Finite Group Databasebeta

← D17×#2488 #17203250

Subgroups — D17×#2488 #17203250

Order 4352.

3114 conjugacy classes of subgroups.

The subgroup lattice has 1696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#123×D17C211yesmaximal, characteristic
2C2×C22⋊Q8×D17C211yesmaximal, characteristic, complemented
3#14533117C211yesmaximal, characteristic, complemented
4#14533116C211yesmaximal, characteristic, complemented
5#14533115C211yesmaximal, characteristic, complemented
6#14533114C211yesmaximal, characteristic, complemented
7#14533113C211yesmaximal, characteristic, complemented
8#14533112C211yesmaximal, characteristic, complemented
9#14533111C211yesmaximal, characteristic, complemented
10#14533110C211yesmaximal, characteristic, complemented
11#14533109C211yesmaximal, characteristic, complemented
12#14533108C211yesmaximal, characteristic, complemented
13#14533107C211yesmaximal, characteristic, complemented
14#14533106C211yesmaximal, characteristic, complemented
15#14533105C211yesmaximal, characteristic, complemented
16#14533104C211yesmaximal, characteristic, complemented
17#14533103C211yesmaximal, characteristic, complemented
18D17×#400C211yesmaximal, characteristic, complemented
19D17×#400C211yesmaximal, characteristic, complemented
20D17×#397C211yesmaximal, characteristic, complemented
21D17×#393C211yesmaximal, characteristic, complemented
22D17×#391C211yesmaximal, characteristic, complemented
23D17×#388C211yesmaximal, characteristic, complemented
24D17×#388C211yesmaximal, characteristic, complemented
25D17×#386C211yesmaximal, characteristic
26D17×#386C211yesmaximal, characteristic
27D17×#382C211yesmaximal, characteristic, complemented
28D17×#381C211yesmaximal, characteristic, complemented
29C4×C22⋊C4×D17C211yesmaximal, characteristic, complemented
30C2×#95×D17C211yesmaximal, characteristic, complemented
31C17×#2488C211yesmaximal, characteristic, complemented
32C22×Q8×D17C2211yescharacteristic
33C22×D4×D17C2211yescharacteristic
34C23×C4×D17C2211yescharacteristic
35C23×C4×D17C2211yescharacteristic
36C23×C4×D17C2211yescharacteristic
37C2×#10587580C2211yescharacteristic
38C2×#10587580C2211yescharacteristic
39C2×#10587572C2211yescharacteristic
40C2×#10587615C2211yescharacteristic
41C2×#10587569C2211yescharacteristic
42C2×#10587569C2211yescharacteristic
43C2×#10587621C2211yescharacteristic
44#123×D17—28no—
45C2×#10587583C2211yescharacteristic, complemented
46C2×#10587610C2211yescharacteristic, complemented
47C2×#10587582C2211yescharacteristic, complemented
48C2×#10587582C2211yescharacteristic, complemented
49C2×#10587564C2211yescharacteristic, complemented
50C2×#10587564C2211yescharacteristic, complemented
51C2×#10587632C2211yescharacteristic, complemented
52C22⋊Q8×D17—28no—
53C2×C4⋊C4×D17C2211yescharacteristic
54C2×C4⋊C4×D17C2211yescharacteristic
55C2×C4⋊C4×D17C2211yescharacteristic
56C2×C4⋊C4×D17C2211yescharacteristic
57C2×C4⋊C4×D17C2211yescharacteristic
58C2×C22⋊C4×D17C2211yescharacteristic
59C2×C22⋊C4×D17C2211yescharacteristic
60C2×C22⋊C4×D17C2211yescharacteristic
61C2×C22⋊C4×D17C2211yescharacteristic
62C2×C22⋊C4×D17C2211yescharacteristic
63C2×C22⋊C4×D17C2211yescharacteristic
64C2×C22⋊C4×D17C2211yescharacteristic
65C2×C22⋊C4×D17C2211yescharacteristic
66C2×C22⋊C4×D17C2211yescharacteristic
67C2×C42×D17C2211yescharacteristic
68C2×C42×D17C2211yescharacteristic
69#11762751C2211yescharacteristic, complemented
70#11762751C2211yescharacteristic, complemented
71#11762751C2211yescharacteristic, complemented
72#11762751C2211yescharacteristic, complemented
73#11762750C2211yescharacteristic, complemented
74#11762750C2211yescharacteristic, complemented
75#11762750C2211yescharacteristic, complemented
76#11762750C2211yescharacteristic, complemented
77#11762749C2211yescharacteristic, complemented
78#11762749C2211yescharacteristic, complemented
79#11762748C2211yescharacteristic, complemented
80#11762748C2211yescharacteristic, complemented
81#11762747C2211yescharacteristic, complemented
82#11762747C2211yescharacteristic, complemented
83#11762738C2211yescharacteristic, complemented
84#11762738C2211yescharacteristic, complemented
85#11762737C2211yescharacteristic, complemented
86#11762737C2211yescharacteristic, complemented
87#11762736C2211yescharacteristic, complemented
88#11762735C2211yescharacteristic, complemented
89#11762734C2211yescharacteristic, complemented
90#11762722C2211yescharacteristic, complemented
91#11762722C2211yescharacteristic, complemented
92#11762722C2211yescharacteristic, complemented
93#11762721C2211yescharacteristic, complemented
94#11762721C2211yescharacteristic, complemented
95#11762721C2211yescharacteristic, complemented
96#11762720C2211yescharacteristic, complemented
97#11762716C2211yescharacteristic, complemented
98#11762715C2211yescharacteristic, complemented
99#11762714C2211yescharacteristic, complemented
100#11762713C2211yescharacteristic, complemented
101#11762713C2211yescharacteristic, complemented
102#11762713C2211yescharacteristic, complemented
103#11762713C2211yescharacteristic, complemented
104#11762703C2211yescharacteristic, complemented
105#11762703C2211yescharacteristic, complemented
106#11762702C2211yescharacteristic, complemented
107#11762702C2211yescharacteristic, complemented
108#11762701C2211yescharacteristic, complemented
109#11762701C2211yescharacteristic, complemented
110#11762700C2211yescharacteristic, complemented
111#11762700C2211yescharacteristic, complemented
112#11762699C2211yescharacteristic, complemented
113#11762699C2211yescharacteristic, complemented
114#11762698C2211yescharacteristic, complemented
115#11762698C2211yescharacteristic, complemented
116#11762697C2211yescharacteristic, complemented
117#11762697C2211yescharacteristic, complemented
118#11762689C2211yescharacteristic
119#11762689C2211yescharacteristic
120#11762688C2211yescharacteristic
121#11762688C2211yescharacteristic
122#11762687C2211yescharacteristic
123#11762687C2211yescharacteristic
124#11762687C2211yescharacteristic
125#11762687C2211yescharacteristic
126#11762686C2211yescharacteristic
127#11762686C2211yescharacteristic
128#11762685C2211yescharacteristic
129#11762685C2211yescharacteristic
130#11762685C2211yescharacteristic
131#11762685C2211yescharacteristic
132#11762675C2211yescharacteristic, complemented
133#11762674C2211yescharacteristic, complemented
134#11762674C2211yescharacteristic, complemented
135#11762673C2211yescharacteristic, complemented
136#11762673C2211yescharacteristic, complemented
137#11762673C2211yescharacteristic, complemented
138#11762673C2211yescharacteristic, complemented
139#11762672C2211yescharacteristic, complemented
140#11762671C2211yescharacteristic, complemented
141#11762671C2211yescharacteristic, complemented
142#11762671C2211yescharacteristic, complemented
143#11762671C2211yescharacteristic, complemented
144#11762670C2211yescharacteristic, complemented
145#11762670C2211yescharacteristic, complemented
146C22⋊C4×Dic17C2211yescharacteristic, complemented
147C22⋊C4×Dic17C2211yescharacteristic, complemented
148C4×#63227C2211yescharacteristic, complemented
149C4×#63227C2211yescharacteristic, complemented
150C4×C22⋊Dic17C2211yescharacteristic, complemented
151#11762656C2211yescharacteristic, complemented
152#11762656C2211yescharacteristic, complemented
153C2×#10587502C2211yescharacteristic, complemented
154C2×#10587502C2211yescharacteristic, complemented
155C2×#10587502C2211yescharacteristic, complemented
156#95×D17C2211yescharacteristic
157#95×D17C2211yescharacteristic
158#95×D17C2211yescharacteristic
159#95×D17C2211yescharacteristic
160#95×D17C2211yescharacteristic
161#95×D17C2211yescharacteristic
162#95×D17C2211yescharacteristic
163#95×D17C2211yescharacteristic
164#95×D17C2211yescharacteristic
165#95×D17C2211yescharacteristic
166#95×D17C2211yescharacteristic
167#95×D17C2211yescharacteristic
168#95×D17C2211yescharacteristic
169#95×D17C2211yescharacteristic
170#95×D17C2211yescharacteristic, complemented
171#95×D17C2211yescharacteristic, complemented
172#95×D17C2211yescharacteristic, complemented
173#95×D17C2211yescharacteristic, complemented
174C2×C17×#123C2211yescharacteristic
175C2×C17×C22⋊Q8C2211yescharacteristic, complemented
176C17×#400C2211yescharacteristic, complemented
177C17×#400C2211yescharacteristic, complemented
178C17×#397C2211yescharacteristic, complemented
179C17×#393C2211yescharacteristic, complemented
180C17×#391C2211yescharacteristic, complemented
181C17×#388C2211yescharacteristic, complemented
182C17×#388C2211yescharacteristic, complemented
183C17×#386C2211yescharacteristic
184C17×#386C2211yescharacteristic
185C17×#382C2211yescharacteristic, complemented
186C17×#381C2211yescharacteristic, complemented
187C4×C22⋊C4×C17C2211yescharacteristic, complemented
188C2×C17×#95C2211yescharacteristic, complemented
189C24×D17C2311yescharacteristic
190C24×D17C2311yescharacteristic
191C22×Q8×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C23×C4×C17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C23×Dic17C2311yescharacteristic
199C23×Dic17C2311yescharacteristic
200C23×Dic17C2311yescharacteristic
201C2×Q8×D17—24no—
202C2×Q8×D17—24no—
203C2×Q8×D17—42no—
204C2×D4×D17—24no—
205C2×D4×D17—24no—
206C2×D4×D17—24no—
207C22×D68C2311yescharacteristic
208C22×C4×D17—24no—
209C22×C4×D17—24no—
210C22×C4×D17—24no—
211C22×C4×D17—24no—
212C22×C4×D17—24no—
213C22×C4×D17—24no—
214C22×C4×D17—24no—
215C22×C4×D17—42no—
216C22×C4×D17—42no—
217C22×C4×D17C2311yescharacteristic
218C22×C4×D17C2311yescharacteristic
219C22×C4×D17C2311yescharacteristic
220C22×C4×D17C2311yescharacteristic
221C22×C4×D17C2311yescharacteristic
222C22×C4×D17C2311yescharacteristic
223C22×C4×D17C2311yescharacteristic
224C22×C4×D17C2311yescharacteristic
225C22×C4×D17C2311yescharacteristic
226C22×C4×D17C2311yescharacteristic
227C22×C4×D17C2311yescharacteristic
228C22×C4×D17C2311yescharacteristic
229C22×C4×D17C2311yescharacteristic
230C22×C4×D17C2311yescharacteristic
231C22×C4×D17C2311yescharacteristic
232C22×C4×D17C2311yescharacteristic
233C22×C4×D17C2311yescharacteristic
234C22×C4×D17C2311yescharacteristic
235C22×C4×D17C2311yescharacteristic
236C22×Dic34C2311yescharacteristic
237C22×Dic34C2311yescharacteristic
238C22×Dic34C2311yescharacteristic
239C17×#123—24no—
240C17×C22⋊Q8—24no—
241C2×C4⋊C4×C17C2311yescharacteristic
242C2×C4⋊C4×C17C2311yescharacteristic
243C2×C4⋊C4×C17C2311yescharacteristic
244C2×C4⋊C4×C17C2311yescharacteristic
245C2×C4⋊C4×C17C2311yescharacteristic
246C2×C22⋊C4×C17C2311yescharacteristic
247C2×C22⋊C4×C17C2311yescharacteristic
248C2×C22⋊C4×C17C2311yescharacteristic
249C2×C22⋊C4×C17C2311yescharacteristic
250C2×C22⋊C4×C17C2311yescharacteristic
251C2×C22⋊C4×C17C2311yescharacteristic
252C2×C22⋊C4×C17C2311yescharacteristic
253C2×C22⋊C4×C17C2311yescharacteristic
254C2×C22⋊C4×C17C2311yescharacteristic
255C2×C42×C17C2311yescharacteristic
256C2×C42×C17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259C2×C22⋊Dic17C2311yescharacteristic
260C2×C22⋊Dic17C2311yescharacteristic
261C2×C22⋊Dic17C2311yescharacteristic
262C2×C22⋊Dic17C2311yescharacteristic
263C2×C22⋊Dic17C2311yescharacteristic
264C2×C22⋊Dic17C2311yescharacteristic
265C2×C22⋊Dic17C2311yescharacteristic
266#10587632—24no—
267#10587621—24no—
268#10587615—24no—
269C2×#63227C2311yescharacteristic
270C2×#63227C2311yescharacteristic
271C2×#63227C2311yescharacteristic
272C2×#63227C2311yescharacteristic
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
275C2×#63227C2311yescharacteristic
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
282C2×#63227C2311yescharacteristic
283C2×#63227C2311yescharacteristic
284C2×#63227C2311yescharacteristic
285C2×#63227C2311yescharacteristic
286C2×#63227C2311yescharacteristic
287C2×C4⋊Dic17C2311yescharacteristic
288C2×C4⋊Dic17C2311yescharacteristic
289C2×C4⋊Dic17C2311yescharacteristic
290C2×C4⋊Dic17C2311yescharacteristic
291C2×C4⋊Dic17C2311yescharacteristic
292#10587610—24no—
293C2×#63225C2311yescharacteristic
294C2×#63225C2311yescharacteristic
295C2×#63225C2311yescharacteristic
296C2×#63225C2311yescharacteristic
297C2×#63225C2311yescharacteristic
298C2×#63225C2311yescharacteristic
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×#63225C2311yescharacteristic
303C2×C4×Dic17C2311yescharacteristic
304C2×C4×Dic17C2311yescharacteristic
305C2×C4×Dic17C2311yescharacteristic
306C2×C4×Dic17C2311yescharacteristic
307C2×C4×Dic17C2311yescharacteristic
308C2×C4×Dic17C2311yescharacteristic
309#10587583—24no—
310#10587582—24no—
311#10587582—24no—
312#10587580—24no—
313#10587580—24no—
314C4⋊C4×D17—24no—
315C4⋊C4×D17—24no—
316C4⋊C4×D17—24no—
317C4⋊C4×D17—24no—
318C4⋊C4×D17—24no—
319#10587572—24no—
320#10587569—24no—
321#10587569—24no—
322C22⋊C4×D17—24no—
323C22⋊C4×D17—24no—
324C22⋊C4×D17—24no—
325C22⋊C4×D17—24no—
326C22⋊C4×D17—24no—
327C22⋊C4×D17—24no—
328C22⋊C4×D17—42no—
329C22⋊C4×D17—42no—
330C22⋊C4×D17D418yes—
331#10587564—24no—
332#10587564—24no—
333C42×D17—24no—
334C42×D17—42no—
335C17×#95C2311yescharacteristic
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338C17×#95C2311yescharacteristic
339C17×#95C2311yescharacteristic
340C17×#95C2311yescharacteristic
341C17×#95C2311yescharacteristic
342C17×#95C2311yescharacteristic
343C17×#95C2311yescharacteristic
344C17×#95C2311yescharacteristic
345C17×#95C2311yescharacteristic
346C17×#95C2311yescharacteristic
347C17×#95C2311yescharacteristic
348C17×#95C2311yescharacteristic
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351#10587502C2311yescharacteristic
352#10587502C2311yescharacteristic
353#10587502C2311yescharacteristic
354#10587502C2311yescharacteristic
355#10587502C2311yescharacteristic
356#10587502C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
376#10587502C2311yescharacteristic
377#10587502C2311yescharacteristic
378#10587502C2311yescharacteristic
379#10587502C2311yescharacteristic
380#10587502C2311yescharacteristic
381#10587502C2311yescharacteristic
382#10587502C2311yescharacteristic
383#10587502C2311yescharacteristic
384#10587502C2311yescharacteristic
385#10587502C2311yescharacteristic
386#10587502C2311yescharacteristic
387#10587502C2311yescharacteristic
388#10587502C2311yescharacteristic
389#10587502C2311yescharacteristic
390#10587502C2311yescharacteristic
391C24×C17C2411yescharacteristic
392C24×C17C2411yescharacteristic
393C23×D17—22no—
394C23×D17—22no—
395C23×D17—22no—
396C23×D17—22no—
397C23×D17—22no—
398C23×D17—22no—
399C23×D17—22no—
400C23×D17—22no—
401C23×D17—22no—
402C23×D17—22no—
403C23×D17—22no—
404C23×D17C2×D414yes—
405C23×D17#4114yes—
406C23×D17#4114yes—
407C23×D17C2411yescharacteristic
408C23×D17C2411yescharacteristic
409C23×D17C2411yescharacteristic
410C2×Q8×C17—22no—
411C2×Q8×C17—22no—
412C2×Q8×C17—41no—
413C2×D4×C17—22no—
414C2×D4×C17—22no—
415C2×D4×C17—22no—
416C22×C4×C17—22no—
417C22×C4×C17—22no—
418C22×C4×C17—22no—
419C22×C4×C17—22no—
420C22×C4×C17—22no—
421C22×C4×C17—22no—
422C22×C4×C17—22no—
423C22×C4×C17—41no—
424C22×C4×C17—41no—
425C22×C4×C17C2411yescharacteristic
426C22×C4×C17C2411yescharacteristic
427C22×C4×C17C2411yescharacteristic
428C22×C4×C17C2411yescharacteristic
429C22×C4×C17C2411yescharacteristic
430C22×C4×C17C2411yescharacteristic
431C22×C4×C17C2411yescharacteristic
432C22×C4×C17C2411yescharacteristic
433C22×C4×C17C2411yescharacteristic
434C22×C4×C17C2411yescharacteristic
435C22×C4×C17C2411yescharacteristic
436C22×C4×C17C2411yescharacteristic
437C22×C4×C17C2411yescharacteristic
438C2×C22⋊D17—22no—
439C2×C22⋊D17—22no—
440C2×C22⋊D17—22no—
441C2×C22⋊D17—22no—
442C2×C22⋊D17—22no—
443C2×C22⋊D17—22no—
444C22×Dic17—22no—
445C22×Dic17—22no—
446C22×Dic17—22no—
447C22×Dic17—22no—
448C22×Dic17—22no—
449C22×Dic17—22no—
450C22×Dic17—22no—
451C22×Dic17—41no—
452C22×Dic17—41no—
453C22×Dic17C2411yescharacteristic
454C22×Dic17C2411yescharacteristic
455C22×Dic17C2411yescharacteristic
456C22×Dic17C2411yescharacteristic
457C22×Dic17C2411yescharacteristic
458C22×Dic17C2411yescharacteristic
459C22×Dic17C2411yescharacteristic
460C22×Dic17C2411yescharacteristic
461C22×Dic17C2411yescharacteristic
462C22×Dic17C2411yescharacteristic
463C22×Dic17C2411yescharacteristic
464C22×Dic17C2411yescharacteristic
465C22×Dic17C2411yescharacteristic
466Q8×D17—416no—
467D4×D17—416no—
468C2×D68—22no—
469C2×D68—22no—
470C2×D68—22no—
471C2×C4×D17—22no—
472C2×C4×D17—22no—
473C2×C4×D17—22no—
474C2×C4×D17—22no—
475C2×C4×D17—22no—
476C2×C4×D17—22no—
477C2×C4×D17—22no—
478C2×C4×D17—22no—
479C2×C4×D17—22no—
480C2×C4×D17—22no—
481C2×C4×D17—22no—
482C2×C4×D17—22no—
483C2×C4×D17—22no—
484C2×C4×D17—22no—
485C2×C4×D17—22no—
486C2×C4×D17—22no—
487C2×C4×D17—22no—
488C2×C4×D17—22no—
489C2×C4×D17—22no—
490C2×C4×D17—22no—
491C2×C4×D17—22no—
492C2×C4×D17—22no—
493C2×C4×D17—22no—
494C2×C4×D17—22no—
495C2×C4×D17—22no—
496C2×C4×D17—22no—
497C2×C4×D17—22no—
498C2×C4×D17—22no—
499C2×C4×D17—22no—
500C2×C4×D17—22no—
501C2×C4×D17—22no—
502C2×C4×D17—22no—
503C2×C4×D17—22no—
504C2×C4×D17—22no—
505C2×C4×D17—22no—
506C2×C4×D17—22no—
507C2×C4×D17—22no—
508C2×C4×D17—22no—
509C2×C4×D17—22no—
510C2×C4×D17—22no—
511C2×C4×D17—22no—
512C2×C4×D17—22no—
513C2×C4×D17—22no—
514C2×C4×D17—22no—
515C2×C4×D17—22no—
516C2×C4×D17—22no—
517C2×C4×D17—22no—
518C2×C4×D17—22no—
519C2×C4×D17—22no—
520C2×C4×D17—416no—
521C2×C4×D17—416no—
522C2×C4×D17—41no—
523C2×C4×D17—41no—
524C2×C4×D17—41no—
525C2×C4×D17—41no—
526C2×C4×D17—416no—
527C2×C4×D17C2×D414yes—
528C2×C4×D17C2×D414yes—
529C2×C4×D17#4114yes—
530C2×C4×D17#4114yes—
531C2×Dic34—22no—
532C2×Dic34—22no—
533C2×Dic34—22no—
534C2×Dic34—22no—
535C2×Dic34—22no—
536C2×Dic34—22no—
537C2×Dic34—41no—
538C2×Dic34—41no—
539C2×Dic34—41no—
540C4⋊C4×C17—22no—
541C4⋊C4×C17—22no—
542C4⋊C4×C17—22no—
543C4⋊C4×C17—22no—
544C4⋊C4×C17—22no—
545C22⋊C4×C17—22no—
546C22⋊C4×C17—22no—
547C22⋊C4×C17—22no—
548C22⋊C4×C17—22no—
549C22⋊C4×C17—22no—
550C22⋊C4×C17—22no—
551C22⋊C4×C17—41no—
552C22⋊C4×C17—41no—
553C22⋊C4×C17C2×D414yes—
554C42×C17—22no—
555C42×C17—41no—
556C22⋊Dic17—22no—
557C22⋊Dic17—22no—
558C22⋊Dic17—22no—
559C22⋊Dic17—22no—
560C22⋊Dic17—22no—
561C22⋊Dic17—22no—
562C22⋊Dic17—41no—
563C22⋊Dic17—41no—
564C22⋊Dic17C2×D414yes—
565#63227—22no—
566#63227—22no—
567#63227—22no—
568#63227—22no—
569#63227—22no—
570#63227—22no—
571#63227—22no—
572#63227—22no—
573#63227—22no—
574#63227—22no—
575#63227—22no—
576#63227—22no—
577#63227—41no—
578#63227—41no—
579#63227—41no—
580#63227—41no—
581#63227C2×D414yes—
582#63227C2×D414yes—
583C4⋊Dic17—22no—
584C4⋊Dic17—22no—
585C4⋊Dic17—22no—
586C4⋊Dic17—22no—
587C4⋊Dic17—22no—
588#63225—22no—
589#63225—22no—
590#63225—22no—
591#63225—22no—
592#63225—22no—
593#63225—22no—
594#63225—22no—
595#63225—22no—
596#63225—22no—
597#63225—22no—
598C4×Dic17—22no—
599C4×Dic17—22no—
600C4×Dic17—22no—
601C4×Dic17—41no—
602C4×Dic17—41no—
603C4×Dic17—41no—
604C2×#2488—171nomaximal, Sylow
605C23×C17—21no—
606C23×C17—21no—
607C23×C17—21no—
608C23×C17—21no—
609C23×C17—21no—
610C23×C17—21no—
611C23×C17—21no—
612C23×C17—21no—
613C23×C17—21no—
614C23×C17—21no—
615C23×C17—21no—
616C23×C17C22×D412yes—
617C23×C17C2×#4112yes—
618C23×C17C2×#4112yes—
619C23×C17C2511yescharacteristic
620C22×D17—21no—
621C22×D17—21no—
622C22×D17—21no—
623C22×D17—21no—
624C22×D17—28no—
625C22×D17—28no—
626C22×D17—28no—
627C22×D17—28no—
628C22×D17—28no—
629C22×D17—28no—
630C22×D17—21no—
631C22×D17—21no—
632C22×D17—21no—
633C22×D17—21no—
634C22×D17—21no—
635C22×D17—21no—
636C22×D17—21no—
637C22×D17—44no—
638C22×D17—44no—
639C22×D17—44no—
640C22×D17—44no—
641C22×D17—44no—
642C22×D17—44no—
643C22×D17—44no—
644C22×D17#124116yes—
645C22×D17C22×D412yes—
646C22×D17C22×D412yes—
647C22×D17C2×#4112yes—
648C22×D17C2×#4112yes—
649C22×D17C2×#4112yes—
650C22×D17C2×#4112yes—
651C22×D17C2×#4112yes—
652C22×D17C2×#4112yes—
653C22×D17H(5,𝔽2)12yes—
654C22×D172−1+412yes—
655Q8×C17—44no—
656D4×C17—44no—
657C2×C4×C17—21no—
658C2×C4×C17—21no—
659C2×C4×C17—21no—
660C2×C4×C17—21no—
661C2×C4×C17—21no—
662C2×C4×C17—21no—
663C2×C4×C17—21no—
664C2×C4×C17—21no—
665C2×C4×C17—21no—
666C2×C4×C17—21no—
667C2×C4×C17—21no—
668C2×C4×C17—21no—
669C2×C4×C17—21no—
670C2×C4×C17—21no—
671C2×C4×C17—21no—
672C2×C4×C17—21no—
673C2×C4×C17—21no—
674C2×C4×C17—21no—
675C2×C4×C17—21no—
676C2×C4×C17—21no—
677C2×C4×C17—21no—
678C2×C4×C17—21no—
679C2×C4×C17—21no—
680C2×C4×C17—21no—
681C2×C4×C17—21no—
682C2×C4×C17—21no—
683C2×C4×C17—21no—
684C2×C4×C17—21no—
685C2×C4×C17—21no—
686C2×C4×C17—21no—
687C2×C4×C17—21no—
688C2×C4×C17—21no—
689C2×C4×C17—21no—
690C2×C4×C17—21no—
691C2×C4×C17—21no—
692C2×C4×C17—44no—
693C2×C4×C17—44no—
694C2×C4×C17—44no—
695C2×C4×C17C22×D412yes—
696C2×C4×C17C22×D412yes—
697C2×C4×C17C2×#4112yes—
698C2×C4×C17C2×#4112yes—
699C22⋊D17—44no—
700C22⋊D17—44no—
701C2×Dic17—21no—
702C2×Dic17—21no—
703C2×Dic17—21no—
704C2×Dic17—21no—
705C2×Dic17—21no—
706C2×Dic17—21no—
707C2×Dic17—21no—
708C2×Dic17—21no—
709C2×Dic17—21no—
710C2×Dic17—21no—
711C2×Dic17—21no—
712C2×Dic17—21no—
713C2×Dic17—21no—
714C2×Dic17—21no—
715C2×Dic17—21no—
716C2×Dic17—21no—
717C2×Dic17—21no—
718C2×Dic17—21no—
719C2×Dic17—21no—
720C2×Dic17—21no—
721C2×Dic17—21no—
722C2×Dic17—21no—
723C2×Dic17—21no—
724C2×Dic17—21no—
725C2×Dic17—21no—
726C2×Dic17—21no—
727C2×Dic17—21no—
728C2×Dic17—21no—
729C2×Dic17—21no—
730C2×Dic17—21no—
731C2×Dic17—21no—
732C2×Dic17—21no—
733C2×Dic17—21no—
734C2×Dic17—21no—
735C2×Dic17—21no—
736C2×Dic17—44no—
737C2×Dic17—44no—
738C2×Dic17—44no—
739C2×Dic17C22×D412yes—
740C2×Dic17C22×D412yes—
741C2×Dic17C2×#4112yes—
742C2×Dic17C2×#4112yes—
743D68—44no—
744C4×D17—28no—
745C4×D17—28no—
746C4×D17—28no—
747C4×D17—28no—
748C4×D17—44no—
749C4×D17—44no—
750C4×D17—44no—
751C4×D17—44no—
752C4×D17—44no—
753C4×D17—44no—
754C4×D17—44no—
755C4×D17—44no—
756C4×D17—44no—
757C4×D17—44no—
758C4×D17—44no—
759C4×D17—44no—
760C4×D17—44no—
761C4×D17—44no—
762C4×D17—44no—
763Dic34—44no—
764Dic34—44no—
765Dic34—44no—
766C22×#123—171no—
767C22×C22⋊Q8—171no—
768#2488—171no—
769#2488—171no—
770#2488—171no—
771#2488—171no—
772#2488—171no—
773#2488—171no—
774#2488—171no—
775#2488—171no—
776#2488—171no—
777#2488—171no—
778#2488—171no—
779#2488—171no—
780#2488—171no—
781#2488—171no—
782#2488—171no—
783#2488D1711yescharacteristic, direct product factor
784C2×#400—171no—
785C2×#400—171no—
786C2×#397—171no—
787C2×#393—171no—
788C2×#391—171no—
789C2×#388—171no—
790C2×#388—171no—
791C2×#386—171no—
792C2×#386—171no—
793C2×#382—171no—
794C2×#381—171no—
795C2×C4×C22⋊C4—171no—
796C22×#95—171no—
797C22×C17—22no—
798C22×C17—22no—
799C22×C17—22no—
800C22×C17—22no—
801C22×C17—22no—
802C22×C17—22no—
803C22×C17—41no—
804C22×C17—41no—
805C22×C17—41no—
806C22×C17—41no—
807C22×C17—41no—
808C22×C17—41no—
809C22×C17—41no—
810C22×C17C2×#12414yes—
811C22×C17C23×D411yescharacteristic
812C22×C17C22×#4111yescharacteristic
813C22×C17C22×#4111yescharacteristic
814C22×C17C22×#4111yescharacteristic
815C22×C17C22×#4111yescharacteristic
816C22×C17C2×H(5,𝔽2)11yescharacteristic
817C22×C17C2×2−1+411yescharacteristic
818C2×D17—22no—
819C2×D17—22no—
820C2×D17—22no—
821C2×D17—22no—
822C2×D17—22no—
823C2×D17—22no—
824C2×D17—232no—
825C2×D17—41no—
826C2×D17—41no—
827C2×D17—41no—
828C2×D17—41no—
829C2×D17—41no—
830C2×D17—41no—
831C2×D17—41no—
832C2×D17—88no—
833C2×D17C2×#12414yes—
834C2×D17C2×#12414yes—
835C2×D17#52914yes—
836C2×D17#53914yes—
837C2×D17#54614yes—
838C2×D17#54714yes—
839C2×D17#55114yes—
840C2×D17#55214yes—
841C4×C17—22no—
842C4×C17—22no—
843C4×C17—22no—
844C4×C17—22no—
845C4×C17—41no—
846C4×C17—41no—
847C4×C17—41no—
848C4×C17—41no—
849C4×C17—41no—
850C4×C17—41no—
851C4×C17—41no—
852C4×C17—41no—
853C4×C17—41no—
854Dic17—22no—
855Dic17—22no—
856Dic17—22no—
857Dic17—22no—
858Dic17—41no—
859Dic17—41no—
860Dic17—41no—
861Dic17—41no—
862Dic17—41no—
863Dic17—41no—
864Dic17—41no—
865Dic17—41no—
866Dic17—41no—
867C23×Q8—171no—
868C23×D4—171no—
869C24×C4—171no—
870C24×C4—171no—
871C24×C4—171no—
872C2×#123—171no—
873C2×#123—171no—
874C2×#123—171no—
875C2×#123—171no—
876C2×#123—171no—
877C2×#123—171no—
878C2×#123—171no—
879C2×#123—348no—
880C2×#123C2×D1711yescharacteristic
881C2×C22⋊Q8—171no—
882C2×C22⋊Q8—171no—
883C2×C22⋊Q8—171no—
884C2×C22⋊Q8—171no—
885C2×C22⋊Q8—171no—
886C2×C22⋊Q8—171no—
887C2×C22⋊Q8—171no—
888C2×C22⋊Q8—348no—
889C2×C22⋊Q8C2×D1711yescharacteristic, complemented
890C22×C4⋊C4—171no—
891C22×C4⋊C4—171no—
892C22×C4⋊C4—171no—
893C22×C4⋊C4—171no—
894C22×C4⋊C4—171no—
895C22×C22⋊C4—171no—
896C22×C22⋊C4—171no—
897C22×C22⋊C4—171no—
898C22×C22⋊C4—171no—
899C22×C22⋊C4—171no—
900C22×C22⋊C4—171no—
901C22×C22⋊C4—171no—
902C22×C22⋊C4—171no—
903C22×C22⋊C4—171no—
904C22×C42—171no—
905C22×C42—171no—
906#400—171no—
907#400—171no—
908#400—171no—
909#400—171no—
910#400—171no—
911#400—171no—
912#400—171no—
913#400—171no—
914#400—171no—
915#400—171no—
916#400—171no—
917#400—171no—
918#400—171no—
919#400—171no—
920#400C2×D1711yescharacteristic, complemented
921#400C2×D1711yescharacteristic, complemented
922#397—171no—
923#397—171no—
924#397—171no—
925#397—171no—
926#397—171no—
927#397—171no—
928#397—171no—
929#397C2×D1711yescharacteristic, complemented
930#393—171no—
931#393—171no—
932#393—171no—
933#393—171no—
934#393—171no—
935#393—171no—
936#393—171no—
937#393C2×D1711yescharacteristic, complemented
938#391—171no—
939#391—171no—
940#391—171no—
941#391—171no—
942#391—171no—
943#391—171no—
944#391—171no—
945#391C2×D1711yescharacteristic, complemented
946#388—171no—
947#388—171no—
948#388—171no—
949#388—171no—
950#388—171no—
951#388—171no—
952#388—171no—
953#388—171no—
954#388—171no—
955#388—171no—
956#388—171no—
957#388—171no—
958#388—171no—
959#388—171no—
960#388C2×D1711yescharacteristic, complemented
961#388C2×D1711yescharacteristic, complemented
962#386—171no—
963#386—171no—
964#386—171no—
965#386—171no—
966#386—171no—
967#386—171no—
968#386—171no—
969#386—171no—
970#386—171no—
971#386—171no—
972#386—171no—
973#386—171no—
974#386—171no—
975#386—171no—
976#386C2×D1711yescharacteristic
977#386C2×D1711yescharacteristic
978#382—171no—
979#382—171no—
980#382—171no—
981#382—171no—
982#382—171no—
983#382—171no—
984#382—171no—
985#382C2×D1711yescharacteristic, complemented
986#381—171no—
987#381—171no—
988#381—171no—
989#381—171no—
990#381—171no—
991#381—171no—
992#381—171no—
993#381C2×D1711yescharacteristic, complemented
994C4×C22⋊C4—171no—
995C4×C22⋊C4—171no—
996C4×C22⋊C4—171no—
997C4×C22⋊C4—171no—
998C4×C22⋊C4—171no—
999C4×C22⋊C4—171no—
1000C4×C22⋊C4—171no—
1001C4×C22⋊C4C2×D1711yescharacteristic, complemented
1002C2×#95—171no—
1003C2×#95—171no—
1004C2×#95—171no—
1005C2×#95—171no—
1006C2×#95—171no—
1007C2×#95—171no—
1008C2×#95—171no—
1009C2×#95—171no—
1010C2×#95—171no—
1011C2×#95—171no—
1012C2×#95—171no—
1013C2×#95—171no—
1014C2×#95—171no—
1015C2×#95—171no—
1016C2×#95—171no—
1017C2×#95—171no—
1018C2×#95—171no—
1019C2×#95—171no—
1020C2×#95—171no—
1021C2×#95—171no—
1022C2×#95—171no—
1023C2×#95C2×D1711yescharacteristic, complemented
1024C2×C17—24no—
1025C2×C17—81no—
1026C2×C17C22×#12411yescharacteristic
1027C2×C17C2×#52911yescharacteristic
1028C2×C17C2×#53911yescharacteristic
1029C2×C17C2×#54611yescharacteristic
1030C2×C17C2×#54711yescharacteristic
1031C2×C17C2×#55111yescharacteristic
1032C2×C17C2×#55211yescharacteristic
1033D17—24no—
1034D17—81no—
1035D17#248818yesdirect product factor
1036C25—171no—
1037C25—171no—
1038C22×Q8—171no—
1039C22×Q8—171no—
1040C22×Q8—171no—
1041C22×Q8—344no—
1042C22×Q8—344no—
1043C22×Q8—682no—
1044C22×Q8C22×D1711yescharacteristic
1045C22×D4—171no—
1046C22×D4—171no—
1047C22×D4—171no—
1048C22×D4—344no—
1049C22×D4—344no—
1050C22×D4—344no—
1051C22×D4C22×D1711yescharacteristic
1052C23×C4—171no—
1053C23×C4—171no—
1054C23×C4—171no—
1055C23×C4—171no—
1056C23×C4—171no—
1057C23×C4—171no—
1058C23×C4—171no—
1059C23×C4—171no—
1060C23×C4—171no—
1061C23×C4—171no—
1062C23×C4—171no—
1063C23×C4—171no—
1064C23×C4—171no—
1065C23×C4—171no—
1066C23×C4—171no—
1067C23×C4—171no—
1068C23×C4—171no—
1069C23×C4—171no—
1070C23×C4—171no—
1071C23×C4—171no—
1072C23×C4—171no—
1073C23×C4—171no—
1074C23×C4—344no—
1075C23×C4—344no—
1076C23×C4—344no—
1077C23×C4—344no—
1078C23×C4—344no—
1079C23×C4—344no—
1080C23×C4—344no—
1081C23×C4—682no—
1082C23×C4—682no—
1083C23×C4C22×D1711yescharacteristic
1084C23×C4C22×D1711yescharacteristic
1085C23×C4C22×D1711yescharacteristic
1086#123—24no—
1087#123—344no—
1088#123—344no—
1089#123—344no—
1090#123—344no—
1091#123—344no—
1092#123—344no—
1093#123—344no—
1094C22⋊Q8—24no—
1095C22⋊Q8—344no—
1096C22⋊Q8—344no—
1097C22⋊Q8—344no—
1098C22⋊Q8—344no—
1099C22⋊Q8—344no—
1100C22⋊Q8—344no—
1101C22⋊Q8—344no—
1102C2×C4⋊C4—171no—
1103C2×C4⋊C4—171no—
1104C2×C4⋊C4—171no—
1105C2×C4⋊C4—171no—
1106C2×C4⋊C4—171no—
1107C2×C4⋊C4—171no—
1108C2×C4⋊C4—171no—
1109C2×C4⋊C4—171no—
1110C2×C4⋊C4—171no—
1111C2×C4⋊C4—171no—
1112C2×C4⋊C4—171no—
1113C2×C4⋊C4—171no—
1114C2×C4⋊C4—171no—
1115C2×C4⋊C4—171no—
1116C2×C4⋊C4—171no—
1117C2×C4⋊C4—344no—
1118C2×C4⋊C4—344no—
1119C2×C4⋊C4—344no—
1120C2×C4⋊C4—344no—
1121C2×C4⋊C4—344no—
1122C2×C4⋊C4C22×D1711yescharacteristic
1123C2×C4⋊C4C22×D1711yescharacteristic
1124C2×C4⋊C4C22×D1711yescharacteristic
1125C2×C4⋊C4C22×D1711yescharacteristic
1126C2×C4⋊C4C22×D1711yescharacteristic
1127C2×C22⋊C4—171no—
1128C2×C22⋊C4—171no—
1129C2×C22⋊C4—171no—
1130C2×C22⋊C4—178no—
1131C2×C22⋊C4—171no—
1132C2×C22⋊C4—171no—
1133C2×C22⋊C4—171no—
1134C2×C22⋊C4—171no—
1135C2×C22⋊C4—171no—
1136C2×C22⋊C4—171no—
1137C2×C22⋊C4—171no—
1138C2×C22⋊C4—171no—
1139C2×C22⋊C4—171no—
1140C2×C22⋊C4—171no—
1141C2×C22⋊C4—171no—
1142C2×C22⋊C4—171no—
1143C2×C22⋊C4—171no—
1144C2×C22⋊C4—171no—
1145C2×C22⋊C4—171no—
1146C2×C22⋊C4—171no—
1147C2×C22⋊C4—171no—
1148C2×C22⋊C4—171no—
1149C2×C22⋊C4—171no—
1150C2×C22⋊C4—171no—
1151C2×C22⋊C4—171no—
1152C2×C22⋊C4—171no—
1153C2×C22⋊C4—171no—
1154C2×C22⋊C4—171no—
1155C2×C22⋊C4—344no—
1156C2×C22⋊C4—344no—
1157C2×C22⋊C4—344no—
1158C2×C22⋊C4—344no—
1159C2×C22⋊C4—344no—
1160C2×C22⋊C4—344no—
1161C2×C22⋊C4—682no—
1162C2×C22⋊C4—682no—
1163C2×C22⋊C4C22×D1711yescharacteristic
1164C2×C22⋊C4C22×D1711yescharacteristic
1165C2×C22⋊C4C22×D1711yescharacteristic
1166C2×C22⋊C4C22×D1711yescharacteristic
1167C2×C22⋊C4C22×D1711yescharacteristic
1168C2×C22⋊C4C22×D1711yescharacteristic
1169C2×C22⋊C4C22×D1711yescharacteristic
1170C2×C22⋊C4C22×D1711yescharacteristic
1171C2×C22⋊C4C22×D1711yescharacteristic
1172C2×C42—171no—
1173C2×C42—171no—
1174C2×C42—171no—
1175C2×C42—171no—
1176C2×C42—171no—
1177C2×C42—171no—
1178C2×C42—344no—
1179C2×C42—682no—
1180C2×C42C22×D1711yescharacteristic
1181C2×C42C22×D1711yescharacteristic
1182#95—171no—
1183#95—171no—
1184#95—171no—
1185#95—171no—
1186#95—171no—
1187#95—171no—
1188#95—171no—
1189#95—171no—
1190#95—171no—
1191#95—171no—
1192#95—171no—
1193#95—171no—
1194#95—171no—
1195#95—171no—
1196#95—171no—
1197#95—171no—
1198#95—171no—
1199#95—171no—
1200#95—171no—
1201#95—171no—
1202#95—171no—
1203#95—171no—
1204#95—171no—
1205#95—171no—
1206#95—171no—
1207#95—171no—
1208#95—171no—
1209#95—171no—
1210#95—171no—
1211#95—171no—
1212#95—171no—
1213#95—171no—
1214#95—171no—
1215#95—171no—
1216#95—171no—
1217#95—171no—
1218#95—171no—
1219#95—171no—
1220#95—171no—
1221#95—171no—
1222#95—171no—
1223#95—171no—
1224#95C22×D1711yescharacteristic
1225#95C22×D1711yescharacteristic
1226#95C22×D1711yescharacteristic
1227#95C22×D1711yescharacteristic
1228#95C22×D1711yescharacteristic
1229#95C22×D1711yescharacteristic
1230#95C22×D1711yescharacteristic
1231#95C22×D1711yescharacteristic
1232#95C22×D1711yescharacteristic
1233#95C22×D1711yescharacteristic
1234#95C22×D1711yescharacteristic
1235#95C22×D1711yescharacteristic
1236#95C22×D1711yescharacteristic
1237#95C22×D1711yescharacteristic
1238C17C2×#248811yescharacteristic, complemented, Sylow
1239C24—171no—
1240C24—174no—
1241C24—174no—
1242C24—174no—
1243C24—171no—
1244C24—171no—
1245C24—342no—
1246C24—342no—
1247C24—342no—
1248C24—342no—
1249C24—342no—
1250C24—342no—
1251C24—342no—
1252C24—342no—
1253C24—342no—
1254C24—342no—
1255C24—342no—
1256C24C23×D1711yescharacteristic
1257C24C23×D1711yescharacteristic
1258C2×Q8—22no—
1259C2×Q8—22no—
1260C2×Q8—41no—
1261C2×Q8—342no—
1262C2×Q8—342no—
1263C2×Q8—342no—
1264C2×Q8—342no—
1265C2×Q8—342no—
1266C2×Q8—342no—
1267C2×Q8—681no—
1268C2×Q8—681no—
1269C2×Q8—681no—
1270C2×Q8—6816no—
1271C2×D4—22no—
1272C2×D4—22no—
1273C2×D4—22no—
1274C2×D4—342no—
1275C2×D4—342no—
1276C2×D4—342no—
1277C2×D4—342no—
1278C2×D4—342no—
1279C2×D4—342no—
1280C2×D4—342no—
1281C2×D4—342no—
1282C2×D4—342no—
1283C2×D4—6816no—
1284C22×C4—22no—
1285C22×C4—22no—
1286C22×C4—22no—
1287C22×C4—22no—
1288C22×C4—22no—
1289C22×C4—22no—
1290C22×C4—22no—
1291C22×C4—41no—
1292C22×C4—41no—
1293C22×C4—171no—
1294C22×C4—171no—
1295C22×C4—171no—
1296C22×C4—171no—
1297C22×C4—174no—
1298C22×C4—174no—
1299C22×C4—174no—
1300C22×C4—174no—
1301C22×C4—171no—
1302C22×C4—171no—
1303C22×C4—171no—
1304C22×C4—171no—
1305C22×C4—171no—
1306C22×C4—171no—
1307C22×C4—171no—
1308C22×C4—171no—
1309C22×C4—171no—
1310C22×C4—342no—
1311C22×C4—342no—
1312C22×C4—342no—
1313C22×C4—342no—
1314C22×C4—342no—
1315C22×C4—342no—
1316C22×C4—342no—
1317C22×C4—342no—
1318C22×C4—342no—
1319C22×C4—342no—
1320C22×C4—342no—
1321C22×C4—342no—
1322C22×C4—342no—
1323C22×C4—342no—
1324C22×C4—342no—
1325C22×C4—342no—
1326C22×C4—342no—
1327C22×C4—342no—
1328C22×C4—342no—
1329C22×C4—342no—
1330C22×C4—342no—
1331C22×C4—342no—
1332C22×C4—342no—
1333C22×C4—342no—
1334C22×C4—342no—
1335C22×C4—342no—
1336C22×C4—342no—
1337C22×C4—342no—
1338C22×C4—342no—
1339C22×C4—342no—
1340C22×C4—342no—
1341C22×C4—342no—
1342C22×C4—342no—
1343C22×C4—342no—
1344C22×C4—342no—
1345C22×C4—342no—
1346C22×C4—342no—
1347C22×C4—342no—
1348C22×C4—342no—
1349C22×C4—342no—
1350C22×C4—342no—
1351C22×C4—342no—
1352C22×C4—342no—
1353C22×C4—342no—
1354C22×C4—342no—
1355C22×C4—342no—
1356C22×C4—342no—
1357C22×C4—342no—
1358C22×C4—342no—
1359C22×C4—342no—
1360C22×C4—342no—
1361C22×C4—342no—
1362C22×C4—342no—
1363C22×C4—342no—
1364C22×C4—342no—
1365C22×C4—342no—
1366C22×C4—681no—
1367C22×C4—681no—
1368C22×C4—681no—
1369C22×C4—681no—
1370C22×C4—6816no—
1371C22×C4—6816no—
1372C22×C4—6816no—
1373C22×C4—681no—
1374C22×C4—681no—
1375C22×C4C23×D1711yescharacteristic
1376C22×C4C23×D1711yescharacteristic
1377C22×C4C23×D1711yescharacteristic
1378C22×C4C23×D1711yescharacteristic
1379C22×C4C23×D1711yescharacteristic
1380C22×C4C23×D1711yescharacteristic
1381C22×C4C23×D1711yescharacteristic
1382C22×C4C23×D1711yescharacteristic
1383C22×C4C23×D1711yescharacteristic
1384C22×C4C23×D1711yescharacteristic
1385C22×C4C23×D1711yescharacteristic
1386C22×C4C23×D1711yescharacteristic
1387C22×C4C23×D1711yescharacteristic
1388C4⋊C4—22no—
1389C4⋊C4—22no—
1390C4⋊C4—22no—
1391C4⋊C4—22no—
1392C4⋊C4—22no—
1393C4⋊C4—342no—
1394C4⋊C4—342no—
1395C4⋊C4—342no—
1396C4⋊C4—342no—
1397C4⋊C4—342no—
1398C4⋊C4—342no—
1399C4⋊C4—342no—
1400C4⋊C4—342no—
1401C4⋊C4—342no—
1402C4⋊C4—342no—
1403C4⋊C4—342no—
1404C4⋊C4—342no—
1405C4⋊C4—342no—
1406C4⋊C4—342no—
1407C4⋊C4—342no—
1408C22⋊C4—22no—
1409C22⋊C4—22no—
1410C22⋊C4—22no—
1411C22⋊C4—22no—
1412C22⋊C4—22no—
1413C22⋊C4—22no—
1414C22⋊C4—41no—
1415C22⋊C4—41no—
1416C22⋊C4—174no—
1417C22⋊C4—174no—
1418C22⋊C4—174no—
1419C22⋊C4—342no—
1420C22⋊C4—342no—
1421C22⋊C4—342no—
1422C22⋊C4—342no—
1423C22⋊C4—342no—
1424C22⋊C4—342no—
1425C22⋊C4—342no—
1426C22⋊C4—342no—
1427C22⋊C4—342no—
1428C22⋊C4—342no—
1429C22⋊C4—342no—
1430C22⋊C4—342no—
1431C22⋊C4—342no—
1432C22⋊C4—342no—
1433C22⋊C4—342no—
1434C22⋊C4—342no—
1435C22⋊C4—342no—
1436C22⋊C4—342no—
1437C22⋊C4—681no—
1438C22⋊C4—681no—
1439C22⋊C4—681no—
1440C22⋊C4—681no—
1441C22⋊C4—681no—
1442C22⋊C4—681no—
1443C22⋊C4D4×D1714yes—
1444C42—22no—
1445C42—41no—
1446C42—342no—
1447C42—342no—
1448C42—342no—
1449C42—681no—
1450C42—681no—
1451C42—681no—
1452C23—21no—
1453C23—21no—
1454C23—21no—
1455C23—21no—
1456C23—21no—
1457C23—21no—
1458C23—21no—
1459C23—21no—
1460C23—21no—
1461C23—21no—
1462C23—21no—
1463C23—172no—
1464C23—172no—
1465C23—172no—
1466C23—172no—
1467C23—172no—
1468C23—172no—
1469C23—172no—
1470C23—1716no—
1471C23—172no—
1472C23—172no—
1473C23—172no—
1474C23—348no—
1475C23—348no—
1476C23—348no—
1477C23—348no—
1478C23—348no—
1479C23—348no—
1480C23—341no—
1481C23—341no—
1482C23—341no—
1483C23—341no—
1484C23—341no—
1485C23—341no—
1486C23—341no—
1487C23—341no—
1488C23—341no—
1489C23—341no—
1490C23—341no—
1491C23—684no—
1492C23—684no—
1493C23—684no—
1494C23—684no—
1495C23—684no—
1496C23—684no—
1497C23—684no—
1498C23C2×D4×D1712yes—
1499C23#41×D1712yes—
1500C23#41×D1712yes—
1501C23C24×D1711yescharacteristic
1502Q8—44no—
1503Q8—684no—
1504Q8—684no—
1505Q8—684no—
1506D4—44no—
1507D4—684no—
1508D4—684no—
1509D4—684no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—21no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—21no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—44no—
1546C2×C4—44no—
1547C2×C4—44no—
1548C2×C4—172no—
1549C2×C4—172no—
1550C2×C4—172no—
1551C2×C4—172no—
1552C2×C4—348no—
1553C2×C4—348no—
1554C2×C4—348no—
1555C2×C4—348no—
1556C2×C4—341no—
1557C2×C4—341no—
1558C2×C4—341no—
1559C2×C4—341no—
1560C2×C4—341no—
1561C2×C4—341no—
1562C2×C4—341no—
1563C2×C4—341no—
1564C2×C4—341no—
1565C2×C4—341no—
1566C2×C4—341no—
1567C2×C4—341no—
1568C2×C4—341no—
1569C2×C4—341no—
1570C2×C4—341no—
1571C2×C4—341no—
1572C2×C4—341no—
1573C2×C4—341no—
1574C2×C4—341no—
1575C2×C4—341no—
1576C2×C4—341no—
1577C2×C4—341no—
1578C2×C4—341no—
1579C2×C4—341no—
1580C2×C4—341no—
1581C2×C4—341no—
1582C2×C4—341no—
1583C2×C4—341no—
1584C2×C4—341no—
1585C2×C4—341no—
1586C2×C4—341no—
1587C2×C4—341no—
1588C2×C4—341no—
1589C2×C4—341no—
1590C2×C4—341no—
1591C2×C4—684no—
1592C2×C4—684no—
1593C2×C4—684no—
1594C2×C4—684no—
1595C2×C4—684no—
1596C2×C4—684no—
1597C2×C4—684no—
1598C2×C4—684no—
1599C2×C4—684no—
1600C2×C4—684no—
1601C2×C4—684no—
1602C2×C4—684no—
1603C2×C4—684no—
1604C2×C4—684no—
1605C2×C4—684no—
1606C2×C4—684no—
1607C2×C4—684no—
1608C2×C4—684no—
1609C2×C4C2×D4×D1712yes—
1610C2×C4C2×D4×D1712yes—
1611C2×C4#41×D1712yes—
1612C2×C4#41×D1712yes—
1613C22—22no—
1614C22—22no—
1615C22—22no—
1616C22—22no—
1617C22—22no—
1618C22—22no—
1619C22—41no—
1620C22—41no—
1621C22—41no—
1622C22—41no—
1623C22—41no—
1624C22—41no—
1625C22—41no—
1626C22—174no—
1627C22—174no—
1628C22—174no—
1629C22—174no—
1630C22—174no—
1631C22—174no—
1632C22—174no—
1633C22—174no—
1634C22—3432no—
1635C22—342no—
1636C22—342no—
1637C22—342no—
1638C22—342no—
1639C22—342no—
1640C22—342no—
1641C22—681no—
1642C22—681no—
1643C22—681no—
1644C22—681no—
1645C22—681no—
1646C22—681no—
1647C22—681no—
1648C22—1368no—
1649C22#124×D1714yes—
1650C22C22×D4×D1711yescharacteristic
1651C22C2×#41×D1711yescharacteristic
1652C22C2×#41×D1711yescharacteristic
1653C22C2×#41×D1711yescharacteristic
1654C22C2×#41×D1711yescharacteristic
1655C22H(5,𝔽2)×D1711yescharacteristic
1656C222−1+4×D1711yescharacteristic
1657C4—22no—
1658C4—22no—
1659C4—22no—
1660C4—22no—
1661C4—41no—
1662C4—41no—
1663C4—41no—
1664C4—41no—
1665C4—41no—
1666C4—41no—
1667C4—41no—
1668C4—41no—
1669C4—41no—
1670C4—342no—
1671C4—342no—
1672C4—342no—
1673C4—342no—
1674C4—681no—
1675C4—681no—
1676C4—681no—
1677C4—681no—
1678C4—681no—
1679C4—681no—
1680C4—681no—
1681C4—681no—
1682C4—681no—
1683C2—24no—
1684C2—81no—
1685C2—178no—
1686C2—344no—
1687C2—1361no—
1688C2C2×#124×D1711yescharacteristic
1689C2D17×#52911yescharacteristic
1690C2D17×#53911yescharacteristic
1691C2D17×#54611yescharacteristic
1692C2D17×#54711yescharacteristic
1693C2D17×#55111yescharacteristic
1694C2D17×#55211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2488C2
prime radicalC22×D4×D17C22
hypercenter#2488D17
hypocenterC17C2×#2488
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2488

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C22⋊Q8×D17C2semidirect
3. #14533117C2semidirect
4. #14533116C2semidirect
5. #14533115C2semidirect
6. #14533114C2semidirect
7. #14533113C2semidirect
8. #14533112C2semidirect
9. #14533111C2semidirect
10. #14533110C2semidirect
11. #14533109C2semidirect
12. #14533108C2semidirect
13. #14533107C2semidirect
14. #14533106C2semidirect
15. #14533105C2semidirect
16. #14533104C2semidirect
17. #14533103C2semidirect
18. D17×#400C2semidirect
19. D17×#400C2semidirect
20. D17×#397C2semidirect
21. D17×#393C2semidirect
22. D17×#391C2semidirect
23. D17×#388C2semidirect
24. D17×#388C2semidirect
27. D17×#382C2semidirect
28. D17×#381C2semidirect
29. C4×C22⋊C4×D17C2semidirect
30. C2×#95×D17C2semidirect
31. C17×#2488C2semidirect
45. C2×#10587583C22semidirect
46. C2×#10587610C22semidirect
47. C2×#10587582C22semidirect
48. C2×#10587582C22semidirect
49. C2×#10587564C22semidirect
50. C2×#10587564C22semidirect
51. C2×#10587632C22semidirect
69. #11762751C22semidirect
70. #11762751C22semidirect
71. #11762751C22semidirect
72. #11762751C22semidirect
73. #11762750C22semidirect
74. #11762750C22semidirect
75. #11762750C22semidirect
76. #11762750C22semidirect
77. #11762749C22semidirect
78. #11762749C22semidirect
79. #11762748C22semidirect
80. #11762748C22semidirect
81. #11762747C22semidirect
82. #11762747C22semidirect
83. #11762738C22semidirect
84. #11762738C22semidirect
85. #11762737C22semidirect
86. #11762737C22semidirect
87. #11762736C22semidirect
88. #11762735C22semidirect
89. #11762734C22semidirect
90. #11762722C22semidirect
91. #11762722C22semidirect
92. #11762722C22semidirect
93. #11762721C22semidirect
94. #11762721C22semidirect
95. #11762721C22semidirect
96. #11762720C22semidirect
97. #11762716C22semidirect
98. #11762715C22semidirect
99. #11762714C22semidirect
100. #11762713C22semidirect
101. #11762713C22semidirect
102. #11762713C22semidirect
103. #11762713C22semidirect
104. #11762703C22semidirect
105. #11762703C22semidirect
106. #11762702C22semidirect
107. #11762702C22semidirect
108. #11762701C22semidirect
109. #11762701C22semidirect
110. #11762700C22semidirect
111. #11762700C22semidirect
112. #11762699C22semidirect
113. #11762699C22semidirect
114. #11762698C22semidirect
115. #11762698C22semidirect
116. #11762697C22semidirect
117. #11762697C22semidirect
132. #11762675C22semidirect
133. #11762674C22semidirect
134. #11762674C22semidirect
135. #11762673C22semidirect
136. #11762673C22semidirect
137. #11762673C22semidirect
138. #11762673C22semidirect
139. #11762672C22semidirect
140. #11762671C22semidirect
141. #11762671C22semidirect
142. #11762671C22semidirect
143. #11762671C22semidirect
144. #11762670C22semidirect
145. #11762670C22semidirect
146. C22⋊C4×Dic17C22semidirect
147. C22⋊C4×Dic17C22semidirect
148. C4×#63227C22semidirect
149. C4×#63227C22semidirect
150. C4×C22⋊Dic17C22semidirect
151. #11762656C22semidirect
152. #11762656C22semidirect
153. C2×#10587502C22semidirect
154. C2×#10587502C22semidirect
155. C2×#10587502C22semidirect
170. #95×D17C22semidirect
171. #95×D17C22semidirect
172. #95×D17C22semidirect
173. #95×D17C22semidirect
175. C2×C17×C22⋊Q8C22semidirect
176. C17×#400C22semidirect
177. C17×#400C22semidirect
178. C17×#397C22semidirect
179. C17×#393C22semidirect
180. C17×#391C22semidirect
181. C17×#388C22semidirect
182. C17×#388C22semidirect
185. C17×#382C22semidirect
186. C17×#381C22semidirect
187. C4×C22⋊C4×C17C22semidirect
188. C2×C17×#95C22semidirect
783. #2488D17direct (N × H)
889. C2×C22⋊Q8C2×D17semidirect
920. #400C2×D17semidirect
921. #400C2×D17semidirect
929. #397C2×D17semidirect
937. #393C2×D17semidirect
945. #391C2×D17semidirect
960. #388C2×D17semidirect
961. #388C2×D17semidirect
985. #382C2×D17semidirect
993. #381C2×D17semidirect
1001. C4×C22⋊C4C2×D17semidirect
1023. C2×#95C2×D17semidirect
1035. D17#2488direct (N × H)
1238. C17C2×#2488semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#123×D172
C2×C22⋊Q8×D172
#145331172
#145331162
#145331152
#145331142
#145331132
#145331122
#145331112
#145331102
#145331092
#145331082
#145331072
#145331062
#145331052
#145331042
#145331032
D17×#4002
D17×#3972
D17×#3932
D17×#3912
D17×#3882
D17×#3862
D17×#3822
D17×#3812
C4×C22⋊C4×D172
C2×#95×D172
C17×#24882
C2×#248817