Finite Group Databasebeta

← #17241320

Subgroups — #17241320

Order 4352.

2450 conjugacy classes of subgroups.

The subgroup lattice has 1638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763434C211yesmaximal, characteristic, complemented
2C2×#123×D17C211yesmaximal, characteristic
3#14537070C211yesmaximal, characteristic, complemented
4#14537068C211yesmaximal, characteristic, complemented
5#14535212C211yesmaximal, characteristic, complemented
6#14535211C211yesmaximal, characteristic, complemented
7#14535208C211yesmaximal, characteristic, complemented
8#14535207C211yesmaximal, characteristic, complemented
9#14535203C211yesmaximal, characteristic, complemented
10#14535202C211yesmaximal, characteristic, complemented
11#14535199C211yesmaximal, characteristic, complemented
12#14535198C211yesmaximal, characteristic, complemented
13#14535128C211yesmaximal, characteristic, complemented
14#14535126C211yesmaximal, characteristic, complemented
15#14535124C211yesmaximal, characteristic, complemented
16#14535123C211yesmaximal, characteristic, complemented
17#14535123C211yesmaximal, characteristic, complemented
18#14535121C211yesmaximal, characteristic, complemented
19#14535120C211yesmaximal, characteristic, complemented
20#14534602C211yesmaximal, characteristic, complemented
21#14534596C211yesmaximal, characteristic, complemented
22#14533940C211yesmaximal, characteristic, complemented
23#14533936C211yesmaximal, characteristic, complemented
24#14533259C211yesmaximal, characteristic, complemented
25#14533257C211yesmaximal, characteristic, complemented
26#14533064C211yesmaximal, characteristic, complemented
27#14533061C211yesmaximal, characteristic, complemented
28#14532108C211yesmaximal, characteristic
29#14532106C211yesmaximal, characteristic
30#14531378C211yesmaximal, characteristic, complemented
31C17×#2680C211yesmaximal, characteristic, complemented
32C22×D4×D17C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34#11763434—28no—
35C2×#10587580C2211yescharacteristic
36C2×#10587580C2211yescharacteristic
37C2×#10587580C2211yescharacteristic
38C2×#10587572C2211yescharacteristic
39C2×#10587615C2211yescharacteristic
40C2×#10587615C2211yescharacteristic
41C2×#10587569C2211yescharacteristic
42C2×#10587569C2211yescharacteristic
43C2×#10587569C2211yescharacteristic
44C2×#10587621C2211yescharacteristic
45#123×D17—28no—
46C2×#10587583C2211yescharacteristic
47C2×#10587583C2211yescharacteristic, complemented
48C2×#10587610C2211yescharacteristic, complemented
49C2×#10587582C2211yescharacteristic
50C2×#10587582C2211yescharacteristic
51C2×#10587582C2211yescharacteristic, complemented
52C2×#10587582C2211yescharacteristic, complemented
53C2×#10587582C2211yescharacteristic, complemented
54C2×#10587564C2211yescharacteristic, complemented
55C2×#10587564C2211yescharacteristic, complemented
56C2×#10587564C2211yescharacteristic, complemented
57C2×#10587632C2211yescharacteristic
58C2×#10587632C2211yescharacteristic, complemented
59C2×#10587632C2211yescharacteristic, complemented
60C2×C4⋊C4×D17C2211yescharacteristic
61C2×C4⋊C4×D17C2211yescharacteristic
62C22×#63227C2211yescharacteristic
63C2×C22⋊C4×D17C2211yescharacteristic
64C2×C22⋊C4×D17C2211yescharacteristic
65C2×C22⋊C4×D17C2211yescharacteristic
66C2×C22⋊C4×D17C2211yescharacteristic
67#11762751C2211yescharacteristic, complemented
68#11762750C2211yescharacteristic, complemented
69#11762749C2211yescharacteristic, complemented
70#11762748C2211yescharacteristic, complemented
71#11762743C2211yescharacteristic, complemented
72#11762743C2211yescharacteristic, complemented
73#11762742C2211yescharacteristic, complemented
74#11762742C2211yescharacteristic, complemented
75#11762742C2211yescharacteristic, complemented
76#11762742C2211yescharacteristic, complemented
77#11762742C2211yescharacteristic, complemented
78#11762742C2211yescharacteristic, complemented
79#11762741C2211yescharacteristic, complemented
80#11762740C2211yescharacteristic, complemented
81#11762740C2211yescharacteristic, complemented
82#11762740C2211yescharacteristic, complemented
83#11762739C2211yescharacteristic, complemented
84#11762739C2211yescharacteristic, complemented
85#11762738C2211yescharacteristic, complemented
86#11762738C2211yescharacteristic, complemented
87#11762738C2211yescharacteristic, complemented
88#11762737C2211yescharacteristic, complemented
89#11762737C2211yescharacteristic, complemented
90#11762737C2211yescharacteristic, complemented
91#11762735C2211yescharacteristic, complemented
92#11762735C2211yescharacteristic, complemented
93#11762735C2211yescharacteristic, complemented
94#11762734C2211yescharacteristic, complemented
95#11762730C2211yescharacteristic, complemented
96#11762729C2211yescharacteristic, complemented
97#11762728C2211yescharacteristic, complemented
98#11762726C2211yescharacteristic
99#11762726C2211yescharacteristic
100#11762725C2211yescharacteristic
101#11762724C2211yescharacteristic
102#11762724C2211yescharacteristic
103#11762724C2211yescharacteristic
104#11762723C2211yescharacteristic
105#11762722C2211yescharacteristic, complemented
106#11762722C2211yescharacteristic, complemented
107#11762721C2211yescharacteristic, complemented
108#11762721C2211yescharacteristic, complemented
109#11762715C2211yescharacteristic, complemented
110#11762714C2211yescharacteristic, complemented
111#11762713C2211yescharacteristic, complemented
112#11762713C2211yescharacteristic, complemented
113#11762703C2211yescharacteristic, complemented
114#11762703C2211yescharacteristic, complemented
115#11762702C2211yescharacteristic, complemented
116#11762702C2211yescharacteristic, complemented
117#11762702C2211yescharacteristic, complemented
118#11762701C2211yescharacteristic, complemented
119#11762701C2211yescharacteristic, complemented
120#11762701C2211yescharacteristic, complemented
121#11762700C2211yescharacteristic, complemented
122#11762700C2211yescharacteristic, complemented
123#11762699C2211yescharacteristic, complemented
124#11762699C2211yescharacteristic, complemented
125#11762698C2211yescharacteristic, complemented
126#11762697C2211yescharacteristic, complemented
127#11762689C2211yescharacteristic
128#11762687C2211yescharacteristic
129#11762686C2211yescharacteristic
130#11762685C2211yescharacteristic
131#11762683C2211yescharacteristic
132#11762683C2211yescharacteristic
133#11762683C2211yescharacteristic, complemented
134#11762683C2211yescharacteristic, complemented
135#11762682C2211yescharacteristic, complemented
136#11762682C2211yescharacteristic, complemented
137#11762681C2211yescharacteristic, complemented
138#11762681C2211yescharacteristic, complemented
139#11762680C2211yescharacteristic
140#11762680C2211yescharacteristic
141#11762680C2211yescharacteristic
142#11762680C2211yescharacteristic
143#11762680C2211yescharacteristic
144#11762680C2211yescharacteristic
145#11762680C2211yescharacteristic, complemented
146#11762680C2211yescharacteristic, complemented
147#11762680C2211yescharacteristic, complemented
148#11762680C2211yescharacteristic, complemented
149#11762678C2211yescharacteristic, complemented
150#11762678C2211yescharacteristic, complemented
151#11762678C2211yescharacteristic, complemented
152#11762671C2211yescharacteristic
153#11762671C2211yescharacteristic
154#11762671C2211yescharacteristic
155#11762671C2211yescharacteristic
156#11762671C2211yescharacteristic, complemented
157#11762671C2211yescharacteristic, complemented
158#11762670C2211yescharacteristic, complemented
159#11762670C2211yescharacteristic, complemented
160#11762669C2211yescharacteristic, complemented
161#11762668C2211yescharacteristic
162#11762668C2211yescharacteristic, complemented
163#11762667C2211yescharacteristic, complemented
164#11762666C2211yescharacteristic
165#11762666C2211yescharacteristic, complemented
166#11762664C2211yescharacteristic
167#11762664C2211yescharacteristic
168#11762664C2211yescharacteristic
169#11762664C2211yescharacteristic
170#11762664C2211yescharacteristic
171#11762664C2211yescharacteristic
172C4×#63227C2211yescharacteristic
173#11762656C2211yescharacteristic
174C2×C17×#123C2211yescharacteristic
175C2×C17×#123C2211yescharacteristic
176C2×C17×C22⋊Q8C2211yescharacteristic, complemented
177C2×C17×C22⋊Q8C2211yescharacteristic, complemented
178C17×#398C2211yescharacteristic, complemented
179C17×#398C2211yescharacteristic, complemented
180C17×#397C2211yescharacteristic, complemented
181C17×#397C2211yescharacteristic, complemented
182C17×#395C2211yescharacteristic, complemented
183C17×#394C2211yescharacteristic
184C17×#388C2211yescharacteristic, complemented
185C17×#388C2211yescharacteristic, complemented
186C17×#385C2211yescharacteristic, complemented
187C17×#385C2211yescharacteristic, complemented
188C17×#384C2211yescharacteristic, complemented
189C24×D17C2311yescharacteristic
190C24×D17C2311yescharacteristic
191C22×Q8×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C23×Dic17C2311yescharacteristic
198C23×Dic17C2311yescharacteristic
199C2×D4×D17—24no—
200C2×D4×D17—42no—
201C2×D4×D17—42no—
202C22×D68C2311yescharacteristic
203C22×C4×D17—24no—
204C22×C4×D17—42no—
205C22×C4×D17—42no—
206C22×C4×D17C2311yescharacteristic
207C22×C4×D17C2311yescharacteristic
208C22×C4×D17C2311yescharacteristic
209C22×C4×D17C2311yescharacteristic
210C22×C4×D17C2311yescharacteristic
211C22×C4×D17C2311yescharacteristic
212C22×C4×D17C2311yescharacteristic
213C22×C4×D17C2311yescharacteristic
214C22×C4×D17C2311yescharacteristic
215C22×Dic34C2311yescharacteristic
216C22×Dic34C2311yescharacteristic
217C22×Dic34C2311yescharacteristic
218C17×#123—24no—
219C17×#123—42no—
220C17×C22⋊Q8—24no—
221C17×C22⋊Q8—42no—
222C2×C4⋊C4×C17C2311yescharacteristic
223C2×C4⋊C4×C17C2311yescharacteristic
224C2×C4⋊C4×C17C2311yescharacteristic
225C2×C4⋊C4×C17C2311yescharacteristic
226C2×C4⋊C4×C17C2311yescharacteristic
227C2×C4⋊C4×C17C2311yescharacteristic
228C2×C4⋊C4×C17C2311yescharacteristic
229C2×C4⋊C4×C17C2311yescharacteristic
230C2×C4⋊C4×C17C2311yescharacteristic
231C2×C4⋊C4×C17C2311yescharacteristic
232C2×C4⋊C4×C17C2311yescharacteristic
233C2×C4⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17C2311yescharacteristic
235C2×C22⋊C4×C17C2311yescharacteristic
236C2×C22⋊C4×C17C2311yescharacteristic
237C2×C22⋊C4×C17C2311yescharacteristic
238C2×C22⋊C4×C17C2311yescharacteristic
239C2×C22⋊C4×C17C2311yescharacteristic
240C2×C22⋊C4×C17C2311yescharacteristic
241C2×C22⋊C4×C17C2311yescharacteristic
242C2×C22⋊C4×C17C2311yescharacteristic
243C2×C22⋊C4×C17C2311yescharacteristic
244C2×C42×C17C2311yescharacteristic
245C2×C22⋊Dic17C2311yescharacteristic
246C2×C22⋊Dic17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
250C2×C22⋊Dic17C2311yescharacteristic
251C2×C22⋊Dic17C2311yescharacteristic
252C2×C22⋊Dic17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255#10587632—24no—
256#10587632—24no—
257#10587632—42no—
258#10587621—24no—
259#10587615—24no—
260#10587615—42no—
261C2×#63227—24no—
262C2×#63227C2311yescharacteristic
263C2×#63227C2311yescharacteristic
264C2×#63227C2311yescharacteristic
265C2×#63227C2311yescharacteristic
266C2×#63227C2311yescharacteristic
267C2×#63227C2311yescharacteristic
268C2×#63227C2311yescharacteristic
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×#63227C2311yescharacteristic
288C2×#63227C2311yescharacteristic
289C2×#63227C2311yescharacteristic
290C2×C4⋊Dic17C2311yescharacteristic
291C2×C4⋊Dic17C2311yescharacteristic
292C2×C4⋊Dic17C2311yescharacteristic
293C2×C4⋊Dic17C2311yescharacteristic
294C2×C4⋊Dic17C2311yescharacteristic
295C2×C4⋊Dic17C2311yescharacteristic
296C2×C4⋊Dic17C2311yescharacteristic
297C2×C4⋊Dic17C2311yescharacteristic
298#10587610—24no—
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×#63225C2311yescharacteristic
303C2×#63225C2311yescharacteristic
304C2×#63225C2311yescharacteristic
305C2×#63225C2311yescharacteristic
306C2×#63225C2311yescharacteristic
307C2×#63225C2311yescharacteristic
308C2×#63225C2311yescharacteristic
309C2×#63225C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×#63225C2311yescharacteristic
312C2×#63225C2311yescharacteristic
313C2×#63225C2311yescharacteristic
314C2×#63225C2311yescharacteristic
315C2×#63225C2311yescharacteristic
316C2×#63225C2311yescharacteristic
317C2×#63225C2311yescharacteristic
318C2×#63225C2311yescharacteristic
319C2×C4×Dic17C2311yescharacteristic
320C2×C4×Dic17C2311yescharacteristic
321C2×C4×Dic17C2311yescharacteristic
322#10587583—24no—
323#10587583—24no—
324#10587582—24no—
325#10587582—24no—
326#10587582—24no—
327#10587582—24no—
328#10587582—42no—
329#10587580—24no—
330#10587580—24no—
331#10587580—42no—
332C4⋊C4×D17—24no—
333C4⋊C4×D17—24no—
334#10587572—24no—
335#10587569—24no—
336#10587569—24no—
337#10587569—42no—
338C22⋊C4×D17—24no—
339C22⋊C4×D17—24no—
340C22⋊C4×D17—24no—
341C22⋊C4×D17D418yes—
342#10587564—24no—
343#10587564—24no—
344#10587564—42no—
345C17×#95C2311yescharacteristic
346C17×#95C2311yescharacteristic
347C17×#95C2311yescharacteristic
348C17×#95C2311yescharacteristic
349C17×#95C2311yescharacteristic
350C17×#95C2311yescharacteristic
351C17×#95C2311yescharacteristic
352C17×#95C2311yescharacteristic
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
385C24×C17C2411yescharacteristic
386C24×C17C2411yescharacteristic
387C23×D17—22no—
388C23×D17—22no—
389C23×D17—22no—
390C23×D17—22no—
391C23×D17—22no—
392C23×D17—22no—
393C23×D17—22no—
394C23×D17—41no—
395C23×D17—41no—
396C23×D17—41no—
397C23×D17—41no—
398C23×D17—41no—
399C23×D17—41no—
400C23×D17C2×D414yes—
401C23×D17C2411yescharacteristic
402C23×D17C2411yescharacteristic
403C23×D17C2411yescharacteristic
404C2×Q8×C17—22no—
405C2×Q8×C17—41no—
406C2×Q8×C17—41no—
407C2×D4×C17—22no—
408C2×D4×C17—22no—
409C2×D4×C17—41no—
410C22×C4×C17—22no—
411C22×C4×C17—22no—
412C22×C4×C17—22no—
413C22×C4×C17—41no—
414C22×C4×C17—41no—
415C22×C4×C17—41no—
416C22×C4×C17C2411yescharacteristic
417C22×C4×C17C2411yescharacteristic
418C22×C4×C17C2411yescharacteristic
419C22×C4×C17C2411yescharacteristic
420C22×C4×C17C2411yescharacteristic
421C22×C4×C17C2411yescharacteristic
422C22×C4×C17C2411yescharacteristic
423C22×C4×C17C2411yescharacteristic
424C22×C4×C17C2411yescharacteristic
425C22×C4×C17C2411yescharacteristic
426C22×C4×C17C2411yescharacteristic
427C22×C4×C17C2411yescharacteristic
428C22×C4×C17C2411yescharacteristic
429C2×C22⋊D17—22no—
430C2×C22⋊D17—22no—
431C2×C22⋊D17—22no—
432C2×C22⋊D17—22no—
433C2×C22⋊D17—41no—
434C2×C22⋊D17—41no—
435C22×Dic17—22no—
436C22×Dic17—22no—
437C22×Dic17—22no—
438C22×Dic17—41no—
439C22×Dic17—41no—
440C22×Dic17—41no—
441C22×Dic17C2411yescharacteristic
442C22×Dic17C2411yescharacteristic
443C22×Dic17C2411yescharacteristic
444C22×Dic17C2411yescharacteristic
445C22×Dic17C2411yescharacteristic
446C22×Dic17C2411yescharacteristic
447C22×Dic17C2411yescharacteristic
448C22×Dic17C2411yescharacteristic
449C22×Dic17C2411yescharacteristic
450C22×Dic17C2411yescharacteristic
451C22×Dic17C2411yescharacteristic
452C22×Dic17C2411yescharacteristic
453C22×Dic17C2411yescharacteristic
454D4×D17—416no—
455C2×D68—22no—
456C2×D68—22no—
457C2×D68—41no—
458C2×C4×D17—22no—
459C2×C4×D17—22no—
460C2×C4×D17—22no—
461C2×C4×D17—22no—
462C2×C4×D17—22no—
463C2×C4×D17—22no—
464C2×C4×D17—22no—
465C2×C4×D17—22no—
466C2×C4×D17—22no—
467C2×C4×D17—22no—
468C2×C4×D17—22no—
469C2×C4×D17—41no—
470C2×C4×D17—41no—
471C2×C4×D17—41no—
472C2×C4×D17—41no—
473C2×C4×D17—41no—
474C2×C4×D17—41no—
475C2×C4×D17—41no—
476C2×C4×D17—41no—
477C2×C4×D17—41no—
478C2×C4×D17—41no—
479C2×C4×D17—416no—
480C2×C4×D17—41no—
481C2×C4×D17—41no—
482C2×C4×D17—41no—
483C2×C4×D17—41no—
484C2×C4×D17C2×D414yes—
485C2×C4×D17C2×D414yes—
486C2×Dic34—22no—
487C2×Dic34—22no—
488C2×Dic34—22no—
489C2×Dic34—41no—
490C2×Dic34—41no—
491C2×Dic34—41no—
492C2×Dic34—41no—
493C2×Dic34—41no—
494C2×Dic34—41no—
495C4⋊C4×C17—22no—
496C4⋊C4×C17—22no—
497C4⋊C4×C17—22no—
498C4⋊C4×C17—22no—
499C4⋊C4×C17—22no—
500C4⋊C4×C17—41no—
501C4⋊C4×C17—41no—
502C4⋊C4×C17—41no—
503C4⋊C4×C17—41no—
504C4⋊C4×C17—41no—
505C4⋊C4×C17—41no—
506C4⋊C4×C17—41no—
507C22⋊C4×C17—22no—
508C22⋊C4×C17—22no—
509C22⋊C4×C17—22no—
510C22⋊C4×C17—22no—
511C22⋊C4×C17—22no—
512C22⋊C4×C17—22no—
513C22⋊C4×C17—41no—
514C22⋊C4×C17—41no—
515C22⋊C4×C17—41no—
516C22⋊C4×C17C2×D414yes—
517C42×C17—41no—
518C22⋊Dic17—22no—
519C22⋊Dic17—22no—
520C22⋊Dic17—22no—
521C22⋊Dic17—22no—
522C22⋊Dic17—41no—
523C22⋊Dic17—41no—
524C22⋊Dic17—41no—
525C22⋊Dic17—41no—
526C22⋊Dic17—41no—
527C22⋊Dic17C2×D414yes—
528#63227—22no—
529#63227—22no—
530#63227—22no—
531#63227—22no—
532#63227—22no—
533#63227—22no—
534#63227—22no—
535#63227—22no—
536#63227—22no—
537#63227—22no—
538#63227—22no—
539#63227—22no—
540#63227—22no—
541#63227—22no—
542#63227—22no—
543#63227—22no—
544#63227—22no—
545#63227—22no—
546#63227—41no—
547#63227—41no—
548#63227—41no—
549#63227—41no—
550#63227—41no—
551#63227—41no—
552#63227—41no—
553#63227—41no—
554#63227C2×D414yes—
555#63227C2×D414yes—
556C4⋊Dic17—22no—
557C4⋊Dic17—22no—
558C4⋊Dic17—22no—
559C4⋊Dic17—22no—
560C4⋊Dic17—22no—
561C4⋊Dic17—41no—
562C4⋊Dic17—41no—
563C4⋊Dic17—41no—
564#63225—22no—
565#63225—22no—
566#63225—22no—
567#63225—22no—
568#63225—22no—
569#63225—22no—
570#63225—22no—
571#63225—22no—
572#63225—22no—
573#63225—22no—
574#63225—41no—
575#63225—41no—
576#63225—41no—
577#63225—41no—
578#63225—41no—
579#63225—41no—
580#63225—41no—
581#63225—41no—
582#63225—41no—
583#63225—41no—
584C4×Dic17—41no—
585C4×Dic17—41no—
586C4×Dic17—41no—
587#36720—171nomaximal, Sylow
588C23×C17—21no—
589C23×C17—21no—
590C23×C17—21no—
591C23×C17—21no—
592C23×C17—21no—
593C23×C17—21no—
594C23×C17—21no—
595C23×C17—21no—
596C23×C17—21no—
597C23×C17—21no—
598C23×C17—21no—
599C23×C17—21no—
600C23×C17C22×D412yes—
601C23×C17H(5,𝔽2)12yes—
602C23×C17C2511yescharacteristic
603C22×D17—21no—
604C22×D17—21no—
605C22×D17—21no—
606C22×D17—21no—
607C22×D17—28no—
608C22×D17—21no—
609C22×D17—21no—
610C22×D17—21no—
611C22×D17—21no—
612C22×D17—21no—
613C22×D17—21no—
614C22×D17—21no—
615C22×D17—21no—
616C22×D17—21no—
617C22×D17—21no—
618C22×D17—21no—
619C22×D17—21no—
620C22×D17—28no—
621C22×D17—44no—
622C22×D17—44no—
623C22×D17—44no—
624C22×D17—44no—
625C22×D17—44no—
626C22×D17—44no—
627C22×D17—44no—
628C22×D17—44no—
629C22×D17—82no—
630C22×D17—82no—
631C22×D17—82no—
632C22×D17—82no—
633C22×D17C22×D412yes—
634C22×D17C22×D412yes—
635C22×D17H(5,𝔽2)12yes—
636C22×D172−1+412yes—
637C22×D172−1+412yes—
638Q8×C17—82no—
639D4×C17—44no—
640C2×C4×C17—21no—
641C2×C4×C17—21no—
642C2×C4×C17—21no—
643C2×C4×C17—21no—
644C2×C4×C17—21no—
645C2×C4×C17—21no—
646C2×C4×C17—21no—
647C2×C4×C17—21no—
648C2×C4×C17—21no—
649C2×C4×C17—21no—
650C2×C4×C17—21no—
651C2×C4×C17—21no—
652C2×C4×C17—21no—
653C2×C4×C17—21no—
654C2×C4×C17—21no—
655C2×C4×C17—21no—
656C2×C4×C17—21no—
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—44no—
678C2×C4×C17—82no—
679C2×C4×C17C22×D412yes—
680C2×C4×C17C22×D412yes—
681C22⋊D17—44no—
682C22⋊D17—44no—
683C2×Dic17—21no—
684C2×Dic17—21no—
685C2×Dic17—21no—
686C2×Dic17—21no—
687C2×Dic17—21no—
688C2×Dic17—21no—
689C2×Dic17—21no—
690C2×Dic17—21no—
691C2×Dic17—21no—
692C2×Dic17—21no—
693C2×Dic17—21no—
694C2×Dic17—21no—
695C2×Dic17—21no—
696C2×Dic17—21no—
697C2×Dic17—21no—
698C2×Dic17—21no—
699C2×Dic17—21no—
700C2×Dic17—21no—
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—44no—
721C2×Dic17—82no—
722C2×Dic17C22×D412yes—
723C2×Dic17C22×D412yes—
724D68—44no—
725C4×D17—44no—
726C4×D17—44no—
727C4×D17—44no—
728C4×D17—44no—
729C4×D17—44no—
730C4×D17—44no—
731C4×D17—44no—
732C4×D17—82no—
733C4×D17—82no—
734Dic34—82no—
735Dic34—82no—
736Dic34—82no—
737C2×#543—171no—
738C22×#123—171no—
739#2848—171no—
740#2848—171no—
741#2687—171no—
742#2687—171no—
743#2687—171no—
744#2687—171no—
745#2687—171no—
746#2687—171no—
747#2687—171no—
748#2687—171no—
749#2680—171no—
750#2680—171no—
751#2680—171no—
752#2680—171no—
753#2680—171no—
754#2680—171no—
755#2680—171no—
756#2680D1711yescharacteristic, complemented
757#2627—171no—
758#2627—171no—
759#2561—171no—
760#2561—171no—
761#2502—171no—
762#2502—171no—
763#2483—171no—
764#2483—171no—
765#2405—171no—
766#2405—171no—
767#2312—171no—
768C22×C17—22no—
769C22×C17—22no—
770C22×C17—22no—
771C22×C17—22no—
772C22×C17—22no—
773C22×C17—22no—
774C22×C17—41no—
775C22×C17—41no—
776C22×C17—41no—
777C22×C17—41no—
778C22×C17—41no—
779C22×C17—41no—
780C22×C17—41no—
781C22×C17—41no—
782C22×C17C23×D411yescharacteristic
783C22×C17C2×H(5,𝔽2)11yescharacteristic
784C22×C17C2×H(5,𝔽2)11yescharacteristic
785C22×C17C2×2−1+411yescharacteristic
786C22×C17C2×2−1+411yescharacteristic
787C22×C17#58511yescharacteristic
788C22×C17#58511yescharacteristic
789C2×D17—22no—
790C2×D17—22no—
791C2×D17—22no—
792C2×D17—22no—
793C2×D17—22no—
794C2×D17—22no—
795C2×D17—22no—
796C2×D17—22no—
797C2×D17—22no—
798C2×D17—22no—
799C2×D17—22no—
800C2×D17—22no—
801C2×D17—416no—
802C2×D17—41no—
803C2×D17—41no—
804C2×D17—41no—
805C2×D17—41no—
806C2×D17—41no—
807C2×D17—41no—
808C2×D17—41no—
809C2×D17—41no—
810C2×D17—88no—
811C2×D17#53614yes—
812C4×C17—22no—
813C4×C17—22no—
814C4×C17—41no—
815C4×C17—41no—
816C4×C17—41no—
817C4×C17—41no—
818C4×C17—41no—
819C4×C17—41no—
820C4×C17—41no—
821C4×C17—41no—
822C4×C17—41no—
823C4×C17—41no—
824C4×C17—41no—
825Dic17—22no—
826Dic17—22no—
827Dic17—41no—
828Dic17—41no—
829Dic17—41no—
830Dic17—41no—
831Dic17—41no—
832Dic17—41no—
833Dic17—41no—
834Dic17—41no—
835Dic17—41no—
836Dic17—41no—
837Dic17—41no—
838C23×D4—171no—
839C24×C4—171no—
840#543—348no—
841C2×#123—171no—
842C2×#123—171no—
843C2×#123—171no—
844C2×#123—171no—
845C2×#123—171no—
846C2×#123—171no—
847C2×#123—171no—
848C2×#123—171no—
849C2×#123—171no—
850C2×#123—171no—
851C2×#123—348no—
852C2×#123C2×D1711yescharacteristic
853C2×#123C2×D1711yescharacteristic
854C2×C22⋊Q8—171no—
855C2×C22⋊Q8—171no—
856C2×C22⋊Q8—171no—
857C2×C22⋊Q8—171no—
858C2×C22⋊Q8—171no—
859C2×C22⋊Q8—171no—
860C2×C22⋊Q8—171no—
861C2×C22⋊Q8—171no—
862C2×C22⋊Q8—171no—
863C2×C22⋊Q8—171no—
864C2×C22⋊Q8—171no—
865C2×C22⋊Q8—171no—
866C2×C22⋊Q8—171no—
867C2×C22⋊Q8—171no—
868C2×C22⋊Q8C2×D1711yescharacteristic, complemented
869C2×C22⋊Q8C2×D1711yescharacteristic, complemented
870C22×C4⋊C4—171no—
871C22×C4⋊C4—171no—
872C22×C22⋊C4—171no—
873C22×C22⋊C4—171no—
874C22×C22⋊C4—171no—
875C22×C22⋊C4—171no—
876C22×C22⋊C4—171no—
877#400—171no—
878#400—171no—
879#400—171no—
880#400—171no—
881#398—171no—
882#398—171no—
883#398—171no—
884#398—171no—
885#398—171no—
886#398—171no—
887#398—171no—
888#398—171no—
889#398—171no—
890#398—171no—
891#398—171no—
892#398—171no—
893#398—171no—
894#398—171no—
895#398C2×D1711yescharacteristic, complemented
896#398C2×D1711yescharacteristic, complemented
897#397—171no—
898#397—171no—
899#397—171no—
900#397—171no—
901#397—171no—
902#397—171no—
903#397—171no—
904#397—171no—
905#397—171no—
906#397—171no—
907#397C2×D1711yescharacteristic, complemented
908#397C2×D1711yescharacteristic, complemented
909#395—171no—
910#395—171no—
911#395—171no—
912#395C2×D1711yescharacteristic, complemented
913#394—171no—
914#394—171no—
915#394—171no—
916#394—171no—
917#394—171no—
918#394—171no—
919#394—171no—
920#394C2×D1711yescharacteristic
921#393—171no—
922#393—171no—
923#393—171no—
924#393—171no—
925#391—171no—
926#391—171no—
927#391—171no—
928#391—171no—
929#388—171no—
930#388—171no—
931#388—171no—
932#388—171no—
933#388—171no—
934#388—171no—
935#388—171no—
936#388—171no—
937#388—171no—
938#388—171no—
939#388—171no—
940#388—171no—
941#388—171no—
942#388—171no—
943#388C2×D1711yescharacteristic, complemented
944#388C2×D1711yescharacteristic, complemented
945#386—171no—
946#386—171no—
947#386—171no—
948#386—171no—
949#385—171no—
950#385—171no—
951#385—171no—
952#385—171no—
953#385—171no—
954#385—171no—
955#385—171no—
956#385—171no—
957#385—171no—
958#385—171no—
959#385—171no—
960#385—171no—
961#385—171no—
962#385—171no—
963#385—171no—
964#385—171no—
965#385—171no—
966#385—171no—
967#385C2×D1711yescharacteristic, complemented
968#385C2×D1711yescharacteristic, complemented
969#384—171no—
970#384—171no—
971#384—171no—
972#384C2×D1711yescharacteristic, complemented
973#381—171no—
974#381—171no—
975#381—171no—
976#381—171no—
977#381—171no—
978#381—171no—
979#381—171no—
980#381—171no—
981#380—171no—
982#380—171no—
983#380—171no—
984#380—171no—
985#380—171no—
986#380—171no—
987#379—171no—
988#379—171no—
989#379—171no—
990#379—171no—
991#379—171no—
992#379—171no—
993C4×C22⋊C4—171no—
994C4×C22⋊C4—171no—
995C2×C17—42no—
996C2×C17—42no—
997C2×C17C2×#53611yescharacteristic
998C2×C17#348411yescharacteristic
999C2×C17#348511yescharacteristic
1000C2×C17#353511yescharacteristic
1001C2×C17#353511yescharacteristic
1002C2×C17#353511yescharacteristic
1003C2×C17#353511yescharacteristic
1004D17—24no—
1005D17—42no—
1006D17—42no—
1007C25—171no—
1008C25—171no—
1009C22×Q8—171no—
1010C22×Q8—171no—
1011C22×Q8—171no—
1012C22×Q8C22×D1711yescharacteristic
1013C22×D4—171no—
1014C22×D4—171no—
1015C22×D4—171no—
1016C22×D4—344no—
1017C22×D4—682no—
1018C22×D4—682no—
1019C22×D4C22×D1711yescharacteristic
1020C23×C4—171no—
1021C23×C4—171no—
1022C23×C4—171no—
1023C23×C4—171no—
1024C23×C4—171no—
1025C23×C4—171no—
1026C23×C4—171no—
1027C23×C4—171no—
1028C23×C4—171no—
1029C23×C4—171no—
1030C23×C4—171no—
1031C23×C4—344no—
1032C23×C4—682no—
1033C23×C4—682no—
1034C23×C4C22×D1711yescharacteristic
1035C23×C4C22×D1711yescharacteristic
1036#123—24no—
1037#123—42no—
1038#123—344no—
1039#123—344no—
1040#123—344no—
1041#123—344no—
1042#123—344no—
1043#123—344no—
1044#123—344no—
1045#123—682no—
1046#123—682no—
1047#123—682no—
1048C22⋊Q8—24no—
1049C22⋊Q8—42no—
1050C22⋊Q8—344no—
1051C22⋊Q8—344no—
1052C22⋊Q8—344no—
1053C22⋊Q8—344no—
1054C22⋊Q8—344no—
1055C22⋊Q8—344no—
1056C22⋊Q8—344no—
1057C22⋊Q8—344no—
1058C22⋊Q8—344no—
1059C22⋊Q8—344no—
1060C22⋊Q8—344no—
1061C22⋊Q8—682no—
1062C22⋊Q8—682no—
1063C22⋊Q8—682no—
1064C2×C4⋊C4—171no—
1065C2×C4⋊C4—171no—
1066C2×C4⋊C4—171no—
1067C2×C4⋊C4—171no—
1068C2×C4⋊C4—171no—
1069C2×C4⋊C4—171no—
1070C2×C4⋊C4—171no—
1071C2×C4⋊C4—171no—
1072C2×C4⋊C4—171no—
1073C2×C4⋊C4—171no—
1074C2×C4⋊C4—171no—
1075C2×C4⋊C4—171no—
1076C2×C4⋊C4—171no—
1077C2×C4⋊C4—171no—
1078C2×C4⋊C4—171no—
1079C2×C4⋊C4—171no—
1080C2×C4⋊C4—171no—
1081C2×C4⋊C4—171no—
1082C2×C4⋊C4—171no—
1083C2×C4⋊C4—171no—
1084C2×C4⋊C4—171no—
1085C2×C4⋊C4—171no—
1086C2×C4⋊C4—171no—
1087C2×C4⋊C4—171no—
1088C2×C4⋊C4—171no—
1089C2×C4⋊C4—171no—
1090C2×C4⋊C4—171no—
1091C2×C4⋊C4—171no—
1092C2×C4⋊C4—344no—
1093C2×C4⋊C4—344no—
1094C2×C4⋊C4C22×D1711yescharacteristic
1095C2×C4⋊C4C22×D1711yescharacteristic
1096C2×C4⋊C4C22×D1711yescharacteristic
1097C2×C4⋊C4C22×D1711yescharacteristic
1098C2×C4⋊C4C22×D1711yescharacteristic
1099C2×C4⋊C4C22×D1711yescharacteristic
1100C2×C4⋊C4C22×D1711yescharacteristic
1101C2×C4⋊C4C22×D1711yescharacteristic
1102C2×C4⋊C4C22×D1711yescharacteristic
1103C2×C4⋊C4C22×D1711yescharacteristic
1104C2×C4⋊C4C22×D1711yescharacteristic
1105C2×C4⋊C4C22×D1711yescharacteristic
1106C2×C22⋊C4—171no—
1107C2×C22⋊C4—171no—
1108C2×C22⋊C4—171no—
1109C2×C22⋊C4—178no—
1110C2×C22⋊C4—171no—
1111C2×C22⋊C4—171no—
1112C2×C22⋊C4—171no—
1113C2×C22⋊C4—171no—
1114C2×C22⋊C4—171no—
1115C2×C22⋊C4—171no—
1116C2×C22⋊C4—171no—
1117C2×C22⋊C4—171no—
1118C2×C22⋊C4—171no—
1119C2×C22⋊C4—171no—
1120C2×C22⋊C4—171no—
1121C2×C22⋊C4—171no—
1122C2×C22⋊C4—171no—
1123C2×C22⋊C4—171no—
1124C2×C22⋊C4—171no—
1125C2×C22⋊C4—171no—
1126C2×C22⋊C4—171no—
1127C2×C22⋊C4—171no—
1128C2×C22⋊C4—171no—
1129C2×C22⋊C4—171no—
1130C2×C22⋊C4—171no—
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—344no—
1146C2×C22⋊C4—344no—
1147C2×C22⋊C4—344no—
1148C2×C22⋊C4—344no—
1149C2×C22⋊C4C22×D1711yescharacteristic
1150C2×C22⋊C4C22×D1711yescharacteristic
1151C2×C22⋊C4C22×D1711yescharacteristic
1152C2×C22⋊C4C22×D1711yescharacteristic
1153C2×C22⋊C4C22×D1711yescharacteristic
1154C2×C22⋊C4C22×D1711yescharacteristic
1155C2×C22⋊C4C22×D1711yescharacteristic
1156C2×C22⋊C4C22×D1711yescharacteristic
1157C2×C22⋊C4C22×D1711yescharacteristic
1158C2×C22⋊C4C22×D1711yescharacteristic
1159C2×C42—171no—
1160C2×C42—171no—
1161C2×C42—171no—
1162C2×C42C22×D1711yescharacteristic
1163#95—171no—
1164#95—171no—
1165#95—171no—
1166#95—171no—
1167#95—171no—
1168#95—171no—
1169#95—171no—
1170#95—171no—
1171#95—171no—
1172#95—171no—
1173#95—171no—
1174#95—171no—
1175#95—171no—
1176#95—171no—
1177#95—171no—
1178#95—171no—
1179#95—171no—
1180#95—171no—
1181#95—171no—
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#95C22×D1711yescharacteristic
1196#95C22×D1711yescharacteristic
1197#95C22×D1711yescharacteristic
1198#95C22×D1711yescharacteristic
1199#95C22×D1711yescharacteristic
1200#95C22×D1711yescharacteristic
1201#95C22×D1711yescharacteristic
1202#95C22×D1711yescharacteristic
1203C17#3672011yescharacteristic, complemented, Sylow
1204C24—171no—
1205C24—171no—
1206C24—171no—
1207C24—174no—
1208C24—342no—
1209C24—342no—
1210C24—342no—
1211C24—342no—
1212C24—342no—
1213C24—342no—
1214C24—342no—
1215C24—681no—
1216C24—681no—
1217C24—681no—
1218C24—681no—
1219C24—681no—
1220C24—681no—
1221C24C23×D1711yescharacteristic
1222C24C23×D1711yescharacteristic
1223C2×Q8—22no—
1224C2×Q8—41no—
1225C2×Q8—41no—
1226C2×Q8—342no—
1227C2×Q8—342no—
1228C2×Q8—342no—
1229C2×Q8—681no—
1230C2×Q8—681no—
1231C2×Q8—681no—
1232C2×Q8—681no—
1233C2×Q8—681no—
1234C2×Q8—681no—
1235C2×D4—22no—
1236C2×D4—22no—
1237C2×D4—41no—
1238C2×D4—342no—
1239C2×D4—342no—
1240C2×D4—342no—
1241C2×D4—342no—
1242C2×D4—342no—
1243C2×D4—342no—
1244C2×D4—681no—
1245C2×D4—681no—
1246C2×D4—681no—
1247C2×D4—6816no—
1248C22×C4—22no—
1249C22×C4—22no—
1250C22×C4—22no—
1251C22×C4—41no—
1252C22×C4—41no—
1253C22×C4—41no—
1254C22×C4—171no—
1255C22×C4—171no—
1256C22×C4—174no—
1257C22×C4—174no—
1258C22×C4—171no—
1259C22×C4—171no—
1260C22×C4—171no—
1261C22×C4—171no—
1262C22×C4—171no—
1263C22×C4—171no—
1264C22×C4—171no—
1265C22×C4—171no—
1266C22×C4—171no—
1267C22×C4—171no—
1268C22×C4—171no—
1269C22×C4—342no—
1270C22×C4—342no—
1271C22×C4—342no—
1272C22×C4—342no—
1273C22×C4—342no—
1274C22×C4—342no—
1275C22×C4—342no—
1276C22×C4—342no—
1277C22×C4—342no—
1278C22×C4—342no—
1279C22×C4—342no—
1280C22×C4—342no—
1281C22×C4—342no—
1282C22×C4—342no—
1283C22×C4—681no—
1284C22×C4—681no—
1285C22×C4—681no—
1286C22×C4—681no—
1287C22×C4—681no—
1288C22×C4—681no—
1289C22×C4—681no—
1290C22×C4—681no—
1291C22×C4—681no—
1292C22×C4—681no—
1293C22×C4—681no—
1294C22×C4—681no—
1295C22×C4—681no—
1296C22×C4—681no—
1297C22×C4—6816no—
1298C22×C4—681no—
1299C22×C4—681no—
1300C22×C4—681no—
1301C22×C4C23×D1711yescharacteristic
1302C22×C4C23×D1711yescharacteristic
1303C22×C4C23×D1711yescharacteristic
1304C22×C4C23×D1711yescharacteristic
1305C22×C4C23×D1711yescharacteristic
1306C22×C4C23×D1711yescharacteristic
1307C22×C4C23×D1711yescharacteristic
1308C22×C4C23×D1711yescharacteristic
1309C22×C4C23×D1711yescharacteristic
1310C22×C4C23×D1711yescharacteristic
1311C22×C4C23×D1711yescharacteristic
1312C22×C4C23×D1711yescharacteristic
1313C22×C4C23×D1711yescharacteristic
1314C4⋊C4—22no—
1315C4⋊C4—22no—
1316C4⋊C4—22no—
1317C4⋊C4—22no—
1318C4⋊C4—22no—
1319C4⋊C4—41no—
1320C4⋊C4—41no—
1321C4⋊C4—41no—
1322C4⋊C4—41no—
1323C4⋊C4—41no—
1324C4⋊C4—41no—
1325C4⋊C4—41no—
1326C4⋊C4—342no—
1327C4⋊C4—342no—
1328C4⋊C4—342no—
1329C4⋊C4—342no—
1330C4⋊C4—342no—
1331C4⋊C4—342no—
1332C4⋊C4—342no—
1333C4⋊C4—342no—
1334C4⋊C4—342no—
1335C4⋊C4—342no—
1336C4⋊C4—342no—
1337C4⋊C4—342no—
1338C4⋊C4—342no—
1339C4⋊C4—342no—
1340C4⋊C4—342no—
1341C4⋊C4—681no—
1342C4⋊C4—681no—
1343C4⋊C4—681no—
1344C4⋊C4—681no—
1345C4⋊C4—681no—
1346C4⋊C4—681no—
1347C4⋊C4—681no—
1348C4⋊C4—681no—
1349C4⋊C4—681no—
1350C4⋊C4—681no—
1351C4⋊C4—681no—
1352C4⋊C4—681no—
1353C4⋊C4—681no—
1354C22⋊C4—22no—
1355C22⋊C4—22no—
1356C22⋊C4—22no—
1357C22⋊C4—22no—
1358C22⋊C4—22no—
1359C22⋊C4—22no—
1360C22⋊C4—41no—
1361C22⋊C4—41no—
1362C22⋊C4—41no—
1363C22⋊C4—174no—
1364C22⋊C4—174no—
1365C22⋊C4—174no—
1366C22⋊C4—342no—
1367C22⋊C4—342no—
1368C22⋊C4—342no—
1369C22⋊C4—342no—
1370C22⋊C4—342no—
1371C22⋊C4—342no—
1372C22⋊C4—342no—
1373C22⋊C4—342no—
1374C22⋊C4—342no—
1375C22⋊C4—342no—
1376C22⋊C4—342no—
1377C22⋊C4—342no—
1378C22⋊C4—342no—
1379C22⋊C4—342no—
1380C22⋊C4—342no—
1381C22⋊C4—342no—
1382C22⋊C4—342no—
1383C22⋊C4—342no—
1384C22⋊C4—342no—
1385C22⋊C4—342no—
1386C22⋊C4—342no—
1387C22⋊C4—342no—
1388C22⋊C4—681no—
1389C22⋊C4—681no—
1390C22⋊C4—681no—
1391C22⋊C4—681no—
1392C22⋊C4—681no—
1393C22⋊C4—681no—
1394C22⋊C4—681no—
1395C22⋊C4—681no—
1396C22⋊C4—681no—
1397C22⋊C4—681no—
1398C22⋊C4—681no—
1399C22⋊C4—681no—
1400C22⋊C4—681no—
1401C22⋊C4D4×D1714yes—
1402C42—41no—
1403C42—681no—
1404C42—681no—
1405C42—681no—
1406C23—21no—
1407C23—21no—
1408C23—21no—
1409C23—21no—
1410C23—21no—
1411C23—21no—
1412C23—21no—
1413C23—21no—
1414C23—21no—
1415C23—21no—
1416C23—21no—
1417C23—21no—
1418C23—172no—
1419C23—172no—
1420C23—172no—
1421C23—172no—
1422C23—172no—
1423C23—348no—
1424C23—348no—
1425C23—341no—
1426C23—341no—
1427C23—341no—
1428C23—341no—
1429C23—341no—
1430C23—341no—
1431C23—341no—
1432C23—341no—
1433C23—341no—
1434C23—341no—
1435C23—341no—
1436C23—341no—
1437C23—341no—
1438C23—341no—
1439C23—341no—
1440C23—341no—
1441C23—684no—
1442C23—684no—
1443C23—684no—
1444C23—684no—
1445C23—684no—
1446C23—684no—
1447C23—684no—
1448C23—684no—
1449C23—1362no—
1450C23—1362no—
1451C23—1362no—
1452C23—1362no—
1453C23C2×D4×D1712yes—
1454C23#1058769112yes—
1455C23C24×D1711yescharacteristic
1456Q8—82no—
1457Q8—1362no—
1458Q8—1362no—
1459Q8—1362no—
1460D4—44no—
1461D4—684no—
1462D4—684no—
1463D4—684no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—44no—
1502C2×C4—82no—
1503C2×C4—172no—
1504C2×C4—172no—
1505C2×C4—341no—
1506C2×C4—341no—
1507C2×C4—341no—
1508C2×C4—341no—
1509C2×C4—341no—
1510C2×C4—341no—
1511C2×C4—341no—
1512C2×C4—341no—
1513C2×C4—341no—
1514C2×C4—341no—
1515C2×C4—341no—
1516C2×C4—341no—
1517C2×C4—341no—
1518C2×C4—341no—
1519C2×C4—341no—
1520C2×C4—341no—
1521C2×C4—341no—
1522C2×C4—341no—
1523C2×C4—341no—
1524C2×C4—341no—
1525C2×C4—341no—
1526C2×C4—341no—
1527C2×C4—341no—
1528C2×C4—341no—
1529C2×C4—341no—
1530C2×C4—341no—
1531C2×C4—341no—
1532C2×C4—341no—
1533C2×C4—341no—
1534C2×C4—341no—
1535C2×C4—341no—
1536C2×C4—341no—
1537C2×C4—341no—
1538C2×C4—341no—
1539C2×C4—341no—
1540C2×C4—341no—
1541C2×C4—341no—
1542C2×C4—684no—
1543C2×C4—684no—
1544C2×C4—684no—
1545C2×C4—684no—
1546C2×C4—684no—
1547C2×C4—684no—
1548C2×C4—684no—
1549C2×C4—684no—
1550C2×C4—1362no—
1551C2×C4—1362no—
1552C2×C4—1362no—
1553C2×C4C2×D4×D1712yes—
1554C2×C4C2×D4×D1712yes—
1555C22—22no—
1556C22—22no—
1557C22—22no—
1558C22—22no—
1559C22—22no—
1560C22—22no—
1561C22—41no—
1562C22—41no—
1563C22—41no—
1564C22—41no—
1565C22—41no—
1566C22—41no—
1567C22—41no—
1568C22—41no—
1569C22—174no—
1570C22—342no—
1571C22—342no—
1572C22—342no—
1573C22—342no—
1574C22—342no—
1575C22—342no—
1576C22—342no—
1577C22—342no—
1578C22—342no—
1579C22—342no—
1580C22—342no—
1581C22—342no—
1582C22—6816no—
1583C22—681no—
1584C22—681no—
1585C22—681no—
1586C22—681no—
1587C22—681no—
1588C22—681no—
1589C22—681no—
1590C22—681no—
1591C22—1368no—
1592C22C22×D4×D1711yescharacteristic
1593C22H(5,𝔽2)×D1711yescharacteristic
1594C22C2×#1058769111yescharacteristic
1595C222−1+4×D1711yescharacteristic
1596C222−1+4×D1711yescharacteristic
1597C22#1176364511yescharacteristic
1598C22#1176364611yescharacteristic
1599C4—22no—
1600C4—22no—
1601C4—41no—
1602C4—41no—
1603C4—41no—
1604C4—41no—
1605C4—41no—
1606C4—41no—
1607C4—41no—
1608C4—41no—
1609C4—41no—
1610C4—41no—
1611C4—41no—
1612C4—342no—
1613C4—342no—
1614C4—681no—
1615C4—681no—
1616C4—681no—
1617C4—681no—
1618C4—681no—
1619C4—681no—
1620C4—681no—
1621C4—681no—
1622C4—681no—
1623C4—681no—
1624C4—681no—
1625C2—42no—
1626C2—42no—
1627C2—344no—
1628C2—682no—
1629C2—682no—
1630C2D17×#53611yescharacteristic
1631C2#1454241211yescharacteristic
1632C2#1454242311yescharacteristic
1633C2#1454298311yescharacteristic
1634C2#1454298511yescharacteristic
1635C2#1454299211yescharacteristic
1636C2#1454299511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2680C2
prime radicalC22×D4×D17C22
hypercenter#2680D17
hypocenterC17#36720
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2680

Complements

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

NH ≅ G/Ntype
1. C2×#11763434C2semidirect
3. #14537070C2semidirect
4. #14537068C2semidirect
5. #14535212C2semidirect
6. #14535211C2semidirect
7. #14535208C2semidirect
8. #14535207C2semidirect
9. #14535203C2semidirect
10. #14535202C2semidirect
11. #14535199C2semidirect
12. #14535198C2semidirect
13. #14535128C2semidirect
14. #14535126C2semidirect
15. #14535124C2semidirect
16. #14535123C2semidirect
17. #14535123C2semidirect
18. #14535121C2semidirect
19. #14535120C2semidirect
20. #14534602C2semidirect
21. #14534596C2semidirect
22. #14533940C2semidirect
23. #14533936C2semidirect
24. #14533259C2semidirect
25. #14533257C2semidirect
26. #14533064C2semidirect
27. #14533061C2semidirect
30. #14531378C2semidirect
31. C17×#2680C2semidirect
47. C2×#10587583C22semidirect
48. C2×#10587610C22semidirect
51. C2×#10587582C22semidirect
52. C2×#10587582C22semidirect
53. C2×#10587582C22semidirect
54. C2×#10587564C22semidirect
55. C2×#10587564C22semidirect
56. C2×#10587564C22semidirect
58. C2×#10587632C22semidirect
59. C2×#10587632C22semidirect
67. #11762751C22semidirect
68. #11762750C22semidirect
69. #11762749C22semidirect
70. #11762748C22semidirect
71. #11762743C22semidirect
72. #11762743C22semidirect
73. #11762742C22semidirect
74. #11762742C22semidirect
75. #11762742C22semidirect
76. #11762742C22semidirect
77. #11762742C22semidirect
78. #11762742C22semidirect
79. #11762741C22semidirect
80. #11762740C22semidirect
81. #11762740C22semidirect
82. #11762740C22semidirect
83. #11762739C22semidirect
84. #11762739C22semidirect
85. #11762738C22semidirect
86. #11762738C22semidirect
87. #11762738C22semidirect
88. #11762737C22semidirect
89. #11762737C22semidirect
90. #11762737C22semidirect
91. #11762735C22semidirect
92. #11762735C22semidirect
93. #11762735C22semidirect
94. #11762734C22semidirect
95. #11762730C22semidirect
96. #11762729C22semidirect
97. #11762728C22semidirect
105. #11762722C22semidirect
106. #11762722C22semidirect
107. #11762721C22semidirect
108. #11762721C22semidirect
109. #11762715C22semidirect
110. #11762714C22semidirect
111. #11762713C22semidirect
112. #11762713C22semidirect
113. #11762703C22semidirect
114. #11762703C22semidirect
115. #11762702C22semidirect
116. #11762702C22semidirect
117. #11762702C22semidirect
118. #11762701C22semidirect
119. #11762701C22semidirect
120. #11762701C22semidirect
121. #11762700C22semidirect
122. #11762700C22semidirect
123. #11762699C22semidirect
124. #11762699C22semidirect
125. #11762698C22semidirect
126. #11762697C22semidirect
133. #11762683C22semidirect
134. #11762683C22semidirect
135. #11762682C22semidirect
136. #11762682C22semidirect
137. #11762681C22semidirect
138. #11762681C22semidirect
145. #11762680C22semidirect
146. #11762680C22semidirect
147. #11762680C22semidirect
148. #11762680C22semidirect
149. #11762678C22semidirect
150. #11762678C22semidirect
151. #11762678C22semidirect
156. #11762671C22semidirect
157. #11762671C22semidirect
158. #11762670C22semidirect
159. #11762670C22semidirect
160. #11762669C22semidirect
162. #11762668C22semidirect
163. #11762667C22semidirect
165. #11762666C22semidirect
176. C2×C17×C22⋊Q8C22semidirect
177. C2×C17×C22⋊Q8C22semidirect
178. C17×#398C22semidirect
179. C17×#398C22semidirect
180. C17×#397C22semidirect
181. C17×#397C22semidirect
182. C17×#395C22semidirect
184. C17×#388C22semidirect
185. C17×#388C22semidirect
186. C17×#385C22semidirect
187. C17×#385C22semidirect
188. C17×#384C22semidirect
756. #2680D17semidirect
868. C2×C22⋊Q8C2×D17semidirect
869. C2×C22⋊Q8C2×D17semidirect
895. #398C2×D17semidirect
896. #398C2×D17semidirect
907. #397C2×D17semidirect
908. #397C2×D17semidirect
912. #395C2×D17semidirect
943. #388C2×D17semidirect
944. #388C2×D17semidirect
967. #385C2×D17semidirect
968. #385C2×D17semidirect
972. #384C2×D17semidirect
1203. C17#36720semidirect

Maximal subgroups

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

subgroupindex
C2×#117634342
C2×#123×D172
#145370702
#145370682
#145352122
#145352112
#145352082
#145352072
#145352032
#145352022
#145351992
#145351982
#145351282
#145351262
#145351242
#145351232
#145351212
#145351202
#145346022
#145345962
#145339402
#145339362
#145332592
#145332572
#145330642
#145330612
#145321082
#145321062
#145313782
C17×#26802
#3672017