Finite Group Databasebeta

← #17194881

Subgroups — #17194881

Order 4352.

2698 conjugacy classes of subgroups.

The subgroup lattice has 1610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763317C211yesmaximal, characteristic
2#14531920C211yesmaximal, characteristic, complemented
3#14531915C211yesmaximal, characteristic, complemented
4#14531915C211yesmaximal, characteristic, complemented
5#14531823C211yesmaximal, characteristic, complemented
6#14531817C211yesmaximal, characteristic, complemented
7#14531812C211yesmaximal, characteristic, complemented
8#14531806C211yesmaximal, characteristic, complemented
9#14531754C211yesmaximal, characteristic, complemented
10#14531753C211yesmaximal, characteristic, complemented
11#14531723C211yesmaximal, characteristic, complemented
12#14531718C211yesmaximal, characteristic, complemented
13#14531674C211yesmaximal, characteristic, complemented
14#14531666C211yesmaximal, characteristic, complemented
15#14531623C211yesmaximal, characteristic, complemented
16#14531610C211yesmaximal, characteristic, complemented
17#14531446C211yesmaximal, characteristic, complemented
18#14531443C211yesmaximal, characteristic, complemented
19#14531440C211yesmaximal, characteristic, complemented
20#14531437C211yesmaximal, characteristic, complemented
21#14531416C211yesmaximal, characteristic, complemented
22#14531414C211yesmaximal, characteristic, complemented
23#14531318C211yesmaximal, characteristic, complemented
24C4×#10587582C211yesmaximal, characteristic, complemented
25#14531296C211yesmaximal, characteristic, complemented
26C4×#10587570C211yesmaximal, characteristic, complemented
27#14531165C211yesmaximal, characteristic, complemented
28#14531144C211yesmaximal, characteristic, complemented
29#14531143C211yesmaximal, characteristic, complemented
30C4×C22⋊C4×D17C211yesmaximal, characteristic, complemented
31C17×#2374C211yesmaximal, characteristic, complemented
32C22×#63254C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34#11763317C4116yescomplemented
35C2×#10587615C2211yescharacteristic
36C2×#10587582C2211yescharacteristic
37C2×#10587582C2211yescharacteristic
38C2×#10587570C2211yescharacteristic
39C2×#10587570C2211yescharacteristic
40C2×#10587568C2211yescharacteristic
41C2×#10587623C2211yescharacteristic
42C2×C4×Dic34C2211yescharacteristic, complemented
43C2×#10587573C2211yescharacteristic, complemented
44C2×C4×D68C2211yescharacteristic
45C2×#10587579C2211yescharacteristic
46C2×#10587579C2211yescharacteristic
47C2×#10587579C2211yescharacteristic
48C2×C4×C22⋊D17C2211yescharacteristic
49C2×C4×C22⋊D17C2211yescharacteristic, complemented
50C2×#10587567C2211yescharacteristic
51C2×#10587567C2211yescharacteristic
52C2×#10587567C2211yescharacteristic
53C2×#10587567C2211yescharacteristic, complemented
54C2×#10587558C2211yescharacteristic
55C2×#10587558C2211yescharacteristic
56C2×#10587563C2211yescharacteristic
57C2×C22⋊C4×D17C2211yescharacteristic
58C2×C22⋊C4×D17C2211yescharacteristic
59C2×C42×D17C2211yescharacteristic
60C2×C42×D17C2211yescharacteristic
61#11762713C2211yescharacteristic, complemented
62#11762713C2211yescharacteristic, complemented
63#11762712C2211yescharacteristic
64#11762711C2211yescharacteristic
65#11762710C2211yescharacteristic
66#11762709C2211yescharacteristic
67#11762709C2211yescharacteristic
68#11762709C2211yescharacteristic
69#11762709C2211yescharacteristic
70#11762709C2211yescharacteristic, complemented
71#11762709C2211yescharacteristic, complemented
72#11762706C2211yescharacteristic, complemented
73#11762706C2211yescharacteristic, complemented
74#11762704C2211yescharacteristic, complemented
75#11762704C2211yescharacteristic, complemented
76#11762703C2211yescharacteristic
77#11762703C2211yescharacteristic
78#11762702C2211yescharacteristic
79#11762702C2211yescharacteristic
80#11762702C2211yescharacteristic, complemented
81#11762702C2211yescharacteristic, complemented
82#11762701C2211yescharacteristic
83#11762701C2211yescharacteristic
84#11762700C2211yescharacteristic
85#11762700C2211yescharacteristic
86#11762700C2211yescharacteristic, complemented
87#11762700C2211yescharacteristic, complemented
88#11762699C2211yescharacteristic
89#11762699C2211yescharacteristic
90#11762698C2211yescharacteristic
91#11762698C2211yescharacteristic
92#11762698C2211yescharacteristic, complemented
93#11762698C2211yescharacteristic, complemented
94#11762697C2211yescharacteristic
95#11762697C2211yescharacteristic
96#11762695C2211yescharacteristic, complemented
97#11762695C2211yescharacteristic, complemented
98#11762693C2211yescharacteristic, complemented
99#11762693C2211yescharacteristic, complemented
100#11762691C2211yescharacteristic, complemented
101#11762691C2211yescharacteristic, complemented
102#11762689C2211yescharacteristic
103#11762688C2211yescharacteristic
104#11762687C2211yescharacteristic
105#11762687C2211yescharacteristic
106#11762687C2211yescharacteristic
107#11762687C2211yescharacteristic
108#11762686C2211yescharacteristic
109#11762685C2211yescharacteristic
110#11762685C2211yescharacteristic
111#11762685C2211yescharacteristic
112#11762685C2211yescharacteristic
113#11762683C2211yescharacteristic
114#11762683C2211yescharacteristic
115#11762680C2211yescharacteristic
116#11762680C2211yescharacteristic
117#11762676C2211yescharacteristic, complemented
118#11762676C2211yescharacteristic, complemented
119#11762674C2211yescharacteristic, complemented
120#11762673C2211yescharacteristic, complemented
121#11762671C2211yescharacteristic
122#11762671C2211yescharacteristic
123#11762671C2211yescharacteristic, complemented
124#11762670C2211yescharacteristic, complemented
125#11762668C2211yescharacteristic
126#11762668C2211yescharacteristic
127#11762667C2211yescharacteristic
128#11762667C2211yescharacteristic
129#11762667C2211yescharacteristic, complemented
130#11762666C2211yescharacteristic, complemented
131#11762664C2211yescharacteristic
132#11762664C2211yescharacteristic
133C4⋊C4×Dic17C2211yescharacteristic, complemented
134C4⋊C4×Dic17C2211yescharacteristic, complemented
135C4⋊C4×Dic17C2211yescharacteristic, complemented
136C4×#63225C2211yescharacteristic, complemented
137C4×#63225C2211yescharacteristic, complemented
138C4×#63225C2211yescharacteristic, complemented
139C4×#63225C2211yescharacteristic, complemented
140C4×#63225C2211yescharacteristic, complemented
141#11762660C2211yescharacteristic, complemented
142#11762660C2211yescharacteristic, complemented
143#11762660C2211yescharacteristic, complemented
144#11762660C2211yescharacteristic, complemented
145C22⋊C4×Dic17C2211yescharacteristic
146C22⋊C4×Dic17C2211yescharacteristic
147C22⋊C4×Dic17C2211yescharacteristic, complemented
148C22⋊C4×Dic17C2211yescharacteristic, complemented
149C22⋊C4×Dic17C2211yescharacteristic, complemented
150C4×#63227C2211yescharacteristic
151C4×#63227C2211yescharacteristic
152C4×#63227C2211yescharacteristic
153C4×#63227C2211yescharacteristic
154C4×#63227C2211yescharacteristic
155C4×#63227C2211yescharacteristic
156C4×#63227C2211yescharacteristic, complemented
157C4×#63227C2211yescharacteristic, complemented
158C4×#63227C2211yescharacteristic, complemented
159C4×C22⋊Dic17C2211yescharacteristic
160C4×C22⋊Dic17C2211yescharacteristic
161#11762656C2211yescharacteristic
162#11762656C2211yescharacteristic
163#11762656C2211yescharacteristic
164#11762656C2211yescharacteristic
165#11762656C2211yescharacteristic, complemented
166#11762656C2211yescharacteristic, complemented
167#11762655C2211yescharacteristic, complemented
168#11762654C2211yescharacteristic, complemented
169C2×#10587502C2211yescharacteristic, complemented
170#95×D17C2211yescharacteristic
171#95×D17C2211yescharacteristic
172#95×D17C2211yescharacteristic, complemented
173C2×C17×#123C2211yescharacteristic
174C17×#390C2211yescharacteristic
175C17×#388C2211yescharacteristic
176C17×#388C2211yescharacteristic
177C17×#388C2211yescharacteristic, complemented
178C17×#388C2211yescharacteristic, complemented
179C17×#387C2211yescharacteristic, complemented
180C17×#387C2211yescharacteristic, complemented
181C17×#386C2211yescharacteristic
182C4×C4⋊C4×C17C2211yescharacteristic, complemented
183C4×C4⋊C4×C17C2211yescharacteristic, complemented
184C4×C22⋊C4×C17C2211yescharacteristic
185C4×C22⋊C4×C17C2211yescharacteristic
186C4×C22⋊C4×C17C2211yescharacteristic, complemented
187C4×C22⋊C4×C17C2211yescharacteristic, complemented
188C24×D17C2311yescharacteristic
189C22×D4×C17C2311yescharacteristic
190C23×C4×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C22×C22⋊D17C2311yescharacteristic
193C22×C22⋊D17C2311yescharacteristic
194C22×C22⋊D17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C23×Dic17C2311yescharacteristic
197C23×Dic17C2311yescharacteristic
198C23×Dic17C2311yescharacteristic
199C2×#63254—42no—
200C2×#63254—42no—
201C2×#63254C2×C418yescomplemented
202C22×D68C2311yescharacteristic
203C22×D68C2311yescharacteristic
204C22×C4×D17—42no—
205C22×C4×D17—42no—
206C22×C4×D17C2×C418yescomplemented
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×C4×D17C2311yescharacteristic
216C22×C4×D17C2311yescharacteristic
217C22×C4×D17C2311yescharacteristic
218C22×Dic34C2311yescharacteristic
219C17×#123C2×C418yescomplemented
220C2×C4⋊C4×C17C2311yescharacteristic
221C2×C4⋊C4×C17C2311yescharacteristic
222C2×C4⋊C4×C17C2311yescharacteristic
223C2×C4⋊C4×C17C2311yescharacteristic
224C2×C4⋊C4×C17C2311yescharacteristic
225C2×C22⋊C4×C17C2311yescharacteristic
226C2×C22⋊C4×C17C2311yescharacteristic
227C2×C22⋊C4×C17C2311yescharacteristic
228C2×C22⋊C4×C17C2311yescharacteristic
229C2×C22⋊C4×C17C2311yescharacteristic
230C2×C22⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17C2311yescharacteristic
232C2×C22⋊C4×C17C2311yescharacteristic
233C2×C22⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17C2311yescharacteristic
235C2×C42×C17C2311yescharacteristic
236C2×C42×C17C2311yescharacteristic
237C2×C42×C17C2311yescharacteristic
238C2×C42×C17C2311yescharacteristic
239C2×C42×C17C2311yescharacteristic
240C2×C42×C17C2311yescharacteristic
241C2×C42×C17C2311yescharacteristic
242C2×C22⋊Dic17C2311yescharacteristic
243C2×C22⋊Dic17C2311yescharacteristic
244C2×C22⋊Dic17C2311yescharacteristic
245C2×C22⋊Dic17C2311yescharacteristic
246C2×C22⋊Dic17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
250#10587623C2×C418yescomplemented
251#10587615C2×C418yescomplemented
252C4×C22⋊D17—24no—
253C4×C22⋊D17—42no—
254C2×#63227C2311yescharacteristic
255C2×#63227C2311yescharacteristic
256C2×#63227C2311yescharacteristic
257C2×#63227C2311yescharacteristic
258C2×#63227C2311yescharacteristic
259C2×#63227C2311yescharacteristic
260C2×#63227C2311yescharacteristic
261C2×#63227C2311yescharacteristic
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×C4⋊Dic17C2311yescharacteristic
279C2×C4⋊Dic17C2311yescharacteristic
280C2×C4⋊Dic17C2311yescharacteristic
281C2×#63225C2311yescharacteristic
282C2×#63225C2311yescharacteristic
283C2×#63225C2311yescharacteristic
284C2×#63225C2311yescharacteristic
285C2×#63225C2311yescharacteristic
286C2×#63225C2311yescharacteristic
287C2×#63225C2311yescharacteristic
288C2×#63225C2311yescharacteristic
289C2×#63225C2311yescharacteristic
290C2×#63225C2311yescharacteristic
291C2×#63225C2311yescharacteristic
292C2×#63225C2311yescharacteristic
293C2×#63225C2311yescharacteristic
294C2×#63225C2311yescharacteristic
295C2×C4×Dic17C2311yescharacteristic
296C2×C4×Dic17C2311yescharacteristic
297C2×C4×Dic17C2311yescharacteristic
298C2×C4×Dic17C2311yescharacteristic
299C2×C4×Dic17C2311yescharacteristic
300C2×C4×Dic17C2311yescharacteristic
301C2×C4×Dic17C2311yescharacteristic
302C2×C4×Dic17C2311yescharacteristic
303C2×C4×Dic17C2311yescharacteristic
304C2×C4×Dic17C2311yescharacteristic
305C2×C4×Dic17C2311yescharacteristic
306C2×C4×Dic17C2311yescharacteristic
307C2×C4×Dic17C2311yescharacteristic
308C2×C4×Dic17C2311yescharacteristic
309C2×C4×Dic17C2311yescharacteristic
310C2×C4×Dic17C2311yescharacteristic
311C2×C4×Dic17C2311yescharacteristic
312C2×C4×Dic17C2311yescharacteristic
313C2×C4×Dic17C2311yescharacteristic
314#10587582C2×C418yescomplemented
315#10587582C2×C418yescomplemented
316#10587579—24no—
317#10587579C2×C418yescomplemented
318#10587579C2×C418yescomplemented
319#10587573—42no—
320#10587570C2×C418yes—
321#10587570C2×C418yescomplemented
322#10587568C2×C418yescomplemented
323#10587567—24no—
324#10587567—42no—
325#10587567C2×C418yescomplemented
326#10587567C2×C418yescomplemented
327C22⋊C4×D17—24no—
328C22⋊C4×D17—24no—
329#10587563C2×C418yescomplemented
330C4×D68—24no—
331#10587558—42no—
332#10587558—42no—
333C42×D17—42no—
334C42×D17—42no—
335C4×Dic34—42no—
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338C17×#95C2311yescharacteristic
339C17×#95C2311yescharacteristic
340C17×#95C2311yescharacteristic
341C17×#95C2311yescharacteristic
342C17×#95C2311yescharacteristic
343C17×#95C2311yescharacteristic
344C17×#95C2311yescharacteristic
345C17×#95C2311yescharacteristic
346#10587502C2311yescharacteristic
347#10587502C2311yescharacteristic
348#10587502C2311yescharacteristic
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
376C24×C17C2411yescharacteristic
377C24×C17C2411yescharacteristic
378C23×D17—22no—
379C23×D17—22no—
380C23×D17—41no—
381C23×D17—41no—
382C23×D17—41no—
383C23×D17—41no—
384C23×D17C22×C414yes—
385C23×D17C2411yescharacteristic
386C23×D17C2411yescharacteristic
387C23×D17C2411yescharacteristic
388C2×D4×C17—41no—
389C2×D4×C17—41no—
390C2×D4×C17C22×C414yes—
391C22×C4×C17—22no—
392C22×C4×C17—41no—
393C22×C4×C17—41no—
394C22×C4×C17—41no—
395C22×C4×C17—41no—
396C22×C4×C17C22×C414yes—
397C22×C4×C17C2411yescharacteristic
398C22×C4×C17C2411yescharacteristic
399C22×C4×C17C2411yescharacteristic
400C22×C4×C17C2411yescharacteristic
401C22×C4×C17C2411yescharacteristic
402C22×C4×C17C2411yescharacteristic
403C22×C4×C17C2411yescharacteristic
404C22×C4×C17C2411yescharacteristic
405C22×C4×C17C2411yescharacteristic
406C22×C4×C17C2411yescharacteristic
407C22×C4×C17C2411yescharacteristic
408C22×C4×C17C2411yescharacteristic
409C22×C4×C17C2411yescharacteristic
410C2×C22⋊D17—22no—
411C2×C22⋊D17—22no—
412C2×C22⋊D17—22no—
413C2×C22⋊D17—22no—
414C2×C22⋊D17—41no—
415C2×C22⋊D17—41no—
416C2×C22⋊D17—41no—
417C2×C22⋊D17—41no—
418C2×C22⋊D17C22×C414yes—
419C2×C22⋊D17C22×C414yes—
420C2×C22⋊D17C22×C414yes—
421C2×C22⋊D17C22×C414yes—
422C22×Dic17—22no—
423C22×Dic17—22no—
424C22×Dic17—22no—
425C22×Dic17—41no—
426C22×Dic17—41no—
427C22×Dic17—41no—
428C22×Dic17—41no—
429C22×Dic17C22×C414yes—
430C22×Dic17C22×C414yes—
431C22×Dic17C2411yescharacteristic
432C22×Dic17C2411yescharacteristic
433C22×Dic17C2411yescharacteristic
434C22×Dic17C2411yescharacteristic
435C22×Dic17C2411yescharacteristic
436C22×Dic17C2411yescharacteristic
437C22×Dic17C2411yescharacteristic
438C22×Dic17C2411yescharacteristic
439C22×Dic17C2411yescharacteristic
440C22×Dic17C2411yescharacteristic
441C22×Dic17C2411yescharacteristic
442C22×Dic17C2411yescharacteristic
443C22×Dic17C2411yescharacteristic
444#63254—416no—
445C2×D68—22no—
446C2×D68—22no—
447C2×D68—41no—
448C2×D68—41no—
449C2×D68C22×C414yes—
450C2×D68C22×C414yes—
451C2×C4×D17—22no—
452C2×C4×D17—22no—
453C2×C4×D17—22no—
454C2×C4×D17—22no—
455C2×C4×D17—22no—
456C2×C4×D17—22no—
457C2×C4×D17—22no—
458C2×C4×D17—22no—
459C2×C4×D17—416no—
460C2×C4×D17—41no—
461C2×C4×D17—41no—
462C2×C4×D17—41no—
463C2×C4×D17—41no—
464C2×C4×D17—41no—
465C2×C4×D17—41no—
466C2×C4×D17—41no—
467C2×C4×D17—41no—
468C2×C4×D17—41no—
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×D17C22×C414yes—
479C2×C4×D17C22×C414yes—
480C2×C4×D17C22×C414yes—
481C2×C4×D17C22×C414yes—
482C2×C4×D17C22×C414yes—
483C2×C4×D17#4114yescomplemented
484C2×C4×D17#4114yescomplemented
485C2×Dic34—22no—
486C2×Dic34—22no—
487C2×Dic34C22×C414yes—
488C4⋊C4×C17—22no—
489C4⋊C4×C17—41no—
490C4⋊C4×C17—41no—
491C4⋊C4×C17C22×C414yes—
492C4⋊C4×C17C22×C414yes—
493C22⋊C4×C17—22no—
494C22⋊C4×C17—22no—
495C22⋊C4×C17—22no—
496C22⋊C4×C17—41no—
497C22⋊C4×C17—41no—
498C22⋊C4×C17—41no—
499C22⋊C4×C17—41no—
500C22⋊C4×C17C22×C414yes—
501C22⋊C4×C17C22×C414yes—
502C22⋊C4×C17C22×C414yes—
503C42×C17—22no—
504C42×C17—41no—
505C42×C17—41no—
506C42×C17—41no—
507C42×C17—41no—
508C42×C17—41no—
509C42×C17—41no—
510C22⋊Dic17—22no—
511C22⋊Dic17—22no—
512C22⋊Dic17—22no—
513C22⋊Dic17—41no—
514C22⋊Dic17—41no—
515C22⋊Dic17—41no—
516C22⋊Dic17—41no—
517C22⋊Dic17C22×C414yes—
518#63227—22no—
519#63227—22no—
520#63227—22no—
521#63227—22no—
522#63227—22no—
523#63227—22no—
524#63227—22no—
525#63227—22no—
526#63227—22no—
527#63227—22no—
528#63227—41no—
529#63227—41no—
530#63227—41no—
531#63227—41no—
532#63227—41no—
533#63227—41no—
534#63227—41no—
535#63227—41no—
536#63227C22×C414yes—
537#63227C22×C414yes—
538#63227C22×C414yes—
539#63227C22×C414yes—
540#63227C22×C414yes—
541#63227C22×C414yes—
542C4⋊Dic17—22no—
543C4⋊Dic17—41no—
544C4⋊Dic17—41no—
545#63225—22no—
546#63225—22no—
547#63225—22no—
548#63225—22no—
549#63225—22no—
550#63225—22no—
551#63225—41no—
552#63225—41no—
553#63225—41no—
554#63225—41no—
555#63225C22×C414yes—
556#63225C22×C414yes—
557#63225C22×C414yes—
558#63225C22×C414yes—
559C4×Dic17—22no—
560C4×Dic17—22no—
561C4×Dic17—22no—
562C4×Dic17—22no—
563C4×Dic17—22no—
564C4×Dic17—22no—
565C4×Dic17—22no—
566C4×Dic17—41no—
567C4×Dic17—41no—
568C4×Dic17—41no—
569C4×Dic17—41no—
570C4×Dic17—41no—
571C4×Dic17—41no—
572C4×Dic17—41no—
573C4×Dic17—41no—
574C4×Dic17—41no—
575C4×Dic17—41no—
576C4×Dic17C22×C414yes—
577C4×Dic17C22×C414yes—
578#34223—171nomaximal, Sylow
579C23×C17—21no—
580C23×C17—21no—
581C23×C17—21no—
582C23×C17—21no—
583C23×C17—21no—
584C23×C17—21no—
585C23×C17—21no—
586C23×C17—21no—
587C23×C17—21no—
588C23×C17—21no—
589C23×C17—21no—
590C23×C17—21no—
591C23×C17C23×C412yes—
592C23×C17C23×C412yes—
593C23×C17C2511yescharacteristic
594C22×D17—21no—
595C22×D17—21no—
596C22×D17—21no—
597C22×D17—21no—
598C22×D17—21no—
599C22×D17—21no—
600C22×D17—21no—
601C22×D17—21no—
602C22×D17—21no—
603C22×D17—21no—
604C22×D17—21no—
605C22×D17—21no—
606C22×D17—21no—
607C22×D17—21no—
608C22×D17—21no—
609C22×D17—21no—
610C22×D17—28no—
611C22×D17—44no—
612C22×D17—44no—
613C22×D17—44no—
614C22×D17—44no—
615C22×D17—44no—
616C22×D17—44no—
617C22×D17C23×C412yes—
618C22×D17C23×C412yes—
619C22×D17C23×C412yes—
620C22×D17C2×#4112yes—
621C22×D17C2×#4112yes—
622D4×C17—44no—
623C2×C4×C17—21no—
624C2×C4×C17—21no—
625C2×C4×C17—21no—
626C2×C4×C17—21no—
627C2×C4×C17—21no—
628C2×C4×C17—21no—
629C2×C4×C17—21no—
630C2×C4×C17—21no—
631C2×C4×C17—21no—
632C2×C4×C17—21no—
633C2×C4×C17—21no—
634C2×C4×C17—21no—
635C2×C4×C17—21no—
636C2×C4×C17—21no—
637C2×C4×C17—21no—
638C2×C4×C17—21no—
639C2×C4×C17—21no—
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—44no—
656C2×C4×C17—82no—
657C2×C4×C17C23×C412yes—
658C2×C4×C17C23×C412yes—
659C2×C4×C17C23×C412yes—
660C2×C4×C17C23×C412yes—
661C2×C4×C17C23×C412yes—
662C2×C4×C17C2×#4112yes—
663C2×C4×C17C2×#4112yes—
664C22⋊D17—28no—
665C22⋊D17—28no—
666C22⋊D17—44no—
667C22⋊D17—44no—
668C2×Dic17—21no—
669C2×Dic17—21no—
670C2×Dic17—21no—
671C2×Dic17—21no—
672C2×Dic17—21no—
673C2×Dic17—21no—
674C2×Dic17—21no—
675C2×Dic17—21no—
676C2×Dic17—21no—
677C2×Dic17—21no—
678C2×Dic17—21no—
679C2×Dic17—21no—
680C2×Dic17—28no—
681C2×Dic17—21no—
682C2×Dic17—21no—
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—44no—
700C2×Dic17—82no—
701C2×Dic17C23×C412yes—
702C2×Dic17C23×C412yes—
703C2×Dic17C23×C412yes—
704C2×Dic17C23×C412yes—
705C2×Dic17C23×C412yes—
706C2×Dic17C2×#4112yes—
707C2×Dic17C2×#4112yes—
708C2×Dic17H(5,𝔽2)12yes—
709C2×Dic17H(5,𝔽2)12yes—
710D68—28no—
711D68—44no—
712C4×D17—28no—
713C4×D17—28no—
714C4×D17—44no—
715C4×D17—44no—
716C4×D17—44no—
717C4×D17—44no—
718C4×D17—44no—
719C4×D17—44no—
720C4×D17—44no—
721C4×D17—82no—
722C4×D17—82no—
723Dic34—28no—
724C2×#525—171no—
725#2374—171no—
726#2374—171no—
727#2374—171no—
728#2374D1711yescharacteristic, complemented
729#2363—171no—
730#2363—171no—
731#2362—171no—
732#2362—171no—
733#2357—171no—
734#2357—171no—
735#2353—171no—
736#2353—171no—
737#2347—171no—
738#2346—171no—
739#2341—171no—
740#2339—171no—
741#2321—171no—
742#2321—171no—
743#2321—171no—
744#2321—171no—
745#2318—171no—
746#2318—171no—
747C4×C22⋊Q8—171no—
748C4×C22⋊Q8—171no—
749C4×#121—171no—
750C4×#121—171no—
751#2280—171no—
752#2275—171no—
753#2275—171no—
754C2×C4×C22⋊C4—171no—
755C22×C17—22no—
756C22×C17—22no—
757C22×C17—22no—
758C22×C17—22no—
759C22×C17—22no—
760C22×C17—22no—
761C22×C17—41no—
762C22×C17—41no—
763C22×C17—41no—
764C22×C17—41no—
765C22×C17—41no—
766C22×C17—41no—
767C22×C17—41no—
768C22×C17—41no—
769C22×C17C24×C411yescharacteristic
770C22×C17C22×#4111yescharacteristic
771C22×C17C22×#4111yescharacteristic
772C22×C17C2×H(5,𝔽2)11yescharacteristic
773C22×C17C2×H(5,𝔽2)11yescharacteristic
774C22×C17#58511yescharacteristic
775C22×C17#58511yescharacteristic
776C2×D17—22no—
777C2×D17—22no—
778C2×D17—22no—
779C2×D17—22no—
780C2×D17—22no—
781C2×D17—22no—
782C2×D17—22no—
783C2×D17—22no—
784C2×D17—22no—
785C2×D17—22no—
786C2×D17—22no—
787C2×D17—22no—
788C2×D17—416no—
789C2×D17—41no—
790C2×D17—41no—
791C2×D17—41no—
792C2×D17—41no—
793C2×D17—41no—
794C2×D17—41no—
795C2×D17—41no—
796C2×D17—41no—
797C2×D17C4×#4114yes—
798C4×C17—22no—
799C4×C17—22no—
800C4×C17—22no—
801C4×C17—22no—
802C4×C17—22no—
803C4×C17—22no—
804C4×C17—22no—
805C4×C17—41no—
806C4×C17—41no—
807C4×C17—41no—
808C4×C17—41no—
809C4×C17—41no—
810C4×C17—41no—
811Dic17—22no—
812Dic17—22no—
813Dic17—22no—
814Dic17—22no—
815Dic17—22no—
816Dic17—22no—
817Dic17—41no—
818Dic17—41no—
819Dic17—41no—
820Dic17—41no—
821Dic17—41no—
822Dic17—41no—
823Dic17#51814yes—
824C22×#41—171no—
825C24×C4—171no—
826#525—1716no—
827C2×#123—171no—
828C2×#123C2×D1711yescharacteristic
829C2×C22⋊Q8—171no—
830C2×C22⋊Q8—171no—
831C2×#121—171no—
832C2×#121—171no—
833C2×#120—171no—
834C2×#120—171no—
835C2×C4×Q8—171no—
836C2×C4×Q8—171no—
837C2×C4×D4—171no—
838C2×C4×D4—171no—
839C2×C4×D4—171no—
840C2×C4×D4—171no—
841C2×C4×D4—171no—
842C2×C4×D4—171no—
843C2×C4×D4—171no—
844C2×C4×D4—171no—
845C2×C4×D4—171no—
846C2×C4×D4—171no—
847C2×#117—171no—
848C2×#117—171no—
849C2×#117—171no—
850C22×C22⋊C4—171no—
851C22×C22⋊C4—171no—
852C22×C42—171no—
853C22×C42—171no—
854#391—171no—
855#391—171no—
856#390—171no—
857#390—171no—
858#390—171no—
859#390—171no—
860#390—171no—
861#390—171no—
862#390—171no—
863#390—171no—
864#390—171no—
865#390C2×D1711yescharacteristic
866#389—171no—
867#389—171no—
868#389—171no—
869#389—171no—
870#388—171no—
871#388—171no—
872#388—171no—
873#388—171no—
874#388—171no—
875#388—171no—
876#388—171no—
877#388—171no—
878#388—171no—
879#388—171no—
880#388—171no—
881#388—171no—
882#388—171no—
883#388—171no—
884#388—171no—
885#388—171no—
886#388—171no—
887#388—171no—
888#388—171no—
889#388—171no—
890#388C2×D1711yescharacteristic
891#388C2×D1711yescharacteristic
892#388C2×D1711yescharacteristic, complemented
893#388C2×D1711yescharacteristic, complemented
894#387—171no—
895#387—171no—
896#387—171no—
897#387—171no—
898#387—171no—
899#387—171no—
900#387C2×D1711yescharacteristic, complemented
901#387C2×D1711yescharacteristic, complemented
902#386—171no—
903#386—171no—
904#386—171no—
905#386—171no—
906#386—171no—
907#386—171no—
908#386—171no—
909#386—171no—
910#386—171no—
911#386—171no—
912#386—171no—
913#386C2×D1711yescharacteristic
914#385—171no—
915#385—171no—
916#385—171no—
917#385—171no—
918#383—171no—
919#383—171no—
920#382—171no—
921#382—171no—
922#381—171no—
923#381—171no—
924#381—171no—
925#381—171no—
926#380—171no—
927#380—171no—
928#380—171no—
929#380—171no—
930#380—171no—
931#380—171no—
932#379—171no—
933#379—171no—
934C4×C4⋊C4—171no—
935C4×C4⋊C4—171no—
936C4×C4⋊C4—171no—
937C4×C4⋊C4—171no—
938C4×C4⋊C4—171no—
939C4×C4⋊C4—171no—
940C4×C4⋊C4—171no—
941C4×C4⋊C4—171no—
942C4×C4⋊C4—171no—
943C4×C4⋊C4—171no—
944C4×C4⋊C4—171no—
945C4×C4⋊C4—171no—
946C4×C4⋊C4C2×D1711yescharacteristic, complemented
947C4×C4⋊C4C2×D1711yescharacteristic, complemented
948C4×C22⋊C4—171no—
949C4×C22⋊C4—171no—
950C4×C22⋊C4—171no—
951C4×C22⋊C4—171no—
952C4×C22⋊C4—171no—
953C4×C22⋊C4—171no—
954C4×C22⋊C4—171no—
955C4×C22⋊C4—171no—
956C4×C22⋊C4—171no—
957C4×C22⋊C4—171no—
958C4×C22⋊C4—171no—
959C4×C22⋊C4—171no—
960C4×C22⋊C4—171no—
961C4×C22⋊C4—171no—
962C4×C22⋊C4—171no—
963C4×C22⋊C4—171no—
964C4×C22⋊C4—171no—
965C4×C22⋊C4—171no—
966C4×C22⋊C4—171no—
967C4×C22⋊C4—171no—
968C4×C22⋊C4—171no—
969C4×C22⋊C4—171no—
970C4×C22⋊C4C2×D1711yescharacteristic
971C4×C22⋊C4C2×D1711yescharacteristic
972C4×C22⋊C4C2×D1711yescharacteristic, complemented
973C4×C22⋊C4C2×D1711yescharacteristic, complemented
974#376—171no—
975#376—171no—
976C2×#95—171no—
977C2×#95—171no—
978C2×#95—171no—
979C2×#95—171no—
980C2×C17—42no—
981C2×C17—42no—
982C2×C17C2×C4×#4111yescharacteristic
983C2×C17C2×#51811yescharacteristic
984C2×C17#342811yescharacteristic
985C2×C17#350511yescharacteristic
986C2×C17#350511yescharacteristic
987C2×C17#350611yescharacteristic
988C2×C17#350611yescharacteristic
989D17—24no—
990D17—42no—
991D17—42no—
992C25—171no—
993C2×#41—178no—
994C2×#41—682no—
995C2×#41—682no—
996C22×Q8—171no—
997C22×D4—171no—
998C22×D4—171no—
999C22×D4—171no—
1000C22×D4—171no—
1001C22×D4—171no—
1002C22×D4—171no—
1003C22×D4C22×D1711yescharacteristic
1004C23×C4—171no—
1005C23×C4—171no—
1006C23×C4—171no—
1007C23×C4—171no—
1008C23×C4—178no—
1009C23×C4—171no—
1010C23×C4—171no—
1011C23×C4—171no—
1012C23×C4—171no—
1013C23×C4—171no—
1014C23×C4—171no—
1015C23×C4—171no—
1016C23×C4—171no—
1017C23×C4—171no—
1018C23×C4—171no—
1019C23×C4—682no—
1020C23×C4—682no—
1021C23×C4C22×D1711yescharacteristic
1022C23×C4C22×D1711yescharacteristic
1023#123—178no—
1024#123C4×D1718yescomplemented
1025C22⋊Q8—178no—
1026C22⋊Q8—178no—
1027#121—178no—
1028#121—178no—
1029#120—178no—
1030#120—178no—
1031C4×Q8—682no—
1032C4×Q8—682no—
1033C4×D4—178no—
1034C4×D4—178no—
1035C4×D4—178no—
1036C4×D4—178no—
1037C4×D4—344no—
1038C4×D4—344no—
1039C4×D4—344no—
1040C4×D4—344no—
1041C4×D4—682no—
1042C4×D4—682no—
1043#117—178no—
1044#117—682no—
1045#117—682no—
1046C2×C4⋊C4—171no—
1047C2×C4⋊C4—171no—
1048C2×C4⋊C4—171no—
1049C2×C4⋊C4—171no—
1050C2×C4⋊C4—171no—
1051C2×C4⋊C4—171no—
1052C2×C4⋊C4—171no—
1053C2×C4⋊C4—171no—
1054C2×C4⋊C4—171no—
1055C2×C4⋊C4—171no—
1056C2×C4⋊C4—171no—
1057C2×C4⋊C4—171no—
1058C2×C4⋊C4—171no—
1059C2×C4⋊C4—171no—
1060C2×C4⋊C4—171no—
1061C2×C4⋊C4—171no—
1062C2×C4⋊C4—171no—
1063C2×C4⋊C4C22×D1711yescharacteristic
1064C2×C4⋊C4C22×D1711yescharacteristic
1065C2×C4⋊C4C22×D1711yescharacteristic
1066C2×C4⋊C4C22×D1711yescharacteristic
1067C2×C4⋊C4C22×D1711yescharacteristic
1068C2×C22⋊C4—171no—
1069C2×C22⋊C4—171no—
1070C2×C22⋊C4—171no—
1071C2×C22⋊C4—171no—
1072C2×C22⋊C4—171no—
1073C2×C22⋊C4—171no—
1074C2×C22⋊C4—171no—
1075C2×C22⋊C4—171no—
1076C2×C22⋊C4—171no—
1077C2×C22⋊C4—171no—
1078C2×C22⋊C4—171no—
1079C2×C22⋊C4—171no—
1080C2×C22⋊C4—171no—
1081C2×C22⋊C4—171no—
1082C2×C22⋊C4—171no—
1083C2×C22⋊C4—171no—
1084C2×C22⋊C4—171no—
1085C2×C22⋊C4—171no—
1086C2×C22⋊C4—171no—
1087C2×C22⋊C4—171no—
1088C2×C22⋊C4—171no—
1089C2×C22⋊C4—171no—
1090C2×C22⋊C4—171no—
1091C2×C22⋊C4—171no—
1092C2×C22⋊C4—171no—
1093C2×C22⋊C4—171no—
1094C2×C22⋊C4—171no—
1095C2×C22⋊C4—171no—
1096C2×C22⋊C4—171no—
1097C2×C22⋊C4—171no—
1098C2×C22⋊C4—171no—
1099C2×C22⋊C4—171no—
1100C2×C22⋊C4—344no—
1101C2×C22⋊C4—344no—
1102C2×C22⋊C4C22×D1711yescharacteristic
1103C2×C22⋊C4C22×D1711yescharacteristic
1104C2×C22⋊C4C22×D1711yescharacteristic
1105C2×C22⋊C4C22×D1711yescharacteristic
1106C2×C22⋊C4C22×D1711yescharacteristic
1107C2×C22⋊C4C22×D1711yescharacteristic
1108C2×C22⋊C4C22×D1711yescharacteristic
1109C2×C22⋊C4C22×D1711yescharacteristic
1110C2×C22⋊C4C22×D1711yescharacteristic
1111C2×C22⋊C4C22×D1711yescharacteristic
1112C2×C42—171no—
1113C2×C42—171no—
1114C2×C42—171no—
1115C2×C42—171no—
1116C2×C42—171no—
1117C2×C42—171no—
1118C2×C42—171no—
1119C2×C42—171no—
1120C2×C42—171no—
1121C2×C42—171no—
1122C2×C42—171no—
1123C2×C42—171no—
1124C2×C42—171no—
1125C2×C42—171no—
1126C2×C42—171no—
1127C2×C42—171no—
1128C2×C42—171no—
1129C2×C42—171no—
1130C2×C42—171no—
1131C2×C42—682no—
1132C2×C42—682no—
1133C2×C42C22×D1711yescharacteristic
1134C2×C42C22×D1711yescharacteristic
1135C2×C42C22×D1711yescharacteristic
1136C2×C42C22×D1711yescharacteristic
1137C2×C42C22×D1711yescharacteristic
1138C2×C42C22×D1711yescharacteristic
1139C2×C42C22×D1711yescharacteristic
1140#95—171no—
1141#95—171no—
1142#95—171no—
1143#95—171no—
1144#95—171no—
1145#95—171no—
1146#95—171no—
1147#95—171no—
1148#95—171no—
1149#95—171no—
1150#95—171no—
1151#95—171no—
1152#95—171no—
1153#95—171no—
1154#95—171no—
1155#95—171no—
1156#95—171no—
1157#95—171no—
1158#95—171no—
1159#95—171no—
1160#95—171no—
1161#95—171no—
1162#95—171no—
1163#95—171no—
1164#95—171no—
1165#95—171no—
1166#95—171no—
1167#95—171no—
1168#95—171no—
1169#95—171no—
1170#95C22×D1711yescharacteristic
1171#95C22×D1711yescharacteristic
1172#95C22×D1711yescharacteristic
1173#95C22×D1711yescharacteristic
1174#95C22×D1711yescharacteristic
1175#95C22×D1711yescharacteristic
1176#95C22×D1711yescharacteristic
1177#95C22×D1711yescharacteristic
1178#95C22×D1711yescharacteristic
1179#95C22×D1711yescharacteristic
1180C17#3422311yescharacteristic, complemented, Sylow
1181C24—171no—
1182C24—171no—
1183C24—171no—
1184C24—174no—
1185C24—342no—
1186C24—342no—
1187C24—681no—
1188C24—681no—
1189C24—681no—
1190C24—681no—
1191C24C23×D1711yescharacteristic
1192C24C23×D1711yescharacteristic
1193#41—6816no—
1194C2×Q8—174no—
1195C2×Q8—342no—
1196C2×Q8—342no—
1197C2×D4—41no—
1198C2×D4—41no—
1199C2×D4—174no—
1200C2×D4—174no—
1201C2×D4—174no—
1202C2×D4—174no—
1203C2×D4—174no—
1204C2×D4—174no—
1205C2×D4—342no—
1206C2×D4—342no—
1207C2×D4—342no—
1208C2×D4—342no—
1209C2×D4—342no—
1210C2×D4—342no—
1211C2×D4—681no—
1212C2×D4—681no—
1213C2×D4—681no—
1214C2×D4—681no—
1215C2×D4—681no—
1216C2×D4—681no—
1217C2×D4C2×C4×D1714yes—
1218C22×C4—22no—
1219C22×C4—41no—
1220C22×C4—41no—
1221C22×C4—41no—
1222C22×C4—41no—
1223C22×C4—171no—
1224C22×C4—174no—
1225C22×C4—171no—
1226C22×C4—171no—
1227C22×C4—171no—
1228C22×C4—171no—
1229C22×C4—171no—
1230C22×C4—171no—
1231C22×C4—174no—
1232C22×C4—174no—
1233C22×C4—174no—
1234C22×C4—174no—
1235C22×C4—174no—
1236C22×C4—174no—
1237C22×C4—174no—
1238C22×C4—174no—
1239C22×C4—171no—
1240C22×C4—171no—
1241C22×C4—171no—
1242C22×C4—171no—
1243C22×C4—171no—
1244C22×C4—171no—
1245C22×C4—342no—
1246C22×C4—342no—
1247C22×C4—342no—
1248C22×C4—342no—
1249C22×C4—342no—
1250C22×C4—342no—
1251C22×C4—342no—
1252C22×C4—342no—
1253C22×C4—342no—
1254C22×C4—342no—
1255C22×C4—342no—
1256C22×C4—681no—
1257C22×C4—681no—
1258C22×C4—681no—
1259C22×C4—681no—
1260C22×C4—681no—
1261C22×C4—681no—
1262C22×C4—681no—
1263C22×C4—681no—
1264C22×C4—681no—
1265C22×C4—681no—
1266C22×C4—681no—
1267C22×C4—681no—
1268C22×C4—681no—
1269C22×C4—681no—
1270C22×C4—681no—
1271C22×C4—681no—
1272C22×C4—681no—
1273C22×C4—681no—
1274C22×C4—6816no—
1275C22×C4—681no—
1276C22×C4—681no—
1277C22×C4—681no—
1278C22×C4—681no—
1279C22×C4C2×C4×D1714yes—
1280C22×C4C23×D1711yescharacteristic
1281C22×C4C23×D1711yescharacteristic
1282C22×C4C23×D1711yescharacteristic
1283C22×C4C23×D1711yescharacteristic
1284C22×C4C23×D1711yescharacteristic
1285C22×C4C23×D1711yescharacteristic
1286C22×C4C23×D1711yescharacteristic
1287C22×C4C23×D1711yescharacteristic
1288C22×C4C23×D1711yescharacteristic
1289C22×C4C23×D1711yescharacteristic
1290C22×C4C23×D1711yescharacteristic
1291C22×C4C23×D1711yescharacteristic
1292C22×C4C23×D1711yescharacteristic
1293C4⋊C4—22no—
1294C4⋊C4—41no—
1295C4⋊C4—41no—
1296C4⋊C4—174no—
1297C4⋊C4—174no—
1298C4⋊C4—174no—
1299C4⋊C4—174no—
1300C4⋊C4—342no—
1301C4⋊C4—342no—
1302C4⋊C4—342no—
1303C4⋊C4—342no—
1304C4⋊C4—342no—
1305C4⋊C4—342no—
1306C4⋊C4—342no—
1307C4⋊C4—681no—
1308C4⋊C4—681no—
1309C4⋊C4—681no—
1310C4⋊C4—681no—
1311C4⋊C4—681no—
1312C4⋊C4—681no—
1313C4⋊C4C2×C4×D1714yes—
1314C4⋊C4C2×C4×D1714yes—
1315C22⋊C4—22no—
1316C22⋊C4—22no—
1317C22⋊C4—22no—
1318C22⋊C4—41no—
1319C22⋊C4—41no—
1320C22⋊C4—41no—
1321C22⋊C4—41no—
1322C22⋊C4—174no—
1323C22⋊C4—174no—
1324C22⋊C4—174no—
1325C22⋊C4—174no—
1326C22⋊C4—174no—
1327C22⋊C4—174no—
1328C22⋊C4—174no—
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—681no—
1343C22⋊C4—681no—
1344C22⋊C4—681no—
1345C22⋊C4—681no—
1346C22⋊C4—681no—
1347C22⋊C4—681no—
1348C22⋊C4—681no—
1349C22⋊C4—681no—
1350C22⋊C4—681no—
1351C22⋊C4—681no—
1352C22⋊C4—681no—
1353C22⋊C4—681no—
1354C22⋊C4C2×C4×D1714yes—
1355C22⋊C4C2×C4×D1714yes—
1356C22⋊C4C2×C4×D1714yes—
1357C42—22no—
1358C42—41no—
1359C42—41no—
1360C42—41no—
1361C42—41no—
1362C42—41no—
1363C42—41no—
1364C42—174no—
1365C42—174no—
1366C42—342no—
1367C42—342no—
1368C42—342no—
1369C42—342no—
1370C42—342no—
1371C42—342no—
1372C42—342no—
1373C42—681no—
1374C42—681no—
1375C42—681no—
1376C42—681no—
1377C42—681no—
1378C42—681no—
1379C42—681no—
1380C42—681no—
1381C42—681no—
1382C42—681no—
1383C23—21no—
1384C23—21no—
1385C23—21no—
1386C23—21no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—172no—
1396C23—172no—
1397C23—172no—
1398C23—172no—
1399C23—172no—
1400C23—348no—
1401C23—341no—
1402C23—341no—
1403C23—341no—
1404C23—341no—
1405C23—341no—
1406C23—341no—
1407C23—341no—
1408C23—341no—
1409C23—341no—
1410C23—341no—
1411C23—341no—
1412C23—341no—
1413C23—341no—
1414C23—341no—
1415C23—341no—
1416C23—341no—
1417C23—684no—
1418C23—684no—
1419C23—684no—
1420C23—684no—
1421C23—684no—
1422C23—684no—
1423C23C22×C4×D1712yes—
1424C23C22×C4×D1712yes—
1425C23C24×D1711yescharacteristic
1426Q8—348no—
1427D4—44no—
1428D4—348no—
1429D4—348no—
1430D4—348no—
1431D4—684no—
1432D4—684no—
1433D4—684no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—44no—
1467C2×C4—82no—
1468C2×C4—172no—
1469C2×C4—172no—
1470C2×C4—172no—
1471C2×C4—172no—
1472C2×C4—172no—
1473C2×C4—172no—
1474C2×C4—172no—
1475C2×C4—172no—
1476C2×C4—172no—
1477C2×C4—348no—
1478C2×C4—348no—
1479C2×C4—348no—
1480C2×C4—341no—
1481C2×C4—341no—
1482C2×C4—341no—
1483C2×C4—341no—
1484C2×C4—341no—
1485C2×C4—341no—
1486C2×C4—341no—
1487C2×C4—341no—
1488C2×C4—341no—
1489C2×C4—341no—
1490C2×C4—341no—
1491C2×C4—341no—
1492C2×C4—341no—
1493C2×C4—341no—
1494C2×C4—341no—
1495C2×C4—341no—
1496C2×C4—341no—
1497C2×C4—341no—
1498C2×C4—341no—
1499C2×C4—341no—
1500C2×C4—341no—
1501C2×C4—341no—
1502C2×C4—341no—
1503C2×C4—341no—
1504C2×C4—341no—
1505C2×C4—341no—
1506C2×C4—341no—
1507C2×C4—341no—
1508C2×C4—341no—
1509C2×C4—341no—
1510C2×C4—684no—
1511C2×C4—684no—
1512C2×C4—684no—
1513C2×C4—684no—
1514C2×C4—684no—
1515C2×C4—684no—
1516C2×C4—684no—
1517C2×C4—684no—
1518C2×C4—1362no—
1519C2×C4—1362no—
1520C2×C4—1362no—
1521C2×C4C22×C4×D1712yes—
1522C2×C4C22×C4×D1712yes—
1523C2×C4C22×C4×D1712yes—
1524C2×C4C22×C4×D1712yes—
1525C2×C4C22×C4×D1712yes—
1526C2×C4#41×D1712yes—
1527C2×C4#41×D1712yes—
1528C22—22no—
1529C22—22no—
1530C22—22no—
1531C22—22no—
1532C22—22no—
1533C22—22no—
1534C22—41no—
1535C22—41no—
1536C22—41no—
1537C22—41no—
1538C22—41no—
1539C22—41no—
1540C22—41no—
1541C22—41no—
1542C22—174no—
1543C22—342no—
1544C22—342no—
1545C22—342no—
1546C22—342no—
1547C22—342no—
1548C22—342no—
1549C22—342no—
1550C22—342no—
1551C22—342no—
1552C22—342no—
1553C22—342no—
1554C22—342no—
1555C22—6816no—
1556C22—681no—
1557C22—681no—
1558C22—681no—
1559C22—681no—
1560C22—681no—
1561C22—681no—
1562C22—681no—
1563C22—681no—
1564C22C23×C4×D1711yescharacteristic
1565C22C2×#41×D1711yescharacteristic
1566C22C2×#41×D1711yescharacteristic
1567C22H(5,𝔽2)×D1711yescharacteristic
1568C22H(5,𝔽2)×D1711yescharacteristic
1569C22#1176364511yescharacteristic
1570C22#1176364511yescharacteristic
1571C4—22no—
1572C4—22no—
1573C4—22no—
1574C4—22no—
1575C4—22no—
1576C4—22no—
1577C4—22no—
1578C4—41no—
1579C4—41no—
1580C4—41no—
1581C4—41no—
1582C4—41no—
1583C4—41no—
1584C4—174no—
1585C4—342no—
1586C4—342no—
1587C4—342no—
1588C4—342no—
1589C4—342no—
1590C4—342no—
1591C4—681no—
1592C4—681no—
1593C4—681no—
1594C4—681no—
1595C4—681no—
1596C4—681no—
1597C2—42no—
1598C2—42no—
1599C2—344no—
1600C2—682no—
1601C2—682no—
1602C2C4×#41×D1711yescharacteristic
1603C2D17×#51811yescharacteristic
1604C2#1454198311yescharacteristic
1605C2#1454261511yescharacteristic
1606C2#1454261711yescharacteristic
1607C2#1454263011yescharacteristic
1608C2#1454263211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2374C2
socle, cosocleC23×C17C25
prime radicalC2×#11763317C2
hypercenter#2374D17
hypocenterC17#34223
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2374

Complements

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

NH ≅ G/Ntype
2. #14531920C2semidirect
3. #14531915C2semidirect
4. #14531915C2semidirect
5. #14531823C2semidirect
6. #14531817C2semidirect
7. #14531812C2semidirect
8. #14531806C2semidirect
9. #14531754C2semidirect
10. #14531753C2semidirect
11. #14531723C2semidirect
12. #14531718C2semidirect
13. #14531674C2semidirect
14. #14531666C2semidirect
15. #14531623C2semidirect
16. #14531610C2semidirect
17. #14531446C2semidirect
18. #14531443C2semidirect
19. #14531440C2semidirect
20. #14531437C2semidirect
21. #14531416C2semidirect
22. #14531414C2semidirect
23. #14531318C2semidirect
24. C4×#10587582C2semidirect
25. #14531296C2semidirect
26. C4×#10587570C2semidirect
27. #14531165C2semidirect
28. #14531144C2semidirect
29. #14531143C2semidirect
30. C4×C22⋊C4×D17C2semidirect
31. C17×#2374C2semidirect
34. #11763317C4semidirect
42. C2×C4×Dic34C22semidirect
43. C2×#10587573C22semidirect
49. C2×C4×C22⋊D17C22semidirect
53. C2×#10587567C22semidirect
61. #11762713C22semidirect
62. #11762713C22semidirect
70. #11762709C22semidirect
71. #11762709C22semidirect
72. #11762706C22semidirect
73. #11762706C22semidirect
74. #11762704C22semidirect
75. #11762704C22semidirect
80. #11762702C22semidirect
81. #11762702C22semidirect
86. #11762700C22semidirect
87. #11762700C22semidirect
92. #11762698C22semidirect
93. #11762698C22semidirect
96. #11762695C22semidirect
97. #11762695C22semidirect
98. #11762693C22semidirect
99. #11762693C22semidirect
100. #11762691C22semidirect
101. #11762691C22semidirect
117. #11762676C22semidirect
118. #11762676C22semidirect
119. #11762674C22semidirect
120. #11762673C22semidirect
123. #11762671C22semidirect
124. #11762670C22semidirect
129. #11762667C22semidirect
130. #11762666C22semidirect
133. C4⋊C4×Dic17C22semidirect
134. C4⋊C4×Dic17C22semidirect
135. C4⋊C4×Dic17C22semidirect
136. C4×#63225C22semidirect
137. C4×#63225C22semidirect
138. C4×#63225C22semidirect
139. C4×#63225C22semidirect
140. C4×#63225C22semidirect
141. #11762660C22semidirect
142. #11762660C22semidirect
143. #11762660C22semidirect
144. #11762660C22semidirect
147. C22⋊C4×Dic17C22semidirect
148. C22⋊C4×Dic17C22semidirect
149. C22⋊C4×Dic17C22semidirect
156. C4×#63227C22semidirect
157. C4×#63227C22semidirect
158. C4×#63227C22semidirect
165. #11762656C22semidirect
166. #11762656C22semidirect
167. #11762655C22semidirect
168. #11762654C22semidirect
169. C2×#10587502C22semidirect
172. #95×D17C22semidirect
177. C17×#388C22semidirect
178. C17×#388C22semidirect
179. C17×#387C22semidirect
180. C17×#387C22semidirect
182. C4×C4⋊C4×C17C22semidirect
183. C4×C4⋊C4×C17C22semidirect
186. C4×C22⋊C4×C17C22semidirect
187. C4×C22⋊C4×C17C22semidirect
201. C2×#63254C2×C4semidirect
206. C22×C4×D17C2×C4semidirect
219. C17×#123C2×C4semidirect
250. #10587623C2×C4semidirect
251. #10587615C2×C4semidirect
314. #10587582C2×C4semidirect
315. #10587582C2×C4semidirect
317. #10587579C2×C4semidirect
318. #10587579C2×C4semidirect
321. #10587570C2×C4semidirect
322. #10587568C2×C4semidirect
325. #10587567C2×C4semidirect
326. #10587567C2×C4semidirect
329. #10587563C2×C4semidirect
483. C2×C4×D17#41semidirect
484. C2×C4×D17#41semidirect
728. #2374D17semidirect
892. #388C2×D17semidirect
893. #388C2×D17semidirect
900. #387C2×D17semidirect
901. #387C2×D17semidirect
946. C4×C4⋊C4C2×D17semidirect
947. C4×C4⋊C4C2×D17semidirect
972. C4×C22⋊C4C2×D17semidirect
973. C4×C22⋊C4C2×D17semidirect
1024. #123C4×D17semidirect
1180. C17#34223semidirect

Maximal subgroups

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

subgroupindex
C2×#117633172
#145319202
#145319152
#145318232
#145318172
#145318122
#145318062
#145317542
#145317532
#145317232
#145317182
#145316742
#145316662
#145316232
#145316102
#145314462
#145314432
#145314402
#145314372
#145314162
#145314142
#145313182
C4×#105875822
#145312962
C4×#105875702
#145311652
#145311442
#145311432
C4×C22⋊C4×D172
C17×#23742
#3422317