Finite Group Databasebeta

← #32868217

Subgroups — #32868217

Order 18176.

2362 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986510C211yesmaximal, characteristic, complemented
2#22599177C214yesmaximal, complemented
3#22599170C212yesmaximal, complemented
4#22599154C212yesmaximal, complemented
5#22599128C214yesmaximal, complemented
6#22599121C212yesmaximal, complemented
7#22599105C212yesmaximal, complemented
8#22598288C211yesmaximal, characteristic, complemented
9#22598280C211yesmaximal, characteristic, complemented
10#22598269C212yesmaximal, complemented
11#22597972C212yesmaximal, complemented
12#22597961C212yesmaximal, complemented
13#22597600C211yesmaximal, characteristic, complemented
14#22597592C211yesmaximal, characteristic, complemented
15#22597580C212yesmaximal, complemented
16C2×#17985963C211yesmaximal, characteristic, complemented
17C2×#525×C71C211yesmaximal, characteristic, complemented
18C22×#11765865C2211yescharacteristic, complemented
19C2×#14556158C2212yescomplemented
20C2×#14556153C2212yescomplemented
21C22×#11765849C2212yescomplemented
22#17986510—21no—
23#17986510—21no—
24#17986510—21no—
25#17986510—21no—
26#17986510C2212yes—
27#17986510C2212yes—
28#17986510C2212yescomplemented
29#17986510C2212yescomplemented
30C2×#14556111—21no—
31C2×#14556107C2211yescharacteristic
32C2×#14556107C2211yescharacteristic, complemented
33C2×#14556102C2211yescharacteristic
34C2×#14556102C2211yescharacteristic, complemented
35C2×#14556097—21no—
36C2×C4×C22⋊D71—21no—
37C2×C4×C22⋊D71—21no—
38C2×#14556087C2211yescharacteristic, complemented
39#17986340C2214yescomplemented
40#17986337C2214yescomplemented
41#17986337C2214yescomplemented
42#17986334C2212yescomplemented
43#17986329C2212yescomplemented
44#17986323C2214yescomplemented
45#17986320C2214yescomplemented
46#17986320C2214yescomplemented
47#17986317C2212yescomplemented
48#17986312C2212yescomplemented
49#17986255C2214yescomplemented
50#17986250C2214yescomplemented
51#17986247C2214yescomplemented
52#17986243C2214yescomplemented
53#17986238C2214yescomplemented
54#17986233C2214yescomplemented
55#17986230C2214yescomplemented
56#17986226C2214yescomplemented
57#17986161C2214yescomplemented
58#17986159C2214yescomplemented
59#17986159C2214yescomplemented
60#17986155C2212yescomplemented
61#17986150C2212yescomplemented
62#17986144C2214yescomplemented
63#17986142C2214yescomplemented
64#17986142C2214yescomplemented
65#17986138C2212yescomplemented
66#17986133C2212yescomplemented
67#17986042C2212yescomplemented
68#17986042C2212yescomplemented
69#17986007C2212yescomplemented
70#17986003C2212yescomplemented
71#17986000C2212yescomplemented
72#17986000C2212yescomplemented
73#17985963C2211yescharacteristic
74#17985963C2211yescharacteristic
75#17985963C2212yescomplemented
76#17985963C2212yescomplemented
77#17985963C2212yescomplemented
78C2×C22⋊(C71⋊C8)C2212yescomplemented
79C2×C22⋊(C71⋊C8)C2212yescomplemented
80C22×#41×C71C2211yescharacteristic
81C24×C4×C71C2211yescharacteristic
82#525×C71—21no—
83#525×C71—21no—
84#525×C71—21no—
85#525×C71—21no—
86#525×C71C2212yes—
87#525×C71C2212yes—
88#525×C71C2212yescomplemented
89#525×C71C2212yescomplemented
90C2×#123×C71—21no—
91C2×C22⋊Q8×C71C2211yescharacteristic, complemented
92C2×C22⋊Q8×C71C2211yescharacteristic, complemented
93C2×#121×C71C2211yescharacteristic, complemented
94C2×#121×C71C2211yescharacteristic, complemented
95C2×#120×C71—21no—
96C2×C4×D4×C71—21no—
97C2×C4×D4×C71—21no—
98C2×#117×C71C2211yescharacteristic
99C2×#11765865—21no—
100C2×#11765865—21no—
101C2×#11765865—44no—
102C2×#11765865C2312yes—
103C2×#11765865C2312yes—
104C22×Dic142C2311yescharacteristic
105C22×D284C2311yescharacteristic
106C22×C22⋊D71—21no—
107C22×C22⋊D71—21no—
108C22×C22⋊D71—21no—
109C22×C4×D71—21no—
110#14556158—44no—
111#14556153—44no—
112C2×#11765855C2314yescomplemented
113C2×#11765853C2314yescomplemented
114C2×#11765852C2314yescomplemented
115C2×#11765850C2314yescomplemented
116C2×#11765849—44no—
117C2×#11765849C2312yes—
118C2×#11765849C2312yes—
119C2×#11765849C2314yes—
120C22×C71⋊C8C2314yes—
121#14556111—22no—
122#14556111—22no—
123#14556111—22no—
124#14556111—22no—
125#14556107—21no—
126#14556107—21no—
127#14556107—21no—
128#14556107—21no—
129#14556107C2312yes—
130#14556107C2312yes—
131#14556107C2312yes—
132#14556107C2312yes—
133#14556102—21no—
134#14556102—21no—
135#14556102—21no—
136#14556102—21no—
137#14556102C2312yes—
138#14556102C2312yes—
139#14556102C2312yes—
140#14556102C2312yes—
141#14556097—22no—
142#14556097—22no—
143#14556097—22no—
144#14556097—22no—
145C4×C22⋊D71—22no—
146C4×C22⋊D71—22no—
147C4×C22⋊D71—22no—
148C4×C22⋊D71—22no—
149C4×C22⋊D71—22no—
150C4×C22⋊D71—22no—
151C4×C22⋊D71—22no—
152C4×C22⋊D71—22no—
153#14556087—21no—
154#14556087—21no—
155#14556087C2312yes—
156#14556087C2312yes—
157C2×C4⋊Dic71C2311yescharacteristic
158C2×C4⋊Dic71C2311yescharacteristic
159C2×Dic71⋊C4—21no—
160C2×Dic71⋊C4—21no—
161C2×C22⋊Dic71—21no—
162C2×C22⋊Dic71—21no—
163C2×C22⋊Dic71—21no—
164C2×(C2×D71)⋊C4—21no—
165C2×(C2×D71)⋊C4—21no—
166C2×C4×Dic71—21no—
167#14556061C2314yescomplemented
168#14556061C2314yescomplemented
169#14556059C2314yescomplemented
170#14556059C2314yescomplemented
171#14556052C2314yescomplemented
172#14556052C2314yescomplemented
173#14556051C2314yescomplemented
174#14556051C2314yescomplemented
175#14556049C2314yescomplemented
176#14556049C2314yescomplemented
177#14556048C2314yescomplemented
178#14556048C2314yescomplemented
179C22⋊(C71⋊C8)C2312yes—
180C22⋊(C71⋊C8)C2314yes—
181C22⋊(C71⋊C8)C2314yes—
182C22⋊(C71⋊C8)C2312yes—
183C22⋊(C71⋊C8)C2312yes—
184C22⋊(C71⋊C8)C2312yes—
185C25×C71D411yescharacteristic
186C2×#41×C71—21no—
187C2×#41×C71—21no—
188C2×#41×C71—44no—
189C2×#41×C71C2312yes—
190C2×#41×C71C2312yes—
191C22×Q8×C71C2311yescharacteristic
192C22×D4×C71—21no—
193C22×D4×C71—21no—
194C22×D4×C71—21no—
195C22×D4×C71C2311yescharacteristic
196C23×C4×C71—21no—
197C23×C4×C71—44no—
198C23×C4×C71D411yescharacteristic
199C23×C4×C71D411yescharacteristic
200C23×C4×C71D411yescharacteristic
201C23×C4×C71D411yescharacteristic
202C23×C4×C71D411yescharacteristic
203C23×C4×C71D411yescharacteristic
204C23×C4×C71D411yescharacteristic
205C23×C4×C71C2311yescharacteristic
206C23×C4×C71C2311yescharacteristic
207C23×C4×C71C2311yescharacteristic
208C23×C4×C71C2311yescharacteristic
209C23×C4×C71C2311yescharacteristic
210C23×C4×C71C2311yescharacteristic
211C23×C4×C71C2311yescharacteristic
212#123×C71—22no—
213#123×C71—22no—
214#123×C71—22no—
215#123×C71—22no—
216C22⋊Q8×C71—21no—
217C22⋊Q8×C71—21no—
218C22⋊Q8×C71—21no—
219C22⋊Q8×C71—21no—
220C22⋊Q8×C71C2312yes—
221C22⋊Q8×C71C2312yes—
222C22⋊Q8×C71C2312yes—
223C22⋊Q8×C71C2312yes—
224#121×C71—21no—
225#121×C71—21no—
226#121×C71—21no—
227#121×C71—21no—
228#121×C71C2312yes—
229#121×C71C2312yes—
230#121×C71C2312yes—
231#121×C71C2312yes—
232#120×C71—22no—
233#120×C71—22no—
234#120×C71—22no—
235#120×C71—22no—
236C4×D4×C71—22no—
237C4×D4×C71—22no—
238C4×D4×C71—22no—
239C4×D4×C71—22no—
240C4×D4×C71—22no—
241C4×D4×C71—22no—
242C4×D4×C71—22no—
243C4×D4×C71—22no—
244#117×C71—21no—
245#117×C71—21no—
246#117×C71C2312yes—
247#117×C71C2312yes—
248C2×C4⋊C4×C71—21no—
249C2×C4⋊C4×C71—21no—
250C2×C4⋊C4×C71C2311yescharacteristic
251C2×C4⋊C4×C71C2311yescharacteristic
252C2×C22⋊C4×C71—21no—
253C2×C22⋊C4×C71—21no—
254C2×C22⋊C4×C71—21no—
255C2×C22⋊C4×C71—21no—
256C2×C22⋊C4×C71—21no—
257C2×C42×C71—21no—
258C23×D71—21no—
259#11765865—44no—
260#11765865—44no—
261#11765865—44no—
262#11765865—44no—
263C2×Dic142—24no—
264C2×Dic142—21no—
265C2×Dic142C2412yes—
266C2×D284—24no—
267C2×D284—21no—
268C2×D284C2412yes—
269C2×C22⋊D71—22no—
270C2×C22⋊D71—22no—
271C2×C22⋊D71—22no—
272C2×C22⋊D71—22no—
273C2×C22⋊D71—22no—
274C2×C22⋊D71—22no—
275C2×C22⋊D71—44no—
276C2×C22⋊D71—44no—
277C2×C22⋊D71—44no—
278C22×Dic71—21no—
279C22×Dic71—21no—
280C22×Dic71—21no—
281C2×C4×D71—22no—
282C2×C4×D71—22no—
283C2×C4×D71—44no—
284#11765855—44no—
285#11765853—44no—
286#11765852—44no—
287#11765850—44no—
288#11765849—24no—
289#11765849—24no—
290#11765849—44no—
291C2×C71⋊C8—44no—
292C2×C71⋊C8C2414yes—
293C2×C71⋊C8C2414yes—
294C4⋊Dic71—21no—
295C4⋊Dic71—21no—
296C4⋊Dic71C2412yes—
297C4⋊Dic71C2412yes—
298Dic71⋊C4—22no—
299Dic71⋊C4—22no—
300Dic71⋊C4—22no—
301Dic71⋊C4—22no—
302C22⋊Dic71—22no—
303C22⋊Dic71—22no—
304C22⋊Dic71—22no—
305C22⋊Dic71—22no—
306C22⋊Dic71—22no—
307C22⋊Dic71—22no—
308(C2×D71)⋊C4—22no—
309(C2×D71)⋊C4—22no—
310(C2×D71)⋊C4—22no—
311(C2×D71)⋊C4—22no—
312C4×Dic71—22no—
313C4×Dic71—22no—
314C24×C71—21no—
315C24×C71—42no—
316C24×C71—42no—
317C24×C71—42no—
318C24×C71C2×D411yescharacteristic
319C24×C71C2×D411yescharacteristic
320C24×C71C2×D411yescharacteristic
321C24×C71C2×D411yescharacteristic
322C24×C71C2×D411yescharacteristic
323C24×C71C2×D411yescharacteristic
324C24×C71C2×D411yescharacteristic
325#41×C71—24no—
326#41×C71—24no—
327#41×C71—42no—
328#41×C71—42no—
329#41×C71—44no—
330#41×C71—44no—
331C2×Q8×C71—21no—
332C2×Q8×C71—42no—
333C2×Q8×C71C2412yes—
334C2×D4×C71—22no—
335C2×D4×C71—22no—
336C2×D4×C71—22no—
337C2×D4×C71—22no—
338C2×D4×C71—22no—
339C2×D4×C71—22no—
340C2×D4×C71—21no—
341C2×D4×C71—42no—
342C2×D4×C71—44no—
343C2×D4×C71—44no—
344C2×D4×C71—44no—
345C2×D4×C71C2412yes—
346C22×C4×C71—24no—
347C22×C4×C71—24no—
348C22×C4×C71—24no—
349C22×C4×C71—21no—
350C22×C4×C71—21no—
351C22×C4×C71—21no—
352C22×C4×C71—22no—
353C22×C4×C71—22no—
354C22×C4×C71—42no—
355C22×C4×C71—42no—
356C22×C4×C71—42no—
357C22×C4×C71—42no—
358C22×C4×C71—42no—
359C22×C4×C71—42no—
360C22×C4×C71—42no—
361C22×C4×C71—42no—
362C22×C4×C71—42no—
363C22×C4×C71—42no—
364C22×C4×C71—42no—
365C22×C4×C71—44no—
366C22×C4×C71C2×D411yescharacteristic
367C22×C4×C71C2×D411yescharacteristic
368C22×C4×C71C2×D411yescharacteristic
369C22×C4×C71C2×D411yescharacteristic
370C22×C4×C71C2×D411yescharacteristic
371C22×C4×C71C2×D411yescharacteristic
372C22×C4×C71C2×D411yescharacteristic
373C22×C4×C71C2×D411yescharacteristic
374C22×C4×C71C2×D411yescharacteristic
375C22×C4×C71C2×D411yescharacteristic
376C22×C4×C71C2×D411yescharacteristic
377C22×C4×C71C2×D411yescharacteristic
378C22×C4×C71C2×D411yescharacteristic
379C22×C4×C71C2×D411yescharacteristic
380C22×C4×C71C2×D411yescharacteristic
381C22×C4×C71C2×D411yescharacteristic
382C22×C4×C71C2×D411yescharacteristic
383C22×C4×C71C2×D411yescharacteristic
384C22×C4×C71C2×D411yescharacteristic
385C22×C4×C71C2×D411yescharacteristic
386C22×C4×C71C2×D411yescharacteristic
387C22×C4×C71C2411yescharacteristic
388C22×C4×C71C2411yescharacteristic
389C22×C4×C71C2411yescharacteristic
390C22×C4×C71C2411yescharacteristic
391C22×C4×C71C2411yescharacteristic
392C22×C4×C71C2411yescharacteristic
393C22×C4×C71C2411yescharacteristic
394C4⋊C4×C71—22no—
395C4⋊C4×C71—22no—
396C4⋊C4×C71—22no—
397C4⋊C4×C71—22no—
398C4⋊C4×C71—21no—
399C4⋊C4×C71—21no—
400C4⋊C4×C71C2412yes—
401C4⋊C4×C71C2412yes—
402C22⋊C4×C71—22no—
403C22⋊C4×C71—22no—
404C22⋊C4×C71—22no—
405C22⋊C4×C71—22no—
406C22⋊C4×C71—22no—
407C22⋊C4×C71—22no—
408C22⋊C4×C71—22no—
409C22⋊C4×C71—22no—
410C22⋊C4×C71—22no—
411C22⋊C4×C71—22no—
412C42×C71—22no—
413C42×C71—22no—
414C23×C71—22no—
415C23×C71—22no—
416C23×C71—22no—
417C23×C71—22no—
418C23×C71—22no—
419C23×C71—22no—
420C23×C71—22no—
421C23×C71—22no—
422C23×C71—22no—
423C23×C71—22no—
424C23×C71—41no—
425C23×C71—41no—
426C23×C71—41no—
427C23×C71—41no—
428C23×C71—41no—
429C23×C71—41no—
430C23×C71—41no—
431C23×C71—41no—
432C23×C71—41no—
433C23×C71—41no—
434C23×C71—41no—
435C23×C71—41no—
436C23×C71—42no—
437C23×C71—42no—
438C23×C71—416no—
439C23×C71—42no—
440C23×C71C22×D411yescharacteristic
441C23×C71C22×D411yescharacteristic
442C23×C71C22×D411yescharacteristic
443C23×C71C22×D411yescharacteristic
444C23×C71C22×D411yescharacteristic
445C23×C71C22×D411yescharacteristic
446C23×C71C22×D411yescharacteristic
447C22×D71—22no—
448C22×D71—42no—
449C22×D71—42no—
450C22×D71—42no—
451Q8×C71—22no—
452Q8×C71—22no—
453Q8×C71—42no—
454D4×C71—22no—
455D4×C71—22no—
456D4×C71—42no—
457D4×C71—44no—
458D4×C71—44no—
459D4×C71—44no—
460D4×C71—44no—
461D4×C71—44no—
462D4×C71—44no—
463C2×C4×C71—22no—
464C2×C4×C71—22no—
465C2×C4×C71—22no—
466C2×C4×C71—22no—
467C2×C4×C71—22no—
468C2×C4×C71—22no—
469C2×C4×C71—22no—
470C2×C4×C71—22no—
471C2×C4×C71—22no—
472C2×C4×C71—22no—
473C2×C4×C71—22no—
474C2×C4×C71—22no—
475C2×C4×C71—22no—
476C2×C4×C71—22no—
477C2×C4×C71—22no—
478C2×C4×C71—22no—
479C2×C4×C71—22no—
480C2×C4×C71—22no—
481C2×C4×C71—41no—
482C2×C4×C71—41no—
483C2×C4×C71—41no—
484C2×C4×C71—41no—
485C2×C4×C71—41no—
486C2×C4×C71—41no—
487C2×C4×C71—41no—
488C2×C4×C71—41no—
489C2×C4×C71—41no—
490C2×C4×C71—41no—
491C2×C4×C71—41no—
492C2×C4×C71—41no—
493C2×C4×C71—44no—
494C2×C4×C71—42no—
495C2×C4×C71—42no—
496C2×C4×C71—42no—
497C2×C4×C71—44no—
498C2×C4×C71C22×D411yescharacteristic
499C2×C4×C71C22×D411yescharacteristic
500C2×C4×C71C22×D411yescharacteristic
501C2×C4×C71C22×D411yescharacteristic
502C2×C4×C71C22×D411yescharacteristic
503C2×C4×C71C22×D411yescharacteristic
504C2×C4×C71C22×D411yescharacteristic
505C2×C4×C71H(5,𝔽2)14yes—
506C2×C4×C71C2511yescharacteristic
507C22⋊D71—44no—
508C22⋊D71—44no—
509C22⋊D71—44no—
510C22⋊D71—44no—
511C22⋊D71—44no—
512C22⋊D71—44no—
513C2×Dic71—22no—
514C2×Dic71—22no—
515C2×Dic71—22no—
516C2×Dic71—42no—
517C2×Dic71—42no—
518C2×Dic71—42no—
519D284—24no—
520D284—42no—
521C4×D71—44no—
522C4×D71—44no—
523Dic142—24no—
524Dic142—42no—
525C71⋊C8—24no—
526C71⋊C8—24no—
527C22×C71—21no—
528C22×C71—21no—
529C22×C71—21no—
530C22×C71—21no—
531C22×C71—21no—
532C22×C71—21no—
533C22×C71—21no—
534C22×C71—21no—
535C22×C71—21no—
536C22×C71—21no—
537C22×C71—21no—
538C22×C71—21no—
539C22×C71—21no—
540C22×C71—21no—
541C22×C71—21no—
542C22×C71—21no—
543C22×C71—21no—
544C22×C71—21no—
545C22×C71—44no—
546C22×C71—44no—
547C22×C71—44no—
548C22×C71—44no—
549C22×C71—44no—
550C22×C71—44no—
551C22×C71—44no—
552C22×C71—42no—
553C22×C71—42no—
554C22×C71—42no—
555C22×C71—84no—
556C22×C71#53412yes—
557C22×C71#57512yes—
558C22×C71#57512yes—
559C22×C71C23×D411yescharacteristic
560C2×D71—42no—
561C2×D71—42no—
562C2×D71—42no—
563C2×D71—84no—
564C4×C71—21no—
565C4×C71—21no—
566C4×C71—21no—
567C4×C71—21no—
568C4×C71—21no—
569C4×C71—21no—
570C4×C71—42no—
571C4×C71—42no—
572C4×C71—42no—
573C4×C71#53412yes—
574C4×C71C2×H(5,𝔽2)12yes—
575Dic71—42no—
576Dic71—42no—
577Dic71—42no—
578#60752—711nomaximal, Sylow
579C2×C71—22no—
580C2×C71—22no—
581C2×C71—22no—
582C2×C71—41no—
583C2×C71—41no—
584C2×C71—41no—
585C2×C71—41no—
586C2×C71—82no—
587C2×C71C2×#53411yescharacteristic
588C2×C71C2×#57511yescharacteristic
589C2×C71C2×#57511yescharacteristic
590D71—82no—
591C2×#525—711no—
592C2×#525D7111yescharacteristic, complemented
593#3197—714no—
594#3196—712no—
595#3194—712no—
596#3191—714no—
597#3190—712no—
598#3188—712no—
599#3095—711no—
600#3094—711no—
601#3093—712no—
602#3056—712no—
603#3055—712no—
604#3007—711no—
605#3006—711no—
606#3005—712no—
607C2×#407—711no—
608C71#6075211yescharacteristic, complemented, Sylow
609C22×#41—711no—
610C22×#41C2×D7111yescharacteristic
611C24×C4C2×D7111yescharacteristic
612C2×#137—712no—
613C2×AGL(1,ℤ/8)—712no—
614C22×M16—712no—
615#525—21no—
616#525—21no—
617#525—21no—
618#525—21no—
619#525—712no—
620#525—712no—
621#525—712no—
622#525—712no—
623#525—1421no—
624#525—1421no—
625#525—1421no—
626#525—1421no—
627#525C2×D7112yes—
628#525C2×D7112yes—
629#525C2×D7112yescomplemented
630#525C2×D7112yescomplemented
631C2×#123—21no—
632C2×#123—1421no—
633C2×C22⋊Q8—711no—
634C2×C22⋊Q8—711no—
635C2×C22⋊Q8C2×D7111yescharacteristic, complemented
636C2×C22⋊Q8C2×D7111yescharacteristic, complemented
637C2×#121—711no—
638C2×#121—711no—
639C2×#121C2×D7111yescharacteristic, complemented
640C2×#121C2×D7111yescharacteristic, complemented
641C2×#120—21no—
642C2×#120—1421no—
643C2×C4×D4—21no—
644C2×C4×D4—21no—
645C2×C4×D4—1421no—
646C2×C4×D4—1421no—
647C2×#117—711no—
648C2×#117C2×D7111yescharacteristic
649#485—714no—
650#485—714no—
651#485—714no—
652#484—712no—
653#483—712no—
654#482—714no—
655#482—714no—
656#482—714no—
657#481—712no—
658#480—712no—
659#470—714no—
660#469—714no—
661#468—714no—
662#468—714no—
663#467—714no—
664#466—714no—
665#465—714no—
666#465—714no—
667#452—714no—
668#452—714no—
669#452—714no—
670#451—712no—
671#450—712no—
672#449—714no—
673#449—714no—
674#449—714no—
675#448—712no—
676#447—712no—
677#428—712no—
678#428—712no—
679#419—712no—
680#418—712no—
681#417—712no—
682#417—712no—
683#407—712no—
684#407—711no—
685#407—711no—
686#407—712no—
687#407—712no—
688C2×C22⋊C8—712no—
689C2×C22⋊C8—712no—
690C25C22⋊D7111yescharacteristic
691C2×#41—21no—
692C2×#41—21no—
693C2×#41—44no—
694C2×#41—2844no—
695C2×#41—712no—
696C2×#41—712no—
697C2×#41—1421no—
698C2×#41—1421no—
699C2×#41C22×D7112yes—
700C2×#41C22×D7112yes—
701C22×Q8—711no—
702C22×Q8C22×D7111yescharacteristic
703C22×D4—21no—
704C22×D4—21no—
705C22×D4—21no—
706C22×D4—711no—
707C22×D4—1421no—
708C22×D4—1421no—
709C22×D4—1421no—
710C22×D4C22×D7111yescharacteristic
711C23×C4—21no—
712C23×C4—44no—
713C23×C4—1421no—
714C23×C4C22⋊D7111yescharacteristic
715C23×C4C22⋊D7111yescharacteristic
716C23×C4C22⋊D7111yescharacteristic
717C23×C4C22⋊D7111yescharacteristic
718C23×C4C22⋊D7111yescharacteristic
719C23×C4C22⋊D7111yescharacteristic
720C23×C4C22⋊D7111yescharacteristic
721C23×C4C22×D7111yescharacteristic
722C23×C4C22×D7111yescharacteristic
723C23×C4C22×D7111yescharacteristic
724C23×C4C22×D7111yescharacteristic
725C23×C4C22×D7111yescharacteristic
726C23×C4C22×D7111yescharacteristic
727C23×C4C22×D7111yescharacteristic
728#137—2844no—
729AGL(1,ℤ/8)—2844no—
730C2×Q16—714no—
731C2×SD16—714no—
732C2×SD16—714no—
733C2×D8—714no—
734C2×M16—2844no—
735C2×M16—714no—
736C2×M16—712no—
737C2×M16—712no—
738C22×C8—714no—
739#123—22no—
740#123—22no—
741#123—22no—
742#123—22no—
743#123—1422no—
744#123—1422no—
745#123—1422no—
746#123—1422no—
747C22⋊Q8—21no—
748C22⋊Q8—21no—
749C22⋊Q8—21no—
750C22⋊Q8—21no—
751C22⋊Q8—712no—
752C22⋊Q8—712no—
753C22⋊Q8—712no—
754C22⋊Q8—712no—
755C22⋊Q8—1421no—
756C22⋊Q8—1421no—
757C22⋊Q8—1421no—
758C22⋊Q8—1421no—
759C22⋊Q8C22×D7112yes—
760C22⋊Q8C22×D7112yes—
761C22⋊Q8C22×D7112yes—
762C22⋊Q8C22×D7112yes—
763#121—21no—
764#121—21no—
765#121—21no—
766#121—21no—
767#121—712no—
768#121—712no—
769#121—712no—
770#121—712no—
771#121—1421no—
772#121—1421no—
773#121—1421no—
774#121—1421no—
775#121C22×D7112yes—
776#121C22×D7112yes—
777#121C22×D7112yes—
778#121C22×D7112yes—
779#120—22no—
780#120—22no—
781#120—22no—
782#120—22no—
783#120—1422no—
784#120—1422no—
785#120—1422no—
786#120—1422no—
787C4×D4—22no—
788C4×D4—22no—
789C4×D4—22no—
790C4×D4—22no—
791C4×D4—22no—
792C4×D4—22no—
793C4×D4—22no—
794C4×D4—22no—
795C4×D4—1422no—
796C4×D4—1422no—
797C4×D4—1422no—
798C4×D4—1422no—
799C4×D4—1422no—
800C4×D4—1422no—
801C4×D4—1422no—
802C4×D4—1422no—
803#117—21no—
804#117—21no—
805#117—712no—
806#117—712no—
807#117—1421no—
808#117—1421no—
809#117C22×D7112yes—
810#117C22×D7112yes—
811C2×C4⋊C4—21no—
812C2×C4⋊C4—21no—
813C2×C4⋊C4—711no—
814C2×C4⋊C4—711no—
815C2×C4⋊C4—1421no—
816C2×C4⋊C4—1421no—
817C2×C4⋊C4C22×D7111yescharacteristic
818C2×C4⋊C4C22×D7111yescharacteristic
819C2×C22⋊C4—21no—
820C2×C22⋊C4—21no—
821C2×C22⋊C4—21no—
822C2×C22⋊C4—21no—
823C2×C22⋊C4—21no—
824C2×C22⋊C4—1421no—
825C2×C22⋊C4—1421no—
826C2×C22⋊C4—1421no—
827C2×C22⋊C4—1421no—
828C2×C22⋊C4—1421no—
829C2×C42—21no—
830C2×C42—1421no—
831#107—714no—
832#107—714no—
833#106—714no—
834#106—714no—
835#103—714no—
836#103—714no—
837#103—714no—
838#103—714no—
839#102—714no—
840#102—714no—
841#102—714no—
842#102—714no—
843C22⋊C8—712no—
844C22⋊C8—712no—
845C22⋊C8—714no—
846C22⋊C8—714no—
847C22⋊C8—712no—
848C22⋊C8—712no—
849C24—21no—
850C24—42no—
851C24—42no—
852C24—42no—
853C24—1421no—
854C24C2×C22⋊D7111yescharacteristic
855C24C2×C22⋊D7111yescharacteristic
856C24C2×C22⋊D7111yescharacteristic
857C24C2×C22⋊D7111yescharacteristic
858C24C2×C22⋊D7111yescharacteristic
859C24C2×C22⋊D7111yescharacteristic
860C24C2×C22⋊D7111yescharacteristic
861#41—24no—
862#41—24no—
863#41—42no—
864#41—42no—
865#41—44no—
866#41—44no—
867#41—2844no—
868#41—2844no—
869#41—2844no—
870#41—2844no—
871C2×Q8—21no—
872C2×Q8—42no—
873C2×Q8—712no—
874C2×Q8—1424no—
875C2×Q8—1421no—
876C2×Q8C23×D7112yes—
877C2×D4—22no—
878C2×D4—22no—
879C2×D4—22no—
880C2×D4—22no—
881C2×D4—22no—
882C2×D4—22no—
883C2×D4—21no—
884C2×D4—42no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—2844no—
889C2×D4—2844no—
890C2×D4—2844no—
891C2×D4—712no—
892C2×D4—1422no—
893C2×D4—1422no—
894C2×D4—1422no—
895C2×D4—1422no—
896C2×D4—1422no—
897C2×D4—1422no—
898C2×D4—1421no—
899C2×D4—1424no—
900C2×D4C23×D7112yes—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—24no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—44no—
921C22×C4—2844no—
922C22×C4—1421no—
923C22×C4—1421no—
924C22×C4—1421no—
925C22×C4—1422no—
926C22×C4—1422no—
927C22×C4C2×C22⋊D7111yescharacteristic
928C22×C4C2×C22⋊D7111yescharacteristic
929C22×C4C2×C22⋊D7111yescharacteristic
930C22×C4C2×C22⋊D7111yescharacteristic
931C22×C4C2×C22⋊D7111yescharacteristic
932C22×C4C2×C22⋊D7111yescharacteristic
933C22×C4C2×C22⋊D7111yescharacteristic
934C22×C4C2×C22⋊D7111yescharacteristic
935C22×C4C2×C22⋊D7111yescharacteristic
936C22×C4C2×C22⋊D7111yescharacteristic
937C22×C4C2×C22⋊D7111yescharacteristic
938C22×C4C2×C22⋊D7111yescharacteristic
939C22×C4C2×C22⋊D7111yescharacteristic
940C22×C4C2×C22⋊D7111yescharacteristic
941C22×C4C2×C22⋊D7111yescharacteristic
942C22×C4C2×C22⋊D7111yescharacteristic
943C22×C4C2×C22⋊D7111yescharacteristic
944C22×C4C2×C22⋊D7111yescharacteristic
945C22×C4C2×C22⋊D7111yescharacteristic
946C22×C4C2×C22⋊D7111yescharacteristic
947C22×C4C2×C22⋊D7111yescharacteristic
948C22×C4C23×D7111yescharacteristic
949C22×C4C23×D7111yescharacteristic
950C22×C4C23×D7111yescharacteristic
951C22×C4C23×D7111yescharacteristic
952C22×C4C23×D7111yescharacteristic
953C22×C4C23×D7111yescharacteristic
954C22×C4C23×D7111yescharacteristic
955Q16—2844no—
956SD16—2844no—
957SD16—2844no—
958D8—2844no—
959M16—2844no—
960M16—1424no—
961M16—1424no—
962C2×C8—2844no—
963C2×C8—714no—
964C2×C8—714no—
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—712no—
972C4⋊C4—712no—
973C4⋊C4—1422no—
974C4⋊C4—1422no—
975C4⋊C4—1422no—
976C4⋊C4—1422no—
977C4⋊C4—1421no—
978C4⋊C4—1421no—
979C4⋊C4C23×D7112yes—
980C4⋊C4C23×D7112yes—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—22no—
990C22⋊C4—22no—
991C22⋊C4—1422no—
992C22⋊C4—1422no—
993C22⋊C4—1422no—
994C22⋊C4—1422no—
995C22⋊C4—1422no—
996C22⋊C4—1422no—
997C22⋊C4—1422no—
998C22⋊C4—1422no—
999C22⋊C4—1422no—
1000C22⋊C4—1422no—
1001C42—22no—
1002C42—22no—
1003C42—1422no—
1004C42—1422no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—42no—
1028C23—42no—
1029C23—416no—
1030C23—42no—
1031C23—2842no—
1032C23—2842no—
1033C23—2842no—
1034C23—1422no—
1035C23C22×C22⋊D7111yescharacteristic
1036C23C22×C22⋊D7111yescharacteristic
1037C23C22×C22⋊D7111yescharacteristic
1038C23C22×C22⋊D7111yescharacteristic
1039C23C22×C22⋊D7111yescharacteristic
1040C23C22×C22⋊D7111yescharacteristic
1041C23C22×C22⋊D7111yescharacteristic
1042Q8—22no—
1043Q8—22no—
1044Q8—42no—
1045Q8—2842no—
1046Q8—1424no—
1047D4—22no—
1048D4—22no—
1049D4—42no—
1050D4—44no—
1051D4—44no—
1052D4—44no—
1053D4—44no—
1054D4—44no—
1055D4—44no—
1056D4—2844no—
1057D4—2844no—
1058D4—2844no—
1059D4—2844no—
1060D4—2844no—
1061D4—2844no—
1062D4—2842no—
1063D4—1424no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—44no—
1095C2×C4—42no—
1096C2×C4—42no—
1097C2×C4—42no—
1098C2×C4—44no—
1099C2×C4—2844no—
1100C2×C4—2844no—
1101C2×C4—2842no—
1102C2×C4—2842no—
1103C2×C4—2842no—
1104C2×C4—1422no—
1105C2×C4—1422no—
1106C2×C4—1422no—
1107C2×C4C22×C22⋊D7111yescharacteristic
1108C2×C4C22×C22⋊D7111yescharacteristic
1109C2×C4C22×C22⋊D7111yescharacteristic
1110C2×C4C22×C22⋊D7111yescharacteristic
1111C2×C4C22×C22⋊D7111yescharacteristic
1112C2×C4C22×C22⋊D7111yescharacteristic
1113C2×C4C22×C22⋊D7111yescharacteristic
1114C2×C4#1455617314yes—
1115C2×C4C24×D7111yescharacteristic
1116C8—1424no—
1117C8—1424no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—21no—
1125C22—21no—
1126C22—21no—
1127C22—21no—
1128C22—21no—
1129C22—21no—
1130C22—21no—
1131C22—21no—
1132C22—21no—
1133C22—21no—
1134C22—21no—
1135C22—21no—
1136C22—44no—
1137C22—44no—
1138C22—44no—
1139C22—44no—
1140C22—44no—
1141C22—44no—
1142C22—44no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—84no—
1147C22—2842no—
1148C22—2842no—
1149C22—2842no—
1150C22—5684no—
1151C22#1798655812yes—
1152C22#1798679712yes—
1153C22#1798679712yes—
1154C22C23×C22⋊D7111yescharacteristic
1155C4—21no—
1156C4—21no—
1157C4—21no—
1158C4—21no—
1159C4—21no—
1160C4—21no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—2842no—
1165C4—2842no—
1166C4—2842no—
1167C4#1798655812yes—
1168C4C2×#1455617312yes—
1169C2—22no—
1170C2—22no—
1171C2—22no—
1172C2—41no—
1173C2—41no—
1174C2—41no—
1175C2—41no—
1176C2—82no—
1177C2—5682no—
1178C2C2×#1798655811yescharacteristic
1179C2C2×#1798679711yescharacteristic
1180C2C2×#1798679711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#525×C71C2
socleC22×C71C23×D4
hypercenterC2×#525D71
hypocenterC71#60752
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#17986510C2semidirect
2. #22599177C2semidirect
3. #22599170C2semidirect
4. #22599154C2semidirect
5. #22599128C2semidirect
6. #22599121C2semidirect
7. #22599105C2semidirect
8. #22598288C2semidirect
9. #22598280C2semidirect
10. #22598269C2semidirect
11. #22597972C2semidirect
12. #22597961C2semidirect
13. #22597600C2semidirect
14. #22597592C2semidirect
15. #22597580C2semidirect
16. C2×#17985963C2semidirect
17. C2×#525×C71C2semidirect
18. C22×#11765865C22semidirect
19. C2×#14556158C22semidirect
20. C2×#14556153C22semidirect
21. C22×#11765849C22semidirect
28. #17986510C22semidirect
29. #17986510C22semidirect
32. C2×#14556107C22semidirect
34. C2×#14556102C22semidirect
38. C2×#14556087C22semidirect
39. #17986340C22semidirect
40. #17986337C22semidirect
41. #17986337C22semidirect
42. #17986334C22semidirect
43. #17986329C22semidirect
44. #17986323C22semidirect
45. #17986320C22semidirect
46. #17986320C22semidirect
47. #17986317C22semidirect
48. #17986312C22semidirect
49. #17986255C22semidirect
50. #17986250C22semidirect
51. #17986247C22semidirect
52. #17986243C22semidirect
53. #17986238C22semidirect
54. #17986233C22semidirect
55. #17986230C22semidirect
56. #17986226C22semidirect
57. #17986161C22semidirect
58. #17986159C22semidirect
59. #17986159C22semidirect
60. #17986155C22semidirect
61. #17986150C22semidirect
62. #17986144C22semidirect
63. #17986142C22semidirect
64. #17986142C22semidirect
65. #17986138C22semidirect
66. #17986133C22semidirect
67. #17986042C22semidirect
68. #17986042C22semidirect
69. #17986007C22semidirect
70. #17986003C22semidirect
71. #17986000C22semidirect
72. #17986000C22semidirect
75. #17985963C22semidirect
76. #17985963C22semidirect
77. #17985963C22semidirect
78. C2×C22⋊(C71⋊C8)C22semidirect
79. C2×C22⋊(C71⋊C8)C22semidirect
88. #525×C71C22semidirect
89. #525×C71C22semidirect
91. C2×C22⋊Q8×C71C22semidirect
92. C2×C22⋊Q8×C71C22semidirect
93. C2×#121×C71C22semidirect
94. C2×#121×C71C22semidirect
112. C2×#11765855C23semidirect
113. C2×#11765853C23semidirect
114. C2×#11765852C23semidirect
115. C2×#11765850C23semidirect
167. #14556061C23semidirect
168. #14556061C23semidirect
169. #14556059C23semidirect
170. #14556059C23semidirect
171. #14556052C23semidirect
172. #14556052C23semidirect
173. #14556051C23semidirect
174. #14556051C23semidirect
175. #14556049C23semidirect
176. #14556049C23semidirect
177. #14556048C23semidirect
178. #14556048C23semidirect
592. C2×#525D71semidirect
608. C71#60752semidirect
629. #525C2×D71semidirect
630. #525C2×D71semidirect
635. C2×C22⋊Q8C2×D71semidirect
636. C2×C22⋊Q8C2×D71semidirect
639. C2×#121C2×D71semidirect
640. C2×#121C2×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179865102
#225991772
#225991702
#225991542
#225991282
#225991212
#225991052
#225982882
#225982802
#225982692
#225979722
#225979612
#225976002
#225975922
#225975802
C2×#179859632
C2×#525×C712
#6075271