Finite Group Databasebeta

← #32868089

Subgroups — #32868089

Order 18176.

2362 conjugacy classes of subgroups.

The subgroup lattice has 1172 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#22599166C212yesmaximal, complemented
5#22599161C211yesmaximal, characteristic, complemented
6#22599154C212yesmaximal, complemented
7#22599150C212yesmaximal, complemented
8#22599146C211yesmaximal, characteristic, complemented
9#22599142C211yesmaximal, characteristic, complemented
10#22599137C211yesmaximal, characteristic, complemented
11#22598253C212yesmaximal, complemented
12#22598249C212yesmaximal, complemented
13#22597946C214yesmaximal, complemented
14#22597558C212yesmaximal, complemented
15#22597556C212yesmaximal, complemented
16C2×#17985963C211yesmaximal, characteristic, complemented
17C2×#525×C71C211yesmaximal, characteristic, complemented
18C22×#11765865C2211yescharacteristic, complemented
19C2×#14556148C2214yescomplemented
20C22×#11765849C2212yescomplemented
21#17986510—21no—
22#17986510—21no—
23#17986510—21no—
24#17986510—21no—
25#17986510C2212yes—
26#17986510C2212yes—
27#17986510C2212yescomplemented
28#17986510C2212yescomplemented
29C2×#14556111—21no—
30C2×#14556107C2211yescharacteristic
31C2×#14556107C2211yescharacteristic, complemented
32C2×#14556102C2211yescharacteristic
33C2×#14556102C2211yescharacteristic, complemented
34C2×#14556097—21no—
35C2×C4×C22⋊D71—21no—
36C2×C4×C22⋊D71—21no—
37C2×#14556087C2211yescharacteristic, complemented
38#17986340C2214yescomplemented
39#17986337C2214yescomplemented
40#17986334C2212yescomplemented
41#17986332C2212yescomplemented
42#17986329C2212yescomplemented
43#17986327C2212yescomplemented
44#17986323C2214yescomplemented
45#17986320C2214yescomplemented
46#17986317C2212yescomplemented
47#17986315C2212yescomplemented
48#17986312C2212yescomplemented
49#17986310C2212yescomplemented
50#17986255C2214yescomplemented
51#17986255C2214yescomplemented
52#17986250C2214yescomplemented
53#17986250C2214yescomplemented
54#17986247C2214yescomplemented
55#17986247C2214yescomplemented
56#17986243C2214yescomplemented
57#17986243C2214yescomplemented
58#17986161C2214yescomplemented
59#17986159C2214yescomplemented
60#17986155C2212yescomplemented
61#17986154C2212yescomplemented
62#17986150C2212yescomplemented
63#17986149C2212yescomplemented
64#17986144C2214yescomplemented
65#17986142C2214yescomplemented
66#17986138C2212yescomplemented
67#17986137C2212yescomplemented
68#17986133C2212yescomplemented
69#17986132C2212yescomplemented
70#17986035C2214yescomplemented
71#17985995C2214yescomplemented
72#17985993C2214yescomplemented
73#17985963C2211yescharacteristic
74#17985963C2211yescharacteristic
75#17985963C2212yescomplemented
76#17985963C2212yescomplemented
77#17985963C2212yescomplemented
78C2×C22⋊(C71⋊C8)C2212yescomplemented
79C2×C22⋊(C71⋊C8)C2212yescomplemented
80C22×#41×C71C2211yescharacteristic, complemented
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
92C2×C22⋊Q8×C71C2211yescharacteristic, complemented
93C2×#121×C71C2211yescharacteristic
94C2×#121×C71C2211yescharacteristic, complemented
95C2×#120×C71—21no—
96C2×C4×D4×C71—21no—
97C2×C4×D4×C71—21no—
98C2×#117×C71C2211yescharacteristic, complemented
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#14556148—48no—
111C2×#11765855C2314yescomplemented
112C2×#11765853C2314yescomplemented
113C2×#11765852C2314yescomplemented
114C2×#11765850C2314yescomplemented
115C2×#11765849—44no—
116C2×#11765849C2312yes—
117C2×#11765849C2312yes—
118C2×#11765849C2314yes—
119C22×C71⋊C8C2314yes—
120#14556111—22no—
121#14556111—22no—
122#14556111—22no—
123#14556111—22no—
124#14556107—21no—
125#14556107—21no—
126#14556107—21no—
127#14556107—21no—
128#14556107C2312yes—
129#14556107C2312yes—
130#14556107C2312yes—
131#14556107C2312yes—
132#14556102—21no—
133#14556102—21no—
134#14556102—21no—
135#14556102—21no—
136#14556102C2312yes—
137#14556102C2312yes—
138#14556102C2312yes—
139#14556102C2312yes—
140#14556097—22no—
141#14556097—22no—
142#14556097—22no—
143#14556097—22no—
144C4×C22⋊D71—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—
152#14556087—21no—
153#14556087—21no—
154#14556087C2312yes—
155#14556087C2312yes—
156C2×C4⋊Dic71C2311yescharacteristic
157C2×C4⋊Dic71C2311yescharacteristic
158C2×Dic71⋊C4—21no—
159C2×Dic71⋊C4—21no—
160C2×C22⋊Dic71—21no—
161C2×C22⋊Dic71—21no—
162C2×C22⋊Dic71—21no—
163C2×(C2×D71)⋊C4—21no—
164C2×(C2×D71)⋊C4—21no—
165C2×C4×Dic71—21no—
166#14556061C2314yescomplemented
167#14556061C2314yescomplemented
168#14556059C2314yescomplemented
169#14556059C2314yescomplemented
170#14556052C2314yescomplemented
171#14556052C2314yescomplemented
172#14556051C2314yescomplemented
173#14556051C2314yescomplemented
174#14556049C2314yescomplemented
175#14556049C2314yescomplemented
176#14556048C2314yescomplemented
177#14556048C2314yescomplemented
178C22⋊(C71⋊C8)C2312yes—
179C22⋊(C71⋊C8)C2312yes—
180C22⋊(C71⋊C8)C2312yes—
181C22⋊(C71⋊C8)C2312yes—
182C22⋊(C71⋊C8)C2314yes—
183C22⋊(C71⋊C8)C2314yes—
184C25×C71D411yescharacteristic
185C2×#41×C71—21no—
186C2×#41×C71—21no—
187C2×#41×C71—44no—
188C2×#41×C71C2312yes—
189C2×#41×C71C2312yes—
190C22×Q8×C71C2311yescharacteristic
191C22×D4×C71—21no—
192C22×D4×C71—21no—
193C22×D4×C71—21no—
194C22×D4×C71C2311yescharacteristic
195C23×C4×C71—21no—
196C23×C4×C71—44no—
197C23×C4×C71D411yescharacteristic
198C23×C4×C71D411yescharacteristic
199C23×C4×C71D411yescharacteristic
200C23×C4×C71D411yescharacteristic
201C23×C4×C71D411yescharacteristic
202C23×C4×C71D411yescharacteristic
203C23×C4×C71D411yescharacteristic
204C23×C4×C71C2311yescharacteristic
205C23×C4×C71C2311yescharacteristic
206C23×C4×C71C2311yescharacteristic
207C23×C4×C71C2311yescharacteristic
208C23×C4×C71C2311yescharacteristic
209C23×C4×C71C2311yescharacteristic
210C23×C4×C71C2311yescharacteristic
211#123×C71—22no—
212#123×C71—22no—
213#123×C71—22no—
214#123×C71—22no—
215C22⋊Q8×C71—21no—
216C22⋊Q8×C71—21no—
217C22⋊Q8×C71—21no—
218C22⋊Q8×C71—21no—
219C22⋊Q8×C71C2312yes—
220C22⋊Q8×C71C2312yes—
221C22⋊Q8×C71C2312yes—
222C22⋊Q8×C71C2312yes—
223#121×C71—21no—
224#121×C71—21no—
225#121×C71—21no—
226#121×C71—21no—
227#121×C71C2312yes—
228#121×C71C2312yes—
229#121×C71C2312yes—
230#121×C71C2312yes—
231#120×C71—22no—
232#120×C71—22no—
233#120×C71—22no—
234#120×C71—22no—
235C4×D4×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—
243#117×C71—21no—
244#117×C71—21no—
245#117×C71C2312yes—
246#117×C71C2312yes—
247C2×C4⋊C4×C71—21no—
248C2×C4⋊C4×C71—21no—
249C2×C4⋊C4×C71C2311yescharacteristic
250C2×C4⋊C4×C71C2311yescharacteristic
251C2×C22⋊C4×C71—21no—
252C2×C22⋊C4×C71—21no—
253C2×C22⋊C4×C71—21no—
254C2×C22⋊C4×C71—21no—
255C2×C22⋊C4×C71—21no—
256C2×C42×C71—21no—
257C23×D71—21no—
258#11765865—28no—
259#11765865—44no—
260#11765865—44no—
261#11765865—44no—
262C2×Dic142—21no—
263C2×Dic142—42no—
264C2×Dic142C2412yes—
265C2×D284—21no—
266C2×D284—42no—
267C2×D284C2412yes—
268C2×C22⋊D71—22no—
269C2×C22⋊D71—22no—
270C2×C22⋊D71—22no—
271C2×C22⋊D71—22no—
272C2×C22⋊D71—22no—
273C2×C22⋊D71—22no—
274C2×C22⋊D71—44no—
275C2×C22⋊D71—44no—
276C2×C22⋊D71—44no—
277C22×Dic71—21no—
278C22×Dic71—21no—
279C22×Dic71—21no—
280C2×C4×D71—22no—
281C2×C4×D71—22no—
282C2×C4×D71—44no—
283#11765855—44no—
284#11765853—44no—
285#11765852—44no—
286#11765850—44no—
287#11765849—42no—
288#11765849—44no—
289#11765849—42no—
290C2×C71⋊C8—28no—
291C2×C71⋊C8C2414yes—
292C2×C71⋊C8C2414yes—
293C4⋊Dic71—21no—
294C4⋊Dic71—21no—
295C4⋊Dic71C2412yes—
296C4⋊Dic71C2412yes—
297Dic71⋊C4—22no—
298Dic71⋊C4—22no—
299Dic71⋊C4—22no—
300Dic71⋊C4—22no—
301C22⋊Dic71—22no—
302C22⋊Dic71—22no—
303C22⋊Dic71—22no—
304C22⋊Dic71—22no—
305C22⋊Dic71—22no—
306C22⋊Dic71—22no—
307(C2×D71)⋊C4—22no—
308(C2×D71)⋊C4—22no—
309(C2×D71)⋊C4—22no—
310(C2×D71)⋊C4—22no—
311C4×Dic71—22no—
312C4×Dic71—22no—
313C24×C71—21no—
314C24×C71—42no—
315C24×C71—42no—
316C24×C71—42no—
317C24×C71C2×D411yescharacteristic
318C24×C71C2×D411yescharacteristic
319C24×C71C2×D411yescharacteristic
320C24×C71C2×D411yescharacteristic
321C24×C71C2×D411yescharacteristic
322C24×C71C2×D411yescharacteristic
323C24×C71C2×D411yescharacteristic
324#41×C71—28no—
325#41×C71—44no—
326#41×C71—44no—
327#41×C71—44no—
328C2×Q8×C71—21no—
329C2×Q8×C71—42no—
330C2×Q8×C71C2412yes—
331C2×D4×C71—22no—
332C2×D4×C71—22no—
333C2×D4×C71—22no—
334C2×D4×C71—22no—
335C2×D4×C71—22no—
336C2×D4×C71—22no—
337C2×D4×C71—21no—
338C2×D4×C71—42no—
339C2×D4×C71—44no—
340C2×D4×C71—44no—
341C2×D4×C71—44no—
342C2×D4×C71C2412yes—
343C22×C4×C71—24no—
344C22×C4×C71—24no—
345C22×C4×C71—24no—
346C22×C4×C71—21no—
347C22×C4×C71—21no—
348C22×C4×C71—21no—
349C22×C4×C71—22no—
350C22×C4×C71—22no—
351C22×C4×C71—42no—
352C22×C4×C71—42no—
353C22×C4×C71—42no—
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—44no—
363C22×C4×C71C2×D411yescharacteristic
364C22×C4×C71C2×D411yescharacteristic
365C22×C4×C71C2×D411yescharacteristic
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×C71C2411yescharacteristic
385C22×C4×C71C2411yescharacteristic
386C22×C4×C71C2411yescharacteristic
387C22×C4×C71C2411yescharacteristic
388C22×C4×C71C2411yescharacteristic
389C22×C4×C71C2411yescharacteristic
390C22×C4×C71C2411yescharacteristic
391C4⋊C4×C71—22no—
392C4⋊C4×C71—22no—
393C4⋊C4×C71—22no—
394C4⋊C4×C71—22no—
395C4⋊C4×C71—21no—
396C4⋊C4×C71—21no—
397C4⋊C4×C71C2412yes—
398C4⋊C4×C71C2412yes—
399C22⋊C4×C71—22no—
400C22⋊C4×C71—22no—
401C22⋊C4×C71—22no—
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—
409C42×C71—22no—
410C42×C71—22no—
411C23×C71—22no—
412C23×C71—22no—
413C23×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—41no—
422C23×C71—41no—
423C23×C71—41no—
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—42no—
434C23×C71—42no—
435C23×C71—416no—
436C23×C71—42no—
437C23×C71C22×D411yescharacteristic
438C23×C71C22×D411yescharacteristic
439C23×C71C22×D411yescharacteristic
440C23×C71C22×D411yescharacteristic
441C23×C71C22×D411yescharacteristic
442C23×C71C22×D411yescharacteristic
443C23×C71C22×D411yescharacteristic
444C22×D71—22no—
445C22×D71—42no—
446C22×D71—42no—
447C22×D71—42no—
448Q8×C71—24no—
449Q8×C71—42no—
450D4×C71—24no—
451D4×C71—42no—
452D4×C71—44no—
453D4×C71—44no—
454D4×C71—44no—
455D4×C71—44no—
456D4×C71—44no—
457D4×C71—44no—
458C2×C4×C71—22no—
459C2×C4×C71—22no—
460C2×C4×C71—22no—
461C2×C4×C71—22no—
462C2×C4×C71—22no—
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—41no—
477C2×C4×C71—41no—
478C2×C4×C71—41no—
479C2×C4×C71—41no—
480C2×C4×C71—41no—
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—44no—
489C2×C4×C71—42no—
490C2×C4×C71—42no—
491C2×C4×C71—42no—
492C2×C4×C71—44no—
493C2×C4×C71C22×D411yescharacteristic
494C2×C4×C71C22×D411yescharacteristic
495C2×C4×C71C22×D411yescharacteristic
496C2×C4×C71C22×D411yescharacteristic
497C2×C4×C71C22×D411yescharacteristic
498C2×C4×C71C22×D411yescharacteristic
499C2×C4×C71C22×D411yescharacteristic
500C2×C4×C71H(5,𝔽2)14yes—
501C2×C4×C71C2511yescharacteristic
502C22⋊D71—44no—
503C22⋊D71—44no—
504C22⋊D71—44no—
505C22⋊D71—44no—
506C22⋊D71—44no—
507C22⋊D71—44no—
508C2×Dic71—22no—
509C2×Dic71—22no—
510C2×Dic71—22no—
511C2×Dic71—42no—
512C2×Dic71—42no—
513C2×Dic71—42no—
514D284—24no—
515D284—42no—
516C4×D71—44no—
517C4×D71—44no—
518Dic142—24no—
519Dic142—42no—
520C71⋊C8—24no—
521C71⋊C8—24no—
522C22×C71—21no—
523C22×C71—21no—
524C22×C71—21no—
525C22×C71—21no—
526C22×C71—21no—
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—44no—
541C22×C71—44no—
542C22×C71—44no—
543C22×C71—44no—
544C22×C71—44no—
545C22×C71—44no—
546C22×C71—44no—
547C22×C71—42no—
548C22×C71—42no—
549C22×C71—42no—
550C22×C71—84no—
551C22×C71#53412yes—
552C22×C71#57512yes—
553C22×C71#57512yes—
554C22×C71C23×D411yescharacteristic
555C2×D71—42no—
556C2×D71—42no—
557C2×D71—42no—
558C2×D71—84no—
559C4×C71—21no—
560C4×C71—21no—
561C4×C71—21no—
562C4×C71—21no—
563C4×C71—21no—
564C4×C71—21no—
565C4×C71—42no—
566C4×C71—42no—
567C4×C71—42no—
568C4×C71#53412yes—
569C4×C71C2×H(5,𝔽2)12yes—
570Dic71—42no—
571Dic71—42no—
572Dic71—42no—
573#60741—711nomaximal, Sylow
574C2×C71—22no—
575C2×C71—22no—
576C2×C71—22no—
577C2×C71—41no—
578C2×C71—41no—
579C2×C71—41no—
580C2×C71—41no—
581C2×C71—82no—
582C2×C71C2×#53411yescharacteristic
583C2×C71C2×#57511yescharacteristic
584C2×C71C2×#57511yescharacteristic
585D71—82no—
586C2×#525—711no—
587C2×#525D7111yescharacteristic, complemented
588#3197—714no—
589#3196—712no—
590#3196—712no—
591#3195—711no—
592#3194—712no—
593#3194—712no—
594#3193—711no—
595#3193—711no—
596#3192—711no—
597#3091—712no—
598#3091—712no—
599#3054—714no—
600#3002—712no—
601#3002—712no—
602C2×#407—711no—
603C71#6074111yescharacteristic, complemented, Sylow
604C22×#41—711no—
605C22×#41C2×D7111yescharacteristic, complemented
606C24×C4C2×D7111yescharacteristic
607C2×#135—714no—
608C22×M16—712no—
609#525—21no—
610#525—21no—
611#525—21no—
612#525—21no—
613#525—712no—
614#525—712no—
615#525—712no—
616#525—712no—
617#525—1421no—
618#525—1421no—
619#525—1421no—
620#525—1421no—
621#525C2×D7112yes—
622#525C2×D7112yes—
623#525C2×D7112yescomplemented
624#525C2×D7112yescomplemented
625C2×#123—21no—
626C2×#123—1421no—
627C2×C22⋊Q8—711no—
628C2×C22⋊Q8—711no—
629C2×C22⋊Q8C2×D7111yescharacteristic
630C2×C22⋊Q8C2×D7111yescharacteristic, complemented
631C2×#121—711no—
632C2×#121—711no—
633C2×#121C2×D7111yescharacteristic
634C2×#121C2×D7111yescharacteristic, complemented
635C2×#120—21no—
636C2×#120—1421no—
637C2×C4×D4—21no—
638C2×C4×D4—21no—
639C2×C4×D4—1421no—
640C2×C4×D4—1421no—
641C2×#117—711no—
642C2×#117C2×D7111yescharacteristic, complemented
643#485—714no—
644#485—714no—
645#484—712no—
646#484—712no—
647#483—712no—
648#483—712no—
649#482—714no—
650#482—714no—
651#481—712no—
652#481—712no—
653#480—712no—
654#480—712no—
655#470—714no—
656#470—714no—
657#469—714no—
658#469—714no—
659#468—714no—
660#468—714no—
661#468—714no—
662#468—714no—
663#452—714no—
664#452—714no—
665#451—712no—
666#451—712no—
667#450—712no—
668#450—712no—
669#449—714no—
670#449—714no—
671#448—712no—
672#448—712no—
673#447—712no—
674#447—712no—
675#427—714no—
676#416—714no—
677#416—714no—
678#407—711no—
679#407—711no—
680#407—712no—
681#407—712no—
682#407—712no—
683C2×C22⋊C8—712no—
684C2×C22⋊C8—712no—
685C25C22⋊D7111yescharacteristic
686C2×#41—21no—
687C2×#41—21no—
688C2×#41—44no—
689C2×#41—2844no—
690C2×#41—712no—
691C2×#41—712no—
692C2×#41—1421no—
693C2×#41—1421no—
694C2×#41C22×D7112yes—
695C2×#41C22×D7112yes—
696C22×Q8—711no—
697C22×Q8C22×D7111yescharacteristic
698C22×D4—21no—
699C22×D4—21no—
700C22×D4—21no—
701C22×D4—711no—
702C22×D4—1421no—
703C22×D4—1421no—
704C22×D4—1421no—
705C22×D4C22×D7111yescharacteristic
706C23×C4—21no—
707C23×C4—44no—
708C23×C4—1421no—
709C23×C4C22⋊D7111yescharacteristic
710C23×C4C22⋊D7111yescharacteristic
711C23×C4C22⋊D7111yescharacteristic
712C23×C4C22⋊D7111yescharacteristic
713C23×C4C22⋊D7111yescharacteristic
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
723#135—2848no—
724C2×Q16—714no—
725C2×SD16—714no—
726C2×SD16—714no—
727C2×D8—714no—
728C2×M16—2844no—
729C2×M16—712no—
730C2×M16—714no—
731C2×M16—712no—
732C22×C8—714no—
733#123—22no—
734#123—22no—
735#123—22no—
736#123—22no—
737#123—1422no—
738#123—1422no—
739#123—1422no—
740#123—1422no—
741C22⋊Q8—21no—
742C22⋊Q8—21no—
743C22⋊Q8—21no—
744C22⋊Q8—21no—
745C22⋊Q8—712no—
746C22⋊Q8—712no—
747C22⋊Q8—712no—
748C22⋊Q8—712no—
749C22⋊Q8—1421no—
750C22⋊Q8—1421no—
751C22⋊Q8—1421no—
752C22⋊Q8—1421no—
753C22⋊Q8C22×D7112yes—
754C22⋊Q8C22×D7112yes—
755C22⋊Q8C22×D7112yes—
756C22⋊Q8C22×D7112yes—
757#121—21no—
758#121—21no—
759#121—21no—
760#121—21no—
761#121—712no—
762#121—712no—
763#121—712no—
764#121—712no—
765#121—1421no—
766#121—1421no—
767#121—1421no—
768#121—1421no—
769#121C22×D7112yes—
770#121C22×D7112yes—
771#121C22×D7112yes—
772#121C22×D7112yes—
773#120—22no—
774#120—22no—
775#120—22no—
776#120—22no—
777#120—1422no—
778#120—1422no—
779#120—1422no—
780#120—1422no—
781C4×D4—22no—
782C4×D4—22no—
783C4×D4—22no—
784C4×D4—22no—
785C4×D4—22no—
786C4×D4—22no—
787C4×D4—22no—
788C4×D4—22no—
789C4×D4—1422no—
790C4×D4—1422no—
791C4×D4—1422no—
792C4×D4—1422no—
793C4×D4—1422no—
794C4×D4—1422no—
795C4×D4—1422no—
796C4×D4—1422no—
797#117—21no—
798#117—21no—
799#117—712no—
800#117—712no—
801#117—1421no—
802#117—1421no—
803#117C22×D7112yes—
804#117C22×D7112yes—
805C2×C4⋊C4—21no—
806C2×C4⋊C4—21no—
807C2×C4⋊C4—711no—
808C2×C4⋊C4—711no—
809C2×C4⋊C4—1421no—
810C2×C4⋊C4—1421no—
811C2×C4⋊C4C22×D7111yescharacteristic
812C2×C4⋊C4C22×D7111yescharacteristic
813C2×C22⋊C4—21no—
814C2×C22⋊C4—21no—
815C2×C22⋊C4—21no—
816C2×C22⋊C4—21no—
817C2×C22⋊C4—21no—
818C2×C22⋊C4—1421no—
819C2×C22⋊C4—1421no—
820C2×C22⋊C4—1421no—
821C2×C22⋊C4—1421no—
822C2×C22⋊C4—1421no—
823C2×C42—21no—
824C2×C42—1421no—
825#107—714no—
826#107—714no—
827#106—714no—
828#106—714no—
829#103—714no—
830#103—714no—
831#103—714no—
832#103—714no—
833#102—714no—
834#102—714no—
835#102—714no—
836#102—714no—
837C22⋊C8—712no—
838C22⋊C8—712no—
839C22⋊C8—712no—
840C22⋊C8—712no—
841C22⋊C8—714no—
842C22⋊C8—714no—
843C24—21no—
844C24—42no—
845C24—42no—
846C24—42no—
847C24—1421no—
848C24C2×C22⋊D7111yescharacteristic
849C24C2×C22⋊D7111yescharacteristic
850C24C2×C22⋊D7111yescharacteristic
851C24C2×C22⋊D7111yescharacteristic
852C24C2×C22⋊D7111yescharacteristic
853C24C2×C22⋊D7111yescharacteristic
854C24C2×C22⋊D7111yescharacteristic
855#41—28no—
856#41—44no—
857#41—44no—
858#41—44no—
859#41—2844no—
860#41—2844no—
861#41—2844no—
862#41—1428no—
863C2×Q8—21no—
864C2×Q8—42no—
865C2×Q8—2842no—
866C2×Q8—712no—
867C2×Q8—1421no—
868C2×Q8C23×D7112yes—
869C2×D4—22no—
870C2×D4—22no—
871C2×D4—22no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—22no—
875C2×D4—21no—
876C2×D4—42no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—2842no—
881C2×D4—2844no—
882C2×D4—2844no—
883C2×D4—2844no—
884C2×D4—712no—
885C2×D4—1422no—
886C2×D4—1422no—
887C2×D4—1422no—
888C2×D4—1422no—
889C2×D4—1422no—
890C2×D4—1422no—
891C2×D4—1421no—
892C2×D4C23×D7112yes—
893C22×C4—24no—
894C22×C4—24no—
895C22×C4—24no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—44no—
913C22×C4—2844no—
914C22×C4—1421no—
915C22×C4—1421no—
916C22×C4—1421no—
917C22×C4—1422no—
918C22×C4—1422no—
919C22×C4C2×C22⋊D7111yescharacteristic
920C22×C4C2×C22⋊D7111yescharacteristic
921C22×C4C2×C22⋊D7111yescharacteristic
922C22×C4C2×C22⋊D7111yescharacteristic
923C22×C4C2×C22⋊D7111yescharacteristic
924C22×C4C2×C22⋊D7111yescharacteristic
925C22×C4C2×C22⋊D7111yescharacteristic
926C22×C4C2×C22⋊D7111yescharacteristic
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×C4C23×D7111yescharacteristic
941C22×C4C23×D7111yescharacteristic
942C22×C4C23×D7111yescharacteristic
943C22×C4C23×D7111yescharacteristic
944C22×C4C23×D7111yescharacteristic
945C22×C4C23×D7111yescharacteristic
946C22×C4C23×D7111yescharacteristic
947Q16—2844no—
948SD16—2844no—
949SD16—2844no—
950D8—2844no—
951M16—2842no—
952M16—2844no—
953M16—2842no—
954C2×C8—714no—
955C2×C8—714no—
956C2×C8—1428no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—712no—
964C4⋊C4—712no—
965C4⋊C4—1422no—
966C4⋊C4—1422no—
967C4⋊C4—1422no—
968C4⋊C4—1422no—
969C4⋊C4—1421no—
970C4⋊C4—1421no—
971C4⋊C4C23×D7112yes—
972C4⋊C4C23×D7112yes—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—22no—
976C22⋊C4—22no—
977C22⋊C4—22no—
978C22⋊C4—22no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—1422no—
984C22⋊C4—1422no—
985C22⋊C4—1422no—
986C22⋊C4—1422no—
987C22⋊C4—1422no—
988C22⋊C4—1422no—
989C22⋊C4—1422no—
990C22⋊C4—1422no—
991C22⋊C4—1422no—
992C22⋊C4—1422no—
993C42—22no—
994C42—22no—
995C42—1422no—
996C42—1422no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—42no—
1020C23—42no—
1021C23—416no—
1022C23—42no—
1023C23—2842no—
1024C23—2842no—
1025C23—2842no—
1026C23—1422no—
1027C23C22×C22⋊D7111yescharacteristic
1028C23C22×C22⋊D7111yescharacteristic
1029C23C22×C22⋊D7111yescharacteristic
1030C23C22×C22⋊D7111yescharacteristic
1031C23C22×C22⋊D7111yescharacteristic
1032C23C22×C22⋊D7111yescharacteristic
1033C23C22×C22⋊D7111yescharacteristic
1034Q8—24no—
1035Q8—42no—
1036Q8—2842no—
1037Q8—1424no—
1038D4—24no—
1039D4—42no—
1040D4—44no—
1041D4—44no—
1042D4—44no—
1043D4—44no—
1044D4—44no—
1045D4—44no—
1046D4—2842no—
1047D4—2844no—
1048D4—2844no—
1049D4—2844no—
1050D4—2844no—
1051D4—2844no—
1052D4—2844no—
1053D4—1424no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
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—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—44no—
1085C2×C4—42no—
1086C2×C4—42no—
1087C2×C4—42no—
1088C2×C4—44no—
1089C2×C4—2844no—
1090C2×C4—2842no—
1091C2×C4—2842no—
1092C2×C4—2842no—
1093C2×C4—2844no—
1094C2×C4—1422no—
1095C2×C4—1422no—
1096C2×C4—1422no—
1097C2×C4C22×C22⋊D7111yescharacteristic
1098C2×C4C22×C22⋊D7111yescharacteristic
1099C2×C4C22×C22⋊D7111yescharacteristic
1100C2×C4C22×C22⋊D7111yescharacteristic
1101C2×C4C22×C22⋊D7111yescharacteristic
1102C2×C4C22×C22⋊D7111yescharacteristic
1103C2×C4C22×C22⋊D7111yescharacteristic
1104C2×C4#1455617314yes—
1105C2×C4C24×D7111yescharacteristic
1106C8—1424no—
1107C8—1424no—
1108C22—21no—
1109C22—21no—
1110C22—21no—
1111C22—21no—
1112C22—21no—
1113C22—21no—
1114C22—21no—
1115C22—21no—
1116C22—21no—
1117C22—21no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—21no—
1125C22—21no—
1126C22—44no—
1127C22—44no—
1128C22—44no—
1129C22—44no—
1130C22—44no—
1131C22—44no—
1132C22—44no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—84no—
1137C22—2842no—
1138C22—2842no—
1139C22—2842no—
1140C22—5684no—
1141C22#1798655812yes—
1142C22#1798679712yes—
1143C22#1798679712yes—
1144C22C23×C22⋊D7111yescharacteristic
1145C4—21no—
1146C4—21no—
1147C4—21no—
1148C4—21no—
1149C4—21no—
1150C4—21no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—2842no—
1155C4—2842no—
1156C4—2842no—
1157C4#1798655812yes—
1158C4C2×#1455617312yes—
1159C2—22no—
1160C2—22no—
1161C2—22no—
1162C2—41no—
1163C2—41no—
1164C2—41no—
1165C2—41no—
1166C2—82no—
1167C2—5682no—
1168C2C2×#1798655811yescharacteristic
1169C2C2×#1798679711yescharacteristic
1170C2C2×#1798679711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#525×C71C2
socleC22×C71C23×D4
hypercenterC2×#525D71
hypocenterC71#60741
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ 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. #22599166C2semidirect
5. #22599161C2semidirect
6. #22599154C2semidirect
7. #22599150C2semidirect
8. #22599146C2semidirect
9. #22599142C2semidirect
10. #22599137C2semidirect
11. #22598253C2semidirect
12. #22598249C2semidirect
13. #22597946C2semidirect
14. #22597558C2semidirect
15. #22597556C2semidirect
16. C2×#17985963C2semidirect
17. C2×#525×C71C2semidirect
18. C22×#11765865C22semidirect
19. C2×#14556148C22semidirect
20. C22×#11765849C22semidirect
27. #17986510C22semidirect
28. #17986510C22semidirect
31. C2×#14556107C22semidirect
33. C2×#14556102C22semidirect
37. C2×#14556087C22semidirect
38. #17986340C22semidirect
39. #17986337C22semidirect
40. #17986334C22semidirect
41. #17986332C22semidirect
42. #17986329C22semidirect
43. #17986327C22semidirect
44. #17986323C22semidirect
45. #17986320C22semidirect
46. #17986317C22semidirect
47. #17986315C22semidirect
48. #17986312C22semidirect
49. #17986310C22semidirect
50. #17986255C22semidirect
51. #17986255C22semidirect
52. #17986250C22semidirect
53. #17986250C22semidirect
54. #17986247C22semidirect
55. #17986247C22semidirect
56. #17986243C22semidirect
57. #17986243C22semidirect
58. #17986161C22semidirect
59. #17986159C22semidirect
60. #17986155C22semidirect
61. #17986154C22semidirect
62. #17986150C22semidirect
63. #17986149C22semidirect
64. #17986144C22semidirect
65. #17986142C22semidirect
66. #17986138C22semidirect
67. #17986137C22semidirect
68. #17986133C22semidirect
69. #17986132C22semidirect
70. #17986035C22semidirect
71. #17985995C22semidirect
72. #17985993C22semidirect
75. #17985963C22semidirect
76. #17985963C22semidirect
77. #17985963C22semidirect
78. C2×C22⋊(C71⋊C8)C22semidirect
79. C2×C22⋊(C71⋊C8)C22semidirect
80. C22×#41×C71C22semidirect
88. #525×C71C22semidirect
89. #525×C71C22semidirect
92. C2×C22⋊Q8×C71C22semidirect
94. C2×#121×C71C22semidirect
98. C2×#117×C71C22semidirect
111. C2×#11765855C23semidirect
112. C2×#11765853C23semidirect
113. C2×#11765852C23semidirect
114. C2×#11765850C23semidirect
166. #14556061C23semidirect
167. #14556061C23semidirect
168. #14556059C23semidirect
169. #14556059C23semidirect
170. #14556052C23semidirect
171. #14556052C23semidirect
172. #14556051C23semidirect
173. #14556051C23semidirect
174. #14556049C23semidirect
175. #14556049C23semidirect
176. #14556048C23semidirect
177. #14556048C23semidirect
587. C2×#525D71semidirect
603. C71#60741semidirect
605. C22×#41C2×D71semidirect
623. #525C2×D71semidirect
624. #525C2×D71semidirect
630. C2×C22⋊Q8C2×D71semidirect
634. C2×#121C2×D71semidirect
642. C2×#117C2×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
#225991662
#225991612
#225991542
#225991502
#225991462
#225991422
#225991372
#225982532
#225982492
#225979462
#225975582
#225975562
C2×#179859632
C2×#525×C712
#6074171