Finite Group Databasebeta

← #32863442

Subgroups — #32863442

Order 18176.

1848 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22601756C211yesmaximal, characteristic
2#22597503C211yesmaximal, characteristic, complemented
3#22597492C211yesmaximal, characteristic, complemented
4#22597476C212yesmaximal, complemented
5#22597454C211yesmaximal, characteristic, complemented
6#22597414C211yesmaximal, characteristic, complemented
7#22597410C212yesmaximal, complemented
8#22597403C211yesmaximal, characteristic, complemented
9#22597399C212yesmaximal, complemented
10#22597387C212yesmaximal, complemented
11#22597374C211yesmaximal, characteristic, complemented
12#22597360C211yesmaximal, characteristic, complemented
13#22597346C211yesmaximal, characteristic, complemented
14#22597320C212yesmaximal, complemented
15#22597314C211yesmaximal, characteristic, complemented
16#22597304C211yesmaximal, characteristic, complemented
17#22597083C212yesmaximal, complemented
18#22597079C211yesmaximal, characteristic, complemented
19#22597075C211yesmaximal, characteristic, complemented
20#22597063C212yesmaximal, complemented
21#22597047C211yesmaximal, characteristic, complemented
22#22597038C212yesmaximal, complemented
23C71×#2990C211yesmaximal, characteristic, complemented
24C2×#14556134C2212yescomplemented
25C2×#14556134C2212yescomplemented
26C2×M16×D71C2212yes—
27#17986627C411yescharacteristic
28#17986621C411yescharacteristic
29#17986621C411yescharacteristic
30#17986620C412yes—
31#17986604C412yes—
32#17986600C411yescharacteristic
33#17986600C411yescharacteristic
34#17986582C412yes—
35#17986582C412yes—
36#17986577C411yescharacteristic
37#17986568C411yescharacteristic
38#17986563C411yescharacteristic
39#17986549C2212yes—
40#17986546C2211yescharacteristic
41#17986546C2211yescharacteristic
42#17986536C2211yescharacteristic
43#17986536C2211yescharacteristic
44#17986533C2212yes—
45#17986508C2212yes—
46#17986508C2212yes—
47C4×#11765865C2211yescharacteristic
48C2×C4×D284C2211yescharacteristic
49#17986128C2212yescomplemented
50#17986128C2211yescharacteristic, complemented
51#17986128C2211yescharacteristic, complemented
52Q8×C71⋊C8C2211yescharacteristic, complemented
53Q8×C71⋊C8C2211yescharacteristic, complemented
54#17986078C2211yescharacteristic
55#17986078C2211yescharacteristic
56#17986077C2212yes—
57#17986077C2212yes—
58#17986077C2211yescharacteristic, complemented
59#17986077C2211yescharacteristic, complemented
60#17986076C2211yescharacteristic
61#17986076C2211yescharacteristic
62#17986076C2212yescomplemented
63#17986076C2212yescomplemented
64#17986075C2212yes—
65#17986074C2211yescharacteristic
66#17986074C2211yescharacteristic
67#17986074C2212yescomplemented
68#17986074C2212yescomplemented
69#17986073C2211yescharacteristic
70#17986073C2211yescharacteristic
71#17986073C2212yescomplemented
72#17986073C2212yescomplemented
73#17986072C2212yescomplemented
74#17986072C2212yescomplemented
75#17986072C2212yescomplemented
76#17986072C2212yescomplemented
77#17986070C2212yescomplemented
78#17986070C2212yescomplemented
79#17986069C2212yes—
80#17986069C2212yes—
81#17986069C2212yes—
82#17986069C2212yes—
83#17986069C2211yescharacteristic, complemented
84#17986069C2212yescomplemented
85#17986069C2211yescharacteristic, complemented
86#17986068C2212yes—
87C8×D284C2211yescharacteristic
88C8×D284C2211yescharacteristic
89#17986064C2211yescharacteristic
90#17986064C2211yescharacteristic
91#17986064C2212yescomplemented
92#17986064C2212yescomplemented
93C8×C22⋊D71C2212yescomplemented
94C8×C22⋊D71C2212yescomplemented
95#17986061C2212yescomplemented
96#17986061C2212yescomplemented
97#17986059C2212yescomplemented
98#17986059C2212yescomplemented
99#17986056C2211yescharacteristic
100#17986056C2212yescomplemented
101#17986055C2211yescharacteristic, complemented
102#17986051C2211yescharacteristic, complemented
103#17986050C2211yescharacteristic, complemented
104#17986050C2211yescharacteristic, complemented
105#17986024C2212yescomplemented
106#17986024C2212yescomplemented
107#17986021C2211yescharacteristic, complemented
108C4⋊C8×D71C2211yescharacteristic, complemented
109#17985965C2212yescomplemented
110#17985965C2212yescomplemented
111#17985964C2212yescomplemented
112#17985964C2212yescomplemented
113#17985964C2212yescomplemented
114#17985964C2212yescomplemented
115#17985962C2212yes—
116#17985961C2212yes—
117C22⋊C8×D71C2212yes—
118#17985956C2212yescomplemented
119#17985956C2212yescomplemented
120C4×#11765849C2211yescharacteristic
121C4×#11765849C2212yescomplemented
122C4×#11765848C2211yescharacteristic, complemented
123C4×C8×D71C2211yescharacteristic, complemented
124C4×#41×C71C2211yescharacteristic
125#446×C71C2211yescharacteristic, complemented
126#446×C71C2211yescharacteristic, complemented
127#435×C71C2212yes—
128#435×C71C2212yes—
129C8×D4×C71C2211yescharacteristic, complemented
130C8×D4×C71C2211yescharacteristic, complemented
131#432×C71C2212yescomplemented
132#431×C71C2211yescharacteristic
133#423×C71C2211yescharacteristic
134C2×C4⋊C8×C71C2212yescomplemented
135C2×#11765865C2×C411yescharacteristic
136C2×#11765865C2312yes—
137C2×#11765865C2312yes—
138C22×D284C2×C411yescharacteristic
139C22×C4×D71C2312yes—
140#14556134—44no—
141#14556134—44no—
142C2×#11765849C2311yescharacteristic
143C2×#11765849C2312yes—
144C2×#11765849C2311yescharacteristic
145C2×#11765849C2312yes—
146C2×#11765848C2312yes—
147C2×#11765848C2311yescharacteristic
148C2×#11765848C2312yes—
149C2×#11765848C2312yes—
150C2×#11765848C2312yes—
151C2×#11765848C2311yescharacteristic
152C2×#11765848C2312yes—
153M16×D71—44no—
154C2×C8×D71C2312yes—
155C2×C8×D71C2311yescharacteristic
156C2×C8×D71C2312yes—
157C2×C8×D71C2312yes—
158C2×C8×D71C2312yes—
159C2×C8×D71C2312yes—
160C2×C8×D71C2311yescharacteristic
161#14556128C2×C412yes—
162#14556127C2×C411yescharacteristic
163#14556127C2×C411yescharacteristic
164#14556125C2×C412yes—
165#14556124C2×C411yescharacteristic
166#14556124C2×C411yescharacteristic
167#14556123C2×C412yes—
168#14556123C2×C412yes—
169#14556122C2×C412yes—
170#14556122C2×C412yes—
171#14556120C2×C412yes—
172#14556119C2×C411yescharacteristic
173#14556119C2×C411yescharacteristic
174#14556117C2×C411yescharacteristic
175#14556117C2×C411yescharacteristic
176#14556116C2×C412yes—
177#14556116C2×C412yes—
178#14556116C2×C412yes—
179#14556114C2×C412yes—
180#14556114C2×C412yes—
181#14556113C2×C412yes—
182#14556113C2×C412yes—
183#14556113C2×C412yes—
184#14556113C2×C412yes—
185#14556111C2×C412yes—
186#14556111C2×C412yes—
187#14556110C2×C412yes—
188#14556110C2×C412yes—
189#14556107C2×C412yes—
190#14556106C2×C412yes—
191#14556106C2×C412yes—
192#14556105C2×C412yes—
193#14556105C2×C412yes—
194#14556104C2×C411yescharacteristic
195#14556104C2×C411yescharacteristic
196#14556103C2×C411yescharacteristic
197#14556103C2×C411yescharacteristic
198#14556103C2×C411yescharacteristic
199#14556103C2×C411yescharacteristic
200#14556102C2×C412yes—
201#14556102C2×C412yes—
202#14556102C2×C412yes—
203#14556102C2×C412yes—
204#14556102C2×C412yes—
205#14556101C2×C412yes—
206#14556101C2×C412yes—
207#14556101C2×C412yes—
208#14556101C2×C412yes—
209#14556100C2×C412yes—
210#14556100C2×C412yes—
211#14556099C2×C411yescharacteristic
212#14556099C2×C411yescharacteristic
213#14556098C2×C412yes—
214#14556098C2×C412yes—
215#14556096C2×C412yes—
216#14556096C2×C412yes—
217C4×Dic142C2×C411yescharacteristic
218C4×Dic142C2311yescharacteristic
219C4×D284C2×C411yescharacteristic
220C4×D284C2×C411yescharacteristic
221C4×D284C2×C411yescharacteristic
222C4×D284C2×C412yes—
223C4×D284C2311yescharacteristic
224C4×D284C2312yes—
225C4×D284C2312yes—
226C4×D284C2311yescharacteristic
227C4×D284C2312yes—
228C4×D284C2311yescharacteristic
229C4×C22⋊D71C2×C411yescharacteristic
230C4×C22⋊D71C2×C411yescharacteristic
231C4×C22⋊D71C2312yes—
232C4×C22⋊D71C2312yes—
233C4×C22⋊D71C2311yescharacteristic
234C4×C22⋊D71C2311yescharacteristic
235#14556087C2×C411yescharacteristic
236#14556085C2×C411yescharacteristic
237#14556085C2×C411yescharacteristic
238#14556085C2312yes—
239#14556085C2312yes—
240C2×C4⋊Dic71C2×C411yescharacteristic
241C2×(C2×D71)⋊C4C2×C412yes—
242C42×D71C2311yescharacteristic
243C42×D71C2311yescharacteristic
244C4⋊(C71⋊C8)C2311yescharacteristic
245C4⋊(C71⋊C8)C2311yescharacteristic
246C4⋊(C71⋊C8)C2312yes—
247C4⋊(C71⋊C8)C2312yes—
248Dic71⋊C8C2311yescharacteristic
249Dic71⋊C8C2311yescharacteristic
250Dic71⋊C8C2311yescharacteristic
251Dic71⋊C8C2311yescharacteristic
252Dic71⋊C8C2312yes—
253Dic71⋊C8C2312yes—
254C22⋊(C71⋊C8)C2312yes—
255C22⋊(C71⋊C8)C2312yes—
256C22⋊(C71⋊C8)C2312yes—
257(C2×D71)⋊C8C2311yescharacteristic
258(C2×D71)⋊C8C2311yescharacteristic
259(C2×D71)⋊C8C2311yescharacteristic
260(C2×D71)⋊C8C2311yescharacteristic
261(C2×D71)⋊C8C2312yes—
262(C2×D71)⋊C8C2312yes—
263(C2×D71)⋊C8C2312yes—
264(C2×D71)⋊C8C2312yes—
265(C2×D71)⋊C8C2312yes—
266(C2×D71)⋊C8C2312yes—
267(C2×D71)⋊C8C2312yes—
268(C2×D71)⋊C8C2312yes—
269(C2×D71)⋊C8C2312yes—
270(C2×D71)⋊C8C2312yes—
271#14556039C2312yes—
272#14556039C2311yescharacteristic
273#14556039C2311yescharacteristic
274#14556038C2312yes—
275#14556038C2311yescharacteristic
276#14556038C2311yescharacteristic
277C4×C71⋊C8C2311yescharacteristic
278C4×C71⋊C8C2312yes—
279C4×C71⋊C8C2311yescharacteristic
280C4×C71⋊C8C2312yes—
281C8×Dic71C2312yes—
282C8×Dic71C2311yescharacteristic
283C8×Dic71C2311yescharacteristic
284C2×#41×C71C2×C411yescharacteristic
285C2×M16×C71C2312yes—
286C22×C8×C71C2312yes—
287C22×C8×C71C2312yes—
288C4×Q8×C71C2×C411yescharacteristic
289C4×Q8×C71C2311yescharacteristic
290C4×D4×C71C2×C412yes—
291C4×D4×C71C2×C411yescharacteristic
292C4×D4×C71C2311yescharacteristic
293C4×D4×C71C2312yes—
294#117×C71C2×C411yescharacteristic
295#117×C71C2×C412yes—
296C2×C42×C71C2311yescharacteristic
297C2×C42×C71C2312yes—
298C4⋊C8×C71C2311yescharacteristic
299C4⋊C8×C71C2311yescharacteristic
300C4⋊C8×C71C2312yes—
301C4⋊C8×C71C2312yes—
302C4⋊C8×C71C2311yescharacteristic
303C4⋊C8×C71C2312yes—
304C4⋊C8×C71C2311yescharacteristic
305C22⋊C8×C71C2311yescharacteristic
306C22⋊C8×C71C2311yescharacteristic
307C22⋊C8×C71C2312yes—
308C22⋊C8×C71C2312yes—
309#97×C71C2312yes—
310#97×C71C2312yes—
311C4×C8×C71C2311yescharacteristic
312C4×C8×C71C2311yescharacteristic
313C23×D71C22×C412yes—
314#11765865—42no—
315#11765865—42no—
316#11765865—42no—
317#11765865—42no—
318#11765865—42no—
319C2×Dic142C22×C411yescharacteristic
320C2×Dic142C22×C412yes—
321C2×Dic142C22×C412yes—
322C2×D284—42no—
323C2×D284C22×C411yescharacteristic
324C2×D284C22×C411yescharacteristic
325C2×D284C22×C412yes—
326C2×D284C22×C411yescharacteristic
327C2×D284C22×C412yes—
328C2×D284C22×C412yes—
329C2×D284C22×C412yes—
330C2×D284C22×C412yes—
331C2×C22⋊D71C22×C411yescharacteristic
332C2×C22⋊D71C22×C411yescharacteristic
333C2×C22⋊D71C22×C412yes—
334C2×C22⋊D71C22×C412yes—
335C2×C22⋊D71C22×C412yes—
336C2×C22⋊D71C22×C412yes—
337C2×C22⋊D71C22×C412yes—
338C2×C22⋊D71C22×C412yes—
339C22×Dic71C22×C412yes—
340C2×C4×D71—42no—
341C2×C4×D71—42no—
342C2×C4×D71C22×C411yescharacteristic
343C2×C4×D71C22×C411yescharacteristic
344C2×C4×D71C22×C412yes—
345C2×C4×D71C22×C412yes—
346C2×C4×D71C22×C411yescharacteristic
347C2×C4×D71C22×C411yescharacteristic
348C2×C4×D71C2412yes—
349C2×C4×D71C2412yes—
350C2×C4×D71C2411yescharacteristic
351C2×C4×D71C2411yescharacteristic
352#11765849—22no—
353#11765849—24no—
354#11765849—41no—
355#11765849—42no—
356#11765848—24no—
357#11765848—22no—
358#11765848—42no—
359#11765848—41no—
360#11765848—42no—
361#11765848—42no—
362#11765848—42no—
363C2×C71⋊C8C2412yes—
364C2×C71⋊C8C2411yescharacteristic
365C2×C71⋊C8C2411yescharacteristic
366C2×C71⋊C8C2411yescharacteristic
367C2×C71⋊C8C2412yes—
368C2×C71⋊C8C2411yescharacteristic
369C8×D71—24no—
370C8×D71—22no—
371C8×D71—42no—
372C8×D71—41no—
373C8×D71—42no—
374C8×D71—42no—
375C8×D71—42no—
376C4⋊Dic71C22×C411yescharacteristic
377C4⋊Dic71C22×C411yescharacteristic
378C4⋊Dic71C22×C412yes—
379C4⋊Dic71C22×C411yescharacteristic
380C4⋊Dic71C22×C411yescharacteristic
381C4⋊Dic71C22×C412yes—
382C4⋊Dic71C22×C412yes—
383Dic71⋊C4C22×C411yescharacteristic
384Dic71⋊C4C22×C411yescharacteristic
385Dic71⋊C4C22×C411yescharacteristic
386Dic71⋊C4C22×C411yescharacteristic
387Dic71⋊C4C22×C412yes—
388Dic71⋊C4C22×C412yes—
389Dic71⋊C4C22×C412yes—
390Dic71⋊C4C22×C412yes—
391Dic71⋊C4C22×C412yes—
392Dic71⋊C4C22×C412yes—
393C22⋊Dic71C22×C411yescharacteristic
394C22⋊Dic71C22×C411yescharacteristic
395C22⋊Dic71C22×C412yes—
396C22⋊Dic71C22×C412yes—
397(C2×D71)⋊C4C22×C412yes—
398(C2×D71)⋊C4C22×C412yes—
399(C2×D71)⋊C4C22×C412yes—
400(C2×D71)⋊C4C22×C412yes—
401(C2×D71)⋊C4C22×C411yescharacteristic
402(C2×D71)⋊C4C22×C411yescharacteristic
403(C2×D71)⋊C4C22×C411yescharacteristic
404(C2×D71)⋊C4C22×C411yescharacteristic
405(C2×D71)⋊C4C22×C412yes—
406(C2×D71)⋊C4C22×C412yes—
407(C2×D71)⋊C4C22×C412yes—
408(C2×D71)⋊C4C22×C412yes—
409(C2×D71)⋊C4C22×C412yes—
410(C2×D71)⋊C4C22×C412yes—
411(C2×D71)⋊C4C22×C412yes—
412(C2×D71)⋊C4C22×C412yes—
413(C2×D71)⋊C4C22×C412yes—
414(C2×D71)⋊C4C22×C412yes—
415C4×Dic71C22×C411yescharacteristic
416C4×Dic71C22×C411yescharacteristic
417C4×Dic71C22×C411yescharacteristic
418C4×Dic71C22×C411yescharacteristic
419C4×Dic71C2411yescharacteristic
420C4×Dic71C2411yescharacteristic
421#41×C71—42no—
422C2×Q8×C71C22×C411yescharacteristic
423C2×D4×C71C22×C411yescharacteristic
424C2×D4×C71C22×C412yes—
425C22×C4×C71C22×C411yescharacteristic
426C22×C4×C71C22×C412yes—
427C22×C4×C71C22×C411yescharacteristic
428C22×C4×C71C22×C412yes—
429C22×C4×C71C2411yescharacteristic
430C22×C4×C71C2412yes—
431M16×C71—42no—
432C2×C8×C71—42no—
433C2×C8×C71—42no—
434C2×C8×C71C2411yescharacteristic
435C2×C8×C71C2411yescharacteristic
436C2×C8×C71C2411yescharacteristic
437C2×C8×C71C2411yescharacteristic
438C2×C8×C71C2412yes—
439C2×C8×C71C2412yes—
440C4⋊C4×C71C22×C411yescharacteristic
441C4⋊C4×C71C22×C412yes—
442C4⋊C4×C71C22×C411yescharacteristic
443C4⋊C4×C71C22×C412yes—
444C22⋊C4×C71C22×C412yes—
445C22⋊C4×C71C22×C412yes—
446C22⋊C4×C71C22×C412yes—
447C42×C71C22×C411yescharacteristic
448C42×C71C22×C412yes—
449C42×C71C22×C411yescharacteristic
450C42×C71C22×C412yes—
451C42×C71C2411yescharacteristic
452C42×C71C2412yes—
453C42×C71C2411yescharacteristic
454C23×C71C23×C411yescharacteristic
455C23×C71C23×C412yes—
456C22×D71—42no—
457C22×D71—42no—
458C22×D71—42no—
459C22×D71C23×C412yes—
460C22×D71C23×C412yes—
461C22×D71C23×C411yescharacteristic
462C22×D71C23×C411yescharacteristic
463Q8×C71—22no—
464D4×C71—22no—
465D4×C71—42no—
466C2×C4×C71—22no—
467C2×C4×C71—22no—
468C2×C4×C71—21no—
469C2×C4×C71—21no—
470C2×C4×C71—22no—
471C2×C4×C71—41no—
472C2×C4×C71—42no—
473C2×C4×C71—42no—
474C2×C4×C71C23×C411yescharacteristic
475C2×C4×C71C23×C411yescharacteristic
476C2×C4×C71C23×C411yescharacteristic
477C2×C4×C71C23×C412yes—
478C2×C4×C71C23×C411yescharacteristic
479C2×C4×C71C23×C412yes—
480C2×C4×C71C23×C412yes—
481C2×C4×C71C23×C411yescharacteristic
482C2×C4×C71C2511yescharacteristic
483C22⋊D71—42no—
484C22⋊D71—42no—
485C22⋊D71—42no—
486C22⋊D71—42no—
487C22⋊D71—42no—
488C22⋊D71—42no—
489C22⋊D71—41no—
490C22⋊D71—41no—
491C2×Dic71—42no—
492C2×Dic71C23×C411yescharacteristic
493C2×Dic71C23×C411yescharacteristic
494C2×Dic71C23×C411yescharacteristic
495C2×Dic71C23×C411yescharacteristic
496C2×Dic71C23×C411yescharacteristic
497C2×Dic71C23×C411yescharacteristic
498C2×Dic71C23×C412yes—
499C2×Dic71C23×C412yes—
500D284—22no—
501D284—22no—
502D284—42no—
503D284—42no—
504D284—42no—
505D284—42no—
506D284—42no—
507D284—41no—
508C4×D71—22no—
509C4×D71—22no—
510C4×D71—22no—
511C4×D71—21no—
512C4×D71—21no—
513C4×D71—22no—
514C4×D71—22no—
515C4×D71—21no—
516C4×D71—22no—
517C4×D71—21no—
518C4×D71—42no—
519C4×D71—42no—
520C4×D71—41no—
521C4×D71—41no—
522Dic142—42no—
523Dic142—42no—
524Dic142—41no—
525C8×C71—21no—
526C8×C71—21no—
527C8×C71—22no—
528C8×C71—22no—
529C8×C71—21no—
530C8×C71—21no—
531C71⋊C8—21no—
532C71⋊C8—22no—
533C71⋊C8—22no—
534C71⋊C8—21no—
535C71⋊C8—21no—
536C71⋊C8H(5,𝔽2)12yes—
537C22×C71—21no—
538C22×C71—22no—
539C22×C71—21no—
540C22×C71—22no—
541C22×C71—22no—
542C22×C71—21no—
543C22×C71C24×C411yescharacteristic
544C2×D71—22no—
545C2×D71—22no—
546C2×D71—21no—
547C2×D71—21no—
548C2×D71—21no—
549C2×D71—21no—
550C2×D71—22no—
551C2×D71—22no—
552C2×D71—21no—
553C2×D71—21no—
554C2×D71—22no—
555C2×D71—22no—
556C2×D71—84no—
557C4×C71—22no—
558C4×C71—21no—
559C4×C71—21no—
560C4×C71—22no—
561C4×C71—21no—
562C4×C71—22no—
563C4×C71—21no—
564C4×C71#56812yes—
565C4×C71C2×H(5,𝔽2)11yescharacteristic
566C4×C71#58511yescharacteristic
567Dic71—21no—
568Dic71—21no—
569Dic71—22no—
570Dic71—22no—
571Dic71—21no—
572Dic71—21no—
573Dic71—21no—
574Dic71—21no—
575#60326—711nomaximal, Sylow
576C2×C71—41no—
577C2×C71—42no—
578C2×C71C4×H(5,𝔽2)11yescharacteristic
579C2×C71C2×#56811yescharacteristic
580C2×C71#357311yescharacteristic
581D71—41no—
582D71—41no—
583D71—42no—
584D71—42no—
585#3460—711no—
586#2994—711no—
587#2993—711no—
588#2992—712no—
589#2990D7111yescharacteristic, complemented
590#2989—711no—
591#2981—711no—
592#2980—712no—
593#2979—711no—
594#2978—712no—
595#2976—712no—
596#2974—711no—
597#2971—711no—
598#2969—711no—
599#2967—712no—
600#2966—711no—
601#2965—711no—
602#2935—711no—
603#2935—712no—
604D4×M16—711no—
605#2933—712no—
606#2931—711no—
607#2930—712no—
608C71#6032611yescharacteristic, complemented, Sylow
609C2×#131—712no—
610C2×#131—712no—
611C22×M16—712no—
612#544—711no—
613#542—711no—
614#542—711no—
615#542—712no—
616#540—711no—
617#540—711no—
618#540—712no—
619#538—712no—
620#538—712no—
621#537—711no—
622#535—711no—
623#535—711no—
624#532—711no—
625#532—711no—
626#532—712no—
627#529—711no—
628#529—711no—
629#529—712no—
630#525—712no—
631#525—712no—
632C4×#41—711no—
633C4×#41C2×D7111yescharacteristic
634C2×C4×D4—711no—
635#446—711no—
636#446—711no—
637#446—712no—
638#446C2×D7111yescharacteristic, complemented
639#446C2×D7111yescharacteristic, complemented
640C8×Q8—711no—
641C8×Q8—711no—
642#436—712no—
643#436—712no—
644#436—712no—
645#436—711no—
646#436—711no—
647#436—711no—
648#436—711no—
649#436—712no—
650#436—712no—
651#436—711no—
652#436—711no—
653#436—712no—
654#436—712no—
655#436—711no—
656#436—711no—
657#435—712no—
658#435—712no—
659#435—712no—
660#435—712no—
661#435—712no—
662#435—712no—
663#435—712no—
664#435—711no—
665#435—712no—
666#435—711no—
667#435—711no—
668#435—711no—
669#435—712no—
670#435—712no—
671#435—712no—
672#435—712no—
673#435—712no—
674#435—712no—
675#435C2×D7112yes—
676#435C2×D7112yes—
677C8×D4—712no—
678C8×D4—712no—
679C8×D4—711no—
680C8×D4—711no—
681C8×D4—712no—
682C8×D4—712no—
683C8×D4—711no—
684C8×D4—711no—
685C8×D4C2×D7111yescharacteristic, complemented
686C8×D4C2×D7111yescharacteristic, complemented
687#433—712no—
688#433—712no—
689#433—712no—
690#433—712no—
691#432—711no—
692#432—712no—
693#432—711no—
694#432C2×D7112yescomplemented
695#431—711no—
696#431—711no—
697#431—711no—
698#431C2×D7111yescharacteristic
699#424—712no—
700#424—712no—
701#423—711no—
702#423C2×D7111yescharacteristic
703C2×C4⋊C8—711no—
704C2×C4⋊C8C2×D7112yescomplemented
705#408—712no—
706#408—712no—
707#408—712no—
708#408—712no—
709#408—712no—
710#408—712no—
711#407—712no—
712#407—712no—
713C2×C22⋊C8—712no—
714#405—712no—
715#405—712no—
716C4×M16—711no—
717C4×M16—712no—
718C4×M16—711no—
719C2×C4×C8—711no—
720C2×#41—711no—
721C2×#41—712no—
722C2×#41—712no—
723C2×#41C4×D7111yescharacteristic
724C22×D4—711no—
725C23×C4—712no—
726#131—2844no—
727#131—2844no—
728C2×M16—2844no—
729C2×M16—711no—
730C2×M16—712no—
731C2×M16—711no—
732C2×M16—712no—
733C2×M16—712no—
734C2×M16—712no—
735C2×M16—712no—
736C2×M16—711no—
737C2×M16—712no—
738C2×M16—712no—
739C2×M16—711no—
740C2×M16C22×D7112yes—
741C22×C8—712no—
742C22×C8—712no—
743C22×C8—712no—
744C22×C8—711no—
745C22×C8—712no—
746C22×C8—712no—
747C22×C8—711no—
748C22×C8C22×D7112yes—
749C22×C8C22×D7112yes—
750C4⋊Q8—711no—
751C4⋊Q8—711no—
752C4⋊Q8—712no—
753#127—711no—
754#127—711no—
755#127—712no—
756#126—712no—
757#126—712no—
758#126—712no—
759#126—712no—
760#125—711no—
761#125—711no—
762#125—712no—
763#124—711no—
764#124—711no—
765#124—712no—
766#124—712no—
767#124—712no—
768#124—712no—
769#124—712no—
770#123—712no—
771#123—712no—
772#123—712no—
773#123—712no—
774#123—712no—
775#123—712no—
776#123—712no—
777#123—712no—
778C22⋊Q8—711no—
779C22⋊Q8—711no—
780C22⋊Q8—712no—
781C22⋊Q8—712no—
782C22⋊Q8—712no—
783C22⋊Q8—712no—
784C22⋊Q8—712no—
785#121—712no—
786#121—712no—
787#121—711no—
788#121—711no—
789#121—712no—
790#121—712no—
791#121—712no—
792#121—712no—
793#121—712no—
794#121—711no—
795#121—711no—
796#121—711no—
797#121—711no—
798#121—712no—
799#121—712no—
800#121—712no—
801#121—712no—
802#120—712no—
803#120—712no—
804#120—712no—
805#120—712no—
806C4×Q8—711no—
807C4×Q8—711no—
808C4×Q8C4×D7111yescharacteristic
809C4×Q8C22×D7111yescharacteristic
810C4×D4—711no—
811C4×D4—711no—
812C4×D4—711no—
813C4×D4—711no—
814C4×D4—712no—
815C4×D4—712no—
816C4×D4—711no—
817C4×D4—711no—
818C4×D4—712no—
819C4×D4—711no—
820C4×D4—711no—
821C4×D4—711no—
822C4×D4—712no—
823C4×D4—711no—
824C4×D4—712no—
825C4×D4—712no—
826C4×D4C4×D7112yes—
827C4×D4C4×D7111yescharacteristic
828C4×D4C22×D7112yes—
829C4×D4C22×D7111yescharacteristic
830#117—711no—
831#117—711no—
832#117—711no—
833#117—712no—
834#117—712no—
835#117C4×D7111yescharacteristic
836#117C4×D7112yes—
837C2×C4⋊C4—711no—
838C2×C22⋊C4—712no—
839C2×C42—711no—
840C2×C42—711no—
841C2×C42C22×D7111yescharacteristic
842C2×C42C22×D7112yes—
843C4⋊C8—712no—
844C4⋊C8—712no—
845C4⋊C8—711no—
846C4⋊C8—711no—
847C4⋊C8—711no—
848C4⋊C8—711no—
849C4⋊C8—711no—
850C4⋊C8—712no—
851C4⋊C8—711no—
852C4⋊C8—712no—
853C4⋊C8C22×D7111yescharacteristic
854C4⋊C8C22×D7111yescharacteristic
855C4⋊C8C22×D7112yes—
856C4⋊C8C22×D7112yes—
857C4⋊C8C22×D7112yes—
858C4⋊C8C22×D7111yescharacteristic
859C4⋊C8C22×D7111yescharacteristic
860C22⋊C8—712no—
861C22⋊C8—712no—
862C22⋊C8—712no—
863C22⋊C8—712no—
864C22⋊C8—712no—
865C22⋊C8—712no—
866C22⋊C8—712no—
867C22⋊C8—712no—
868C22⋊C8—712no—
869C22⋊C8—712no—
870C22⋊C8—712no—
871C22⋊C8—711no—
872C22⋊C8—711no—
873C22⋊C8—712no—
874C22⋊C8—711no—
875C22⋊C8—711no—
876C22⋊C8—712no—
877C22⋊C8C22×D7111yescharacteristic
878C22⋊C8C22×D7111yescharacteristic
879C22⋊C8C22×D7112yes—
880C22⋊C8C22×D7112yes—
881#97—711no—
882#97—711no—
883#97—712no—
884#97—711no—
885#97—712no—
886#97—711no—
887#97C22×D7112yes—
888#97C22×D7112yes—
889C4×C8—711no—
890C4×C8—711no—
891C4×C8—712no—
892C4×C8—711no—
893C4×C8—712no—
894C4×C8—711no—
895C4×C8—712no—
896C4×C8C22×D7111yescharacteristic
897C4×C8C22×D7111yescharacteristic
898C24—712no—
899#41—42no—
900#41—2842no—
901#41—2842no—
902#41—2842no—
903#41—2842no—
904#41—2842no—
905C2×Q8—711no—
906C2×Q8—712no—
907C2×Q8—712no—
908C2×Q8C2×C4×D7111yescharacteristic
909C2×D4—2842no—
910C2×D4—711no—
911C2×D4—711no—
912C2×D4—712no—
913C2×D4—712no—
914C2×D4—712no—
915C2×D4—712no—
916C2×D4—712no—
917C2×D4—712no—
918C2×D4—712no—
919C2×D4—711no—
920C2×D4—712no—
921C2×D4—712no—
922C2×D4—712no—
923C2×D4—712no—
924C2×D4—711no—
925C2×D4—711no—
926C2×D4C2×C4×D7111yescharacteristic
927C2×D4C2×C4×D7112yes—
928C22×C4—2842no—
929C22×C4—2842no—
930C22×C4—712no—
931C22×C4—711no—
932C22×C4—711no—
933C22×C4—712no—
934C22×C4—712no—
935C22×C4—711no—
936C22×C4—711no—
937C22×C4—711no—
938C22×C4—711no—
939C22×C4—712no—
940C22×C4—712no—
941C22×C4C2×C4×D7111yescharacteristic
942C22×C4C2×C4×D7111yescharacteristic
943C22×C4C2×C4×D7112yes—
944C22×C4C2×C4×D7112yes—
945C22×C4C23×D7112yes—
946C22×C4C23×D7111yescharacteristic
947M16—42no—
948M16—2842no—
949M16—2841no—
950M16—2842no—
951M16—2842no—
952M16—2842no—
953M16—2841no—
954M16—2842no—
955M16—1424no—
956M16—1422no—
957M16—1422no—
958M16—1424no—
959C2×C8—42no—
960C2×C8—42no—
961C2×C8—2842no—
962C2×C8—2841no—
963C2×C8—2842no—
964C2×C8—2842no—
965C2×C8—2842no—
966C2×C8—711no—
967C2×C8—711no—
968C2×C8—711no—
969C2×C8—712no—
970C2×C8—711no—
971C2×C8—712no—
972C2×C8—1424no—
973C2×C8—1422no—
974C2×C8C23×D7111yescharacteristic
975C2×C8C23×D7111yescharacteristic
976C2×C8C23×D7112yes—
977C2×C8C23×D7111yescharacteristic
978C2×C8C23×D7111yescharacteristic
979C2×C8C23×D7112yes—
980C4⋊C4—711no—
981C4⋊C4—711no—
982C4⋊C4—711no—
983C4⋊C4—711no—
984C4⋊C4—712no—
985C4⋊C4—712no—
986C4⋊C4—712no—
987C4⋊C4—712no—
988C4⋊C4—712no—
989C4⋊C4—712no—
990C4⋊C4—712no—
991C4⋊C4—711no—
992C4⋊C4—711no—
993C4⋊C4—711no—
994C4⋊C4—711no—
995C4⋊C4—712no—
996C4⋊C4—712no—
997C4⋊C4C2×C4×D7111yescharacteristic
998C4⋊C4C2×C4×D7112yes—
999C4⋊C4C2×C4×D7111yescharacteristic
1000C4⋊C4C2×C4×D7112yes—
1001C22⋊C4—711no—
1002C22⋊C4—711no—
1003C22⋊C4—712no—
1004C22⋊C4—712no—
1005C22⋊C4—712no—
1006C22⋊C4—712no—
1007C22⋊C4—712no—
1008C22⋊C4—712no—
1009C22⋊C4—711no—
1010C22⋊C4—711no—
1011C22⋊C4—711no—
1012C22⋊C4—711no—
1013C22⋊C4—712no—
1014C22⋊C4—712no—
1015C22⋊C4—712no—
1016C22⋊C4—712no—
1017C22⋊C4—712no—
1018C22⋊C4—712no—
1019C22⋊C4—712no—
1020C22⋊C4—712no—
1021C22⋊C4—712no—
1022C22⋊C4—712no—
1023C22⋊C4C2×C4×D7112yes—
1024C22⋊C4C2×C4×D7112yes—
1025C22⋊C4C2×C4×D7112yes—
1026C42—711no—
1027C42—711no—
1028C42—711no—
1029C42—711no—
1030C42—711no—
1031C42—711no—
1032C42C2×C4×D7111yescharacteristic
1033C42C2×C4×D7111yescharacteristic
1034C42C2×C4×D7112yes—
1035C42C2×C4×D7112yes—
1036C42C23×D7111yescharacteristic
1037C42C23×D7112yes—
1038C42C23×D7111yescharacteristic
1039C23—2842no—
1040C23—2842no—
1041C23—2842no—
1042C23—712no—
1043C23—712no—
1044C23—711no—
1045C23—711no—
1046C23C22×C4×D7111yescharacteristic
1047C23C22×C4×D7112yes—
1048Q8—22no—
1049Q8—2841no—
1050Q8—2842no—
1051Q8—2842no—
1052D4—22no—
1053D4—42no—
1054D4—2842no—
1055D4—2841no—
1056D4—2842no—
1057D4—2842no—
1058D4—2842no—
1059D4—2842no—
1060D4—2841no—
1061D4—2841no—
1062D4—2842no—
1063D4—2842no—
1064D4—2842no—
1065D4—2842no—
1066D4—2842no—
1067D4—2842no—
1068D4—1422no—
1069D4—1422no—
1070C2×C4—22no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—42no—
1076C2×C4—41no—
1077C2×C4—42no—
1078C2×C4—2842no—
1079C2×C4—2842no—
1080C2×C4—2841no—
1081C2×C4—2841no—
1082C2×C4—2842no—
1083C2×C4—711no—
1084C2×C4—711no—
1085C2×C4—711no—
1086C2×C4—711no—
1087C2×C4—711no—
1088C2×C4—711no—
1089C2×C4—712no—
1090C2×C4—712no—
1091C2×C4—1421no—
1092C2×C4—1422no—
1093C2×C4—1422no—
1094C2×C4—1421no—
1095C2×C4—1422no—
1096C2×C4—1421no—
1097C2×C4—1422no—
1098C2×C4—1421no—
1099C2×C4—1422no—
1100C2×C4—1422no—
1101C2×C4C22×C4×D7111yescharacteristic
1102C2×C4C22×C4×D7111yescharacteristic
1103C2×C4C22×C4×D7111yescharacteristic
1104C2×C4C22×C4×D7111yescharacteristic
1105C2×C4C22×C4×D7112yes—
1106C2×C4C22×C4×D7112yes—
1107C2×C4C22×C4×D7112yes—
1108C2×C4C22×C4×D7111yescharacteristic
1109C2×C4C24×D7111yescharacteristic
1110C8—21no—
1111C8—21no—
1112C8—22no—
1113C8—22no—
1114C8—21no—
1115C8—21no—
1116C8—712no—
1117C8—1421no—
1118C8—1422no—
1119C8—1422no—
1120C8—1421no—
1121C8—1421no—
1122C22—21no—
1123C22—22no—
1124C22—22no—
1125C22—21no—
1126C22—21no—
1127C22—22no—
1128C22—5684no—
1129C22—1421no—
1130C22—1421no—
1131C22—1422no—
1132C22—1422no—
1133C22—1421no—
1134C22—1421no—
1135C22—1422no—
1136C22—1422no—
1137C22—1422no—
1138C22—1422no—
1139C22—1421no—
1140C22—1421no—
1141C22C23×C4×D7111yescharacteristic
1142C4—21no—
1143C4—22no—
1144C4—21no—
1145C4—21no—
1146C4—22no—
1147C4—21no—
1148C4—22no—
1149C4—1421no—
1150C4—1421no—
1151C4—1421no—
1152C4—1421no—
1153C4—1422no—
1154C4—1422no—
1155C4—1421no—
1156C4—1421no—
1157C4#1798676512yes—
1158C4H(5,𝔽2)×D7111yescharacteristic
1159C4#1798683611yescharacteristic
1160C2—41no—
1161C2—42no—
1162C2—2842no—
1163C2—2842no—
1164C2—2841no—
1165C2—2841no—
1166C2#2260154611yescharacteristic
1167C2C2×#1798676511yescharacteristic
1168C2#2260305111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D71
commutator, socleC22×C71C24×C4
FittingC71×#2990C2
prime radical#22601756C2
cosocleC2×C4×C71C25
hypercenter#2990D71
hypocenterC71#60326
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ #2990

Complements

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

NH ≅ G/Ntype
2. #22597503C2semidirect
3. #22597492C2semidirect
4. #22597476C2semidirect
5. #22597454C2semidirect
6. #22597414C2semidirect
7. #22597410C2semidirect
8. #22597403C2semidirect
9. #22597399C2semidirect
10. #22597387C2semidirect
11. #22597374C2semidirect
12. #22597360C2semidirect
13. #22597346C2semidirect
14. #22597320C2semidirect
15. #22597314C2semidirect
16. #22597304C2semidirect
17. #22597083C2semidirect
18. #22597079C2semidirect
19. #22597075C2semidirect
20. #22597063C2semidirect
21. #22597047C2semidirect
22. #22597038C2semidirect
23. C71×#2990C2semidirect
24. C2×#14556134C22semidirect
25. C2×#14556134C22semidirect
49. #17986128C22semidirect
50. #17986128C22semidirect
51. #17986128C22semidirect
52. Q8×C71⋊C8C22semidirect
53. Q8×C71⋊C8C22semidirect
58. #17986077C22semidirect
59. #17986077C22semidirect
62. #17986076C22semidirect
63. #17986076C22semidirect
67. #17986074C22semidirect
68. #17986074C22semidirect
71. #17986073C22semidirect
72. #17986073C22semidirect
73. #17986072C22semidirect
74. #17986072C22semidirect
75. #17986072C22semidirect
76. #17986072C22semidirect
77. #17986070C22semidirect
78. #17986070C22semidirect
83. #17986069C22semidirect
84. #17986069C22semidirect
85. #17986069C22semidirect
91. #17986064C22semidirect
92. #17986064C22semidirect
93. C8×C22⋊D71C22semidirect
94. C8×C22⋊D71C22semidirect
95. #17986061C22semidirect
96. #17986061C22semidirect
97. #17986059C22semidirect
98. #17986059C22semidirect
100. #17986056C22semidirect
101. #17986055C22semidirect
102. #17986051C22semidirect
103. #17986050C22semidirect
104. #17986050C22semidirect
105. #17986024C22semidirect
106. #17986024C22semidirect
107. #17986021C22semidirect
108. C4⋊C8×D71C22semidirect
109. #17985965C22semidirect
110. #17985965C22semidirect
111. #17985964C22semidirect
112. #17985964C22semidirect
113. #17985964C22semidirect
114. #17985964C22semidirect
118. #17985956C22semidirect
119. #17985956C22semidirect
121. C4×#11765849C22semidirect
122. C4×#11765848C22semidirect
123. C4×C8×D71C22semidirect
125. #446×C71C22semidirect
126. #446×C71C22semidirect
129. C8×D4×C71C22semidirect
130. C8×D4×C71C22semidirect
131. #432×C71C22semidirect
134. C2×C4⋊C8×C71C22semidirect
589. #2990D71semidirect
608. C71#60326semidirect
638. #446C2×D71semidirect
639. #446C2×D71semidirect
685. C8×D4C2×D71semidirect
686. C8×D4C2×D71semidirect
694. #432C2×D71semidirect
704. C2×C4⋊C8C2×D71semidirect

Maximal subgroups

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

subgroupindex
#226017562
#225975032
#225974922
#225974762
#225974542
#225974142
#225974102
#225974032
#225973992
#225973872
#225973742
#225973602
#225973462
#225973202
#225973142
#225973042
#225970832
#225970792
#225970752
#225970632
#225970472
#225970382
C71×#29902
#6032671