Finite Group Databasebeta

← #32863520

Subgroups — #32863520

Order 18176.

1926 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14556175C211yesmaximal, characteristic
2#22597469C212yesmaximal, complemented
3#22597468C212yesmaximal, complemented
4#22597457C211yesmaximal, characteristic, complemented
5#22597453C211yesmaximal, characteristic, complemented
6#22597452C214yesmaximal, complemented
7#22597427C212yesmaximal, complemented
8#22597426C212yesmaximal, complemented
9#22597420C211yesmaximal, characteristic, complemented
10#22597358C212yesmaximal, complemented
11#22597356C212yesmaximal, complemented
12#22597306C211yesmaximal, characteristic, complemented
13#22597300C214yesmaximal, complemented
14M16×Dic142C212yesmaximal, complemented
15#22597292C212yesmaximal, complemented
16C2×C8×Dic142C211yesmaximal, characteristic, complemented
17C71×#2965C211yesmaximal, characteristic, complemented
18C2×#14556175C411yescharacteristic
19#17986482C411yescharacteristic
20#17986479C412yes—
21#17986479C411yescharacteristic
22#17986478C412yes—
23#17986478C414yes—
24#17986476C412yes—
25#17986476C411yescharacteristic
26#17986475C412yes—
27C4×#11765865C2211yescharacteristic
28C4×#11765865C2212yes—
29C4×#11765864C2214yes—
30C4×#11765864C2212yes—
31C2×C4×Dic142C2211yescharacteristic
32C2×C4×Dic142C2212yes—
33C4×Q8×D71C2212yes—
34#17986130C2212yes—
35#17986129C2211yescharacteristic
36#17986129C2212yes—
37#17986129C2211yescharacteristic
38#17986128C2214yes—
39#17986128C2214yes—
40#17986127C2214yes—
41#17986127C2214yes—
42C8×Dic142C2212yes—
43C8×Dic142C2212yes—
44C8×Dic142C2212yes—
45C8×Dic142C2212yes—
46C8×Dic142C2212yes—
47C8×Dic142C2212yes—
48#17986123C2212yes—
49#17986123C2212yes—
50#17986078C2212yes—
51#17986078C2211yescharacteristic
52#17986078C2211yescharacteristic
53#17986077C2212yes—
54#17986075C2214yes—
55#17986075C2214yes—
56#17986074C2214yes—
57#17986074C2214yes—
58#17986071C2214yes—
59#17986070C2212yes—
60#17986070C2212yes—
61#17986067C2214yes—
62#17986056C2212yes—
63#17986055C2212yes—
64#17986054C2214yes—
65#17986053C2214yes—
66#17986052C2211yescharacteristic
67#17986051C2214yes—
68#17986050C2212yes—
69#17986049C2214yes—
70#17986049C2214yes—
71#17986023C2212yes—
72#17986022C2214yes—
73#17986021C2214yes—
74#17986021C2212yes—
75C2×C4⋊(C71⋊C8)C2211yescharacteristic
76C2×Dic71⋊C8C2212yes—
77#17985951C2214yes—
78M16×Dic71C2214yes—
79C4×#11765848C2212yes—
80C2×C8×Dic71C2212yes—
81C4×#41×C71C2211yescharacteristic
82#446×C71C2211yescharacteristic
83#446×C71C2211yescharacteristic
84#436×C71C2211yescharacteristic
85#436×C71C2211yescharacteristic
86#435×C71C2212yes—
87#435×C71C2212yes—
88#431×C71C2211yescharacteristic
89#431×C71C2212yes—
90C4×M16×C71C2212yes—
91C2×C4×C8×C71C2211yescharacteristic
92#14556175—28no—
93C2×#11765865C2×C412yes—
94C2×#11765865C2×C411yescharacteristic
95C2×#11765864C2×C412yes—
96C2×#11765864C2×C414yes—
97C22×Dic142C2×C412yes—
98C22×Dic142C2×C411yescharacteristic
99C2×Q8×D71C2×C412yes—
100C2×#11765849C2314yes—
101C2×#11765848C2312yes—
102C2×#11765848C2314yes—
103C2×#11765848C2312yes—
104C22×C71⋊C8C2312yes—
105Q8×Dic71C2×C412yes—
106C4×Dic142C2×C414yes—
107C4×Dic142C2×C412yes—
108C4×Dic142C2×C412yes—
109C4×Dic142C2×C412yes—
110C4×Dic142C2×C412yes—
111C4×Dic142C2×C411yescharacteristic
112C4×Dic142C2×C412yes—
113C4×Dic142C2312yes—
114C4×Dic142C2312yes—
115C4×Dic142C2314yes—
116C4×Dic142C2311yescharacteristic
117#14556093C2×C414yes—
118#14556093C2×C412yes—
119#14556093C2×C414yes—
120#14556093C2×C412yes—
121C4×D284C2×C411yescharacteristic
122C4×D284C2×C412yes—
123C4×D284C2311yescharacteristic
124D4×Dic71C2×C414yes—
125D4×Dic71C2×C412yes—
126C4×C22⋊D71C2×C412yes—
127C4×C22⋊D71C2×C414yes—
128C4×C22⋊D71C2312yes—
129C4×C22⋊D71C2314yes—
130(C22⋊D71)⋊C4C2×C414yes—
131(C22⋊D71)⋊C4C2×C414yes—
132(C22⋊D71)⋊C4C2×C414yes—
133#14556087C2×C412yes—
134#14556087C2×C411yescharacteristic
135#14556086C2×C414yes—
136#14556086C2×C412yes—
137#14556085C2×C412yes—
138#14556085C2×C414yes—
139#14556084C2×C414yes—
140#14556084C2×C414yes—
141#14556084C2×C414yes—
142C2×C4⋊Dic71C2×C412yes—
143C2×C4⋊Dic71C2×C411yescharacteristic
144C2×Dic71⋊C4C2×C414yes—
145C2×Dic71⋊C4C2×C412yes—
146C4⋊C4×D71C2×C414yes—
147C4⋊C4×D71C2×C412yes—
148C2×C4×Dic71C2312yes—
149C2×C4×Dic71C2314yes—
150C42×D71C2312yes—
151C42×D71C2314yes—
152C4⋊(C71⋊C8)C2314yes—
153C4⋊(C71⋊C8)C2311yescharacteristic
154C4⋊(C71⋊C8)C2311yescharacteristic
155C4⋊(C71⋊C8)C2312yes—
156C4⋊(C71⋊C8)C2312yes—
157Dic71⋊C8C2312yes—
158Dic71⋊C8C2314yes—
159Dic71⋊C8C2314yes—
160Dic71⋊C8C2314yes—
161Dic71⋊C8C2312yes—
162Dic71⋊C8C2314yes—
163Dic71⋊C8C2314yes—
164C22⋊(C71⋊C8)C2312yes—
165C22⋊(C71⋊C8)C2314yes—
166(C2×D71)⋊C8C2312yes—
167(C2×D71)⋊C8C2312yes—
168(C2×D71)⋊C8C2314yes—
169#14556039C2314yes—
170#14556038C2312yes—
171#14556038C2314yes—
172#14556038C2312yes—
173C4×C71⋊C8C2312yes—
174C8×Dic71C2314yes—
175C8×Dic71C2314yes—
176C8×Dic71C2314yes—
177C8×Dic71C2314yes—
178C2×#41×C71C2×C411yescharacteristic
179C2×M16×C71C2312yes—
180C2×M16×C71C2312yes—
181C22×C8×C71C2311yescharacteristic
182C22×C8×C71C2311yescharacteristic
183C4×Q8×C71C2×C411yescharacteristic
184C4×Q8×C71C2311yescharacteristic
185C4×D4×C71C2×C412yes—
186C4×D4×C71C2×C411yescharacteristic
187C4×D4×C71C2312yes—
188C4×D4×C71C2311yescharacteristic
189#117×C71C2×C412yes—
190#117×C71C2×C411yescharacteristic
191C2×C42×C71C2311yescharacteristic
192C2×C42×C71C2312yes—
193C4⋊C8×C71C2312yes—
194C4⋊C8×C71C2311yescharacteristic
195C4⋊C8×C71C2312yes—
196C4⋊C8×C71C2311yescharacteristic
197C22⋊C8×C71C2312yes—
198C22⋊C8×C71C2312yes—
199C22⋊C8×C71C2312yes—
200#97×C71C2312yes—
201#97×C71C2312yes—
202C4×C8×C71C2311yescharacteristic
203C4×C8×C71C2311yescharacteristic
204C4×C8×C71C2312yes—
205C4×C8×C71C2311yescharacteristic
206C4×C8×C71C2311yescharacteristic
207#11765865—24no—
208#11765865—28no—
209#11765864—216no—
210#11765864—28no—
211C2×Dic142—28no—
212C2×Dic142M1618yescomplemented
213C2×Dic142C22×C414yes—
214C2×Dic142C22×C411yescharacteristic
215C2×Dic142C22×C412yes—
216C2×Dic142C22×C412yes—
217Q8×D71—28no—
218C2×D284C22×C411yescharacteristic
219C2×C22⋊D71C22×C412yes—
220C2×C22⋊D71C22×C414yes—
221C22×Dic71C22×C414yes—
222C22×Dic71C22×C414yes—
223C22×Dic71C22×C412yes—
224C22×Dic71C22×C412yes—
225C2×C4×D71C22×C412yes—
226C2×C4×D71C22×C414yes—
227C2×C4×D71C22×C412yes—
228C2×C4×D71C22×C414yes—
229C2×C4×D71C2412yes—
230#11765849—44no—
231#11765848—24no—
232#11765848—44no—
233#11765848—42no—
234C2×C71⋊C8—42no—
235C2×C71⋊C8C2412yes—
236C2×C71⋊C8C2412yes—
237C2×C71⋊C8C2414yes—
238C4⋊Dic71C22×C414yes—
239C4⋊Dic71C22×C412yes—
240C4⋊Dic71C22×C412yes—
241C4⋊Dic71C22×C411yescharacteristic
242C4⋊Dic71C22×C411yescharacteristic
243Dic71⋊C4C22×C414yes—
244Dic71⋊C4C22×C414yes—
245Dic71⋊C4C22×C414yes—
246Dic71⋊C4C22×C412yes—
247Dic71⋊C4C22×C414yes—
248Dic71⋊C4C22×C412yes—
249Dic71⋊C4C22×C414yes—
250C22⋊Dic71C22×C414yes—
251C22⋊Dic71C22×C412yes—
252(C2×D71)⋊C4C22×C412yes—
253(C2×D71)⋊C4C22×C412yes—
254(C2×D71)⋊C4C22×C414yes—
255C4×Dic71C22×C412yes—
256C4×Dic71C22×C414yes—
257C4×Dic71C22×C414yes—
258C4×Dic71C22×C412yes—
259C4×Dic71C22×C414yes—
260C4×Dic71C22×C414yes—
261C4×Dic71C22×C414yes—
262C4×Dic71C2414yes—
263C4×Dic71C2412yes—
264#41×C71—24no—
265C2×Q8×C71C22×C411yescharacteristic
266C2×D4×C71C22×C412yes—
267C2×D4×C71C22×C411yescharacteristic
268C22×C4×C71C22×C412yes—
269C22×C4×C71C22×C412yes—
270C22×C4×C71C22×C411yescharacteristic
271C22×C4×C71C22×C411yescharacteristic
272C22×C4×C71C2411yescharacteristic
273C22×C4×C71C2412yes—
274M16×C71—24no—
275M16×C71—42no—
276C2×C8×C71—22no—
277C2×C8×C71—41no—
278C2×C8×C71C2411yescharacteristic
279C2×C8×C71C2411yescharacteristic
280C2×C8×C71C2411yescharacteristic
281C2×C8×C71C2412yes—
282C2×C8×C71C2412yes—
283C2×C8×C71C2411yescharacteristic
284C4⋊C4×C71C22×C412yes—
285C4⋊C4×C71C22×C411yescharacteristic
286C4⋊C4×C71C22×C412yes—
287C4⋊C4×C71C22×C411yescharacteristic
288C22⋊C4×C71C22×C412yes—
289C22⋊C4×C71C22×C412yes—
290C22⋊C4×C71C22×C412yes—
291C42×C71C22×C411yescharacteristic
292C42×C71C22×C412yes—
293C42×C71C22×C412yes—
294C42×C71C22×C411yescharacteristic
295C42×C71C2411yescharacteristic
296C42×C71C2411yescharacteristic
297C42×C71C2412yes—
298C23×C71C23×C412yes—
299C23×C71C23×C411yescharacteristic
300C22×D71C23×C412yes—
301Q8×C71—22no—
302D4×C71—24no—
303D4×C71—22no—
304C2×C4×C71—24no—
305C2×C4×C71—21no—
306C2×C4×C71—22no—
307C2×C4×C71—21no—
308C2×C4×C71—22no—
309C2×C4×C71—41no—
310C2×C4×C71—42no—
311C2×C4×C71C2×M1614yes—
312C2×C4×C71C23×C411yescharacteristic
313C2×C4×C71C23×C411yescharacteristic
314C2×C4×C71C23×C412yes—
315C2×C4×C71C23×C411yescharacteristic
316C2×C4×C71C23×C412yes—
317C2×C4×C71C23×C412yes—
318C2×C4×C71C23×C411yescharacteristic
319C2×C4×C71C23×C411yescharacteristic
320C2×C4×C71C2511yescharacteristic
321C22⋊D71—24no—
322C22⋊D71—28no—
323C2×Dic71—28no—
324C2×Dic71—42no—
325C2×Dic71—44no—
326C2×Dic71C2×M1618yes—
327C2×Dic71C23×C412yes—
328C2×Dic71C23×C414yes—
329C2×Dic71C23×C412yes—
330C2×Dic71C23×C412yes—
331C2×Dic71C23×C414yes—
332D284—22no—
333C4×D71—24no—
334C4×D71—22no—
335C4×D71—22no—
336C4×D71—28no—
337C4×D71—42no—
338C4×D71—44no—
339Dic142—22no—
340Dic142—28no—
341Dic142C2×M1618yes—
342Dic142C2×M1618yes—
343C8×C71—21no—
344C8×C71—22no—
345C8×C71—21no—
346C8×C71—21no—
347C8×C71—22no—
348C8×C712−1+412yescomplemented
349C71⋊C8—22no—
350C71⋊C8—24no—
351C71⋊C8—22no—
352C22×C71—21no—
353C22×C71—21no—
354C22×C71—22no—
355C22×C71—22no—
356C22×C71—22no—
357C22×C71C22×M1612yes—
358C22×C71C24×C411yescharacteristic
359C2×D71—22no—
360C2×D71—22no—
361C2×D71—22no—
362C4×C71—21no—
363C4×C71—22no—
364C4×C71—22no—
365C4×C71—21no—
366C4×C71—22no—
367C4×C71—21no—
368C4×C71C22×M1612yes—
369C4×C71C22×M1612yes—
370C4×C71C2×2−1+411yescharacteristic
371C4×C71#58511yescharacteristic
372Dic71—22no—
373Dic71—22no—
374Dic71—24no—
375Dic71—22no—
376Dic71C22×M1618yes—
377#60333—711nomaximal, Sylow
378C2×C71—22no—
379C2×C71—42no—
380C2×C71C4×2−1+411yescharacteristic
381C2×C71C23×M1611yescharacteristic
382C2×C71#357311yescharacteristic
383D71—42no—
384C4×2−1+4—711no—
385#2991—712no—
386#2991—712no—
387#2989—714no—
388#2989—711no—
389#2989—711no—
390#2984—712no—
391#2984—712no—
392#2982—711no—
393#2971—712no—
394#2971—712no—
395#2965—714no—
396#2965—711no—
397#2965D7111yescharacteristic, complemented
398Q8×M16—712no—
399Q8×M16—712no—
400C2×C8×Q8—711no—
401C71#6033311yescharacteristic, complemented, Sylow
402C2×2−1+4—711no—
403#520—711no—
404#520—714no—
405#520—712no—
406#520—712no—
407#520—711no—
408#519—712no—
409#519—711no—
410#519—712no—
411C4×#41—714no—
412C4×#41—712no—
413C4×#41—711no—
414C4×#41—712no—
415C4×#41C2×D7111yescharacteristic
416C2×C4×Q8—712no—
417C2×C4×Q8—711no—
418C2×C4×Q8—712no—
419#446—712no—
420#446—714no—
421#446—714no—
422#446—714no—
423#446—714no—
424#446—711no—
425#446—712no—
426#446—711no—
427#446C2×D7111yescharacteristic
428#446C2×D7111yescharacteristic
429C8×Q8—712no—
430C8×Q8—712no—
431C8×Q8—712no—
432C8×Q8—712no—
433C8×Q8—712no—
434C8×Q8—712no—
435C8×Q8—712no—
436C8×Q8—712no—
437#436—714no—
438#436—714no—
439#436—712no—
440#436—714no—
441#436—714no—
442#436—711no—
443#436—711no—
444#436—712no—
445#436C2×D7111yescharacteristic
446#436C2×D7111yescharacteristic
447#435—712no—
448#435—712no—
449#435—714no—
450#435—714no—
451#435C2×D7112yes—
452#435C2×D7112yes—
453#432—712no—
454#432—712no—
455#432—714no—
456#432—714no—
457#431—711no—
458#431—714no—
459#431—714no—
460#431—714no—
461#431—712no—
462#431C2×D7111yescharacteristic
463#431C2×D7112yes—
464#423—714no—
465#423—712no—
466#423—714no—
467#423—712no—
468C2×C4⋊C8—712no—
469C2×C4⋊C8—711no—
470C4×M16—714no—
471C4×M16—714no—
472C4×M16—712no—
473C4×M16C2×D7112yes—
474C2×C4×C8—712no—
475C2×C4×C8C2×D7111yescharacteristic
4762−1+4—1428no—
477C2×#41—714no—
478C2×#41—712no—
479C2×#41—712no—
480C2×#41—711no—
481C2×#41C4×D7111yescharacteristic
482C22×Q8—712no—
483C22×Q8—711no—
484C22×Q8—712no—
485C2×M16—714no—
486C2×M16—712no—
487C2×M16—714no—
488C2×M16—712no—
489C2×M16C22×D7112yes—
490C2×M16C22×D7112yes—
491C22×C8—712no—
492C22×C8C22×D7111yescharacteristic
493C22×C8C22×D7111yescharacteristic
494C4×Q8—712no—
495C4×Q8—712no—
496C4×Q8—714no—
497C4×Q8—712no—
498C4×Q8—714no—
499C4×Q8—712no—
500C4×Q8—714no—
501C4×Q8—712no—
502C4×Q8—712no—
503C4×Q8—712no—
504C4×Q8—712no—
505C4×Q8—711no—
506C4×Q8—712no—
507C4×Q8—712no—
508C4×Q8—714no—
509C4×Q8—711no—
510C4×Q8C4×D7111yescharacteristic
511C4×Q8C22×D7111yescharacteristic
512C4×D4—714no—
513C4×D4—712no—
514C4×D4—712no—
515C4×D4—714no—
516C4×D4—712no—
517C4×D4—714no—
518C4×D4—714no—
519C4×D4—714no—
520C4×D4—714no—
521C4×D4—711no—
522C4×D4—712no—
523C4×D4—711no—
524C4×D4C4×D7112yes—
525C4×D4C4×D7111yescharacteristic
526C4×D4C22×D7112yes—
527C4×D4C22×D7111yescharacteristic
528#117—712no—
529#117—711no—
530#117—714no—
531#117—712no—
532#117—714no—
533#117—714no—
534#117—714no—
535#117—712no—
536#117—714no—
537#117C4×D7112yes—
538#117C4×D7111yescharacteristic
539C2×C4⋊C4—712no—
540C2×C4⋊C4—714no—
541C2×C4⋊C4—712no—
542C2×C4⋊C4—711no—
543C2×C4⋊C4—714no—
544C2×C4⋊C4—712no—
545C2×C42—712no—
546C2×C42—714no—
547C2×C42—714no—
548C2×C42—712no—
549C2×C42C22×D7111yescharacteristic
550C2×C42C22×D7112yes—
551C4⋊C8—714no—
552C4⋊C8—714no—
553C4⋊C8—712no—
554C4⋊C8—714no—
555C4⋊C8—714no—
556C4⋊C8—712no—
557C4⋊C8—714no—
558C4⋊C8—712no—
559C4⋊C8—712no—
560C4⋊C8—714no—
561C4⋊C8—711no—
562C4⋊C8—711no—
563C4⋊C8C22×D7112yes—
564C4⋊C8C22×D7111yescharacteristic
565C4⋊C8C22×D7112yes—
566C4⋊C8C22×D7111yescharacteristic
567C22⋊C8—712no—
568C22⋊C8—714no—
569C22⋊C8—712no—
570C22⋊C8—712no—
571C22⋊C8—714no—
572C22⋊C8C22×D7112yes—
573C22⋊C8C22×D7112yes—
574C22⋊C8C22×D7112yes—
575#97—712no—
576#97—712no—
577#97—714no—
578#97—714no—
579#97C22×D7112yes—
580#97C22×D7112yes—
581C4×C8—714no—
582C4×C8—714no—
583C4×C8—714no—
584C4×C8—714no—
585C4×C8—712no—
586C4×C8C22×D7111yescharacteristic
587C4×C8C22×D7111yescharacteristic
588C4×C8C22×D7111yescharacteristic
589C4×C8C22×D7111yescharacteristic
590C4×C8C22×D7112yes—
591#41—24no—
592#41—1428no—
593#41—14216no—
594#41—1428no—
595#41—1424no—
596C2×Q8—712no—
597C2×Q8—712no—
598C2×Q8—714no—
599C2×Q8—711no—
600C2×Q8—718no—
601C2×Q8—1428no—
602C2×Q8—1428no—
603C2×Q8C2×C4×D7111yescharacteristic
604C2×D4—714no—
605C2×D4—712no—
606C2×D4—711no—
607C2×D4C2×C4×D7112yes—
608C2×D4C2×C4×D7111yescharacteristic
609C22×C4—714no—
610C22×C4—712no—
611C22×C4—714no—
612C22×C4—712no—
613C22×C4—712no—
614C22×C4—714no—
615C22×C4—714no—
616C22×C4—712no—
617C22×C4—712no—
618C22×C4C2×C4×D7112yes—
619C22×C4C2×C4×D7112yes—
620C22×C4C2×C4×D7111yescharacteristic
621C22×C4C2×C4×D7111yescharacteristic
622C22×C4C23×D7111yescharacteristic
623C22×C4C23×D7112yes—
624M16—24no—
625M16—42no—
626M16—2842no—
627M16—2844no—
628M16—2844no—
629M16—1424no—
630C2×C8—22no—
631C2×C8—41no—
632C2×C8—2842no—
633C2×C8—712no—
634C2×C8—712no—
635C2×C8—714no—
636C2×C8C23×D7111yescharacteristic
637C2×C8C23×D7112yes—
638C2×C8C23×D7112yes—
639C2×C8C23×D7111yescharacteristic
640C2×C8C23×D7111yescharacteristic
641C2×C8C23×D7111yescharacteristic
642C4⋊C4—714no—
643C4⋊C4—714no—
644C4⋊C4—714no—
645C4⋊C4—714no—
646C4⋊C4—712no—
647C4⋊C4—714no—
648C4⋊C4—712no—
649C4⋊C4—714no—
650C4⋊C4—712no—
651C4⋊C4—712no—
652C4⋊C4—711no—
653C4⋊C4—711no—
654C4⋊C4C2×C4×D7112yes—
655C4⋊C4C2×C4×D7111yescharacteristic
656C4⋊C4C2×C4×D7112yes—
657C4⋊C4C2×C4×D7111yescharacteristic
658C22⋊C4—714no—
659C22⋊C4—712no—
660C22⋊C4—712no—
661C22⋊C4—712no—
662C22⋊C4—714no—
663C22⋊C4C2×C4×D7112yes—
664C22⋊C4C2×C4×D7112yes—
665C22⋊C4C2×C4×D7112yes—
666C42—714no—
667C42—714no—
668C42—714no—
669C42—714no—
670C42—712no—
671C42—712no—
672C42—714no—
673C42—714no—
674C42—712no—
675C42C2×C4×D7112yes—
676C42C2×C4×D7111yescharacteristic
677C42C2×C4×D7111yescharacteristic
678C42C2×C4×D7112yes—
679C42C23×D7111yescharacteristic
680C42C23×D7111yescharacteristic
681C42C23×D7112yes—
682C23—712no—
683C23C22×C4×D7112yes—
684C23C22×C4×D7111yescharacteristic
685Q8—22no—
686Q8—718no—
687Q8—718no—
688Q8—1428no—
689Q8—1422no—
690D4—24no—
691D4—22no—
692D4—1428no—
693D4—1424no—
694D4—1422no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—2842no—
703C2×C4—2844no—
704C2×C4—2842no—
705C2×C4—2844no—
706C2×C4—714no—
707C2×C4—718no—
708C2×C4—712no—
709C2×C4—714no—
710C2×C4—712no—
711C2×C4—712no—
712C2×C4—1428no—
713C2×C4—1428no—
714C2×C4—1422no—
715C2×C4—1422no—
716C2×C4—1424no—
717C2×C4M16×D7114yes—
718C2×C4C22×C4×D7111yescharacteristic
719C2×C4C22×C4×D7112yes—
720C2×C4C22×C4×D7111yescharacteristic
721C2×C4C22×C4×D7112yes—
722C2×C4C22×C4×D7112yes—
723C2×C4C22×C4×D7111yescharacteristic
724C2×C4C22×C4×D7111yescharacteristic
725C2×C4C22×C4×D7111yescharacteristic
726C2×C4C24×D7111yescharacteristic
727C8—21no—
728C8—22no—
729C8—21no—
730C8—21no—
731C8—22no—
732C8—1422no—
733C8—1424no—
734C8—1422no—
735C8#1455617512yescomplemented
736C22—21no—
737C22—21no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—1422no—
742C22—1422no—
743C22—1422no—
744C22C2×M16×D7112yes—
745C22C23×C4×D7111yescharacteristic
746C4—22no—
747C4—21no—
748C4—21no—
749C4—22no—
750C4—21no—
751C4—22no—
752C4—718no—
753C4—1422no—
754C4—1424no—
755C4—1422no—
756C4—1422no—
757C4C2×M16×D7112yes—
758C4C2×M16×D7112yes—
759C4C2×#1455617511yescharacteristic
760C4#1798683511yescharacteristic
761C2—22no—
762C2—42no—
763C2—2842no—
764C2C4×#1455617511yescharacteristic
765C2C22×M16×D7111yescharacteristic
766C2#2260305111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D71
commutator, socleC22×C71C24×C4
FittingC71×#2965C2
prime radicalC2×#14556175C4
cosocleC2×C4×C71C25
hypercenter#2965D71
hypocenterC71#60333
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ #2965

Complements

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

NH ≅ G/Ntype
2. #22597469C2semidirect
3. #22597468C2semidirect
4. #22597457C2semidirect
5. #22597453C2semidirect
6. #22597452C2semidirect
7. #22597427C2semidirect
8. #22597426C2semidirect
9. #22597420C2semidirect
10. #22597358C2semidirect
11. #22597356C2semidirect
12. #22597306C2semidirect
13. #22597300C2semidirect
14. M16×Dic142C2semidirect
15. #22597292C2semidirect
16. C2×C8×Dic142C2semidirect
17. C71×#2965C2semidirect
212. C2×Dic142M16semidirect
348. C8×C712−1+4semidirect
397. #2965D71semidirect
401. C71#60333semidirect
735. C8#14556175semidirect

Maximal subgroups

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

subgroupindex
C4×#145561752
#225974692
#225974682
#225974572
#225974532
#225974522
#225974272
#225974262
#225974202
#225973582
#225973562
#225973062
#225973002
M16×Dic1422
#225972922
C2×C8×Dic1422
C71×#29652
#6033371