Finite Group Databasebeta

← C2×#22600721 #32875901

Subgroups — C2×#22600721 #32875901

Order 18176.

1930 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986695C211yesmaximal, characteristic
2C2×#17986689C211yesmaximal, characteristic, complemented
3#22600721C2116yesmaximal, direct product factor
4C2×#17986401C211yesmaximal, characteristic, complemented
5C2×#17986335C211yesmaximal, characteristic, complemented
6C2×#17986341C211yesmaximal, characteristic, complemented
7C2×#17986324C211yesmaximal, characteristic, complemented
8C2×#17986313C211yesmaximal, characteristic, complemented
9C2×#17986307C211yesmaximal, characteristic, complemented
10C2×#17986300C211yesmaximal, characteristic, complemented
11C2×#17986228C211yesmaximal, characteristic, complemented
12C2×#17986228C211yesmaximal, characteristic, complemented
13C2×C4×#11765854C211yesmaximal, characteristic, complemented
14C2×#17986037C211yesmaximal, characteristic, complemented
15C22×#14556060C211yesmaximal, characteristic, complemented
16C2×C8×D4×C71C211yesmaximal, characteristic, complemented
17C22×#11765854C2211yescharacteristic
18#17986695—24no—
19#17986695C2218yes—
20#17986689—24no—
21#17986689C2218yescomplemented
22C2×#14556123—21no—
23C2×#14556121—21no—
24C2×#14556120C2211yescharacteristic
25C2×#14556120C2211yescharacteristic
26C2×#14556118—21no—
27C2×#14556110—21no—
28C2×#14556109—21no—
29C2×#14556107C2211yescharacteristic
30C2×#14556107C2211yescharacteristic
31C2×#14556102C2211yescharacteristic
32C2×#14556102C2211yescharacteristic
33C2×#14556100—21no—
34C2×C4×Dic142C2211yescharacteristic
35C2×C4×D284C2211yescharacteristic
36C2×(C22⋊D71)⋊C4—21no—
37C2×#14556087C2211yescharacteristic
38C2×#14556087C2211yescharacteristic
39C2×#14556084—21no—
40C22×C4⋊Dic71C2211yescharacteristic
41C22×C4⋊Dic71C2211yescharacteristic
42#17986401C2218yescomplemented
43#17986341C2218yescomplemented
44#17986335C2218yescomplemented
45#17986324C2218yescomplemented
46#17986313C2218yescomplemented
47#17986307C2218yescomplemented
48#17986300C2218yescomplemented
49#17986228C2218yescomplemented
50#17986228C2218yescomplemented
51C4×#11765854C2218yescomplemented
52#17986037C2218yescomplemented
53C2×#14556062C2211yescharacteristic
54C2×#14556062C2211yescharacteristic
55C2×#14556062C2211yescharacteristic
56C2×#14556062C2211yescharacteristic
57C2×#14556060C2211yescharacteristic
58C2×#14556060C2211yescharacteristic
59C2×#14556060C2211yescharacteristic
60C2×#14556060C2211yescharacteristic
61C2×#14556060C2211yescharacteristic
62C2×#14556060C2218yescomplemented
63C2×#14556053C2211yescharacteristic
64C2×#14556053C2211yescharacteristic
65C2×#14556053C2211yescharacteristic
66C2×#14556050C2211yescharacteristic
67C2×#14556050C2211yescharacteristic
68C2×#14556050C2211yescharacteristic
69C23×C8×C71C2211yescharacteristic
70C23×C8×C71C2211yescharacteristic
71C2×C4×D4×C71C2211yescharacteristic
72C8×D4×C71C2218yescomplemented
73C2×C4⋊C8×C71C2211yescharacteristic
74C2×C22⋊C8×C71C2211yescharacteristic
75C2×C22⋊C8×C71C2211yescharacteristic
76C2×C4×C8×C71C2211yescharacteristic
77C22×Dic142C2311yescharacteristic
78C22×D284C2311yescharacteristic
79C22×C22⋊D71—21no—
80C22×C22⋊D71—21no—
81C23×Dic71—21no—
82C23×Dic71—21no—
83C22×C4×D71—21no—
84C2×#11765854—24no—
85C2×#11765854C2314yes—
86#14556123—28no—
87#14556121—28no—
88#14556120—22no—
89#14556120—22no—
90#14556120C2314yes—
91#14556120C2314yes—
92#14556118—28no—
93#14556110—28no—
94#14556109—28no—
95#14556107—22no—
96#14556107—22no—
97#14556107C2314yes—
98#14556107C2314yes—
99#14556102—22no—
100#14556102—22no—
101#14556102C2314yes—
102#14556102C2314yes—
103#14556100—28no—
104C4×Dic142—22no—
105C4×Dic142C2314yes—
106C4×D284—22no—
107C4×D284C2314yes—
108(C22⋊D71)⋊C4—28no—
109#14556087—22no—
110#14556087—22no—
111#14556087C2314yes—
112#14556087C2314yes—
113#14556084—28no—
114C2×C4⋊Dic71—22no—
115C2×C4⋊Dic71—22no—
116C2×C4⋊Dic71—21no—
117C2×C4⋊Dic71—21no—
118C2×C4⋊Dic71C2314yes—
119C2×C4⋊Dic71C2314yes—
120C2×C4⋊Dic71C2311yescharacteristic
121C2×C4⋊Dic71C2311yescharacteristic
122C2×C4⋊Dic71C2311yescharacteristic
123C2×C4⋊Dic71C2311yescharacteristic
124C2×C4⋊Dic71C2311yescharacteristic
125C2×C4⋊Dic71C2311yescharacteristic
126C2×Dic71⋊C4—21no—
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—21no—
129C2×Dic71⋊C4—21no—
130C2×Dic71⋊C4—21no—
131C2×Dic71⋊C4—21no—
132C2×Dic71⋊C4—21no—
133C2×C22⋊Dic71—21no—
134C2×C22⋊Dic71—21no—
135C2×C22⋊Dic71—21no—
136C2×C22⋊Dic71—21no—
137C2×(C2×D71)⋊C4—21no—
138C2×(C2×D71)⋊C4—21no—
139C2×(C2×D71)⋊C4—21no—
140C2×C4×Dic71—21no—
141C2×C4×Dic71—21no—
142C2×C4×Dic71—21no—
143#14556062C2314yes—
144#14556062C2314yes—
145#14556062C2314yes—
146#14556062C2314yes—
147#14556060C2314yes—
148#14556060C2314yes—
149#14556060C2314yes—
150#14556060C2314yes—
151#14556060C2314yes—
152#14556053C2314yes—
153#14556053C2314yes—
154#14556053C2314yes—
155#14556050C2314yes—
156#14556050C2314yes—
157#14556050C2314yes—
158C22×D4×C71D411yescharacteristic
159C23×C4×C71C2311yescharacteristic
160C23×C4×C71C2311yescharacteristic
161C22×C8×C71—24no—
162C22×C8×C71—24no—
163C22×C8×C71C2311yescharacteristic
164C22×C8×C71C2311yescharacteristic
165C22×C8×C71C2311yescharacteristic
166C22×C8×C71C2314yes—
167C22×C8×C71C2314yes—
168C22×C8×C71C2311yescharacteristic
169C4×D4×C71D414yes—
170C4×D4×C71C2314yes—
171C2×C4⋊C4×C71D411yescharacteristic
172C2×C22⋊C4×C71D411yescharacteristic
173C2×C22⋊C4×C71D411yescharacteristic
174C2×C42×C71C2311yescharacteristic
175C4⋊C8×C71C2314yes—
176C22⋊C8×C71C2314yes—
177C22⋊C8×C71C2314yes—
178C4×C8×C71C2314yes—
179C23×D71—21no—
180C2×Dic142—22no—
181C2×Dic142—22no—
182C2×Dic142—21no—
183C2×Dic142C2412yes—
184C2×D284—22no—
185C2×D284—22no—
186C2×D284—21no—
187C2×D284C2412yes—
188C2×C22⋊D71—24no—
189C2×C22⋊D71—24no—
190C2×C22⋊D71—44no—
191C2×C22⋊D71—82no—
192C22×Dic71—21no—
193C22×Dic71—21no—
194C22×Dic71—21no—
195C22×Dic71—21no—
196C22×Dic71—24no—
197C22×Dic71—21no—
198C22×Dic71—21no—
199C22×Dic71—21no—
200C22×Dic71—24no—
201C22×Dic71—44no—
202C22×Dic71—82no—
203C2×C4×D71—24no—
204C2×C4×D71—82no—
205#11765854—28no—
206C4⋊Dic71—21no—
207C4⋊Dic71—21no—
208C4⋊Dic71—21no—
209C4⋊Dic71—21no—
210C4⋊Dic71—24no—
211C4⋊Dic71—24no—
212C4⋊Dic71—21no—
213C4⋊Dic71—21no—
214C4⋊Dic71C2412yes—
215C4⋊Dic71C2412yes—
216C4⋊Dic71C2412yes—
217C4⋊Dic71C2412yes—
218C4⋊Dic71C2412yes—
219C4⋊Dic71C2412yes—
220Dic71⋊C4—24no—
221Dic71⋊C4—24no—
222Dic71⋊C4—24no—
223Dic71⋊C4—24no—
224Dic71⋊C4—24no—
225Dic71⋊C4—24no—
226Dic71⋊C4—24no—
227C22⋊Dic71—24no—
228C22⋊Dic71—24no—
229C22⋊Dic71—24no—
230C22⋊Dic71—24no—
231(C2×D71)⋊C4—24no—
232(C2×D71)⋊C4—24no—
233(C2×D71)⋊C4—24no—
234C4×Dic71—24no—
235C4×Dic71—24no—
236C4×Dic71—24no—
237C24×C71C2×D411yescharacteristic
238C24×C71C2×D411yescharacteristic
239C2×D4×C71—24no—
240C2×D4×C71C2×D414yes—
241C22×C4×C71—22no—
242C22×C4×C71—22no—
243C22×C4×C71—22no—
244C22×C4×C71—22no—
245C22×C4×C71C2×D411yescharacteristic
246C22×C4×C71C2×D411yescharacteristic
247C22×C4×C71C2×D411yescharacteristic
248C22×C4×C71C2×D411yescharacteristic
249C22×C4×C71C2×D412yes—
250C22×C4×C71C2×D412yes—
251C22×C4×C71C2412yes—
252C22×C4×C71C2412yes—
253C22×C4×C71C2411yescharacteristic
254C2×C8×C71—22no—
255C2×C8×C71—22no—
256C2×C8×C71—22no—
257C2×C8×C71—28no—
258C2×C8×C71—28no—
259C2×C8×C71#4114yes—
260C2×C8×C71C2412yes—
261C2×C8×C71C2412yes—
262C2×C8×C71C2412yes—
263C2×C8×C71C2412yes—
264C4⋊C4×C71C2×D414yes—
265C22⋊C4×C71C2×D414yes—
266C22⋊C4×C71C2×D414yes—
267C42×C71C2×D412yes—
268C42×C71C2412yes—
269C23×C71—22no—
270C23×C71—22no—
271C23×C71—22no—
272C23×C71—22no—
273C23×C71—22no—
274C23×C71#13514yes—
275C23×C71C22×D412yes—
276C23×C71C22×D412yes—
277C23×C71C22×D411yescharacteristic
278C22×D71—22no—
279C22×D71—42no—
280C22×D71—42no—
281C22×D71—42no—
282D4×C71—28no—
283C2×C4×C71—22no—
284C2×C4×C71—22no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—24no—
288C2×C4×C71—24no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71C22×D412yes—
294C2×C4×C71C22×D412yes—
295C2×C4×C71C22×D412yes—
296C2×C4×C71C22×D412yes—
297C2×C4×C71C22×D411yescharacteristic
298C2×C4×C71C2×#4112yes—
299C2×C4×C712−1+412yes—
300C2×C4×C71C2511yescharacteristic
301C22⋊D71—48no—
302C22⋊D71—84no—
303C2×Dic71—22no—
304C2×Dic71—22no—
305C2×Dic71—22no—
306C2×Dic71—22no—
307C2×Dic71—22no—
308C2×Dic71—22no—
309C2×Dic71—22no—
310C2×Dic71—42no—
311C2×Dic71—48no—
312C2×Dic71—42no—
313C2×Dic71—42no—
314C2×Dic71—42no—
315C2×Dic71—42no—
316C2×Dic71—42no—
317C2×Dic71—42no—
318C2×Dic71—84no—
319D284—22no—
320D284—22no—
321D284—42no—
322C4×D71—84no—
323Dic142—22no—
324Dic142—22no—
325Dic142—42no—
326C8×C71—22no—
327C8×C71—22no—
328C8×C71—22no—
329C8×C71C2×#4114yes—
330C22×C71—28no—
331C22×C71—22no—
332C22×C71—22no—
333C22×C71—22no—
334C22×C71—22no—
335C22×C71—22no—
336C22×C71—44no—
337C22×C71#54712yes—
338C22×C71C2×#13514yes—
339C22×C71C2×#13512yes—
340C22×C71#57712yes—
341C22×C71C23×D411yescharacteristic
342C2×D71—42no—
343C2×D71—42no—
344C2×D71—42no—
345C2×D71—84no—
346C4×C71—22no—
347C4×C71—22no—
348C4×C71—22no—
349C4×C71—22no—
350C4×C71#54712yes—
351C4×C71C22×#4111yescharacteristic
352C4×C71C2×2−1+411yescharacteristic
353Dic71—42no—
354Dic71—42no—
355Dic71—42no—
356Dic71—42no—
357Dic71—42no—
358Dic71—42no—
359Dic71—42no—
360C2×#3337—711nomaximal, Sylow
361C2×C71—24no—
362C2×C71—42no—
363C2×C71#333714yescomplemented
364C2×C71C2×#54711yescharacteristic
365C2×C71C22×#13511yescharacteristic
366C2×C71C2×#57711yescharacteristic
367D71—82no—
368C2×#553—711no—
369C2×#552—711no—
370#3337—7116no—
371C2×#499—711no—
372C2×#484—711no—
373C2×#485—711no—
374C2×#482—711no—
375C2×#480—711no—
376C2×#479—711no—
377C2×#478—711no—
378C2×#465—711no—
379C2×#465—711no—
380C2×C4×SD16—711no—
381C2×C8×D4D7111yescharacteristic, complemented
382C2×#427—711no—
383C22×#106—711no—
384C71C2×#333711yescharacteristic, complemented, Sylow
385C22×SD16—711no—
386C23×C8C2×D7111yescharacteristic
387C23×C8C2×D7111yescharacteristic
388#553—718no—
389#553—1424no—
390#552—718no—
391#552—1424no—
392C2×#126—1421no—
393C2×#126—1421no—
394C2×#125—711no—
395C2×#125—711no—
396C2×#125—1421no—
397C2×#123—1421no—
398C2×#123—1421no—
399C2×C22⋊Q8—711no—
400C2×C22⋊Q8—711no—
401C2×#121—711no—
402C2×#121—711no—
403C2×#121—1421no—
404C2×C4×Q8—711no—
405C2×C4×D4—711no—
406C2×C4×D4—1421no—
407C2×C4×D4C2×D7111yescharacteristic
408C2×#117—711no—
409C2×#117—711no—
410C2×#117—1421no—
411C22×C4⋊C4—711no—
412C22×C4⋊C4—711no—
413#499—718no—
414#485—718no—
415#484—718no—
416#482—718no—
417#480—718no—
418#479—718no—
419#478—718no—
420#465—718no—
421#465—718no—
422C4×SD16—718no—
423C8×D4C2×D7118yescomplemented
424#427—718no—
425C2×#107—711no—
426C2×#107—711no—
427C2×#107—711no—
428C2×#107—711no—
429C2×#106—711no—
430C2×#106—711no—
431C2×#106—718no—
432C2×#106—711no—
433C2×#106—711no—
434C2×#106—711no—
435C2×C4⋊C8C2×D7111yescharacteristic
436C2×#103—711no—
437C2×#103—711no—
438C2×#103—711no—
439C2×#102—711no—
440C2×#102—711no—
441C2×#102—711no—
442C2×C22⋊C8C2×D7111yescharacteristic
443C2×C22⋊C8C2×D7111yescharacteristic
444C2×C4×C8C2×D7111yescharacteristic
445C22×Q8—711no—
446C22×D4—711no—
447C22×D4—1421no—
448C22×D4—1421no—
449C22×D4D28411yescharacteristic
450C23×C4—1421no—
451C23×C4—1421no—
452C23×C4—1421no—
453C23×C4C22×D7111yescharacteristic
454C23×C4C22×D7111yescharacteristic
455C2×SD16—714no—
456C2×SD16—1424no—
457C22×C8—24no—
458C22×C8—24no—
459C22×C8C22×D7111yescharacteristic
460C22×C8C22×D7111yescharacteristic
461C22×C8C22×D7114yes—
462C22×C8C22×D7114yes—
463C22×C8C22×D7111yescharacteristic
464C22×C8C22×D7111yescharacteristic
465#126—1428no—
466#126—1428no—
467#125—714no—
468#125—714no—
469#125—1428no—
470#125—1422no—
471#125—1422no—
472#123—1428no—
473#123—1428no—
474C22⋊Q8—714no—
475C22⋊Q8—714no—
476C22⋊Q8—1422no—
477C22⋊Q8—1422no—
478#121—714no—
479#121—714no—
480#121—1428no—
481#121—1422no—
482#121—1422no—
483C4×Q8—714no—
484C4×Q8—1422no—
485C4×D4—714no—
486C4×D4—1428no—
487C4×D4—1422no—
488C4×D4D28414yes—
489C4×D4C22×D7114yes—
490#117—714no—
491#117—714no—
492#117—1422no—
493#117—1422no—
494#117—1428no—
495C2×C4⋊C4—711no—
496C2×C4⋊C4—711no—
497C2×C4⋊C4—711no—
498C2×C4⋊C4—711no—
499C2×C4⋊C4—714no—
500C2×C4⋊C4—714no—
501C2×C4⋊C4—711no—
502C2×C4⋊C4—711no—
503C2×C4⋊C4—1421no—
504C2×C4⋊C4—1421no—
505C2×C4⋊C4—1422no—
506C2×C4⋊C4—1422no—
507C2×C4⋊C4—1421no—
508C2×C4⋊C4—1421no—
509C2×C4⋊C4—1421no—
510C2×C4⋊C4—1421no—
511C2×C4⋊C4—1421no—
512C2×C4⋊C4—1421no—
513C2×C4⋊C4—1421no—
514C2×C4⋊C4D28411yescharacteristic
515C2×C22⋊C4—1421no—
516C2×C22⋊C4—1421no—
517C2×C22⋊C4—1421no—
518C2×C22⋊C4—1421no—
519C2×C22⋊C4—1421no—
520C2×C22⋊C4—1421no—
521C2×C22⋊C4—1421no—
522C2×C22⋊C4D28411yescharacteristic
523C2×C22⋊C4D28411yescharacteristic
524C2×C42—1421no—
525C2×C42—1421no—
526C2×C42—1421no—
527C2×C42C22×D7111yescharacteristic
528#107—714no—
529#107—714no—
530#107—714no—
531#107—714no—
532#106—714no—
533#106—714no—
534#106—714no—
535#106—714no—
536#106—714no—
537C4⋊C8C22×D7114yes—
538#103—714no—
539#103—714no—
540#103—714no—
541#102—714no—
542#102—714no—
543#102—714no—
544C22⋊C8C22×D7114yes—
545C22⋊C8C22×D7114yes—
546C4×C8C22×D7114yes—
547C24—1421no—
548C24C2×D28411yescharacteristic
549C24C2×D28411yescharacteristic
550C2×Q8—712no—
551C2×Q8—1422no—
552C2×Q8—1422no—
553C2×Q8—1421no—
554C2×D4—24no—
555C2×D4—2844no—
556C2×D4—5682no—
557C2×D4—712no—
558C2×D4—1424no—
559C2×D4—1424no—
560C2×D4—1421no—
561C2×D4—1422no—
562C2×D4—1422no—
563C2×D4C2×D28414yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—2844no—
569C22×C4—5682no—
570C22×C4—5682no—
571C22×C4—1424no—
572C22×C4—1421no—
573C22×C4—1421no—
574C22×C4—1421no—
575C22×C4—1421no—
576C22×C4—1421no—
577C22×C4—1421no—
578C22×C4—1421no—
579C22×C4—1424no—
580C22×C4—1424no—
581C22×C4C2×D28412yes—
582C22×C4C2×D28412yes—
583C22×C4C2×D28411yescharacteristic
584C22×C4C2×D28411yescharacteristic
585C22×C4C2×D28411yescharacteristic
586C22×C4C2×D28411yescharacteristic
587C22×C4C23×D7112yes—
588C22×C4C23×D7112yes—
589C22×C4C23×D7111yescharacteristic
590SD16—1428no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—28no—
595C2×C8—28no—
596C2×C8#1176586414yes—
597C2×C8C23×D7112yes—
598C2×C8C23×D7112yes—
599C2×C8C23×D7112yes—
600C2×C8C23×D7112yes—
601C4⋊C4—712no—
602C4⋊C4—712no—
603C4⋊C4—712no—
604C4⋊C4—712no—
605C4⋊C4—712no—
606C4⋊C4—712no—
607C4⋊C4—1424no—
608C4⋊C4—1424no—
609C4⋊C4—1424no—
610C4⋊C4—1424no—
611C4⋊C4—1424no—
612C4⋊C4—1424no—
613C4⋊C4—1424no—
614C4⋊C4—1421no—
615C4⋊C4—1421no—
616C4⋊C4—1421no—
617C4⋊C4—1421no—
618C4⋊C4—1424no—
619C4⋊C4—1424no—
620C4⋊C4—1421no—
621C4⋊C4—1421no—
622C4⋊C4C2×D28414yes—
623C22⋊C4—1424no—
624C22⋊C4—1424no—
625C22⋊C4—1424no—
626C22⋊C4—1424no—
627C22⋊C4—1424no—
628C22⋊C4—1424no—
629C22⋊C4—1424no—
630C22⋊C4C2×D28414yes—
631C22⋊C4C2×D28414yes—
632C42—1424no—
633C42—1424no—
634C42—1424no—
635C42C2×D28412yes—
636C42C23×D7112yes—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—2842no—
643C23—2842no—
644C23—2842no—
645C23—1422no—
646C23#1455615014yes—
647C23C22×D28412yes—
648C23C22×D28412yes—
649C23C22×D28411yescharacteristic
650Q8—2842no—
651Q8—1422no—
652Q8—1422no—
653D4—28no—
654D4—2848no—
655D4—2842no—
656D4—5684no—
657D4—1422no—
658D4—1422no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—2842no—
670C2×C4—2848no—
671C2×C4—2842no—
672C2×C4—2842no—
673C2×C4—2842no—
674C2×C4—2842no—
675C2×C4—2842no—
676C2×C4—2842no—
677C2×C4—5684no—
678C2×C4—5684no—
679C2×C4—1422no—
680C2×C4—1422no—
681C2×C4—1422no—
682C2×C4—1422no—
683C2×C4—1422no—
684C2×C4—1422no—
685C2×C4—1422no—
686C2×C4C22×D28412yes—
687C2×C4C22×D28412yes—
688C2×C4C22×D28412yes—
689C2×C4C22×D28412yes—
690C2×C4C22×D28411yescharacteristic
691C2×C4C2×#1176586412yes—
692C2×C4#1455617512yes—
693C2×C4C24×D7111yescharacteristic
694C8—22no—
695C8—22no—
696C8—22no—
697C8C2×#1176586414yes—
698C22—28no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—2842no—
706C22—2842no—
707C22—2842no—
708C22—5684no—
709C22#1798665312yes—
710C22C2×#1455615014yes—
711C22C2×#1455615012yes—
712C22#1798681112yes—
713C22C23×D28411yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—2842no—
719C4—2842no—
720C4—2842no—
721C4—2842no—
722C4—2842no—
723C4—2842no—
724C4—2842no—
725C4#1798665312yes—
726C4C22×#1176586411yescharacteristic
727C4C2×#1455617511yescharacteristic
728C2—24no—
729C2—42no—
730C2—5682no—
731C2#2260072114yesdirect product factor
732C2C2×#1798665311yescharacteristic
733C2C22×#1455615011yescharacteristic
734C2C2×#1798681111yescharacteristic
subgroupG/H
centerC23C22×D284
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×C8×D4×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986695C2
hypercenterC2×C8×D4D71
hypocenterC71C2×#3337
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
2. C2×#17986689C2semidirect
3. #22600721C2direct (N × H)
4. C2×#17986401C2semidirect
5. C2×#17986335C2semidirect
6. C2×#17986341C2semidirect
7. C2×#17986324C2semidirect
8. C2×#17986313C2semidirect
9. C2×#17986307C2semidirect
10. C2×#17986300C2semidirect
11. C2×#17986228C2semidirect
12. C2×#17986228C2semidirect
13. C2×C4×#11765854C2semidirect
14. C2×#17986037C2semidirect
15. C22×#14556060C2semidirect
16. C2×C8×D4×C71C2semidirect
21. #17986689C22semidirect
42. #17986401C22semidirect
43. #17986341C22semidirect
44. #17986335C22semidirect
45. #17986324C22semidirect
46. #17986313C22semidirect
47. #17986307C22semidirect
48. #17986300C22semidirect
49. #17986228C22semidirect
50. #17986228C22semidirect
51. C4×#11765854C22semidirect
52. #17986037C22semidirect
62. C2×#14556060C22semidirect
72. C8×D4×C71C22semidirect
363. C2×C71#3337semidirect
381. C2×C8×D4D71semidirect
384. C71C2×#3337semidirect
423. C8×D4C2×D71semidirect
731. C2#22600721direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866952
C2×#179866892
#226007212
C2×#179864012
C2×#179863352
C2×#179863412
C2×#179863242
C2×#179863132
C2×#179863072
C2×#179863002
C2×#179862282
C2×C4×#117658542
C2×#179860372
C22×#145560602
C2×C8×D4×C712
C2×#333771