Finite Group Databasebeta

← C2×#22600780 #32875983

Subgroups — C2×#22600780 #32875983

Order 18176.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986653C211yesmaximal, characteristic
2#22600780C2116yesmaximal, direct product factor
3C2×#17986409C211yesmaximal, characteristic, complemented
4C2×#17986332C211yesmaximal, characteristic, complemented
5C2×#17986323C211yesmaximal, characteristic, complemented
6C2×#17986327C211yesmaximal, characteristic, complemented
7C2×#17986312C211yesmaximal, characteristic, complemented
8C2×#17986294C211yesmaximal, characteristic, complemented
9C2×#17986296C211yesmaximal, characteristic, complemented
10C2×#17986247C211yesmaximal, characteristic, complemented
11C2×#17986230C211yesmaximal, characteristic, complemented
12C2×#17986097C211yesmaximal, characteristic, complemented
13C2×#17986071C211yesmaximal, characteristic, complemented
14C2×#17986042C211yesmaximal, characteristic, complemented
15C22×#14556061C211yesmaximal, characteristic, complemented
16C2×#552×C71C211yesmaximal, characteristic, complemented
17C22×#11765864—21no—
18C22×#11765852C2211yescharacteristic
19C22×#11765849C2211yescharacteristic
20C23×C71⋊C8C2211yescharacteristic
21#17986653—24no—
22#17986653C2218yes—
23C2×#14556128C2211yescharacteristic
24C2×#14556112—21no—
25C2×#14556112—21no—
26C2×#14556108—21no—
27C2×#14556102C2211yescharacteristic
28C2×#14556102C2211yescharacteristic
29C2×C4×D284C2211yescharacteristic
30C22×C4⋊Dic71C2211yescharacteristic
31C22×C4⋊Dic71C2211yescharacteristic
32#17986409C2218yescomplemented
33#17986332C2218yescomplemented
34#17986327C2218yescomplemented
35#17986323C2218yescomplemented
36#17986312C2218yescomplemented
37#17986296C2218yescomplemented
38#17986294C2218yescomplemented
39#17986247C2218yescomplemented
40#17986230C2218yescomplemented
41#17986097C2218yescomplemented
42#17986071C2218yescomplemented
43#17986042C2218yescomplemented
44C2×#14556061C2211yescharacteristic
45C2×#14556061C2211yescharacteristic
46C2×#14556061C2211yescharacteristic
47C2×#14556061C2211yescharacteristic
48C2×#14556061C2211yescharacteristic
49C2×#14556061C2211yescharacteristic
50C2×#14556061C2218yescomplemented
51C2×#14556059C2211yescharacteristic
52C2×#14556059C2211yescharacteristic
53C2×#14556059C2211yescharacteristic
54C2×C4⋊(C71⋊C8)C2211yescharacteristic
55C2×#14556052C2211yescharacteristic
56C2×#14556052C2211yescharacteristic
57C2×#14556052C2211yescharacteristic
58C2×#14556048C2211yescharacteristic
59C2×#14556048C2211yescharacteristic
60C2×#14556048C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×C22⋊(C71⋊C8)C2211yescharacteristic
63C2×#14556039C2211yescharacteristic
64#552×C71—24no—
65#552×C71C2218yescomplemented
66C2×#126×C71—21no—
67C2×#125×C71—21no—
68C2×#125×C71C2211yescharacteristic
69C2×#123×C71—21no—
70C2×C22⋊Q8×C71C2211yescharacteristic
71C2×C22⋊Q8×C71C2211yescharacteristic
72C2×C4×Q8×C71C2211yescharacteristic
73C2×C4×D4×C71C2211yescharacteristic
74C2×#117×C71—21no—
75C2×#117×C71C2211yescharacteristic
76C22×C4⋊C4×C71C2211yescharacteristic
77C2×#11765864—28no—
78C2×#11765864—48no—
79C22×Dic142—21no—
80C22×D284C2311yescharacteristic
81C22×C22⋊D71—21no—
82C22×C22⋊D71—21no—
83C23×Dic71—21no—
84C23×Dic71—21no—
85C22×C4×D71—21no—
86C2×#11765852—24no—
87C2×#11765852C2314yes—
88C2×#11765849—24no—
89C2×#11765849C2314yes—
90C22×C71⋊C8—24no—
91C22×C71⋊C8C2314yes—
92C22×C71⋊C8C2311yescharacteristic
93C22×C71⋊C8C2311yescharacteristic
94C22×C71⋊C8C2311yescharacteristic
95C22×C71⋊C8C2311yescharacteristic
96#14556128—22no—
97#14556128C2314yes—
98#14556112—28no—
99#14556112—28no—
100#14556108—28no—
101#14556102—22no—
102#14556102—22no—
103#14556102C2314yes—
104#14556102C2314yes—
105C4×D284—22no—
106C4×D284C2314yes—
107C2×C4⋊Dic71—22no—
108C2×C4⋊Dic71—22no—
109C2×C4⋊Dic71—21no—
110C2×C4⋊Dic71—21no—
111C2×C4⋊Dic71—21no—
112C2×C4⋊Dic71C2314yes—
113C2×C4⋊Dic71C2314yes—
114C2×C4⋊Dic71C2311yescharacteristic
115C2×C4⋊Dic71C2311yescharacteristic
116C2×C4⋊Dic71C2311yescharacteristic
117C2×(C2×D71)⋊C4—21no—
118C2×(C2×D71)⋊C4—21no—
119C2×(C2×D71)⋊C4—21no—
120#14556061C2314yes—
121#14556061C2314yes—
122#14556061C2314yes—
123#14556061C2314yes—
124#14556061C2314yes—
125#14556061C2314yes—
126#14556059C2314yes—
127#14556059C2314yes—
128#14556059C2314yes—
129C4⋊(C71⋊C8)C2314yes—
130#14556052C2314yes—
131#14556052C2314yes—
132#14556052C2314yes—
133#14556048C2314yes—
134#14556048C2314yes—
135#14556048C2314yes—
136C22⋊(C71⋊C8)C2314yes—
137C22⋊(C71⋊C8)C2314yes—
138#14556039C2314yes—
139C22×Q8×C71C2311yescharacteristic
140C22×D4×C71D411yescharacteristic
141C23×C4×C71—21no—
142C23×C4×C71C2311yescharacteristic
143C23×C4×C71C2311yescharacteristic
144#126×C71—28no—
145#125×C71—28no—
146#125×C71—22no—
147#125×C71C2314yes—
148#123×C71—28no—
149C22⋊Q8×C71—22no—
150C22⋊Q8×C71—22no—
151C22⋊Q8×C71C2314yes—
152C22⋊Q8×C71C2314yes—
153C4×Q8×C71—22no—
154C4×Q8×C71C2314yes—
155C4×D4×C71D414yes—
156C4×D4×C71C2314yes—
157#117×C71—22no—
158#117×C71—28no—
159#117×C71C2314yes—
160C2×C4⋊C4×C71—21no—
161C2×C4⋊C4×C71—22no—
162C2×C4⋊C4×C71—21no—
163C2×C4⋊C4×C71—21no—
164C2×C4⋊C4×C71—21no—
165C2×C4⋊C4×C71—21no—
166C2×C4⋊C4×C71—21no—
167C2×C4⋊C4×C71D411yescharacteristic
168C2×C4⋊C4×C71C2314yes—
169C2×C4⋊C4×C71C2311yescharacteristic
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C22⋊C4×C71—21no—
173C2×C22⋊C4×C71—21no—
174C2×C22⋊C4×C71—21no—
175C2×C22⋊C4×C71D411yescharacteristic
176C2×C22⋊C4×C71D411yescharacteristic
177C2×C42×C71—21no—
178C2×C42×C71—21no—
179C2×C42×C71C2311yescharacteristic
180C23×D71—21no—
181#11765864—432no—
182C2×Dic142—24no—
183C2×Dic142—44no—
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—44no—
192C22×Dic71—21no—
193C22×Dic71—21no—
194C22×Dic71—21no—
195C22×Dic71—24no—
196C22×Dic71—24no—
197C22×Dic71—44no—
198C22×Dic71—44no—
199C2×C4×D71—24no—
200C2×C4×D71—44no—
201#11765852—28no—
202#11765849—28no—
203C2×C71⋊C8—22no—
204C2×C71⋊C8—22no—
205C2×C71⋊C8—22no—
206C2×C71⋊C8—28no—
207C2×C71⋊C8#4114yescomplemented
208C2×C71⋊C8C2412yes—
209C2×C71⋊C8C2412yes—
210C2×C71⋊C8C2412yes—
211C2×C71⋊C8C2412yes—
212C4⋊Dic71—21no—
213C4⋊Dic71—21no—
214C4⋊Dic71—21no—
215C4⋊Dic71—24no—
216C4⋊Dic71—24no—
217C4⋊Dic71—24no—
218C4⋊Dic71C2412yes—
219C4⋊Dic71C2412yes—
220C4⋊Dic71C2412yes—
221(C2×D71)⋊C4—24no—
222(C2×D71)⋊C4—24no—
223(C2×D71)⋊C4—24no—
224C24×C71C2×D411yescharacteristic
225C24×C71C2×D411yescharacteristic
226C2×Q8×C71—21no—
227C2×Q8×C71—22no—
228C2×Q8×C71—22no—
229C2×Q8×C71C2412yes—
230C2×D4×C71—24no—
231C2×D4×C71C2×D414yes—
232C22×C4×C71—22no—
233C22×C4×C71—22no—
234C22×C4×C71—22no—
235C22×C4×C71—22no—
236C22×C4×C71—21no—
237C22×C4×C71—21no—
238C22×C4×C71—21no—
239C22×C4×C71—21no—
240C22×C4×C71—24no—
241C22×C4×C71—44no—
242C22×C4×C71C2×D411yescharacteristic
243C22×C4×C71C2×D411yescharacteristic
244C22×C4×C71C2×D411yescharacteristic
245C22×C4×C71C2×D411yescharacteristic
246C22×C4×C71C2×D412yes—
247C22×C4×C71C2×D412yes—
248C22×C4×C71C2412yes—
249C22×C4×C71C2412yes—
250C22×C4×C71C2411yescharacteristic
251C4⋊C4×C71—21no—
252C4⋊C4×C71—21no—
253C4⋊C4×C71—24no—
254C4⋊C4×C71—24no—
255C4⋊C4×C71—24no—
256C4⋊C4×C71—24no—
257C4⋊C4×C71—24no—
258C4⋊C4×C71—24no—
259C4⋊C4×C71—21no—
260C4⋊C4×C71C2×D414yes—
261C4⋊C4×C71C2412yes—
262C4⋊C4×C71C2412yes—
263C4⋊C4×C71C2412yes—
264C22⋊C4×C71—24no—
265C22⋊C4×C71—24no—
266C22⋊C4×C71—24no—
267C22⋊C4×C71C2×D414yes—
268C22⋊C4×C71C2×D414yes—
269C42×C71—24no—
270C42×C71—24no—
271C42×C71C2×D412yes—
272C42×C71C2412yes—
273C23×C71—22no—
274C23×C71—22no—
275C23×C71—22no—
276C23×C71—22no—
277C23×C71—22no—
278C23×C71AGL(1,ℤ/8)14yes—
279C23×C71C22×D412yes—
280C23×C71C22×D412yes—
281C23×C71C22×D411yescharacteristic
282C22×D71—22no—
283C22×D71—42no—
284C22×D71—42no—
285C22×D71—42no—
286Q8×C71—22no—
287Q8×C71—22no—
288Q8×C71—42no—
289D4×C71—28no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71—24no—
295C2×C4×C71—24no—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—22no—
302C2×C4×C71—22no—
303C2×C4×C71—22no—
304C2×C4×C71—42no—
305C2×C4×C71—48no—
306C2×C4×C71—42no—
307C2×C4×C71—42no—
308C2×C4×C71—42no—
309C2×C4×C71C22×D412yes—
310C2×C4×C71C22×D412yes—
311C2×C4×C71C22×D412yes—
312C2×C4×C71C22×D412yes—
313C2×C4×C71C22×D411yescharacteristic
314C2×C4×C71C2×#4112yes—
315C2×C4×C712−1+412yes—
316C2×C4×C71C2511yescharacteristic
317C22⋊D71—48no—
318C22⋊D71—48no—
319C2×Dic71—22no—
320C2×Dic71—22no—
321C2×Dic71—22no—
322C2×Dic71—48no—
323C2×Dic71—42no—
324C2×Dic71—42no—
325C2×Dic71—42no—
326C2×Dic71—48no—
327D284—22no—
328D284—22no—
329D284—42no—
330C4×D71—48no—
331Dic142—48no—
332C71⋊C8—22no—
333C71⋊C8—22no—
334C71⋊C8—22no—
335C71⋊C8C2×#4114yescomplemented
336C22×C71—28no—
337C22×C71—22no—
338C22×C71—22no—
339C22×C71—22no—
340C22×C71—22no—
341C22×C71—22no—
342C22×C71—44no—
343C22×C71#54712yes—
344C22×C71C2×AGL(1,ℤ/8)14yes—
345C22×C71C2×AGL(1,ℤ/8)12yes—
346C22×C71#57812yes—
347C22×C71C23×D411yescharacteristic
348C2×D71—42no—
349C2×D71—42no—
350C2×D71—42no—
351C2×D71—84no—
352C4×C71—22no—
353C4×C71—22no—
354C4×C71—22no—
355C4×C71—22no—
356C4×C71—42no—
357C4×C71—42no—
358C4×C71—42no—
359C4×C71—42no—
360C4×C71#54712yes—
361C4×C71C22×#4111yescharacteristic
362C4×C71C2×2−1+411yescharacteristic
363Dic71—42no—
364Dic71—42no—
365Dic71—42no—
366C2×#3343—711nomaximal, Sylow
367C2×C71—24no—
368C2×C71—42no—
369C2×C71#334314yescomplemented
370C2×C71C2×#54711yescharacteristic
371C2×C71C22×AGL(1,ℤ/8)11yescharacteristic
372C2×C71C2×#57811yescharacteristic
373D71—82no—
374C2×#552D7111yescharacteristic, complemented
375C2×#547—711no—
376#3343—7116no—
377C2×#501—711no—
378C2×#484—711no—
379C2×#482—711no—
380C2×#483—711no—
381C2×#480—711no—
382C2×#477—711no—
383C2×#478—711no—
384C2×#468—711no—
385C2×#465—711no—
386C2×#440—711no—
387C2×#435—711no—
388C2×#428—711no—
389C22×#107—711no—
390C71C2×#334311yescharacteristic, complemented, Sylow
391C22×#41—1421no—
392C22×SD16—711no—
393C22×M16—711no—
394C23×C8—711no—
395#552—24no—
396#552C2×D7118yescomplemented
397#547—718no—
398#547—1424no—
399C2×C4⋊Q8—711no—
400C2×#126—21no—
401C2×#125—21no—
402C2×#125C2×D7111yescharacteristic
403C2×#123—21no—
404C2×#123—1421no—
405C2×#123—1421no—
406C2×C22⋊Q8—1421no—
407C2×C22⋊Q8C2×D7111yescharacteristic
408C2×C22⋊Q8C2×D7111yescharacteristic
409C2×#121—711no—
410C2×#121—711no—
411C2×C4×Q8C2×D7111yescharacteristic
412C2×C4×D4—711no—
413C2×C4×D4C2×D7111yescharacteristic
414C2×#117—21no—
415C2×#117C2×D7111yescharacteristic
416C22×C4⋊C4—711no—
417C22×C4⋊C4—711no—
418C22×C4⋊C4C2×D7111yescharacteristic
419#501—718no—
420#484—718no—
421#483—718no—
422#482—718no—
423#480—718no—
424#478—718no—
425#477—718no—
426#468—718no—
427#465—718no—
428#440—718no—
429#435—718no—
430#428—718no—
431C2×#107—711no—
432C2×#107—711no—
433C2×#107—711no—
434C2×#107—711no—
435C2×#107—718no—
436C2×#107—711no—
437C2×#107—711no—
438C2×#106—711no—
439C2×#106—711no—
440C2×#106—711no—
441C2×C4⋊C8—711no—
442C2×#103—711no—
443C2×#103—711no—
444C2×#103—711no—
445C2×#102—711no—
446C2×#102—711no—
447C2×#102—711no—
448C2×C22⋊C8—711no—
449C2×C22⋊C8—711no—
450C2×#97—711no—
451C2×#41—2848no—
452C2×#41—1428no—
453C22×Q8—1421no—
454C22×Q8C22×D7111yescharacteristic
455C22×D4—711no—
456C22×D4—1421no—
457C22×D4—1421no—
458C22×D4C22⋊D7111yescharacteristic
459C23×C4—21no—
460C23×C4—1421no—
461C23×C4—1421no—
462C23×C4—1421no—
463C23×C4C22×D7111yescharacteristic
464C23×C4C22×D7111yescharacteristic
465C2×SD16—714no—
466C2×SD16—1424no—
467C2×M16—714no—
468C2×M16—1424no—
469C22×C8—711no—
470C22×C8—711no—
471C22×C8—714no—
472C22×C8—711no—
473C22×C8—711no—
474C22×C8—1424no—
475C4⋊Q8—714no—
476C4⋊Q8—1422no—
477#126—28no—
478#125—28no—
479#125—22no—
480#125C22×D7114yes—
481#123—28no—
482#123—1428no—
483#123—1428no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—1428no—
487C22⋊Q8C22×D7114yes—
488C22⋊Q8C22×D7114yes—
489#121—714no—
490#121—714no—
491#121—1422no—
492#121—1422no—
493C4×Q8—22no—
494C4×Q8C22×D7114yes—
495C4×D4—714no—
496C4×D4—1422no—
497C4×D4C22⋊D7114yes—
498C4×D4C22×D7114yes—
499#117—22no—
500#117—28no—
501#117C22×D7114yes—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—711no—
510C2×C4⋊C4—711no—
511C2×C4⋊C4—711no—
512C2×C4⋊C4—714no—
513C2×C4⋊C4—714no—
514C2×C4⋊C4—1421no—
515C2×C4⋊C4—1421no—
516C2×C4⋊C4—1422no—
517C2×C4⋊C4—1422no—
518C2×C4⋊C4—1421no—
519C2×C4⋊C4C22⋊D7111yescharacteristic
520C2×C4⋊C4C22×D7111yescharacteristic
521C2×C4⋊C4C22×D7111yescharacteristic
522C2×C4⋊C4C22×D7114yes—
523C2×C4⋊C4C22×D7111yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—1421no—
528C2×C22⋊C4—1421no—
529C2×C22⋊C4—1421no—
530C2×C22⋊C4C22⋊D7111yescharacteristic
531C2×C22⋊C4C22⋊D7111yescharacteristic
532C2×C42—21no—
533C2×C42—21no—
534C2×C42C22×D7111yescharacteristic
535#107—714no—
536#107—714no—
537#107—714no—
538#107—714no—
539#107—714no—
540#107—714no—
541#106—714no—
542#106—714no—
543#106—714no—
544C4⋊C8—714no—
545#103—714no—
546#103—714no—
547#103—714no—
548#102—714no—
549#102—714no—
550#102—714no—
551C22⋊C8—714no—
552C22⋊C8—714no—
553#97—714no—
554C24—1421no—
555C24C2×C22⋊D7111yescharacteristic
556C24C2×C22⋊D7111yescharacteristic
557#41—28432no—
558C2×Q8—21no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—2844no—
562C2×Q8—1424no—
563C2×Q8C23×D7112yes—
564C2×D4—24no—
565C2×D4—2844no—
566C2×D4—2844no—
567C2×D4—712no—
568C2×D4—1424no—
569C2×D4—1424no—
570C2×D4—1421no—
571C2×D4—1422no—
572C2×D4—1422no—
573C2×D4C2×C22⋊D7114yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—44no—
584C22×C4—2844no—
585C22×C4—2844no—
586C22×C4—2844no—
587C22×C4—1424no—
588C22×C4—1424no—
589C22×C4—1421no—
590C22×C4—1421no—
591C22×C4—1421no—
592C22×C4—1424no—
593C22×C4C2×C22⋊D7112yes—
594C22×C4C2×C22⋊D7112yes—
595C22×C4C2×C22⋊D7111yescharacteristic
596C22×C4C2×C22⋊D7111yescharacteristic
597C22×C4C2×C22⋊D7111yescharacteristic
598C22×C4C2×C22⋊D7111yescharacteristic
599C22×C4C23×D7112yes—
600C22×C4C23×D7112yes—
601C22×C4C23×D7111yescharacteristic
602SD16—1428no—
603M16—1428no—
604C2×C8—714no—
605C2×C8—712no—
606C2×C8—712no—
607C2×C8—712no—
608C2×C8—712no—
609C2×C8—1428no—
610C2×C8—1422no—
611C2×C8—1422no—
612C2×C8—1422no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—21no—
622C4⋊C4—712no—
623C4⋊C4—712no—
624C4⋊C4—712no—
625C4⋊C4—1421no—
626C4⋊C4—1421no—
627C4⋊C4—1421no—
628C4⋊C4—1424no—
629C4⋊C4—1424no—
630C4⋊C4—1424no—
631C4⋊C4C2×C22⋊D7114yes—
632C4⋊C4C23×D7112yes—
633C4⋊C4C23×D7112yes—
634C4⋊C4C23×D7112yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—1424no—
639C22⋊C4—1424no—
640C22⋊C4—1424no—
641C22⋊C4C2×C22⋊D7114yes—
642C22⋊C4C2×C22⋊D7114yes—
643C42—24no—
644C42—24no—
645C42C2×C22⋊D7112yes—
646C42C23×D7112yes—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—2842no—
653C23—2842no—
654C23—2842no—
655C23—1422no—
656C23#1455615314yes—
657C23C22×C22⋊D7112yes—
658C23C22×C22⋊D7112yes—
659C23C22×C22⋊D7111yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—2848no—
664D4—28no—
665D4—2848no—
666D4—2848no—
667D4—2842no—
668D4—1422no—
669D4—1422no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—48no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—2848no—
690C2×C4—2848no—
691C2×C4—2842no—
692C2×C4—2842no—
693C2×C4—2842no—
694C2×C4—2848no—
695C2×C4—1422no—
696C2×C4—1422no—
697C2×C4—1422no—
698C2×C4C22×C22⋊D7112yes—
699C2×C4C22×C22⋊D7112yes—
700C2×C4C22×C22⋊D7112yes—
701C2×C4C22×C22⋊D7112yes—
702C2×C4C22×C22⋊D7111yescharacteristic
703C2×C4#41×D7112yes—
704C2×C4#1455617512yes—
705C2×C4C24×D7111yescharacteristic
706C8—714no—
707C8—1422no—
708C8—1422no—
709C8—1422no—
710C22—22no—
711C22—28no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—2842no—
718C22—2842no—
719C22—2842no—
720C22—5684no—
721C22#1798664812yes—
722C22C2×#1455615314yes—
723C22C2×#1455615312yes—
724C22#1798681412yes—
725C22C23×C22⋊D7111yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—2842no—
735C4—2842no—
736C4—2842no—
737C4#1798664812yes—
738C4C2×#41×D7111yescharacteristic
739C4C2×#1455617511yescharacteristic
740C2—24no—
741C2—42no—
742C2—5682no—
743C2#2260078014yesdirect product factor
744C2C2×#1798664811yescharacteristic
745C2C22×#1455615311yescharacteristic
746C2C2×#1798681411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#552×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986653C2
hypercenterC2×#552D71
hypocenterC71C2×#3343
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #22600780C2direct (N × H)
3. C2×#17986409C2semidirect
4. C2×#17986332C2semidirect
5. C2×#17986323C2semidirect
6. C2×#17986327C2semidirect
7. C2×#17986312C2semidirect
8. C2×#17986294C2semidirect
9. C2×#17986296C2semidirect
10. C2×#17986247C2semidirect
11. C2×#17986230C2semidirect
12. C2×#17986097C2semidirect
13. C2×#17986071C2semidirect
14. C2×#17986042C2semidirect
15. C22×#14556061C2semidirect
16. C2×#552×C71C2semidirect
32. #17986409C22semidirect
33. #17986332C22semidirect
34. #17986327C22semidirect
35. #17986323C22semidirect
36. #17986312C22semidirect
37. #17986296C22semidirect
38. #17986294C22semidirect
39. #17986247C22semidirect
40. #17986230C22semidirect
41. #17986097C22semidirect
42. #17986071C22semidirect
43. #17986042C22semidirect
50. C2×#14556061C22semidirect
65. #552×C71C22semidirect
207. C2×C71⋊C8#41semidirect
335. C71⋊C8C2×#41semidirect
369. C2×C71#3343semidirect
374. C2×#552D71semidirect
390. C71C2×#3343semidirect
396. #552C2×D71semidirect
743. C2#22600780direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866532
#226007802
C2×#179864092
C2×#179863322
C2×#179863232
C2×#179863272
C2×#179863122
C2×#179862942
C2×#179862962
C2×#179862472
C2×#179862302
C2×#179860972
C2×#179860712
C2×#179860422
C22×#145560612
C2×#552×C712
C2×#334371