Finite Group Databasebeta

← C2×#22600885 #32876095

Subgroups — C2×#22600885 #32876095

Order 18176.

1898 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
2#22600885C2116yesmaximal, direct product factor
3C2×#17986405C211yesmaximal, characteristic, complemented
4C2×#17986337C211yesmaximal, characteristic, complemented
5C2×#17986323C211yesmaximal, characteristic, complemented
6C2×#17986323C211yesmaximal, characteristic, complemented
7C2×#17986327C211yesmaximal, characteristic, complemented
8C2×#17986306C211yesmaximal, characteristic, complemented
9C2×#17986286C211yesmaximal, characteristic, complemented
10C2×#17986247C211yesmaximal, characteristic, complemented
11C2×#17986230C211yesmaximal, characteristic, complemented
12C2×#17986097C211yesmaximal, characteristic, complemented
13C2×#17986071C211yesmaximal, characteristic, complemented
14C2×#17986042C211yesmaximal, characteristic, complemented
15C2×#17986035C211yesmaximal, characteristic, complemented
16C2×#556×C71C211yesmaximal, characteristic, complemented
17C22×#11765852C2211yescharacteristic
18C22×#11765849C2211yescharacteristic
19C23×C71⋊C8C2211yescharacteristic
20#17986695—24no—
21#17986695C2218yes—
22C2×#14556123—21no—
23C2×#14556120C2211yescharacteristic
24C2×#14556110—21no—
25C2×#14556102C2211yescharacteristic
26C2×#14556102C2211yescharacteristic
27C2×#14556100—21no—
28C2×C4×D284C2211yescharacteristic
29C2×(C22⋊D71)⋊C4—21no—
30C2×#14556087C2211yescharacteristic
31C22×C4⋊Dic71C2211yescharacteristic
32#17986405C2218yescomplemented
33#17986337C2218yescomplemented
34#17986327C2218yescomplemented
35#17986323C2218yescomplemented
36#17986323C2218yescomplemented
37#17986306C2218yescomplemented
38#17986286C2218yescomplemented
39#17986247C2218yescomplemented
40#17986230C2218yescomplemented
41#17986097C2218yescomplemented
42#17986071C2218yescomplemented
43#17986042C2218yescomplemented
44#17986035C2218yescomplemented
45C2×#14556061C2211yescharacteristic
46C2×#14556061C2211yescharacteristic
47C2×#14556061C2211yescharacteristic
48C2×#14556061C2211yescharacteristic
49C2×#14556059C2211yescharacteristic
50C2×#14556059C2211yescharacteristic
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#556×C71—24no—
65#556×C71C2218yescomplemented
66C2×C4⋊Q8×C71C2211yescharacteristic
67C2×#126×C71—21no—
68C2×#126×C71—21no—
69C2×#124×C71—21no—
70C2×C22⋊Q8×C71C2211yescharacteristic
71C2×C22⋊Q8×C71C2211yescharacteristic
72C2×C4×Q8×C71—21no—
73C2×C4×Q8×C71C2211yescharacteristic
74C2×C4×D4×C71C2211yescharacteristic
75C2×#117×C71C2211yescharacteristic
76C2×#117×C71C2211yescharacteristic
77C22×D284C2311yescharacteristic
78C22×C22⋊D71—21no—
79C22×C22⋊D71—21no—
80C23×Dic71—21no—
81C22×C4×D71—21no—
82C2×#11765852—24no—
83C2×#11765852C2314yes—
84C2×#11765849—24no—
85C2×#11765849C2314yes—
86C22×C71⋊C8—24no—
87C22×C71⋊C8C2314yes—
88C22×C71⋊C8C2311yescharacteristic
89C22×C71⋊C8C2311yescharacteristic
90C22×C71⋊C8C2311yescharacteristic
91C22×C71⋊C8C2311yescharacteristic
92#14556123—28no—
93#14556120—22no—
94#14556120C2314yes—
95#14556110—28no—
96#14556102—22no—
97#14556102—22no—
98#14556102C2314yes—
99#14556102C2314yes—
100#14556100—28no—
101C4×D284—22no—
102C4×D284C2314yes—
103(C22⋊D71)⋊C4—28no—
104#14556087—22no—
105#14556087C2314yes—
106C2×C4⋊Dic71—22no—
107C2×C4⋊Dic71—21no—
108C2×C4⋊Dic71C2314yes—
109C2×C4⋊Dic71C2311yescharacteristic
110C2×C4⋊Dic71C2311yescharacteristic
111C2×C4⋊Dic71C2311yescharacteristic
112C2×Dic71⋊C4—21no—
113C2×Dic71⋊C4—21no—
114C2×C22⋊Dic71—21no—
115C2×(C2×D71)⋊C4—21no—
116C2×(C2×D71)⋊C4—21no—
117C2×(C2×D71)⋊C4—21no—
118C2×C4×Dic71—21no—
119#14556061C2314yes—
120#14556061C2314yes—
121#14556061C2314yes—
122#14556061C2314yes—
123#14556059C2314yes—
124#14556059C2314yes—
125#14556059C2314yes—
126#14556059C2314yes—
127#14556059C2314yes—
128C4⋊(C71⋊C8)C2314yes—
129#14556052C2314yes—
130#14556052C2314yes—
131#14556052C2314yes—
132#14556048C2314yes—
133#14556048C2314yes—
134#14556048C2314yes—
135C22⋊(C71⋊C8)C2314yes—
136C22⋊(C71⋊C8)C2314yes—
137#14556039C2314yes—
138C22×Q8×C71—21no—
139C22×Q8×C71C2311yescharacteristic
140C22×D4×C71D411yescharacteristic
141C23×C4×C71C2311yescharacteristic
142C23×C4×C71C2311yescharacteristic
143C4⋊Q8×C71—22no—
144C4⋊Q8×C71C2314yes—
145#126×C71—28no—
146#126×C71—28no—
147#124×C71—28no—
148C22⋊Q8×C71—22no—
149C22⋊Q8×C71—22no—
150C22⋊Q8×C71C2314yes—
151C22⋊Q8×C71C2314yes—
152C4×Q8×C71—28no—
153C4×Q8×C71—22no—
154C4×Q8×C71C2314yes—
155C4×D4×C71D414yes—
156C4×D4×C71C2314yes—
157#117×C71—22no—
158#117×C71—22no—
159#117×C71C2314yes—
160#117×C71C2314yes—
161C2×C4⋊C4×C71—21no—
162C2×C4⋊C4×C71—21no—
163C2×C4⋊C4×C71—21no—
164C2×C4⋊C4×C71—21no—
165C2×C4⋊C4×C71D411yescharacteristic
166C2×C4⋊C4×C71C2311yescharacteristic
167C2×C4⋊C4×C71C2311yescharacteristic
168C2×C4⋊C4×C71C2311yescharacteristic
169C2×C22⋊C4×C71—21no—
170C2×C22⋊C4×C71—21no—
171C2×C22⋊C4×C71—21no—
172C2×C22⋊C4×C71—21no—
173C2×C22⋊C4×C71D411yescharacteristic
174C2×C22⋊C4×C71D411yescharacteristic
175C2×C42×C71—21no—
176C2×C42×C71—21no—
177C2×C42×C71—21no—
178C2×C42×C71C2311yescharacteristic
179C23×D71—21no—
180C2×D284—22no—
181C2×D284—22no—
182C2×D284—21no—
183C2×D284C2412yes—
184C2×C22⋊D71—24no—
185C2×C22⋊D71—24no—
186C2×C22⋊D71—44no—
187C2×C22⋊D71—82no—
188C22×Dic71—21no—
189C22×Dic71—21no—
190C22×Dic71—21no—
191C22×Dic71—24no—
192C22×Dic71—82no—
193C2×C4×D71—24no—
194C2×C4×D71—82no—
195#11765852—28no—
196#11765849—28no—
197C2×C71⋊C8—22no—
198C2×C71⋊C8—22no—
199C2×C71⋊C8—22no—
200C2×C71⋊C8—28no—
201C2×C71⋊C8#4114yes—
202C2×C71⋊C8C2412yes—
203C2×C71⋊C8C2412yes—
204C2×C71⋊C8C2412yes—
205C2×C71⋊C8C2412yes—
206C4⋊Dic71—21no—
207C4⋊Dic71—21no—
208C4⋊Dic71—24no—
209C4⋊Dic71—21no—
210C4⋊Dic71C2412yes—
211C4⋊Dic71C2412yes—
212C4⋊Dic71C2412yes—
213Dic71⋊C4—24no—
214Dic71⋊C4—24no—
215C22⋊Dic71—24no—
216(C2×D71)⋊C4—24no—
217(C2×D71)⋊C4—24no—
218(C2×D71)⋊C4—24no—
219C4×Dic71—24no—
220C24×C71C2×D411yescharacteristic
221C24×C71C2×D411yescharacteristic
222C2×Q8×C71—21no—
223C2×Q8×C71—24no—
224C2×Q8×C71—22no—
225C2×Q8×C71—22no—
226C2×Q8×C71—44no—
227C2×Q8×C71C2412yes—
228C2×D4×C71—42no—
229C2×D4×C71C2×D414yes—
230C22×C4×C71—22no—
231C22×C4×C71—22no—
232C22×C4×C71—22no—
233C22×C4×C71—22no—
234C22×C4×C71—21no—
235C22×C4×C71—21no—
236C22×C4×C71—21no—
237C22×C4×C71—21no—
238C22×C4×C71C2×D411yescharacteristic
239C22×C4×C71C2×D411yescharacteristic
240C22×C4×C71C2×D411yescharacteristic
241C22×C4×C71C2×D411yescharacteristic
242C22×C4×C71C2×D412yes—
243C22×C4×C71C2×D412yes—
244C22×C4×C71C2412yes—
245C22×C4×C71C2412yes—
246C22×C4×C71C2411yescharacteristic
247C4⋊C4×C71—24no—
248C4⋊C4×C71—24no—
249C4⋊C4×C71—24no—
250C4⋊C4×C71—24no—
251C4⋊C4×C71—21no—
252C4⋊C4×C71—21no—
253C4⋊C4×C71—21no—
254C4⋊C4×C71C2×D414yes—
255C4⋊C4×C71C2412yes—
256C4⋊C4×C71C2412yes—
257C4⋊C4×C71C2412yes—
258C22⋊C4×C71—24no—
259C22⋊C4×C71—24no—
260C22⋊C4×C71—24no—
261C22⋊C4×C71—24no—
262C22⋊C4×C71C2×D414yes—
263C22⋊C4×C71C2×D414yes—
264C42×C71—24no—
265C42×C71—24no—
266C42×C71—24no—
267C42×C71C2×D412yes—
268C42×C71C2412yes—
269C23×C71—22no—
270C23×C71—22no—
271C23×C71—22no—
272C23×C71—22no—
273C23×C71—22no—
274C23×C71—22no—
275C23×C71C22×D412yes—
276C23×C71C22×D412yes—
277C23×C71C22×D411yescharacteristic
278C22×D71—22no—
279C22×D71—42no—
280C22×D71—42no—
281C22×D71—42no—
282Q8×C71—22no—
283Q8×C71—22no—
284Q8×C71—48no—
285Q8×C71—42no—
286D4×C71—44no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—24no—
292C2×C4×C71—24no—
293C2×C4×C71—22no—
294C2×C4×C71—22no—
295C2×C4×C71—22no—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—42no—
302C2×C4×C71—42no—
303C2×C4×C71—42no—
304C2×C4×C71—42no—
305C2×C4×C71C22×D412yes—
306C2×C4×C71C22×D412yes—
307C2×C4×C71C22×D412yes—
308C2×C4×C71C22×D412yes—
309C2×C4×C71C22×D411yescharacteristic
310C2×C4×C71C2×#4112yes—
311C2×C4×C712−1+412yes—
312C2×C4×C71C2511yescharacteristic
313C22⋊D71—48no—
314C22⋊D71—84no—
315C2×Dic71—22no—
316C2×Dic71—22no—
317C2×Dic71—22no—
318C2×Dic71—42no—
319C2×Dic71—42no—
320C2×Dic71—42no—
321C2×Dic71—84no—
322D284—22no—
323D284—22no—
324D284—42no—
325C4×D71—84no—
326C71⋊C8—22no—
327C71⋊C8—22no—
328C71⋊C8—22no—
329C71⋊C8C2×#4114yes—
330C22×C71—22no—
331C22×C71—22no—
332C22×C71—22no—
333C22×C71—22no—
334C22×C71—22no—
335C22×C71—22no—
336C22×C71—44no—
337C22×C71—44no—
338C22×C71#54712yes—
339C22×C71#57512yes—
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—42no—
351C4×C71—42no—
352C4×C71—42no—
353C4×C71—42no—
354C4×C71#54712yes—
355C4×C71C22×#4111yescharacteristic
356C4×C71C2×2−1+411yescharacteristic
357Dic71—42no—
358Dic71—42no—
359Dic71—42no—
360C2×#3350—711nomaximal, Sylow
361C2×C71—42no—
362C2×C71—42no—
363C2×C71#335014yescomplemented
364C2×C71C2×#54711yescharacteristic
365C2×C71C2×#57511yescharacteristic
366C2×C71C2×#57711yescharacteristic
367D71—82no—
368C2×#556D7111yescharacteristic, complemented
369C2×#553—711no—
370#3350—7116no—
371C2×#501—711no—
372C2×#485—711no—
373C2×#482—711no—
374C2×#482—711no—
375C2×#483—711no—
376C2×#479—711no—
377C2×#476—711no—
378C2×#468—711no—
379C2×#465—711no—
380C2×#440—711no—
381C2×#435—711no—
382C2×#428—711no—
383C2×#427—711no—
384C71C2×#335011yescharacteristic, complemented, Sylow
385C22×SD16—711no—
386C22×M16—711no—
387C23×C8—711no—
388#556—24no—
389#556C2×D7118yescomplemented
390#553—718no—
391#553—1424no—
392C2×C4⋊Q8C2×D7111yescharacteristic
393C2×#126—21no—
394C2×#126—21no—
395C2×#126—1421no—
396C2×#125—711no—
397C2×#124—21no—
398C2×#123—1421no—
399C2×C22⋊Q8C2×D7111yescharacteristic
400C2×C22⋊Q8C2×D7111yescharacteristic
401C2×#121—711no—
402C2×#121—711no—
403C2×#121—1421no—
404C2×C4×Q8—21no—
405C2×C4×Q8C2×D7111yescharacteristic
406C2×C4×D4—711no—
407C2×C4×D4—1421no—
408C2×C4×D4C2×D7111yescharacteristic
409C2×#117—711no—
410C2×#117C2×D7111yescharacteristic
411C2×#117C2×D7111yescharacteristic
412C22×C4⋊C4—711no—
413#501—718no—
414#485—718no—
415#483—718no—
416#482—718no—
417#482—718no—
418#479—718no—
419#476—718no—
420#468—718no—
421#465—718no—
422#440—718no—
423#435—718no—
424#428—718no—
425#427—718no—
426C2×#107—711no—
427C2×#107—711no—
428C2×#107—711no—
429C2×#107—711no—
430C2×#106—711no—
431C2×#106—711no—
432C2×#106—711no—
433C2×#106—711no—
434C2×#106—711no—
435C2×C4⋊C8—711no—
436C2×#103—711no—
437C2×#103—711no—
438C2×#103—711no—
439C2×#102—711no—
440C2×#102—711no—
441C2×#102—711no—
442C2×C22⋊C8—711no—
443C2×C22⋊C8—711no—
444C2×#97—711no—
445C22×Q8—21no—
446C22×Q8C22×D7111yescharacteristic
447C22×D4—711no—
448C22×D4—1421no—
449C22×D4—1421no—
450C22×D4C22⋊D7111yescharacteristic
451C23×C4—1421no—
452C23×C4—1421no—
453C23×C4C22×D7111yescharacteristic
454C23×C4C22×D7111yescharacteristic
455C2×SD16—714no—
456C2×SD16—1424no—
457C2×M16—714no—
458C2×M16—1424no—
459C22×C8—711no—
460C22×C8—711no—
461C22×C8—714no—
462C22×C8—711no—
463C22×C8—711no—
464C22×C8—1424no—
465C4⋊Q8—22no—
466C4⋊Q8C22×D7114yes—
467#126—28no—
468#126—28no—
469#126—1428no—
470#125—714no—
471#125—1422no—
472#124—28no—
473#123—1428no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476C22⋊Q8C22×D7114yes—
477C22⋊Q8C22×D7114yes—
478#121—714no—
479#121—714no—
480#121—1428no—
481#121—1422no—
482#121—1422no—
483C4×Q8—28no—
484C4×Q8—22no—
485C4×Q8C22×D7114yes—
486C4×D4—714no—
487C4×D4—1428no—
488C4×D4—1422no—
489C4×D4C22⋊D7114yes—
490C4×D4C22×D7114yes—
491#117—22no—
492#117—22no—
493#117—714no—
494#117—1422no—
495#117C22×D7114yes—
496#117C22×D7114yes—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—711no—
502C2×C4⋊C4—711no—
503C2×C4⋊C4—714no—
504C2×C4⋊C4—711no—
505C2×C4⋊C4—1421no—
506C2×C4⋊C4—1422no—
507C2×C4⋊C4—1421no—
508C2×C4⋊C4—1421no—
509C2×C4⋊C4C22⋊D7111yescharacteristic
510C2×C4⋊C4C22×D7111yescharacteristic
511C2×C4⋊C4C22×D7111yescharacteristic
512C2×C4⋊C4C22×D7111yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—1421no—
518C2×C22⋊C4—1421no—
519C2×C22⋊C4—1421no—
520C2×C22⋊C4—1421no—
521C2×C22⋊C4C22⋊D7111yescharacteristic
522C2×C22⋊C4C22⋊D7111yescharacteristic
523C2×C42—21no—
524C2×C42—21no—
525C2×C42—21no—
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⋊C8—714no—
538#103—714no—
539#103—714no—
540#103—714no—
541#102—714no—
542#102—714no—
543#102—714no—
544C22⋊C8—714no—
545C22⋊C8—714no—
546#97—714no—
547C24—1421no—
548C24C2×C22⋊D7111yescharacteristic
549C24C2×C22⋊D7111yescharacteristic
550C2×Q8—21no—
551C2×Q8—24no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—44no—
555C2×Q8C23×D7112yes—
556C2×D4—42no—
557C2×D4—2844no—
558C2×D4—5682no—
559C2×D4—712no—
560C2×D4—1424no—
561C2×D4—1424no—
562C2×D4—1421no—
563C2×D4—1422no—
564C2×D4—1422no—
565C2×D4C2×C22⋊D7114yes—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—5682no—
575C22×C4—5682no—
576C22×C4—1421no—
577C22×C4—1421no—
578C22×C4—1421no—
579C22×C4—1424no—
580C22×C4—1424no—
581C22×C4C2×C22⋊D7112yes—
582C22×C4C2×C22⋊D7112yes—
583C22×C4C2×C22⋊D7111yescharacteristic
584C22×C4C2×C22⋊D7111yescharacteristic
585C22×C4C2×C22⋊D7111yescharacteristic
586C22×C4C2×C22⋊D7111yescharacteristic
587C22×C4C23×D7112yes—
588C22×C4C23×D7112yes—
589C22×C4C23×D7111yescharacteristic
590SD16—1428no—
591M16—1428no—
592C2×C8—714no—
593C2×C8—712no—
594C2×C8—712no—
595C2×C8—712no—
596C2×C8—712no—
597C2×C8—1428no—
598C2×C8—1422no—
599C2×C8—1422no—
600C2×C8—1422no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—712no—
609C4⋊C4—712no—
610C4⋊C4—712no—
611C4⋊C4—1424no—
612C4⋊C4—1424no—
613C4⋊C4—1421no—
614C4⋊C4—1421no—
615C4⋊C4—1424no—
616C4⋊C4—1421no—
617C4⋊C4C2×C22⋊D7114yes—
618C4⋊C4C23×D7112yes—
619C4⋊C4C23×D7112yes—
620C4⋊C4C23×D7112yes—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—1424no—
626C22⋊C4—1424no—
627C22⋊C4—1424no—
628C22⋊C4—1424no—
629C22⋊C4C2×C22⋊D7114yes—
630C22⋊C4C2×C22⋊D7114yes—
631C42—24no—
632C42—24no—
633C42—24no—
634C42—1424no—
635C42C2×C22⋊D7112yes—
636C42C23×D7112yes—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—2842no—
644C23—2842no—
645C23—2842no—
646C23—1422no—
647C23C22×C22⋊D7112yes—
648C23C22×C22⋊D7112yes—
649C23C22×C22⋊D7111yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—48no—
653Q8—42no—
654D4—44no—
655D4—2848no—
656D4—2842no—
657D4—5684no—
658D4—1422no—
659D4—1422no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—2842no—
679C2×C4—2842no—
680C2×C4—2842no—
681C2×C4—5684no—
682C2×C4—5684no—
683C2×C4—1422no—
684C2×C4—1422no—
685C2×C4—1422no—
686C2×C4C22×C22⋊D7112yes—
687C2×C4C22×C22⋊D7112yes—
688C2×C4C22×C22⋊D7112yes—
689C2×C4C22×C22⋊D7112yes—
690C2×C4C22×C22⋊D7111yescharacteristic
691C2×C4#41×D7112yes—
692C2×C4#1455617512yes—
693C2×C4C24×D7111yescharacteristic
694C8—714no—
695C8—1422no—
696C8—1422no—
697C8—1422no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—44no—
706C22—2842no—
707C22—2842no—
708C22—2842no—
709C22—5684no—
710C22#1798664812yes—
711C22#1798679712yes—
712C22#1798680712yes—
713C22C23×C22⋊D7111yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—2842no—
723C4—2842no—
724C4—2842no—
725C4#1798664812yes—
726C4C2×#41×D7111yescharacteristic
727C4C2×#1455617511yescharacteristic
728C2—42no—
729C2—42no—
730C2—5682no—
731C2#2260088514yesdirect product factor
732C2C2×#1798664811yescharacteristic
733C2C2×#1798679711yescharacteristic
734C2C2×#1798680711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#556×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986695C2
hypercenterC2×#556D71
hypocenterC71C2×#3350
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
2. #22600885C2direct (N × H)
3. C2×#17986405C2semidirect
4. C2×#17986337C2semidirect
5. C2×#17986323C2semidirect
6. C2×#17986323C2semidirect
7. C2×#17986327C2semidirect
8. C2×#17986306C2semidirect
9. C2×#17986286C2semidirect
10. C2×#17986247C2semidirect
11. C2×#17986230C2semidirect
12. C2×#17986097C2semidirect
13. C2×#17986071C2semidirect
14. C2×#17986042C2semidirect
15. C2×#17986035C2semidirect
16. C2×#556×C71C2semidirect
32. #17986405C22semidirect
33. #17986337C22semidirect
34. #17986327C22semidirect
35. #17986323C22semidirect
36. #17986323C22semidirect
37. #17986306C22semidirect
38. #17986286C22semidirect
39. #17986247C22semidirect
40. #17986230C22semidirect
41. #17986097C22semidirect
42. #17986071C22semidirect
43. #17986042C22semidirect
44. #17986035C22semidirect
65. #556×C71C22semidirect
363. C2×C71#3350semidirect
368. C2×#556D71semidirect
384. C71C2×#3350semidirect
389. #556C2×D71semidirect
731. C2#22600885direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866952
#226008852
C2×#179864052
C2×#179863372
C2×#179863232
C2×#179863272
C2×#179863062
C2×#179862862
C2×#179862472
C2×#179862302
C2×#179860972
C2×#179860712
C2×#179860422
C2×#179860352
C2×#556×C712
C2×#335071