Finite Group Databasebeta

← C2×#22599063 #32867400

Subgroups — C2×#22599063 #32867400

Order 18176.

2018 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986533C211yesmaximal, characteristic, complemented
2#22599063C2116yesmaximal, direct product factor
3C2×#17986398C211yesmaximal, characteristic, complemented
4C2×#17986381C211yesmaximal, characteristic, complemented
5C2×#17986356C211yesmaximal, characteristic, complemented
6C2×#17986353C211yesmaximal, characteristic, complemented
7C2×#17986255C211yesmaximal, characteristic, complemented
8C2×#17986250C211yesmaximal, characteristic
9C2×#17986247C211yesmaximal, characteristic, complemented
10C2×#17986243C211yesmaximal, characteristic, complemented
11C2×#17986109C211yesmaximal, characteristic, complemented
12C2×#17986104C211yesmaximal, characteristic, complemented
13C2×#17986099C211yesmaximal, characteristic, complemented
14C2×#17986097C211yesmaximal, characteristic, complemented
15C2×C4×#11765849C211yesmaximal, characteristic, complemented
16C2×#529×C71C211yesmaximal, characteristic, complemented
17C22×#11765855C2211yescharacteristic
18C22×#11765853C2211yescharacteristic
19C22×#11765852C2211yescharacteristic
20C22×#11765850C2211yescharacteristic
21C22×#11765849C2211yescharacteristic
22C22×#11765849C2211yescharacteristic
23#17986533—24no—
24#17986533C2218yescomplemented
25C2×#14556122—21no—
26C2×#14556120C2211yescharacteristic
27C2×#14556116C2211yescharacteristic
28C2×#14556111—21no—
29C2×#14556107C2211yescharacteristic
30C2×#14556102C2211yescharacteristic
31C2×C4×Dic142C2211yescharacteristic
32C2×C4×D284C2211yescharacteristic
33C2×C4×C22⋊D71—21no—
34C2×#14556085—21no—
35#17986398C2218yescomplemented
36#17986381C2218yescomplemented
37#17986356C2218yescomplemented
38#17986353C2218yescomplemented
39#17986255C2218yescomplemented
40#17986250C2218yes—
41#17986247C2218yescomplemented
42#17986243C2218yescomplemented
43#17986109C2218yescomplemented
44#17986104C2218yescomplemented
45#17986099C2218yescomplemented
46#17986097C2218yescomplemented
47C2×#14556061C2211yescharacteristic
48C2×#14556061C2211yescharacteristic
49C2×#14556059C2211yescharacteristic
50C2×#14556059C2211yescharacteristic
51C2×#14556052C2211yescharacteristic
52C2×#14556052C2211yescharacteristic
53C2×#14556051C2211yescharacteristic
54C2×#14556051C2211yescharacteristic
55C2×#14556049C2211yescharacteristic
56C2×#14556049C2211yescharacteristic
57C2×#14556048C2211yescharacteristic
58C2×#14556048C2211yescharacteristic
59C4×#11765849C2218yescomplemented
60C2×#14556039C2211yescharacteristic
61C2×#14556039C2211yescharacteristic
62C2×C4×C71⋊C8C2211yescharacteristic
63C2×C4×C71⋊C8C2211yescharacteristic
64#529×C71—24no—
65#529×C71C2218yescomplemented
66C2×#126×C71—21no—
67C2×#125×C71C2211yescharacteristic
68C2×#124×C71C2211yescharacteristic
69C2×#123×C71—21no—
70C2×C22⋊Q8×C71C2211yescharacteristic
71C2×#121×C71C2211yescharacteristic
72C2×C4×Q8×C71C2211yescharacteristic
73C2×C4×D4×C71—21no—
74C2×C4×D4×C71C2211yescharacteristic
75C2×#117×C71—21no—
76C22×C42×C71C2211yescharacteristic
77C22×Dic142C2311yescharacteristic
78C22×D284C2311yescharacteristic
79C22×C22⋊D71—21no—
80C22×C4×D71—21no—
81C2×#11765855—24no—
82C2×#11765855C2314yes—
83C2×#11765853—24no—
84C2×#11765853C2314yes—
85C2×#11765852—24no—
86C2×#11765852C2314yes—
87C2×#11765850—24no—
88C2×#11765850C2314yes—
89C2×#11765849—24no—
90C2×#11765849—24no—
91C2×#11765849C2314yes—
92C2×#11765849C2314yes—
93C22×C71⋊C8C2311yescharacteristic
94C22×C71⋊C8C2311yescharacteristic
95C22×C71⋊C8C2311yescharacteristic
96C22×C71⋊C8C2311yescharacteristic
97#14556122—28no—
98#14556120—22no—
99#14556120C2314yes—
100#14556116—22no—
101#14556116C2314yes—
102#14556111—28no—
103#14556107—22no—
104#14556107C2314yes—
105#14556102—22no—
106#14556102C2314yes—
107C4×Dic142—22no—
108C4×Dic142C2314yes—
109C4×D284—22no—
110C4×D284C2314yes—
111C4×C22⋊D71—28no—
112#14556085—28no—
113C2×C4⋊Dic71C2311yescharacteristic
114C2×C4⋊Dic71C2311yescharacteristic
115C2×Dic71⋊C4—21no—
116C2×Dic71⋊C4—21no—
117C2×Dic71⋊C4—21no—
118C2×Dic71⋊C4—21no—
119C2×C22⋊Dic71—21no—
120C2×(C2×D71)⋊C4—21no—
121C2×(C2×D71)⋊C4—21no—
122C2×(C2×D71)⋊C4—21no—
123C2×(C2×D71)⋊C4—21no—
124C2×C4×Dic71—21no—
125#14556061C2314yes—
126#14556061C2314yes—
127#14556059C2314yes—
128#14556059C2314yes—
129#14556052C2314yes—
130#14556052C2314yes—
131#14556051C2314yes—
132#14556051C2314yes—
133#14556049C2314yes—
134#14556049C2314yes—
135#14556048C2314yes—
136#14556048C2314yes—
137#14556039C2314yes—
138#14556039C2314yes—
139C4×C71⋊C8C2314yes—
140C4×C71⋊C8C2314yes—
141C22×Q8×C71C2311yescharacteristic
142C22×D4×C71—21no—
143C22×D4×C71C2311yescharacteristic
144C23×C4×C71—21no—
145C23×C4×C71D411yescharacteristic
146C23×C4×C71D411yescharacteristic
147C23×C4×C71C2311yescharacteristic
148#126×C71—28no—
149#125×C71—22no—
150#125×C71C2314yes—
151#124×C71—22no—
152#124×C71C2314yes—
153#123×C71—28no—
154C22⋊Q8×C71—22no—
155C22⋊Q8×C71C2314yes—
156#121×C71—22no—
157#121×C71C2314yes—
158C4×Q8×C71—22no—
159C4×Q8×C71C2314yes—
160C4×D4×C71—28no—
161C4×D4×C71—22no—
162C4×D4×C71C2314yes—
163#117×C71—28no—
164C2×C4⋊C4×C71—21no—
165C2×C4⋊C4×C71—21no—
166C2×C4⋊C4×C71—21no—
167C2×C4⋊C4×C71—21no—
168C2×C4⋊C4×C71C2311yescharacteristic
169C2×C4⋊C4×C71C2311yescharacteristic
170C2×C22⋊C4×C71—21no—
171C2×C22⋊C4×C71—21no—
172C2×C22⋊C4×C71—21no—
173C2×C22⋊C4×C71—21no—
174C2×C22⋊C4×C71—21no—
175C2×C42×C71—21no—
176C2×C42×C71D411yescharacteristic
177C2×C42×C71D411yescharacteristic
178C2×C42×C71D414yes—
179C2×C42×C71C2311yescharacteristic
180C2×C42×C71C2311yescharacteristic
181C2×C42×C71C2314yes—
182C23×D71—21no—
183C2×Dic142—22no—
184C2×Dic142—22no—
185C2×Dic142—21no—
186C2×Dic142C2412yes—
187C2×D284—22no—
188C2×D284—22no—
189C2×D284—21no—
190C2×D284C2412yes—
191C2×C22⋊D71—24no—
192C2×C22⋊D71—44no—
193C22×Dic71—21no—
194C22×Dic71—21no—
195C22×Dic71—21no—
196C2×C4×D71—24no—
197C2×C4×D71—44no—
198#11765855—28no—
199#11765853—28no—
200#11765852—28no—
201#11765850—28no—
202#11765849—28no—
203#11765849—28no—
204C2×C71⋊C8—22no—
205C2×C71⋊C8—22no—
206C2×C71⋊C8#4114yes—
207C2×C71⋊C8#4114yes—
208C2×C71⋊C8C2412yes—
209C2×C71⋊C8C2412yes—
210C2×C71⋊C8C2412yes—
211C2×C71⋊C8C2412yes—
212C4⋊Dic71—21no—
213C4⋊Dic71—21no—
214C4⋊Dic71C2412yes—
215C4⋊Dic71C2412yes—
216Dic71⋊C4—24no—
217Dic71⋊C4—24no—
218Dic71⋊C4—24no—
219Dic71⋊C4—24no—
220C22⋊Dic71—24no—
221(C2×D71)⋊C4—24no—
222(C2×D71)⋊C4—24no—
223(C2×D71)⋊C4—24no—
224(C2×D71)⋊C4—24no—
225C4×Dic71—24no—
226C24×C71—21no—
227C24×C71C2×D411yescharacteristic
228C2×Q8×C71—21no—
229C2×Q8×C71—22no—
230C2×Q8×C71—22no—
231C2×Q8×C71C2412yes—
232C2×D4×C71—24no—
233C2×D4×C71—21no—
234C2×D4×C71—22no—
235C2×D4×C71—22no—
236C2×D4×C71—44no—
237C2×D4×C71C2412yes—
238C22×C4×C71—22no—
239C22×C4×C71—22no—
240C22×C4×C71—21no—
241C22×C4×C71—21no—
242C22×C4×C71—21no—
243C22×C4×C71—24no—
244C22×C4×C71—42no—
245C22×C4×C71—42no—
246C22×C4×C71—44no—
247C22×C4×C71C2×D411yescharacteristic
248C22×C4×C71C2×D411yescharacteristic
249C22×C4×C71C2×D411yescharacteristic
250C22×C4×C71C2×D412yes—
251C22×C4×C71C2×D411yescharacteristic
252C22×C4×C71C2×D411yescharacteristic
253C22×C4×C71C2×D414yes—
254C22×C4×C71C2×D414yes—
255C22×C4×C71C2412yes—
256C22×C4×C71C2411yescharacteristic
257C4⋊C4×C71—24no—
258C4⋊C4×C71—24no—
259C4⋊C4×C71—24no—
260C4⋊C4×C71—24no—
261C4⋊C4×C71—21no—
262C4⋊C4×C71—21no—
263C4⋊C4×C71C2412yes—
264C4⋊C4×C71C2412yes—
265C22⋊C4×C71—24no—
266C22⋊C4×C71—24no—
267C22⋊C4×C71—24no—
268C22⋊C4×C71—24no—
269C22⋊C4×C71—24no—
270C42×C71—24no—
271C42×C71C2×D414yes—
272C42×C71C2×D412yes—
273C42×C71C2×D412yes—
274C42×C71C2×D414yes—
275C42×C71C2412yes—
276C42×C71C2412yes—
277C23×C71—22no—
278C23×C71—22no—
279C23×C71—22no—
280C23×C71—22no—
281C23×C71—42no—
282C23×C71—42no—
283C23×C71—42no—
284C23×C71C22×D412yes—
285C23×C71C22×D411yescharacteristic
286C22×D71—22no—
287C22×D71—42no—
288C22×D71—42no—
289C22×D71—42no—
290Q8×C71—22no—
291Q8×C71—22no—
292Q8×C71—42no—
293D4×C71—22no—
294D4×C71—22no—
295D4×C71—48no—
296D4×C71—42no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—22no—
302C2×C4×C71—24no—
303C2×C4×C71—22no—
304C2×C4×C71—22no—
305C2×C4×C71—22no—
306C2×C4×C71—22no—
307C2×C4×C71—22no—
308C2×C4×C71—44no—
309C2×C4×C71—44no—
310C2×C4×C71—48no—
311C2×C4×C71—42no—
312C2×C4×C71—42no—
313C2×C4×C71—42no—
314C2×C4×C71C22×D412yes—
315C2×C4×C71C22×D412yes—
316C2×C4×C71C22×D412yes—
317C2×C4×C71C22×D412yes—
318C2×C4×C71C22×D412yes—
319C2×C4×C71C22×D411yescharacteristic
320C2×C4×C71C2×#4112yes—
321C2×C4×C71C2×#4112yes—
322C2×C4×C71C2511yescharacteristic
323C22⋊D71—48no—
324C2×Dic71—22no—
325C2×Dic71—22no—
326C2×Dic71—22no—
327C2×Dic71—42no—
328C2×Dic71—42no—
329C2×Dic71—42no—
330D284—22no—
331D284—22no—
332D284—42no—
333C4×D71—48no—
334Dic142—22no—
335Dic142—22no—
336Dic142—42no—
337C71⋊C8—22no—
338C71⋊C8—22no—
339C71⋊C8C2×#4114yes—
340C71⋊C8C2×#4114yes—
341C22×C71—22no—
342C22×C71—22no—
343C22×C71—22no—
344C22×C71—44no—
345C22×C71—42no—
346C22×C71—42no—
347C22×C71—42no—
348C22×C71—84no—
349C22×C71#53212yes—
350C22×C71#57512yes—
351C22×C71#57512yes—
352C22×C71C23×D411yescharacteristic
353C2×D71—42no—
354C2×D71—42no—
355C2×D71—42no—
356C2×D71—84no—
357C4×C71—22no—
358C4×C71—22no—
359C4×C71—22no—
360C4×C71—22no—
361C4×C71—22no—
362C4×C71—42no—
363C4×C71—42no—
364C4×C71—42no—
365C4×C71#53212yes—
366C4×C71C22×#4111yescharacteristic
367C4×C71C22×#4111yescharacteristic
368Dic71—42no—
369Dic71—42no—
370Dic71—42no—
371C2×#3183—711nomaximal, Sylow
372C2×C71—42no—
373C2×C71—82no—
374C2×C71#318314yescomplemented
375C2×C71C2×#53211yescharacteristic
376C2×C71C2×#57511yescharacteristic
377C2×C71C2×#57511yescharacteristic
378D71—82no—
379C2×#529—711no—
380C2×#529D7111yescharacteristic, complemented
381#3183—7116no—
382C2×#499—711no—
383C2×#495—711no—
384C2×#488—711no—
385C2×#488—711no—
386C2×#470—711no—
387C2×#469—711no—
388C2×#468—711no—
389C2×#468—711no—
390C2×#442—711no—
391C2×#441—711no—
392C2×#440—711no—
393C2×#440—711no—
394C2×C4×M16—711no—
395C71C2×#318311yescharacteristic, complemented, Sylow
396C22×Q16—711no—
397C22×SD16—711no—
398C22×SD16—711no—
399C22×D8—711no—
400C22×M16—711no—
401C22×M16—711no—
402#529—24no—
403#529—718no—
404#529—1424no—
405#529C2×D7118yescomplemented
406C2×#126—21no—
407C2×#126—1421no—
408C2×#125—711no—
409C2×#125C2×D7111yescharacteristic
410C2×#124—711no—
411C2×#124C2×D7111yescharacteristic
412C2×#123—21no—
413C2×#123—1421no—
414C2×C22⋊Q8—711no—
415C2×C22⋊Q8C2×D7111yescharacteristic
416C2×#121—711no—
417C2×#121C2×D7111yescharacteristic
418C2×C4×Q8—711no—
419C2×C4×Q8C2×D7111yescharacteristic
420C2×C4×D4—21no—
421C2×C4×D4—711no—
422C2×C4×D4—1421no—
423C2×C4×D4C2×D7111yescharacteristic
424C2×#117—21no—
425C2×#117—1421no—
426C22×C42C2×D7111yescharacteristic
427#499—718no—
428#495—718no—
429#488—718no—
430#488—718no—
431#470—718no—
432#469—718no—
433#468—718no—
434#468—718no—
435#442—718no—
436#441—718no—
437#440—718no—
438#440—718no—
439C2×#107—711no—
440C2×#107—711no—
441C2×#106—711no—
442C2×#106—711no—
443C2×#103—711no—
444C2×#103—711no—
445C2×#103—711no—
446C2×#103—711no—
447C2×#102—711no—
448C2×#102—711no—
449C2×#102—711no—
450C2×#102—711no—
451C4×M16—718no—
452C2×#97—711no—
453C2×#97—711no—
454C2×C4×C8—711no—
455C2×C4×C8—711no—
456C22×Q8—711no—
457C22×Q8C22×D7111yescharacteristic
458C22×D4—21no—
459C22×D4—711no—
460C22×D4—1421no—
461C22×D4C22×D7111yescharacteristic
462C23×C4—21no—
463C23×C4—1421no—
464C23×C4C22⋊D7111yescharacteristic
465C23×C4C22⋊D7111yescharacteristic
466C23×C4C22×D7111yescharacteristic
467C2×Q16—714no—
468C2×Q16—1424no—
469C2×SD16—714no—
470C2×SD16—714no—
471C2×SD16—1424no—
472C2×SD16—1424no—
473C2×D8—714no—
474C2×D8—1424no—
475C2×M16—714no—
476C2×M16—714no—
477C2×M16—1424no—
478C2×M16—1424no—
479C22×C8—711no—
480C22×C8—711no—
481C22×C8—711no—
482C22×C8—711no—
483#126—28no—
484#126—1428no—
485#125—22no—
486#125—714no—
487#125—1422no—
488#125C22×D7114yes—
489#124—22no—
490#124—714no—
491#124—1422no—
492#124C22×D7114yes—
493#123—28no—
494#123—1428no—
495C22⋊Q8—22no—
496C22⋊Q8—714no—
497C22⋊Q8—1422no—
498C22⋊Q8C22×D7114yes—
499#121—22no—
500#121—714no—
501#121—1422no—
502#121C22×D7114yes—
503C4×Q8—22no—
504C4×Q8—714no—
505C4×Q8—1422no—
506C4×Q8C22×D7114yes—
507C4×D4—28no—
508C4×D4—22no—
509C4×D4—714no—
510C4×D4—1428no—
511C4×D4—1422no—
512C4×D4C22×D7114yes—
513#117—28no—
514#117—1428no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—711no—
520C2×C4⋊C4—711no—
521C2×C4⋊C4—1421no—
522C2×C4⋊C4—1421no—
523C2×C4⋊C4—1421no—
524C2×C4⋊C4—1421no—
525C2×C4⋊C4C22×D7111yescharacteristic
526C2×C4⋊C4C22×D7111yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—1421no—
533C2×C22⋊C4—1421no—
534C2×C22⋊C4—1421no—
535C2×C22⋊C4—1421no—
536C2×C22⋊C4—1421no—
537C2×C42—21no—
538C2×C42—1421no—
539C2×C42C22⋊D7111yescharacteristic
540C2×C42C22⋊D7111yescharacteristic
541C2×C42C22⋊D7114yes—
542C2×C42C22×D7111yescharacteristic
543C2×C42C22×D7111yescharacteristic
544C2×C42C22×D7114yes—
545#107—714no—
546#107—714no—
547#106—714no—
548#106—714no—
549#103—714no—
550#103—714no—
551#103—714no—
552#103—714no—
553#102—714no—
554#102—714no—
555#102—714no—
556#102—714no—
557#97—714no—
558#97—714no—
559C4×C8—714no—
560C4×C8—714no—
561C24—21no—
562C24—1421no—
563C24C2×C22⋊D7111yescharacteristic
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—712no—
568C2×Q8—1422no—
569C2×Q8—1422no—
570C2×Q8—1421no—
571C2×Q8C23×D7112yes—
572C2×D4—24no—
573C2×D4—21no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—44no—
577C2×D4—2844no—
578C2×D4—712no—
579C2×D4—1424no—
580C2×D4—1421no—
581C2×D4—1422no—
582C2×D4—1422no—
583C2×D4C23×D7112yes—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—24no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—44no—
593C22×C4—2844no—
594C22×C4—1421no—
595C22×C4—1421no—
596C22×C4—1421no—
597C22×C4—1424no—
598C22×C4C2×C22⋊D7112yes—
599C22×C4C2×C22⋊D7111yescharacteristic
600C22×C4C2×C22⋊D7111yescharacteristic
601C22×C4C2×C22⋊D7111yescharacteristic
602C22×C4C2×C22⋊D7111yescharacteristic
603C22×C4C2×C22⋊D7111yescharacteristic
604C22×C4C2×C22⋊D7114yes—
605C22×C4C2×C22⋊D7114yes—
606C22×C4C23×D7112yes—
607C22×C4C23×D7111yescharacteristic
608Q16—1428no—
609SD16—1428no—
610SD16—1428no—
611D8—1428no—
612M16—1428no—
613M16—1428no—
614C2×C8—714no—
615C2×C8—714no—
616C2×C8—712no—
617C2×C8—712no—
618C2×C8—712no—
619C2×C8—712no—
620C2×C8—1422no—
621C2×C8—1422no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—712no—
629C4⋊C4—712no—
630C4⋊C4—1424no—
631C4⋊C4—1424no—
632C4⋊C4—1424no—
633C4⋊C4—1424no—
634C4⋊C4—1421no—
635C4⋊C4—1421no—
636C4⋊C4C23×D7112yes—
637C4⋊C4C23×D7112yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—1424no—
644C22⋊C4—1424no—
645C22⋊C4—1424no—
646C22⋊C4—1424no—
647C22⋊C4—1424no—
648C42—24no—
649C42—1424no—
650C42C2×C22⋊D7114yes—
651C42C2×C22⋊D7114yes—
652C42C2×C22⋊D7112yes—
653C42C2×C22⋊D7112yes—
654C42C23×D7112yes—
655C42C23×D7112yes—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—2842no—
664C23—2842no—
665C23—2842no—
666C23—1422no—
667C23C22×C22⋊D7112yes—
668C23C22×C22⋊D7111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—2842no—
673Q8—1422no—
674Q8—1422no—
675D4—22no—
676D4—22no—
677D4—48no—
678D4—42no—
679D4—2848no—
680D4—2842no—
681D4—1422no—
682D4—1422no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—48no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—2848no—
701C2×C4—2842no—
702C2×C4—2842no—
703C2×C4—2842no—
704C2×C4—1422no—
705C2×C4—1422no—
706C2×C4—1422no—
707C2×C4C22×C22⋊D7112yes—
708C2×C4C22×C22⋊D7112yes—
709C2×C4C22×C22⋊D7112yes—
710C2×C4C22×C22⋊D7112yes—
711C2×C4C22×C22⋊D7112yes—
712C2×C4C22×C22⋊D7111yescharacteristic
713C2×C4#41×D7112yes—
714C2×C4#41×D7112yes—
715C2×C4C24×D7111yescharacteristic
716C8—714no—
717C8—714no—
718C8—1422no—
719C8—1422no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—84no—
728C22—2842no—
729C22—2842no—
730C22—2842no—
731C22—5684no—
732C22#1798654512yes—
733C22#1798679712yes—
734C22#1798679712yes—
735C22C23×C22⋊D7111yescharacteristic
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—22no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—2842no—
745C4—2842no—
746C4—2842no—
747C4#1798654512yes—
748C4C2×#41×D7111yescharacteristic
749C4C2×#41×D7111yescharacteristic
750C2—42no—
751C2—82no—
752C2—5682no—
753C2#2259906314yesdirect product factor
754C2C2×#1798654511yescharacteristic
755C2C2×#1798679711yescharacteristic
756C2C2×#1798679711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#529×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986250C2
hypercenterC2×#529D71
hypocenterC71C2×#3183
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#17986533C2semidirect
2. #22599063C2direct (N × H)
3. C2×#17986398C2semidirect
4. C2×#17986381C2semidirect
5. C2×#17986356C2semidirect
6. C2×#17986353C2semidirect
7. C2×#17986255C2semidirect
9. C2×#17986247C2semidirect
10. C2×#17986243C2semidirect
11. C2×#17986109C2semidirect
12. C2×#17986104C2semidirect
13. C2×#17986099C2semidirect
14. C2×#17986097C2semidirect
15. C2×C4×#11765849C2semidirect
16. C2×#529×C71C2semidirect
24. #17986533C22semidirect
35. #17986398C22semidirect
36. #17986381C22semidirect
37. #17986356C22semidirect
38. #17986353C22semidirect
39. #17986255C22semidirect
41. #17986247C22semidirect
42. #17986243C22semidirect
43. #17986109C22semidirect
44. #17986104C22semidirect
45. #17986099C22semidirect
46. #17986097C22semidirect
59. C4×#11765849C22semidirect
65. #529×C71C22semidirect
374. C2×C71#3183semidirect
380. C2×#529D71semidirect
395. C71C2×#3183semidirect
405. #529C2×D71semidirect
753. C2#22599063direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179865332
#225990632
C2×#179863982
C2×#179863812
C2×#179863562
C2×#179863532
C2×#179862552
C2×#179862502
C2×#179862472
C2×#179862432
C2×#179861092
C2×#179861042
C2×#179860992
C2×#179860972
C2×C4×#117658492
C2×#529×C712
C2×#318371