Finite Group Databasebeta

← C2×#22598533 #32865693

Subgroups — C2×#22598533 #32865693

Order 18176.

2198 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986479C211yesmaximal, characteristic, complemented
2#22598533C2116yesmaximal, direct product factor
3C2×#17986315C211yesmaximal, characteristic, complemented
4C2×#17986310C211yesmaximal, characteristic, complemented
5C2×#17986303C211yesmaximal, characteristic, complemented
6C2×#17986296C211yesmaximal, characteristic, complemented
7C2×#17986196C211yesmaximal, characteristic, complemented
8C2×#17986191C211yesmaximal, characteristic, complemented
9C2×#17986142C211yesmaximal, characteristic, complemented
10C2×#17986142C211yesmaximal, characteristic, complemented
11C2×#17986109C211yesmaximal, characteristic, complemented
12C2×#17986099C211yesmaximal, characteristic, complemented
13C2×C4×#11765853C211yesmaximal, characteristic, complemented
14C2×C4×#11765850C211yesmaximal, characteristic, complemented
15C2×#17986060C211yesmaximal, characteristic, complemented
16C2×#540×C71C211yesmaximal, characteristic, complemented
17C22×#11765865C2211yescharacteristic
18C22×#11765853C2211yescharacteristic
19C22×#11765853C2211yescharacteristic
20C22×#11765850C2211yescharacteristic
21C22×#11765850C2211yescharacteristic
22#17986479—24no—
23#17986479C2218yescomplemented
24C2×C4×Dic142C2211yescharacteristic
25C2×C4×Dic142C2211yescharacteristic
26C2×C4×D284C2211yescharacteristic
27C2×C4×D284C2211yescharacteristic
28C2×(C22⋊D71)⋊C4—21no—
29C2×(C22⋊D71)⋊C4—21no—
30C2×#14556086—21no—
31C22×C4⋊Dic71C2211yescharacteristic
32C2×C4⋊C4×D71—21no—
33#17986315C2218yescomplemented
34#17986310C2218yescomplemented
35#17986303C2218yescomplemented
36#17986296C2218yescomplemented
37#17986196C2218yescomplemented
38#17986191C2218yescomplemented
39#17986142C2218yescomplemented
40#17986142C2218yescomplemented
41#17986109C2218yescomplemented
42#17986099C2218yescomplemented
43C4×#11765853C2218yescomplemented
44C4×#11765850C2218yescomplemented
45#17986060C2218yescomplemented
46C2×#14556061C2211yescharacteristic
47C2×#14556061C2211yescharacteristic
48C2×#14556059C2211yescharacteristic
49C2×#14556059C2211yescharacteristic
50C2×C4⋊(C71⋊C8)C2211yescharacteristic
51C2×C4⋊(C71⋊C8)C2211yescharacteristic
52C2×#14556051C2211yescharacteristic
53C2×#14556051C2211yescharacteristic
54C2×#14556049C2211yescharacteristic
55C2×#14556049C2211yescharacteristic
56C2×#14556049C2211yescharacteristic
57C2×#14556049C2211yescharacteristic
58C2×#14556048C2211yescharacteristic
59C2×#14556048C2211yescharacteristic
60C2×C22⋊(C71⋊C8)C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×#14556039C2211yescharacteristic
63C2×C4×C71⋊C8C2211yescharacteristic
64#540×C71—24no—
65#540×C71C2218yescomplemented
66C2×#127×C71C2211yescharacteristic
67C2×#125×C71C2211yescharacteristic
68C2×#123×C71—21no—
69C2×#123×C71—21no—
70C2×#121×C71—21no—
71C2×#121×C71—21no—
72C2×#121×C71C2211yescharacteristic
73C2×#121×C71C2211yescharacteristic
74C2×C4×D4×C71C2211yescharacteristic
75C2×C4×D4×C71C2211yescharacteristic
76C2×#117×C71C2211yescharacteristic
77C2×#11765865—24no—
78C2×#11765865—24no—
79C2×#11765865—22no—
80C2×#11765865C2314yes—
81C22×Dic142C2311yescharacteristic
82C22×D284C2311yescharacteristic
83C22×C22⋊D71—21no—
84C23×Dic71—21no—
85C22×C4×D71—21no—
86C22×C4×D71—21no—
87C22×C4×D71—21no—
88C2×#11765853—24no—
89C2×#11765853—24no—
90C2×#11765853C2314yes—
91C2×#11765853C2314yes—
92C2×#11765850—24no—
93C2×#11765850—24no—
94C2×#11765850C2314yes—
95C2×#11765850C2314yes—
96C22×C71⋊C8C2311yescharacteristic
97C22×C71⋊C8C2311yescharacteristic
98C22×C71⋊C8C2311yescharacteristic
99C22×C71⋊C8C2311yescharacteristic
100C4×Dic142—22no—
101C4×Dic142—22no—
102C4×Dic142C2314yes—
103C4×Dic142C2314yes—
104C4×D284—22no—
105C4×D284—22no—
106C4×D284C2314yes—
107C4×D284C2314yes—
108(C22⋊D71)⋊C4—28no—
109(C22⋊D71)⋊C4—28no—
110#14556086—28no—
111C2×C4⋊Dic71—21no—
112C2×C4⋊Dic71—22no—
113C2×C4⋊Dic71C2314yes—
114C2×C4⋊Dic71C2311yescharacteristic
115C2×C4⋊Dic71C2311yescharacteristic
116C2×Dic71⋊C4—21no—
117C2×Dic71⋊C4—21no—
118C4⋊C4×D71—28no—
119C2×(C2×D71)⋊C4—21no—
120C2×(C2×D71)⋊C4—21no—
121C2×C4×Dic71—21no—
122C2×C4×Dic71—21no—
123#14556061C2314yes—
124#14556061C2314yes—
125#14556059C2314yes—
126#14556059C2314yes—
127C4⋊(C71⋊C8)C2314yes—
128C4⋊(C71⋊C8)C2314yes—
129#14556051C2314yes—
130#14556051C2314yes—
131#14556049C2314yes—
132#14556049C2314yes—
133#14556049C2314yes—
134#14556049C2314yes—
135#14556048C2314yes—
136#14556048C2314yes—
137C22⋊(C71⋊C8)C2314yes—
138C22⋊(C71⋊C8)C2314yes—
139#14556039C2314yes—
140C4×C71⋊C8C2314yes—
141C22×D4×C71—21no—
142C22×D4×C71—21no—
143C22×D4×C71—21no—
144C22×D4×C71—21no—
145C22×D4×C71C2311yescharacteristic
146C22×D4×C71C2311yescharacteristic
147C23×C4×C71—21no—
148C23×C4×C71—21no—
149C23×C4×C71C2311yescharacteristic
150#127×C71—22no—
151#127×C71C2314yes—
152#125×C71—22no—
153#125×C71C2314yes—
154#123×C71—28no—
155#123×C71—28no—
156#121×C71—22no—
157#121×C71—22no—
158#121×C71—28no—
159#121×C71—28no—
160#121×C71C2314yes—
161#121×C71C2314yes—
162C4×D4×C71—22no—
163C4×D4×C71—22no—
164C4×D4×C71C2314yes—
165C4×D4×C71C2314yes—
166#117×C71D414yes—
167#117×C71C2314yes—
168C2×C4⋊C4×C71—21no—
169C2×C4⋊C4×C71—21no—
170C2×C4⋊C4×C71D411yescharacteristic
171C2×C4⋊C4×C71D411yescharacteristic
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C4⋊C4×C71C2311yescharacteristic
174C2×C22⋊C4×C71—21no—
175C2×C22⋊C4×C71—21no—
176C2×C22⋊C4×C71—21no—
177C2×C22⋊C4×C71—21no—
178C2×C22⋊C4×C71D411yescharacteristic
179C2×C22⋊C4×C71D411yescharacteristic
180C2×C42×C71C2311yescharacteristic
181C2×C42×C71C2311yescharacteristic
182C23×D71—21no—
183#11765865—216no—
184#11765865—28no—
185#11765865—28no—
186C2×Dic142—21no—
187C2×Dic142—22no—
188C2×Dic142#4114yes—
189C2×Dic142C2412yes—
190C2×D284—21no—
191C2×D284—22no—
192C2×D284#4114yes—
193C2×D284C2412yes—
194C2×C22⋊D71—28no—
195C2×C22⋊D71—24no—
196C22×Dic71—21no—
197C22×Dic71—21no—
198C22×Dic71—21no—
199C22×Dic71—24no—
200C22×Dic71—82no—
201C2×C4×D71—28no—
202C2×C4×D71—24no—
203C2×C4×D71—24no—
204C2×C4×D71—24no—
205C2×C4×D71—82no—
206C2×C4×D71—82no—
207#11765853—28no—
208#11765853—28no—
209#11765850—28no—
210#11765850—28no—
211C2×C71⋊C8—22no—
212C2×C71⋊C8—22no—
213C2×C71⋊C8—22no—
214C2×C71⋊C8—22no—
215C2×C71⋊C8C2412yes—
216C2×C71⋊C8C2412yes—
217C2×C71⋊C8C2412yes—
218C2×C71⋊C8C2412yes—
219C4⋊Dic71—24no—
220C4⋊Dic71—21no—
221C4⋊Dic71—21no—
222C4⋊Dic71C2412yes—
223C4⋊Dic71C2412yes—
224Dic71⋊C4—24no—
225Dic71⋊C4—24no—
226(C2×D71)⋊C4—24no—
227(C2×D71)⋊C4—24no—
228C4×Dic71—24no—
229C4×Dic71—24no—
230C24×C71—21no—
231C24×C71—21no—
232C24×C71C2×D411yescharacteristic
233C2×D4×C71—24no—
234C2×D4×C71—24no—
235C2×D4×C71—21no—
236C2×D4×C71—21no—
237C2×D4×C71—24no—
238C2×D4×C71—24no—
239C2×D4×C71—22no—
240C2×D4×C71—22no—
241C2×D4×C71—22no—
242C2×D4×C71—22no—
243C2×D4×C71—82no—
244C2×D4×C71—82no—
245C2×D4×C71—82no—
246C2×D4×C71—82no—
247C2×D4×C71C2412yes—
248C2×D4×C71C2412yes—
249C22×C4×C71—22no—
250C22×C4×C71—22no—
251C22×C4×C71—21no—
252C22×C4×C71—21no—
253C22×C4×C71—24no—
254C22×C4×C71—24no—
255C22×C4×C71—82no—
256C22×C4×C71—82no—
257C22×C4×C71C2×D411yescharacteristic
258C22×C4×C71C2×D411yescharacteristic
259C22×C4×C71C2×D411yescharacteristic
260C22×C4×C71C2×D412yes—
261C22×C4×C71C2×D411yescharacteristic
262C22×C4×C71C2×D411yescharacteristic
263C22×C4×C71C2412yes—
264C22×C4×C71C2411yescharacteristic
265C4⋊C4×C71—24no—
266C4⋊C4×C71—24no—
267C4⋊C4×C71—21no—
268C4⋊C4×C71—21no—
269C4⋊C4×C71C2×D414yes—
270C4⋊C4×C71C2×D414yes—
271C4⋊C4×C71C2412yes—
272C4⋊C4×C71C2412yes—
273C22⋊C4×C71—24no—
274C22⋊C4×C71—24no—
275C22⋊C4×C71—24no—
276C22⋊C4×C71—24no—
277C22⋊C4×C71C2×D414yes—
278C22⋊C4×C71C2×D414yes—
279C42×C71C2×D412yes—
280C42×C71C2×D412yes—
281C42×C71C2412yes—
282C42×C71C2412yes—
283C23×C71—22no—
284C23×C71—22no—
285C23×C71—22no—
286C23×C71—22no—
287C23×C71—22no—
288C23×C71—42no—
289C23×C71—42no—
290C23×C71—42no—
291C23×C71—42no—
292C23×C71—42no—
293C23×C71—42no—
294C23×C71C22×D412yes—
295C23×C71C22×D411yescharacteristic
296C22×D71—24no—
297C22×D71—22no—
298C22×D71—42no—
299C22×D71—42no—
300D4×C71—22no—
301D4×C71—22no—
302D4×C71—22no—
303D4×C71—22no—
304D4×C71—42no—
305D4×C71—42no—
306D4×C71—84no—
307D4×C71—84no—
308D4×C71—84no—
309D4×C71—84no—
310C2×C4×C71—22no—
311C2×C4×C71—22no—
312C2×C4×C71—22no—
313C2×C4×C71—22no—
314C2×C4×C71—22no—
315C2×C4×C71—24no—
316C2×C4×C71—22no—
317C2×C4×C71—22no—
318C2×C4×C71—22no—
319C2×C4×C71—22no—
320C2×C4×C71—42no—
321C2×C4×C71—42no—
322C2×C4×C71—84no—
323C2×C4×C71—84no—
324C2×C4×C71C22×D412yes—
325C2×C4×C71C22×D412yes—
326C2×C4×C71C22×D412yes—
327C2×C4×C71C22×D412yes—
328C2×C4×C71C22×D412yes—
329C2×C4×C71C22×D411yescharacteristic
330C2×C4×C71C2×#4112yes—
331C2×C4×C71C2×#4112yes—
332C2×C4×C71C2511yescharacteristic
333C22⋊D71—216no—
334C2×Dic71—24no—
335C2×Dic71—22no—
336C2×Dic71—22no—
337C2×Dic71—22no—
338C2×Dic71—42no—
339C2×Dic71—42no—
340C2×Dic71—84no—
341D284—24no—
342D284—22no—
343D284C2×#4114yes—
344C4×D71—216no—
345C4×D71—84no—
346C4×D71—84no—
347Dic142—24no—
348Dic142—22no—
349Dic142C2×#4114yes—
350C71⋊C8—22no—
351C71⋊C8—22no—
352C71⋊C8—22no—
353C71⋊C8—22no—
354C22×C71—22no—
355C22×C71—22no—
356C22×C71—22no—
357C22×C71—44no—
358C22×C71—42no—
359C22×C71—42no—
360C22×C71—42no—
361C22×C71—42no—
362C22×C71—42no—
363C22×C71—42no—
364C22×C71—84no—
365C22×C71—84no—
366C22×C71#52512yes—
367C22×C71#57612yes—
368C22×C71#57712yes—
369C22×C71C23×D411yescharacteristic
370C2×D71—24no—
371C2×D71—48no—
372C2×D71—42no—
373C2×D71—42no—
374C4×C71—22no—
375C4×C71—22no—
376C4×C71—22no—
377C4×C71—22no—
378C4×C71—22no—
379C4×C71—42no—
380C4×C71—42no—
381C4×C71#52512yes—
382C4×C71C22×#4111yescharacteristic
383C4×C71C22×#4111yescharacteristic
384Dic71—24no—
385Dic71—42no—
386Dic71—42no—
387C2×#3119—711nomaximal, Sylow
388C2×C71—42no—
389C2×C71—82no—
390C2×C71—82no—
391C2×C71#311914yescomplemented
392C2×C71C2×#52511yescharacteristic
393C2×C71C2×#57611yescharacteristic
394C2×C71C2×#57711yescharacteristic
395D71—44no—
396C2×#540D7111yescharacteristic, complemented
397C2×#520—711no—
398#3119—7116no—
399C2×#481—711no—
400C2×#480—711no—
401C2×#479—711no—
402C2×#478—711no—
403C2×#460—711no—
404C2×#459—711no—
405C2×#449—711no—
406C2×#449—711no—
407C2×#442—711no—
408C2×#440—711no—
409C2×C4×SD16—711no—
410C2×C4×D8—711no—
411C2×#433—711no—
412C71C2×#311911yescharacteristic, complemented, Sylow
413C22×#41—711no—
414C22×SD16—711no—
415C22×SD16—711no—
416C22×D8—711no—
417C22×D8—711no—
418#540—24no—
419#540C2×D7118yescomplemented
420C2×#127C2×D7111yescharacteristic
421C2×#125C2×D7111yescharacteristic
422C2×#123—21no—
423C2×#123—21no—
424C2×#121—21no—
425C2×#121—21no—
426C2×#121C2×D7111yescharacteristic
427C2×#121C2×D7111yescharacteristic
428#520—718no—
429#520—1424no—
430C2×C4×Q8—711no—
431C2×C4×Q8—711no—
432C2×C4×D4—711no—
433C2×C4×D4—711no—
434C2×C4×D4—1421no—
435C2×C4×D4—1421no—
436C2×C4×D4C2×D7111yescharacteristic
437C2×C4×D4C2×D7111yescharacteristic
438C2×#117—1421no—
439C2×#117C2×D7111yescharacteristic
440C22×C4⋊C4—711no—
441C22×C4⋊C4—1421no—
442#481—718no—
443#480—718no—
444#479—718no—
445#478—718no—
446#460—718no—
447#459—718no—
448#449—718no—
449#449—718no—
450#442—718no—
451#440—718no—
452C4×SD16—718no—
453C4×D8—718no—
454#433—718no—
455C2×#107—711no—
456C2×#107—711no—
457C2×#106—711no—
458C2×#106—711no—
459C2×C4⋊C8—711no—
460C2×C4⋊C8—711no—
461C2×#103—711no—
462C2×#103—711no—
463C2×#102—711no—
464C2×#102—711no—
465C2×#102—711no—
466C2×#102—711no—
467C2×#102—711no—
468C2×#102—711no—
469C2×C22⋊C8—711no—
470C2×C22⋊C8—711no—
471C2×#97—711no—
472C2×C4×C8—711no—
473C2×#41—714no—
474C2×#41—1424no—
475C2×#41—1424no—
476C2×#41—1422no—
477C22×Q8—711no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—21no—
482C22×D4—711no—
483C22×D4—1421no—
484C22×D4C22×D7111yescharacteristic
485C22×D4C22×D7111yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—1421no—
489C23×C4—1421no—
490C23×C4—1421no—
491C23×C4—1421no—
492C23×C4C22×D7111yescharacteristic
493C2×SD16—714no—
494C2×SD16—714no—
495C2×SD16—1424no—
496C2×SD16—1424no—
497C2×D8—714no—
498C2×D8—714no—
499C2×D8—1424no—
500C2×D8—1424no—
501C22×C8—711no—
502C22×C8—711no—
503C22×C8—711no—
504C22×C8—711no—
505#127—22no—
506#127C22×D7114yes—
507#125—22no—
508#125C22×D7114yes—
509#123—28no—
510#123—28no—
511#121—22no—
512#121—22no—
513#121—28no—
514#121—28no—
515#121C22×D7114yes—
516#121C22×D7114yes—
517C4×Q8—714no—
518C4×Q8—714no—
519C4×Q8—1422no—
520C4×Q8—1422no—
521C4×D4—22no—
522C4×D4—22no—
523C4×D4—714no—
524C4×D4—714no—
525C4×D4—1428no—
526C4×D4—1428no—
527C4×D4—1422no—
528C4×D4—1422no—
529C4×D4C22×D7114yes—
530C4×D4C22×D7114yes—
531#117—1428no—
532#117C22⋊D7114yes—
533#117C22×D7114yes—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—711no—
537C2×C4⋊C4—711no—
538C2×C4⋊C4—714no—
539C2×C4⋊C4—1421no—
540C2×C4⋊C4—1422no—
541C2×C4⋊C4—1421no—
542C2×C4⋊C4—1421no—
543C2×C4⋊C4—1428no—
544C2×C4⋊C4C22⋊D7111yescharacteristic
545C2×C4⋊C4C22⋊D7111yescharacteristic
546C2×C4⋊C4C22×D7111yescharacteristic
547C2×C4⋊C4C22×D7111yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—1421no—
553C2×C22⋊C4—1421no—
554C2×C22⋊C4C22⋊D7111yescharacteristic
555C2×C22⋊C4C22⋊D7111yescharacteristic
556C2×C42—1421no—
557C2×C42—1421no—
558C2×C42C22×D7111yescharacteristic
559C2×C42C22×D7111yescharacteristic
560#107—714no—
561#107—714no—
562#106—714no—
563#106—714no—
564C4⋊C8—714no—
565C4⋊C8—714no—
566#103—714no—
567#103—714no—
568#102—714no—
569#102—714no—
570#102—714no—
571#102—714no—
572#102—714no—
573#102—714no—
574C22⋊C8—714no—
575C22⋊C8—714no—
576#97—714no—
577C4×C8—714no—
578C24—21no—
579C24—21no—
580C24—1421no—
581C24C2×C22⋊D7111yescharacteristic
582#41—1428no—
583#41—1428no—
584#41—14216no—
585C2×Q8—714no—
586C2×Q8—712no—
587C2×Q8—1421no—
588C2×Q8—1422no—
589C2×D4—24no—
590C2×D4—24no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—24no—
594C2×D4—24no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—82no—
600C2×D4—82no—
601C2×D4—82no—
602C2×D4—82no—
603C2×D4—714no—
604C2×D4—712no—
605C2×D4—1428no—
606C2×D4—1424no—
607C2×D4—1421no—
608C2×D4—1422no—
609C2×D4C23×D7112yes—
610C2×D4C23×D7112yes—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—82no—
618C22×C4—82no—
619C22×C4—5682no—
620C22×C4—5682no—
621C22×C4—5682no—
622C22×C4—1428no—
623C22×C4—1421no—
624C22×C4—1421no—
625C22×C4—1424no—
626C22×C4—1424no—
627C22×C4—1424no—
628C22×C4—1421no—
629C22×C4—1424no—
630C22×C4C2×C22⋊D7112yes—
631C22×C4C2×C22⋊D7111yescharacteristic
632C22×C4C2×C22⋊D7111yescharacteristic
633C22×C4C2×C22⋊D7111yescharacteristic
634C22×C4C2×C22⋊D7111yescharacteristic
635C22×C4C2×C22⋊D7111yescharacteristic
636C22×C4C23×D7112yes—
637C22×C4C23×D7111yescharacteristic
638SD16—1428no—
639SD16—1428no—
640D8—1428no—
641D8—1428no—
642C2×C8—712no—
643C2×C8—712no—
644C2×C8—712no—
645C2×C8—712no—
646C2×C8—1422no—
647C2×C8—1422no—
648C2×C8—1422no—
649C2×C8—1422no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—712no—
655C4⋊C4—712no—
656C4⋊C4—1424no—
657C4⋊C4—1424no—
658C4⋊C4—1424no—
659C4⋊C4—1421no—
660C4⋊C4—1421no—
661C4⋊C4C2×C22⋊D7114yes—
662C4⋊C4C2×C22⋊D7114yes—
663C4⋊C4C23×D7112yes—
664C4⋊C4C23×D7112yes—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—1424no—
670C22⋊C4—1424no—
671C22⋊C4C2×C22⋊D7114yes—
672C22⋊C4C2×C22⋊D7114yes—
673C42—1424no—
674C42—1424no—
675C42C2×C22⋊D7112yes—
676C42C2×C22⋊D7112yes—
677C42C23×D7112yes—
678C42C23×D7112yes—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—2842no—
691C23—2842no—
692C23—1422no—
693C23—1424no—
694C23C22×C22⋊D7112yes—
695C23C22×C22⋊D7111yescharacteristic
696Q8—714no—
697Q8—1422no—
698Q8—1424no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—22no—
703D4—42no—
704D4—42no—
705D4—84no—
706D4—84no—
707D4—84no—
708D4—84no—
709D4—714no—
710D4—14216no—
711D4—1422no—
712D4—1424no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4—2842no—
728C2×C4—2842no—
729C2×C4—5684no—
730C2×C4—5684no—
731C2×C4—5684no—
732C2×C4—14216no—
733C2×C4—1422no—
734C2×C4—1422no—
735C2×C4—1422no—
736C2×C4—1424no—
737C2×C4C22×C22⋊D7112yes—
738C2×C4C22×C22⋊D7112yes—
739C2×C4C22×C22⋊D7112yes—
740C2×C4C22×C22⋊D7112yes—
741C2×C4C22×C22⋊D7112yes—
742C2×C4C22×C22⋊D7111yescharacteristic
743C2×C4#41×D7112yes—
744C2×C4#41×D7112yes—
745C2×C4C24×D7111yescharacteristic
746C8—1422no—
747C8—1422no—
748C8—1422no—
749C8—1422no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—84no—
761C22—84no—
762C22—2842no—
763C22—2842no—
764C22—2848no—
765C22—1424no—
766C22#1798650612yes—
767C22#1798680212yes—
768C22#1798681012yes—
769C22C23×C22⋊D7111yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—42no—
776C4—42no—
777C4—2842no—
778C4—2842no—
779C4—1424no—
780C4#1798650612yes—
781C4C2×#41×D7111yescharacteristic
782C4C2×#41×D7111yescharacteristic
783C2—42no—
784C2—82no—
785C2—82no—
786C2—2844no—
787C2#2259853314yesdirect product factor
788C2C2×#1798650611yescharacteristic
789C2C2×#1798680211yescharacteristic
790C2C2×#1798681011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#540×C71C2
socleC23×C71C22×D4
hypercenterC2×#540D71
hypocenterC71C2×#3119
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×#17986479C2semidirect
2. #22598533C2direct (N × H)
3. C2×#17986315C2semidirect
4. C2×#17986310C2semidirect
5. C2×#17986303C2semidirect
6. C2×#17986296C2semidirect
7. C2×#17986196C2semidirect
8. C2×#17986191C2semidirect
9. C2×#17986142C2semidirect
10. C2×#17986142C2semidirect
11. C2×#17986109C2semidirect
12. C2×#17986099C2semidirect
13. C2×C4×#11765853C2semidirect
14. C2×C4×#11765850C2semidirect
15. C2×#17986060C2semidirect
16. C2×#540×C71C2semidirect
23. #17986479C22semidirect
33. #17986315C22semidirect
34. #17986310C22semidirect
35. #17986303C22semidirect
36. #17986296C22semidirect
37. #17986196C22semidirect
38. #17986191C22semidirect
39. #17986142C22semidirect
40. #17986142C22semidirect
41. #17986109C22semidirect
42. #17986099C22semidirect
43. C4×#11765853C22semidirect
44. C4×#11765850C22semidirect
45. #17986060C22semidirect
65. #540×C71C22semidirect
391. C2×C71#3119semidirect
396. C2×#540D71semidirect
412. C71C2×#3119semidirect
419. #540C2×D71semidirect
787. C2#22598533direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179864792
#225985332
C2×#179863152
C2×#179863102
C2×#179863032
C2×#179862962
C2×#179861962
C2×#179861912
C2×#179861422
C2×#179861092
C2×#179860992
C2×C4×#117658532
C2×C4×#117658502
C2×#179860602
C2×#540×C712
C2×#311971