Finite Group Databasebeta

← C2×#20257270 #27124719

Subgroups — C2×#20257270 #27124719

Order 12032.

7022 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257270C2132yesmaximal, direct product factor
2C2×#15689850C214yesmaximal, complemented
3C2×#15689840C214yesmaximal, complemented
4C2×#15689809C214yesmaximal, complemented
5C2×#15689805C214yesmaximal, complemented
6C2×#15689736C211yesmaximal, characteristic, complemented
7C2×#15689735C211yesmaximal, characteristic, complemented
8C2×#15689734C211yesmaximal, characteristic, complemented
9C2×#15689696C212yesmaximal
10C2×#15689679C211yesmaximal, characteristic, complemented
11C2×#15689677C212yesmaximal, complemented
12C2×#15689675C212yesmaximal, complemented
13C2×C4⋊Q8×D47C211yesmaximal, characteristic, complemented
14C2×#15689599C212yesmaximal, complemented
15C2×#15689591C211yesmaximal, characteristic
16C2×C47×#541C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×Q8×D47C2212yes—
19#15689850C22164yescomplemented
20#15689840C22164yescomplemented
21#15689809C22164yescomplemented
22#15689805C22164yescomplemented
23#15689736C22116yescomplemented
24#15689735C22116yescomplemented
25#15689734C22116yescomplemented
26#15689696C22132yes—
27#15689679C22116yescomplemented
28#15689677C22132yescomplemented
29#15689675C22132yescomplemented
30C2×#13094024C2211yescharacteristic
31C2×#13094023C2214yes—
32C2×#13094023C2212yes—
33C2×#13094023C2214yes—
34C2×#13094022C2212yes—
35C4⋊Q8×D47C22116yescomplemented
36C2×#13094019C2214yes—
37C2×#13094019C2214yes—
38C2×#13094017C2214yes—
39C2×#13094016C2211yescharacteristic
40C2×#13094015C2214yes—
41C2×#13094014C2214yes—
42C2×#13094014C2214yes—
43C2×#13094014C2214yes—
44C2×#13094014C2214yes—
45C2×#13094010C2214yes—
46C2×#13094009C2214yes—
47C2×#13094006C2214yes—
48C2×#13094004C2212yes—
49C2×#13094003C2212yes—
50C2×#13094002C2214yes—
51C2×#13094002C2214yes—
52C2×#13094001C2214yes—
53C2×#13094000C2212yes—
54#15689599C22132yescomplemented
55#15689591C22116yes—
56C2×Q8×Dic47C2212yes—
57C2×C4×Dic94C2214yes—
58C2×C4×Dic94C2212yes—
59C2×C4×Dic94C2214yes—
60C2×#13093989C2212yes—
61C2×#13093989C2212yes—
62C2×#13093989C2214yes—
63C2×#13093989C2214yes—
64C2×#13093989C2214yes—
65C2×#13093986C2212yes—
66C2×(C22⋊D47)⋊C4C2212yes—
67C2×(C22⋊D47)⋊C4C2212yes—
68C2×#13093982C2214yes—
69C2×#13093982C2212yes—
70C2×#13093981C2211yescharacteristic
71C2×#13093981C2211yescharacteristic
72C2×#13093981C2214yes—
73C2×#13093981C2214yes—
74C2×#13093980C2214yes—
75C2×C4⋊C4×D47C2214yes—
76C22×C4×Dic47C2211yescharacteristic
77C2×C42×D47C2211yescharacteristic
78C2×C42×D47C2211yescharacteristic
79C47×#541C22116yescomplemented
80C2×C4⋊Q8×C47C2211yescharacteristic
81C2×#126×C47C2214yes—
82C2×#125×C47C2214yes—
83C2×#125×C47C2211yescharacteristic
84C2×C22⋊Q8×C47C2212yes—
85C2×C4×Q8×C47C2212yes—
86C2×#117×C47C2211yescharacteristic
87C2×#10625350—28no—
88C2×#10625350C2318yes—
89C22×Dic94C2314yes—
90C22×Dic94C2311yescharacteristic
91C22×Dic94C2312yes—
92C22×Dic94C2314yes—
93C2×Q8×D47—216no—
94C2×Q8×D47C23116yes—
95C22×D188C2311yescharacteristic
96C22×C22⋊D47C2311yescharacteristic
97C22×C22⋊D47C2311yescharacteristic
98C23×Dic47C2312yes—
99C22×C4×D47C2312yes—
100C22×C4×D47C2312yes—
101C22×C4×D47C2311yescharacteristic
102C22×C4×D47C2314yes—
103C22×C4×D47C2311yescharacteristic
104#13094024C2318yes—
105#13094023C23132yes—
106#13094023C23132yes—
107#13094023C23116yes—
108#13094022C23116yes—
109#13094019C23132yes—
110#13094019C23132yes—
111#13094017C23132yes—
112#13094016C2318yes—
113#13094015C23132yes—
114#13094014C23132yes—
115#13094014C23132yes—
116#13094014C23132yes—
117#13094014C23132yes—
118#13094010C23132yes—
119#13094009C23132yes—
120#13094006C23132yes—
121#13094004C23116yes—
122#13094003C23116yes—
123#13094002C23132yes—
124#13094002C23132yes—
125#13094001C23132yes—
126#13094000C23116yes—
127Q8×Dic47C23116yes—
128C4×Dic94C23116yes—
129C4×Dic94C23132yes—
130C4×Dic94C23132yes—
131#13093989C23116yes—
132#13093989C23132yes—
133#13093989C23132yes—
134#13093989C23132yes—
135#13093989C23116yes—
136#13093986C23116yes—
137(C22⋊D47)⋊C4C23116yes—
138(C22⋊D47)⋊C4C23116yes—
139#13093982C23132yes—
140#13093982C23116yes—
141#13093981C2318yes—
142#13093981C23132yes—
143#13093981C23132yes—
144#13093981C2318yes—
145#13093980C23132yes—
146C2×C4⋊Dic47C2314yes—
147C2×C4⋊Dic47C2312yes—
148C2×C4⋊Dic47C2314yes—
149C2×C4⋊Dic47C2314yes—
150C2×Dic47⋊C4C2314yes—
151C2×Dic47⋊C4C2314yes—
152C2×Dic47⋊C4C2314yes—
153C2×Dic47⋊C4C2312yes—
154C2×Dic47⋊C4C2312yes—
155C2×Dic47⋊C4C2314yes—
156C2×Dic47⋊C4C2314yes—
157C2×Dic47⋊C4C2314yes—
158C2×Dic47⋊C4C2314yes—
159C2×Dic47⋊C4C2314yes—
160C4⋊C4×D47C23132yes—
161C2×C22⋊Dic47C2314yes—
162C2×(C2×D47)⋊C4C2312yes—
163C2×(C2×D47)⋊C4C2314yes—
164C2×(C2×D47)⋊C4C2312yes—
165C2×(C2×D47)⋊C4C2314yes—
166C2×(C2×D47)⋊C4C2314yes—
167C2×C4×Dic47C2311yescharacteristic
168C2×C4×Dic47C2312yes—
169C2×C4×Dic47C2312yes—
170C2×C4×Dic47C2311yescharacteristic
171C2×C4×Dic47C2312yes—
172C2×C4×Dic47C2318yes—
173C2×C4×Dic47C2314yes—
174C2×C4×Dic47C2314yes—
175C2×C4×Dic47C2314yes—
176C2×C4×Dic47C2314yes—
177C42×D47C2318yes—
178C42×D47C2318yes—
179C22×Q8×C47C2312yes—
180C23×C4×C47C2311yescharacteristic
181C4⋊Q8×C47C2318yes—
182#126×C47C23132yes—
183#125×C47C2318yes—
184#125×C47C23132yes—
185C22⋊Q8×C47C23116yes—
186C4×Q8×C47C23116yes—
187#117×C47C2318yes—
188C2×C4⋊C4×C47C2312yes—
189C2×C4⋊C4×C47C2312yes—
190C2×C4⋊C4×C47C2314yes—
191C2×C4⋊C4×C47C2314yes—
192C2×C4⋊C4×C47C2314yes—
193C2×C4⋊C4×C47C2314yes—
194C2×C22⋊C4×C47C2312yes—
195C2×C22⋊C4×C47C2314yes—
196C2×C42×C47C2311yescharacteristic
197C2×C42×C47C2311yescharacteristic
198C2×C42×C47C2314yes—
199C24×C47C2411yescharacteristic
200C23×D47C2411yescharacteristic
201C23×D47C2411yescharacteristic
202C2×Q8×C47—28no—
203C2×Q8×C47C2418yes—
204C22×C4×C47—24no—
205C22×C4×C47C2412yes—
206C22×C4×C47C2414yes—
207C22×C4×C47C2412yes—
208C22×C4×C47C2414yes—
209C22×C4×C47C2411yescharacteristic
210C22×C4×C47C2414yes—
211C22×C4×C47C2411yescharacteristic
212C2×C22⋊D47—24no—
213C2×C22⋊D47—24no—
214C2×C22⋊D47C2414yes—
215C2×C22⋊D47C2414yes—
216C22×Dic47—28no—
217C22×Dic47C2412yes—
218C22×Dic47C2414yes—
219C22×Dic47C2414yes—
220C22×Dic47C2411yescharacteristic
221C22×Dic47C2418yes—
222C22×Dic47C2411yescharacteristic
223C22×Dic47C2412yes—
224Q8×D47—264no—
225#10625350—232no—
226C2×D188—24no—
227C2×D188C2414yes—
228C2×C4×D47—216no—
229C2×C4×D47—24no—
230C2×C4×D47—28no—
231C2×C4×D47—28no—
232C2×C4×D47#4118yes—
233C2×C4×D47C2418yes—
234C2×C4×D47C2418yes—
235C2×C4×D47C2414yes—
236C2×C4×D47C24116yes—
237C2×C4×D47C2414yes—
238C2×Dic94—28no—
239C2×Dic94—216no—
240C2×Dic94—24no—
241C2×Dic94—216no—
242C2×Dic94C24116yes—
243C2×Dic94C2414yes—
244C2×Dic94C2418yes—
245C2×Dic94C24116yes—
246C4⋊C4×C47C2418yes—
247C4⋊C4×C47C2418yes—
248C4⋊C4×C47C24116yes—
249C4⋊C4×C47C24116yes—
250C4⋊C4×C47C24116yes—
251C4⋊C4×C47C24116yes—
252C22⋊C4×C47C2418yes—
253C22⋊C4×C47C24116yes—
254C42×C47C2414yes—
255C42×C47C2414yes—
256C42×C47C24116yes—
257C22⋊Dic47C24116yes—
258(C2×D47)⋊C4C2418yes—
259(C2×D47)⋊C4C24116yes—
260(C2×D47)⋊C4C2418yes—
261(C2×D47)⋊C4C24116yes—
262(C2×D47)⋊C4C24116yes—
263C4⋊Dic47C24116yes—
264C4⋊Dic47C2418yes—
265C4⋊Dic47C24116yes—
266C4⋊Dic47C24116yes—
267Dic47⋊C4C24116yes—
268Dic47⋊C4C24116yes—
269Dic47⋊C4C24116yes—
270Dic47⋊C4C2418yes—
271Dic47⋊C4C2418yes—
272Dic47⋊C4C24116yes—
273Dic47⋊C4C24116yes—
274Dic47⋊C4C24116yes—
275Dic47⋊C4C24116yes—
276Dic47⋊C4C24116yes—
277C4×Dic47C2414yes—
278C4×Dic47C2418yes—
279C4×Dic47C2418yes—
280C4×Dic47C2414yes—
281C4×Dic47C2418yes—
282C4×Dic47C24116yes—
283C4×Dic47C24116yes—
284C4×Dic47C24116yes—
285C4×Dic47C24116yes—
286C23×C47—22no—
287C23×C47—24no—
288C23×C47C2512yes—
289C23×C47C2511yescharacteristic
290C22×D47—24no—
291C22×D47—22no—
292C22×D47—24no—
293C22×D47C2×#4114yes—
294C22×D47C2512yes—
295C22×D47C2512yes—
296Q8×C47—216no—
297C2×C4×C47—28no—
298C2×C4×C47—22no—
299C2×C4×C47—28no—
300C2×C4×C47—24no—
301C2×C4×C47—24no—
302C2×C4×C47—28no—
303C2×C4×C47C2×#4114yes—
304C2×C4×C47C2514yes—
305C2×C4×C47C2512yes—
306C2×C4×C47C2518yes—
307C2×C4×C47C2514yes—
308C2×C4×C47C2518yes—
309C2×C4×C47C2512yes—
310C22⋊D47—28no—
311C22⋊D47—28no—
312C2×Dic47—28no—
313C2×Dic47—22no—
314C2×Dic47—28no—
315C2×Dic47—24no—
316C2×Dic47—216no—
317C2×Dic47C2×#4114yes—
318C2×Dic472−1+418yes—
319C2×Dic47C2514yes—
320C2×Dic47C2518yes—
321C2×Dic47C2512yes—
322C2×Dic47C2518yes—
323C2×Dic47C2512yes—
324C2×Dic47C2514yes—
325D188—28no—
326C4×D47—232no—
327C4×D47—28no—
328C4×D47—216no—
329C4×D47—216no—
330C4×D47C2×#41116yes—
331Dic94—216no—
332Dic94—28no—
333Dic94—232no—
334Dic94—232no—
335C2×#3509—471nomaximal, Sylow
336C22×C47—22no—
337C22×C47—24no—
338C22×C47—44no—
339C22×C47C22×#4112yes—
340C22×C47C2×2−1+414yes—
341C22×C47C2611yescharacteristic
342C2×D47—24no—
343C2×D47—28no—
344C2×D47—22no—
345C2×D47—24no—
346C2×D47—44no—
347C2×D47C22×#4114yes—
348C4×C47—28no—
349C4×C47—22no—
350C4×C47—28no—
351C4×C47—24no—
352C4×C47—24no—
353C4×C47C22×#4114yes—
354Dic47—28no—
355Dic47—22no—
356Dic47—28no—
357Dic47—24no—
358Dic47C22×#4114yes—
359Dic47C2×2−1+418yes—
360#3509—4732no—
361C2×#557—474no—
362C2×#556—474no—
363C2×#552—474no—
364C2×#552—474no—
365C2×#541—471no—
366C2×#541—471no—
367C2×#541—471no—
368C2×#541D4711yescharacteristic, complemented
369C2×#536—472no—
370C2×#533—471no—
371C2×#533—472no—
372C2×#533—472no—
373C22×C4⋊Q8—471no—
374C2×#519—472no—
375C2×C4×#41—471no—
376C2×C47—42no—
377C2×C47#350914yescomplemented
378C2×C47C23×#4111yescharacteristic
379C2×C47C22×2−1+412yes—
380D47—24no—
381D47—42no—
382C22×#41—471no—
383C23×Q8—472no—
384#557—4764no—
385#556—4764no—
386#552—4764no—
387#552—4764no—
388#541—4716no—
389#541—4716no—
390#541—4716no—
391#541C2×D47116yescomplemented
392#536—4732no—
393#533—4716no—
394#533—4732no—
395#533—4732no—
396C2×C4⋊Q8—472no—
397C2×C4⋊Q8—4716no—
398C2×C4⋊Q8—474no—
399C2×C4⋊Q8—472no—
400C2×C4⋊Q8—474no—
401C2×C4⋊Q8—471no—
402C2×C4⋊Q8C2×D4711yescharacteristic
403C2×#126—474no—
404C2×#126—474no—
405C2×#126—474no—
406C2×#126C2×D4714yes—
407C2×#125—474no—
408C2×#125—474no—
409C2×#125—474no—
410C2×#125—474no—
411C2×#125—474no—
412C2×#125—471no—
413C2×#125C2×D4711yescharacteristic
414C2×#125C2×D4714yes—
415C2×#124—474no—
416C2×#123—474no—
417C2×#123—474no—
418C2×C22⋊Q8—472no—
419C2×C22⋊Q8—472no—
420C2×C22⋊Q8—472no—
421C2×C22⋊Q8—474no—
422C2×C22⋊Q8—474no—
423C2×C22⋊Q8—474no—
424C2×C22⋊Q8C2×D4712yes—
425#519—4732no—
426C4×#41—4716no—
427C2×C4×Q8—472no—
428C2×C4×Q8—472no—
429C2×C4×Q8—472no—
430C2×C4×Q8—474no—
431C2×C4×Q8—474no—
432C2×C4×Q8—474no—
433C2×C4×Q8—472no—
434C2×C4×Q8—474no—
435C2×C4×Q8—474no—
436C2×C4×Q8C2×D4712yes—
437C2×C4×D4—472no—
438C2×C4×D4—472no—
439C2×C4×D4—472no—
440C2×#117—472no—
441C2×#117—474no—
442C2×#117—474no—
443C2×#117—471no—
444C2×#117—471no—
445C2×#117—474no—
446C2×#117—474no—
447C2×#117C2×D4711yescharacteristic
448C22×C4⋊C4—474no—
449C22×C42—471no—
450C22×C42—471no—
451C22×C42—471no—
452C47C2×#350911yescharacteristic, complemented, Sylow
453C2×#41—478no—
454C2×#41—948no—
455C22×Q8—4716no—
456C22×Q8—474no—
457C22×Q8—472no—
458C22×Q8—474no—
459C22×Q8—471no—
460C22×Q8—9416no—
461C22×Q8C22×D4712yes—
462C22×D4—471no—
463C22×D4—471no—
464C22×D4—471no—
465C23×C4—471no—
466C23×C4—472no—
467C23×C4—474no—
468C23×C4—472no—
469C23×C4—472no—
470C23×C4—471no—
471C23×C4C22×D4711yescharacteristic
472C4⋊Q8—4716no—
473C4⋊Q8—4732no—
474C4⋊Q8—4716no—
475C4⋊Q8—4732no—
476C4⋊Q8—478no—
477C4⋊Q8C22×D4718yes—
478#126—4732no—
479#126—4732no—
480#126—4732no—
481#126C22×D47132yes—
482#125—4732no—
483#125—4732no—
484#125—4732no—
485#125—4732no—
486#125—4732no—
487#125—478no—
488#125C22×D4718yes—
489#125C22×D47132yes—
490#124—4732no—
491#123—4732no—
492#123—4732no—
493C22⋊Q8—4716no—
494C22⋊Q8—4716no—
495C22⋊Q8—4716no—
496C22⋊Q8—4732no—
497C22⋊Q8—4732no—
498C22⋊Q8—4732no—
499C22⋊Q8C22×D47116yes—
500C4×Q8—4716no—
501C4×Q8—4716no—
502C4×Q8—4716no—
503C4×Q8—4732no—
504C4×Q8—4732no—
505C4×Q8—4732no—
506C4×Q8—4716no—
507C4×Q8—4732no—
508C4×Q8—4732no—
509C4×Q8C22×D47116yes—
510C4×D4—4716no—
511C4×D4—4716no—
512C4×D4—4716no—
513#117—4716no—
514#117—4732no—
515#117—4732no—
516#117—478no—
517#117—478no—
518#117—4732no—
519#117—4732no—
520#117C22×D4718yes—
521C2×C4⋊C4—474no—
522C2×C4⋊C4—474no—
523C2×C4⋊C4—474no—
524C2×C4⋊C4—474no—
525C2×C4⋊C4—472no—
526C2×C4⋊C4—472no—
527C2×C4⋊C4—472no—
528C2×C4⋊C4—474no—
529C2×C4⋊C4—474no—
530C2×C4⋊C4—474no—
531C2×C4⋊C4—474no—
532C2×C4⋊C4—474no—
533C2×C4⋊C4—474no—
534C2×C4⋊C4—474no—
535C2×C4⋊C4—4732no—
536C2×C4⋊C4C22×D4714yes—
537C2×C4⋊C4C22×D4712yes—
538C2×C4⋊C4C22×D4714yes—
539C2×C4⋊C4C22×D4712yes—
540C2×C4⋊C4C22×D4714yes—
541C2×C4⋊C4C22×D4714yes—
542C2×C22⋊C4—474no—
543C2×C22⋊C4—472no—
544C2×C22⋊C4—474no—
545C2×C22⋊C4—472no—
546C2×C22⋊C4—474no—
547C2×C22⋊C4—474no—
548C2×C22⋊C4C22×D4714yes—
549C2×C22⋊C4C22×D4712yes—
550C2×C42—471no—
551C2×C42—474no—
552C2×C42—474no—
553C2×C42—474no—
554C2×C42—474no—
555C2×C42—472no—
556C2×C42—472no—
557C2×C42—472no—
558C2×C42—478no—
559C2×C42—471no—
560C2×C42—478no—
561C2×C42—478no—
562C2×C42C22×D4714yes—
563C2×C42C22×D4711yescharacteristic
564C2×C42C22×D4711yescharacteristic
565C24—471no—
566C24—471no—
567C24C23×D4711yescharacteristic
568#41—9432no—
569C2×Q8—28no—
570C2×Q8—4716no—
571C2×Q8—478no—
572C2×Q8—4716no—
573C2×Q8—474no—
574C2×Q8—9416no—
575C2×Q8—9416no—
576C2×Q8—944no—
577C2×Q8—9464no—
578C2×Q8—948no—
579C2×Q8C23×D4718yes—
580C2×D4—474no—
581C2×D4—474no—
582C2×D4—474no—
583C2×D4—944no—
584C2×D4—944no—
585C2×D4—944no—
586C22×C4—24no—
587C22×C4—471no—
588C22×C4—472no—
589C22×C4—478no—
590C22×C4—474no—
591C22×C4—478no—
592C22×C4—472no—
593C22×C4—474no—
594C22×C4—474no—
595C22×C4—471no—
596C22×C4—478no—
597C22×C4—478no—
598C22×C4—474no—
599C22×C4—4716no—
600C22×C4—948no—
601C22×C4—948no—
602C22×C4—9416no—
603C22×C4—948no—
604C22×C4—944no—
605C22×C4C23×D4714yes—
606C22×C4C23×D4712yes—
607C22×C4C23×D4714yes—
608C22×C4C23×D4711yescharacteristic
609C22×C4C23×D4712yes—
610C22×C4C23×D4714yes—
611C22×C4C23×D4711yescharacteristic
612C4⋊C4—4716no—
613C4⋊C4—4716no—
614C4⋊C4—4716no—
615C4⋊C4—478no—
616C4⋊C4—478no—
617C4⋊C4—4716no—
618C4⋊C4—4716no—
619C4⋊C4—4716no—
620C4⋊C4—4716no—
621C4⋊C4—4716no—
622C4⋊C4—4716no—
623C4⋊C4—478no—
624C4⋊C4—4716no—
625C4⋊C4—4716no—
626C4⋊C4C23×D47116yes—
627C4⋊C4C23×D4718yes—
628C4⋊C4C23×D47116yes—
629C4⋊C4C23×D4718yes—
630C4⋊C4C23×D47116yes—
631C4⋊C4C23×D47116yes—
632C22⋊C4—4716no—
633C22⋊C4—478no—
634C22⋊C4—4716no—
635C22⋊C4—478no—
636C22⋊C4—4716no—
637C22⋊C4—4716no—
638C22⋊C4C23×D47116yes—
639C22⋊C4C23×D4718yes—
640C42—474no—
641C42—474no—
642C42—478no—
643C42—478no—
644C42—478no—
645C42—4716no—
646C42—4716no—
647C42—4716no—
648C42—4716no—
649C42C23×D4714yes—
650C42C23×D4714yes—
651C42C23×D47116yes—
652C23—22no—
653C23—24no—
654C23—474no—
655C23—472no—
656C23—472no—
657C23—944no—
658C23—942no—
659C23—944no—
660C23C24×D4712yes—
661C23C24×D4711yescharacteristic
662Q8—216no—
663Q8—9432no—
664Q8—9432no—
665Q8—948no—
666Q8—9416no—
667D4—948no—
668D4—948no—
669D4—948no—
670C2×C4—22no—
671C2×C4—28no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—28no—
675C2×C4—28no—
676C2×C4—474no—
677C2×C4—478no—
678C2×C4—472no—
679C2×C4—474no—
680C2×C4—4716no—
681C2×C4—474no—
682C2×C4—478no—
683C2×C4—478no—
684C2×C4—472no—
685C2×C4—9416no—
686C2×C4—9416no—
687C2×C4—9432no—
688C2×C4—9416no—
689C2×C4—942no—
690C2×C4—948no—
691C2×C4—944no—
692C2×C4—948no—
693C2×C4—948no—
694C2×C4#41×D4714yes—
695C2×C4C24×D4714yes—
696C2×C4C24×D4718yes—
697C2×C4C24×D4712yes—
698C2×C4C24×D4714yes—
699C2×C4C24×D4718yes—
700C2×C4C24×D4712yes—
701C22—22no—
702C22—24no—
703C22—44no—
704C22—474no—
705C22—944no—
706C22—948no—
707C22—942no—
708C22—944no—
709C22—1884no—
710C22C2×#41×D4712yes—
711C222−1+4×D4714yes—
712C22C25×D4711yescharacteristic
713C4—22no—
714C4—28no—
715C4—24no—
716C4—24no—
717C4—28no—
718C4—474no—
719C4—478no—
720C4—942no—
721C4—948no—
722C4—944no—
723C4—948no—
724C4C2×#41×D4714yes—
725C2—42no—
726C2—944no—
727C2—1882no—
728C2#2025727014yesdirect product factor
729C2C22×#41×D4711yescharacteristic
730C2C2×2−1+4×D4712yes—
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#541C2
socleC23×C47C25
prime radicalC22×#10625350C22
hypercenterC2×#541D47
hypocenterC47C2×#3509
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. #20257270C2direct (N × H)
2. C2×#15689850C2semidirect
3. C2×#15689840C2semidirect
4. C2×#15689809C2semidirect
5. C2×#15689805C2semidirect
6. C2×#15689736C2semidirect
7. C2×#15689735C2semidirect
8. C2×#15689734C2semidirect
10. C2×#15689679C2semidirect
11. C2×#15689677C2semidirect
12. C2×#15689675C2semidirect
13. C2×C4⋊Q8×D47C2semidirect
14. C2×#15689599C2semidirect
16. C2×C47×#541C2semidirect
19. #15689850C22semidirect
20. #15689840C22semidirect
21. #15689809C22semidirect
22. #15689805C22semidirect
23. #15689736C22semidirect
24. #15689735C22semidirect
25. #15689734C22semidirect
27. #15689679C22semidirect
28. #15689677C22semidirect
29. #15689675C22semidirect
35. C4⋊Q8×D47C22semidirect
54. #15689599C22semidirect
79. C47×#541C22semidirect
368. C2×#541D47semidirect
377. C2×C47#3509semidirect
391. #541C2×D47semidirect
452. C47C2×#3509semidirect
728. C2#20257270direct (N × H)

Maximal subgroups

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

subgroupindex
#202572702
C2×#156898502
C2×#156898402
C2×#156898092
C2×#156898052
C2×#156897362
C2×#156897352
C2×#156897342
C2×#156896962
C2×#156896792
C2×#156896772
C2×#156896752
C2×C4⋊Q8×D472
C2×#156895992
C2×#156895912
C2×C47×#5412
C2×#350947