Finite Group Databasebeta

← C2×#20252228 #27080384

Subgroups — C2×#20252228 #27080384

Order 12032.

2730 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094053C211yesmaximal, characteristic
2C2×#15689602C211yesmaximal, characteristic
3C2×#15689599C211yesmaximal, characteristic, complemented
4#20252228C2116yesmaximal, direct product factor
5C2×#15689231C211yesmaximal, characteristic, complemented
6C2×#15689227C211yesmaximal, characteristic, complemented
7C2×#15689220C211yesmaximal, characteristic, complemented
8C2×#15689217C211yesmaximal, characteristic, complemented
9C2×C4×#10625337C211yesmaximal, characteristic, complemented
10C2×SD16×Dic47C211yesmaximal, characteristic, complemented
11C2×C4×#10625335C211yesmaximal, characteristic, complemented
12C2×#15689164C211yesmaximal, characteristic, complemented
13C2×#15689116C211yesmaximal, characteristic
14C2×#103×D47C211yesmaximal, characteristic, complemented
15C2×#15689080C211yesmaximal, characteristic, complemented
16C2×C47×#440C211yesmaximal, characteristic, complemented
17C22×#10625352C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic
19C2×#13094053C4116yescomplemented
20C2×#13094053C2218yes—
21C22×Dic188C2211yescharacteristic
22C22×#10625337C2211yescharacteristic
23C22×#10625335C2211yescharacteristic
24C22×#10625324C2211yescharacteristic
25C22×C8×D47C2211yescharacteristic
26#15689602—24no—
27#15689602C2218yes—
28#15689599—24no—
29#15689599C2218yescomplemented
30C2×Q8×Dic47C2211yescharacteristic
31C2×C4×Dic94—21no—
32C2×C4×Dic94C2211yescharacteristic
33C2×C4×Dic94C2211yescharacteristic
34C2×#13093989—21no—
35C2×#13093989C2211yescharacteristic
36C2×#13093989C2211yescharacteristic
37C2×D4×Dic47C2211yescharacteristic
38C2×C4×C22⋊D47—21no—
39C2×(C22⋊D47)⋊C4—21no—
40C2×#13093982—21no—
41C2×#13093982C2211yescharacteristic
42C2×#13093981—21no—
43C2×#13093981C2211yescharacteristic
44C2×#13093980—21no—
45C22×Dic47⋊C4—21no—
46C2×C4⋊C4×D47C2211yescharacteristic
47#15689231C2218yescomplemented
48#15689227C2218yescomplemented
49#15689220C2218yescomplemented
50#15689217C2218yescomplemented
51C4×#10625337C2218yescomplemented
52SD16×Dic47C2218yescomplemented
53C4×#10625335C2218yescomplemented
54#15689164C2218yescomplemented
55C2×#13093957C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58#15689116C2218yes—
59C2×#13093949C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093947C2211yescharacteristic
63C2×#13093947C2211yescharacteristic
64#103×D47C2218yescomplemented
65C2×#13093945C2211yescharacteristic
66#15689080C2218yescomplemented
67C2×#13093934C2211yescharacteristic
68C2×C4×C47⋊C8C2211yescharacteristic
69C2×C8×Dic47C2211yescharacteristic
70C22×SD16×C47C2211yescharacteristic
71C2×C4×Q8×C47C2211yescharacteristic
72C2×C4×D4×C47C2211yescharacteristic
73C47×#440C2218yescomplemented
74C2×#107×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C2×#97×C47C2211yescharacteristic
78C2×#10625352—22no—
79C2×#10625352—24no—
80C2×#10625352C2×C418yes—
81C2×#10625352C2314yes—
82C22×Dic94—21no—
83C22×Dic94C2311yescharacteristic
84C22×Dic94C2311yescharacteristic
85C2×Q8×D47—22no—
86C2×Q8×D47—24no—
87C2×Q8×D47C2×C418yescomplemented
88C2×Q8×D47C2314yes—
89C22×C22⋊D47—21no—
90C23×Dic47—21no—
91C23×Dic47—21no—
92C22×C4×D47—21no—
93C22×C4×D47—21no—
94C22×C4×D47C2311yescharacteristic
95#13094053C2×C4164yescomplemented
96C2×Dic188C2×C418yescomplemented
97C2×Dic188C2314yes—
98C2×#10625337C2×C418yescomplemented
99C2×#10625337C2314yes—
100C2×#10625335C2×C418yescomplemented
101C2×#10625335C2314yes—
102C2×#10625324C2×C418yescomplemented
103C2×#10625324C2314yes—
104C22×C47⋊C8C2311yescharacteristic
105C22×C47⋊C8C2311yescharacteristic
106C2×C8×D47—24no—
107C2×C8×D47C2314yes—
108Q8×Dic47—22no—
109Q8×Dic47C2314yes—
110C4×Dic94—22no—
111C4×Dic94—22no—
112C4×Dic94—28no—
113C4×Dic94C2314yes—
114C4×Dic94C2314yes—
115#13093989—28no—
116#13093989—22no—
117#13093989—22no—
118#13093989C2314yes—
119#13093989C2314yes—
120D4×Dic47—22no—
121D4×Dic47C2314yes—
122C4×C22⋊D47—28no—
123(C22⋊D47)⋊C4—28no—
124#13093982—22no—
125#13093982—28no—
126#13093982C2314yes—
127#13093981—28no—
128#13093981D414yes—
129#13093981C2314yes—
130#13093980—28no—
131C2×C4⋊Dic47—21no—
132C2×C4⋊Dic47C2311yescharacteristic
133C2×C4⋊Dic47C2311yescharacteristic
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4—21no—
138C2×Dic47⋊C4—21no—
139C2×Dic47⋊C4—28no—
140C2×Dic47⋊C4D411yescharacteristic
141C2×Dic47⋊C4D411yescharacteristic
142C4⋊C4×D47—22no—
143C4⋊C4×D47C2314yes—
144C2×C22⋊Dic47—21no—
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4D411yescharacteristic
147C2×(C2×D47)⋊C4D411yescharacteristic
148C2×C4×Dic47—21no—
149C2×C4×Dic47—21no—
150C2×C4×Dic47—21no—
151C2×C4×Dic47—21no—
152C2×C4×Dic47—21no—
153C2×C4×Dic47—21no—
154C2×C4×Dic47C2311yescharacteristic
155#13093957C2314yes—
156#13093956C2314yes—
157#13093955C2314yes—
158#13093949C2314yes—
159#13093949C2314yes—
160#13093948C2314yes—
161#13093947C2314yes—
162#13093947C2314yes—
163#13093945C2314yes—
164#13093934C2314yes—
165C4×C47⋊C8C2314yes—
166C8×Dic47C2314yes—
167C22×Q8×C47C2311yescharacteristic
168C22×D4×C47C2311yescharacteristic
169C23×C4×C47—21no—
170C2×SD16×C47C2×C418yescomplemented
171C2×SD16×C47C2314yes—
172C22×C8×C47C2311yescharacteristic
173C22×C8×C47C2311yescharacteristic
174C4×Q8×C47—22no—
175C4×Q8×C47C2314yes—
176C4×D4×C47—22no—
177C4×D4×C47C2314yes—
178C2×C4⋊C4×C47—21no—
179C2×C4⋊C4×C47C2311yescharacteristic
180C2×C4⋊C4×C47C2311yescharacteristic
181C2×C22⋊C4×C47—21no—
182C2×C42×C47—21no—
183C2×C42×C47C2311yescharacteristic
184#107×C47C2314yes—
185#103×C47C2314yes—
186#102×C47C2314yes—
187#97×C47C2314yes—
188C24×C47—21no—
189C23×D47C2×D411yescharacteristic
190C2×Q8×C47—21no—
191C2×Q8×C47—22no—
192C2×Q8×C47C22×C414yes—
193C2×Q8×C47C2412yes—
194C2×D4×C47—21no—
195C2×D4×C47—22no—
196C2×D4×C47C22×C414yes—
197C2×D4×C47C2412yes—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—24no—
202C22×C4×C47—82no—
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2411yescharacteristic
206C2×C22⋊D47—28no—
207C2×C22⋊D47—24no—
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47—28no—
211C22×Dic47—24no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—24no—
215C22×Dic47—82no—
216C22×Dic47C2×D411yescharacteristic
217C22×Dic47C2×D411yescharacteristic
218C22×Dic47C2×D411yescharacteristic
219Q8×D47—216no—
220Q8×D47—28no—
221Q8×D47C22×C4116yescomplemented
222#10625352—216no—
223#10625352—28no—
224#10625352C22×C4116yes—
225C2×C4×D47—28no—
226C2×C4×D47—24no—
227C2×C4×D47—24no—
228C2×C4×D47—82no—
229C2×C4×D47C22×C414yes—
230C2×C4×D47C2×D412yes—
231C2×C4×D47#4114yes—
232C2×C4×D47C2412yes—
233C2×Dic94—21no—
234C2×Dic94—21no—
235C2×Dic94—22no—
236C2×Dic94—22no—
237C2×Dic94—28no—
238C2×Dic94—24no—
239C2×Dic94C22×C414yes—
240C2×Dic94C22×C414yes—
241C2×Dic94C2412yes—
242C2×Dic94C2412yes—
243SD16×C47C22×C4116yescomplemented
244C2×C8×C47—22no—
245C2×C8×C47C22×C414yes—
246C2×C8×C47C2412yes—
247C2×C8×C47C2412yes—
248C4⋊C4×C47—24no—
249C4⋊C4×C47—21no—
250C4⋊C4×C47—21no—
251C4⋊C4×C47C2412yes—
252C4⋊C4×C47C2412yes—
253C22⋊C4×C47—24no—
254C42×C47—24no—
255C42×C47C2×D412yes—
256C42×C47C2412yes—
257C22⋊Dic47—24no—
258#10625337C22×C4116yescomplemented
259#10625335C22×C4116yescomplemented
260(C2×D47)⋊C4—24no—
261(C2×D47)⋊C4C2×D414yes—
262(C2×D47)⋊C4C2×D414yes—
263C4⋊Dic47—21no—
264C4⋊Dic47—21no—
265C4⋊Dic47—24no—
266C4⋊Dic47C2412yes—
267C4⋊Dic47C2412yes—
268Dic47⋊C4—24no—
269Dic47⋊C4—24no—
270Dic47⋊C4—24no—
271Dic47⋊C4—24no—
272Dic47⋊C4—24no—
273Dic47⋊C4C2×D414yes—
274Dic47⋊C4C2×D414yes—
275C4×Dic47—24no—
276C4×Dic47—24no—
277C4×Dic47—24no—
278C4×Dic47—24no—
279C4×Dic47—24no—
280C4×Dic47—24no—
281C4×Dic47C2×D412yes—
282C4×Dic47C2412yes—
283C2×C47⋊C8—22no—
284C2×C47⋊C8C22×C414yes—
285C2×C47⋊C8C2412yes—
286C2×C47⋊C8C2412yes—
287Dic188C22×C4116yescomplemented
288#10625324C22×C4116yescomplemented
289C8×D47—28no—
290C23×C47—24no—
291C23×C47—22no—
292C23×C47—42no—
293C23×C47—42no—
294C23×C47C22×D411yescharacteristic
295C22×D47—22no—
296C22×D47—22no—
297C22×D47C4×D414yes—
298C22×D47C22×D412yes—
299Q8×C47—24no—
300Q8×C47—22no—
301Q8×C47C23×C414yes—
302D4×C47—24no—
303D4×C47—22no—
304D4×C47C23×C414yes—
305C2×C4×C47—24no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—42no—
312C2×C4×C47—42no—
313C2×C4×C47—84no—
314C2×C4×C47C23×C412yes—
315C2×C4×C47C22×D412yes—
316C2×C4×C47C22×D412yes—
317C2×C4×C47C22×D411yescharacteristic
318C2×C4×C47C2×#4112yes—
319C2×C4×C47C2511yescharacteristic
320C22⋊D47—216no—
321C2×Dic47—24no—
322C2×Dic47—24no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—216no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—42no—
331C2×Dic47—42no—
332C2×Dic47—84no—
333C2×Dic47C4×D414yes—
334C2×Dic47C22×D412yes—
335C2×Dic47C22×D412yes—
336C2×Dic47C22×D412yes—
337C4×D47—216no—
338C4×D47—84no—
339C4×D47C4×D418yes—
340C4×D47C23×C414yes—
341C4×D47C2×#4114yes—
342Dic94—24no—
343Dic94—24no—
344Dic94—22no—
345Dic94—22no—
346Dic94—216no—
347Dic94C23×C414yes—
348Dic94C23×C414yes—
349C8×C47—22no—
350C8×C47C23×C414yes—
351C47⋊C8—22no—
352C47⋊C8C23×C414yes—
353C2×#2947—471nomaximal, Sylow
354C22×C47—24no—
355C22×C47—48no—
356C22×C47—42no—
357C22×C47—42no—
358C22×C47C2×C4×D412yes—
359C22×C47#57712yes—
360C22×C47#57812yes—
361C22×C47C23×D411yescharacteristic
362C2×D47—28no—
363C2×D47—22no—
364C2×D47—22no—
365C2×D47C2×C4×D414yes—
366C4×C47—24no—
367C4×C47—22no—
368C4×C47—22no—
369C4×C47—42no—
370C4×C47—42no—
371C4×C47C2×C4×D412yes—
372C4×C47C24×C411yescharacteristic
373C4×C47C22×#4111yescharacteristic
374Dic47—24no—
375Dic47—24no—
376Dic47—22no—
377Dic47—22no—
378Dic47—42no—
379Dic47—42no—
380Dic47C2×C4×D414yes—
381C22×#137—471no—
382C2×#520—471no—
383C2×#519—471no—
384#2947—4716no—
385C2×#441—471no—
386C2×#441—471no—
387C2×#440—471no—
388C2×#440D4711yescharacteristic, complemented
389C2×C4×Q16—471no—
390C2×C4×Q16—471no—
391C2×C4×SD16—471no—
392C2×C4×SD16—471no—
393C2×#428—471no—
394C2×#416—471no—
395C22×#103—471no—
396C2×#405—471no—
397C2×C47—44no—
398C2×C47#294714yescomplemented
399C2×C47C22×C4×D411yescharacteristic
400C2×C47C2×#57711yescharacteristic
401C2×C47C2×#57811yescharacteristic
402D47—24no—
403C22×#41—471no—
404C23×Q8—471no—
405C2×#137—4716no—
406C2×#137—478no—
407C22×Q16—471no—
408C22×Q16—471no—
409C22×SD16—471no—
410C22×SD16C2×D4711yescharacteristic
411C22×M16—471no—
412C23×C8—471no—
413#520—478no—
414#520—944no—
415#519—478no—
416#519—944no—
417C2×C4×Q8—471no—
418C2×C4×Q8—471no—
419C2×C4×Q8—471no—
420C2×C4×Q8—471no—
421C2×C4×Q8—471no—
422C2×C4×Q8—941no—
423C2×C4×Q8—941no—
424C2×C4×Q8C2×D4711yescharacteristic
425C2×C4×D4—471no—
426C2×C4×D4—941no—
427C2×C4×D4—941no—
428C2×C4×D4C2×D4711yescharacteristic
429C2×#117—471no—
430C2×#117—471no—
431C2×#117—941no—
432C2×#117—941no—
433C2×#117—941no—
434C22×C4⋊C4—471no—
435C22×C4⋊C4—941no—
436#441—478no—
437#441—478no—
438#440—478no—
439#440C2×D4718yescomplemented
440C4×Q16—478no—
441C4×Q16—478no—
442C4×SD16—478no—
443C4×SD16—478no—
444#428—478no—
445C2×#107—471no—
446C2×#107C2×D4711yescharacteristic
447C2×#106—471no—
448C2×#106—471no—
449#416—478no—
450C2×#103—471no—
451C2×#103—471no—
452C2×#103—471no—
453C2×#103—471no—
454C2×#103—471no—
455C2×#103—478no—
456C2×#103C2×D4711yescharacteristic
457C2×#102—471no—
458C2×#102C2×D4711yescharacteristic
459#405—478no—
460C2×#97—471no—
461C2×#97C2×D4711yescharacteristic
462C2×C4×C8—471no—
463C2×C4×C8—471no—
464C47C2×#294711yescharacteristic, complemented, Sylow
465C2×#41—478no—
466C2×#41—474no—
467C2×#41—942no—
468C2×#41—944no—
469C22×Q8—478no—
470C22×Q8—474no—
471C22×Q8—471no—
472C22×Q8—471no—
473C22×Q8—941no—
474C22×Q8—942no—
475C22×Q8—944no—
476C22×Q8C22×D4711yescharacteristic
477C22×D4—941no—
478C22×D4C22×D4711yescharacteristic
479C23×C4—21no—
480C23×C4—471no—
481C23×C4—941no—
482C23×C4—941no—
483C23×C4—941no—
484C23×C4—941no—
485#137—4764no—
486C2×Q16—478no—
487C2×Q16—474no—
488C2×Q16—478no—
489C2×Q16—474no—
490C2×SD16—478no—
491C2×SD16—474no—
492C2×SD16C4×D4718yescomplemented
493C2×SD16C22×D4714yes—
494C2×M16—478no—
495C2×M16—474no—
496C22×C8—471no—
497C22×C8—471no—
498C22×C8—474no—
499C22×C8—944no—
500C22×C8C22×D4711yescharacteristic
501C22×C8C22×D4711yescharacteristic
502C4×Q8—22no—
503C4×Q8—474no—
504C4×Q8—474no—
505C4×Q8—474no—
506C4×Q8—474no—
507C4×Q8—474no—
508C4×Q8—948no—
509C4×Q8—942no—
510C4×Q8—942no—
511C4×Q8—942no—
512C4×Q8—948no—
513C4×Q8—942no—
514C4×Q8—942no—
515C4×Q8C22×D4714yes—
516C4×D4—22no—
517C4×D4—474no—
518C4×D4—942no—
519C4×D4—948no—
520C4×D4—948no—
521C4×D4C22×D4714yes—
522#117—474no—
523#117—474no—
524#117—474no—
525#117—948no—
526#117—948no—
527#117—948no—
528#117—942no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—471no—
531C2×C4⋊C4—471no—
532C2×C4⋊C4—471no—
533C2×C4⋊C4—471no—
534C2×C4⋊C4—474no—
535C2×C4⋊C4—942no—
536C2×C4⋊C4—948no—
537C2×C4⋊C4—941no—
538C2×C4⋊C4—941no—
539C2×C4⋊C4—941no—
540C2×C4⋊C4—941no—
541C2×C4⋊C4—941no—
542C2×C4⋊C4—941no—
543C2×C4⋊C4C22×D4711yescharacteristic
544C2×C4⋊C4C22×D4711yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—471no—
547C2×C22⋊C4—471no—
548C2×C22⋊C4—941no—
549C2×C22⋊C4—941no—
550C2×C42—21no—
551C2×C42—471no—
552C2×C42—941no—
553C2×C42—941no—
554C2×C42—941no—
555C2×C42—941no—
556C2×C42—941no—
557C2×C42—941no—
558C2×C42C22×D4711yescharacteristic
559#107—474no—
560#107C22×D4714yes—
561#106—474no—
562#106—474no—
563#103—474no—
564#103—474no—
565#103—474no—
566#103—474no—
567#103—474no—
568#103C22×D4714yes—
569#102—474no—
570#102C22×D4714yes—
571#97—474no—
572#97C22×D4714yes—
573C4×C8—474no—
574C4×C8—474no—
575C24—21no—
576C24—471no—
577#41—4716no—
578#41—9416no—
579#41—948no—
580C2×Q8—21no—
581C2×Q8—22no—
582C2×Q8—4716no—
583C2×Q8—474no—
584C2×Q8—474no—
585C2×Q8—472no—
586C2×Q8—472no—
587C2×Q8—944no—
588C2×Q8—948no—
589C2×Q8—9416no—
590C2×Q8—948no—
591C2×Q8—941no—
592C2×Q8—941no—
593C2×Q8—942no—
594C2×Q8—942no—
595C2×Q8C2×C4×D4714yes—
596C2×Q8C23×D4712yes—
597C2×D4—21no—
598C2×D4—22no—
599C2×D4—944no—
600C2×D4—948no—
601C2×D4C2×C4×D4714yes—
602C2×D4C23×D4712yes—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—24no—
607C22×C4—82no—
608C22×C4—471no—
609C22×C4—474no—
610C22×C4—472no—
611C22×C4—474no—
612C22×C4—472no—
613C22×C4—471no—
614C22×C4—471no—
615C22×C4—944no—
616C22×C4—948no—
617C22×C4—944no—
618C22×C4—944no—
619C22×C4—948no—
620C22×C4—944no—
621C22×C4—941no—
622C22×C4—941no—
623C22×C4—941no—
624C22×C4—941no—
625C22×C4—3762no—
626C22×C4—3762no—
627C22×C4D4×D4711yescharacteristic
628C22×C4D4×D4711yescharacteristic
629C22×C4C23×D4711yescharacteristic
630Q16—4716no—
631Q16—4716no—
632SD16—4716no—
633SD16C2×C4×D47116yescomplemented
634M16—4716no—
635C2×C8—22no—
636C2×C8—474no—
637C2×C8—472no—
638C2×C8—472no—
639C2×C8—948no—
640C2×C8—942no—
641C2×C8C2×C4×D4714yes—
642C2×C8C23×D4712yes—
643C2×C8C23×D4712yes—
644C4⋊C4—24no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—474no—
648C4⋊C4—474no—
649C4⋊C4—472no—
650C4⋊C4—472no—
651C4⋊C4—944no—
652C4⋊C4—944no—
653C4⋊C4—944no—
654C4⋊C4—944no—
655C4⋊C4—944no—
656C4⋊C4—944no—
657C4⋊C4—941no—
658C4⋊C4—941no—
659C4⋊C4C23×D4712yes—
660C4⋊C4C23×D4712yes—
661C22⋊C4—24no—
662C22⋊C4—474no—
663C22⋊C4—474no—
664C22⋊C4—944no—
665C22⋊C4—944no—
666C42—24no—
667C42—472no—
668C42—472no—
669C42—944no—
670C42—944no—
671C42—944no—
672C42—944no—
673C42—944no—
674C42—944no—
675C42D4×D4712yes—
676C42C23×D4712yes—
677C23—24no—
678C23—22no—
679C23—42no—
680C23—42no—
681C23—474no—
682C23—472no—
683C23—942no—
684C23—942no—
685C23C2×D4×D4711yescharacteristic
686Q8—24no—
687Q8—22no—
688Q8—474no—
689Q8—474no—
690Q8—9416no—
691Q8—944no—
692Q8—944no—
693Q8—942no—
694Q8—942no—
695Q8C22×C4×D4714yes—
696D4—24no—
697D4—22no—
698D4—9416no—
699D4C22×C4×D4714yes—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—84no—
709C2×C4—474no—
710C2×C4—472no—
711C2×C4—478no—
712C2×C4—474no—
713C2×C4—474no—
714C2×C4—472no—
715C2×C4—472no—
716C2×C4—9416no—
717C2×C4—9416no—
718C2×C4—944no—
719C2×C4—944no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—942no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—3764no—
727C2×C4—3764no—
728C2×C4—1882no—
729C2×C4—1882no—
730C2×C4C22×C4×D4712yes—
731C2×C4C2×D4×D4712yes—
732C2×C4C2×D4×D4712yes—
733C2×C4C2×D4×D4711yescharacteristic
734C2×C4#41×D4712yes—
735C2×C4C24×D4711yescharacteristic
736C8—22no—
737C8—474no—
738C8—942no—
739C8C22×C4×D4714yes—
740C22—24no—
741C22—48no—
742C22—42no—
743C22—42no—
744C22—474no—
745C22—948no—
746C22—942no—
747C22—942no—
748C22C4×D4×D4712yes—
749C22#1568993312yes—
750C22#1568993912yes—
751C22C22×D4×D4711yescharacteristic
752C4—24no—
753C4—22no—
754C4—22no—
755C4—42no—
756C4—42no—
757C4—474no—
758C4—944no—
759C4—944no—
760C4—942no—
761C4—942no—
762C4—1882no—
763C4—1882no—
764C4C4×D4×D4712yes—
765C4C23×C4×D4711yescharacteristic
766C4C2×#41×D4711yescharacteristic
767C2—44no—
768C2—944no—
769C2#2025222814yesdirect product factor
770C2C2×C4×D4×D4711yescharacteristic
771C2C2×#1568993311yescharacteristic
772C2C2×#1568993911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC4×C47C24×C4
FrattiniC2×C4C24×D47
FittingC2×C47×#440C2
socleC23×C47C22×D4
prime radicalC22×#10625352C22
cosocleC2×C4×C47C25
hypercenterC2×#440D47
hypocenterC47C2×#2947
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
3. C2×#15689599C2semidirect
4. #20252228C2direct (N × H)
5. C2×#15689231C2semidirect
6. C2×#15689227C2semidirect
7. C2×#15689220C2semidirect
8. C2×#15689217C2semidirect
9. C2×C4×#10625337C2semidirect
10. C2×SD16×Dic47C2semidirect
11. C2×C4×#10625335C2semidirect
12. C2×#15689164C2semidirect
14. C2×#103×D47C2semidirect
15. C2×#15689080C2semidirect
16. C2×C47×#440C2semidirect
19. C2×#13094053C4semidirect
29. #15689599C22semidirect
47. #15689231C22semidirect
48. #15689227C22semidirect
49. #15689220C22semidirect
50. #15689217C22semidirect
51. C4×#10625337C22semidirect
52. SD16×Dic47C22semidirect
53. C4×#10625335C22semidirect
54. #15689164C22semidirect
64. #103×D47C22semidirect
66. #15689080C22semidirect
73. C47×#440C22semidirect
87. C2×Q8×D47C2×C4semidirect
95. #13094053C2×C4semidirect
96. C2×Dic188C2×C4semidirect
98. C2×#10625337C2×C4semidirect
100. C2×#10625335C2×C4semidirect
102. C2×#10625324C2×C4semidirect
170. C2×SD16×C47C2×C4semidirect
221. Q8×D47C22×C4semidirect
243. SD16×C47C22×C4semidirect
258. #10625337C22×C4semidirect
259. #10625335C22×C4semidirect
287. Dic188C22×C4semidirect
288. #10625324C22×C4semidirect
388. C2×#440D47semidirect
398. C2×C47#2947semidirect
439. #440C2×D47semidirect
464. C47C2×#2947semidirect
492. C2×SD16C4×D47semidirect
633. SD16C2×C4×D47semidirect
769. C2#20252228direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940532
C2×#156896022
C2×#156895992
#202522282
C2×#156892312
C2×#156892272
C2×#156892202
C2×#156892172
C2×C4×#106253372
C2×SD16×Dic472
C2×C4×#106253352
C2×#156891642
C2×#156891162
C2×#103×D472
C2×#156890802
C2×C47×#4402
C2×#294747