Finite Group Databasebeta

← #27080490

Subgroups — #27080490

Order 12032.

2742 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689921C211yesmaximal, characteristic
2#20256591C211yesmaximal, characteristic, complemented
3C2×#15689604C211yesmaximal, characteristic, complemented
4#20252267C214yesmaximal, complemented
5#20252259C214yesmaximal, complemented
6#20252225C214yesmaximal, complemented
7#20252214C214yesmaximal, complemented
8#20252212C214yesmaximal, complemented
9#20252201C214yesmaximal, complemented
10C2×#15689163C211yesmaximal, characteristic, complemented
11#20251908C211yesmaximal, characteristic, complemented
12#20251806C211yesmaximal, characteristic, complemented
13C2×C47×#417C211yesmaximal, characteristic, complemented
14C22×#10625350C2211yescharacteristic
15#15689921C4116yescomplemented
16C2×#13094055C2212yes—
17C2×#13094054C2212yes—
18C2×#13094050C2212yes—
19C2×#13094049C2212yes—
20C2×#13094044C2214yes—
21C22×#10625329C2211yescharacteristic
22#15689606—21no—
23#15689606—21no—
24#15689606C2212yescomplemented
25#15689606C2212yescomplemented
26#15689604—22no—
27#15689604—22no—
28#15689604C2214yes—
29#15689604C2214yescomplemented
30#15689601C2212yescomplemented
31#15689598—22no—
32#15689598C2212yescomplemented
33#41×Dic47—22no—
34#41×Dic47C2214yes—
35C2×#13093989C2212yescomplemented
36C2×#13093986C2212yescomplemented
37C2×C4×C22⋊D47—22no—
38C2×#13093983—22no—
39C2×#13093983C2211yescharacteristic
40C2×#13093983C2211yescharacteristic
41C2×#13093982—21no—
42C2×C4⋊C4×D47—21no—
43#15689232C2218yescomplemented
44#15689227C2218yescomplemented
45#15689226C2218yescomplemented
46#15689220C2218yescomplemented
47#15689215C2218yescomplemented
48#15689214C2218yescomplemented
49#15689208C2218yescomplemented
50#15689203C2218yescomplemented
51#15689163C2214yescomplemented
52#15689163C2214yescomplemented
53C2×#13093957C2212yescomplemented
54C2×#13093955C2212yescomplemented
55#15689133C2212yescomplemented
56#15689129C2212yescomplemented
57#15689125C2212yescomplemented
58#15689125C2212yescomplemented
59#15689120C2214yes—
60#15689081C2214yescomplemented
61#15689078C2214yescomplemented
62M16×Dic47C2214yescomplemented
63C22×#41×C47C2211yescharacteristic
64C22×M16×C47C2211yescharacteristic
65C22×C4⋊C4×C47C2211yescharacteristic
66C47×#417C2214yes—
67C47×#417C2214yescomplemented
68C2×#103×C47C2212yescomplemented
69C2×#102×C47C2212yescomplemented
70C2×#10625350—21no—
71C2×#10625350—21no—
72C2×#10625350—24no—
73C2×#10625350C2×C418yescomplemented
74C2×#10625350C2312yes—
75C2×#10625350C2312yes—
76C22×Dic94C2311yescharacteristic
77C22×D188C2311yescharacteristic
78C22×C22⋊D47—21no—
79C22×C4×D47—21no—
80C22×C4×D47—22no—
81#13094055C2×C4116yescomplemented
82#13094054C2×C4116yescomplemented
83#13094050C2×C4116yescomplemented
84#13094049C2×C4116yescomplemented
85#13094044C2×C4132yescomplemented
86C2×#10625337C2314yes—
87C2×#10625335C2314yes—
88C2×#10625336C2314yes—
89C2×#10625334C2314yes—
90C2×#10625329C2×C418yescomplemented
91C2×#10625329C2312yes—
92C2×#10625329C2312yes—
93C22×C47⋊C8C2312yes—
94Q8×Dic47—22no—
95Q8×Dic47—22no—
96Q8×Dic47C2314yes—
97Q8×Dic47C2314yes—
98#13093989—24no—
99#13093989C2318yes—
100D4×Dic47—24no—
101D4×Dic47—24no—
102D4×Dic47—24no—
103D4×Dic47—24no—
104D4×Dic47—22no—
105D4×Dic47—22no—
106D4×Dic47C2314yes—
107D4×Dic47C2314yes—
108#13093986—24no—
109#13093986C2318yes—
110C4×C22⋊D47—28no—
111C4×C22⋊D47—28no—
112#13093983—21no—
113#13093983—21no—
114#13093983—24no—
115#13093983—22no—
116#13093983—22no—
117#13093983—24no—
118#13093983D412yes—
119#13093983D412yes—
120#13093983C2312yes—
121#13093983C2312yes—
122#13093983C2312yes—
123#13093983C2312yes—
124#13093982—24no—
125#13093982—24no—
126C2×C4⋊Dic47—22no—
127C2×C4⋊Dic47—22no—
128C2×C4⋊Dic47D411yescharacteristic
129C2×C4⋊Dic47D411yescharacteristic
130C2×C4⋊Dic47C2311yescharacteristic
131C2×C4⋊Dic47C2311yescharacteristic
132C2×Dic47⋊C4—22no—
133C4⋊C4×D47—24no—
134C4⋊C4×D47—24no—
135C2×C22⋊Dic47—21no—
136C2×C22⋊Dic47—24no—
137C2×C22⋊Dic47D412yes—
138C2×(C2×D47)⋊C4—22no—
139C2×C4×Dic47—21no—
140C2×C4×Dic47—22no—
141C2×C4×Dic47—24no—
142C2×C4×Dic47C2312yes—
143#13093957C2318yes—
144#13093955C2318yes—
145#13093949C2314yes—
146#13093949C2314yes—
147#13093946C2314yes—
148#13093946C2314yes—
149#13093934C2318yes—
150C8×Dic47C2318yes—
151C2×#41×C47—21no—
152C2×#41×C47—21no—
153C2×#41×C47—24no—
154C2×#41×C47C2×C418yescomplemented
155C2×#41×C47C2312yes—
156C2×#41×C47C2312yes—
157C22×Q8×C47C2311yescharacteristic
158C22×D4×C47—21no—
159C22×D4×C47C2311yescharacteristic
160C23×C4×C47—21no—
161C23×C4×C47—21no—
162C23×C4×C47C2311yescharacteristic
163C2×M16×C47—24no—
164C2×M16×C47C2312yes—
165C2×M16×C47C2312yes—
166C22×C8×C47C2312yes—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47—21no—
169C2×C4⋊C4×C47—21no—
170C2×C4⋊C4×C47C2312yes—
171C2×C4⋊C4×C47C2312yes—
172C2×C4⋊C4×C47C2312yes—
173#103×C47C2318yes—
174#102×C47C2318yes—
175C24×C47—21no—
176C24×C47C2×D411yescharacteristic
177C23×D47—21no—
178#41×C47—28no—
179#41×C47—28no—
180#41×C47—24no—
181#41×C47—24no—
182#41×C47C22×C418yes—
183#41×C47C22×C418yescomplemented
184C2×Q8×C47—21no—
185C2×Q8×C47—22no—
186C2×Q8×C47C22×C414yescomplemented
187C2×Q8×C47C2412yes—
188C2×D4×C47—28no—
189C2×D4×C47—22no—
190C2×D4×C47—22no—
191C2×D4×C47—21no—
192C2×D4×C47—22no—
193C2×D4×C47C22×C414yescomplemented
194C2×D4×C47C2412yes—
195C22×C4×C47—21no—
196C22×C4×C47—28no—
197C22×C4×C47—22no—
198C22×C4×C47—22no—
199C22×C4×C47—22no—
200C22×C4×C47—22no—
201C22×C4×C47—22no—
202C22×C4×C47—82no—
203C22×C4×C47C22×C414yes—
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47#4114yes—
208C22×C4×C47C2411yescharacteristic
209C22×C4×C47C2411yescharacteristic
210C22×C4×C47C2411yescharacteristic
211C2×C22⋊D47—28no—
212C2×C22⋊D47—22no—
213C2×C22⋊D47—22no—
214C22×Dic47—21no—
215C22×Dic47—21no—
216C22×Dic47—21no—
217C22×Dic47—24no—
218C22×Dic47—24no—
219C22×Dic47C2×D412yes—
220C22×Dic47C2×D412yes—
221#10625350—28no—
222#10625350—28no—
223#10625350—24no—
224#10625350—24no—
225#10625350C22×C418yes—
226#10625350C22×C418yes—
227C2×D188—21no—
228C2×D188—22no—
229C2×D188C22×C414yes—
230C2×D188C2412yes—
231C2×C4×D47—28no—
232C2×C4×D47—22no—
233C2×C4×D47—22no—
234C2×C4×D47—28no—
235C2×C4×D47—84no—
236C2×Dic94—21no—
237C2×Dic94—22no—
238C2×Dic94C22×C414yes—
239C2×Dic94C2412yes—
240M16×C47—24no—
241M16×C47—24no—
242C2×C8×C47—24no—
243C2×C8×C47C2414yes—
244C4⋊C4×C47—22no—
245C4⋊C4×C47—22no—
246C4⋊C4×C47—22no—
247C4⋊C4×C47C2414yes—
248C22⋊Dic47—22no—
249C22⋊Dic47—22no—
250C22⋊Dic47—24no—
251C22⋊Dic47—24no—
252C22⋊Dic47C2×D414yes—
253C22⋊Dic47C2×D414yes—
254#10625337C22×C4116yescomplemented
255#10625336C22×C4116yescomplemented
256#10625335C22×C4116yescomplemented
257#10625334C22×C4116yescomplemented
258(C2×D47)⋊C4—28no—
259C4⋊Dic47—21no—
260C4⋊Dic47—21no—
261C4⋊Dic47—24no—
262C4⋊Dic47—24no—
263C4⋊Dic47C2×D412yes—
264C4⋊Dic47C2×D412yes—
265C4⋊Dic47C2×D412yes—
266C4⋊Dic47C2×D412yes—
267C4⋊Dic47C2412yes—
268C4⋊Dic47C2412yes—
269Dic47⋊C4—28no—
270C4×Dic47—22no—
271C4×Dic47—22no—
272C4×Dic47—28no—
273C4×Dic47—24no—
274C4×Dic47—24no—
275C4×Dic47C2×D414yes—
276C4×Dic47C2414yes—
277#10625329C22×C418yes—
278#10625329C22×C418yescomplemented
279C2×C47⋊C8C22×C418yescomplemented
280C2×C47⋊C8C2414yes—
281C23×C47—22no—
282C23×C47—24no—
283C23×C47—41no—
284C23×C47—41no—
285C23×C47—81no—
286C23×C47—81no—
287C23×C47C4×D414yes—
288C23×C47C22×D411yescharacteristic
289C23×C47C22×D411yescharacteristic
290C23×C47C22×D411yescharacteristic
291C22×D47—24no—
292C22×D47—22no—
293C22×D47—42no—
294C22×D47—42no—
295Q8×C47—24no—
296Q8×C47—22no—
297Q8×C47C23×C414yes—
298D4×C47—28no—
299D4×C47—28no—
300D4×C47—24no—
301D4×C47—22no—
302D4×C47C23×C414yes—
303C2×C4×C47—24no—
304C2×C4×C47—22no—
305C2×C4×C47—28no—
306C2×C4×C47—28no—
307C2×C4×C47—24no—
308C2×C4×C47—44no—
309C2×C4×C47—82no—
310C2×C4×C47—82no—
311C2×C4×C47C4×D414yes—
312C2×C4×C47C4×D414yes—
313C2×C4×C47C4×D414yes—
314C2×C4×C47C23×C412yes—
315C2×C4×C47C23×C412yes—
316C2×C4×C47C23×C412yes—
317C2×C4×C47C22×D411yescharacteristic
318C2×C4×C47C22×D411yescharacteristic
319C2×C4×C47C22×D411yescharacteristic
320C2×C4×C47C2×#4112yes—
321C2×C4×C47C2×#4112yes—
322C2×C4×C47C2×#4112yes—
323C2×C4×C47C2511yescharacteristic
324C22⋊D47—28no—
325C22⋊D47—28no—
326C2×Dic47—24no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—42no—
331C2×Dic47—42no—
332C2×Dic47—84no—
333C2×Dic47—84no—
334C2×Dic47—81no—
335C2×Dic47—81no—
336C2×Dic47C22×D414yes—
337C2×Dic47C22×D414yes—
338D188—24no—
339D188—22no—
340D188C23×C414yes—
341C4×D47—28no—
342C4×D47—28no—
343C4×D47—88no—
344Dic94—24no—
345Dic94—22no—
346Dic94C23×C414yes—
347C8×C47—24no—
348C47⋊C8C23×C418yes—
349#60170—471nomaximal, Sylow
350C22×C47—21no—
351C22×C47—21no—
352C22×C47—21no—
353C22×C47—21no—
354C22×C47—21no—
355C22×C47—21no—
356C22×C47—24no—
357C22×C47—44no—
358C22×C47—42no—
359C22×C47—42no—
360C22×C47—84no—
361C22×C47C2×C4×D412yes—
362C22×C47C2×C4×D412yes—
363C22×C47C2×C4×D412yes—
364C22×C47C23×D411yescharacteristic
365C2×D47—24no—
366C2×D47—48no—
367C2×D47—42no—
368C2×D47—42no—
369C4×C47—24no—
370C4×C47—44no—
371C4×C47C2×C4×D412yes—
372C4×C47C2×C4×D412yes—
373C4×C47C2×C4×D412yes—
374C4×C47C24×C411yescharacteristic
375C4×C47C22×#4111yescharacteristic
376Dic47—24no—
377Dic47—24no—
378Dic47—24no—
379Dic47—42no—
380Dic47—42no—
381C2×#575—471no—
382#3428—471no—
383C2×#520—471no—
384#2952—474no—
385#2951—474no—
386#2947—474no—
387#2946—474no—
388C4×#137—474no—
389C4×AGL(1,ℤ/8)—474no—
390C2×#428—471no—
391#2896—471no—
392C2×#417D4711yescharacteristic, complemented
393#2873—471no—
394C2×C47—22no—
395C2×C47—22no—
396C2×C47—22no—
397C2×C47—44no—
398C2×C47C22×C4×D411yescharacteristic
399C2×C47#358511yescharacteristic
400C2×C47#358611yescharacteristic
401D47—44no—
402C22×#41—471no—
403C22×#41C2×D4711yescharacteristic
404#575—4716no—
405C2×#137—472no—
406C2×#137—472no—
407C2×AGL(1,ℤ/8)—472no—
408C2×AGL(1,ℤ/8)—472no—
409C2×#135—474no—
410C22×M16—471no—
411C22×M16C2×D4711yescharacteristic
412#520—472no—
413#520—472no—
414#520—474no—
415#520—474no—
416#520—942no—
417#520—942no—
418#520—941no—
419#520—941no—
420#519—472no—
421#518—472no—
422#518—942no—
423C4×#41—474no—
424C4×#41—942no—
425C2×C4×Q8—472no—
426C2×C4×D4—472no—
427C2×C4×D4—942no—
428C2×#117—471no—
429C2×#117—471no—
430C2×#117—941no—
431C2×#117—942no—
432C22×C4⋊C4—941no—
433C22×C4⋊C4C2×D4711yescharacteristic
434#442—478no—
435#441—478no—
436#440—478no—
437#440—478no—
438C4×Q16—478no—
439C4×SD16—478no—
440C4×SD16—478no—
441C4×D8—478no—
442#428—474no—
443#428—474no—
444C2×#107—472no—
445C2×#106—472no—
446#419—472no—
447#418—472no—
448#417—472no—
449#417—472no—
450#417C2×D4714yes—
451#417C2×D4714yescomplemented
452#416—474no—
453C2×#103C2×D4712yescomplemented
454C2×#102C2×D4712yescomplemented
455#405—474no—
456#405—474no—
457C4×M16—474no—
458C47#6017011yescharacteristic, complemented, Sylow
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—24no—
462C2×#41—478no—
463C2×#41—472no—
464C2×#41—472no—
465C2×#41—941no—
466C2×#41—941no—
467C2×#41—944no—
468C2×#41C4×D4718yescomplemented
469C2×#41C22×D4712yes—
470C2×#41C22×D4712yes—
471C22×Q8—471no—
472C22×Q8C22×D4711yescharacteristic
473C22×D4—21no—
474C22×D4—471no—
475C22×D4—941no—
476C22×D4C22×D4711yescharacteristic
477C23×C4—21no—
478C23×C4—21no—
479C23×C4—942no—
480C23×C4—941no—
481C23×C4C22×D4711yescharacteristic
482#137—4716no—
483#137—4716no—
484AGL(1,ℤ/8)—4716no—
485AGL(1,ℤ/8)—4716no—
486#135—4732no—
487C2×Q16—474no—
488C2×SD16—474no—
489C2×SD16—474no—
490C2×D8—474no—
491C2×M16—24no—
492C2×M16—478no—
493C2×M16—472no—
494C2×M16—472no—
495C2×M16C22×D4712yes—
496C2×M16C22×D4712yes—
497C22×C8—472no—
498C22×C8C22×D4712yes—
499C4×Q8—474no—
500C4×Q8—474no—
501C4×Q8—478no—
502C4×Q8—944no—
503C4×Q8—942no—
504C4×Q8—942no—
505C4×D4—474no—
506C4×D4—474no—
507C4×D4—478no—
508C4×D4—944no—
509C4×D4—948no—
510C4×D4—948no—
511C4×D4—944no—
512C4×D4—944no—
513C4×D4—942no—
514C4×D4—942no—
515C4×D4—944no—
516C4×D4—944no—
517#117—472no—
518#117—472no—
519#117—472no—
520#117—472no—
521#117—472no—
522#117—472no—
523#117—944no—
524#117—944no—
525#117—944no—
526#117—944no—
527#117—942no—
528#117—942no—
529#117—941no—
530#117—941no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—471no—
535C2×C4⋊C4—471no—
536C2×C4⋊C4—471no—
537C2×C4⋊C4—471no—
538C2×C4⋊C4—944no—
539C2×C4⋊C4—944no—
540C2×C4⋊C4—942no—
541C2×C4⋊C4—942no—
542C2×C4⋊C4—942no—
543C2×C4⋊C4C22×D4712yes—
544C2×C4⋊C4C22×D4712yes—
545C2×C4⋊C4C22×D4712yes—
546C2×C22⋊C4—472no—
547C2×C22⋊C4—944no—
548C2×C22⋊C4—942no—
549C2×C22⋊C4—941no—
550C2×C42—472no—
551C2×C42—944no—
552C2×C42—942no—
553C2×C42—941no—
554#107—478no—
555#106—478no—
556#103—474no—
557#103—474no—
558#103C22×D4718yes—
559#102—474no—
560#102—474no—
561#102C22×D4718yes—
562#97—478no—
563C4×C8—478no—
564C24—21no—
565C24—941no—
566C24D4×D4711yescharacteristic
567#41—28no—
568#41—28no—
569#41—24no—
570#41—24no—
571#41—478no—
572#41—478no—
573#41—948no—
574#41—948no—
575#41—944no—
576#41—944no—
577#41C2×C4×D4718yes—
578#41C2×C4×D4718yescomplemented
579C2×Q8—21no—
580C2×Q8—22no—
581C2×Q8—474no—
582C2×Q8—472no—
583C2×Q8—941no—
584C2×Q8—942no—
585C2×Q8C2×C4×D4714yescomplemented
586C2×Q8C23×D4712yes—
587C2×D4—28no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—21no—
591C2×D4—22no—
592C2×D4—474no—
593C2×D4—472no—
594C2×D4—948no—
595C2×D4—942no—
596C2×D4—942no—
597C2×D4—941no—
598C2×D4—942no—
599C2×D4C2×C4×D4714yescomplemented
600C2×D4C23×D4712yes—
601C22×C4—21no—
602C22×C4—28no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—82no—
609C22×C4—472no—
610C22×C4—472no—
611C22×C4—948no—
612C22×C4—944no—
613C22×C4—944no—
614C22×C4—941no—
615C22×C4—948no—
616C22×C4—942no—
617C22×C4—942no—
618C22×C4—941no—
619C22×C4—941no—
620C22×C4—3764no—
621C22×C4C2×C4×D4714yes—
622C22×C4D4×D4711yescharacteristic
623C22×C4D4×D4711yescharacteristic
624C22×C4D4×D4711yescharacteristic
625C22×C4#1062535214yes—
626C22×C4C23×D4711yescharacteristic
627C22×C4C23×D4711yescharacteristic
628C22×C4C23×D4711yescharacteristic
629Q16—4716no—
630SD16—4716no—
631SD16—4716no—
632D8—4716no—
633M16—24no—
634M16—24no—
635M16—478no—
636M16—478no—
637C2×C8—24no—
638C2×C8—478no—
639C2×C8—474no—
640C2×C8C23×D4714yes—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—472no—
645C4⋊C4—472no—
646C4⋊C4—472no—
647C4⋊C4—472no—
648C4⋊C4—472no—
649C4⋊C4—472no—
650C4⋊C4—948no—
651C4⋊C4—944no—
652C4⋊C4—944no—
653C4⋊C4—941no—
654C4⋊C4—941no—
655C4⋊C4C23×D4714yes—
656C22⋊C4—474no—
657C22⋊C4—474no—
658C22⋊C4—948no—
659C22⋊C4—944no—
660C22⋊C4—944no—
661C22⋊C4—942no—
662C22⋊C4—942no—
663C42—474no—
664C42—474no—
665C42—944no—
666C42—944no—
667C42—948no—
668C42—942no—
669C42—942no—
670C23—22no—
671C23—24no—
672C23—41no—
673C23—41no—
674C23—81no—
675C23—81no—
676C23—944no—
677C23—942no—
678C23—1882no—
679C23—1882no—
680C23(C22⋊D47)⋊C414yes—
681C23C2×D4×D4711yescharacteristic
682C23C2×D4×D4711yescharacteristic
683C23C2×D4×D4711yescharacteristic
684Q8—24no—
685Q8—22no—
686Q8—474no—
687Q8—944no—
688Q8—942no—
689Q8C22×C4×D4714yes—
690D4—28no—
691D4—28no—
692D4—24no—
693D4—22no—
694D4—474no—
695D4—948no—
696D4—948no—
697D4—944no—
698D4—942no—
699D4C22×C4×D4714yes—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—28no—
703C2×C4—28no—
704C2×C4—24no—
705C2×C4—44no—
706C2×C4—82no—
707C2×C4—82no—
708C2×C4—474no—
709C2×C4—474no—
710C2×C4—944no—
711C2×C4—942no—
712C2×C4—948no—
713C2×C4—948no—
714C2×C4—942no—
715C2×C4—942no—
716C2×C4—3768no—
717C2×C4—3764no—
718C2×C4—3764no—
719C2×C4—3761no—
720C2×C4—3761no—
721C2×C4—1882no—
722C2×C4—1882no—
723C2×C4(C22⋊D47)⋊C414yes—
724C2×C4(C22⋊D47)⋊C414yes—
725C2×C4(C22⋊D47)⋊C414yes—
726C2×C4C22×C4×D4712yes—
727C2×C4C22×C4×D4712yes—
728C2×C4C22×C4×D4712yes—
729C2×C4C2×D4×D4711yescharacteristic
730C2×C4C2×D4×D4711yescharacteristic
731C2×C4C2×D4×D4711yescharacteristic
732C2×C4C2×#1062535212yes—
733C2×C4C2×#1062535212yes—
734C2×C4C2×#1062535212yes—
735C2×C4C24×D4711yescharacteristic
736C8—24no—
737C8—478no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—24no—
745C22—44no—
746C22—42no—
747C22—42no—
748C22—84no—
749C22—944no—
750C22—1888no—
751C22—1882no—
752C22—1882no—
753C22C2×(C22⋊D47)⋊C412yes—
754C22C2×(C22⋊D47)⋊C412yes—
755C22C2×(C22⋊D47)⋊C412yes—
756C22C22×D4×D4711yescharacteristic
757C4—24no—
758C4—44no—
759C4—944no—
760C4—944no—
761C4—944no—
762C4—1882no—
763C4—1882no—
764C4C2×(C22⋊D47)⋊C412yes—
765C4C2×(C22⋊D47)⋊C412yes—
766C4C2×(C22⋊D47)⋊C412yes—
767C4C23×C4×D4711yescharacteristic
768C4C22×#1062535211yescharacteristic
769C2—22no—
770C2—22no—
771C2—22no—
772C2—44no—
773C2—1884no—
774C2C22×(C22⋊D47)⋊C411yescharacteristic
775C2#2025816411yescharacteristic
776C2#2025817111yescharacteristic
subgroupG/H
centerC22C22×D4×D47
commutatorC4×C47C24×C4
FrattiniC2×C4C24×D47
FittingC2×C47×#417C2
socleC22×C47C23×D4
prime radicalC2×#15689921C2
cosocleC2×C4×C47C25
hypercenterC2×#417D47
hypocenterC47#60170
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. #20256591C2semidirect
3. C2×#15689604C2semidirect
4. #20252267C2semidirect
5. #20252259C2semidirect
6. #20252225C2semidirect
7. #20252214C2semidirect
8. #20252212C2semidirect
9. #20252201C2semidirect
10. C2×#15689163C2semidirect
11. #20251908C2semidirect
12. #20251806C2semidirect
13. C2×C47×#417C2semidirect
15. #15689921C4semidirect
24. #15689606C22semidirect
25. #15689606C22semidirect
29. #15689604C22semidirect
30. #15689601C22semidirect
32. #15689598C22semidirect
35. C2×#13093989C22semidirect
36. C2×#13093986C22semidirect
43. #15689232C22semidirect
44. #15689227C22semidirect
45. #15689226C22semidirect
46. #15689220C22semidirect
47. #15689215C22semidirect
48. #15689214C22semidirect
49. #15689208C22semidirect
50. #15689203C22semidirect
51. #15689163C22semidirect
52. #15689163C22semidirect
53. C2×#13093957C22semidirect
54. C2×#13093955C22semidirect
55. #15689133C22semidirect
56. #15689129C22semidirect
57. #15689125C22semidirect
58. #15689125C22semidirect
60. #15689081C22semidirect
61. #15689078C22semidirect
62. M16×Dic47C22semidirect
67. C47×#417C22semidirect
68. C2×#103×C47C22semidirect
69. C2×#102×C47C22semidirect
73. C2×#10625350C2×C4semidirect
81. #13094055C2×C4semidirect
82. #13094054C2×C4semidirect
83. #13094050C2×C4semidirect
84. #13094049C2×C4semidirect
85. #13094044C2×C4semidirect
90. C2×#10625329C2×C4semidirect
154. C2×#41×C47C2×C4semidirect
183. #41×C47C22×C4semidirect
186. C2×Q8×C47C22×C4semidirect
193. C2×D4×C47C22×C4semidirect
254. #10625337C22×C4semidirect
255. #10625336C22×C4semidirect
256. #10625335C22×C4semidirect
257. #10625334C22×C4semidirect
278. #10625329C22×C4semidirect
279. C2×C47⋊C8C22×C4semidirect
392. C2×#417D47semidirect
451. #417C2×D47semidirect
453. C2×#103C2×D47semidirect
454. C2×#102C2×D47semidirect
458. C47#60170semidirect
468. C2×#41C4×D47semidirect
578. #41C2×C4×D47semidirect
585. C2×Q8C2×C4×D47semidirect
599. C2×D4C2×C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156899212
#202565912
C2×#156896042
#202522672
#202522592
#202522252
#202522142
#202522122
#202522012
C2×#156891632
#202519082
#202518062
C2×C47×#4172
#6017047