Finite Group Databasebeta

← #27083904

Subgroups — #27083904

Order 12032.

2038 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256791C211yesmaximal, characteristic, complemented
2C2×#15689602C211yesmaximal, characteristic
3#20253251C214yesmaximal, complemented
4#20253245C214yesmaximal, complemented
5#20253240C214yesmaximal, complemented
6#20253234C214yesmaximal, complemented
7#20253195C211yesmaximal, characteristic, complemented
8#20253192C212yesmaximal, complemented
9#20253189C211yesmaximal, characteristic, complemented
10#20253185C211yesmaximal, characteristic, complemented
11#20253182C212yesmaximal, complemented
12#428×D47C212yesmaximal, complemented
13#20251950C211yesmaximal, characteristic, complemented
14#20251902C212yesmaximal
15C47×#3077C211yesmaximal, characteristic, complemented
16C22×#10625352C2211yescharacteristic
17C2×M16×D47C2212yes—
18#15689753C2212yescomplemented
19#15689753C2212yescomplemented
20#15689752—21no—
21#15689752—21no—
22#15689750C2212yescomplemented
23#15689750C2212yescomplemented
24#15689748—21no—
25#15689748—21no—
26#15689680C2211yescharacteristic
27#15689677—22no—
28#15689677—22no—
29#15689676C2212yes—
30#15689602—22no—
31#15689602—22no—
32#15689602C2214yes—
33#15689602C2214yes—
34C2×C4×Dic94C2211yescharacteristic
35C2×#13093989C2211yescharacteristic
36C2×D4×Dic47C2211yescharacteristic
37C2×C4×C22⋊D47—21no—
38C2×(C22⋊D47)⋊C4—21no—
39C2×#13093981C2211yescharacteristic
40C2×#13093980—21no—
41#117×D47C2212yes—
42C22×Dic47⋊C4—21no—
43C2×C4⋊C4×D47C2211yescharacteristic
44#15689433C2214yescomplemented
45#15689431C2214yescomplemented
46#15689429C2214yescomplemented
47#15689427C2214yescomplemented
48#15689425C2214yescomplemented
49#15689423C2214yescomplemented
50#15689421C2214yescomplemented
51#15689419C2212yescomplemented
52#15689417C2214yescomplemented
53#15689415C2212yescomplemented
54#15689413C2212yescomplemented
55#15689411C2214yescomplemented
56#15689409C2212yescomplemented
57#15689407C2214yescomplemented
58#15689405C2212yescomplemented
59#15689403C2212yescomplemented
60#15689401C2214yescomplemented
61#15689166C2212yes—
62#15689165C2212yes—
63#15689164C2214yescomplemented
64#15689163C2212yes—
65#15689162C2214yescomplemented
66#107×D47C2214yescomplemented
67#106×D47C2214yescomplemented
68#15689148C2214yescomplemented
69#15689148C2214yescomplemented
70#15689147C2211yescharacteristic
71#15689146C2212yes—
72#15689133C2212yes—
73#15689131C2212yes—
74#15689128C2212yes—
75#15689121C2214yes—
76#15689121C2214yes—
77#15689116C2214yes—
78#15689116C2214yes—
79C47×#533C2211yescharacteristic
80C2×C4×D4×C47C2211yescharacteristic
81C47×#478C2214yescomplemented
82C47×#476C2212yescomplemented
83C47×#474C2212yescomplemented
84C47×#428C2212yes—
85C47×#423C2211yescharacteristic
86C47×#418C2212yes—
87C2×#10625352—22no—
88C2×#10625352—24no—
89C2×#10625352Q818yescomplemented
90C2×#10625352C2314yes—
91C22×Dic94C2311yescharacteristic
92C22×C22⋊D47—21no—
93C23×Dic47—21no—
94C23×Dic47—21no—
95C22×C4×D47—21no—
96C22×C4×D47C2311yescharacteristic
97C2×#10625329C2312yes—
98C2×#10625324C2314yes—
99M16×D47—28no—
100C2×C8×D47C2314yes—
101#13094024C2311yescharacteristic
102#13094024C2311yescharacteristic
103#13094023—22no—
104#13094023—22no—
105#13094023C2312yes—
106#13094023C2312yes—
107#13094022—22no—
108#13094022—22no—
109#13094016C2312yes—
110#13094015C2312yes—
111#13094015C2312yes—
112#13094014—22no—
113#13094014—22no—
114#13094014—22no—
115#13094014—22no—
116#13094004—22no—
117#13094004—22no—
118#13094003—21no—
119#13094003—21no—
120#13094002—22no—
121#13094002—22no—
122#13094002—22no—
123#13094002—22no—
124#13094001—22no—
125#13094001—22no—
126#13094000—22no—
127#13094000—22no—
128C4×Dic94—21no—
129C4×Dic94—21no—
130C4×Dic94—21no—
131C4×Dic94—21no—
132C4×Dic94—22no—
133C4×Dic94—22no—
134C4×Dic94C2312yes—
135C4×Dic94C2312yes—
136#13093989—22no—
137#13093989C2314yes—
138D4×Dic47—22no—
139D4×Dic47C2314yes—
140C4×C22⋊D47—24no—
141C4×C22⋊D47—24no—
142(C22⋊D47)⋊C4—24no—
143(C22⋊D47)⋊C4—24no—
144#13093983C2312yes—
145#13093982C2312yes—
146#13093982C2312yes—
147#13093981—22no—
148#13093981D412yes—
149#13093981D412yes—
150#13093981C2312yes—
151#13093981C2312yes—
152#13093980—22no—
153#13093980—24no—
154#13093980—24no—
155C2×C4⋊Dic47C2311yescharacteristic
156C2×Dic47⋊C4—21no—
157C2×Dic47⋊C4—21no—
158C2×Dic47⋊C4—21no—
159C2×Dic47⋊C4—24no—
160C2×Dic47⋊C4—24no—
161C2×Dic47⋊C4D411yescharacteristic
162C2×Dic47⋊C4D411yescharacteristic
163C4⋊C4×D47—22no—
164C4⋊C4×D47C2312yes—
165C4⋊C4×D47C2312yes—
166C4⋊C4×D47C2314yes—
167C2×C22⋊Dic47—21no—
168C2×(C2×D47)⋊C4D411yescharacteristic
169C2×(C2×D47)⋊C4D411yescharacteristic
170C22⋊C4×D47—22no—
171C2×C4×Dic47—21no—
172C2×C4×Dic47—21no—
173C2×C4×Dic47C2311yescharacteristic
174C42×D47—22no—
175#13093958C2314yes—
176#13093957C2314yes—
177#13093957C2314yes—
178#13093956C2314yes—
179#13093955C2314yes—
180#13093955C2314yes—
181C4⋊(C47⋊C8)C2312yes—
182C4⋊(C47⋊C8)C2312yes—
183Dic47⋊C8C2314yes—
184Dic47⋊C8C2314yes—
185#13093949C2314yes—
186#13093949C2314yes—
187#13093947C2314yes—
188#13093947C2314yes—
189#13093945C2314yes—
190#13093945C2314yes—
191C22×D4×C47C2311yescharacteristic
192C23×C4×C47—21no—
193C2×M16×C47C2312yes—
194C4⋊Q8×C47C2311yescharacteristic
195C4⋊Q8×C47C2311yescharacteristic
196#125×C47C2312yes—
197C22⋊Q8×C47—21no—
198C22⋊Q8×C47—21no—
199C4×Q8×C47—21no—
200C4×Q8×C47—21no—
201C4×D4×C47—21no—
202C4×D4×C47—21no—
203C4×D4×C47C2312yes—
204C4×D4×C47C2312yes—
205#117×C47C2312yes—
206C2×C4⋊C4×C47C2311yescharacteristic
207C2×C22⋊C4×C47—21no—
208C2×C42×C47C2311yescharacteristic
209#107×C47C2314yes—
210#106×C47C2314yes—
211C4⋊C8×C47C2312yes—
212C4⋊C8×C47C2312yes—
213#102×C47C2314yes—
214#102×C47C2314yes—
215C24×C47—21no—
216C23×D47C2×D411yescharacteristic
217C2×Q8×C47—21no—
218C2×Q8×C47—21no—
219C2×D4×C47—21no—
220C2×D4×C47—22no—
221C2×D4×C47C2×Q814yes—
222C2×D4×C47C2412yes—
223C22×C4×C47—21no—
224C22×C4×C47—22no—
225C22×C4×C47—22no—
226C22×C4×C47—82no—
227C22×C4×C47C2×D411yescharacteristic
228C22×C4×C47C2×D411yescharacteristic
229C22×C4×C47C2411yescharacteristic
230C2×C22⋊D47—28no—
231C2×C22⋊D47—24no—
232C22×Dic47—21no—
233C22×Dic47—28no—
234C22×Dic47—24no—
235C22×Dic47—21no—
236C22×Dic47—24no—
237C22×Dic47—82no—
238C22×Dic47C2×D411yescharacteristic
239C22×Dic47C2×D411yescharacteristic
240C22×Dic47C2×D411yescharacteristic
241#10625352—216no—
242#10625352—28no—
243#10625352C2×Q8116yes—
244C2×C4×D47—22no—
245C2×C4×D47—22no—
246C2×C4×D47—24no—
247C2×C4×D47—82no—
248C2×C4×D47C2×D412yes—
249C2×C4×D47C2×Q814yes—
250C2×C4×D47#4114yes—
251C2×C4×D47C2412yes—
252C2×Dic94—21no—
253C2×Dic94—22no—
254C2×Dic94—21no—
255C2×Dic94—21no—
256C2×Dic94—22no—
257C2×Dic94—22no—
258C2×Dic94C2×Q814yes—
259C2×Dic94C2412yes—
260M16×C47—24no—
261C2×C8×C47C2414yes—
262C4⋊C4×C47—21no—
263C4⋊C4×C47—22no—
264C4⋊C4×C47—22no—
265C4⋊C4×C47—21no—
266C4⋊C4×C47—21no—
267C4⋊C4×C47C2412yes—
268C4⋊C4×C47C2412yes—
269C4⋊C4×C47C2412yes—
270C22⋊C4×C47—22no—
271C22⋊C4×C47—22no—
272C22⋊C4×C47—22no—
273C42×C47—22no—
274C42×C47C2×D411yescharacteristic
275C42×C47C2×D411yescharacteristic
276C42×C47C2411yescharacteristic
277C42×C47C2411yescharacteristic
278C22⋊Dic47—22no—
279C22⋊Dic47—24no—
280(C2×D47)⋊C4—22no—
281(C2×D47)⋊C4—22no—
282(C2×D47)⋊C4C2×D412yes—
283(C2×D47)⋊C4C2×D412yes—
284(C2×D47)⋊C4C2×D412yes—
285(C2×D47)⋊C4C2×D412yes—
286C4⋊Dic47—21no—
287C4⋊Dic47—21no—
288C4⋊Dic47—21no—
289C4⋊Dic47—22no—
290C4⋊Dic47—22no—
291C4⋊Dic47C2412yes—
292C4⋊Dic47C2412yes—
293C4⋊Dic47C2412yes—
294Dic47⋊C4—22no—
295Dic47⋊C4—22no—
296Dic47⋊C4—22no—
297Dic47⋊C4—22no—
298Dic47⋊C4—24no—
299Dic47⋊C4—22no—
300Dic47⋊C4—22no—
301Dic47⋊C4—24no—
302Dic47⋊C4—22no—
303Dic47⋊C4—22no—
304Dic47⋊C4—22no—
305Dic47⋊C4—22no—
306Dic47⋊C4C2×D412yes—
307Dic47⋊C4C2×D412yes—
308Dic47⋊C4C2×D412yes—
309Dic47⋊C4C2×D412yes—
310C4×Dic47—22no—
311C4×Dic47—22no—
312C4×Dic47—22no—
313C4×Dic47—22no—
314C4×Dic47—22no—
315C4×Dic47—24no—
316C4×Dic47C2×D412yes—
317C4×Dic47C2412yes—
318#10625329—24no—
319C2×C47⋊C8C2414yes—
320#10625324—28no—
321C8×D47—28no—
322C23×C47—24no—
323C23×C47—22no—
324C23×C47—42no—
325C23×C47—42no—
326C23×C47C22×D411yescharacteristic
327C22×D47—41no—
328C22×D47—41no—
329C22×D47C22⋊Q814yes—
330C22×D47C22×D412yes—
331Q8×C47—81no—
332Q8×C47—81no—
333D4×C47—24no—
334D4×C47—22no—
335D4×C47C22×Q814yes—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—41no—
340C2×C4×C47—41no—
341C2×C4×C47—42no—
342C2×C4×C47—82no—
343C2×C4×C47—82no—
344C2×C4×C47C22×D411yescharacteristic
345C2×C4×C47C22×D411yescharacteristic
346C2×C4×C47C22×D411yescharacteristic
347C2×C4×C47C22×D411yescharacteristic
348C2×C4×C47C22×D411yescharacteristic
349C2×C4×C47C22×Q812yes—
350C2×C4×C47C2×#4112yes—
351C2×C4×C47C2511yescharacteristic
352C22⋊D47—216no—
353C2×Dic47—24no—
354C2×Dic47—22no—
355C2×Dic47—216no—
356C2×Dic47—22no—
357C2×Dic47—22no—
358C2×Dic47—22no—
359C2×Dic47—41no—
360C2×Dic47—41no—
361C2×Dic47—42no—
362C2×Dic47—84no—
363C2×Dic47C22⋊Q814yes—
364C2×Dic47C22×D412yes—
365C2×Dic47C22×D412yes—
366C2×Dic47C22×D412yes—
367C4×D47—82no—
368C4×D47—82no—
369C4×D47—84no—
370C4×D47C22⋊Q818yes—
371C4×D47C22×Q814yes—
372C4×D47C2×#4114yes—
373Dic94—24no—
374Dic94—22no—
375Dic94—82no—
376Dic94—82no—
377Dic94—81no—
378Dic94—81no—
379Dic94C22×Q814yes—
380C8×C47—24no—
381C47⋊C8—24no—
382#60492—471nomaximal, Sylow
383C22×C47—21no—
384C22×C47—21no—
385C22×C47—24no—
386C22×C47—48no—
387C22×C47—42no—
388C22×C47—42no—
389C22×C47C2×C22⋊Q812yes—
390C22×C47C23×D411yescharacteristic
391C2×D47—22no—
392C2×D47—22no—
393C2×D47—44no—
394C2×D47C2×C22⋊Q814yes—
395C4×C47—21no—
396C4×C47—21no—
397C4×C47—21no—
398C4×C47—21no—
399C4×C47—42no—
400C4×C47—42no—
401C4×C47—42no—
402C4×C47C2×C22⋊Q812yes—
403C4×C47C23×Q811yescharacteristic
404C4×C47C22×#4111yescharacteristic
405Dic47—22no—
406Dic47—22no—
407Dic47—24no—
408Dic47—42no—
409Dic47—42no—
410Dic47—42no—
411Dic47C2×C22⋊Q814yes—
412#3458—471no—
413C2×#520—471no—
414#3084—474no—
415#3084—474no—
416#3083—474no—
417#3083—474no—
418#3078—472no—
419#3078—471no—
420#3078—471no—
421#3077—472no—
422#3077—471no—
423#3077D4711yescharacteristic, complemented
424C2×#428—472no—
425#2905—471no—
426#2896—472no—
427C2×C47—22no—
428C2×C47—44no—
429C2×C47C22×C22⋊Q811yescharacteristic
430C2×C47#358511yescharacteristic
431C2×C47#358611yescharacteristic
432D47—24no—
433C22×#41—471no—
434C22×M16—472no—
435#544—472no—
436#544—472no—
437#544—472no—
438#544—472no—
439#544—941no—
440#544—941no—
441#543—941no—
442#543—941no—
443#533—472no—
444#533—471no—
445#533—942no—
446#533—942no—
447#533C2×D4711yescharacteristic
448#520—474no—
449#520—474no—
450#520—942no—
451#520—942no—
452C2×C4×Q8—471no—
453C2×C4×Q8—471no—
454C2×C4×D4—471no—
455C2×C4×D4—941no—
456C2×C4×D4—941no—
457C2×C4×D4C2×D4711yescharacteristic
458C2×#117—471no—
459C2×#117—472no—
460C2×#117—941no—
461C22×C4⋊C4—471no—
462C22×C4⋊C4—941no—
463#479—474no—
464#479—474no—
465#479—474no—
466#479—474no—
467#478—474no—
468#478—474no—
469#478—474no—
470#478C2×D4714yescomplemented
471#477—472no—
472#477—474no—
473#477—472no—
474#476—472no—
475#476—474no—
476#476C2×D4712yescomplemented
477#475—472no—
478#475—474no—
479#475—472no—
480#474—472no—
481#474—474no—
482#474C2×D4712yescomplemented
483#428—472no—
484#428—472no—
485#428—472no—
486#428—474no—
487#428—474no—
488#428C2×D4712yes—
489C2×#107—474no—
490C2×#106—474no—
491#424—474no—
492#424—474no—
493#423—472no—
494#423—471no—
495#423C2×D4711yescharacteristic
496#419—472no—
497#419—472no—
498#418—472no—
499#418C2×D4712yes—
500#417—474no—
501#417—474no—
502#416—474no—
503#416—474no—
504C47#6049211yescharacteristic, complemented, Sylow
505C2×#41—478no—
506C2×#41—474no—
507C2×#41—942no—
508C2×#41—944no—
509C22×Q8—471no—
510C22×D4—941no—
511C22×D4C22×D4711yescharacteristic
512C23×C4—21no—
513C23×C4—471no—
514C23×C4—941no—
515C23×C4—941no—
516C23×C4—941no—
517C2×M16—472no—
518C2×M16—474no—
519C2×M16—948no—
520C2×M16C22×D4712yes—
521C22×C8—474no—
522C4⋊Q8—472no—
523C4⋊Q8—472no—
524C4⋊Q8—471no—
525C4⋊Q8—471no—
526C4⋊Q8—942no—
527C4⋊Q8—942no—
528C4⋊Q8—942no—
529C4⋊Q8—942no—
530C4⋊Q8C22×D4711yescharacteristic
531C4⋊Q8C22×D4711yescharacteristic
532#125—472no—
533#125—472no—
534#125—472no—
535#125—942no—
536#125—942no—
537#125—942no—
538#125—942no—
539#125C22×D4712yes—
540C22⋊Q8—21no—
541C22⋊Q8—21no—
542C22⋊Q8—942no—
543C22⋊Q8—942no—
544C22⋊Q8—942no—
545C22⋊Q8—942no—
546C22⋊Q8—942no—
547C22⋊Q8—942no—
548C22⋊Q8—942no—
549C22⋊Q8—942no—
550C22⋊Q8—942no—
551C22⋊Q8—942no—
552C22⋊Q8—941no—
553C22⋊Q8—941no—
554C4×Q8—21no—
555C4×Q8—21no—
556C4×Q8—474no—
557C4×Q8—472no—
558C4×Q8—472no—
559C4×Q8—942no—
560C4×Q8—942no—
561C4×Q8—942no—
562C4×Q8—941no—
563C4×Q8—941no—
564C4×Q8—941no—
565C4×Q8—941no—
566C4×D4—21no—
567C4×D4—21no—
568C4×D4—474no—
569C4×D4—942no—
570C4×D4—944no—
571C4×D4—944no—
572C4×D4—944no—
573C4×D4—944no—
574C4×D4C22×D4712yes—
575C4×D4C22×D4712yes—
576#117—472no—
577#117—472no—
578#117—472no—
579#117—472no—
580#117—472no—
581#117—472no—
582#117—472no—
583#117—942no—
584#117—944no—
585#117—944no—
586#117—942no—
587#117C22×D4712yes—
588C2×C4⋊C4—471no—
589C2×C4⋊C4—471no—
590C2×C4⋊C4—471no—
591C2×C4⋊C4—474no—
592C2×C4⋊C4—472no—
593C2×C4⋊C4—472no—
594C2×C4⋊C4—942no—
595C2×C4⋊C4—944no—
596C2×C4⋊C4—944no—
597C2×C4⋊C4—941no—
598C2×C4⋊C4—941no—
599C2×C4⋊C4—941no—
600C2×C4⋊C4C22×D4711yescharacteristic
601C2×C22⋊C4—21no—
602C2×C22⋊C4—471no—
603C2×C22⋊C4—471no—
604C2×C22⋊C4—942no—
605C2×C22⋊C4—941no—
606C2×C42—471no—
607C2×C42—942no—
608C2×C42—941no—
609C2×C42—941no—
610C2×C42C22×D4711yescharacteristic
611#107—474no—
612#107—474no—
613#107—474no—
614#107C22×D4714yes—
615#106—474no—
616#106—474no—
617#106—474no—
618#106C22×D4714yes—
619C4⋊C8—474no—
620C4⋊C8—474no—
621C4⋊C8—472no—
622C4⋊C8—472no—
623C4⋊C8C22×D4712yes—
624C4⋊C8C22×D4712yes—
625#103—474no—
626#103—474no—
627#103—474no—
628#103—474no—
629#102—474no—
630#102—474no—
631#102C22×D4714yes—
632#102C22×D4714yes—
633C24—21no—
634C24—471no—
635#41—4716no—
636#41—9416no—
637#41—948no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—474no—
641C2×Q8—472no—
642C2×Q8—942no—
643C2×Q8—942no—
644C2×Q8—941no—
645C2×Q8—941no—
646C2×Q8—941no—
647C2×Q8—942no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—944no—
651C2×D4—948no—
652C2×D4Q8×D4714yes—
653C2×D4C23×D4712yes—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—82no—
658C22×C4—471no—
659C22×C4—472no—
660C22×C4—474no—
661C22×C4—474no—
662C22×C4—472no—
663C22×C4—471no—
664C22×C4—471no—
665C22×C4—942no—
666C22×C4—942no—
667C22×C4—944no—
668C22×C4—944no—
669C22×C4—948no—
670C22×C4—944no—
671C22×C4—941no—
672C22×C4—941no—
673C22×C4—3762no—
674C22×C4—3762no—
675C22×C4D4×D4711yescharacteristic
676C22×C4D4×D4711yescharacteristic
677C22×C4C23×D4711yescharacteristic
678M16—24no—
679M16—948no—
680M16—944no—
681C2×C8—474no—
682C2×C8—948no—
683C2×C8C23×D4714yes—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—472no—
690C4⋊C4—472no—
691C4⋊C4—472no—
692C4⋊C4—472no—
693C4⋊C4—472no—
694C4⋊C4—472no—
695C4⋊C4—472no—
696C4⋊C4—944no—
697C4⋊C4—942no—
698C4⋊C4—942no—
699C4⋊C4—944no—
700C4⋊C4—942no—
701C4⋊C4—942no—
702C4⋊C4—942no—
703C4⋊C4—942no—
704C4⋊C4—942no—
705C4⋊C4—942no—
706C4⋊C4—942no—
707C4⋊C4—942no—
708C4⋊C4—942no—
709C4⋊C4—942no—
710C4⋊C4—941no—
711C4⋊C4—941no—
712C4⋊C4—941no—
713C4⋊C4C23×D4712yes—
714C4⋊C4C23×D4712yes—
715C4⋊C4C23×D4712yes—
716C22⋊C4—22no—
717C22⋊C4—22no—
718C22⋊C4—22no—
719C22⋊C4—472no—
720C22⋊C4—472no—
721C22⋊C4—472no—
722C22⋊C4—472no—
723C22⋊C4—942no—
724C22⋊C4—942no—
725C22⋊C4—944no—
726C22⋊C4—942no—
727C42—22no—
728C42—472no—
729C42—472no—
730C42—942no—
731C42—942no—
732C42—944no—
733C42—942no—
734C42—942no—
735C42—942no—
736C42D4×D4711yescharacteristic
737C42D4×D4711yescharacteristic
738C42C23×D4711yescharacteristic
739C42C23×D4711yescharacteristic
740C23—24no—
741C23—22no—
742C23—42no—
743C23—42no—
744C23—472no—
745C23—474no—
746C23—1881no—
747C23—1881no—
748C23C2×D4×D4711yescharacteristic
749Q8—81no—
750Q8—81no—
751Q8—474no—
752Q8—944no—
753Q8—942no—
754Q8—3761no—
755Q8—3761no—
756Q8—3762no—
757Q8—3762no—
758D4—24no—
759D4—22no—
760D4—9416no—
761D4C2×Q8×D4714yes—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—82no—
769C2×C4—82no—
770C2×C4—474no—
771C2×C4—472no—
772C2×C4—478no—
773C2×C4—474no—
774C2×C4—474no—
775C2×C4—472no—
776C2×C4—472no—
777C2×C4—9416no—
778C2×C4—944no—
779C2×C4—942no—
780C2×C4—942no—
781C2×C4—942no—
782C2×C4—942no—
783C2×C4—3762no—
784C2×C4—3762no—
785C2×C4—3764no—
786C2×C4—3764no—
787C2×C4—1881no—
788C2×C4—1881no—
789C2×C4—1882no—
790C2×C4C2×D4×D4711yescharacteristic
791C2×C4C2×D4×D4711yescharacteristic
792C2×C4C2×D4×D4711yescharacteristic
793C2×C4C2×D4×D4711yescharacteristic
794C2×C4C2×D4×D4711yescharacteristic
795C2×C4C2×Q8×D4712yes—
796C2×C4#41×D4712yes—
797C2×C4C24×D4711yescharacteristic
798C8—24no—
799C8—944no—
800C22—21no—
801C22—21no—
802C22—24no—
803C22—48no—
804C22—42no—
805C22—42no—
806C22—474no—
807C22—942no—
808C22—942no—
809C22—1884no—
810C22C22⋊Q8×D4712yes—
811C22C22×D4×D4711yescharacteristic
812C4—21no—
813C4—21no—
814C4—21no—
815C4—21no—
816C4—42no—
817C4—42no—
818C4—42no—
819C4—474no—
820C4—944no—
821C4—942no—
822C4—942no—
823C4—1882no—
824C4—1882no—
825C4—1882no—
826C4C22⋊Q8×D4712yes—
827C4C22×Q8×D4711yescharacteristic
828C4C2×#41×D4711yescharacteristic
829C2—22no—
830C2—44no—
831C2—944no—
832C2C2×C22⋊Q8×D4711yescharacteristic
833C2#2025816411yescharacteristic
834C2#2025817211yescharacteristic
subgroupG/H
centerC22C22×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#3077C2
socleC22×C47C23×D4
prime radicalC22×#10625352C22
hypercenter#3077D47
hypocenterC47#60492
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #20256791C2semidirect
3. #20253251C2semidirect
4. #20253245C2semidirect
5. #20253240C2semidirect
6. #20253234C2semidirect
7. #20253195C2semidirect
8. #20253192C2semidirect
9. #20253189C2semidirect
10. #20253185C2semidirect
11. #20253182C2semidirect
12. #428×D47C2semidirect
13. #20251950C2semidirect
15. C47×#3077C2semidirect
18. #15689753C22semidirect
19. #15689753C22semidirect
22. #15689750C22semidirect
23. #15689750C22semidirect
44. #15689433C22semidirect
45. #15689431C22semidirect
46. #15689429C22semidirect
47. #15689427C22semidirect
48. #15689425C22semidirect
49. #15689423C22semidirect
50. #15689421C22semidirect
51. #15689419C22semidirect
52. #15689417C22semidirect
53. #15689415C22semidirect
54. #15689413C22semidirect
55. #15689411C22semidirect
56. #15689409C22semidirect
57. #15689407C22semidirect
58. #15689405C22semidirect
59. #15689403C22semidirect
60. #15689401C22semidirect
63. #15689164C22semidirect
65. #15689162C22semidirect
66. #107×D47C22semidirect
67. #106×D47C22semidirect
68. #15689148C22semidirect
69. #15689148C22semidirect
81. C47×#478C22semidirect
82. C47×#476C22semidirect
83. C47×#474C22semidirect
89. C2×#10625352Q8semidirect
423. #3077D47semidirect
470. #478C2×D47semidirect
476. #476C2×D47semidirect
482. #474C2×D47semidirect
504. C47#60492semidirect

Maximal subgroups

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

subgroupindex
#202567912
C2×#156896022
#202532512
#202532452
#202532402
#202532342
#202531952
#202531922
#202531892
#202531852
#202531822
#428×D472
#202519502
#202519022
C47×#30772
#6049247