Finite Group Databasebeta

← #27083897

Subgroups — #27083897

Order 12032.

1962 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256791C211yesmaximal, characteristic
2C2×#15689599C211yesmaximal, characteristic
3#20253229C214yesmaximal, complemented
4#20253227C214yesmaximal, complemented
5#20253225C214yesmaximal, complemented
6#20253223C214yesmaximal, complemented
7#20253195C211yesmaximal, characteristic, complemented
8#20253193C211yesmaximal, characteristic, complemented
9#20253192C212yesmaximal, complemented
10#20253190C212yesmaximal, complemented
11#20253189C211yesmaximal, characteristic, complemented
12#20251975C212yesmaximal
13#20251950C211yesmaximal, characteristic
14#419×D47C212yesmaximal
15C47×#3078C211yesmaximal, characteristic, complemented
16C22×Q8×D47C2211yescharacteristic
17C2×M16×D47C2212yes—
18#15689753C2212yes—
19#15689753C2212yes—
20#15689752—21no—
21#15689752—21no—
22#15689750C2212yes—
23#15689750C2212yes—
24#15689748—21no—
25#15689748—21no—
26#15689680C2211yescharacteristic
27#15689677—22no—
28#15689677—22no—
29#15689676C2212yes—
30#15689599—22no—
31#15689599—22no—
32#15689599C2214yes—
33#15689599C2214yes—
34C2×Q8×Dic47C2211yescharacteristic
35C2×C4×Dic94—21no—
36C2×C4×Dic94C2211yescharacteristic
37C2×#13093989—21no—
38C2×#13093989C2211yescharacteristic
39C2×#13093982—21no—
40C2×#13093982C2211yescharacteristic
41C2×#13093981—21no—
42C2×#13093981C2211yescharacteristic
43#117×D47C2212yes—
44#15689433C2214yescomplemented
45#15689432C2214yescomplemented
46#15689431C2214yescomplemented
47#15689430C2214yescomplemented
48#15689429C2214yescomplemented
49#15689428C2214yescomplemented
50#15689427C2214yescomplemented
51#15689419C2212yescomplemented
52#15689418C2212yescomplemented
53#15689417C2214yescomplemented
54#15689416C2214yescomplemented
55#15689415C2212yescomplemented
56#15689409C2212yescomplemented
57#15689408C2212yescomplemented
58#15689407C2214yescomplemented
59#15689406C2214yescomplemented
60#15689405C2212yescomplemented
61#15689166C2212yes—
62#15689165C2212yes—
63#15689164C2214yes—
64#15689163C2212yes—
65#15689162C2214yes—
66#15689160C2214yes—
67#15689158C2214yes—
68#15689148C2214yes—
69#15689148C2214yes—
70#15689147C2211yescharacteristic
71#15689146C2212yes—
72#15689133C2212yes—
73#15689132C2212yes—
74#15689131C2212yes—
75#15689130C2214yes—
76#15689130C2214yes—
77#103×D47C2214yes—
78#103×D47C2214yes—
79C47×#533C2211yescharacteristic
80C2×C4×Q8×C47C2211yescharacteristic
81C47×#479C2214yescomplemented
82C47×#477C2212yescomplemented
83C47×#475C2212yescomplemented
84C47×#428C2212yes—
85C47×#423C2211yescharacteristic
86C47×#419C2212yes—
87C22×Dic94—21no—
88C22×Dic94C2311yescharacteristic
89C2×Q8×D47—22no—
90C2×Q8×D47—24no—
91C2×Q8×D47Q818yescomplemented
92C2×Q8×D47C2314yes—
93C22×C4×D47—21no—
94C22×C4×D47C2311yescharacteristic
95C2×#10625329C2312yes—
96C2×#10625324C2314yes—
97M16×D47—28no—
98C2×C8×D47C2314yes—
99#13094024C2311yescharacteristic
100#13094024C2311yescharacteristic
101#13094023—22no—
102#13094023—22no—
103#13094023C2312yes—
104#13094023C2312yes—
105#13094022—22no—
106#13094022—22no—
107#13094016C2312yes—
108#13094015C2312yes—
109#13094015C2312yes—
110#13094014—22no—
111#13094014—22no—
112#13094014—22no—
113#13094014—22no—
114#13094004—22no—
115#13094004—22no—
116#13094003—21no—
117#13094003—21no—
118#13094002—22no—
119#13094002—22no—
120#13094002—22no—
121#13094002—22no—
122#13094001—22no—
123#13094001—22no—
124#13094000—22no—
125#13094000—22no—
126Q8×Dic47—22no—
127Q8×Dic47C2314yes—
128C4×Dic94—21no—
129C4×Dic94—21no—
130C4×Dic94—21no—
131C4×Dic94—21no—
132C4×Dic94—24no—
133C4×Dic94—24no—
134C4×Dic94—22no—
135C4×Dic94—22no—
136C4×Dic94C2312yes—
137C4×Dic94C2312yes—
138#13093989—24no—
139#13093989—24no—
140#13093989—22no—
141#13093989C2314yes—
142#13093983C2312yes—
143#13093982—22no—
144#13093982—24no—
145#13093982—24no—
146#13093982C2312yes—
147#13093982C2312yes—
148#13093982C2314yes—
149#13093981—22no—
150#13093981—24no—
151#13093981—24no—
152#13093981D412yes—
153#13093981D412yes—
154#13093981C2312yes—
155#13093981C2312yes—
156#13093980—22no—
157C2×C4⋊Dic47—21no—
158C2×C4⋊Dic47C2311yescharacteristic
159C2×Dic47⋊C4—21no—
160C2×Dic47⋊C4—21no—
161C2×Dic47⋊C4D411yescharacteristic
162C2×Dic47⋊C4D411yescharacteristic
163C4⋊C4×D47C2312yes—
164C4⋊C4×D47C2312yes—
165C2×(C2×D47)⋊C4—21no—
166C2×(C2×D47)⋊C4D411yescharacteristic
167C2×(C2×D47)⋊C4D411yescharacteristic
168C22⋊C4×D47—22no—
169C2×C4×Dic47—21no—
170C2×C4×Dic47—21no—
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#13093948C2314yes—
188#13093948C2314yes—
189#13093947C2314yes—
190#13093947C2314yes—
191C22×Q8×C47C2311yescharacteristic
192C2×M16×C47C2312yes—
193C4⋊Q8×C47C2311yescharacteristic
194C4⋊Q8×C47C2311yescharacteristic
195#125×C47C2312yes—
196C22⋊Q8×C47—21no—
197C22⋊Q8×C47—21no—
198C4×Q8×C47—21no—
199C4×Q8×C47—21no—
200C4×Q8×C47—21no—
201C4×Q8×C47—21no—
202C4×Q8×C47C2312yes—
203C4×Q8×C47C2312yes—
204#117×C47C2312yes—
205C2×C4⋊C4×C47—21no—
206C2×C4⋊C4×C47C2311yescharacteristic
207C2×C42×C47—21no—
208C2×C42×C47C2311yescharacteristic
209#107×C47C2314yes—
210#106×C47C2314yes—
211C4⋊C8×C47C2312yes—
212C4⋊C8×C47C2312yes—
213#103×C47C2314yes—
214#103×C47C2314yes—
215C23×D47C2×D411yescharacteristic
216C2×Q8×C47—21no—
217C2×Q8×C47—21no—
218C2×Q8×C47—21no—
219C2×Q8×C47—22no—
220C2×Q8×C47C2×Q814yes—
221C2×Q8×C47C2412yes—
222C22×C4×C47—21no—
223C22×C4×C47—21no—
224C22×C4×C47C2×D411yescharacteristic
225C22×C4×C47C2×D411yescharacteristic
226C22×C4×C47C2411yescharacteristic
227C22×Dic47—21no—
228C22×Dic47—21no—
229C22×Dic47C2×D411yescharacteristic
230C22×Dic47C2×D411yescharacteristic
231C22×Dic47C2×D411yescharacteristic
232Q8×D47—216no—
233Q8×D47—28no—
234Q8×D47C2×Q8116yes—
235C2×C4×D47—28no—
236C2×C4×D47—24no—
237C2×C4×D47—22no—
238C2×C4×D47—22no—
239C2×C4×D47C2×D412yes—
240C2×C4×D47C2×Q814yes—
241C2×C4×D47#4114yes—
242C2×C4×D47C2412yes—
243C2×Dic94—21no—
244C2×Dic94—22no—
245C2×Dic94—28no—
246C2×Dic94—24no—
247C2×Dic94—21no—
248C2×Dic94—21no—
249C2×Dic94—22no—
250C2×Dic94—22no—
251C2×Dic94C2×Q814yes—
252C2×Dic94C2412yes—
253M16×C47—24no—
254C2×C8×C47C2414yes—
255C4⋊C4×C47—22no—
256C4⋊C4×C47—22no—
257C4⋊C4×C47—21no—
258C4⋊C4×C47—22no—
259C4⋊C4×C47—22no—
260C4⋊C4×C47—21no—
261C4⋊C4×C47—21no—
262C4⋊C4×C47C2412yes—
263C4⋊C4×C47C2412yes—
264C4⋊C4×C47C2412yes—
265C22⋊C4×C47—22no—
266C42×C47—22no—
267C42×C47—22no—
268C42×C47—22no—
269C42×C47C2×D411yescharacteristic
270C42×C47C2×D411yescharacteristic
271C42×C47C2411yescharacteristic
272C42×C47C2411yescharacteristic
273C22⋊Dic47—22no—
274(C2×D47)⋊C4—22no—
275(C2×D47)⋊C4—22no—
276(C2×D47)⋊C4—24no—
277(C2×D47)⋊C4C2×D412yes—
278(C2×D47)⋊C4C2×D412yes—
279(C2×D47)⋊C4C2×D412yes—
280(C2×D47)⋊C4C2×D412yes—
281C4⋊Dic47—21no—
282C4⋊Dic47—21no—
283C4⋊Dic47—21no—
284C4⋊Dic47—24no—
285C4⋊Dic47—22no—
286C4⋊Dic47—22no—
287C4⋊Dic47C2412yes—
288C4⋊Dic47C2412yes—
289C4⋊Dic47C2412yes—
290Dic47⋊C4—22no—
291Dic47⋊C4—22no—
292Dic47⋊C4—22no—
293Dic47⋊C4—22no—
294Dic47⋊C4—22no—
295Dic47⋊C4—22no—
296Dic47⋊C4—24no—
297Dic47⋊C4—22no—
298Dic47⋊C4—22no—
299Dic47⋊C4—22no—
300Dic47⋊C4—22no—
301Dic47⋊C4C2×D412yes—
302Dic47⋊C4C2×D412yes—
303Dic47⋊C4C2×D412yes—
304Dic47⋊C4C2×D412yes—
305C4×Dic47—22no—
306C4×Dic47—22no—
307C4×Dic47—22no—
308C4×Dic47—22no—
309C4×Dic47—22no—
310C4×Dic47—24no—
311C4×Dic47—24no—
312C4×Dic47—24no—
313C4×Dic47C2×D412yes—
314C4×Dic47C2412yes—
315#10625329—24no—
316C2×C47⋊C8C2414yes—
317#10625324—28no—
318C8×D47—28no—
319C23×C47C22×D411yescharacteristic
320C22×D47—41no—
321C22×D47—41no—
322C22×D47C22⋊Q814yes—
323C22×D47C22×D412yes—
324Q8×C47—24no—
325Q8×C47—22no—
326Q8×C47—81no—
327Q8×C47—81no—
328Q8×C47C22×Q814yes—
329C2×C4×C47—24no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—22no—
334C2×C4×C47—41no—
335C2×C4×C47—41no—
336C2×C4×C47—42no—
337C2×C4×C47C22×D411yescharacteristic
338C2×C4×C47C22×D411yescharacteristic
339C2×C4×C47C22×D411yescharacteristic
340C2×C4×C47C22×D411yescharacteristic
341C2×C4×C47C22×D411yescharacteristic
342C2×C4×C47C22×Q812yes—
343C2×C4×C47C2×#4112yes—
344C2×C4×C47C2511yescharacteristic
345C2×Dic47—24no—
346C2×Dic47—22no—
347C2×Dic47—22no—
348C2×Dic47—22no—
349C2×Dic47—22no—
350C2×Dic47—41no—
351C2×Dic47—41no—
352C2×Dic47—42no—
353C2×Dic47C22⋊Q814yes—
354C2×Dic47C22×D412yes—
355C2×Dic47C22×D412yes—
356C2×Dic47C22×D412yes—
357C4×D47—216no—
358C4×D47—82no—
359C4×D47—82no—
360C4×D47C22⋊Q818yes—
361C4×D47C22×Q814yes—
362C4×D47C2×#4114yes—
363Dic94—24no—
364Dic94—22no—
365Dic94—216no—
366Dic94—82no—
367Dic94—82no—
368Dic94—81no—
369Dic94—81no—
370Dic94C22×Q814yes—
371C8×C47—24no—
372C47⋊C8—24no—
373#60491—471nomaximal, Sylow
374C22×C47—21no—
375C22×C47—21no—
376C22×C47C2×C22⋊Q812yes—
377C22×C47C23×D411yescharacteristic
378C2×D47—22no—
379C2×D47—22no—
380C2×D47—44no—
381C2×D47C2×C22⋊Q814yes—
382C4×C47—21no—
383C4×C47—21no—
384C4×C47—21no—
385C4×C47—21no—
386C4×C47—24no—
387C4×C47—42no—
388C4×C47—42no—
389C4×C47—42no—
390C4×C47C2×C22⋊Q812yes—
391C4×C47C23×Q811yescharacteristic
392C4×C47C22×#4111yescharacteristic
393Dic47—22no—
394Dic47—22no—
395Dic47—24no—
396Dic47—42no—
397Dic47—42no—
398Dic47—42no—
399Dic47C2×C22⋊Q814yes—
400#3458—471no—
401C2×#519—471no—
402#3082—474no—
403#3082—474no—
404#3082—474no—
405#3082—474no—
406#3078—472no—
407#3078—471no—
408#3078—472no—
409#3078—471no—
410#3078—471no—
411#3078D4711yescharacteristic, complemented
412#2911—472no—
413#2905—471no—
414C2×#419—472no—
415C2×C47—22no—
416C2×C47C22×C22⋊Q811yescharacteristic
417C2×C47#358611yescharacteristic
418C2×C47#358611yescharacteristic
419D47—24no—
420C23×Q8—471no—
421C22×M16—472no—
422#544—472no—
423#544—472no—
424#544—472no—
425#544—472no—
426#544—941no—
427#544—941no—
428#543—941no—
429#543—941no—
430#533—472no—
431#533—471no—
432#533—942no—
433#533—942no—
434#533C2×D4711yescharacteristic
435#519—474no—
436#519—474no—
437#519—942no—
438#519—942no—
439C2×C4×Q8—471no—
440C2×C4×Q8—471no—
441C2×C4×Q8—471no—
442C2×C4×Q8—941no—
443C2×C4×Q8—941no—
444C2×C4×Q8C2×D4711yescharacteristic
445C2×#117—471no—
446C2×#117—472no—
447C2×#117—471no—
448C2×#117—941no—
449C2×#117—941no—
450#479—474no—
451#479—474no—
452#479—474no—
453#479—474no—
454#479—474no—
455#479—474no—
456#479—474no—
457#479C2×D4714yescomplemented
458#477—472no—
459#477—472no—
460#477—474no—
461#477—472no—
462#477—474no—
463#477C2×D4712yescomplemented
464#475—472no—
465#475—472no—
466#475—474no—
467#475—472no—
468#475—474no—
469#475C2×D4712yescomplemented
470#428—472no—
471#428—472no—
472#428—472no—
473#428—474no—
474#428—474no—
475#428C2×D4712yes—
476#427—474no—
477#427—474no—
478#424—474no—
479#424—474no—
480#423—472no—
481#423—471no—
482#423C2×D4711yescharacteristic
483#419—472no—
484#419—472no—
485#419—472no—
486#419—474no—
487#419—474no—
488#419C2×D4712yes—
489C2×#103—474no—
490C2×#103—474no—
491C47#6049111yescharacteristic, complemented, Sylow
492C22×Q8—478no—
493C22×Q8—474no—
494C22×Q8—471no—
495C22×Q8—941no—
496C22×Q8—942no—
497C22×Q8—944no—
498C22×Q8C22×D4711yescharacteristic
499C23×C4—471no—
500C23×C4—941no—
501C2×M16—472no—
502C2×M16—474no—
503C2×M16—948no—
504C2×M16C22×D4712yes—
505C22×C8—474no—
506C4⋊Q8—472no—
507C4⋊Q8—472no—
508C4⋊Q8—471no—
509C4⋊Q8—471no—
510C4⋊Q8—942no—
511C4⋊Q8—942no—
512C4⋊Q8—942no—
513C4⋊Q8—942no—
514C4⋊Q8C22×D4711yescharacteristic
515C4⋊Q8C22×D4711yescharacteristic
516#125—472no—
517#125—472no—
518#125—472no—
519#125—942no—
520#125—942no—
521#125—942no—
522#125—942no—
523#125C22×D4712yes—
524C22⋊Q8—21no—
525C22⋊Q8—21no—
526C22⋊Q8—942no—
527C22⋊Q8—942no—
528C22⋊Q8—942no—
529C22⋊Q8—942no—
530C22⋊Q8—942no—
531C22⋊Q8—942no—
532C22⋊Q8—942no—
533C22⋊Q8—942no—
534C22⋊Q8—942no—
535C22⋊Q8—942no—
536C22⋊Q8—941no—
537C22⋊Q8—941no—
538C4×Q8—21no—
539C4×Q8—21no—
540C4×Q8—21no—
541C4×Q8—21no—
542C4×Q8—474no—
543C4×Q8—474no—
544C4×Q8—472no—
545C4×Q8—472no—
546C4×Q8—942no—
547C4×Q8—942no—
548C4×Q8—944no—
549C4×Q8—944no—
550C4×Q8—942no—
551C4×Q8—942no—
552C4×Q8—944no—
553C4×Q8—944no—
554C4×Q8—941no—
555C4×Q8—941no—
556C4×Q8—941no—
557C4×Q8—941no—
558C4×Q8C22×D4712yes—
559C4×Q8C22×D4712yes—
560#117—472no—
561#117—472no—
562#117—472no—
563#117—472no—
564#117—472no—
565#117—474no—
566#117—472no—
567#117—472no—
568#117—944no—
569#117—944no—
570#117—942no—
571#117—942no—
572#117—944no—
573#117—944no—
574#117—942no—
575#117C22×D4712yes—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—471no—
578C2×C4⋊C4—471no—
579C2×C4⋊C4—471no—
580C2×C4⋊C4—472no—
581C2×C4⋊C4—472no—
582C2×C4⋊C4—941no—
583C2×C4⋊C4—941no—
584C2×C4⋊C4—941no—
585C2×C4⋊C4C22×D4711yescharacteristic
586C2×C22⋊C4—471no—
587C2×C22⋊C4—471no—
588C2×C22⋊C4—942no—
589C2×C22⋊C4—941no—
590C2×C42—21no—
591C2×C42—471no—
592C2×C42—942no—
593C2×C42—941no—
594C2×C42—941no—
595C2×C42—941no—
596C2×C42—941no—
597C2×C42C22×D4711yescharacteristic
598#107—474no—
599#107—474no—
600#107—474no—
601#107C22×D4714yes—
602#106—474no—
603#106—474no—
604#106—474no—
605#106C22×D4714yes—
606C4⋊C8—474no—
607C4⋊C8—474no—
608C4⋊C8—472no—
609C4⋊C8—472no—
610C4⋊C8C22×D4712yes—
611C4⋊C8C22×D4712yes—
612#103—474no—
613#103—474no—
614#103—474no—
615#103—474no—
616#103—474no—
617#103—474no—
618#103C22×D4714yes—
619#103C22×D4714yes—
620C24—471no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—22no—
625C2×Q8—4716no—
626C2×Q8—474no—
627C2×Q8—472no—
628C2×Q8—944no—
629C2×Q8—948no—
630C2×Q8—942no—
631C2×Q8—942no—
632C2×Q8—9416no—
633C2×Q8—948no—
634C2×Q8—941no—
635C2×Q8—941no—
636C2×Q8—941no—
637C2×Q8—942no—
638C2×Q8Q8×D4714yes—
639C2×Q8C23×D4712yes—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—471no—
643C22×C4—472no—
644C22×C4—474no—
645C22×C4—474no—
646C22×C4—472no—
647C22×C4—471no—
648C22×C4—471no—
649C22×C4—944no—
650C22×C4—948no—
651C22×C4—942no—
652C22×C4—942no—
653C22×C4—941no—
654C22×C4—941no—
655C22×C4D4×D4711yescharacteristic
656C22×C4D4×D4711yescharacteristic
657C22×C4C23×D4711yescharacteristic
658M16—24no—
659M16—948no—
660M16—944no—
661C2×C8—474no—
662C2×C8—948no—
663C2×C8C23×D4714yes—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—472no—
672C4⋊C4—472no—
673C4⋊C4—472no—
674C4⋊C4—472no—
675C4⋊C4—472no—
676C4⋊C4—472no—
677C4⋊C4—472no—
678C4⋊C4—942no—
679C4⋊C4—942no—
680C4⋊C4—944no—
681C4⋊C4—942no—
682C4⋊C4—942no—
683C4⋊C4—942no—
684C4⋊C4—942no—
685C4⋊C4—944no—
686C4⋊C4—942no—
687C4⋊C4—942no—
688C4⋊C4—942no—
689C4⋊C4—942no—
690C4⋊C4—942no—
691C4⋊C4—942no—
692C4⋊C4—941no—
693C4⋊C4—941no—
694C4⋊C4—941no—
695C4⋊C4C23×D4712yes—
696C4⋊C4C23×D4712yes—
697C4⋊C4C23×D4712yes—
698C22⋊C4—22no—
699C22⋊C4—472no—
700C22⋊C4—472no—
701C22⋊C4—472no—
702C22⋊C4—472no—
703C22⋊C4—944no—
704C22⋊C4—942no—
705C22⋊C4—942no—
706C22⋊C4—942no—
707C42—22no—
708C42—22no—
709C42—22no—
710C42—472no—
711C42—472no—
712C42—944no—
713C42—942no—
714C42—942no—
715C42—944no—
716C42—944no—
717C42—942no—
718C42—942no—
719C42—942no—
720C42D4×D4711yescharacteristic
721C42D4×D4711yescharacteristic
722C42C23×D4711yescharacteristic
723C42C23×D4711yescharacteristic
724C23—472no—
725C23—474no—
726C23—1881no—
727C23—1881no—
728C23C2×D4×D4711yescharacteristic
729Q8—24no—
730Q8—22no—
731Q8—81no—
732Q8—81no—
733Q8—474no—
734Q8—9416no—
735Q8—944no—
736Q8—942no—
737Q8—3761no—
738Q8—3761no—
739Q8—3762no—
740Q8—3762no—
741Q8C2×Q8×D4714yes—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—474no—
751C2×C4—472no—
752C2×C4—478no—
753C2×C4—474no—
754C2×C4—474no—
755C2×C4—472no—
756C2×C4—472no—
757C2×C4—9416no—
758C2×C4—944no—
759C2×C4—942no—
760C2×C4—942no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—3762no—
764C2×C4—3762no—
765C2×C4—1881no—
766C2×C4—1881no—
767C2×C4—1882no—
768C2×C4C2×D4×D4711yescharacteristic
769C2×C4C2×D4×D4711yescharacteristic
770C2×C4C2×D4×D4711yescharacteristic
771C2×C4C2×D4×D4711yescharacteristic
772C2×C4C2×D4×D4711yescharacteristic
773C2×C4C2×Q8×D4712yes—
774C2×C4#41×D4712yes—
775C2×C4C24×D4711yescharacteristic
776C8—24no—
777C8—944no—
778C22—21no—
779C22—21no—
780C22—474no—
781C22—942no—
782C22—942no—
783C22—1884no—
784C22C22⋊Q8×D4712yes—
785C22C22×D4×D4711yescharacteristic
786C4—24no—
787C4—21no—
788C4—21no—
789C4—21no—
790C4—21no—
791C4—42no—
792C4—42no—
793C4—42no—
794C4—474no—
795C4—944no—
796C4—942no—
797C4—942no—
798C4—1882no—
799C4—1882no—
800C4—1882no—
801C4C22⋊Q8×D4712yes—
802C4C22×Q8×D4711yescharacteristic
803C4C2×#41×D4711yescharacteristic
804C2—22no—
805C2—944no—
806C2C2×C22⋊Q8×D4711yescharacteristic
807C2#2025817111yescharacteristic
808C2#2025817211yescharacteristic
subgroupG/H
centerC22C22×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#3078C2
socleC22×C47C23×D4
prime radicalC23×D47C2×D4
hypercenter#3078D47
hypocenterC47#60491
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
3. #20253229C2semidirect
4. #20253227C2semidirect
5. #20253225C2semidirect
6. #20253223C2semidirect
7. #20253195C2semidirect
8. #20253193C2semidirect
9. #20253192C2semidirect
10. #20253190C2semidirect
11. #20253189C2semidirect
15. C47×#3078C2semidirect
44. #15689433C22semidirect
45. #15689432C22semidirect
46. #15689431C22semidirect
47. #15689430C22semidirect
48. #15689429C22semidirect
49. #15689428C22semidirect
50. #15689427C22semidirect
51. #15689419C22semidirect
52. #15689418C22semidirect
53. #15689417C22semidirect
54. #15689416C22semidirect
55. #15689415C22semidirect
56. #15689409C22semidirect
57. #15689408C22semidirect
58. #15689407C22semidirect
59. #15689406C22semidirect
60. #15689405C22semidirect
81. C47×#479C22semidirect
82. C47×#477C22semidirect
83. C47×#475C22semidirect
91. C2×Q8×D47Q8semidirect
411. #3078D47semidirect
457. #479C2×D47semidirect
463. #477C2×D47semidirect
469. #475C2×D47semidirect
491. C47#60491semidirect

Maximal subgroups

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

subgroupindex
#202567912
C2×#156895992
#202532292
#202532272
#202532252
#202532232
#202531952
#202531932
#202531922
#202531902
#202531892
#202519752
#202519502
#419×D472
C47×#30782
#6049147