Finite Group Databasebeta

← #27124813

Subgroups — #27124813

Order 12032.

11534 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689960C211yesmaximal, characteristic, complemented
2C23×#10625354C211yesmaximal, characteristic, complemented
3#20257065C218yesmaximal, complemented
4#20257054C218yesmaximal, complemented
5#20257047C211yesmaximal, characteristic, complemented
6#20257043C211yesmaximal, characteristic, complemented
7#20257039C211yesmaximal, characteristic, complemented
8#20257031C216yesmaximal, complemented
9#20257021C216yesmaximal, complemented
10D4×#10625354C218yesmaximal, complemented
11#20256877C218yesmaximal, complemented
12#20256720C216yesmaximal, complemented
13#525×D47C216yesmaximal, complemented
14#20256590C211yesmaximal, characteristic, complemented
15C47×#3486C211yesmaximal, characteristic, complemented
16#15689960—216no—
17C2×#13094072C2211yescharacteristic, complemented
18C2×#13094072C2214yescomplemented
19C2×#13094070C2216yescomplemented
20C2×#13094070C2214yescomplemented
21C22×#10625354—216no—
22C22×#10625354C2211yescharacteristic
23C22×#10625354C2213yescomplemented
24C22×#10625354C2211yescharacteristic, complemented
25C22×#10625354C2218yescomplemented
26C22×#10625354C2218yescomplemented
27C22×#10625354C2213yescomplemented
28C22×#10625354C2214yescomplemented
29C2×#41×D47C2216yescomplemented
30C2×#41×D47C2214yescomplemented
31C23×D188C2213yescomplemented
32C23×C4×D47C2213yescomplemented
33#15689795C2218yescomplemented
34#15689792C2218yescomplemented
35Q8×C22⋊D47C2218yescomplemented
36#15689785C2218yescomplemented
37#15689784C2218yescomplemented
38#15689784C2218yescomplemented
39#15689776C22124yescomplemented
40#15689775C22124yescomplemented
41#15689769C22124yescomplemented
42#15689766C22124yescomplemented
43#15689764C22124yescomplemented
44#15689764C22124yescomplemented
45D4×D188C22124yescomplemented
46#15689757C22124yescomplemented
47#15689703C22124yescomplemented
48#15689698C22112yescomplemented
49#15689697C2216yescomplemented
50#15689692C2216yescomplemented
51#15689691C22112yescomplemented
52#15689687C2216yescomplemented
53#15689684C22124yescomplemented
54#15689674C22112yescomplemented
55#15689672C22112yescomplemented
56#15689636C22112yescomplemented
57#15689636C22124yescomplemented
58#15689635C2216yescomplemented
59#15689634C2216yescomplemented
60#15689633C22112yescomplemented
61#15689632C22124yescomplemented
62#15689631C22112yescomplemented
63#15689630C2216yescomplemented
64#15689629C2214yescomplemented
65#123×D47C22112yescomplemented
66C22⋊Q8×D47C22112yescomplemented
67#121×D47C22112yescomplemented
68#120×D47C22112yescomplemented
69#15689605C2218yescomplemented
70#15689601C2211yescharacteristic, complemented
71#15689597C2216yescomplemented
72C4×#10625354C2218yescomplemented
73C4×D4×D47C22124yescomplemented
74#117×D47C2216yescomplemented
75C2×2−1+4×C47C2211yescharacteristic, complemented
76C23×Q8×C47C2211yescharacteristic, complemented
77D4×Q8×C47C2218yescomplemented
78C47×#548C2218yescomplemented
79C47×#536C2216yescomplemented
80C47×#525C2216yescomplemented
81C47×#519C2211yescharacteristic, complemented
82C24×D47C2313yes—
83#13094072—28no—
84#13094072—232no—
85#13094070—232no—
86#13094070—248no—
87C2×#10625354—28no—
88C2×#10625354—264no—
89C2×#10625354—264no—
90C2×#10625354—232no—
91C2×#10625354—224no—
92C2×#10625354—224no—
93C2×#10625354D4116yescomplemented
94C2×#10625354C23124yes—
95C2×#10625354C2318yes—
96C2×#10625354C23112yes—
97C2×#10625354C23112yes—
98C2×#10625354C2314yes—
99C2×#10625354C2314yes—
100C2×#10625354C23112yescomplemented
101C2×#10625354C2314yescomplemented
102C2×#10625354C2316yescomplemented
103C2×#10625350C2316yes—
104C2×#10625350C23112yescomplemented
105C2×#10625350C23112yescomplemented
106C2×#10625352C2314yes—
107C2×#10625352C2316yescomplemented
108#41×D47—232no—
109#41×D47—248no—
110C2×Q8×D47C2314yescomplemented
111C2×Q8×D47C2316yescomplemented
112C22×D188—224no—
113C22×D188C23124yes—
114C22×D188C2316yes—
115C22×D188C2313yes—
116C22×D188C2313yes—
117C22×D188C23112yescomplemented
118C2×D4×D47C23112yes—
119C2×D4×D47C23124yes—
120C2×D4×D47C23112yescomplemented
121C2×D4×D47C2316yescomplemented
122C23×Dic47C2311yescharacteristic
123C22×C4×D47—224no—
124C22×C4×D47C23112yes—
125C22×C4×D47C23112yes—
126C22×C4×D47C2313yes—
127C22×C4×D47C2313yes—
128C22×C4×D47C2313yes—
129C22×C4×D47C2313yes—
130C22×C4×D47C23112yescomplemented
131#13094022C23112yescomplemented
132#13094021C23112yescomplemented
133#13094020C23112yescomplemented
134#13094013C23112yescomplemented
135#13094013C23112yescomplemented
136#13094012C23112yescomplemented
137#13094009C23124yescomplemented
138#13094009C23148yescomplemented
139#13094008C2314yes—
140#13094007C23112yes—
141#13094006C23124yescomplemented
142#13094005C2314yes—
143#13094004C23112yescomplemented
144#13094003C23112yes—
145#13094002C23124yescomplemented
146#13094001C2318yes—
147#13094000C23124yescomplemented
148#13094000C23112yescomplemented
149#13093999C23124yescomplemented
150#13093999C23148yescomplemented
151#13093999C23112yescomplemented
152#13093998C23112yes—
153#13093998C23124yescomplemented
154#13093997C23148yescomplemented
155#13093997C23124yescomplemented
156#13093996C2318yes—
157#13093995C23112yescomplemented
158#13093994C23124yes—
159#13093994C23112yes—
160#13093994C23148yescomplemented
161#13093993C2314yes—
162#13093992C23124yes—
163#13093992C23112yes—
164Q8×Dic47C2318yescomplemented
165C4×D188C23124yescomplemented
166C4×D188C23124yescomplemented
167D4×Dic47C2318yes—
168#13093986C23124yescomplemented
169#13093986C23124yescomplemented
170C4×C22⋊D47C23124yes—
171C4×C22⋊D47C23124yescomplemented
172(C22⋊D47)⋊C4C2318yes—
173(C22⋊D47)⋊C4C23124yescomplemented
174#13093983C2316yes—
175#13093982C23112yescomplemented
176#13093981C23112yescomplemented
177#13093980C2314yes—
178C4⋊C4×D47C23124yescomplemented
179C4⋊C4×D47C23112yescomplemented
180C22⋊C4×D47C23124yes—
181C22⋊C4×D47C23112yes—
182C22⋊C4×D47C23124yescomplemented
183C42×D47C23112yescomplemented
1842−1+4×C47—28no—
185C2×#41×C47C2316yes—
186C2×#41×C47C2314yescomplemented
187C22×Q8×C47—28no—
188C22×Q8×C47C2318yes—
189C22×Q8×C47C2313yes—
190C22×Q8×C47C2311yescharacteristic
191C22×Q8×C47C2314yescomplemented
192C23×C4×C47C2313yes—
193C4⋊Q8×C47C23112yescomplemented
194#124×C47C23112yescomplemented
195#123×C47C23112yes—
196C22⋊Q8×C47C23112yes—
197C22⋊Q8×C47C23124yescomplemented
198#121×C47C23112yes—
199#120×C47C2314yes—
200C4×Q8×C47C2318yescomplemented
201C4×D4×C47C23124yes—
202#117×C47C2316yes—
203C24×C47C2411yescharacteristic
204C23×D47—212no—
205C23×D47—412no—
206C23×D47C24112yes—
207C23×D47C24112yes—
208C23×D47C2413yes—
209C23×D47C2413yes—
210#41×C47—216no—
211#41×C47—224no—
212C2×Q8×C47—232no—
213C2×Q8×C47—216no—
214C2×Q8×C47—212no—
215C2×Q8×C47C2×D418yescomplemented
216C2×Q8×C47C2416yes—
217C2×Q8×C47C24112yes—
218C2×Q8×C47C2414yes—
219C2×D4×C47C2418yes—
220C2×D4×C47C2414yes—
221C2×D4×C47C2416yes—
222C22×C4×C47—212no—
223C22×C4×C47C24112yes—
224C22×C4×C47C24112yes—
225C22×C4×C47C2413yes—
226C22×C4×C47C2413yes—
227C2×C22⋊D47C2418yes—
228C2×C22⋊D47C24112yes—
229C2×C22⋊D47C2414yes—
230C2×C22⋊D47C2414yes—
231C2×C22⋊D47C24124yes—
232C22×Dic47—24no—
233C22×Dic47C2412yes—
234C22×Dic47C2414yes—
235C22×Dic47C2412yes—
236C22×Dic47C2411yescharacteristic
237C22×Dic47C2411yescharacteristic
238#10625354—232no—
239#10625354—216no—
240#10625354—296no—
241#10625354—248no—
242#10625354—224no—
243#10625354—248no—
244#10625354—248no—
245#10625354C2×D4132yescomplemented
246#10625354C2×D4132yescomplemented
247Q8×D47—216no—
248Q8×D47—224no—
249#10625352—216no—
250#10625352—224no—
251D4×D47—248no—
252D4×D47—248no—
253D4×D47—224no—
254D4×D47—448no—
255#10625350—224no—
256#10625350—248no—
257#10625350—248no—
258C2×D188—224no—
259C2×D188—212no—
260C2×D188—296no—
261C2×D188—248no—
262C2×D188C2×D4124yescomplemented
263C2×D188C24112yes—
264C2×D188C24124yes—
265C2×D188C2416yes—
266C2×D188C24112yes—
267C2×D188C24124yes—
268C2×D188C24112yes—
269C2×C4×D47—212no—
270C2×C4×D47—212no—
271C2×C4×D47—212no—
272C2×C4×D47—248no—
273C2×C4×D47—248no—
274C2×C4×D47—248no—
275C2×C4×D47C2×D4124yescomplemented
276C2×C4×D47C24112yes—
277C2×C4×D47C24112yes—
278C2×C4×D47C2414yes—
279C2×C4×D47C2416yes—
280C2×C4×D47C24112yes—
281C2×C4×D47C24112yes—
282C2×C4×D47C2416yes—
283C2×C4×D47C24124yes—
284C2×C4×D47C2416yes—
285C2×C4×D47C2416yes—
286C2×Dic94C2414yes—
287C2×Dic94C2416yes—
288C4⋊C4×C47C24112yes—
289C4⋊C4×C47C24124yes—
290C22⋊C4×C47C2414yes—
291C22⋊C4×C47C2418yes—
292C22⋊C4×C47C24124yes—
293C42×C47C24112yes—
294C22⋊Dic47C2414yes—
295C22⋊Dic47C2418yes—
296C22⋊Dic47C2418yes—
297(C2×D47)⋊C4C24124yes—
298(C2×D47)⋊C4C24124yes—
299(C2×D47)⋊C4C24124yes—
300(C2×D47)⋊C4C2418yes—
301(C2×D47)⋊C4C24124yes—
302C4⋊Dic47C2418yes—
303C4⋊Dic47C24112yes—
304Dic47⋊C4C2418yes—
305Dic47⋊C4C2418yes—
306Dic47⋊C4C24124yes—
307C4×Dic47C2418yes—
308C4×Dic47C24112yes—
309C23×C47—22no—
310C23×C47—24no—
311C23×C47C2514yes—
312C23×C47C2511yescharacteristic
313C23×C47C2512yes—
314C22×D47—26no—
315C22×D47—224no—
316C22×D47—224no—
317C22×D47—224no—
318C22×D47—46no—
319C22×D47—412no—
320C22×D47—46no—
321C22×D47—424no—
322C22×D47—448no—
323C22×D47C22×D4112yes—
324C22×D47C2516yes—
325C22×D47C2514yes—
326C22×D47C2516yes—
327Q8×C47—212no—
328Q8×C47—224no—
329Q8×C47C22×D4116yes—
330D4×C47—28no—
331D4×C47—216no—
332D4×C47—212no—
333C2×C4×C47—26no—
334C2×C4×C47—224no—
335C2×C4×C47—224no—
336C2×C4×C47C22×D4112yes—
337C2×C4×C47C2518yes—
338C2×C4×C47C2516yes—
339C2×C4×C47C2514yes—
340C2×C4×C47C2516yes—
341C22⋊D47—28no—
342C22⋊D47—216no—
343C22⋊D47—224no—
344C22⋊D47—28no—
345C22⋊D47—424no—
346C2×Dic47—22no—
347C2×Dic47—24no—
348C2×Dic47—24no—
349C2×Dic47—28no—
350C2×Dic47C22×D414yes—
351C2×Dic47C2518yes—
352C2×Dic47C2514yes—
353C2×Dic47C2512yes—
354C2×Dic47C2511yescharacteristic
355C2×Dic47C2511yescharacteristic
356D188—248no—
357D188—224no—
358D188—224no—
359D188—212no—
360D188—424no—
361D188C22×D4148yes—
362C4×D47—224no—
363C4×D47—224no—
364C4×D47—224no—
365C4×D47—224no—
366C4×D47—28no—
367C4×D47—212no—
368C4×D47—212no—
369C4×D47—424no—
370C4×D47C22×D4124yes—
371C4×D47C22×D4124yes—
372Dic94—212no—
373Dic94—28no—
374#62811—471nomaximal, Sylow
375C22×C47—28no—
376C22×C47—22no—
377C22×C47—22no—
378C22×C47—22no—
379C22×C47—24no—
380C22×C47—28no—
381C22×C47C23×D412yes—
382C22×C47#58514yescomplemented
383C22×C47C2611yescharacteristic
384C2×D47—212no—
385C2×D47—26no—
386C2×D47—24no—
387C2×D47—28no—
388C2×D47—212no—
389C2×D47—412no—
390C2×D47—448no—
391C2×D47—412no—
392C2×D47—824no—
393C2×D47C23×D4112yes—
394C4×C47—24no—
395C4×C47—26no—
396C4×C47—28no—
397C4×C47C23×D4112yes—
398Dic47—24no—
399Dic47—22no—
400Dic47—28no—
401Dic47C23×D412yes—
402Dic47C23×D412yes—
403C2×#585—471no—
404C23×#41—471no—
405#3489—478no—
406#3488—478no—
407#3487—471no—
408#3487—471no—
409#3486—471no—
410#3486D4711yescharacteristic, complemented
411#3485—476no—
412#3484—476no—
413D4×#41—478no—
414D4×#41—478no—
415#3449—476no—
416C2×#525—476no—
417#3428—471no—
418C2×C47—22no—
419C2×C47—24no—
420C2×C47—44no—
421C2×C47C24×D411yescharacteristic
422C2×C47C2×#58512yes—
423D47—212no—
424D47—46no—
425D47—44no—
426#585—9416no—
427C2×2−1+4—471no—
428C2×2−1+4—474no—
429C2×2−1+4C2×D4711yescharacteristic, complemented
430C2×H(5,𝔽2)—476no—
431C2×H(5,𝔽2)—474no—
432C22×#41—476no—
433C22×#41—474no—
434C22×#41—471no—
435C22×#41—473no—
436C22×#41—478no—
437C22×#41—473no—
438C22×#41—471no—
439C22×#41—478no—
440C22×#41—474no—
441C22×#41—9416no—
442C23×Q8C2×D4711yescharacteristic, complemented
443C23×D4—473no—
444C24×C4—473no—
445#550—478no—
446#550—478no—
447D4×Q8—478no—
448D4×Q8C2×D4718yescomplemented
449#548—478no—
450#548—478no—
451#548—478no—
452#548C2×D4718yescomplemented
453#547—4724no—
454#547—4724no—
455#546—4724no—
456#546—4724no—
457#546—4724no—
458#546—4724no—
459D42—4724no—
460D42—4724no—
461#537—4724no—
462#536—476no—
463#536—4712no—
464#536C2×D4716yescomplemented
465#535—476no—
466#535—4712no—
467#535—476no—
468#534—4724no—
469#532—4712no—
470#532—4712no—
471#525—476no—
472#525—476no—
473#525—4712no—
474#525—4712no—
475#525—4724no—
476#525—4712no—
477#525—474no—
478#525—4724no—
479#525—476no—
480#525C2×D4716yescomplemented
481C2×#123—4712no—
482C2×C22⋊Q8—4712no—
483C2×#121—4712no—
484C2×#120—4712no—
485#520—478no—
486#519—471no—
487#519C2×D4711yescharacteristic, complemented
488#518—476no—
489C4×#41—478no—
490C2×C4×D4—4724no—
491C2×#117—476no—
492C47#6281111yescharacteristic, complemented, Sylow
493C25—473no—
4942−1+4—28no—
4952−1+4—9432no—
4962−1+4—948no—
497H(5,𝔽2)—9448no—
498H(5,𝔽2)—9432no—
499C2×#41—4716no—
500C2×#41—474no—
501C2×#41—474no—
502C2×#41—4712no—
503C2×#41—476no—
504C2×#41—4712no—
505C2×#41—4724no—
506C2×#41—4712no—
507C2×#41—478no—
508C2×#41—474no—
509C2×#41—474no—
510C2×#41—476no—
511C2×#41—476no—
512C2×#41—4712no—
513C2×#41—4712no—
514C2×#41—9424no—
515C2×#41—9448no—
516C2×#41—9424no—
517C2×#41—9464no—
518C2×#41—9464no—
519C2×#41—9432no—
520C2×#41—9432no—
521C2×#41—948no—
522C2×#41C22×D4716yes—
523C2×#41C22×D4714yescomplemented
524C22×Q8—28no—
525C22×Q8—476no—
526C22×Q8—474no—
527C22×Q8C22×D4713yes—
528C22×Q8C22×D4718yes—
529C22×Q8C22×D4711yescharacteristic
530C22×Q8C22×D4714yescomplemented
531C22×D4—4712no—
532C22×D4—476no—
533C22×D4—4712no—
534C22×D4—4724no—
535C22×D4—473no—
536C22×D4—476no—
537C22×D4—473no—
538C22×D4—4724no—
539C22×D4—4712no—
540C22×D4—9424no—
541C23×C4—473no—
542C23×C4—471no—
543C23×C4—4712no—
544C23×C4—4712no—
545C23×C4—4712no—
546C23×C4—473no—
547C23×C4—473no—
548C23×C4—473no—
549C23×C4—9424no—
550C23×C4C22×D4713yes—
551C4⋊Q8—4712no—
552C4⋊Q8C22×D47112yescomplemented
553#127—4712no—
554#127—4712no—
555#124—4712no—
556#124—4712no—
557#124—4712no—
558#124C22×D47112yescomplemented
559#123—474no—
560#123—4712no—
561#123—4724no—
562#123—4748no—
563#123—474no—
564#123—4724no—
565#123C22×D47112yes—
566C22⋊Q8—4712no—
567C22⋊Q8—4724no—
568C22⋊Q8—4712no—
569C22⋊Q8—4724no—
570C22⋊Q8—4712no—
571C22⋊Q8—478no—
572C22⋊Q8C22×D47112yes—
573C22⋊Q8C22×D47124yescomplemented
574#121—478no—
575#121—4712no—
576#121—4712no—
577#121—4724no—
578#121—4712no—
579#121—4724no—
580#121—4748no—
581#121—4724no—
582#121—4748no—
583#121C22×D47112yes—
584#120—474no—
585#120—4712no—
586#120—4724no—
587#120—4712no—
588#120—4724no—
589#120—4748no—
590#120C22×D4714yes—
591C4×Q8—478no—
592C4×Q8C22×D4718yescomplemented
593C4×D4—478no—
594C4×D4—4724no—
595C4×D4—4724no—
596C4×D4—4724no—
597C4×D4—4724no—
598C4×D4—478no—
599C4×D4—4724no—
600C4×D4—4724no—
601C4×D4—4724no—
602C4×D4C22×D47124yes—
603#117—476no—
604#117—4712no—
605#117—474no—
606#117—4712no—
607#117C22×D4716yes—
608C2×C4⋊C4—4712no—
609C2×C4⋊C4—4724no—
610C2×C22⋊C4—4712no—
611C2×C22⋊C4—4724no—
612C2×C22⋊C4—4724no—
613C2×C42—4712no—
614C24—473no—
615C24—4712no—
616C24—4712no—
617C24—473no—
618C24—9412no—
619C24—18812no—
620C24C23×D4711yescharacteristic
621#41—216no—
622#41—224no—
623#41—4732no—
624#41—4732no—
625#41—9448no—
626#41—9448no—
627#41—9416no—
628#41—9424no—
629#41—9448no—
630#41—9424no—
631#41—9448no—
632#41—9496no—
633#41—9448no—
634#41—9432no—
635#41—9416no—
636#41—9424no—
637C2×Q8—232no—
638C2×Q8—216no—
639C2×Q8—212no—
640C2×Q8—474no—
641C2×Q8—476no—
642C2×Q8—9424no—
643C2×Q8—9416no—
644C2×Q8D4×D4718yescomplemented
645C2×Q8C23×D4716yes—
646C2×Q8C23×D47112yes—
647C2×Q8C23×D4714yes—
648C2×D4—478no—
649C2×D4—474no—
650C2×D4—4712no—
651C2×D4—474no—
652C2×D4—4724no—
653C2×D4—4724no—
654C2×D4—4712no—
655C2×D4—4712no—
656C2×D4—4724no—
657C2×D4—476no—
658C2×D4—4712no—
659C2×D4—4724no—
660C2×D4—9496no—
661C2×D4—9448no—
662C2×D4—9424no—
663C2×D4—9424no—
664C2×D4—9448no—
665C2×D4—9448no—
666C2×D4—9412no—
667C2×D4—18848no—
668C2×D4C23×D4718yes—
669C2×D4C23×D4714yes—
670C2×D4C23×D4716yes—
671C22×C4—212no—
672C22×C4—471no—
673C22×C4—4724no—
674C22×C4—476no—
675C22×C4—476no—
676C22×C4—472no—
677C22×C4—474no—
678C22×C4—472no—
679C22×C4—471no—
680C22×C4—4712no—
681C22×C4—4712no—
682C22×C4—474no—
683C22×C4—476no—
684C22×C4—4712no—
685C22×C4—4712no—
686C22×C4—476no—
687C22×C4—4724no—
688C22×C4—9412no—
689C22×C4—9448no—
690C22×C4—9448no—
691C22×C4—9448no—
692C22×C4—9412no—
693C22×C4—944no—
694C22×C4—9412no—
695C22×C4C23×D47112yes—
696C22×C4C23×D47112yes—
697C22×C4C23×D4713yes—
698C22×C4C23×D4713yes—
699C4⋊C4—478no—
700C4⋊C4—478no—
701C4⋊C4—4724no—
702C4⋊C4—478no—
703C4⋊C4—4712no—
704C4⋊C4C23×D47112yes—
705C4⋊C4C23×D47124yes—
706C22⋊C4—474no—
707C22⋊C4—478no—
708C22⋊C4—478no—
709C22⋊C4—478no—
710C22⋊C4—4724no—
711C22⋊C4—4724no—
712C22⋊C4—4724no—
713C22⋊C4—4724no—
714C22⋊C4C23×D4714yes—
715C22⋊C4C23×D4718yes—
716C22⋊C4C23×D47124yes—
717C42—478no—
718C42—4712no—
719C42C23×D47112yes—
720C23—22no—
721C23—24no—
722C23—476no—
723C23—4712no—
724C23—474no—
725C23—476no—
726C23—9424no—
727C23—9424no—
728C23—946no—
729C23—9424no—
730C23—18824no—
731C23—1886no—
732C23—18812no—
733C23—1886no—
734C23—18848no—
735C23C24×D4714yes—
736C23C24×D4711yescharacteristic
737C23C24×D4712yes—
738Q8—224no—
739Q8—212no—
740Q8—948no—
741Q8—9412no—
742Q8C2×D4×D47116yes—
743D4—28no—
744D4—216no—
745D4—212no—
746D4—4748no—
747D4—9424no—
748D4—9448no—
749D4—948no—
750D4—9424no—
751D4—948no—
752D4—9416no—
753D4—9424no—
754D4—9412no—
755D4—18824no—
756D4—18824no—
757C2×C4—26no—
758C2×C4—224no—
759C2×C4—224no—
760C2×C4—474no—
761C2×C4—471no—
762C2×C4—471no—
763C2×C4—4724no—
764C2×C4—4724no—
765C2×C4—478no—
766C2×C4—472no—
767C2×C4—474no—
768C2×C4—948no—
769C2×C4—9412no—
770C2×C4—9412no—
771C2×C4—9424no—
772C2×C4—9424no—
773C2×C4—944no—
774C2×C4—944no—
775C2×C4—948no—
776C2×C4—942no—
777C2×C4—9424no—
778C2×C4—9424no—
779C2×C4—18824no—
780C2×C4C2×D4×D47112yes—
781C2×C4C24×D4718yes—
782C2×C4C24×D4714yes—
783C2×C4C24×D4716yes—
784C2×C4C24×D4716yes—
785C22—28no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—24no—
790C22—28no—
791C22—4712no—
792C22—9412no—
793C22—944no—
794C22—946no—
795C22—948no—
796C22—9412no—
797C22—37624no—
798C22—18812no—
799C22—18848no—
800C22—18812no—
801C22C22×D4×D4712yes—
802C22#1568996014yescomplemented
803C22C25×D4711yescharacteristic
804C4—24no—
805C4—26no—
806C4—28no—
807C4—472no—
808C4—472no—
809C4—942no—
810C4—944no—
811C4—948no—
812C4C22×D4×D47112yes—
813C2—22no—
814C2—24no—
815C2—44no—
816C2—9412no—
817C2—1884no—
818C2—1886no—
819C2C23×D4×D4711yescharacteristic
820C2C2×#1568996012yes—
subgroupG/H
center, FrattiniC22C25×D47
commutator, socle, cosocleC22×C47C26
FittingC47×#3486C2
hypercenter#3486D47
hypocenterC47#62811
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #3486

Complements

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

NH ≅ G/Ntype
1. C2×#15689960C2semidirect
2. C23×#10625354C2semidirect
3. #20257065C2semidirect
4. #20257054C2semidirect
5. #20257047C2semidirect
6. #20257043C2semidirect
7. #20257039C2semidirect
8. #20257031C2semidirect
9. #20257021C2semidirect
10. D4×#10625354C2semidirect
11. #20256877C2semidirect
12. #20256720C2semidirect
13. #525×D47C2semidirect
14. #20256590C2semidirect
15. C47×#3486C2semidirect
17. C2×#13094072C22semidirect
18. C2×#13094072C22semidirect
19. C2×#13094070C22semidirect
20. C2×#13094070C22semidirect
23. C22×#10625354C22semidirect
24. C22×#10625354C22semidirect
25. C22×#10625354C22semidirect
26. C22×#10625354C22semidirect
27. C22×#10625354C22semidirect
28. C22×#10625354C22semidirect
29. C2×#41×D47C22semidirect
30. C2×#41×D47C22semidirect
31. C23×D188C22semidirect
32. C23×C4×D47C22semidirect
33. #15689795C22semidirect
34. #15689792C22semidirect
35. Q8×C22⋊D47C22semidirect
36. #15689785C22semidirect
37. #15689784C22semidirect
38. #15689784C22semidirect
39. #15689776C22semidirect
40. #15689775C22semidirect
41. #15689769C22semidirect
42. #15689766C22semidirect
43. #15689764C22semidirect
44. #15689764C22semidirect
45. D4×D188C22semidirect
46. #15689757C22semidirect
47. #15689703C22semidirect
48. #15689698C22semidirect
49. #15689697C22semidirect
50. #15689692C22semidirect
51. #15689691C22semidirect
52. #15689687C22semidirect
53. #15689684C22semidirect
54. #15689674C22semidirect
55. #15689672C22semidirect
56. #15689636C22semidirect
57. #15689636C22semidirect
58. #15689635C22semidirect
59. #15689634C22semidirect
60. #15689633C22semidirect
61. #15689632C22semidirect
62. #15689631C22semidirect
63. #15689630C22semidirect
64. #15689629C22semidirect
65. #123×D47C22semidirect
66. C22⋊Q8×D47C22semidirect
67. #121×D47C22semidirect
68. #120×D47C22semidirect
69. #15689605C22semidirect
70. #15689601C22semidirect
71. #15689597C22semidirect
72. C4×#10625354C22semidirect
73. C4×D4×D47C22semidirect
74. #117×D47C22semidirect
75. C2×2−1+4×C47C22semidirect
76. C23×Q8×C47C22semidirect
77. D4×Q8×C47C22semidirect
78. C47×#548C22semidirect
79. C47×#536C22semidirect
80. C47×#525C22semidirect
81. C47×#519C22semidirect
93. C2×#10625354D4semidirect
100. C2×#10625354C23semidirect
101. C2×#10625354C23semidirect
102. C2×#10625354C23semidirect
104. C2×#10625350C23semidirect
105. C2×#10625350C23semidirect
107. C2×#10625352C23semidirect
110. C2×Q8×D47C23semidirect
111. C2×Q8×D47C23semidirect
117. C22×D188C23semidirect
120. C2×D4×D47C23semidirect
121. C2×D4×D47C23semidirect
130. C22×C4×D47C23semidirect
131. #13094022C23semidirect
132. #13094021C23semidirect
133. #13094020C23semidirect
134. #13094013C23semidirect
135. #13094013C23semidirect
136. #13094012C23semidirect
137. #13094009C23semidirect
138. #13094009C23semidirect
141. #13094006C23semidirect
143. #13094004C23semidirect
145. #13094002C23semidirect
147. #13094000C23semidirect
148. #13094000C23semidirect
149. #13093999C23semidirect
150. #13093999C23semidirect
151. #13093999C23semidirect
153. #13093998C23semidirect
154. #13093997C23semidirect
155. #13093997C23semidirect
157. #13093995C23semidirect
160. #13093994C23semidirect
164. Q8×Dic47C23semidirect
165. C4×D188C23semidirect
166. C4×D188C23semidirect
168. #13093986C23semidirect
169. #13093986C23semidirect
171. C4×C22⋊D47C23semidirect
173. (C22⋊D47)⋊C4C23semidirect
175. #13093982C23semidirect
176. #13093981C23semidirect
178. C4⋊C4×D47C23semidirect
179. C4⋊C4×D47C23semidirect
182. C22⋊C4×D47C23semidirect
183. C42×D47C23semidirect
186. C2×#41×C47C23semidirect
191. C22×Q8×C47C23semidirect
193. C4⋊Q8×C47C23semidirect
194. #124×C47C23semidirect
197. C22⋊Q8×C47C23semidirect
200. C4×Q8×C47C23semidirect
215. C2×Q8×C47C2×D4semidirect
245. #10625354C2×D4semidirect
246. #10625354C2×D4semidirect
262. C2×D188C2×D4semidirect
275. C2×C4×D47C2×D4semidirect
382. C22×C47#585semidirect
410. #3486D47semidirect
429. C2×2−1+4C2×D47semidirect
442. C23×Q8C2×D47semidirect
448. D4×Q8C2×D47semidirect
452. #548C2×D47semidirect
464. #536C2×D47semidirect
480. #525C2×D47semidirect
487. #519C2×D47semidirect
492. C47#62811semidirect
523. C2×#41C22×D47semidirect
530. C22×Q8C22×D47semidirect
552. C4⋊Q8C22×D47semidirect
558. #124C22×D47semidirect
573. C22⋊Q8C22×D47semidirect
592. C4×Q8C22×D47semidirect
644. C2×Q8D4×D47semidirect
802. C22#15689960semidirect

Maximal subgroups

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

subgroupindex
C2×#156899602
C23×#106253542
#202570652
#202570542
#202570472
#202570432
#202570392
#202570312
#202570212
D4×#106253542
#202568772
#202567202
#525×D472
#202565902
C47×#34862
#6281147