Finite Group Databasebeta

← #26379548

Subgroups — #26379548

Order 12032.

1990 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689658C211yesmaximal, characteristic
2#20246535C212yesmaximal, complemented
3#20246533C212yesmaximal, complemented
4#20246513C212yesmaximal, complemented
5#20246501C212yesmaximal, complemented
6#20246357C212yesmaximal, complemented
7#20246327C212yesmaximal, complemented
8#20246272C212yesmaximal, complemented
9#20246247C212yesmaximal, complemented
10#20246201C211yesmaximal, characteristic, complemented
11#20246198C211yesmaximal, characteristic, complemented
12#20246194C211yesmaximal, characteristic, complemented
13#20246152C212yesmaximal
14#20246140C212yesmaximal, complemented
15#20246037C212yesmaximal, complemented
16#20246020C212yesmaximal, complemented
17#20245785C211yesmaximal, characteristic, complemented
18#20245784C211yesmaximal, characteristic, complemented
19C47×#2336C211yesmaximal, characteristic, complemented
20#15689658C4116yescomplemented
21C2×#13094019C2212yes—
22C2×#13094012C2211yescharacteristic
23C2×#13094009C2212yes—
24C2×#13094004C2211yescharacteristic
25C2×#13093999C2211yescharacteristic
26C2×#13093989C2211yescharacteristic
27C2×#13093986C2211yescharacteristic
28C2×#13093986C2212yes—
29C2×#13093982C2212yes—
30C2×C42×D47C2211yescharacteristic
31#15689027C2212yes—
32#15689027C2212yes—
33#15689025C2212yes—
34#15689024C2212yes—
35#15689022C2212yes—
36#15689020C2212yes—
37#15689018C2212yes—
38#15689015C2212yes—
39#15689015C2212yes—
40#15689015C2212yes—
41#15689014C2212yes—
42#15689014C2212yes—
43#15689014C2212yes—
44#15689013C2212yes—
45#15689013C2212yes—
46#15689013C2212yes—
47#15689012C2212yes—
48#15689012C2212yes—
49#15689012C2212yes—
50#15689009C2212yes—
51#15689009C2212yes—
52#15689009C2212yes—
53#15689009C2212yes—
54#15689008C2212yes—
55#15689007C2212yes—
56#15689006C2212yes—
57#15689005C2212yes—
58#15689001C2212yes—
59#15689001C2212yes—
60#15689001C2212yes—
61#15689001C2212yes—
62#15688997C2212yes—
63#15688997C2212yes—
64#15688994C2212yes—
65#15688994C2212yes—
66#15688991C2211yescharacteristic
67#15688990C2212yes—
68#15688990C2212yes—
69#15688988C2212yes—
70#15688988C2212yes—
71#15688987C2212yes—
72#15688985C2212yes—
73#15688985C2212yes—
74#15688985C2212yes—
75#15688982C2211yescharacteristic
76#15688982C2211yescharacteristic
77#15688980C2212yes—
78#15688980C2212yes—
79C4⋊C4×Dic47C2212yes—
80C4⋊C4×Dic47C2212yes—
81C4×Dic47⋊C4C2212yes—
82C4×C4⋊Dic47C2212yes—
83C4×C4⋊Dic47C2211yescharacteristic
84#15688974C2212yes—
85C4×(C2×D47)⋊C4C2212yes—
86C4×(C2×D47)⋊C4C2211yescharacteristic
87C4×(C2×D47)⋊C4C2211yescharacteristic
88C4×(C2×D47)⋊C4C2212yes—
89C4×(C2×D47)⋊C4C2212yes—
90#15688970C2212yes—
91#15688970C2212yes—
92#15688970C2212yes—
93#15688969C2211yescharacteristic
94#15688969C2211yescharacteristic
95#15688968C2211yescharacteristic
96#15688968C2212yes—
97#15688968C2211yescharacteristic
98#95×D47C2212yes—
99C2×#125×C47C2211yescharacteristic
100C47×#389C2212yes—
101C47×#387C2212yes—
102C47×#387C2212yes—
103C47×#387C2212yes—
104C47×#387C2212yes—
105C47×#383C2211yescharacteristic
106C4×C4⋊C4×C47C2211yescharacteristic
107C4×C4⋊C4×C47C2212yes—
108C22×Dic94C2311yescharacteristic
109C22×D188C2311yescharacteristic
110C22×D188C2312yes—
111C22×C4×D47C2312yes—
112C22×C4×D47C2312yes—
113C22×C4×D47C2312yes—
114C22×C4×D47C2311yescharacteristic
115C22×C4×D47C2311yescharacteristic
116C22×C4×D47C2311yescharacteristic
117#13094019C2×C4116yescomplemented
118#13094012C2×C418yes—
119#13094009C2×C4116yescomplemented
120#13094004C2×C418yescomplemented
121#13093999C2×C418yes—
122#13093989C2×C418yescomplemented
123#13093986C2×C418yes—
124#13093986C2×C4116yescomplemented
125#13093982C2×C4116yescomplemented
126C2×C4⋊Dic47C2312yes—
127C2×C4⋊Dic47C2312yes—
128C2×C4⋊Dic47C2312yes—
129C2×C4⋊Dic47C2312yes—
130C2×Dic47⋊C4C2312yes—
131C2×Dic47⋊C4C2312yes—
132C2×Dic47⋊C4C2312yes—
133C2×Dic47⋊C4C2312yes—
134C2×Dic47⋊C4C2312yes—
135C2×(C2×D47)⋊C4C2312yes—
136C2×(C2×D47)⋊C4C2312yes—
137C2×(C2×D47)⋊C4C2312yes—
138C2×(C2×D47)⋊C4C2312yes—
139C2×(C2×D47)⋊C4C2312yes—
140C2×(C2×D47)⋊C4C2312yes—
141C2×(C2×D47)⋊C4C2312yes—
142C2×(C2×D47)⋊C4C2312yes—
143C2×(C2×D47)⋊C4C2312yes—
144C2×(C2×D47)⋊C4C2312yes—
145C2×(C2×D47)⋊C4C2312yes—
146C2×(C2×D47)⋊C4C2312yes—
147C2×(C2×D47)⋊C4C2312yes—
148C2×(C2×D47)⋊C4C2312yes—
149C2×(C2×D47)⋊C4C2312yes—
150C2×C4×Dic47C2312yes—
151C2×C4×Dic47C2312yes—
152C2×C4×Dic47C2312yes—
153C2×C4×Dic47C2312yes—
154C2×C4×Dic47C2311yescharacteristic
155C2×C4×Dic47C2311yescharacteristic
156C2×C4×Dic47C2312yes—
157C2×C4×Dic47C2312yes—
158C2×C4×Dic47C2311yescharacteristic
159C2×C4×Dic47C2312yes—
160C2×C4×Dic47C2311yescharacteristic
161C2×C4×Dic47C2311yescharacteristic
162C42×D47C2×C418yescomplemented
163C47⋊#95C2312yes—
164C47⋊#95C2312yes—
165C47⋊#95C2312yes—
166C47⋊#95C2312yes—
167C47⋊#95C2311yescharacteristic
168C47⋊#95C2311yescharacteristic
169C47⋊#95C2312yes—
170C47⋊#95C2312yes—
171C47⋊#95C2312yes—
172C47⋊#95C2312yes—
173C47⋊#95C2312yes—
174C47⋊#95C2312yes—
175C47⋊#95C2312yes—
176C47⋊#95C2312yes—
177C47⋊#95C2312yes—
178C47⋊#95C2312yes—
179C47⋊#95C2312yes—
180C47⋊#95C2312yes—
181C47⋊#95C2312yes—
182C47⋊#95C2312yes—
183C47⋊#95C2312yes—
184#125×C47C2×C418yescomplemented
185C2×C4⋊C4×C47C2312yes—
186C2×C4⋊C4×C47C2312yes—
187C2×C4⋊C4×C47C2312yes—
188C2×C4⋊C4×C47C2312yes—
189C2×C4⋊C4×C47C2311yescharacteristic
190C2×C4⋊C4×C47C2311yescharacteristic
191C2×C4⋊C4×C47C2312yes—
192C2×C42×C47C2311yescharacteristic
193C2×C42×C47C2311yescharacteristic
194C2×C42×C47C2312yes—
195C2×C42×C47C2312yes—
196C2×C42×C47C2311yescharacteristic
197#95×C47C2312yes—
198#95×C47C2311yescharacteristic
199#95×C47C2311yescharacteristic
200#95×C47C2312yes—
201#95×C47C2312yes—
202#95×C47C2312yes—
203#95×C47C2312yes—
204#95×C47C2312yes—
205#95×C47C2312yes—
206C23×D47C2411yescharacteristic
207C23×D47C2412yes—
208C22×C4×C47C2412yes—
209C22×C4×C47C2412yes—
210C22×C4×C47C2412yes—
211C22×C4×C47C2412yes—
212C22×C4×C47C2411yescharacteristic
213C22×C4×C47C2412yes—
214C22×C4×C47C2412yes—
215C22×C4×C47C2411yescharacteristic
216C22×C4×C47C2411yescharacteristic
217C22×Dic47C2412yes—
218C22×Dic47C2412yes—
219C22×Dic47C2412yes—
220C22×Dic47C2412yes—
221C22×Dic47C2411yescharacteristic
222C22×Dic47C2411yescharacteristic
223C22×Dic47C2412yes—
224C22×Dic47C2411yescharacteristic
225C2×D188—42no—
226C2×D188—42no—
227C2×D188—42no—
228C2×D188C22×C414yes—
229C2×D188C22×C418yes—
230C2×C4×D47—42no—
231C2×C4×D47—42no—
232C2×C4×D47—41no—
233C2×C4×D47—42no—
234C2×C4×D47—41no—
235C2×C4×D47—42no—
236C2×C4×D47—42no—
237C2×C4×D47—42no—
238C2×C4×D47—42no—
239C2×C4×D47—42no—
240C2×C4×D47—42no—
241C2×C4×D47—42no—
242C2×C4×D47C22×C414yes—
243C2×C4×D47C22×C414yes—
244C2×C4×D47C22×C414yes—
245C2×C4×D47C22×C418yes—
246C2×Dic94—42no—
247C2×Dic94C22×C414yes—
248C4⋊C4×C47—42no—
249C4⋊C4×C47—42no—
250C4⋊C4×C47—42no—
251C4⋊C4×C47C22×C418yes—
252C4⋊C4×C47C22×C414yes—
253C4⋊C4×C47C22×C418yes—
254C4⋊C4×C47C22×C414yes—
255C42×C47—42no—
256C42×C47—41no—
257C42×C47—41no—
258C42×C47—42no—
259C42×C47C22×C414yes—
260(C2×D47)⋊C4—42no—
261(C2×D47)⋊C4—42no—
262(C2×D47)⋊C4—42no—
263(C2×D47)⋊C4—42no—
264(C2×D47)⋊C4—42no—
265(C2×D47)⋊C4—42no—
266(C2×D47)⋊C4—42no—
267(C2×D47)⋊C4—42no—
268(C2×D47)⋊C4—42no—
269(C2×D47)⋊C4—42no—
270(C2×D47)⋊C4C22×C418yes—
271(C2×D47)⋊C4C22×C418yes—
272(C2×D47)⋊C4C22×C418yes—
273(C2×D47)⋊C4C22×C418yes—
274(C2×D47)⋊C4C22×C418yes—
275C4⋊Dic47—42no—
276C4⋊Dic47—42no—
277C4⋊Dic47—42no—
278C4⋊Dic47C22×C418yes—
279Dic47⋊C4—42no—
280Dic47⋊C4—42no—
281Dic47⋊C4—42no—
282Dic47⋊C4—42no—
283Dic47⋊C4C22×C418yes—
284C4×Dic47—42no—
285C4×Dic47—42no—
286C4×Dic47—42no—
287C4×Dic47—42no—
288C4×Dic47—41no—
289C4×Dic47—42no—
290C4×Dic47—42no—
291C4×Dic47—41no—
292C4×Dic47C22×C414yes—
293C4×Dic47C22×C414yes—
294C4×Dic47C22×C414yes—
295C4×Dic47C22×C418yes—
296C23×C47C2511yescharacteristic
297C22×D47—21no—
298C22×D47—21no—
299C22×D47—22no—
300C22×D47—22no—
301C22×D47—22no—
302C22×D47—22no—
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—22no—
307C22×D47C23×C414yes—
308C22×D47C23×C412yes—
309C2×C4×C47—21no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—21no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47C23×C414yes—
330C2×C4×C47C23×C412yes—
331C2×C4×C47C23×C412yes—
332C2×C4×C47C23×C412yes—
333C2×C4×C47C23×C414yes—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—21no—
339C2×Dic47—21no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—22no—
346C2×Dic47—22no—
347C2×Dic47—22no—
348C2×Dic47—22no—
349C2×Dic47—22no—
350C2×Dic47—22no—
351C2×Dic47—22no—
352C2×Dic47C23×C412yes—
353C2×Dic47C23×C412yes—
354C2×Dic47C23×C412yes—
355C2×Dic47C23×C414yes—
356D188—44no—
357D188—48no—
358C4×D47—44no—
359C4×D47—48no—
360C4×D47—44no—
361C4×D47—44no—
362C4×D47—84no—
363C4×D47—84no—
364Dic94—44no—
365#34400—471nomaximal, Sylow
366C22×C47C24×C411yescharacteristic
367C22×C47#58511yescharacteristic
368C22×C47#58512yes—
369C22×C47#58511yescharacteristic
370C22×C47#58512yes—
371C2×D47—22no—
372C2×D47—22no—
373C2×D47—24no—
374C2×D47—22no—
375C2×D47—24no—
376C2×D47—24no—
377C2×D47—42no—
378C2×D47—42no—
379C2×D47—42no—
380C2×D47—42no—
381C2×D47—42no—
382C2×D47—42no—
383C4×C47—22no—
384C4×C47—22no—
385C4×C47—22no—
386C4×C47—24no—
387C4×C47—24no—
388C4×C47—42no—
389C4×C47—42no—
390C4×C47—42no—
391C4×C47—42no—
392Dic47—24no—
393Dic47—22no—
394Dic47—22no—
395Dic47—22no—
396Dic47—42no—
397Dic47—42no—
398Dic47—42no—
399Dic47—42no—
400C2×#529—471no—
401#2376—472no—
402#2376—472no—
403#2373—472no—
404#2373—472no—
405#2357—472no—
406#2353—472no—
407#2346—472no—
408#2343—472no—
409#2337—471no—
410#2337—471no—
411#2336—471no—
412#2336D4711yescharacteristic, complemented
413#2333—472no—
414#2332—472no—
415#2320—472no—
416#2318—472no—
417#2283—471no—
418#2283—471no—
419C2×C47#342811yescharacteristic
420C2×C47#342811yescharacteristic
421C2×C47#342811yescharacteristic
422C2×C47#356612yes—
423C2×C47#356612yes—
424D47—42no—
425D47—44no—
426#529—4716no—
427C2×#126—472no—
428C2×#125C2×D4711yescharacteristic
429C2×#124—471no—
430C2×#123—472no—
431C2×C22⋊Q8—471no—
432C2×#121—471no—
433C2×C4×Q8—471no—
434C2×C4×D4—471no—
435C2×C4×D4—472no—
436C2×#117—472no—
437C22×C42—471no—
438#391—472no—
439#391—472no—
440#390—472no—
441#390—472no—
442#389—472no—
443#389—472no—
444#389—472no—
445#389C2×D4712yes—
446#388—472no—
447#388—472no—
448#388—472no—
449#388—472no—
450#388—472no—
451#388—472no—
452#388—472no—
453#388—472no—
454#388—472no—
455#388—472no—
456#388—472no—
457#388—472no—
458#387—472no—
459#387—472no—
460#387—472no—
461#387—472no—
462#387—472no—
463#387—472no—
464#387—472no—
465#387—472no—
466#387C2×D4712yes—
467#387C2×D4712yes—
468#387C2×D4712yes—
469#387C2×D4712yes—
470#386—472no—
471#386—472no—
472#386—472no—
473#386—472no—
474#385—472no—
475#385—472no—
476#385—472no—
477#385—472no—
478#383—471no—
479#383—472no—
480#383—472no—
481#383C2×D4711yescharacteristic
482#382—472no—
483#382—472no—
484#382—472no—
485#381—472no—
486#381—472no—
487#381—472no—
488#380—472no—
489#380—472no—
490#380—471no—
491#380—471no—
492C4×C4⋊C4—472no—
493C4×C4⋊C4—472no—
494C4×C4⋊C4—472no—
495C4×C4⋊C4—471no—
496C4×C4⋊C4—472no—
497C4×C4⋊C4—472no—
498C4×C4⋊C4C2×D4711yescharacteristic
499C4×C4⋊C4C2×D4712yes—
500C4×C22⋊C4—472no—
501C4×C22⋊C4—472no—
502C4×C22⋊C4—472no—
503C4×C22⋊C4—471no—
504C4×C22⋊C4—471no—
505C4×C22⋊C4—472no—
506C4×C22⋊C4—472no—
507C4×C22⋊C4—472no—
508#376—471no—
509#376—471no—
510#376—472no—
511#376—471no—
512#376—471no—
513C2×#95—472no—
514C47#3440011yescharacteristic, complemented, Sylow
515C22×Q8—471no—
516C22×D4—472no—
517C22×D4—471no—
518C23×C4—472no—
519C23×C4—471no—
520C23×C4—471no—
521C23×C4—471no—
522C23×C4—472no—
523C23×C4—472no—
524#126—4716no—
525#125C4×D4718yescomplemented
526#124—478no—
527#123—4716no—
528C22⋊Q8—478no—
529#121—478no—
530C4×Q8—478no—
531C4×D4—478no—
532C4×D4—4716no—
533#117—4716no—
534C2×C4⋊C4—472no—
535C2×C4⋊C4—472no—
536C2×C4⋊C4—472no—
537C2×C4⋊C4—472no—
538C2×C4⋊C4—472no—
539C2×C4⋊C4—472no—
540C2×C4⋊C4—472no—
541C2×C4⋊C4—472no—
542C2×C4⋊C4—472no—
543C2×C4⋊C4C22×D4712yes—
544C2×C4⋊C4C22×D4712yes—
545C2×C4⋊C4C22×D4712yes—
546C2×C4⋊C4C22×D4712yes—
547C2×C4⋊C4C22×D4711yescharacteristic
548C2×C4⋊C4C22×D4712yes—
549C2×C4⋊C4C22×D4711yescharacteristic
550C2×C22⋊C4—472no—
551C2×C22⋊C4—472no—
552C2×C22⋊C4—472no—
553C2×C22⋊C4—472no—
554C2×C22⋊C4—472no—
555C2×C22⋊C4—472no—
556C2×C22⋊C4—472no—
557C2×C22⋊C4—472no—
558C2×C22⋊C4—472no—
559C2×C22⋊C4—472no—
560C2×C22⋊C4—472no—
561C2×C22⋊C4—472no—
562C2×C22⋊C4—472no—
563C2×C22⋊C4—472no—
564C2×C22⋊C4—472no—
565C2×C42—471no—
566C2×C42—472no—
567C2×C42—471no—
568C2×C42—471no—
569C2×C42—478no—
570C2×C42—472no—
571C2×C42—471no—
572C2×C42—472no—
573C2×C42—471no—
574C2×C42—472no—
575C2×C42—472no—
576C2×C42—472no—
577C2×C42—472no—
578C2×C42C22×D4711yescharacteristic
579C2×C42C22×D4711yescharacteristic
580C2×C42C22×D4712yes—
581C2×C42C22×D4712yes—
582C2×C42C22×D4711yescharacteristic
583#95—472no—
584#95—472no—
585#95—472no—
586#95—472no—
587#95—472no—
588#95—472no—
589#95—471no—
590#95—472no—
591#95—472no—
592#95—471no—
593#95—472no—
594#95—472no—
595#95—472no—
596#95—472no—
597#95—472no—
598#95—472no—
599#95—472no—
600#95—472no—
601#95—472no—
602#95—472no—
603#95—472no—
604#95C22×D4712yes—
605#95C22×D4711yescharacteristic
606#95C22×D4711yescharacteristic
607#95C22×D4712yes—
608#95C22×D4712yes—
609#95C22×D4712yes—
610#95C22×D4712yes—
611#95C22×D4712yes—
612#95C22×D4712yes—
613C24—472no—
614C24—471no—
615C2×Q8—474no—
616C2×Q8—1882no—
617C2×D4—478no—
618C2×D4—474no—
619C2×D4—1882no—
620C2×D4—1882no—
621C2×D4—1882no—
622C22×C4—471no—
623C22×C4—471no—
624C22×C4—472no—
625C22×C4—471no—
626C22×C4—474no—
627C22×C4—474no—
628C22×C4—474no—
629C22×C4—478no—
630C22×C4—472no—
631C22×C4—472no—
632C22×C4—472no—
633C22×C4—472no—
634C22×C4—1882no—
635C22×C4—1882no—
636C22×C4—1882no—
637C22×C4—1882no—
638C22×C4—1882no—
639C22×C4—1882no—
640C22×C4—1881no—
641C22×C4—1882no—
642C22×C4—1882no—
643C22×C4—1881no—
644C22×C4—1882no—
645C22×C4—1882no—
646C22×C4C23×D4712yes—
647C22×C4C23×D4712yes—
648C22×C4C23×D4712yes—
649C22×C4C23×D4712yes—
650C22×C4C23×D4711yescharacteristic
651C22×C4C23×D4711yescharacteristic
652C22×C4C23×D4712yes—
653C22×C4C23×D4712yes—
654C22×C4C23×D4711yescharacteristic
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—478no—
659C4⋊C4—478no—
660C4⋊C4—1882no—
661C4⋊C4—1882no—
662C4⋊C4—1882no—
663C4⋊C4—1882no—
664C4⋊C4—1882no—
665C4⋊C4—1882no—
666C4⋊C4—1882no—
667C4⋊C4C2×C4×D4718yes—
668C4⋊C4C2×C4×D4714yes—
669C4⋊C4C2×C4×D4718yes—
670C4⋊C4C2×C4×D4714yes—
671C22⋊C4—478no—
672C22⋊C4—478no—
673C22⋊C4—478no—
674C22⋊C4—478no—
675C22⋊C4—478no—
676C22⋊C4—1882no—
677C22⋊C4—1882no—
678C22⋊C4—1882no—
679C22⋊C4—1882no—
680C22⋊C4—1882no—
681C22⋊C4—1882no—
682C22⋊C4—1882no—
683C22⋊C4—1882no—
684C22⋊C4—1882no—
685C22⋊C4—1882no—
686C42—41no—
687C42—41no—
688C42—42no—
689C42—42no—
690C42—474no—
691C42—474no—
692C42—474no—
693C42—478no—
694C42—1882no—
695C42—1881no—
696C42—1881no—
697C42—1882no—
698C42—1882no—
699C42—1882no—
700C42—1882no—
701C42—1882no—
702C42C2×C4×D4714yes—
703C23—474no—
704C23—472no—
705C23—941no—
706C23—942no—
707C23—942no—
708C23—942no—
709C23—942no—
710C23—941no—
711C23—942no—
712C23—942no—
713C23—942no—
714C23—942no—
715C23C24×D4711yescharacteristic
716Q8—1884no—
717D4—1888no—
718D4—1884no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—472no—
740C2×C4—472no—
741C2×C4—472no—
742C2×C4—474no—
743C2×C4—941no—
744C2×C4—942no—
745C2×C4—942no—
746C2×C4—942no—
747C2×C4—942no—
748C2×C4—941no—
749C2×C4—942no—
750C2×C4—942no—
751C2×C4—942no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—942no—
755C2×C4—942no—
756C2×C4—942no—
757C2×C4—942no—
758C2×C4—942no—
759C2×C4—942no—
760C2×C4—942no—
761C2×C4—3764no—
762C2×C4—3764no—
763C2×C4—1884no—
764C2×C4—1884no—
765C2×C4—1888no—
766C2×C4—1884no—
767C2×C4C22×C4×D4712yes—
768C2×C4C22×C4×D4712yes—
769C2×C4C22×C4×D4712yes—
770C2×C4C22×C4×D4714yes—
771C2×C4C22×C4×D4714yes—
772C22—942no—
773C22—944no—
774C22—944no—
775C22—942no—
776C22—942no—
777C22—944no—
778C22—1882no—
779C22—1882no—
780C22—1882no—
781C22—1882no—
782C22—1882no—
783C22—1882no—
784C22C23×C4×D4711yescharacteristic
785C22#1568995811yescharacteristic
786C22#1568995912yes—
787C22#1568996011yescharacteristic
788C22#1568996012yes—
789C4—22no—
790C4—24no—
791C4—22no—
792C4—24no—
793C4—22no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—942no—
799C4—942no—
800C4—942no—
801C4—944no—
802C4—1882no—
803C4—1882no—
804C4—1882no—
805C4—1882no—
806C2—1882no—
807C2—1884no—
808C2#2025658711yescharacteristic
809C2#2025658811yescharacteristic
810C2#2025659011yescharacteristic
811C2#2025804712yes—
812C2#2025807112yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2336C2
socle, cosocleC23×C47C25
prime radicalC2×#13093999C22
hypercenter#2336D47
hypocenterC47#34400
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2336

Complements

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

NH ≅ G/Ntype
2. #20246535C2semidirect
3. #20246533C2semidirect
4. #20246513C2semidirect
5. #20246501C2semidirect
6. #20246357C2semidirect
7. #20246327C2semidirect
8. #20246272C2semidirect
9. #20246247C2semidirect
10. #20246201C2semidirect
11. #20246198C2semidirect
12. #20246194C2semidirect
14. #20246140C2semidirect
15. #20246037C2semidirect
16. #20246020C2semidirect
17. #20245785C2semidirect
18. #20245784C2semidirect
19. C47×#2336C2semidirect
20. #15689658C4semidirect
117. #13094019C2×C4semidirect
119. #13094009C2×C4semidirect
120. #13094004C2×C4semidirect
122. #13093989C2×C4semidirect
124. #13093986C2×C4semidirect
125. #13093982C2×C4semidirect
162. C42×D47C2×C4semidirect
184. #125×C47C2×C4semidirect
412. #2336D47semidirect
514. C47#34400semidirect
525. #125C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896582
#202465352
#202465332
#202465132
#202465012
#202463572
#202463272
#202462722
#202462472
#202462012
#202461982
#202461942
#202461522
#202461402
#202460372
#202460202
#202457852
#202457842
C47×#23362
#3440047