Finite Group Databasebeta

← #26382592

Subgroups — #26382592

Order 12032.

2082 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
1#20246692C212yesmaximal, complemented
2#20246689C212yesmaximal, complemented
3#20246687C212yesmaximal, complemented
4#20246687C212yesmaximal, complemented
5#20246677C212yesmaximal, complemented
6#20246674C211yesmaximal, characteristic, complemented
7#20246665C212yesmaximal, complemented
8#20246660C211yesmaximal, characteristic, complemented
9#20246654C212yesmaximal, complemented
10#20246652C212yesmaximal, complemented
11#20246651C212yesmaximal, complemented
12#20246629C212yesmaximal
13#20246628C211yesmaximal, characteristic
14C4×#13093989C211yesmaximal, characteristic, complemented
15C4×#13093986C211yesmaximal, characteristic, complemented
16C4×#13093986C212yesmaximal, complemented
17C4×#13093982C212yesmaximal, complemented
18#20245727C211yesmaximal, characteristic, complemented
19C47×#2402C211yesmaximal, characteristic, complemented
20C2×C4×Dic94C2211yescharacteristic
21C2×#13093989C2212yes—
22C2×C4×D188C2212yes—
23C2×C4×D188C2211yescharacteristic
24C2×#13093986C2212yes—
25C2×#13093986C2212yes—
26C2×#13093986C2212yes—
27C2×#13093982C2212yes—
28C2×#13093982C2212yes—
29C2×#13093981C2211yescharacteristic
30C2×#13093981C2211yescharacteristic
31C2×C42×D47C2211yescharacteristic
32C2×C42×D47C2212yes—
33C47⋊#401C2212yes—
34#15689065C2212yes—
35#15689065C2212yes—
36#15689063C2211yescharacteristic
37#15689063C2212yes—
38#15689062C2212yes—
39#15689061C2212yes—
40#15689060C2211yescharacteristic
41#15689058C2212yes—
42#15689056C2212yes—
43#15689055C2211yescharacteristic
44#15689053C2212yes—
45#15689052C2212yes—
46#15689052C2212yes—
47#15689052C2212yes—
48#15689050C2211yescharacteristic
49#15689050C2212yes—
50#15689050C2212yes—
51#15689049C2212yes—
52#15689049C2212yes—
53#15689045C2212yes—
54#15689045C2212yes—
55#15689045C2212yes—
56#15689044C2211yescharacteristic
57#15689041C2211yescharacteristic
58#15689041C2212yes—
59#15689041C2212yes—
60#15689040C2212yes—
61#15689040C2212yes—
62#15689036C2211yescharacteristic
63#15689036C2212yes—
64#15689033C2211yescharacteristic
65C4⋊C4×Dic47C2212yes—
66C4⋊C4×Dic47C2212yes—
67C4⋊C4×Dic47C2212yes—
68C4⋊C4×Dic47C2212yes—
69C4⋊C4×Dic47C2212yes—
70C4⋊C4×Dic47C2212yes—
71C4×Dic47⋊C4C2212yes—
72C4×C4⋊Dic47C2212yes—
73#15688974C2212yes—
74#15688974C2212yes—
75#15688974C2212yes—
76#15688974C2212yes—
77C4×(C2×D47)⋊C4C2212yes—
78C4×(C2×D47)⋊C4C2212yes—
79C4×(C2×D47)⋊C4C2212yes—
80C4×(C2×D47)⋊C4C2212yes—
81C4×(C2×D47)⋊C4C2212yes—
82#15688970C2212yes—
83#15688970C2212yes—
84#15688970C2212yes—
85#15688970C2212yes—
86#15688970C2212yes—
87#15688970C2212yes—
88#15688970C2212yes—
89#15688970C2212yes—
90#15688970C2212yes—
91#15688970C2212yes—
92#15688969C2211yescharacteristic
93#15688968C2212yes—
94#15688968C2212yes—
95C42×Dic47C2211yescharacteristic
96C42×Dic47C2211yescharacteristic
97C42×Dic47C2212yes—
98C47×#400C2212yes—
99C47×#400C2212yes—
100C47×#398C2212yes—
101C47×#398C2212yes—
102C4×C4⋊C4×C47C2211yescharacteristic
103C4×C4⋊C4×C47C2212yes—
104C4×C4⋊C4×C47C2211yescharacteristic
105C4×C4⋊C4×C47C2212yes—
106C47×#376C2211yescharacteristic
107C22×Dic94C2311yescharacteristic
108C22×D188C2312yes—
109C22×D188C2311yescharacteristic
110C22×C4×D47C2312yes—
111C22×C4×D47C2312yes—
112C22×C4×D47C2312yes—
113C22×C4×D47C2312yes—
114C22×C4×D47C2311yescharacteristic
115C4×Dic94—24no—
116#13093989—28no—
117C4×D188—28no—
118C4×D188—24no—
119#13093986—28no—
120#13093986—28no—
121#13093986—28no—
122#13093982—28no—
123#13093982—28no—
124#13093981—24no—
125#13093981—24no—
126C2×C4⋊Dic47C2312yes—
127C2×C4⋊Dic47C2312yes—
128C2×C4⋊Dic47C2312yes—
129C2×C4⋊Dic47C2311yescharacteristic
130C2×C4⋊Dic47C2311yescharacteristic
131C2×Dic47⋊C4C2312yes—
132C2×Dic47⋊C4C2311yescharacteristic
133C2×Dic47⋊C4C2311yescharacteristic
134C2×Dic47⋊C4C2312yes—
135C2×Dic47⋊C4C2312yes—
136C2×Dic47⋊C4C2312yes—
137C2×(C2×D47)⋊C4C2311yescharacteristic
138C2×(C2×D47)⋊C4C2311yescharacteristic
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×(C2×D47)⋊C4C2312yes—
151C2×(C2×D47)⋊C4C2312yes—
152C2×(C2×D47)⋊C4C2312yes—
153C2×C4×Dic47C2312yes—
154C2×C4×Dic47C2312yes—
155C2×C4×Dic47C2312yes—
156C2×C4×Dic47C2311yescharacteristic
157C2×C4×Dic47C2311yescharacteristic
158C2×C4×Dic47C2312yes—
159C2×C4×Dic47C2312yes—
160C2×C4×Dic47C2312yes—
161C2×C4×Dic47C2312yes—
162C2×C4×Dic47C2312yes—
163C2×C4×Dic47C2312yes—
164C2×C4×Dic47C2312yes—
165C2×C4×Dic47C2312yes—
166C2×C4×Dic47C2311yescharacteristic
167C2×C4×Dic47C2312yes—
168C42×D47—24no—
169C42×D47—28no—
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—
184C47⋊#95C2312yes—
185C47⋊#95C2312yes—
186C2×C4⋊C4×C47C2312yes—
187C2×C4⋊C4×C47C2312yes—
188C2×C4⋊C4×C47C2312yes—
189C2×C4⋊C4×C47C2312yes—
190C2×C4⋊C4×C47C2312yes—
191C2×C4⋊C4×C47C2312yes—
192C2×C42×C47C2311yescharacteristic
193C2×C42×C47C2312yes—
194C2×C42×C47C2311yescharacteristic
195C2×C42×C47C2312yes—
196C2×C42×C47C2311yescharacteristic
197#95×C47C2312yes—
198#95×C47C2312yes—
199#95×C47C2311yescharacteristic
200#95×C47C2311yescharacteristic
201#95×C47C2312yes—
202#95×C47C2312yes—
203#95×C47C2312yes—
204#95×C47C2312yes—
205#95×C47C2311yescharacteristic
206#95×C47C2311yescharacteristic
207C23×D47C2411yescharacteristic
208C23×D47C2412yes—
209C22×C4×C47C2412yes—
210C22×C4×C47C2412yes—
211C22×C4×C47C2412yes—
212C22×C4×C47C2412yes—
213C22×C4×C47C2412yes—
214C22×C4×C47C2412yes—
215C22×C4×C47C2411yescharacteristic
216C22×C4×C47C2411yescharacteristic
217C22×C4×C47C2411yescharacteristic
218C22×Dic47C2412yes—
219C22×Dic47C2412yes—
220C22×Dic47C2412yes—
221C22×Dic47C2411yescharacteristic
222C22×Dic47C2411yescharacteristic
223C22×Dic47C2412yes—
224C22×Dic47C2411yescharacteristic
225C22×Dic47C2412yes—
226C2×D188—24no—
227C2×D188—24no—
228C2×D188—24no—
229C2×D188—24no—
230C2×D188—22no—
231C2×C4×D47—22no—
232C2×C4×D47—22no—
233C2×C4×D47—24no—
234C2×C4×D47—24no—
235C2×C4×D47—24no—
236C2×C4×D47—24no—
237C2×C4×D47—24no—
238C2×C4×D47—24no—
239C2×C4×D47—24no—
240C2×C4×D47—24no—
241C2×C4×D47—24no—
242C2×C4×D47—24no—
243C2×C4×D47—24no—
244C2×C4×D47#4114yes—
245C2×C4×D47#4118yes—
246C2×Dic94—22no—
247C2×Dic94—24no—
248C4⋊C4×C47—24no—
249C4⋊C4×C47—24no—
250C4⋊C4×C47—24no—
251C4⋊C4×C47—24no—
252C4⋊C4×C47—24no—
253C4⋊C4×C47—24no—
254C42×C47—24no—
255C42×C47—22no—
256C42×C47—22no—
257C42×C47—24no—
258C42×C47#4114yes—
259(C2×D47)⋊C4—24no—
260(C2×D47)⋊C4—24no—
261(C2×D47)⋊C4—24no—
262(C2×D47)⋊C4—24no—
263(C2×D47)⋊C4—24no—
264(C2×D47)⋊C4—24no—
265(C2×D47)⋊C4—22no—
266(C2×D47)⋊C4—22no—
267(C2×D47)⋊C4—24no—
268(C2×D47)⋊C4—24no—
269(C2×D47)⋊C4—24no—
270(C2×D47)⋊C4—24no—
271(C2×D47)⋊C4—24no—
272(C2×D47)⋊C4—24no—
273(C2×D47)⋊C4—24no—
274(C2×D47)⋊C4—24no—
275C4⋊Dic47—24no—
276C4⋊Dic47—22no—
277C4⋊Dic47—22no—
278C4⋊Dic47—24no—
279C4⋊Dic47—24no—
280Dic47⋊C4—22no—
281Dic47⋊C4—22no—
282Dic47⋊C4—24no—
283Dic47⋊C4—24no—
284Dic47⋊C4—24no—
285Dic47⋊C4—24no—
286C4×Dic47—22no—
287C4×Dic47—22no—
288C4×Dic47—24no—
289C4×Dic47—24no—
290C4×Dic47—24no—
291C4×Dic47—24no—
292C4×Dic47—24no—
293C4×Dic47—24no—
294C4×Dic47—24no—
295C4×Dic47—24no—
296C4×Dic47—24no—
297C4×Dic47—24no—
298C4×Dic47—24no—
299C4×Dic47#4114yes—
300C4×Dic47#4118yes—
301C23×C47C2511yescharacteristic
302C22×D47—22no—
303C22×D47—21no—
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—22no—
307C22×D47—22no—
308C22×D47—22no—
309C22×D47—22no—
310C22×D47—21no—
311C22×D47—22no—
312C22×D47C2×#4112yes—
313C22×D47C2×#4114yes—
314C2×C4×C47—22no—
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×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47C2×#4114yes—
333C2×C4×C47C2×#4114yes—
334C2×C4×C47C2×#4112yes—
335C2×C4×C47C2×#4112yes—
336C2×C4×C47C2×#4112yes—
337C2×C4×C47C2×#4112yes—
338C2×C4×C47C2×#4112yes—
339C2×Dic47—21no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—21no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—22no—
346C2×Dic47—22no—
347C2×Dic47—21no—
348C2×Dic47—21no—
349C2×Dic47—22no—
350C2×Dic47—22no—
351C2×Dic47—22no—
352C2×Dic47—22no—
353C2×Dic47—22no—
354C2×Dic47—22no—
355C2×Dic47—22no—
356C2×Dic47C2×#4114yes—
357C2×Dic47C2×#4112yes—
358C2×Dic47C2×#4114yes—
359C2×Dic47C2×#4114yes—
360C2×Dic47C2×#4114yes—
361D188—28no—
362D188—216no—
363C4×D47—28no—
364C4×D47—216no—
365C4×D47—48no—
366C4×D47—48no—
367C4×D47—48no—
368Dic94—28no—
369#34551—471nomaximal, Sylow
370C22×C47C22×#4111yescharacteristic
371C22×C47C22×#4112yes—
372C22×C47C22×#4111yescharacteristic
373C22×C47C22×#4112yes—
374C22×C47C22×#4111yescharacteristic
375C2×D47—24no—
376C2×D47—22no—
377C2×D47—24no—
378C2×D47—24no—
379C2×D47—24no—
380C2×D47—42no—
381C2×D47—42no—
382C2×D47—42no—
383C2×D47—42no—
384C2×D47—42no—
385C2×D47—41no—
386C2×D47—41no—
387C4×C47—24no—
388C4×C47—22no—
389C4×C47—24no—
390C4×C47—22no—
391C4×C47—42no—
392C4×C47—42no—
393C4×C47—42no—
394C4×C47—42no—
395C4×C47#52914yes—
396Dic47—22no—
397Dic47—24no—
398Dic47—42no—
399Dic47—42no—
400Dic47—41no—
401Dic47—42no—
402Dic47—41no—
403Dic47#52918yes—
404#2402—472no—
405#2402D4711yescharacteristic, complemented
406#2401—472no—
407#2401—472no—
408#2401—472no—
409#2398—472no—
410#2398—471no—
411#2396—472no—
412#2396—471no—
413#2395—472no—
414#2395—472no—
415#2395—472no—
416#2392—472no—
417#2392—471no—
418C42×Q8—471no—
419C42×D4—471no—
420C42×D4—472no—
421C4×#117—472no—
422C4×#117—471no—
423C2×C47C2×#52912yes—
424C2×C47C2×#52911yescharacteristic
425C2×C47#344412yes—
426C2×C47#344411yescharacteristic
427C2×C47#344411yescharacteristic
428D47—44no—
429D47—42no—
430C2×C4×Q8—472no—
431C2×C4×Q8—471no—
432C2×C4×D4—472no—
433C2×C4×D4—472no—
434C2×C4×D4—472no—
435C2×C4×D4—472no—
436C2×C4×D4—471no—
437C2×#117—472no—
438C2×#117—472no—
439C2×#117—471no—
440C2×#117—471no—
441C22×C42—472no—
442C22×C42—471no—
443#401—472no—
444#400—472no—
445#400—472no—
446#400—472no—
447#400—471no—
448#400—472no—
449#400—472no—
450#400C2×D4712yes—
451#400C2×D4712yes—
452#399—472no—
453#399—471no—
454#398—472no—
455#398—472no—
456#398—471no—
457#398C2×D4712yes—
458#398C2×D4712yes—
459#397—472no—
460#397—472no—
461#397—471no—
462#397—472no—
463#397—472no—
464#397—472no—
465#397—472no—
466#397—472no—
467#396—472no—
468#396—472no—
469#396—472no—
470#395—471no—
471#394—472no—
472#394—472no—
473#394—471no—
474#394—472no—
475#394—472no—
476#393—471no—
477#393—472no—
478#392—471no—
479C4×C4⋊C4—472no—
480C4×C4⋊C4—472no—
481C4×C4⋊C4—472no—
482C4×C4⋊C4—472no—
483C4×C4⋊C4—472no—
484C4×C4⋊C4—472no—
485C4×C4⋊C4—472no—
486C4×C4⋊C4—472no—
487C4×C4⋊C4—472no—
488C4×C4⋊C4—472no—
489C4×C4⋊C4—472no—
490C4×C4⋊C4—472no—
491C4×C4⋊C4C2×D4711yescharacteristic
492C4×C4⋊C4C2×D4712yes—
493C4×C4⋊C4C2×D4711yescharacteristic
494C4×C4⋊C4C2×D4712yes—
495C4×C22⋊C4—472no—
496C4×C22⋊C4—472no—
497C4×C22⋊C4—472no—
498C4×C22⋊C4—472no—
499C4×C22⋊C4—472no—
500C4×C22⋊C4—472no—
501C4×C22⋊C4—472no—
502C4×C22⋊C4—472no—
503C4×C22⋊C4—472no—
504C4×C22⋊C4—472no—
505C4×C22⋊C4—472no—
506C4×C22⋊C4—472no—
507C4×C22⋊C4—472no—
508C4×C22⋊C4—472no—
509C4×C22⋊C4—472no—
510#376—471no—
511#376—472no—
512#376—472no—
513#376C2×D4711yescharacteristic
514C43—471no—
515C43—472no—
516C43—471no—
517C47#3455111yescharacteristic, complemented, Sylow
518C22×Q8—471no—
519C22×D4—472no—
520C22×D4—471no—
521C23×C4—472no—
522C23×C4—471no—
523C23×C4—472no—
524C23×C4—472no—
525C23×C4—472no—
526C4×Q8—948no—
527C4×Q8—944no—
528C4×D4—948no—
529C4×D4—948no—
530C4×D4—948no—
531C4×D4—948no—
532C4×D4—944no—
533#117—944no—
534#117—948no—
535#117—948no—
536#117—944no—
537C2×C4⋊C4—471no—
538C2×C4⋊C4—471no—
539C2×C4⋊C4—472no—
540C2×C4⋊C4—472no—
541C2×C4⋊C4—472no—
542C2×C4⋊C4—472no—
543C2×C4⋊C4—471no—
544C2×C4⋊C4—472no—
545C2×C4⋊C4—472no—
546C2×C4⋊C4—472no—
547C2×C4⋊C4—471no—
548C2×C4⋊C4C22×D4712yes—
549C2×C4⋊C4C22×D4712yes—
550C2×C4⋊C4C22×D4712yes—
551C2×C4⋊C4C22×D4712yes—
552C2×C4⋊C4C22×D4712yes—
553C2×C4⋊C4C22×D4712yes—
554C2×C22⋊C4—472no—
555C2×C22⋊C4—471no—
556C2×C22⋊C4—472no—
557C2×C22⋊C4—471no—
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×C22⋊C4—472no—
566C2×C22⋊C4—472no—
567C2×C22⋊C4—472no—
568C2×C22⋊C4—472no—
569C2×C22⋊C4—472no—
570C2×C42—472no—
571C2×C42—471no—
572C2×C42—472no—
573C2×C42—472no—
574C2×C42—472no—
575C2×C42—472no—
576C2×C42—472no—
577C2×C42—472no—
578C2×C42—472no—
579C2×C42—472no—
580C2×C42—472no—
581C2×C42—472no—
582C2×C42—471no—
583C2×C42—471no—
584C2×C42—472no—
585C2×C42—948no—
586C2×C42—944no—
587C2×C42C22×D4711yescharacteristic
588C2×C42C22×D4712yes—
589C2×C42C22×D4711yescharacteristic
590C2×C42C22×D4712yes—
591C2×C42C22×D4711yescharacteristic
592#95—472no—
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#95—472no—
605#95—472no—
606#95—472no—
607#95—472no—
608#95C22×D4712yes—
609#95C22×D4712yes—
610#95C22×D4712yes—
611#95C22×D4712yes—
612#95C22×D4711yescharacteristic
613#95C22×D4711yescharacteristic
614#95C22×D4712yes—
615#95C22×D4712yes—
616#95C22×D4711yescharacteristic
617#95C22×D4711yescharacteristic
618C24—472no—
619C24—471no—
620C2×Q8—944no—
621C2×Q8—942no—
622C2×D4—944no—
623C2×D4—944no—
624C2×D4—944no—
625C2×D4—944no—
626C2×D4—942no—
627C22×C4—472no—
628C22×C4—472no—
629C22×C4—471no—
630C22×C4—478no—
631C22×C4—474no—
632C22×C4—472no—
633C22×C4—472no—
634C22×C4—472no—
635C22×C4—471no—
636C22×C4—471no—
637C22×C4—944no—
638C22×C4—944no—
639C22×C4—944no—
640C22×C4—944no—
641C22×C4—944no—
642C22×C4—944no—
643C22×C4—944no—
644C22×C4—944no—
645C22×C4—942no—
646C22×C4—942no—
647C22×C4—944no—
648C22×C4—944no—
649C22×C4—944no—
650C22×C4C23×D4712yes—
651C22×C4C23×D4712yes—
652C22×C4C23×D4712yes—
653C22×C4C23×D4712yes—
654C22×C4C23×D4712yes—
655C22×C4C23×D4712yes—
656C22×C4C23×D4711yescharacteristic
657C22×C4C23×D4711yescharacteristic
658C22×C4C23×D4711yescharacteristic
659C4⋊C4—24no—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—24no—
663C4⋊C4—24no—
664C4⋊C4—24no—
665C4⋊C4—944no—
666C4⋊C4—944no—
667C4⋊C4—944no—
668C4⋊C4—944no—
669C4⋊C4—944no—
670C4⋊C4—944no—
671C4⋊C4—942no—
672C4⋊C4—942no—
673C4⋊C4—944no—
674C4⋊C4—942no—
675C4⋊C4—942no—
676C22⋊C4—944no—
677C22⋊C4—944no—
678C22⋊C4—944no—
679C22⋊C4—944no—
680C22⋊C4—944no—
681C22⋊C4—944no—
682C22⋊C4—944no—
683C22⋊C4—944no—
684C22⋊C4—944no—
685C22⋊C4—944no—
686C22⋊C4—944no—
687C22⋊C4—944no—
688C22⋊C4—944no—
689C22⋊C4—942no—
690C22⋊C4—942no—
691C22⋊C4—944no—
692C42—24no—
693C42—22no—
694C42—22no—
695C42—24no—
696C42—474no—
697C42—478no—
698C42—944no—
699C42—944no—
700C42—944no—
701C42—944no—
702C42—944no—
703C42—944no—
704C42—944no—
705C42—944no—
706C42—944no—
707C42—944no—
708C42—942no—
709C42—942no—
710C42—944no—
711C42#1062535414yes—
712C23—474no—
713C23—472no—
714C23—942no—
715C23—942no—
716C23—942no—
717C23—942no—
718C23—942no—
719C23—942no—
720C23—942no—
721C23—941no—
722C23—941no—
723C23—942no—
724C23C24×D4711yescharacteristic
725Q8—948no—
726D4—9416no—
727D4—948no—
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—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—474no—
747C2×C4—474no—
748C2×C4—474no—
749C2×C4—474no—
750C2×C4—472no—
751C2×C4—9416no—
752C2×C4—941no—
753C2×C4—942no—
754C2×C4—942no—
755C2×C4—941no—
756C2×C4—948no—
757C2×C4—942no—
758C2×C4—942no—
759C2×C4—942no—
760C2×C4—942no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—942no—
764C2×C4—942no—
765C2×C4—942no—
766C2×C4—941no—
767C2×C4—941no—
768C2×C4—942no—
769C2×C4—942no—
770C2×C4—1888no—
771C2×C4—1888no—
772C2×C4—1888no—
773C2×C4#41×D4714yes—
774C2×C4#41×D4714yes—
775C2×C4#41×D4712yes—
776C2×C4#41×D4712yes—
777C2×C4C2×#1062535412yes—
778C2×C4C2×#1062535412yes—
779C2×C4C2×#1062535412yes—
780C22—944no—
781C22—942no—
782C22—944no—
783C22—944no—
784C22—944no—
785C22—1882no—
786C22—1882no—
787C22—1882no—
788C22—1882no—
789C22—1882no—
790C22—1881no—
791C22—1881no—
792C22C2×#41×D4711yescharacteristic
793C22C2×#41×D4712yes—
794C22C2×#41×D4712yes—
795C22C2×#41×D4711yescharacteristic
796C22C22×#1062535411yescharacteristic
797C4—24no—
798C4—24no—
799C4—22no—
800C4—22no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—478no—
806C4—942no—
807C4—944no—
808C4—1882no—
809C4—1882no—
810C4—1881no—
811C4—1882no—
812C4—1881no—
813C4#1568965814yes—
814C2—1884no—
815C2—1882no—
816C2#529×D4712yes—
817C2C2×#1568965811yescharacteristic
818C2#2025668212yes—
819C2#2025668511yescharacteristic
820C2#2025668511yescharacteristic
subgroupG/H
centerC22×C4C23×D47
commutator, socle, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC47×#2402C2
prime radical#15689033C22
hypercenter#2402D47
hypocenterC47#34551
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #2402

Complements

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

NH ≅ G/Ntype
1. #20246692C2semidirect
2. #20246689C2semidirect
3. #20246687C2semidirect
4. #20246687C2semidirect
5. #20246677C2semidirect
6. #20246674C2semidirect
7. #20246665C2semidirect
8. #20246660C2semidirect
9. #20246654C2semidirect
10. #20246652C2semidirect
11. #20246651C2semidirect
14. C4×#13093989C2semidirect
15. C4×#13093986C2semidirect
16. C4×#13093986C2semidirect
17. C4×#13093982C2semidirect
18. #20245727C2semidirect
19. C47×#2402C2semidirect
405. #2402D47semidirect
517. C47#34551semidirect

Maximal subgroups

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

subgroupindex
#202466922
#202466892
#202466872
#202466772
#202466742
#202466652
#202466602
#202466542
#202466522
#202466512
#202466292
#202466282
C4×#130939892
C4×#130939862
C4×#130939822
#202457272
C47×#24022
#3455147