Finite Group Databasebeta

← #25262911

Subgroups — #25262911

Order 11008.

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#19137899C212yesmaximal, complemented
2#19137896C212yesmaximal, complemented
3#19137894C212yesmaximal, complemented
4#19137894C212yesmaximal, complemented
5#19137884C212yesmaximal, complemented
6#19137881C211yesmaximal, characteristic, complemented
7#19137872C212yesmaximal, complemented
8#19137867C211yesmaximal, characteristic, complemented
9#19137861C212yesmaximal, complemented
10#19137859C212yesmaximal, complemented
11#19137858C212yesmaximal, complemented
12#19137836C212yesmaximal
13#19137835C211yesmaximal, characteristic
14C4×#13063290C211yesmaximal, characteristic, complemented
15C4×#13063287C212yesmaximal, complemented
16C4×#13063287C211yesmaximal, characteristic, complemented
17C4×#13063283C212yesmaximal, complemented
18#19136934C211yesmaximal, characteristic, complemented
19C43×#2402C211yesmaximal, characteristic, complemented
20C2×C4×Dic86C2211yescharacteristic
21C2×#13063290C2212yes—
22C2×C4×D172C2212yes—
23C2×C4×D172C2211yescharacteristic
24C2×#13063287C2212yes—
25C2×#13063287C2212yes—
26C2×#13063287C2212yes—
27C2×#13063283C2212yes—
28C2×#13063283C2212yes—
29C2×#13063282C2211yescharacteristic
30C2×#13063282C2211yescharacteristic
31C2×C42×D43C2211yescharacteristic
32C2×C42×D43C2212yes—
33C43⋊#401C2212yes—
34#14582841C2212yes—
35#14582841C2212yes—
36#14582839C2211yescharacteristic
37#14582839C2212yes—
38#14582838C2212yes—
39#14582837C2212yes—
40#14582836C2211yescharacteristic
41#14582834C2212yes—
42#14582832C2212yes—
43#14582831C2211yescharacteristic
44#14582829C2212yes—
45#14582828C2212yes—
46#14582828C2212yes—
47#14582828C2212yes—
48#14582826C2211yescharacteristic
49#14582826C2212yes—
50#14582826C2212yes—
51#14582825C2212yes—
52#14582825C2212yes—
53#14582821C2212yes—
54#14582821C2212yes—
55#14582821C2212yes—
56#14582820C2211yescharacteristic
57#14582817C2211yescharacteristic
58#14582817C2212yes—
59#14582817C2212yes—
60#14582816C2212yes—
61#14582816C2212yes—
62#14582812C2211yescharacteristic
63#14582812C2212yes—
64#14582809C2211yescharacteristic
65C4⋊C4×Dic43C2212yes—
66C4⋊C4×Dic43C2212yes—
67C4⋊C4×Dic43C2212yes—
68C4⋊C4×Dic43C2212yes—
69C4⋊C4×Dic43C2212yes—
70C4⋊C4×Dic43C2212yes—
71C4×Dic43⋊C4C2212yes—
72C4×C4⋊Dic43C2212yes—
73#14582750C2212yes—
74#14582750C2212yes—
75#14582750C2212yes—
76#14582750C2212yes—
77C4×(C2×D43)⋊C4C2212yes—
78C4×(C2×D43)⋊C4C2212yes—
79C4×(C2×D43)⋊C4C2212yes—
80C4×(C2×D43)⋊C4C2212yes—
81C4×(C2×D43)⋊C4C2212yes—
82#14582746C2212yes—
83#14582746C2212yes—
84#14582746C2212yes—
85#14582746C2212yes—
86#14582746C2212yes—
87#14582746C2212yes—
88#14582746C2212yes—
89#14582746C2212yes—
90#14582746C2212yes—
91#14582746C2212yes—
92#14582745C2211yescharacteristic
93#14582744C2212yes—
94#14582744C2212yes—
95C42×Dic43C2211yescharacteristic
96C42×Dic43C2211yescharacteristic
97C42×Dic43C2212yes—
98C43×#400C2212yes—
99C43×#400C2212yes—
100C43×#398C2212yes—
101C43×#398C2212yes—
102C4×C4⋊C4×C43C2211yescharacteristic
103C4×C4⋊C4×C43C2212yes—
104C4×C4⋊C4×C43C2211yescharacteristic
105C4×C4⋊C4×C43C2212yes—
106C43×#376C2211yescharacteristic
107C22×Dic86C2311yescharacteristic
108C22×D172C2312yes—
109C22×D172C2311yescharacteristic
110C22×C4×D43C2312yes—
111C22×C4×D43C2312yes—
112C22×C4×D43C2312yes—
113C22×C4×D43C2311yescharacteristic
114C22×C4×D43C2312yes—
115C4×Dic86—24no—
116#13063290—28no—
117C4×D172—28no—
118C4×D172—24no—
119#13063287—28no—
120#13063287—28no—
121#13063287—28no—
122#13063283—28no—
123#13063283—28no—
124#13063282—24no—
125#13063282—24no—
126C2×C4⋊Dic43C2312yes—
127C2×C4⋊Dic43C2312yes—
128C2×C4⋊Dic43C2311yescharacteristic
129C2×C4⋊Dic43C2312yes—
130C2×C4⋊Dic43C2311yescharacteristic
131C2×Dic43⋊C4C2312yes—
132C2×Dic43⋊C4C2312yes—
133C2×Dic43⋊C4C2311yescharacteristic
134C2×Dic43⋊C4C2311yescharacteristic
135C2×Dic43⋊C4C2312yes—
136C2×Dic43⋊C4C2312yes—
137C2×(C2×D43)⋊C4C2312yes—
138C2×(C2×D43)⋊C4C2311yescharacteristic
139C2×(C2×D43)⋊C4C2311yescharacteristic
140C2×(C2×D43)⋊C4C2312yes—
141C2×(C2×D43)⋊C4C2312yes—
142C2×(C2×D43)⋊C4C2312yes—
143C2×(C2×D43)⋊C4C2312yes—
144C2×(C2×D43)⋊C4C2312yes—
145C2×(C2×D43)⋊C4C2312yes—
146C2×(C2×D43)⋊C4C2312yes—
147C2×(C2×D43)⋊C4C2312yes—
148C2×(C2×D43)⋊C4C2312yes—
149C2×(C2×D43)⋊C4C2312yes—
150C2×(C2×D43)⋊C4C2312yes—
151C2×(C2×D43)⋊C4C2312yes—
152C2×(C2×D43)⋊C4C2312yes—
153C2×C4×Dic43C2312yes—
154C2×C4×Dic43C2312yes—
155C2×C4×Dic43C2312yes—
156C2×C4×Dic43C2311yescharacteristic
157C2×C4×Dic43C2311yescharacteristic
158C2×C4×Dic43C2312yes—
159C2×C4×Dic43C2312yes—
160C2×C4×Dic43C2312yes—
161C2×C4×Dic43C2312yes—
162C2×C4×Dic43C2312yes—
163C2×C4×Dic43C2312yes—
164C2×C4×Dic43C2312yes—
165C2×C4×Dic43C2312yes—
166C2×C4×Dic43C2311yescharacteristic
167C2×C4×Dic43C2312yes—
168C42×D43—24no—
169C42×D43—28no—
170C43⋊#95C2312yes—
171C43⋊#95C2312yes—
172C43⋊#95C2312yes—
173C43⋊#95C2312yes—
174C43⋊#95C2312yes—
175C43⋊#95C2312yes—
176C43⋊#95C2312yes—
177C43⋊#95C2312yes—
178C43⋊#95C2312yes—
179C43⋊#95C2312yes—
180C43⋊#95C2312yes—
181C43⋊#95C2312yes—
182C43⋊#95C2312yes—
183C43⋊#95C2312yes—
184C43⋊#95C2312yes—
185C43⋊#95C2312yes—
186C2×C4⋊C4×C43C2312yes—
187C2×C4⋊C4×C43C2312yes—
188C2×C4⋊C4×C43C2312yes—
189C2×C4⋊C4×C43C2312yes—
190C2×C4⋊C4×C43C2312yes—
191C2×C4⋊C4×C43C2312yes—
192C2×C42×C43C2311yescharacteristic
193C2×C42×C43C2312yes—
194C2×C42×C43C2311yescharacteristic
195C2×C42×C43C2312yes—
196C2×C42×C43C2311yescharacteristic
197#95×C43C2311yescharacteristic
198#95×C43C2312yes—
199#95×C43C2311yescharacteristic
200#95×C43C2311yescharacteristic
201#95×C43C2312yes—
202#95×C43C2312yes—
203#95×C43C2311yescharacteristic
204#95×C43C2312yes—
205#95×C43C2312yes—
206#95×C43C2312yes—
207C23×D43C2412yes—
208C23×D43C2411yescharacteristic
209C22×C4×C43C2412yes—
210C22×C4×C43C2412yes—
211C22×C4×C43C2412yes—
212C22×C4×C43C2412yes—
213C22×C4×C43C2411yescharacteristic
214C22×C4×C43C2411yescharacteristic
215C22×C4×C43C2412yes—
216C22×C4×C43C2412yes—
217C22×C4×C43C2411yescharacteristic
218C22×Dic43C2412yes—
219C22×Dic43C2412yes—
220C22×Dic43C2412yes—
221C22×Dic43C2411yescharacteristic
222C22×Dic43C2411yescharacteristic
223C22×Dic43C2412yes—
224C22×Dic43C2411yescharacteristic
225C22×Dic43C2412yes—
226C2×D172—24no—
227C2×D172—22no—
228C2×D172—24no—
229C2×D172—24no—
230C2×D172—24no—
231C2×C4×D43—22no—
232C2×C4×D43—22no—
233C2×C4×D43—24no—
234C2×C4×D43—24no—
235C2×C4×D43—24no—
236C2×C4×D43—24no—
237C2×C4×D43—24no—
238C2×C4×D43—24no—
239C2×C4×D43—24no—
240C2×C4×D43—24no—
241C2×C4×D43—24no—
242C2×C4×D43—24no—
243C2×C4×D43—24no—
244C2×C4×D43#4114yes—
245C2×C4×D43#4118yes—
246C2×Dic86—22no—
247C2×Dic86—24no—
248C4⋊C4×C43—24no—
249C4⋊C4×C43—24no—
250C4⋊C4×C43—24no—
251C4⋊C4×C43—24no—
252C4⋊C4×C43—24no—
253C4⋊C4×C43—24no—
254C42×C43—24no—
255C42×C43—22no—
256C42×C43—22no—
257C42×C43—24no—
258C42×C43#4114yes—
259(C2×D43)⋊C4—22no—
260(C2×D43)⋊C4—22no—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4—24no—
264(C2×D43)⋊C4—24no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4—24no—
269(C2×D43)⋊C4—24no—
270(C2×D43)⋊C4—24no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4—24no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—24no—
275C4⋊Dic43—24no—
276C4⋊Dic43—22no—
277C4⋊Dic43—22no—
278C4⋊Dic43—24no—
279C4⋊Dic43—24no—
280Dic43⋊C4—22no—
281Dic43⋊C4—22no—
282Dic43⋊C4—24no—
283Dic43⋊C4—24no—
284Dic43⋊C4—24no—
285Dic43⋊C4—24no—
286C4×Dic43—22no—
287C4×Dic43—22no—
288C4×Dic43—24no—
289C4×Dic43—24no—
290C4×Dic43—24no—
291C4×Dic43—24no—
292C4×Dic43—24no—
293C4×Dic43—24no—
294C4×Dic43—24no—
295C4×Dic43—24no—
296C4×Dic43—24no—
297C4×Dic43—24no—
298C4×Dic43—24no—
299C4×Dic43#4114yes—
300C4×Dic43#4118yes—
301C23×C43C2511yescharacteristic
302C22×D43—22no—
303C22×D43—21no—
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—22no—
308C22×D43—22no—
309C22×D43—22no—
310C22×D43—21no—
311C22×D43—22no—
312C22×D43C2×#4112yes—
313C22×D43C2×#4114yes—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43C2×#4114yes—
333C2×C4×C43C2×#4114yes—
334C2×C4×C43C2×#4112yes—
335C2×C4×C43C2×#4112yes—
336C2×C4×C43C2×#4112yes—
337C2×C4×C43C2×#4112yes—
338C2×C4×C43C2×#4112yes—
339C2×Dic43—21no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—21no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—21no—
348C2×Dic43—21no—
349C2×Dic43—22no—
350C2×Dic43—22no—
351C2×Dic43—22no—
352C2×Dic43—22no—
353C2×Dic43—22no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43C2×#4114yes—
357C2×Dic43C2×#4112yes—
358C2×Dic43C2×#4114yes—
359C2×Dic43C2×#4114yes—
360C2×Dic43C2×#4114yes—
361D172—216no—
362D172—28no—
363C4×D43—28no—
364C4×D43—216no—
365C4×D43—48no—
366C4×D43—48no—
367C4×D43—48no—
368Dic86—28no—
369#34551—431nomaximal, Sylow
370C22×C43C22×#4111yescharacteristic
371C22×C43C22×#4112yes—
372C22×C43C22×#4112yes—
373C22×C43C22×#4111yescharacteristic
374C22×C43C22×#4111yescharacteristic
375C2×D43—24no—
376C2×D43—22no—
377C2×D43—24no—
378C2×D43—24no—
379C2×D43—24no—
380C2×D43—42no—
381C2×D43—42no—
382C2×D43—42no—
383C2×D43—42no—
384C2×D43—42no—
385C2×D43—41no—
386C2×D43—41no—
387C4×C43—24no—
388C4×C43—22no—
389C4×C43—24no—
390C4×C43—22no—
391C4×C43—42no—
392C4×C43—42no—
393C4×C43—42no—
394C4×C43—42no—
395C4×C43#52914yes—
396Dic43—22no—
397Dic43—24no—
398Dic43—42no—
399Dic43—42no—
400Dic43—41no—
401Dic43—42no—
402Dic43—41no—
403Dic43#52918yes—
404#2402—432no—
405#2402D4311yescharacteristic, complemented
406#2401—432no—
407#2401—432no—
408#2401—432no—
409#2398—432no—
410#2398—431no—
411#2396—432no—
412#2396—431no—
413#2395—432no—
414#2395—432no—
415#2395—432no—
416#2392—432no—
417#2392—431no—
418C42×Q8—431no—
419C42×D4—431no—
420C42×D4—432no—
421C4×#117—432no—
422C4×#117—431no—
423C2×C43C2×#52912yes—
424C2×C43C2×#52911yescharacteristic
425C2×C43#344412yes—
426C2×C43#344411yescharacteristic
427C2×C43#344411yescharacteristic
428D43—44no—
429D43—42no—
430C2×C4×Q8—432no—
431C2×C4×Q8—431no—
432C2×C4×D4—432no—
433C2×C4×D4—432no—
434C2×C4×D4—432no—
435C2×C4×D4—432no—
436C2×C4×D4—431no—
437C2×#117—432no—
438C2×#117—432no—
439C2×#117—431no—
440C2×#117—431no—
441C22×C42—432no—
442C22×C42—431no—
443#401—432no—
444#400—432no—
445#400—432no—
446#400—431no—
447#400—432no—
448#400—432no—
449#400—432no—
450#400C2×D4312yes—
451#400C2×D4312yes—
452#399—432no—
453#399—431no—
454#398—432no—
455#398—432no—
456#398—431no—
457#398C2×D4312yes—
458#398C2×D4312yes—
459#397—432no—
460#397—432no—
461#397—431no—
462#397—432no—
463#397—432no—
464#397—432no—
465#397—432no—
466#397—432no—
467#396—432no—
468#396—432no—
469#396—432no—
470#395—431no—
471#394—432no—
472#394—432no—
473#394—431no—
474#394—432no—
475#394—432no—
476#393—431no—
477#393—432no—
478#392—431no—
479C4×C4⋊C4—432no—
480C4×C4⋊C4—432no—
481C4×C4⋊C4—432no—
482C4×C4⋊C4—432no—
483C4×C4⋊C4—432no—
484C4×C4⋊C4—432no—
485C4×C4⋊C4—432no—
486C4×C4⋊C4—432no—
487C4×C4⋊C4—432no—
488C4×C4⋊C4—432no—
489C4×C4⋊C4—432no—
490C4×C4⋊C4—432no—
491C4×C4⋊C4C2×D4311yescharacteristic
492C4×C4⋊C4C2×D4312yes—
493C4×C4⋊C4C2×D4311yescharacteristic
494C4×C4⋊C4C2×D4312yes—
495C4×C22⋊C4—432no—
496C4×C22⋊C4—432no—
497C4×C22⋊C4—432no—
498C4×C22⋊C4—432no—
499C4×C22⋊C4—432no—
500C4×C22⋊C4—432no—
501C4×C22⋊C4—432no—
502C4×C22⋊C4—432no—
503C4×C22⋊C4—432no—
504C4×C22⋊C4—432no—
505C4×C22⋊C4—432no—
506C4×C22⋊C4—432no—
507C4×C22⋊C4—432no—
508C4×C22⋊C4—432no—
509C4×C22⋊C4—432no—
510#376—431no—
511#376—432no—
512#376—432no—
513#376C2×D4311yescharacteristic
514C43—431no—
515C43—432no—
516C43—431no—
517C43#3455111yescharacteristic, complemented, Sylow
518C22×Q8—431no—
519C22×D4—432no—
520C22×D4—431no—
521C23×C4—432no—
522C23×C4—431no—
523C23×C4—432no—
524C23×C4—432no—
525C23×C4—432no—
526C4×Q8—868no—
527C4×Q8—864no—
528C4×D4—868no—
529C4×D4—868no—
530C4×D4—868no—
531C4×D4—868no—
532C4×D4—864no—
533#117—864no—
534#117—868no—
535#117—868no—
536#117—864no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—431no—
539C2×C4⋊C4—432no—
540C2×C4⋊C4—432no—
541C2×C4⋊C4—432no—
542C2×C4⋊C4—432no—
543C2×C4⋊C4—431no—
544C2×C4⋊C4—432no—
545C2×C4⋊C4—432no—
546C2×C4⋊C4—432no—
547C2×C4⋊C4—431no—
548C2×C4⋊C4C22×D4312yes—
549C2×C4⋊C4C22×D4312yes—
550C2×C4⋊C4C22×D4312yes—
551C2×C4⋊C4C22×D4312yes—
552C2×C4⋊C4C22×D4312yes—
553C2×C4⋊C4C22×D4312yes—
554C2×C22⋊C4—432no—
555C2×C22⋊C4—431no—
556C2×C22⋊C4—432no—
557C2×C22⋊C4—431no—
558C2×C22⋊C4—432no—
559C2×C22⋊C4—432no—
560C2×C22⋊C4—432no—
561C2×C22⋊C4—432no—
562C2×C22⋊C4—432no—
563C2×C22⋊C4—432no—
564C2×C22⋊C4—432no—
565C2×C22⋊C4—432no—
566C2×C22⋊C4—432no—
567C2×C22⋊C4—432no—
568C2×C22⋊C4—432no—
569C2×C22⋊C4—432no—
570C2×C42—432no—
571C2×C42—431no—
572C2×C42—432no—
573C2×C42—432no—
574C2×C42—432no—
575C2×C42—432no—
576C2×C42—432no—
577C2×C42—432no—
578C2×C42—432no—
579C2×C42—432no—
580C2×C42—432no—
581C2×C42—432no—
582C2×C42—431no—
583C2×C42—431no—
584C2×C42—432no—
585C2×C42—868no—
586C2×C42—864no—
587C2×C42C22×D4311yescharacteristic
588C2×C42C22×D4312yes—
589C2×C42C22×D4311yescharacteristic
590C2×C42C22×D4312yes—
591C2×C42C22×D4311yescharacteristic
592#95—432no—
593#95—432no—
594#95—432no—
595#95—432no—
596#95—432no—
597#95—432no—
598#95—432no—
599#95—432no—
600#95—432no—
601#95—432no—
602#95—432no—
603#95—432no—
604#95—432no—
605#95—432no—
606#95—432no—
607#95—432no—
608#95C22×D4312yes—
609#95C22×D4312yes—
610#95C22×D4312yes—
611#95C22×D4312yes—
612#95C22×D4311yescharacteristic
613#95C22×D4311yescharacteristic
614#95C22×D4312yes—
615#95C22×D4312yes—
616#95C22×D4311yescharacteristic
617#95C22×D4311yescharacteristic
618C24—432no—
619C24—431no—
620C2×Q8—864no—
621C2×Q8—862no—
622C2×D4—864no—
623C2×D4—864no—
624C2×D4—864no—
625C2×D4—864no—
626C2×D4—862no—
627C22×C4—432no—
628C22×C4—432no—
629C22×C4—431no—
630C22×C4—438no—
631C22×C4—434no—
632C22×C4—432no—
633C22×C4—432no—
634C22×C4—432no—
635C22×C4—431no—
636C22×C4—431no—
637C22×C4—864no—
638C22×C4—864no—
639C22×C4—864no—
640C22×C4—864no—
641C22×C4—864no—
642C22×C4—864no—
643C22×C4—864no—
644C22×C4—864no—
645C22×C4—862no—
646C22×C4—862no—
647C22×C4—864no—
648C22×C4—864no—
649C22×C4—864no—
650C22×C4C23×D4312yes—
651C22×C4C23×D4312yes—
652C22×C4C23×D4312yes—
653C22×C4C23×D4312yes—
654C22×C4C23×D4312yes—
655C22×C4C23×D4312yes—
656C22×C4C23×D4311yescharacteristic
657C22×C4C23×D4311yescharacteristic
658C22×C4C23×D4311yescharacteristic
659C4⋊C4—24no—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—24no—
663C4⋊C4—24no—
664C4⋊C4—24no—
665C4⋊C4—864no—
666C4⋊C4—864no—
667C4⋊C4—864no—
668C4⋊C4—864no—
669C4⋊C4—864no—
670C4⋊C4—864no—
671C4⋊C4—862no—
672C4⋊C4—862no—
673C4⋊C4—862no—
674C4⋊C4—864no—
675C4⋊C4—862no—
676C22⋊C4—864no—
677C22⋊C4—864no—
678C22⋊C4—864no—
679C22⋊C4—864no—
680C22⋊C4—864no—
681C22⋊C4—864no—
682C22⋊C4—864no—
683C22⋊C4—864no—
684C22⋊C4—864no—
685C22⋊C4—864no—
686C22⋊C4—864no—
687C22⋊C4—864no—
688C22⋊C4—864no—
689C22⋊C4—862no—
690C22⋊C4—862no—
691C22⋊C4—864no—
692C42—24no—
693C42—22no—
694C42—22no—
695C42—24no—
696C42—434no—
697C42—438no—
698C42—864no—
699C42—864no—
700C42—864no—
701C42—864no—
702C42—864no—
703C42—864no—
704C42—864no—
705C42—864no—
706C42—864no—
707C42—864no—
708C42—862no—
709C42—862no—
710C42—864no—
711C42#1062190214yes—
712C23—434no—
713C23—432no—
714C23—862no—
715C23—862no—
716C23—862no—
717C23—862no—
718C23—862no—
719C23—862no—
720C23—862no—
721C23—861no—
722C23—861no—
723C23—862no—
724C23C24×D4311yescharacteristic
725Q8—868no—
726D4—8616no—
727D4—868no—
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—434no—
747C2×C4—434no—
748C2×C4—434no—
749C2×C4—434no—
750C2×C4—432no—
751C2×C4—8616no—
752C2×C4—861no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—861no—
756C2×C4—868no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—862no—
766C2×C4—861no—
767C2×C4—861no—
768C2×C4—862no—
769C2×C4—862no—
770C2×C4—1728no—
771C2×C4—1728no—
772C2×C4—1728no—
773C2×C4#41×D4314yes—
774C2×C4#41×D4314yes—
775C2×C4#41×D4312yes—
776C2×C4#41×D4312yes—
777C2×C4C2×#1062190212yes—
778C2×C4C2×#1062190212yes—
779C2×C4C2×#1062190212yes—
780C22—864no—
781C22—862no—
782C22—864no—
783C22—864no—
784C22—864no—
785C22—1722no—
786C22—1722no—
787C22—1722no—
788C22—1722no—
789C22—1722no—
790C22—1721no—
791C22—1721no—
792C22C2×#41×D4311yescharacteristic
793C22C2×#41×D4312yes—
794C22C2×#41×D4312yes—
795C22C2×#41×D4311yescharacteristic
796C22C22×#1062190211yescharacteristic
797C4—24no—
798C4—24no—
799C4—22no—
800C4—22no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—438no—
806C4—862no—
807C4—864no—
808C4—1722no—
809C4—1722no—
810C4—1721no—
811C4—1722no—
812C4—1721no—
813C4#1458343414yes—
814C2—1724no—
815C2—1722no—
816C2#529×D4312yes—
817C2C2×#1458343411yescharacteristic
818C2#1914788912yes—
819C2#1914789211yescharacteristic
820C2#1914789211yescharacteristic
subgroupG/H
centerC22×C4C23×D43
commutator, socle, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC43×#2402C2
prime radical#14582809C22
hypercenter#2402D43
hypocenterC43#34551
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #2402

Complements

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

NH ≅ G/Ntype
1. #19137899C2semidirect
2. #19137896C2semidirect
3. #19137894C2semidirect
4. #19137894C2semidirect
5. #19137884C2semidirect
6. #19137881C2semidirect
7. #19137872C2semidirect
8. #19137867C2semidirect
9. #19137861C2semidirect
10. #19137859C2semidirect
11. #19137858C2semidirect
14. C4×#13063290C2semidirect
15. C4×#13063287C2semidirect
16. C4×#13063287C2semidirect
17. C4×#13063283C2semidirect
18. #19136934C2semidirect
19. C43×#2402C2semidirect
405. #2402D43semidirect
517. C43#34551semidirect

Maximal subgroups

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

subgroupindex
#191378992
#191378962
#191378942
#191378842
#191378812
#191378722
#191378672
#191378612
#191378592
#191378582
#191378362
#191378352
C4×#130632902
C4×#130632872
C4×#130632832
#191369342
C43×#24022
#3455143