Finite Group Databasebeta

← #14960535

Subgroups — #14960535

Order 2816.

3018 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623336C211yesmaximal, characteristic, complemented
2#13076908C212yesmaximal, complemented
3#13075048C214yesmaximal, complemented
4#13075018C214yesmaximal, complemented
5#13074878C214yesmaximal, complemented
6#13074848C214yesmaximal, complemented
7#13074328C212yesmaximal, complemented
8#13072903C211yesmaximal, characteristic, complemented
9#13072890C211yesmaximal, characteristic, complemented
10#13072012C212yesmaximal, complemented
11#13071990C212yesmaximal, complemented
12#13071951C211yesmaximal, characteristic, complemented
13#13071935C211yesmaximal, characteristic, complemented
14#13071194C211yesmaximal, characteristic, complemented
15C22×C11×#121C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C22×#4339C2211yescharacteristic
21C2×C11×#121—28no—
22C2×C11×#121C2214yes—
23C2×C11×#121C2214yes—
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C2×#67006C2212yes—
28C2×#67006C2212yes—
29C2×#67006C2212yes—
30C22×C22⋊Dic11C2212yes—
31#10623336—28no—
32C2×#66993C2212yescomplemented
33C2×#66992C2214yescomplemented
34C2×#66991C2212yescomplemented
35C2×#66991C2212yescomplemented
36C2×#66989C2212yescomplemented
37C2×#66982C2212yes—
38C2×#66982C2214yescomplemented
39C2×#66979C2211yescharacteristic
40#10622860C2212yes—
41#10622860C2212yes—
42#10622836C2214yescomplemented
43#10622836C2214yescomplemented
44#10622836C2214yescomplemented
45#10622835C2214yescomplemented
46#10622835C2214yescomplemented
47#10622835C2214yescomplemented
48#10622833C2214yescomplemented
49#10622833C2214yescomplemented
50#10622833C2214yescomplemented
51#10622826C2212yes—
52#10622826C2212yes—
53#10622826C2214yescomplemented
54#10622824C2211yescharacteristic
55#10622824C2212yes—
56#10622824C2211yescharacteristic
57#10622824C2214yescomplemented
58#10622823C2212yes—
59#10622823C2212yes—
60#10622823C2214yescomplemented
61#10622604C2212yescomplemented
62#10622602C2214yescomplemented
63#10622599C2212yescomplemented
64#10622596C2212yescomplemented
65#10622592C2212yescomplemented
66#10622591C2214yescomplemented
67#10622573C2212yescomplemented
68#10622572C2214yescomplemented
69#10622571C2214yescomplemented
70#10622569C2214yescomplemented
71#10622566C2212yescomplemented
72#10622565C2214yescomplemented
73#10622562C2212yescomplemented
74#10622560C2212yescomplemented
75#10622557C2214yescomplemented
76#10622555C2214yescomplemented
77C25×C11C2311yescharacteristic
78C25×C11C2311yescharacteristic
79C25×C11C2311yescharacteristic
80C22×D4×C11—24no—
81C22×D4×C11—24no—
82C22×D4×C11—44no—
83C22×D4×C11—44no—
84C22×D4×C11—44no—
85C22×D4×C11D418yescomplemented
86C22×D4×C11C2314yes—
87C22×D4×C11C2314yes—
88C22×D4×C11C2312yes—
89C22×D4×C11C2312yes—
90C23×C4×C11—24no—
91C23×C4×C11—44no—
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2314yes—
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C22×C22⋊D11C2312yes—
98C22×C22⋊D11C2312yes—
99C22×C22⋊D11C2312yes—
100C22×C22⋊D11C2312yes—
101C22×C22⋊D11C2312yes—
102C22×C22⋊D11C2314yes—
103C23×Dic11C2314yes—
104C2×#4339—24no—
105C2×#4339—44no—
106C22×D44C2311yescharacteristic
107C22×C4×D11C2312yes—
108C22×Dic22C2311yescharacteristic
109C11×#121—216no—
110C11×#121—216no—
111C2×C11×C4⋊C4—24no—
112C2×C11×C4⋊C4C2312yes—
113C2×C11×C4⋊C4C2312yes—
114C2×C11×C22⋊C4—24no—
115C2×C11×C22⋊C4—24no—
116C2×C11×C22⋊C4C2314yes—
117C2×C11×C22⋊C4C2312yes—
118C2×C11×C22⋊C4C2312yes—
119#67006—28no—
120#67006—28no—
121#67006—44no—
122C2×C22⋊Dic11—44no—
123C2×C22⋊Dic11C2312yes—
124C2×C22⋊Dic11C2312yes—
125C2×C22⋊Dic11C2312yes—
126C2×C22⋊Dic11C2312yes—
127C2×C22⋊Dic11C2312yes—
128C2×C22⋊Dic11C2312yes—
129C2×C22⋊Dic11C2312yes—
130C2×C22⋊Dic11C2314yes—
131C2×C22⋊Dic11C2314yes—
132C2×C22⋊Dic11C2314yes—
133C2×C22⋊Dic11C2314yes—
134C2×C22⋊Dic11C2314yes—
135C2×C22⋊Dic11C2314yes—
136#66993—28no—
137#66992—48no—
138#66991—28no—
139#66991—28no—
140#66989—28no—
141#66982—48no—
142#66982—44no—
143C2×(C2×D11)⋊C4C2314yes—
144C2×(C2×D11)⋊C4C2314yes—
145C2×(C2×D11)⋊C4C2314yes—
146#66979—24no—
147C2×C4⋊Dic11C2311yescharacteristic
148C2×C4⋊Dic11C2311yescharacteristic
149C2×Dic11⋊C4C2314yes—
150C2×Dic11⋊C4C2314yes—
151C2×Dic11⋊C4C2314yes—
152C2×C4×Dic11C2312yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2312yes—
156C11⋊#95C2314yes—
157C11⋊#95C2312yes—
158C11⋊#95C2312yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2312yes—
163#36704—111nomaximal, Sylow
164C24×C11—24no—
165C24×C11—24no—
166C24×C11—22no—
167C24×C11—24no—
168C24×C11—42no—
169C24×C11—42no—
170C24×C11—42no—
171C24×C11—42no—
172C24×C11—42no—
173C24×C11—42no—
174C24×C11C2×D414yes—
175C24×C11C2×D414yes—
176C24×C11C2412yes—
177C24×C11C2412yes—
178C24×C11C2412yes—
179C24×C11C2411yescharacteristic
180C23×D11C2412yes—
181C2×D4×C11—28no—
182C2×D4×C11—28no—
183C2×D4×C11—28no—
184C2×D4×C11—416no—
185C2×D4×C11—42no—
186C2×D4×C11—42no—
187C2×D4×C11—42no—
188C2×D4×C11—42no—
189C2×D4×C11—44no—
190C2×D4×C11—44no—
191C2×D4×C11—44no—
192C2×D4×C11—416no—
193C2×D4×C11—416no—
194C2×D4×C11C2×D418yes—
195C2×D4×C11C2×D418yes—
196C22×C4×C11—22no—
197C22×C4×C11—24no—
198C22×C4×C11—24no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—28no—
202C22×C4×C11—24no—
203C22×C4×C11—28no—
204C22×C4×C11—44no—
205C22×C4×C11—42no—
206C22×C4×C11—416no—
207C22×C4×C11C2×D414yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2411yescharacteristic
211C22×C4×C11C2411yescharacteristic
212C22×C4×C11C2412yes—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—24no—
215C2×C22⋊D11—24no—
216C2×C22⋊D11—24no—
217C2×C22⋊D11—24no—
218C2×C22⋊D11—24no—
219C2×C22⋊D11—24no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11—44no—
222C2×C22⋊D11—44no—
223C2×C22⋊D11—44no—
224C2×C22⋊D11—44no—
225C2×C22⋊D11—44no—
226C2×C22⋊D11—44no—
227C22×Dic11—44no—
228C22×Dic11—44no—
229C22×Dic11—44no—
230C22×Dic11C2412yes—
231C22×Dic11C2414yes—
232C22×Dic11C2414yes—
233C22×Dic11C2412yes—
234C22×Dic11C2412yes—
235#4339—416no—
236C2×D44—22no—
237C2×D44—42no—
238C2×C4×D11—24no—
239C2×C4×D11—42no—
240C2×C4×D11—42no—
241C2×Dic22—22no—
242C2×Dic22—42no—
243C11×C4⋊C4—24no—
244C11×C4⋊C4—24no—
245C11×C22⋊C4—28no—
246C11×C22⋊C4—24no—
247C11×C22⋊C4—24no—
248C22⋊Dic11—24no—
249C22⋊Dic11—24no—
250C22⋊Dic11—24no—
251C22⋊Dic11—24no—
252C22⋊Dic11—24no—
253C22⋊Dic11—24no—
254C22⋊Dic11—24no—
255C22⋊Dic11—44no—
256C22⋊Dic11—44no—
257C22⋊Dic11—44no—
258C22⋊Dic11—44no—
259C22⋊Dic11—44no—
260C22⋊Dic11—44no—
261(C2×D11)⋊C4—28no—
262(C2×D11)⋊C4—44no—
263(C2×D11)⋊C4—44no—
264C4⋊Dic11—22no—
265C4⋊Dic11—22no—
266Dic11⋊C4—28no—
267Dic11⋊C4—44no—
268Dic11⋊C4—44no—
269C4×Dic11—24no—
270C2×#535—111no—
271C22×#121D1111yescharacteristic, complemented
272#2849—112no—
273#2688—114no—
274#2686—114no—
275#2673—114no—
276#2671—114no—
277#2613—112no—
278#2484—111no—
279#2482—111no—
280#2412—112no—
281#2410—112no—
282#2406—111no—
283#2404—111no—
284#2308—111no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—28no—
288C23×C11—22no—
289C23×C11—24no—
290C23×C11—22no—
291C23×C11—24no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—24no—
295C23×C11—24no—
296C23×C11—28no—
297C23×C11—22no—
298C23×C11—24no—
299C23×C11—24no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—44no—
303C23×C11—44no—
304C23×C11—44no—
305C23×C11—44no—
306C23×C11—416no—
307C23×C11—44no—
308C23×C11—44no—
309C23×C11—44no—
310C23×C11—88no—
311C23×C11—88no—
312C23×C11C22×D414yes—
313C23×C11C22×D414yes—
314C23×C11C22×D412yes—
315C23×C11H(5,𝔽2)14yes—
316C23×C11C2511yescharacteristic
317C22×D11—22no—
318C22×D11—24no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—24no—
322D4×C11—48no—
323D4×C11—48no—
324D4×C11—416no—
325D4×C11—416no—
326C2×C4×C11—28no—
327C2×C4×C11—28no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—24no—
335C2×C4×C11—24no—
336C2×C4×C11—416no—
337C2×C4×C11—44no—
338C2×C4×C11—44no—
339C2×C4×C11C22×D412yes—
340C2×C4×C11C22×D412yes—
341C2×C4×C11H(5,𝔽2)14yes—
342C22⋊D11—48no—
343C22⋊D11—84no—
344C22⋊D11—84no—
345C22⋊D11—84no—
346C22⋊D11—84no—
347C22⋊D11—88no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—24no—
352C2×Dic11—24no—
353C2×Dic11—22no—
354C2×Dic11—24no—
355C2×Dic11—24no—
356C2×Dic11—24no—
357C2×Dic11—22no—
358C2×Dic11—24no—
359C2×Dic11—24no—
360C2×Dic11—24no—
361C2×Dic11—88no—
362D44—44no—
363C4×D11—48no—
364Dic22—44no—
365C22×#41—111no—
366C23×D4C2×D1111yescharacteristic
367C23×D4C2×D1111yescharacteristic
368C23×D4C2×D1111yescharacteristic
369C24×C4C2×D1111yescharacteristic
370#535—228no—
371C2×#127—112no—
372C2×#124—112no—
373C2×#123—114no—
374C2×#123—112no—
375C2×#121—28no—
376C2×#121—112no—
377C2×#121—112no—
378C2×#121—114no—
379C2×#121C2×D1114yes—
380C2×#121C2×D1114yes—
381C2×#120—112no—
382C2×#120—112no—
383C2×#120—112no—
384C2×#117—111no—
385C22×C4⋊C4C2×D1111yescharacteristic
386C22×C22⋊C4—112no—
387C22×C22⋊C4C2×D1111yescharacteristic
388C22×C22⋊C4C2×D1111yescharacteristic
389#400—112no—
390#399—112no—
391#398—112no—
392#397—114no—
393#397—112no—
394#395—112no—
395#394—114no—
396#394—114no—
397#394—114no—
398#394—112no—
399#394—114no—
400#393—112no—
401#392—114no—
402#392—114no—
403#392—114no—
404#392—112no—
405#388—114no—
406#387—114no—
407#386—114no—
408#386—114no—
409#386—114no—
410#386—112no—
411#386—112no—
412#386—114no—
413#386—114no—
414#386—114no—
415#385—112no—
416#385—112no—
417#385—114no—
418#385—114no—
419#381—111no—
420#381—111no—
421#381—114no—
422#381—112no—
423#380—114no—
424#379—112no—
425#379—112no—
426C22×C11—22no—
427C22×C11—22no—
428C22×C11—28no—
429C22×C11—24no—
430C22×C11—24no—
431C22×C11—24no—
432C22×C11—24no—
433C22×C11—24no—
434C22×C11—24no—
435C22×C11—416no—
436C22×C11—44no—
437C22×C11—44no—
438C22×C11—44no—
439C22×C11—44no—
440C22×C11—42no—
441C22×C11—42no—
442C22×C11—42no—
443C22×C11—44no—
444C22×C11—44no—
445C22×C11—88no—
446C22×C11—88no—
447C22×C11#53414yes—
448C22×C11C23×D411yescharacteristic
449C22×C11C2×H(5,𝔽2)12yes—
450C22×C11C2×H(5,𝔽2)12yes—
451C22×C11#58512yes—
452C2×D11—42no—
453C2×D11—42no—
454C2×D11—42no—
455C2×D11—44no—
456C2×D11—44no—
457C4×C11—22no—
458C4×C11—22no—
459C4×C11—24no—
460C4×C11—42no—
461C4×C11—42no—
462Dic11—42no—
463Dic11—42no—
464Dic11—42no—
465Dic11—44no—
466Dic11—44no—
467C25C22×D1111yescharacteristic
468C25C22×D1111yescharacteristic
469C25C22×D1111yescharacteristic
470C2×#41—224no—
471C2×#41—444no—
472C22×Q8—111no—
473C22×D4—24no—
474C22×D4—24no—
475C22×D4—44no—
476C22×D4—44no—
477C22×D4—44no—
478C22×D4—112no—
479C22×D4—112no—
480C22×D4—112no—
481C22×D4—112no—
482C22×D4—112no—
483C22×D4—114no—
484C22×D4—111no—
485C22×D4C22⋊D1118yescomplemented
486C22×D4C22×D1114yes—
487C22×D4C22×D1114yes—
488C22×D4C22×D1112yes—
489C22×D4C22×D1112yes—
490C23×C4—24no—
491C23×C4—44no—
492C23×C4—114no—
493C23×C4—112no—
494C23×C4C22×D1111yescharacteristic
495C23×C4C22×D1111yescharacteristic
496C23×C4C22×D1114yes—
497C23×C4C22×D1111yescharacteristic
498C23×C4C22×D1111yescharacteristic
499#127—228no—
500#124—228no—
501#123—448no—
502#123—444no—
503#121—216no—
504#121—216no—
505#121—228no—
506#121—228no—
507#121—448no—
508#120—228no—
509#120—228no—
510#120—444no—
511#117—224no—
512C2×C4⋊C4—24no—
513C2×C4⋊C4—111no—
514C2×C4⋊C4—111no—
515C2×C4⋊C4—114no—
516C2×C4⋊C4—114no—
517C2×C4⋊C4—114no—
518C2×C4⋊C4C22×D1112yes—
519C2×C4⋊C4C22×D1112yes—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—112no—
523C2×C22⋊C4—112no—
524C2×C22⋊C4—112no—
525C2×C22⋊C4—112no—
526C2×C22⋊C4—112no—
527C2×C22⋊C4—112no—
528C2×C22⋊C4—112no—
529C2×C22⋊C4—114no—
530C2×C22⋊C4—114no—
531C2×C22⋊C4—114no—
532C2×C22⋊C4—114no—
533C2×C22⋊C4—114no—
534C2×C22⋊C4—114no—
535C2×C22⋊C4—114no—
536C2×C22⋊C4—114no—
537C2×C22⋊C4—114no—
538C2×C22⋊C4—444no—
539C2×C22⋊C4C22×D1114yes—
540C2×C22⋊C4C22×D1112yes—
541C2×C22⋊C4C22×D1112yes—
542C2×C42—112no—
543#95—114no—
544#95—114no—
545#95—114no—
546#95—112no—
547#95—114no—
548#95—114no—
549#95—112no—
550#95—112no—
551#95—112no—
552#95—114no—
553C2×C11—24no—
554C2×C11—44no—
555C2×C11—44no—
556C2×C11—82no—
557C2×C11C2×#53411yescharacteristic
558C2×C11#348411yescharacteristic
559C2×C11#348511yescharacteristic
560C2×C11#354214yes—
561D11—82no—
562C24—24no—
563C24—24no—
564C24—22no—
565C24—24no—
566C24—42no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—42no—
571C24—42no—
572C24—112no—
573C24C2×C22⋊D1114yes—
574C24C2×C22⋊D1114yes—
575C24C23×D1112yes—
576C24C23×D1112yes—
577C24C23×D1112yes—
578C24C23×D1111yescharacteristic
579#41—4416no—
580C2×Q8—222no—
581C2×Q8—442no—
582C2×D4—28no—
583C2×D4—28no—
584C2×D4—28no—
585C2×D4—44no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—44no—
591C2×D4—44no—
592C2×D4—416no—
593C2×D4—416no—
594C2×D4—416no—
595C2×D4—224no—
596C2×D4—224no—
597C2×D4—224no—
598C2×D4—224no—
599C2×D4—224no—
600C2×D4—224no—
601C2×D4—224no—
602C2×D4—222no—
603C2×D4—442no—
604C2×D4—444no—
605C2×D4—444no—
606C2×D4—444no—
607C2×D4—444no—
608C2×D4—444no—
609C2×D4—444no—
610C2×D4—444no—
611C2×D4C2×C22⋊D1118yes—
612C2×D4C2×C22⋊D1118yes—
613C22×C4—24no—
614C22×C4—22no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—28no—
620C22×C4—28no—
621C22×C4—44no—
622C22×C4—42no—
623C22×C4—416no—
624C22×C4—112no—
625C22×C4—114no—
626C22×C4—114no—
627C22×C4—112no—
628C22×C4—112no—
629C22×C4—224no—
630C22×C4—442no—
631C22×C4—442no—
632C22×C4—444no—
633C22×C4—444no—
634C22×C4—444no—
635C22×C4C2×C22⋊D1114yes—
636C22×C4C23×D1112yes—
637C22×C4C23×D1112yes—
638C22×C4C23×D1112yes—
639C22×C4C23×D1111yescharacteristic
640C22×C4C23×D1111yescharacteristic
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—228no—
644C4⋊C4—222no—
645C4⋊C4—222no—
646C4⋊C4—444no—
647C4⋊C4—444no—
648C22⋊C4—28no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—224no—
652C22⋊C4—224no—
653C22⋊C4—224no—
654C22⋊C4—224no—
655C22⋊C4—224no—
656C22⋊C4—224no—
657C22⋊C4—224no—
658C22⋊C4—228no—
659C22⋊C4—444no—
660C22⋊C4—444no—
661C22⋊C4—444no—
662C22⋊C4—444no—
663C22⋊C4—444no—
664C22⋊C4—444no—
665C22⋊C4—444no—
666C22⋊C4—444no—
667C42—224no—
668C11#3670411yescharacteristic, complemented, Sylow
669C23—22no—
670C23—22no—
671C23—28no—
672C23—22no—
673C23—24no—
674C23—22no—
675C23—24no—
676C23—22no—
677C23—22no—
678C23—24no—
679C23—24no—
680C23—28no—
681C23—24no—
682C23—24no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—416no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—88no—
695C23—88no—
696C23—224no—
697C23—222no—
698C23—222no—
699C23—224no—
700C23—222no—
701C23#6703714yes—
702C23C22×C22⋊D1114yes—
703C23C22×C22⋊D1114yes—
704C23C22×C22⋊D1112yes—
705C23C24×D1111yescharacteristic
706Q8—444no—
707D4—48no—
708D4—48no—
709D4—416no—
710D4—416no—
711D4—444no—
712D4—448no—
713D4—884no—
714D4—884no—
715D4—884no—
716D4—884no—
717D4—888no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—416no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—224no—
732C2×C4—224no—
733C2×C4—224no—
734C2×C4—224no—
735C2×C4—222no—
736C2×C4—224no—
737C2×C4—222no—
738C2×C4—224no—
739C2×C4—224no—
740C2×C4—224no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—448no—
745C2×C4—888no—
746C2×C4#6703714yes—
747C2×C4C22×C22⋊D1112yes—
748C2×C4C22×C22⋊D1112yes—
749C22—28no—
750C22—22no—
751C22—22no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—24no—
758C22—416no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—88no—
769C22—88no—
770C22—444no—
771C22—444no—
772C22—442no—
773C22—442no—
774C22—442no—
775C22#1062333514yes—
776C22C2×#6703712yes—
777C22C2×#6703712yes—
778C22#1062345312yes—
779C22C23×C22⋊D1111yescharacteristic
780C4—22no—
781C4—22no—
782C4—24no—
783C4—42no—
784C4—42no—
785C4—444no—
786C4—444no—
787C4—442no—
788C4—442no—
789C4—442no—
790C2—24no—
791C2—44no—
792C2—44no—
793C2—82no—
794C2—882no—
795C2C2×#1062333511yescharacteristic
796C2#1308225111yescharacteristic
797C2#1308226011yescharacteristic
798C2#1308293614yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC22×C11×#121C2
hypercenterC22×#121D11
hypocenterC11#36704
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10623336C2semidirect
2. #13076908C2semidirect
3. #13075048C2semidirect
4. #13075018C2semidirect
5. #13074878C2semidirect
6. #13074848C2semidirect
7. #13074328C2semidirect
8. #13072903C2semidirect
9. #13072890C2semidirect
10. #13072012C2semidirect
11. #13071990C2semidirect
12. #13071951C2semidirect
13. #13071935C2semidirect
14. #13071194C2semidirect
15. C22×C11×#121C2semidirect
32. C2×#66993C22semidirect
33. C2×#66992C22semidirect
34. C2×#66991C22semidirect
35. C2×#66991C22semidirect
36. C2×#66989C22semidirect
38. C2×#66982C22semidirect
42. #10622836C22semidirect
43. #10622836C22semidirect
44. #10622836C22semidirect
45. #10622835C22semidirect
46. #10622835C22semidirect
47. #10622835C22semidirect
48. #10622833C22semidirect
49. #10622833C22semidirect
50. #10622833C22semidirect
53. #10622826C22semidirect
57. #10622824C22semidirect
60. #10622823C22semidirect
61. #10622604C22semidirect
62. #10622602C22semidirect
63. #10622599C22semidirect
64. #10622596C22semidirect
65. #10622592C22semidirect
66. #10622591C22semidirect
67. #10622573C22semidirect
68. #10622572C22semidirect
69. #10622571C22semidirect
70. #10622569C22semidirect
71. #10622566C22semidirect
72. #10622565C22semidirect
73. #10622562C22semidirect
74. #10622560C22semidirect
75. #10622557C22semidirect
76. #10622555C22semidirect
85. C22×D4×C11D4semidirect
271. C22×#121D11semidirect
485. C22×D4C22⋊D11semidirect
668. C11#36704semidirect

Maximal subgroups

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

subgroupindex
C2×#106233362
#130769082
#130750482
#130750182
#130748782
#130748482
#130743282
#130729032
#130728902
#130720122
#130719902
#130719512
#130719352
#130711942
C22×C11×#1212
#3670411