Finite Group Databasebeta

← #14960605

Subgroups — #14960605

Order 2816.

2630 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623175C211yesmaximal, characteristic, complemented
2C22×#66982C211yesmaximal, characteristic, complemented
3#13076898C211yesmaximal, characteristic, complemented
4#13075155C214yesmaximal, complemented
5#13075125C214yesmaximal, complemented
6#13074863C214yesmaximal, complemented
7#13074856C214yesmaximal, complemented
8#13074431C211yesmaximal, characteristic, complemented
9#13074361C211yesmaximal, characteristic, complemented
10#13073509C212yesmaximal, complemented
11#13072932C212yesmaximal, complemented
12#13072010C212yesmaximal, complemented
13#13071992C212yesmaximal, complemented
14#13071229C211yesmaximal, characteristic, complemented
15C11×#2848C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×C22⋊Q8C2212yescomplemented
20C2×#67006C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C2×#67000C2212yescomplemented
23C2×#66983C2211yescharacteristic
24C2×#66983C2212yescomplemented
25C2×#66982—28no—
26C2×#66982C2214yes—
27C2×#66982C2214yes—
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32#10623175—28no—
33C2×#66951C2212yescomplemented
34C2×#66948C2212yescomplemented
35C2×#66947C2212yescomplemented
36C2×#66939C2212yes—
37C2×#66937C2214yes—
38C2×#66935C2212yes—
39C2×(C22⋊D11)⋊C4C2212yes—
40C2×C22⋊C4×D11C2212yes—
41C11×#385C2212yes—
42C11×#385C2214yescomplemented
43C11×#380C2211yescharacteristic
44C11×#380C2212yescomplemented
45C11×#379C2212yes—
46#10622842C2212yescomplemented
47#10622826C2212yes—
48#10622826C2214yescomplemented
49#10622825C2211yescharacteristic
50#10622825C2212yescomplemented
51#10622607C2214yescomplemented
52#10622605C2214yescomplemented
53#10622604C2214yescomplemented
54#10622602C2214yescomplemented
55#10622600C2214yescomplemented
56#10622597C2214yescomplemented
57#10622595C2212yescomplemented
58#10622585C2214yescomplemented
59#10622573C2214yes—
60#10622572C2214yes—
61#10622572C2214yescomplemented
62#10622571C2212yes—
63#10622569C2214yes—
64#10622569C2214yescomplemented
65#10622564C2214yescomplemented
66#10622561C2214yescomplemented
67#10622559C2212yes—
68#10622556C2212yes—
69#10622555C2212yes—
70#10622287C2214yescomplemented
71#10622285C2212yescomplemented
72#10622281C2214yescomplemented
73#10622280C2214yescomplemented
74#10622278C2214yescomplemented
75#10622274C2212yescomplemented
76#10622271C2214yescomplemented
77C25×C11C2311yescharacteristic
78C24×D11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C23×C4×C11—24no—
81C23×C4×C11—44no—
82C23×C4×C11C2312yes—
83C23×C4×C11C2312yes—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11—24no—
87C22×C22⋊D11—44no—
88C22×C22⋊D11C2312yes—
89C22×C22⋊D11C2314yes—
90C22×C22⋊D11C2314yes—
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C22×D44C2312yes—
95C22×D44C2312yes—
96C22×D44C2311yescharacteristic
97C22×C4×D11C2312yes—
98C22×C4×D11C2314yes—
99C11×C22⋊Q8—24no—
100C11×C22⋊Q8—44no—
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2312yes—
103C2×C11×C4⋊C4C2314yes—
104C2×C11×C4⋊C4C2312yes—
105C2×C11×C22⋊C4C2312yes—
106C2×C11×C22⋊C4C2312yes—
107C2×C11×C22⋊C4C2314yes—
108C2×C11×C22⋊C4C2314yes—
109#67006—44no—
110C2×C22⋊Dic11—24no—
111C2×C22⋊Dic11C2312yes—
112C2×C22⋊Dic11C2314yes—
113C2×C22⋊Dic11C2314yes—
114#67000—28no—
115#66983—24no—
116#66983—44no—
117#66982—216no—
118#66982—216no—
119C2×(C2×D11)⋊C4—24no—
120C2×(C2×D11)⋊C4D418yescomplemented
121C2×(C2×D11)⋊C4C2312yes—
122C2×(C2×D11)⋊C4C2312yes—
123C2×(C2×D11)⋊C4C2312yes—
124C2×(C2×D11)⋊C4C2312yes—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
130C2×(C2×D11)⋊C4C2312yes—
131C2×(C2×D11)⋊C4C2312yes—
132C2×C4⋊Dic11C2311yescharacteristic
133C2×C4⋊Dic11C2314yes—
134C2×C4⋊Dic11C2312yes—
135C2×Dic11⋊C4—24no—
136C2×Dic11⋊C4—24no—
137C2×Dic11⋊C4C2312yes—
138C2×Dic11⋊C4C2314yes—
139C2×Dic11⋊C4C2312yes—
140C2×Dic11⋊C4C2312yes—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×C4×Dic11C2312yes—
144#66951—28no—
145#66948—28no—
146#66947—28no—
147#66939—44no—
148#66937—48no—
149#66935—28no—
150(C22⋊D11)⋊C4—28no—
151C22⋊C4×D11—44no—
152C11×#95C2314yes—
153C11×#95C2312yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2312yes—
161#36709—111nomaximal, Sylow
162C24×C11—22no—
163C24×C11—24no—
164C24×C11—22no—
165C24×C11—22no—
166C24×C11—42no—
167C24×C11C2412yes—
168C24×C11C2411yescharacteristic
169C23×D11—22no—
170C23×D11—22no—
171C23×D11—42no—
172C23×D11—42no—
173C23×D11C2×D414yes—
174C23×D11C2412yes—
175C23×D11C2412yes—
176C2×Q8×C11—22no—
177C2×Q8×C11—42no—
178C22×C4×C11—22no—
179C22×C4×C11—24no—
180C22×C4×C11—24no—
181C22×C4×C11—24no—
182C22×C4×C11—24no—
183C22×C4×C11—42no—
184C22×C4×C11—42no—
185C22×C4×C11—42no—
186C22×C4×C11—42no—
187C22×C4×C11—416no—
188C22×C4×C11C2×D414yes—
189C22×C4×C11C2412yes—
190C22×C4×C11C2412yes—
191C22×C4×C11C2414yes—
192C22×C4×C11C2412yes—
193C22×C4×C11C2411yescharacteristic
194C22×C4×C11C2411yescharacteristic
195C2×C22⋊D11—24no—
196C2×C22⋊D11—28no—
197C2×C22⋊D11—24no—
198C2×C22⋊D11—28no—
199C2×C22⋊D11—24no—
200C2×C22⋊D11—28no—
201C2×C22⋊D11—44no—
202C2×C22⋊D11—44no—
203C2×C22⋊D11—44no—
204C2×C22⋊D11—416no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—42no—
210C22×Dic11—42no—
211C22×Dic11C2×D414yes—
212C22×Dic11C2414yes—
213C22×Dic11C2412yes—
214C22×Dic11C2412yes—
215C22×Dic11C2412yes—
216C22×Dic11C2412yes—
217C2×D44—24no—
218C2×D44—24no—
219C2×D44—22no—
220C2×D44—44no—
221C2×D44—42no—
222C2×D44—44no—
223C2×C4×D11—24no—
224C2×C4×D11—44no—
225C2×C4×D11—44no—
226C2×C4×D11—44no—
227C2×C4×D11—44no—
228C11×C4⋊C4—22no—
229C11×C4⋊C4—24no—
230C11×C4⋊C4—42no—
231C11×C4⋊C4—44no—
232C11×C22⋊C4—24no—
233C11×C22⋊C4—24no—
234C11×C22⋊C4—28no—
235C11×C22⋊C4—44no—
236C22⋊Dic11—28no—
237C22⋊Dic11—24no—
238C22⋊Dic11—44no—
239(C2×D11)⋊C4—24no—
240(C2×D11)⋊C4—24no—
241(C2×D11)⋊C4—24no—
242(C2×D11)⋊C4—28no—
243(C2×D11)⋊C4—24no—
244(C2×D11)⋊C4—44no—
245(C2×D11)⋊C4—44no—
246(C2×D11)⋊C4—44no—
247(C2×D11)⋊C4—44no—
248(C2×D11)⋊C4C2×D418yes—
249(C2×D11)⋊C4C2×D418yes—
250C4⋊Dic11—22no—
251C4⋊Dic11—44no—
252C4⋊Dic11—42no—
253Dic11⋊C4—24no—
254Dic11⋊C4—28no—
255Dic11⋊C4—24no—
256Dic11⋊C4—24no—
257Dic11⋊C4—44no—
258Dic11⋊C4—44no—
259C4×Dic11—24no—
260C2×#538—111no—
261C22×#123—111no—
262#2848D1111yescharacteristic, complemented
263#2847—111no—
264#2695—114no—
265#2693—114no—
266#2672—114no—
267#2671—114no—
268#2627—111no—
269#2618—111no—
270#2534—112no—
271#2487—112no—
272#2412—112no—
273#2410—112no—
274#2315—111no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—28no—
278C23×C11—22no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—48no—
285C23×C11—48no—
286C23×C11—44no—
287C23×C11—44no—
288C23×C11C22×D412yes—
289C23×C11H(5,𝔽2)14yes—
290C23×C11H(5,𝔽2)12yes—
291C23×C112−1+412yes—
292C23×C11C2511yescharacteristic
293C22×D11—22no—
294C22×D11—24no—
295C22×D11—22no—
296C22×D11—24no—
297C22×D11—28no—
298C22×D11—22no—
299C22×D11—24no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—24no—
303C22×D11—44no—
304C22×D11—44no—
305C22×D11—84no—
306C22×D11—84no—
307C22×D11C22×D414yes—
308Q8×C11—82no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—24no—
315C2×C4×C11—24no—
316C2×C4×C11—22no—
317C2×C4×C11—24no—
318C2×C4×C11—22no—
319C2×C4×C11—24no—
320C2×C4×C11—24no—
321C2×C4×C11—44no—
322C2×C4×C11—48no—
323C2×C4×C11—48no—
324C2×C4×C11—44no—
325C2×C4×C11C22×D412yes—
326C2×C4×C11C22×D412yes—
327C22⋊D11—416no—
328C22⋊D11—48no—
329C22⋊D11—88no—
330C2×Dic11—24no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—24no—
335C2×Dic11—24no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—24no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—24no—
342C2×Dic11—44no—
343C2×Dic11—44no—
344C2×Dic11—44no—
345C2×Dic11C22×D414yes—
346D44—82no—
347D44—84no—
348D44—84no—
349C4×D11—84no—
350C4×D11—88no—
351C23×D4—111no—
352C24×C4C2×D1111yescharacteristic
353#538—228no—
354C2×#126—112no—
355C2×#124—112no—
356C2×#123—114no—
357C2×#123—114no—
358C2×#123—112no—
359C2×#123—112no—
360C2×#123—228no—
361C2×C22⋊Q8C2×D1111yescharacteristic
362C2×C22⋊Q8C2×D1112yescomplemented
363C2×#121—111no—
364C2×#121—112no—
365C2×#121—112no—
366C2×#121—114no—
367C2×#120—112no—
368C2×#120—112no—
369C2×C4×D4—112no—
370C22×C4⋊C4—111no—
371C22×C4⋊C4—111no—
372C22×C22⋊C4—111no—
373C22×C22⋊C4—111no—
374C22×C22⋊C4—111no—
375C22×C22⋊C4—112no—
376#400—112no—
377#400—114no—
378#399—114no—
379#398—114no—
380#398—112no—
381#397—114no—
382#396—114no—
383#396—114no—
384#395—112no—
385#394—114no—
386#394—114no—
387#394—114no—
388#394—112no—
389#392—114no—
390#389—114no—
391#388—114no—
392#386—112no—
393#386—114no—
394#386—112no—
395#386—114no—
396#386—114no—
397#386—114no—
398#385—114no—
399#385—112no—
400#385—114no—
401#385C2×D1112yes—
402#385C2×D1114yescomplemented
403#381—112no—
404#380—111no—
405#380—112no—
406#380—114no—
407#380—112no—
408#380—114no—
409#380C2×D1111yescharacteristic
410#380C2×D1112yescomplemented
411#379C2×D1112yes—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11—24no—
415C22×C11—24no—
416C22×C11—24no—
417C22×C11—24no—
418C22×C11—24no—
419C22×C11—416no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11#53714yes—
425C22×C11C23×D411yescharacteristic
426C22×C11C2×H(5,𝔽2)12yes—
427C22×C11C2×H(5,𝔽2)11yescharacteristic
428C22×C11C2×2−1+411yescharacteristic
429C22×C11#58512yes—
430C2×D11—24no—
431C2×D11—24no—
432C2×D11—24no—
433C2×D11—44no—
434C2×D11—44no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—44no—
439C2×D11—44no—
440C2×D11—88no—
441C4×C11—22no—
442C4×C11—22no—
443C4×C11—42no—
444C4×C11—42no—
445C4×C11—42no—
446C4×C11—44no—
447Dic11—24no—
448Dic11—42no—
449Dic11—42no—
450Dic11—42no—
451Dic11—44no—
452C25—111no—
453C25C22×D1111yescharacteristic
454C22×Q8C22×D1111yescharacteristic
455C22×D4—112no—
456C22×D4—114no—
457C22×D4—114no—
458C22×D4—112no—
459C22×D4—112no—
460C22×D4—111no—
461C22×D4—224no—
462C22×D4—444no—
463C23×C4—24no—
464C23×C4—44no—
465C23×C4—111no—
466C23×C4—111no—
467C23×C4—111no—
468C23×C4—112no—
469C23×C4—114no—
470C23×C4C22×D1112yes—
471C23×C4C22×D1112yes—
472C23×C4C22×D1111yescharacteristic
473C23×C4C22×D1111yescharacteristic
474#126—228no—
475#124—228no—
476#123—228no—
477#123—2216no—
478#123—2216no—
479#123—444no—
480C22⋊Q8—24no—
481C22⋊Q8—44no—
482#121—228no—
483#121—224no—
484#121—448no—
485#121—444no—
486#120—228no—
487#120—444no—
488C4×D4—228no—
489C2×C4⋊C4—114no—
490C2×C4⋊C4—112no—
491C2×C4⋊C4—112no—
492C2×C4⋊C4—112no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—112no—
495C2×C4⋊C4—114no—
496C2×C4⋊C4—114no—
497C2×C4⋊C4—114no—
498C2×C4⋊C4—224no—
499C2×C4⋊C4—224no—
500C2×C4⋊C4C22×D1112yes—
501C2×C4⋊C4C22×D1111yescharacteristic
502C2×C4⋊C4C22×D1114yes—
503C2×C4⋊C4C22×D1112yes—
504C2×C22⋊C4—118no—
505C2×C22⋊C4—112no—
506C2×C22⋊C4—112no—
507C2×C22⋊C4—112no—
508C2×C22⋊C4—114no—
509C2×C22⋊C4—114no—
510C2×C22⋊C4—112no—
511C2×C22⋊C4—112no—
512C2×C22⋊C4—112no—
513C2×C22⋊C4—112no—
514C2×C22⋊C4—114no—
515C2×C22⋊C4—114no—
516C2×C22⋊C4—114no—
517C2×C22⋊C4—114no—
518C2×C22⋊C4—114no—
519C2×C22⋊C4—224no—
520C2×C22⋊C4—224no—
521C2×C22⋊C4—444no—
522C2×C22⋊C4C22×D1112yes—
523C2×C22⋊C4C22×D1112yes—
524C2×C22⋊C4C22×D1114yes—
525C2×C22⋊C4C22×D1114yes—
526C2×C42—112no—
527#95—114no—
528#95—114no—
529#95—112no—
530#95—114no—
531#95—114no—
532#95—114no—
533#95—114no—
534#95C22×D1114yes—
535#95C22×D1112yes—
536C2×C11—24no—
537C2×C11—44no—
538C2×C11C2×#53711yescharacteristic
539C2×C11#348411yescharacteristic
540C2×C11#348511yescharacteristic
541C2×C11#353412yes—
542C2×C11#353512yes—
543D11—44no—
544D11—82no—
545C24—22no—
546C24—24no—
547C24—22no—
548C24—22no—
549C24—42no—
550C24—112no—
551C24—114no—
552C24—112no—
553C24—222no—
554C24—222no—
555C24—442no—
556C24—442no—
557C24C23×D1112yes—
558C24C23×D1111yescharacteristic
559C2×Q8—22no—
560C2×Q8—42no—
561C2×D4—224no—
562C2×D4—224no—
563C2×D4—228no—
564C2×D4—224no—
565C2×D4—228no—
566C2×D4—224no—
567C2×D4—224no—
568C2×D4—228no—
569C2×D4—222no—
570C2×D4—442no—
571C2×D4—444no—
572C2×D4—444no—
573C2×D4—444no—
574C2×D4—444no—
575C2×D4—444no—
576C2×D4—4416no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—416no—
587C22×C4—112no—
588C22×C4—114no—
589C22×C4—114no—
590C22×C4—112no—
591C22×C4—112no—
592C22×C4—112no—
593C22×C4—224no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—444no—
599C22×C4—444no—
600C22×C4—444no—
601C22×C4—444no—
602C22×C4—442no—
603C22×C4—442no—
604C22×C4D4×D1114yes—
605C22×C4C23×D1112yes—
606C22×C4C23×D1112yes—
607C22×C4C23×D1114yes—
608C22×C4C23×D1112yes—
609C22×C4C23×D1111yescharacteristic
610C22×C4C23×D1111yescharacteristic
611C4⋊C4—24no—
612C4⋊C4—22no—
613C4⋊C4—42no—
614C4⋊C4—44no—
615C4⋊C4—228no—
616C4⋊C4—224no—
617C4⋊C4—224no—
618C4⋊C4—224no—
619C4⋊C4—222no—
620C4⋊C4—444no—
621C4⋊C4—442no—
622C4⋊C4—444no—
623C4⋊C4—444no—
624C22⋊C4—24no—
625C22⋊C4—28no—
626C22⋊C4—24no—
627C22⋊C4—44no—
628C22⋊C4—118no—
629C22⋊C4—118no—
630C22⋊C4—224no—
631C22⋊C4—228no—
632C22⋊C4—224no—
633C22⋊C4—224no—
634C22⋊C4—228no—
635C22⋊C4—224no—
636C22⋊C4—224no—
637C22⋊C4—444no—
638C22⋊C4—444no—
639C22⋊C4—444no—
640C22⋊C4—444no—
641C22⋊C4—444no—
642C42—224no—
643C11#3670911yescharacteristic, complemented, Sylow
644C23—22no—
645C23—22no—
646C23—28no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—48no—
654C23—48no—
655C23—44no—
656C23—44no—
657C23—114no—
658C23—224no—
659C23—222no—
660C23—222no—
661C23—224no—
662C23—228no—
663C23—222no—
664C23—224no—
665C23—222no—
666C23—222no—
667C23—224no—
668C23—444no—
669C23—444no—
670C23—884no—
671C23—884no—
672C23C2×D4×D1112yes—
673C23#6703714yes—
674C23#6704012yes—
675C23#6704212yes—
676C23C24×D1111yescharacteristic
677Q8—82no—
678D4—4416no—
679D4—448no—
680D4—882no—
681D4—884no—
682D4—884no—
683D4—888no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—44no—
697C2×C4—48no—
698C2×C4—48no—
699C2×C4—44no—
700C2×C4—114no—
701C2×C4—224no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—224no—
706C2×C4—224no—
707C2×C4—222no—
708C2×C4—222no—
709C2×C4—224no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—224no—
713C2×C4—444no—
714C2×C4—444no—
715C2×C4—444no—
716C2×C4—884no—
717C2×C4—888no—
718C2×C4C2×D4×D1112yes—
719C2×C4C2×D4×D1112yes—
720C22—22no—
721C22—22no—
722C22—24no—
723C22—24no—
724C22—24no—
725C22—24no—
726C22—24no—
727C22—416no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—224no—
733C22—224no—
734C22—224no—
735C22—444no—
736C22—444no—
737C22—442no—
738C22—442no—
739C22—442no—
740C22—444no—
741C22—444no—
742C22—888no—
743C22#1062316014yes—
744C22C22×D4×D1111yescharacteristic
745C22C2×#6703712yes—
746C22C2×#6704011yescharacteristic
747C22C2×#6704211yescharacteristic
748C22#1062345312yes—
749C4—22no—
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—44no—
755C4—224no—
756C4—442no—
757C4—442no—
758C4—442no—
759C4—444no—
760C2—24no—
761C2—44no—
762C2—444no—
763C2—882no—
764C2C2×#1062316011yescharacteristic
765C2#1308224511yescharacteristic
766C2#1308225811yescharacteristic
767C2#1308280012yes—
768C2#1308282512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2848C2
hypercenter#2848D11
hypocenterC11#36709
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2848

Complements

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

NH ≅ G/Ntype
1. C2×#10623175C2semidirect
2. C22×#66982C2semidirect
3. #13076898C2semidirect
4. #13075155C2semidirect
5. #13075125C2semidirect
6. #13074863C2semidirect
7. #13074856C2semidirect
8. #13074431C2semidirect
9. #13074361C2semidirect
10. #13073509C2semidirect
11. #13072932C2semidirect
12. #13072010C2semidirect
13. #13071992C2semidirect
14. #13071229C2semidirect
15. C11×#2848C2semidirect
19. C2×C11×C22⋊Q8C22semidirect
22. C2×#67000C22semidirect
24. C2×#66983C22semidirect
33. C2×#66951C22semidirect
34. C2×#66948C22semidirect
35. C2×#66947C22semidirect
42. C11×#385C22semidirect
44. C11×#380C22semidirect
46. #10622842C22semidirect
48. #10622826C22semidirect
50. #10622825C22semidirect
51. #10622607C22semidirect
52. #10622605C22semidirect
53. #10622604C22semidirect
54. #10622602C22semidirect
55. #10622600C22semidirect
56. #10622597C22semidirect
57. #10622595C22semidirect
58. #10622585C22semidirect
61. #10622572C22semidirect
64. #10622569C22semidirect
65. #10622564C22semidirect
66. #10622561C22semidirect
70. #10622287C22semidirect
71. #10622285C22semidirect
72. #10622281C22semidirect
73. #10622280C22semidirect
74. #10622278C22semidirect
75. #10622274C22semidirect
76. #10622271C22semidirect
120. C2×(C2×D11)⋊C4D4semidirect
262. #2848D11semidirect
362. C2×C22⋊Q8C2×D11semidirect
402. #385C2×D11semidirect
410. #380C2×D11semidirect
643. C11#36709semidirect

Maximal subgroups

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

subgroupindex
C2×#106231752
C22×#669822
#130768982
#130751552
#130751252
#130748632
#130748562
#130744312
#130743612
#130735092
#130729322
#130720102
#130719922
#130712292
C11×#28482
#3670911