Finite Group Databasebeta

← #14960602

Subgroups — #14960602

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×#10623025C211yesmaximal, characteristic, complemented
2#13076903C211yesmaximal, characteristic, complemented
3#13076898C211yesmaximal, characteristic, complemented
4#13075147C214yesmaximal, complemented
5#13075121C214yesmaximal, complemented
6#13074867C214yesmaximal, complemented
7#13074852C214yesmaximal, complemented
8#13074429C211yesmaximal, characteristic, complemented
9#13074358C211yesmaximal, characteristic, complemented
10#13073506C212yesmaximal, complemented
11#13072927C212yesmaximal, complemented
12#13072012C212yesmaximal, complemented
13#13071990C212yesmaximal, complemented
14#13071230C211yesmaximal, characteristic, complemented
15C22×C11×#123C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C2×C11×#123—28no—
19C2×C11×#123C2214yes—
20C2×C11×#123C2214yes—
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C2×#67006C2212yes—
27C2×#67006C2212yes—
28C22×C22⋊Dic11C2212yes—
29C2×#66992C2214yes—
30C2×#66983C2211yescharacteristic
31C2×#66983C2212yescomplemented
32C2×#66982C2212yes—
33C2×C4×C22⋊D11C2212yes—
34C2×#66977C2211yescharacteristic
35C2×#66977C2212yescomplemented
36#10623025—28no—
37C2×#66938C2212yescomplemented
38C2×#66937C2212yescomplemented
39C2×#66936C2212yescomplemented
40C2×#66932C2212yescomplemented
41#10622860C2212yes—
42#10622836C2214yes—
43#10622835C2214yes—
44#10622833C2214yes—
45#10622826C2212yes—
46#10622826C2212yes—
47#10622826C2214yescomplemented
48#10622825C2212yes—
49#10622825C2211yescharacteristic
50#10622825C2211yescharacteristic
51#10622825C2212yescomplemented
52#10622825C2212yescomplemented
53#10622824C2212yes—
54#10622823C2212yes—
55#10622823C2212yes—
56#10622823C2214yescomplemented
57#10622607C2214yescomplemented
58#10622605C2214yescomplemented
59#10622604C2212yescomplemented
60#10622600C2214yescomplemented
61#10622599C2212yescomplemented
62#10622597C2214yescomplemented
63#10622596C2212yescomplemented
64#10622595C2214yescomplemented
65#10622592C2212yescomplemented
66#10622586C2214yescomplemented
67#10622574C2214yescomplemented
68#10622572C2214yescomplemented
69#10622571C2214yescomplemented
70#10622569C2214yescomplemented
71#10622565C2214yescomplemented
72#10622563C2214yescomplemented
73#10622563C2214yescomplemented
74#10622561C2214yescomplemented
75#10622557C2214yescomplemented
76#10622555C2214yescomplemented
77C25×C11C2311yescharacteristic
78C25×C11C2311yescharacteristic
79C22×D4×C11—24no—
80C22×D4×C11—44no—
81C22×D4×C11C2314yes—
82C23×C4×C11—24no—
83C23×C4×C11—44no—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2312yes—
86C23×C4×C11C2312yes—
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C22×C22⋊D11C2312yes—
92C22×C22⋊D11C2312yes—
93C22×C22⋊D11C2312yes—
94C22×C22⋊D11C2314yes—
95C23×Dic11C2314yes—
96C22×D44C2311yescharacteristic
97C22×C4×D11C2312yes—
98C22×Dic22C2311yescharacteristic
99C11×#123—216no—
100C11×#123—216no—
101C2×C11×C4⋊C4—24no—
102C2×C11×C4⋊C4—24no—
103C2×C11×C4⋊C4C2314yes—
104C2×C11×C4⋊C4C2312yes—
105C2×C11×C4⋊C4C2312yes—
106C2×C11×C22⋊C4—24no—
107C2×C11×C22⋊C4—24no—
108C2×C11×C22⋊C4D418yescomplemented
109C2×C11×C22⋊C4C2314yes—
110C2×C11×C22⋊C4C2314yes—
111C2×C11×C22⋊C4C2312yes—
112C2×C11×C22⋊C4C2312yes—
113#67006—28no—
114#67006—44no—
115C2×C22⋊Dic11—44no—
116C2×C22⋊Dic11C2312yes—
117C2×C22⋊Dic11C2312yes—
118C2×C22⋊Dic11C2312yes—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2312yes—
121C2×C22⋊Dic11C2312yes—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2314yes—
125#66992—48no—
126#66983—24no—
127#66983—44no—
128#66982—44no—
129C4×C22⋊D11—28no—
130C2×(C2×D11)⋊C4C2312yes—
131C2×(C2×D11)⋊C4C2312yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×C4⋊Dic11C2311yescharacteristic
136C2×C4⋊Dic11C2311yescharacteristic
137C2×C4⋊Dic11C2312yes—
138C2×C4⋊Dic11C2312yes—
139C2×C4⋊Dic11C2314yes—
140#66977—24no—
141#66977—44no—
142C2×Dic11⋊C4C2312yes—
143C2×Dic11⋊C4C2312yes—
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×Dic11⋊C4C2314yes—
147C2×C4×Dic11C2312yes—
148#66938—28no—
149#66937—28no—
150#66936—28no—
151#66932—28no—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2312yes—
157C11⋊#95C2312yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161#36709—111nomaximal, Sylow
162C24×C11—22no—
163C24×C11—24no—
164C24×C11—22no—
165C24×C11—22no—
166C24×C11—22no—
167C24×C11—22no—
168C24×C11—42no—
169C24×C11—42no—
170C24×C11—42no—
171C24×C11C2×D414yes—
172C24×C11C2412yes—
173C24×C11C2412yes—
174C24×C11C2411yescharacteristic
175C23×D11C2412yes—
176C2×D4×C11—28no—
177C2×D4×C11—28no—
178C2×D4×C11—44no—
179C2×D4×C11—416no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—24no—
184C22×C4×C11—22no—
185C22×C4×C11—24no—
186C22×C4×C11—22no—
187C22×C4×C11—24no—
188C22×C4×C11—24no—
189C22×C4×C11—42no—
190C22×C4×C11—42no—
191C22×C4×C11—42no—
192C22×C4×C11—42no—
193C22×C4×C11—42no—
194C22×C4×C11—42no—
195C22×C4×C11—416no—
196C22×C4×C11C2×D414yes—
197C22×C4×C11C2×D414yes—
198C22×C4×C11C2412yes—
199C22×C4×C11C2412yes—
200C22×C4×C11C2412yes—
201C22×C4×C11C2412yes—
202C22×C4×C11C2411yescharacteristic
203C22×C4×C11C2411yescharacteristic
204C2×C22⋊D11—24no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—24no—
207C2×C22⋊D11—24no—
208C2×C22⋊D11—28no—
209C2×C22⋊D11—24no—
210C2×C22⋊D11—44no—
211C2×C22⋊D11—44no—
212C2×C22⋊D11—44no—
213C2×C22⋊D11—44no—
214C22×Dic11—44no—
215C22×Dic11—44no—
216C22×Dic11—44no—
217C22×Dic11C2412yes—
218C22×Dic11C2414yes—
219C22×Dic11C2412yes—
220C22×Dic11C2414yes—
221C22×Dic11C2412yes—
222C2×D44—22no—
223C2×D44—42no—
224C2×C4×D11—24no—
225C2×C4×D11—44no—
226C2×Dic22—22no—
227C2×Dic22—42no—
228C11×C4⋊C4—24no—
229C11×C4⋊C4—24no—
230C11×C4⋊C4—28no—
231C11×C22⋊C4—28no—
232C11×C22⋊C4—28no—
233C11×C22⋊C4C2×D418yes—
234C11×C22⋊C4C2×D418yes—
235C22⋊Dic11—24no—
236C22⋊Dic11—24no—
237C22⋊Dic11—24no—
238C22⋊Dic11—28no—
239C22⋊Dic11—24no—
240C22⋊Dic11—24no—
241C22⋊Dic11—44no—
242C22⋊Dic11—44no—
243C22⋊Dic11—44no—
244(C2×D11)⋊C4—24no—
245(C2×D11)⋊C4—24no—
246(C2×D11)⋊C4—44no—
247(C2×D11)⋊C4—44no—
248(C2×D11)⋊C4—44no—
249C4⋊Dic11—22no—
250C4⋊Dic11—22no—
251C4⋊Dic11—42no—
252C4⋊Dic11—44no—
253C4⋊Dic11—42no—
254Dic11⋊C4—24no—
255Dic11⋊C4—24no—
256Dic11⋊C4—44no—
257Dic11⋊C4—44no—
258Dic11⋊C4—44no—
259C4×Dic11—24no—
260C2×#538—111no—
261C22×#123D1111yescharacteristic, complemented
262#2848—111no—
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—24no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—24no—
287C23×C11—22no—
288C23×C11—28no—
289C23×C11—44no—
290C23×C11—44no—
291C23×C11—48no—
292C23×C11—48no—
293C23×C11—44no—
294C23×C11—44no—
295C23×C11—84no—
296C23×C11—84no—
297C23×C11C22×D414yes—
298C23×C11C22×D412yes—
299C23×C11H(5,𝔽2)14yes—
300C23×C11H(5,𝔽2)12yes—
301C23×C112−1+412yes—
302C23×C11C2511yescharacteristic
303C22×D11—22no—
304C22×D11—24no—
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—24no—
308D4×C11—416no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—24no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—24no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—44no—
321C2×C4×C11—44no—
322C2×C4×C11—48no—
323C2×C4×C11—48no—
324C2×C4×C11—44no—
325C2×C4×C11—44no—
326C2×C4×C11—44no—
327C2×C4×C11C22×D414yes—
328C2×C4×C11C22×D412yes—
329C2×C4×C11C22×D412yes—
330C22⋊D11—48no—
331C22⋊D11—84no—
332C22⋊D11—84no—
333C22⋊D11—88no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—24no—
338C2×Dic11—22no—
339C2×Dic11—24no—
340C2×Dic11—24no—
341C2×Dic11—24no—
342C2×Dic11—24no—
343C2×Dic11—22no—
344C2×Dic11—24no—
345C2×Dic11—24no—
346C2×Dic11—24no—
347C2×Dic11—88no—
348D44—82no—
349C4×D11—84no—
350Dic22—82no—
351C23×D4C2×D1111yescharacteristic
352C24×C4C2×D1111yescharacteristic
353#538—228no—
354C2×#126—112no—
355C2×#124—112no—
356C2×#123—28no—
357C2×#123—112no—
358C2×#123—112no—
359C2×#123C2×D1114yes—
360C2×#123C2×D1114yes—
361C2×C22⋊Q8—111no—
362C2×C22⋊Q8—112no—
363C2×#121—111no—
364C2×#121—114no—
365C2×#121—112no—
366C2×#121—112no—
367C2×#120—112no—
368C2×#120—112no—
369C2×C4×D4—112no—
370C22×C4⋊C4C2×D1111yescharacteristic
371C22×C4⋊C4C2×D1111yescharacteristic
372C22×C22⋊C4—112no—
373C22×C22⋊C4C2×D1111yescharacteristic
374C22×C22⋊C4C2×D1111yescharacteristic
375C22×C22⋊C4C2×D1111yescharacteristic
376#400—112no—
377#400—114no—
378#399—114no—
379#398—112no—
380#398—114no—
381#397—114no—
382#396—114no—
383#396—114no—
384#395—112no—
385#394—114no—
386#394—112no—
387#394—114no—
388#394—114no—
389#392—114no—
390#389—114no—
391#388—114no—
392#386—114no—
393#386—112no—
394#386—114no—
395#386—112no—
396#386—114no—
397#386—114no—
398#385—112no—
399#385—114no—
400#385—112no—
401#385—114no—
402#385—114no—
403#381—112no—
404#380—111no—
405#380—111no—
406#380—112no—
407#380—112no—
408#380—112no—
409#380—114no—
410#380—114no—
411#379—112no—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11—24no—
415C22×C11—24no—
416C22×C11—24no—
417C22×C11—24no—
418C22×C11—24no—
419C22×C11—24no—
420C22×C11—24no—
421C22×C11—24no—
422C22×C11—416no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11—42no—
426C22×C11—44no—
427C22×C11—42no—
428C22×C11—44no—
429C22×C11—88no—
430C22×C11#53714yes—
431C22×C11C23×D411yescharacteristic
432C22×C11C2×H(5,𝔽2)12yes—
433C22×C11C2×H(5,𝔽2)11yescharacteristic
434C22×C11C2×2−1+411yescharacteristic
435C22×C11#58512yes—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—42no—
439C2×D11—44no—
440C2×D11—44no—
441C4×C11—22no—
442C4×C11—22no—
443C4×C11—24no—
444C4×C11—42no—
445C4×C11—42no—
446C4×C11—42no—
447Dic11—42no—
448Dic11—42no—
449Dic11—42no—
450Dic11—44no—
451Dic11—44no—
452C25C22×D1111yescharacteristic
453C25C22×D1111yescharacteristic
454C22×Q8—111no—
455C22×D4—24no—
456C22×D4—44no—
457C22×D4—112no—
458C22×D4—112no—
459C22×D4—114no—
460C22×D4—112no—
461C22×D4—111no—
462C22×D4C22×D1114yes—
463C23×C4—24no—
464C23×C4—44no—
465C23×C4—114no—
466C23×C4—112no—
467C23×C4C22×D1111yescharacteristic
468C23×C4C22×D1112yes—
469C23×C4C22×D1112yes—
470C23×C4C22×D1111yescharacteristic
471C23×C4C22×D1111yescharacteristic
472C23×C4C22×D1111yescharacteristic
473C23×C4C22×D1111yescharacteristic
474#126—228no—
475#124—228no—
476#123—216no—
477#123—216no—
478#123—228no—
479#123—444no—
480C22⋊Q8—224no—
481C22⋊Q8—444no—
482#121—224no—
483#121—228no—
484#121—448no—
485#121—444no—
486#120—228no—
487#120—444no—
488C4×D4—228no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—24no—
491C2×C4⋊C4—112no—
492C2×C4⋊C4—112no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—112no—
496C2×C4⋊C4—114no—
497C2×C4⋊C4—112no—
498C2×C4⋊C4—114no—
499C2×C4⋊C4—114no—
500C2×C4⋊C4—114no—
501C2×C4⋊C4C22×D1114yes—
502C2×C4⋊C4C22×D1112yes—
503C2×C4⋊C4C22×D1112yes—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—112no—
507C2×C22⋊C4—112no—
508C2×C22⋊C4—112no—
509C2×C22⋊C4—112no—
510C2×C22⋊C4—112no—
511C2×C22⋊C4—114no—
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—114no—
520C2×C22⋊C4—444no—
521C2×C22⋊C4C22⋊D1118yescomplemented
522C2×C22⋊C4C22×D1114yes—
523C2×C22⋊C4C22×D1114yes—
524C2×C22⋊C4C22×D1112yes—
525C2×C22⋊C4C22×D1112yes—
526C2×C42—112no—
527#95—114no—
528#95—114no—
529#95—114no—
530#95—112no—
531#95—112no—
532#95—114no—
533#95—114no—
534#95—114no—
535#95—114no—
536C2×C11—24no—
537C2×C11—44no—
538C2×C11—44no—
539C2×C11C2×#53711yescharacteristic
540C2×C11#348411yescharacteristic
541C2×C11#348511yescharacteristic
542C2×C11#353412yes—
543C2×C11#353512yes—
544D11—82no—
545C24—24no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—42no—
552C24—42no—
553C24—42no—
554C24—112no—
555C24C2×C22⋊D1114yes—
556C24C23×D1112yes—
557C24C23×D1112yes—
558C24C23×D1111yescharacteristic
559C2×Q8—222no—
560C2×Q8—442no—
561C2×D4—28no—
562C2×D4—28no—
563C2×D4—44no—
564C2×D4—416no—
565C2×D4—224no—
566C2×D4—224no—
567C2×D4—224no—
568C2×D4—228no—
569C2×D4—224no—
570C2×D4—224no—
571C2×D4—222no—
572C2×D4—442no—
573C2×D4—444no—
574C2×D4—444no—
575C2×D4—444no—
576C2×D4—444no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—416no—
593C22×C4—114no—
594C22×C4—112no—
595C22×C4—112no—
596C22×C4—114no—
597C22×C4—112no—
598C22×C4—224no—
599C22×C4—444no—
600C22×C4—444no—
601C22×C4—444no—
602C22×C4—444no—
603C22×C4C2×C22⋊D1114yes—
604C22×C4C2×C22⋊D1114yes—
605C22×C4C23×D1112yes—
606C22×C4C23×D1112yes—
607C22×C4C23×D1112yes—
608C22×C4C23×D1112yes—
609C22×C4C23×D1111yescharacteristic
610C22×C4C23×D1111yescharacteristic
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—28no—
614C4⋊C4—224no—
615C4⋊C4—224no—
616C4⋊C4—222no—
617C4⋊C4—222no—
618C4⋊C4—444no—
619C4⋊C4—442no—
620C4⋊C4—444no—
621C4⋊C4—442no—
622C4⋊C4—444no—
623C4⋊C4—444no—
624C22⋊C4—28no—
625C22⋊C4—28no—
626C22⋊C4—228no—
627C22⋊C4—224no—
628C22⋊C4—224no—
629C22⋊C4—224no—
630C22⋊C4—224no—
631C22⋊C4—224no—
632C22⋊C4—224no—
633C22⋊C4—224no—
634C22⋊C4—444no—
635C22⋊C4—444no—
636C22⋊C4—444no—
637C22⋊C4—444no—
638C22⋊C4—444no—
639C22⋊C4—444no—
640C22⋊C4C2×C22⋊D1118yes—
641C22⋊C4C2×C22⋊D1118yes—
642C42—224no—
643C11#3670911yescharacteristic, complemented, Sylow
644C23—22no—
645C23—22no—
646C23—28no—
647C23—22no—
648C23—24no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—22no—
656C23—22no—
657C23—28no—
658C23—44no—
659C23—44no—
660C23—48no—
661C23—48no—
662C23—44no—
663C23—44no—
664C23—84no—
665C23—84no—
666C23—224no—
667C23—222no—
668C23—222no—
669C23—224no—
670C23—222no—
671C23#6703714yes—
672C23#6704212yes—
673C23#6704312yes—
674C23C22×C22⋊D1114yes—
675C23C22×C22⋊D1112yes—
676C23C24×D1111yescharacteristic
677Q8—882no—
678D4—416no—
679D4—448no—
680D4—882no—
681D4—884no—
682D4—884no—
683D4—888no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—48no—
698C2×C4—48no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—224no—
703C2×C4—224no—
704C2×C4—224no—
705C2×C4—224no—
706C2×C4—224no—
707C2×C4—222no—
708C2×C4—222no—
709C2×C4—224no—
710C2×C4—224no—
711C2×C4—224no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—884no—
716C2×C4—888no—
717C2×C4C22×C22⋊D1114yes—
718C2×C4C22×C22⋊D1112yes—
719C2×C4C22×C22⋊D1112yes—
720C22—22no—
721C22—22no—
722C22—24no—
723C22—24no—
724C22—24no—
725C22—24no—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—416no—
731C22—42no—
732C22—42no—
733C22—44no—
734C22—42no—
735C22—42no—
736C22—44no—
737C22—88no—
738C22—442no—
739C22—442no—
740C22—442no—
741C22—444no—
742C22—444no—
743C22#1062336414yes—
744C22C2×#6703712yes—
745C22C2×#6704211yescharacteristic
746C22C2×#6704311yescharacteristic
747C22#1062345312yes—
748C22C23×C22⋊D1111yescharacteristic
749C4—22no—
750C4—22no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—442no—
756C4—442no—
757C4—442no—
758C4—444no—
759C4—444no—
760C2—24no—
761C2—44no—
762C2—44no—
763C2—882no—
764C2C2×#1062336411yescharacteristic
765C2#1308225111yescharacteristic
766C2#1308226011yescharacteristic
767C2#1308281012yes—
768C2#1308282912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC22×C11×#123C2
hypercenterC22×#123D11
hypocenterC11#36709
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C2×#10623025C2semidirect
2. #13076903C2semidirect
3. #13076898C2semidirect
4. #13075147C2semidirect
5. #13075121C2semidirect
6. #13074867C2semidirect
7. #13074852C2semidirect
8. #13074429C2semidirect
9. #13074358C2semidirect
10. #13073506C2semidirect
11. #13072927C2semidirect
12. #13072012C2semidirect
13. #13071990C2semidirect
14. #13071230C2semidirect
15. C22×C11×#123C2semidirect
31. C2×#66983C22semidirect
35. C2×#66977C22semidirect
37. C2×#66938C22semidirect
38. C2×#66937C22semidirect
39. C2×#66936C22semidirect
40. C2×#66932C22semidirect
47. #10622826C22semidirect
51. #10622825C22semidirect
52. #10622825C22semidirect
56. #10622823C22semidirect
57. #10622607C22semidirect
58. #10622605C22semidirect
59. #10622604C22semidirect
60. #10622600C22semidirect
61. #10622599C22semidirect
62. #10622597C22semidirect
63. #10622596C22semidirect
64. #10622595C22semidirect
65. #10622592C22semidirect
66. #10622586C22semidirect
67. #10622574C22semidirect
68. #10622572C22semidirect
69. #10622571C22semidirect
70. #10622569C22semidirect
71. #10622565C22semidirect
72. #10622563C22semidirect
73. #10622563C22semidirect
74. #10622561C22semidirect
75. #10622557C22semidirect
76. #10622555C22semidirect
108. C2×C11×C22⋊C4D4semidirect
261. C22×#123D11semidirect
521. C2×C22⋊C4C22⋊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×#106230252
#130769032
#130768982
#130751472
#130751212
#130748672
#130748522
#130744292
#130743582
#130735062
#130729272
#130720122
#130719902
#130712302
C22×C11×#1232
#3670911