Finite Group Databasebeta

← #14797626

Subgroups — #14797626

Order 2816.

1156 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622659C211yesmaximal, characteristic
2C2×#10622401C211yesmaximal, characteristic, complemented
3#13072137C211yesmaximal, characteristic, complemented
4#13071436C211yesmaximal, characteristic
5#13070146C211yesmaximal, characteristic, complemented
6#13070052C211yesmaximal, characteristic, complemented
7#13069930C211yesmaximal, characteristic, complemented
8#13069297C211yesmaximal, characteristic, complemented
9#13069225C211yesmaximal, characteristic, complemented
10#13068969C211yesmaximal, characteristic, complemented
11#13068947C211yesmaximal, characteristic, complemented
12#13068874C211yesmaximal, characteristic, complemented
13#13068615C211yesmaximal, characteristic, complemented
14#13068548C211yesmaximal, characteristic
15C11×#2035C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic, complemented
19C22×#4325C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C2×#66946C2211yescharacteristic
22C2×#66946C2211yescharacteristic
23C2×C22⋊C4×D11—21no—
24C2×C11×#106C2211yescharacteristic, complemented
25C2×C11×#103C2211yescharacteristic, complemented
26C2×C11×#103C2211yescharacteristic, complemented
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#380C2211yescharacteristic
29#10622843C2211yescharacteristic, complemented
30#10622825C2211yescharacteristic
31C4×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×#66885C2211yescharacteristic
36C2×#66885C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic, complemented
38C2×C8×Dic11C2211yescharacteristic, complemented
39#10622659—24no—
40#10622601C2211yescharacteristic
41#10622601C2211yescharacteristic
42#10622596—21no—
43#10622591—21no—
44#10622589C2211yescharacteristic, complemented
45#10622586C2211yescharacteristic, complemented
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66872C2211yescharacteristic, complemented
49#10622568—21no—
50#10622562—21no—
51#10622557—21no—
52#10622401—24no—
53#10622278—21no—
54#10622278—21no—
55C11×#340C2211yescharacteristic, complemented
56#10622188C2211yescharacteristic, complemented
57#10622188C2211yescharacteristic, complemented
58#10622167C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61C24×D11—21no—
62C22×Q8×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×D44—21no—
65C22×D44—22no—
66C22×D44—22no—
67C22×D44—22no—
68C22×D44—22no—
69C22×D44—41no—
70C22×D44—41no—
71C22×D44C2311yescharacteristic
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×C4×D11—21no—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8—41no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11D411yescharacteristic
87C2×C22⋊Dic11D411yescharacteristic
88Q8×Dic11—22no—
89Q8×Dic11—41no—
90C2×#4325—22no—
91C2×#4325—22no—
92C2×#4325—22no—
93C2×#4325—22no—
94C2×#4325—41no—
95C2×#4325D414yes—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4—21no—
108C2×C4×Dic11—21no—
109C2×C4×Dic11C2311yescharacteristic
110C2×C4×Dic11C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113#66946—22no—
114#66946—22no—
115#66946—41no—
116#66946—41no—
117C22⋊C4×D11—44no—
118C11×#106—41no—
119C11×#103—22no—
120C11×#103—41no—
121C11×C22⋊C8—41no—
122C11×#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95D411yescharacteristic
128C11⋊#95D411yescharacteristic
129C22⋊(C11⋊C8)—22no—
130#66885—22no—
131#66885—22no—
132#66885—22no—
133#66885—41no—
134Dic11⋊C8—41no—
135C8×Dic11—22no—
136#66873—22no—
137#66873—22no—
138#66872—22no—
139#24901—111nomaximal, Sylow
140C24×C11C2×D411yescharacteristic
141C23×D11—21no—
142C23×D11—21no—
143C23×D11—24no—
144C23×D11—42no—
145C23×D11—42no—
146C23×D11—42no—
147C23×D11—42no—
148C23×D11—81no—
149C23×D11—81no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11C2×D412yes—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2411yescharacteristic
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172C22×Dic11C2×D411yescharacteristic
173C22×Dic11C2×D411yescharacteristic
174C2×D44—24no—
175C2×D44—21no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—21no—
180C2×D44—21no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—42no—
184C2×D44—42no—
185C2×D44—44no—
186C2×D44—44no—
187C2×D44—44no—
188C2×D44—44no—
189C2×D44C2×D412yes—
190C2×D44#4112yes—
191C2×D44#4112yes—
192C2×D44#4112yes—
193C2×C4×D11—42no—
194C2×C4×D11—42no—
195C2×C4×D11—42no—
196C2×C4×D11—42no—
197C2×C4×D11—81no—
198C2×C4×D11—81no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—42no—
212C11×C22⋊C4—42no—
213C11×C22⋊C4—42no—
214C22⋊Dic11—41no—
215C22⋊Dic11—81no—
216C22⋊Dic11SD1614yescomplemented
217#4325—28no—
218#4325—44no—
219(C2×D11)⋊C4—42no—
220(C2×D11)⋊C4—42no—
221(C2×D11)⋊C4—42no—
222(C2×D11)⋊C4—42no—
223(C2×D11)⋊C4—81no—
224(C2×D11)⋊C4—81no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—42no—
230Dic11⋊C4—42no—
231Dic11⋊C4—81no—
232Dic11⋊C4—81no—
233C4×Dic11—21no—
234C4×Dic11—21no—
235C4×Dic11—21no—
236C4×Dic11—21no—
237C4×Dic11—42no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8C2×D412yes—
244C2×#450—111no—
245C2×C4×SD16—111no—
246#2423—111no—
247D4×C22⋊C4—111no—
248#2094—111no—
249#2077—111no—
250#2055—111no—
251#2035D1111yescharacteristic, complemented
252#1934—111no—
253#1923—111no—
254#1880—111no—
255#1877—111no—
256#1864—111no—
257#1802—111no—
258#1786—111no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11C2×SD1612yes—
266C23×C11C22×D411yescharacteristic
267C22×D11—22no—
268C22×D11—22no—
269C22×D11—22no—
270C22×D11—22no—
271C22×D11—48no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—48no—
277C22×D11—41no—
278C22×D11—41no—
279C22×D11—41no—
280C22×D11—41no—
281C22×D11—41no—
282C22×D11—41no—
283C22×D11—84no—
284C22×D11—84no—
285C22×D11—84no—
286C22×D11—84no—
287C22×D11—84no—
288Q8×C11—22no—
289Q8×C11—22no—
290Q8×C11—41no—
291Q8×C11—41no—
292C2×C4×C11—21no—
293C2×C4×C11—22no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11C22×D411yescharacteristic
312C2×C4×C11C2×#4111yescharacteristic
313C2×C4×C11C2×#4111yescharacteristic
314C2×C4×C11C2×#4111yescharacteristic
315C2×C4×C11H(5,𝔽2)11yescharacteristic
316C2×C4×C11H(5,𝔽2)11yescharacteristic
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—21no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11C2×SD1612yes—
334C2×Dic11C2×SD1612yes—
335D44—22no—
336D44—22no—
337D44—22no—
338D44—22no—
339D44—22no—
340D44—48no—
341D44—41no—
342D44—41no—
343D44#12314yes—
344C4×D11—84no—
345C4×D11—84no—
346C8×C11—41no—
347C8×C11—41no—
348C11⋊C8—22no—
349C11⋊C8—41no—
350C23×D4—111no—
351C22×SD16—111no—
352C22×SD16—111no—
353C2×C22⋊Q8C2×D1111yescharacteristic
354C2×C4×Q8—111no—
355C2×C4×D4—111no—
356C2×C4×D4—111no—
357C22×C22⋊C4—221no—
358#450—224no—
359C4×SD16—224no—
360C2×#106—111no—
361C2×#106C2×D1111yescharacteristic, complemented
362C2×C4⋊C8—111no—
363C2×#103C2×D1111yescharacteristic, complemented
364C2×#103C2×D1111yescharacteristic, complemented
365C2×#102—111no—
366C2×#102—111no—
367C2×#102—111no—
368C2×#102—111no—
369C2×#102—111no—
370C2×#102—111no—
371C2×C22⋊C8—111no—
372C2×C22⋊C8C2×D1111yescharacteristic
373C2×C4×C8—111no—
374#399—221no—
375#398—221no—
376#391—111no—
377#390—111no—
378#390—111no—
379#389—111no—
380#388—221no—
381#387—221no—
382#386—221no—
383#386—221no—
384#384—111no—
385#380—111no—
386#380C2×D1111yescharacteristic
387#379—221no—
388C4×C22⋊C4—111no—
389#340—111no—
390#340—111no—
391#340—111no—
392#340C2×D1111yescharacteristic, complemented
393#336—111no—
394#336—111no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11#52511yescharacteristic
403C22×C11D4211yescharacteristic
404C22×C11#54611yescharacteristic
405C22×C11C22×SD1611yescharacteristic
406C22×C11#57511yescharacteristic
407C22×C11#57611yescharacteristic
408C22×C11#57711yescharacteristic
409C2×D11—24no—
410C2×D11—42no—
411C2×D11—42no—
412C2×D11—42no—
413C2×D11—42no—
414C2×D11—42no—
415C2×D11—42no—
416C2×D11—42no—
417C2×D11—42no—
418C2×D11—42no—
419C2×D11—816no—
420C2×D11—81no—
421C2×D11—81no—
422C2×D11—81no—
423C2×D11—81no—
424C4×C11—41no—
425C4×C11—42no—
426C4×C11—81no—
427C4×C11—81no—
428C4×C11—81no—
429C4×C11C2×#12311yescharacteristic
430C4×C11#53811yescharacteristic
431C4×C11#54611yescharacteristic
432C4×C11#55111yescharacteristic
433Dic11—22no—
434Dic11—22no—
435Dic11—41no—
436Dic11—41no—
437Dic11—81no—
438Dic11—81no—
439C25—221no—
440C22×Q8C22×D1111yescharacteristic
441C22×D4—111no—
442C22×D4—111no—
443C22×D4—222no—
444C22×D4—222no—
445C22×D4—222no—
446C22×D4—222no—
447C22×D4—221no—
448C22×D4—441no—
449C22×D4—441no—
450C23×C4—221no—
451C23×C4—221no—
452C23×C4C22×D1111yescharacteristic
453C2×SD16—114no—
454C2×SD16—222no—
455C2×SD16—222no—
456C2×SD16—222no—
457C2×SD16—222no—
458C2×SD16—441no—
459C22×C8—111no—
460C22×C8—111no—
461C22×C8C22×D1111yescharacteristic
462C22×C8C22×D1111yescharacteristic
463C22⋊Q8—22no—
464C22⋊Q8—41no—
465C4×Q8—222no—
466C4×Q8—441no—
467C4×D4—222no—
468C4×D4—222no—
469C4×D4—441no—
470C4×D4—441no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—111no—
473C2×C4⋊C4—111no—
474C2×C4⋊C4—221no—
475C2×C4⋊C4—221no—
476C2×C4⋊C4—221no—
477C2×C4⋊C4—221no—
478C2×C4⋊C4C22×D1111yescharacteristic
479C2×C4⋊C4C22×D1111yescharacteristic
480C2×C4⋊C4C22×D1111yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—111no—
484C2×C22⋊C4—111no—
485C2×C22⋊C4—221no—
486C2×C22⋊C4—221no—
487C2×C22⋊C4—221no—
488C2×C22⋊C4—221no—
489C2×C22⋊C4—221no—
490C2×C22⋊C4—221no—
491C2×C22⋊C4—221no—
492C2×C22⋊C4—444no—
493C2×C42—111no—
494C2×C42—111no—
495C2×C42—221no—
496#106—41no—
497#106—222no—
498C4⋊C8—441no—
499#103—22no—
500#103—41no—
501#102—222no—
502#102—222no—
503#102—222no—
504#102—222no—
505#102—222no—
506#102—441no—
507C22⋊C8—41no—
508C22⋊C8—222no—
509C4×C8—222no—
510#95—21no—
511#95—111no—
512#95—111no—
513#95—221no—
514#95—221no—
515#95—221no—
516#95—221no—
517C2×C11—42no—
518C2×C11#241811yescharacteristic
519C2×C11#310111yescharacteristic
520C2×C11#311811yescharacteristic
521C2×C11#326811yescharacteristic
522C2×C11D4×SD1611yescharacteristic
523C2×C11#329511yescharacteristic
524C2×C11#332311yescharacteristic
525D11—44no—
526D11—82no—
527C24—224no—
528C24—221no—
529C24—221no—
530C24—442no—
531C24—442no—
532C24—442no—
533C24—442no—
534C24—881no—
535C24—881no—
536C24D4×D1111yescharacteristic
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8D4×D1112yes—
543C2×D4—112no—
544C2×D4—112no—
545C2×D4—112no—
546C2×D4—112no—
547C2×D4—224no—
548C2×D4—221no—
549C2×D4—221no—
550C2×D4—221no—
551C2×D4—221no—
552C2×D4—221no—
553C2×D4—221no—
554C2×D4—221no—
555C2×D4—221no—
556C2×D4—442no—
557C2×D4—442no—
558C2×D4—444no—
559C2×D4—444no—
560C2×D4—444no—
561C2×D4—444no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—111no—
573C22×C4—111no—
574C22×C4—111no—
575C22×C4—111no—
576C22×C4—221no—
577C22×C4—221no—
578C22×C4—442no—
579C22×C4—442no—
580C22×C4—442no—
581C22×C4—442no—
582C22×C4—881no—
583C22×C4—881no—
584C22×C4D4×D1111yescharacteristic
585C22×C4C23×D1111yescharacteristic
586SD16—228no—
587SD16—444no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—112no—
595C2×C8—221no—
596C2×C8—221no—
597C2×C8—221no—
598C2×C8—221no—
599C2×C8—221no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—42no—
607C4⋊C4—221no—
608C4⋊C4—221no—
609C4⋊C4—221no—
610C4⋊C4—221no—
611C4⋊C4—442no—
612C4⋊C4—442no—
613C4⋊C4—881no—
614C4⋊C4—881no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—114no—
618C22⋊C4—442no—
619C22⋊C4—442no—
620C22⋊C4—442no—
621C22⋊C4—442no—
622C22⋊C4—441no—
623C22⋊C4—881no—
624C22⋊C4—881no—
625C22⋊C4—881no—
626C42—221no—
627C42—221no—
628C42—221no—
629C42—221no—
630C42—442no—
631C11#2490111yescharacteristic, complemented, Sylow
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—222no—
639C23—222no—
640C23—222no—
641C23—222no—
642C23—448no—
643C23—448no—
644C23—441no—
645C23—441no—
646C23—441no—
647C23—441no—
648C23—441no—
649C23—441no—
650C23—441no—
651C23—441no—
652C23—441no—
653C23—441no—
654C23—884no—
655C23—884no—
656C23—884no—
657C23—884no—
658C23—884no—
659C23SD16×D1112yes—
660C23C2×D4×D1111yescharacteristic
661Q8—22no—
662Q8—22no—
663Q8—41no—
664Q8—41no—
665D4—114no—
666D4—222no—
667D4—222no—
668D4—222no—
669D4—222no—
670D4—222no—
671D4—448no—
672D4—441no—
673D4—441no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—112no—
694C2×C4—112no—
695C2×C4—221no—
696C2×C4—221no—
697C2×C4—221no—
698C2×C4—221no—
699C2×C4—221no—
700C2×C4—221no—
701C2×C4—221no—
702C2×C4—221no—
703C2×C4—221no—
704C2×C4—221no—
705C2×C4—441no—
706C2×C4—441no—
707C2×C4—441no—
708C2×C4—441no—
709C2×C4—441no—
710C2×C4—441no—
711C2×C4—884no—
712C2×C4—884no—
713C2×C4C2×D4×D1111yescharacteristic
714C2×C4#6703711yescharacteristic
715C2×C4#6703711yescharacteristic
716C2×C4#41×D1111yescharacteristic
717C2×C4#41×D1111yescharacteristic
718C2×C4#41×D1111yescharacteristic
719C8—41no—
720C8—41no—
721C8—222no—
722C8—441no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—224no—
731C22—442no—
732C22—442no—
733C22—442no—
734C22—442no—
735C22—442no—
736C22—442no—
737C22—442no—
738C22—442no—
739C22—442no—
740C22—8816no—
741C22—881no—
742C22—881no—
743C22—881no—
744C22—881no—
745C22#1062312111yescharacteristic
746C22#1062314111yescharacteristic
747C22#1062318711yescharacteristic
748C22C2×SD16×D1111yescharacteristic
749C22#1062330011yescharacteristic
750C22#1062330811yescharacteristic
751C22#1062330911yescharacteristic
752C4—41no—
753C4—42no—
754C4—81no—
755C4—81no—
756C4—81no—
757C4—222no—
758C4—222no—
759C4—441no—
760C4—441no—
761C4—881no—
762C4—881no—
763C4#1062314111yescharacteristic
764C4#1062314411yescharacteristic
765C4D11×#12311yescharacteristic
766C4#1062321011yescharacteristic
767C2—42no—
768C2—444no—
769C2—882no—
770C2#1307207111yescharacteristic
771C2#1307862111yescharacteristic
772C2#1307880311yescharacteristic
773C2#1308015911yescharacteristic
774C2#1308030511yescharacteristic
775C2#1308043511yescharacteristic
776C2#1308083811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2035C2
socleC23×C11C22×D4
prime radicalC23×D44C22
hypercenter#2035D11
hypocenterC11#24901
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2035

Complements

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

NH ≅ G/Ntype
2. C2×#10622401C2semidirect
3. #13072137C2semidirect
5. #13070146C2semidirect
6. #13070052C2semidirect
7. #13069930C2semidirect
8. #13069297C2semidirect
9. #13069225C2semidirect
10. #13068969C2semidirect
11. #13068947C2semidirect
12. #13068874C2semidirect
13. #13068615C2semidirect
15. C11×#2035C2semidirect
18. C2×Q8×Dic11C22semidirect
24. C2×C11×#106C22semidirect
25. C2×C11×#103C22semidirect
26. C2×C11×#103C22semidirect
29. #10622843C22semidirect
37. C2×Dic11⋊C8C22semidirect
38. C2×C8×Dic11C22semidirect
44. #10622589C22semidirect
45. #10622586C22semidirect
48. C2×#66872C22semidirect
55. C11×#340C22semidirect
56. #10622188C22semidirect
57. #10622188C22semidirect
58. #10622167C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
216. C22⋊Dic11SD16semidirect
251. #2035D11semidirect
361. C2×#106C2×D11semidirect
363. C2×#103C2×D11semidirect
364. C2×#103C2×D11semidirect
392. #340C2×D11semidirect
631. C11#24901semidirect

Maximal subgroups

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

subgroupindex
C2×#106226592
C2×#106224012
#130721372
#130714362
#130701462
#130700522
#130699302
#130692972
#130692252
#130689692
#130689472
#130688742
#130686152
#130685482
C11×#20352
#2490111