Finite Group Databasebeta

← #14770610

Subgroups — #14770610

Order 2816.

1366 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623084C211yesmaximal, characteristic
2C2×#10622314C211yesmaximal, characteristic, complemented
3#13071574C211yesmaximal, characteristic, complemented
4#13069543C211yesmaximal, characteristic, complemented
5#13069541C211yesmaximal, characteristic, complemented
6#13069541C211yesmaximal, characteristic, complemented
7#13069440C211yesmaximal, characteristic, complemented
8#13069438C211yesmaximal, characteristic, complemented
9#13069420C211yesmaximal, characteristic, complemented
10#13068626C211yesmaximal, characteristic, complemented
11#13068625C211yesmaximal, characteristic, complemented
12#13068615C211yesmaximal, characteristic, complemented
13#13068440C211yesmaximal, characteristic, complemented
14#13068430C211yesmaximal, characteristic, complemented
15C11×#1762C211yesmaximal, characteristic, complemented
16C22×#4339—21no—
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66993C2211yescharacteristic
19C2×#66993C2211yescharacteristic
20C2×#66983—21no—
21#10623084—24no—
22#10623084C418yescomplemented
23C2×#66946C2211yescharacteristic
24C2×#66946C2211yescharacteristic
25C2×#66937—21no—
26C2×#66937—21no—
27C2×#66927C2211yescharacteristic
28C2×C4×Dic22C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#97C2211yescharacteristic
32C4×C11×C4⋊C4C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66885C2211yescharacteristic
36C2×#66885C2211yescharacteristic
37C2×#66885C2211yescharacteristic
38C2×#66885C2211yescharacteristic
39C2×#66879C2211yescharacteristic
40C2×Dic11⋊C8C2211yescharacteristic
41C2×Dic11⋊C8C2211yescharacteristic
42C2×C8×Dic11C2211yescharacteristic
43#10622590C2211yescharacteristic
44#10622589C2211yescharacteristic
45C4⋊C4×Dic11C2211yescharacteristic
46C4⋊C4×Dic11C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66873C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51#10622549C2211yescharacteristic
52#10622546—21no—
53C4×Dic11⋊C4—21no—
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55#10622314—24no—
56#10622267—21no—
57#10622259—21no—
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C22×C22⋊D11—21no—
65C22×C22⋊D11—21no—
66C22×C22⋊D11—21no—
67C22×C22⋊D11—21no—
68C2×#4339—28no—
69C2×#4339—44no—
70C2×#4339—44no—
71C22×D44—21no—
72C22×D44—21no—
73C22×D44C2311yescharacteristic
74C22×D44C2311yescharacteristic
75C22×C4×D11—21no—
76C22×C4×D11—21no—
77C22×Dic22D411yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C4×D4×C11—22no—
81C4×D4×C11C2×C414yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C42×C11—21no—
87C2×C42×C11C2311yescharacteristic
88#66993—22no—
89#66993—22no—
90#66993C2×C414yes—
91#66993C2×C414yes—
92#66983—28no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×C4⋊Dic11D411yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4D411yescharacteristic
101C2×Dic11⋊C4D411yescharacteristic
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11C2311yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108#66946—22no—
109#66946—22no—
110#66946C2×C414yes—
111#66946C2×C414yes—
112#66937—28no—
113#66937—28no—
114#66927—22no—
115#66927C2×C414yes—
116C4×Dic22C2×C414yes—
117C4×Dic22D414yes—
118C11×#102—22no—
119C11×#102—22no—
120C11×#97—22no—
121C11×#95—21no—
122#66896—41no—
123#66896—41no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130#66885—22no—
131#66885—22no—
132#66885—41no—
133#66885—41no—
134#66879—22no—
135Dic11⋊C8—22no—
136Dic11⋊C8—22no—
137C8×Dic11—22no—
138#66873—22no—
139#66873—22no—
140#66873—41no—
141#66873—41no—
142C4⋊(C11⋊C8)—22no—
143#22545—111nomaximal, Sylow
144C24×C11—21no—
145C23×D11—21no—
146C23×D11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11C22×C412yes—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—24no—
156C22×C4×C11—21no—
157C22×C4×C11—42no—
158C22×C4×C11—42no—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2411yescharacteristic
162C2×C22⋊D11—24no—
163C2×C22⋊D11—24no—
164C2×C22⋊D11—24no—
165C2×C22⋊D11—24no—
166C2×C22⋊D11—42no—
167C2×C22⋊D11—42no—
168C2×C22⋊D11—42no—
169C2×C22⋊D11—42no—
170C2×C22⋊D11—81no—
171C2×C22⋊D11—81no—
172C2×C22⋊D11—81no—
173C2×C22⋊D11—81no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11C2×D411yescharacteristic
177C22×Dic11C2×D411yescharacteristic
178C22×Dic11C2×D411yescharacteristic
179C22×Dic11C2×D411yescharacteristic
180#4339—432no—
181C2×D44—24no—
182C2×D44—24no—
183C2×D44—21no—
184C2×D44—21no—
185C2×D44—21no—
186C2×D44—21no—
187C2×D44—21no—
188C2×D44—21no—
189C2×D44—21no—
190C2×D44—21no—
191C2×D44—21no—
192C2×D44—21no—
193C2×D44—42no—
194C2×D44—42no—
195C2×D44—81no—
196C2×D44—81no—
197C2×D44C22×C412yes—
198C2×D44C22×C412yes—
199C2×C4×D11—24no—
200C2×C4×D11—24no—
201C2×C4×D11—42no—
202C2×C4×D11—42no—
203C2×C4×D11—42no—
204C2×C4×D11—42no—
205C2×Dic22—22no—
206C2×Dic22—22no—
207C2×Dic22C22⋊C414yes—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11—21no—
213C2×C8×C11#4112yescomplemented
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4C22×C412yes—
219C11×C4⋊C4#4112yescomplemented
220C11×C22⋊C4—24no—
221C42×C11—81no—
222C42×C11C22×C412yes—
223C42×C11C2×D412yes—
224(C2×D11)⋊C4—24no—
225(C2×D11)⋊C4—24no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11C22⋊C414yes—
231Dic11⋊C4—42no—
232Dic11⋊C4—81no—
233Dic11⋊C4C22⋊C414yes—
234Dic11⋊C4C22⋊C414yes—
235C4×Dic11—42no—
236C4×Dic11—81no—
237C4×Dic11C22×C412yes—
238C4×Dic11C22×C412yes—
239C4×Dic11C2×D412yes—
240C4×Dic11C2×D412yes—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×#550—111no—
248C2×#446—111no—
249#2355—111no—
250#1982—111no—
251#1982—111no—
252#1982—111no—
253#1961—111no—
254#1961—111no—
255#1957—111no—
256#1804—111no—
257#1804—111no—
258#1802—111no—
259#1762—111no—
260#1762D1111yescharacteristic, complemented
261C4×#102—111no—
262C23×C11—22no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11C22×D411yescharacteristic
270C22×D11—22no—
271C22×D11—22no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—41no—
279C22×D11—41no—
280C22×D11—41no—
281C22×D11—41no—
282C22×D11—41no—
283C22×D11—41no—
284D4×C11—22no—
285D4×C11—22no—
286D4×C11—41no—
287D4×C11—41no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—48no—
295C2×C4×C11—41no—
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×C11C2×C22⋊C412yes—
303C2×C4×C11C2×C22⋊C412yes—
304C2×C4×C11C23×C411yescharacteristic
305C2×C4×C11C22×D411yescharacteristic
306C2×C4×C11C2×#4111yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11H(5,𝔽2)11yescharacteristic
309C2×C4×C112−1+411yescharacteristic
310C22⋊D11—48no—
311C22⋊D11—48no—
312C22⋊D11—84no—
313C22⋊D11—84no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11C2×C22⋊C412yes—
327C2×Dic11C2×C22⋊C412yes—
328C2×Dic11C2×C22⋊C412yes—
329C2×Dic11C2×C22⋊C412yes—
330C2×Dic11AGL(1,ℤ/8)12yes—
331C2×Dic11AGL(1,ℤ/8)12yes—
332D44—22no—
333D44—22no—
334D44—22no—
335D44—22no—
336D44—48no—
337D44—41no—
338D44—41no—
339D44—41no—
340D44—41no—
341D44—84no—
342C4×D11—48no—
343C4×D11—48no—
344Dic22—28no—
345C8×C11—22no—
346C8×C11—41no—
347C11⋊C8—41no—
348C11⋊C8—41no—
349C22×#41—221no—
350#550—118no—
351#550—224no—
352C2×#127—111no—
353C2×#127—111no—
354C2×#127—111no—
355C2×#121—221no—
356C2×#121—221no—
357C2×#121—221no—
358C2×C4×Q8—111no—
359C2×C4×D4—111no—
360C2×C4×D4—111no—
361C2×C4×D4C2×D1111yescharacteristic
362#446—224no—
363C2×C4⋊C8—111no—
364C2×C4⋊C8—111no—
365C2×C4⋊C8—111no—
366C2×#102—111no—
367C2×#102—111no—
368C2×#102—111no—
369C2×#102—111no—
370C2×#102—111no—
371C2×#102—111no—
372C2×#102—111no—
373C2×#102—111no—
374C2×#102—111no—
375C2×#102—111no—
376C2×#102C2×D1111yescharacteristic
377C2×#102C2×D1111yescharacteristic
378C2×#97—111no—
379C2×#97C2×D1111yescharacteristic
380C2×C4×C8—111no—
381#391—221no—
382#387—221no—
383#387—221no—
384#384—111no—
385#382—111no—
386#382—111no—
387C4×C4⋊C4—111no—
388C4×C4⋊C4—111no—
389C4×C4⋊C4—221no—
390C4×C4⋊C4C2×D1111yescharacteristic
391#340—111no—
392#340—111no—
393#340C2×D1111yescharacteristic
394#340C2×D1111yescharacteristic
395C22×C11—42no—
396C22×C11—42no—
397C22×C11—42no—
398C22×C11—81no—
399C22×C11—81no—
400C22×C11—81no—
401C22×C11—81no—
402C22×C11C22×C22⋊C411yescharacteristic
403C22×C11#54811yescharacteristic
404C22×C11#55011yescharacteristic
405C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
406C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
407C22×C11#57611yescharacteristic
408C22×C11#57711yescharacteristic
409C2×D11—42no—
410C2×D11—42no—
411C2×D11—42no—
412C2×D11—42no—
413C2×D11—42no—
414C2×D11—42no—
415C2×D11—81no—
416C2×D11—81no—
417C2×D11—81no—
418C2×D11—81no—
419C2×D11—81no—
420C2×D11—81no—
421C2×D11—81no—
422C2×D11—81no—
423C4×C11—22no—
424C4×C11—22no—
425C4×C11—42no—
426C4×C11—42no—
427C4×C11—81no—
428C4×C11C4×#4111yescharacteristic
429C4×C11#52011yescharacteristic
430C4×C11#54811yescharacteristic
431C4×C11#55011yescharacteristic
432Dic11—22no—
433Dic11—22no—
434Dic11—22no—
435Dic11—81no—
436Dic11—81no—
437Dic11#41814yes—
438C2×#41—228no—
439C2×#41—444no—
440C2×#41—444no—
441C22×Q8—111no—
442C22×D4—111no—
443C22×D4—111no—
444C22×D4—221no—
445C22×D4—221no—
446C22×D4—221no—
447C22×D4—221no—
448C22×D4—221no—
449C22×D4—221no—
450C22×D4C22×D1111yescharacteristic
451C23×C4—21no—
452C23×C4—221no—
453C23×C4—221no—
454C22×C8—111no—
455C22×C8—111no—
456C22×C8C22×D1111yescharacteristic
457C22×C8C22×D1111yescharacteristic
458#127—114no—
459#127—114no—
460#127—114no—
461#127—222no—
462#127—222no—
463#127—222no—
464#121—228no—
465#121—228no—
466#121—228no—
467C4×Q8—114no—
468C4×Q8—114no—
469C4×D4—22no—
470C4×D4—114no—
471C4×D4—114no—
472C4×D4—222no—
473C4×D4—222no—
474C4×D4C4×D1114yes—
475C2×C4⋊C4—111no—
476C2×C4⋊C4—111no—
477C2×C4⋊C4—111no—
478C2×C4⋊C4—111no—
479C2×C4⋊C4—111no—
480C2×C4⋊C4—221no—
481C2×C4⋊C4—221no—
482C2×C4⋊C4C22×D1111yescharacteristic
483C2×C4⋊C4C22×D1111yescharacteristic
484C2×C4⋊C4C22×D1111yescharacteristic
485C2×C22⋊C4—21no—
486C2×C22⋊C4—221no—
487C2×C22⋊C4—221no—
488C2×C42—21no—
489C2×C42—111no—
490C2×C42—111no—
491C2×C42—221no—
492C2×C42—221no—
493C2×C42C22×D1111yescharacteristic
494C4⋊C8—222no—
495C4⋊C8—222no—
496C4⋊C8—222no—
497#102—22no—
498#102—22no—
499#102—222no—
500#102—222no—
501#102—222no—
502#102—222no—
503#102—441no—
504#102—441no—
505#102—441no—
506#102—441no—
507#102—441no—
508#102—441no—
509#97—22no—
510#97—222no—
511C4×C8—222no—
512#95—21no—
513#95—221no—
514#95—221no—
515#95—221no—
516#95—221no—
517#95—221no—
518#95—221no—
519C2×C11—82no—
520C2×C11#234111yescharacteristic
521C2×C11C2×#41811yescharacteristic
522C2×C11#289711yescharacteristic
523C2×C11#336611yescharacteristic
524C2×C11#336811yescharacteristic
525C2×C11#339711yescharacteristic
526C2×C11#339911yescharacteristic
527D11—82no—
528D11—82no—
529C24—21no—
530C24—221no—
531C24—221no—
532#41—4432no—
533C2×Q8—114no—
534C2×Q8—222no—
535C2×Q8—222no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—112no—
542C2×D4—112no—
543C2×D4—224no—
544C2×D4—224no—
545C2×D4—224no—
546C2×D4—224no—
547C2×D4—224no—
548C2×D4—224no—
549C2×D4—221no—
550C2×D4—221no—
551C2×D4—221no—
552C2×D4—221no—
553C2×D4—221no—
554C2×D4—221no—
555C2×D4—221no—
556C2×D4—221no—
557C2×D4—221no—
558C2×D4—221no—
559C2×D4—442no—
560C2×D4—442no—
561C2×D4—442no—
562C2×D4—442no—
563C2×D4—442no—
564C2×D4—442no—
565C2×D4—881no—
566C2×D4—881no—
567C2×D4—881no—
568C2×D4—881no—
569C2×D4—881no—
570C2×D4—881no—
571C2×D4C2×C4×D1112yes—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—24no—
575C22×C4—21no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—111no—
579C22×C4—111no—
580C22×C4—111no—
581C22×C4—111no—
582C22×C4—224no—
583C22×C4—224no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—442no—
587C22×C4—442no—
588C22×C4—442no—
589C22×C4—442no—
590C22×C4D4×D1111yescharacteristic
591C22×C4D4×D1111yescharacteristic
592C22×C4C23×D1111yescharacteristic
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—221no—
599C2×C8—221no—
600C2×C8—221no—
601C2×C8—221no—
602C2×C8—221no—
603C2×C8—221no—
604C2×C8#433912yescomplemented
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—114no—
610C4⋊C4—114no—
611C4⋊C4—114no—
612C4⋊C4—221no—
613C4⋊C4—221no—
614C4⋊C4—221no—
615C4⋊C4—221no—
616C4⋊C4—442no—
617C4⋊C4—881no—
618C4⋊C4C2×C4×D1112yes—
619C4⋊C4#433912yescomplemented
620C22⋊C4—24no—
621C22⋊C4—224no—
622C22⋊C4—224no—
623C42—81no—
624C42—112no—
625C42—112no—
626C42—112no—
627C42—112no—
628C42—442no—
629C42—881no—
630C42C2×C4×D1112yes—
631C42D4×D1112yes—
632C11#2254511yescharacteristic, complemented, Sylow
633C23—22no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—222no—
641C23—222no—
642C23—441no—
643C23—441no—
644C23—441no—
645C23—441no—
646C23—441no—
647C23—441no—
648C23—441no—
649C23—441no—
650C23—441no—
651C23—441no—
652C23—441no—
653C23—441no—
654C23C2×D4×D1111yescharacteristic
655Q8—228no—
656D4—22no—
657D4—22no—
658D4—41no—
659D4—41no—
660D4—222no—
661D4—222no—
662D4—222no—
663D4—222no—
664D4—448no—
665D4—448no—
666D4—448no—
667D4—441no—
668D4—441no—
669D4—441no—
670D4—441no—
671D4—884no—
672D4—884no—
673D4—884no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—48no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—112no—
689C2×C4—112no—
690C2×C4—112no—
691C2×C4—112no—
692C2×C4—112no—
693C2×C4—112no—
694C2×C4—221no—
695C2×C4—221no—
696C2×C4—221no—
697C2×C4—221no—
698C2×C4—221no—
699C2×C4—221no—
700C2×C4—448no—
701C2×C4—448no—
702C2×C4—441no—
703C2×C4—441no—
704C2×C4—441no—
705C2×C4—441no—
706C2×C4—441no—
707C2×C4—441no—
708C2×C4C22⋊C4×D1112yes—
709C2×C4C22⋊C4×D1112yes—
710C2×C4C22×C4×D1111yescharacteristic
711C2×C4C2×#433911yescharacteristic
712C2×C4C2×#433911yescharacteristic
713C2×C4C2×D4×D1111yescharacteristic
714C2×C4#6704211yescharacteristic
715C2×C4#6704311yescharacteristic
716C8—22no—
717C8—41no—
718C8—441no—
719C8—441no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—442no—
728C22—442no—
729C22—442no—
730C22—442no—
731C22—442no—
732C22—442no—
733C22—881no—
734C22—881no—
735C22—881no—
736C22—881no—
737C22—881no—
738C22—881no—
739C22—881no—
740C22—881no—
741C22C2×C22⋊C4×D1111yescharacteristic
742C22#1062308311yescharacteristic
743C22#1062308411yescharacteristic
744C22D11×AGL(1,ℤ/8)11yescharacteristic
745C22D11×AGL(1,ℤ/8)11yescharacteristic
746C22#1062330511yescharacteristic
747C22#1062330911yescharacteristic
748C4—22no—
749C4—22no—
750C4—42no—
751C4—42no—
752C4—81no—
753C4—114no—
754C4—222no—
755C4—222no—
756C4—222no—
757C4—881no—
758C4—881no—
759C4C4×#433911yescharacteristic
760C4#1062305411yescharacteristic
761C4#1062308311yescharacteristic
762C4#1062308411yescharacteristic
763C2—82no—
764C2—882no—
765C2—882no—
766C2#1307145611yescharacteristic
767C2D11×#41811yescharacteristic
768C2#1307714011yescharacteristic
769C2#1308132411yescharacteristic
770C2#1308134611yescharacteristic
771C2#1308163711yescharacteristic
772C2#1308165911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1762C2
socleC23×C11C22×D4
prime radicalC2×#10623084C2
cosocleC22×C4×C11C24
hypercenter#1762D11
hypocenterC11#22545
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. C2×#10622314C2semidirect
3. #13071574C2semidirect
4. #13069543C2semidirect
5. #13069541C2semidirect
6. #13069541C2semidirect
7. #13069440C2semidirect
8. #13069438C2semidirect
9. #13069420C2semidirect
10. #13068626C2semidirect
11. #13068625C2semidirect
12. #13068615C2semidirect
13. #13068440C2semidirect
14. #13068430C2semidirect
15. C11×#1762C2semidirect
22. #10623084C4semidirect
213. C2×C8×C11#41semidirect
219. C11×C4⋊C4#41semidirect
260. #1762D11semidirect
604. C2×C8#4339semidirect
619. C4⋊C4#4339semidirect
632. C11#22545semidirect

Maximal subgroups

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

subgroupindex
C2×#106230842
C2×#106223142
#130715742
#130695432
#130695412
#130694402
#130694382
#130694202
#130686262
#130686252
#130686152
#130684402
#130684302
C11×#17622
#2254511