Finite Group Databasebeta

← #14774161

Subgroups — #14774161

Order 2816.

1190 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×#10622851C211yesmaximal, characteristic
2C2×#10622639C211yesmaximal, characteristic, complemented
3C2×#10622845C211yesmaximal, characteristic, complemented
4#13071630C211yesmaximal, characteristic, complemented
5#13069481C211yesmaximal, characteristic, complemented
6#13069316C211yesmaximal, characteristic, complemented
7#13069233C211yesmaximal, characteristic, complemented
8#13069052C211yesmaximal, characteristic, complemented
9#13068971C211yesmaximal, characteristic, complemented
10#13068967C211yesmaximal, characteristic, complemented
11#13068870C211yesmaximal, characteristic, complemented
12#13068803C211yesmaximal, characteristic, complemented
13C4×#66899C211yesmaximal, characteristic, complemented
14#13068400C211yesmaximal, characteristic, complemented
15C11×#2341C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C22×#4323C2211yescharacteristic
21C2×#66983C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24C2×(C22⋊D11)⋊C4—21no—
25C2×C4×D44C2211yescharacteristic
26C11×#390—21no—
27C11×#390—21no—
28C11×#390C2211yescharacteristic
29C11×#390C2211yescharacteristic
30C11×#380—21no—
31C11×#380C2211yescharacteristic
32C4×C11×C22⋊C4—21no—
33C4×C11×C22⋊C4C2211yescharacteristic
34#10622851C418yescomplemented
35#10622845—24no—
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43#10622639—24no—
44C2×#66873C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48#10622571—21no—
49#10622552C2211yescharacteristic
50C4×C4⋊Dic11C2211yescharacteristic
51#10622541C2211yescharacteristic
52C2×#66867C2211yescharacteristic
53C2×C4×C11⋊C8C2211yescharacteristic
54#10622283—21no—
55#10622281—21no—
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61#10622162C2211yescharacteristic
62C2×C11×#41—22no—
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—41no—
66C2×C11×#41—41no—
67C2×C11×#41C2×C414yescomplemented
68C22×Q8×C11C2311yescharacteristic
69C22×D4×C11—21no—
70C22×D4×C11C2311yescharacteristic
71C23×C4×C11—21no—
72C23×C4×C11C2311yescharacteristic
73C22×C22⋊D11—21no—
74C23×Dic11—21no—
75C22×D44C2311yescharacteristic
76C22×C4×D11—21no—
77C4×Q8×C11—22no—
78C4×Q8×C11—22no—
79C4×Q8×C11—41no—
80C4×Q8×C11—41no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4D411yescharacteristic
91C2×C11×C22⋊C4D411yescharacteristic
92C2×C42×C11—21no—
93C2×C42×C11—21no—
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×#4325—22no—
97C2×#4325—22no—
98C2×#4325C2×C414yescomplemented
99C2×#4323—41no—
100C2×#4323—41no—
101C2×#4323C2×C414yescomplemented
102#66983—22no—
103#66983C2×C414yes—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×C4⋊Dic11—22no—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11—41no—
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114C2×Dic11⋊C4—21no—
115C2×C4×Dic11—21no—
116C2×#4318—22no—
117C2×#4318—22no—
118C2×#4318—41no—
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123(C22⋊D11)⋊C4—44no—
124C4×D44—22no—
125C4×D44—41no—
126C11×#95—21no—
127C11×#95D411yescharacteristic
128C11×#95D411yescharacteristic
129#66899—22no—
130#66899C2×C414yescomplemented
131#66899D414yescomplemented
132#66896—22no—
133#66896—22no—
134#66896C2×C414yescomplemented
135C11⋊#95—21no—
136C11⋊#95—21no—
137C22⋊(C11⋊C8)C2×C414yescomplemented
138#66873—22no—
139#66873—41no—
140#66871—22no—
141#66871—41no—
142#66867—22no—
143C4×C11⋊C8—41no—
144#22863—111nomaximal, Sylow
145C24×C11—21no—
146C24×C11C2×D411yescharacteristic
147C23×D11—21no—
148C11×#41—28no—
149C11×#41—44no—
150C11×#41—44no—
151C11×#41—44no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11C22×C412yes—
156C2×Q8×C11C2×D412yes—
157C2×Q8×C11#4112yes—
158C2×D4×C11—24no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—42no—
165C2×D4×C11—42no—
166C2×D4×C11C22×C412yes—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—24no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—42no—
176C22×C4×C11—42no—
177C22×C4×C11C22×C412yes—
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11#4112yes—
184C22×C4×C11C2411yescharacteristic
185C2×C22⋊D11—24no—
186C2×C22⋊D11—42no—
187C2×C22⋊D11—42no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—42no—
192C22×Dic11—42no—
193C22×Dic11—81no—
194C2×D44—21no—
195C2×D44—21no—
196C2×D44—21no—
197C2×D44—21no—
198C2×D44—21no—
199C2×D44C22×C412yes—
200C2×C4×D11—42no—
201C2×C4×D11—42no—
202C2×C4×D11—81no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—42no—
208C11×C4⋊C4—42no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—41no—
211C11×C22⋊C4—42no—
212C11×C22⋊C4—42no—
213C11×C22⋊C4—81no—
214C11×C22⋊C4—81no—
215C11×C22⋊C4—81no—
216C42×C11—21no—
217C42×C11—21no—
218C42×C11—21no—
219C42×C11—21no—
220C42×C11—42no—
221C42×C11—42no—
222#4325—28no—
223#4323—44no—
224(C2×D11)⋊C4—24no—
225(C2×D11)⋊C4—42no—
226(C2×D11)⋊C4—42no—
227(C2×D11)⋊C4—81no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11—42no—
233C4⋊Dic11C22×C412yes—
234C4⋊Dic11C2×D412yes—
235Dic11⋊C4—42no—
236C4×Dic11—42no—
237#4318—44no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
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×C11⋊C8C22×C412yes—
248C2×C11⋊C8C22×C412yes—
249C2×C11⋊C8C2×D412yes—
250C2×#449—111no—
251C2×#440—111no—
252C2×#417—111no—
253#2361—111no—
254#2341D1111yescharacteristic, complemented
255#1970—111no—
256#1936—111no—
257#1925—111no—
258#1895—111no—
259#1880—111no—
260#1879—111no—
261#1863—111no—
262#1852—111no—
263C4×#103—111no—
264#1753—111no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—22no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11C4×D412yes—
279C23×C11C22×D411yescharacteristic
280C22×D11—22no—
281C22×D11—41no—
282C22×D11—41no—
283C22×D11—41no—
284C22×D11—41no—
285C22×D11—41no—
286C22×D11—41no—
287Q8×C11—22no—
288Q8×C11—22no—
289Q8×C11—22no—
290Q8×C11C4×D414yescomplemented
291D4×C11—22no—
292D4×C11—22no—
293D4×C11—48no—
294D4×C11—41no—
295D4×C11—41no—
296C2×C4×C11—22no—
297C2×C4×C11—21no—
298C2×C4×C11—22no—
299C2×C4×C11—21no—
300C2×C4×C11—22no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—48no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11C4×D412yes—
324C2×C4×C11AGL(1,ℤ/8)12yes—
325C2×C4×C11C23×C411yescharacteristic
326C2×C4×C11C22×D411yescharacteristic
327C2×C4×C11C2×#4111yescharacteristic
328C2×C4×C11C2×#4111yescharacteristic
329C2×C4×C11H(5,𝔽2)11yescharacteristic
330C2×C4×C11H(5,𝔽2)11yescharacteristic
331C22⋊D11—48no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—84no—
342D44—22no—
343D44—22no—
344D44—41no—
345D44—41no—
346C4×D11—84no—
347C11⋊C8—22no—
348C11⋊C8—22no—
349C11⋊C8—22no—
350C11⋊C8—41no—
351C22×#41C2×D1111yescharacteristic
352C22×SD16—111no—
353C22×D8—111no—
354C22×M16—111no—
355C2×#121—111no—
356C2×C4×Q8C2×D1111yescharacteristic
357C2×C4×Q8C2×D1111yescharacteristic
358C2×C4×D4—111no—
359C2×C4×D4—221no—
360C22×C4⋊C4—111no—
361#449—118no—
362#440—224no—
363C2×#107—111no—
364C2×#107—111no—
365#417—224no—
366C2×#103—111no—
367C2×#103—111no—
368C2×#103—111no—
369C2×#102—111no—
370C2×#102—111no—
371C2×#102—111no—
372C2×#102—111no—
373C2×#102—111no—
374C2×C22⋊C8—111no—
375C2×#97—111no—
376C2×C4×C8—111no—
377#390—21no—
378#390—21no—
379#390—111no—
380#390C2×D1111yescharacteristic
381#390C2×D1111yescharacteristic
382#389—111no—
383#388—221no—
384#386—221no—
385#385—221no—
386#380—21no—
387#380C2×D1111yescharacteristic
388C4×C4⋊C4—111no—
389C4×C22⋊C4—21no—
390C4×C22⋊C4C2×D1111yescharacteristic
391#340—111no—
392#340—111no—
393#340—111no—
394#340—111no—
395#336—111no—
396#336—111no—
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—22no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—42no—
405C22×C11—42no—
406C22×C11—42no—
407C22×C11—81no—
408C22×C11—81no—
409C22×C11—81no—
410C22×C11—81no—
411C22×C11C2×C4×D411yescharacteristic
412C22×C11D4211yescharacteristic
413C22×C11#54611yescharacteristic
414C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
415C22×C11#57511yescharacteristic
416C22×C11#57611yescharacteristic
417C22×C11#57811yescharacteristic
418C2×D11—42no—
419C2×D11—42no—
420C2×D11—42no—
421C2×D11—81no—
422C2×D11—81no—
423C2×D11—81no—
424C2×D11—81no—
425C4×C11—22no—
426C4×C11—24no—
427C4×C11—22no—
428C4×C11—41no—
429C4×C11—41no—
430C4×C11—41no—
431C4×C11—81no—
432C4×C11—81no—
433C4×C11C2×C4×D411yescharacteristic
434C4×C11#51811yescharacteristic
435C4×C11#54611yescharacteristic
436C4×C11#55111yescharacteristic
437Dic11—42no—
438Dic11—42no—
439Dic11—81no—
440C2×#41—22no—
441C2×#41—22no—
442C2×#41—22no—
443C2×#41—41no—
444C2×#41—41no—
445C2×#41C4×D1114yescomplemented
446C22×Q8C22×D1111yescharacteristic
447C22×D4—21no—
448C22×D4—111no—
449C22×D4—221no—
450C22×D4C22×D1111yescharacteristic
451C23×C4—21no—
452C23×C4—221no—
453C23×C4—221no—
454C23×C4C22×D1111yescharacteristic
455C2×SD16—114no—
456C2×SD16—222no—
457C2×SD16—222no—
458C2×D8—114no—
459C2×D8—441no—
460C2×D8—441no—
461C2×M16—222no—
462C2×M16—222no—
463C2×M16—441no—
464C22×C8—111no—
465C22×C8—111no—
466C22×C8—111no—
467C22×C8—111no—
468#121—114no—
469#121—222no—
470C4×Q8—22no—
471C4×Q8—22no—
472C4×Q8—41no—
473C4×Q8—41no—
474C4×D4—222no—
475C4×D4—441no—
476C4×D4—444no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—111no—
480C2×C4⋊C4—111no—
481C2×C4⋊C4—111no—
482C2×C4⋊C4—222no—
483C2×C4⋊C4—221no—
484C2×C4⋊C4—221no—
485C2×C4⋊C4—441no—
486C2×C4⋊C4C22×D1111yescharacteristic
487C2×C4⋊C4C22×D1111yescharacteristic
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—221no—
494C2×C22⋊C4—221no—
495C2×C22⋊C4—221no—
496C2×C22⋊C4—221no—
497C2×C22⋊C4C22⋊D1111yescharacteristic
498C2×C22⋊C4C22⋊D1111yescharacteristic
499C2×C42—21no—
500C2×C42—21no—
501C2×C42—221no—
502C2×C42C22×D1111yescharacteristic
503C2×C42C22×D1111yescharacteristic
504#107—222no—
505#107—441no—
506#103—114no—
507#103—114no—
508#103—222no—
509#102—114no—
510#102—222no—
511#102—222no—
512#102—222no—
513#102—441no—
514C22⋊C8—114no—
515#97—222no—
516C4×C8—441no—
517#95—21no—
518#95—221no—
519#95—221no—
520#95C22⋊D1111yescharacteristic
521#95C22⋊D1111yescharacteristic
522C2×C11—42no—
523C2×C11—82no—
524C2×C11#235811yescharacteristic
525C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
526C2×C11#295111yescharacteristic
527C2×C11#327411yescharacteristic
528C2×C11#327711yescharacteristic
529C2×C11#330811yescharacteristic
530C2×C11#330911yescharacteristic
531D11—82no—
532C24—21no—
533C24—221no—
534C24C2×C22⋊D1111yescharacteristic
535#41—28no—
536#41—44no—
537#41—44no—
538#41—44no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8C2×C4×D1112yes—
543C2×Q8D4×D1112yes—
544C2×Q8#434112yes—
545C2×D4—24no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—112no—
554C2×D4—224no—
555C2×D4—221no—
556C2×D4—221no—
557C2×D4—221no—
558C2×D4—221no—
559C2×D4—221no—
560C2×D4—442no—
561C2×D4—442no—
562C2×D4C2×C4×D1112yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—24no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—221no—
576C22×C4—442no—
577C22×C4—442no—
578C22×C4—442no—
579C22×C4—442no—
580C22×C4—881no—
581C22×C4—881no—
582C22×C4C2×C4×D1112yes—
583C22×C4#433912yes—
584C22×C4C2×C22⋊D1111yescharacteristic
585C22×C4C2×C22⋊D1111yescharacteristic
586C22×C4C2×C22⋊D1111yescharacteristic
587C22×C4C2×C22⋊D1111yescharacteristic
588C22×C4C2×C22⋊D1111yescharacteristic
589C22×C4C23×D1111yescharacteristic
590SD16—228no—
591D8—444no—
592M16—444no—
593C2×C8—112no—
594C2×C8—112no—
595C2×C8—112no—
596C2×C8—221no—
597C2×C8—221no—
598C2×C8—221no—
599C2×C8—221no—
600C2×C8—221no—
601C2×C8—221no—
602C2×C8—221no—
603C2×C8—221no—
604C2×C8—221no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—112no—
612C4⋊C4—112no—
613C4⋊C4—221no—
614C4⋊C4—221no—
615C4⋊C4—221no—
616C4⋊C4—221no—
617C4⋊C4—442no—
618C4⋊C4—442no—
619C22⋊C4—22no—
620C22⋊C4—41no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—81no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4—224no—
627C22⋊C4—442no—
628C22⋊C4—442no—
629C22⋊C4—881no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—42no—
635C42—42no—
636C42—442no—
637C11#2286311yescharacteristic, complemented, Sylow
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—22no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—222no—
652C23—441no—
653C23—441no—
654C23—441no—
655C23—441no—
656C23—441no—
657C23—441no—
658C23C4×C22⋊D1112yes—
659C23C22×C22⋊D1111yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—22no—
663Q8(C22⋊D11)⋊C414yescomplemented
664D4—22no—
665D4—22no—
666D4—48no—
667D4—41no—
668D4—41no—
669D4—222no—
670D4—222no—
671D4—448no—
672D4—441no—
673D4—441no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—48no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—441no—
704C2×C4—441no—
705C2×C4—441no—
706C2×C4—441no—
707C2×C4—441no—
708C2×C4—441no—
709C2×C4—441no—
710C2×C4—884no—
711C2×C4—884no—
712C2×C4C4×C22⋊D1112yes—
713C2×C4#6700212yes—
714C2×C4C22×C4×D1111yescharacteristic
715C2×C4C2×#433911yescharacteristic
716C2×C4C2×D4×D1111yescharacteristic
717C2×C4C2×#434111yescharacteristic
718C2×C4#6703711yescharacteristic
719C2×C4#6703711yescharacteristic
720C8—222no—
721C8—222no—
722C8—222no—
723C8—441no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—442no—
739C22—442no—
740C22—442no—
741C22—881no—
742C22—881no—
743C22—881no—
744C22—881no—
745C22C2×C4×C22⋊D1111yescharacteristic
746C22D4×C22⋊D1111yescharacteristic
747C22#1062333711yescharacteristic
748C22C2×#6700211yescharacteristic
749C22#1062335311yescharacteristic
750C22#1062336611yescharacteristic
751C22#1062336911yescharacteristic
752C4—22no—
753C4—22no—
754C4—24no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—81no—
759C4—81no—
760C4—442no—
761C4—442no—
762C4—881no—
763C4C2×(C22⋊D11)⋊C411yescharacteristic
764C4#1062301711yescharacteristic
765C4#1062302111yescharacteristic
766C4#1062302611yescharacteristic
767C2—42no—
768C2—82no—
769C2—882no—
770C2#1307159511yescharacteristic
771C2C4×#6700211yescharacteristic
772C2#1307748911yescharacteristic
773C2#1308023611yescharacteristic
774C2#1308026911yescharacteristic
775C2#1308060711yescharacteristic
776C2#1308062211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2341C2
socleC23×C11C22×D4
prime radicalC2×#10622851C2
cosocleC22×C4×C11C24
hypercenter#2341D11
hypocenterC11#22863
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×#10622639C2semidirect
3. C2×#10622845C2semidirect
4. #13071630C2semidirect
5. #13069481C2semidirect
6. #13069316C2semidirect
7. #13069233C2semidirect
8. #13069052C2semidirect
9. #13068971C2semidirect
10. #13068967C2semidirect
11. #13068870C2semidirect
12. #13068803C2semidirect
13. C4×#66899C2semidirect
14. #13068400C2semidirect
15. C11×#2341C2semidirect
34. #10622851C4semidirect
67. C2×C11×#41C2×C4semidirect
98. C2×#4325C2×C4semidirect
101. C2×#4323C2×C4semidirect
130. #66899C2×C4semidirect
131. #66899D4semidirect
134. #66896C2×C4semidirect
137. C22⋊(C11⋊C8)C2×C4semidirect
254. #2341D11semidirect
290. Q8×C11C4×D4semidirect
445. C2×#41C4×D11semidirect
637. C11#22863semidirect
663. Q8(C22⋊D11)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#106228512
C2×#106226392
C2×#106228452
#130716302
#130694812
#130693162
#130692332
#130690522
#130689712
#130689672
#130688702
#130688032
C4×#668992
#130684002
C11×#23412
#2286311