Finite Group Databasebeta

← #14787748

Subgroups — #14787748

Order 2816.

1216 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622679C211yesmaximal, characteristic, complemented
2C2×C4×#4323C211yesmaximal, characteristic, complemented
3#13073517C211yesmaximal, characteristic, complemented
4#13069802C211yesmaximal, characteristic, complemented
5#13069795C211yesmaximal, characteristic, complemented
6#13069612C211yesmaximal, characteristic, complemented
7#13069612C211yesmaximal, characteristic, complemented
8#13069582C211yesmaximal, characteristic, complemented
9#13069411C211yesmaximal, characteristic, complemented
10#13068938C211yesmaximal, characteristic, complemented
11#13068933C211yesmaximal, characteristic, complemented
12#13068815C211yesmaximal, characteristic, complemented
13#13068804C211yesmaximal, characteristic, complemented
14#13068626C211yesmaximal, characteristic, complemented
15C2×C11×#553C211yesmaximal, characteristic, complemented
16C11×#553—24no—
17C11×#553—24no—
18C2×C11×#126—21no—
19C2×C11×#125C2211yescharacteristic
20C2×C11×#123—21no—
21C2×C11×#121—21no—
22C2×C11×#121C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×C4×D4×C11—21no—
25C2×C4×D4×C11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C11×#117C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C22×#4323C2211yescharacteristic
30C2×#66983C2211yescharacteristic
31C2×#66983C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33#10622836—21no—
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37#10622825C2211yescharacteristic
38#10622825C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43#10622679—24no—
44C4×#4323—24no—
45#10622606—21no—
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×#66871C2211yescharacteristic
51C2×#66871C2211yescharacteristic
52#10622569—21no—
53#10622569—21no—
54#10622549C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4×C11⋊C8C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11—21no—
65C22×D4×C11D411yescharacteristic
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C23×C4×C11—21no—
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C22×C22⋊D11—21no—
72C22×C22⋊D11—21no—
73C22×D44C2311yescharacteristic
74C22×C4×D11—21no—
75C11×#126—28no—
76C11×#125—22no—
77C11×#125D414yescomplemented
78C11×#123—28no—
79C11×#121—28no—
80C11×#121—22no—
81C11×#121—22no—
82C11×#121—22no—
83C11×#121—22no—
84C4×D4×C11—28no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11D414yescomplemented
89C11×#117—22no—
90C11×#117—22no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4D411yescharacteristic
105C2×C11×C22⋊C4D411yescharacteristic
106C2×C42×C11—21no—
107C2×C42×C11C2311yescharacteristic
108C2×C22⋊Dic11—21no—
109C2×C22⋊Dic11—21no—
110C2×#4323—22no—
111C2×#4323—22no—
112C2×#4323—22no—
113#66983—22no—
114#66983—22no—
115#66983—41no—
116#66983—41no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122C2×C4⋊Dic11C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C4×D44—22no—
128C4×D44—22no—
129#66896—22no—
130#66896—41no—
131#66896—41no—
132C11⋊#95—21no—
133C11⋊#95—21no—
134C11⋊#95—21no—
135C11⋊#95—21no—
136C22⋊(C11⋊C8)—22no—
137C22⋊(C11⋊C8)—22no—
138C22⋊(C11⋊C8)—41no—
139C22⋊(C11⋊C8)—41no—
140#66873—22no—
141#66873—22no—
142#66873—22no—
143#66872—22no—
144#66871—22no—
145#66871—22no—
146C4⋊(C11⋊C8)—22no—
147C4×C11⋊C8—22no—
148#24124—111nomaximal, Sylow
149C24×C11—21no—
150C24×C11C2×D411yescharacteristic
151C24×C11C2×D411yescharacteristic
152C23×D11—21no—
153C2×D4×C11—24no—
154C2×D4×C11—22no—
155C2×D4×C11—24no—
156C2×D4×C11—22no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—41no—
163C2×D4×C11—42no—
164C2×D4×C11—42no—
165C2×D4×C11—81no—
166C2×D4×C11—81no—
167C2×D4×C11C2×D412yes—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—24no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—24no—
185C22×C4×C11—81no—
186C22×C4×C11—81no—
187C22×C4×C11—81no—
188C22×C4×C11—81no—
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2411yescharacteristic
194C2×C22⋊D11—42no—
195C2×C22⋊D11—42no—
196C2×C22⋊D11—42no—
197C2×C22⋊D11—42no—
198C2×C22⋊D11—81no—
199C2×C22⋊D11—81no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C2×D44—21no—
204C2×D44—21no—
205C2×D44—21no—
206C2×D44—21no—
207C2×D44—21no—
208C2×D44#4112yes—
209C2×C4×D11—42no—
210C2×C4×D11—81no—
211C2×C4×D11—81no—
212C11×C4⋊C4—24no—
213C11×C4⋊C4—24no—
214C11×C4⋊C4—24no—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4C2×D412yes—
220C11×C4⋊C4C2×D412yes—
221C11×C4⋊C4C2×D412yes—
222C11×C22⋊C4—24no—
223C11×C22⋊C4—24no—
224C11×C22⋊C4—24no—
225C11×C22⋊C4—24no—
226C11×C22⋊C4—22no—
227C11×C22⋊C4—22no—
228C42×C11—24no—
229C42×C11C2×D412yes—
230C42×C11C2×D412yes—
231C22⋊Dic11—81no—
232C22⋊Dic11—81no—
233#4323—28no—
234(C2×D11)⋊C4—42no—
235(C2×D11)⋊C4—42no—
236(C2×D11)⋊C4—42no—
237C4⋊Dic11—21no—
238C4⋊Dic11—21no—
239C4⋊Dic11—21no—
240C4⋊Dic11—21no—
241C4⋊Dic11—21no—
242C4⋊Dic11—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8#4112yes—
255C2×#553D1111yescharacteristic, complemented
256C2×#478—111no—
257C2×C4×D8—111no—
258#2535—111no—
259#2034—111no—
260#2033—111no—
261#1999—111no—
262#1999—111no—
263#1991—111no—
264#1954—111no—
265#1875—111no—
266#1874—111no—
267#1854—111no—
268#1852—111no—
269#1804—111no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—22no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11#13512yes—
291C23×C11C22×D411yescharacteristic
292C22×D11—22no—
293C22×D11—41no—
294C22×D11—41no—
295C22×D11—41no—
296C22×D11—41no—
297C22×D11—41no—
298C22×D11—41no—
299D4×C11—22no—
300D4×C11—22no—
301D4×C11—44no—
302D4×C11—48no—
303D4×C11—41no—
304D4×C11—41no—
305D4×C11—84no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—21no—
314C2×C4×C11—22no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—84no—
334C2×C4×C11—84no—
335C2×C4×C11#12012yes—
336C2×C4×C11#12012yes—
337C2×C4×C11C22×D411yescharacteristic
338C2×C4×C11C22×D411yescharacteristic
339C2×C4×C11C2×#4111yescharacteristic
340C2×C4×C11C2×#4111yescharacteristic
341C2×C4×C11H(5,𝔽2)11yescharacteristic
342C2×C4×C112−1+411yescharacteristic
343C22⋊D11—84no—
344C22⋊D11—84no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354D44—22no—
355D44—22no—
356D44—41no—
357D44—41no—
358C4×D11—84no—
359C11⋊C8—22no—
360C11⋊C8—41no—
361C11⋊C8—41no—
362C11⋊C8—41no—
363C22×D8—111no—
364#553—24no—
365#553—24no—
366C2×#126—21no—
367C2×#125C2×D1111yescharacteristic
368C2×#123—21no—
369C2×#121—21no—
370C2×#121—111no—
371C2×#121—111no—
372C2×#121C2×D1111yescharacteristic
373C2×#121C2×D1111yescharacteristic
374C2×C4×D4—21no—
375C2×C4×D4—111no—
376C2×C4×D4C2×D1111yescharacteristic
377C2×C4×D4C2×D1111yescharacteristic
378C2×#117C2×D1111yescharacteristic
379C22×C4⋊C4C2×D1111yescharacteristic
380#478—224no—
381C4×D8—224no—
382C2×#107—111no—
383C2×#107—111no—
384C2×#106—111no—
385C2×C4⋊C8—111no—
386C2×#102—111no—
387C2×#102—111no—
388C2×#102—111no—
389C2×#102—111no—
390C2×#102—111no—
391C2×#102—111no—
392C2×C22⋊C8—111no—
393C2×C22⋊C8—111no—
394C2×C22⋊C8—111no—
395C2×C22⋊C8—111no—
396C2×C4×C8—111no—
397#397—221no—
398#392—221no—
399#386—221no—
400#386—221no—
401#382—111no—
402#380—111no—
403#380—111no—
404#340—111no—
405#340—111no—
406#340—111no—
407#340—111no—
408#340—111no—
409#340—111no—
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—41no—
416C22×C11—41no—
417C22×C11—41no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—42no—
421C22×C11—41no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—41no—
425C22×C11—41no—
426C22×C11—41no—
427C22×C11—81no—
428C22×C11—81no—
429C22×C11—81no—
430C22×C11—81no—
431C22×C11C2×#12011yescharacteristic
432C22×C11#54611yescharacteristic
433C22×C11#54711yescharacteristic
434C22×C11C2×#13511yescharacteristic
435C22×C11#57511yescharacteristic
436C22×C11#57611yescharacteristic
437C22×C11#57611yescharacteristic
438C2×D11—42no—
439C2×D11—42no—
440C2×D11—42no—
441C2×D11—81no—
442C2×D11—81no—
443C2×D11—81no—
444C2×D11—81no—
445C4×C11—22no—
446C4×C11—22no—
447C4×C11—41no—
448C4×C11—41no—
449C4×C11—42no—
450C4×C11—42no—
451C4×C11—42no—
452C4×C11#52511yescharacteristic
453C4×C11#53711yescharacteristic
454C4×C11#54811yescharacteristic
455C4×C11#55011yescharacteristic
456Dic11—81no—
457Dic11—81no—
458Dic11—81no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—111no—
462C22×D4—221no—
463C22×D4—221no—
464C22×D4C22⋊D1111yescharacteristic
465C22×D4C22×D1111yescharacteristic
466C23×C4—21no—
467C23×C4—21no—
468C23×C4—221no—
469C23×C4C22×D1111yescharacteristic
470C23×C4C22×D1111yescharacteristic
471C2×D8—222no—
472C2×D8—222no—
473C2×D8—222no—
474C22×C8—111no—
475C22×C8—111no—
476C22×C8—111no—
477C22×C8—111no—
478#126—28no—
479#125—22no—
480#125C22⋊D1114yescomplemented
481#123—28no—
482#121—28no—
483#121—22no—
484#121—22no—
485#121—22no—
486#121—22no—
487#121—222no—
488#121—222no—
489#121—441no—
490#121—441no—
491C4×D4—28no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—222no—
496C4×D4—222no—
497C4×D4C22⋊D1114yescomplemented
498#117—22no—
499#117—22no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—111no—
506C2×C4⋊C4—111no—
507C2×C4⋊C4—111no—
508C2×C4⋊C4C22⋊D1111yescharacteristic
509C2×C4⋊C4C22×D1111yescharacteristic
510C2×C4⋊C4C22×D1111yescharacteristic
511C2×C4⋊C4C22×D1111yescharacteristic
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—221no—
517C2×C22⋊C4—221no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C22⋊C4C22⋊D1111yescharacteristic
522C2×C22⋊C4C22⋊D1111yescharacteristic
523C2×C42—21no—
524C2×C42C22×D1111yescharacteristic
525#107—222no—
526#107—222no—
527#106—222no—
528C4⋊C8—222no—
529#102—222no—
530#102—222no—
531#102—222no—
532#102—222no—
533#102—441no—
534#102—441no—
535C22⋊C8—222no—
536C22⋊C8—222no—
537C22⋊C8—441no—
538C22⋊C8—441no—
539C4×C8—222no—
540#95—221no—
541#95—221no—
542#95—221no—
543#95—221no—
544C2×C11—42no—
545C2×C11—81no—
546C2×C11—82no—
547C2×C11#240711yescharacteristic
548C2×C11#300211yescharacteristic
549C2×C11#300811yescharacteristic
550C2×C11#329711yescharacteristic
551C2×C11#332211yescharacteristic
552C2×C11#333911yescharacteristic
553C2×C11#335511yescharacteristic
554D11—82no—
555C24—21no—
556C24—221no—
557C24C2×C22⋊D1111yescharacteristic
558C24C2×C22⋊D1111yescharacteristic
559C2×D4—24no—
560C2×D4—22no—
561C2×D4—24no—
562C2×D4—22no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—41no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4—112no—
574C2×D4—221no—
575C2×D4—221no—
576C2×D4—221no—
577C2×D4—221no—
578C2×D4—221no—
579C2×D4—442no—
580C2×D4—442no—
581C2×D4—442no—
582C2×D4—442no—
583C2×D4—881no—
584C2×D4—881no—
585C2×D4C2×C22⋊D1112yes—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—24no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—24no—
603C22×C4—81no—
604C22×C4—81no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—221no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—442no—
611C22×C4—881no—
612C22×C4—881no—
613C22×C4C2×C22⋊D1111yescharacteristic
614C22×C4C2×C22⋊D1111yescharacteristic
615C22×C4C2×C22⋊D1111yescharacteristic
616C22×C4C2×C22⋊D1111yescharacteristic
617C22×C4C23×D1111yescharacteristic
618D8—228no—
619C2×C8—112no—
620C2×C8—221no—
621C2×C8—221no—
622C2×C8—221no—
623C2×C8—221no—
624C2×C8—221no—
625C2×C8—221no—
626C2×C8—221no—
627C2×C8—221no—
628C2×C8—221no—
629C2×C8—221no—
630C2×C8—221no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—22no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—221no—
639C4⋊C4—221no—
640C4⋊C4—221no—
641C4⋊C4—221no—
642C4⋊C4—221no—
643C4⋊C4—221no—
644C4⋊C4C2×C22⋊D1112yes—
645C4⋊C4C2×C22⋊D1112yes—
646C4⋊C4C2×C22⋊D1112yes—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—442no—
654C22⋊C4—442no—
655C22⋊C4—442no—
656C22⋊C4—881no—
657C22⋊C4—881no—
658C42—24no—
659C42C2×C22⋊D1112yes—
660C42C2×C22⋊D1112yes—
661C11#2412411yescharacteristic, complemented, Sylow
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—222no—
683C23—441no—
684C23—441no—
685C23—441no—
686C23—441no—
687C23—441no—
688C23—441no—
689C23#6700312yes—
690C23C22×C22⋊D1111yescharacteristic
691D4—22no—
692D4—22no—
693D4—44no—
694D4—48no—
695D4—41no—
696D4—41no—
697D4—84no—
698D4—222no—
699D4—222no—
700D4—441no—
701D4—441no—
702D4—884no—
703D4—884no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—84no—
732C2×C4—84no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—441no—
742C2×C4—884no—
743C2×C4#6700612yes—
744C2×C4#6700612yes—
745C2×C4#41×D1111yescharacteristic
746C2×C4#41×D1111yescharacteristic
747C2×C4#6704211yescharacteristic
748C2×C4#6704311yescharacteristic
749C2×C4C22×C22⋊D1111yescharacteristic
750C2×C4C22×C22⋊D1111yescharacteristic
751C8—222no—
752C8—441no—
753C8—441no—
754C8—441no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—442no—
777C22—442no—
778C22—442no—
779C22—881no—
780C22—881no—
781C22—881no—
782C22—881no—
783C22C2×#6700311yescharacteristic
784C22#1062335311yescharacteristic
785C22#1062335511yescharacteristic
786C22#1062336011yescharacteristic
787C22#1062336611yescharacteristic
788C22#1062336611yescharacteristic
789C22C2×#6700611yescharacteristic
790C4—22no—
791C4—22no—
792C4—42no—
793C4—41no—
794C4—41no—
795C4—42no—
796C4—42no—
797C4—881no—
798C4—881no—
799C4—881no—
800C4#1062335911yescharacteristic
801C4#1062336211yescharacteristic
802C4#1062336411yescharacteristic
803C4#1062336511yescharacteristic
804C2—42no—
805C2—81no—
806C2—82no—
807C2—882no—
808C2#1307195511yescharacteristic
809C2#1307783411yescharacteristic
810C2#1307788411yescharacteristic
811C2#1308046011yescharacteristic
812C2#1308081111yescharacteristic
813C2#1308101211yescharacteristic
814C2#1308121611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#553C2
socleC23×C11C22×D4
hypercenterC2×#553D11
hypocenterC11#24124
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#10622679C2semidirect
2. C2×C4×#4323C2semidirect
3. #13073517C2semidirect
4. #13069802C2semidirect
5. #13069795C2semidirect
6. #13069612C2semidirect
7. #13069612C2semidirect
8. #13069582C2semidirect
9. #13069411C2semidirect
10. #13068938C2semidirect
11. #13068933C2semidirect
12. #13068815C2semidirect
13. #13068804C2semidirect
14. #13068626C2semidirect
15. C2×C11×#553C2semidirect
77. C11×#125D4semidirect
88. C4×D4×C11D4semidirect
255. C2×#553D11semidirect
480. #125C22⋊D11semidirect
497. C4×D4C22⋊D11semidirect
661. C11#24124semidirect

Maximal subgroups

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

subgroupindex
C2×#106226792
C2×C4×#43232
#130735172
#130698022
#130697952
#130696122
#130695822
#130694112
#130689382
#130689332
#130688152
#130688042
#130686262
C2×C11×#5532
#2412411