Finite Group Databasebeta

← #14788222

Subgroups — #14788222

Order 2816.

1206 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622679C211yesmaximal, characteristic, complemented
2C2×#10622685C211yesmaximal, characteristic, complemented
3#13071309C211yesmaximal, characteristic, complemented
4#13069802C211yesmaximal, characteristic, complemented
5#13069795C211yesmaximal, characteristic, complemented
6#13069612C211yesmaximal, characteristic, complemented
7#13069612C211yesmaximal, characteristic, complemented
8#13069574C211yesmaximal, characteristic, complemented
9#13069544C211yesmaximal, characteristic, complemented
10#13068964C211yesmaximal, characteristic, complemented
11#13068964C211yesmaximal, characteristic, complemented
12#13068877C211yesmaximal, characteristic, complemented
13#13068863C211yesmaximal, characteristic, complemented
14#13068600C211yesmaximal, characteristic, complemented
15C2×C11×#540C211yesmaximal, characteristic, complemented
16C11×#540—24no—
17C11×#540—24no—
18C2×C11×#127C2211yescharacteristic
19C2×C11×#125C2211yescharacteristic
20C2×C11×#123—21no—
21C2×C11×#123—21no—
22C2×C11×#121—21no—
23C2×C11×#121—21no—
24C2×C11×#121C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic
29C22×#4323C2211yescharacteristic
30C22×#4323C2211yescharacteristic
31C2×#66983C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39#10622825C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42#10622685—24no—
43#10622679—24no—
44#10622603—21no—
45#10622602—21no—
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66872C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50#10622570—21no—
51#10622569—21no—
52#10622552C2211yescharacteristic
53C4×C4⋊Dic11C2211yescharacteristic
54#10622541C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4⋊(C11⋊C8)C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11—21no—
65C22×D4×C11—21no—
66C22×D4×C11—21no—
67C22×D4×C11C2311yescharacteristic
68C22×D4×C11C2311yescharacteristic
69C23×C4×C11—21no—
70C23×C4×C11—21no—
71C23×C4×C11C2311yescharacteristic
72C22×C22⋊D11—21no—
73C22×D44C2311yescharacteristic
74C22×C4×D11—21no—
75C11×#127—22no—
76C11×#127D414yescomplemented
77C11×#125—22no—
78C11×#125D414yescomplemented
79C11×#123—28no—
80C11×#123—28no—
81C11×#121—28no—
82C11×#121—28no—
83C11×#121—22no—
84C11×#121—22no—
85C11×#121—22no—
86C11×#121—22no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C11×#117—22no—
92C11×#117—22no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4D411yescharacteristic
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4D411yescharacteristic
104C2×C11×C22⋊C4D411yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C2×C22⋊Dic11—21no—
108C2×#4323—22no—
109C2×#4323—22no—
110C2×#4323—22no—
111C2×#4323—22no—
112C2×#4323—41no—
113C2×#4323—41no—
114#66983—22no—
115#66983—22no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122C2×C4⋊Dic11C2311yescharacteristic
123C2×Dic11⋊C4—21no—
124C2×C4×Dic11—21no—
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C4×D44—22no—
130C4×D44—22no—
131#66896—22no—
132#66896—22no—
133#66896—22no—
134#66896—22no—
135#66896—41no—
136#66896—41no—
137C11⋊#95—21no—
138C11⋊#95—21no—
139C11⋊#95—21no—
140C22⋊(C11⋊C8)—41no—
141C22⋊(C11⋊C8)—41no—
142#66873—22no—
143#66873—22no—
144#66872—22no—
145#66871—22no—
146C4⋊(C11⋊C8)—22no—
147C4⋊(C11⋊C8)—22no—
148#24162—111nomaximal, Sylow
149C24×C11—21no—
150C24×C11—21no—
151C24×C11C2×D411yescharacteristic
152C23×D11—21no—
153C2×D4×C11—24no—
154C2×D4×C11—24no—
155C2×D4×C11—24no—
156C2×D4×C11—24no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—81no—
168C2×D4×C11—81no—
169C2×D4×C11—81no—
170C2×D4×C11—81no—
171C2×D4×C11—81no—
172C2×D4×C11—81no—
173C2×D4×C11—81no—
174C2×D4×C11—81no—
175C2×D4×C11C2×D412yes—
176C2×D4×C11C2×D412yes—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—24no—
180C22×C4×C11—24no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—81no—
188C22×C4×C11—81no—
189C22×C4×C11—81no—
190C22×C4×C11—81no—
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2411yescharacteristic
197C2×C22⋊D11—24no—
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—22no—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4C2×D412yes—
219C11×C4⋊C4C2×D412yes—
220C11×C22⋊C4—24no—
221C11×C22⋊C4—24no—
222C11×C22⋊C4—24no—
223C11×C22⋊C4—24no—
224C11×C22⋊C4—22no—
225C11×C22⋊C4—22no—
226C42×C11—21no—
227C42×C11—21no—
228C42×C11C2×D412yes—
229C42×C11C2×D412yes—
230C22⋊Dic11—81no—
231#4323—44no—
232#4323—44no—
233(C2×D11)⋊C4—24no—
234(C2×D11)⋊C4—42no—
235(C2×D11)⋊C4—81no—
236(C2×D11)⋊C4—81no—
237C4⋊Dic11—21no—
238C4⋊Dic11—21no—
239C4⋊Dic11—21no—
240C4⋊Dic11—21no—
241C4⋊Dic11—21no—
242C4⋊Dic11#4112yes—
243Dic11⋊C4—81no—
244C4×Dic11—81no—
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—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×#540D1111yescharacteristic, complemented
258C2×#478—111no—
259C2×#459—111no—
260#2324—111no—
261#2034—111no—
262#2033—111no—
263#1999—111no—
264#1999—111no—
265#1989—111no—
266#1982—111no—
267#1879—111no—
268#1879—111no—
269#1864—111no—
270#1862—111no—
271#1798—111no—
272C23×C11—21no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11C22×D411yescharacteristic
294C22×D11—22no—
295C22×D11—41no—
296C22×D11—41no—
297C22×D11—41no—
298C22×D11—41no—
299C22×D11—41no—
300C22×D11—41no—
301D4×C11—22no—
302D4×C11—22no—
303D4×C11—22no—
304D4×C11—22no—
305D4×C11—41no—
306D4×C11—41no—
307D4×C11—41no—
308D4×C11—41no—
309D4×C11—84no—
310D4×C11—84no—
311D4×C11—84no—
312D4×C11—84no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—84no—
337C2×C4×C11—84no—
338C2×C4×C11#12012yes—
339C2×C4×C11#12012yes—
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C2×#4111yescharacteristic
343C2×C4×C11C2×#4111yescharacteristic
344C2×C4×C11H(5,𝔽2)11yescharacteristic
345C2×C4×C112−1+411yescharacteristic
346C22⋊D11—84no—
347C2×Dic11—22no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356D44—22no—
357D44—22no—
358D44—41no—
359D44—41no—
360C4×D11—84no—
361C11⋊C8—41no—
362C11⋊C8—41no—
363C11⋊C8—41no—
364C11⋊C8—41no—
365C22×D8—111no—
366C22×D8—111no—
367#540—24no—
368#540—24no—
369C2×#127C2×D1111yescharacteristic
370C2×#125C2×D1111yescharacteristic
371C2×#123—21no—
372C2×#123—21no—
373C2×#121—21no—
374C2×#121—21no—
375C2×#121—111no—
376C2×#121C2×D1111yescharacteristic
377C2×#121C2×D1111yescharacteristic
378C2×C4×D4—111no—
379C2×C4×D4C2×D1111yescharacteristic
380C2×C4×D4C2×D1111yescharacteristic
381C2×#117C2×D1111yescharacteristic
382#478—224no—
383#459—224no—
384C2×#107—111no—
385C2×#106—111no—
386C2×C4⋊C8—111no—
387C2×C4⋊C8—111no—
388C2×#102—111no—
389C2×#102—111no—
390C2×#102—111no—
391C2×#102—111no—
392C2×#102—111no—
393C2×#102—111no—
394C2×#102—111no—
395C2×#102—111no—
396C2×C22⋊C8—111no—
397C2×C22⋊C8—111no—
398#390—111no—
399#390—221no—
400#389—111no—
401#388—221no—
402#386—221no—
403#385—221no—
404#380—111no—
405C4×C4⋊C4—111no—
406#340—111no—
407#340—111no—
408#340—111no—
409#340—111no—
410#336—111no—
411#336—111no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11—41no—
418C22×C11—41no—
419C22×C11—42no—
420C22×C11—41no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—41no—
424C22×C11—42no—
425C22×C11—81no—
426C22×C11—81no—
427C22×C11—81no—
428C22×C11—81no—
429C22×C11—81no—
430C22×C11—81no—
431C22×C11—81no—
432C22×C11—81no—
433C22×C11C2×#12011yescharacteristic
434C22×C11#52511yescharacteristic
435C22×C11#53711yescharacteristic
436C22×C11#57611yescharacteristic
437C22×C11#57611yescharacteristic
438C22×C11#57611yescharacteristic
439C22×C11#57711yescharacteristic
440C2×D11—42no—
441C2×D11—42no—
442C2×D11—42no—
443C2×D11—81no—
444C2×D11—81no—
445C2×D11—81no—
446C2×D11—81no—
447C4×C11—22no—
448C4×C11—22no—
449C4×C11—41no—
450C4×C11—41no—
451C4×C11—42no—
452C4×C11—41no—
453C4×C11—42no—
454C4×C11#54611yescharacteristic
455C4×C11#54711yescharacteristic
456C4×C11#54811yescharacteristic
457C4×C11#55011yescharacteristic
458Dic11—42no—
459Dic11—81no—
460Dic11—81no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—111no—
466C22×D4—221no—
467C22×D4C22×D1111yescharacteristic
468C22×D4C22×D1111yescharacteristic
469C23×C4—21no—
470C23×C4—21no—
471C23×C4—221no—
472C23×C4C22×D1111yescharacteristic
473C2×D8—222no—
474C2×D8—222no—
475C2×D8—222no—
476C2×D8—222no—
477C2×D8—441no—
478C2×D8—441no—
479C22×C8—111no—
480C22×C8—111no—
481C22×C8—111no—
482C22×C8—111no—
483#127—22no—
484#127C22⋊D1114yescomplemented
485#125—22no—
486#125C22⋊D1114yescomplemented
487#123—28no—
488#123—28no—
489#121—28no—
490#121—28no—
491#121—22no—
492#121—22no—
493#121—22no—
494#121—22no—
495#121—222no—
496#121—222no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—222no—
502C4×D4—222no—
503#117—22no—
504#117—22no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—111no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—111no—
510C2×C4⋊C4—221no—
511C2×C4⋊C4C22⋊D1111yescharacteristic
512C2×C4⋊C4C22⋊D1111yescharacteristic
513C2×C4⋊C4C22×D1111yescharacteristic
514C2×C4⋊C4C22×D1111yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C22⋊C4—221no—
522C2×C22⋊C4—221no—
523C2×C22⋊C4—221no—
524C2×C22⋊C4C22⋊D1111yescharacteristic
525C2×C22⋊C4C22⋊D1111yescharacteristic
526C2×C42—221no—
527C2×C42C22×D1111yescharacteristic
528C2×C42C22×D1111yescharacteristic
529#107—222no—
530#106—222no—
531C4⋊C8—222no—
532C4⋊C8—222no—
533#102—222no—
534#102—222no—
535#102—222no—
536#102—222no—
537#102—222no—
538#102—222no—
539#102—441no—
540#102—441no—
541C22⋊C8—441no—
542C22⋊C8—441no—
543#95—221no—
544#95—221no—
545#95—221no—
546C2×C11—81no—
547C2×C11—82no—
548C2×C11—82no—
549C2×C11#240711yescharacteristic
550C2×C11#300811yescharacteristic
551C2×C11#301211yescharacteristic
552C2×C11#311911yescharacteristic
553C2×C11#312211yescharacteristic
554C2×C11#325711yescharacteristic
555C2×C11#325911yescharacteristic
556D11—82no—
557C24—21no—
558C24—21no—
559C24—221no—
560C24C2×C22⋊D1111yescharacteristic
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—81no—
576C2×D4—81no—
577C2×D4—81no—
578C2×D4—81no—
579C2×D4—81no—
580C2×D4—81no—
581C2×D4—81no—
582C2×D4—81no—
583C2×D4—112no—
584C2×D4—224no—
585C2×D4—221no—
586C2×D4—221no—
587C2×D4—221no—
588C2×D4—221no—
589C2×D4—221no—
590C2×D4—881no—
591C2×D4—881no—
592C2×D4C2×C22⋊D1112yes—
593C2×D4C2×C22⋊D1112yes—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—81no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—442no—
612C22×C4—881no—
613C22×C4—881no—
614C22×C4C2×C22⋊D1111yescharacteristic
615C22×C4C2×C22⋊D1111yescharacteristic
616C22×C4C2×C22⋊D1111yescharacteristic
617C22×C4C2×C22⋊D1111yescharacteristic
618C22×C4C2×C22⋊D1111yescharacteristic
619C22×C4C23×D1111yescharacteristic
620D8—444no—
621D8—444no—
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—
631C2×C8—221no—
632C2×C8—221no—
633C2×C8—221no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—112no—
641C4⋊C4—221no—
642C4⋊C4—221no—
643C4⋊C4—221no—
644C4⋊C4—221no—
645C4⋊C4—221no—
646C4⋊C4—881no—
647C4⋊C4C2×C22⋊D1112yes—
648C4⋊C4C2×C22⋊D1112yes—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—224no—
656C22⋊C4—442no—
657C22⋊C4—881no—
658C22⋊C4—881no—
659C22⋊C4—881no—
660C42—21no—
661C42—21no—
662C42—881no—
663C42C2×C22⋊D1112yes—
664C42C2×C22⋊D1112yes—
665C11#2416211yescharacteristic, complemented, Sylow
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—22no—
674C23—22no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—222no—
688C23—441no—
689C23—441no—
690C23—441no—
691C23—441no—
692C23—441no—
693C23—441no—
694C23C22×C22⋊D1111yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—84no—
704D4—84no—
705D4—84no—
706D4—84no—
707D4—222no—
708D4—222no—
709D4—441no—
710D4—441no—
711D4—884no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—84no—
736C2×C4—84no—
737C2×C4—222no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—441no—
742C2×C4—441no—
743C2×C4—441no—
744C2×C4—441no—
745C2×C4—441no—
746C2×C4—884no—
747C2×C4#6700612yes—
748C2×C4#6700612yes—
749C2×C4#41×D1111yescharacteristic
750C2×C4#41×D1111yescharacteristic
751C2×C4#6704211yescharacteristic
752C2×C4#6704311yescharacteristic
753C2×C4C22×C22⋊D1111yescharacteristic
754C2×C4C22×C22⋊D1111yescharacteristic
755C8—441no—
756C8—441no—
757C8—441no—
758C8—441no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—41no—
766C22—42no—
767C22—42no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—41no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—442no—
781C22—442no—
782C22—442no—
783C22—881no—
784C22—881no—
785C22—881no—
786C22—881no—
787C22#1062335911yescharacteristic
788C22#1062336411yescharacteristic
789C22#1062336611yescharacteristic
790C22#1062336611yescharacteristic
791C22#1062336611yescharacteristic
792C22#1062336711yescharacteristic
793C22C2×#6700611yescharacteristic
794C4—22no—
795C4—22no—
796C4—41no—
797C4—41no—
798C4—42no—
799C4—41no—
800C4—42no—
801C4—442no—
802C4—881no—
803C4—881no—
804C4#1062335511yescharacteristic
805C4#1062336011yescharacteristic
806C4#1062336211yescharacteristic
807C4#1062336511yescharacteristic
808C2—81no—
809C2—82no—
810C2—82no—
811C2—882no—
812C2#1307195511yescharacteristic
813C2#1307788411yescharacteristic
814C2#1307792011yescharacteristic
815C2#1307880911yescharacteristic
816C2#1307885411yescharacteristic
817C2#1308002111yescharacteristic
818C2#1308005111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#540C2
socleC23×C11C22×D4
hypercenterC2×#540D11
hypocenterC11#24162
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×#10622679C2semidirect
2. C2×#10622685C2semidirect
3. #13071309C2semidirect
4. #13069802C2semidirect
5. #13069795C2semidirect
6. #13069612C2semidirect
7. #13069612C2semidirect
8. #13069574C2semidirect
9. #13069544C2semidirect
10. #13068964C2semidirect
11. #13068964C2semidirect
12. #13068877C2semidirect
13. #13068863C2semidirect
14. #13068600C2semidirect
15. C2×C11×#540C2semidirect
76. C11×#127D4semidirect
78. C11×#125D4semidirect
257. C2×#540D11semidirect
484. #127C22⋊D11semidirect
486. #125C22⋊D11semidirect
665. C11#24162semidirect

Maximal subgroups

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

subgroupindex
C2×#106226792
C2×#106226852
#130713092
#130698022
#130697952
#130696122
#130695742
#130695442
#130689642
#130688772
#130688632
#130686002
C2×C11×#5402
#2416211