Finite Group Databasebeta

← #14788740

Subgroups — #14788740

Order 2816.

1208 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622670C211yesmaximal, characteristic, complemented
2C2×#10622627C211yesmaximal, characteristic, complemented
3#13073534C211yesmaximal, characteristic, complemented
4#13069852C211yesmaximal, characteristic, complemented
5#13069847C211yesmaximal, characteristic, complemented
6#13069693C211yesmaximal, characteristic, complemented
7#13069687C211yesmaximal, characteristic
8#13069557C211yesmaximal, characteristic, complemented
9#13069433C211yesmaximal, characteristic, complemented
10#13068971C211yesmaximal, characteristic, complemented
11#13068964C211yesmaximal, characteristic, complemented
12#13068884C211yesmaximal, characteristic, complemented
13#13068877C211yesmaximal, characteristic, complemented
14#13068616C211yesmaximal, characteristic, complemented
15C2×C11×#559C211yesmaximal, characteristic, complemented
16C11×#559—24no—
17C11×#559—24no—
18C2×C11×#127C2211yescharacteristic
19C2×C11×#124—21no—
20C2×C11×#124C2211yescharacteristic
21C2×C11×#124C2211yescharacteristic
22C2×C11×#123—21no—
23C2×C11×#123—21no—
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×D4×C11—21no—
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×#66999—21no—
30C22×#4325C2211yescharacteristic
31C22×#4323C2211yescharacteristic
32C22×#4323C2211yescharacteristic
33C2×C4×D44C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43#10622670—24no—
44#10622627—24no—
45#10622607—21no—
46#10622607—21no—
47#10622600—21no—
48C2×#66873C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50#10622552C2211yescharacteristic
51#10622552C2211yescharacteristic
52#10622548C2211yescharacteristic
53#10622541C2211yescharacteristic
54#10622541C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×#66867C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11D411yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11—21no—
66C22×D4×C11—21no—
67C22×D4×C11C2311yescharacteristic
68C22×D4×C11C2311yescharacteristic
69C23×C4×C11—21no—
70C23×C4×C11—21no—
71C22×D44C2311yescharacteristic
72C22×C4×D11—21no—
73C11×#127—22no—
74C11×#127—22no—
75C11×#124—28no—
76C11×#124—22no—
77C11×#124—22no—
78C11×#124—22no—
79C11×#124D414yes—
80C11×#123—28no—
81C11×#123—28no—
82C4×Q8×C11—22no—
83C4×Q8×C11—22no—
84C4×Q8×C11—22no—
85C4×Q8×C11—22no—
86C4×D4×C11—28no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11—22no—
90C4×D4×C11D414yes—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4D411yescharacteristic
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C42×C11—21no—
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106#66999—44no—
107C2×#4325—22no—
108C2×#4325—22no—
109C2×#4325—41no—
110C2×#4323—22no—
111C2×#4323—22no—
112C2×#4323—22no—
113C2×#4323—22no—
114C2×#4323—22no—
115C2×#4323—41no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×C4⋊Dic11—21no—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C22×C11⋊C8C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132C4×D44—22no—
133C4×D44—22no—
134#66899—22no—
135#66899—22no—
136#66899—41no—
137#66896—22no—
138#66896—22no—
139#66896—22no—
140#66896—41no—
141#66896—41no—
142#66896—41no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145#66873—22no—
146#66872—22no—
147C4⋊(C11⋊C8)—22no—
148#66867—22no—
149#24204—111nomaximal, Sylow
150C24×C11—21no—
151C24×C11—21no—
152C23×D11—21no—
153C2×Q8×C11—22no—
154C2×Q8×C11—22no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—41no—
161C2×Q8×C11C2×D412yes—
162C2×D4×C11—24no—
163C2×D4×C11—24no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11—21no—
174C2×D4×C11—42no—
175C2×D4×C11—42no—
176C2×D4×C11—81no—
177C2×D4×C11—81no—
178C2×D4×C11C2×D412yes—
179C2×D4×C11C2×D412yes—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—24no—
183C22×C4×C11—24no—
184C22×C4×C11—81no—
185C22×C4×C11—81no—
186C22×C4×C11—81no—
187C22×C4×C11—81no—
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2411yescharacteristic
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C2×D44—21no—
199C2×D44—21no—
200C2×D44—21no—
201C2×D44—21no—
202C2×D44—21no—
203C2×D44#4112yes—
204C2×C4×D11—42no—
205C2×C4×D11—42no—
206C2×C4×D11—42no—
207C11×C4⋊C4—24no—
208C11×C4⋊C4—22no—
209C11×C4⋊C4—22no—
210C11×C4⋊C4—22no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4C2×D412yes—
213C11×C22⋊C4—24no—
214C11×C22⋊C4—24no—
215C11×C22⋊C4—24no—
216C11×C22⋊C4—24no—
217C11×C22⋊C4—24no—
218C11×C22⋊C4—24no—
219C42×C11—24no—
220C42×C11—21no—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11—21no—
224C42×C11C2×D412yes—
225C42×C11C2×D412yes—
226#4325—44no—
227#4323—28no—
228#4323—44no—
229(C2×D11)⋊C4—42no—
230(C2×D11)⋊C4—42no—
231(C2×D11)⋊C4—42no—
232(C2×D11)⋊C4—81no—
233(C2×D11)⋊C4—81no—
234C4⋊Dic11—21no—
235C4⋊Dic11—21no—
236C4⋊Dic11—21no—
237C4⋊Dic11—21no—
238C4⋊Dic11—21no—
239C4⋊Dic11—21no—
240C4⋊Dic11—42no—
241C4⋊Dic11—81no—
242Dic11⋊C4—42no—
243Dic11⋊C4—42no—
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—21no—
255C2×C11⋊C8#4112yes—
256C2×#559D1111yescharacteristic, complemented
257C2×#463—111no—
258C2×#442—111no—
259#2538—111no—
260#2042—111no—
261#2041—111no—
262#2012—111no—
263#2011—111no—
264#1985—111no—
265#1959—111no—
266#1880—111no—
267#1879—111no—
268#1865—111no—
269#1864—111no—
270#1802—111no—
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11C22×D411yescharacteristic
286C22×D11—22no—
287C22×D11—41no—
288C22×D11—41no—
289C22×D11—41no—
290C22×D11—41no—
291C22×D11—41no—
292C22×D11—41no—
293Q8×C11—22no—
294Q8×C11—22no—
295Q8×C11—44no—
296Q8×C11—41no—
297Q8×C11—41no—
298D4×C11—22no—
299D4×C11—22no—
300D4×C11—22no—
301D4×C11—22no—
302D4×C11—48no—
303D4×C11—41no—
304D4×C11—41no—
305D4×C11—41no—
306D4×C11—41no—
307D4×C11—84no—
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—22no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—22no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—84no—
330C2×C4×C11—84no—
331C2×C4×C11#12012yes—
332C2×C4×C11#12012yes—
333C2×C4×C11AGL(1,ℤ/8)12yes—
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11C2×#4111yescharacteristic
337C2×C4×C11C2×#4111yescharacteristic
338C2×C4×C11H(5,𝔽2)11yescharacteristic
339C2×C4×C112−1+411yescharacteristic
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349D44—22no—
350D44—22no—
351D44—41no—
352D44—41no—
353C4×D11—84no—
354C11⋊C8—22no—
355C11⋊C8—41no—
356C11⋊C8—41no—
357C11⋊C8—41no—
358C22×SD16—111no—
359C22×D8—111no—
360C22×D8—111no—
361#559—24no—
362#559—24no—
363C2×#127C2×D1111yescharacteristic
364C2×#124—21no—
365C2×#124C2×D1111yescharacteristic
366C2×#124C2×D1111yescharacteristic
367C2×#123—21no—
368C2×#123—21no—
369C2×C22⋊Q8—221no—
370C2×C4×Q8C2×D1111yescharacteristic
371C2×C4×Q8C2×D1111yescharacteristic
372C2×C4×D4—21no—
373C2×C4×D4—111no—
374C2×C4×D4C2×D1111yescharacteristic
375C2×C4×D4C2×D1111yescharacteristic
376#463—224no—
377#442—224no—
378C2×#106—111no—
379C2×C4⋊C8—111no—
380C2×#103—111no—
381C2×#103—111no—
382C2×#103—111no—
383C2×#102—111no—
384C2×#102—111no—
385C2×#102—111no—
386C2×#102—111no—
387C2×#102—111no—
388C2×#102—111no—
389C2×#102—111no—
390C2×#97—111no—
391#396—221no—
392#396—221no—
393#390—111no—
394#390—111no—
395#389—111no—
396#389—111no—
397#384—111no—
398#380—221no—
399#340—111no—
400#340—111no—
401#336—111no—
402#336—111no—
403#336—111no—
404#336—111no—
405C22×C11—42no—
406C22×C11—42no—
407C22×C11—42no—
408C22×C11—42no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—81no—
412C22×C11—81no—
413C22×C11—81no—
414C22×C11—81no—
415C22×C11—81no—
416C22×C11—81no—
417C22×C11—81no—
418C22×C11—81no—
419C22×C11C2×#12011yescharacteristic
420C22×C11#54811yescharacteristic
421C22×C11#55011yescharacteristic
422C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
423C22×C11#57511yescharacteristic
424C22×C11#57611yescharacteristic
425C22×C11#57711yescharacteristic
426C2×D11—42no—
427C2×D11—42no—
428C2×D11—42no—
429C2×D11—81no—
430C2×D11—81no—
431C2×D11—81no—
432C2×D11—81no—
433C4×C11—22no—
434C4×C11—22no—
435C4×C11—22no—
436C4×C11—42no—
437C4×C11—41no—
438C4×C11—41no—
439C4×C11—41no—
440C4×C11—42no—
441C4×C11#52511yescharacteristic
442C4×C11#53711yescharacteristic
443C4×C11#54611yescharacteristic
444C4×C11#54711yescharacteristic
445Dic11—81no—
446Dic11—81no—
447Dic11—81no—
448C22×Q8C22⋊D1111yescharacteristic
449C22×Q8C22×D1111yescharacteristic
450C22×D4—21no—
451C22×D4—21no—
452C22×D4—111no—
453C22×D4C22×D1111yescharacteristic
454C22×D4C22×D1111yescharacteristic
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—221no—
458C2×SD16—222no—
459C2×SD16—222no—
460C2×SD16—441no—
461C2×D8—222no—
462C2×D8—222no—
463C2×D8—222no—
464C2×D8—222no—
465C2×D8—222no—
466C2×D8—441no—
467C22×C8—111no—
468C22×C8—111no—
469C22×C8—111no—
470C22×C8—111no—
471#127—22no—
472#127—22no—
473#124—28no—
474#124—22no—
475#124—22no—
476#124—22no—
477#124C22⋊D1114yes—
478#123—28no—
479#123—28no—
480C22⋊Q8—444no—
481C4×Q8—22no—
482C4×Q8—22no—
483C4×Q8—22no—
484C4×Q8—22no—
485C4×D4—28no—
486C4×D4—22no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—222no—
490C4×D4—222no—
491C4×D4C22⋊D1114yes—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—221no—
497C2×C4⋊C4—221no—
498C2×C4⋊C4—221no—
499C2×C4⋊C4—221no—
500C2×C4⋊C4C22⋊D1111yescharacteristic
501C2×C4⋊C4C22⋊D1111yescharacteristic
502C2×C4⋊C4C22⋊D1111yescharacteristic
503C2×C4⋊C4C22×D1111yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—221no—
511C2×C22⋊C4—221no—
512C2×C22⋊C4—221no—
513C2×C22⋊C4—221no—
514C2×C22⋊C4—221no—
515C2×C42—21no—
516C2×C42C22×D1111yescharacteristic
517C2×C42C22×D1111yescharacteristic
518C2×C42C22×D1111yescharacteristic
519#106—222no—
520C4⋊C8—222no—
521#103—222no—
522#103—222no—
523#103—441no—
524#102—222no—
525#102—222no—
526#102—222no—
527#102—222no—
528#102—441no—
529#102—441no—
530#102—441no—
531#97—222no—
532#95—221no—
533#95—221no—
534C2×C11—82no—
535C2×C11—82no—
536C2×C11#240711yescharacteristic
537C2×C11#300611yescharacteristic
538C2×C11#301211yescharacteristic
539C2×C11#337011yescharacteristic
540C2×C11#337311yescharacteristic
541C2×C11#339911yescharacteristic
542C2×C11#340111yescharacteristic
543D11—82no—
544C24—21no—
545C24—21no—
546C24—221no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—41no—
555C2×Q8C2×C22⋊D1112yes—
556C2×D4—24no—
557C2×D4—24no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4—112no—
573C2×D4—221no—
574C2×D4—221no—
575C2×D4—221no—
576C2×D4—221no—
577C2×D4—221no—
578C2×D4C2×C22⋊D1112yes—
579C2×D4C2×C22⋊D1112yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—81no—
585C22×C4—81no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—442no—
592C22×C4—442no—
593C22×C4—442no—
594C22×C4C2×C22⋊D1111yescharacteristic
595C22×C4C2×C22⋊D1111yescharacteristic
596C22×C4C2×C22⋊D1111yescharacteristic
597C22×C4C2×C22⋊D1111yescharacteristic
598C22×C4C2×C22⋊D1111yescharacteristic
599C22×C4C2×C22⋊D1111yescharacteristic
600C22×C4C23×D1111yescharacteristic
601SD16—444no—
602D8—228no—
603D8—444no—
604C2×C8—112no—
605C2×C8—221no—
606C2×C8—221no—
607C2×C8—221no—
608C2×C8—221no—
609C2×C8—221no—
610C2×C8—221no—
611C2×C8—221no—
612C2×C8—221no—
613C2×C8—221no—
614C2×C8—221no—
615C2×C8—221no—
616C4⋊C4—24no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—21no—
621C4⋊C4—221no—
622C4⋊C4—221no—
623C4⋊C4—221no—
624C4⋊C4—221no—
625C4⋊C4—221no—
626C4⋊C4—221no—
627C4⋊C4—442no—
628C4⋊C4—442no—
629C4⋊C4—442no—
630C4⋊C4—881no—
631C4⋊C4C2×C22⋊D1112yes—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—442no—
639C22⋊C4—442no—
640C22⋊C4—442no—
641C22⋊C4—881no—
642C22⋊C4—881no—
643C42—24no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—21no—
648C42C2×C22⋊D1112yes—
649C42C2×C22⋊D1112yes—
650C11#2420411yescharacteristic, complemented, Sylow
651C23—22no—
652C23—22no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—222no—
666C23—441no—
667C23—441no—
668C23—441no—
669C23—441no—
670C23—441no—
671C23—441no—
672C23C22×C22⋊D1111yescharacteristic
673Q8—22no—
674Q8—22no—
675Q8—44no—
676Q8—41no—
677Q8—41no—
678D4—22no—
679D4—22no—
680D4—22no—
681D4—22no—
682D4—48no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—84no—
688D4—222no—
689D4—222no—
690D4—441no—
691D4—441no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—84no—
714C2×C4—84no—
715C2×C4—441no—
716C2×C4—441no—
717C2×C4—441no—
718C2×C4—441no—
719C2×C4—441no—
720C2×C4—441no—
721C2×C4—441no—
722C2×C4—441no—
723C2×C4—441no—
724C2×C4—884no—
725C2×C4#6700212yes—
726C2×C4#6700612yes—
727C2×C4#6700612yes—
728C2×C4#41×D1111yescharacteristic
729C2×C4#41×D1111yescharacteristic
730C2×C4#6704211yescharacteristic
731C2×C4#6704311yescharacteristic
732C2×C4C22×C22⋊D1111yescharacteristic
733C2×C4C22×C22⋊D1111yescharacteristic
734C8—222no—
735C8—441no—
736C8—441no—
737C8—441no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—442no—
753C22—442no—
754C22—442no—
755C22—881no—
756C22—881no—
757C22—881no—
758C22—881no—
759C22C2×#6700211yescharacteristic
760C22#1062335311yescharacteristic
761C22#1062336211yescharacteristic
762C22#1062336511yescharacteristic
763C22#1062336611yescharacteristic
764C22#1062336711yescharacteristic
765C22C2×#6700611yescharacteristic
766C4—22no—
767C4—22no—
768C4—22no—
769C4—42no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—42no—
774C4—881no—
775C4—881no—
776C4—881no—
777C4#1062335511yescharacteristic
778C4#1062335911yescharacteristic
779C4#1062336011yescharacteristic
780C4#1062336411yescharacteristic
781C2—82no—
782C2—82no—
783C2—882no—
784C2#1307195511yescharacteristic
785C2#1307786811yescharacteristic
786C2#1307792011yescharacteristic
787C2#1308136311yescharacteristic
788C2#1308140411yescharacteristic
789C2#1308165411yescharacteristic
790C2#1308167611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#559C2
socleC23×C11C22×D4
prime radical#13069687C2
hypercenterC2×#559D11
hypocenterC11#24204
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#10622670C2semidirect
2. C2×#10622627C2semidirect
3. #13073534C2semidirect
4. #13069852C2semidirect
5. #13069847C2semidirect
6. #13069693C2semidirect
8. #13069557C2semidirect
9. #13069433C2semidirect
10. #13068971C2semidirect
11. #13068964C2semidirect
12. #13068884C2semidirect
13. #13068877C2semidirect
14. #13068616C2semidirect
15. C2×C11×#559C2semidirect
256. C2×#559D11semidirect
650. C11#24204semidirect

Maximal subgroups

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

subgroupindex
C2×#106226702
C2×#106226272
#130735342
#130698522
#130698472
#130696932
#130696872
#130695572
#130694332
#130689712
#130689642
#130688842
#130688772
#130686162
C2×C11×#5592
#2420411