Finite Group Databasebeta

← #14806891

Subgroups — #14806891

Order 2816.

1124 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623074C211yesmaximal, characteristic
2C2×#10622656C211yesmaximal, characteristic, complemented
3C2×#10622665C211yesmaximal, characteristic, complemented
4#13069949C211yesmaximal, characteristic, complemented
5#13069812C211yesmaximal, characteristic, complemented
6#13069757C211yesmaximal, characteristic, complemented
7#13069624C211yesmaximal, characteristic, complemented
8#13068960C211yesmaximal, characteristic, complemented
9#13068928C211yesmaximal, characteristic, complemented
10#13068924C211yesmaximal, characteristic, complemented
11#13068914C211yesmaximal, characteristic
12#13068883C211yesmaximal, characteristic, complemented
13#13068808C211yesmaximal, characteristic, complemented
14#13068337C211yesmaximal, characteristic, complemented
15C11×#2415C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C2×D4×Dic11—21no—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C2×#66977C2211yescharacteristic
26C22×#4318C2211yescharacteristic
27#10623074—24no—
28#10623074—24no—
29C2×#66943—21no—
30C2×#66931—21no—
31C2×#66931—21no—
32C2×#66922C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C11×#397—21no—
35C11×#394—21no—
36C11×#391C2211yescharacteristic
37C11×#389—21no—
38C11×#389C2211yescharacteristic
39C11×#388—21no—
40C11×#380C2211yescharacteristic
41C2×#66899C2211yescharacteristic
42C2×#66899C2211yescharacteristic
43C2×#66899C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46C2×C22⋊(C11⋊C8)C2211yescharacteristic
47#10622665—24no—
48#10622656—24no—
49C2×#66874C2211yescharacteristic
50C2×#66874C2211yescharacteristic
51C2×#66874C2211yescharacteristic
52C2×#66872C2211yescharacteristic
53C2×#66872C2211yescharacteristic
54C2×#66872C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11D411yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×Dic11—21no—
68C23×Dic11—21no—
69C22×Dic22—21no—
70C22×Dic22C2311yescharacteristic
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—41no—
75C4×D4×C11—22no—
76C4×D4×C11—22no—
77C11×#117—22no—
78C11×#117—41no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
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×C11C2311yescharacteristic
94C2×C22⋊Dic11—21no—
95C2×C22⋊Dic11—21no—
96C2×#4326—22no—
97C2×#4326—22no—
98C2×#4326—41no—
99D4×Dic11—28no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11—22no—
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11D414yes—
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2311yescharacteristic
110#66977—22no—
111#66977—22no—
112#66977—22no—
113#66977D414yes—
114C2×Dic11⋊C4—21no—
115C2×Dic11⋊C4—21no—
116C2×Dic11⋊C4—21no—
117C2×C4×Dic11—21no—
118C2×#4318—22no—
119C2×#4318—22no—
120C2×#4318—41no—
121C22×C11⋊C8C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125#66943—28no—
126#66931—28no—
127#66931—28no—
128#66922—22no—
129#66922—22no—
130C4×Dic22—22no—
131C4×Dic22—22no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136#66899—22no—
137#66899—22no—
138#66899—22no—
139C22⋊(C11⋊C8)—22no—
140C22⋊(C11⋊C8)—22no—
141C22⋊(C11⋊C8)—41no—
142#66874—22no—
143#66874—22no—
144#66874—41no—
145#66872—22no—
146#66872—22no—
147#66872—22no—
148#25561—111nomaximal, Sylow
149C24×C11C2×D411yescharacteristic
150C24×C11C2×D411yescharacteristic
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D412yes—
178C22×C4×C11C2×D412yes—
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2411yescharacteristic
181C22×Dic11—24no—
182C22×Dic11—24no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—81no—
188C22×Dic11—81no—
189C22×Dic11—81no—
190C22×Dic11—81no—
191C2×Dic22—24no—
192C2×Dic22—21no—
193C2×Dic22—21no—
194C2×Dic22—21no—
195C2×Dic22—21no—
196C2×Dic22—21no—
197C2×Dic22—81no—
198C2×Dic22—81no—
199C2×Dic22C2×D412yes—
200C11×C4⋊C4—22no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—42no—
207C11×C4⋊C4—42no—
208C11×C4⋊C4—42no—
209C11×C4⋊C4#4112yes—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—22no—
212C11×C22⋊C4—42no—
213C11×C22⋊C4—42no—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—42no—
216C42×C11—21no—
217C42×C11—21no—
218C42×C11—42no—
219C22⋊Dic11—24no—
220C22⋊Dic11—24no—
221#4326—44no—
222C4⋊Dic11—24no—
223C4⋊Dic11—24no—
224C4⋊Dic11—24no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11C2×D412yes—
229C4⋊Dic11C2×D412yes—
230C4⋊Dic11C2×D412yes—
231Dic11⋊C4—24no—
232Dic11⋊C4—24no—
233Dic11⋊C4—24no—
234C4×Dic11—24no—
235#4318—44no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
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⋊C8#4112yes—
248C2×#554—111no—
249C2×#483—111no—
250C2×#470—111no—
251#2415D1111yescharacteristic
252#2058—111no—
253#2035—111no—
254#2024—111no—
255#2001—111no—
256#1878—111no—
257#1873—111no—
258#1872—111no—
259#1870—111no—
260#1865—111no—
261#1853—111no—
262#1736—111no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11#12012yes—
276C23×C11#13712yes—
277C23×C11C22×D411yescharacteristic
278Q8×C11—41no—
279Q8×C11—41no—
280Q8×C11—41no—
281Q8×C11—41no—
282D4×C11—28no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—22no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11#12012yes—
314C2×C4×C11#13712yes—
315C2×C4×C11C22×D411yescharacteristic
316C2×C4×C11C22×D411yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11C2×#4111yescharacteristic
319C2×C4×C11H(5,𝔽2)11yescharacteristic
320C2×C4×C112−1+411yescharacteristic
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—84no—
334C2×Dic11—84no—
335Dic22—22no—
336Dic22—22no—
337Dic22—41no—
338Dic22—41no—
339Dic22—84no—
340C11⋊C8—22no—
341C11⋊C8—41no—
342C11⋊C8—41no—
343C11⋊C8—41no—
344C22×Q16—111no—
345C22×M16—111no—
346#554—224no—
347#554—224no—
348C2×C4⋊Q8—111no—
349C2×#125—221no—
350C2×C22⋊Q8—111no—
351C2×C22⋊Q8—111no—
352C2×C22⋊Q8—221no—
353C2×C22⋊Q8—221no—
354C2×C22⋊Q8C2×D1111yescharacteristic
355C2×C22⋊Q8C2×D1111yescharacteristic
356C2×C4×Q8—111no—
357C2×C4×D4—221no—
358C2×C4×D4C2×D1111yescharacteristic
359C2×#117C2×D1111yescharacteristic
360C22×C4⋊C4—111no—
361C22×C4⋊C4—111no—
362#483—224no—
363#470—224no—
364C2×#106—111no—
365C2×#106—111no—
366C2×#106—111no—
367C2×#103—111no—
368C2×#103—111no—
369C2×#103—111no—
370C2×#103—111no—
371C2×#103—111no—
372C2×#103—111no—
373C2×C22⋊C8—111no—
374C2×C22⋊C8—111no—
375C2×C22⋊C8—111no—
376#397—21no—
377#394—21no—
378#391C2×D1111yescharacteristic
379#389—21no—
380#389C2×D1111yescharacteristic
381#388—21no—
382#380C2×D1111yescharacteristic
383#340—111no—
384#340—111no—
385#340—111no—
386#340—111no—
387#340—111no—
388#340—111no—
389#336—111no—
390#336—111no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11C2×#12011yescharacteristic
406C22×C11#54611yescharacteristic
407C22×C11#54711yescharacteristic
408C22×C11C2×#13711yescharacteristic
409C22×C11C2×#13711yescharacteristic
410C22×C11#57711yescharacteristic
411C22×C11#57711yescharacteristic
412C4×C11—22no—
413C4×C11—22no—
414C4×C11—42no—
415C4×C11—41no—
416C4×C11—41no—
417C4×C11—81no—
418C4×C11—81no—
419C4×C11—81no—
420C4×C11#53211yescharacteristic
421C4×C11#53711yescharacteristic
422C4×C11#54611yescharacteristic
423C4×C11#54711yescharacteristic
424Dic11—42no—
425Dic11—42no—
426Dic11—42no—
427Dic11—42no—
428C22×Q8—111no—
429C22×Q8—221no—
430C22×Q8C22×D1111yescharacteristic
431C22×D4C22⋊D1111yescharacteristic
432C23×C4—221no—
433C23×C4—221no—
434C23×C4C22×D1111yescharacteristic
435C23×C4C22×D1111yescharacteristic
436C2×Q16—222no—
437C2×Q16—222no—
438C2×Q16—441no—
439C2×M16—222no—
440C2×M16—222no—
441C2×M16—441no—
442C22×C8—111no—
443C22×C8—111no—
444C22×C8—111no—
445C22×C8—111no—
446C4⋊Q8—222no—
447C4⋊Q8—222no—
448#125—228no—
449C22⋊Q8—22no—
450C22⋊Q8—22no—
451C22⋊Q8—22no—
452C22⋊Q8—41no—
453C22⋊Q8—114no—
454C22⋊Q8—228no—
455C22⋊Q8—228no—
456C22⋊Q8—222no—
457C22⋊Q8—222no—
458C22⋊Q8—222no—
459C4×Q8—222no—
460C4×Q8—222no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—228no—
464#117—22no—
465#117—41no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—114no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4—111no—
472C2×C4⋊C4—111no—
473C2×C4⋊C4—222no—
474C2×C4⋊C4—222no—
475C2×C4⋊C4—222no—
476C2×C4⋊C4—221no—
477C2×C4⋊C4—221no—
478C2×C4⋊C4—221no—
479C2×C4⋊C4—221no—
480C2×C4⋊C4—221no—
481C2×C4⋊C4—221no—
482C2×C4⋊C4C22⋊D1111yescharacteristic
483C2×C4⋊C4C22×D1111yescharacteristic
484C2×C4⋊C4C22×D1111yescharacteristic
485C2×C4⋊C4C22×D1111yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—221no—
491C2×C22⋊C4—221no—
492C2×C22⋊C4C22⋊D1111yescharacteristic
493C2×C22⋊C4C22⋊D1111yescharacteristic
494C2×C42—21no—
495C2×C42—221no—
496C2×C42C22×D1111yescharacteristic
497#106—222no—
498#106—222no—
499#106—222no—
500#103—222no—
501#103—222no—
502#103—222no—
503#103—222no—
504#103—222no—
505#103—441no—
506C22⋊C8—222no—
507C22⋊C8—222no—
508C22⋊C8—441no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513C2×C11—42no—
514C2×C11—42no—
515C2×C11#243011yescharacteristic
516C2×C11#300411yescharacteristic
517C2×C11#300911yescharacteristic
518C2×C11#331611yescharacteristic
519C2×C11#333111yescharacteristic
520C2×C11#334411yescharacteristic
521C2×C11#335611yescharacteristic
522C24C2×C22⋊D1111yescharacteristic
523C24C2×C22⋊D1111yescharacteristic
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—112no—
531C2×Q8—224no—
532C2×Q8—221no—
533C2×Q8—221no—
534C2×Q8—221no—
535C2×Q8—221no—
536C2×Q8—221no—
537C2×Q8—881no—
538C2×Q8—881no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—221no—
557C22×C4—221no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—224no—
561C22×C4—224no—
562C22×C4—881no—
563C22×C4—881no—
564C22×C4—881no—
565C22×C4—881no—
566C22×C4D4×D1112yes—
567C22×C4D4×D1112yes—
568C22×C4C2×C22⋊D1111yescharacteristic
569C22×C4C2×C22⋊D1111yescharacteristic
570C22×C4C2×C22⋊D1111yescharacteristic
571C22×C4C2×C22⋊D1111yescharacteristic
572C22×C4C23×D1111yescharacteristic
573Q16—444no—
574M16—444no—
575C2×C8—112no—
576C2×C8—221no—
577C2×C8—221no—
578C2×C8—221no—
579C2×C8—221no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8—221no—
587C4⋊C4—22no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—112no—
597C4⋊C4—112no—
598C4⋊C4—112no—
599C4⋊C4—224no—
600C4⋊C4—224no—
601C4⋊C4—224no—
602C4⋊C4—224no—
603C4⋊C4—224no—
604C4⋊C4—224no—
605C4⋊C4—221no—
606C4⋊C4—221no—
607C4⋊C4—221no—
608C4⋊C4#434112yes—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—224no—
616C22⋊C4—224no—
617C42—21no—
618C42—21no—
619C42—42no—
620C42—224no—
621C11#2556111yescharacteristic, complemented, Sylow
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23#6699012yes—
635C23#6700412yes—
636C23C22×C22⋊D1111yescharacteristic
637Q8—41no—
638Q8—41no—
639Q8—41no—
640Q8—41no—
641Q8—222no—
642Q8—222no—
643Q8—441no—
644Q8—441no—
645Q8—884no—
646D4—28no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—222no—
678C2×C4—222no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—441no—
682C2×C4—441no—
683C2×C4—441no—
684C2×C4—441no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4—884no—
690C2×C4—884no—
691C2×C4#6699012yes—
692C2×C4#6700412yes—
693C2×C4C2×D4×D1111yescharacteristic
694C2×C4C2×D4×D1111yescharacteristic
695C2×C4C2×#434111yescharacteristic
696C2×C4#6703711yescharacteristic
697C2×C4#41×D1111yescharacteristic
698C2×C4#6704311yescharacteristic
699C8—222no—
700C8—441no—
701C8—441no—
702C8—441no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22C2×#6699011yescharacteristic
718C22#1062333711yescharacteristic
719C22C2×#6700411yescharacteristic
720C22C2×#6700411yescharacteristic
721C22#1062335511yescharacteristic
722C22#1062336811yescharacteristic
723C22#1062336811yescharacteristic
724C4—22no—
725C4—22no—
726C4—41no—
727C4—42no—
728C4—41no—
729C4—81no—
730C4—81no—
731C4—81no—
732C4—442no—
733C4—442no—
734C4—442no—
735C4—442no—
736C4#1062312711yescharacteristic
737C4#1062312811yescharacteristic
738C4#1062314111yescharacteristic
739C4#1062314211yescharacteristic
740C2—42no—
741C2—42no—
742C2#1307222211yescharacteristic
743C2#1307784911yescharacteristic
744C2#1307789111yescharacteristic
745C2#1308072711yescharacteristic
746C2#1308093211yescharacteristic
747C2#1308107111yescharacteristic
748C2#1308122511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2415C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#2415D11
hypocenterC11#25561
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2415

Complements

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

NH ≅ G/Ntype
2. C2×#10622656C2semidirect
3. C2×#10622665C2semidirect
4. #13069949C2semidirect
5. #13069812C2semidirect
6. #13069757C2semidirect
7. #13069624C2semidirect
8. #13068960C2semidirect
9. #13068928C2semidirect
10. #13068924C2semidirect
12. #13068883C2semidirect
13. #13068808C2semidirect
14. #13068337C2semidirect
621. C11#25561semidirect

Maximal subgroups

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

subgroupindex
C2×#106230742
C2×#106226562
C2×#106226652
#130699492
#130698122
#130697572
#130696242
#130689602
#130689282
#130689242
#130689142
#130688832
#130688082
#130683372
C11×#24152
#2556111