Finite Group Databasebeta

← #14770815

Subgroups — #14770815

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622333C211yesmaximal, characteristic, complemented
2C2×#10622847C211yesmaximal, characteristic
3#13071107C211yesmaximal, characteristic
4#13069232C211yesmaximal, characteristic, complemented
5#13069226C211yesmaximal, characteristic, complemented
6#13069226C211yesmaximal, characteristic, complemented
7#13069225C211yesmaximal, characteristic, complemented
8#13068798C211yesmaximal, characteristic, complemented
9#13068793C211yesmaximal, characteristic, complemented
10#13068685C211yesmaximal, characteristic, complemented
11#13068594C211yesmaximal, characteristic, complemented
12#13068402C211yesmaximal, characteristic, complemented
13#13068395C211yesmaximal, characteristic, complemented
14#13068380C211yesmaximal, characteristic, complemented
15C11×#1780C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622847—24no—
28#10622843C411yescharacteristic
29#10622843C411yescharacteristic
30#10622834C411yescharacteristic
31#10622834C411yescharacteristic
32#10622833C411yescharacteristic
33#10622833C411yescharacteristic
34#10622833C411yescharacteristic
35#10622833C411yescharacteristic
36C4×C22⋊Dic11C2211yescharacteristic
37C4×C22⋊Dic11C2211yescharacteristic
38C4×C22⋊Dic11C2211yescharacteristic
39C4×C22⋊Dic11C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44C2×#66879C2211yescharacteristic
45C2×#66879C2211yescharacteristic
46C2×#66879C2211yescharacteristic
47C2×Dic11⋊C8C2211yescharacteristic
48C2×Dic11⋊C8C2211yescharacteristic
49C2×Dic11⋊C8C2211yescharacteristic
50C2×Dic11⋊C8C2211yescharacteristic
51C2×C8×Dic11C2211yescharacteristic
52#10622333—24no—
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—41no—
66C2×C11×#41—41no—
67C22×Q8×C11C2×C411yescharacteristic
68C22×D4×C11C2×C411yescharacteristic
69C22×D4×C11C2×C411yescharacteristic
70C22×D4×C11C2×C411yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×Dic11C2×C411yescharacteristic
75C23×Dic11C2×C411yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C2×C22⋊Dic11C2×C411yescharacteristic
81C2×C22⋊Dic11C2×C411yescharacteristic
82C2×C22⋊Dic11C2×C411yescharacteristic
83C2×C22⋊Dic11C2×C411yescharacteristic
84C2×C22⋊Dic11C2×C411yescharacteristic
85C2×C22⋊Dic11C2×C411yescharacteristic
86C2×C22⋊Dic11C2×C411yescharacteristic
87C2×C22⋊Dic11C2×C411yescharacteristic
88C2×C22⋊Dic11C2×C411yescharacteristic
89C2×C22⋊Dic11C2×C411yescharacteristic
90#66979—22no—
91#66979—22no—
92C2×C4⋊Dic11C2×C411yescharacteristic
93C2×C4⋊Dic11C2×C411yescharacteristic
94C2×C4×Dic11—41no—
95C2×C4×Dic11—41no—
96C2×C4×Dic11C2×C411yescharacteristic
97C2×C4×Dic11C2×C411yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C2×#4318—22no—
103C2×#4318—22no—
104C2×#4318—41no—
105C22×C11⋊C8—22no—
106C22×C11⋊C8—22no—
107C22×C11⋊C8—41no—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C11×C22⋊C8—22no—
113C11×C22⋊C8—22no—
114C11×C22⋊C8—22no—
115C11×C22⋊C8—22no—
116C11×C22⋊C8—41no—
117C11×C22⋊C8—41no—
118C11⋊#95C2×C411yescharacteristic
119C11⋊#95C2×C411yescharacteristic
120C11⋊#95C2×C411yescharacteristic
121C11⋊#95C2×C411yescharacteristic
122C11⋊#95C2×C411yescharacteristic
123C11⋊#95C2×C411yescharacteristic
124C11⋊#95C2×C411yescharacteristic
125C11⋊#95C2×C411yescharacteristic
126C22⋊(C11⋊C8)—22no—
127C22⋊(C11⋊C8)—22no—
128C22⋊(C11⋊C8)—22no—
129C22⋊(C11⋊C8)D414yes—
130#66879—22no—
131#66879—41no—
132#66879—41no—
133Dic11⋊C8—22no—
134Dic11⋊C8—22no—
135Dic11⋊C8—41no—
136Dic11⋊C8—41no—
137C8×Dic11—22no—
138#22561—111nomaximal, Sylow
139C24×C11C22×C411yescharacteristic
140C24×C11C22×C411yescharacteristic
141C24×C11C22×C411yescharacteristic
142C11×#41—44no—
143C11×#41—44no—
144C11×#41—44no—
145C11×#41—44no—
146C2×Q8×C11—22no—
147C2×Q8×C11—22no—
148C2×Q8×C11—41no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—22no—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—41no—
156C2×D4×C11—41no—
157C2×D4×C11—41no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
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×C11C22×C411yescharacteristic
173C22×C4×C11C22×C411yescharacteristic
174C22×C4×C11C22×C411yescharacteristic
175C22×C4×C11C2×D412yes—
176C22×C4×C11#4112yes—
177C22×C4×C11#4112yes—
178C22×C4×C11#4112yes—
179C22×C4×C11C2411yescharacteristic
180C22×Dic11—22no—
181C22×Dic11—41no—
182C22×Dic11—41no—
183C22×Dic11—41no—
184C22×Dic11—41no—
185C22×Dic11—41no—
186C22×Dic11C22×C411yescharacteristic
187C22×Dic11C22×C411yescharacteristic
188C22×Dic11C22×C411yescharacteristic
189C22×Dic11C22×C411yescharacteristic
190C22×Dic11C22×C411yescharacteristic
191C22×Dic11C22×C411yescharacteristic
192C22×Dic11C22×C411yescharacteristic
193C22×Dic11C22×C411yescharacteristic
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C22⋊Dic11—22no—
207C22⋊Dic11—22no—
208C22⋊Dic11—22no—
209C22⋊Dic11—22no—
210C22⋊Dic11—41no—
211C22⋊Dic11—41no—
212C22⋊Dic11—41no—
213C22⋊Dic11—41no—
214C22⋊Dic11—41no—
215C22⋊Dic11—41no—
216C4⋊Dic11—22no—
217C4⋊Dic11—22no—
218C4×Dic11—21no—
219C4×Dic11—21no—
220C4×Dic11—21no—
221C4×Dic11—21no—
222C4×Dic11—21no—
223C4×Dic11—21no—
224C4×Dic11—21no—
225C4×Dic11—21no—
226C4×Dic11—41no—
227C4×Dic11—41no—
228#4318—44no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—44no—
240C2×C11⋊C8C2×D412yes—
241C2×C11⋊C8C2×D412yes—
242C2×#433—111no—
243C2×#408—111no—
244#2297—111no—
245#1924—111no—
246#1924—111no—
247#1924—111no—
248#1923—111no—
249#1851—111no—
250#1850—111no—
251#1818—111no—
252#1797—111no—
253#1780D1111yescharacteristic
254#1753—111no—
255#1752—111no—
256#1749—111no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
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—21no—
276C23×C11#11712yes—
277C23×C11C4×D412yes—
278C23×C11C23×C411yescharacteristic
279Q8×C11—44no—
280D4×C11—44no—
281D4×C11—44no—
282D4×C11—44no—
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—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
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#11712yes—
303C2×C4×C11C4×D412yes—
304C2×C4×C11C22×D411yescharacteristic
305C2×C4×C11C2×#4111yescharacteristic
306C2×C4×C11C2×#4111yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11H(5,𝔽2)11yescharacteristic
309C2×C4×C11H(5,𝔽2)11yescharacteristic
310C2×Dic11—21no—
311C2×Dic11—21no—
312C2×Dic11—21no—
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—21no—
327C2×Dic11—21no—
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11—21no—
331C2×Dic11—21no—
332C2×Dic11—21no—
333C2×Dic11—44no—
334C2×Dic11—44no—
335C2×Dic11#13112yes—
336C8×C11—41no—
337C8×C11—41no—
338C8×C11—41no—
339C8×C11—41no—
340C11⋊C8—22no—
341C11⋊C8—22no—
342C11⋊C8—41no—
343C11⋊C8—41no—
344C22×#41C2×D1111yescharacteristic
345C22×M16—111no—
346C23×C8—111no—
347C2×#117—111no—
348C22×C42—111no—
349#433—224no—
350C2×C4⋊C8—111no—
351C2×C4⋊C8—111no—
352C2×C4⋊C8—111no—
353C2×C4⋊C8—111no—
354#408—224no—
355C2×C22⋊C8—111no—
356C2×C22⋊C8—111no—
357C2×C22⋊C8—111no—
358C2×C22⋊C8—111no—
359C2×C22⋊C8C2×D1111yescharacteristic
360C2×C22⋊C8C2×D1111yescharacteristic
361C2×C22⋊C8C2×D1111yescharacteristic
362C2×C22⋊C8C2×D1111yescharacteristic
363C2×C22⋊C8C2×D1111yescharacteristic
364C2×C22⋊C8C2×D1111yescharacteristic
365C2×#97—111no—
366C2×#97—111no—
367C2×#97—111no—
368C2×C4×C8—111no—
369#391—111no—
370#391—111no—
371#390—111no—
372#390—111no—
373#386—111no—
374#386—111no—
375#386—111no—
376#386—111no—
377C4×C22⋊C4—111no—
378C4×C22⋊C4—111no—
379C4×C22⋊C4—111no—
380C4×C22⋊C4—111no—
381#336—111no—
382#336—111no—
383#336—111no—
384#336—111no—
385#336—111no—
386#336—111no—
387#336—111no—
388#336—111no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—41no—
396C22×C11—41no—
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×C11—41no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11—41no—
409C22×C11—41no—
410C22×C11C2×#11711yescharacteristic
411C22×C11C2×C4×D411yescharacteristic
412C22×C11#51811yescharacteristic
413C22×C11C2×#13111yescharacteristic
414C22×C11#56811yescharacteristic
415C22×C11#56811yescharacteristic
416C22×C11#56811yescharacteristic
417C4×C11—22no—
418C4×C11—22no—
419C4×C11—41no—
420C4×C11#54611yescharacteristic
421C4×C11#54611yescharacteristic
422C4×C11#55111yescharacteristic
423C4×C11#55111yescharacteristic
424Dic11—22no—
425Dic11—41no—
426Dic11—41no—
427Dic11—41no—
428Dic11—41no—
429Dic11—41no—
430Dic11—41no—
431Dic11—41no—
432C2×#41—22no—
433C2×#41—22no—
434C2×#41—22no—
435C2×#41—22no—
436C2×#41—41no—
437C2×#41—41no—
438C22×Q8C4×D1111yescharacteristic
439C22×D4C4×D1111yescharacteristic
440C22×D4C4×D1111yescharacteristic
441C22×D4C4×D1111yescharacteristic
442C23×C4—111no—
443C23×C4—111no—
444C23×C4C22×D1111yescharacteristic
445C23×C4C22×D1111yescharacteristic
446C23×C4C22×D1111yescharacteristic
447C2×M16—222no—
448C2×M16—222no—
449C2×M16—441no—
450C22×C8—111no—
451C22×C8—111no—
452C22×C8—111no—
453C22×C8—111no—
454C22×C8—222no—
455C22×C8—222no—
456C22×C8—441no—
457C22×C8C22×D1111yescharacteristic
458C22×C8C22×D1111yescharacteristic
459C22×C8C22×D1111yescharacteristic
460C22×C8C22×D1111yescharacteristic
461#117—222no—
462#117—222no—
463C2×C4⋊C4—111no—
464C2×C4⋊C4—111no—
465C2×C22⋊C4—111no—
466C2×C22⋊C4—111no—
467C2×C22⋊C4—111no—
468C2×C22⋊C4—111no—
469C2×C22⋊C4—111no—
470C2×C22⋊C4—111no—
471C2×C22⋊C4—111no—
472C2×C22⋊C4—111no—
473C2×C22⋊C4—111no—
474C2×C22⋊C4—111no—
475C2×C42—111no—
476C2×C42—111no—
477C2×C42—111no—
478C2×C42—111no—
479C2×C42—111no—
480C2×C42—111no—
481C2×C42—441no—
482C2×C42—441no—
483C4⋊C8—222no—
484C4⋊C8—222no—
485C4⋊C8—441no—
486C4⋊C8—441no—
487C22⋊C8—22no—
488C22⋊C8—22no—
489C22⋊C8—22no—
490C22⋊C8—22no—
491C22⋊C8—41no—
492C22⋊C8—41no—
493C22⋊C8—114no—
494C22⋊C8—222no—
495C22⋊C8—222no—
496C22⋊C8—222no—
497#97—222no—
498#97—441no—
499#97—441no—
500C4×C8—222no—
501#95—111no—
502#95—111no—
503#95—111no—
504#95—111no—
505#95—111no—
506#95—111no—
507#95—111no—
508#95—111no—
509C2×C11—42no—
510C2×C11—42no—
511C2×C11—81no—
512C2×C11#234211yescharacteristic
513C2×C11#292311yescharacteristic
514C2×C11#292511yescharacteristic
515C2×C11#293211yescharacteristic
516C2×C11#293511yescharacteristic
517C2×C11#297611yescharacteristic
518C2×C11#297811yescharacteristic
519C24C2×C4×D1111yescharacteristic
520C24C2×C4×D1111yescharacteristic
521C24C2×C4×D1111yescharacteristic
522#41—44no—
523#41—44no—
524#41—44no—
525#41—44no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—41no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—41no—
536C2×D4—41no—
537C2×D4—41no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
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—111no—
553C22×C4—111no—
554C22×C4—111no—
555C22×C4—111no—
556C22×C4—111no—
557C22×C4—111no—
558C22×C4—111no—
559C22×C4—111no—
560C22×C4—222no—
561C22×C4—441no—
562C22×C4—441no—
563C22×C4—441no—
564C22×C4—441no—
565C22×C4—441no—
566C22×C4C2×C4×D1111yescharacteristic
567C22×C4C2×C4×D1111yescharacteristic
568C22×C4C2×C4×D1111yescharacteristic
569C22×C4D4×D1112yes—
570C22×C4#434112yes—
571C22×C4#434112yes—
572C22×C4#434112yes—
573C22×C4C23×D1111yescharacteristic
574M16—444no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—112no—
588C2×C8—112no—
589C2×C8—221no—
590C2×C8—221no—
591C2×C8—221no—
592C2×C8—221no—
593C2×C8—221no—
594C2×C8—221no—
595C2×C8—221no—
596C2×C8—221no—
597C2×C8—221no—
598C2×C8—221no—
599C2×C8—444no—
600C4⋊C4—222no—
601C4⋊C4—222no—
602C22⋊C4—222no—
603C22⋊C4—222no—
604C22⋊C4—222no—
605C22⋊C4—222no—
606C22⋊C4—441no—
607C22⋊C4—441no—
608C22⋊C4—441no—
609C22⋊C4—441no—
610C22⋊C4—441no—
611C22⋊C4—441no—
612C42—221no—
613C42—221no—
614C42—221no—
615C42—221no—
616C42—221no—
617C42—221no—
618C42—221no—
619C42—221no—
620C42—441no—
621C42—441no—
622C11#2256111yescharacteristic, complemented, Sylow
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23#6693012yes—
643C23(C22⋊D11)⋊C412yes—
644C23C22×C4×D1111yescharacteristic
645Q8—44no—
646D4—44no—
647D4—44no—
648D4—44no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—112no—
669C2×C4—221no—
670C2×C4—221no—
671C2×C4—221no—
672C2×C4—221no—
673C2×C4—221no—
674C2×C4—221no—
675C2×C4—221no—
676C2×C4—221no—
677C2×C4—221no—
678C2×C4—221no—
679C2×C4—221no—
680C2×C4—221no—
681C2×C4—221no—
682C2×C4—221no—
683C2×C4—221no—
684C2×C4—221no—
685C2×C4—221no—
686C2×C4—221no—
687C2×C4—221no—
688C2×C4—221no—
689C2×C4—221no—
690C2×C4—221no—
691C2×C4—221no—
692C2×C4—444no—
693C2×C4—444no—
694C2×C4#6693012yes—
695C2×C4(C22⋊D11)⋊C412yes—
696C2×C4C2×D4×D1111yescharacteristic
697C2×C4C2×#434111yescharacteristic
698C2×C4C2×#434111yescharacteristic
699C2×C4C2×#434111yescharacteristic
700C2×C4#6703711yescharacteristic
701C2×C4#6703711yescharacteristic
702C8—41no—
703C8—41no—
704C8—41no—
705C8—41no—
706C8—222no—
707C8—222no—
708C8—441no—
709C8—441no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22C2×#6693011yescharacteristic
732C22C2×(C22⋊D11)⋊C411yescharacteristic
733C22#1062301711yescharacteristic
734C22D11×#13111yescharacteristic
735C22#1062328111yescharacteristic
736C22#1062328111yescharacteristic
737C22#1062328111yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—222no—
742C4—441no—
743C4—441no—
744C4—441no—
745C4—441no—
746C4—441no—
747C4—441no—
748C4—441no—
749C4#1062311811yescharacteristic
750C4#1062311811yescharacteristic
751C4#1062312211yescharacteristic
752C4#1062312211yescharacteristic
753C2—42no—
754C2—42no—
755C2—81no—
756C2#1307146711yescharacteristic
757C2#1307726311yescharacteristic
758C2#1307727811yescharacteristic
759C2#1307733111yescharacteristic
760C2#1307735611yescharacteristic
761C2#1307765911yescharacteristic
762C2#1307767411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1780C2
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenter#1780D11
hypocenterC11#22561
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1780

Complements

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

NH ≅ G/Ntype
1. C2×#10622333C2semidirect
4. #13069232C2semidirect
5. #13069226C2semidirect
6. #13069226C2semidirect
7. #13069225C2semidirect
8. #13068798C2semidirect
9. #13068793C2semidirect
10. #13068685C2semidirect
11. #13068594C2semidirect
12. #13068402C2semidirect
13. #13068395C2semidirect
14. #13068380C2semidirect
622. C11#22561semidirect

Maximal subgroups

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

subgroupindex
C2×#106223332
C2×#106228472
#130711072
#130692322
#130692262
#130692252
#130687982
#130687932
#130686852
#130685942
#130684022
#130683952
#130683802
C11×#17802
#2256111