Finite Group Databasebeta

← #14770808

Subgroups — #14770808

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×#10622340C211yesmaximal, characteristic
3#13071106C211yesmaximal, characteristic
4#13069228C211yesmaximal, characteristic, complemented
5#13069227C211yesmaximal, characteristic, complemented
6#13069227C211yesmaximal, characteristic, complemented
7#13069221C211yesmaximal, characteristic, complemented
8#13068797C211yesmaximal, characteristic, complemented
9#13068792C211yesmaximal, characteristic, complemented
10#13068685C211yesmaximal, characteristic, complemented
11#13068527C211yesmaximal, characteristic
12#13068398C211yesmaximal, characteristic, complemented
13#13068391C211yesmaximal, characteristic, complemented
14#13068378C211yesmaximal, characteristic, complemented
15C11×#1797C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20C22×C8×D11C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25#10622826C411yescharacteristic
26#10622826C411yescharacteristic
27#10622826C411yescharacteristic
28#10622826C411yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×#66879C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40C2×C8×Dic11C2211yescharacteristic
41#10622552C411yescharacteristic
42#10622552C411yescharacteristic
43C4×(C2×D11)⋊C4C2211yescharacteristic
44C4×(C2×D11)⋊C4C2211yescharacteristic
45C4×(C2×D11)⋊C4C2211yescharacteristic
46C4×(C2×D11)⋊C4C2211yescharacteristic
47#10622542C411yescharacteristic
48#10622542C411yescharacteristic
49C2×#66867C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51#10622340—24no—
52#10622333—24no—
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C23×C4×C11C2×C411yescharacteristic
62C23×C4×C11C2×C411yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11C2×C411yescharacteristic
65C22×C22⋊D11C2×C411yescharacteristic
66C2×#4339—22no—
67C2×#4339—22no—
68C2×#4339—22no—
69C2×#4339—22no—
70C2×#4339—41no—
71C2×#4339—41no—
72C22×D44C2×C411yescharacteristic
73C22×C4×D11C2311yescharacteristic
74C22×C4×D11C2311yescharacteristic
75C22×Dic22C2×C411yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C2×C42×C11—41no—
81C2×C42×C11—41no—
82C2×C42×C11C2×C411yescharacteristic
83C2×C42×C11C2×C411yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11C2×C411yescharacteristic
87C2×C22⋊Dic11C2×C411yescharacteristic
88C2×(C2×D11)⋊C4C2×C411yescharacteristic
89C2×(C2×D11)⋊C4C2×C411yescharacteristic
90C2×(C2×D11)⋊C4C2×C411yescharacteristic
91C2×(C2×D11)⋊C4C2×C411yescharacteristic
92C2×(C2×D11)⋊C4C2×C411yescharacteristic
93C2×(C2×D11)⋊C4C2×C411yescharacteristic
94C2×(C2×D11)⋊C4C2×C411yescharacteristic
95C2×(C2×D11)⋊C4C2×C411yescharacteristic
96#66979—22no—
97#66979—22no—
98C2×C4⋊Dic11C2×C411yescharacteristic
99C2×C4⋊Dic11C2×C411yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C2×#4313—22no—
107C2×#4313—22no—
108C2×#4313—41no—
109C2×C8×D11—22no—
110C2×C8×D11—22no—
111C2×C8×D11—41no—
112C11×C4⋊C8—41no—
113C11×C4⋊C8—41no—
114C11×C22⋊C8—22no—
115C11×C22⋊C8—22no—
116C11⋊#95C2×C411yescharacteristic
117C11⋊#95C2×C411yescharacteristic
118C11⋊#95C2×C411yescharacteristic
119C11⋊#95C2×C411yescharacteristic
120C11⋊#95C2×C411yescharacteristic
121C11⋊#95C2×C411yescharacteristic
122C11⋊#95C2×C411yescharacteristic
123C11⋊#95C2×C411yescharacteristic
124C22⋊(C11⋊C8)—22no—
125C22⋊(C11⋊C8)D414yes—
126(C2×D11)⋊C8—22no—
127(C2×D11)⋊C8—22no—
128(C2×D11)⋊C8—22no—
129(C2×D11)⋊C8—22no—
130(C2×D11)⋊C8—41no—
131(C2×D11)⋊C8—41no—
132#66879—22no—
133Dic11⋊C8—22no—
134Dic11⋊C8—22no—
135C8×Dic11—22no—
136#66867—41no—
137#66867—41no—
138#22561—111nomaximal, Sylow
139C24×C11C22×C411yescharacteristic
140C23×D11C22×C411yescharacteristic
141C23×D11C22×C411yescharacteristic
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—22no—
147C22×C4×C11—41no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11—41no—
151C22×C4×C11—41no—
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C22×C411yescharacteristic
155C22×C4×C11C22×C411yescharacteristic
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C2×D412yes—
158C22×C4×C11#4112yes—
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—22no—
161C2×C22⋊D11—22no—
162C2×C22⋊D11—22no—
163C2×C22⋊D11—22no—
164C2×C22⋊D11—41no—
165C2×C22⋊D11—41no—
166C22×Dic11C22×C411yescharacteristic
167C22×Dic11C22×C411yescharacteristic
168C22×Dic11C22×C411yescharacteristic
169C22×Dic11C22×C411yescharacteristic
170C22×Dic11C22×C411yescharacteristic
171C22×Dic11C22×C411yescharacteristic
172#4339—44no—
173#4339—44no—
174#4339—44no—
175#4339—44no—
176C2×D44—22no—
177C2×D44—22no—
178C2×D44—41no—
179C2×C4×D11—21no—
180C2×C4×D11—21no—
181C2×C4×D11—21no—
182C2×C4×D11—21no—
183C2×C4×D11—21no—
184C2×C4×D11—21no—
185C2×C4×D11—21no—
186C2×C4×D11—21no—
187C2×C4×D11—21no—
188C2×C4×D11—21no—
189C2×C4×D11#4112yes—
190C2×C4×D11#4112yes—
191C2×Dic22—22no—
192C2×Dic22—22no—
193C2×Dic22—41no—
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—
206C42×C11—21no—
207C42×C11—21no—
208C42×C11—21no—
209C42×C11—21no—
210C42×C11—41no—
211C42×C11—41no—
212C22⋊Dic11—22no—
213C22⋊Dic11—22no—
214(C2×D11)⋊C4—22no—
215(C2×D11)⋊C4—22no—
216(C2×D11)⋊C4—41no—
217(C2×D11)⋊C4—41no—
218(C2×D11)⋊C4—41no—
219(C2×D11)⋊C4—41no—
220(C2×D11)⋊C4—41no—
221(C2×D11)⋊C4—41no—
222C4⋊Dic11—22no—
223C4⋊Dic11—22no—
224C4×Dic11—21no—
225C4×Dic11—21no—
226C4×Dic11—21no—
227C4×Dic11—21no—
228C2×C11⋊C8—21no—
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⋊C8C2×D412yes—
239C2×C11⋊C8C2×D412yes—
240#4313—44no—
241C8×D11—44no—
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#1797D1111yescharacteristic, complemented
253#1780—111no—
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×C11C4×D412yes—
264C23×C11C23×C411yescharacteristic
265C22×D11—21no—
266C22×D11—21no—
267C22×D11—21no—
268C22×D11—21no—
269C22×D11—21no—
270C22×D11—21no—
271C22×D11—21no—
272C22×D11—21no—
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—21no—
276C22×D11—21no—
277C22×D11—21no—
278C22×D11#11712yes—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—44no—
297C2×C4×C11—44no—
298C2×C4×C11C4×D412yes—
299C2×C4×C11#13112yes—
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C2×#4111yescharacteristic
302C2×C4×C11C2×#4111yescharacteristic
303C2×C4×C11C2×#4111yescharacteristic
304C2×C4×C11H(5,𝔽2)11yescharacteristic
305C2×C4×C11H(5,𝔽2)11yescharacteristic
306C22⋊D11—44no—
307C22⋊D11—44no—
308C2×Dic11—21no—
309C2×Dic11—21no—
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#11712yes—
326D44—44no—
327C4×D11—22no—
328C4×D11—22no—
329C4×D11—22no—
330C4×D11—22no—
331C4×D11—41no—
332C4×D11—41no—
333C4×D11—41no—
334C4×D11—41no—
335Dic22—44no—
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×#41—111no—
345C22×M16—111no—
346C23×C8—111no—
347C2×#117—111no—
348C22×C42C2×D1111yescharacteristic
349#433—224no—
350C2×C4⋊C8—111no—
351C2×C4⋊C8—111no—
352C2×C4⋊C8C2×D1111yescharacteristic
353C2×C4⋊C8C2×D1111yescharacteristic
354#408—224no—
355C2×C22⋊C8—111no—
356C2×C22⋊C8—111no—
357C2×C22⋊C8—111no—
358C2×C22⋊C8—111no—
359C2×C22⋊C8—111no—
360C2×C22⋊C8—111no—
361C2×C22⋊C8—111no—
362C2×C22⋊C8—111no—
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#336C2×D1111yescharacteristic
388#336C2×D1111yescharacteristic
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11C2×#11711yescharacteristic
397C22×C11C2×C4×D411yescharacteristic
398C22×C11#51811yescharacteristic
399C22×C11C2×#13111yescharacteristic
400C22×C11#56811yescharacteristic
401C22×C11#56811yescharacteristic
402C22×C11#56811yescharacteristic
403C2×D11—22no—
404C2×D11—22no—
405C2×D11—22no—
406C2×D11—41no—
407C2×D11—41no—
408C2×D11—41no—
409C2×D11—41no—
410C2×D11—41no—
411C2×D11—41no—
412C2×D11—41no—
413C2×D11—41no—
414C2×D11—41no—
415C2×D11—41no—
416C2×D11—41no—
417C4×C11—22no—
418C4×C11—22no—
419C4×C11—41no—
420C4×C11—41no—
421C4×C11—41no—
422C4×C11#54611yescharacteristic
423C4×C11#54611yescharacteristic
424C4×C11#55111yescharacteristic
425C4×C11#55111yescharacteristic
426Dic11—22no—
427Dic11—41no—
428Dic11—41no—
429Dic11—41no—
430Dic11—41no—
431Dic11—41no—
432C2×#41—222no—
433C2×#41—222no—
434C2×#41—222no—
435C2×#41—222no—
436C2×#41—441no—
437C2×#41—441no—
438C22×Q8—111no—
439C22×D4—111no—
440C22×D4—111no—
441C22×D4—111no—
442C23×C4—111no—
443C23×C4—111no—
444C23×C4C4×D1111yescharacteristic
445C23×C4C4×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—41no—
476C2×C42—41no—
477C2×C42—111no—
478C2×C42—111no—
479C2×C42C4×D1111yescharacteristic
480C2×C42C4×D1111yescharacteristic
481C2×C42C22×D1111yescharacteristic
482C2×C42C22×D1111yescharacteristic
483C4⋊C8—41no—
484C4⋊C8—41no—
485C4⋊C8—222no—
486C4⋊C8—222no—
487C22⋊C8—22no—
488C22⋊C8—22no—
489C22⋊C8—114no—
490C22⋊C8—222no—
491C22⋊C8—222no—
492C22⋊C8—222no—
493C22⋊C8—222no—
494C22⋊C8—222no—
495C22⋊C8—441no—
496C22⋊C8—441no—
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#234211yescharacteristic
511C2×C11#292311yescharacteristic
512C2×C11#292511yescharacteristic
513C2×C11#293211yescharacteristic
514C2×C11#293511yescharacteristic
515C2×C11#297611yescharacteristic
516C2×C11#297811yescharacteristic
517D11—42no—
518D11—81no—
519C24—111no—
520C24—111no—
521C24C2×C4×D1111yescharacteristic
522#41—444no—
523#41—444no—
524#41—444no—
525#41—444no—
526C2×Q8—222no—
527C2×Q8—222no—
528C2×Q8—441no—
529C2×D4—222no—
530C2×D4—222no—
531C2×D4—222no—
532C2×D4—222no—
533C2×D4—222no—
534C2×D4—222no—
535C2×D4—441no—
536C2×D4—441no—
537C2×D4—441no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—111no—
549C22×C4—112no—
550C22×C4—112no—
551C22×C4—111no—
552C22×C4—111no—
553C22×C4—111no—
554C22×C4—111no—
555C22×C4—111no—
556C22×C4—221no—
557C22×C4—221no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4C2×C4×D1111yescharacteristic
567C22×C4C2×C4×D1111yescharacteristic
568C22×C4C2×C4×D1111yescharacteristic
569C22×C4C2×C4×D1111yescharacteristic
570C22×C4C2×C4×D1111yescharacteristic
571C22×C4D4×D1112yes—
572C22×C4#434312yes—
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—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—41no—
617C42—41no—
618C42—221no—
619C42—221no—
620C42—221no—
621C42—221no—
622C11#2256111yescharacteristic, complemented, Sylow
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—112no—
630C23—221no—
631C23—221no—
632C23—221no—
633C23—221no—
634C23—221no—
635C23—221no—
636C23—221no—
637C23—221no—
638C23—221no—
639C23—221no—
640C23—221no—
641C23—221no—
642C23—221no—
643C23#6694612yes—
644C23C22×C4×D1111yescharacteristic
645Q8—444no—
646D4—444no—
647D4—444no—
648D4—444no—
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—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—112no—
669C2×C4—221no—
670C2×C4—221no—
671C2×C4—222no—
672C2×C4—222no—
673C2×C4—222no—
674C2×C4—222no—
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—441no—
691C2×C4—441no—
692C2×C4—441no—
693C2×C4—441no—
694C2×C4#6694612yes—
695C2×C4#6695412yes—
696C2×C4C2×D4×D1111yescharacteristic
697C2×C4#6703711yescharacteristic
698C2×C4#6703711yescharacteristic
699C2×C4C2×#434311yescharacteristic
700C2×C4#41×D1111yescharacteristic
701C2×C4#41×D1111yescharacteristic
702C8—41no—
703C8—41no—
704C8—41no—
705C8—41no—
706C8—222no—
707C8—222no—
708C8—441no—
709C8—441no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—222no—
718C22—222no—
719C22—222no—
720C22—441no—
721C22—441no—
722C22—441no—
723C22—441no—
724C22—441no—
725C22—441no—
726C22—441no—
727C22—441no—
728C22—441no—
729C22—441no—
730C22—441no—
731C22#1062301711yescharacteristic
732C22C2×#6694611yescharacteristic
733C22D11×#11711yescharacteristic
734C22C2×#6695411yescharacteristic
735C22#1062327611yescharacteristic
736C22#1062327611yescharacteristic
737C22#1062327611yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—222no—
744C4—441no—
745C4—441no—
746C4—441no—
747C4—441no—
748C4—441no—
749C4#1062314111yescharacteristic
750C4#1062314111yescharacteristic
751C4#1062316811yescharacteristic
752C4#1062316811yescharacteristic
753C2—42no—
754C2—442no—
755C2—881no—
756C2#1307146211yescharacteristic
757C2#1307726211yescharacteristic
758C2#1307727711yescharacteristic
759C2#1307733311yescharacteristic
760C2#1307735911yescharacteristic
761C2#1307766111yescharacteristic
762C2#1307767611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1797C2
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#1797D11
hypocenterC11#22561
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1797

Complements

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

NH ≅ G/Ntype
1. C2×#10622333C2semidirect
4. #13069228C2semidirect
5. #13069227C2semidirect
6. #13069227C2semidirect
7. #13069221C2semidirect
8. #13068797C2semidirect
9. #13068792C2semidirect
10. #13068685C2semidirect
12. #13068398C2semidirect
13. #13068391C2semidirect
14. #13068378C2semidirect
15. C11×#1797C2semidirect
252. #1797D11semidirect
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×#106223402
#130711062
#130692282
#130692272
#130692212
#130687972
#130687922
#130686852
#130685272
#130683982
#130683912
#130683782
C11×#17972
#2256111