Finite Group Databasebeta

← #14775951

Subgroups — #14775951

Order 2816.

1040 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622449C211yesmaximal, characteristic, complemented
2C2×C8×D44C211yesmaximal, characteristic, complemented
3C2×#10622447C211yesmaximal, characteristic, complemented
4C2×#10622452C211yesmaximal, characteristic, complemented
5#13071856C211yesmaximal, characteristic
6#13069413C211yesmaximal, characteristic, complemented
7#13069227C211yesmaximal, characteristic, complemented
8#13069220C211yesmaximal, characteristic, complemented
9#13068912C211yesmaximal, characteristic, complemented
10#13068907C211yesmaximal, characteristic, complemented
11#13068792C211yesmaximal, characteristic, complemented
12#13068792C211yesmaximal, characteristic, complemented
13#13068491C211yesmaximal, characteristic, complemented
14#13068383C211yesmaximal, characteristic, complemented
15C11×#1939C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×#66925C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
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×Dic11⋊C8C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39#10622607C411yescharacteristic
40#10622607C411yescharacteristic
41#10622604C411yescharacteristic
42#10622604C411yescharacteristic
43C4×(C2×D11)⋊C4C2211yescharacteristic
44C4×(C2×D11)⋊C4C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47C2×#66867C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622452—24no—
50#10622449—24no—
51#10622447—24no—
52C8×D44—24no—
53#10622287C411yescharacteristic
54#10622285C411yescharacteristic
55#10622284C411yescharacteristic
56#10622274C411yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×D44C2×C411yescharacteristic
64C22×D44C2×C411yescharacteristic
65C22×D44C2×C411yescharacteristic
66C22×C4×D11C2311yescharacteristic
67C22×C4×D11C2311yescharacteristic
68C22×C4×D11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C2×C11×C4⋊C4C2×C411yescharacteristic
74C2×C11×C4⋊C4C2×C411yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×(C2×D11)⋊C4C2×C411yescharacteristic
79C2×(C2×D11)⋊C4C2×C411yescharacteristic
80C2×(C2×D11)⋊C4C2×C411yescharacteristic
81C2×(C2×D11)⋊C4C2×C411yescharacteristic
82C2×(C2×D11)⋊C4C2×C411yescharacteristic
83C2×(C2×D11)⋊C4C2×C411yescharacteristic
84C2×(C2×D11)⋊C4C2×C411yescharacteristic
85C2×(C2×D11)⋊C4C2×C411yescharacteristic
86C2×(C2×D11)⋊C4C2×C411yescharacteristic
87C2×(C2×D11)⋊C4C2×C411yescharacteristic
88C2×(C2×D11)⋊C4C2×C411yescharacteristic
89C2×(C2×D11)⋊C4C2×C411yescharacteristic
90C2×C4⋊Dic11C2×C411yescharacteristic
91C2×C4⋊Dic11C2×C411yescharacteristic
92C2×C4⋊Dic11C2×C411yescharacteristic
93C2×Dic11⋊C4C2×C411yescharacteristic
94C2×Dic11⋊C4C2×C411yescharacteristic
95C2×C4×Dic11C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C2×#4313—22no—
101C2×#4313—22no—
102C2×#4313—41no—
103C2×C8×D11—22no—
104C2×C8×D11—22no—
105C2×C8×D11—22no—
106C2×C8×D11—22no—
107C2×C8×D11—22no—
108C2×C8×D11—22no—
109C2×C8×D11—41no—
110C2×C8×D11—41no—
111C2×C8×D11—41no—
112C4×D44—22no—
113C4×D44—22no—
114C4×D44—22no—
115C4×D44—22no—
116C4×D44—22no—
117C4×D44—22no—
118#66925—22no—
119#66925—22no—
120C11×C4⋊C8—22no—
121C11×C4⋊C8—22no—
122C11×C4⋊C8—22no—
123C4×C8×C11—22no—
124C11×#95C2×C411yescharacteristic
125C11×#95C2×C411yescharacteristic
126C11⋊#95C2×C411yescharacteristic
127C11⋊#95C2×C411yescharacteristic
128C11⋊#95C2×C411yescharacteristic
129C11⋊#95C2×C411yescharacteristic
130(C2×D11)⋊C8—22no—
131(C2×D11)⋊C8—22no—
132(C2×D11)⋊C8—22no—
133(C2×D11)⋊C8—22no—
134(C2×D11)⋊C8—22no—
135(C2×D11)⋊C8—41no—
136(C2×D11)⋊C8—41no—
137(C2×D11)⋊C8D414yescomplemented
138Dic11⋊C8—22no—
139Dic11⋊C8—22no—
140C4⋊(C11⋊C8)D414yescomplemented
141#66867—22no—
142#66867—22no—
143C4×C11⋊C8—22no—
144#22991—111nomaximal, Sylow
145C23×D11C22×C411yescharacteristic
146C23×D11C22×C411yescharacteristic
147C23×D11C22×C411yescharacteristic
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C22×Dic11C22×C411yescharacteristic
156C22×Dic11C22×C411yescharacteristic
157C22×Dic11C22×C411yescharacteristic
158C22×Dic11C22×C411yescharacteristic
159C22×Dic11C22×C411yescharacteristic
160C2×D44—22no—
161C2×D44—22no—
162C2×D44—22no—
163C2×D44—22no—
164C2×D44—22no—
165C2×D44—22no—
166C2×D44—22no—
167C2×D44—22no—
168C2×D44—41no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C2×C4×D11—21no—
173C2×C4×D11—21no—
174C2×C4×D11—21no—
175C2×C4×D11—21no—
176C2×C4×D11—21no—
177C2×C4×D11—21no—
178C2×C4×D11—21no—
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×D11C2×D412yes—
186C2×C4×D11#4112yes—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11C2×D412yes—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—41no—
201C42×C11—21no—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11C2×D412yes—
206C42×C11#4112yes—
207(C2×D11)⋊C4—22no—
208(C2×D11)⋊C4—22no—
209(C2×D11)⋊C4—22no—
210(C2×D11)⋊C4—22no—
211(C2×D11)⋊C4—22no—
212(C2×D11)⋊C4—22no—
213(C2×D11)⋊C4—22no—
214(C2×D11)⋊C4—22no—
215(C2×D11)⋊C4—22no—
216(C2×D11)⋊C4—22no—
217(C2×D11)⋊C4—22no—
218(C2×D11)⋊C4—41no—
219C4⋊Dic11—22no—
220C4⋊Dic11—22no—
221C4⋊Dic11—22no—
222Dic11⋊C4—22no—
223Dic11⋊C4—22no—
224C4×Dic11—21no—
225C4×Dic11—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—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⋊C8C2×D412yes—
236C2×C11⋊C8C2×D412yes—
237C2×C11⋊C8C2×D412yes—
238#4313—44no—
239C8×D11—44no—
240C8×D11—44no—
241C8×D11—44no—
242C2×#435—111no—
243C2×C8×D4—111no—
244C2×C8×D4—111no—
245C2×#424—111no—
246#2392—111no—
247#1955—111no—
248#1939D1111yescharacteristic, complemented
249#1924—111no—
250#1923—111no—
251#1870—111no—
252#1869—111no—
253#1850—111no—
254#1850—111no—
255#1771—111no—
256#1750—111no—
257C23×C11C23×C411yescharacteristic
258C22×D11—21no—
259C22×D11—21no—
260C22×D11—21no—
261C22×D11—21no—
262C22×D11—21no—
263C22×D11—21no—
264C22×D11—21no—
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×D11C4×D412yes—
277C22×D11#13112yes—
278C22×D11#13112yes—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
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×C11C4×D412yes—
295C2×C4×C11C4×D412yes—
296C2×C4×C11#13112yes—
297C2×C4×C11C22×D411yescharacteristic
298C2×C4×C11C22×D411yescharacteristic
299C2×C4×C11C2×#4111yescharacteristic
300C2×C4×C11C2×#4111yescharacteristic
301C2×C4×C11H(5,𝔽2)11yescharacteristic
302C2×C4×C112−1+411yescharacteristic
303C2×Dic11—21no—
304C2×Dic11—21no—
305C2×Dic11—21no—
306C2×Dic11—21no—
307C2×Dic11—21no—
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×Dic11C4×D412yes—
318D44—28no—
319D44—28no—
320D44—44no—
321C4×D11—22no—
322C4×D11—22no—
323C4×D11—22no—
324C4×D11—22no—
325C4×D11—41no—
326C4×D11—41no—
327C4×D11—41no—
328C4×D11—41no—
329C4×D11—41no—
330C4×D11—41no—
331C4×D11—41no—
332C4×D11—41no—
333C8×C11—22no—
334C8×C11—41no—
335C8×C11—41no—
336C8×C11—41no—
337C11⋊C8—22no—
338C11⋊C8—22no—
339C11⋊C8—22no—
340C11⋊C8—41no—
341C22×M16—111no—
342C23×C8—111no—
343C23×C8—111no—
344C23×C8—111no—
345C2×C4×D4—111no—
346C2×C4×D4—111no—
347C2×C4×D4—111no—
348C2×#117—111no—
349#435—224no—
350C8×D4—224no—
351C8×D4—224no—
352#424—224no—
353C2×C4⋊C8—111no—
354C2×C4⋊C8—111no—
355C2×C4⋊C8—111no—
356C2×C4⋊C8C2×D1111yescharacteristic
357C2×C4⋊C8C2×D1111yescharacteristic
358C2×C4⋊C8C2×D1111yescharacteristic
359C2×C22⋊C8—111no—
360C2×C22⋊C8—111no—
361C2×C22⋊C8—111no—
362C2×C22⋊C8—111no—
363C2×C22⋊C8—111no—
364C2×C22⋊C8—111no—
365C2×C22⋊C8—111no—
366C2×C22⋊C8—111no—
367C2×#97—111no—
368C2×#97—111no—
369C2×C4×C8—111no—
370C2×C4×C8C2×D1111yescharacteristic
371#398—111no—
372#397—111no—
373#396—111no—
374#396—111no—
375#394—111no—
376#394—111no—
377#394—111no—
378#392—111no—
379C4×C4⋊C4C2×D1111yescharacteristic
380C4×C22⋊C4—111no—
381C4×C22⋊C4—111no—
382#336—111no—
383#336—111no—
384#336—111no—
385#336—111no—
386#336C2×D1111yescharacteristic
387#336C2×D1111yescharacteristic
388C22×C11C2×C4×D411yescharacteristic
389C22×C11C2×C4×D411yescharacteristic
390C22×C11#52011yescharacteristic
391C22×C11C2×#13111yescharacteristic
392C22×C11C2×#13111yescharacteristic
393C22×C11C2×#13111yescharacteristic
394C22×C11#56811yescharacteristic
395C2×D11—22no—
396C2×D11—22no—
397C2×D11—22no—
398C2×D11—22no—
399C2×D11—22no—
400C2×D11—22no—
401C2×D11—22no—
402C2×D11—22no—
403C2×D11—22no—
404C2×D11—41no—
405C2×D11—41no—
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—
416C4×C11—22no—
417C4×C11—22no—
418C4×C11—22no—
419C4×C11—41no—
420C4×C11—41no—
421C4×C11—41no—
422C4×C11D4211yescharacteristic
423C4×C11#54711yescharacteristic
424C4×C11#54811yescharacteristic
425C4×C11#55311yescharacteristic
426Dic11—22no—
427Dic11—41no—
428Dic11—41no—
429Dic11—41no—
430Dic11—41no—
431C22×D4—111no—
432C22×D4—111no—
433C22×D4—111no—
434C23×C4—111no—
435C23×C4—111no—
436C23×C4—111no—
437C2×M16—222no—
438C2×M16—222no—
439C2×M16—441no—
440C22×C8—111no—
441C22×C8—111no—
442C22×C8—111no—
443C22×C8—111no—
444C22×C8—222no—
445C22×C8—222no—
446C22×C8—222no—
447C22×C8—222no—
448C22×C8—222no—
449C22×C8—222no—
450C22×C8—441no—
451C22×C8—441no—
452C22×C8—441no—
453C22×C8C22×D1111yescharacteristic
454C22×C8C22×D1111yescharacteristic
455C22×C8C22×D1111yescharacteristic
456C22×C8C22×D1111yescharacteristic
457C4×D4—222no—
458C4×D4—222no—
459C4×D4—222no—
460C4×D4—222no—
461C4×D4—222no—
462C4×D4—222no—
463#117—222no—
464#117—222no—
465C2×C4⋊C4—111no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—111no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—111no—
470C2×C4⋊C4C4×D1111yescharacteristic
471C2×C4⋊C4C4×D1111yescharacteristic
472C2×C22⋊C4—111no—
473C2×C22⋊C4—111no—
474C2×C22⋊C4—111no—
475C2×C22⋊C4—111no—
476C2×C22⋊C4—111no—
477C2×C22⋊C4—111no—
478C2×C22⋊C4—111no—
479C2×C22⋊C4—111no—
480C2×C22⋊C4—111no—
481C2×C22⋊C4—111no—
482C2×C22⋊C4—111no—
483C2×C22⋊C4—111no—
484C2×C42—111no—
485C2×C42C22×D1111yescharacteristic
486C2×C42C22×D1111yescharacteristic
487C2×C42C22×D1111yescharacteristic
488C4⋊C8—22no—
489C4⋊C8—22no—
490C4⋊C8—22no—
491C4⋊C8—114no—
492C4⋊C8—222no—
493C4⋊C8—222no—
494C22⋊C8—114no—
495C22⋊C8—222no—
496C22⋊C8—222no—
497C22⋊C8—222no—
498C22⋊C8—222no—
499C22⋊C8—222no—
500C22⋊C8—441no—
501C22⋊C8—441no—
502#97—222no—
503#97—222no—
504C4×C8—22no—
505C4×C8—222no—
506#95—111no—
507#95—111no—
508#95—111no—
509#95—111no—
510#95C4×D1111yescharacteristic
511#95C4×D1111yescharacteristic
512C2×C11#236111yescharacteristic
513C2×C11#292911yescharacteristic
514C2×C11#292911yescharacteristic
515C2×C11#293311yescharacteristic
516C2×C11#293511yescharacteristic
517C2×C11#299211yescharacteristic
518C2×C11#299411yescharacteristic
519D11—42no—
520D11—42no—
521D11—42no—
522C24—111no—
523C24—111no—
524C24—111no—
525C2×D4—222no—
526C2×D4—222no—
527C2×D4—222no—
528C2×D4—222no—
529C2×D4—222no—
530C2×D4—222no—
531C2×D4—222no—
532C2×D4—222no—
533C2×D4—441no—
534C22×C4—111no—
535C22×C4—112no—
536C22×C4—112no—
537C22×C4—111no—
538C22×C4—111no—
539C22×C4—111no—
540C22×C4—111no—
541C22×C4—221no—
542C22×C4—221no—
543C22×C4—221no—
544C22×C4—221no—
545C22×C4—221no—
546C22×C4—221no—
547C22×C4—221no—
548C22×C4—221no—
549C22×C4—221no—
550C22×C4—221no—
551C22×C4—221no—
552C22×C4—221no—
553C22×C4—221no—
554C22×C4—221no—
555C22×C4—221no—
556C22×C4—221no—
557C22×C4C2×C4×D1111yescharacteristic
558C22×C4C2×C4×D1111yescharacteristic
559C22×C4C2×C4×D1111yescharacteristic
560C22×C4C2×C4×D1111yescharacteristic
561C22×C4C2×C4×D1111yescharacteristic
562C22×C4C2×C4×D1111yescharacteristic
563C22×C4C23×D1111yescharacteristic
564M16—444no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—112no—
577C2×C8—112no—
578C2×C8—112no—
579C2×C8—221no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8—221no—
587C2×C8—221no—
588C2×C8—444no—
589C2×C8—444no—
590C2×C8—444no—
591C2×C8D4×D1112yes—
592C4⋊C4—22no—
593C4⋊C4—41no—
594C4⋊C4—222no—
595C4⋊C4—222no—
596C4⋊C4—222no—
597C4⋊C4—222no—
598C4⋊C4—222no—
599C22⋊C4—222no—
600C22⋊C4—222no—
601C22⋊C4—222no—
602C22⋊C4—222no—
603C22⋊C4—222no—
604C22⋊C4—222no—
605C22⋊C4—222no—
606C22⋊C4—222no—
607C22⋊C4—222no—
608C22⋊C4—222no—
609C22⋊C4—222no—
610C22⋊C4—441no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—221no—
616C42—221no—
617C42D4×D1112yes—
618C42#434312yes—
619C11#2299111yescharacteristic, complemented, Sylow
620C23—112no—
621C23—112no—
622C23—112no—
623C23—221no—
624C23—221no—
625C23—221no—
626C23—221no—
627C23—221no—
628C23—221no—
629C23—221no—
630C23—221no—
631C23—221no—
632C23—221no—
633C23—221no—
634C23—221no—
635C23—221no—
636C23—221no—
637C23—221no—
638C23—221no—
639C23—221no—
640C23—221no—
641C23C22×C4×D1111yescharacteristic
642D4—228no—
643D4—228no—
644D4—444no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—112no—
661C2×C4—221no—
662C2×C4—221no—
663C2×C4—222no—
664C2×C4—222no—
665C2×C4—222no—
666C2×C4—222no—
667C2×C4—221no—
668C2×C4—221no—
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—441no—
680C2×C4—441no—
681C2×C4—441no—
682C2×C4—441no—
683C2×C4—441no—
684C2×C4—441no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4#6694612yes—
688C2×C4#6694612yes—
689C2×C4#6695412yes—
690C2×C4C2×D4×D1111yescharacteristic
691C2×C4C2×D4×D1111yescharacteristic
692C2×C4C2×#434311yescharacteristic
693C2×C4#6704011yescharacteristic
694C2×C4#41×D1111yescharacteristic
695C2×C4#6704211yescharacteristic
696C8—22no—
697C8—41no—
698C8—41no—
699C8—41no—
700C8—222no—
701C8—222no—
702C8—222no—
703C8—441no—
704C22—222no—
705C22—222no—
706C22—222no—
707C22—222no—
708C22—222no—
709C22—222no—
710C22—222no—
711C22—222no—
712C22—222no—
713C22—441no—
714C22—441no—
715C22—441no—
716C22—441no—
717C22—441no—
718C22—441no—
719C22—441no—
720C22—441no—
721C22—441no—
722C22—441no—
723C22—441no—
724C22—441no—
725C22C2×#6694611yescharacteristic
726C22C4×D4×D1111yescharacteristic
727C22#1062310511yescharacteristic
728C22C2×#6695411yescharacteristic
729C22#1062327611yescharacteristic
730C22D11×#13111yescharacteristic
731C22D11×#13111yescharacteristic
732C4—22no—
733C4—22no—
734C4—22no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—222no—
739C4—441no—
740C4—441no—
741C4—441no—
742C4—441no—
743C4#1062314011yescharacteristic
744C4#1062316411yescharacteristic
745C4#1062322611yescharacteristic
746C4#1062325711yescharacteristic
747C2—442no—
748C2—442no—
749C2—442no—
750C2#1307163111yescharacteristic
751C2#1307730511yescharacteristic
752C2#1307730911yescharacteristic
753C2#1307734511yescharacteristic
754C2#1307735911yescharacteristic
755C2#1307775411yescharacteristic
756C2#1307777511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1939C2
prime radical#10622284C4
cosocleC22×C4×C11C24
hypercenter#1939D11
hypocenterC11#22991
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1939

Complements

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

NH ≅ G/Ntype
1. C2×#10622449C2semidirect
2. C2×C8×D44C2semidirect
3. C2×#10622447C2semidirect
4. C2×#10622452C2semidirect
6. #13069413C2semidirect
7. #13069227C2semidirect
8. #13069220C2semidirect
9. #13068912C2semidirect
10. #13068907C2semidirect
11. #13068792C2semidirect
12. #13068792C2semidirect
13. #13068491C2semidirect
14. #13068383C2semidirect
15. C11×#1939C2semidirect
137. (C2×D11)⋊C8D4semidirect
140. C4⋊(C11⋊C8)D4semidirect
248. #1939D11semidirect
619. C11#22991semidirect

Maximal subgroups

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

subgroupindex
C2×#106224492
C2×C8×D442
C2×#106224472
C2×#106224522
#130718562
#130694132
#130692272
#130692202
#130689122
#130689072
#130687922
#130684912
#130683832
C11×#19392
#2299111