Finite Group Databasebeta

← #14775949

Subgroups — #14775949

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×#10622341C211yesmaximal, characteristic, complemented
2C2×C8×D44C211yesmaximal, characteristic, complemented
3C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
4C2×#10622612C211yesmaximal, characteristic, complemented
5#13071852C211yesmaximal, characteristic
6#13069414C211yesmaximal, characteristic, complemented
7#13069334C211yesmaximal, characteristic, complemented
8#13069230C211yesmaximal, characteristic, complemented
9#13069223C211yesmaximal, characteristic, complemented
10#13068911C211yesmaximal, characteristic, complemented
11#13068906C211yesmaximal, characteristic, complemented
12#13068795C211yesmaximal, characteristic, complemented
13#13068795C211yesmaximal, characteristic, complemented
14#13068488C211yesmaximal, characteristic, complemented
15C11×#1750C211yesmaximal, characteristic, complemented
16C2×C11×#117C2211yescharacteristic
17C2×C4×C22⋊D11C2211yescharacteristic
18C2×C4×C22⋊D11C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22C22×C8×D11C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×#97C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38#10622612—24no—
39#10622607C411yescharacteristic
40#10622607C411yescharacteristic
41#10622604C411yescharacteristic
42#10622596C411yescharacteristic
43#10622574C411yescharacteristic
44#10622574C411yescharacteristic
45#10622573C411yescharacteristic
46#10622566C411yescharacteristic
47C4×(C2×D11)⋊C4C2211yescharacteristic
48C4×(C2×D11)⋊C4C2211yescharacteristic
49C4×C4⋊Dic11C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54#10622341—24no—
55(C22⋊D11)⋊C8—24no—
56C8×D44—24no—
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622188C2211yescharacteristic
62#10622188C2211yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11C2×C411yescharacteristic
65C22×C22⋊D11C2×C411yescharacteristic
66C22×D44C2×C411yescharacteristic
67C22×C4×D11C2311yescharacteristic
68C22×C4×D11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×#117—22no—
74C11×#117—22no—
75C2×C11×C4⋊C4C2×C411yescharacteristic
76C2×C11×C4⋊C4C2×C411yescharacteristic
77C2×C11×C22⋊C4C2×C411yescharacteristic
78C2×C11×C22⋊C4C2×C411yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C22⋊Dic11C2×C411yescharacteristic
82C2×C22⋊Dic11C2×C411yescharacteristic
83C4×C22⋊D11—22no—
84C4×C22⋊D11—22no—
85C4×C22⋊D11—22no—
86C4×C22⋊D11—22no—
87C2×(C2×D11)⋊C4C2×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×C4⋊Dic11C2×C411yescharacteristic
96C2×C4⋊Dic11C2×C411yescharacteristic
97C2×C4⋊Dic11C2×C411yescharacteristic
98C2×Dic11⋊C4C2×C411yescharacteristic
99C2×Dic11⋊C4C2×C411yescharacteristic
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
112C2×C8×D11—22no—
113C2×C8×D11—22no—
114C2×C8×D11—22no—
115C2×C8×D11—22no—
116C2×C8×D11—41no—
117C2×C8×D11—41no—
118C4×D44—22no—
119C4×D44—22no—
120C11×C22⋊C8—22no—
121C11×C22⋊C8D414yescomplemented
122C11×#97—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—41no—
135(C2×D11)⋊C8—41no—
136#66879—22no—
137Dic11⋊C8—22no—
138Dic11⋊C8—22no—
139C8×Dic11—22no—
140C4⋊(C11⋊C8)—22no—
141C4⋊(C11⋊C8)—22no—
142C4⋊(C11⋊C8)—22no—
143C4⋊(C11⋊C8)D414yescomplemented
144#22991—111nomaximal, Sylow
145C24×C11C22×C411yescharacteristic
146C23×D11C22×C411yescharacteristic
147C23×D11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
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—22no—
165C2×C22⋊D11—41no—
166C22×Dic11C22×C411yescharacteristic
167C22×Dic11C22×C411yescharacteristic
168C22×Dic11C22×C411yescharacteristic
169C22×Dic11C22×C411yescharacteristic
170C22×Dic11C22×C411yescharacteristic
171C22×Dic11C22×C411yescharacteristic
172C2×D44—22no—
173C2×D44—22no—
174C2×D44—22no—
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×D11—21no—
186C2×C4×D11—21no—
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×C11C2×D412yes—
198C2×C8×C11C2×D412yes—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—22no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—22no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11C2×D412yes—
206C42×C11#4112yes—
207C22⋊Dic11—22no—
208C22⋊Dic11—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—41no—
217C4⋊Dic11—22no—
218C4⋊Dic11—22no—
219C4⋊Dic11—41no—
220Dic11⋊C4—22no—
221Dic11⋊C4—22no—
222C4×Dic11—21no—
223C4×Dic11—21no—
224C4×Dic11—21no—
225C4×Dic11—21no—
226#4318—44no—
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⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—44no—
238C2×C11⋊C8C2×D412yes—
239C2×C11⋊C8C2×D412yes—
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#1939—111no—
249#1924—111no—
250#1923—111no—
251#1870—111no—
252#1869—111no—
253#1850—111no—
254#1850—111no—
255#1771—111no—
256#1750D1111yescharacteristic, complemented
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#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—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
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×C11C4×D412yes—
296C2×C4×C11C4×D412yes—
297C2×C4×C11C4×D412yes—
298C2×C4×C11C22×D411yescharacteristic
299C2×C4×C11C22×D411yescharacteristic
300C2×C4×C11C2×#4111yescharacteristic
301C2×C4×C11C2×#4111yescharacteristic
302C2×C4×C11H(5,𝔽2)11yescharacteristic
303C2×C4×C112−1+411yescharacteristic
304C22⋊D11—28no—
305C22⋊D11—44no—
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×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11#13112yes—
324D44—28no—
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—22no—
335C8×C11—41no—
336C8×C11—41no—
337C11⋊C8—22no—
338C11⋊C8—22no—
339C11⋊C8—41no—
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×#117C2×D1111yescharacteristic
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⋊C8—111no—
357C2×C4⋊C8—111no—
358C2×C4⋊C8—111no—
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⋊C8C2×D1111yescharacteristic
366C2×C22⋊C8C2×D1111yescharacteristic
367C2×#97—111no—
368C2×#97C2×D1111yescharacteristic
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⋊C4—111no—
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×C11—22no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11C2×C4×D411yescharacteristic
396C22×C11C2×C4×D411yescharacteristic
397C22×C11#52011yescharacteristic
398C22×C11C2×#13111yescharacteristic
399C22×C11C2×#13111yescharacteristic
400C22×C11C2×#13111yescharacteristic
401C22×C11#56811yescharacteristic
402C2×D11—22no—
403C2×D11—22no—
404C2×D11—22no—
405C2×D11—22no—
406C2×D11—22no—
407C2×D11—22no—
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×C11D4211yescharacteristic
422C4×C11#54711yescharacteristic
423C4×C11#54811yescharacteristic
424C4×C11#55311yescharacteristic
425Dic11—22no—
426Dic11—41no—
427Dic11—41no—
428Dic11—41no—
429Dic11—41no—
430Dic11—41no—
431C22×D4—111no—
432C22×D4—111no—
433C22×D4—111no—
434C23×C4—111no—
435C23×C4—111no—
436C23×C4C22×D1111yescharacteristic
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—22no—
464#117—22no—
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⋊C4C4×D1111yescharacteristic
483C2×C22⋊C4C4×D1111yescharacteristic
484C2×C42—111no—
485C2×C42—111no—
486C2×C42C22×D1111yescharacteristic
487C2×C42C22×D1111yescharacteristic
488C4⋊C8—114no—
489C4⋊C8—222no—
490C4⋊C8—222no—
491C4⋊C8—222no—
492C4⋊C8—222no—
493C4⋊C8—222no—
494C22⋊C8—22no—
495C22⋊C8—222no—
496C22⋊C8—222no—
497C22⋊C8—222no—
498C22⋊C8—222no—
499C22⋊C8—441no—
500C22⋊C8—441no—
501C22⋊C8D4414yescomplemented
502#97—22no—
503#97—222no—
504C4×C8—22no—
505C4×C8—222no—
506#95—111no—
507#95—111no—
508#95—111no—
509#95—111no—
510#95—111no—
511#95—111no—
512C2×C11—42no—
513C2×C11#236111yescharacteristic
514C2×C11#292911yescharacteristic
515C2×C11#292911yescharacteristic
516C2×C11#293311yescharacteristic
517C2×C11#293511yescharacteristic
518C2×C11#299211yescharacteristic
519C2×C11#299411yescharacteristic
520D11—42no—
521D11—42no—
522C24—111no—
523C24—111no—
524C24C2×C4×D1111yescharacteristic
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—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—111no—
539C22×C4—111no—
540C22×C4—111no—
541C22×C4—111no—
542C22×C4—111no—
543C22×C4—111no—
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×C4C2×C4×D1111yescharacteristic
557C22×C4C2×C4×D1111yescharacteristic
558C22×C4C2×C4×D1111yescharacteristic
559C22×C4C2×C4×D1111yescharacteristic
560C22×C4C2×C4×D1111yescharacteristic
561C22×C4C2×D4412yes—
562C22×C4#433912yes—
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—112no—
576C2×C8—112no—
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—
587C2×C8—444no—
588C2×C8—444no—
589C2×C8—444no—
590C2×C8C2×D4412yes—
591C2×C8C2×D4412yes—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—222no—
595C4⋊C4—222no—
596C4⋊C4—222no—
597C4⋊C4—222no—
598C4⋊C4—441no—
599C22⋊C4—22no—
600C22⋊C4—22no—
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—221no—
614C42—221no—
615C42—221no—
616C42—221no—
617C42D4×D1112yes—
618C42#434112yes—
619C11#2299111yescharacteristic, complemented, Sylow
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—112no—
627C23—112no—
628C23—221no—
629C23—221no—
630C23—221no—
631C23—221no—
632C23—221no—
633C23—221no—
634C23—221no—
635C23—221no—
636C23—221no—
637C23—221no—
638C23—221no—
639C23—221no—
640C23C4×D4412yes—
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—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—112no—
662C2×C4—221no—
663C2×C4—221no—
664C2×C4—221no—
665C2×C4—221no—
666C2×C4—221no—
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×C4C4×D4412yes—
688C2×C4(C22⋊D11)⋊C412yes—
689C2×C4(C22⋊D11)⋊C412yes—
690C2×C4C22×D4411yescharacteristic
691C2×C4C2×#433911yescharacteristic
692C2×C4C2×D4×D1111yescharacteristic
693C2×C4C2×#434111yescharacteristic
694C2×C4#6704211yescharacteristic
695C2×C4#6704311yescharacteristic
696C8—22no—
697C8—22no—
698C8—41no—
699C8—41no—
700C8—222no—
701C8—222no—
702C8—441no—
703C8—441no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—222no—
712C22—222no—
713C22—222no—
714C22—222no—
715C22—222no—
716C22—222no—
717C22—441no—
718C22—441no—
719C22—441no—
720C22—441no—
721C22—441no—
722C22—441no—
723C22—441no—
724C22—441no—
725C22C2×C4×D4411yescharacteristic
726C22C2×(C22⋊D11)⋊C411yescharacteristic
727C22#1062305411yescharacteristic
728C22D11×#13111yescharacteristic
729C22D11×#13111yescharacteristic
730C22D11×#13111yescharacteristic
731C22#1062328111yescharacteristic
732C4—22no—
733C4—22no—
734C4—22no—
735C4—41no—
736C4—41no—
737C4—222no—
738C4—441no—
739C4—441no—
740C4—441no—
741C4—441no—
742C4—441no—
743C4D4×D4411yescharacteristic
744C4#1062308311yescharacteristic
745C4#1062308611yescharacteristic
746C4#1062309611yescharacteristic
747C2—42no—
748C2—442no—
749C2—442no—
750C2#1307163011yescharacteristic
751C2#1307731211yescharacteristic
752C2#1307731311yescharacteristic
753C2#1307734411yescharacteristic
754C2#1307735611yescharacteristic
755C2#1307775011yescharacteristic
756C2#1307777011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1750C2
prime radical#10622573C4
cosocleC22×C4×C11C24
hypercenter#1750D11
hypocenterC11#22991
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1750

Complements

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

NH ≅ G/Ntype
1. C2×#10622341C2semidirect
2. C2×C8×D44C2semidirect
3. C2×(C22⋊D11)⋊C8C2semidirect
4. C2×#10622612C2semidirect
6. #13069414C2semidirect
7. #13069334C2semidirect
8. #13069230C2semidirect
9. #13069223C2semidirect
10. #13068911C2semidirect
11. #13068906C2semidirect
12. #13068795C2semidirect
13. #13068795C2semidirect
14. #13068488C2semidirect
15. C11×#1750C2semidirect
121. C11×C22⋊C8D4semidirect
143. C4⋊(C11⋊C8)D4semidirect
256. #1750D11semidirect
501. C22⋊C8D44semidirect
619. C11#22991semidirect

Maximal subgroups

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

subgroupindex
C2×#106223412
C2×C8×D442
C2×(C22⋊D11)⋊C82
C2×#106226122
#130718522
#130694142
#130693342
#130692302
#130692232
#130689112
#130689062
#130687952
#130684882
C11×#17502
#2299111