Finite Group Databasebeta

← #14775953

Subgroups — #14775953

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×#10622740C211yesmaximal, characteristic, complemented
2C2×#10622447C211yesmaximal, characteristic, complemented
3C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
4#13071852C211yesmaximal, characteristic
5#13069413C211yesmaximal, characteristic, complemented
6#13069332C211yesmaximal, characteristic, complemented
7#13069228C211yesmaximal, characteristic, complemented
8#13069221C211yesmaximal, characteristic, complemented
9#13068913C211yesmaximal, characteristic, complemented
10#13068908C211yesmaximal, characteristic, complemented
11#13068792C211yesmaximal, characteristic, complemented
12#13068792C211yesmaximal, characteristic, complemented
13#13068493C211yesmaximal, characteristic, complemented
14#13068382C211yesmaximal, characteristic, complemented
15C2×C11×#424C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22C22×C8×D11C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C11×#424—24no—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31#10622740—24no—
32C8×C22⋊D11—24no—
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×(C2×D11)⋊C8C2211yescharacteristic
39C2×#66879C2211yescharacteristic
40C2×Dic11⋊C8C2211yescharacteristic
41C2×Dic11⋊C8C2211yescharacteristic
42C2×C8×Dic11C2211yescharacteristic
43#10622607C411yescharacteristic
44#10622607C411yescharacteristic
45#10622604C411yescharacteristic
46#10622596C411yescharacteristic
47#10622574C411yescharacteristic
48#10622574C411yescharacteristic
49#10622573C411yescharacteristic
50#10622566C411yescharacteristic
51C4×(C2×D11)⋊C4C2211yescharacteristic
52C4×(C2×D11)⋊C4C2211yescharacteristic
53C4×C4⋊Dic11C2211yescharacteristic
54C2×#66867C2211yescharacteristic
55C2×C4×C11⋊C8C2211yescharacteristic
56#10622447—24no—
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11C2×C411yescharacteristic
65C22×C22⋊D11C2×C411yescharacteristic
66C22×D44C2×C411yescharacteristic
67C22×C4×D11C2311yescharacteristic
68C22×C4×D11C2311yescharacteristic
69C2×C11×M16—22no—
70C2×C11×M16—22no—
71C2×C11×M16—41no—
72C22×C8×C11—22no—
73C22×C8×C11—22no—
74C22×C8×C11—41no—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C11×#117—22no—
80C11×#117—22no—
81C2×C11×C4⋊C4C2×C411yescharacteristic
82C2×C11×C4⋊C4C2×C411yescharacteristic
83C2×C11×C22⋊C4C2×C411yescharacteristic
84C2×C11×C22⋊C4C2×C411yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C22⋊Dic11C2×C411yescharacteristic
88C2×C22⋊Dic11C2×C411yescharacteristic
89C4×C22⋊D11—22no—
90C4×C22⋊D11—22no—
91C4×C22⋊D11—22no—
92C4×C22⋊D11—22no—
93C2×(C2×D11)⋊C4C2×C411yescharacteristic
94C2×(C2×D11)⋊C4C2×C411yescharacteristic
95C2×(C2×D11)⋊C4C2×C411yescharacteristic
96C2×(C2×D11)⋊C4C2×C411yescharacteristic
97C2×(C2×D11)⋊C4C2×C411yescharacteristic
98C2×(C2×D11)⋊C4C2×C411yescharacteristic
99C2×(C2×D11)⋊C4C2×C411yescharacteristic
100C2×(C2×D11)⋊C4C2×C411yescharacteristic
101C2×C4⋊Dic11C2×C411yescharacteristic
102C2×C4⋊Dic11C2×C411yescharacteristic
103C2×C4⋊Dic11C2×C411yescharacteristic
104C2×Dic11⋊C4C2×C411yescharacteristic
105C2×Dic11⋊C4C2×C411yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
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×C4⋊C8—22no—
121C11×C4⋊C8—22no—
122C11×C4⋊C8—22no—
123C11×C4⋊C8D414yescomplemented
124C11⋊#95C2×C411yescharacteristic
125C11⋊#95C2×C411yescharacteristic
126C11⋊#95C2×C411yescharacteristic
127C11⋊#95C2×C411yescharacteristic
128C11⋊#95C2×C411yescharacteristic
129C11⋊#95C2×C411yescharacteristic
130C22⋊(C11⋊C8)—22no—
131C22⋊(C11⋊C8)D414yescomplemented
132(C2×D11)⋊C8—22no—
133(C2×D11)⋊C8—22no—
134(C2×D11)⋊C8—22no—
135(C2×D11)⋊C8—22no—
136(C2×D11)⋊C8—41no—
137(C2×D11)⋊C8—41no—
138#66879—22no—
139Dic11⋊C8—22no—
140Dic11⋊C8—22no—
141C8×Dic11—22no—
142#66867—22no—
143C4×C11⋊C8—22no—
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—
187C11×M16—44no—
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×C11—44no—
199C2×C8×C11C2×D412yes—
200C2×C8×C11C2×D412yes—
201C11×C4⋊C4—22no—
202C11×C4⋊C4—22no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—22no—
205C42×C11—21no—
206C42×C11—21no—
207C42×C11C2×D412yes—
208C42×C11#4112yes—
209C22⋊Dic11—22no—
210C22⋊Dic11—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—41no—
222Dic11⋊C4—22no—
223Dic11⋊C4—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—
240C8×D11—44no—
241C8×D11—44no—
242C2×#435—111no—
243C2×C8×D4—111no—
244C2×C8×D4—111no—
245C2×#424D1111yescharacteristic, complemented
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#1750—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#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×M16C2×D1111yescharacteristic
342C23×C8—111no—
343C23×C8—111no—
344C23×C8C2×D1111yescharacteristic
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—24no—
353C2×C4⋊C8—111no—
354C2×C4⋊C8—111no—
355C2×C4⋊C8C2×D1111yescharacteristic
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×C8—111no—
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#336—111no—
387#336—111no—
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—22no—
438C2×M16—22no—
439C2×M16—41no—
440C22×C8—22no—
441C22×C8—22no—
442C22×C8—41no—
443C22×C8—111no—
444C22×C8—111no—
445C22×C8—111no—
446C22×C8—111no—
447C22×C8—222no—
448C22×C8—222no—
449C22×C8—222no—
450C22×C8—222no—
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—22no—
489C4⋊C8—22no—
490C4⋊C8—22no—
491C4⋊C8—222no—
492C4⋊C8—222no—
493C4⋊C8C22⋊D1114yescomplemented
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—222no—
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×C4D4×D1112yes—
562C22×C4#434312yes—
563C22×C4C23×D1111yescharacteristic
564M16—44no—
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—44no—
576C2×C8—112no—
577C2×C8—112no—
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—221no—
588C2×C8—444no—
589C2×C8—444no—
590C2×C8C2×C22⋊D1112yes—
591C2×C8C2×C22⋊D1112yes—
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—
617C42#433912yes—
618C42C2×C22⋊D1112yes—
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—
640C23#6694612yes—
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×C4#6694612yes—
688C2×C4C4×C22⋊D1112yes—
689C2×C4C4×C22⋊D1112yes—
690C2×C4C2×#433911yescharacteristic
691C2×C4C2×D4×D1111yescharacteristic
692C2×C4#6703711yescharacteristic
693C2×C4C2×#434311yescharacteristic
694C2×C4#6704011yescharacteristic
695C2×C4C22×C22⋊D1111yescharacteristic
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×#6694611yescharacteristic
726C22#1062303511yescharacteristic
727C22D11×#13111yescharacteristic
728C22D11×#13111yescharacteristic
729C22D11×#13111yescharacteristic
730C22#1062328111yescharacteristic
731C22C2×C4×C22⋊D1111yescharacteristic
732C4—22no—
733C4—22no—
734C4—22no—
735C4—41no—
736C4—41no—
737C4—222no—
738C4—441no—
739C4—441no—
740C4—441no—
741C4—441no—
742C4—441no—
743C4#1062303811yescharacteristic
744C4#1062304511yescharacteristic
745C4D4×C22⋊D1111yescharacteristic
746C4#1062334811yescharacteristic
747C2—42no—
748C2—442no—
749C2—442no—
750C2#1307163211yescharacteristic
751C2#1307730811yescharacteristic
752C2#1307730911yescharacteristic
753C2#1307734011yescharacteristic
754C2#1307735811yescharacteristic
755C2#1307775311yescharacteristic
756C2#1307777411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC2×C11×#424C2
prime radical#10622573C4
cosocleC22×C4×C11C24
hypercenterC2×#424D11
hypocenterC11#22991
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
1. C2×#10622740C2semidirect
2. C2×#10622447C2semidirect
3. C2×C8×C22⋊D11C2semidirect
5. #13069413C2semidirect
6. #13069332C2semidirect
7. #13069228C2semidirect
8. #13069221C2semidirect
9. #13068913C2semidirect
10. #13068908C2semidirect
11. #13068792C2semidirect
12. #13068792C2semidirect
13. #13068493C2semidirect
14. #13068382C2semidirect
15. C2×C11×#424C2semidirect
123. C11×C4⋊C8D4semidirect
131. C22⋊(C11⋊C8)D4semidirect
245. C2×#424D11semidirect
493. C4⋊C8C22⋊D11semidirect
619. C11#22991semidirect

Maximal subgroups

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

subgroupindex
C2×#106227402
C2×#106224472
C2×C8×C22⋊D112
#130718522
#130694132
#130693322
#130692282
#130692212
#130689132
#130689082
#130687922
#130684932
#130683822
C2×C11×#4242
#2299111