Finite Group Databasebeta

← #14772789

Subgroups — #14772789

Order 2816.

1052 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622298C211yesmaximal, characteristic, complemented
2C2×D11×C4⋊C8C211yesmaximal, characteristic, complemented
3C4×#66946C211yesmaximal, characteristic
4#13069223C211yesmaximal, characteristic, complemented
5#13069221C211yesmaximal, characteristic, complemented
6#13069175C211yesmaximal, characteristic, complemented
7#13068907C211yesmaximal, characteristic
8#13068907C211yesmaximal, characteristic
9#13068731C211yesmaximal, characteristic, complemented
10#13068595C211yesmaximal, characteristic, complemented
11#13068595C211yesmaximal, characteristic, complemented
12#13068464C211yesmaximal, characteristic, complemented
13C8×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
14#13068386C211yesmaximal, characteristic, complemented
15C11×#1916C211yesmaximal, characteristic, complemented
16C22×C8×D11C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18C2×#66946C411yescharacteristic
19C2×#66946C411yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×C42×D11C2211yescharacteristic
22C2×C42×D11C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38C4⋊C4×Dic11C411yescharacteristic
39C4⋊C4×Dic11C411yescharacteristic
40C4×(C2×D11)⋊C4C2211yescharacteristic
41C4×(C2×D11)⋊C4C2211yescharacteristic
42C42×Dic11C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45D11×C4⋊C8—24no—
46#10622298—24no—
47#10622279C411yescharacteristic
48#10622279C411yescharacteristic
49#10622279C411yescharacteristic
50#10622279C411yescharacteristic
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D44C2×C411yescharacteristic
62C22×C4×D11C2×C411yescharacteristic
63C22×C4×D11C2×C411yescharacteristic
64C22×C4×D11C2×C411yescharacteristic
65C22×C4×D11C2×C411yescharacteristic
66C22×C4×D11C2311yescharacteristic
67C22×C4×D11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C2×C11×C4⋊C4C2×C411yescharacteristic
73C2×C11×C4⋊C4C2×C411yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×(C2×D11)⋊C4C2×C411yescharacteristic
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×C4⋊Dic11C2×C411yescharacteristic
84C2×C4×Dic11C2×C411yescharacteristic
85C2×C4×Dic11C2×C411yescharacteristic
86C2×C4×Dic11C2×C411yescharacteristic
87C2×C4×Dic11C2×C411yescharacteristic
88C2×C4×Dic11C2×C411yescharacteristic
89C2×C4×Dic11C2×C411yescharacteristic
90C2×C4×Dic11C2×C411yescharacteristic
91C2×C4×Dic11C2×C411yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C2×C8×D11—22no—
99C2×C8×D11—22no—
100C2×C8×D11—22no—
101C2×C8×D11—22no—
102C2×C8×D11—41no—
103C2×C8×D11—41no—
104#66946—24no—
105#66946C818yescomplemented
106C4×D44—22no—
107C4×D44—22no—
108C42×D11—22no—
109C42×D11—22no—
110C42×D11—22no—
111C42×D11—22no—
112C11×C4⋊C8—22no—
113C4×C8×C11—22no—
114C11×#95C2×C411yescharacteristic
115C11×#95C2×C411yescharacteristic
116C11⋊#95C2×C411yescharacteristic
117C11⋊#95C2×C411yescharacteristic
118C11⋊#95C2×C411yescharacteristic
119C11⋊#95C2×C411yescharacteristic
120(C2×D11)⋊C8—22no—
121(C2×D11)⋊C8—22no—
122(C2×D11)⋊C8—22no—
123(C2×D11)⋊C8—22no—
124(C2×D11)⋊C8—41no—
125(C2×D11)⋊C8—41no—
126Dic11⋊C8—22no—
127Dic11⋊C8—22no—
128Dic11⋊C8—22no—
129Dic11⋊C8D414yescomplemented
130C8×Dic11—41no—
131C8×Dic11—41no—
132C4⋊(C11⋊C8)—22no—
133C4×C11⋊C8—22no—
134#22748—111nomaximal, Sylow
135C23×D11C22×C411yescharacteristic
136C23×D11C22×C411yescharacteristic
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C22×C411yescharacteristic
140C22×C4×C11C22×C411yescharacteristic
141C22×C4×C11C22×C411yescharacteristic
142C22×C4×C11C22×C411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11C22×C411yescharacteristic
145C22×Dic11C22×C411yescharacteristic
146C22×Dic11C22×C411yescharacteristic
147C22×Dic11C22×C411yescharacteristic
148C22×Dic11C22×C411yescharacteristic
149C22×Dic11C22×C411yescharacteristic
150C2×D44—22no—
151C2×D44—22no—
152C2×D44C2×C814yes—
153C2×C4×D11—22no—
154C2×C4×D11—22no—
155C2×C4×D11—22no—
156C2×C4×D11—22no—
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×C4×D11—22no—
160C2×C4×D11—22no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—41no—
172C2×C4×D11—41no—
173C2×C4×D11C2×C814yes—
174C2×C4×D11C2×C814yescomplemented
175C2×C4×D11#4112yes—
176C2×C4×D11#4112yes—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11C2×D412yes—
189C11×C4⋊C4—22no—
190C11×C4⋊C4C2×C814yescomplemented
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—21no—
197(C2×D11)⋊C4—22no—
198(C2×D11)⋊C4—22no—
199(C2×D11)⋊C4—22no—
200(C2×D11)⋊C4C2×C814yes—
201(C2×D11)⋊C4C2×C814yescomplemented
202(C2×D11)⋊C4M1614yes—
203C4⋊Dic11—22no—
204C4×Dic11—22no—
205C4×Dic11—22no—
206C4×Dic11—22no—
207C4×Dic11—22no—
208C4×Dic11—22no—
209C4×Dic11—22no—
210C4×Dic11—21no—
211C4×Dic11—21no—
212C4×Dic11—41no—
213C4×Dic11C2×C814yescomplemented
214C4×Dic11C2×D412yes—
215C4×Dic11#4112yes—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8C2×D412yes—
228C8×D11—44no—
229C8×D11—44no—
230C2×#431—111no—
231C22×C4⋊C8—111no—
232C42×D4—111no—
233#1923—111no—
234#1923—111no—
235#1916—111no—
236#1916D1111yescharacteristic, complemented
237#1869—111no—
238#1869—111no—
239#1831—111no—
240#1797—111no—
241#1797—111no—
242C4×C4⋊C8—111no—
243C8×C22⋊C4—111no—
244C8×C22⋊C4—111no—
245C23×C11C23×C411yescharacteristic
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11—21no—
251C22×D11—21no—
252C22×D11—21no—
253C22×D11—21no—
254C22×D11—21no—
255C22×D11—21no—
256C22×D11#11712yes—
257C22×D11C22×C812yes—
258C22×D11C22×C812yes—
259C22×D11C2×M1612yes—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11C22×C812yes—
275C2×C4×C11C22×C812yes—
276C2×C4×C11C22×C812yes—
277C2×C4×C11C2×M1612yes—
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11H(5,𝔽2)11yescharacteristic
283C2×C4×C112−1+411yescharacteristic
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11#11712yes—
296C2×Dic11C4×D412yes—
297C2×Dic11C4×D412yes—
298C2×Dic11C22×C812yes—
299C2×Dic11C22×C812yes—
300C2×Dic11C2×M1612yes—
301C2×Dic11#13112yes—
302D44—28no—
303C4×D11—22no—
304C4×D11—22no—
305C4×D11—22no—
306C4×D11—22no—
307C4×D11—28no—
308C4×D11—28no—
309C4×D11—44no—
310C4×D11—44no—
311C4×D11—41no—
312C4×D11—41no—
313C4×D11—41no—
314C4×D11—41no—
315C8×C11—22no—
316C8×C11—41no—
317C8×C11—41no—
318C8×C11—41no—
319C11⋊C8—22no—
320C11⋊C8—41no—
321C11⋊C8—41no—
322C11⋊C8—41no—
323C23×C8—111no—
324C23×C8—111no—
325C2×C4×D4—111no—
326C2×C4×D4—111no—
327C2×C4×D4—111no—
328C22×C42—111no—
329C22×C42—111no—
330#431—224no—
331C2×C4⋊C8—111no—
332C2×C4⋊C8—111no—
333C2×C4⋊C8—111no—
334C2×C4⋊C8—111no—
335C2×C4⋊C8—111no—
336C2×C4⋊C8—224no—
337C2×C4⋊C8C2×D1111yescharacteristic
338C2×C22⋊C8—111no—
339C2×C22⋊C8—111no—
340C2×C22⋊C8—111no—
341C2×C22⋊C8—111no—
342C2×C22⋊C8—111no—
343C2×C22⋊C8—111no—
344C2×C4×C8—111no—
345C2×C4×C8—111no—
346C2×C4×C8—111no—
347C2×C4×C8C2×D1111yescharacteristic
348C4×C4⋊C4—111no—
349C4×C4⋊C4—111no—
350C4×C4⋊C4C2×D1111yescharacteristic
351C4×C22⋊C4—111no—
352C4×C22⋊C4—111no—
353C4×C22⋊C4—111no—
354C4×C22⋊C4—111no—
355C4×C22⋊C4—111no—
356C4×C22⋊C4—111no—
357C43—111no—
358#336—111no—
359#336—111no—
360#336—111no—
361#336—111no—
362#336—111no—
363#336—111no—
364#336C2×D1111yescharacteristic
365#336C2×D1111yescharacteristic
366#336C2×D1111yescharacteristic
367#336C2×D1111yescharacteristic
368C22×C11C2×#11711yescharacteristic
369C22×C11C2×C4×D411yescharacteristic
370C22×C11#52011yescharacteristic
371C22×C11C23×C811yescharacteristic
372C22×C11C22×M1611yescharacteristic
373C22×C11C2×#13111yescharacteristic
374C22×C11#56811yescharacteristic
375C2×D11—22no—
376C2×D11—22no—
377C2×D11—22no—
378C2×D11—22no—
379C2×D11—22no—
380C2×D11—22no—
381C2×D11—22no—
382C2×D11—22no—
383C2×D11—22no—
384C2×D11—41no—
385C2×D11—41no—
386C2×D11—41no—
387C2×D11—41no—
388C2×D11#43114yescomplemented
389C4×C11—22no—
390C4×C11—22no—
391C4×C11—22no—
392C4×C11—22no—
393C4×C11—41no—
394C4×C11—41no—
395C4×C11#54611yescharacteristic
396C4×C11#54811yescharacteristic
397C4×C11#55211yescharacteristic
398C4×C11#55311yescharacteristic
399Dic11—22no—
400Dic11—22no—
401Dic11—22no—
402Dic11—22no—
403Dic11—41no—
404Dic11C8×D414yes—
405C22×D4—111no—
406C23×C4—111no—
407C23×C4—111no—
408C23×C4—111no—
409C23×C4—111no—
410C23×C4—111no—
411C23×C4—111no—
412C22×C8—111no—
413C22×C8—111no—
414C22×C8—111no—
415C22×C8—111no—
416C22×C8—222no—
417C22×C8—222no—
418C22×C8—222no—
419C22×C8—222no—
420C22×C8—441no—
421C22×C8—441no—
422C22×C8C22×D1111yescharacteristic
423C22×C8C22×D1111yescharacteristic
424C22×C8C22×D1111yescharacteristic
425C22×C8C22×D1111yescharacteristic
426C4×D4—118no—
427C4×D4—222no—
428C4×D4—222no—
429C4×D4—224no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4C4×D1111yescharacteristic
432C2×C4⋊C4C4×D1111yescharacteristic
433C2×C22⋊C4—111no—
434C2×C22⋊C4—111no—
435C2×C22⋊C4—111no—
436C2×C22⋊C4—111no—
437C2×C22⋊C4—111no—
438C2×C22⋊C4—111no—
439C2×C42—111no—
440C2×C42—111no—
441C2×C42—111no—
442C2×C42—111no—
443C2×C42—111no—
444C2×C42—111no—
445C2×C42—111no—
446C2×C42—111no—
447C2×C42—111no—
448C2×C42—111no—
449C2×C42—222no—
450C2×C42—222no—
451C2×C42—222no—
452C2×C42—222no—
453C2×C42C22×D1111yescharacteristic
454C2×C42C22×D1111yescharacteristic
455C2×C42C22×D1111yescharacteristic
456C4⋊C8—22no—
457C4⋊C8—114no—
458C4⋊C8—222no—
459C4⋊C8—222no—
460C4⋊C8—222no—
461C4⋊C8—222no—
462C22⋊C8—222no—
463C22⋊C8—222no—
464C22⋊C8—222no—
465C22⋊C8—222no—
466C22⋊C8—441no—
467C22⋊C8—441no—
468C4×C8—22no—
469C4×C8—222no—
470C4×C8—441no—
471C4×C8—441no—
472#95—111no—
473#95—111no—
474#95—111no—
475#95—111no—
476#95C4×D1111yescharacteristic
477#95C4×D1111yescharacteristic
478C2×C11#235211yescharacteristic
479C2×C11C2×#43111yescharacteristic
480C2×C11#292511yescharacteristic
481C2×C11C2×C8×D411yescharacteristic
482C2×C11D4×M1611yescharacteristic
483C2×C11#298811yescharacteristic
484C2×C11#299011yescharacteristic
485D11—24no—
486D11—42no—
487C24—111no—
488C24—111no—
489C2×D4—114no—
490C2×D4—222no—
491C2×D4—222no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—111no—
496C22×C4—111no—
497C22×C4—114no—
498C22×C4—114no—
499C22×C4—112no—
500C22×C4—112no—
501C22×C4—111no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—222no—
506C22×C4—222no—
507C22×C4—222no—
508C22×C4—222no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—222no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—441no—
521C22×C4—441no—
522C22×C4C2×C4×D1111yescharacteristic
523C22×C4C2×C4×D1111yescharacteristic
524C22×C4C2×C4×D1111yescharacteristic
525C22×C4C2×C4×D1111yescharacteristic
526C22×C4C2×C4×D1111yescharacteristic
527C22×C4C2×C4×D1111yescharacteristic
528C22×C4C23×D1111yescharacteristic
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—112no—
541C2×C8—221no—
542C2×C8—221no—
543C2×C8—221no—
544C2×C8—221no—
545C2×C8—221no—
546C2×C8—221no—
547C2×C8—221no—
548C2×C8—221no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8—444no—
553C2×C8—444no—
554C2×C8D4×D1112yes—
555C4⋊C4—22no—
556C4⋊C4—222no—
557C4⋊C4C8×D1114yescomplemented
558C22⋊C4—114no—
559C22⋊C4—114no—
560C22⋊C4—114no—
561C22⋊C4—222no—
562C22⋊C4—222no—
563C22⋊C4—222no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—114no—
571C42—112no—
572C42—112no—
573C42—222no—
574C42—222no—
575C42—222no—
576C42—222no—
577C42—222no—
578C42—222no—
579C42—221no—
580C42—221no—
581C42—441no—
582C11#2274811yescharacteristic, complemented, Sylow
583C23—112no—
584C23—112no—
585C23—112no—
586C23—112no—
587C23—221no—
588C23—221no—
589C23—221no—
590C23—221no—
591C23—221no—
592C23—221no—
593C23—221no—
594C23—221no—
595C23—221no—
596C23—221no—
597C23C22×C4×D1111yescharacteristic
598D4—228no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—112no—
614C2×C4—112no—
615C2×C4—112no—
616C2×C4—112no—
617C2×C4—112no—
618C2×C4—112no—
619C2×C4—112no—
620C2×C4—228no—
621C2×C4—228no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—221no—
626C2×C4—221no—
627C2×C4—221no—
628C2×C4—221no—
629C2×C4—221no—
630C2×C4—222no—
631C2×C4—222no—
632C2×C4—222no—
633C2×C4—222no—
634C2×C4—221no—
635C2×C4—221no—
636C2×C4—221no—
637C2×C4—444no—
638C2×C4—444no—
639C2×C4—441no—
640C2×C4—441no—
641C2×C4—441no—
642C2×C4—441no—
643C2×C4C2×C8×D1112yes—
644C2×C4C2×C8×D1112yes—
645C2×C4C2×C8×D1112yes—
646C2×C4M16×D1112yes—
647C2×C4C2×D4×D1111yescharacteristic
648C2×C4#6704011yescharacteristic
649C2×C4#41×D1111yescharacteristic
650C2×C4#41×D1111yescharacteristic
651C2×C4#41×D1111yescharacteristic
652C2×C4#6704211yescharacteristic
653C8—22no—
654C8—41no—
655C8—41no—
656C8—41no—
657C8—222no—
658C8—441no—
659C8—441no—
660C8—441no—
661C22—114no—
662C22—222no—
663C22—222no—
664C22—222no—
665C22—222no—
666C22—222no—
667C22—222no—
668C22—222no—
669C22—222no—
670C22—222no—
671C22—441no—
672C22—441no—
673C22—441no—
674C22—441no—
675C22D11×#11711yescharacteristic
676C22C4×D4×D1111yescharacteristic
677C22#1062310511yescharacteristic
678C22C22×C8×D1111yescharacteristic
679C22C2×M16×D1111yescharacteristic
680C22D11×#13111yescharacteristic
681C22#1062328111yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—22no—
686C4—41no—
687C4—41no—
688C4—114no—
689C4—222no—
690C4—222no—
691C4—222no—
692C4—222no—
693C4—441no—
694C4#1062316411yescharacteristic
695C4#1062318511yescharacteristic
696C4#1062322411yescharacteristic
697C4#1062324011yescharacteristic
698C2—224no—
699C2—442no—
700C2#1307154011yescharacteristic
701C2D11×#43111yescharacteristic
702C2#1307727911yescharacteristic
703C2C8×D4×D1111yescharacteristic
704C2#1307734911yescharacteristic
705C2#1307772611yescharacteristic
706C2#1307774011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C23×C8
FittingC11×#1916C2
socleC23×C11C23×C4
prime radicalC22×D44C2×C4
cosocleC22×C4×C11C24
hypercenter#1916D11
hypocenterC11#22748
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
1. C2×#10622298C2semidirect
2. C2×D11×C4⋊C8C2semidirect
4. #13069223C2semidirect
5. #13069221C2semidirect
6. #13069175C2semidirect
9. #13068731C2semidirect
10. #13068595C2semidirect
11. #13068595C2semidirect
12. #13068464C2semidirect
13. C8×(C2×D11)⋊C4C2semidirect
14. #13068386C2semidirect
15. C11×#1916C2semidirect
105. #66946C8semidirect
129. Dic11⋊C8D4semidirect
174. C2×C4×D11C2×C8semidirect
190. C11×C4⋊C4C2×C8semidirect
201. (C2×D11)⋊C4C2×C8semidirect
213. C4×Dic11C2×C8semidirect
236. #1916D11semidirect
388. C2×D11#431semidirect
557. C4⋊C4C8×D11semidirect
582. C11#22748semidirect

Maximal subgroups

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

subgroupindex
C2×#106222982
C2×D11×C4⋊C82
C4×#669462
#130692232
#130692212
#130691752
#130689072
#130687312
#130685952
#130684642
C8×(C2×D11)⋊C42
#130683862
C11×#19162
#2274811