Finite Group Databasebeta

← C8×#66936 #14760730

Subgroups — C8×#66936 #14760730

Order 2816.

1034 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×C22⋊D11C211yesmaximal, characteristic
2C2×C4×C8×D11C211yesmaximal, characteristic, complemented
3C4×#66936C211yesmaximal, characteristic
4#13069225C211yesmaximal, characteristic, complemented
5#13069224C211yesmaximal, characteristic, complemented
6#13069172C211yesmaximal, characteristic, complemented
7#13069171C211yesmaximal, characteristic, complemented
8#13068905C211yesmaximal, characteristic
9#13068795C211yesmaximal, characteristic, complemented
10#13068683C211yesmaximal, characteristic, complemented
11C8×Dic11⋊C4C211yesmaximal, characteristic, complemented
12C8×C4⋊Dic11C211yesmaximal, characteristic, complemented
13C8×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
14C8×C22⋊Dic11C211yesmaximal, characteristic, complemented
15C8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C2×C4×C22⋊D11C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20C2×#66936C411yescharacteristic
21C2×C42×D11C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C4×C11×C22⋊C4C2211yescharacteristic
26C4×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C8×C22⋊D11—24no—
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38#10622569C411yescharacteristic
39#10622564C411yescharacteristic
40#10622558C411yescharacteristic
41C4×(C2×D11)⋊C4C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43C4×Dic11⋊C4C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45C2×C4×C11⋊C8C2211yescharacteristic
46C4×C8×D11—24no—
47#10622281C411yescharacteristic
48#10622277C411yescharacteristic
49#10622267C411yescharacteristic
50#10622265C411yescharacteristic
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11C2×C411yescharacteristic
63C22×C4×D11C2×C411yescharacteristic
64C22×C4×D11C2×C411yescharacteristic
65C22×C4×D11C2311yescharacteristic
66C22×C8×C11—22no—
67C22×C8×C11—22no—
68C22×C8×C11—22no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C2×C11×C22⋊C4C2×C411yescharacteristic
74C2×C11×C22⋊C4C2×C411yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11C2×C411yescharacteristic
78C2×C22⋊Dic11C2×C411yescharacteristic
79C2×C22⋊Dic11C2×C411yescharacteristic
80C4×C22⋊D11—22no—
81C4×C22⋊D11—22no—
82C2×(C2×D11)⋊C4C2×C411yescharacteristic
83C2×(C2×D11)⋊C4C2×C411yescharacteristic
84C2×(C2×D11)⋊C4C2×C411yescharacteristic
85C2×C4⋊Dic11C2×C411yescharacteristic
86C2×C4⋊Dic11C2×C411yescharacteristic
87C2×Dic11⋊C4C2×C411yescharacteristic
88C2×Dic11⋊C4C2×C411yescharacteristic
89C2×Dic11⋊C4C2×C411yescharacteristic
90C2×C4×Dic11C2×C411yescharacteristic
91C2×C4×Dic11C2×C411yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C2×C8×D11—22no—
100C2×C8×D11—22no—
101C2×C8×D11—22no—
102C2×C8×D11—22no—
103C2×C8×D11—22no—
104C2×C8×D11D414yes—
105#66936C818yesdirect product factor
106C42×D11—22no—
107C42×D11—22no—
108C11×C22⋊C8—22no—
109C4×C8×C11—22no—
110C4×C8×C11—22no—
111C11×#95C2×C411yescharacteristic
112C11×#95C2×C411yescharacteristic
113C11⋊#95C2×C411yescharacteristic
114C11⋊#95C2×C411yescharacteristic
115C11⋊#95C2×C411yescharacteristic
116C11⋊#95C2×C411yescharacteristic
117C11⋊#95C2×C411yescharacteristic
118C11⋊#95C2×C411yescharacteristic
119C11⋊#95C2×C411yescharacteristic
120C11⋊#95C2×C411yescharacteristic
121C22⋊(C11⋊C8)—22no—
122C22⋊(C11⋊C8)—22no—
123(C2×D11)⋊C8—22no—
124(C2×D11)⋊C8—22no—
125Dic11⋊C8—22no—
126Dic11⋊C8—22no—
127C8×Dic11—22no—
128C8×Dic11—22no—
129C8×Dic11—22no—
130C8×Dic11—22no—
131C4⋊(C11⋊C8)—22no—
132C4×C11⋊C8—22no—
133C8×#123—111nomaximal, Sylow
134C24×C11C22×C411yescharacteristic
135C23×D11C22×C411yescharacteristic
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11C22×C411yescharacteristic
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C2×C22⋊D11—22no—
149C2×C22⋊D11—22no—
150C2×C22⋊D11C2×C814yes—
151C22×Dic11C22×C411yescharacteristic
152C22×Dic11C22×C411yescharacteristic
153C22×Dic11C22×C411yescharacteristic
154C22×Dic11C22×C411yescharacteristic
155C22×Dic11C22×C411yescharacteristic
156C22×Dic11C22×C411yescharacteristic
157C22×Dic11C22×C411yescharacteristic
158C2×C4×D11—22no—
159C2×C4×D11—22no—
160C2×C4×D11—22no—
161C2×C4×D11—22no—
162C2×C4×D11—22no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11C2×C814yescomplemented
168C2×C4×D11C2×D412yes—
169C2×C4×D11#4112yes—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—44no—
179C2×C8×C11C2×D412yes—
180C2×C8×C11#4112yes—
181C2×C8×C11#4112yes—
182C2×C8×C11#4112yes—
183C11×C22⋊C4—22no—
184C11×C22⋊C4C2×C814yescomplemented
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C22⋊Dic11—22no—
190C22⋊Dic11—22no—
191C22⋊Dic11C2×C814yescomplemented
192(C2×D11)⋊C4—22no—
193(C2×D11)⋊C4—22no—
194(C2×D11)⋊C4C2×C814yescomplemented
195C4⋊Dic11—22no—
196C4⋊Dic11C2×C814yescomplemented
197Dic11⋊C4—22no—
198Dic11⋊C4—22no—
199Dic11⋊C4C2×C814yescomplemented
200C4×Dic11—22no—
201C4×Dic11—22no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8C2×D412yes—
219C2×C11⋊C8#4112yes—
220C8×D11—28no—
221C8×D11—28no—
222C2×C8×D4—111no—
223C22×C4×C8—111no—
224C4×#123—111no—
225#1923—111no—
226#1923—111no—
227#1916—111no—
228#1916—111no—
229#1869—111no—
230#1850—111no—
231#1817—111no—
232C8×C4⋊C4—111no—
233C8×C4⋊C4—111no—
234C8×C22⋊C4—111no—
235C8×C22⋊C4—111no—
236C8×C22⋊C4D1111yescharacteristic, complemented
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11C22×C812yes—
244C23×C11C23×C411yescharacteristic
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11C4×D412yes—
250C22×D11C22×C812yes—
251C22×D11#13112yes—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11C22×C812yes—
269C2×C4×C11C22×C812yes—
270C2×C4×C11#13112yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C22⋊D11—28no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
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×Dic11C4×D412yes—
295C2×Dic11C22×C812yes—
296C2×Dic11C22×C812yes—
297C2×Dic11C22×C812yes—
298C2×Dic11#13112yes—
299C4×D11—28no—
300C4×D11—28no—
301C4×D11—22no—
302C4×D11—22no—
303C4×D11—22no—
304C4×D11—22no—
305C8×C11—22no—
306C8×C11—41no—
307C8×C11—41no—
308C8×C11#12314yescomplemented
309C11⋊C8—22no—
310C11⋊C8—22no—
311C11⋊C8—41no—
312C11⋊C8—41no—
313C23×C8—111no—
314C23×C8—111no—
315C23×C8C2×D1111yescharacteristic
316C2×#123—111no—
317C2×C4×D4—111no—
318C22×C42—111no—
319C8×D4—224no—
320C2×C4⋊C8—111no—
321C2×C4⋊C8—111no—
322C2×C4⋊C8—111no—
323C2×C22⋊C8—111no—
324C2×C22⋊C8—111no—
325C2×C22⋊C8—111no—
326C2×C22⋊C8—111no—
327C2×C22⋊C8C2×D1111yescharacteristic
328C2×C4×C8—111no—
329C2×C4×C8—111no—
330C2×C4×C8—111no—
331C2×C4×C8—111no—
332C2×C4×C8—111no—
333C2×C4×C8—224no—
334C2×C4×C8C2×D1111yescharacteristic
335C2×C4×C8C2×D1111yescharacteristic
336#388—111no—
337#388—111no—
338#387—111no—
339#387—111no—
340#386—111no—
341#385—111no—
342#381—111no—
343C4×C4⋊C4—111no—
344C4×C4⋊C4—111no—
345C4×C22⋊C4—111no—
346C4×C22⋊C4—111no—
347C4×C22⋊C4C2×D1111yescharacteristic
348#336—111no—
349#336—111no—
350#336—111no—
351#336—111no—
352#336—111no—
353#336—111no—
354#336—111no—
355#336—111no—
356#336C2×D1111yescharacteristic
357#336C2×D1111yescharacteristic
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11C2×C4×D411yescharacteristic
366C22×C11C4×#4111yescharacteristic
367C22×C11C4×#4111yescharacteristic
368C22×C11C23×C811yescharacteristic
369C22×C11C2×#13111yescharacteristic
370C22×C11C2×#13111yescharacteristic
371C22×C11C2×#13111yescharacteristic
372C2×D11—22no—
373C2×D11—22no—
374C2×D11—22no—
375C2×D11—22no—
376C2×D11—22no—
377C2×D11—22no—
378C2×D11C8×D414yes—
379C4×C11—22no—
380C4×C11—22no—
381C4×C11—22no—
382C4×C11—41no—
383C4×C11—41no—
384C4×C11C2×#12311yescharacteristic
385C4×C11#52511yescharacteristic
386C4×C11#52911yescharacteristic
387C4×C11#52911yescharacteristic
388Dic11—22no—
389Dic11—22no—
390Dic11—22no—
391Dic11—22no—
392Dic11—22no—
393Dic11—41no—
394Dic11—41no—
395C22×D4—111no—
396C23×C4—111no—
397C23×C4—111no—
398C23×C4—111no—
399C23×C4C22×D1111yescharacteristic
400C22×C8—22no—
401C22×C8—22no—
402C22×C8—22no—
403C22×C8—111no—
404C22×C8—111no—
405C22×C8—114no—
406C22×C8—111no—
407C22×C8—111no—
408C22×C8—222no—
409C22×C8—222no—
410C22×C8—222no—
411C22×C8—222no—
412C22×C8—222no—
413C22×C8C22×D1111yescharacteristic
414C22×C8C22×D1111yescharacteristic
415C22×C8C22×D1111yescharacteristic
416C22×C8C22×D1111yescharacteristic
417#123—118no—
418C4×D4—222no—
419C4×D4—222no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C22⋊C4—111no—
426C2×C22⋊C4—111no—
427C2×C22⋊C4—111no—
428C2×C22⋊C4—111no—
429C2×C22⋊C4—111no—
430C2×C22⋊C4—111no—
431C2×C22⋊C4C4×D1111yescharacteristic
432C2×C22⋊C4C4×D1111yescharacteristic
433C2×C42—111no—
434C2×C42—111no—
435C2×C42—111no—
436C2×C42—111no—
437C2×C42—111no—
438C2×C42—222no—
439C2×C42—222no—
440C2×C42C22×D1111yescharacteristic
441C2×C42C22×D1111yescharacteristic
442C4⋊C8—222no—
443C4⋊C8—222no—
444C4⋊C8—222no—
445C22⋊C8—22no—
446C22⋊C8—222no—
447C22⋊C8—222no—
448C22⋊C8—222no—
449C22⋊C8—222no—
450C4×C8—22no—
451C4×C8—22no—
452C4×C8—222no—
453C4×C8—222no—
454C4×C8—222no—
455C4×C8—222no—
456C4×C8—222no—
457#95—111no—
458#95—111no—
459#95—111no—
460#95—111no—
461#95—111no—
462#95—111no—
463#95—111no—
464#95—111no—
465#95C4×D1111yescharacteristic
466#95C4×D1111yescharacteristic
467C2×C11—42no—
468C2×C11C4×#12311yescharacteristic
469C2×C11C2×C8×D411yescharacteristic
470C2×C11#292911yescharacteristic
471C2×C11C8×#4111yescharacteristic
472C2×C11C8×#4111yescharacteristic
473C2×C11#296611yescharacteristic
474C2×C11#296611yescharacteristic
475D11—24no—
476C24—111no—
477C24C2×C4×D1111yescharacteristic
478C2×D4—114no—
479C2×D4—222no—
480C2×D4—222no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—111no—
488C22×C4—111no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—111no—
492C22×C4—114no—
493C22×C4—112no—
494C22×C4—112no—
495C22×C4—111no—
496C22×C4—111no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4C2×C4×D1111yescharacteristic
507C22×C4C2×C4×D1111yescharacteristic
508C22×C4C2×C4×D1111yescharacteristic
509C22×C4C2×C4×D1111yescharacteristic
510C22×C4C2×C4×D1111yescharacteristic
511C22×C4C23×D1111yescharacteristic
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—44no—
521C2×C8—112no—
522C2×C8—112no—
523C2×C8—228no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8—228no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8#433912yes—
536C2×C8#433912yes—
537C2×C8D4×D1112yes—
538C2×C8#434112yes—
539C4⋊C4—114no—
540C4⋊C4—114no—
541C4⋊C4—222no—
542C4⋊C4—222no—
543C4⋊C4—222no—
544C22⋊C4—22no—
545C22⋊C4—114no—
546C22⋊C4—114no—
547C22⋊C4—222no—
548C22⋊C4—222no—
549C22⋊C4—222no—
550C22⋊C4—222no—
551C22⋊C4C8×D1114yescomplemented
552C42—21no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—222no—
557C42—222no—
558C42—221no—
559C42—221no—
560C42—221no—
561C42—221no—
562C42—221no—
563C42—221no—
564C11C8×#12311yescharacteristic, complemented, Sylow
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—112no—
572C23—112no—
573C23—112no—
574C23—221no—
575C23—221no—
576C23—221no—
577C23—221no—
578C23C2×C8×D1112yes—
579C23C22×C4×D1111yescharacteristic
580D4—228no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—112no—
598C2×C4—112no—
599C2×C4—112no—
600C2×C4—112no—
601C2×C4—112no—
602C2×C4—228no—
603C2×C4—228no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—221no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—221no—
610C2×C4—221no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—221no—
614C2×C4—222no—
615C2×C4—222no—
616C2×C4—222no—
617C2×C4—222no—
618C2×C4—221no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4C2×C8×D1112yes—
625C2×C4C2×C8×D1112yes—
626C2×C4#6695412yes—
627C2×C4C2×#433911yescharacteristic
628C2×C4C2×#433911yescharacteristic
629C2×C4C2×D4×D1111yescharacteristic
630C2×C4C2×#434111yescharacteristic
631C2×C4#41×D1111yescharacteristic
632C2×C4#41×D1111yescharacteristic
633C8—22no—
634C8—41no—
635C8—41no—
636C8—222no—
637C8—222no—
638C8—441no—
639C8—441no—
640C8#6693614yesdirect product factor
641C22—22no—
642C22—22no—
643C22—22no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—114no—
649C22—222no—
650C22—222no—
651C22—222no—
652C22—222no—
653C22—222no—
654C22—222no—
655C22C4×#433911yescharacteristic
656C22C4×#434111yescharacteristic
657C22C4×D4×D1111yescharacteristic
658C22C22×C8×D1111yescharacteristic
659C22C2×#6695411yescharacteristic
660C22D11×#13111yescharacteristic
661C22D11×#13111yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—41no—
666C4—41no—
667C4—222no—
668C4—222no—
669C4—222no—
670C4—222no—
671C4—222no—
672C4—441no—
673C4—441no—
674C4C2×#6693611yescharacteristic
675C4#1062305911yescharacteristic
676C4#1062307811yescharacteristic
677C4#1062308811yescharacteristic
678C2—42no—
679C2—224no—
680C2C4×#6693611yescharacteristic
681C2C8×D4×D1111yescharacteristic
682C2#1307730511yescharacteristic
683C2C8×#434111yescharacteristic
684C2C8×#433911yescharacteristic
685C2#1307758711yescharacteristic
686C2#1307758811yescharacteristic
subgroupG/H
centerC22×C8C22×D11
commutatorC22×C11C23×C8
FrattiniC22×C4C23×D11
FittingC8×C11×C22⋊C4C2
socleC23×C11C23×C4
prime radicalC22×C22⋊D11C2×C4
cosocleC22×C4×C11C24
hypercenterC8×C22⋊C4D11
hypocenterC11C8×#123
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C8 ◁ C8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C8×D11C2semidirect
4. #13069225C2semidirect
5. #13069224C2semidirect
6. #13069172C2semidirect
7. #13069171C2semidirect
9. #13068795C2semidirect
10. #13068683C2semidirect
11. C8×Dic11⋊C4C2semidirect
12. C8×C4⋊Dic11C2semidirect
13. C8×(C2×D11)⋊C4C2semidirect
14. C8×C22⋊Dic11C2semidirect
15. C8×C11×C22⋊C4C2semidirect
105. #66936C8direct (N × H)
167. C2×C4×D11C2×C8semidirect
184. C11×C22⋊C4C2×C8semidirect
191. C22⋊Dic11C2×C8semidirect
194. (C2×D11)⋊C4C2×C8semidirect
196. C4⋊Dic11C2×C8semidirect
199. Dic11⋊C4C2×C8semidirect
236. C8×C22⋊C4D11semidirect
308. C8×C11#123semidirect
551. C22⋊C4C8×D11semidirect
564. C11C8×#123semidirect
640. C8#66936direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C8×C22⋊D112
C2×C4×C8×D112
C4×#669362
#130692252
#130692242
#130691722
#130691712
#130689052
#130687952
#130686832
C8×Dic11⋊C42
C8×C4⋊Dic112
C8×(C2×D11)⋊C42
C8×C22⋊Dic112
C8×C11×C22⋊C42
C8×#12311