Finite Group Databasebeta

← #14775872

Subgroups — #14775872

Order 2816.

1168 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
2C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
3C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
4C22×Dic11⋊C8C211yesmaximal, characteristic, complemented
5C4×#66992C211yesmaximal, characteristic
6#13069408C211yesmaximal, characteristic, complemented
7#13069333C211yesmaximal, characteristic, complemented
8#13069225C211yesmaximal, characteristic, complemented
9#13069220C211yesmaximal, characteristic, complemented
10#13068906C211yesmaximal, characteristic, complemented
11#13068795C211yesmaximal, characteristic, complemented
12#13068793C211yesmaximal, characteristic, complemented
13#13068477C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic11C211yesmaximal, characteristic, complemented
15C11×#1869C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66992C411yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C23×C11⋊C8C2211yescharacteristic
24C22×C8×D11C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28#10622833C411yescharacteristic
29C4×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C8×C22⋊D11—24no—
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×Dic11⋊C8—24no—
37C2×Dic11⋊C8C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40C2×Dic11⋊C8C2211yescharacteristic
41C2×Dic11⋊C8C2211yescharacteristic
42C2×C8×Dic11C2211yescharacteristic
43C2×C8×Dic11C2211yescharacteristic
44C2×C8×Dic11C2211yescharacteristic
45D4×C11⋊C8—24no—
46#10622603C411yescharacteristic
47#10622585C411yescharacteristic
48#10622571C411yescharacteristic
49#10622570C411yescharacteristic
50#10622558C411yescharacteristic
51#10622555C411yescharacteristic
52C4×(C2×D11)⋊C4C2211yescharacteristic
53C4×Dic11⋊C4C2211yescharacteristic
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55C2×C4×C11⋊C8C2211yescharacteristic
56(C22⋊D11)⋊C8—24no—
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622188C2211yescharacteristic
62#10622188C2211yescharacteristic
63C22×D4×C11C2×C411yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11C2×C411yescharacteristic
67C22×C22⋊D11C2×C411yescharacteristic
68C23×Dic11C2×C411yescharacteristic
69C23×Dic11C2×C411yescharacteristic
70C22×C4×D11C2311yescharacteristic
71C22×C8×C11—22no—
72C22×C8×C11—22no—
73C22×C8×C11—41no—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C2×C11×C4⋊C4C2×C411yescharacteristic
81C2×C11×C22⋊C4C2×C411yescharacteristic
82C2×C11×C22⋊C4C2×C411yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11C2×C411yescharacteristic
85C2×C22⋊Dic11C2×C411yescharacteristic
86C2×C22⋊Dic11C2×C411yescharacteristic
87C2×C22⋊Dic11C2×C411yescharacteristic
88#66992C818yescomplemented
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×Dic11⋊C4C2×C411yescharacteristic
98C2×Dic11⋊C4C2×C411yescharacteristic
99C2×Dic11⋊C4C2×C411yescharacteristic
100C2×Dic11⋊C4C2×C411yescharacteristic
101C2×C4×Dic11—22no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11C2×C411yescharacteristic
104C2×C4×Dic11C2×C411yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C22×C11⋊C8—22no—
109C22×C11⋊C8—22no—
110C22×C11⋊C8—22no—
111C22×C11⋊C8—22no—
112C22×C11⋊C8—41no—
113C22×C11⋊C8—41no—
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C2×C8×D11—22no—
119C2×C8×D11—22no—
120C2×C8×D11—41no—
121C11×C22⋊C8—22no—
122C11×C22⋊C8—22no—
123C11×C22⋊C8—41no—
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—41no—
135Dic11⋊C8—22no—
136Dic11⋊C8—22no—
137Dic11⋊C8—22no—
138Dic11⋊C8—22no—
139Dic11⋊C8D414yescomplemented
140C8×Dic11—22no—
141C8×Dic11—22no—
142C8×Dic11—22no—
143C4⋊(C11⋊C8)—22no—
144C4×C11⋊C8—22no—
145#22985—111nomaximal, Sylow
146C24×C11C22×C411yescharacteristic
147C24×C11C22×C411yescharacteristic
148C23×D11C22×C411yescharacteristic
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11C2×C814yescomplemented
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11C22×C411yescharacteristic
163C22×C4×C11C22×C411yescharacteristic
164C22×C4×C11C22×C411yescharacteristic
165C22×C4×C11C22×C411yescharacteristic
166C22×C4×C11C2×D412yes—
167C22×C4×C11#4112yes—
168C22×C4×C11C2411yescharacteristic
169C2×C22⋊D11—22no—
170C2×C22⋊D11—22no—
171C2×C22⋊D11—22no—
172C2×C22⋊D11—22no—
173C2×C22⋊D11C2×C814yescomplemented
174C2×C22⋊D11C2×C814yescomplemented
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—41no—
180C22×Dic11C2×C814yescomplemented
181C22×Dic11C22×C411yescharacteristic
182C22×Dic11C22×C411yescharacteristic
183C22×Dic11C22×C411yescharacteristic
184C22×Dic11C22×C411yescharacteristic
185C22×Dic11C22×C411yescharacteristic
186C22×Dic11C22×C411yescharacteristic
187C22×Dic11C22×C411yescharacteristic
188C2×C4×D11—21no—
189C2×C4×D11—21no—
190C2×C4×D11—21no—
191C2×C4×D11—21no—
192C2×C4×D11—21no—
193C2×C4×D11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—44no—
206C2×C8×C11C2×D412yes—
207C11×C4⋊C4—22no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—22no—
210C42×C11—21no—
211C42×C11—21no—
212C22⋊Dic11—22no—
213C22⋊Dic11—22no—
214C22⋊Dic11—41no—
215C22⋊Dic11C2×C814yescomplemented
216(C2×D11)⋊C4—22no—
217(C2×D11)⋊C4—22no—
218(C2×D11)⋊C4—41no—
219(C2×D11)⋊C4C2×C814yescomplemented
220Dic11⋊C4—22no—
221Dic11⋊C4—22no—
222Dic11⋊C4—22no—
223Dic11⋊C4C2×C814yescomplemented
224C4×Dic11—22no—
225C4×Dic11—22no—
226C4×Dic11—21no—
227C4×Dic11—21no—
228C4×Dic11—21no—
229C4×Dic11—21no—
230C4×Dic11C2×D412yes—
231C4×Dic11#4112yes—
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⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—44no—
242C2×C11⋊C8—44no—
243C2×C11⋊C8C2×D412yes—
244C2×C11⋊C8C2×D412yes—
245C2×C11⋊C8C2×D412yes—
246C8×D11—44no—
247C2×C8×D4—111no—
248C2×C8×D4—111no—
249C2×C8×D4—111no—
250C22×C4⋊C8—111no—
251C4×#121—111no—
252#1954—111no—
253#1939—111no—
254#1923—111no—
255#1923—111no—
256#1869—111no—
257#1869D1111yescharacteristic, complemented
258#1850—111no—
259#1850—111no—
260C8×C4⋊C4—111no—
261C4×C22⋊C8—111no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11C4×D412yes—
273C23×C11C22×C812yes—
274C23×C11C22×C812yes—
275C23×C11#13112yes—
276C23×C11C23×C411yescharacteristic
277C22×D11—21no—
278C22×D11—21no—
279C22×D11—21no—
280C22×D11—21no—
281C22×D11—21no—
282C22×D11—21no—
283C22×D11C22×C812yes—
284D4×C11—28no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11C4×D412yes—
304C2×C4×C11C22×C812yes—
305C2×C4×C11C22×D411yescharacteristic
306C2×C4×C11C22×D411yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11H(5,𝔽2)11yescharacteristic
310C2×C4×C112−1+411yescharacteristic
311C22⋊D11—28no—
312C22⋊D11—28no—
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—28no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—21no—
327C2×Dic11—21no—
328C2×Dic11—21no—
329C2×Dic11—44no—
330C2×Dic11C4×D412yes—
331C2×Dic11C4×D412yes—
332C2×Dic11C22×C812yes—
333C2×Dic11C22×C812yes—
334C2×Dic11C22×C812yes—
335C2×Dic11#13112yes—
336C4×D11—41no—
337C4×D11—41no—
338C4×D11—41no—
339C4×D11—41no—
340C8×C11—22no—
341C8×C11—41no—
342C8×C11—41no—
343C8×C11—41no—
344C11⋊C8—22no—
345C11⋊C8—22no—
346C11⋊C8—22no—
347C11⋊C8—41no—
348C23×C8—111no—
349C23×C8—111no—
350C23×C8—111no—
351C23×C8C2×D1111yescharacteristic
352C2×#121—111no—
353C2×C4×D4—111no—
354C2×C4×D4—111no—
355C2×C4×D4C2×D1111yescharacteristic
356C22×C42—111no—
357C8×D4—224no—
358C8×D4—224no—
359C8×D4—224no—
360C2×C4⋊C8—111no—
361C2×C4⋊C8—111no—
362C2×C4⋊C8—111no—
363C2×C4⋊C8—111no—
364C2×C4⋊C8—111no—
365C2×C4⋊C8—111no—
366C2×C4⋊C8—224no—
367C2×C22⋊C8—111no—
368C2×C22⋊C8—111no—
369C2×C22⋊C8—111no—
370C2×C22⋊C8—111no—
371C2×C22⋊C8—111no—
372C2×C22⋊C8C2×D1111yescharacteristic
373C2×C22⋊C8C2×D1111yescharacteristic
374C2×C22⋊C8C2×D1111yescharacteristic
375C2×C4×C8—111no—
376C2×C4×C8—111no—
377C2×C4×C8—111no—
378C2×C4×C8—111no—
379#390—111no—
380#389—111no—
381#388—111no—
382#388—111no—
383#386—111no—
384#386—111no—
385#380—111no—
386C4×C4⋊C4—111no—
387C4×C22⋊C4—111no—
388C4×C22⋊C4—111no—
389#336—111no—
390#336—111no—
391#336—111no—
392#336—111no—
393#336C2×D1111yescharacteristic
394#336C2×D1111yescharacteristic
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—22no—
400C22×C11—22no—
401C22×C11—22no—
402C22×C11—22no—
403C22×C11—22no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11C8×D414yescomplemented
409C22×C11C2×C4×D411yescharacteristic
410C22×C11C2×C4×D411yescharacteristic
411C22×C11#52011yescharacteristic
412C22×C11C23×C811yescharacteristic
413C22×C11C2×#13111yescharacteristic
414C22×C11C2×#13111yescharacteristic
415C22×C11#56811yescharacteristic
416C2×D11—22no—
417C2×D11—22no—
418C2×D11—22no—
419C2×D11—41no—
420C2×D11—41no—
421C2×D11—41no—
422C2×D11—41no—
423C4×C11—22no—
424C4×C11—22no—
425C4×C11—41no—
426C4×C11—41no—
427C4×C11D4211yescharacteristic
428C4×C11#54711yescharacteristic
429C4×C11#54811yescharacteristic
430C4×C11#55311yescharacteristic
431Dic11—22no—
432Dic11—22no—
433Dic11—22no—
434Dic11—41no—
435Dic11—41no—
436Dic11—41no—
437Dic11C8×D414yescomplemented
438C22×D4—111no—
439C22×D4—111no—
440C22×D4C4×D1111yescharacteristic
441C23×C4—111no—
442C23×C4—111no—
443C23×C4—111no—
444C23×C4C22×D1111yescharacteristic
445C23×C4C22×D1111yescharacteristic
446C22×C8—22no—
447C22×C8—22no—
448C22×C8—41no—
449C22×C8—111no—
450C22×C8—111no—
451C22×C8—111no—
452C22×C8—111no—
453C22×C8—222no—
454C22×C8—222no—
455C22×C8—222no—
456C22×C8—222no—
457C22×C8—222no—
458C22×C8—222no—
459C22×C8—441no—
460C22×C8—441no—
461C22×C8—441no—
462C22×C8C22×D1111yescharacteristic
463C22×C8C22×D1111yescharacteristic
464C22×C8C22×D1111yescharacteristic
465C22×C8C22×D1111yescharacteristic
466#121—118no—
467C4×D4—22no—
468C4×D4—22no—
469C4×D4—222no—
470C4×D4—222no—
471C4×D4—222no—
472C4×D4—222no—
473C2×C4⋊C4—111no—
474C2×C4⋊C4—111no—
475C2×C4⋊C4—111no—
476C2×C4⋊C4—111no—
477C2×C4⋊C4C4×D1111yescharacteristic
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×C22⋊C4—111no—
485C2×C22⋊C4—111no—
486C2×C22⋊C4C4×D1111yescharacteristic
487C2×C22⋊C4C4×D1111yescharacteristic
488C2×C42—111no—
489C2×C42—111no—
490C2×C42—111no—
491C2×C42—111no—
492C2×C42—111no—
493C2×C42—222no—
494C2×C42—222no—
495C2×C42C22×D1111yescharacteristic
496C4⋊C8—114no—
497C4⋊C8—222no—
498C4⋊C8—222no—
499C4⋊C8—222no—
500C4⋊C8—222no—
501C4⋊C8—222no—
502C22⋊C8—22no—
503C22⋊C8—22no—
504C22⋊C8—41no—
505C22⋊C8—114no—
506C22⋊C8—222no—
507C22⋊C8—222no—
508C22⋊C8—222no—
509C22⋊C8—441no—
510C4×C8—222no—
511C4×C8—222no—
512C4×C8—222no—
513C4×C8—222no—
514#95—111no—
515#95—111no—
516#95—111no—
517#95—111no—
518#95—111no—
519#95—111no—
520C2×C11—24no—
521C2×C11—42no—
522C2×C11#236111yescharacteristic
523C2×C11C2×C8×D411yescharacteristic
524C2×C11C2×C8×D411yescharacteristic
525C2×C11#293311yescharacteristic
526C2×C11#293511yescharacteristic
527C2×C11#298811yescharacteristic
528C2×C11#299411yescharacteristic
529D11—42no—
530C24—111no—
531C24C2×C4×D1111yescharacteristic
532C24C2×C4×D1111yescharacteristic
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—114no—
536C2×D4—114no—
537C2×D4—222no—
538C2×D4—222no—
539C2×D4—222no—
540C2×D4—222no—
541C2×D4C8×D1114yescomplemented
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—111no—
553C22×C4—114no—
554C22×C4—111no—
555C22×C4—111no—
556C22×C4—111no—
557C22×C4—111no—
558C22×C4—111no—
559C22×C4—111no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—222no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—441no—
571C22×C4C2×C4×D1111yescharacteristic
572C22×C4C2×C4×D1111yescharacteristic
573C22×C4C2×C4×D1111yescharacteristic
574C22×C4C2×C4×D1111yescharacteristic
575C22×C4D4×D1112yes—
576C22×C4#434112yes—
577C22×C4C23×D1111yescharacteristic
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—44no—
590C2×C8—112no—
591C2×C8—112no—
592C2×C8—112no—
593C2×C8—221no—
594C2×C8—221no—
595C2×C8—221no—
596C2×C8—221no—
597C2×C8—221no—
598C2×C8—221no—
599C2×C8—221no—
600C2×C8—221no—
601C2×C8—221no—
602C2×C8—444no—
603C2×C8—444no—
604C2×C8—444no—
605C2×C8D4×D1112yes—
606C4⋊C4—22no—
607C4⋊C4—114no—
608C4⋊C4—222no—
609C4⋊C4—222no—
610C4⋊C4—222no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—114no—
614C22⋊C4—114no—
615C22⋊C4—222no—
616C22⋊C4—222no—
617C22⋊C4—222no—
618C22⋊C4—222no—
619C22⋊C4—441no—
620C22⋊C4—441no—
621C42—21no—
622C42—21no—
623C42—112no—
624C42—112no—
625C42—222no—
626C42—222no—
627C42—221no—
628C42—221no—
629C42—221no—
630C42—221no—
631C11#2298511yescharacteristic, complemented, Sylow
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—112no—
643C23—221no—
644C23—221no—
645C23—221no—
646C23—221no—
647C23—221no—
648C23—221no—
649C23(C22⋊D11)⋊C412yes—
650C23C2×C8×D1112yes—
651C23C2×C8×D1112yes—
652C23#6696012yes—
653C23C22×C4×D1111yescharacteristic
654D4—28no—
655D4—228no—
656D4—228no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—112no—
676C2×C4—112no—
677C2×C4—112no—
678C2×C4—112no—
679C2×C4—112no—
680C2×C4—112no—
681C2×C4—228no—
682C2×C4—221no—
683C2×C4—221no—
684C2×C4—221no—
685C2×C4—221no—
686C2×C4—221no—
687C2×C4—221no—
688C2×C4—221no—
689C2×C4—221no—
690C2×C4—221no—
691C2×C4—221no—
692C2×C4—221no—
693C2×C4—221no—
694C2×C4—221no—
695C2×C4—221no—
696C2×C4—221no—
697C2×C4—444no—
698C2×C4—441no—
699C2×C4—441no—
700C2×C4—441no—
701C2×C4—441no—
702C2×C4(C22⋊D11)⋊C412yes—
703C2×C4C2×C8×D1112yes—
704C2×C4C2×D4×D1111yescharacteristic
705C2×C4C2×D4×D1111yescharacteristic
706C2×C4C2×#434111yescharacteristic
707C2×C4#6703711yescharacteristic
708C2×C4#41×D1111yescharacteristic
709C2×C4#6704311yescharacteristic
710C8—22no—
711C8—41no—
712C8—41no—
713C8—41no—
714C8—222no—
715C8—222no—
716C8—222no—
717C8—441no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—222no—
732C22—222no—
733C22—222no—
734C22—441no—
735C22—441no—
736C22—441no—
737C22—441no—
738C22(C22⋊D11)⋊C814yescomplemented
739C22C2×(C22⋊D11)⋊C411yescharacteristic
740C22C4×D4×D1111yescharacteristic
741C22#1062307711yescharacteristic
742C22C22×C8×D1111yescharacteristic
743C22C2×#6696011yescharacteristic
744C22D11×#13111yescharacteristic
745C22#1062328111yescharacteristic
746C4—22no—
747C4—22no—
748C4—41no—
749C4—41no—
750C4—114no—
751C4—222no—
752C4—222no—
753C4—222no—
754C4—441no—
755C4—441no—
756C4—441no—
757C4#1062312111yescharacteristic
758C4#1062312911yescharacteristic
759C4#1062313211yescharacteristic
760C4#1062318611yescharacteristic
761C2—24no—
762C2—42no—
763C2—442no—
764C2#1307162711yescharacteristic
765C2C8×D4×D1111yescharacteristic
766C2C2×(C22⋊D11)⋊C811yescharacteristic
767C2#1307734211yescharacteristic
768C2#1307735611yescharacteristic
769C2#1307772311yescharacteristic
770C2#1307776911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C23×C8
FittingC11×#1869C2
socleC23×C11C23×C4
prime radicalC2×#66992C4
cosocleC22×C4×C11C24
hypercenter#1869D11
hypocenterC11#22985
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
1. C2×D4×C11⋊C8C2semidirect
2. C2×C8×C22⋊D11C2semidirect
3. C2×(C22⋊D11)⋊C8C2semidirect
4. C22×Dic11⋊C8C2semidirect
6. #13069408C2semidirect
7. #13069333C2semidirect
8. #13069225C2semidirect
9. #13069220C2semidirect
10. #13068906C2semidirect
11. #13068795C2semidirect
12. #13068793C2semidirect
13. #13068477C2semidirect
14. C22⋊C8×Dic11C2semidirect
15. C11×#1869C2semidirect
88. #66992C8semidirect
131. C22⋊(C11⋊C8)D4semidirect
139. Dic11⋊C8D4semidirect
151. C2×D4×C11C2×C8semidirect
173. C2×C22⋊D11C2×C8semidirect
174. C2×C22⋊D11C2×C8semidirect
180. C22×Dic11C2×C8semidirect
215. C22⋊Dic11C2×C8semidirect
219. (C2×D11)⋊C4C2×C8semidirect
223. Dic11⋊C4C2×C8semidirect
257. #1869D11semidirect
408. C22×C11C8×D4semidirect
437. Dic11C8×D4semidirect
541. C2×D4C8×D11semidirect
631. C11#22985semidirect
738. C22(C22⋊D11)⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C11⋊C82
C2×C8×C22⋊D112
C2×(C22⋊D11)⋊C82
C22×Dic11⋊C82
C4×#669922
#130694082
#130693332
#130692252
#130692202
#130689062
#130687952
#130687932
#130684772
C22⋊C8×Dic112
C11×#18692
#2298511