Finite Group Databasebeta

← #14769824

Subgroups — #14769824

Order 2816.

1500 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4341C211yesmaximal, characteristic
2C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
3C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
4#13069550C211yesmaximal, characteristic, complemented
5#13069550C211yesmaximal, characteristic, complemented
6#13068909C211yesmaximal, characteristic, complemented
7#13068905C211yesmaximal, characteristic, complemented
8#13068905C211yesmaximal, characteristic, complemented
9#13068683C211yesmaximal, characteristic, complemented
10#13068682C211yesmaximal, characteristic, complemented
11#13068594C211yesmaximal, characteristic, complemented
12C22⋊C8×Dic11C211yesmaximal, characteristic, complemented
13C2×#10622188C211yesmaximal, characteristic, complemented
14D11×#336C211yesmaximal, characteristic, complemented
15C11×#1869C211yesmaximal, characteristic, complemented
16C22×#4341C411yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×D4×Dic11C411yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C23×C11⋊C8C2211yescharacteristic
25C22×C8×D11C2211yescharacteristic
26C22×C8×D11C2211yescharacteristic
27C4×#4341—24no—
28C4×#4341—24no—
29C2×#66945C411yescharacteristic
30C2×#66940C411yescharacteristic
31C2×(C22⋊D11)⋊C4C411yescharacteristic
32C2×(C22⋊D11)⋊C4C411yescharacteristic
33C2×#66930C411yescharacteristic
34C2×#66930C411yescharacteristic
35C2×C42×D11C2211yescharacteristic
36C2×C4×Dic22C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C8×C22⋊D11—24no—
44C2×(C2×D11)⋊C8C2211yescharacteristic
45C2×(C2×D11)⋊C8C2211yescharacteristic
46C2×Dic11⋊C8C2211yescharacteristic
47C2×Dic11⋊C8C2211yescharacteristic
48C2×C8×Dic11C2211yescharacteristic
49C2×C8×Dic11C2211yescharacteristic
50(C22⋊D11)⋊C8—24no—
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×D4×C11C2×C411yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11C2×C411yescharacteristic
67C22×C22⋊D11C2×C411yescharacteristic
68C23×Dic11C2×C411yescharacteristic
69C23×Dic11C2×C411yescharacteristic
70C23×Dic11C2×C411yescharacteristic
71C23×Dic11C2×C411yescharacteristic
72C2×#4341—24no—
73C2×#4341—24no—
74C2×#4341C818yescomplemented
75C22×C4×D11C2×C411yescharacteristic
76C22×C4×D11C2×C411yescharacteristic
77C22×C4×D11C2311yescharacteristic
78C22×Dic22C2×C411yescharacteristic
79C22×C8×C11—22no—
80C22×C8×C11—22no—
81C22×C8×C11—41no—
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C2×C11×C4⋊C4C2×C411yescharacteristic
89C2×C11×C22⋊C4C2×C411yescharacteristic
90C2×C11×C22⋊C4C2×C411yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×C22⋊Dic11C2×C411yescharacteristic
93C2×C22⋊Dic11C2×C411yescharacteristic
94D4×Dic11—24no—
95C4×C22⋊D11—22no—
96C4×C22⋊D11—22no—
97C4×C22⋊D11D414yes—
98C4×C22⋊D11D414yes—
99C2×(C2×D11)⋊C4C2×C411yescharacteristic
100C2×(C2×D11)⋊C4C2×C411yescharacteristic
101C2×C4⋊Dic11C2×C411yescharacteristic
102C2×Dic11⋊C4C2×C411yescharacteristic
103C2×Dic11⋊C4C2×C411yescharacteristic
104C2×Dic11⋊C4C2×C411yescharacteristic
105C2×Dic11⋊C4C2×C411yescharacteristic
106C2×C4×Dic11—22no—
107C2×C4×Dic11—22no—
108C2×C4×Dic11—22no—
109C2×C4×Dic11—22no—
110C2×C4×Dic11C2×C411yescharacteristic
111C2×C4×Dic11C2×C411yescharacteristic
112C2×C4×Dic11C2×C411yescharacteristic
113C2×C4×Dic11C2×C411yescharacteristic
114C2×C4×Dic11C2×C411yescharacteristic
115C2×C4×Dic11C2×C411yescharacteristic
116C2×C4×Dic11C2311yescharacteristic
117C2×C4×Dic11C2311yescharacteristic
118C2×C4×Dic11C2311yescharacteristic
119C22×C11⋊C8—22no—
120C22×C11⋊C8—22no—
121C22×C11⋊C8—41no—
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C2×C8×D11—22no—
127C2×C8×D11—22no—
128C2×C8×D11—22no—
129C2×C8×D11—22no—
130C2×C8×D11—41no—
131C2×C8×D11—41no—
132#66945—24no—
133#66940—24no—
134(C22⋊D11)⋊C4—24no—
135(C22⋊D11)⋊C4—24no—
136#66930—24no—
137#66930—24no—
138C42×D11—22no—
139C42×D11—22no—
140C4×Dic22—22no—
141C4×Dic22—22no—
142C11×C22⋊C8—22no—
143C11×C22⋊C8—22no—
144C11×C22⋊C8—41no—
145C22⋊(C11⋊C8)—22no—
146C22⋊(C11⋊C8)—22no—
147C22⋊(C11⋊C8)—41no—
148(C2×D11)⋊C8—22no—
149(C2×D11)⋊C8—22no—
150Dic11⋊C8—22no—
151Dic11⋊C8—22no—
152C8×Dic11—22no—
153C8×Dic11—22no—
154#22469—111nomaximal, Sylow
155C24×C11C22×C411yescharacteristic
156C24×C11C22×C411yescharacteristic
157C23×D11C22×C411yescharacteristic
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11C2×C814yescomplemented
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11C22×C411yescharacteristic
172C22×C4×C11C22×C411yescharacteristic
173C22×C4×C11C22×C411yescharacteristic
174C22×C4×C11C22×C411yescharacteristic
175C22×C4×C11C2×D412yes—
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2411yescharacteristic
178C2×C22⋊D11—22no—
179C2×C22⋊D11—22no—
180C2×C22⋊D11C22⋊C414yes—
181C2×C22⋊D11C2×C814yes—
182C2×C22⋊D11C2×C814yescomplemented
183C2×C22⋊D11M1614yes—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—41no—
193C22×Dic11—41no—
194C22×Dic11C2×C814yescomplemented
195C22×Dic11C2×C814yescomplemented
196C22×Dic11C22×C411yescharacteristic
197C22×Dic11C22×C411yescharacteristic
198C22×Dic11C22×C411yescharacteristic
199C22×Dic11C22×C411yescharacteristic
200C22×Dic11C22×C411yescharacteristic
201C22×Dic11C22×C411yescharacteristic
202C22×Dic11C22×C411yescharacteristic
203#4341—232no—
204C2×C4×D11—22no—
205C2×C4×D11—22no—
206C2×C4×D11—22no—
207C2×C4×D11—22no—
208C2×C4×D11—21no—
209C2×C4×D11—21no—
210C2×C4×D11—21no—
211C2×C4×D11—21no—
212C2×C4×D11—41no—
213C2×C4×D11C2×C814yescomplemented
214C2×C4×D11C2×D412yes—
215C2×C4×D11C2×D412yes—
216C2×Dic22—22no—
217C2×Dic22—22no—
218C2×Dic22C2×C814yescomplemented
219C2×C8×C11—21no—
220C2×C8×C11—21no—
221C2×C8×C11—21no—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C2×C8×C11—21no—
226C2×C8×C11—21no—
227C2×C8×C11—21no—
228C2×C8×C11—21no—
229C2×C8×C11—21no—
230C2×C8×C11—44no—
231C2×C8×C11#4112yescomplemented
232C11×C4⋊C4—22no—
233C11×C22⋊C4—22no—
234C11×C22⋊C4—22no—
235C42×C11—21no—
236C42×C11—21no—
237C22⋊Dic11—22no—
238C22⋊Dic11C22⋊C414yes—
239(C2×D11)⋊C4—22no—
240(C2×D11)⋊C4C22⋊C414yes—
241C4⋊Dic11—22no—
242Dic11⋊C4—22no—
243Dic11⋊C4—22no—
244Dic11⋊C4—22no—
245Dic11⋊C4C22⋊C414yes—
246C4×Dic11—22no—
247C4×Dic11—22no—
248C4×Dic11—22no—
249C4×Dic11—22no—
250C4×Dic11—22no—
251C4×Dic11—22no—
252C4×Dic11—21no—
253C4×Dic11—21no—
254C4×Dic11—21no—
255C4×Dic11—21no—
256C4×Dic11C2×D412yes—
257C4×Dic11C2×D412yes—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8—21no—
265C2×C11⋊C8—21no—
266C2×C11⋊C8—21no—
267C2×C11⋊C8—21no—
268C2×C11⋊C8—21no—
269C2×C11⋊C8—44no—
270C2×C11⋊C8#4112yescomplemented
271C8×D11—44no—
272C8×D11—44no—
273C2×C4×#41—111no—
274C2×C8×D4—111no—
275C2×C8×D4—111no—
276#1984—111no—
277#1984—111no—
278#1869—111no—
279#1869—111no—
280#1869—111no—
281#1869D1111yescharacteristic, complemented
282#1817—111no—
283#1817—111no—
284#1797—111no—
285C4×C22⋊C8—111no—
286C2×#336—111no—
287C2×#336—111no—
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11C2×C22⋊C412yes—
299C23×C11C22×C812yes—
300C23×C11C22×C812yes—
301C23×C11C2×M1612yes—
302C23×C11C23×C411yescharacteristic
303C22×D11—21no—
304C22×D11—21no—
305C22×D11—21no—
306C22×D11—21no—
307C22×D11C2×C22⋊C412yes—
308C22×D11C22×C812yes—
309C22×D11C2×M1612yes—
310D4×C11—28no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11C2×C22⋊C412yes—
330C2×C4×C11C22×C812yes—
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11C2×#4111yescharacteristic
334C2×C4×C11C2×#4111yescharacteristic
335C2×C4×C11H(5,𝔽2)11yescharacteristic
336C2×C4×C112−1+411yescharacteristic
337C22⋊D11—28no—
338C22⋊D11C22⋊C8116yescomplemented
339C2×Dic11—21no—
340C2×Dic11—21no—
341C2×Dic11—21no—
342C2×Dic11—21no—
343C2×Dic11—21no—
344C2×Dic11—21no—
345C2×Dic11—21no—
346C2×Dic11—21no—
347C2×Dic11—21no—
348C2×Dic11—21no—
349C2×Dic11—28no—
350C2×Dic11—28no—
351C2×Dic11—21no—
352C2×Dic11—21no—
353C2×Dic11—21no—
354C2×Dic11—44no—
355C2×Dic11—44no—
356C2×Dic11C2×C22⋊C412yes—
357C2×Dic11C2×C22⋊C412yes—
358C2×Dic11C2×C22⋊C412yes—
359C2×Dic11C22×C812yes—
360C2×Dic11C22×C812yes—
361C2×Dic11C22×C812yes—
362C2×Dic11C2×M1612yes—
363C2×Dic11#13112yes—
364C4×D11—28no—
365C4×D11—22no—
366C4×D11—22no—
367C4×D11—22no—
368C4×D11—22no—
369C4×D11—44no—
370Dic22—28no—
371C8×C11—22no—
372C8×C11—41no—
373C8×C11—41no—
374C8×C11—41no—
375C11⋊C8—22no—
376C11⋊C8—41no—
377C11⋊C8—41no—
378C11⋊C8—41no—
379C22×#41—111no—
380C23×C8—111no—
381C23×C8—111no—
382C23×C8—111no—
383C23×C8C2×D1111yescharacteristic
384C4×#41—224no—
385C4×#41—224no—
386C2×C4×Q8—111no—
387C2×C4×Q8—111no—
388C2×C4×D4—111no—
389C2×C4×D4—111no—
390C2×C4×D4—111no—
391C2×C4×D4—111no—
392C2×C4×D4—111no—
393C2×C4×D4C2×D1111yescharacteristic
394C2×#117—111no—
395C2×#117—111no—
396C2×#117—111no—
397C22×C42—111no—
398C22×C42—111no—
399C22×C42—111no—
400C8×D4—224no—
401C8×D4—224no—
402C2×C4⋊C8—111no—
403C2×C4⋊C8—111no—
404C2×C22⋊C8—111no—
405C2×C22⋊C8—111no—
406C2×C22⋊C8—111no—
407C2×C22⋊C8—111no—
408C2×C22⋊C8—111no—
409C2×C22⋊C8C2×D1111yescharacteristic
410C2×C22⋊C8C2×D1111yescharacteristic
411C2×C22⋊C8C2×D1111yescharacteristic
412C2×C4×C8—111no—
413C2×C4×C8—111no—
414#336—111no—
415#336—111no—
416#336—111no—
417#336—111no—
418#336—111no—
419#336—111no—
420#336—111no—
421#336—111no—
422#336—111no—
423#336—111no—
424#336C2×D1111yescharacteristic
425#336C2×D1111yescharacteristic
426C22×C11—22no—
427C22×C11—22no—
428C22×C11—22no—
429C22×C11—22no—
430C22×C11—22no—
431C22×C11—22no—
432C22×C11—22no—
433C22×C11—22no—
434C22×C11—22no—
435C22×C11—41no—
436C22×C11—41no—
437C22×C11—41no—
438C22×C11—41no—
439C22×C11C2×C22⋊C814yes—
440C22×C11C22×C22⋊C411yescharacteristic
441C22×C11C4×#4111yescharacteristic
442C22×C11#52011yescharacteristic
443C22×C11C23×C811yescharacteristic
444C22×C11C22×M1611yescharacteristic
445C22×C11C2×#13111yescharacteristic
446C22×C11#56811yescharacteristic
447C2×D11—22no—
448C2×D11—22no—
449C2×D11—22no—
450C2×D11—22no—
451C2×D11—22no—
452C2×D11—22no—
453C2×D11C2×C22⋊C814yes—
454C4×C11—22no—
455C4×C11—22no—
456C4×C11—41no—
457C4×C11—41no—
458C4×C11#54611yescharacteristic
459C4×C11#54611yescharacteristic
460C4×C11#54711yescharacteristic
461C4×C11#54711yescharacteristic
462Dic11—22no—
463Dic11—22no—
464Dic11—22no—
465Dic11—22no—
466Dic11—22no—
467Dic11—41no—
468Dic11C2×C22⋊C814yes—
469C2×#41—118no—
470C2×#41—224no—
471C2×#41—224no—
472C22×Q8—111no—
473C22×D4—111no—
474C22×D4—111no—
475C22×D4C4×D1111yescharacteristic
476C23×C4—111no—
477C23×C4—111no—
478C23×C4—111no—
479C23×C4—111no—
480C23×C4—111no—
481C23×C4—111no—
482C23×C4—111no—
483C23×C4C22×D1111yescharacteristic
484C23×C4C22×D1111yescharacteristic
485C22×C8—22no—
486C22×C8—22no—
487C22×C8—41no—
488C22×C8—111no—
489C22×C8—111no—
490C22×C8—111no—
491C22×C8—111no—
492C22×C8—222no—
493C22×C8—222no—
494C22×C8—222no—
495C22×C8—222no—
496C22×C8—222no—
497C22×C8—222no—
498C22×C8—441no—
499C22×C8—441no—
500C22×C8—441no—
501C22×C8C22×D1111yescharacteristic
502C22×C8C22×D1111yescharacteristic
503C22×C8C22×D1111yescharacteristic
504C22×C8C22×D1111yescharacteristic
505C4×Q8—222no—
506C4×Q8—222no—
507C4×Q8—224no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—114no—
511C4×D4—114no—
512C4×D4—224no—
513C4×D4—224no—
514C4×D4—224no—
515C4×D4—222no—
516C4×D4—222no—
517#117—224no—
518#117—224no—
519#117—224no—
520C2×C4⋊C4—111no—
521C2×C4⋊C4—111no—
522C2×C4⋊C4—111no—
523C2×C4⋊C4—111no—
524C2×C4⋊C4—111no—
525C2×C4⋊C4C4×D1111yescharacteristic
526C2×C22⋊C4—111no—
527C2×C22⋊C4—111no—
528C2×C22⋊C4—111no—
529C2×C22⋊C4—111no—
530C2×C22⋊C4C4×D1111yescharacteristic
531C2×C22⋊C4C4×D1111yescharacteristic
532C2×C42—111no—
533C2×C42—111no—
534C2×C42—111no—
535C2×C42—111no—
536C2×C42—111no—
537C2×C42—111no—
538C2×C42—111no—
539C2×C42—111no—
540C2×C42—111no—
541C2×C42—222no—
542C2×C42—222no—
543C2×C42—222no—
544C2×C42—222no—
545C2×C42—222no—
546C2×C42—222no—
547C2×C42C22×D1111yescharacteristic
548C4⋊C8—222no—
549C4⋊C8—222no—
550C22⋊C8—22no—
551C22⋊C8—22no—
552C22⋊C8—41no—
553C22⋊C8—222no—
554C22⋊C8—222no—
555C22⋊C8—222no—
556C22⋊C8—222no—
557C22⋊C8—441no—
558C4×C8—222no—
559C4×C8—222no—
560C2×C11—24no—
561C2×C11—42no—
562C2×C11#233911yescharacteristic
563C2×C11C22×C22⋊C811yescharacteristic
564C2×C11#288011yescharacteristic
565C2×C11C8×#4111yescharacteristic
566C2×C11#297011yescharacteristic
567C2×C11#298811yescharacteristic
568C2×C11#299011yescharacteristic
569D11—24no—
570C24—111no—
571C24C2×C4×D1111yescharacteristic
572C24C2×C4×D1111yescharacteristic
573#41—2232no—
574C2×Q8—114no—
575C2×Q8—222no—
576C2×Q8—222no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—114no—
580C2×D4—114no—
581C2×D4—114no—
582C2×D4—114no—
583C2×D4—222no—
584C2×D4—222no—
585C2×D4C8×D1114yescomplemented
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—111no—
597C22×C4—114no—
598C22×C4—114no—
599C22×C4—111no—
600C22×C4—111no—
601C22×C4—111no—
602C22×C4—111no—
603C22×C4—111no—
604C22×C4—114no—
605C22×C4—112no—
606C22×C4—112no—
607C22×C4—111no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—222no—
613C22×C4—222no—
614C22×C4—222no—
615C22×C4—222no—
616C22×C4—222no—
617C22×C4—222no—
618C22×C4—222no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—221no—
622C22×C4—221no—
623C22×C4—222no—
624C22×C4—441no—
625C22×C4—441no—
626C22×C4—441no—
627C22×C4C2×C4×D1111yescharacteristic
628C22×C4C2×C4×D1111yescharacteristic
629C22×C4C2×C4×D1111yescharacteristic
630C22×C4C2×C4×D1111yescharacteristic
631C22×C4D4×D1112yes—
632C22×C4D4×D1112yes—
633C22×C4C23×D1111yescharacteristic
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—44no—
646C2×C8—112no—
647C2×C8—221no—
648C2×C8—221no—
649C2×C8—221no—
650C2×C8—221no—
651C2×C8—221no—
652C2×C8—221no—
653C2×C8—221no—
654C2×C8—221no—
655C2×C8—221no—
656C2×C8—221no—
657C2×C8—221no—
658C2×C8—444no—
659C2×C8—444no—
660C2×C8—444no—
661C2×C8#434112yescomplemented
662C4⋊C4—22no—
663C4⋊C4—114no—
664C4⋊C4—222no—
665C4⋊C4—222no—
666C4⋊C4—222no—
667C4⋊C4—222no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—114no—
671C22⋊C4—114no—
672C22⋊C4—222no—
673C22⋊C4—222no—
674C42—21no—
675C42—21no—
676C42—112no—
677C42—112no—
678C42—222no—
679C42—222no—
680C42—222no—
681C42—222no—
682C42—222no—
683C42—222no—
684C42—221no—
685C42—221no—
686C42—221no—
687C42—221no—
688C11#2246911yescharacteristic, complemented, Sylow
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—112no—
700C23—112no—
701C23—112no—
702C23—221no—
703C23—221no—
704C23—221no—
705C23—221no—
706C23C22⋊C4×D1112yes—
707C23C2×C8×D1112yes—
708C23C2×C8×D1112yes—
709C23M16×D1112yes—
710C23C22×C4×D1111yescharacteristic
711Q8—228no—
712D4—28no—
713D4—1116no—
714D4—228no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—112no—
734C2×C4—112no—
735C2×C4—112no—
736C2×C4—112no—
737C2×C4—112no—
738C2×C4—112no—
739C2×C4—112no—
740C2×C4—112no—
741C2×C4—228no—
742C2×C4—228no—
743C2×C4—221no—
744C2×C4—221no—
745C2×C4—221no—
746C2×C4—221no—
747C2×C4—221no—
748C2×C4—221no—
749C2×C4—221no—
750C2×C4—221no—
751C2×C4—221no—
752C2×C4—221no—
753C2×C4—228no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—221no—
759C2×C4—221no—
760C2×C4—221no—
761C2×C4—444no—
762C2×C4—444no—
763C2×C4—444no—
764C2×C4C22⋊C4×D1112yes—
765C2×C4C2×C8×D1112yes—
766C2×C4C2×D4×D1111yescharacteristic
767C2×C4C2×D4×D1111yescharacteristic
768C2×C4C2×#434111yescharacteristic
769C2×C4#6703711yescharacteristic
770C2×C4#41×D1111yescharacteristic
771C2×C4#6704311yescharacteristic
772C8—22no—
773C8—41no—
774C8—41no—
775C8—41no—
776C8—222no—
777C8—441no—
778C8—441no—
779C8—441no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—114no—
794C22—222no—
795C22—222no—
796C22—222no—
797C22—222no—
798C22—222no—
799C22—222no—
800C22D11×C22⋊C814yes—
801C22C2×C22⋊C4×D1111yescharacteristic
802C22C4×#434111yescharacteristic
803C22#1062307711yescharacteristic
804C22C22×C8×D1111yescharacteristic
805C22C2×M16×D1111yescharacteristic
806C22D11×#13111yescharacteristic
807C22#1062328111yescharacteristic
808C4—22no—
809C4—22no—
810C4—41no—
811C4—41no—
812C4—114no—
813C4—222no—
814C4—222no—
815C4—222no—
816C4—222no—
817C4—222no—
818C4—441no—
819C4#1062312211yescharacteristic
820C4#1062314111yescharacteristic
821C4#1062314211yescharacteristic
822C4#1062318611yescharacteristic
823C2—24no—
824C2—42no—
825C2—224no—
826C2#1307144211yescharacteristic
827C2C2×D11×C22⋊C811yescharacteristic
828C2#1307706411yescharacteristic
829C2C8×#434111yescharacteristic
830C2#1307762611yescharacteristic
831C2#1307772311yescharacteristic
832C2#1307773611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C23×C8
FittingC11×#1869C2
socleC23×C11C23×C4
prime radicalC22×#4341C4
cosocleC22×C4×C11C24
hypercenter#1869D11
hypocenterC11#22469
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
2. C2×C8×C22⋊D11C2semidirect
3. C2×(C22⋊D11)⋊C8C2semidirect
4. #13069550C2semidirect
5. #13069550C2semidirect
6. #13068909C2semidirect
7. #13068905C2semidirect
8. #13068905C2semidirect
9. #13068683C2semidirect
10. #13068682C2semidirect
11. #13068594C2semidirect
12. C22⋊C8×Dic11C2semidirect
13. C2×#10622188C2semidirect
14. D11×#336C2semidirect
15. C11×#1869C2semidirect
74. C2×#4341C8semidirect
160. C2×D4×C11C2×C8semidirect
182. C2×C22⋊D11C2×C8semidirect
194. C22×Dic11C2×C8semidirect
195. C22×Dic11C2×C8semidirect
213. C2×C4×D11C2×C8semidirect
218. C2×Dic22C2×C8semidirect
231. C2×C8×C11#41semidirect
270. C2×C11⋊C8#41semidirect
281. #1869D11semidirect
338. C22⋊D11C22⋊C8semidirect
585. C2×D4C8×D11semidirect
661. C2×C8#4341semidirect
688. C11#22469semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43412
C2×C8×C22⋊D112
C2×(C22⋊D11)⋊C82
#130695502
#130689092
#130689052
#130686832
#130686822
#130685942
C22⋊C8×Dic112
C2×#106221882
D11×#3362
C11×#18692
#2246911