Finite Group Databasebeta

← #14677429

Subgroups — #14677429

Order 2816.

2222 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D11C211yesmaximal, characteristic
2C2×#10622546C211yesmaximal, characteristic, complemented
3C2×#10622602C211yesmaximal, characteristic
4C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
5#13066874C211yesmaximal, characteristic, complemented
6#13066872C211yesmaximal, characteristic, complemented
7#13066869C211yesmaximal, characteristic, complemented
8#13066867C211yesmaximal, characteristic, complemented
9#13066851C211yesmaximal, characteristic, complemented
10#13066848C211yesmaximal, characteristic, complemented
11(C2×D11)⋊#95C211yesmaximal, characteristic
12(C2×D11)⋊#95C211yesmaximal, characteristic
13(C2×D11)⋊#95C211yesmaximal, characteristic
14(C2×D11)⋊#95C211yesmaximal, characteristic
15C2×C11×#387C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C2×C4⋊C4×D11—24no—
32C2×C4⋊C4×D11—24no—
33C2×C4⋊C4×D11—24no—
34C11×#387—24no—
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55#10622602C418yescomplemented
56C4×(C2×D11)⋊C4—24no—
57#10622546—24no—
58C24×D11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C22×C4×D11—22no—
74C22×C4×D11—22no—
75C22×C4×D11—22no—
76C22×C4×D11—22no—
77C22×C4×D11—22no—
78C22×C4×D11—22no—
79C22×C4×D11—22no—
80C22×C4×D11—22no—
81C22×C4×D11—22no—
82C22×C4×D11—22no—
83C22×C4×D11—22no—
84C22×C4×D11—22no—
85C22×C4×D11—22no—
86C22×C4×D11—22no—
87C22×C4×D11—22no—
88C22×C4×D11—41no—
89C22×C4×D11—41no—
90C22×C4×D11—41no—
91C22×C4×D11—41no—
92C22×C4×D11C2×C414yes—
93C22×C4×D11D414yes—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4—22no—
98C2×C11×C4⋊C4C2×C414yescomplemented
99C2×C11×C4⋊C4D414yes—
100C2×C42×C11—22no—
101C2×C42×C11—22no—
102C2×C42×C11—22no—
103C2×(C2×D11)⋊C4—22no—
104C2×(C2×D11)⋊C4—22no—
105C2×(C2×D11)⋊C4—22no—
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—22no—
109C2×(C2×D11)⋊C4—22no—
110C2×(C2×D11)⋊C4—22no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4C2×C414yes—
113C2×(C2×D11)⋊C4C2×C414yes—
114C2×(C2×D11)⋊C4Q814yes—
115C2×C4⋊Dic11—22no—
116C2×C4⋊Dic11—22no—
117C2×C4⋊Dic11—22no—
118C2×Dic11⋊C4—22no—
119C2×Dic11⋊C4—22no—
120C2×Dic11⋊C4—22no—
121C2×Dic11⋊C4—22no—
122C2×Dic11⋊C4—22no—
123C2×Dic11⋊C4—22no—
124C2×Dic11⋊C4—22no—
125C2×Dic11⋊C4C2×C414yescomplemented
126C2×Dic11⋊C4D414yes—
127C2×C4×Dic11—22no—
128C2×C4×Dic11—41no—
129C2×C4×Dic11—41no—
130C4⋊C4×D11—232no—
131C11×#95—22no—
132C11×#95—22no—
133C11×#95—22no—
134C11×#95—22no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—22no—
139C11⋊#95—22no—
140C11⋊#95—22no—
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—41no—
144C11⋊#95—41no—
145C11⋊#95—41no—
146C11⋊#95—41no—
147C11⋊#95—41no—
148C11⋊#95—41no—
149C11⋊#95C2×C414yescomplemented
150C11⋊#95C2×C414yescomplemented
151#14039—111nomaximal, Sylow
152C24×C11C2411yescharacteristic
153C23×D11—21no—
154C23×D11—21no—
155C23×D11—21no—
156C23×D11—21no—
157C23×D11—21no—
158C23×D11—21no—
159C23×D11—21no—
160C23×D11—21no—
161C23×D11C22×C412yes—
162C23×D11C2×D412yes—
163C23×D11C2×Q812yes—
164C23×D11#4112yes—
165C23×D11#4112yes—
166C23×D11#4112yes—
167C23×D11#4112yes—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11C22×C412yes—
208C22×C4×C11C22×C412yes—
209C22×C4×C11C22×C412yes—
210C22×C4×C11C2×D412yes—
211C22×C4×C11C2×D412yes—
212C22×C4×C11C2×D412yes—
213C22×C4×C11C2×D412yes—
214C22×C4×C11C2×D412yes—
215C22×C4×C11C2×Q812yes—
216C22×C4×C11#4112yes—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11C22×C412yes—
259C22×Dic11C22×C412yes—
260C22×Dic11C22×C412yes—
261C22×Dic11C2×D412yes—
262C22×Dic11C2×D412yes—
263C22×Dic11C2×D412yes—
264C22×Dic11C2×Q812yes—
265C22×Dic11#4112yes—
266C2×C4×D11—28no—
267C2×C4×D11—28no—
268C2×C4×D11—28no—
269C2×C4×D11—28no—
270C2×C4×D11—28no—
271C2×C4×D11—28no—
272C2×C4×D11—28no—
273C2×C4×D11—28no—
274C2×C4×D11—28no—
275C2×C4×D11—28no—
276C2×C4×D11—44no—
277C2×C4×D11—44no—
278C2×C4×D11—44no—
279C2×C4×D11—44no—
280C2×C4×D11—44no—
281C2×C4×D11—44no—
282C2×C4×D11—44no—
283C2×C4×D11—44no—
284C2×C4×D11—44no—
285C2×C4×D11—44no—
286C2×C4×D11—44no—
287C11×C4⋊C4—28no—
288C11×C4⋊C4—28no—
289C42×C11—44no—
290(C2×D11)⋊C4—28no—
291(C2×D11)⋊C4—28no—
292(C2×D11)⋊C4—28no—
293(C2×D11)⋊C4—44no—
294C4⋊Dic11—28no—
295Dic11⋊C4—28no—
296Dic11⋊C4—28no—
297Dic11⋊C4—28no—
298C4×Dic11—44no—
299C23×C4⋊C4—111no—
300C2×#387—111no—
301C2×#387D1111yescharacteristic, complemented
302C2×#385—111no—
303C2×C4×C22⋊C4—111no—
304#1442—111no—
305#1442—111no—
306#1441—111no—
307#1441—111no—
308#1436—111no—
309#1436—111no—
310C22⋊#95—111no—
311C22⋊#95—111no—
312C22⋊#95—111no—
313C22⋊#95—111no—
314C23×C11C23×C411yescharacteristic
315C23×C11C22×D411yescharacteristic
316C23×C11C22×D411yescharacteristic
317C23×C11C22×D411yescharacteristic
318C23×C11C22×Q811yescharacteristic
319C23×C11C2×#4111yescharacteristic
320C23×C11C2×#4111yescharacteristic
321C23×C11C2×#4111yescharacteristic
322C23×C11C2×#4111yescharacteristic
323C23×C11C2×#4111yescharacteristic
324C23×C11C2×#4111yescharacteristic
325C23×C11H(5,𝔽2)11yescharacteristic
326C23×C11H(5,𝔽2)11yescharacteristic
327C23×C112−1+411yescharacteristic
328C23×C112−1+411yescharacteristic
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11#11714yes—
358C22×D11C4×D414yes—
359C22×D11C4×Q814yes—
360C22×D11C22⋊Q814yes—
361C22×D11#12314yes—
362C22×D11#12514yes—
363C22×D11#12614yes—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11C4×D414yes—
412C2×C4×C11#12014yes—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—41no—
435C2×Dic11—41no—
436C2×Dic11—41no—
437C2×Dic11—41no—
438C2×Dic11—41no—
439C2×Dic11—41no—
440C2×Dic11—41no—
441C2×Dic11—41no—
442C2×Dic11—41no—
443C2×Dic11—41no—
444C2×Dic11—41no—
445C2×Dic11—41no—
446C2×Dic11—41no—
447C2×Dic11—41no—
448C2×Dic11—41no—
449C2×Dic11—41no—
450C2×Dic11—41no—
451C2×Dic11—41no—
452C2×Dic11—41no—
453C2×Dic11—41no—
454C2×Dic11—41no—
455C2×Dic11—41no—
456C2×Dic11—41no—
457C2×Dic11—41no—
458C2×Dic11—41no—
459C2×Dic11—41no—
460C2×Dic11—41no—
461C2×Dic11C4×D414yes—
462C4×D11—232no—
463C4×D11—416no—
464C4×D11—416no—
465C24×C4—111no—
466C24×C4—111no—
467C24×C4—111no—
468C22×C4⋊C4—111no—
469C22×C4⋊C4—111no—
470C22×C4⋊C4—111no—
471C22×C4⋊C4—111no—
472C22×C4⋊C4—224no—
473C22×C4⋊C4—224no—
474C22×C4⋊C4—224no—
475C22×C4⋊C4C2×D1111yescharacteristic
476C22×C4⋊C4C2×D1111yescharacteristic
477C22×C22⋊C4—111no—
478C22×C22⋊C4—111no—
479C22×C22⋊C4—111no—
480C22×C22⋊C4—111no—
481C22×C42—111no—
482C22×C42C2×D1111yescharacteristic
483#387—24no—
484#387—224no—
485#385—118no—
486C4×C22⋊C4—224no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95—111no—
491C2×#95—111no—
492C2×#95—111no—
493C2×#95—111no—
494C2×#95—111no—
495C2×#95—111no—
496C2×#95—111no—
497C2×#95—111no—
498C2×#95—111no—
499C2×#95—111no—
500C2×#95—111no—
501C2×#95—111no—
502C2×#95—111no—
503C2×#95C2×D1111yescharacteristic
504C2×#95C2×D1111yescharacteristic
505C2×#95C2×D1111yescharacteristic
506C2×#95C2×D1111yescharacteristic
507C22×C11C2×#11711yescharacteristic
508C22×C11C2×C4×D411yescharacteristic
509C22×C11C2×C4×D411yescharacteristic
510C22×C11C2×C4×D411yescharacteristic
511C22×C11C2×C4×Q811yescharacteristic
512C22×C11#52011yescharacteristic
513C22×C11#52011yescharacteristic
514C22×C11C2×#12011yescharacteristic
515C22×C11C2×C22⋊Q811yescharacteristic
516C22×C11C2×#12311yescharacteristic
517C22×C11#52511yescharacteristic
518C22×C11#52511yescharacteristic
519C22×C11#52511yescharacteristic
520C22×C11C2×#12511yescharacteristic
521C22×C11C2×#12611yescharacteristic
522C22×C11#53411yescharacteristic
523C22×C11#53611yescharacteristic
524C22×C11#53911yescharacteristic
525C22×C11#53911yescharacteristic
526C22×C11#54611yescharacteristic
527C22×C11#54611yescharacteristic
528C22×C11#54611yescharacteristic
529C22×C11#54611yescharacteristic
530C22×C11#54811yescharacteristic
531C22×C11#54811yescharacteristic
532C22×C11D4×Q811yescharacteristic
533C22×C11D4×Q811yescharacteristic
534C22×C11#55211yescharacteristic
535C22×C11#55211yescharacteristic
536C22×C11#55211yescharacteristic
537C22×C11#55211yescharacteristic
538C22×C11#55311yescharacteristic
539C22×C11#55311yescharacteristic
540C22×C11#55411yescharacteristic
541C22×C11#55411yescharacteristic
542C2×D11—24no—
543C2×D11—24no—
544C2×D11—24no—
545C2×D11—24no—
546C2×D11—24no—
547C2×D11—24no—
548C2×D11—24no—
549C2×D11—24no—
550C2×D11—24no—
551C2×D11—24no—
552C2×D11—24no—
553C2×D11—24no—
554C2×D11—24no—
555C2×D11—24no—
556C2×D11#38718yescomplemented
557C4×C11—24no—
558C4×C11—24no—
559C4×C11—42no—
560C4×C11—42no—
561C4×C11—42no—
562C4×C11—42no—
563C4×C11—81no—
564Dic11—24no—
565Dic11—42no—
566Dic11—42no—
567Dic11—42no—
568Dic11—42no—
569Dic11—42no—
570Dic11—81no—
571C25—111no—
572C23×C4—111no—
573C23×C4—111no—
574C23×C4—111no—
575C23×C4—111no—
576C23×C4—111no—
577C23×C4—111no—
578C23×C4—114no—
579C23×C4—114no—
580C23×C4—111no—
581C23×C4—222no—
582C23×C4—222no—
583C23×C4—222no—
584C23×C4—222no—
585C23×C4—222no—
586C23×C4—222no—
587C23×C4—222no—
588C23×C4—222no—
589C23×C4—222no—
590C23×C4—222no—
591C23×C4—222no—
592C23×C4—222no—
593C23×C4—222no—
594C23×C4—222no—
595C23×C4—222no—
596C23×C4—441no—
597C23×C4—441no—
598C23×C4—441no—
599C23×C4—441no—
600C23×C4C22×D1111yescharacteristic
601C23×C4C22×D1111yescharacteristic
602C23×C4C22×D1111yescharacteristic
603C23×C4C22×D1111yescharacteristic
604C23×C4C22×D1111yescharacteristic
605C23×C4C22×D1111yescharacteristic
606C23×C4C22×D1111yescharacteristic
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—114no—
612C2×C4⋊C4—114no—
613C2×C4⋊C4—2232no—
614C2×C4⋊C4—222no—
615C2×C4⋊C4—222no—
616C2×C4⋊C4—222no—
617C2×C4⋊C4—222no—
618C2×C4⋊C4—222no—
619C2×C4⋊C4—222no—
620C2×C4⋊C4—222no—
621C2×C4⋊C4—222no—
622C2×C4⋊C4—222no—
623C2×C4⋊C4—222no—
624C2×C4⋊C4C4×D1114yescomplemented
625C2×C4⋊C4C22⋊D1114yes—
626C2×C22⋊C4—114no—
627C2×C22⋊C4—114no—
628C2×C22⋊C4—114no—
629C2×C22⋊C4—222no—
630C2×C22⋊C4—222no—
631C2×C22⋊C4—222no—
632C2×C22⋊C4—222no—
633C2×C22⋊C4—222no—
634C2×C22⋊C4—222no—
635C2×C22⋊C4—222no—
636C2×C22⋊C4—222no—
637C2×C22⋊C4—222no—
638C2×C42—22no—
639C2×C42—22no—
640C2×C42—22no—
641C2×C42—222no—
642C2×C42—441no—
643C2×C42—441no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—114no—
649#95—114no—
650#95—222no—
651#95—222no—
652#95—222no—
653#95—222no—
654#95—222no—
655#95—222no—
656#95—222no—
657#95—222no—
658#95—441no—
659#95—441no—
660#95—441no—
661#95—441no—
662#95—441no—
663#95—441no—
664C2×C11C2×#38711yescharacteristic
665C2×C11C4×#12011yescharacteristic
666C2×C11#232211yescharacteristic
667C2×C11#235211yescharacteristic
668C2×C11#235211yescharacteristic
669C2×C11#236011yescharacteristic
670C2×C11#236011yescharacteristic
671C2×C11#240511yescharacteristic
672C2×C11#240911yescharacteristic
673C2×C11#247311yescharacteristic
674C2×C11#247311yescharacteristic
675C2×C11#248111yescharacteristic
676C2×C11#248111yescharacteristic
677C2×C11#248411yescharacteristic
678C2×C11#257911yescharacteristic
679D11—28no—
680C24—112no—
681C24—112no—
682C24—112no—
683C24—112no—
684C24—112no—
685C24—112no—
686C24—112no—
687C24—221no—
688C24—221no—
689C24—221no—
690C24—221no—
691C24—221no—
692C24—221no—
693C24—221no—
694C24—221no—
695C24C23×D1111yescharacteristic
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—112no—
736C22×C4—112no—
737C22×C4—112no—
738C22×C4—112no—
739C22×C4—112no—
740C22×C4—112no—
741C22×C4—112no—
742C22×C4—112no—
743C22×C4—228no—
744C22×C4—228no—
745C22×C4—228no—
746C22×C4—228no—
747C22×C4—228no—
748C22×C4—228no—
749C22×C4—228no—
750C22×C4—228no—
751C22×C4—221no—
752C22×C4—221no—
753C22×C4—221no—
754C22×C4—221no—
755C22×C4—228no—
756C22×C4—221no—
757C22×C4—221no—
758C22×C4—221no—
759C22×C4—221no—
760C22×C4—221no—
761C22×C4—221no—
762C22×C4—221no—
763C22×C4—221no—
764C22×C4—221no—
765C22×C4—221no—
766C22×C4—221no—
767C22×C4—221no—
768C22×C4—221no—
769C22×C4—221no—
770C22×C4—221no—
771C22×C4—221no—
772C22×C4—221no—
773C22×C4—221no—
774C22×C4—221no—
775C22×C4—221no—
776C22×C4—221no—
777C22×C4—221no—
778C22×C4—221no—
779C22×C4—221no—
780C22×C4—221no—
781C22×C4—221no—
782C22×C4—221no—
783C22×C4—221no—
784C22×C4—221no—
785C22×C4—221no—
786C22×C4—228no—
787C22×C4—221no—
788C22×C4—221no—
789C22×C4—221no—
790C22×C4—221no—
791C22×C4—221no—
792C22×C4—221no—
793C22×C4—221no—
794C22×C4—444no—
795C22×C4—444no—
796C22×C4—444no—
797C22×C4—444no—
798C22×C4—444no—
799C22×C4—444no—
800C22×C4—444no—
801C22×C4—444no—
802C22×C4—444no—
803C22×C4—444no—
804C22×C4—444no—
805C22×C4C2×C4×D1112yes—
806C22×C4C2×C4×D1112yes—
807C22×C4C2×C4×D1112yes—
808C22×C4#433912yes—
809C22×C4D4×D1112yes—
810C22×C4D4×D1112yes—
811C22×C4Q8×D1112yes—
812C22×C4C2×C22⋊D1112yes—
813C22×C4C2×C22⋊D1112yes—
814C22×C4C2×C22⋊D1112yes—
815C4⋊C4—28no—
816C4⋊C4—28no—
817C4⋊C4—228no—
818C4⋊C4—228no—
819C4⋊C4—228no—
820C4⋊C4—228no—
821C22⋊C4—228no—
822C22⋊C4—228no—
823C22⋊C4—228no—
824C22⋊C4—444no—
825C42—44no—
826C42—444no—
827C11#1403911yescharacteristic, complemented, Sylow
828C23—114no—
829C23—114no—
830C23—114no—
831C23—114no—
832C23—114no—
833C23—114no—
834C23—114no—
835C23—222no—
836C23—222no—
837C23—222no—
838C23—222no—
839C23—222no—
840C23—222no—
841C23—222no—
842C23—222no—
843C23—222no—
844C23—222no—
845C23—222no—
846C23—222no—
847C23—222no—
848C23—222no—
849C23—222no—
850C23—222no—
851C23—222no—
852C23—222no—
853C23—222no—
854C23—222no—
855C23—222no—
856C23—222no—
857C23—222no—
858C23—222no—
859C23—222no—
860C23—222no—
861C23—222no—
862C23—222no—
863C23C22×C4×D1111yescharacteristic
864C23C2×#433911yescharacteristic
865C23C2×D4×D1111yescharacteristic
866C23C2×D4×D1111yescharacteristic
867C23C2×Q8×D1111yescharacteristic
868C23#6704011yescharacteristic
869C23#41×D1111yescharacteristic
870C23#41×D1111yescharacteristic
871C23#41×D1111yescharacteristic
872C23#41×D1111yescharacteristic
873C23#41×D1111yescharacteristic
874C23#6704211yescharacteristic
875C23#6704211yescharacteristic
876C23#6704311yescharacteristic
877C23C22×C22⋊D1111yescharacteristic
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—114no—
926C2×C4—2232no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—222no—
932C2×C4—222no—
933C2×C4—222no—
934C2×C4—222no—
935C2×C4—222no—
936C2×C4—222no—
937C2×C4—222no—
938C2×C4—222no—
939C2×C4—222no—
940C2×C4—222no—
941C2×C4—222no—
942C2×C4—222no—
943C2×C4—222no—
944C2×C4—222no—
945C2×C4—222no—
946C2×C4—222no—
947C2×C4—222no—
948C2×C4—4416no—
949C2×C4—4416no—
950C2×C4—441no—
951C2×C4—441no—
952C2×C4—441no—
953C2×C4—441no—
954C2×C4—441no—
955C2×C4—441no—
956C2×C4—441no—
957C2×C4—441no—
958C2×C4—441no—
959C2×C4—441no—
960C2×C4—441no—
961C2×C4—441no—
962C2×C4—441no—
963C2×C4—441no—
964C2×C4—441no—
965C2×C4—441no—
966C2×C4—441no—
967C2×C4—441no—
968C2×C4—441no—
969C2×C4—441no—
970C2×C4—441no—
971C2×C4—441no—
972C2×C4—441no—
973C2×C4—441no—
974C2×C4—441no—
975C2×C4—441no—
976C2×C4—441no—
977C2×C4C4×C22⋊D1114yes—
978C2×C4#6699014yes—
979C22—118no—
980C22—224no—
981C22—224no—
982C22—224no—
983C22—224no—
984C22—224no—
985C22—224no—
986C22—224no—
987C22—224no—
988C22—224no—
989C22—224no—
990C22—224no—
991C22—224no—
992C22—224no—
993C22—224no—
994C22D11×#11711yescharacteristic
995C22#1062305411yescharacteristic
996C22#1062306011yescharacteristic
997C22#1062306111yescharacteristic
998C22C4×D4×D1111yescharacteristic
999C22C4×D4×D1111yescharacteristic
1000C22#1062307811yescharacteristic
1001C22#1062307811yescharacteristic
1002C22C4×Q8×D1111yescharacteristic
1003C22#1062310511yescharacteristic
1004C22#1062311011yescharacteristic
1005C22#1062311211yescharacteristic
1006C22D11×C22⋊Q811yescharacteristic
1007C22#1062315911yescharacteristic
1008C22#1062316311yescharacteristic
1009C22#1062316411yescharacteristic
1010C22D11×#12311yescharacteristic
1011C22#1062318411yescharacteristic
1012C22#1062318511yescharacteristic
1013C22#1062318511yescharacteristic
1014C22D11×#12511yescharacteristic
1015C22#1062322111yescharacteristic
1016C22#1062322311yescharacteristic
1017C22#1062322411yescharacteristic
1018C22D11×#12611yescharacteristic
1019C22#1062323811yescharacteristic
1020C22#1062323911yescharacteristic
1021C22#1062324011yescharacteristic
1022C22C2×C4×C22⋊D1111yescharacteristic
1023C22C2×#6699011yescharacteristic
1024C22Q8×C22⋊D1111yescharacteristic
1025C22#1062335911yescharacteristic
1026C22#1062336011yescharacteristic
1027C22#1062336011yescharacteristic
1028C22#1062336211yescharacteristic
1029C4—24no—
1030C4—24no—
1031C4—42no—
1032C4—42no—
1033C4—42no—
1034C4—42no—
1035C4—81no—
1036C4—224no—
1037C4—442no—
1038C4—442no—
1039C4—442no—
1040C4—442no—
1041C4—442no—
1042C4—881no—
1043C2—228no—
1044C2D11×#38711yescharacteristic
1045C2C4×#6699011yescharacteristic
1046C2#1307128911yescharacteristic
1047C2#1307154011yescharacteristic
1048C2#1307154611yescharacteristic
1049C2#1307161711yescharacteristic
1050C2#1307162411yescharacteristic
1051C2#1307194011yescharacteristic
1052C2#1307197711yescharacteristic
1053C2#1307275311yescharacteristic
1054C2#1307276111yescharacteristic
1055C2#1307287311yescharacteristic
1056C2#1307288111yescharacteristic
1057C2#1307290111yescharacteristic
1058C2#1307396711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#387C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#387D11
hypocenterC11#14039
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. C2×#10622546C2semidirect
5. #13066874C2semidirect
6. #13066872C2semidirect
7. #13066869C2semidirect
8. #13066867C2semidirect
9. #13066851C2semidirect
10. #13066848C2semidirect
15. C2×C11×#387C2semidirect
55. #10622602C4semidirect
98. C2×C11×C4⋊C4C2×C4semidirect
125. C2×Dic11⋊C4C2×C4semidirect
149. C11⋊#95C2×C4semidirect
150. C11⋊#95C2×C4semidirect
301. C2×#387D11semidirect
556. C2×D11#387semidirect
624. C2×C4⋊C4C4×D11semidirect
827. C11#14039semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D112
C2×#106225462
C2×#106226022
C2×C4×(C2×D11)⋊C42
#130668742
#130668722
#130668692
#130668672
#130668512
#130668482
(C2×D11)⋊#952
C2×C11×#3872
#1403911