Finite Group Databasebeta

← #14678223

Subgroups — #14678223

Order 2816.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66947C211yesmaximal, characteristic
2C2×#10622603C211yesmaximal, characteristic, complemented
3C2×#10622278C211yesmaximal, characteristic
4C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
5C2×#10622279C211yesmaximal, characteristic, complemented
6#13066884C211yesmaximal, characteristic, complemented
7#13066864C211yesmaximal, characteristic, complemented
8#13066858C211yesmaximal, characteristic, complemented
9#13066856C211yesmaximal, characteristic
10#13066854C211yesmaximal, characteristic, complemented
11#13066847C211yesmaximal, characteristic, complemented
12#13066847C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×C4⋊#95C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×#66947—24no—
36C2×#66947—24no—
37C2×#66947C418yescomplemented
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
54#10622603—24no—
55C4×(C2×D11)⋊C4—24no—
56#10622279—24no—
57#10622278—24no—
58C24×D11C2311yescharacteristic
59C24×D11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C22×D44—22no—
74C22×D44—22no—
75C22×D44—22no—
76C22×D44—22no—
77C22×D44—41no—
78C22×D44—41no—
79C22×D44C2×C414yes—
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—22no—
89C22×C4×D11—41no—
90C22×C4×D11—41no—
91C22×C4×D11—41no—
92C22×C4×D11—41no—
93C22×C4×D11C2×C414yescomplemented
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4—22no—
98C2×C11×C4⋊C4—41no—
99C2×C11×C4⋊C4C2×C414yescomplemented
100C2×C42×C11—22no—
101C2×C42×C11—22no—
102C2×C42×C11—41no—
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)⋊C4—22no—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—22no—
115C2×(C2×D11)⋊C4—22no—
116C2×(C2×D11)⋊C4—22no—
117C2×(C2×D11)⋊C4—22no—
118C2×(C2×D11)⋊C4—22no—
119C2×(C2×D11)⋊C4—22no—
120C2×(C2×D11)⋊C4—22no—
121C2×(C2×D11)⋊C4—22no—
122C2×(C2×D11)⋊C4—22no—
123C2×(C2×D11)⋊C4—41no—
124C2×(C2×D11)⋊C4—41no—
125C2×(C2×D11)⋊C4—41no—
126C2×(C2×D11)⋊C4—41no—
127C2×(C2×D11)⋊C4C2×C414yes—
128C2×(C2×D11)⋊C4C2×C414yes—
129C2×(C2×D11)⋊C4C2×C414yescomplemented
130C2×(C2×D11)⋊C4D414yes—
131C2×(C2×D11)⋊C4D414yes—
132C2×(C2×D11)⋊C4D414yes—
133C2×Dic11⋊C4—22no—
134C2×Dic11⋊C4—22no—
135C2×Dic11⋊C4C2×C414yescomplemented
136C2×C4×Dic11—22no—
137C2×C4×Dic11—22no—
138C2×C4×Dic11—22no—
139C2×C4×Dic11—22no—
140C2×C4×Dic11—41no—
141C2×C4×Dic11—41no—
142#66947—232no—
143C11×#95—22no—
144C11×#95—22no—
145C11×#95—41no—
146C11×#95—41no—
147C11⋊#95—22no—
148C11⋊#95—22no—
149C11⋊#95—22no—
150C11⋊#95—22no—
151C11⋊#95—22no—
152C11⋊#95—22no—
153C11⋊#95—22no—
154C11⋊#95—22no—
155C11⋊#95—22no—
156C11⋊#95—22no—
157C11⋊#95—41no—
158C11⋊#95—41no—
159#14096—111nomaximal, Sylow
160C24×C11C2411yescharacteristic
161C23×D11—21no—
162C23×D11—21no—
163C23×D11—21no—
164C23×D11—21no—
165C23×D11—21no—
166C23×D11—21no—
167C23×D11—21no—
168C23×D11—21no—
169C23×D11—21no—
170C23×D11—21no—
171C23×D11—21no—
172C23×D11—21no—
173C23×D11—21no—
174C23×D11—21no—
175C23×D11—21no—
176C23×D11—21no—
177C23×D11—21no—
178C23×D11—21no—
179C23×D11—21no—
180C23×D11—21no—
181C23×D11—21no—
182C23×D11—21no—
183C23×D11—21no—
184C23×D11—21no—
185C23×D11C22×C412yes—
186C23×D11C22×C412yes—
187C23×D11C2×D412yes—
188C23×D11C2×D412yes—
189C23×D11C2×D412yes—
190C23×D11#4112yes—
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×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11C22×C412yes—
231C22×C4×C11C22×C412yes—
232C22×C4×C11C22×C412yes—
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2×D412yes—
235C22×C4×C11C2×D412yes—
236C22×C4×C11#4112yes—
237C22×C4×C11#4112yes—
238C22×C4×C11#4112yes—
239C22×C4×C11#4112yes—
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×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—21no—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11C22×C412yes—
276C22×Dic11C22×C412yes—
277C22×Dic11C2×D412yes—
278C22×Dic11C2×D412yes—
279C22×Dic11C2×D412yes—
280C22×Dic11#4112yes—
281C22×Dic11#4112yes—
282C2×D44—28no—
283C2×D44—28no—
284C2×D44—44no—
285C2×D44—44no—
286C2×D44—44no—
287C2×D44—44no—
288C2×D44—44no—
289C2×C4×D11—28no—
290C2×C4×D11—28no—
291C2×C4×D11—28no—
292C2×C4×D11—44no—
293C2×C4×D11—44no—
294C2×C4×D11—44no—
295C2×C4×D11—44no—
296C2×C4×D11—44no—
297C2×C4×D11—44no—
298C2×C4×D11—44no—
299C2×C4×D11—44no—
300C2×C4×D11—44no—
301C2×C4×D11—44no—
302C2×C4×D11—44no—
303C11×C4⋊C4—28no—
304C11×C4⋊C4—44no—
305C42×C11—44no—
306(C2×D11)⋊C4—28no—
307(C2×D11)⋊C4—28no—
308(C2×D11)⋊C4—28no—
309(C2×D11)⋊C4—28no—
310(C2×D11)⋊C4—28no—
311(C2×D11)⋊C4—44no—
312(C2×D11)⋊C4—44no—
313(C2×D11)⋊C4—44no—
314(C2×D11)⋊C4—44no—
315(C2×D11)⋊C4C22⋊C4116yescomplemented
316Dic11⋊C4—28no—
317C4×Dic11—44no—
318C4×Dic11—44no—
319C22×#123—111no—
320C2×#388—111no—
321C2×#386—111no—
322C2×C4×C22⋊C4—111no—
323C2×C4×C22⋊C4—111no—
324#1445—111no—
325#1440—111no—
326#1439—111no—
327#1438—111no—
328#1437—111no—
329#1436—111no—
330#1436—111no—
331C4⋊#95D1111yescharacteristic, complemented
332C22⋊#95—111no—
333C22⋊#95—111no—
334C23×C11C23×C411yescharacteristic
335C23×C11C22×D411yescharacteristic
336C23×C11C22×D411yescharacteristic
337C23×C11C22×D411yescharacteristic
338C23×C11C2×#4111yescharacteristic
339C23×C11C2×#4111yescharacteristic
340C23×C11C2×#4111yescharacteristic
341C23×C11C2×#4111yescharacteristic
342C23×C11C2×#4111yescharacteristic
343C23×C11C2×#4111yescharacteristic
344C23×C11C2×#4111yescharacteristic
345C23×C11H(5,𝔽2)11yescharacteristic
346C23×C11H(5,𝔽2)11yescharacteristic
347C23×C11H(5,𝔽2)11yescharacteristic
348C23×C112−1+411yescharacteristic
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—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—22no—
384C22×D11—22no—
385C22×D11—41no—
386C22×D11—41no—
387C22×D11—41no—
388C22×D11—41no—
389C22×D11—41no—
390C22×D11—41no—
391C22×D11—41no—
392C22×D11—41no—
393C22×D11—41no—
394C22×D11—41no—
395C22×D11—41no—
396C22×D11—41no—
397C22×D11—41no—
398C22×D11—41no—
399C22×D11—41no—
400C22×D11—41no—
401C22×D11—41no—
402C22×D11—41no—
403C22×D11—41no—
404C22×D11—41no—
405C22×D11—41no—
406C22×D11—41no—
407C22×D11—41no—
408C22×D11—41no—
409C22×D11—41no—
410C22×D11—41no—
411C22×D11—41no—
412C22×D11—41no—
413C22×D11—41no—
414C22×D11—41no—
415C22×D11—41no—
416C22×D11—41no—
417C22×D11C2×C22⋊C414yes—
418C22×D11C4×D414yes—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
455C2×C4×C11—41no—
456C2×C4×C11—41no—
457C2×C4×C11—41no—
458C2×C4×C11—41no—
459C2×C4×C11—41no—
460C2×C4×C11—41no—
461C2×C4×C11—41no—
462C2×C4×C11—41no—
463C2×C4×C11—41no—
464C2×C4×C11—41no—
465C2×C4×C11—41no—
466C2×C4×C11C2×C22⋊C414yes—
467C2×C4×C11#12314yescomplemented
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—22no—
486C2×Dic11—41no—
487C2×Dic11—41no—
488C2×Dic11—41no—
489C2×Dic11—41no—
490C2×Dic11—41no—
491C2×Dic11—41no—
492C2×Dic11—41no—
493C2×Dic11—41no—
494C2×Dic11—41no—
495C2×Dic11—41no—
496C2×Dic11—41no—
497C2×Dic11—41no—
498C2×Dic11—41no—
499C2×Dic11—41no—
500C2×Dic11—41no—
501C2×Dic11—41no—
502C2×Dic11—41no—
503C2×Dic11—41no—
504C2×Dic11—41no—
505C2×Dic11—41no—
506C2×Dic11—41no—
507C2×Dic11—41no—
508C2×Dic11—41no—
509C2×Dic11C2×C22⋊C414yes—
510D44—416no—
511C4×D11—416no—
512C4×D11—416no—
513C23×D4—111no—
514C24×C4—111no—
515C24×C4—111no—
516C2×#123—118no—
517C2×#123—224no—
518C2×#123—224no—
519C22×C4⋊C4—111no—
520C22×C4⋊C4C2×D1111yescharacteristic
521C22×C4⋊C4C2×D1111yescharacteristic
522C22×C22⋊C4—111no—
523C22×C22⋊C4—111no—
524C22×C22⋊C4—111no—
525C22×C22⋊C4—111no—
526C22×C22⋊C4—111no—
527C22×C22⋊C4—111no—
528C22×C22⋊C4—111no—
529C22×C22⋊C4—111no—
530C22×C22⋊C4—111no—
531C22×C22⋊C4—111no—
532C22×C42—111no—
533C22×C42—111no—
534C22×C42C2×D1111yescharacteristic
535#388—224no—
536#386—224no—
537C4×C22⋊C4—224no—
538C4×C22⋊C4—224no—
539C2×#95—111no—
540C2×#95—111no—
541C2×#95—111no—
542C2×#95—111no—
543C2×#95—111no—
544C2×#95—111no—
545C2×#95—111no—
546C2×#95—111no—
547C2×#95—111no—
548C2×#95—111no—
549C2×#95—111no—
550C2×#95—111no—
551C2×#95C2×D1111yescharacteristic
552C2×#95C2×D1111yescharacteristic
553C2×#95C2×D1111yescharacteristic
554C2×#95C2×D1111yescharacteristic
555C22×C11C22×C22⋊C411yescharacteristic
556C22×C11C2×C4×D411yescharacteristic
557C22×C11C4×#4111yescharacteristic
558C22×C11C4×#4111yescharacteristic
559C22×C11C4×#4111yescharacteristic
560C22×C11#51811yescharacteristic
561C22×C11#52011yescharacteristic
562C22×C11C2×#12311yescharacteristic
563C22×C11#52511yescharacteristic
564C22×C11#52511yescharacteristic
565C22×C11#52511yescharacteristic
566C22×C11#52911yescharacteristic
567C22×C11#52911yescharacteristic
568C22×C11#53211yescharacteristic
569C22×C11#53211yescharacteristic
570C22×C11#53811yescharacteristic
571C22×C11#53911yescharacteristic
572C22×C11#54011yescharacteristic
573C22×C11#54211yescharacteristic
574C22×C11D4211yescharacteristic
575C22×C11D4211yescharacteristic
576C22×C11#54611yescharacteristic
577C22×C11#54611yescharacteristic
578C22×C11#54611yescharacteristic
579C22×C11#54611yescharacteristic
580C22×C11#54611yescharacteristic
581C22×C11#54711yescharacteristic
582C22×C11#54711yescharacteristic
583C22×C11#54711yescharacteristic
584C22×C11#55111yescharacteristic
585C22×C11#55111yescharacteristic
586C22×C11#55211yescharacteristic
587C22×C11#55311yescharacteristic
588C22×C11#55311yescharacteristic
589C22×C11#55911yescharacteristic
590C2×D11—24no—
591C2×D11—24no—
592C2×D11—24no—
593C2×D11—24no—
594C2×D11—24no—
595C2×D11—24no—
596C2×D11—42no—
597C2×D11—42no—
598C2×D11—42no—
599C2×D11—42no—
600C2×D11—42no—
601C2×D11—42no—
602C2×D11—42no—
603C2×D11—42no—
604C2×D11—42no—
605C2×D11—42no—
606C2×D11—42no—
607C2×D11—42no—
608C2×D11—42no—
609C2×D11—42no—
610C2×D11—42no—
611C2×D11—42no—
612C2×D11—42no—
613C2×D11—42no—
614C2×D11—42no—
615C2×D11—42no—
616C2×D11—42no—
617C2×D11—42no—
618C2×D11—42no—
619C2×D11—42no—
620C4×C11—24no—
621C4×C11—24no—
622C4×C11—42no—
623C4×C11—42no—
624C4×C11—42no—
625C4×C11—42no—
626C4×C11—81no—
627Dic11—24no—
628Dic11—42no—
629Dic11—42no—
630Dic11—42no—
631Dic11—42no—
632Dic11—81no—
633C25—111no—
634C25—111no—
635C22×D4—114no—
636C22×D4—222no—
637C22×D4—222no—
638C22×D4—222no—
639C22×D4—222no—
640C22×D4—441no—
641C22×D4—441no—
642C23×C4—111no—
643C23×C4—111no—
644C23×C4—111no—
645C23×C4—111no—
646C23×C4—111no—
647C23×C4—114no—
648C23×C4—111no—
649C23×C4—222no—
650C23×C4—222no—
651C23×C4—222no—
652C23×C4—222no—
653C23×C4—222no—
654C23×C4—222no—
655C23×C4—222no—
656C23×C4—222no—
657C23×C4—222no—
658C23×C4—441no—
659C23×C4—441no—
660C23×C4—441no—
661C23×C4—441no—
662C23×C4C22×D1111yescharacteristic
663C23×C4C22×D1111yescharacteristic
664C23×C4C22×D1111yescharacteristic
665C23×C4C22×D1111yescharacteristic
666C23×C4C22×D1111yescharacteristic
667C23×C4C22×D1111yescharacteristic
668C23×C4C22×D1111yescharacteristic
669#123—2232no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—22no—
672C2×C4⋊C4—22no—
673C2×C4⋊C4—22no—
674C2×C4⋊C4—41no—
675C2×C4⋊C4—114no—
676C2×C4⋊C4—222no—
677C2×C4⋊C4—222no—
678C2×C4⋊C4C4×D1114yescomplemented
679C2×C22⋊C4—114no—
680C2×C22⋊C4—114no—
681C2×C22⋊C4—114no—
682C2×C22⋊C4—114no—
683C2×C22⋊C4—114no—
684C2×C22⋊C4—114no—
685C2×C22⋊C4—222no—
686C2×C22⋊C4—222no—
687C2×C22⋊C4—222no—
688C2×C22⋊C4—222no—
689C2×C22⋊C4—222no—
690C2×C22⋊C4—222no—
691C2×C22⋊C4—222no—
692C2×C22⋊C4—222no—
693C2×C22⋊C4—222no—
694C2×C22⋊C4—222no—
695C2×C22⋊C4—222no—
696C2×C22⋊C4—222no—
697C2×C22⋊C4—222no—
698C2×C22⋊C4—222no—
699C2×C22⋊C4—222no—
700C2×C22⋊C4—222no—
701C2×C22⋊C4—222no—
702C2×C22⋊C4—222no—
703C2×C22⋊C4—222no—
704C2×C22⋊C4—222no—
705C2×C22⋊C4—441no—
706C2×C22⋊C4—441no—
707C2×C22⋊C4—441no—
708C2×C22⋊C4—441no—
709C2×C42—22no—
710C2×C42—22no—
711C2×C42—41no—
712C2×C42—222no—
713C2×C42—222no—
714C2×C42—222no—
715C2×C42—222no—
716C2×C42—441no—
717C2×C42—441no—
718#95—22no—
719#95—22no—
720#95—41no—
721#95—41no—
722#95—222no—
723#95—222no—
724#95—222no—
725#95—222no—
726#95—222no—
727#95—222no—
728#95—222no—
729#95—222no—
730#95—222no—
731#95—222no—
732#95—441no—
733#95—441no—
734C2×C11#229711yescharacteristic
735C2×C11C4×#12311yescharacteristic
736C2×C11#233511yescharacteristic
737C2×C11D4×C22⋊C411yescharacteristic
738C2×C11#233911yescharacteristic
739C2×C11#235911yescharacteristic
740C2×C11#237411yescharacteristic
741C2×C11#241811yescharacteristic
742C2×C11#242211yescharacteristic
743C2×C11#245511yescharacteristic
744C2×C11#245711yescharacteristic
745C2×C11#246411yescharacteristic
746C2×C11#247011yescharacteristic
747C2×C11#255311yescharacteristic
748C2×C11#255711yescharacteristic
749D11—44no—
750D11—44no—
751C24—112no—
752C24—112no—
753C24—112no—
754C24—112no—
755C24—112no—
756C24—112no—
757C24—221no—
758C24—221no—
759C24—221no—
760C24—221no—
761C24—221no—
762C24—221no—
763C24—221no—
764C24—221no—
765C24—221no—
766C24—221no—
767C24—221no—
768C24—221no—
769C24—221no—
770C24—221no—
771C24—221no—
772C24—221no—
773C24—221no—
774C24—221no—
775C24—221no—
776C24—221no—
777C24—221no—
778C24—221no—
779C24—221no—
780C24—221no—
781C24C23×D1111yescharacteristic
782C2×D4—228no—
783C2×D4—228no—
784C2×D4—444no—
785C2×D4—444no—
786C2×D4—444no—
787C2×D4—444no—
788C2×D4—444no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—112no—
829C22×C4—112no—
830C22×C4—112no—
831C22×C4—112no—
832C22×C4—112no—
833C22×C4—112no—
834C22×C4—112no—
835C22×C4—228no—
836C22×C4—228no—
837C22×C4—228no—
838C22×C4—221no—
839C22×C4—221no—
840C22×C4—221no—
841C22×C4—221no—
842C22×C4—221no—
843C22×C4—221no—
844C22×C4—221no—
845C22×C4—221no—
846C22×C4—221no—
847C22×C4—221no—
848C22×C4—221no—
849C22×C4—221no—
850C22×C4—221no—
851C22×C4—221no—
852C22×C4—221no—
853C22×C4—221no—
854C22×C4—221no—
855C22×C4—221no—
856C22×C4—221no—
857C22×C4—221no—
858C22×C4—221no—
859C22×C4—221no—
860C22×C4—221no—
861C22×C4—221no—
862C22×C4—221no—
863C22×C4—221no—
864C22×C4—221no—
865C22×C4—221no—
866C22×C4—221no—
867C22×C4—221no—
868C22×C4—221no—
869C22×C4—221no—
870C22×C4—221no—
871C22×C4—221no—
872C22×C4—221no—
873C22×C4—444no—
874C22×C4—444no—
875C22×C4—444no—
876C22×C4—444no—
877C22×C4—444no—
878C22×C4—444no—
879C22×C4—444no—
880C22×C4—444no—
881C22×C4—444no—
882C22×C4—444no—
883C22×C4—444no—
884C22×C4C2×C4×D1112yes—
885C22×C4C2×C4×D1112yes—
886C22×C4C2×C4×D1112yes—
887C22×C4#433912yes—
888C22×C4#433912yes—
889C22×C4D4×D1112yes—
890C22×C4D4×D1112yes—
891C22×C4D4×D1112yes—
892C22×C4#434312yes—
893C22×C4#434312yes—
894C4⋊C4—28no—
895C4⋊C4—44no—
896C4⋊C4—228no—
897C22⋊C4—1116no—
898C22⋊C4—228no—
899C22⋊C4—228no—
900C22⋊C4—228no—
901C22⋊C4—228no—
902C22⋊C4—228no—
903C22⋊C4—444no—
904C22⋊C4—444no—
905C22⋊C4—444no—
906C22⋊C4—444no—
907C42—44no—
908C42—444no—
909C42—444no—
910C11#1409611yescharacteristic, complemented, Sylow
911C23—114no—
912C23—114no—
913C23—222no—
914C23—222no—
915C23—222no—
916C23—222no—
917C23—222no—
918C23—222no—
919C23—222no—
920C23—222no—
921C23—222no—
922C23—222no—
923C23—222no—
924C23—222no—
925C23—222no—
926C23—222no—
927C23—222no—
928C23—222no—
929C23—222no—
930C23—222no—
931C23—222no—
932C23—222no—
933C23—222no—
934C23—222no—
935C23—222no—
936C23—222no—
937C23—222no—
938C23—222no—
939C23—222no—
940C23—222no—
941C23—222no—
942C23—222no—
943C23—222no—
944C23—222no—
945C23—222no—
946C23—222no—
947C23—222no—
948C23—222no—
949C23—441no—
950C23—441no—
951C23—441no—
952C23—441no—
953C23—441no—
954C23—441no—
955C23—441no—
956C23—441no—
957C23—441no—
958C23—441no—
959C23—441no—
960C23—441no—
961C23—441no—
962C23—441no—
963C23—441no—
964C23—441no—
965C23—441no—
966C23—441no—
967C23—441no—
968C23—441no—
969C23—441no—
970C23—441no—
971C23—441no—
972C23—441no—
973C23—441no—
974C23—441no—
975C23—441no—
976C23—441no—
977C23—441no—
978C23—441no—
979C23—441no—
980C23—441no—
981C23C22×C4×D1111yescharacteristic
982C23C2×#433911yescharacteristic
983C23C2×#433911yescharacteristic
984C23C2×D4×D1111yescharacteristic
985C23C2×D4×D1111yescharacteristic
986C23C2×D4×D1111yescharacteristic
987C23#6703711yescharacteristic
988C23#6703711yescharacteristic
989C23C2×#434311yescharacteristic
990C23C2×#434311yescharacteristic
991C23#6704011yescharacteristic
992C23#41×D1111yescharacteristic
993C23#41×D1111yescharacteristic
994C23#41×D1111yescharacteristic
995C23#6704211yescharacteristic
996D4—4416no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—114no—
1045C2×C4—222no—
1046C2×C4—222no—
1047C2×C4—222no—
1048C2×C4—222no—
1049C2×C4—222no—
1050C2×C4—222no—
1051C2×C4—222no—
1052C2×C4—222no—
1053C2×C4—222no—
1054C2×C4—222no—
1055C2×C4—222no—
1056C2×C4—222no—
1057C2×C4—222no—
1058C2×C4—222no—
1059C2×C4—222no—
1060C2×C4—222no—
1061C2×C4—222no—
1062C2×C4—222no—
1063C2×C4—4416no—
1064C2×C4—4416no—
1065C2×C4—441no—
1066C2×C4—441no—
1067C2×C4—441no—
1068C2×C4—441no—
1069C2×C4—441no—
1070C2×C4—441no—
1071C2×C4—441no—
1072C2×C4—441no—
1073C2×C4—441no—
1074C2×C4—441no—
1075C2×C4—441no—
1076C2×C4—441no—
1077C2×C4—441no—
1078C2×C4—441no—
1079C2×C4—441no—
1080C2×C4—441no—
1081C2×C4—441no—
1082C2×C4—441no—
1083C2×C4—441no—
1084C2×C4—441no—
1085C2×C4—441no—
1086C2×C4—441no—
1087C2×C4—441no—
1088C2×C4C22⋊C4×D1114yes—
1089C2×C4#6694714yescomplemented
1090C22—224no—
1091C22—224no—
1092C22—224no—
1093C22—224no—
1094C22—224no—
1095C22—224no—
1096C22—442no—
1097C22—442no—
1098C22—442no—
1099C22—442no—
1100C22—442no—
1101C22—442no—
1102C22—442no—
1103C22—442no—
1104C22—442no—
1105C22—442no—
1106C22—442no—
1107C22—442no—
1108C22—442no—
1109C22—442no—
1110C22—442no—
1111C22—442no—
1112C22—442no—
1113C22—442no—
1114C22—442no—
1115C22—442no—
1116C22—442no—
1117C22—442no—
1118C22—442no—
1119C22—442no—
1120C22C4×#433911yescharacteristic
1121C22C2×C22⋊C4×D1111yescharacteristic
1122C22#1062302111yescharacteristic
1123C22#1062302111yescharacteristic
1124C22#1062303511yescharacteristic
1125C22C2×#6694711yescharacteristic
1126C22#1062303811yescharacteristic
1127C22#1062303811yescharacteristic
1128C22#1062304511yescharacteristic
1129C22#1062305811yescharacteristic
1130C22#1062305911yescharacteristic
1131C22#1062307111yescharacteristic
1132C22C4×D4×D1111yescharacteristic
1133C22#1062307611yescharacteristic
1134C22#1062307811yescharacteristic
1135C22C4×#434311yescharacteristic
1136C22C4×#434311yescharacteristic
1137C22#1062311111yescharacteristic
1138C22#1062311611yescharacteristic
1139C22#1062314011yescharacteristic
1140C22#1062314111yescharacteristic
1141C22#1062314311yescharacteristic
1142C22#1062314611yescharacteristic
1143C22#1062315811yescharacteristic
1144C22#1062315811yescharacteristic
1145C22#1062316811yescharacteristic
1146C22#1062317511yescharacteristic
1147C22#1062319911yescharacteristic
1148C22#1062320711yescharacteristic
1149C22#1062322311yescharacteristic
1150C22#1062322411yescharacteristic
1151C22#1062324811yescharacteristic
1152C22#1062325611yescharacteristic
1153C22#1062325711yescharacteristic
1154C22#1062326411yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—42no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—81no—
1162C4—224no—
1163C4—442no—
1164C4—442no—
1165C4—442no—
1166C4—442no—
1167C4—881no—
1168C2—444no—
1169C2—444no—
1170C2#1307110511yescharacteristic
1171C2C4×#6694711yescharacteristic
1172C2#1307140911yescharacteristic
1173C2#1307143711yescharacteristic
1174C2#1307144311yescharacteristic
1175C2#1307160311yescharacteristic
1176C2#1307174511yescharacteristic
1177C2#1307208411yescharacteristic
1178C2#1307213311yescharacteristic
1179C2#1307250011yescharacteristic
1180C2#1307253011yescharacteristic
1181C2#1307262811yescharacteristic
1182C2#1307271911yescharacteristic
1183C2#1307366811yescharacteristic
1184C2#1307372211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC4⋊#95D11
hypocenterC11#14096
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622603C2semidirect
4. C2×C4×(C2×D11)⋊C4C2semidirect
5. C2×#10622279C2semidirect
6. #13066884C2semidirect
7. #13066864C2semidirect
8. #13066858C2semidirect
10. #13066854C2semidirect
11. #13066847C2semidirect
12. #13066847C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×C4⋊#95C2semidirect
37. C2×#66947C4semidirect
93. C22×C4×D11C2×C4semidirect
99. C2×C11×C4⋊C4C2×C4semidirect
129. C2×(C2×D11)⋊C4C2×C4semidirect
135. C2×Dic11⋊C4C2×C4semidirect
315. (C2×D11)⋊C4C22⋊C4semidirect
331. C4⋊#95D11semidirect
467. C2×C4×C11#123semidirect
678. C2×C4⋊C4C4×D11semidirect
910. C11#14096semidirect
1089. C2×C4#66947semidirect

Maximal subgroups

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

subgroupindex
C22×#669472
C2×#106226032
C2×#106222782
C2×C4×(C2×D11)⋊C42
C2×#106222792
#130668842
#130668642
#130668582
#130668562
#130668542
#130668472
(C2×D11)⋊#952
C11×C4⋊#952
#1409611