Finite Group Databasebeta

← #14682948

Subgroups — #14682948

Order 2816.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66947C211yesmaximal, characteristic
2C2×#10622553C211yesmaximal, characteristic, complemented
3C2×#10622603C211yesmaximal, characteristic, complemented
4#13066884C211yesmaximal, characteristic, complemented
5#13066882C211yesmaximal, characteristic, complemented
6#13066860C211yesmaximal, characteristic, complemented
7#13066858C211yesmaximal, characteristic, complemented
8#13066856C211yesmaximal, characteristic
9#13066856C211yesmaximal, characteristic
10#13066854C211yesmaximal, characteristic, complemented
11#13066852C211yesmaximal, characteristic, complemented
12Dic11⋊#95C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×C4⋊#95C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic
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—
55#10622553—24no—
56C24×D11C2311yescharacteristic
57C24×D11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C22×D44—22no—
72C22×D44—22no—
73C22×D44—41no—
74C22×D44—41no—
75C22×D44—41no—
76C22×D44—41no—
77C22×D44C2×C414yes—
78C22×C4×D11—22no—
79C22×C4×D11—22no—
80C22×C4×D11—41no—
81C22×C4×D11—41no—
82C22×C4×D11—41no—
83C22×C4×D11—41no—
84C22×C4×D11C2×C414yes—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—41no—
90C2×C11×C4⋊C4C2×C414yes—
91C2×C42×C11—22no—
92C2×C42×C11—22no—
93C2×C42×C11—41no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—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—41no—
111C2×(C2×D11)⋊C4—41no—
112C2×(C2×D11)⋊C4—41no—
113C2×(C2×D11)⋊C4—41no—
114C2×(C2×D11)⋊C4—41no—
115C2×(C2×D11)⋊C4—41no—
116C2×(C2×D11)⋊C4—41no—
117C2×(C2×D11)⋊C4—41no—
118C2×(C2×D11)⋊C4—41no—
119C2×(C2×D11)⋊C4—41no—
120C2×(C2×D11)⋊C4—41no—
121C2×(C2×D11)⋊C4—41no—
122C2×(C2×D11)⋊C4C2×C414yes—
123C2×(C2×D11)⋊C4C2×C414yes—
124C2×(C2×D11)⋊C4C2×C414yes—
125C2×(C2×D11)⋊C4D414yes—
126C2×(C2×D11)⋊C4D414yes—
127C2×Dic11⋊C4—22no—
128C2×Dic11⋊C4—22no—
129C2×Dic11⋊C4—22no—
130C2×Dic11⋊C4—22no—
131C2×Dic11⋊C4—41no—
132C2×Dic11⋊C4C2×C414yes—
133C2×C4×Dic11—22no—
134C2×C4×Dic11—22no—
135C2×C4×Dic11—41no—
136#66947—232no—
137C11×#95—41no—
138C11×#95—41no—
139C11×#95—41no—
140C11×#95—41no—
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—22no—
145C11⋊#95—41no—
146C11⋊#95—41no—
147C11⋊#95—41no—
148C11⋊#95—41no—
149C11⋊#95—41no—
150C11⋊#95—41no—
151C11⋊#95—41no—
152C11⋊#95—41no—
153#14506—111nomaximal, Sylow
154C24×C11C2411yescharacteristic
155C23×D11—21no—
156C23×D11—21no—
157C23×D11—21no—
158C23×D11—21no—
159C23×D11—21no—
160C23×D11—21no—
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×D11C22×C412yes—
182C23×D11C22×C412yes—
183C23×D11C2×D412yes—
184C23×D11C2×D412yes—
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×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×C11C22×C412yes—
227C22×C4×C11C22×C412yes—
228C22×C4×C11C22×C412yes—
229C22×C4×C11C2×D412yes—
230C22×C4×C11C2×D412yes—
231C22×C4×C11#4112yes—
232C22×C4×C11#4112yes—
233C22×C4×C11#4112yes—
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×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×Dic11C22×C412yes—
272C22×Dic11C22×C412yes—
273C22×Dic11C2×D412yes—
274C22×Dic11C2×D412yes—
275C22×Dic11#4112yes—
276C2×D44—28no—
277C2×D44—44no—
278C2×D44—44no—
279C2×D44—44no—
280C2×D44—44no—
281C2×D44—44no—
282C2×D44—44no—
283C2×C4×D11—28no—
284C2×C4×D11—44no—
285C2×C4×D11—44no—
286C2×C4×D11—44no—
287C2×C4×D11—44no—
288C2×C4×D11—44no—
289C2×C4×D11—44no—
290C11×C4⋊C4—28no—
291C11×C4⋊C4—44no—
292C42×C11—44no—
293(C2×D11)⋊C4—28no—
294(C2×D11)⋊C4—28no—
295(C2×D11)⋊C4—44no—
296(C2×D11)⋊C4—44no—
297(C2×D11)⋊C4—44no—
298(C2×D11)⋊C4—44no—
299(C2×D11)⋊C4—44no—
300(C2×D11)⋊C4—44no—
301(C2×D11)⋊C4—44no—
302(C2×D11)⋊C4—44no—
303(C2×D11)⋊C4C22⋊C4116yescomplemented
304Dic11⋊C4—28no—
305Dic11⋊C4—44no—
306C4×Dic11—44no—
307C22×#123—111no—
308C2×#388—111no—
309C2×#388—111no—
310#1445—111no—
311#1445—111no—
312#1439—111no—
313#1439—111no—
314#1438—111no—
315#1438—111no—
316#1437—111no—
317#1437—111no—
318C4⋊#95—111no—
319C4⋊#95D1111yescharacteristic, complemented
320C22⋊#95—111no—
321C22⋊#95—111no—
322C23×C11C23×C411yescharacteristic
323C23×C11C22×D411yescharacteristic
324C23×C11C22×D411yescharacteristic
325C23×C11C2×#4111yescharacteristic
326C23×C11C2×#4111yescharacteristic
327C23×C11C2×#4111yescharacteristic
328C23×C11C2×#4111yescharacteristic
329C23×C11H(5,𝔽2)11yescharacteristic
330C23×C11H(5,𝔽2)11yescharacteristic
331C23×C11H(5,𝔽2)11yescharacteristic
332C23×C11H(5,𝔽2)11yescharacteristic
333C23×C11H(5,𝔽2)11yescharacteristic
334C23×C11H(5,𝔽2)11yescharacteristic
335C23×C112−1+411yescharacteristic
336C23×C112−1+411yescharacteristic
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—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—41no—
363C22×D11—41no—
364C22×D11—41no—
365C22×D11—41no—
366C22×D11—41no—
367C22×D11—41no—
368C22×D11—41no—
369C22×D11—41no—
370C22×D11—41no—
371C22×D11—41no—
372C22×D11—41no—
373C22×D11—41no—
374C22×D11—41no—
375C22×D11—41no—
376C22×D11—41no—
377C22×D11—41no—
378C22×D11—41no—
379C22×D11—41no—
380C22×D11—41no—
381C22×D11—41no—
382C22×D11—41no—
383C22×D11—41no—
384C22×D11—41no—
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×D11C2×C22⋊C414yes—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
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—41no—
429C2×C4×C11—41no—
430C2×C4×C11—41no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
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×C11C2×C22⋊C414yes—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—22no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—41no—
469C2×Dic11—41no—
470C2×Dic11—41no—
471C2×Dic11—41no—
472C2×Dic11—41no—
473C2×Dic11—41no—
474C2×Dic11—41no—
475C2×Dic11—41no—
476C2×Dic11—41no—
477C2×Dic11—41no—
478C2×Dic11—41no—
479C2×Dic11—41no—
480C2×Dic11—41no—
481C2×Dic11—41no—
482C2×Dic11—41no—
483C2×Dic11—41no—
484C2×Dic11—41no—
485C2×Dic11—41no—
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×Dic11C2×C22⋊C414yes—
498D44—416no—
499C4×D11—416no—
500C23×D4—111no—
501C24×C4—111no—
502C2×#123—118no—
503C2×#123—224no—
504C2×#123—224no—
505C22×C4⋊C4—111no—
506C22×C4⋊C4—111no—
507C22×C4⋊C4C2×D1111yescharacteristic
508C22×C4⋊C4C2×D1111yescharacteristic
509C22×C22⋊C4—111no—
510C22×C22⋊C4—111no—
511C22×C22⋊C4—111no—
512C22×C22⋊C4—111no—
513C22×C22⋊C4—111no—
514C22×C22⋊C4—111no—
515C22×C22⋊C4—111no—
516C22×C22⋊C4—111no—
517C22×C22⋊C4—111no—
518C22×C22⋊C4—111no—
519C22×C22⋊C4—111no—
520C22×C42—111no—
521C22×C42C2×D1111yescharacteristic
522#388—224no—
523#388—224no—
524C2×#95—111no—
525C2×#95—111no—
526C2×#95—111no—
527C2×#95—111no—
528C2×#95—111no—
529C2×#95—111no—
530C2×#95—111no—
531C2×#95—111no—
532C2×#95—111no—
533C2×#95—111no—
534C2×#95—111no—
535C2×#95—111no—
536C2×#95C2×D1111yescharacteristic
537C2×#95C2×D1111yescharacteristic
538C2×#95C2×D1111yescharacteristic
539C2×#95C2×D1111yescharacteristic
540C22×C11C22×C22⋊C411yescharacteristic
541C22×C11C4×#4111yescharacteristic
542C22×C11C4×#4111yescharacteristic
543C22×C11#51811yescharacteristic
544C22×C11#51811yescharacteristic
545C22×C11#52011yescharacteristic
546C22×C11#52011yescharacteristic
547C22×C11#53511yescharacteristic
548C22×C11#53511yescharacteristic
549C22×C11#53511yescharacteristic
550C22×C11#53511yescharacteristic
551C22×C11#53811yescharacteristic
552C22×C11#53811yescharacteristic
553C22×C11#53911yescharacteristic
554C22×C11#53911yescharacteristic
555C22×C11#54011yescharacteristic
556C22×C11#54011yescharacteristic
557C22×C11#54211yescharacteristic
558C22×C11#54211yescharacteristic
559C22×C11#54611yescharacteristic
560C22×C11#54611yescharacteristic
561C22×C11#54611yescharacteristic
562C22×C11#54611yescharacteristic
563C22×C11#54711yescharacteristic
564C22×C11#54711yescharacteristic
565C22×C11#54711yescharacteristic
566C22×C11#54711yescharacteristic
567C22×C11#55111yescharacteristic
568C22×C11#55311yescharacteristic
569C22×C11#55311yescharacteristic
570C22×C11#55911yescharacteristic
571C22×C11#56011yescharacteristic
572C22×C11#56211yescharacteristic
573C22×C11#56211yescharacteristic
574C22×C11#56311yescharacteristic
575C2×D11—24no—
576C2×D11—24no—
577C2×D11—24no—
578C2×D11—42no—
579C2×D11—42no—
580C2×D11—42no—
581C2×D11—42no—
582C2×D11—42no—
583C2×D11—42no—
584C2×D11—42no—
585C2×D11—42no—
586C2×D11—42no—
587C2×D11—42no—
588C2×D11—42no—
589C2×D11—42no—
590C2×D11—42no—
591C2×D11—42no—
592C2×D11—42no—
593C2×D11—42no—
594C2×D11—42no—
595C2×D11—42no—
596C2×D11—42no—
597C2×D11—81no—
598C2×D11—81no—
599C2×D11—81no—
600C2×D11—81no—
601C2×D11—81no—
602C2×D11—81no—
603C2×D11—81no—
604C2×D11—81no—
605C4×C11—24no—
606C4×C11—42no—
607C4×C11—42no—
608C4×C11—42no—
609C4×C11—42no—
610C4×C11—42no—
611C4×C11—81no—
612Dic11—24no—
613Dic11—42no—
614Dic11—42no—
615Dic11—81no—
616Dic11—81no—
617Dic11—81no—
618C25—111no—
619C25—111no—
620C22×D4—114no—
621C22×D4—222no—
622C22×D4—222no—
623C22×D4—441no—
624C22×D4—441no—
625C22×D4—441no—
626C22×D4—441no—
627C23×C4—111no—
628C23×C4—111no—
629C23×C4—111no—
630C23×C4—114no—
631C23×C4—111no—
632C23×C4—111no—
633C23×C4—111no—
634C23×C4—222no—
635C23×C4—222no—
636C23×C4—441no—
637C23×C4—441no—
638C23×C4—441no—
639C23×C4—441no—
640C23×C4C22×D1111yescharacteristic
641C23×C4C22×D1111yescharacteristic
642C23×C4C22×D1111yescharacteristic
643C23×C4C22×D1111yescharacteristic
644C23×C4C22×D1111yescharacteristic
645C23×C4C22×D1111yescharacteristic
646C23×C4C22×D1111yescharacteristic
647#123—2232no—
648C2×C4⋊C4—22no—
649C2×C4⋊C4—22no—
650C2×C4⋊C4—22no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—41no—
653C2×C4⋊C4—114no—
654C2×C4⋊C4—222no—
655C2×C4⋊C4—222no—
656C2×C4⋊C4—222no—
657C2×C4⋊C4—222no—
658C2×C4⋊C4—441no—
659C2×C4⋊C4C4×D1114yes—
660C2×C22⋊C4—114no—
661C2×C22⋊C4—114no—
662C2×C22⋊C4—114no—
663C2×C22⋊C4—114no—
664C2×C22⋊C4—114no—
665C2×C22⋊C4—222no—
666C2×C22⋊C4—222no—
667C2×C22⋊C4—222no—
668C2×C22⋊C4—222no—
669C2×C22⋊C4—222no—
670C2×C22⋊C4—222no—
671C2×C22⋊C4—222no—
672C2×C22⋊C4—222no—
673C2×C22⋊C4—222no—
674C2×C22⋊C4—222no—
675C2×C22⋊C4—222no—
676C2×C22⋊C4—222no—
677C2×C22⋊C4—222no—
678C2×C22⋊C4—222no—
679C2×C22⋊C4—222no—
680C2×C22⋊C4—222no—
681C2×C22⋊C4—441no—
682C2×C22⋊C4—441no—
683C2×C22⋊C4—441no—
684C2×C22⋊C4—441no—
685C2×C22⋊C4—441no—
686C2×C22⋊C4—441no—
687C2×C22⋊C4—441no—
688C2×C22⋊C4—441no—
689C2×C22⋊C4—441no—
690C2×C22⋊C4—441no—
691C2×C22⋊C4—441no—
692C2×C22⋊C4—441no—
693C2×C42—22no—
694C2×C42—22no—
695C2×C42—41no—
696C2×C42—222no—
697C2×C42—222no—
698C2×C42—441no—
699#95—41no—
700#95—41no—
701#95—41no—
702#95—41no—
703#95—222no—
704#95—222no—
705#95—222no—
706#95—222no—
707#95—441no—
708#95—441no—
709#95—441no—
710#95—441no—
711#95—441no—
712#95—441no—
713#95—441no—
714#95—441no—
715C2×C11#230911yescharacteristic
716C2×C11#233511yescharacteristic
717C2×C11#233511yescharacteristic
718C2×C11#233911yescharacteristic
719C2×C11#233911yescharacteristic
720C2×C11#237411yescharacteristic
721C2×C11#237611yescharacteristic
722C2×C11#270311yescharacteristic
723C2×C11#270311yescharacteristic
724C2×C11#270611yescharacteristic
725C2×C11#270611yescharacteristic
726C2×C11#271011yescharacteristic
727C2×C11#271011yescharacteristic
728C2×C11#271811yescharacteristic
729C2×C11#271811yescharacteristic
730D11—44no—
731D11—82no—
732C24—112no—
733C24—112no—
734C24—112no—
735C24—112no—
736C24—221no—
737C24—221no—
738C24—221no—
739C24—221no—
740C24—221no—
741C24—221no—
742C24—221no—
743C24—221no—
744C24—221no—
745C24—221no—
746C24—221no—
747C24—221no—
748C24—221no—
749C24—221no—
750C24—221no—
751C24—221no—
752C24—221no—
753C24—221no—
754C24—221no—
755C24—221no—
756C24—221no—
757C24—221no—
758C24—221no—
759C24—221no—
760C24—221no—
761C24—221no—
762C24C23×D1111yescharacteristic
763C2×D4—228no—
764C2×D4—444no—
765C2×D4—444no—
766C2×D4—444no—
767C2×D4—444no—
768C2×D4—444no—
769C2×D4—444no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
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—112no—
812C22×C4—112no—
813C22×C4—112no—
814C22×C4—112no—
815C22×C4—112no—
816C22×C4—228no—
817C22×C4—221no—
818C22×C4—221no—
819C22×C4—221no—
820C22×C4—221no—
821C22×C4—221no—
822C22×C4—221no—
823C22×C4—221no—
824C22×C4—221no—
825C22×C4—221no—
826C22×C4—221no—
827C22×C4—221no—
828C22×C4—221no—
829C22×C4—221no—
830C22×C4—221no—
831C22×C4—221no—
832C22×C4—221no—
833C22×C4—221no—
834C22×C4—221no—
835C22×C4—221no—
836C22×C4—221no—
837C22×C4—221no—
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—444no—
855C22×C4—444no—
856C22×C4—444no—
857C22×C4—444no—
858C22×C4—444no—
859C22×C4—444no—
860C22×C4C2×C4×D1112yes—
861C22×C4C2×C4×D1112yes—
862C22×C4C2×C4×D1112yes—
863C22×C4#433912yes—
864C22×C4#433912yes—
865C22×C4D4×D1112yes—
866C22×C4D4×D1112yes—
867C22×C4#434312yes—
868C4⋊C4—28no—
869C4⋊C4—44no—
870C4⋊C4—228no—
871C4⋊C4—444no—
872C22⋊C4—1116no—
873C22⋊C4—228no—
874C22⋊C4—228no—
875C22⋊C4—444no—
876C22⋊C4—444no—
877C22⋊C4—444no—
878C22⋊C4—444no—
879C22⋊C4—444no—
880C22⋊C4—444no—
881C22⋊C4—444no—
882C22⋊C4—444no—
883C42—44no—
884C42—444no—
885C11#1450611yescharacteristic, complemented, Sylow
886C23—114no—
887C23—222no—
888C23—222no—
889C23—222no—
890C23—222no—
891C23—222no—
892C23—222no—
893C23—222no—
894C23—222no—
895C23—222no—
896C23—222no—
897C23—222no—
898C23—222no—
899C23—222no—
900C23—222no—
901C23—222no—
902C23—222no—
903C23—222no—
904C23—222no—
905C23—222no—
906C23—222no—
907C23—222no—
908C23—222no—
909C23—222no—
910C23—222no—
911C23—222no—
912C23—441no—
913C23—441no—
914C23—441no—
915C23—441no—
916C23—441no—
917C23—441no—
918C23—441no—
919C23—441no—
920C23—441no—
921C23—441no—
922C23—441no—
923C23—441no—
924C23—441no—
925C23—441no—
926C23—441no—
927C23—441no—
928C23—441no—
929C23—441no—
930C23—441no—
931C23—441no—
932C23—441no—
933C23—441no—
934C23—441no—
935C23—441no—
936C23—441no—
937C23—441no—
938C23—441no—
939C23—441no—
940C23—441no—
941C23—441no—
942C23—441no—
943C23—441no—
944C23—441no—
945C23—441no—
946C23—441no—
947C23—441no—
948C23—441no—
949C23—441no—
950C23—441no—
951C23—441no—
952C23—441no—
953C23—441no—
954C23—441no—
955C23—441no—
956C23C22×C4×D1111yescharacteristic
957C23C2×#433911yescharacteristic
958C23C2×#433911yescharacteristic
959C23C2×D4×D1111yescharacteristic
960C23C2×D4×D1111yescharacteristic
961C23#6703711yescharacteristic
962C23#6703711yescharacteristic
963C23#6703711yescharacteristic
964C23C2×#434311yescharacteristic
965C23#6704011yescharacteristic
966C23#6704011yescharacteristic
967C23#41×D1111yescharacteristic
968C23#6704211yescharacteristic
969C23#6704211yescharacteristic
970C23#6704211yescharacteristic
971D4—4416no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—114no—
1021C2×C4—222no—
1022C2×C4—222no—
1023C2×C4—222no—
1024C2×C4—222no—
1025C2×C4—222no—
1026C2×C4—222no—
1027C2×C4—222no—
1028C2×C4—222no—
1029C2×C4—222no—
1030C2×C4—222no—
1031C2×C4—222no—
1032C2×C4—222no—
1033C2×C4—4416no—
1034C2×C4—441no—
1035C2×C4—441no—
1036C2×C4—441no—
1037C2×C4—441no—
1038C2×C4—441no—
1039C2×C4—441no—
1040C2×C4—441no—
1041C2×C4—441no—
1042C2×C4—441no—
1043C2×C4—441no—
1044C2×C4—441no—
1045C2×C4—441no—
1046C2×C4—441no—
1047C2×C4—441no—
1048C2×C4—441no—
1049C2×C4—441no—
1050C2×C4—441no—
1051C2×C4—441no—
1052C2×C4—441no—
1053C2×C4—441no—
1054C2×C4—441no—
1055C2×C4—441no—
1056C2×C4—441no—
1057C2×C4—441no—
1058C2×C4—441no—
1059C2×C4—441no—
1060C2×C4—441no—
1061C2×C4—441no—
1062C2×C4—441no—
1063C2×C4C22⋊C4×D1114yes—
1064C22—224no—
1065C22—224no—
1066C22—224no—
1067C22—442no—
1068C22—442no—
1069C22—442no—
1070C22—442no—
1071C22—442no—
1072C22—442no—
1073C22—442no—
1074C22—442no—
1075C22—442no—
1076C22—442no—
1077C22—442no—
1078C22—442no—
1079C22—442no—
1080C22—442no—
1081C22—442no—
1082C22—442no—
1083C22—442no—
1084C22—442no—
1085C22—442no—
1086C22—881no—
1087C22—881no—
1088C22—881no—
1089C22—881no—
1090C22—881no—
1091C22—881no—
1092C22—881no—
1093C22—881no—
1094C22C4×#433911yescharacteristic
1095C22C2×C22⋊C4×D1111yescharacteristic
1096C22#1062302111yescharacteristic
1097C22#1062302111yescharacteristic
1098C22#1062303511yescharacteristic
1099C22#1062303811yescharacteristic
1100C22#1062303811yescharacteristic
1101C22#1062304511yescharacteristic
1102C22#1062304611yescharacteristic
1103C22#1062305811yescharacteristic
1104C22#1062306611yescharacteristic
1105C22#1062307111yescharacteristic
1106C22#1062307611yescharacteristic
1107C22#1062307611yescharacteristic
1108C22#1062309111yescharacteristic
1109C22C4×#434311yescharacteristic
1110C22#1062310511yescharacteristic
1111C22#1062311311yescharacteristic
1112C22#1062311611yescharacteristic
1113C22#1062313811yescharacteristic
1114C22#1062313811yescharacteristic
1115C22#1062314611yescharacteristic
1116C22#1062315111yescharacteristic
1117C22#1062316111yescharacteristic
1118C22#1062316211yescharacteristic
1119C22#1062317511yescharacteristic
1120C22#1062317811yescharacteristic
1121C22#1062320511yescharacteristic
1122C22#1062320711yescharacteristic
1123C22#1062322311yescharacteristic
1124C22#1062323111yescharacteristic
1125C22#1062324611yescharacteristic
1126C22#1062325711yescharacteristic
1127C22#1062326411yescharacteristic
1128C22#1062326611yescharacteristic
1129C4—24no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—81no—
1136C4—224no—
1137C4—442no—
1138C4—442no—
1139C4—881no—
1140C4—881no—
1141C4—881no—
1142C2—444no—
1143C2—882no—
1144C2#1307119511yescharacteristic
1145C2#1307140011yescharacteristic
1146C2#1307140911yescharacteristic
1147C2#1307144311yescharacteristic
1148C2#1307144511yescharacteristic
1149C2#1307174511yescharacteristic
1150C2#1307176111yescharacteristic
1151C2#1307525611yescharacteristic
1152C2#1307525911yescharacteristic
1153C2#1307530111yescharacteristic
1154C2#1307530411yescharacteristic
1155C2#1307535311yescharacteristic
1156C2#1307535911yescharacteristic
1157C2#1307546111yescharacteristic
1158C2#1307546711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC4⋊#95D11
hypocenterC11#14506
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622553C2semidirect
3. C2×#10622603C2semidirect
4. #13066884C2semidirect
5. #13066882C2semidirect
6. #13066860C2semidirect
7. #13066858C2semidirect
10. #13066854C2semidirect
11. #13066852C2semidirect
12. Dic11⋊#95C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×C4⋊#95C2semidirect
37. C2×#66947C4semidirect
303. (C2×D11)⋊C4C22⋊C4semidirect
319. C4⋊#95D11semidirect
885. C11#14506semidirect

Maximal subgroups

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

subgroupindex
C22×#669472
C2×#106225532
C2×#106226032
#130668842
#130668822
#130668602
#130668582
#130668562
#130668542
#130668522
Dic11⋊#952
(C2×D11)⋊#952
C11×C4⋊#952
#1450611