Finite Group Databasebeta

← #14676562

Subgroups — #14676562

Order 2816.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66949C211yesmaximal, characteristic
2C22×#66940C211yesmaximal, characteristic, complemented
3C2×#10622259C211yesmaximal, characteristic, complemented
4C2×#10622280C211yesmaximal, characteristic
5C2×#10622279C211yesmaximal, characteristic
6#13066867C211yesmaximal, characteristic, complemented
7#13066860C211yesmaximal, characteristic
8#13066858C211yesmaximal, characteristic
9#13066852C211yesmaximal, characteristic
10#13066852C211yesmaximal, characteristic
11#13066848C211yesmaximal, characteristic, complemented
12#13066847C211yesmaximal, characteristic, complemented
13Dic11⋊#95C211yesmaximal, characteristic, complemented
14Dic11⋊#95C211yesmaximal, characteristic, complemented
15C11×#1441C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×#66949—24no—
36C2×#66949—24no—
37C2×#66949C418yescomplemented
38C2×#66940—24no—
39C2×#66940—24no—
40C2×#66940—24no—
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
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622280—24no—
58#10622279—24no—
59#10622259—24no—
60C24×D11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
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×D11C2×C414yes—
82C22×Dic22—22no—
83C22×Dic22—22no—
84C22×Dic22—22no—
85C22×Dic22—22no—
86C22×Dic22C2×C414yes—
87C22×Dic22D414yes—
88C22×Dic22D414yes—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4C2×C414yes—
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—41no—
109C2×(C2×D11)⋊C4—41no—
110C2×(C2×D11)⋊C4C2×C414yes—
111C2×(C2×D11)⋊C4C2×C414yes—
112C2×(C2×D11)⋊C4Q814yescomplemented
113C2×Dic11⋊C4—22no—
114C2×Dic11⋊C4—22no—
115C2×Dic11⋊C4—22no—
116C2×Dic11⋊C4—22no—
117C2×Dic11⋊C4—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×C414yes—
126C2×Dic11⋊C4C2×C414yes—
127C2×Dic11⋊C4D414yes—
128C2×C4×Dic11—22no—
129C2×C4×Dic11—22no—
130C2×C4×Dic11—22no—
131C2×C4×Dic11—22no—
132C2×C4×Dic11—22no—
133C2×C4×Dic11—22no—
134C2×C4×Dic11—22no—
135C2×C4×Dic11—22no—
136C2×C4×Dic11—22no—
137C2×C4×Dic11—22no—
138C2×C4×Dic11—22no—
139C2×C4×Dic11D414yes—
140#66949—232no—
141#66940—232no—
142C11×#95—22no—
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—41no—
157C11⋊#95—41no—
158#13969—111nomaximal, Sylow
159C24×C11C2411yescharacteristic
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×D11C22×C412yes—
173C23×D11C2×Q812yes—
174C23×D11#4112yes—
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×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×C11C22×C412yes—
217C22×C4×C11C22×C412yes—
218C22×C4×C11C22×C412yes—
219C22×C4×C11C2×D412yes—
220C22×C4×C11C2×D412yes—
221C22×C4×C11C2×D412yes—
222C22×C4×C11C2×D412yes—
223C22×C4×C11C2×Q812yes—
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×Dic11C22×C412yes—
258C22×Dic11C22×C412yes—
259C22×Dic11C22×C412yes—
260C22×Dic11C2×D412yes—
261C22×Dic11C2×D412yes—
262C22×Dic11C2×D412yes—
263C22×Dic11C2×D412yes—
264C22×Dic11C2×D412yes—
265C22×Dic11C2×D412yes—
266C22×Dic11C2×D412yes—
267C22×Dic11C2×D412yes—
268C22×Dic11C2×Q812yes—
269C22×Dic11#4112yes—
270C22×Dic11#4112yes—
271C22×Dic11#4112yes—
272C22×Dic11#4112yes—
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×Dic22—28no—
281C2×Dic22—28no—
282C2×Dic22—28no—
283C2×Dic22—28no—
284C2×Dic22—28no—
285C2×Dic22—28no—
286C2×Dic22C22⋊C4116yescomplemented
287C11×C4⋊C4—28no—
288C11×C4⋊C4—28no—
289(C2×D11)⋊C4—28no—
290(C2×D11)⋊C4—28no—
291(C2×D11)⋊C4—28no—
292(C2×D11)⋊C4—28no—
293(C2×D11)⋊C4—44no—
294(C2×D11)⋊C4—44no—
295Dic11⋊C4—28no—
296Dic11⋊C4—28no—
297Dic11⋊C4—28no—
298Dic11⋊C4—28no—
299Dic11⋊C4—44no—
300C4×Dic11—28no—
301C4×Dic11—28no—
302C4×Dic11—28no—
303C4×Dic11—44no—
304C22×C22⋊Q8—111no—
305C22×C4×Q8—111no—
306C2×#391—111no—
307C2×#380—111no—
308C2×C4×C22⋊C4—111no—
309#1441—111no—
310#1441D1111yescharacteristic, complemented
311#1439—111no—
312#1439—111no—
313#1437—111no—
314#1437—111no—
315#1436—111no—
316#1436—111no—
317C4⋊#95—111no—
318C4⋊#95—111no—
319C23×C11C23×C411yescharacteristic
320C23×C11C22×D411yescharacteristic
321C23×C11C22×D411yescharacteristic
322C23×C11C22×D411yescharacteristic
323C23×C11C22×D411yescharacteristic
324C23×C11C22×Q811yescharacteristic
325C23×C11C2×#4111yescharacteristic
326C23×C11C2×#4111yescharacteristic
327C23×C11C2×#4111yescharacteristic
328C23×C11C2×#4111yescharacteristic
329C23×C11C2×#4111yescharacteristic
330C23×C11H(5,𝔽2)11yescharacteristic
331C23×C112−1+411yescharacteristic
332C23×C112−1+411yescharacteristic
333C23×C112−1+411yescharacteristic
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—41no—
353C22×D11—41no—
354C22×D11—41no—
355C22×D11—41no—
356C22×D11—41no—
357C22×D11—41no—
358C22×D11—41no—
359C22×D11—41no—
360C22×D11—41no—
361C22×D11—41no—
362C22×D11—41no—
363C22×D11—41no—
364C22×D11—41no—
365C22×D11—41no—
366C22×D11—41no—
367C22×D11—41no—
368C22×D11C4×Q814yescomplemented
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—22no—
389C2×C4×C11—22no—
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×C11—41no—
412C2×C4×C11—41no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11C2×C22⋊C414yes—
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—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
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×Dic11C2×C22⋊C414yes—
459C2×Dic11C2×C22⋊C414yes—
460C2×Dic11C4×D414yes—
461C2×Dic11C4×D414yes—
462C2×Dic11#12014yes—
463C2×Dic11#12114yes—
464C2×Dic11#12114yes—
465C2×Dic11C22⋊Q814yescomplemented
466C2×Dic11#12314yes—
467C4×D11—416no—
468Dic22—232no—
469C23×Q8—111no—
470C24×C4—111no—
471C2×C22⋊Q8—118no—
472C2×C22⋊Q8—224no—
473C2×C22⋊Q8—224no—
474C2×C4×Q8—224no—
475C2×C4×Q8—224no—
476C2×C4×Q8—224no—
477C22×C4⋊C4—111no—
478C22×C4⋊C4—111no—
479C22×C4⋊C4—111no—
480C22×C4⋊C4—111no—
481C22×C4⋊C4—111no—
482C22×C4⋊C4C2×D1111yescharacteristic
483C22×C4⋊C4C2×D1111yescharacteristic
484C22×C22⋊C4—111no—
485C22×C22⋊C4—111no—
486C22×C22⋊C4—111no—
487C22×C22⋊C4—111no—
488C22×C22⋊C4—111no—
489C22×C22⋊C4—111no—
490C22×C42—111no—
491C22×C42—111no—
492C22×C42—111no—
493C22×C42—111no—
494#391—224no—
495#380—224no—
496C4×C22⋊C4—224no—
497C2×#95—111no—
498C2×#95—111no—
499C2×#95—111no—
500C2×#95—111no—
501C2×#95—111no—
502C2×#95—111no—
503C2×#95—111no—
504C2×#95—111no—
505C2×#95—111no—
506C2×#95—111no—
507C2×#95—111no—
508C2×#95C2×D1111yescharacteristic
509C2×#95C2×D1111yescharacteristic
510C2×#95C2×D1111yescharacteristic
511C2×#95C2×D1111yescharacteristic
512C2×#95C2×D1111yescharacteristic
513C22×C11C22×C22⋊C411yescharacteristic
514C22×C11C2×C4×D411yescharacteristic
515C22×C11C2×C4×D411yescharacteristic
516C22×C11C2×C4×Q811yescharacteristic
517C22×C11C4×#4111yescharacteristic
518C22×C11#51911yescharacteristic
519C22×C11#52011yescharacteristic
520C22×C11C2×#12011yescharacteristic
521C22×C11C2×#12111yescharacteristic
522C22×C11C2×#12111yescharacteristic
523C22×C11C2×C22⋊Q811yescharacteristic
524C22×C11C2×#12311yescharacteristic
525C22×C11#52511yescharacteristic
526C22×C11#52911yescharacteristic
527C22×C11#53311yescharacteristic
528C22×C11#53611yescharacteristic
529C22×C11#53711yescharacteristic
530C22×C11#54111yescharacteristic
531C22×C11#54211yescharacteristic
532C22×C11#54611yescharacteristic
533C22×C11#54711yescharacteristic
534C22×C11#54811yescharacteristic
535C22×C11#54811yescharacteristic
536C22×C11#54811yescharacteristic
537C22×C11#54811yescharacteristic
538C22×C11#54811yescharacteristic
539C22×C11D4×Q811yescharacteristic
540C22×C11D4×Q811yescharacteristic
541C22×C11D4×Q811yescharacteristic
542C22×C11#55011yescharacteristic
543C22×C11#55011yescharacteristic
544C22×C11#55211yescharacteristic
545C22×C11#55211yescharacteristic
546C22×C11#55411yescharacteristic
547C22×C11#55611yescharacteristic
548C2×D11—24no—
549C2×D11—24no—
550C2×D11—24no—
551C2×D11—42no—
552C2×D11—42no—
553C2×D11—42no—
554C2×D11—42no—
555C2×D11—42no—
556C2×D11—42no—
557C2×D11—42no—
558C2×D11—42no—
559C2×D11—42no—
560C2×D11—42no—
561C2×D11—42no—
562C2×D11—42no—
563C4×C11—24no—
564C4×C11—42no—
565C4×C11—42no—
566C4×C11—42no—
567C4×C11—42no—
568C4×C11—42no—
569C4×C11—81no—
570Dic11—24no—
571Dic11—24no—
572Dic11—42no—
573Dic11—42no—
574Dic11—42no—
575Dic11—81no—
576Dic11#38618yes—
577C25—111no—
578C22×Q8—114no—
579C22×Q8—114no—
580C22×Q8—114no—
581C22×Q8—222no—
582C22×Q8—222no—
583C22×Q8—222no—
584C22×Q8—222no—
585C23×C4—111no—
586C23×C4—111no—
587C23×C4—111no—
588C23×C4—111no—
589C23×C4—111no—
590C23×C4—111no—
591C23×C4—114no—
592C23×C4—111no—
593C23×C4—222no—
594C23×C4—222no—
595C23×C4—222no—
596C23×C4—222no—
597C23×C4—222no—
598C23×C4—222no—
599C23×C4C22×D1111yescharacteristic
600C23×C4C22×D1111yescharacteristic
601C23×C4C22×D1111yescharacteristic
602C23×C4C22×D1111yescharacteristic
603C23×C4C22×D1111yescharacteristic
604C23×C4C22×D1111yescharacteristic
605C23×C4C22×D1111yescharacteristic
606C22⋊Q8—2232no—
607C4×Q8—2232no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—114no—
614C2×C4⋊C4—114no—
615C2×C4⋊C4—114no—
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⋊C4—222no—
625C2×C4⋊C4—222no—
626C2×C4⋊C4—222no—
627C2×C4⋊C4—222no—
628C2×C4⋊C4C4×D1114yes—
629C2×C22⋊C4—114no—
630C2×C22⋊C4—114no—
631C2×C22⋊C4—114no—
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×C22⋊C4—222no—
639C2×C22⋊C4—222no—
640C2×C22⋊C4—222no—
641C2×C22⋊C4—222no—
642C2×C22⋊C4—222no—
643C2×C22⋊C4—222no—
644C2×C22⋊C4—222no—
645C2×C22⋊C4—441no—
646C2×C22⋊C4—441no—
647C2×C42—114no—
648C2×C42—222no—
649C2×C42—222no—
650C2×C42—222no—
651C2×C42—222no—
652C2×C42—222no—
653C2×C42—222no—
654C2×C42—222no—
655C2×C42—222no—
656C2×C42—222no—
657C2×C42—222no—
658C2×C42—222no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—41no—
663#95—41no—
664#95—222no—
665#95—222no—
666#95—222no—
667#95—222no—
668#95—222no—
669#95—222no—
670#95—222no—
671#95—222no—
672#95—222no—
673#95—441no—
674#95—441no—
675C2×C11C2×#38611yescharacteristic
676C2×C11C4×C22⋊Q811yescharacteristic
677C2×C11#232311yescharacteristic
678C2×C11Q8×C22⋊C411yescharacteristic
679C2×C11#234111yescharacteristic
680C2×C11#236011yescharacteristic
681C2×C11#236211yescharacteristic
682C2×C11#240711yescharacteristic
683C2×C11#240911yescharacteristic
684C2×C11#242111yescharacteristic
685C2×C11#242311yescharacteristic
686C2×C11#242611yescharacteristic
687C2×C11#242911yescharacteristic
688C2×C11#253611yescharacteristic
689C2×C11#253811yescharacteristic
690D11—44no—
691C24—112no—
692C24—112no—
693C24—112no—
694C24—221no—
695C24—221no—
696C24—221no—
697C24—221no—
698C24—221no—
699C24—221no—
700C24—221no—
701C24—221no—
702C24—221no—
703C24—221no—
704C24—221no—
705C24—221no—
706C24C23×D1111yescharacteristic
707C2×Q8—1116no—
708C2×Q8—228no—
709C2×Q8—228no—
710C2×Q8—228no—
711C2×Q8—228no—
712C2×Q8—228no—
713C2×Q8—228no—
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—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—112no—
756C22×C4—112no—
757C22×C4—112no—
758C22×C4—112no—
759C22×C4—112no—
760C22×C4—112no—
761C22×C4—112no—
762C22×C4—112no—
763C22×C4—112no—
764C22×C4—112no—
765C22×C4—112no—
766C22×C4—112no—
767C22×C4—112no—
768C22×C4—112no—
769C22×C4—112no—
770C22×C4—112no—
771C22×C4—228no—
772C22×C4—228no—
773C22×C4—228no—
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—221no—
787C22×C4—221no—
788C22×C4—221no—
789C22×C4—221no—
790C22×C4—221no—
791C22×C4—221no—
792C22×C4—221no—
793C22×C4—221no—
794C22×C4—221no—
795C22×C4—221no—
796C22×C4—221no—
797C22×C4—221no—
798C22×C4—221no—
799C22×C4—221no—
800C22×C4—221no—
801C22×C4—221no—
802C22×C4—221no—
803C22×C4—221no—
804C22×C4—221no—
805C22×C4—221no—
806C22×C4—221no—
807C22×C4—444no—
808C22×C4—444no—
809C22×C4—444no—
810C22×C4—444no—
811C22×C4C2×C4×D1112yes—
812C22×C4C2×C4×D1112yes—
813C22×C4C2×C4×D1112yes—
814C22×C4D4×D1112yes—
815C22×C4D4×D1112yes—
816C22×C4D4×D1112yes—
817C22×C4D4×D1112yes—
818C22×C4Q8×D1112yes—
819C4⋊C4—28no—
820C4⋊C4—28no—
821C4⋊C4—228no—
822C4⋊C4—228no—
823C4⋊C4—228no—
824C4⋊C4—228no—
825C4⋊C4—444no—
826C22⋊C4—228no—
827C22⋊C4—228no—
828C22⋊C4—228no—
829C22⋊C4—228no—
830C22⋊C4—444no—
831C22⋊C4—444no—
832C42—228no—
833C42—228no—
834C42—228no—
835C42—444no—
836C11#1396911yescharacteristic, complemented, Sylow
837C23—114no—
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—441no—
857C23—441no—
858C23—441no—
859C23—441no—
860C23—441no—
861C23—441no—
862C23—441no—
863C23—441no—
864C23—441no—
865C23—441no—
866C23—441no—
867C23—441no—
868C23—441no—
869C23—441no—
870C23—441no—
871C23—441no—
872C23C22×C4×D1111yescharacteristic
873C23C2×D4×D1111yescharacteristic
874C23C2×D4×D1111yescharacteristic
875C23C2×D4×D1111yescharacteristic
876C23C2×D4×D1111yescharacteristic
877C23#6703711yescharacteristic
878C23C2×Q8×D1111yescharacteristic
879C23#6704011yescharacteristic
880C23#6704011yescharacteristic
881C23#41×D1111yescharacteristic
882C23#41×D1111yescharacteristic
883C23#41×D1111yescharacteristic
884C23#41×D1111yescharacteristic
885C23#41×D1111yescharacteristic
886C23#6704311yescharacteristic
887Q8—2232no—
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—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
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—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—114no—
937C2×C4—114no—
938C2×C4—114no—
939C2×C4—114no—
940C2×C4—114no—
941C2×C4—114no—
942C2×C4—114no—
943C2×C4—114no—
944C2×C4—114no—
945C2×C4—222no—
946C2×C4—222no—
947C2×C4—222no—
948C2×C4—222no—
949C2×C4—222no—
950C2×C4—222no—
951C2×C4—222no—
952C2×C4—222no—
953C2×C4—222no—
954C2×C4—222no—
955C2×C4—222no—
956C2×C4—222no—
957C2×C4—222no—
958C2×C4—222no—
959C2×C4—222no—
960C2×C4—222no—
961C2×C4—222no—
962C2×C4—222no—
963C2×C4—222no—
964C2×C4—222no—
965C2×C4—222no—
966C2×C4—4416no—
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×C4—441no—
978C2×C4—441no—
979C2×C4—441no—
980C2×C4—441no—
981C2×C4—441no—
982C2×C4—441no—
983C2×C4—441no—
984C2×C4—441no—
985C2×C4—441no—
986C2×C4C22⋊C4×D1114yes—
987C22—224no—
988C22—224no—
989C22—224no—
990C22—442no—
991C22—442no—
992C22—442no—
993C22—442no—
994C22—442no—
995C22—442no—
996C22—442no—
997C22—442no—
998C22—442no—
999C22—442no—
1000C22—442no—
1001C22—442no—
1002C22C2×C22⋊C4×D1111yescharacteristic
1003C22#1062303511yescharacteristic
1004C22#1062305311yescharacteristic
1005C22C4×D4×D1111yescharacteristic
1006C22C4×D4×D1111yescharacteristic
1007C22C4×Q8×D1111yescharacteristic
1008C22#1062310311yescharacteristic
1009C22D11×#12011yescharacteristic
1010C22#1062312811yescharacteristic
1011C22#1062313011yescharacteristic
1012C22#1062313011yescharacteristic
1013C22D11×#12111yescharacteristic
1014C22D11×#12111yescharacteristic
1015C22#1062314111yescharacteristic
1016C22D11×C22⋊Q811yescharacteristic
1017C22#1062316311yescharacteristic
1018C22#1062316411yescharacteristic
1019C22#1062316411yescharacteristic
1020C22#1062316411yescharacteristic
1021C22#1062316411yescharacteristic
1022C22#1062316711yescharacteristic
1023C22#1062317111yescharacteristic
1024C22D11×#12311yescharacteristic
1025C22#1062318611yescharacteristic
1026C22#1062318711yescharacteristic
1027C22#1062320811yescharacteristic
1028C22#1062321911yescharacteristic
1029C22#1062322411yescharacteristic
1030C22#1062322411yescharacteristic
1031C22#1062322711yescharacteristic
1032C22#1062323311yescharacteristic
1033C22#1062323711yescharacteristic
1034C22#1062325511yescharacteristic
1035C22#1062325811yescharacteristic
1036C22#1062325811yescharacteristic
1037C4—24no—
1038C4—42no—
1039C4—42no—
1040C4—42no—
1041C4—42no—
1042C4—42no—
1043C4—81no—
1044C4—118no—
1045C4—224no—
1046C4—224no—
1047C4—442no—
1048C4—442no—
1049C4—442no—
1050C4—881no—
1051C2—444no—
1052C2D11×#38611yescharacteristic
1053C2#1307115011yescharacteristic
1054C2#1307129311yescharacteristic
1055C2#1307145011yescharacteristic
1056C2#1307145311yescharacteristic
1057C2#1307161811yescharacteristic
1058C2#1307163811yescharacteristic
1059C2#1307195611yescharacteristic
1060C2#1307197611yescharacteristic
1061C2#1307211411yescharacteristic
1062C2#1307213611yescharacteristic
1063C2#1307217711yescharacteristic
1064C2#1307221011yescharacteristic
1065C2#1307352211yescharacteristic
1066C2#1307353311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1441C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1441D11
hypocenterC11#13969
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
2. C22×#66940C2semidirect
3. C2×#10622259C2semidirect
6. #13066867C2semidirect
11. #13066848C2semidirect
12. #13066847C2semidirect
13. Dic11⋊#95C2semidirect
14. Dic11⋊#95C2semidirect
15. C11×#1441C2semidirect
37. C2×#66949C4semidirect
112. C2×(C2×D11)⋊C4Q8semidirect
286. C2×Dic22C22⋊C4semidirect
310. #1441D11semidirect
368. C22×D11C4×Q8semidirect
465. C2×Dic11C22⋊Q8semidirect
836. C11#13969semidirect

Maximal subgroups

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

subgroupindex
C22×#669492
C22×#669402
C2×#106222592
C2×#106222802
C2×#106222792
#130668672
#130668602
#130668582
#130668522
#130668482
#130668472
Dic11⋊#952
C11×#14412
#1396911