Finite Group Databasebeta

← #14676904

Subgroups — #14676904

Order 2816.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66931C211yesmaximal, characteristic
2C2×#10622259C211yesmaximal, characteristic, complemented
3C2×#10622259C211yesmaximal, characteristic, complemented
4C2×#10622260C211yesmaximal, characteristic, complemented
5C2×#10622555C211yesmaximal, characteristic
6C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
7C2×C22⋊C4×Dic11C211yesmaximal, characteristic
8#13066885C211yesmaximal, characteristic, complemented
9#13066882C211yesmaximal, characteristic, complemented
10#13066861C211yesmaximal, characteristic
11#13066859C211yesmaximal, characteristic
12#13066853C211yesmaximal, characteristic
13#13066846C211yesmaximal, characteristic, complemented
14Dic11⋊#95C211yesmaximal, characteristic, complemented
15C11×#1437C211yesmaximal, characteristic
16C24×Dic11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×#66931—24no—
36C2×#66931—24no—
37C2×#66931C418yescomplemented
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#10622555—24no—
55C22⋊C4×Dic11—24no—
56C4×Dic11⋊C4—24no—
57#10622260—24no—
58#10622259—24no—
59#10622259—24no—
60C25×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×Dic11—22no—
68C23×Dic11—22no—
69C23×Dic11—22no—
70C23×Dic11—22no—
71C23×Dic11—22no—
72C23×Dic11—22no—
73C23×Dic11C2×C414yes—
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C22×Dic22—22no—
83C22×Dic22—22no—
84C22×Dic22—22no—
85C22×Dic22—22no—
86C22×Dic22—22no—
87C22×Dic22—22no—
88C22×Dic22C2×C414yes—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—41no—
96C2×C11×C22⋊C4C2×C414yes—
97C2×C11×C22⋊C4Q814yescomplemented
98C2×C42×C11—22no—
99C2×C42×C11—22no—
100C2×C42×C11—41no—
101C2×C22⋊Dic11—22no—
102C2×C22⋊Dic11—22no—
103C2×C22⋊Dic11—22no—
104C2×C22⋊Dic11—22no—
105C2×C22⋊Dic11—22no—
106C2×C22⋊Dic11—22no—
107C2×C22⋊Dic11—22no—
108C2×C22⋊Dic11—41no—
109C2×C22⋊Dic11C2×C414yes—
110C2×C4⋊Dic11—22no—
111C2×C4⋊Dic11—22no—
112C2×C4⋊Dic11—22no—
113C2×C4⋊Dic11—22no—
114C2×C4⋊Dic11—41no—
115C2×C4⋊Dic11C2×C414yes—
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⋊C4—41no—
126C2×Dic11⋊C4C2×C414yes—
127C2×Dic11⋊C4C2×C414yes—
128C2×Dic11⋊C4D414yes—
129C2×Dic11⋊C4D414yes—
130C2×Dic11⋊C4D414yes—
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—41no—
139C2×C4×Dic11D414yes—
140#66931—232no—
141C11×#95—22no—
142C11×#95—22no—
143C11×#95—22no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146C11⋊#95—22no—
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—
157#13997—111nomaximal, Sylow
158C24×C11—21no—
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11—21no—
165C24×C11—21no—
166C24×C11—21no—
167C24×C11—21no—
168C24×C11—21no—
169C24×C11—21no—
170C24×C11C22×C412yes—
171C24×C11C2×Q812yes—
172C24×C11#4112yes—
173C24×C11C2411yescharacteristic
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×C11C2×D412yes—
210C22×C4×C11C2×D412yes—
211C22×C4×C11C2×D412yes—
212C22×C4×C11C2×D412yes—
213C22×C4×C11C2×Q812yes—
214C22×C4×C11C2×Q812yes—
215C22×C4×C11#4112yes—
216C22×Dic11—28no—
217C22×Dic11—28no—
218C22×Dic11—28no—
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×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—44no—
261C22×Dic11—44no—
262C22×Dic11—44no—
263C22×Dic11—44no—
264C22×Dic11C22×C412yes—
265C22×Dic11C22×C412yes—
266C22×Dic11C22×C412yes—
267C22×Dic11C22×C412yes—
268C22×Dic11C2×D412yes—
269C22×Dic11C2×D412yes—
270C22×Dic11C2×D412yes—
271C22×Dic11C2×D412yes—
272C22×Dic11C2×D412yes—
273C22×Dic11C2×D412yes—
274C22×Dic11C2×D412yes—
275C22×Dic11C2×D412yes—
276C22×Dic11#4112yes—
277C22×Dic11#4112yes—
278C22×Dic11#4112yes—
279C2×Dic22—28no—
280C2×Dic22—28no—
281C2×Dic22—28no—
282C2×Dic22—44no—
283C2×Dic22—44no—
284C2×Dic22—44no—
285C2×Dic22—44no—
286C11×C22⋊C4—28no—
287C11×C22⋊C4—28no—
288C11×C22⋊C4—44no—
289C42×C11—44no—
290C22⋊Dic11—28no—
291C22⋊Dic11—28no—
292C22⋊Dic11—44no—
293C4⋊Dic11—28no—
294C4⋊Dic11—44no—
295Dic11⋊C4—28no—
296Dic11⋊C4—28no—
297Dic11⋊C4—44no—
298Dic11⋊C4—44no—
299Dic11⋊C4C22⋊C4116yescomplemented
300C4×Dic11—28no—
301C4×Dic11—44no—
302C4×Dic11—44no—
303C22×C22⋊Q8—111no—
304C2×#391—111no—
305C2×#391—111no—
306C2×#389—111no—
307C2×#380—111no—
308C2×C4×C4⋊C4—111no—
309C2×C4×C22⋊C4—111no—
310#1445—111no—
311#1445—111no—
312#1439—111no—
313#1439—111no—
314#1437—111no—
315#1437D1111yescharacteristic
316C4⋊#95—111no—
317C4⋊#95—111no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—41no—
337C23×C11—41no—
338C23×C11—41no—
339C23×C11—41no—
340C23×C11—41no—
341C23×C11—41no—
342C23×C11—41no—
343C23×C11—41no—
344C23×C11—41no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—41no—
349C23×C11—41no—
350C23×C11—41no—
351C23×C11—41no—
352C23×C11C4×Q814yes—
353C23×C11C23×C411yescharacteristic
354C23×C11C22×D411yescharacteristic
355C23×C11C22×D411yescharacteristic
356C23×C11C22×D411yescharacteristic
357C23×C11C22×D411yescharacteristic
358C23×C11C22×Q811yescharacteristic
359C23×C11C2×#4111yescharacteristic
360C23×C11C2×#4111yescharacteristic
361C23×C11C2×#4111yescharacteristic
362C23×C11C2×#4111yescharacteristic
363C23×C11C2×#4111yescharacteristic
364C23×C11H(5,𝔽2)11yescharacteristic
365C23×C112−1+411yescharacteristic
366C23×C112−1+411yescharacteristic
367C23×C112−1+411yescharacteristic
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—22no—
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×C11C2×C22⋊C414yes—
409C2×C4×C11C22⋊Q814yescomplemented
410C2×Dic11—22no—
411C2×Dic11—22no—
412C2×Dic11—22no—
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—41no—
432C2×Dic11—41no—
433C2×Dic11—41no—
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—416no—
452C2×Dic11—41no—
453C2×Dic11—41no—
454C2×Dic11—41no—
455C2×Dic11—41no—
456C2×Dic11—41no—
457C2×Dic11—41no—
458C2×Dic11—41no—
459C2×Dic11C2×C22⋊C414yes—
460C2×Dic11C2×C22⋊C414yes—
461C2×Dic11C4×D414yes—
462C2×Dic11C4×D414yes—
463C2×Dic11#12114yes—
464C2×Dic11#12114yes—
465C2×Dic11#12414yes—
466C2×Dic11#12714yes—
467Dic22—416no—
468C23×Q8—111no—
469C24×C4—111no—
470C2×C22⋊Q8—118no—
471C2×C22⋊Q8—224no—
472C2×C22⋊Q8—224no—
473C22×C4⋊C4—111no—
474C22×C4⋊C4—111no—
475C22×C4⋊C4—111no—
476C22×C4⋊C4—111no—
477C22×C4⋊C4—111no—
478C22×C4⋊C4—111no—
479C22×C4⋊C4—111no—
480C22×C22⋊C4—111no—
481C22×C22⋊C4—111no—
482C22×C22⋊C4—111no—
483C22×C22⋊C4C2×D1111yescharacteristic
484C22×C22⋊C4C2×D1111yescharacteristic
485C22×C22⋊C4C2×D1111yescharacteristic
486C22×C42—111no—
487C22×C42—111no—
488C22×C42—111no—
489C22×C42C2×D1111yescharacteristic
490#391—224no—
491#391—224no—
492#389—224no—
493#380—224no—
494C4×C4⋊C4—224no—
495C4×C22⋊C4—224no—
496C2×#95—111no—
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×#95—111no—
509C2×#95C2×D1111yescharacteristic
510C2×#95C2×D1111yescharacteristic
511C2×#95C2×D1111yescharacteristic
512C22×C11—24no—
513C22×C11—24no—
514C22×C11—24no—
515C22×C11—42no—
516C22×C11—42no—
517C22×C11—42no—
518C22×C11—42no—
519C22×C11—42no—
520C22×C11—42no—
521C22×C11—42no—
522C22×C11—42no—
523C22×C11—42no—
524C22×C11—42no—
525C22×C11—42no—
526C22×C11—42no—
527C22×C11C22×C22⋊C411yescharacteristic
528C22×C11C2×C4×D411yescharacteristic
529C22×C11C2×C4×D411yescharacteristic
530C22×C11C2×C4×Q811yescharacteristic
531C22×C11C4×#4111yescharacteristic
532C22×C11#51911yescharacteristic
533C22×C11#52011yescharacteristic
534C22×C11C2×#12111yescharacteristic
535C22×C11C2×#12111yescharacteristic
536C22×C11C2×C22⋊Q811yescharacteristic
537C22×C11#52511yescharacteristic
538C22×C11C2×#12411yescharacteristic
539C22×C11#52911yescharacteristic
540C22×C11C2×#12711yescharacteristic
541C22×C11#53311yescharacteristic
542C22×C11#53611yescharacteristic
543C22×C11#53711yescharacteristic
544C22×C11#54111yescharacteristic
545C22×C11#54211yescharacteristic
546C22×C11#54611yescharacteristic
547C22×C11#54611yescharacteristic
548C22×C11#54611yescharacteristic
549C22×C11#54711yescharacteristic
550C22×C11#54711yescharacteristic
551C22×C11#54711yescharacteristic
552C22×C11#54811yescharacteristic
553C22×C11#54811yescharacteristic
554C22×C11#54811yescharacteristic
555C22×C11D4×Q811yescharacteristic
556C22×C11D4×Q811yescharacteristic
557C22×C11D4×Q811yescharacteristic
558C22×C11#55211yescharacteristic
559C22×C11#55211yescharacteristic
560C22×C11#55411yescharacteristic
561C22×C11#55611yescharacteristic
562C4×C11—24no—
563C4×C11—24no—
564C4×C11—42no—
565C4×C11—42no—
566C4×C11—42no—
567C4×C11—81no—
568Dic11—24no—
569Dic11—42no—
570Dic11—42no—
571Dic11—42no—
572Dic11—42no—
573Dic11—42no—
574Dic11—81no—
575Dic11#39018yes—
576C25C22×D1111yescharacteristic
577C22×Q8—114no—
578C22×Q8—222no—
579C22×Q8—222no—
580C22×Q8—222no—
581C22×Q8—222no—
582C22×Q8—222no—
583C22×Q8—222no—
584C23×C4—111no—
585C23×C4—111no—
586C23×C4—114no—
587C23×C4—111no—
588C23×C4—111no—
589C23×C4—111no—
590C23×C4—111no—
591C23×C4—111no—
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
605C22⋊Q8—2232no—
606C2×C4⋊C4—114no—
607C2×C4⋊C4—114no—
608C2×C4⋊C4—114no—
609C2×C4⋊C4—114no—
610C2×C4⋊C4—114no—
611C2×C4⋊C4—114no—
612C2×C4⋊C4—222no—
613C2×C4⋊C4—222no—
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⋊C4—222no—
625C2×C4⋊C4—441no—
626C2×C4⋊C4—441no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—41no—
634C2×C22⋊C4—114no—
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—441no—
643C2×C22⋊C4Dic2214yescomplemented
644C2×C22⋊C4C4×D1114yes—
645C2×C42—22no—
646C2×C42—22no—
647C2×C42—41no—
648C2×C42—114no—
649C2×C42—222no—
650C2×C42—222no—
651C2×C42—222no—
652C2×C42—222no—
653C2×C42—222no—
654C2×C42—222no—
655C2×C42—222no—
656C2×C42—441no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—222no—
661#95—222no—
662#95—222no—
663#95—222no—
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—
673C2×C11—44no—
674C2×C11C2×#39011yescharacteristic
675C2×C11C4×C22⋊Q811yescharacteristic
676C2×C11#232311yescharacteristic
677C2×C11#233911yescharacteristic
678C2×C11Q8×C22⋊C411yescharacteristic
679C2×C11#236011yescharacteristic
680C2×C11#236211yescharacteristic
681C2×C11#241511yescharacteristic
682C2×C11#241711yescharacteristic
683C2×C11#242711yescharacteristic
684C2×C11#242911yescharacteristic
685C2×C11#248911yescharacteristic
686C2×C11#249211yescharacteristic
687C2×C11#254011yescharacteristic
688C2×C11#254211yescharacteristic
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24C2×Dic2212yes—
702C24C2×C4×D1112yes—
703C24#433912yes—
704C24C23×D1111yescharacteristic
705C2×Q8—228no—
706C2×Q8—228no—
707C2×Q8—228no—
708C2×Q8—444no—
709C2×Q8—444no—
710C2×Q8—444no—
711C2×Q8—444no—
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—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—112no—
746C22×C4—112no—
747C22×C4—112no—
748C22×C4—112no—
749C22×C4—112no—
750C22×C4—112no—
751C22×C4—112no—
752C22×C4—112no—
753C22×C4—112no—
754C22×C4—112no—
755C22×C4—112no—
756C22×C4—112no—
757C22×C4—112no—
758C22×C4—112no—
759C22×C4—112no—
760C22×C4—228no—
761C22×C4—228no—
762C22×C4—228no—
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—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—444no—
805C22×C4—444no—
806C22×C4—444no—
807C22×C4—444no—
808C22×C4C2×Dic2212yes—
809C22×C4C2×Dic2212yes—
810C22×C4C2×C4×D1112yes—
811C22×C4C2×C4×D1112yes—
812C22×C4D4×D1112yes—
813C22×C4D4×D1112yes—
814C22×C4D4×D1112yes—
815C22×C4D4×D1112yes—
816C22×C4#434112yes—
817C4⋊C4—1116no—
818C4⋊C4—228no—
819C4⋊C4—228no—
820C4⋊C4—228no—
821C4⋊C4—444no—
822C4⋊C4—444no—
823C4⋊C4—444no—
824C22⋊C4—28no—
825C22⋊C4—28no—
826C22⋊C4—44no—
827C22⋊C4—228no—
828C22⋊C4—228no—
829C22⋊C4—444no—
830C42—44no—
831C42—228no—
832C42—444no—
833C42—444no—
834C11#1399711yescharacteristic, complemented, Sylow
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23C4×Dic2214yes—
870C23C22×Dic2211yescharacteristic
871C23C22×C4×D1111yescharacteristic
872C23C2×#433911yescharacteristic
873C23C2×D4×D1111yescharacteristic
874C23C2×D4×D1111yescharacteristic
875C23C2×D4×D1111yescharacteristic
876C23C2×D4×D1111yescharacteristic
877C23C2×#434111yescharacteristic
878C23#6703711yescharacteristic
879C23#41×D1111yescharacteristic
880C23#41×D1111yescharacteristic
881C23#41×D1111yescharacteristic
882C23#6704311yescharacteristic
883C23#6704311yescharacteristic
884C23#6704311yescharacteristic
885Q8—4416no—
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—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
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—41no—
926C2×C4—114no—
927C2×C4—114no—
928C2×C4—114no—
929C2×C4—114no—
930C2×C4—114no—
931C2×C4—114no—
932C2×C4—114no—
933C2×C4—114no—
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—222no—
949C2×C4—222no—
950C2×C4—222no—
951C2×C4—222no—
952C2×C4—222no—
953C2×C4—222no—
954C2×C4—222no—
955C2×C4—4416no—
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×C4—441no—
978C2×C4—441no—
979C2×C4—441no—
980C2×C4—441no—
981C2×C4—441no—
982C2×C4—441no—
983C2×C4#6693114yescomplemented
984C2×C4C22⋊C4×D1114yes—
985C22—24no—
986C22—24no—
987C22—24no—
988C22—42no—
989C22—42no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22—42no—
998C22—42no—
999C22—42no—
1000C22C2×C4×Dic2211yescharacteristic
1001C22C2×#6693111yescharacteristic
1002C22C2×C22⋊C4×D1111yescharacteristic
1003C22#1062302111yescharacteristic
1004C22#1062304711yescharacteristic
1005C22#1062304811yescharacteristic
1006C22#1062306211yescharacteristic
1007C22C4×#434111yescharacteristic
1008C22D4×Dic2211yescharacteristic
1009C22D4×Dic2211yescharacteristic
1010C22D4×Dic2211yescharacteristic
1011C22#1062306911yescharacteristic
1012C22#1062307011yescharacteristic
1013C22C4×D4×D1111yescharacteristic
1014C22C4×D4×D1111yescharacteristic
1015C22#1062307711yescharacteristic
1016C22#1062307811yescharacteristic
1017C22#1062308311yescharacteristic
1018C22#1062308311yescharacteristic
1019C22#1062312211yescharacteristic
1020C22#1062312811yescharacteristic
1021C22D11×#12111yescharacteristic
1022C22D11×#12111yescharacteristic
1023C22#1062314111yescharacteristic
1024C22#1062314211yescharacteristic
1025C22#1062314211yescharacteristic
1026C22#1062318111yescharacteristic
1027C22#1062318611yescharacteristic
1028C22#1062319311yescharacteristic
1029C22D11×#12411yescharacteristic
1030C22#1062320611yescharacteristic
1031C22#1062320811yescharacteristic
1032C22#1062323211yescharacteristic
1033C22#1062323311yescharacteristic
1034C22D11×#12711yescharacteristic
1035C4—24no—
1036C4—24no—
1037C4—42no—
1038C4—42no—
1039C4—42no—
1040C4—81no—
1041C4—118no—
1042C4—224no—
1043C4—442no—
1044C4—442no—
1045C4—442no—
1046C4—442no—
1047C4—442no—
1048C4—881no—
1049C2—44no—
1050C2D11×#39011yescharacteristic
1051C2C4×#6693111yescharacteristic
1052C2#1307129111yescharacteristic
1053C2#1307144211yescharacteristic
1054C2C22⋊C4×Dic2211yescharacteristic
1055C2#1307162211yescharacteristic
1056C2#1307164011yescharacteristic
1057C2#1307204211yescharacteristic
1058C2#1307206411yescharacteristic
1059C2#1307219011yescharacteristic
1060C2#1307221211yescharacteristic
1061C2#1307295411yescharacteristic
1062C2#1307298711yescharacteristic
1063C2#1307355311yescharacteristic
1064C2#1307356711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1437C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenter#1437D11
hypocenterC11#13997
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C2×#10622259C2semidirect
3. C2×#10622259C2semidirect
4. C2×#10622260C2semidirect
6. C2×C4×Dic11⋊C4C2semidirect
8. #13066885C2semidirect
9. #13066882C2semidirect
13. #13066846C2semidirect
14. Dic11⋊#95C2semidirect
37. C2×#66931C4semidirect
97. C2×C11×C22⋊C4Q8semidirect
299. Dic11⋊C4C22⋊C4semidirect
409. C2×C4×C11C22⋊Q8semidirect
643. C2×C22⋊C4Dic22semidirect
834. C11#13997semidirect
983. C2×C4#66931semidirect

Maximal subgroups

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

subgroupindex
C22×#669312
C2×#106222592
C2×#106222602
C2×#106225552
C2×C4×Dic11⋊C42
C2×C22⋊C4×Dic112
#130668852
#130668822
#130668612
#130668592
#130668532
#130668462
Dic11⋊#952
C11×#14372
#1399711