Finite Group Databasebeta

← #14675717

Subgroups — #14675717

Order 2816.

1846 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622558C211yesmaximal, characteristic
2C2×#10622557C211yesmaximal, characteristic
3C2×#10622589C211yesmaximal, characteristic, complemented
4C2×#10622555C211yesmaximal, characteristic
5C2×#10622555C211yesmaximal, characteristic
6C2×#10622262C211yesmaximal, characteristic, complemented
7C2×C22⋊C4×Dic11C211yesmaximal, characteristic
8#13066874C211yesmaximal, characteristic, complemented
9#13066871C211yesmaximal, characteristic, complemented
10#13066861C211yesmaximal, characteristic
11#13066850C211yesmaximal, characteristic, complemented
12#13066848C211yesmaximal, characteristic, complemented
13Dic11⋊#95C211yesmaximal, characteristic, complemented
14Dic11⋊#95C211yesmaximal, characteristic, complemented
15C11×#1439C211yesmaximal, characteristic
16C24×Dic11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×Dic11⋊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×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51#10622589—24no—
52#10622558—24no—
53#10622557—24no—
54#10622555—24no—
55#10622555—24no—
56C22⋊C4×Dic11C418yescomplemented
57#10622262—24no—
58C25×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—22no—
66C23×Dic11—22no—
67C23×Dic11—22no—
68C23×Dic11—22no—
69C23×Dic11—22no—
70C23×Dic11—22no—
71C23×Dic11C2×C414yes—
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—41no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—41no—
90C2×C11×C22⋊C4—41no—
91C2×C11×C22⋊C4C2×C414yes—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—41no—
97C2×C22⋊Dic11—41no—
98C2×C22⋊Dic11C2×C414yes—
99C2×C22⋊Dic11D414yes—
100C2×C22⋊Dic11Q814yes—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—41no—
104C2×Dic11⋊C4—22no—
105C2×Dic11⋊C4—22no—
106C2×Dic11⋊C4—22no—
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—22no—
111C2×Dic11⋊C4—22no—
112C2×Dic11⋊C4—22no—
113C2×Dic11⋊C4—22no—
114C2×Dic11⋊C4—22no—
115C2×Dic11⋊C4—22no—
116C2×Dic11⋊C4—22no—
117C2×Dic11⋊C4—22no—
118C2×Dic11⋊C4—41no—
119C2×Dic11⋊C4—41no—
120C2×Dic11⋊C4D414yes—
121C2×Dic11⋊C4D414yes—
122C2×C4×Dic11—22no—
123C2×C4×Dic11—22no—
124C2×C4×Dic11—22no—
125C2×C4×Dic11—22no—
126C2×C4×Dic11—22no—
127C2×C4×Dic11—22no—
128C2×C4×Dic11—22no—
129C2×C4×Dic11—22no—
130C2×C4×Dic11—41no—
131C2×C4×Dic11—41no—
132C2×C4×Dic11C2×C414yes—
133C2×C4×Dic11C2×C414yes—
134C11×#95—22no—
135C11×#95—22no—
136C11×#95—41no—
137C11⋊#95—22no—
138C11⋊#95—22no—
139C11⋊#95—22no—
140C11⋊#95—22no—
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146C11⋊#95—22no—
147C11⋊#95—41no—
148C11⋊#95C2×C414yes—
149C11⋊#95C2×C414yes—
150#13876—111nomaximal, Sylow
151C24×C11—21no—
152C24×C11—21no—
153C24×C11—21no—
154C24×C11—21no—
155C24×C11—21no—
156C24×C11—21no—
157C24×C11—21no—
158C24×C11—21no—
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11C22×C412yes—
164C24×C11C2×D412yes—
165C24×C11C2×Q812yes—
166C24×C11C2411yescharacteristic
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11C22×C412yes—
204C22×C4×C11C22×C412yes—
205C22×C4×C11C2×D412yes—
206C22×C4×C11C2×D412yes—
207C22×C4×C11#4112yes—
208C22×C4×C11#4112yes—
209C22×Dic11—28no—
210C22×Dic11—28no—
211C22×Dic11—28no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—44no—
253C22×Dic11—44no—
254C22×Dic11—44no—
255C22×Dic11—44no—
256C22×Dic11C22×C412yes—
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×Q812yes—
267C22×Dic11C2×Q812yes—
268C22×Dic11#4112yes—
269C22×Dic11#4112yes—
270C22×Dic11#4112yes—
271C22×Dic11#4112yes—
272C11×C4⋊C4—44no—
273C11×C22⋊C4—28no—
274C11×C22⋊C4—44no—
275C11×C22⋊C4—44no—
276C22⋊Dic11—44no—
277C22⋊Dic11—44no—
278C22⋊Dic11C4⋊C4116yescomplemented
279C4⋊Dic11—44no—
280Dic11⋊C4—28no—
281Dic11⋊C4—28no—
282Dic11⋊C4—44no—
283Dic11⋊C4—44no—
284Dic11⋊C4—44no—
285Dic11⋊C4—44no—
286C4×Dic11—28no—
287C4×Dic11—28no—
288C4×Dic11—44no—
289C4×Dic11—44no—
290C2×#388—111no—
291C2×#388—111no—
292C2×#384—111no—
293C2×#380—111no—
294C2×#380—111no—
295C2×C4×C4⋊C4—111no—
296C2×C4×C22⋊C4—111no—
297#1442—111no—
298#1442—111no—
299#1439—111no—
300#1439D1111yescharacteristic
301#1436—111no—
302#1436—111no—
303C4⋊#95—111no—
304C4⋊#95—111no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—41no—
337C23×C11—41no—
338C23×C11—41no—
339C23×C11C2×C4⋊C414yes—
340C23×C11C23×C411yescharacteristic
341C23×C11C22×D411yescharacteristic
342C23×C11C22×D411yescharacteristic
343C23×C11C22×D411yescharacteristic
344C23×C11C22×Q811yescharacteristic
345C23×C11C2×#4111yescharacteristic
346C23×C11C2×#4111yescharacteristic
347C23×C11C2×#4111yescharacteristic
348C23×C11C2×#4111yescharacteristic
349C23×C11C2×#4111yescharacteristic
350C23×C11C2×#4111yescharacteristic
351C23×C11H(5,𝔽2)11yescharacteristic
352C23×C11H(5,𝔽2)11yescharacteristic
353C23×C112−1+411yescharacteristic
354C23×C112−1+411yescharacteristic
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11#11714yes—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—22no—
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—41no—
419C2×Dic11—41no—
420C2×Dic11—41no—
421C2×Dic11—41no—
422C2×Dic11—41no—
423C2×Dic11—41no—
424C2×Dic11—41no—
425C2×Dic11—41no—
426C2×Dic11—41no—
427C2×Dic11—41no—
428C2×Dic11—41no—
429C2×Dic11—41no—
430C2×Dic11—416no—
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×Dic11C2×C4⋊C414yes—
446C2×Dic11C2×C4⋊C414yes—
447C2×Dic11#11714yes—
448C2×Dic11C4×D414yes—
449C2×Dic11C4×D414yes—
450C2×Dic11#12114yes—
451C2×Dic11#12314yes—
452C2×Dic11#12414yes—
453C2×Dic11#12614yes—
454C24×C4—111no—
455C22×C4⋊C4—111no—
456C22×C4⋊C4—111no—
457C22×C4⋊C4—111no—
458C22×C4⋊C4—111no—
459C22×C4⋊C4—111no—
460C22×C4⋊C4—111no—
461C22×C4⋊C4—111no—
462C22×C4⋊C4C2×D1111yescharacteristic
463C22×C22⋊C4—111no—
464C22×C22⋊C4—111no—
465C22×C22⋊C4—111no—
466C22×C22⋊C4C2×D1111yescharacteristic
467C22×C22⋊C4C2×D1111yescharacteristic
468C22×C22⋊C4C2×D1111yescharacteristic
469C22×C42—111no—
470C22×C42—111no—
471C22×C42—111no—
472C22×C42—111no—
473#388—224no—
474#388—224no—
475#384—224no—
476#380—224no—
477#380—224no—
478C4×C4⋊C4—224no—
479C4×C22⋊C4—118no—
480C2×#95—111no—
481C2×#95—111no—
482C2×#95—111no—
483C2×#95—111no—
484C2×#95—111no—
485C2×#95—111no—
486C2×#95—111no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95—111no—
491C2×#95—111no—
492C2×#95—111no—
493C2×#95C2×D1111yescharacteristic
494C2×#95C2×D1111yescharacteristic
495C2×#95C2×D1111yescharacteristic
496C22×C11—24no—
497C22×C11—24no—
498C22×C11—24no—
499C22×C11—42no—
500C22×C11—42no—
501C22×C11—42no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—42no—
509C22×C11—42no—
510C22×C11—42no—
511C22×C11C22×C4⋊C411yescharacteristic
512C22×C11C2×#11711yescharacteristic
513C22×C11C2×#11711yescharacteristic
514C22×C11C2×C4×D411yescharacteristic
515C22×C11C2×C4×D411yescharacteristic
516C22×C11#52011yescharacteristic
517C22×C11#52011yescharacteristic
518C22×C11C2×#12111yescharacteristic
519C22×C11C2×#12311yescharacteristic
520C22×C11C2×#12411yescharacteristic
521C22×C11C2×#12611yescharacteristic
522C22×C11#53211yescharacteristic
523C22×C11#53211yescharacteristic
524C22×C11#53311yescharacteristic
525C22×C11#53311yescharacteristic
526C22×C11#54011yescharacteristic
527C22×C11#54111yescharacteristic
528C22×C11#54211yescharacteristic
529C22×C11#54211yescharacteristic
530C22×C11D4211yescharacteristic
531C22×C11D4211yescharacteristic
532C22×C11#54611yescharacteristic
533C22×C11#54711yescharacteristic
534C22×C11#54711yescharacteristic
535C22×C11#54711yescharacteristic
536C22×C11#54811yescharacteristic
537C22×C11D4×Q811yescharacteristic
538C22×C11D4×Q811yescharacteristic
539C22×C11#55011yescharacteristic
540C22×C11#55211yescharacteristic
541C22×C11#55311yescharacteristic
542C22×C11#55411yescharacteristic
543C22×C11#55411yescharacteristic
544C22×C11#55511yescharacteristic
545C22×C11#55611yescharacteristic
546C4×C11—24no—
547C4×C11—42no—
548C4×C11—42no—
549C4×C11—42no—
550C4×C11—81no—
551C4×C11—81no—
552Dic11—24no—
553Dic11—24no—
554Dic11—42no—
555Dic11—42no—
556Dic11—42no—
557Dic11—81no—
558Dic11—81no—
559Dic11#38818yescomplemented
560C25C22×D1111yescharacteristic
561C23×C4—111no—
562C23×C4—111no—
563C23×C4—111no—
564C23×C4—114no—
565C23×C4—111no—
566C23×C4—111no—
567C23×C4—111no—
568C23×C4—111no—
569C23×C4—111no—
570C23×C4—222no—
571C23×C4—222no—
572C23×C4—222no—
573C23×C4—222no—
574C23×C4—222no—
575C23×C4—222no—
576C23×C4C22×D1111yescharacteristic
577C23×C4C22×D1111yescharacteristic
578C23×C4C22×D1111yescharacteristic
579C23×C4C22×D1111yescharacteristic
580C23×C4C22×D1111yescharacteristic
581C23×C4C22×D1111yescharacteristic
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—41no—
585C2×C4⋊C4—114no—
586C2×C4⋊C4—114no—
587C2×C4⋊C4—222no—
588C2×C4⋊C4—222no—
589C2×C4⋊C4—222no—
590C2×C4⋊C4—222no—
591C2×C4⋊C4—222no—
592C2×C4⋊C4—222no—
593C2×C4⋊C4—222no—
594C2×C4⋊C4—222no—
595C2×C4⋊C4—222no—
596C2×C4⋊C4—222no—
597C2×C4⋊C4—222no—
598C2×C4⋊C4—222no—
599C2×C4⋊C4—222no—
600C2×C4⋊C4—222no—
601C2×C4⋊C4—222no—
602C2×C4⋊C4—222no—
603C2×C4⋊C4—441no—
604C2×C4⋊C4—441no—
605C2×C4⋊C4—441no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—41no—
613C2×C22⋊C4—41no—
614C2×C22⋊C4—114no—
615C2×C22⋊C4—114no—
616C2×C22⋊C4—114no—
617C2×C22⋊C4—222no—
618C2×C22⋊C4—222no—
619C2×C22⋊C4—222no—
620C2×C22⋊C4—222no—
621C2×C22⋊C4—441no—
622C2×C22⋊C4—441no—
623C2×C22⋊C4C4×D1114yes—
624C2×C42—114no—
625C2×C42—114no—
626C2×C42—222no—
627C2×C42—222no—
628C2×C42—222no—
629C2×C42—222no—
630C2×C42—222no—
631C2×C42—222no—
632C2×C42—222no—
633C2×C42—222no—
634C2×C42—441no—
635C2×C42—441no—
636#95—22no—
637#95—22no—
638#95—41no—
639#95—114no—
640#95—114no—
641#95—222no—
642#95—222no—
643#95—222no—
644#95—222no—
645#95—222no—
646#95—222no—
647#95—222no—
648#95—222no—
649#95—222no—
650#95—222no—
651#95—441no—
652C2×C11—44no—
653C2×C11#228511yescharacteristic
654C2×C11C2×#38811yescharacteristic
655C2×C11#231411yescharacteristic
656C2×C11D4×C4⋊C411yescharacteristic
657C2×C11D4×C4⋊C411yescharacteristic
658C2×C11#235211yescharacteristic
659C2×C11#235411yescharacteristic
660C2×C11#242211yescharacteristic
661C2×C11#242311yescharacteristic
662C2×C11#242811yescharacteristic
663C2×C11#242911yescharacteristic
664C2×C11#249111yescharacteristic
665C2×C11#249211yescharacteristic
666C2×C11#249611yescharacteristic
667C2×C11#249711yescharacteristic
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24C2×C4×D1112yes—
681C24D4×D1112yes—
682C24Q8×D1112yes—
683C24C23×D1111yescharacteristic
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—112no—
721C22×C4—112no—
722C22×C4—112no—
723C22×C4—112no—
724C22×C4—112no—
725C22×C4—112no—
726C22×C4—112no—
727C22×C4—112no—
728C22×C4—112no—
729C22×C4—112no—
730C22×C4—112no—
731C22×C4—112no—
732C22×C4—112no—
733C22×C4—112no—
734C22×C4—112no—
735C22×C4—112no—
736C22×C4—228no—
737C22×C4—228no—
738C22×C4—228no—
739C22×C4—221no—
740C22×C4—221no—
741C22×C4—221no—
742C22×C4—221no—
743C22×C4—221no—
744C22×C4—221no—
745C22×C4—221no—
746C22×C4—221no—
747C22×C4—221no—
748C22×C4—221no—
749C22×C4—221no—
750C22×C4—221no—
751C22×C4—221no—
752C22×C4—221no—
753C22×C4—221no—
754C22×C4—221no—
755C22×C4—221no—
756C22×C4—221no—
757C22×C4—221no—
758C22×C4—221no—
759C22×C4—221no—
760C22×C4—221no—
761C22×C4—221no—
762C22×C4—221no—
763C22×C4—221no—
764C22×C4—221no—
765C22×C4—221no—
766C22×C4—221no—
767C22×C4—221no—
768C22×C4—221no—
769C22×C4—221no—
770C22×C4—221no—
771C22×C4—221no—
772C22×C4—221no—
773C22×C4—221no—
774C22×C4—221no—
775C22×C4—221no—
776C22×C4—221no—
777C22×C4—221no—
778C22×C4—221no—
779C22×C4—444no—
780C22×C4—444no—
781C22×C4—444no—
782C22×C4—444no—
783C22×C4C2×C4×D1112yes—
784C22×C4C2×C4×D1112yes—
785C22×C4D4×D1112yes—
786C22×C4D4×D1112yes—
787C22×C4#434112yes—
788C22×C4#434112yes—
789C4⋊C4—44no—
790C4⋊C4—228no—
791C4⋊C4—228no—
792C4⋊C4—444no—
793C4⋊C4—444no—
794C4⋊C4—444no—
795C4⋊C4—444no—
796C4⋊C4—444no—
797C22⋊C4—28no—
798C22⋊C4—44no—
799C22⋊C4—44no—
800C22⋊C4—1116no—
801C22⋊C4—444no—
802C22⋊C4—444no—
803C42—228no—
804C42—228no—
805C42—444no—
806C42—444no—
807C11#1387611yescharacteristic, complemented, Sylow
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C4⋊C4×D1114yes—
843C23C22×C4×D1111yescharacteristic
844C23C2×D4×D1111yescharacteristic
845C23C2×D4×D1111yescharacteristic
846C23C2×D4×D1111yescharacteristic
847C23C2×#434111yescharacteristic
848C23C2×#434111yescharacteristic
849C23#6703711yescharacteristic
850C23#6703711yescharacteristic
851C23C2×Q8×D1111yescharacteristic
852C23#41×D1111yescharacteristic
853C23#41×D1111yescharacteristic
854C23#41×D1111yescharacteristic
855C23#41×D1111yescharacteristic
856C23#6704311yescharacteristic
857C23#6704311yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—114no—
900C2×C4—114no—
901C2×C4—114no—
902C2×C4—114no—
903C2×C4—114no—
904C2×C4—114no—
905C2×C4—114no—
906C2×C4—114no—
907C2×C4—114no—
908C2×C4—222no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—222no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—222no—
916C2×C4—222no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—222no—
921C2×C4—222no—
922C2×C4—222no—
923C2×C4—222no—
924C2×C4—222no—
925C2×C4—222no—
926C2×C4—222no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—4416no—
930C2×C4—441no—
931C2×C4—441no—
932C2×C4—441no—
933C2×C4—441no—
934C2×C4—441no—
935C2×C4—441no—
936C2×C4—441no—
937C2×C4—441no—
938C2×C4—441no—
939C2×C4—441no—
940C2×C4—441no—
941C2×C4—441no—
942C2×C4—441no—
943C2×C4—441no—
944C2×C4—441no—
945C2×C4—441no—
946C2×C4—441no—
947C2×C4—441no—
948C2×C4—441no—
949C2×C4—441no—
950C2×C4—441no—
951C2×C4—441no—
952C2×C4—441no—
953C2×C4—441no—
954C2×C4—441no—
955C2×C4—441no—
956C2×C4#6693014yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C2×#6693011yescharacteristic
973C22C2×C4⋊C4×D1111yescharacteristic
974C22D11×#11711yescharacteristic
975C22C4×D4×D1111yescharacteristic
976C22C4×D4×D1111yescharacteristic
977C22#1062307711yescharacteristic
978C22#1062307711yescharacteristic
979C22#1062312111yescharacteristic
980C22#1062312111yescharacteristic
981C22#1062312211yescharacteristic
982C22#1062312711yescharacteristic
983C22#1062312711yescharacteristic
984C22#1062312911yescharacteristic
985C22#1062313211yescharacteristic
986C22D11×#12111yescharacteristic
987C22#1062314211yescharacteristic
988C22#1062314611yescharacteristic
989C22#1062314711yescharacteristic
990C22#1062315311yescharacteristic
991C22#1062315311yescharacteristic
992C22#1062316311yescharacteristic
993C22#1062316311yescharacteristic
994C22#1062316711yescharacteristic
995C22#1062316711yescharacteristic
996C22#1062318111yescharacteristic
997C22D11×#12311yescharacteristic
998C22#1062318611yescharacteristic
999C22#1062318611yescharacteristic
1000C22#1062319311yescharacteristic
1001C22#1062320011yescharacteristic
1002C22#1062320211yescharacteristic
1003C22D11×#12411yescharacteristic
1004C22#1062323211yescharacteristic
1005C22D11×#12611yescharacteristic
1006C22#1062324911yescharacteristic
1007C4—24no—
1008C4—42no—
1009C4—42no—
1010C4—42no—
1011C4—81no—
1012C4—81no—
1013C4—118no—
1014C4—224no—
1015C4—224no—
1016C4—442no—
1017C4—442no—
1018C4—442no—
1019C4—881no—
1020C4—881no—
1021C2—44no—
1022C2#1307101811yescharacteristic
1023C2D11×#38811yescharacteristic
1024C2#1307122011yescharacteristic
1025C2#1307151411yescharacteristic
1026C2#1307151411yescharacteristic
1027C2#1307154311yescharacteristic
1028C2#1307156411yescharacteristic
1029C2#1307212311yescharacteristic
1030C2#1307213411yescharacteristic
1031C2#1307219711yescharacteristic
1032C2#1307220811yescharacteristic
1033C2#1307297211yescharacteristic
1034C2#1307298311yescharacteristic
1035C2#1307303111yescharacteristic
1036C2#1307304211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenter#1439D11
hypocenterC11#13876
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
3. C2×#10622589C2semidirect
6. C2×#10622262C2semidirect
8. #13066874C2semidirect
9. #13066871C2semidirect
11. #13066850C2semidirect
12. #13066848C2semidirect
13. Dic11⋊#95C2semidirect
14. Dic11⋊#95C2semidirect
56. C22⋊C4×Dic11C4semidirect
278. C22⋊Dic11C4⋊C4semidirect
559. Dic11#388semidirect
807. C11#13876semidirect

Maximal subgroups

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

subgroupindex
C2×#106225582
C2×#106225572
C2×#106225892
C2×#106225552
C2×#106222622
C2×C22⋊C4×Dic112
#130668742
#130668712
#130668612
#130668502
#130668482
Dic11⋊#952
C11×#14392
#1387611