Finite Group Databasebeta

← #14679133

Subgroups — #14679133

Order 2816.

1694 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622565C211yesmaximal, characteristic
2C2×#10622558C211yesmaximal, characteristic
3C2×#10622823C211yesmaximal, characteristic
4C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
5#13066882C211yesmaximal, characteristic, complemented
6#13066871C211yesmaximal, characteristic, complemented
7#13066865C211yesmaximal, characteristic
8#13066853C211yesmaximal, characteristic
9#13066851C211yesmaximal, characteristic, complemented
10#13066849C211yesmaximal, characteristic, complemented
11#13066849C211yesmaximal, characteristic, complemented
12#13066847C211yesmaximal, characteristic, complemented
13#13066843C211yesmaximal, characteristic, complemented
14#13066839C211yesmaximal, characteristic
15C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
16C24×C4×C11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C4×C11×C22⋊C4—24no—
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34#10622823—24no—
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
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53#10622565C418yescomplemented
54#10622558—24no—
55C4×Dic11⋊C4—24no—
56C25×C11C2311yescharacteristic
57C23×C4×C11—22no—
58C23×C4×C11—22no—
59C23×C4×C11—22no—
60C23×C4×C11—22no—
61C23×C4×C11—22no—
62C23×C4×C11—41no—
63C23×C4×C11—41no—
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4C2×C414yes—
83C2×C11×C22⋊C4D414yes—
84C2×C42×C11—22no—
85C2×C42×C11—22no—
86C2×C42×C11—22no—
87C2×C42×C11—22no—
88C2×C42×C11—41no—
89C2×C42×C11—41no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11—41no—
99C2×C22⋊Dic11—41no—
100C2×C22⋊Dic11C2×C414yes—
101C2×C22⋊Dic11C2×C414yes—
102C2×Dic11⋊C4—22no—
103C2×Dic11⋊C4—22no—
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—41no—
112C2×Dic11⋊C4C2×C414yescomplemented
113C2×Dic11⋊C4D414yes—
114C2×C4×Dic11—22no—
115C2×C4×Dic11—22no—
116C2×C4×Dic11—22no—
117C2×C4×Dic11—22no—
118C2×C4×Dic11—22no—
119C2×C4×Dic11—41no—
120C11×#95—22no—
121C11×#95—22no—
122C11⋊#95—22no—
123C11⋊#95—22no—
124C11⋊#95—22no—
125C11⋊#95—22no—
126C11⋊#95—22no—
127C11⋊#95—22no—
128C11⋊#95—22no—
129C11⋊#95—22no—
130C11⋊#95—22no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—41no—
134C11⋊#95—41no—
135C11⋊#95—41no—
136C11⋊#95—41no—
137C11⋊#95C2×C414yescomplemented
138C11⋊#95C2×C414yescomplemented
139C11⋊#95C2×C414yescomplemented
140#14177—111nomaximal, Sylow
141C24×C11—21no—
142C24×C11—21no—
143C24×C11—21no—
144C24×C11—21no—
145C24×C11—21no—
146C24×C11—21no—
147C24×C11—21no—
148C24×C11—21no—
149C24×C11—21no—
150C24×C11—21no—
151C24×C11—21no—
152C24×C11—21no—
153C24×C11C22×C412yes—
154C24×C11C2×D412yes—
155C24×C11#4112yes—
156C24×C11C2411yescharacteristic
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—28no—
166C22×C4×C11—21no—
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—44no—
191C22×C4×C11—44no—
192C22×C4×C11—44no—
193C22×C4×C11—44no—
194C22×C4×C11—44no—
195C22×C4×C11—44no—
196C22×C4×C11C22×C412yes—
197C22×C4×C11C22×C412yes—
198C22×C4×C11C2×D412yes—
199C22×C4×C11C2×D412yes—
200C22×C4×C11C2×D412yes—
201C22×C4×C11#4112yes—
202C22×C4×C11#4112yes—
203C22×C4×C11#4112yes—
204C22×C4×C11#4112yes—
205C22×C4×C11#4112yes—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
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—21no—
253C22×Dic11—21no—
254C22×Dic11C22×C412yes—
255C22×Dic11C22×C412yes—
256C22×Dic11C22×C412yes—
257C22×Dic11C22×C412yes—
258C22×Dic11C2×D412yes—
259C22×Dic11C2×D412yes—
260C22×Dic11#4112yes—
261C22×Dic11#4112yes—
262C11×C22⋊C4—28no—
263C11×C22⋊C4—28no—
264C42×C11—44no—
265C42×C11—44no—
266C22⋊Dic11—28no—
267C22⋊Dic11—28no—
268C22⋊Dic11—44no—
269C22⋊Dic11—44no—
270Dic11⋊C4—28no—
271Dic11⋊C4—28no—
272Dic11⋊C4—44no—
273Dic11⋊C4—44no—
274C4×Dic11—28no—
275C4×Dic11—44no—
276C2×#397—111no—
277C2×#388—111no—
278C2×#385—111no—
279C2×C4×C4⋊C4—111no—
280C2×C4×C22⋊C4D1111yescharacteristic
281#1445—111no—
282#1442—111no—
283#1440—111no—
284#1437—111no—
285#1436—111no—
286#1436—111no—
287#1436—111no—
288#1436—111no—
289#1434—111no—
290C22⋊#95—111no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11C4×D414yes—
326C23×C11C23×C411yescharacteristic
327C23×C11C22×D411yescharacteristic
328C23×C11C22×D411yescharacteristic
329C23×C11C2×#4111yescharacteristic
330C23×C11C2×#4111yescharacteristic
331C23×C11C2×#4111yescharacteristic
332C23×C11C2×#4111yescharacteristic
333C23×C11C2×#4111yescharacteristic
334C23×C11C2×#4111yescharacteristic
335C23×C11C2×#4111yescharacteristic
336C23×C11C2×#4111yescharacteristic
337C23×C11H(5,𝔽2)11yescharacteristic
338C23×C11H(5,𝔽2)11yescharacteristic
339C23×C112−1+411yescharacteristic
340C23×C112−1+411yescharacteristic
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
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—416no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
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#12314yes—
383C2×C4×C11#12314yes—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
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—41no—
406C2×Dic11—41no—
407C2×Dic11—41no—
408C2×Dic11—41no—
409C2×Dic11—41no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C2×Dic11—41no—
413C2×Dic11—41no—
414C2×Dic11—41no—
415C2×Dic11—41no—
416C2×Dic11—41no—
417C2×Dic11—41no—
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—41no—
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×Dic11C4×D414yes—
440C24×C4C2×D1111yescharacteristic
441C22×C4⋊C4—111no—
442C22×C4⋊C4—111no—
443C22×C4⋊C4—111no—
444C22×C4⋊C4—111no—
445C22×C22⋊C4—111no—
446C22×C22⋊C4—111no—
447C22×C22⋊C4—111no—
448C22×C22⋊C4—111no—
449C22×C22⋊C4C2×D1111yescharacteristic
450C22×C22⋊C4C2×D1111yescharacteristic
451C22×C42—111no—
452C22×C42—111no—
453C22×C42C2×D1111yescharacteristic
454C22×C42C2×D1111yescharacteristic
455#397—118no—
456#388—224no—
457#385—224no—
458C4×C4⋊C4—224no—
459C4×C22⋊C4—24no—
460C2×#95—111no—
461C2×#95—111no—
462C2×#95—111no—
463C2×#95—111no—
464C2×#95—111no—
465C2×#95—111no—
466C2×#95—111no—
467C2×#95—111no—
468C2×#95—111no—
469C2×#95—111no—
470C2×#95—111no—
471C2×#95—111no—
472C2×#95—111no—
473C2×#95—111no—
474C2×#95—111no—
475C2×#95—111no—
476C2×#95—111no—
477C2×#95—111no—
478C2×#95C2×D1111yescharacteristic
479C2×#95C2×D1111yescharacteristic
480C22×C11—24no—
481C22×C11—24no—
482C22×C11—24no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11C2×C4×D411yescharacteristic
496C22×C11C2×C4×D411yescharacteristic
497C22×C11C4×#4111yescharacteristic
498C22×C11C4×#4111yescharacteristic
499C22×C11C4×#4111yescharacteristic
500C22×C11#52011yescharacteristic
501C22×C11#52011yescharacteristic
502C22×C11C2×#12311yescharacteristic
503C22×C11C2×#12311yescharacteristic
504C22×C11#52511yescharacteristic
505C22×C11#52511yescharacteristic
506C22×C11#52911yescharacteristic
507C22×C11#52911yescharacteristic
508C22×C11#52911yescharacteristic
509C22×C11#52911yescharacteristic
510C22×C11#53811yescharacteristic
511C22×C11#53911yescharacteristic
512C22×C11#54111yescharacteristic
513C22×C11#54211yescharacteristic
514C22×C11D4211yescharacteristic
515C22×C11#54611yescharacteristic
516C22×C11#54611yescharacteristic
517C22×C11#54711yescharacteristic
518C22×C11#54711yescharacteristic
519C22×C11#54811yescharacteristic
520C22×C11#54811yescharacteristic
521C22×C11#55111yescharacteristic
522C22×C11#55111yescharacteristic
523C22×C11#55211yescharacteristic
524C22×C11#55211yescharacteristic
525C22×C11#55311yescharacteristic
526C22×C11#55311yescharacteristic
527C22×C11#55611yescharacteristic
528C22×C11#55611yescharacteristic
529C22×C11#55911yescharacteristic
530C4×C11—24no—
531C4×C11—24no—
532C4×C11—42no—
533C4×C11—42no—
534C4×C11—42no—
535C4×C11—42no—
536Dic11—24no—
537Dic11—42no—
538Dic11—42no—
539Dic11—42no—
540Dic11—42no—
541Dic11—42no—
542Dic11—81no—
543Dic11—81no—
544C25C22×D1111yescharacteristic
545C23×C4—22no—
546C23×C4—22no—
547C23×C4—22no—
548C23×C4—22no—
549C23×C4—22no—
550C23×C4—41no—
551C23×C4—41no—
552C23×C4—111no—
553C23×C4—111no—
554C23×C4—111no—
555C23×C4—111no—
556C23×C4—111no—
557C23×C4—111no—
558C23×C4—111no—
559C23×C4—111no—
560C23×C4C22×D1111yescharacteristic
561C23×C4C22×D1111yescharacteristic
562C23×C4C22×D1111yescharacteristic
563C23×C4C22×D1111yescharacteristic
564C23×C4C22×D1111yescharacteristic
565C23×C4C22×D1111yescharacteristic
566C2×C4⋊C4—114no—
567C2×C4⋊C4—114no—
568C2×C4⋊C4—222no—
569C2×C4⋊C4—222no—
570C2×C4⋊C4—222no—
571C2×C4⋊C4—222no—
572C2×C4⋊C4—222no—
573C2×C4⋊C4—222no—
574C2×C4⋊C4—222no—
575C2×C4⋊C4—222no—
576C2×C4⋊C4—222no—
577C2×C4⋊C4—441no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—114no—
583C2×C22⋊C4—114no—
584C2×C22⋊C4—222no—
585C2×C22⋊C4—222no—
586C2×C22⋊C4—222no—
587C2×C22⋊C4—222no—
588C2×C22⋊C4—222no—
589C2×C22⋊C4—222no—
590C2×C22⋊C4—222no—
591C2×C22⋊C4—222no—
592C2×C22⋊C4—441no—
593C2×C22⋊C4—441no—
594C2×C22⋊C4C4×D1114yes—
595C2×C22⋊C4C22⋊D1114yes—
596C2×C42—22no—
597C2×C42—22no—
598C2×C42—22no—
599C2×C42—22no—
600C2×C42—41no—
601C2×C42—41no—
602C2×C42—222no—
603C2×C42—222no—
604C2×C42—222no—
605C2×C42—222no—
606C2×C42—222no—
607C2×C42—441no—
608#95—22no—
609#95—22no—
610#95—114no—
611#95—114no—
612#95—114no—
613#95—222no—
614#95—222no—
615#95—222no—
616#95—222no—
617#95—222no—
618#95—222no—
619#95—222no—
620#95—222no—
621#95—222no—
622#95—222no—
623#95—222no—
624#95—441no—
625#95—441no—
626#95—441no—
627#95—441no—
628C2×C11—44no—
629C2×C11C4×#12311yescharacteristic
630C2×C11C4×#12311yescharacteristic
631C2×C11#233411yescharacteristic
632C2×C11#235911yescharacteristic
633C2×C11#236111yescharacteristic
634C2×C11#236711yescharacteristic
635C2×C11#237311yescharacteristic
636C2×C11#241811yescharacteristic
637C2×C11#242111yescharacteristic
638C2×C11#244311yescharacteristic
639C2×C11#244711yescharacteristic
640C2×C11#247711yescharacteristic
641C2×C11#247811yescharacteristic
642C2×C11#257711yescharacteristic
643C2×C11#259711yescharacteristic
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24C2×C4×D1112yes—
657C24#433912yes—
658C24C2×C22⋊D1112yes—
659C24C23×D1111yescharacteristic
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—28no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
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—44no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—112no—
700C22×C4—112no—
701C22×C4—112no—
702C22×C4—112no—
703C22×C4—112no—
704C22×C4—112no—
705C22×C4—112no—
706C22×C4—112no—
707C22×C4—221no—
708C22×C4—221no—
709C22×C4—221no—
710C22×C4—221no—
711C22×C4—221no—
712C22×C4—221no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—221no—
726C22×C4—221no—
727C22×C4—221no—
728C22×C4—221no—
729C22×C4—221no—
730C22×C4—221no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—221no—
736C22×C4—221no—
737C22×C4—221no—
738C22×C4—221no—
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×C4C2×C4×D1112yes—
756C22×C4C2×C4×D1112yes—
757C22×C4#433912yes—
758C22×C4#433912yes—
759C22×C4#433912yes—
760C22×C4#433912yes—
761C22×C4D4×D1112yes—
762C22×C4#434112yes—
763C22×C4C2×C22⋊D1112yes—
764C22×C4C2×C22⋊D1112yes—
765C4⋊C4—228no—
766C4⋊C4—228no—
767C4⋊C4—444no—
768C4⋊C4—444no—
769C22⋊C4—28no—
770C22⋊C4—28no—
771C22⋊C4—228no—
772C22⋊C4—228no—
773C22⋊C4—444no—
774C22⋊C4—444no—
775C42—44no—
776C42—44no—
777C42—228no—
778C42—444no—
779C11#1417711yescharacteristic, complemented, Sylow
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23C4×C22⋊D1114yes—
815C23C22×C4×D1111yescharacteristic
816C23C2×#433911yescharacteristic
817C23C2×#433911yescharacteristic
818C23C2×#433911yescharacteristic
819C23C2×#433911yescharacteristic
820C23C2×#433911yescharacteristic
821C23C2×D4×D1111yescharacteristic
822C23C2×#434111yescharacteristic
823C23#6703711yescharacteristic
824C23#6703711yescharacteristic
825C23#41×D1111yescharacteristic
826C23#41×D1111yescharacteristic
827C23#6704311yescharacteristic
828C23#6704311yescharacteristic
829C23C22×C22⋊D1111yescharacteristic
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—416no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—114no—
872C2×C4—222no—
873C2×C4—222no—
874C2×C4—222no—
875C2×C4—222no—
876C2×C4—222no—
877C2×C4—222no—
878C2×C4—222no—
879C2×C4—222no—
880C2×C4—222no—
881C2×C4—222no—
882C2×C4—222no—
883C2×C4—222no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—222no—
887C2×C4—222no—
888C2×C4—222no—
889C2×C4—222no—
890C2×C4—222no—
891C2×C4—222no—
892C2×C4—222no—
893C2×C4—441no—
894C2×C4—441no—
895C2×C4—441no—
896C2×C4—441no—
897C2×C4—441no—
898C2×C4—441no—
899C2×C4—441no—
900C2×C4—441no—
901C2×C4—441no—
902C2×C4—441no—
903C2×C4—441no—
904C2×C4—441no—
905C2×C4—441no—
906C2×C4—441no—
907C2×C4—441no—
908C2×C4—441no—
909C2×C4—441no—
910C2×C4—441no—
911C2×C4—441no—
912C2×C4—441no—
913C2×C4—441no—
914C2×C4—441no—
915C2×C4—441no—
916C2×C4—441no—
917C2×C4—441no—
918C2×C4—441no—
919C2×C4—441no—
920C2×C4—441no—
921C2×C4—441no—
922C2×C4—441no—
923C2×C4—441no—
924C2×C4—441no—
925C2×C4—441no—
926C2×C4—441no—
927C2×C4#6693614yes—
928C2×C4#6698214yes—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22C4×#433911yescharacteristic
945C22C4×#433911yescharacteristic
946C22#1062301011yescharacteristic
947C22#1062301011yescharacteristic
948C22C2×#6693611yescharacteristic
949C22#1062302111yescharacteristic
950C22#1062302511yescharacteristic
951C22#1062302611yescharacteristic
952C22#1062304911yescharacteristic
953C22#1062305911yescharacteristic
954C22#1062306011yescharacteristic
955C22#1062306411yescharacteristic
956C22C4×#434111yescharacteristic
957C22#1062307111yescharacteristic
958C22#1062307111yescharacteristic
959C22#1062307211yescharacteristic
960C22#1062307311yescharacteristic
961C22C4×D4×D1111yescharacteristic
962C22#1062307711yescharacteristic
963C22#1062307711yescharacteristic
964C22#1062307811yescharacteristic
965C22#1062308311yescharacteristic
966C22#1062308311yescharacteristic
967C22#1062308711yescharacteristic
968C22#1062308811yescharacteristic
969C22#1062309011yescharacteristic
970C22#1062309211yescharacteristic
971C22#1062309511yescharacteristic
972C22C2×C4×C22⋊D1111yescharacteristic
973C22C2×#6698211yescharacteristic
974C22#1062332211yescharacteristic
975C22D4×C22⋊D1111yescharacteristic
976C22#1062333711yescharacteristic
977C22#1062335511yescharacteristic
978C22#1062335511yescharacteristic
979C4—24no—
980C4—24no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—224no—
986C4—442no—
987C4—442no—
988C4—442no—
989C4—442no—
990C4—442no—
991C4—881no—
992C4—881no—
993C2—44no—
994C2C4×#6693611yescharacteristic
995C2C4×#6698211yescharacteristic
996C2#1307139311yescharacteristic
997C2#1307160211yescharacteristic
998C2#1307163311yescharacteristic
999C2#1307168811yescharacteristic
1000C2#1307173711yescharacteristic
1001C2#1307207811yescharacteristic
1002C2#1307211911yescharacteristic
1003C2#1307234511yescharacteristic
1004C2#1307239711yescharacteristic
1005C2#1307281711yescharacteristic
1006C2#1307282611yescharacteristic
1007C2#1307393511yescharacteristic
1008C2#1307416111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#14177
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C4×Dic11⋊C4C2semidirect
5. #13066882C2semidirect
6. #13066871C2semidirect
9. #13066851C2semidirect
10. #13066849C2semidirect
11. #13066849C2semidirect
12. #13066847C2semidirect
13. #13066843C2semidirect
53. #10622565C4semidirect
112. C2×Dic11⋊C4C2×C4semidirect
137. C11⋊#95C2×C4semidirect
138. C11⋊#95C2×C4semidirect
139. C11⋊#95C2×C4semidirect
779. C11#14177semidirect

Maximal subgroups

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

subgroupindex
C2×#106225652
C2×#106225582
C2×#106228232
C2×C4×Dic11⋊C42
#130668822
#130668712
#130668652
#130668532
#130668512
#130668492
#130668472
#130668432
#130668392
C2×C4×C11×C22⋊C42
#1417711