Finite Group Databasebeta

← #14675124

Subgroups — #14675124

Order 2816.

1826 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622564C211yesmaximal, characteristic
2C2×#10622563C211yesmaximal, characteristic
3C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic11C211yesmaximal, characteristic
5#13066853C211yesmaximal, characteristic
6#13066853C211yesmaximal, characteristic
7#13066850C211yesmaximal, characteristic, complemented
8#13066850C211yesmaximal, characteristic, complemented
9#13066850C211yesmaximal, characteristic, complemented
10#13066848C211yesmaximal, characteristic, complemented
11#13066845C211yesmaximal, characteristic, complemented
12#13066843C211yesmaximal, characteristic, complemented
13#13066838C211yesmaximal, characteristic
14#95×Dic11C211yesmaximal, characteristic, complemented
15C2×C11×#388C211yesmaximal, characteristic
16C24×Dic11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C11×#388C418yescomplemented
34C2×C11×#95C2211yescharacteristic
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
52#10622564C418yescomplemented
53#10622563C418yescomplemented
54C22⋊C4×Dic11—24no—
55C4×C4⋊Dic11—24no—
56C25×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11—22no—
64C23×Dic11—22no—
65C23×Dic11—41no—
66C23×Dic11—41no—
67C23×Dic11—41no—
68C23×Dic11—41no—
69C23×Dic11C2×C414yes—
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C2×C11×C4⋊C4—41no—
79C2×C11×C4⋊C4—41no—
80C2×C11×C4⋊C4C2×C414yescomplemented
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—41no—
84C2×C11×C22⋊C4—41no—
85C2×C11×C22⋊C4C2×C414yes—
86C2×C11×C22⋊C4C2×C414yes—
87C2×C11×C22⋊C4C2×C414yes—
88C2×C11×C22⋊C4C2×C414yes—
89C2×C11×C22⋊C4C2×C414yes—
90C2×C42×C11—22no—
91C2×C42×C11—22no—
92C2×C42×C11C2×C414yescomplemented
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—41no—
96C2×C22⋊Dic11—41no—
97C2×C22⋊Dic11—41no—
98C2×C22⋊Dic11—41no—
99C2×C22⋊Dic11C2×C414yes—
100C2×C22⋊Dic11C2×C414yes—
101C2×C22⋊Dic11C2×C414yes—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11—22no—
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11—41no—
107C2×C4⋊Dic11—41no—
108C2×C4⋊Dic11C2×C414yes—
109C2×C4⋊Dic11C2×C414yes—
110C2×C4⋊Dic11C2×C414yescomplemented
111C2×C4×Dic11—22no—
112C2×C4×Dic11—22no—
113C2×C4×Dic11—22no—
114C2×C4×Dic11—41no—
115C2×C4×Dic11—41no—
116C2×C4×Dic11—41no—
117C2×C4×Dic11—41no—
118C2×C4×Dic11—41no—
119C2×C4×Dic11—41no—
120C2×C4×Dic11—41no—
121C2×C4×Dic11—41no—
122C2×C4×Dic11—41no—
123C2×C4×Dic11—41no—
124C2×C4×Dic11C2×C414yescomplemented
125C2×C4×Dic11D414yes—
126C11×#95C2×C414yescomplemented
127C11×#95C2×C414yescomplemented
128C11⋊#95—22no—
129C11⋊#95—22no—
130C11⋊#95—22no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—22no—
134C11⋊#95—41no—
135C11⋊#95—41no—
136C11⋊#95—41no—
137C11⋊#95—41no—
138C11⋊#95—41no—
139C11⋊#95—41no—
140C11⋊#95C2×C414yes—
141C11⋊#95C2×C414yes—
142C11⋊#95C2×C414yescomplemented
143C11⋊#95C2×C414yescomplemented
144#13789—111nomaximal, Sylow
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×C11—21no—
154C24×C11—21no—
155C24×C11—21no—
156C24×C11—21no—
157C24×C11C22×C412yes—
158C24×C11C22×C412yes—
159C24×C11C22×C412yes—
160C24×C11C2411yescharacteristic
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
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—21no—
191C22×C4×C11C22×C412yes—
192C22×C4×C11C22×C412yes—
193C22×C4×C11C22×C412yes—
194C22×C4×C11C22×C412yes—
195C22×C4×C11C22×C412yes—
196C22×C4×C11C22×C412yes—
197C22×C4×C11C22×C412yes—
198C22×C4×C11C22×C412yes—
199C22×C4×C11C22×C412yes—
200C22×C4×C11C22×C412yes—
201C22×C4×C11C2×D412yes—
202C22×C4×C11#4112yes—
203C22×Dic11—28no—
204C22×Dic11—21no—
205C22×Dic11—21no—
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—44no—
249C22×Dic11—44no—
250C22×Dic11—44no—
251C22×Dic11—44no—
252C22×Dic11—44no—
253C22×Dic11—44no—
254C22×Dic11C22×C412yes—
255C22×Dic11C22×C412yes—
256C22×Dic11C22×C412yes—
257C22×Dic11C22×C412yes—
258C22×Dic11C22×C412yes—
259C22×Dic11C22×C412yes—
260C22×Dic11C22×C412yes—
261C22×Dic11C22×C412yes—
262C22×Dic11C2×D412yes—
263C22×Dic11C2×D412yes—
264C22×Dic11#4112yes—
265C22×Dic11#4112yes—
266C11×C4⋊C4—44no—
267C11×C22⋊C4—28no—
268C11×C22⋊C4—44no—
269C11×C22⋊C4C42116yescomplemented
270C42×C11—28no—
271C22⋊Dic11—28no—
272C22⋊Dic11—44no—
273C22⋊Dic11—44no—
274C4⋊Dic11—28no—
275C4⋊Dic11—28no—
276C4⋊Dic11—44no—
277C4×Dic11—44no—
278C4×Dic11—44no—
279C4×Dic11—44no—
280C4×Dic11—44no—
281C4×Dic11—44no—
282C2×#388—111no—
283C2×#388D1111yescharacteristic
284C2×#385—111no—
285C2×C4×C4⋊C4—111no—
286C2×C4×C22⋊C4—111no—
287#1437—111no—
288#1437—111no—
289#1436—111no—
290#1436—111no—
291#1436—111no—
292#1436—111no—
293C4⋊#95—111no—
294#1434—111no—
295C22⋊#95—111no—
296C4×#95—111no—
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—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
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×C11—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11C2×C4214yes—
332C23×C11C23×C411yescharacteristic
333C23×C11C23×C411yescharacteristic
334C23×C11C23×C411yescharacteristic
335C23×C11C22×D411yescharacteristic
336C23×C11C2×#4111yescharacteristic
337C23×C11C2×#4111yescharacteristic
338C23×C11C2×#4111yescharacteristic
339C23×C11H(5,𝔽2)11yescharacteristic
340C23×C11H(5,𝔽2)11yescharacteristic
341C23×C11H(5,𝔽2)11yescharacteristic
342C23×C11H(5,𝔽2)11yescharacteristic
343C23×C11H(5,𝔽2)11yescharacteristic
344C23×C112−1+411yescharacteristic
345C23×C112−1+411yescharacteristic
346C23×C112−1+411yescharacteristic
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—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
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—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×C11C2×C4214yes—
387C2×C4×C11C2×C4214yes—
388C2×C4×C11C4×D414yes—
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—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—22no—
419C2×Dic11—416no—
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×Dic11—41no—
440C2×Dic11—41no—
441C2×Dic11—41no—
442C2×Dic11—41no—
443C2×Dic11—41no—
444C2×Dic11C4×D414yes—
445C2×Dic11C4×D414yes—
446C24×C4—111no—
447C22×C4⋊C4—111no—
448C22×C4⋊C4—111no—
449C22×C4⋊C4—111no—
450C22×C4⋊C4C2×D1111yescharacteristic
451C22×C22⋊C4—111no—
452C22×C22⋊C4—111no—
453C22×C22⋊C4—111no—
454C22×C22⋊C4C2×D1111yescharacteristic
455C22×C22⋊C4C2×D1111yescharacteristic
456C22×C22⋊C4C2×D1111yescharacteristic
457C22×C42—111no—
458C22×C42—111no—
459C22×C42—111no—
460C22×C42—111no—
461C22×C42—111no—
462C22×C42C2×D1111yescharacteristic
463#388—118no—
464#388Dic1118yescomplemented
465#385—118no—
466C4×C4⋊C4—224no—
467C4×C22⋊C4—224no—
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×#95—111no—
479C2×#95—111no—
480C2×#95—111no—
481C2×#95—111no—
482C2×#95—111no—
483C2×#95—111no—
484C2×#95C2×D1111yescharacteristic
485C2×#95C2×D1111yescharacteristic
486C22×C11—24no—
487C22×C11—24no—
488C22×C11—24no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—42no—
501C22×C11C22×C4211yescharacteristic
502C22×C11C2×C4×D411yescharacteristic
503C22×C11C2×C4×D411yescharacteristic
504C22×C11C2×C4×D411yescharacteristic
505C22×C11C4×#4111yescharacteristic
506C22×C11C4×#4111yescharacteristic
507C22×C11C4×#4111yescharacteristic
508C22×C11#51811yescharacteristic
509C22×C11#51811yescharacteristic
510C22×C11#51811yescharacteristic
511C22×C11#51811yescharacteristic
512C22×C11#51911yescharacteristic
513C22×C11#52011yescharacteristic
514C22×C11#52011yescharacteristic
515C22×C11#52011yescharacteristic
516C22×C11#52011yescharacteristic
517C22×C11#52011yescharacteristic
518C22×C11#52011yescharacteristic
519C22×C11#52011yescharacteristic
520C22×C11#53411yescharacteristic
521C22×C11#53511yescharacteristic
522C22×C11#53611yescharacteristic
523C22×C11#53711yescharacteristic
524C22×C11#53811yescharacteristic
525C22×C11#53811yescharacteristic
526C22×C11#53811yescharacteristic
527C22×C11#53911yescharacteristic
528C22×C11#53911yescharacteristic
529C22×C11#53911yescharacteristic
530C22×C11#54011yescharacteristic
531C22×C11#54111yescharacteristic
532C22×C11#54211yescharacteristic
533C22×C11#54211yescharacteristic
534C22×C11#54211yescharacteristic
535C22×C11#54211yescharacteristic
536C4×C11—24no—
537C4×C11—24no—
538C4×C11—24no—
539C4×C11—42no—
540C4×C11—42no—
541C4×C11—42no—
542Dic11—24no—
543Dic11—24no—
544Dic11—42no—
545Dic11—42no—
546Dic11—42no—
547Dic11—42no—
548Dic11—42no—
549Dic11—42no—
550C25C22×D1111yescharacteristic
551C23×C4—111no—
552C23×C4—111no—
553C23×C4—111no—
554C23×C4—111no—
555C23×C4—111no—
556C23×C4—111no—
557C23×C4—111no—
558C23×C4—111no—
559C23×C4—114no—
560C23×C4—222no—
561C23×C4—222no—
562C23×C4—441no—
563C23×C4—441no—
564C23×C4—441no—
565C23×C4—441no—
566C23×C4C22×D1111yescharacteristic
567C23×C4C22×D1111yescharacteristic
568C23×C4C22×D1111yescharacteristic
569C23×C4C22×D1111yescharacteristic
570C23×C4C22×D1111yescharacteristic
571C23×C4C22×D1111yescharacteristic
572C2×C4⋊C4—41no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—114no—
575C2×C4⋊C4—114no—
576C2×C4⋊C4—114no—
577C2×C4⋊C4—222no—
578C2×C4⋊C4—222no—
579C2×C4⋊C4—222no—
580C2×C4⋊C4—222no—
581C2×C4⋊C4—441no—
582C2×C4⋊C4—441no—
583C2×C4⋊C4C2×Dic1114yescomplemented
584C2×C22⋊C4—22no—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—41no—
587C2×C22⋊C4—41no—
588C2×C22⋊C4—114no—
589C2×C22⋊C4—114no—
590C2×C22⋊C4—114no—
591C2×C22⋊C4—222no—
592C2×C22⋊C4—222no—
593C2×C22⋊C4—441no—
594C2×C22⋊C4—441no—
595C2×C22⋊C4—441no—
596C2×C22⋊C4—441no—
597C2×C22⋊C4C4×D1114yes—
598C2×C22⋊C4C4×D1114yes—
599C2×C22⋊C4C2×Dic1114yes—
600C2×C22⋊C4C2×Dic1114yes—
601C2×C22⋊C4C2×Dic1114yes—
602C2×C42—22no—
603C2×C42—22no—
604C2×C42—114no—
605C2×C42—114no—
606C2×C42—222no—
607C2×C42—222no—
608C2×C42—222no—
609C2×C42—441no—
610C2×C42—441no—
611C2×C42—441no—
612C2×C42—441no—
613C2×C42—441no—
614C2×C42—441no—
615C2×C42—441no—
616C2×C42—441no—
617C2×C42—441no—
618C2×C42—441no—
619C2×C42C2×Dic1114yescomplemented
620#95—114no—
621#95—114no—
622#95—114no—
623#95—114no—
624#95—222no—
625#95—222no—
626#95—222no—
627#95—222no—
628#95—222no—
629#95—222no—
630#95—441no—
631#95—441no—
632#95—441no—
633#95—441no—
634#95—441no—
635#95—441no—
636#95C2×Dic1114yescomplemented
637#95C2×Dic1114yescomplemented
638C2×C11—44no—
639C2×C11C42×D411yescharacteristic
640C2×C11#227411yescharacteristic
641C2×C11#227511yescharacteristic
642C2×C11#232111yescharacteristic
643C2×C11#232211yescharacteristic
644C2×C11#232311yescharacteristic
645C2×C11#232411yescharacteristic
646C2×C11#232511yescharacteristic
647C2×C11#232611yescharacteristic
648C2×C11#233211yescharacteristic
649C2×C11#233411yescharacteristic
650C2×C11#233411yescharacteristic
651C2×C11#233511yescharacteristic
652C2×C11#233511yescharacteristic
653C2×C11#233711yescharacteristic
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24C2×C4×D1112yes—
667C24C2×C4×D1112yes—
668C24C22×Dic1112yes—
669C24C23×D1111yescharacteristic
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—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—112no—
701C22×C4—112no—
702C22×C4—112no—
703C22×C4—112no—
704C22×C4—112no—
705C22×C4—112no—
706C22×C4—112no—
707C22×C4—112no—
708C22×C4—112no—
709C22×C4—112no—
710C22×C4—112no—
711C22×C4—112no—
712C22×C4—228no—
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×C4—221no—
756C22×C4—221no—
757C22×C4—444no—
758C22×C4—444no—
759C22×C4—444no—
760C22×C4—444no—
761C22×C4—444no—
762C22×C4—444no—
763C22×C4C2×C4×D1112yes—
764C22×C4C2×C4×D1112yes—
765C22×C4C2×C4×D1112yes—
766C22×C4C2×C4×D1112yes—
767C22×C4D4×D1112yes—
768C22×C4#434112yes—
769C22×C4C22×Dic1112yes—
770C22×C4C22×Dic1112yes—
771C22×C4C22×Dic1112yes—
772C22×C4C22×Dic1112yes—
773C22×C4C22×Dic1112yes—
774C22×C4C22×Dic1112yes—
775C4⋊C4—44no—
776C4⋊C4—228no—
777C4⋊C4—228no—
778C4⋊C4—444no—
779C22⋊C4—28no—
780C22⋊C4—44no—
781C22⋊C4—228no—
782C22⋊C4—444no—
783C22⋊C4—444no—
784C22⋊C4C4×Dic11116yescomplemented
785C42—28no—
786C42—444no—
787C42—444no—
788C42—444no—
789C42—444no—
790C42—444no—
791C11#1378911yescharacteristic, complemented, Sylow
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4×Dic1114yes—
827C23C22×C4×D1111yescharacteristic
828C23C22×C4×D1111yescharacteristic
829C23C2×D4×D1111yescharacteristic
830C23C2×#434111yescharacteristic
831C23#6703711yescharacteristic
832C23#6703711yescharacteristic
833C23#41×D1111yescharacteristic
834C23#41×D1111yescharacteristic
835C23#6704211yescharacteristic
836C23#6704211yescharacteristic
837C23#6704211yescharacteristic
838C23#6704311yescharacteristic
839C23#6704311yescharacteristic
840C23#6704311yescharacteristic
841C23C23×Dic1111yescharacteristic
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—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
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—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
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—114no—
882C2×C4—114no—
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—222no—
894C2×C4—222no—
895C2×C4—222no—
896C2×C4—222no—
897C2×C4—222no—
898C2×C4—222no—
899C2×C4—222no—
900C2×C4—222no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—222no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—222no—
908C2×C4—222no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—222no—
913C2×C4—4416no—
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—441no—
928C2×C4—441no—
929C2×C4—441no—
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×C4C2×C4×Dic1114yes—
939C2×C4C2×C4×Dic1114yes—
940C2×C4D4×Dic1114yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22#1062304711yescharacteristic
957C22#1062305211yescharacteristic
958C22#1062305411yescharacteristic
959C22#1062305411yescharacteristic
960C22C4×#434111yescharacteristic
961C22C4×#434111yescharacteristic
962C22C4×D4×D1111yescharacteristic
963C22C4×D4×D1111yescharacteristic
964C22#1062307611yescharacteristic
965C22#1062307611yescharacteristic
966C22#1062307711yescharacteristic
967C22#1062307711yescharacteristic
968C22#1062313411yescharacteristic
969C22#1062313811yescharacteristic
970C22#1062313911yescharacteristic
971C22#1062315011yescharacteristic
972C22#1062317911yescharacteristic
973C22#1062318411yescharacteristic
974C22#1062319611yescharacteristic
975C22#1062319611yescharacteristic
976C22#1062320011yescharacteristic
977C22#1062320011yescharacteristic
978C22#1062320911yescharacteristic
979C22#1062320911yescharacteristic
980C22#1062323211yescharacteristic
981C22#1062323511yescharacteristic
982C22#1062323811yescharacteristic
983C22#1062324111yescharacteristic
984C22C22×C4×Dic1111yescharacteristic
985C22C2×D4×Dic1111yescharacteristic
986C22#1062332911yescharacteristic
987C22#41×Dic1111yescharacteristic
988C22#1062335811yescharacteristic
989C22#1062335811yescharacteristic
990C22#1062335811yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—224no—
998C4—224no—
999C4—442no—
1000C4—442no—
1001C4—442no—
1002C4—442no—
1003C4—442no—
1004C4—442no—
1005C2—44no—
1006C2C4×D4×Dic1111yescharacteristic
1007C2#1307097211yescharacteristic
1008C2#1307097711yescharacteristic
1009C2#1307127811yescharacteristic
1010C2#1307128811yescharacteristic
1011C2#1307129511yescharacteristic
1012C2#1307131111yescharacteristic
1013C2#1307132011yescharacteristic
1014C2#1307132511yescharacteristic
1015C2#1307137311yescharacteristic
1016C2#1307139511yescharacteristic
1017C2#1307139811yescharacteristic
1018C2#1307141111yescharacteristic
1019C2#1307141311yescharacteristic
1020C2#1307143111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC2×C11×#388C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#388D11
hypocenterC11#13789
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C2×C4×C4⋊Dic11C2semidirect
7. #13066850C2semidirect
8. #13066850C2semidirect
9. #13066850C2semidirect
10. #13066848C2semidirect
11. #13066845C2semidirect
12. #13066843C2semidirect
14. #95×Dic11C2semidirect
33. C11×#388C4semidirect
52. #10622564C4semidirect
53. #10622563C4semidirect
80. C2×C11×C4⋊C4C2×C4semidirect
92. C2×C42×C11C2×C4semidirect
110. C2×C4⋊Dic11C2×C4semidirect
124. C2×C4×Dic11C2×C4semidirect
126. C11×#95C2×C4semidirect
127. C11×#95C2×C4semidirect
142. C11⋊#95C2×C4semidirect
143. C11⋊#95C2×C4semidirect
269. C11×C22⋊C4C42semidirect
464. #388Dic11semidirect
583. C2×C4⋊C4C2×Dic11semidirect
619. C2×C42C2×Dic11semidirect
636. #95C2×Dic11semidirect
637. #95C2×Dic11semidirect
784. C22⋊C4C4×Dic11semidirect
791. C11#13789semidirect

Maximal subgroups

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

subgroupindex
C2×#106225642
C2×#106225632
C2×C4×C4⋊Dic112
C2×C22⋊C4×Dic112
#130668532
#130668502
#130668482
#130668452
#130668432
#130668382
#95×Dic112
C2×C11×#3882
#1378911