Finite Group Databasebeta

← #14679228

Subgroups — #14679228

Order 2816.

1578 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622565C211yesmaximal, characteristic
2C2×C22⋊C4×Dic11C211yesmaximal, characteristic
3#13066877C211yesmaximal, characteristic, complemented
4#13066866C211yesmaximal, characteristic, complemented
5#13066863C211yesmaximal, characteristic
6#13066853C211yesmaximal, characteristic
7#13066848C211yesmaximal, characteristic, complemented
8#13066847C211yesmaximal, characteristic, complemented
9#13066843C211yesmaximal, characteristic, complemented
10#13066842C211yesmaximal, characteristic, complemented
11#13066840C211yesmaximal, characteristic, complemented
12#13066838C211yesmaximal, characteristic
13#13066838C211yesmaximal, characteristic
14C4×C11⋊#95C211yesmaximal, 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×Dic11⋊C4C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C11×#388—24no—
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2211yescharacteristic
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#10622565C418yescomplemented
53C22⋊C4×Dic11—24no—
54C25×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×Dic11—22no—
62C23×Dic11—22no—
63C23×Dic11—22no—
64C23×Dic11—22no—
65C23×Dic11—22no—
66C23×Dic11—41no—
67C23×Dic11—41no—
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—41no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—41no—
86C2×C11×C22⋊C4C2×C414yes—
87C2×C11×C22⋊C4D414yes—
88C2×C42×C11—22no—
89C2×C42×C11—22no—
90C2×C42×C11—22no—
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—41no—
96C2×C22⋊Dic11—41no—
97C2×C22⋊Dic11—41no—
98C2×C22⋊Dic11C2×C414yes—
99C2×C22⋊Dic11C2×C414yes—
100C2×Dic11⋊C4—41no—
101C2×Dic11⋊C4—41no—
102C2×Dic11⋊C4C2×C414yescomplemented
103C2×C4×Dic11—22no—
104C2×C4×Dic11—22no—
105C2×C4×Dic11—22no—
106C2×C4×Dic11—22no—
107C2×C4×Dic11—22no—
108C2×C4×Dic11—22no—
109C2×C4×Dic11—41no—
110C2×C4×Dic11—41no—
111C2×C4×Dic11—41no—
112C11×#95—22no—
113C11×#95—22no—
114C11⋊#95—22no—
115C11⋊#95—22no—
116C11⋊#95—22no—
117C11⋊#95—22no—
118C11⋊#95—22no—
119C11⋊#95—22no—
120C11⋊#95—22no—
121C11⋊#95—22no—
122C11⋊#95—22no—
123C11⋊#95—22no—
124C11⋊#95—22no—
125C11⋊#95—41no—
126C11⋊#95—41no—
127C11⋊#95—41no—
128C11⋊#95—41no—
129C11⋊#95—41no—
130C11⋊#95—41no—
131C11⋊#95C2×C414yescomplemented
132C11⋊#95C2×C414yescomplemented
133C11⋊#95C2×C414yescomplemented
134#14184—111nomaximal, Sylow
135C24×C11—21no—
136C24×C11—21no—
137C24×C11—21no—
138C24×C11—21no—
139C24×C11—21no—
140C24×C11—21no—
141C24×C11—21no—
142C24×C11—21no—
143C24×C11—21no—
144C24×C11—21no—
145C24×C11—21no—
146C24×C11—21no—
147C24×C11C22×C412yes—
148C24×C11C2×D412yes—
149C24×C11#4112yes—
150C24×C11C2411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
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—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×C11C22×C412yes—
187C22×C4×C11C22×C412yes—
188C22×C4×C11C2×D412yes—
189C22×C4×C11C2×D412yes—
190C22×C4×C11#4112yes—
191C22×C4×C11#4112yes—
192C22×C4×C11#4112yes—
193C22×Dic11—28no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
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—44no—
242C22×Dic11—44no—
243C22×Dic11—44no—
244C22×Dic11—44no—
245C22×Dic11—44no—
246C22×Dic11—44no—
247C22×Dic11C22×C412yes—
248C22×Dic11C22×C412yes—
249C22×Dic11C22×C412yes—
250C22×Dic11C22×C412yes—
251C22×Dic11#4112yes—
252C22×Dic11#4112yes—
253C22×Dic11#4112yes—
254C22×Dic11#4112yes—
255C22×Dic11#4112yes—
256C11×C4⋊C4—44no—
257C11×C22⋊C4—28no—
258C11×C22⋊C4—28no—
259C11×C22⋊C4—44no—
260C42×C11—44no—
261C22⋊Dic11—28no—
262C22⋊Dic11—44no—
263C22⋊Dic11—44no—
264Dic11⋊C4—44no—
265C4×Dic11—44no—
266C4×Dic11—44no—
267C4×Dic11—44no—
268C2×#397—111no—
269C2×#388D1111yescharacteristic
270C2×C4×C22⋊C4—111no—
271#1443—111no—
272#1441—111no—
273#1440—111no—
274#1437—111no—
275#1436—111no—
276#1436—111no—
277#1434—111no—
278#1434—111no—
279#1434—111no—
280C22⋊#95—111no—
281C22⋊#95—111no—
282C4×#95—111no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—22no—
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—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
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×C11C4×D414yes—
318C23×C11C23×C411yescharacteristic
319C23×C11C22×D411yescharacteristic
320C23×C11C2×#4111yescharacteristic
321C23×C11C2×#4111yescharacteristic
322C23×C11C2×#4111yescharacteristic
323C23×C11C2×#4111yescharacteristic
324C23×C11C2×#4111yescharacteristic
325C23×C11C2×#4111yescharacteristic
326C23×C11C2×#4111yescharacteristic
327C23×C11C2×#4111yescharacteristic
328C23×C11C2×#4111yescharacteristic
329C23×C11H(5,𝔽2)11yescharacteristic
330C23×C11H(5,𝔽2)11yescharacteristic
331C23×C11H(5,𝔽2)11yescharacteristic
332C23×C112−1+411yescharacteristic
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
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—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
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#12314yes—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
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—416no—
400C2×Dic11—41no—
401C2×Dic11—41no—
402C2×Dic11—41no—
403C2×Dic11—41no—
404C2×Dic11—41no—
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#12614yes—
432C24×C4—111no—
433C22×C4⋊C4—111no—
434C22×C4⋊C4C2×D1111yescharacteristic
435C22×C22⋊C4—111no—
436C22×C22⋊C4—111no—
437C22×C22⋊C4—111no—
438C22×C22⋊C4C2×D1111yescharacteristic
439C22×C22⋊C4C2×D1111yescharacteristic
440C22×C22⋊C4C2×D1111yescharacteristic
441C22×C42—111no—
442C22×C42—111no—
443C22×C42—111no—
444C22×C42C2×D1111yescharacteristic
445#397—118no—
446#388—24no—
447C4×C22⋊C4—224no—
448C2×#95—111no—
449C2×#95—111no—
450C2×#95—111no—
451C2×#95—111no—
452C2×#95—111no—
453C2×#95—111no—
454C2×#95—111no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95—111no—
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×#95C2×D1111yescharacteristic
469C2×#95C2×D1111yescharacteristic
470C22×C11—24no—
471C22×C11—24no—
472C22×C11—24no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11C2×C4×D411yescharacteristic
486C22×C11C4×#4111yescharacteristic
487C22×C11C4×#4111yescharacteristic
488C22×C11C4×#4111yescharacteristic
489C22×C11C4×#4111yescharacteristic
490C22×C11#51811yescharacteristic
491C22×C11#52011yescharacteristic
492C22×C11C2×#12311yescharacteristic
493C22×C11#52511yescharacteristic
494C22×C11C2×#12611yescharacteristic
495C22×C11#52911yescharacteristic
496C22×C11#52911yescharacteristic
497C22×C11#52911yescharacteristic
498C22×C11#52911yescharacteristic
499C22×C11#52911yescharacteristic
500C22×C11#53811yescharacteristic
501C22×C11#53911yescharacteristic
502C22×C11#54011yescharacteristic
503C22×C11#54211yescharacteristic
504C22×C11#54611yescharacteristic
505C22×C11#54611yescharacteristic
506C22×C11#54611yescharacteristic
507C22×C11#54711yescharacteristic
508C22×C11#55111yescharacteristic
509C22×C11#55111yescharacteristic
510C22×C11#55111yescharacteristic
511C22×C11#55111yescharacteristic
512C22×C11#55211yescharacteristic
513C22×C11#55211yescharacteristic
514C22×C11#55311yescharacteristic
515C22×C11#55311yescharacteristic
516C22×C11#55311yescharacteristic
517C22×C11#55511yescharacteristic
518C22×C11#55511yescharacteristic
519C22×C11#55611yescharacteristic
520C4×C11—24no—
521C4×C11—42no—
522C4×C11—42no—
523C4×C11—42no—
524C4×C11—42no—
525C4×C11—81no—
526Dic11—24no—
527Dic11—42no—
528Dic11—42no—
529Dic11—42no—
530Dic11—42no—
531Dic11—42no—
532Dic11—42no—
533Dic11—81no—
534C25C22×D1111yescharacteristic
535C23×C4—111no—
536C23×C4—111no—
537C23×C4—111no—
538C23×C4—111no—
539C23×C4—111no—
540C23×C4—111no—
541C23×C4—111no—
542C23×C4—111no—
543C23×C4—222no—
544C23×C4—222no—
545C23×C4—222no—
546C23×C4—222no—
547C23×C4—222no—
548C23×C4—441no—
549C23×C4—441no—
550C23×C4C22×D1111yescharacteristic
551C23×C4C22×D1111yescharacteristic
552C23×C4C22×D1111yescharacteristic
553C23×C4C22×D1111yescharacteristic
554C23×C4C22×D1111yescharacteristic
555C23×C4C22×D1111yescharacteristic
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—41no—
559C2×C4⋊C4—114no—
560C2×C4⋊C4—441no—
561C2×C4⋊C4—441no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—41no—
569C2×C22⋊C4—114no—
570C2×C22⋊C4—114no—
571C2×C22⋊C4—222no—
572C2×C22⋊C4—222no—
573C2×C22⋊C4—222no—
574C2×C22⋊C4—222no—
575C2×C22⋊C4—441no—
576C2×C22⋊C4—441no—
577C2×C22⋊C4—441no—
578C2×C22⋊C4C4×D1114yes—
579C2×C22⋊C4C22⋊D1114yes—
580C2×C42—22no—
581C2×C42—22no—
582C2×C42—22no—
583C2×C42—222no—
584C2×C42—222no—
585C2×C42—222no—
586C2×C42—222no—
587C2×C42—222no—
588C2×C42—222no—
589C2×C42—441no—
590C2×C42—441no—
591C2×C42—441no—
592#95—22no—
593#95—22no—
594#95—114no—
595#95—114no—
596#95—114no—
597#95—222no—
598#95—222no—
599#95—222no—
600#95—222no—
601#95—222no—
602#95—222no—
603#95—222no—
604#95—222no—
605#95—222no—
606#95—222no—
607#95—222no—
608#95—441no—
609#95—441no—
610#95—441no—
611#95—441no—
612#95—441no—
613#95—441no—
614C2×C11—44no—
615C2×C11C4×#12311yescharacteristic
616C2×C11C4×#12611yescharacteristic
617C2×C11#233511yescharacteristic
618C2×C11#235911yescharacteristic
619C2×C11#236411yescharacteristic
620C2×C11#237211yescharacteristic
621C2×C11#237311yescharacteristic
622C2×C11#241911yescharacteristic
623C2×C11#242011yescharacteristic
624C2×C11#247411yescharacteristic
625C2×C11#248011yescharacteristic
626C2×C11#249511yescharacteristic
627C2×C11#253111yescharacteristic
628C2×C11#257611yescharacteristic
629C2×C11#257711yescharacteristic
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24C2×C4×D1112yes—
643C24#433912yes—
644C24C2×C22⋊D1112yes—
645C24C23×D1111yescharacteristic
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
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—21no—
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—112no—
682C22×C4—112no—
683C22×C4—112no—
684C22×C4—112no—
685C22×C4—112no—
686C22×C4—112no—
687C22×C4—112no—
688C22×C4—112no—
689C22×C4—112no—
690C22×C4—221no—
691C22×C4—221no—
692C22×C4—221no—
693C22×C4—221no—
694C22×C4—228no—
695C22×C4—221no—
696C22×C4—221no—
697C22×C4—221no—
698C22×C4—221no—
699C22×C4—221no—
700C22×C4—221no—
701C22×C4—221no—
702C22×C4—221no—
703C22×C4—221no—
704C22×C4—221no—
705C22×C4—221no—
706C22×C4—221no—
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—444no—
739C22×C4—444no—
740C22×C4—444no—
741C22×C4—444no—
742C22×C4—444no—
743C22×C4—444no—
744C22×C4C2×C4×D1112yes—
745C22×C4C2×C4×D1112yes—
746C22×C4#434112yes—
747C22×C4#434112yes—
748C22×C4#434112yes—
749C22×C4C2×C22⋊D1112yes—
750C22×C4C2×C22⋊D1112yes—
751C4⋊C4—44no—
752C4⋊C4—444no—
753C22⋊C4—28no—
754C22⋊C4—28no—
755C22⋊C4—44no—
756C22⋊C4—228no—
757C22⋊C4—444no—
758C22⋊C4—444no—
759C42—44no—
760C42—444no—
761C42—444no—
762C42—444no—
763C11#1418411yescharacteristic, complemented, Sylow
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23C4×C22⋊D1114yes—
799C23C22×C4×D1111yescharacteristic
800C23C2×#433911yescharacteristic
801C23C2×#434111yescharacteristic
802C23C2×#434111yescharacteristic
803C23C2×#434111yescharacteristic
804C23#6703711yescharacteristic
805C23#41×D1111yescharacteristic
806C23#41×D1111yescharacteristic
807C23#41×D1111yescharacteristic
808C23#41×D1111yescharacteristic
809C23#41×D1111yescharacteristic
810C23#6704211yescharacteristic
811C23#6704211yescharacteristic
812C23#6704311yescharacteristic
813C23C22×C22⋊D1111yescharacteristic
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—114no—
856C2×C4—222no—
857C2×C4—222no—
858C2×C4—222no—
859C2×C4—222no—
860C2×C4—222no—
861C2×C4—222no—
862C2×C4—222no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—222no—
869C2×C4—222no—
870C2×C4—222no—
871C2×C4—222no—
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—4416no—
881C2×C4—441no—
882C2×C4—441no—
883C2×C4—441no—
884C2×C4—441no—
885C2×C4—441no—
886C2×C4—441no—
887C2×C4—441no—
888C2×C4—441no—
889C2×C4—441no—
890C2×C4—441no—
891C2×C4—441no—
892C2×C4—441no—
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#6698814yes—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22#1062305311yescharacteristic
929C22#1062305411yescharacteristic
930C22#1062305811yescharacteristic
931C22#1062306211yescharacteristic
932C22C4×#434111yescharacteristic
933C22C4×#434111yescharacteristic
934C22C4×#434111yescharacteristic
935C22#1062306911yescharacteristic
936C22#1062306911yescharacteristic
937C22#1062307111yescharacteristic
938C22#1062307611yescharacteristic
939C22#1062309611yescharacteristic
940C22#1062313111yescharacteristic
941C22#1062314711yescharacteristic
942C22#1062314911yescharacteristic
943C22#1062315011yescharacteristic
944C22#1062318011yescharacteristic
945C22#1062318111yescharacteristic
946C22#1062318911yescharacteristic
947C22#1062319611yescharacteristic
948C22#1062320011yescharacteristic
949C22#1062320111yescharacteristic
950C22#1062320211yescharacteristic
951C22#1062321111yescharacteristic
952C22D11×#12611yescharacteristic
953C22#1062323511yescharacteristic
954C22#1062323611yescharacteristic
955C22#1062323611yescharacteristic
956C22C2×C4×C22⋊D1111yescharacteristic
957C22C2×#6698811yescharacteristic
958C22#1062333711yescharacteristic
959C22#1062335511yescharacteristic
960C22#1062335911yescharacteristic
961C22#1062336011yescharacteristic
962C22#1062336011yescharacteristic
963C4—24no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—81no—
969C4—224no—
970C4—442no—
971C4—442no—
972C4—442no—
973C4—442no—
974C4—442no—
975C4—442no—
976C4—881no—
977C2—44no—
978C2C4×#6698811yescharacteristic
979C2#1307117011yescharacteristic
980C2#1307141311yescharacteristic
981C2#1307160811yescharacteristic
982C2#1307166111yescharacteristic
983C2#1307172311yescharacteristic
984C2#1307174311yescharacteristic
985C2#1307208911yescharacteristic
986C2#1307210411yescharacteristic
987C2#1307276811yescharacteristic
988C2#1307285811yescharacteristic
989C2#1307302411yescharacteristic
990C2#1307346011yescharacteristic
991C2#1307392611yescharacteristic
992C2#1307393211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#388C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#388D11
hypocenterC11#14184
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. #13066877C2semidirect
4. #13066866C2semidirect
7. #13066848C2semidirect
8. #13066847C2semidirect
9. #13066843C2semidirect
10. #13066842C2semidirect
11. #13066840C2semidirect
14. C4×C11⋊#95C2semidirect
52. #10622565C4semidirect
102. C2×Dic11⋊C4C2×C4semidirect
131. C11⋊#95C2×C4semidirect
132. C11⋊#95C2×C4semidirect
133. C11⋊#95C2×C4semidirect
763. C11#14184semidirect

Maximal subgroups

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

subgroupindex
C2×#106225652
C2×C22⋊C4×Dic112
#130668772
#130668662
#130668632
#130668532
#130668482
#130668472
#130668432
#130668422
#130668402
#130668382
C4×C11⋊#952
C2×C11×#3882
#1418411