Finite Group Databasebeta

← #14680566

Subgroups — #14680566

Order 2816.

1774 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622835C211yesmaximal, characteristic
2C2×#10622833C211yesmaximal, characteristic
3C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
4#13066882C211yesmaximal, characteristic, complemented
5#13066877C211yesmaximal, characteristic, complemented
6#13066863C211yesmaximal, characteristic, complemented
7#13066863C211yesmaximal, characteristic, complemented
8#13066859C211yesmaximal, characteristic, complemented
9#13066859C211yesmaximal, characteristic, complemented
10#13066853C211yesmaximal, characteristic, complemented
11#13066853C211yesmaximal, characteristic, complemented
12#13066851C211yesmaximal, characteristic, complemented
13#13066847C211yesmaximal, characteristic, complemented
14#13066838C211yesmaximal, characteristic, complemented
15C11×#1438C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34C2×C11×#95C2211yescharacteristic
35#10622835C418yescomplemented
36#10622833—24no—
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
53C22⋊C4×Dic11—24no—
54C25×C11C2311yescharacteristic
55C25×C11C2311yescharacteristic
56C22×D4×C11—22no—
57C22×D4×C11—22no—
58C22×D4×C11—41no—
59C22×D4×C11—41no—
60C22×D4×C11—41no—
61C22×D4×C11—41no—
62C22×D4×C11C2×C414yes—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×Dic11—22no—
69C23×Dic11—22no—
70C23×Dic11—41no—
71C23×Dic11—41no—
72C23×Dic11—41no—
73C23×Dic11—41no—
74C23×Dic11D414yes—
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
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⋊C4—41no—
92C2×C11×C22⋊C4—41no—
93C2×C11×C22⋊C4—41no—
94C2×C11×C22⋊C4—41no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11—22no—
99C2×C22⋊Dic11—22no—
100C2×C22⋊Dic11—22no—
101C2×C22⋊Dic11—22no—
102C2×C22⋊Dic11—41no—
103C2×C22⋊Dic11—41no—
104C2×C22⋊Dic11—41no—
105C2×C22⋊Dic11—41no—
106C2×C22⋊Dic11—41no—
107C2×C22⋊Dic11—41no—
108C2×C22⋊Dic11—41no—
109C2×C22⋊Dic11—41no—
110C2×C22⋊Dic11—41no—
111C2×C22⋊Dic11—41no—
112C2×C22⋊Dic11C2×C414yes—
113C2×C22⋊Dic11C2×C414yes—
114C2×C22⋊Dic11C2×C414yescomplemented
115C2×C22⋊Dic11C2×C414yescomplemented
116C2×Dic11⋊C4—22no—
117C2×Dic11⋊C4—41no—
118C2×Dic11⋊C4—41no—
119C2×Dic11⋊C4—41no—
120C2×Dic11⋊C4—41no—
121C2×Dic11⋊C4C2×C414yescomplemented
122C2×C4×Dic11—22no—
123C2×C4×Dic11—22no—
124C2×C4×Dic11—41no—
125C2×C4×Dic11—41no—
126C2×C4×Dic11—41no—
127C2×C4×Dic11—41no—
128C11×#95—41no—
129C11×#95—41no—
130C11⋊#95—22no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—22no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95—41no—
138C11⋊#95—41no—
139C11⋊#95—41no—
140C11⋊#95—41no—
141C11⋊#95—41no—
142C11⋊#95—41no—
143C11⋊#95—41no—
144C11⋊#95—41no—
145C11⋊#95C2×C414yescomplemented
146#14303—111nomaximal, Sylow
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×C11—21no—
158C24×C11—21no—
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11—21no—
165C24×C11—21no—
166C24×C11—21no—
167C24×C11—21no—
168C24×C11—21no—
169C24×C11—21no—
170C24×C11—21no—
171C24×C11—21no—
172C24×C11—21no—
173C24×C11C22×C412yes—
174C24×C11C22×C412yes—
175C24×C11C2×D412yes—
176C24×C11#4112yes—
177C24×C11C2411yescharacteristic
178C2×D4×C11—28no—
179C2×D4×C11—44no—
180C2×D4×C11—44no—
181C2×D4×C11—44no—
182C2×D4×C11—44no—
183C2×D4×C11—44no—
184C2×D4×C11—44no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11C22×C412yes—
218C22×C4×C11#4112yes—
219C22×C4×C11#4112yes—
220C22×Dic11—28no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—44no—
270C22×Dic11—44no—
271C22×Dic11—44no—
272C22×Dic11—44no—
273C22×Dic11—44no—
274C22×Dic11—44no—
275C22×Dic11C22×C412yes—
276C22×Dic11C22×C412yes—
277C22×Dic11C22×C412yes—
278C22×Dic11C22×C412yes—
279C22×Dic11C2×D412yes—
280C22×Dic11C2×D412yes—
281C22×Dic11#4112yes—
282C22×Dic11#4112yes—
283C11×C22⋊C4—28no—
284C11×C22⋊C4—44no—
285C11×C22⋊C4—44no—
286C11×C22⋊C4—44no—
287C22⋊Dic11—28no—
288C22⋊Dic11—44no—
289C22⋊Dic11—44no—
290C22⋊Dic11—44no—
291C22⋊Dic11—44no—
292C22⋊Dic11—44no—
293C22⋊Dic11—44no—
294Dic11⋊C4—44no—
295Dic11⋊C4—44no—
296C4×Dic11—44no—
297C4×Dic11—44no—
298C2×#394—111no—
299C2×#386—111no—
300C2×C4×C22⋊C4—111no—
301#1445—111no—
302#1443—111no—
303#1440—111no—
304#1440—111no—
305#1439—111no—
306#1439—111no—
307#1438D1111yescharacteristic
308#1437—111no—
309#1437—111no—
310#1436—111no—
311#1436—111no—
312C22⋊#95—111no—
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—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—41no—
339C23×C11—41no—
340C23×C11—41no—
341C23×C11—41no—
342C23×C11—41no—
343C23×C11—41no—
344C23×C11—41no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—41no—
349C23×C11—41no—
350C23×C11—41no—
351C23×C11—41no—
352C23×C11—41no—
353C23×C11—41no—
354C23×C11—41no—
355C23×C11—41no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11—41no—
365C23×C11—41no—
366C23×C11—41no—
367C23×C11—41no—
368C23×C11—41no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—41no—
373C23×C11—41no—
374C23×C11—41no—
375C23×C11—41no—
376C23×C11—41no—
377C23×C11—41no—
378C23×C11—41no—
379C23×C11—41no—
380C23×C11—41no—
381C23×C11—41no—
382C23×C11C4×D414yes—
383C23×C11C23×C411yescharacteristic
384C23×C11C22×D411yescharacteristic
385C23×C11C2×#4111yescharacteristic
386C23×C11C2×#4111yescharacteristic
387C23×C11C2×#4111yescharacteristic
388C23×C11C2×#4111yescharacteristic
389C23×C11C2×#4111yescharacteristic
390C23×C11H(5,𝔽2)11yescharacteristic
391C23×C11H(5,𝔽2)11yescharacteristic
392C23×C11H(5,𝔽2)11yescharacteristic
393C23×C11H(5,𝔽2)11yescharacteristic
394C23×C11H(5,𝔽2)11yescharacteristic
395C23×C11H(5,𝔽2)11yescharacteristic
396C23×C11H(5,𝔽2)11yescharacteristic
397C23×C112−1+411yescharacteristic
398D4×C11—416no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11—41no—
412C2×C4×C11—41no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11—41no—
418C2×C4×C11—41no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C2×C4×C11—41no—
422C2×C4×C11—41no—
423C2×C4×C11—41no—
424C2×C4×C11—41no—
425C2×C4×C11—41no—
426C2×C4×C11—41no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11—41no—
430C2×C4×C11—41no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—416no—
456C2×Dic11—41no—
457C2×Dic11—41no—
458C2×Dic11—41no—
459C2×Dic11—41no—
460C2×Dic11—41no—
461C2×Dic11—41no—
462C2×Dic11—41no—
463C2×Dic11—41no—
464C2×Dic11—41no—
465C2×Dic11—41no—
466C2×Dic11—41no—
467C2×Dic11—41no—
468C2×Dic11—41no—
469C2×Dic11—41no—
470C2×Dic11—41no—
471C2×Dic11—41no—
472C2×Dic11—41no—
473C2×Dic11—41no—
474C2×Dic11—41no—
475C2×Dic11—41no—
476C2×Dic11—41no—
477C2×Dic11—41no—
478C2×Dic11—41no—
479C2×Dic11—41no—
480C2×Dic11—41no—
481C2×Dic11—41no—
482C2×Dic11—41no—
483C2×Dic11—41no—
484C2×Dic11—41no—
485C2×Dic11—41no—
486C2×Dic11—41no—
487C2×Dic11—41no—
488C2×Dic11—41no—
489C2×Dic11—41no—
490C2×Dic11#12314yes—
491C23×D4C2×D1111yescharacteristic
492C24×C4—111no—
493C22×C4⋊C4—111no—
494C22×C4⋊C4—111no—
495C22×C22⋊C4—111no—
496C22×C22⋊C4—111no—
497C22×C22⋊C4—111no—
498C22×C22⋊C4—111no—
499C22×C22⋊C4—111no—
500C22×C22⋊C4—111no—
501C22×C22⋊C4—111no—
502C22×C22⋊C4C2×D1111yescharacteristic
503C22×C22⋊C4C2×D1111yescharacteristic
504C22×C22⋊C4C2×D1111yescharacteristic
505C22×C22⋊C4C2×D1111yescharacteristic
506C22×C42—111no—
507C22×C42—111no—
508#394—118no—
509#386—224no—
510C4×C22⋊C4—224no—
511C2×#95—111no—
512C2×#95—111no—
513C2×#95—111no—
514C2×#95—111no—
515C2×#95—111no—
516C2×#95—111no—
517C2×#95—111no—
518C2×#95—111no—
519C2×#95—111no—
520C2×#95—111no—
521C2×#95—111no—
522C2×#95—111no—
523C2×#95—111no—
524C2×#95—111no—
525C2×#95—111no—
526C2×#95—111no—
527C2×#95C2×D1111yescharacteristic
528C2×#95C2×D1111yescharacteristic
529C22×C11—24no—
530C22×C11—24no—
531C22×C11—24no—
532C22×C11—42no—
533C22×C11—42no—
534C22×C11—42no—
535C22×C11—42no—
536C22×C11—42no—
537C22×C11—42no—
538C22×C11—42no—
539C22×C11—42no—
540C22×C11—42no—
541C22×C11—42no—
542C22×C11—42no—
543C22×C11—42no—
544C22×C11—42no—
545C22×C11—42no—
546C22×C11—42no—
547C22×C11—42no—
548C22×C11—42no—
549C22×C11—42no—
550C22×C11—42no—
551C22×C11—81no—
552C22×C11—81no—
553C22×C11—81no—
554C22×C11—81no—
555C22×C11—81no—
556C22×C11—81no—
557C22×C11—81no—
558C22×C11—81no—
559C22×C11C2×C4×D411yescharacteristic
560C22×C11C4×#4111yescharacteristic
561C22×C11C4×#4111yescharacteristic
562C22×C11#51811yescharacteristic
563C22×C11#51811yescharacteristic
564C22×C11#51811yescharacteristic
565C22×C11#52011yescharacteristic
566C22×C11C2×#12311yescharacteristic
567C22×C11#52511yescharacteristic
568C22×C11#52911yescharacteristic
569C22×C11#52911yescharacteristic
570C22×C11#53411yescharacteristic
571C22×C11#53411yescharacteristic
572C22×C11#53511yescharacteristic
573C22×C11#53711yescharacteristic
574C22×C11#53811yescharacteristic
575C22×C11#53811yescharacteristic
576C22×C11#53811yescharacteristic
577C22×C11#53811yescharacteristic
578C22×C11#53811yescharacteristic
579C22×C11#53811yescharacteristic
580C22×C11#53811yescharacteristic
581C22×C11#53811yescharacteristic
582C22×C11#53811yescharacteristic
583C22×C11#53811yescharacteristic
584C22×C11#53911yescharacteristic
585C22×C11#53911yescharacteristic
586C22×C11#54011yescharacteristic
587C22×C11#54011yescharacteristic
588C22×C11#54011yescharacteristic
589C22×C11#54011yescharacteristic
590C22×C11#54011yescharacteristic
591C22×C11#54211yescharacteristic
592C22×C11#54211yescharacteristic
593C22×C11#54211yescharacteristic
594C4×C11—42no—
595C4×C11—42no—
596C4×C11—42no—
597C4×C11—81no—
598C4×C11—81no—
599Dic11—24no—
600Dic11—42no—
601Dic11—42no—
602Dic11—42no—
603Dic11—42no—
604Dic11—42no—
605Dic11—81no—
606Dic11—81no—
607C25C22×D1111yescharacteristic
608C25C22×D1111yescharacteristic
609C22×D4—22no—
610C22×D4—22no—
611C22×D4—41no—
612C22×D4—41no—
613C22×D4—41no—
614C22×D4—41no—
615C22×D4C4×D1114yes—
616C23×C4—111no—
617C23×C4—111no—
618C23×C4—111no—
619C23×C4—111no—
620C23×C4—111no—
621C23×C4—111no—
622C23×C4—114no—
623C23×C4—111no—
624C23×C4—111no—
625C23×C4—222no—
626C23×C4—222no—
627C23×C4—441no—
628C23×C4—441no—
629C23×C4—441no—
630C23×C4—441no—
631C23×C4C22×D1111yescharacteristic
632C23×C4C22×D1111yescharacteristic
633C23×C4C22×D1111yescharacteristic
634C23×C4C22×D1111yescharacteristic
635C23×C4C22×D1111yescharacteristic
636C2×C4⋊C4—114no—
637C2×C4⋊C4—222no—
638C2×C4⋊C4—441no—
639C2×C4⋊C4—441no—
640C2×C4⋊C4—441no—
641C2×C4⋊C4—441no—
642C2×C22⋊C4—22no—
643C2×C22⋊C4—22no—
644C2×C22⋊C4—22no—
645C2×C22⋊C4—22no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—41no—
649C2×C22⋊C4—41no—
650C2×C22⋊C4—41no—
651C2×C22⋊C4—41no—
652C2×C22⋊C4—41no—
653C2×C22⋊C4—41no—
654C2×C22⋊C4—114no—
655C2×C22⋊C4—114no—
656C2×C22⋊C4—114no—
657C2×C22⋊C4—114no—
658C2×C22⋊C4—222no—
659C2×C22⋊C4—222no—
660C2×C22⋊C4—222no—
661C2×C22⋊C4—222no—
662C2×C22⋊C4—222no—
663C2×C22⋊C4—222no—
664C2×C22⋊C4—222no—
665C2×C22⋊C4—441no—
666C2×C22⋊C4—441no—
667C2×C22⋊C4—441no—
668C2×C22⋊C4—441no—
669C2×C22⋊C4—441no—
670C2×C22⋊C4—441no—
671C2×C22⋊C4—441no—
672C2×C22⋊C4—441no—
673C2×C22⋊C4—441no—
674C2×C22⋊C4—441no—
675C2×C42—222no—
676C2×C42—222no—
677C2×C42—441no—
678C2×C42—441no—
679C2×C42—441no—
680C2×C42—441no—
681#95—41no—
682#95—41no—
683#95—114no—
684#95—222no—
685#95—222no—
686#95—222no—
687#95—222no—
688#95—222no—
689#95—222no—
690#95—222no—
691#95—441no—
692#95—441no—
693#95—441no—
694#95—441no—
695#95—441no—
696#95—441no—
697#95—441no—
698#95—441no—
699C2×C11—44no—
700C2×C11—82no—
701C2×C11C4×#12311yescharacteristic
702C2×C11#232111yescharacteristic
703C2×C11#232511yescharacteristic
704C2×C11#233311yescharacteristic
705C2×C11#233311yescharacteristic
706C2×C11#233511yescharacteristic
707C2×C11#233711yescharacteristic
708C2×C11#262211yescharacteristic
709C2×C11#262411yescharacteristic
710C2×C11#263011yescharacteristic
711C2×C11#263511yescharacteristic
712C2×C11#264811yescharacteristic
713C2×C11#264811yescharacteristic
714C2×C11#264911yescharacteristic
715C2×C11#265311yescharacteristic
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24C2×C4×D1112yes—
743C24C2×C4×D1112yes—
744C24D4×D1112yes—
745C24#434112yes—
746C24C23×D1111yescharacteristic
747C2×D4—28no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—112no—
787C22×C4—112no—
788C22×C4—112no—
789C22×C4—112no—
790C22×C4—112no—
791C22×C4—112no—
792C22×C4—112no—
793C22×C4—112no—
794C22×C4—228no—
795C22×C4—221no—
796C22×C4—221no—
797C22×C4—221no—
798C22×C4—221no—
799C22×C4—221no—
800C22×C4—221no—
801C22×C4—221no—
802C22×C4—221no—
803C22×C4—221no—
804C22×C4—221no—
805C22×C4—221no—
806C22×C4—221no—
807C22×C4—221no—
808C22×C4—221no—
809C22×C4—221no—
810C22×C4—221no—
811C22×C4—221no—
812C22×C4—221no—
813C22×C4—221no—
814C22×C4—221no—
815C22×C4—221no—
816C22×C4—221no—
817C22×C4—221no—
818C22×C4—221no—
819C22×C4—221no—
820C22×C4—221no—
821C22×C4—221no—
822C22×C4—221no—
823C22×C4—221no—
824C22×C4—221no—
825C22×C4—221no—
826C22×C4—221no—
827C22×C4—221no—
828C22×C4—221no—
829C22×C4—221no—
830C22×C4—221no—
831C22×C4—221no—
832C22×C4—221no—
833C22×C4—221no—
834C22×C4—221no—
835C22×C4—221no—
836C22×C4—221no—
837C22×C4—221no—
838C22×C4—221no—
839C22×C4—221no—
840C22×C4—221no—
841C22×C4—221no—
842C22×C4—221no—
843C22×C4—444no—
844C22×C4—444no—
845C22×C4—444no—
846C22×C4—444no—
847C22×C4—444no—
848C22×C4—444no—
849C22×C4C2×C4×D1112yes—
850C22×C4#434112yes—
851C22×C4#434112yes—
852C4⋊C4—444no—
853C4⋊C4—444no—
854C22⋊C4—28no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—228no—
859C22⋊C4—444no—
860C22⋊C4—444no—
861C22⋊C4—444no—
862C22⋊C4—444no—
863C22⋊C4—444no—
864C22⋊C4—444no—
865C42—444no—
866C42—444no—
867C11#1430311yescharacteristic, complemented, Sylow
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23(C22⋊D11)⋊C414yes—
938C23C22×C4×D1111yescharacteristic
939C23C2×D4×D1111yescharacteristic
940C23C2×#434111yescharacteristic
941C23C2×#434111yescharacteristic
942C23C2×#434111yescharacteristic
943C23#6703711yescharacteristic
944C23#6703711yescharacteristic
945C23#6703711yescharacteristic
946C23#6703711yescharacteristic
947C23#6703711yescharacteristic
948C23#6703711yescharacteristic
949C23#41×D1111yescharacteristic
950C23#41×D1111yescharacteristic
951C23#6704211yescharacteristic
952C23#6704311yescharacteristic
953D4—416no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—114no—
990C2×C4—222no—
991C2×C4—222no—
992C2×C4—222no—
993C2×C4—222no—
994C2×C4—222no—
995C2×C4—222no—
996C2×C4—222no—
997C2×C4—222no—
998C2×C4—222no—
999C2×C4—222no—
1000C2×C4—222no—
1001C2×C4—222no—
1002C2×C4—222no—
1003C2×C4—222no—
1004C2×C4—222no—
1005C2×C4—222no—
1006C2×C4—222no—
1007C2×C4—222no—
1008C2×C4—222no—
1009C2×C4—222no—
1010C2×C4—222no—
1011C2×C4—4416no—
1012C2×C4—441no—
1013C2×C4—441no—
1014C2×C4—441no—
1015C2×C4—441no—
1016C2×C4—441no—
1017C2×C4—441no—
1018C2×C4—441no—
1019C2×C4—441no—
1020C2×C4—441no—
1021C2×C4—441no—
1022C2×C4—441no—
1023C2×C4—441no—
1024C2×C4—441no—
1025C2×C4—441no—
1026C2×C4—441no—
1027C2×C4—441no—
1028C2×C4—441no—
1029C2×C4—441no—
1030C2×C4—441no—
1031C2×C4—441no—
1032C2×C4—441no—
1033C2×C4—441no—
1034C2×C4—441no—
1035C2×C4—441no—
1036C2×C4—441no—
1037C2×C4—441no—
1038C2×C4—441no—
1039C2×C4—441no—
1040C2×C4—441no—
1041C2×C4—441no—
1042C2×C4—441no—
1043C2×C4—441no—
1044C2×C4—441no—
1045C2×C4—441no—
1046C22—24no—
1047C22—24no—
1048C22—24no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—81no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22C2×(C22⋊D11)⋊C411yescharacteristic
1077C22#1062301711yescharacteristic
1078C22#1062301711yescharacteristic
1079C22C4×#434111yescharacteristic
1080C22C4×#434111yescharacteristic
1081C22#1062307611yescharacteristic
1082C22#1062307711yescharacteristic
1083C22#1062311711yescharacteristic
1084C22#1062312011yescharacteristic
1085C22#1062312311yescharacteristic
1086C22#1062312411yescharacteristic
1087C22#1062312411yescharacteristic
1088C22#1062312411yescharacteristic
1089C22#1062312411yescharacteristic
1090C22#1062312411yescharacteristic
1091C22#1062312811yescharacteristic
1092C22#1062313111yescharacteristic
1093C22#1062313111yescharacteristic
1094C22#1062313311yescharacteristic
1095C22#1062313411yescharacteristic
1096C22#1062313611yescharacteristic
1097C22#1062314411yescharacteristic
1098C22#1062314411yescharacteristic
1099C22#1062314611yescharacteristic
1100C22#1062314611yescharacteristic
1101C22#1062314811yescharacteristic
1102C22#1062315011yescharacteristic
1103C22D11×#12311yescharacteristic
1104C22#1062318811yescharacteristic
1105C22#1062319311yescharacteristic
1106C22#1062319611yescharacteristic
1107C22#1062320011yescharacteristic
1108C22#1062320911yescharacteristic
1109C22#1062325011yescharacteristic
1110C22#1062325011yescharacteristic
1111C4—42no—
1112C4—42no—
1113C4—42no—
1114C4—81no—
1115C4—81no—
1116C4—224no—
1117C4—442no—
1118C4—442no—
1119C4—442no—
1120C4—442no—
1121C4—442no—
1122C4—881no—
1123C4—881no—
1124C2—44no—
1125C2—82no—
1126C2#1307114111yescharacteristic
1127C2#1307127111yescharacteristic
1128C2#1307131711yescharacteristic
1129C2#1307137511yescharacteristic
1130C2#1307137711yescharacteristic
1131C2#1307140311yescharacteristic
1132C2#1307142511yescharacteristic
1133C2#1307438811yescharacteristic
1134C2#1307440411yescharacteristic
1135C2#1307445211yescharacteristic
1136C2#1307449911yescharacteristic
1137C2#1307460511yescharacteristic
1138C2#1307460511yescharacteristic
1139C2#1307462011yescharacteristic
1140C2#1307468011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenter#1438D11
hypocenterC11#14303
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
3. C2×C22⋊C4×Dic11C2semidirect
4. #13066882C2semidirect
5. #13066877C2semidirect
6. #13066863C2semidirect
7. #13066863C2semidirect
8. #13066859C2semidirect
9. #13066859C2semidirect
10. #13066853C2semidirect
11. #13066853C2semidirect
12. #13066851C2semidirect
13. #13066847C2semidirect
14. #13066838C2semidirect
35. #10622835C4semidirect
114. C2×C22⋊Dic11C2×C4semidirect
115. C2×C22⋊Dic11C2×C4semidirect
121. C2×Dic11⋊C4C2×C4semidirect
145. C11⋊#95C2×C4semidirect
867. C11#14303semidirect

Maximal subgroups

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

subgroupindex
C2×#106228352
C2×#106228332
C2×C22⋊C4×Dic112
#130668822
#130668772
#130668632
#130668592
#130668532
#130668512
#130668472
#130668382
C11×#14382
#1430311