Finite Group Databasebeta

← #14682009

Subgroups — #14682009

Order 2816.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622564C211yesmaximal, characteristic, complemented
2C2×#10622833C211yesmaximal, characteristic
3#13066878C211yesmaximal, characteristic, complemented
4#13066878C211yesmaximal, characteristic, complemented
5#13066873C211yesmaximal, characteristic, complemented
6#13066865C211yesmaximal, characteristic, complemented
7#13066861C211yesmaximal, characteristic, complemented
8#13066857C211yesmaximal, characteristic
9#13066853C211yesmaximal, characteristic, complemented
10#13066841C211yesmaximal, characteristic, complemented
11#13066839C211yesmaximal, characteristic, complemented
12#13066839C211yesmaximal, characteristic, complemented
13#13066838C211yesmaximal, characteristic, complemented
14#13066838C211yesmaximal, characteristic, complemented
15C2×C11×#386C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C11×#386C418yescomplemented
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34#10622833—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#10622564—24no—
54C25×C11C2311yescharacteristic
55C25×C11C2311yescharacteristic
56C22×D4×C11—22no—
57C22×D4×C11—22no—
58C22×D4×C11—22no—
59C22×D4×C11—22no—
60C22×D4×C11—41no—
61C22×D4×C11—41no—
62C22×D4×C11C2×C414yes—
63C23×C4×C11—41no—
64C23×C4×C11—41no—
65C23×C4×C11—41no—
66C23×C4×C11—41no—
67C23×C4×C11—41no—
68C23×C4×C11—41no—
69C23×C4×C11C2×C414yescomplemented
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×Dic11—22no—
76C23×Dic11—22no—
77C23×Dic11—22no—
78C23×Dic11—41no—
79C23×Dic11—41no—
80C23×Dic11—41no—
81C23×Dic11—41no—
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—41no—
93C2×C11×C22⋊C4—41no—
94C2×C11×C22⋊C4—41no—
95C2×C11×C22⋊C4—41no—
96C2×C11×C22⋊C4C2×C414yes—
97C2×C11×C22⋊C4C2×C414yes—
98C2×C11×C22⋊C4C2×C414yescomplemented
99C2×C22⋊Dic11—22no—
100C2×C22⋊Dic11—22no—
101C2×C22⋊Dic11—22no—
102C2×C22⋊Dic11—22no—
103C2×C22⋊Dic11—22no—
104C2×C22⋊Dic11—22no—
105C2×C22⋊Dic11—22no—
106C2×C22⋊Dic11—22no—
107C2×C22⋊Dic11—22no—
108C2×C22⋊Dic11—22no—
109C2×C22⋊Dic11—41no—
110C2×C22⋊Dic11—41no—
111C2×C22⋊Dic11—41no—
112C2×C22⋊Dic11—41no—
113C2×C22⋊Dic11—41no—
114C2×C22⋊Dic11—41no—
115C2×C22⋊Dic11—41no—
116C2×C22⋊Dic11—41no—
117C2×C22⋊Dic11—41no—
118C2×C22⋊Dic11—41no—
119C2×C22⋊Dic11D414yes—
120C2×C4⋊Dic11—22no—
121C2×C4⋊Dic11—41no—
122C2×C4⋊Dic11—41no—
123C2×C4×Dic11—22no—
124C2×C4×Dic11—22no—
125C2×C4×Dic11—41no—
126C11×#95C2×C414yescomplemented
127C11×#95C2×C414yescomplemented
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⋊#95—41no—
138C11⋊#95—41no—
139C11⋊#95—41no—
140C11⋊#95—41no—
141C11⋊#95—41no—
142C11⋊#95—41no—
143C11⋊#95—41no—
144C11⋊#95—41no—
145C11⋊#95—41no—
146#14427—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×C11C22×C412yes—
172C24×C11C22×C412yes—
173C24×C11C2×D412yes—
174C24×C11#4112yes—
175C24×C11#4112yes—
176C24×C11#4112yes—
177C24×C11C2411yescharacteristic
178C2×D4×C11—28no—
179C2×D4×C11—28no—
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—44no—
216C22×C4×C11—44no—
217C22×C4×C11—44no—
218C22×C4×C11—44no—
219C22×C4×C11—44no—
220C22×C4×C11—44no—
221C22×C4×C11—44no—
222C22×C4×C11C22×C412yes—
223C22×C4×C11C22×C412yes—
224C22×C4×C11C22×C412yes—
225C22×C4×C11C22×C412yes—
226C22×C4×C11C22×C412yes—
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—21no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—21no—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11—21no—
277C22×Dic11—21no—
278C22×Dic11—21no—
279C22×Dic11—44no—
280C22×Dic11—44no—
281C22×Dic11—44no—
282C22×Dic11—44no—
283C22×Dic11—44no—
284C22×Dic11—44no—
285C22×Dic11—44no—
286C22×Dic11C2×D412yes—
287C22×Dic11C2×D412yes—
288C22×Dic11#4112yes—
289C22×Dic11#4112yes—
290C11×C22⋊C4—28no—
291C11×C22⋊C4—44no—
292C11×C22⋊C4—44no—
293C22⋊Dic11—44no—
294C22⋊Dic11—44no—
295C22⋊Dic11—44no—
296C22⋊Dic11—44no—
297C22⋊Dic11—44no—
298C22⋊Dic11—44no—
299C22⋊Dic11—44no—
300C4⋊Dic11—44no—
301C4×Dic11—44no—
302C2×#388—111no—
303C2×#386—111no—
304C2×#386D1111yescharacteristic
305#1443—111no—
306#1443—111no—
307#1442—111no—
308#1440—111no—
309#1439—111no—
310#1438—111no—
311#1437—111no—
312#1434—111no—
313C22⋊#95—111no—
314C22⋊#95—111no—
315C22⋊#95—111no—
316C22⋊#95—111no—
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—22no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—22no—
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×C11—41no—
383C23×C11—41no—
384C23×C11—41no—
385C23×C11#11714yes—
386C23×C11C4×D414yes—
387C23×C11C23×C411yescharacteristic
388C23×C11C22×D411yescharacteristic
389C23×C11C2×#4111yescharacteristic
390C23×C11C2×#4111yescharacteristic
391C23×C11C2×#4111yescharacteristic
392C23×C11C2×#4111yescharacteristic
393C23×C11C2×#4111yescharacteristic
394C23×C11H(5,𝔽2)11yescharacteristic
395C23×C11H(5,𝔽2)11yescharacteristic
396C23×C11H(5,𝔽2)11yescharacteristic
397C23×C11H(5,𝔽2)11yescharacteristic
398C23×C11H(5,𝔽2)11yescharacteristic
399C23×C11H(5,𝔽2)11yescharacteristic
400C23×C11H(5,𝔽2)11yescharacteristic
401C23×C112−1+411yescharacteristic
402D4×C11—416no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—416no—
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×C4×C11—41no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
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—416no—
452C2×Dic11—41no—
453C2×Dic11—41no—
454C2×Dic11—41no—
455C2×Dic11—41no—
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—41no—
491C2×Dic11—41no—
492C2×Dic11—41no—
493C2×Dic11—41no—
494C2×Dic11—41no—
495C2×Dic11—41no—
496C23×D4C2×D1111yescharacteristic
497C24×C4—111no—
498C24×C4C2×D1111yescharacteristic
499C22×C4⋊C4—111no—
500C22×C22⋊C4—111no—
501C22×C22⋊C4—111no—
502C22×C22⋊C4—111no—
503C22×C22⋊C4—111no—
504C22×C22⋊C4—111no—
505C22×C22⋊C4—111no—
506C22×C22⋊C4—111no—
507C22×C22⋊C4C2×D1111yescharacteristic
508C22×C22⋊C4C2×D1111yescharacteristic
509C22×C22⋊C4C2×D1111yescharacteristic
510C22×C42—111no—
511#388—224no—
512#386—224no—
513#386Dic1118yescomplemented
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×#95—111no—
528C2×#95—111no—
529C2×#95—111no—
530C2×#95—111no—
531C2×#95—111no—
532C2×#95C2×D1111yescharacteristic
533C2×#95C2×D1111yescharacteristic
534C22×C11—24no—
535C22×C11—24no—
536C22×C11—24no—
537C22×C11—24no—
538C22×C11—24no—
539C22×C11—24no—
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—42no—
552C22×C11—42no—
553C22×C11—42no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—42no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11—42no—
560C22×C11—42no—
561C22×C11—42no—
562C22×C11—42no—
563C22×C11—42no—
564C22×C11C2×#11711yescharacteristic
565C22×C11C2×C4×D411yescharacteristic
566C22×C11C4×#4111yescharacteristic
567C22×C11#51811yescharacteristic
568C22×C11#51811yescharacteristic
569C22×C11#51811yescharacteristic
570C22×C11#52011yescharacteristic
571C22×C11#53411yescharacteristic
572C22×C11#53711yescharacteristic
573C22×C11#53811yescharacteristic
574C22×C11#53811yescharacteristic
575C22×C11#53811yescharacteristic
576C22×C11#53811yescharacteristic
577C22×C11#53911yescharacteristic
578C22×C11#53911yescharacteristic
579C22×C11#53911yescharacteristic
580C22×C11#53911yescharacteristic
581C22×C11#54011yescharacteristic
582C22×C11#54211yescharacteristic
583C22×C11#54611yescharacteristic
584C22×C11#54611yescharacteristic
585C22×C11#54611yescharacteristic
586C22×C11#54611yescharacteristic
587C22×C11#55111yescharacteristic
588C22×C11#55111yescharacteristic
589C22×C11#55111yescharacteristic
590C22×C11#55111yescharacteristic
591C22×C11#55311yescharacteristic
592C22×C11#55311yescharacteristic
593C22×C11#55311yescharacteristic
594C22×C11#55311yescharacteristic
595C22×C11#56011yescharacteristic
596C22×C11#56011yescharacteristic
597C22×C11#56011yescharacteristic
598C22×C11H(3,𝔽4)11yescharacteristic
599C4×C11—42no—
600C4×C11—42no—
601C4×C11—42no—
602C4×C11—42no—
603C4×C11—42no—
604Dic11—42no—
605Dic11—42no—
606Dic11—42no—
607Dic11—42no—
608Dic11—81no—
609Dic11—81no—
610Dic11—81no—
611Dic11—81no—
612C25C22×D1111yescharacteristic
613C25C22×D1111yescharacteristic
614C22×D4—22no—
615C22×D4—22no—
616C22×D4—22no—
617C22×D4—22no—
618C22×D4—41no—
619C22×D4—41no—
620C22×D4C2×Dic1114yes—
621C23×C4—41no—
622C23×C4—41no—
623C23×C4—41no—
624C23×C4—41no—
625C23×C4—41no—
626C23×C4—41no—
627C23×C4—111no—
628C23×C4—111no—
629C23×C4—111no—
630C23×C4—111no—
631C23×C4—111no—
632C23×C4—111no—
633C23×C4—111no—
634C23×C4—111no—
635C23×C4—222no—
636C23×C4—222no—
637C23×C4—222no—
638C23×C4—441no—
639C23×C4—441no—
640C23×C4—441no—
641C23×C4—441no—
642C23×C4C2×Dic1114yescomplemented
643C23×C4C22×D1111yescharacteristic
644C23×C4C22×D1111yescharacteristic
645C23×C4C22×D1111yescharacteristic
646C23×C4C22×D1111yescharacteristic
647C23×C4C22×D1111yescharacteristic
648C2×C4⋊C4—222no—
649C2×C4⋊C4—441no—
650C2×C4⋊C4—441no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—41no—
654C2×C22⋊C4—41no—
655C2×C22⋊C4—41no—
656C2×C22⋊C4—41no—
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—222no—
666C2×C22⋊C4—222no—
667C2×C22⋊C4—222no—
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×C22⋊C4—441no—
676C2×C22⋊C4—441no—
677C2×C22⋊C4—441no—
678C2×C22⋊C4C2×Dic1114yes—
679C2×C22⋊C4C2×Dic1114yes—
680C2×C22⋊C4C2×Dic1114yescomplemented
681C2×C42—222no—
682C2×C42—222no—
683C2×C42—441no—
684#95—222no—
685#95—222no—
686#95—222no—
687#95—222no—
688#95—222no—
689#95—441no—
690#95—441no—
691#95—441no—
692#95—441no—
693#95—441no—
694#95—441no—
695#95—441no—
696#95—441no—
697#95—441no—
698#95—441no—
699#95—441no—
700#95—441no—
701#95—441no—
702#95C2×Dic1114yescomplemented
703#95C2×Dic1114yescomplemented
704C2×C11—44no—
705C2×C11—44no—
706C2×C11#231811yescharacteristic
707C2×C11#232511yescharacteristic
708C2×C11#233511yescharacteristic
709C2×C11#234211yescharacteristic
710C2×C11#235311yescharacteristic
711C2×C11#236411yescharacteristic
712C2×C11#237511yescharacteristic
713C2×C11#268411yescharacteristic
714C2×C11#268811yescharacteristic
715C2×C11#269111yescharacteristic
716C2×C11#269311yescharacteristic
717C2×C11#274611yescharacteristic
718C2×C11#274911yescharacteristic
719C2×C11#277811yescharacteristic
720C2×C11#278211yescharacteristic
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—
742C24—21no—
743C24—21no—
744C24—21no—
745C24#433912yes—
746C24#433912yes—
747C24D4×D1112yes—
748C24#434112yes—
749C24C22×Dic1112yes—
750C24C22×Dic1112yes—
751C24C23×D1111yescharacteristic
752C2×D4—28no—
753C2×D4—28no—
754C2×D4—44no—
755C2×D4—44no—
756C2×D4—44no—
757C2×D4—44no—
758C2×D4—44no—
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—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—112no—
797C22×C4—112no—
798C22×C4—112no—
799C22×C4—112no—
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—221no—
844C22×C4—221no—
845C22×C4—221no—
846C22×C4—221no—
847C22×C4—221no—
848C22×C4—221no—
849C22×C4—221no—
850C22×C4—221no—
851C22×C4—221no—
852C22×C4—444no—
853C22×C4—444no—
854C22×C4—444no—
855C22×C4—444no—
856C22×C4—444no—
857C22×C4—444no—
858C22×C4—444no—
859C22×C4C22×Dic1112yes—
860C22×C4C22×Dic1112yes—
861C22×C4C22×Dic1112yes—
862C22×C4C22×Dic1112yes—
863C22×C4C22×Dic1112yes—
864C4⋊C4—444no—
865C22⋊C4—28no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C22⋊C4—444no—
869C22⋊C4—444no—
870C22⋊C4—444no—
871C22⋊C4—444no—
872C22⋊C4—444no—
873C22⋊C4—444no—
874C22⋊C4—444no—
875C42—444no—
876C11#1442711yescharacteristic, complemented, Sylow
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—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
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—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23#6697914yes—
946C23D4×Dic1114yes—
947C23C2×#433911yescharacteristic
948C23C2×#433911yescharacteristic
949C23C2×D4×D1111yescharacteristic
950C23C2×#434111yescharacteristic
951C23#6703711yescharacteristic
952C23#6703711yescharacteristic
953C23#6703711yescharacteristic
954C23#6703711yescharacteristic
955C23#6703711yescharacteristic
956C23#6703711yescharacteristic
957C23#41×D1111yescharacteristic
958C23#41×D1111yescharacteristic
959C23#6704211yescharacteristic
960C23#6704311yescharacteristic
961C23C23×Dic1111yescharacteristic
962D4—416no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—416no—
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—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
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—
1046C2×C4—441no—
1047C2×C4—441no—
1048C2×C4—441no—
1049C2×C4—441no—
1050C2×C4—441no—
1051C2×C4—441no—
1052C2×C4—441no—
1053C2×C4—441no—
1054C2×C4—441no—
1055C2×C4—441no—
1056C22—24no—
1057C22—24no—
1058C22—24no—
1059C22—24no—
1060C22—24no—
1061C22—24no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22#1062302111yescharacteristic
1087C22#1062302111yescharacteristic
1088C22#1062302611yescharacteristic
1089C22#1062302611yescharacteristic
1090C22#1062307111yescharacteristic
1091C22#1062307111yescharacteristic
1092C22#1062308711yescharacteristic
1093C22#1062308711yescharacteristic
1094C22#1062309111yescharacteristic
1095C22#1062309111yescharacteristic
1096C22#1062309511yescharacteristic
1097C22#1062309511yescharacteristic
1098C22#1062312511yescharacteristic
1099C22#1062312611yescharacteristic
1100C22#1062312611yescharacteristic
1101C22#1062312611yescharacteristic
1102C22#1062312811yescharacteristic
1103C22#1062313211yescharacteristic
1104C22#1062313211yescharacteristic
1105C22#1062313311yescharacteristic
1106C22#1062313611yescharacteristic
1107C22#1062314111yescharacteristic
1108C22#1062314111yescharacteristic
1109C22#1062314811yescharacteristic
1110C22#1062318811yescharacteristic
1111C22#1062319111yescharacteristic
1112C22#1062319311yescharacteristic
1113C22#1062319411yescharacteristic
1114C22C2×#6697911yescharacteristic
1115C22C2×D4×Dic1111yescharacteristic
1116C22#1062332911yescharacteristic
1117C22#1062332911yescharacteristic
1118C22#1062332911yescharacteristic
1119C22#41×Dic1111yescharacteristic
1120C22#1062335811yescharacteristic
1121C4—42no—
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4—442no—
1127C4—442no—
1128C4—442no—
1129C4—442no—
1130C4—881no—
1131C4—881no—
1132C4—881no—
1133C4—881no—
1134C2—44no—
1135C2—44no—
1136C2#1307124911yescharacteristic
1137C2#1307132111yescharacteristic
1138C2#1307141011yescharacteristic
1139C2#1307146511yescharacteristic
1140C2#1307155611yescharacteristic
1141C2#1307166811yescharacteristic
1142C2#1307175711yescharacteristic
1143C2#1307499311yescharacteristic
1144C2#1307504911yescharacteristic
1145C2#1307509411yescharacteristic
1146C2#1307512211yescharacteristic
1147C2#1307579811yescharacteristic
1148C2#1307583311yescharacteristic
1149C2#1307623511yescharacteristic
1150C2#1307628911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#386C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#386D11
hypocenterC11#14427
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C2×#10622564C2semidirect
3. #13066878C2semidirect
4. #13066878C2semidirect
5. #13066873C2semidirect
6. #13066865C2semidirect
7. #13066861C2semidirect
9. #13066853C2semidirect
10. #13066841C2semidirect
11. #13066839C2semidirect
12. #13066839C2semidirect
13. #13066838C2semidirect
14. #13066838C2semidirect
31. C11×#386C4semidirect
69. C23×C4×C11C2×C4semidirect
98. C2×C11×C22⋊C4C2×C4semidirect
126. C11×#95C2×C4semidirect
127. C11×#95C2×C4semidirect
513. #386Dic11semidirect
642. C23×C4C2×Dic11semidirect
680. C2×C22⋊C4C2×Dic11semidirect
702. #95C2×Dic11semidirect
703. #95C2×Dic11semidirect
876. C11#14427semidirect

Maximal subgroups

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

subgroupindex
C2×#106225642
C2×#106228332
#130668782
#130668732
#130668652
#130668612
#130668572
#130668532
#130668412
#130668392
#130668382
C2×C11×#3862
#1442711