Finite Group Databasebeta

← #14682018

Subgroups — #14682018

Order 2816.

1766 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×#10622557C211yesmaximal, characteristic, complemented
2C2×#10622833C211yesmaximal, characteristic
3#13066875C211yesmaximal, characteristic, complemented
4#13066863C211yesmaximal, characteristic, complemented
5#13066863C211yesmaximal, characteristic, complemented
6#13066863C211yesmaximal, characteristic, complemented
7#13066859C211yesmaximal, characteristic, complemented
8#13066857C211yesmaximal, characteristic
9#13066853C211yesmaximal, characteristic, complemented
10#13066849C211yesmaximal, characteristic, complemented
11#13066848C211yesmaximal, characteristic, complemented
12#13066843C211yesmaximal, characteristic, complemented
13#13066838C211yesmaximal, characteristic, complemented
14#13066838C211yesmaximal, characteristic, complemented
15C2×C11×#390C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C11×#390—24no—
34#10622833C418yescomplemented
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#10622557—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×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×Dic11—41no—
69C23×Dic11—41no—
70C23×Dic11—41no—
71C23×Dic11—41no—
72C23×Dic11—41no—
73C23×Dic11—41no—
74C23×Dic11C2×C414yes—
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—41no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—41no—
92C2×C11×C22⋊C4—41no—
93C2×C11×C22⋊C4—41no—
94C2×C11×C22⋊C4—41no—
95C2×C11×C22⋊C4—41no—
96C2×C11×C22⋊C4—41no—
97C2×C11×C22⋊C4D414yes—
98C2×C42×C11—22no—
99C2×C42×C11—22no—
100C2×C42×C11—41no—
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—41no—
108C2×C22⋊Dic11—41no—
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⋊Dic11C2×C414yes—
120C2×C22⋊Dic11C2×C414yes—
121C2×C22⋊Dic11C2×C414yes—
122C2×Dic11⋊C4—22no—
123C2×Dic11⋊C4—22no—
124C2×Dic11⋊C4—41no—
125C2×C4×Dic11—22no—
126C2×C4×Dic11—41no—
127C2×C4×Dic11—41no—
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⋊#95C2×C414yes—
145C11⋊#95C2×C414yes—
146#14428—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—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×C11C22×C412yes—
215C22×C4×C11C2×D412yes—
216C22×C4×C11C2×D412yes—
217C22×C4×C11#4112yes—
218C22×C4×C11#4112yes—
219C22×C4×C11#4112yes—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×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—44no—
272C22×Dic11—44no—
273C22×Dic11—44no—
274C22×Dic11—44no—
275C22×Dic11—44no—
276C22×Dic11—44no—
277C22×Dic11—44no—
278C22×Dic11C22×C412yes—
279C22×Dic11C22×C412yes—
280C22×Dic11C22×C412yes—
281C22×Dic11C22×C412yes—
282C22×Dic11#4112yes—
283C11×C4⋊C4—44no—
284C11×C22⋊C4—44no—
285C11×C22⋊C4—44no—
286C11×C22⋊C4—44no—
287C11×C22⋊C4—44no—
288C42×C11—44no—
289C22⋊Dic11—28no—
290C22⋊Dic11—44no—
291C22⋊Dic11—44no—
292C22⋊Dic11—44no—
293C22⋊Dic11—44no—
294C22⋊Dic11—44no—
295C22⋊Dic11—44no—
296Dic11⋊C4—44no—
297C4×Dic11—44no—
298C2×#390D1111yescharacteristic
299C2×#388—111no—
300C2×#386—111no—
301#1442—111no—
302#1440—111no—
303#1440—111no—
304#1440—111no—
305#1439—111no—
306#1438—111no—
307#1437—111no—
308#1436—111no—
309#1436—111no—
310#1434—111no—
311C22⋊#95—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—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
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#11714yes—
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—416no—
450C2×Dic11—41no—
451C2×Dic11—41no—
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—
491C23×D4C2×D1111yescharacteristic
492C24×C4—111no—
493C22×C4⋊C4—111no—
494C22×C4⋊C4C2×D1111yescharacteristic
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×C42C2×D1111yescharacteristic
508#390—24no—
509#388—224no—
510#386—118no—
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×#95—111no—
528C2×#95—111no—
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×#11711yescharacteristic
560C22×C11C2×C4×D411yescharacteristic
561C22×C11C4×#4111yescharacteristic
562C22×C11#51811yescharacteristic
563C22×C11#51811yescharacteristic
564C22×C11#51811yescharacteristic
565C22×C11#52011yescharacteristic
566C22×C11#53411yescharacteristic
567C22×C11#53711yescharacteristic
568C22×C11#53811yescharacteristic
569C22×C11#53811yescharacteristic
570C22×C11#53911yescharacteristic
571C22×C11#53911yescharacteristic
572C22×C11#54011yescharacteristic
573C22×C11#54011yescharacteristic
574C22×C11#54011yescharacteristic
575C22×C11#54211yescharacteristic
576C22×C11#54211yescharacteristic
577C22×C11#54211yescharacteristic
578C22×C11#54611yescharacteristic
579C22×C11#54611yescharacteristic
580C22×C11#54611yescharacteristic
581C22×C11#54611yescharacteristic
582C22×C11#55111yescharacteristic
583C22×C11#55111yescharacteristic
584C22×C11#55311yescharacteristic
585C22×C11#55311yescharacteristic
586C22×C11#55311yescharacteristic
587C22×C11#55311yescharacteristic
588C22×C11#55911yescharacteristic
589C22×C11#55911yescharacteristic
590C22×C11#56011yescharacteristic
591C22×C11#56011yescharacteristic
592C22×C11#56011yescharacteristic
593C22×C11H(3,𝔽4)11yescharacteristic
594C4×C11—24no—
595C4×C11—42no—
596C4×C11—42no—
597C4×C11—42no—
598C4×C11—81no—
599Dic11—42no—
600Dic11—42no—
601Dic11—42no—
602Dic11—42no—
603Dic11—42no—
604Dic11—81no—
605Dic11—81no—
606Dic11—81no—
607C25C22×D1111yescharacteristic
608C25C22×D1111yescharacteristic
609C22×D4—22no—
610C22×D4—22no—
611C22×D4—22no—
612C22×D4—22no—
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—114no—
622C23×C4—111no—
623C23×C4—111no—
624C23×C4—111no—
625C23×C4—441no—
626C23×C4—441no—
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—22no—
637C2×C4⋊C4—22no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4—222no—
640C2×C4⋊C4—222no—
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—41no—
648C2×C22⋊C4—41no—
649C2×C22⋊C4—41no—
650C2×C22⋊C4—41no—
651C2×C22⋊C4—41no—
652C2×C22⋊C4—41no—
653C2×C22⋊C4—114no—
654C2×C22⋊C4—114no—
655C2×C22⋊C4—114no—
656C2×C22⋊C4—222no—
657C2×C22⋊C4—222no—
658C2×C22⋊C4—222no—
659C2×C22⋊C4—222no—
660C2×C22⋊C4—222no—
661C2×C22⋊C4—222no—
662C2×C22⋊C4—441no—
663C2×C22⋊C4—441no—
664C2×C22⋊C4—441no—
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⋊C4C22⋊D1114yes—
675C2×C42—22no—
676C2×C42—22no—
677C2×C42—41no—
678C2×C42—222no—
679C2×C42—441no—
680C2×C42—441no—
681#95—114no—
682#95—114no—
683#95—222no—
684#95—222no—
685#95—222no—
686#95—222no—
687#95—222no—
688#95—441no—
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—
699C2×C11—44no—
700C2×C11—82no—
701C2×C11#231911yescharacteristic
702C2×C11#232511yescharacteristic
703C2×C11#233511yescharacteristic
704C2×C11#234211yescharacteristic
705C2×C11#235711yescharacteristic
706C2×C11#236411yescharacteristic
707C2×C11#237511yescharacteristic
708C2×C11#268811yescharacteristic
709C2×C11#269111yescharacteristic
710C2×C11#270911yescharacteristic
711C2×C11#271211yescharacteristic
712C2×C11#275311yescharacteristic
713C2×C11#275711yescharacteristic
714C2×C11#279611yescharacteristic
715C2×C11#279711yescharacteristic
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—
744C24#433912yes—
745C24C2×C22⋊D1112yes—
746C24C23×D1111yescharacteristic
747C2×D4—28no—
748C2×D4—28no—
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—112no—
784C22×C4—112no—
785C22×C4—112no—
786C22×C4—112no—
787C22×C4—112no—
788C22×C4—221no—
789C22×C4—221no—
790C22×C4—221no—
791C22×C4—221no—
792C22×C4—221no—
793C22×C4—221no—
794C22×C4—221no—
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—444no—
840C22×C4—444no—
841C22×C4—444no—
842C22×C4—444no—
843C22×C4—444no—
844C22×C4—444no—
845C22×C4—444no—
846C22×C4C2×C4×D1112yes—
847C22×C4#434112yes—
848C22×C4#434112yes—
849C22×C4#434112yes—
850C22×C4C2×C22⋊D1112yes—
851C22×C4C2×C22⋊D1112yes—
852C4⋊C4—44no—
853C4⋊C4—444no—
854C22⋊C4—44no—
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—44no—
866C42—444no—
867C11#1442811yescharacteristic, 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—
937C23C4×C22⋊D1114yes—
938C23C22×C4×D1111yescharacteristic
939C23C2×#433911yescharacteristic
940C23C2×#434111yescharacteristic
941C23C2×#434111yescharacteristic
942C23C2×#434111yescharacteristic
943C23#6703711yescharacteristic
944C23#6703711yescharacteristic
945C23#6703711yescharacteristic
946C23#6703711yescharacteristic
947C23#6703711yescharacteristic
948C23#41×D1111yescharacteristic
949C23#6704211yescharacteristic
950C23#6704211yescharacteristic
951C23#6704311yescharacteristic
952C23C22×C22⋊D1111yescharacteristic
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—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
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—222no—
989C2×C4—222no—
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—4416no—
1004C2×C4—441no—
1005C2×C4—441no—
1006C2×C4—441no—
1007C2×C4—441no—
1008C2×C4—441no—
1009C2×C4—441no—
1010C2×C4—441no—
1011C2×C4—441no—
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#6693014yes—
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×#6693011yescharacteristic
1077C22#1062301711yescharacteristic
1078C22#1062302611yescharacteristic
1079C22#1062302611yescharacteristic
1080C22C4×#434111yescharacteristic
1081C22#1062307111yescharacteristic
1082C22#1062307611yescharacteristic
1083C22#1062307611yescharacteristic
1084C22#1062307711yescharacteristic
1085C22#1062309111yescharacteristic
1086C22#1062309511yescharacteristic
1087C22#1062309611yescharacteristic
1088C22#1062313311yescharacteristic
1089C22#1062313411yescharacteristic
1090C22#1062314411yescharacteristic
1091C22#1062314511yescharacteristic
1092C22#1062314911yescharacteristic
1093C22#1062315011yescharacteristic
1094C22#1062315111yescharacteristic
1095C22#1062315111yescharacteristic
1096C22#1062320011yescharacteristic
1097C22#1062321211yescharacteristic
1098C22#1062321311yescharacteristic
1099C22#1062321411yescharacteristic
1100C22#1062324411yescharacteristic
1101C22#1062325011yescharacteristic
1102C22#1062325011yescharacteristic
1103C22#1062325111yescharacteristic
1104C22C2×C4×C22⋊D1111yescharacteristic
1105C22#1062333511yescharacteristic
1106C22#1062333711yescharacteristic
1107C22#1062333711yescharacteristic
1108C22#1062333711yescharacteristic
1109C22#1062336011yescharacteristic
1110C22#1062336411yescharacteristic
1111C4—24no—
1112C4—42no—
1113C4—42no—
1114C4—42no—
1115C4—81no—
1116C4—442no—
1117C4—442no—
1118C4—442no—
1119C4—442no—
1120C4—442no—
1121C4—881no—
1122C4—881no—
1123C4—881no—
1124C2—44no—
1125C2—82no—
1126C2#1307125311yescharacteristic
1127C2#1307131411yescharacteristic
1128C2#1307140311yescharacteristic
1129C2#1307146111yescharacteristic
1130C2#1307158811yescharacteristic
1131C2#1307166111yescharacteristic
1132C2#1307175311yescharacteristic
1133C2#1307504811yescharacteristic
1134C2#1307509311yescharacteristic
1135C2#1307534311yescharacteristic
1136C2#1307538211yescharacteristic
1137C2#1307589311yescharacteristic
1138C2#1307595311yescharacteristic
1139C2#1307645211yescharacteristic
1140C2#1307646711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#390C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#390D11
hypocenterC11#14428
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C2×#10622557C2semidirect
3. #13066875C2semidirect
4. #13066863C2semidirect
5. #13066863C2semidirect
6. #13066863C2semidirect
7. #13066859C2semidirect
9. #13066853C2semidirect
10. #13066849C2semidirect
11. #13066848C2semidirect
12. #13066843C2semidirect
13. #13066838C2semidirect
14. #13066838C2semidirect
34. #10622833C4semidirect
867. C11#14428semidirect

Maximal subgroups

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

subgroupindex
C2×#106225572
C2×#106228332
#130668752
#130668632
#130668592
#130668572
#130668532
#130668492
#130668482
#130668432
#130668382
C2×C11×#3902
#1442811