Finite Group Databasebeta

← #14684053

Subgroups — #14684053

Order 2816.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622835C211yesmaximal, characteristic
2C2×#10622558C211yesmaximal, characteristic, complemented
3C2×#10622557C211yesmaximal, characteristic, complemented
4#13066867C211yesmaximal, characteristic, complemented
5#13066859C211yesmaximal, characteristic, complemented
6#13066859C211yesmaximal, characteristic, complemented
7#13066857C211yesmaximal, characteristic
8#13066853C211yesmaximal, characteristic, complemented
9#13066853C211yesmaximal, characteristic, complemented
10#13066853C211yesmaximal, characteristic, complemented
11#13066853C211yesmaximal, characteristic, complemented
12Dic11⋊#95C211yesmaximal, characteristic, complemented
13#13066842C211yesmaximal, characteristic, complemented
14#13066840C211yesmaximal, characteristic, complemented
15C11×#1438C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37#10622835C418yescomplemented
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#10622558—24no—
53#10622557—24no—
54C25×C11C2311yescharacteristic
55C25×C11C2311yescharacteristic
56C22×D4×C11—41no—
57C22×D4×C11—41no—
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×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—41no—
83C2×C11×C22⋊C4—41no—
84C2×C11×C22⋊C4—41no—
85C2×C11×C22⋊C4—41no—
86C2×C11×C22⋊C4—41no—
87C2×C11×C22⋊C4—41no—
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11—41no—
99C2×C22⋊Dic11—41no—
100C2×C22⋊Dic11—41no—
101C2×C22⋊Dic11—41no—
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⋊Dic11C2×C414yes—
109C2×C22⋊Dic11C2×C414yes—
110C2×C22⋊Dic11C2×C414yes—
111C2×C22⋊Dic11C2×C414yes—
112C2×Dic11⋊C4—41no—
113C2×Dic11⋊C4—41no—
114C2×Dic11⋊C4—41no—
115C2×Dic11⋊C4—41no—
116C2×Dic11⋊C4—41no—
117C2×Dic11⋊C4—41no—
118C2×Dic11⋊C4—41no—
119C2×Dic11⋊C4C2×C414yes—
120C2×Dic11⋊C4D414yescomplemented
121C2×C4×Dic11—22no—
122C2×C4×Dic11—22no—
123C2×C4×Dic11—22no—
124C2×C4×Dic11—22no—
125C2×C4×Dic11—22no—
126C2×C4×Dic11—41no—
127C2×C4×Dic11—41no—
128C2×C4×Dic11—41no—
129C2×C4×Dic11—41no—
130C11×#95—41no—
131C11×#95—41no—
132C11⋊#95—22no—
133C11⋊#95—22no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—41no—
139C11⋊#95—41no—
140C11⋊#95—41no—
141C11⋊#95—41no—
142C11⋊#95—41no—
143C11⋊#95—41no—
144C11⋊#95—41no—
145C11⋊#95C2×C414yes—
146#14589—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×C11—21no—
174C24×C11—21no—
175C24×C11C22×C412yes—
176C24×C11C22×C412yes—
177C24×C11C2411yescharacteristic
178C2×D4×C11—44no—
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×C11C22×C412yes—
217C22×C4×C11C2×D412yes—
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×Dic11C22×C412yes—
268C22×Dic11C22×C412yes—
269C22×Dic11C22×C412yes—
270C22×Dic11C22×C412yes—
271C22×Dic11C2×D412yes—
272C22×Dic11C2×D412yes—
273C22×Dic11#4112yes—
274C22×Dic11#4112yes—
275C22×Dic11#4112yes—
276C11×C22⋊C4—44no—
277C11×C22⋊C4—44no—
278C11×C22⋊C4—44no—
279C11×C22⋊C4—44no—
280C22⋊Dic11—28no—
281C22⋊Dic11—28no—
282C22⋊Dic11—44no—
283C22⋊Dic11—44no—
284C22⋊Dic11—44no—
285C22⋊Dic11—44no—
286C22⋊Dic11—44no—
287C22⋊Dic11—44no—
288Dic11⋊C4—44no—
289Dic11⋊C4—44no—
290Dic11⋊C4—44no—
291C4×Dic11—44no—
292C4×Dic11—44no—
293C4×Dic11—44no—
294C2×#394—111no—
295C2×#388—111no—
296C2×#388—111no—
297#1441—111no—
298#1439—111no—
299#1439—111no—
300#1438—111no—
301#1438D1111yescharacteristic
302#1437—111no—
303#1437—111no—
304#1437—111no—
305#1437—111no—
306C4⋊#95—111no—
307#1434—111no—
308#1434—111no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
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—41no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—41no—
337C23×C11—41no—
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×C11C23×C411yescharacteristic
380C23×C11C22×D411yescharacteristic
381C23×C11C2×#4111yescharacteristic
382C23×C11C2×#4111yescharacteristic
383C23×C11C2×#4111yescharacteristic
384C23×C11C2×#4111yescharacteristic
385C23×C11C2×#4111yescharacteristic
386C23×C11H(5,𝔽2)11yescharacteristic
387C23×C11H(5,𝔽2)11yescharacteristic
388C23×C11H(5,𝔽2)11yescharacteristic
389C23×C11H(5,𝔽2)11yescharacteristic
390C23×C11H(5,𝔽2)11yescharacteristic
391C23×C11H(5,𝔽2)11yescharacteristic
392C23×C11H(5,𝔽2)11yescharacteristic
393C23×C112−1+411yescharacteristic
394D4×C11—416no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
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—41no—
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×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
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—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×Dic11C4×D414yes—
486C23×D4C2×D1111yescharacteristic
487C22×C4⋊C4—111no—
488C22×C4⋊C4—111no—
489C22×C4⋊C4—111no—
490C22×C22⋊C4—111no—
491C22×C22⋊C4—111no—
492C22×C22⋊C4—111no—
493C22×C22⋊C4—111no—
494C22×C22⋊C4—111no—
495C22×C22⋊C4—111no—
496C22×C22⋊C4—111no—
497C22×C22⋊C4—111no—
498C22×C22⋊C4C2×D1111yescharacteristic
499C22×C22⋊C4C2×D1111yescharacteristic
500C22×C22⋊C4C2×D1111yescharacteristic
501C22×C22⋊C4C2×D1111yescharacteristic
502C22×C42—111no—
503C22×C42—111no—
504C22×C42—111no—
505#394—118no—
506#388—224no—
507#388—224no—
508C2×#95—111no—
509C2×#95—111no—
510C2×#95—111no—
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×#95C2×D1111yescharacteristic
523C2×#95C2×D1111yescharacteristic
524C22×C11—42no—
525C22×C11—42no—
526C22×C11—42no—
527C22×C11—42no—
528C22×C11—42no—
529C22×C11—42no—
530C22×C11—42no—
531C22×C11—42no—
532C22×C11—42no—
533C22×C11—42no—
534C22×C11—42no—
535C22×C11—42no—
536C22×C11—42no—
537C22×C11—42no—
538C22×C11—81no—
539C22×C11—81no—
540C22×C11—81no—
541C22×C11—81no—
542C22×C11—81no—
543C22×C11—81no—
544C22×C11—81no—
545C22×C11—81no—
546C22×C11—81no—
547C22×C11—81no—
548C22×C11—81no—
549C22×C11—81no—
550C22×C11—81no—
551C22×C11—81no—
552C22×C11—81no—
553C22×C11—81no—
554C22×C11C2×C4×D411yescharacteristic
555C22×C11C4×#4111yescharacteristic
556C22×C11C4×#4111yescharacteristic
557C22×C11#51811yescharacteristic
558C22×C11#51811yescharacteristic
559C22×C11#51811yescharacteristic
560C22×C11#52011yescharacteristic
561C22×C11#53411yescharacteristic
562C22×C11#53711yescharacteristic
563C22×C11#53811yescharacteristic
564C22×C11#53811yescharacteristic
565C22×C11#53811yescharacteristic
566C22×C11#53911yescharacteristic
567C22×C11#53911yescharacteristic
568C22×C11#53911yescharacteristic
569C22×C11#54011yescharacteristic
570C22×C11#54011yescharacteristic
571C22×C11#54211yescharacteristic
572C22×C11#54211yescharacteristic
573C22×C11#54611yescharacteristic
574C22×C11#54611yescharacteristic
575C22×C11#55011yescharacteristic
576C22×C11#55011yescharacteristic
577C22×C11#55111yescharacteristic
578C22×C11#55111yescharacteristic
579C22×C11#55311yescharacteristic
580C22×C11#55311yescharacteristic
581C22×C11#55511yescharacteristic
582C22×C11#55511yescharacteristic
583C22×C11#55511yescharacteristic
584C22×C11#55511yescharacteristic
585C22×C11#56011yescharacteristic
586C22×C11#56011yescharacteristic
587C22×C11#56011yescharacteristic
588C22×C11H(3,𝔽4)11yescharacteristic
589C4×C11—42no—
590C4×C11—42no—
591C4×C11—42no—
592C4×C11—42no—
593C4×C11—81no—
594Dic11—24no—
595Dic11—42no—
596Dic11—42no—
597Dic11—42no—
598Dic11—42no—
599Dic11—42no—
600Dic11—42no—
601Dic11—81no—
602C25C22×D1111yescharacteristic
603C25C22×D1111yescharacteristic
604C22×D4—41no—
605C22×D4—41no—
606C22×D4—41no—
607C22×D4—41no—
608C22×D4—41no—
609C22×D4—41no—
610C22×D4C4×D1114yes—
611C23×C4—111no—
612C23×C4—111no—
613C23×C4—111no—
614C23×C4—111no—
615C23×C4—111no—
616C23×C4—111no—
617C23×C4—111no—
618C23×C4—111no—
619C23×C4C22×D1111yescharacteristic
620C23×C4C22×D1111yescharacteristic
621C23×C4C22×D1111yescharacteristic
622C23×C4C22×D1111yescharacteristic
623C23×C4C22×D1111yescharacteristic
624C2×C4⋊C4—114no—
625C2×C4⋊C4—114no—
626C2×C4⋊C4—441no—
627C2×C4⋊C4—441no—
628C2×C4⋊C4—441no—
629C2×C4⋊C4—441no—
630C2×C4⋊C4—441no—
631C2×C4⋊C4—441no—
632C2×C4⋊C4—441no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—41no—
640C2×C22⋊C4—41no—
641C2×C22⋊C4—41no—
642C2×C22⋊C4—41no—
643C2×C22⋊C4—41no—
644C2×C22⋊C4—41no—
645C2×C22⋊C4—114no—
646C2×C22⋊C4—114no—
647C2×C22⋊C4—114no—
648C2×C22⋊C4—114no—
649C2×C22⋊C4—222no—
650C2×C22⋊C4—222no—
651C2×C22⋊C4—222no—
652C2×C22⋊C4—222no—
653C2×C22⋊C4—222no—
654C2×C22⋊C4—222no—
655C2×C22⋊C4—222no—
656C2×C22⋊C4—222no—
657C2×C22⋊C4—222no—
658C2×C22⋊C4—222no—
659C2×C22⋊C4—441no—
660C2×C22⋊C4—441no—
661C2×C22⋊C4—441no—
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×C42—222no—
670C2×C42—222no—
671C2×C42—222no—
672C2×C42—222no—
673C2×C42—222no—
674C2×C42—441no—
675C2×C42—441no—
676C2×C42—441no—
677C2×C42—441no—
678#95—41no—
679#95—41no—
680#95—114no—
681#95—222no—
682#95—222no—
683#95—222no—
684#95—222no—
685#95—222no—
686#95—222no—
687#95—441no—
688#95—441no—
689#95—441no—
690#95—441no—
691#95—441no—
692#95—441no—
693#95—441no—
694C2×C11—82no—
695C2×C11—82no—
696C2×C11#232511yescharacteristic
697C2×C11#233511yescharacteristic
698C2×C11#233511yescharacteristic
699C2×C11#236311yescharacteristic
700C2×C11#236311yescharacteristic
701C2×C11#237211yescharacteristic
702C2×C11#237511yescharacteristic
703C2×C11#269911yescharacteristic
704C2×C11#270511yescharacteristic
705C2×C11#270511yescharacteristic
706C2×C11#273311yescharacteristic
707C2×C11#275611yescharacteristic
708C2×C11#275611yescharacteristic
709C2×C11#278511yescharacteristic
710C2×C11#279511yescharacteristic
711C24—21no—
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
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—
739C24C2×C4×D1112yes—
740C24C2×C4×D1112yes—
741C24C23×D1111yescharacteristic
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
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—112no—
781C22×C4—112no—
782C22×C4—112no—
783C22×C4—112no—
784C22×C4—112no—
785C22×C4—112no—
786C22×C4—112no—
787C22×C4—112no—
788C22×C4—112no—
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×C4C2×C4×D1112yes—
837C22×C4D4×D1112yes—
838C22×C4#434112yes—
839C22×C4#434112yes—
840C4⋊C4—444no—
841C4⋊C4—444no—
842C4⋊C4—444no—
843C22⋊C4—44no—
844C22⋊C4—44no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—228no—
848C22⋊C4—228no—
849C22⋊C4—444no—
850C22⋊C4—444no—
851C22⋊C4—444no—
852C22⋊C4—444no—
853C22⋊C4—444no—
854C22⋊C4—444no—
855C42—444no—
856C42—444no—
857C42—444no—
858C11#1458911yescharacteristic, complemented, Sylow
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
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—
929C23C22×C4×D1111yescharacteristic
930C23C2×D4×D1111yescharacteristic
931C23C2×#434111yescharacteristic
932C23C2×#434111yescharacteristic
933C23#6703711yescharacteristic
934C23#6703711yescharacteristic
935C23#6703711yescharacteristic
936C23#6703711yescharacteristic
937C23#6703711yescharacteristic
938C23#6703711yescharacteristic
939C23#6703711yescharacteristic
940C23#41×D1111yescharacteristic
941C23#41×D1111yescharacteristic
942C23#41×D1111yescharacteristic
943C23#6704311yescharacteristic
944D4—416no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
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—114no—
981C2×C4—222no—
982C2×C4—222no—
983C2×C4—222no—
984C2×C4—222no—
985C2×C4—222no—
986C2×C4—222no—
987C2×C4—222no—
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—222no—
1004C2×C4—222no—
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—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—42no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—81no—
1051C22—81no—
1052C22—81no—
1053C22—81no—
1054C22—81no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—81no—
1059C22—81no—
1060C22—81no—
1061C22—81no—
1062C22—81no—
1063C22—81no—
1064C22—81no—
1065C22—81no—
1066C22#1062301711yescharacteristic
1067C22#1062301711yescharacteristic
1068C22#1062301711yescharacteristic
1069C22C4×#434111yescharacteristic
1070C22C4×#434111yescharacteristic
1071C22C4×D4×D1111yescharacteristic
1072C22#1062307711yescharacteristic
1073C22#1062311811yescharacteristic
1074C22#1062312011yescharacteristic
1075C22#1062312211yescharacteristic
1076C22#1062312411yescharacteristic
1077C22#1062312511yescharacteristic
1078C22#1062312611yescharacteristic
1079C22#1062312611yescharacteristic
1080C22#1062312611yescharacteristic
1081C22#1062313011yescharacteristic
1082C22#1062313211yescharacteristic
1083C22#1062313311yescharacteristic
1084C22#1062313411yescharacteristic
1085C22#1062313911yescharacteristic
1086C22#1062314111yescharacteristic
1087C22#1062314411yescharacteristic
1088C22#1062314411yescharacteristic
1089C22#1062314611yescharacteristic
1090C22#1062314711yescharacteristic
1091C22#1062314711yescharacteristic
1092C22#1062314711yescharacteristic
1093C22#1062319011yescharacteristic
1094C22#1062319111yescharacteristic
1095C22#1062319111yescharacteristic
1096C22#1062319211yescharacteristic
1097C22#1062320011yescharacteristic
1098C22#1062320111yescharacteristic
1099C22#1062324911yescharacteristic
1100C22#1062325011yescharacteristic
1101C4—42no—
1102C4—42no—
1103C4—42no—
1104C4—42no—
1105C4—81no—
1106C4—224no—
1107C4—442no—
1108C4—442no—
1109C4—442no—
1110C4—442no—
1111C4—442no—
1112C4—442no—
1113C4—881no—
1114C2—82no—
1115C2—82no—
1116C2#1307131811yescharacteristic
1117C2#1307140311yescharacteristic
1118C2#1307140711yescharacteristic
1119C2#1307165111yescharacteristic
1120C2#1307165711yescharacteristic
1121C2#1307172511yescharacteristic
1122C2#1307175511yescharacteristic
1123C2#1307520611yescharacteristic
1124C2#1307529511yescharacteristic
1125C2#1307529611yescharacteristic
1126C2#1307564411yescharacteristic
1127C2#1307594011yescharacteristic
1128C2#1307594311yescharacteristic
1129C2#1307632311yescharacteristic
1130C2#1307644711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenter#1438D11
hypocenterC11#14589
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#10622558C2semidirect
3. C2×#10622557C2semidirect
4. #13066867C2semidirect
5. #13066859C2semidirect
6. #13066859C2semidirect
8. #13066853C2semidirect
9. #13066853C2semidirect
10. #13066853C2semidirect
11. #13066853C2semidirect
12. Dic11⋊#95C2semidirect
13. #13066842C2semidirect
14. #13066840C2semidirect
37. #10622835C4semidirect
120. C2×Dic11⋊C4D4semidirect
858. C11#14589semidirect

Maximal subgroups

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

subgroupindex
C2×#106228352
C2×#106225582
C2×#106225572
#130668672
#130668592
#130668572
#130668532
Dic11⋊#952
#130668422
#130668402
C11×#14382
#1458911