Finite Group Databasebeta

← #14683068

Subgroups — #14683068

Order 2816.

1666 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622278C211yesmaximal, characteristic
2#13066876C211yesmaximal, characteristic, complemented
3#13066864C211yesmaximal, characteristic, complemented
4#13066864C211yesmaximal, characteristic, complemented
5#13066856C211yesmaximal, characteristic
6#13066856C211yesmaximal, characteristic
7#13066852C211yesmaximal, characteristic, complemented
8#13066852C211yesmaximal, characteristic, complemented
9#13066852C211yesmaximal, characteristic, complemented
10#13066852C211yesmaximal, characteristic, complemented
11#13066841C211yesmaximal, characteristic, complemented
12#13066840C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1443C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C2×C11×#95C2211yescharacteristic
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51#10622278C418yescomplemented
52C24×D11C2311yescharacteristic
53C24×D11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C22×D44—22no—
68C22×D44—22no—
69C22×D44—41no—
70C22×D44—41no—
71C22×D44—41no—
72C22×D44—41no—
73C22×D44C2×C414yes—
74C22×C4×D11—41no—
75C22×C4×D11—41no—
76C22×C4×D11—41no—
77C22×C4×D11—41no—
78C22×C4×D11—41no—
79C22×C4×D11—41no—
80C22×C4×D11C2×C414yes—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—22no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—41no—
94C2×(C2×D11)⋊C4—41no—
95C2×(C2×D11)⋊C4—41no—
96C2×(C2×D11)⋊C4—41no—
97C2×(C2×D11)⋊C4—41no—
98C2×(C2×D11)⋊C4—41no—
99C2×(C2×D11)⋊C4—41no—
100C2×(C2×D11)⋊C4—41no—
101C2×(C2×D11)⋊C4—41no—
102C2×(C2×D11)⋊C4—41no—
103C2×(C2×D11)⋊C4—41no—
104C2×(C2×D11)⋊C4—41no—
105C2×(C2×D11)⋊C4—41no—
106C2×(C2×D11)⋊C4—41no—
107C2×(C2×D11)⋊C4—41no—
108C2×(C2×D11)⋊C4—41no—
109C2×(C2×D11)⋊C4—41no—
110C2×(C2×D11)⋊C4—41no—
111C2×(C2×D11)⋊C4C2×C414yes—
112C2×(C2×D11)⋊C4C2×C414yes—
113C2×(C2×D11)⋊C4C2×C414yes—
114C2×C4×Dic11—22no—
115C2×C4×Dic11—22no—
116C2×C4×Dic11—41no—
117C2×C4×Dic11—41no—
118C2×C4×Dic11—41no—
119C2×C4×Dic11—41no—
120C11×#95—41no—
121C11×#95—41no—
122C11×#95—41no—
123C11×#95—41no—
124C11×#95—41no—
125C11×#95—41no—
126C11×#95C2×C414yes—
127C11⋊#95—22no—
128C11⋊#95—22no—
129C11⋊#95—41no—
130C11⋊#95—41no—
131C11⋊#95—41no—
132C11⋊#95—41no—
133C11⋊#95—41no—
134C11⋊#95—41no—
135C11⋊#95—41no—
136C11⋊#95—41no—
137C11⋊#95—41no—
138C11⋊#95—41no—
139C11⋊#95C2×C414yes—
140#14516—111nomaximal, Sylow
141C24×C11C2411yescharacteristic
142C23×D11—21no—
143C23×D11—21no—
144C23×D11—21no—
145C23×D11—21no—
146C23×D11—21no—
147C23×D11—21no—
148C23×D11—21no—
149C23×D11—21no—
150C23×D11—21no—
151C23×D11—21no—
152C23×D11—21no—
153C23×D11—21no—
154C23×D11—21no—
155C23×D11—21no—
156C23×D11—21no—
157C23×D11—21no—
158C23×D11—21no—
159C23×D11—21no—
160C23×D11—21no—
161C23×D11—21no—
162C23×D11—21no—
163C23×D11—21no—
164C23×D11—21no—
165C23×D11—21no—
166C23×D11—21no—
167C23×D11—21no—
168C23×D11C22×C412yes—
169C23×D11C22×C412yes—
170C23×D11#4112yes—
171C23×D11#4112yes—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×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×C11C22×C412yes—
219C22×C4×C11C22×C412yes—
220C22×C4×C11#4112yes—
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×Dic11C22×C412yes—
259C22×Dic11C22×C412yes—
260C22×Dic11#4112yes—
261C22×Dic11#4112yes—
262C22×Dic11#4112yes—
263C2×D44—28no—
264C2×D44—44no—
265C2×D44—44no—
266C2×D44—44no—
267C2×D44—44no—
268C2×D44—44no—
269C2×D44—44no—
270C2×C4×D11—44no—
271C2×C4×D11—44no—
272C2×C4×D11—44no—
273C2×C4×D11—44no—
274C2×C4×D11—44no—
275C2×C4×D11—44no—
276C2×C4×D11—44no—
277(C2×D11)⋊C4—44no—
278(C2×D11)⋊C4—44no—
279(C2×D11)⋊C4—44no—
280(C2×D11)⋊C4—44no—
281(C2×D11)⋊C4—44no—
282(C2×D11)⋊C4—44no—
283(C2×D11)⋊C4—44no—
284(C2×D11)⋊C4—44no—
285(C2×D11)⋊C4—44no—
286(C2×D11)⋊C4—44no—
287(C2×D11)⋊C4—44no—
288C4×Dic11—44no—
289C4×Dic11—44no—
290C2×#386—111no—
291#1443—111no—
292#1443D1111yescharacteristic, complemented
293#1440—111no—
294#1440—111no—
295#1438—111no—
296#1438—111no—
297#1437—111no—
298#1437—111no—
299#1437—111no—
300#1437—111no—
301#1434—111no—
302#1434—111no—
303C22⋊#95—111no—
304C22⋊#95—111no—
305C23×C11C23×C411yescharacteristic
306C23×C11C2×#4111yescharacteristic
307C23×C11C2×#4111yescharacteristic
308C23×C11C2×#4111yescharacteristic
309C23×C11C2×#4111yescharacteristic
310C23×C11C2×#4111yescharacteristic
311C23×C11C2×#4111yescharacteristic
312C23×C11H(5,𝔽2)11yescharacteristic
313C23×C11H(5,𝔽2)11yescharacteristic
314C23×C11H(5,𝔽2)11yescharacteristic
315C23×C11H(5,𝔽2)11yescharacteristic
316C23×C11H(5,𝔽2)11yescharacteristic
317C23×C11H(5,𝔽2)11yescharacteristic
318C23×C11H(5,𝔽2)11yescharacteristic
319C23×C11H(5,𝔽2)11yescharacteristic
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—41no—
346C22×D11—41no—
347C22×D11—41no—
348C22×D11—41no—
349C22×D11—41no—
350C22×D11—41no—
351C22×D11—41no—
352C22×D11—41no—
353C22×D11—41no—
354C22×D11—41no—
355C22×D11—41no—
356C22×D11—41no—
357C22×D11—41no—
358C22×D11—41no—
359C22×D11—41no—
360C22×D11—41no—
361C22×D11—41no—
362C22×D11—41no—
363C22×D11—41no—
364C22×D11—41no—
365C22×D11—41no—
366C22×D11—41no—
367C22×D11—41no—
368C22×D11—41no—
369C22×D11—41no—
370C22×D11—41no—
371C22×D11—41no—
372C22×D11—41no—
373C22×D11—41no—
374C22×D11—41no—
375C22×D11—41no—
376C22×D11—41no—
377C22×D11—41no—
378C22×D11—41no—
379C22×D11—41no—
380C22×D11—41no—
381C22×D11—41no—
382C22×D11—41no—
383C22×D11—41no—
384C22×D11—41no—
385C22×D11—41no—
386C22×D11—41no—
387C22×D11—41no—
388C22×D11—41no—
389C22×D11#11714yes—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
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—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
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×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—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—
481D44—416no—
482C4×D11—416no—
483C23×D4—111no—
484C24×C4—111no—
485C22×C22⋊C4—111no—
486C22×C22⋊C4—111no—
487C22×C22⋊C4—111no—
488C22×C22⋊C4—111no—
489C22×C22⋊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×C42—111no—
497C22×C42—111no—
498#386—118no—
499C2×#95—111no—
500C2×#95—111no—
501C2×#95—111no—
502C2×#95—111no—
503C2×#95—111no—
504C2×#95—111no—
505C2×#95—111no—
506C2×#95—111no—
507C2×#95—111no—
508C2×#95—111no—
509C2×#95—111no—
510C2×#95—111no—
511C2×#95—111no—
512C2×#95C2×D1111yescharacteristic
513C2×#95C2×D1111yescharacteristic
514C2×#95C2×D1111yescharacteristic
515C2×#95C2×D1111yescharacteristic
516C2×#95C2×D1111yescharacteristic
517C2×#95C2×D1111yescharacteristic
518C2×#95C2×D1111yescharacteristic
519C22×C11C2×#11711yescharacteristic
520C22×C11C4×#4111yescharacteristic
521C22×C11C4×#4111yescharacteristic
522C22×C11#51811yescharacteristic
523C22×C11#51811yescharacteristic
524C22×C11#51811yescharacteristic
525C22×C11#51811yescharacteristic
526C22×C11#53811yescharacteristic
527C22×C11#53811yescharacteristic
528C22×C11#53811yescharacteristic
529C22×C11#53811yescharacteristic
530C22×C11#53811yescharacteristic
531C22×C11#53811yescharacteristic
532C22×C11#53811yescharacteristic
533C22×C11#53811yescharacteristic
534C22×C11#54011yescharacteristic
535C22×C11#54011yescharacteristic
536C22×C11#54011yescharacteristic
537C22×C11#54011yescharacteristic
538C22×C11#55111yescharacteristic
539C22×C11#55111yescharacteristic
540C22×C11#55111yescharacteristic
541C22×C11#55111yescharacteristic
542C22×C11#55111yescharacteristic
543C22×C11#55311yescharacteristic
544C22×C11#55311yescharacteristic
545C22×C11#55311yescharacteristic
546C22×C11#55311yescharacteristic
547C22×C11#55311yescharacteristic
548C22×C11#55311yescharacteristic
549C22×C11#55911yescharacteristic
550C22×C11#56011yescharacteristic
551C22×C11#56011yescharacteristic
552C22×C11#56011yescharacteristic
553C22×C11H(3,𝔽4)11yescharacteristic
554C2×D11—24no—
555C2×D11—24no—
556C2×D11—24no—
557C2×D11—42no—
558C2×D11—42no—
559C2×D11—42no—
560C2×D11—42no—
561C2×D11—42no—
562C2×D11—42no—
563C2×D11—42no—
564C2×D11—42no—
565C2×D11—42no—
566C2×D11—42no—
567C2×D11—42no—
568C2×D11—42no—
569C2×D11—42no—
570C2×D11—42no—
571C2×D11—42no—
572C2×D11—42no—
573C2×D11—42no—
574C2×D11—42no—
575C2×D11—42no—
576C2×D11—81no—
577C2×D11—81no—
578C2×D11—81no—
579C2×D11—81no—
580C2×D11—81no—
581C2×D11—81no—
582C2×D11—81no—
583C2×D11—81no—
584C4×C11—42no—
585C4×C11—42no—
586C4×C11—42no—
587C4×C11—42no—
588C4×C11—81no—
589C4×C11—81no—
590C4×C11—81no—
591Dic11—42no—
592Dic11—42no—
593Dic11—42no—
594Dic11—42no—
595Dic11—42no—
596Dic11—81no—
597C25—111no—
598C25—111no—
599C22×D4—114no—
600C22×D4—222no—
601C22×D4—222no—
602C22×D4—441no—
603C22×D4—441no—
604C22×D4—441no—
605C22×D4—441no—
606C23×C4—111no—
607C23×C4—111no—
608C23×C4—111no—
609C23×C4—111no—
610C23×C4—111no—
611C23×C4—114no—
612C23×C4—111no—
613C23×C4—441no—
614C23×C4—441no—
615C23×C4—441no—
616C23×C4—441no—
617C23×C4—441no—
618C23×C4—441no—
619C23×C4C22×D1111yescharacteristic
620C23×C4C22×D1111yescharacteristic
621C23×C4C22×D1111yescharacteristic
622C23×C4C22×D1111yescharacteristic
623C23×C4C22×D1111yescharacteristic
624C23×C4C22×D1111yescharacteristic
625C23×C4C22×D1111yescharacteristic
626C2×C22⋊C4—114no—
627C2×C22⋊C4—114no—
628C2×C22⋊C4—114no—
629C2×C22⋊C4—222no—
630C2×C22⋊C4—222no—
631C2×C22⋊C4—222no—
632C2×C22⋊C4—222no—
633C2×C22⋊C4—222no—
634C2×C22⋊C4—222no—
635C2×C22⋊C4—222no—
636C2×C22⋊C4—222no—
637C2×C22⋊C4—222no—
638C2×C22⋊C4—222no—
639C2×C22⋊C4—222no—
640C2×C22⋊C4—222no—
641C2×C22⋊C4—441no—
642C2×C22⋊C4—441no—
643C2×C22⋊C4—441no—
644C2×C22⋊C4—441no—
645C2×C22⋊C4—441no—
646C2×C22⋊C4—441no—
647C2×C22⋊C4—441no—
648C2×C22⋊C4—441no—
649C2×C22⋊C4—441no—
650C2×C22⋊C4—441no—
651C2×C22⋊C4—441no—
652C2×C22⋊C4—441no—
653C2×C22⋊C4—441no—
654C2×C22⋊C4—441no—
655C2×C22⋊C4—441no—
656C2×C22⋊C4—441no—
657C2×C22⋊C4—441no—
658C2×C22⋊C4—441no—
659C2×C42—222no—
660C2×C42—222no—
661C2×C42—441no—
662C2×C42—441no—
663C2×C42—441no—
664C2×C42—441no—
665#95—41no—
666#95—41no—
667#95—41no—
668#95—41no—
669#95—41no—
670#95—41no—
671#95—114no—
672#95—222no—
673#95—222no—
674#95—441no—
675#95—441no—
676#95—441no—
677#95—441no—
678#95—441no—
679#95—441no—
680#95—441no—
681#95—441no—
682#95—441no—
683#95—441no—
684#95C4×D1114yes—
685C2×C11#231211yescharacteristic
686C2×C11#233311yescharacteristic
687C2×C11#233311yescharacteristic
688C2×C11#235311yescharacteristic
689C2×C11#235311yescharacteristic
690C2×C11#237411yescharacteristic
691C2×C11#237511yescharacteristic
692C2×C11#274911yescharacteristic
693C2×C11#274911yescharacteristic
694C2×C11#275311yescharacteristic
695C2×C11#275311yescharacteristic
696C2×C11#277811yescharacteristic
697C2×C11#277811yescharacteristic
698C2×C11#279711yescharacteristic
699C2×C11#279711yescharacteristic
700D11—44no—
701D11—82no—
702C24—112no—
703C24—112no—
704C24—112no—
705C24—112no—
706C24—221no—
707C24—221no—
708C24—221no—
709C24—221no—
710C24—221no—
711C24—221no—
712C24—221no—
713C24—221no—
714C24—221no—
715C24—221no—
716C24—221no—
717C24—221no—
718C24—221no—
719C24—221no—
720C24—221no—
721C24—221no—
722C24—221no—
723C24—221no—
724C24—221no—
725C24—221no—
726C24—221no—
727C24—221no—
728C24—221no—
729C24—221no—
730C24—221no—
731C24—221no—
732C24C23×D1111yescharacteristic
733C2×D4—228no—
734C2×D4—444no—
735C2×D4—444no—
736C2×D4—444no—
737C2×D4—444no—
738C2×D4—444no—
739C2×D4—444no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
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—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—112no—
786C22×C4—112no—
787C22×C4—112no—
788C22×C4—112no—
789C22×C4—112no—
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—444no—
828C22×C4—444no—
829C22×C4—444no—
830C22×C4—444no—
831C22×C4—444no—
832C22×C4—444no—
833C22×C4—444no—
834C22×C4C2×C4×D1112yes—
835C22×C4C2×C4×D1112yes—
836C22×C4C2×C4×D1112yes—
837C22×C4#434312yes—
838C22⋊C4—444no—
839C22⋊C4—444no—
840C22⋊C4—444no—
841C22⋊C4—444no—
842C22⋊C4—444no—
843C22⋊C4—444no—
844C22⋊C4—444no—
845C22⋊C4—444no—
846C22⋊C4—444no—
847C22⋊C4—444no—
848C22⋊C4—444no—
849C42—444no—
850C42—444no—
851C11#1451611yescharacteristic, complemented, Sylow
852C23—114no—
853C23—222no—
854C23—222no—
855C23—222no—
856C23—222no—
857C23—222no—
858C23—222no—
859C23—222no—
860C23—222no—
861C23—222no—
862C23—222no—
863C23—222no—
864C23—222no—
865C23—222no—
866C23—222no—
867C23—222no—
868C23—222no—
869C23—222no—
870C23—222no—
871C23—222no—
872C23—222no—
873C23—222no—
874C23—222no—
875C23—222no—
876C23—222no—
877C23—222no—
878C23—441no—
879C23—441no—
880C23—441no—
881C23—441no—
882C23—441no—
883C23—441no—
884C23—441no—
885C23—441no—
886C23—441no—
887C23—441no—
888C23—441no—
889C23—441no—
890C23—441no—
891C23—441no—
892C23—441no—
893C23—441no—
894C23—441no—
895C23—441no—
896C23—441no—
897C23—441no—
898C23—441no—
899C23—441no—
900C23—441no—
901C23—441no—
902C23—441no—
903C23—441no—
904C23—441no—
905C23—441no—
906C23—441no—
907C23—441no—
908C23—441no—
909C23—441no—
910C23—441no—
911C23—441no—
912C23—441no—
913C23—441no—
914C23—441no—
915C23—441no—
916C23—441no—
917C23—441no—
918C23—441no—
919C23—441no—
920C23—441no—
921C23—441no—
922C23C22×C4×D1111yescharacteristic
923C23#6703711yescharacteristic
924C23#6703711yescharacteristic
925C23#6703711yescharacteristic
926C23C2×#434311yescharacteristic
927C23#41×D1111yescharacteristic
928C23#41×D1111yescharacteristic
929C23#41×D1111yescharacteristic
930C23#41×D1111yescharacteristic
931C23#41×D1111yescharacteristic
932C23#6704211yescharacteristic
933C23#6704211yescharacteristic
934C23#6704211yescharacteristic
935C23#6704211yescharacteristic
936C23#6704211yescharacteristic
937D4—4416no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
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—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
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—4416no—
1003C2×C4—441no—
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—
1030C22—224no—
1031C22—224no—
1032C22—224no—
1033C22—442no—
1034C22—442no—
1035C22—442no—
1036C22—442no—
1037C22—442no—
1038C22—442no—
1039C22—442no—
1040C22—442no—
1041C22—442no—
1042C22—442no—
1043C22—442no—
1044C22—442no—
1045C22—442no—
1046C22—442no—
1047C22—442no—
1048C22—442no—
1049C22—442no—
1050C22—442no—
1051C22—442no—
1052C22—881no—
1053C22—881no—
1054C22—881no—
1055C22—881no—
1056C22—881no—
1057C22—881no—
1058C22—881no—
1059C22—881no—
1060C22D11×#11711yescharacteristic
1061C22#1062305211yescharacteristic
1062C22#1062305311yescharacteristic
1063C22#1062307611yescharacteristic
1064C22#1062307611yescharacteristic
1065C22#1062307611yescharacteristic
1066C22C4×#434311yescharacteristic
1067C22#1062314411yescharacteristic
1068C22#1062314611yescharacteristic
1069C22#1062315111yescharacteristic
1070C22#1062316811yescharacteristic
1071C22#1062316811yescharacteristic
1072C22#1062317511yescharacteristic
1073C22#1062318811yescharacteristic
1074C22#1062319211yescharacteristic
1075C22#1062319411yescharacteristic
1076C22#1062319411yescharacteristic
1077C22#1062319511yescharacteristic
1078C22#1062319711yescharacteristic
1079C22#1062320911yescharacteristic
1080C22#1062320911yescharacteristic
1081C22#1062321411yescharacteristic
1082C22#1062322611yescharacteristic
1083C22#1062322611yescharacteristic
1084C22#1062322911yescharacteristic
1085C22#1062323511yescharacteristic
1086C22#1062323511yescharacteristic
1087C22#1062323511yescharacteristic
1088C22#1062323611yescharacteristic
1089C22#1062323611yescharacteristic
1090C22#1062323611yescharacteristic
1091C22#1062324011yescharacteristic
1092C22#1062324011yescharacteristic
1093C22#1062324011yescharacteristic
1094C22#1062324211yescharacteristic
1095C4—42no—
1096C4—42no—
1097C4—42no—
1098C4—42no—
1099C4—81no—
1100C4—81no—
1101C4—81no—
1102C4—442no—
1103C4—442no—
1104C4—442no—
1105C4—442no—
1106C4—442no—
1107C4—881no—
1108C2—444no—
1109C2—882no—
1110C2#1307121011yescharacteristic
1111C2#1307137911yescharacteristic
1112C2#1307138011yescharacteristic
1113C2#1307154911yescharacteristic
1114C2#1307155511yescharacteristic
1115C2#1307174811yescharacteristic
1116C2#1307175611yescharacteristic
1117C2#1307584511yescharacteristic
1118C2#1307584611yescharacteristic
1119C2#1307589911yescharacteristic
1120C2#1307590011yescharacteristic
1121C2#1307624011yescharacteristic
1122C2#1307624111yescharacteristic
1123C2#1307647211yescharacteristic
1124C2#1307647811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1443C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1443D11
hypocenterC11#14516
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
2. #13066876C2semidirect
3. #13066864C2semidirect
4. #13066864C2semidirect
7. #13066852C2semidirect
8. #13066852C2semidirect
9. #13066852C2semidirect
10. #13066852C2semidirect
11. #13066841C2semidirect
12. #13066840C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1443C2semidirect
51. #10622278C4semidirect
292. #1443D11semidirect
851. C11#14516semidirect

Maximal subgroups

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

subgroupindex
C2×#106222782
#130668762
#130668642
#130668562
#130668522
#130668412
#130668402
(C2×D11)⋊#952
C11×#14432
#1451611