Finite Group Databasebeta

← #14682226

Subgroups — #14682226

Order 2816.

1658 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×#10622601C211yesmaximal, characteristic
2C2×#10622553C211yesmaximal, characteristic, complemented
3C2×#10622282C211yesmaximal, characteristic, complemented
4#13066864C211yesmaximal, characteristic, complemented
5#13066864C211yesmaximal, characteristic, complemented
6#13066860C211yesmaximal, characteristic, complemented
7#13066860C211yesmaximal, characteristic, complemented
8#13066856C211yesmaximal, characteristic
9#13066856C211yesmaximal, characteristic
10#13066854C211yesmaximal, characteristic, complemented
11#13066852C211yesmaximal, characteristic, complemented
12#13066848C211yesmaximal, characteristic, complemented
13Dic11⋊#95C211yesmaximal, characteristic, complemented
14#13066842C211yesmaximal, characteristic, complemented
15C11×#1436C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
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#10622601C418yescomplemented
52#10622553—24no—
53#10622282—24no—
54C24×D11C2311yescharacteristic
55C24×D11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C22×D44—22no—
70C22×D44—22no—
71C22×D44—41no—
72C22×D44—41no—
73C22×D44—41no—
74C22×D44—41no—
75C22×D44C2×C414yes—
76C2×C11×C4⋊C4—41no—
77C2×C11×C4⋊C4—41no—
78C2×C11×C4⋊C4C2×C414yes—
79C2×C42×C11—22no—
80C2×C42×C11—41no—
81C2×C42×C11—41no—
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—22no—
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)⋊C4—41no—
112C2×(C2×D11)⋊C4—41no—
113C2×(C2×D11)⋊C4—41no—
114C2×(C2×D11)⋊C4C2×C414yes—
115C2×(C2×D11)⋊C4C2×C414yes—
116C2×(C2×D11)⋊C4C2×C414yes—
117C2×(C2×D11)⋊C4C2×C414yes—
118C2×Dic11⋊C4—22no—
119C2×Dic11⋊C4—22no—
120C2×Dic11⋊C4—22no—
121C2×Dic11⋊C4—22no—
122C2×Dic11⋊C4—41no—
123C2×Dic11⋊C4—41no—
124C2×C4×Dic11—22no—
125C2×C4×Dic11—41no—
126C2×C4×Dic11—41no—
127C2×C4×Dic11—41no—
128C2×C4×Dic11—41no—
129C2×C4×Dic11C2×C414yes—
130C11×#95—22no—
131C11×#95—22no—
132C11×#95—22no—
133C11×#95—41no—
134C11×#95—41no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—22no—
139C11⋊#95—41no—
140C11⋊#95—41no—
141C11⋊#95—41no—
142C11⋊#95—41no—
143C11⋊#95—41no—
144C11⋊#95—41no—
145C11⋊#95D414yescomplemented
146#14444—111nomaximal, Sylow
147C24×C11C2411yescharacteristic
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×D11—21no—
169C23×D11—21no—
170C23×D11—21no—
171C23×D11—21no—
172C23×D11—21no—
173C23×D11—21no—
174C23×D11—21no—
175C23×D11—21no—
176C23×D11C22×C412yes—
177C23×D11C22×C412yes—
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×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11C22×C412yes—
221C22×C4×C11C22×C412yes—
222C22×C4×C11C22×C412yes—
223C22×C4×C11C2×D412yes—
224C22×C4×C11#4112yes—
225C22×C4×C11#4112yes—
226C22×C4×C11#4112yes—
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×Dic11C22×C412yes—
264C22×Dic11C22×C412yes—
265C22×Dic11C2×D412yes—
266C22×Dic11C2×D412yes—
267C22×Dic11#4112yes—
268C22×Dic11#4112yes—
269C2×D44—28no—
270C2×D44—44no—
271C2×D44—44no—
272C2×D44—44no—
273C2×D44—44no—
274C2×D44—44no—
275C2×D44—44no—
276C11×C4⋊C4—44no—
277C42×C11—44no—
278(C2×D11)⋊C4—28no—
279(C2×D11)⋊C4—28no—
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—
288(C2×D11)⋊C4—44no—
289(C2×D11)⋊C4—44no—
290Dic11⋊C4—44no—
291Dic11⋊C4—44no—
292C4×Dic11—44no—
293C4×Dic11—44no—
294C2×#390—111no—
295C2×#388—111no—
296C2×#388—111no—
297#1440—111no—
298#1440—111no—
299#1439—111no—
300#1439—111no—
301#1438—111no—
302#1438—111no—
303#1437—111no—
304#1437—111no—
305#1436—111no—
306#1436D1111yescharacteristic, complemented
307C4⋊#95—111no—
308#1434—111no—
309C23×C11C23×C411yescharacteristic
310C23×C11C22×D411yescharacteristic
311C23×C11C2×#4111yescharacteristic
312C23×C11C2×#4111yescharacteristic
313C23×C11C2×#4111yescharacteristic
314C23×C11C2×#4111yescharacteristic
315C23×C11C2×#4111yescharacteristic
316C23×C11H(5,𝔽2)11yescharacteristic
317C23×C11H(5,𝔽2)11yescharacteristic
318C23×C11H(5,𝔽2)11yescharacteristic
319C23×C11H(5,𝔽2)11yescharacteristic
320C23×C11H(5,𝔽2)11yescharacteristic
321C23×C11H(5,𝔽2)11yescharacteristic
322C23×C11H(5,𝔽2)11yescharacteristic
323C23×C112−1+411yescharacteristic
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—41no—
339C22×D11—41no—
340C22×D11—41no—
341C22×D11—41no—
342C22×D11—41no—
343C22×D11—41no—
344C22×D11—41no—
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—41no—
390C22×D11—41no—
391C22×D11—41no—
392C22×D11—41no—
393C22×D11—41no—
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—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—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×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11#11714yes—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—22no—
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×Dic11C4×D414yes—
485D44—416no—
486C23×D4—111no—
487C22×C4⋊C4—111no—
488C22×C4⋊C4—111no—
489C22×C4⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
499C22×C22⋊C4—111no—
500C22×C22⋊C4—111no—
501C22×C22⋊C4—111no—
502C22×C42—111no—
503C22×C42—111no—
504C22×C42C2×D1111yescharacteristic
505#390—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×#95C2×D1111yescharacteristic
520C2×#95C2×D1111yescharacteristic
521C2×#95C2×D1111yescharacteristic
522C2×#95C2×D1111yescharacteristic
523C2×#95C2×D1111yescharacteristic
524C22×C11C2×#11711yescharacteristic
525C22×C11C2×C4×D411yescharacteristic
526C22×C11C4×#4111yescharacteristic
527C22×C11#51811yescharacteristic
528C22×C11#51811yescharacteristic
529C22×C11#51811yescharacteristic
530C22×C11#52011yescharacteristic
531C22×C11#53511yescharacteristic
532C22×C11#53511yescharacteristic
533C22×C11#53811yescharacteristic
534C22×C11#53811yescharacteristic
535C22×C11#53811yescharacteristic
536C22×C11#53811yescharacteristic
537C22×C11#53811yescharacteristic
538C22×C11#53811yescharacteristic
539C22×C11#54011yescharacteristic
540C22×C11#54011yescharacteristic
541C22×C11#54211yescharacteristic
542C22×C11#54211yescharacteristic
543C22×C11#54611yescharacteristic
544C22×C11#54611yescharacteristic
545C22×C11#54711yescharacteristic
546C22×C11#55011yescharacteristic
547C22×C11#55311yescharacteristic
548C22×C11#55311yescharacteristic
549C22×C11#55311yescharacteristic
550C22×C11#55311yescharacteristic
551C22×C11#55511yescharacteristic
552C22×C11#55611yescharacteristic
553C22×C11#55911yescharacteristic
554C22×C11#55911yescharacteristic
555C22×C11#56011yescharacteristic
556C22×C11#56011yescharacteristic
557C22×C11#56211yescharacteristic
558C22×C11#56211yescharacteristic
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—81no—
574C2×D11—81no—
575C2×D11—81no—
576C2×D11—81no—
577C2×D11—81no—
578C2×D11—81no—
579C2×D11—81no—
580C2×D11—81no—
581C2×D11—81no—
582C2×D11—81no—
583C2×D11—81no—
584C2×D11—81no—
585C2×D11—81no—
586C2×D11—81no—
587C2×D11—81no—
588C2×D11—81no—
589C4×C11—24no—
590C4×C11—42no—
591C4×C11—42no—
592C4×C11—42no—
593C4×C11—42no—
594C4×C11—81no—
595C4×C11—81no—
596Dic11—24no—
597Dic11—42no—
598Dic11—42no—
599Dic11—42no—
600Dic11—81no—
601Dic11—81no—
602C25—111no—
603C25—111no—
604C22×D4—114no—
605C22×D4—222no—
606C22×D4—222no—
607C22×D4—441no—
608C22×D4—441no—
609C22×D4—441no—
610C22×D4—441no—
611C23×C4—111no—
612C23×C4—111no—
613C23×C4—111no—
614C23×C4—111no—
615C23×C4—111no—
616C23×C4—111no—
617C23×C4C22×D1111yescharacteristic
618C23×C4C22×D1111yescharacteristic
619C23×C4C22×D1111yescharacteristic
620C23×C4C22×D1111yescharacteristic
621C23×C4C22×D1111yescharacteristic
622C23×C4C22×D1111yescharacteristic
623C23×C4C22×D1111yescharacteristic
624C2×C4⋊C4—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—222no—
627C2×C4⋊C4—222no—
628C2×C4⋊C4—222no—
629C2×C4⋊C4—222no—
630C2×C4⋊C4—441no—
631C2×C4⋊C4—441no—
632C2×C4⋊C4C4×D1114yes—
633C2×C22⋊C4—114no—
634C2×C22⋊C4—114no—
635C2×C22⋊C4—114no—
636C2×C22⋊C4—114no—
637C2×C22⋊C4—222no—
638C2×C22⋊C4—222no—
639C2×C22⋊C4—222no—
640C2×C22⋊C4—222no—
641C2×C22⋊C4—222no—
642C2×C22⋊C4—222no—
643C2×C22⋊C4—222no—
644C2×C22⋊C4—222no—
645C2×C22⋊C4—222no—
646C2×C22⋊C4—222no—
647C2×C22⋊C4—222no—
648C2×C22⋊C4—222no—
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×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—22no—
670C2×C42—41no—
671C2×C42—41no—
672C2×C42—114no—
673C2×C42—222no—
674C2×C42—441no—
675C2×C42—441no—
676C2×C42—441no—
677C2×C42—441no—
678#95—22no—
679#95—22no—
680#95—22no—
681#95—41no—
682#95—41no—
683#95—114no—
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—
694C2×C11#231211yescharacteristic
695C2×C11#232811yescharacteristic
696C2×C11#233711yescharacteristic
697C2×C11#235411yescharacteristic
698C2×C11#235711yescharacteristic
699C2×C11#236411yescharacteristic
700C2×C11#237711yescharacteristic
701C2×C11#271011yescharacteristic
702C2×C11#271011yescharacteristic
703C2×C11#271411yescharacteristic
704C2×C11#271411yescharacteristic
705C2×C11#280011yescharacteristic
706C2×C11#280011yescharacteristic
707C2×C11#280311yescharacteristic
708C2×C11#280311yescharacteristic
709D11—82no—
710D11—82no—
711C24—112no—
712C24—112no—
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—
732C24—221no—
733C24—221no—
734C24—221no—
735C24—221no—
736C24—221no—
737C24—221no—
738C24—221no—
739C24—221no—
740C24—221no—
741C24C23×D1111yescharacteristic
742C2×D4—228no—
743C2×D4—444no—
744C2×D4—444no—
745C2×D4—444no—
746C2×D4—444no—
747C2×D4—444no—
748C2×D4—444no—
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—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—112no—
792C22×C4—112no—
793C22×C4—112no—
794C22×C4—112no—
795C22×C4—112no—
796C22×C4—112no—
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×C4C2×C4×D1112yes—
834C22×C4C2×C4×D1112yes—
835C22×C4C2×C4×D1112yes—
836C22×C4#433912yes—
837C22×C4#433912yes—
838C22×C4D4×D1112yes—
839C22×C4#434312yes—
840C4⋊C4—44no—
841C4⋊C4—444no—
842C4⋊C4—444no—
843C22⋊C4—228no—
844C22⋊C4—228no—
845C22⋊C4—444no—
846C22⋊C4—444no—
847C22⋊C4—444no—
848C22⋊C4—444no—
849C22⋊C4—444no—
850C22⋊C4—444no—
851C22⋊C4—444no—
852C22⋊C4—444no—
853C22⋊C4—444no—
854C22⋊C4—444no—
855C42—44no—
856C42—444no—
857C42—444no—
858C11#1444411yescharacteristic, complemented, Sylow
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—441no—
874C23—441no—
875C23—441no—
876C23—441no—
877C23—441no—
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—
922C23—441no—
923C23—441no—
924C23—441no—
925C23—441no—
926C23—441no—
927C23—441no—
928C23—441no—
929C23C22×C4×D1111yescharacteristic
930C23C2×#433911yescharacteristic
931C23C2×#433911yescharacteristic
932C23C2×D4×D1111yescharacteristic
933C23#6703711yescharacteristic
934C23#6703711yescharacteristic
935C23#6703711yescharacteristic
936C23C2×#434311yescharacteristic
937C23#6704011yescharacteristic
938C23#41×D1111yescharacteristic
939C23#41×D1111yescharacteristic
940C23#6704211yescharacteristic
941C23#6704211yescharacteristic
942C23#6704211yescharacteristic
943C23#6704211yescharacteristic
944D4—4416no—
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—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—114no—
994C2×C4—222no—
995C2×C4—222no—
996C2×C4—222no—
997C2×C4—222no—
998C2×C4—222no—
999C2×C4—222no—
1000C2×C4—222no—
1001C2×C4—222no—
1002C2×C4—222no—
1003C2×C4—222no—
1004C2×C4—222no—
1005C2×C4—222no—
1006C2×C4—222no—
1007C2×C4—222no—
1008C2×C4—222no—
1009C2×C4—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#6692514yes—
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—881no—
1051C22—881no—
1052C22—881no—
1053C22—881no—
1054C22—881no—
1055C22—881no—
1056C22—881no—
1057C22—881no—
1058C22—881no—
1059C22—881no—
1060C22—881no—
1061C22—881no—
1062C22—881no—
1063C22—881no—
1064C22—881no—
1065C22—881no—
1066C22C2×#6692511yescharacteristic
1067C22#1062301711yescharacteristic
1068C22#1062303811yescharacteristic
1069C22#1062304511yescharacteristic
1070C22#1062305211yescharacteristic
1071C22#1062306111yescharacteristic
1072C22#1062306311yescharacteristic
1073C22C4×D4×D1111yescharacteristic
1074C22#1062307611yescharacteristic
1075C22#1062308411yescharacteristic
1076C22#1062309011yescharacteristic
1077C22#1062309111yescharacteristic
1078C22#1062309111yescharacteristic
1079C22#1062309111yescharacteristic
1080C22#1062309111yescharacteristic
1081C22#1062309911yescharacteristic
1082C22C4×#434311yescharacteristic
1083C22#1062310511yescharacteristic
1084C22#1062311611yescharacteristic
1085C22#1062312311yescharacteristic
1086C22#1062313811yescharacteristic
1087C22#1062314611yescharacteristic
1088C22#1062316111yescharacteristic
1089C22#1062317111yescharacteristic
1090C22#1062317511yescharacteristic
1091C22#1062317811yescharacteristic
1092C22#1062318511yescharacteristic
1093C22#1062319411yescharacteristic
1094C22#1062319711yescharacteristic
1095C22#1062320911yescharacteristic
1096C22#1062322611yescharacteristic
1097C22#1062323111yescharacteristic
1098C22#1062324011yescharacteristic
1099C22#1062324211yescharacteristic
1100C22#1062326411yescharacteristic
1101C4—24no—
1102C4—42no—
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—81no—
1107C4—81no—
1108C4—224no—
1109C4—442no—
1110C4—442no—
1111C4—442no—
1112C4—881no—
1113C4—881no—
1114C2—882no—
1115C2—882no—
1116C2#1307121111yescharacteristic
1117C2#1307133711yescharacteristic
1118C2#1307142811yescharacteristic
1119C2#1307156111yescharacteristic
1120C2#1307158511yescharacteristic
1121C2#1307166211yescharacteristic
1122C2#1307177111yescharacteristic
1123C2#1307535911yescharacteristic
1124C2#1307536211yescharacteristic
1125C2#1307541311yescharacteristic
1126C2#1307541611yescharacteristic
1127C2#1307650911yescharacteristic
1128C2#1307651611yescharacteristic
1129C2#1307654611yescharacteristic
1130C2#1307655311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1436D11
hypocenterC11#14444
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#10622553C2semidirect
3. C2×#10622282C2semidirect
4. #13066864C2semidirect
5. #13066864C2semidirect
6. #13066860C2semidirect
7. #13066860C2semidirect
10. #13066854C2semidirect
11. #13066852C2semidirect
12. #13066848C2semidirect
13. Dic11⋊#95C2semidirect
14. #13066842C2semidirect
15. C11×#1436C2semidirect
51. #10622601C4semidirect
145. C11⋊#95D4semidirect
306. #1436D11semidirect
858. C11#14444semidirect

Maximal subgroups

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

subgroupindex
C2×#106226012
C2×#106225532
C2×#106222822
#130668642
#130668602
#130668562
#130668542
#130668522
#130668482
Dic11⋊#952
#130668422
C11×#14362
#1444411