Finite Group Databasebeta

← #14684669

Subgroups — #14684669

Order 2816.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622285C211yesmaximal, characteristic
2#13066882C211yesmaximal, characteristic, complemented
3#13066878C211yesmaximal, characteristic, complemented
4#13066867C211yesmaximal, characteristic, complemented
5#13066864C211yesmaximal, characteristic, complemented
6#13066864C211yesmaximal, characteristic, complemented
7#13066860C211yesmaximal, characteristic, complemented
8#13066860C211yesmaximal, characteristic, complemented
9#13066858C211yesmaximal, characteristic, complemented
10#13066858C211yesmaximal, characteristic, complemented
11#13066856C211yesmaximal, characteristic
12#13066856C211yesmaximal, characteristic
13#13066854C211yesmaximal, characteristic, complemented
14#13066854C211yesmaximal, 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
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#10622285C418yescomplemented
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—41no—
68C22×D44—41no—
69C22×D44—41no—
70C22×D44—41no—
71C22×D44—41no—
72C22×D44—41no—
73C22×D44C2×C414yes—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—41no—
76C2×C11×C4⋊C4—41no—
77C2×C42×C11—41no—
78C2×C42×C11—41no—
79C2×C42×C11—41no—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—22no—
84C2×(C2×D11)⋊C4—41no—
85C2×(C2×D11)⋊C4—41no—
86C2×(C2×D11)⋊C4—41no—
87C2×(C2×D11)⋊C4—41no—
88C2×(C2×D11)⋊C4—41no—
89C2×(C2×D11)⋊C4—41no—
90C2×(C2×D11)⋊C4—41no—
91C2×(C2×D11)⋊C4—41no—
92C2×(C2×D11)⋊C4—41no—
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)⋊C4—41no—
112C2×(C2×D11)⋊C4C2×C414yes—
113C2×(C2×D11)⋊C4C2×C414yes—
114C2×(C2×D11)⋊C4C2×C414yes—
115C2×(C2×D11)⋊C4C2×C414yes—
116C2×Dic11⋊C4—41no—
117C2×Dic11⋊C4—41no—
118C2×Dic11⋊C4—41no—
119C2×Dic11⋊C4—41no—
120C2×Dic11⋊C4—41no—
121C2×Dic11⋊C4C2×C414yes—
122C11×#95—22no—
123C11×#95—41no—
124C11×#95—41no—
125C11×#95—41no—
126C11×#95C2×C414yes—
127C11⋊#95—41no—
128C11⋊#95—41no—
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⋊#95—41no—
140#14645—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×D11—21no—
169C23×D11—21no—
170C23×D11C22×C412yes—
171C23×D11C22×C412yes—
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×C11C22×C412yes—
217C22×C4×C11C22×C412yes—
218C22×C4×C11C22×C412yes—
219C22×C4×C11#4112yes—
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×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11C22×C412yes—
262C22×Dic11C22×C412yes—
263C2×D44—44no—
264C2×D44—44no—
265C2×D44—44no—
266C2×D44—44no—
267C2×D44—44no—
268C2×D44—44no—
269C2×D44—44no—
270C11×C4⋊C4—44no—
271C42×C11—44no—
272(C2×D11)⋊C4—44no—
273(C2×D11)⋊C4—44no—
274(C2×D11)⋊C4—44no—
275(C2×D11)⋊C4—44no—
276(C2×D11)⋊C4—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—
284Dic11⋊C4—44no—
285Dic11⋊C4—44no—
286C2×#394—111no—
287#1445—111no—
288#1443—111no—
289#1441—111no—
290#1440—111no—
291#1440—111no—
292#1439—111no—
293#1439—111no—
294#1439—111no—
295#1439—111no—
296#1438—111no—
297#1438—111no—
298#1437—111no—
299#1437—111no—
300#1436D1111yescharacteristic, complemented
301C23×C11C23×C411yescharacteristic
302C23×C11C2×#4111yescharacteristic
303C23×C11C2×#4111yescharacteristic
304C23×C11H(5,𝔽2)11yescharacteristic
305C23×C11H(5,𝔽2)11yescharacteristic
306C23×C11H(5,𝔽2)11yescharacteristic
307C23×C11H(5,𝔽2)11yescharacteristic
308C23×C11H(5,𝔽2)11yescharacteristic
309C23×C11H(5,𝔽2)11yescharacteristic
310C23×C11H(5,𝔽2)11yescharacteristic
311C23×C11H(5,𝔽2)11yescharacteristic
312C23×C11H(5,𝔽2)11yescharacteristic
313C23×C11H(5,𝔽2)11yescharacteristic
314C23×C112−1+411yescharacteristic
315C23×C112−1+411yescharacteristic
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
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—41no—
331C22×D11—41no—
332C22×D11—41no—
333C22×D11—41no—
334C22×D11—41no—
335C22×D11—41no—
336C22×D11—41no—
337C22×D11—41no—
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—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
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—41no—
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×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—41no—
442C2×Dic11—41no—
443C2×Dic11—41no—
444C2×Dic11—41no—
445C2×Dic11—41no—
446C2×Dic11—41no—
447C2×Dic11—41no—
448C2×Dic11—41no—
449C2×Dic11—41no—
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—
477D44—416no—
478C23×D4—111no—
479C22×C4⋊C4—111no—
480C22×C4⋊C4—111no—
481C22×C4⋊C4C2×D1111yescharacteristic
482C22×C22⋊C4—111no—
483C22×C22⋊C4—111no—
484C22×C22⋊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×C42C2×D1111yescharacteristic
495#394—118no—
496C2×#95—111no—
497C2×#95—111no—
498C2×#95—111no—
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×#95C2×D1111yescharacteristic
510C2×#95C2×D1111yescharacteristic
511C2×#95C2×D1111yescharacteristic
512C2×#95C2×D1111yescharacteristic
513C2×#95C2×D1111yescharacteristic
514C22×C11C4×#4111yescharacteristic
515C22×C11#51811yescharacteristic
516C22×C11#51811yescharacteristic
517C22×C11#51811yescharacteristic
518C22×C11#51811yescharacteristic
519C22×C11#52011yescharacteristic
520C22×C11#52011yescharacteristic
521C22×C11#53811yescharacteristic
522C22×C11#53811yescharacteristic
523C22×C11#53811yescharacteristic
524C22×C11#53811yescharacteristic
525C22×C11#53811yescharacteristic
526C22×C11#53911yescharacteristic
527C22×C11#54011yescharacteristic
528C22×C11#54011yescharacteristic
529C22×C11#54011yescharacteristic
530C22×C11#54211yescharacteristic
531C22×C11#54211yescharacteristic
532C22×C11#54211yescharacteristic
533C22×C11#56011yescharacteristic
534C22×C11#56011yescharacteristic
535C22×C11#56011yescharacteristic
536C22×C11#56011yescharacteristic
537C22×C11#56011yescharacteristic
538C22×C11#56011yescharacteristic
539C22×C11#56011yescharacteristic
540C22×C11#56011yescharacteristic
541C22×C11H(3,𝔽4)11yescharacteristic
542C22×C11#56211yescharacteristic
543C22×C11#56211yescharacteristic
544C22×C11#56211yescharacteristic
545C22×C11#56211yescharacteristic
546C22×C11#56211yescharacteristic
547C22×C11#56211yescharacteristic
548C22×C11#56311yescharacteristic
549C2×D11—42no—
550C2×D11—42no—
551C2×D11—42no—
552C2×D11—42no—
553C2×D11—42no—
554C2×D11—42no—
555C2×D11—42no—
556C2×D11—42no—
557C2×D11—42no—
558C2×D11—42no—
559C2×D11—42no—
560C2×D11—42no—
561C2×D11—42no—
562C2×D11—42no—
563C2×D11—81no—
564C2×D11—81no—
565C2×D11—81no—
566C2×D11—81no—
567C2×D11—81no—
568C2×D11—81no—
569C2×D11—81no—
570C2×D11—81no—
571C2×D11—81no—
572C2×D11—81no—
573C2×D11—81no—
574C2×D11—81no—
575C2×D11—81no—
576C2×D11—81no—
577C2×D11—81no—
578C2×D11—81no—
579C4×C11—42no—
580C4×C11—42no—
581C4×C11—42no—
582C4×C11—42no—
583C4×C11—42no—
584C4×C11—81no—
585C4×C11—81no—
586Dic11—42no—
587Dic11—42no—
588Dic11—81no—
589Dic11—81no—
590Dic11—81no—
591Dic11—81no—
592C25—111no—
593C25—111no—
594C22×D4—114no—
595C22×D4—441no—
596C22×D4—441no—
597C22×D4—441no—
598C22×D4—441no—
599C22×D4—441no—
600C22×D4—441no—
601C23×C4—111no—
602C23×C4—111no—
603C23×C4—111no—
604C23×C4—111no—
605C23×C4—111no—
606C23×C4—111no—
607C23×C4C22×D1111yescharacteristic
608C23×C4C22×D1111yescharacteristic
609C23×C4C22×D1111yescharacteristic
610C23×C4C22×D1111yescharacteristic
611C23×C4C22×D1111yescharacteristic
612C23×C4C22×D1111yescharacteristic
613C23×C4C22×D1111yescharacteristic
614C2×C4⋊C4—22no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4—41no—
617C2×C4⋊C4—114no—
618C2×C4⋊C4—441no—
619C2×C4⋊C4—441no—
620C2×C4⋊C4—441no—
621C2×C4⋊C4—441no—
622C2×C4⋊C4—441no—
623C2×C22⋊C4—114no—
624C2×C22⋊C4—114no—
625C2×C22⋊C4—114no—
626C2×C22⋊C4—114no—
627C2×C22⋊C4—222no—
628C2×C22⋊C4—222no—
629C2×C22⋊C4—222no—
630C2×C22⋊C4—222no—
631C2×C22⋊C4—441no—
632C2×C22⋊C4—441no—
633C2×C22⋊C4—441no—
634C2×C22⋊C4—441no—
635C2×C22⋊C4—441no—
636C2×C22⋊C4—441no—
637C2×C22⋊C4—441no—
638C2×C22⋊C4—441no—
639C2×C22⋊C4—441no—
640C2×C22⋊C4—441no—
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—41no—
660C2×C42—41no—
661C2×C42—41no—
662#95—22no—
663#95—41no—
664#95—41no—
665#95—41no—
666#95—441no—
667#95—441no—
668#95—441no—
669#95—441no—
670#95—441no—
671#95—441no—
672#95—441no—
673#95—441no—
674#95—441no—
675#95—441no—
676#95—441no—
677#95—441no—
678#95—441no—
679#95C4×D1114yes—
680C2×C11#233311yescharacteristic
681C2×C11#233511yescharacteristic
682C2×C11#233711yescharacteristic
683C2×C11#237511yescharacteristic
684C2×C11#237611yescharacteristic
685C2×C11#237711yescharacteristic
686C2×C11#237711yescharacteristic
687C2×C11#282511yescharacteristic
688C2×C11#282611yescharacteristic
689C2×C11#282811yescharacteristic
690C2×C11#282911yescharacteristic
691C2×C11#282911yescharacteristic
692C2×C11#282911yescharacteristic
693C2×C11#283211yescharacteristic
694C2×C11#283711yescharacteristic
695D11—82no—
696D11—82no—
697C24—112no—
698C24—112no—
699C24—221no—
700C24—221no—
701C24—221no—
702C24—221no—
703C24—221no—
704C24—221no—
705C24—221no—
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—
727C24C23×D1111yescharacteristic
728C2×D4—444no—
729C2×D4—444no—
730C2×D4—444no—
731C2×D4—444no—
732C2×D4—444no—
733C2×D4—444no—
734C2×D4—444no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
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—112no—
780C22×C4—112no—
781C22×C4—221no—
782C22×C4—221no—
783C22×C4—221no—
784C22×C4—221no—
785C22×C4—221no—
786C22×C4—221no—
787C22×C4—221no—
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×C4C2×C4×D1112yes—
822C22×C4C2×C4×D1112yes—
823C22×C4C2×C4×D1112yes—
824C22×C4#433912yes—
825C22×C4#433912yes—
826C4⋊C4—44no—
827C4⋊C4—444no—
828C4⋊C4—444no—
829C22⋊C4—444no—
830C22⋊C4—444no—
831C22⋊C4—444no—
832C22⋊C4—444no—
833C22⋊C4—444no—
834C22⋊C4—444no—
835C22⋊C4—444no—
836C22⋊C4—444no—
837C22⋊C4—444no—
838C22⋊C4—444no—
839C22⋊C4—444no—
840C22⋊C4—444no—
841C42—44no—
842C11#1464511yescharacteristic, complemented, Sylow
843C23—222no—
844C23—222no—
845C23—222no—
846C23—222no—
847C23—222no—
848C23—222no—
849C23—222no—
850C23—222no—
851C23—222no—
852C23—222no—
853C23—222no—
854C23—222no—
855C23—222no—
856C23—222no—
857C23—441no—
858C23—441no—
859C23—441no—
860C23—441no—
861C23—441no—
862C23—441no—
863C23—441no—
864C23—441no—
865C23—441no—
866C23—441no—
867C23—441no—
868C23—441no—
869C23—441no—
870C23—441no—
871C23—441no—
872C23—441no—
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—
913C23C22×C4×D1111yescharacteristic
914C23C2×#433911yescharacteristic
915C23C2×#433911yescharacteristic
916C23#6703711yescharacteristic
917C23#6703711yescharacteristic
918C23#6703711yescharacteristic
919C23#6703711yescharacteristic
920C23#6704011yescharacteristic
921C23#6704011yescharacteristic
922C23#6704211yescharacteristic
923C23#6704211yescharacteristic
924C23#6704211yescharacteristic
925C23#6704211yescharacteristic
926C23#6704211yescharacteristic
927C23#6704211yescharacteristic
928D4—4416no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
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—222no—
979C2×C4—222no—
980C2×C4—222no—
981C2×C4—222no—
982C2×C4—222no—
983C2×C4—222no—
984C2×C4—441no—
985C2×C4—441no—
986C2×C4—441no—
987C2×C4—441no—
988C2×C4—441no—
989C2×C4—441no—
990C2×C4—441no—
991C2×C4—441no—
992C2×C4—441no—
993C2×C4—441no—
994C2×C4—441no—
995C2×C4—441no—
996C2×C4—441no—
997C2×C4—441no—
998C2×C4—441no—
999C2×C4—441no—
1000C2×C4—441no—
1001C2×C4—441no—
1002C2×C4—441no—
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—
1020C22—442no—
1021C22—442no—
1022C22—442no—
1023C22—442no—
1024C22—442no—
1025C22—442no—
1026C22—442no—
1027C22—442no—
1028C22—442no—
1029C22—442no—
1030C22—442no—
1031C22—442no—
1032C22—442no—
1033C22—442no—
1034C22—881no—
1035C22—881no—
1036C22—881no—
1037C22—881no—
1038C22—881no—
1039C22—881no—
1040C22—881no—
1041C22—881no—
1042C22—881no—
1043C22—881no—
1044C22—881no—
1045C22—881no—
1046C22—881no—
1047C22—881no—
1048C22—881no—
1049C22—881no—
1050C22C4×#433911yescharacteristic
1051C22#1062302511yescharacteristic
1052C22#1062303511yescharacteristic
1053C22#1062304611yescharacteristic
1054C22#1062305211yescharacteristic
1055C22#1062306611yescharacteristic
1056C22#1062306611yescharacteristic
1057C22#1062307611yescharacteristic
1058C22#1062307611yescharacteristic
1059C22#1062307611yescharacteristic
1060C22#1062309111yescharacteristic
1061C22#1062309111yescharacteristic
1062C22#1062309111yescharacteristic
1063C22#1062309111yescharacteristic
1064C22#1062309311yescharacteristic
1065C22#1062310511yescharacteristic
1066C22#1062311311yescharacteristic
1067C22#1062311311yescharacteristic
1068C22#1062311311yescharacteristic
1069C22#1062312611yescharacteristic
1070C22#1062315111yescharacteristic
1071C22#1062315111yescharacteristic
1072C22#1062317811yescharacteristic
1073C22#1062317811yescharacteristic
1074C22#1062317811yescharacteristic
1075C22#1062317811yescharacteristic
1076C22#1062319711yescharacteristic
1077C22#1062319711yescharacteristic
1078C22#1062319711yescharacteristic
1079C22#1062321411yescharacteristic
1080C22#1062323111yescharacteristic
1081C22#1062323111yescharacteristic
1082C22#1062324211yescharacteristic
1083C22#1062324211yescharacteristic
1084C22#1062326611yescharacteristic
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—42no—
1089C4—42no—
1090C4—81no—
1091C4—81no—
1092C4—442no—
1093C4—442no—
1094C4—881no—
1095C4—881no—
1096C4—881no—
1097C4—881no—
1098C2—882no—
1099C2—882no—
1100C2#1307137611yescharacteristic
1101C2#1307140011yescharacteristic
1102C2#1307142911yescharacteristic
1103C2#1307175611yescharacteristic
1104C2#1307176111yescharacteristic
1105C2#1307177111yescharacteristic
1106C2#1307177211yescharacteristic
1107C2#1307670211yescharacteristic
1108C2#1307670911yescharacteristic
1109C2#1307673311yescharacteristic
1110C2#1307674611yescharacteristic
1111C2#1307674611yescharacteristic
1112C2#1307674611yescharacteristic
1113C2#1307678311yescharacteristic
1114C2#1307682611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1436D11
hypocenterC11#14645
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. #13066882C2semidirect
3. #13066878C2semidirect
4. #13066867C2semidirect
5. #13066864C2semidirect
6. #13066864C2semidirect
7. #13066860C2semidirect
8. #13066860C2semidirect
9. #13066858C2semidirect
10. #13066858C2semidirect
13. #13066854C2semidirect
14. #13066854C2semidirect
15. C11×#1436C2semidirect
51. #10622285C4semidirect
300. #1436D11semidirect
842. C11#14645semidirect

Maximal subgroups

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

subgroupindex
C2×#106222852
#130668822
#130668782
#130668672
#130668642
#130668602
#130668582
#130668562
#130668542
C11×#14362
#1464511