Finite Group Databasebeta

← #14681699

Subgroups — #14681699

Order 2816.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622586C211yesmaximal, characteristic, complemented
2C2×#10622585C211yesmaximal, characteristic, complemented
3C2×#10622603C211yesmaximal, characteristic
4C2×#10622282C211yesmaximal, characteristic
5C2×#10622281C211yesmaximal, characteristic
6C2×#10622280C211yesmaximal, characteristic
7C2×#10622600C211yesmaximal, characteristic
8#13066879C211yesmaximal, characteristic, complemented
9#13066870C211yesmaximal, characteristic, complemented
10#13066868C211yesmaximal, characteristic, complemented
11#13066860C211yesmaximal, characteristic
12#13066858C211yesmaximal, characteristic
13#13066850C211yesmaximal, characteristic, complemented
14#13066847C211yesmaximal, characteristic, complemented
15C11×#1444C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊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×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊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#10622603—24no—
52#10622600—24no—
53#10622586—24no—
54#10622585—24no—
55#10622282—24no—
56#10622281C418yescomplemented
57#10622280—24no—
58C24×D11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C22×C4×D11—22no—
74C22×C4×D11—22no—
75C22×C4×D11—22no—
76C22×C4×D11—22no—
77C22×C4×D11—41no—
78C22×C4×D11—41no—
79C22×C4×D11C2×C414yes—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—41no—
85C2×C11×C4⋊C4—41no—
86C2×C11×C4⋊C4—41no—
87C2×C11×C4⋊C4—41no—
88C2×C11×C4⋊C4—41no—
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—22no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
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)⋊C4C2×C414yes—
104C2×(C2×D11)⋊C4C2×C414yes—
105C2×(C2×D11)⋊C4D414yes—
106C2×(C2×D11)⋊C4Q814yes—
107C2×C4⋊Dic11—22no—
108C2×C4⋊Dic11—22no—
109C2×C4⋊Dic11—22no—
110C2×C4⋊Dic11—22no—
111C2×C4⋊Dic11—41no—
112C2×C4⋊Dic11C2×C414yes—
113C2×Dic11⋊C4—22no—
114C2×Dic11⋊C4—22no—
115C2×Dic11⋊C4—22no—
116C2×Dic11⋊C4—22no—
117C2×Dic11⋊C4—22no—
118C2×Dic11⋊C4—22no—
119C2×Dic11⋊C4—22no—
120C2×Dic11⋊C4—22no—
121C2×Dic11⋊C4—22no—
122C2×Dic11⋊C4—22no—
123C2×Dic11⋊C4—41no—
124C2×Dic11⋊C4—41no—
125C2×Dic11⋊C4—41no—
126C2×Dic11⋊C4—41no—
127C2×Dic11⋊C4C2×C414yes—
128C2×C4×Dic11—22no—
129C2×C4×Dic11—22no—
130C2×C4×Dic11—22no—
131C2×C4×Dic11—22no—
132C2×C4×Dic11—41no—
133C2×C4×Dic11—41no—
134C11×#95—22no—
135C11×#95—22no—
136C11×#95—41no—
137C11×#95C2×C414yes—
138C11⋊#95—22no—
139C11⋊#95—22no—
140C11⋊#95—22no—
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—41no—
145C11⋊#95—41no—
146C11⋊#95—41no—
147C11⋊#95C2×C414yes—
148C11⋊#95D414yes—
149C11⋊#95D414yes—
150#14402—111nomaximal, Sylow
151C24×C11C2411yescharacteristic
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×D11C22×C412yes—
165C23×D11C2×D412yes—
166C23×D11C2×Q812yes—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
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×C11C22×C412yes—
209C22×C4×C11C22×C412yes—
210C22×C4×C11C22×C412yes—
211C22×C4×C11C2×D412yes—
212C22×C4×C11C2×D412yes—
213C22×C4×C11C2×D412yes—
214C22×C4×C11C2×Q812yes—
215C22×C4×C11#4112yes—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
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×Dic11C22×C412yes—
256C22×Dic11C22×C412yes—
257C22×Dic11C22×C412yes—
258C22×Dic11C2×D412yes—
259C22×Dic11C2×D412yes—
260C22×Dic11C2×D412yes—
261C22×Dic11C2×D412yes—
262C22×Dic11C2×D412yes—
263C22×Dic11C2×Q812yes—
264C22×Dic11#4112yes—
265C2×C4×D11—28no—
266C2×C4×D11—28no—
267C2×C4×D11—44no—
268C2×C4×D11—44no—
269C2×C4×D11—44no—
270C2×C4×D11—44no—
271C2×C4×D11—44no—
272C11×C4⋊C4—44no—
273C11×C4⋊C4—44no—
274C11×C4⋊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)⋊C4C4⋊C4116yescomplemented
281C4⋊Dic11—28no—
282C4⋊Dic11—44no—
283Dic11⋊C4—28no—
284Dic11⋊C4—44no—
285Dic11⋊C4—44no—
286Dic11⋊C4—44no—
287Dic11⋊C4—44no—
288C4×Dic11—44no—
289C4×Dic11—44no—
290C2×#389—111no—
291C2×#389—111no—
292C2×#388—111no—
293C2×#388—111no—
294C2×#385—111no—
295C2×#380—111no—
296C2×#380—111no—
297#1444—111no—
298#1444D1111yescharacteristic, complemented
299#1441—111no—
300#1441—111no—
301#1439—111no—
302#1439—111no—
303#1436—111no—
304#1436—111no—
305C23×C11C23×C411yescharacteristic
306C23×C11C22×D411yescharacteristic
307C23×C11C22×D411yescharacteristic
308C23×C11C22×D411yescharacteristic
309C23×C11C22×Q811yescharacteristic
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×C112−1+411yescharacteristic
317C23×C112−1+411yescharacteristic
318C23×C112−1+411yescharacteristic
319C23×C112−1+411yescharacteristic
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—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×D11C2×C4⋊C414yes—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11C2×C4⋊C414yes—
403C2×C4×C11C4×D414yes—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—22no—
410C2×Dic11—22no—
411C2×Dic11—22no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—41no—
429C2×Dic11—41no—
430C2×Dic11—41no—
431C2×Dic11—41no—
432C2×Dic11—41no—
433C2×Dic11—41no—
434C2×Dic11—41no—
435C2×Dic11—41no—
436C2×Dic11—41no—
437C2×Dic11—41no—
438C2×Dic11—41no—
439C2×Dic11—41no—
440C2×Dic11—41no—
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×Dic11C2×C4⋊C414yes—
452C2×Dic11C4×D414yes—
453C4×D11—416no—
454C24×C4—111no—
455C22×C4⋊C4—111no—
456C22×C4⋊C4—111no—
457C22×C4⋊C4—111no—
458C22×C4⋊C4—111no—
459C22×C4⋊C4—111no—
460C22×C4⋊C4—111no—
461C22×C4⋊C4—111no—
462C22×C4⋊C4C2×D1111yescharacteristic
463C22×C4⋊C4C2×D1111yescharacteristic
464C22×C4⋊C4C2×D1111yescharacteristic
465C22×C22⋊C4—111no—
466C22×C22⋊C4—111no—
467C22×C22⋊C4—111no—
468C22×C22⋊C4—111no—
469C22×C22⋊C4—111no—
470C22×C22⋊C4—111no—
471C22×C42—111no—
472C22×C42—111no—
473#389—224no—
474#389—224no—
475#388—224no—
476#388—224no—
477#385—118no—
478#380—224no—
479#380—224no—
480C2×#95—111no—
481C2×#95—111no—
482C2×#95—111no—
483C2×#95—111no—
484C2×#95—111no—
485C2×#95—111no—
486C2×#95—111no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95—111no—
491C2×#95—111no—
492C2×#95C2×D1111yescharacteristic
493C2×#95C2×D1111yescharacteristic
494C2×#95C2×D1111yescharacteristic
495C2×#95C2×D1111yescharacteristic
496C22×C11C22×C4⋊C411yescharacteristic
497C22×C11C2×C4×D411yescharacteristic
498C22×C11C2×C4×D411yescharacteristic
499C22×C11#51811yescharacteristic
500C22×C11#51911yescharacteristic
501C22×C11#52011yescharacteristic
502C22×C11#52011yescharacteristic
503C22×C11#53611yescharacteristic
504C22×C11#53611yescharacteristic
505C22×C11#53711yescharacteristic
506C22×C11#53711yescharacteristic
507C22×C11#53711yescharacteristic
508C22×C11#53711yescharacteristic
509C22×C11#54111yescharacteristic
510C22×C11#54111yescharacteristic
511C22×C11#54211yescharacteristic
512C22×C11#54211yescharacteristic
513C22×C11#54411yescharacteristic
514C22×C11#54411yescharacteristic
515C22×C11D4211yescharacteristic
516C22×C11D4211yescharacteristic
517C22×C11D4211yescharacteristic
518C22×C11#54611yescharacteristic
519C22×C11#54611yescharacteristic
520C22×C11#54711yescharacteristic
521C22×C11#54711yescharacteristic
522C22×C11D4×Q811yescharacteristic
523C22×C11D4×Q811yescharacteristic
524C22×C11#55111yescharacteristic
525C22×C11#55411yescharacteristic
526C22×C11#55411yescharacteristic
527C22×C11#56011yescharacteristic
528C22×C11#56211yescharacteristic
529C22×C11#56211yescharacteristic
530C22×C11#56311yescharacteristic
531C2×D11—24no—
532C2×D11—24no—
533C2×D11—24no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—42no—
539C2×D11—42no—
540C2×D11—42no—
541C2×D11—42no—
542C2×D11—42no—
543C2×D11—42no—
544C2×D11—42no—
545C2×D11—42no—
546C4×C11—24no—
547C4×C11—24no—
548C4×C11—42no—
549C4×C11—42no—
550C4×C11—81no—
551C4×C11—81no—
552C4×C11—81no—
553Dic11—24no—
554Dic11—24no—
555Dic11—42no—
556Dic11—42no—
557Dic11—42no—
558Dic11—42no—
559Dic11—81no—
560C25—111no—
561C23×C4—111no—
562C23×C4—111no—
563C23×C4—111no—
564C23×C4—111no—
565C23×C4—111no—
566C23×C4—111no—
567C23×C4—114no—
568C23×C4—111no—
569C23×C4—222no—
570C23×C4—222no—
571C23×C4—222no—
572C23×C4—222no—
573C23×C4—441no—
574C23×C4—441no—
575C23×C4C22×D1111yescharacteristic
576C23×C4C22×D1111yescharacteristic
577C23×C4C22×D1111yescharacteristic
578C23×C4C22×D1111yescharacteristic
579C23×C4C22×D1111yescharacteristic
580C23×C4C22×D1111yescharacteristic
581C23×C4C22×D1111yescharacteristic
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4—114no—
592C2×C4⋊C4—114no—
593C2×C4⋊C4—222no—
594C2×C4⋊C4—222no—
595C2×C4⋊C4—222no—
596C2×C4⋊C4—222no—
597C2×C4⋊C4—222no—
598C2×C4⋊C4—222no—
599C2×C4⋊C4—222no—
600C2×C4⋊C4—222no—
601C2×C4⋊C4—222no—
602C2×C4⋊C4—222no—
603C2×C4⋊C4—222no—
604C2×C4⋊C4—222no—
605C2×C4⋊C4—222no—
606C2×C4⋊C4—222no—
607C2×C4⋊C4—441no—
608C2×C4⋊C4—441no—
609C2×C4⋊C4—441no—
610C2×C4⋊C4—441no—
611C2×C4⋊C4—441no—
612C2×C22⋊C4—114no—
613C2×C22⋊C4—114no—
614C2×C22⋊C4—114no—
615C2×C22⋊C4—114no—
616C2×C22⋊C4—222no—
617C2×C22⋊C4—222no—
618C2×C22⋊C4—222no—
619C2×C22⋊C4—222no—
620C2×C22⋊C4—222no—
621C2×C22⋊C4—222no—
622C2×C22⋊C4—222no—
623C2×C22⋊C4—222no—
624C2×C22⋊C4—441no—
625C2×C22⋊C4—441no—
626C2×C22⋊C4—441no—
627C2×C22⋊C4—441no—
628C2×C22⋊C4—441no—
629C2×C22⋊C4—441no—
630C2×C42—222no—
631C2×C42—222no—
632C2×C42—222no—
633C2×C42—222no—
634C2×C42—441no—
635C2×C42—441no—
636#95—22no—
637#95—22no—
638#95—41no—
639#95—114no—
640#95—114no—
641#95—114no—
642#95—222no—
643#95—222no—
644#95—222no—
645#95—222no—
646#95—222no—
647#95—222no—
648#95—441no—
649#95—441no—
650#95—441no—
651#95C4×D1114yes—
652C2×C11#231611yescharacteristic
653C2×C11#232311yescharacteristic
654C2×C11#232311yescharacteristic
655C2×C11D4×C4⋊C411yescharacteristic
656C2×C11D4×C4⋊C411yescharacteristic
657C2×C11#235811yescharacteristic
658C2×C11#237611yescharacteristic
659C2×C11#267211yescharacteristic
660C2×C11#267211yescharacteristic
661C2×C11#267511yescharacteristic
662C2×C11#267711yescharacteristic
663C2×C11#270411yescharacteristic
664C2×C11#270411yescharacteristic
665C2×C11#272211yescharacteristic
666C2×C11#274211yescharacteristic
667D11—44no—
668C24—112no—
669C24—112no—
670C24—112no—
671C24—221no—
672C24—221no—
673C24—221no—
674C24—221no—
675C24—221no—
676C24—221no—
677C24—221no—
678C24—221no—
679C24—221no—
680C24—221no—
681C24—221no—
682C24—221no—
683C24C23×D1111yescharacteristic
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—112no—
726C22×C4—112no—
727C22×C4—112no—
728C22×C4—112no—
729C22×C4—112no—
730C22×C4—112no—
731C22×C4—112no—
732C22×C4—112no—
733C22×C4—112no—
734C22×C4—112no—
735C22×C4—228no—
736C22×C4—221no—
737C22×C4—221no—
738C22×C4—221no—
739C22×C4—221no—
740C22×C4—221no—
741C22×C4—221no—
742C22×C4—221no—
743C22×C4—221no—
744C22×C4—221no—
745C22×C4—221no—
746C22×C4—221no—
747C22×C4—221no—
748C22×C4—221no—
749C22×C4—221no—
750C22×C4—221no—
751C22×C4—221no—
752C22×C4—221no—
753C22×C4—221no—
754C22×C4—221no—
755C22×C4—221no—
756C22×C4—221no—
757C22×C4—221no—
758C22×C4—221no—
759C22×C4—221no—
760C22×C4—221no—
761C22×C4—221no—
762C22×C4—221no—
763C22×C4—221no—
764C22×C4—221no—
765C22×C4—221no—
766C22×C4—221no—
767C22×C4—221no—
768C22×C4—228no—
769C22×C4—221no—
770C22×C4—221no—
771C22×C4—221no—
772C22×C4—221no—
773C22×C4—221no—
774C22×C4—221no—
775C22×C4—221no—
776C22×C4—444no—
777C22×C4—444no—
778C22×C4—444no—
779C22×C4—444no—
780C22×C4—444no—
781C22×C4C2×C4×D1112yes—
782C22×C4C2×C4×D1112yes—
783C22×C4C2×C4×D1112yes—
784C22×C4D4×D1112yes—
785C22×C4D4×D1112yes—
786C22×C4D4×D1112yes—
787C22×C4Q8×D1112yes—
788C22×C4#434312yes—
789C4⋊C4—44no—
790C4⋊C4—44no—
791C4⋊C4—44no—
792C4⋊C4—228no—
793C4⋊C4—228no—
794C4⋊C4—444no—
795C4⋊C4—444no—
796C4⋊C4—444no—
797C4⋊C4—444no—
798C4⋊C4—444no—
799C22⋊C4—1116no—
800C22⋊C4—444no—
801C22⋊C4—444no—
802C22⋊C4—444no—
803C22⋊C4—444no—
804C22⋊C4—444no—
805C42—444no—
806C42—444no—
807C11#1440211yescharacteristic, complemented, Sylow
808C23—114no—
809C23—222no—
810C23—222no—
811C23—222no—
812C23—222no—
813C23—222no—
814C23—222no—
815C23—222no—
816C23—222no—
817C23—222no—
818C23—222no—
819C23—222no—
820C23—222no—
821C23—222no—
822C23—222no—
823C23—222no—
824C23—222no—
825C23—222no—
826C23—222no—
827C23—441no—
828C23—441no—
829C23—441no—
830C23—441no—
831C23—441no—
832C23—441no—
833C23—441no—
834C23—441no—
835C23—441no—
836C23—441no—
837C23—441no—
838C23—441no—
839C23—441no—
840C23—441no—
841C23—441no—
842C23—441no—
843C23C22×C4×D1111yescharacteristic
844C23C2×D4×D1111yescharacteristic
845C23C2×D4×D1111yescharacteristic
846C23C2×D4×D1111yescharacteristic
847C23#6703711yescharacteristic
848C23#6703711yescharacteristic
849C23#6703711yescharacteristic
850C23C2×Q8×D1111yescharacteristic
851C23C2×#434311yescharacteristic
852C23#6704011yescharacteristic
853C23#6704011yescharacteristic
854C23#41×D1111yescharacteristic
855C23#6704211yescharacteristic
856C23#6704311yescharacteristic
857C23#6704311yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—114no—
906C2×C4—114no—
907C2×C4—222no—
908C2×C4—222no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—222no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—222no—
916C2×C4—222no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—222no—
921C2×C4—222no—
922C2×C4—222no—
923C2×C4—222no—
924C2×C4—222no—
925C2×C4—222no—
926C2×C4—222no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—4416no—
932C2×C4—441no—
933C2×C4—441no—
934C2×C4—441no—
935C2×C4—441no—
936C2×C4—441no—
937C2×C4—441no—
938C2×C4—441no—
939C2×C4—441no—
940C2×C4—441no—
941C2×C4—441no—
942C2×C4—441no—
943C2×C4—441no—
944C2×C4—441no—
945C2×C4—441no—
946C2×C4—441no—
947C2×C4—441no—
948C2×C4—441no—
949C2×C4—441no—
950C2×C4—441no—
951C2×C4—441no—
952C2×C4—441no—
953C2×C4—441no—
954C2×C4—441no—
955C2×C4C4⋊C4×D1114yes—
956C2×C4#6694614yes—
957C22—224no—
958C22—224no—
959C22—224no—
960C22—442no—
961C22—442no—
962C22—442no—
963C22—442no—
964C22—442no—
965C22—442no—
966C22—442no—
967C22—442no—
968C22—442no—
969C22—442no—
970C22—442no—
971C22—442no—
972C22C2×C4⋊C4×D1111yescharacteristic
973C22C2×#6694611yescharacteristic
974C22#1062303511yescharacteristic
975C22C4×D4×D1111yescharacteristic
976C22#1062307611yescharacteristic
977C22#1062307711yescharacteristic
978C22#1062310311yescharacteristic
979C22#1062312111yescharacteristic
980C22#1062312111yescharacteristic
981C22#1062312611yescharacteristic
982C22#1062312811yescharacteristic
983C22#1062313911yescharacteristic
984C22#1062313911yescharacteristic
985C22#1062315911yescharacteristic
986C22#1062316011yescharacteristic
987C22#1062316111yescharacteristic
988C22#1062316311yescharacteristic
989C22#1062316711yescharacteristic
990C22#1062316811yescharacteristic
991C22#1062317111yescharacteristic
992C22#1062317711yescharacteristic
993C22#1062317811yescharacteristic
994C22#1062318511yescharacteristic
995C22#1062318611yescharacteristic
996C22#1062319811yescharacteristic
997C22#1062322011yescharacteristic
998C22#1062322711yescharacteristic
999C22#1062322811yescharacteristic
1000C22#1062324811yescharacteristic
1001C22#1062325511yescharacteristic
1002C22#1062325711yescharacteristic
1003C22#1062325811yescharacteristic
1004C22#1062326011yescharacteristic
1005C22#1062326111yescharacteristic
1006C22#1062326411yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—42no—
1010C4—42no—
1011C4—81no—
1012C4—81no—
1013C4—81no—
1014C4—224no—
1015C4—224no—
1016C4—442no—
1017C4—442no—
1018C4—442no—
1019C4—442no—
1020C4—881no—
1021C2—444no—
1022C2#1307123111yescharacteristic
1023C2#1307129311yescharacteristic
1024C2#1307129611yescharacteristic
1025C2#1307151411yescharacteristic
1026C2#1307151611yescharacteristic
1027C2#1307159211yescharacteristic
1028C2#1307176511yescharacteristic
1029C2#1307486611yescharacteristic
1030C2#1307487211yescharacteristic
1031C2#1307490811yescharacteristic
1032C2#1307493011yescharacteristic
1033C2#1307527311yescharacteristic
1034C2#1307527611yescharacteristic
1035C2#1307552511yescharacteristic
1036C2#1307574711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1444C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1444D11
hypocenterC11#14402
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
1. C2×#10622586C2semidirect
2. C2×#10622585C2semidirect
8. #13066879C2semidirect
9. #13066870C2semidirect
10. #13066868C2semidirect
13. #13066850C2semidirect
14. #13066847C2semidirect
15. C11×#1444C2semidirect
56. #10622281C4semidirect
280. (C2×D11)⋊C4C4⋊C4semidirect
298. #1444D11semidirect
807. C11#14402semidirect

Maximal subgroups

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

subgroupindex
C2×#106225862
C2×#106225852
C2×#106226032
C2×#106222822
C2×#106222812
C2×#106222802
C2×#106226002
#130668792
#130668702
#130668682
#130668602
#130668582
#130668502
#130668472
C11×#14442
#1440211