Finite Group Databasebeta

← #14681743

Subgroups — #14681743

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×#10622541C211yesmaximal, characteristic, complemented
2C2×#10622283C211yesmaximal, characteristic
3C2×#10622553C211yesmaximal, characteristic
4C2×#10622281C211yesmaximal, characteristic
5C2×#10622281C211yesmaximal, characteristic
6C2×#10622602C211yesmaximal, characteristic
7C2×#10622589C211yesmaximal, characteristic, complemented
8#13066881C211yesmaximal, characteristic, complemented
9#13066880C211yesmaximal, characteristic, complemented
10#13066871C211yesmaximal, characteristic, complemented
11#13066868C211yesmaximal, characteristic, complemented
12#13066862C211yesmaximal, characteristic
13#13066860C211yesmaximal, characteristic
14#13066840C211yesmaximal, characteristic, complemented
15C11×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
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#10622602—24no—
52#10622589—24no—
53#10622553—24no—
54#10622541—24no—
55#10622283C418yescomplemented
56#10622281—24no—
57#10622281—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—41no—
77C22×C4×D11—41no—
78C22×C4×D11—41no—
79C22×C4×D11—41no—
80C2×C11×C4⋊C4—41no—
81C2×C11×C4⋊C4—41no—
82C2×C11×C4⋊C4D414yes—
83C2×C42×C11—22no—
84C2×C42×C11—22no—
85C2×C42×C11—41no—
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—22no—
95C2×(C2×D11)⋊C4—41no—
96C2×(C2×D11)⋊C4—41no—
97C2×(C2×D11)⋊C4—41no—
98C2×(C2×D11)⋊C4—41no—
99C2×(C2×D11)⋊C4C2×C414yes—
100C2×(C2×D11)⋊C4C2×C414yes—
101C2×(C2×D11)⋊C4C2×C414yes—
102C2×(C2×D11)⋊C4D414yes—
103C2×(C2×D11)⋊C4Q814yes—
104C2×C4⋊Dic11—22no—
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11—22no—
107C2×C4⋊Dic11—22no—
108C2×C4⋊Dic11—22no—
109C2×C4⋊Dic11—22no—
110C2×C4⋊Dic11—41no—
111C2×C4⋊Dic11—41no—
112C2×C4⋊Dic11—41no—
113C2×C4⋊Dic11—41no—
114C2×C4⋊Dic11—41no—
115C2×C4⋊Dic11C2×C414yescomplemented
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—22no—
124C2×Dic11⋊C4—22no—
125C2×Dic11⋊C4—22no—
126C2×Dic11⋊C4—41no—
127C2×Dic11⋊C4—41no—
128C2×Dic11⋊C4—41no—
129C2×Dic11⋊C4—41no—
130C2×Dic11⋊C4—41no—
131C2×C4×Dic11—22no—
132C2×C4×Dic11—22no—
133C2×C4×Dic11C2×C414yescomplemented
134C11×#95—22no—
135C11×#95—22no—
136C11×#95—22no—
137C11×#95—41no—
138C11×#95C2×C414yescomplemented
139C11⋊#95—22no—
140C11⋊#95—22no—
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146C11⋊#95—41no—
147C11⋊#95—41no—
148C11⋊#95C2×C414yescomplemented
149C11⋊#95D414yes—
150#14405—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×C11C22×C412yes—
207C22×C4×C11C22×C412yes—
208C22×C4×C11C22×C412yes—
209C22×C4×C11C2×D412yes—
210C22×C4×C11C2×D412yes—
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×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11C22×C412yes—
258C22×Dic11C22×C412yes—
259C22×Dic11C22×C412yes—
260C22×Dic11C2×D412yes—
261C22×Dic11C2×D412yes—
262C22×Dic11C2×D412yes—
263C22×Dic11C2×Q812yes—
264C22×Dic11#4112yes—
265C2×C4×D11—44no—
266C2×C4×D11—44no—
267C2×C4×D11—44no—
268C2×C4×D11—44no—
269C2×C4×D11—44no—
270C2×C4×D11—44no—
271C2×C4×D11—44no—
272C11×C4⋊C4—44no—
273C42×C11—44no—
274(C2×D11)⋊C4—28no—
275(C2×D11)⋊C4—28no—
276(C2×D11)⋊C4—44no—
277(C2×D11)⋊C4—44no—
278(C2×D11)⋊C4—44no—
279(C2×D11)⋊C4C4⋊C4116yescomplemented
280C4⋊Dic11—28no—
281C4⋊Dic11—44no—
282C4⋊Dic11—44no—
283C4⋊Dic11—44no—
284Dic11⋊C4—44no—
285Dic11⋊C4—44no—
286Dic11⋊C4—44no—
287Dic11⋊C4—44no—
288Dic11⋊C4—44no—
289C4×Dic11—28no—
290C2×#389—111no—
291C2×#388—111no—
292C2×#388—111no—
293C2×#385—111no—
294C2×#385—111no—
295C2×#385—111no—
296C2×#384—111no—
297#1444—111no—
298#1444—111no—
299#1442—111no—
300#1441—111no—
301#1439—111no—
302#1439—111no—
303#1436D1111yescharacteristic, complemented
304#1434—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—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
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—41no—
423C2×Dic11—41no—
424C2×Dic11—41no—
425C2×Dic11—41no—
426C2×Dic11—41no—
427C2×Dic11—41no—
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⋊C4—111no—
463C22×C4⋊C4—111no—
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×C42C2×D1111yescharacteristic
473#389—224no—
474#388—118no—
475#388—224no—
476#385—224no—
477#385—224no—
478#385—224no—
479#384—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×#95C2×D1111yescharacteristic
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#52011yescharacteristic
500C22×C11#52011yescharacteristic
501C22×C11#52011yescharacteristic
502C22×C11#52011yescharacteristic
503C22×C11#53411yescharacteristic
504C22×C11#53511yescharacteristic
505C22×C11#53511yescharacteristic
506C22×C11#53611yescharacteristic
507C22×C11#53611yescharacteristic
508C22×C11#53611yescharacteristic
509C22×C11#53911yescharacteristic
510C22×C11#53911yescharacteristic
511C22×C11#54211yescharacteristic
512C22×C11#54211yescharacteristic
513C22×C11#54411yescharacteristic
514C22×C11#54411yescharacteristic
515C22×C11D4211yescharacteristic
516C22×C11D4211yescharacteristic
517C22×C11D4211yescharacteristic
518C22×C11#54711yescharacteristic
519C22×C11#54711yescharacteristic
520C22×C11#54711yescharacteristic
521C22×C11#54811yescharacteristic
522C22×C11D4×Q811yescharacteristic
523C22×C11D4×Q811yescharacteristic
524C22×C11#55311yescharacteristic
525C22×C11#55411yescharacteristic
526C22×C11#55411yescharacteristic
527C22×C11#56011yescharacteristic
528C22×C11#56311yescharacteristic
529C22×C11#56311yescharacteristic
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—42no—
551C4×C11—42no—
552C4×C11—81no—
553Dic11—24no—
554Dic11—24no—
555Dic11—42no—
556Dic11—42no—
557Dic11—81no—
558Dic11—81no—
559Dic11—81no—
560C25—111no—
561C23×C4—111no—
562C23×C4—111no—
563C23×C4—111no—
564C23×C4—111no—
565C23×C4—111no—
566C23×C4—111no—
567C23×C4—111no—
568C23×C4—222no—
569C23×C4—222no—
570C23×C4—222no—
571C23×C4—441no—
572C23×C4—441no—
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—41no—
583C2×C4⋊C4—41no—
584C2×C4⋊C4—114no—
585C2×C4⋊C4—222no—
586C2×C4⋊C4—222no—
587C2×C4⋊C4—222no—
588C2×C4⋊C4—222no—
589C2×C4⋊C4—222no—
590C2×C4⋊C4—222no—
591C2×C4⋊C4—222no—
592C2×C4⋊C4—222no—
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—441no—
602C2×C4⋊C4—441no—
603C2×C4⋊C4—441no—
604C2×C4⋊C4—441no—
605C2×C4⋊C4—441no—
606C2×C4⋊C4—441no—
607C2×C4⋊C4—441no—
608C2×C4⋊C4—441no—
609C2×C4⋊C4—441no—
610C2×C4⋊C4—441no—
611C2×C4⋊C4D4414yes—
612C2×C22⋊C4—114no—
613C2×C22⋊C4—114no—
614C2×C22⋊C4—114no—
615C2×C22⋊C4—114no—
616C2×C22⋊C4—114no—
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—222no—
625C2×C22⋊C4—222no—
626C2×C22⋊C4—441no—
627C2×C22⋊C4—441no—
628C2×C22⋊C4—441no—
629C2×C22⋊C4—441no—
630C2×C42—22no—
631C2×C42—22no—
632C2×C42—41no—
633C2×C42—114no—
634C2×C42—222no—
635C2×C42—222no—
636#95—22no—
637#95—22no—
638#95—22no—
639#95—41no—
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—222no—
649#95—441no—
650#95—441no—
651#95C4×D1114yescomplemented
652C2×C11#231711yescharacteristic
653C2×C11#232211yescharacteristic
654C2×C11#232611yescharacteristic
655C2×C11D4×C4⋊C411yescharacteristic
656C2×C11D4×C4⋊C411yescharacteristic
657C2×C11#236111yescharacteristic
658C2×C11#238311yescharacteristic
659C2×C11#266911yescharacteristic
660C2×C11#267411yescharacteristic
661C2×C11#267711yescharacteristic
662C2×C11#268011yescharacteristic
663C2×C11#271811yescharacteristic
664C2×C11#272011yescharacteristic
665C2×C11#272911yescharacteristic
666C2×C11#279011yescharacteristic
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—112no—
724C22×C4—112no—
725C22×C4—112no—
726C22×C4—112no—
727C22×C4—112no—
728C22×C4—112no—
729C22×C4—112no—
730C22×C4—112no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—221no—
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—221no—
769C22×C4—221no—
770C22×C4—221no—
771C22×C4—221no—
772C22×C4—444no—
773C22×C4—444no—
774C22×C4—444no—
775C22×C4—444no—
776C22×C4—444no—
777C22×C4—444no—
778C22×C4—444no—
779C22×C4C2×C4×D1112yes—
780C22×C4C2×C4×D1112yes—
781C22×C4C2×C4×D1112yes—
782C22×C4C2×D4412yes—
783C22×C4C2×D4412yes—
784C22×C4C2×D4412yes—
785C22×C4#433912yes—
786C22×C4D4×D1112yes—
787C22×C4D4×D1112yes—
788C22×C4Q8×D1112yes—
789C4⋊C4—44no—
790C4⋊C4—228no—
791C4⋊C4—444no—
792C4⋊C4—444no—
793C4⋊C4—444no—
794C4⋊C4—444no—
795C4⋊C4—444no—
796C4⋊C4—444no—
797C4⋊C4—444no—
798C4⋊C4—444no—
799C22⋊C4—1116no—
800C22⋊C4—228no—
801C22⋊C4—228no—
802C22⋊C4—444no—
803C22⋊C4—444no—
804C22⋊C4—444no—
805C42—44no—
806C42—228no—
807C11#1440511yescharacteristic, 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
844C23C22×D4411yescharacteristic
845C23C2×#433911yescharacteristic
846C23C2×D4×D1111yescharacteristic
847C23C2×D4×D1111yescharacteristic
848C23#6703711yescharacteristic
849C23#6703711yescharacteristic
850C23C2×Q8×D1111yescharacteristic
851C23#6704011yescharacteristic
852C23#41×D1111yescharacteristic
853C23#6704211yescharacteristic
854C23#6704211yescharacteristic
855C23#6704311yescharacteristic
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—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
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—4416no—
926C2×C4—441no—
927C2×C4—441no—
928C2×C4—441no—
929C2×C4—441no—
930C2×C4—441no—
931C2×C4—441no—
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×D4414yes—
956C2×C4C4⋊C4×D1114yes—
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×D4411yescharacteristic
973C22#1062302411yescharacteristic
974C22C2×C4⋊C4×D1111yescharacteristic
975C22#1062303811yescharacteristic
976C22#1062305411yescharacteristic
977C22#1062305711yescharacteristic
978C22#1062306111yescharacteristic
979C22C4×D4×D1111yescharacteristic
980C22#1062307711yescharacteristic
981C22#1062307711yescharacteristic
982C22D4×D4411yescharacteristic
983C22D4×D4411yescharacteristic
984C22#1062308211yescharacteristic
985C22#1062309511yescharacteristic
986C22#1062309511yescharacteristic
987C22#1062310511yescharacteristic
988C22Q8×D4411yescharacteristic
989C22#1062310711yescharacteristic
990C22#1062311011yescharacteristic
991C22#1062312111yescharacteristic
992C22#1062313811yescharacteristic
993C22#1062313811yescharacteristic
994C22#1062315911yescharacteristic
995C22#1062316311yescharacteristic
996C22#1062316711yescharacteristic
997C22#1062317711yescharacteristic
998C22#1062317911yescharacteristic
999C22#1062318611yescharacteristic
1000C22#1062319711yescharacteristic
1001C22#1062320011yescharacteristic
1002C22#1062322011yescharacteristic
1003C22#1062323011yescharacteristic
1004C22#1062324111yescharacteristic
1005C22#1062324311yescharacteristic
1006C22#1062326011yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—42no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—81no—
1014C4—224no—
1015C4—224no—
1016C4—442no—
1017C4—442no—
1018C4—881no—
1019C4—881no—
1020C4—881no—
1021C2—444no—
1022C2#1307123811yescharacteristic
1023C2#1307128711yescharacteristic
1024C2#1307132511yescharacteristic
1025C2#1307151411yescharacteristic
1026C2C4⋊C4×D4411yescharacteristic
1027C2#1307163411yescharacteristic
1028C2#1307180611yescharacteristic
1029C2#1307483411yescharacteristic
1030C2#1307490011yescharacteristic
1031C2#1307492911yescharacteristic
1032C2#1307495811yescharacteristic
1033C2#1307546911yescharacteristic
1034C2#1307549611yescharacteristic
1035C2#1307559611yescharacteristic
1036C2#1307638411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1436D11
hypocenterC11#14405
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
1. C2×#10622541C2semidirect
7. C2×#10622589C2semidirect
8. #13066881C2semidirect
9. #13066880C2semidirect
10. #13066871C2semidirect
11. #13066868C2semidirect
14. #13066840C2semidirect
15. C11×#1436C2semidirect
55. #10622283C4semidirect
115. C2×C4⋊Dic11C2×C4semidirect
133. C2×C4×Dic11C2×C4semidirect
138. C11×#95C2×C4semidirect
148. C11⋊#95C2×C4semidirect
279. (C2×D11)⋊C4C4⋊C4semidirect
303. #1436D11semidirect
651. #95C4×D11semidirect
807. C11#14405semidirect

Maximal subgroups

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

subgroupindex
C2×#106225412
C2×#106222832
C2×#106225532
C2×#106222812
C2×#106226022
C2×#106225892
#130668812
#130668802
#130668712
#130668682
#130668622
#130668602
#130668402
C11×#14362
#1440511