Finite Group Databasebeta

← #14675364

Subgroups — #14675364

Order 2816.

2022 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×#10622558C211yesmaximal, characteristic
2C2×#10622557C211yesmaximal, characteristic
3C2×#10622823C211yesmaximal, characteristic
4C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
5C2×#10622262C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Dic11C211yesmaximal, characteristic
7#13066853C211yesmaximal, characteristic
8#13066853C211yesmaximal, characteristic
9#13066851C211yesmaximal, characteristic, complemented
10#13066849C211yesmaximal, characteristic, complemented
11#13066849C211yesmaximal, characteristic, complemented
12#13066847C211yesmaximal, characteristic, complemented
13C4×C11⋊#95C211yesmaximal, characteristic, complemented
14#95×Dic11C211yesmaximal, characteristic, complemented
15C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
16C24×C4×C11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C4×C11×C22⋊C4—24no—
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38#10622823C418yescomplemented
39C4×C22⋊Dic11—24no—
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
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54#10622558C418yescomplemented
55#10622557C418yescomplemented
56C4×Dic11⋊C4—24no—
57#10622262—24no—
58C25×C11C2311yescharacteristic
59C23×C4×C11—22no—
60C23×C4×C11—22no—
61C23×C4×C11—22no—
62C23×C4×C11—22no—
63C23×C4×C11—41no—
64C23×C4×C11—41no—
65C23×C4×C11C2×C414yes—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4C2×C414yes—
85C2×C11×C22⋊C4C2×C414yes—
86C2×C42×C11—22no—
87C2×C42×C11—22no—
88C2×C42×C11—22no—
89C2×C42×C11—22no—
90C2×C42×C11—41no—
91C2×C42×C11—41no—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—41no—
97C2×C22⋊Dic11—41no—
98C2×C22⋊Dic11C2×C414yes—
99C2×C22⋊Dic11C2×C414yes—
100C2×C22⋊Dic11C2×C414yes—
101C2×C22⋊Dic11C2×C414yes—
102C2×C22⋊Dic11C2×C414yes—
103C2×C22⋊Dic11C2×C414yes—
104C2×Dic11⋊C4—22no—
105C2×Dic11⋊C4—22no—
106C2×Dic11⋊C4—22no—
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—22no—
111C2×Dic11⋊C4—22no—
112C2×Dic11⋊C4C2×C414yes—
113C2×Dic11⋊C4C2×C414yes—
114C2×Dic11⋊C4C2×C414yescomplemented
115C2×Dic11⋊C4C2×C414yescomplemented
116C2×C4×Dic11—22no—
117C2×C4×Dic11—22no—
118C2×C4×Dic11—22no—
119C2×C4×Dic11—22no—
120C2×C4×Dic11—22no—
121C2×C4×Dic11—22no—
122C2×C4×Dic11—22no—
123C2×C4×Dic11—22no—
124C2×C4×Dic11—22no—
125C2×C4×Dic11—22no—
126C2×C4×Dic11—22no—
127C2×C4×Dic11—22no—
128C2×C4×Dic11—41no—
129C2×C4×Dic11—41no—
130C2×C4×Dic11—41no—
131C2×C4×Dic11—41no—
132C2×C4×Dic11C2×C414yescomplemented
133C2×C4×Dic11C2×C414yescomplemented
134C11×#95—22no—
135C11×#95D414yes—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—22no—
139C11⋊#95—22no—
140C11⋊#95—22no—
141C11⋊#95—41no—
142C11⋊#95—41no—
143C11⋊#95C2×C414yes—
144C11⋊#95C2×C414yes—
145C11⋊#95C2×C414yescomplemented
146C11⋊#95C2×C414yescomplemented
147C11⋊#95C2×C414yescomplemented
148C11⋊#95C2×C414yescomplemented
149C11⋊#95D414yes—
150#13823—111nomaximal, Sylow
151C24×C11—21no—
152C24×C11—21no—
153C24×C11—21no—
154C24×C11—21no—
155C24×C11—21no—
156C24×C11—21no—
157C24×C11—21no—
158C24×C11—21no—
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11C22×C412yes—
164C24×C11C22×C412yes—
165C24×C11C22×C412yes—
166C24×C11C2411yescharacteristic
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—28no—
196C22×C4×C11—28no—
197C22×C4×C11—44no—
198C22×C4×C11—44no—
199C22×C4×C11—44no—
200C22×C4×C11—44no—
201C22×C4×C11—44no—
202C22×C4×C11C22×C412yes—
203C22×C4×C11C22×C412yes—
204C22×C4×C11C22×C412yes—
205C22×C4×C11C22×C412yes—
206C22×C4×C11C22×C412yes—
207C22×C4×C11C22×C412yes—
208C22×C4×C11C2×D412yes—
209C22×C4×C11C2×D412yes—
210C22×C4×C11C2×D412yes—
211C22×C4×C11C2×D412yes—
212C22×C4×C11#4112yes—
213C22×C4×C11#4112yes—
214C22×C4×C11#4112yes—
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×Dic11C22×C412yes—
257C22×Dic11C22×C412yes—
258C22×Dic11C22×C412yes—
259C22×Dic11C22×C412yes—
260C22×Dic11C22×C412yes—
261C22×Dic11C22×C412yes—
262C22×Dic11C22×C412yes—
263C22×Dic11C22×C412yes—
264C22×Dic11C22×C412yes—
265C22×Dic11C22×C412yes—
266C22×Dic11C22×C412yes—
267C22×Dic11C22×C412yes—
268C22×Dic11C2×D412yes—
269C22×Dic11C2×D412yes—
270C22×Dic11#4112yes—
271C22×Dic11#4112yes—
272C11×C22⋊C4—28no—
273C11×C22⋊C4—28no—
274C42×C11—44no—
275C42×C11—44no—
276C22⋊Dic11—28no—
277C22⋊Dic11—28no—
278C22⋊Dic11—44no—
279C22⋊Dic11C42116yescomplemented
280Dic11⋊C4—28no—
281Dic11⋊C4—28no—
282Dic11⋊C4—28no—
283Dic11⋊C4—28no—
284C4×Dic11—28no—
285C4×Dic11—28no—
286C4×Dic11—44no—
287C4×Dic11—44no—
288C4×Dic11—44no—
289C4×Dic11—44no—
290C2×#388—111no—
291C2×#388—111no—
292C2×#385—111no—
293C2×C4×C4⋊C4—111no—
294C2×C4×C4⋊C4—111no—
295C2×C4×C22⋊C4—111no—
296C2×C4×C22⋊C4D1111yescharacteristic
297#1437—111no—
298#1437—111no—
299#1436—111no—
300#1436—111no—
301#1436—111no—
302#1436—111no—
303C4×#95—111no—
304C4×#95—111no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—41no—
337C23×C11—41no—
338C23×C11—41no—
339C23×C11C2×C4214yes—
340C23×C11C23×C411yescharacteristic
341C23×C11C23×C411yescharacteristic
342C23×C11C23×C411yescharacteristic
343C23×C11C22×D411yescharacteristic
344C23×C11C22×D411yescharacteristic
345C23×C11C2×#4111yescharacteristic
346C23×C11C2×#4111yescharacteristic
347C23×C11C2×#4111yescharacteristic
348C23×C11C2×#4111yescharacteristic
349C23×C11C2×#4111yescharacteristic
350C23×C11C2×#4111yescharacteristic
351C23×C11H(5,𝔽2)11yescharacteristic
352C23×C11H(5,𝔽2)11yescharacteristic
353C23×C112−1+411yescharacteristic
354C23×C112−1+411yescharacteristic
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—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—416no—
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×C11C4×D414yes—
395C2×C4×C11C4×D414yes—
396C2×C4×C11C4×D414yes—
397C2×C4×C11C4×D414yes—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
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—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
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×Dic11C2×C4214yes—
451C2×Dic11C2×C4214yes—
452C2×Dic11C4×D414yes—
453C2×Dic11C4×D414yes—
454C24×C4C2×D1111yescharacteristic
455C22×C4⋊C4—111no—
456C22×C4⋊C4—111no—
457C22×C4⋊C4—111no—
458C22×C4⋊C4—111no—
459C22×C22⋊C4—111no—
460C22×C22⋊C4—111no—
461C22×C22⋊C4—111no—
462C22×C22⋊C4—111no—
463C22×C22⋊C4C2×D1111yescharacteristic
464C22×C22⋊C4C2×D1111yescharacteristic
465C22×C42—111no—
466C22×C42—111no—
467C22×C42—111no—
468C22×C42—111no—
469C22×C42—111no—
470C22×C42—111no—
471C22×C42C2×D1111yescharacteristic
472C22×C42C2×D1111yescharacteristic
473#388—118no—
474#388—118no—
475#385—118no—
476C4×C4⋊C4—224no—
477C4×C4⋊C4—224no—
478C4×C22⋊C4—24no—
479C4×C22⋊C4—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×#95—111no—
493C2×#95—111no—
494C2×#95C2×D1111yescharacteristic
495C2×#95C2×D1111yescharacteristic
496C22×C11—24no—
497C22×C11—24no—
498C22×C11—24no—
499C22×C11—42no—
500C22×C11—42no—
501C22×C11—42no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—42no—
509C22×C11—42no—
510C22×C11—42no—
511C22×C11C22×C4211yescharacteristic
512C22×C11C2×C4×D411yescharacteristic
513C22×C11C2×C4×D411yescharacteristic
514C22×C11C2×C4×D411yescharacteristic
515C22×C11C2×C4×D411yescharacteristic
516C22×C11C2×C4×D411yescharacteristic
517C22×C11C2×C4×D411yescharacteristic
518C22×C11C4×#4111yescharacteristic
519C22×C11C4×#4111yescharacteristic
520C22×C11C4×#4111yescharacteristic
521C22×C11C4×#4111yescharacteristic
522C22×C11C4×#4111yescharacteristic
523C22×C11C4×#4111yescharacteristic
524C22×C11#51811yescharacteristic
525C22×C11#51911yescharacteristic
526C22×C11#52011yescharacteristic
527C22×C11#52011yescharacteristic
528C22×C11#52011yescharacteristic
529C22×C11#52011yescharacteristic
530C22×C11D4211yescharacteristic
531C22×C11#54611yescharacteristic
532C22×C11#54611yescharacteristic
533C22×C11#54711yescharacteristic
534C22×C11#54711yescharacteristic
535C22×C11#54811yescharacteristic
536C22×C11#54811yescharacteristic
537C22×C11#55111yescharacteristic
538C22×C11#55111yescharacteristic
539C22×C11#55211yescharacteristic
540C22×C11#55211yescharacteristic
541C22×C11#55311yescharacteristic
542C22×C11#55311yescharacteristic
543C22×C11#55611yescharacteristic
544C22×C11#55611yescharacteristic
545C22×C11#55911yescharacteristic
546C4×C11—24no—
547C4×C11—24no—
548C4×C11—24no—
549C4×C11—24no—
550C4×C11—42no—
551C4×C11—42no—
552Dic11—24no—
553Dic11—24no—
554Dic11—24no—
555Dic11—24no—
556Dic11—42no—
557Dic11—42no—
558Dic11—42no—
559Dic11—42no—
560C25C22×D1111yescharacteristic
561C23×C4—22no—
562C23×C4—22no—
563C23×C4—22no—
564C23×C4—22no—
565C23×C4—41no—
566C23×C4—41no—
567C23×C4—111no—
568C23×C4—111no—
569C23×C4—111no—
570C23×C4—111no—
571C23×C4—111no—
572C23×C4—111no—
573C23×C4—111no—
574C23×C4—111no—
575C23×C4C4×D1114yes—
576C23×C4C22×D1111yescharacteristic
577C23×C4C22×D1111yescharacteristic
578C23×C4C22×D1111yescharacteristic
579C23×C4C22×D1111yescharacteristic
580C23×C4C22×D1111yescharacteristic
581C23×C4C22×D1111yescharacteristic
582C2×C4⋊C4—114no—
583C2×C4⋊C4—114no—
584C2×C4⋊C4—114no—
585C2×C4⋊C4—114no—
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×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—114no—
599C2×C22⋊C4—114no—
600C2×C22⋊C4—114no—
601C2×C22⋊C4—114no—
602C2×C22⋊C4—114no—
603C2×C22⋊C4—114no—
604C2×C22⋊C4—222no—
605C2×C22⋊C4—222no—
606C2×C22⋊C4—222no—
607C2×C22⋊C4—222no—
608C2×C22⋊C4—441no—
609C2×C22⋊C4—441no—
610C2×C22⋊C4C4×D1114yes—
611C2×C22⋊C4C4×D1114yes—
612C2×C42—22no—
613C2×C42—22no—
614C2×C42—22no—
615C2×C42—22no—
616C2×C42—41no—
617C2×C42—41no—
618C2×C42—114no—
619C2×C42—114no—
620C2×C42—222no—
621C2×C42—222no—
622C2×C42—222no—
623C2×C42—222no—
624C2×C42—222no—
625C2×C42—222no—
626C2×C42—222no—
627C2×C42—222no—
628C2×C42—222no—
629C2×C42—222no—
630C2×C42—222no—
631C2×C42—222no—
632C2×C42—441no—
633C2×C42—441no—
634C2×C42—441no—
635C2×C42—441no—
636#95—22no—
637#95—114no—
638#95—114no—
639#95—114no—
640#95—114no—
641#95—114no—
642#95—114no—
643#95—114no—
644#95—222no—
645#95—222no—
646#95—222no—
647#95—222no—
648#95—222no—
649#95—441no—
650#95—441no—
651#95C22⋊D1114yes—
652C2×C11—44no—
653C2×C11C42×D411yescharacteristic
654C2×C11C42×D411yescharacteristic
655C2×C11#227411yescharacteristic
656C2×C11#235811yescharacteristic
657C2×C11#235911yescharacteristic
658C2×C11#235911yescharacteristic
659C2×C11#236111yescharacteristic
660C2×C11#236111yescharacteristic
661C2×C11#236211yescharacteristic
662C2×C11#236211yescharacteristic
663C2×C11#236711yescharacteristic
664C2×C11#236711yescharacteristic
665C2×C11#237311yescharacteristic
666C2×C11#237311yescharacteristic
667C2×C11#237411yescharacteristic
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24C2×C4×D1112yes—
681C24C2×C4×D1112yes—
682C24C2×C4×D1112yes—
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—28no—
713C22×C4—28no—
714C22×C4—44no—
715C22×C4—44no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—112no—
720C22×C4—112no—
721C22×C4—112no—
722C22×C4—112no—
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—112no—
732C22×C4—112no—
733C22×C4—112no—
734C22×C4—112no—
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—221no—
773C22×C4—221no—
774C22×C4—221no—
775C22×C4C2×C4×D1112yes—
776C22×C4C2×C4×D1112yes—
777C22×C4C2×C4×D1112yes—
778C22×C4C2×C4×D1112yes—
779C22×C4C2×C4×D1112yes—
780C22×C4C2×C4×D1112yes—
781C22×C4#433912yes—
782C22×C4#433912yes—
783C22×C4#433912yes—
784C22×C4D4×D1112yes—
785C22×C4#434112yes—
786C22×C4C2×C22⋊D1112yes—
787C22×C4C2×C22⋊D1112yes—
788C22×C4C2×C22⋊D1112yes—
789C4⋊C4—228no—
790C4⋊C4—228no—
791C4⋊C4—228no—
792C4⋊C4—228no—
793C22⋊C4—28no—
794C22⋊C4—28no—
795C22⋊C4—1116no—
796C22⋊C4—228no—
797C22⋊C4—228no—
798C22⋊C4—444no—
799C42—44no—
800C42—44no—
801C42—228no—
802C42—228no—
803C42—444no—
804C42—444no—
805C42—444no—
806C42—444no—
807C11#1382311yescharacteristic, complemented, Sylow
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C42×D1114yes—
843C23C22×C4×D1111yescharacteristic
844C23C22×C4×D1111yescharacteristic
845C23C22×C4×D1111yescharacteristic
846C23C2×#433911yescharacteristic
847C23C2×#433911yescharacteristic
848C23C2×#433911yescharacteristic
849C23C2×D4×D1111yescharacteristic
850C23C2×#434111yescharacteristic
851C23#6703711yescharacteristic
852C23#6703711yescharacteristic
853C23#41×D1111yescharacteristic
854C23#41×D1111yescharacteristic
855C23#6704311yescharacteristic
856C23#6704311yescharacteristic
857C23C22×C22⋊D1111yescharacteristic
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—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—416no—
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—114no—
898C2×C4—114no—
899C2×C4—114no—
900C2×C4—114no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—222no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—222no—
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—222no—
932C2×C4—222no—
933C2×C4—222no—
934C2×C4—222no—
935C2×C4—222no—
936C2×C4—222no—
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(C22⋊D11)⋊C414yes—
954C2×C4C4×C22⋊D1114yes—
955C2×C4C4×C22⋊D1114yes—
956C2×C4C4×C22⋊D1114yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C2×C42×D1111yescharacteristic
973C22C4×#433911yescharacteristic
974C22C4×#433911yescharacteristic
975C22C4×#433911yescharacteristic
976C22C2×(C22⋊D11)⋊C411yescharacteristic
977C22#1062301711yescharacteristic
978C22#1062302111yescharacteristic
979C22#1062302611yescharacteristic
980C22#1062304711yescharacteristic
981C22#1062305311yescharacteristic
982C22#1062306011yescharacteristic
983C22#1062306411yescharacteristic
984C22C4×#434111yescharacteristic
985C22C4×#434111yescharacteristic
986C22#1062307111yescharacteristic
987C22#1062307211yescharacteristic
988C22#1062307311yescharacteristic
989C22C4×D4×D1111yescharacteristic
990C22C4×D4×D1111yescharacteristic
991C22#1062307711yescharacteristic
992C22#1062307711yescharacteristic
993C22#1062307711yescharacteristic
994C22#1062307711yescharacteristic
995C22#1062308211yescharacteristic
996C22#1062308311yescharacteristic
997C22#1062308711yescharacteristic
998C22#1062308911yescharacteristic
999C22#1062309011yescharacteristic
1000C22C2×C4×C22⋊D1111yescharacteristic
1001C22C2×C4×C22⋊D1111yescharacteristic
1002C22C2×C4×C22⋊D1111yescharacteristic
1003C22D4×C22⋊D1111yescharacteristic
1004C22#1062333711yescharacteristic
1005C22#1062335511yescharacteristic
1006C22#1062336211yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—42no—
1012C4—42no—
1013C4—224no—
1014C4—224no—
1015C4—224no—
1016C4—224no—
1017C4—442no—
1018C4—442no—
1019C4—442no—
1020C4—442no—
1021C2—44no—
1022C2C4×(C22⋊D11)⋊C411yescharacteristic
1023C2C42×C22⋊D1111yescharacteristic
1024C2#1307097111yescharacteristic
1025C2#1307159511yescharacteristic
1026C2#1307160211yescharacteristic
1027C2#1307160911yescharacteristic
1028C2#1307162811yescharacteristic
1029C2#1307163311yescharacteristic
1030C2#1307164111yescharacteristic
1031C2#1307164311yescharacteristic
1032C2#1307168811yescharacteristic
1033C2#1307168911yescharacteristic
1034C2#1307173711yescharacteristic
1035C2#1307173811yescharacteristic
1036C2#1307174711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#13823
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C4×Dic11⋊C4C2semidirect
5. C2×#10622262C2semidirect
9. #13066851C2semidirect
10. #13066849C2semidirect
11. #13066849C2semidirect
12. #13066847C2semidirect
13. C4×C11⋊#95C2semidirect
14. #95×Dic11C2semidirect
38. #10622823C4semidirect
54. #10622558C4semidirect
55. #10622557C4semidirect
114. C2×Dic11⋊C4C2×C4semidirect
115. C2×Dic11⋊C4C2×C4semidirect
132. C2×C4×Dic11C2×C4semidirect
133. C2×C4×Dic11C2×C4semidirect
145. C11⋊#95C2×C4semidirect
146. C11⋊#95C2×C4semidirect
147. C11⋊#95C2×C4semidirect
148. C11⋊#95C2×C4semidirect
279. C22⋊Dic11C42semidirect
807. C11#13823semidirect

Maximal subgroups

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

subgroupindex
C2×#106225582
C2×#106225572
C2×#106228232
C2×C4×Dic11⋊C42
C2×#106222622
C2×C4×C22⋊Dic112
#130668532
#130668512
#130668492
#130668472
C4×C11⋊#952
#95×Dic112
C2×C4×C11×C22⋊C42
#1382311