Finite Group Databasebeta

← #14681906

Subgroups — #14681906

Order 2816.

2602 conjugacy classes of subgroups.

The subgroup lattice has 1354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66937C211yesmaximal, characteristic
2C2×#10622278C211yesmaximal, characteristic, complemented
3C2×#10622571C211yesmaximal, characteristic, complemented
4C2×#10622571C211yesmaximal, characteristic, complemented
5C2×#10622569C211yesmaximal, characteristic, complemented
6#13066882C211yesmaximal, characteristic, complemented
7#13066882C211yesmaximal, characteristic, complemented
8#13066864C211yesmaximal, characteristic, complemented
9#13066856C211yesmaximal, characteristic, complemented
10#13066855C211yesmaximal, characteristic, complemented
11#13066838C211yesmaximal, characteristic, complemented
12(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1440C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C2×#66937—24no—
36C2×#66937—24no—
37C2×#66937C418yescomplemented
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
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54#10622571—24no—
55#10622571—24no—
56#10622569—24no—
57#10622278—24no—
58C25×C11C2311yescharacteristic
59C24×D11C2311yescharacteristic
60C24×D11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—22no—
68C22×C22⋊D11—22no—
69C22×C22⋊D11—22no—
70C22×C22⋊D11—22no—
71C22×C22⋊D11—41no—
72C22×C22⋊D11—41no—
73C22×C22⋊D11—41no—
74C22×C22⋊D11—41no—
75C22×C22⋊D11—41no—
76C22×C22⋊D11—41no—
77C22×C22⋊D11C2×C414yes—
78C22×C22⋊D11C2×C414yescomplemented
79C22×C22⋊D11D414yes—
80C22×C22⋊D11D414yes—
81C23×Dic11—22no—
82C23×Dic11—22no—
83C23×Dic11—22no—
84C23×Dic11—41no—
85C23×Dic11—41no—
86C23×Dic11—41no—
87C23×Dic11—41no—
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C22×D44—22no—
95C22×D44—22no—
96C22×D44—22no—
97C22×D44—22no—
98C22×D44—41no—
99C22×D44—41no—
100C22×D44C2×C414yescomplemented
101C22×C4×D11—22no—
102C22×C4×D11—22no—
103C22×C4×D11—22no—
104C22×C4×D11—22no—
105C22×C4×D11—22no—
106C22×C4×D11—41no—
107C22×C4×D11—41no—
108C22×C4×D11—41no—
109C22×C4×D11—41no—
110C22×C4×D11—41no—
111C22×C4×D11—41no—
112C22×C4×D11—41no—
113C22×C4×D11—41no—
114C22×C4×D11C2×C414yescomplemented
115C2×C11×C22⋊C4—22no—
116C2×C11×C22⋊C4—22no—
117C2×C11×C22⋊C4—22no—
118C2×C11×C22⋊C4—22no—
119C2×C11×C22⋊C4—22no—
120C2×C11×C22⋊C4—41no—
121C2×C11×C22⋊C4—41no—
122C2×C11×C22⋊C4—41no—
123C2×C11×C22⋊C4C2×C414yescomplemented
124C2×C22⋊Dic11—22no—
125C2×C22⋊Dic11—22no—
126C2×C22⋊Dic11—41no—
127C2×(C2×D11)⋊C4—22no—
128C2×(C2×D11)⋊C4—22no—
129C2×(C2×D11)⋊C4—22no—
130C2×(C2×D11)⋊C4—22no—
131C2×(C2×D11)⋊C4—22no—
132C2×(C2×D11)⋊C4—22no—
133C2×(C2×D11)⋊C4—22no—
134C2×(C2×D11)⋊C4—22no—
135C2×(C2×D11)⋊C4—22no—
136C2×(C2×D11)⋊C4—22no—
137C2×(C2×D11)⋊C4—22no—
138C2×(C2×D11)⋊C4—22no—
139C2×(C2×D11)⋊C4—41no—
140C2×(C2×D11)⋊C4—41no—
141C2×(C2×D11)⋊C4—41no—
142C2×(C2×D11)⋊C4—41no—
143C2×(C2×D11)⋊C4—41no—
144C2×(C2×D11)⋊C4—41no—
145C2×(C2×D11)⋊C4—41no—
146C2×(C2×D11)⋊C4—41no—
147C2×(C2×D11)⋊C4—41no—
148C2×(C2×D11)⋊C4—41no—
149C2×(C2×D11)⋊C4C2×C414yescomplemented
150C2×(C2×D11)⋊C4D414yescomplemented
151C2×Dic11⋊C4—22no—
152C2×Dic11⋊C4—22no—
153C2×Dic11⋊C4C2×C414yescomplemented
154#66937—232no—
155C11×#95—22no—
156C11×#95—41no—
157C11×#95—41no—
158C11×#95—41no—
159C11⋊#95—22no—
160C11⋊#95—22no—
161C11⋊#95—22no—
162C11⋊#95—22no—
163C11⋊#95—22no—
164C11⋊#95—22no—
165C11⋊#95—22no—
166C11⋊#95—41no—
167C11⋊#95—41no—
168C11⋊#95—41no—
169C11⋊#95—41no—
170C11⋊#95—41no—
171#14417—111nomaximal, Sylow
172C24×C11—21no—
173C24×C11—21no—
174C24×C11—21no—
175C24×C11—21no—
176C24×C11—21no—
177C24×C11—21no—
178C24×C11—21no—
179C24×C11—21no—
180C24×C11—21no—
181C24×C11—21no—
182C24×C11—21no—
183C24×C11—21no—
184C24×C11C22×C412yes—
185C24×C11C2×D412yes—
186C24×C11C2×D412yes—
187C24×C11C2411yescharacteristic
188C23×D11—21no—
189C23×D11—21no—
190C23×D11—21no—
191C23×D11—21no—
192C23×D11—21no—
193C23×D11—21no—
194C23×D11—21no—
195C23×D11—21no—
196C23×D11—21no—
197C23×D11—21no—
198C23×D11—21no—
199C23×D11—21no—
200C23×D11—21no—
201C23×D11—21no—
202C23×D11—21no—
203C23×D11—21no—
204C23×D11—21no—
205C23×D11—21no—
206C23×D11—21no—
207C23×D11—21no—
208C23×D11—21no—
209C23×D11—21no—
210C23×D11—21no—
211C23×D11—21no—
212C23×D11C22×C412yes—
213C23×D11C22×C412yes—
214C23×D11C2×D412yes—
215C23×D11C2×D412yes—
216C23×D11C2×D412yes—
217C23×D11#4112yes—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11—21no—
257C22×C4×C11C22×C412yes—
258C22×C4×C11C22×C412yes—
259C22×C4×C11C2×D412yes—
260C2×C22⋊D11—28no—
261C2×C22⋊D11—28no—
262C2×C22⋊D11—44no—
263C2×C22⋊D11—44no—
264C2×C22⋊D11—44no—
265C2×C22⋊D11—44no—
266C2×C22⋊D11—44no—
267C2×C22⋊D11—44no—
268C2×C22⋊D11—44no—
269C2×C22⋊D11—44no—
270C2×C22⋊D11—44no—
271C2×C22⋊D11—44no—
272C2×C22⋊D11—44no—
273C2×C22⋊D11C22⋊C4116yescomplemented
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11—21no—
277C22×Dic11—21no—
278C22×Dic11—21no—
279C22×Dic11—21no—
280C22×Dic11—21no—
281C22×Dic11—21no—
282C22×Dic11—21no—
283C22×Dic11—21no—
284C22×Dic11—21no—
285C22×Dic11—21no—
286C22×Dic11—21no—
287C22×Dic11—21no—
288C22×Dic11—21no—
289C22×Dic11—21no—
290C22×Dic11—21no—
291C22×Dic11—21no—
292C22×Dic11—21no—
293C22×Dic11—21no—
294C22×Dic11—21no—
295C22×Dic11—21no—
296C22×Dic11—21no—
297C22×Dic11—21no—
298C22×Dic11—21no—
299C22×Dic11—21no—
300C22×Dic11—21no—
301C22×Dic11—21no—
302C22×Dic11—21no—
303C22×Dic11—21no—
304C22×Dic11—21no—
305C22×Dic11—21no—
306C22×Dic11—21no—
307C22×Dic11—21no—
308C22×Dic11—21no—
309C22×Dic11—44no—
310C22×Dic11—44no—
311C22×Dic11—44no—
312C22×Dic11—44no—
313C22×Dic11—44no—
314C22×Dic11—44no—
315C22×Dic11—44no—
316C22×Dic11C22×C412yes—
317C22×Dic11C22×C412yes—
318C22×Dic11C2×D412yes—
319C22×Dic11C2×D412yes—
320C22×Dic11C2×D412yes—
321C22×Dic11#4112yes—
322C22×Dic11#4112yes—
323C2×D44—28no—
324C2×D44—28no—
325C2×D44—44no—
326C2×D44—44no—
327C2×D44—44no—
328C2×D44—44no—
329C2×D44—44no—
330C2×C4×D11—28no—
331C2×C4×D11—44no—
332C2×C4×D11—44no—
333C2×C4×D11—44no—
334C2×C4×D11—44no—
335C2×C4×D11—44no—
336C2×C4×D11—44no—
337C2×C4×D11—44no—
338C2×C4×D11—44no—
339C2×C4×D11—44no—
340C2×C4×D11—44no—
341C2×C4×D11—44no—
342C2×C4×D11—44no—
343C2×C4×D11—44no—
344C11×C22⋊C4—28no—
345C11×C22⋊C4—44no—
346C11×C22⋊C4—44no—
347C22⋊Dic11—44no—
348(C2×D11)⋊C4—28no—
349(C2×D11)⋊C4—44no—
350(C2×D11)⋊C4—44no—
351(C2×D11)⋊C4—44no—
352(C2×D11)⋊C4—44no—
353(C2×D11)⋊C4—44no—
354(C2×D11)⋊C4—44no—
355(C2×D11)⋊C4—44no—
356Dic11⋊C4—28no—
357C22×#121—111no—
358C2×#386—111no—
359C2×#386—111no—
360C2×#386—111no—
361C2×#386—111no—
362#1445—111no—
363#1445—111no—
364#1440—111no—
365#1440D1111yescharacteristic, complemented
366#1438—111no—
367#1438—111no—
368C22⋊#95—111no—
369C22⋊#95—111no—
370C22⋊#95—111no—
371C22⋊#95—111no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—22no—
380C23×C11—22no—
381C23×C11—22no—
382C23×C11—22no—
383C23×C11—22no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—22no—
388C23×C11—22no—
389C23×C11—22no—
390C23×C11—41no—
391C23×C11—41no—
392C23×C11—41no—
393C23×C11—41no—
394C23×C11—41no—
395C23×C11—41no—
396C23×C11—41no—
397C23×C11—41no—
398C23×C11—41no—
399C23×C11—41no—
400C23×C11—41no—
401C23×C11—41no—
402C23×C11—41no—
403C23×C11—41no—
404C23×C11—41no—
405C23×C11—41no—
406C23×C11C2×C22⋊C414yes—
407C23×C11C23×C411yescharacteristic
408C23×C11C22×D411yescharacteristic
409C23×C11C22×D411yescharacteristic
410C23×C11C22×D411yescharacteristic
411C23×C11C2×#4111yescharacteristic
412C23×C11C2×#4111yescharacteristic
413C23×C11C2×#4111yescharacteristic
414C23×C11H(5,𝔽2)11yescharacteristic
415C23×C11H(5,𝔽2)11yescharacteristic
416C23×C11H(5,𝔽2)11yescharacteristic
417C23×C11H(5,𝔽2)11yescharacteristic
418C23×C11H(5,𝔽2)11yescharacteristic
419C23×C11H(5,𝔽2)11yescharacteristic
420C23×C11H(5,𝔽2)11yescharacteristic
421C23×C112−1+411yescharacteristic
422C22×D11—22no—
423C22×D11—22no—
424C22×D11—22no—
425C22×D11—22no—
426C22×D11—22no—
427C22×D11—22no—
428C22×D11—22no—
429C22×D11—22no—
430C22×D11—22no—
431C22×D11—22no—
432C22×D11—22no—
433C22×D11—22no—
434C22×D11—22no—
435C22×D11—22no—
436C22×D11—22no—
437C22×D11—22no—
438C22×D11—22no—
439C22×D11—22no—
440C22×D11—22no—
441C22×D11—22no—
442C22×D11—22no—
443C22×D11—22no—
444C22×D11—22no—
445C22×D11—22no—
446C22×D11—22no—
447C22×D11—22no—
448C22×D11—22no—
449C22×D11—22no—
450C22×D11—22no—
451C22×D11—22no—
452C22×D11—22no—
453C22×D11—22no—
454C22×D11—22no—
455C22×D11—22no—
456C22×D11—22no—
457C22×D11—22no—
458C22×D11—41no—
459C22×D11—41no—
460C22×D11—41no—
461C22×D11—41no—
462C22×D11—41no—
463C22×D11—41no—
464C22×D11—41no—
465C22×D11—41no—
466C22×D11—41no—
467C22×D11—41no—
468C22×D11—41no—
469C22×D11—41no—
470C22×D11—41no—
471C22×D11—41no—
472C22×D11—41no—
473C22×D11—41no—
474C22×D11—41no—
475C22×D11—41no—
476C22×D11—41no—
477C22×D11—41no—
478C22×D11—41no—
479C22×D11—41no—
480C22×D11—41no—
481C22×D11—41no—
482C22×D11—41no—
483C22×D11—41no—
484C22×D11—41no—
485C22×D11—41no—
486C22×D11—41no—
487C22×D11—41no—
488C22×D11—41no—
489C22×D11—41no—
490C22×D11C2×C22⋊C414yes—
491C22×D11C4×D414yes—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—41no—
502C2×C4×C11—41no—
503C2×C4×C11—41no—
504C2×C4×C11—41no—
505C2×C4×C11—41no—
506C2×C4×C11—41no—
507C2×C4×C11—41no—
508C2×C4×C11—41no—
509C2×C4×C11—41no—
510C2×C4×C11—41no—
511C2×C4×C11—41no—
512C2×C4×C11—41no—
513C2×C4×C11—41no—
514C2×C4×C11—41no—
515C2×C4×C11—41no—
516C2×C4×C11—41no—
517C2×C4×C11—41no—
518C2×C4×C11—41no—
519C2×C4×C11—41no—
520C2×C4×C11—41no—
521C2×C4×C11—41no—
522C2×C4×C11—41no—
523C2×C4×C11—41no—
524C2×C4×C11—41no—
525C2×C4×C11—41no—
526C2×C4×C11—41no—
527C2×C4×C11—41no—
528C2×C4×C11—41no—
529C2×C4×C11—41no—
530C2×C4×C11—41no—
531C2×C4×C11—41no—
532C2×C4×C11—41no—
533C2×C4×C11—41no—
534C22⋊D11—416no—
535C22⋊D11—416no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—22no—
543C2×Dic11—22no—
544C2×Dic11—22no—
545C2×Dic11—22no—
546C2×Dic11—22no—
547C2×Dic11—22no—
548C2×Dic11—22no—
549C2×Dic11—22no—
550C2×Dic11—22no—
551C2×Dic11—22no—
552C2×Dic11—22no—
553C2×Dic11—22no—
554C2×Dic11—416no—
555C2×Dic11—41no—
556C2×Dic11—41no—
557C2×Dic11—41no—
558C2×Dic11—41no—
559C2×Dic11—41no—
560C2×Dic11—41no—
561C2×Dic11—41no—
562C2×Dic11—41no—
563C2×Dic11—41no—
564C2×Dic11—41no—
565C2×Dic11—41no—
566C2×Dic11—41no—
567C2×Dic11—41no—
568C2×Dic11—41no—
569C2×Dic11—41no—
570C2×Dic11—41no—
571C2×Dic11—41no—
572C2×Dic11—41no—
573C2×Dic11—41no—
574C2×Dic11—41no—
575C2×Dic11—41no—
576C2×Dic11—41no—
577C2×Dic11—41no—
578C2×Dic11C2×C22⋊C414yes—
579D44—416no—
580C4×D11—416no—
581C4×D11—416no—
582C23×D4—111no—
583C23×D4—111no—
584C23×D4—111no—
585C24×C4—111no—
586C24×C4—111no—
587C24×C4—111no—
588C2×#121—118no—
589C2×#121—224no—
590C2×#121—224no—
591C22×C4⋊C4—111no—
592C22×C22⋊C4—111no—
593C22×C22⋊C4—111no—
594C22×C22⋊C4—111no—
595C22×C22⋊C4—111no—
596C22×C22⋊C4—111no—
597C22×C22⋊C4—111no—
598C22×C22⋊C4—111no—
599C22×C22⋊C4—111no—
600C22×C22⋊C4—111no—
601C22×C22⋊C4C2×D1111yescharacteristic
602C22×C22⋊C4C2×D1111yescharacteristic
603C22×C22⋊C4C2×D1111yescharacteristic
604#386—224no—
605#386—224no—
606#386—224no—
607#386—224no—
608C2×#95—111no—
609C2×#95—111no—
610C2×#95—111no—
611C2×#95—111no—
612C2×#95—111no—
613C2×#95—111no—
614C2×#95—111no—
615C2×#95—111no—
616C2×#95—111no—
617C2×#95—111no—
618C2×#95—111no—
619C2×#95—111no—
620C2×#95C2×D1111yescharacteristic
621C2×#95C2×D1111yescharacteristic
622C2×#95C2×D1111yescharacteristic
623C2×#95C2×D1111yescharacteristic
624C22×C11—24no—
625C22×C11—24no—
626C22×C11—24no—
627C22×C11—42no—
628C22×C11—42no—
629C22×C11—42no—
630C22×C11—42no—
631C22×C11—42no—
632C22×C11—42no—
633C22×C11—42no—
634C22×C11—42no—
635C22×C11—42no—
636C22×C11—42no—
637C22×C11—42no—
638C22×C11—42no—
639C22×C11C22×C22⋊C411yescharacteristic
640C22×C11C2×C4×D411yescharacteristic
641C22×C11C4×#4111yescharacteristic
642C22×C11#51811yescharacteristic
643C22×C11#51811yescharacteristic
644C22×C11#51811yescharacteristic
645C22×C11#52011yescharacteristic
646C22×C11#53411yescharacteristic
647C22×C11#53411yescharacteristic
648C22×C11#53411yescharacteristic
649C22×C11#53411yescharacteristic
650C22×C11#53411yescharacteristic
651C22×C11#53711yescharacteristic
652C22×C11#53811yescharacteristic
653C22×C11#53811yescharacteristic
654C22×C11#53811yescharacteristic
655C22×C11#53911yescharacteristic
656C22×C11#54011yescharacteristic
657C22×C11#54011yescharacteristic
658C22×C11D4211yescharacteristic
659C22×C11D4211yescharacteristic
660C22×C11#54611yescharacteristic
661C22×C11#54611yescharacteristic
662C22×C11#54611yescharacteristic
663C22×C11#54611yescharacteristic
664C22×C11#54611yescharacteristic
665C22×C11#54611yescharacteristic
666C22×C11#54711yescharacteristic
667C22×C11#54711yescharacteristic
668C22×C11#55311yescharacteristic
669C22×C11#55311yescharacteristic
670C22×C11#56011yescharacteristic
671C22×C11#56011yescharacteristic
672C22×C11#56211yescharacteristic
673C22×C11#56211yescharacteristic
674C2×D11—24no—
675C2×D11—24no—
676C2×D11—24no—
677C2×D11—24no—
678C2×D11—24no—
679C2×D11—24no—
680C2×D11—42no—
681C2×D11—42no—
682C2×D11—42no—
683C2×D11—42no—
684C2×D11—42no—
685C2×D11—42no—
686C2×D11—42no—
687C2×D11—42no—
688C2×D11—42no—
689C2×D11—42no—
690C2×D11—42no—
691C2×D11—42no—
692C2×D11—42no—
693C2×D11—42no—
694C2×D11—42no—
695C2×D11—42no—
696C2×D11—42no—
697C2×D11—42no—
698C2×D11—42no—
699C2×D11—42no—
700C2×D11—42no—
701C2×D11—42no—
702C2×D11—42no—
703C2×D11—42no—
704C4×C11—42no—
705C4×C11—42no—
706C4×C11—42no—
707C4×C11—81no—
708C4×C11—81no—
709C4×C11—81no—
710Dic11—24no—
711Dic11—42no—
712Dic11—42no—
713Dic11—42no—
714Dic11—42no—
715Dic11—81no—
716C25—111no—
717C25—111no—
718C25C22×D1111yescharacteristic
719C22×D4—114no—
720C22×D4—114no—
721C22×D4—114no—
722C22×D4—114no—
723C22×D4—114no—
724C22×D4—222no—
725C22×D4—222no—
726C22×D4—222no—
727C22×D4—222no—
728C22×D4—222no—
729C22×D4—222no—
730C22×D4—222no—
731C22×D4—222no—
732C22×D4—441no—
733C22×D4—441no—
734C22×D4—441no—
735C22×D4—441no—
736C22×D4—441no—
737C22×D4—441no—
738C22×D4—441no—
739C22×D4—441no—
740C23×C4—111no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—111no—
744C23×C4—111no—
745C23×C4—114no—
746C23×C4—111no—
747C23×C4—222no—
748C23×C4—222no—
749C23×C4—222no—
750C23×C4—222no—
751C23×C4—222no—
752C23×C4—222no—
753C23×C4—222no—
754C23×C4—222no—
755C23×C4—441no—
756C23×C4—441no—
757C23×C4—441no—
758C23×C4—441no—
759C23×C4—441no—
760C23×C4—441no—
761C23×C4—441no—
762C23×C4—441no—
763C23×C4—441no—
764C23×C4—441no—
765C23×C4—441no—
766C23×C4—441no—
767C23×C4C22×D1111yescharacteristic
768C23×C4C22×D1111yescharacteristic
769C23×C4C22×D1111yescharacteristic
770C23×C4C22×D1111yescharacteristic
771C23×C4C22×D1111yescharacteristic
772C23×C4C22×D1111yescharacteristic
773#121—2232no—
774C2×C4⋊C4—114no—
775C2×C4⋊C4—222no—
776C2×C4⋊C4—222no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—114no—
786C2×C22⋊C4—114no—
787C2×C22⋊C4—222no—
788C2×C22⋊C4—222no—
789C2×C22⋊C4—222no—
790C2×C22⋊C4—222no—
791C2×C22⋊C4—222no—
792C2×C22⋊C4—222no—
793C2×C22⋊C4—222no—
794C2×C22⋊C4—222no—
795C2×C22⋊C4—222no—
796C2×C22⋊C4—222no—
797C2×C22⋊C4—222no—
798C2×C22⋊C4—222no—
799C2×C22⋊C4—222no—
800C2×C22⋊C4—222no—
801C2×C22⋊C4—441no—
802C2×C22⋊C4—441no—
803C2×C22⋊C4—441no—
804C2×C22⋊C4—441no—
805C2×C22⋊C4—441no—
806C2×C22⋊C4—441no—
807C2×C22⋊C4—441no—
808C2×C22⋊C4—441no—
809C2×C22⋊C4—441no—
810C2×C22⋊C4—441no—
811C2×C22⋊C4—441no—
812C2×C22⋊C4C4×D1114yescomplemented
813#95—22no—
814#95—41no—
815#95—41no—
816#95—41no—
817#95—222no—
818#95—222no—
819#95—222no—
820#95—222no—
821#95—222no—
822#95—222no—
823#95—222no—
824#95—441no—
825#95—441no—
826#95—441no—
827#95—441no—
828#95—441no—
829C2×C11—44no—
830C2×C11#230811yescharacteristic
831C2×C11#232511yescharacteristic
832C2×C11#233311yescharacteristic
833C2×C11D4×C22⋊C411yescharacteristic
834C2×C11#233911yescharacteristic
835C2×C11#236411yescharacteristic
836C2×C11#237711yescharacteristic
837C2×C11#266811yescharacteristic
838C2×C11#266811yescharacteristic
839C2×C11#267111yescharacteristic
840C2×C11#267111yescharacteristic
841C2×C11#268811yescharacteristic
842C2×C11#268811yescharacteristic
843C2×C11#270811yescharacteristic
844C2×C11#270811yescharacteristic
845D11—44no—
846D11—44no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—112no—
860C24—112no—
861C24—112no—
862C24—112no—
863C24—112no—
864C24—112no—
865C24—221no—
866C24—221no—
867C24—221no—
868C24—221no—
869C24—221no—
870C24—221no—
871C24—221no—
872C24—221no—
873C24—221no—
874C24—221no—
875C24—221no—
876C24—221no—
877C24—221no—
878C24—221no—
879C24—221no—
880C24—221no—
881C24—221no—
882C24—221no—
883C24—221no—
884C24—221no—
885C24—221no—
886C24—221no—
887C24—221no—
888C24—221no—
889C24C2×C4×D1112yes—
890C24D4×D1112yes—
891C24D4×D1112yes—
892C24C23×D1111yescharacteristic
893C2×D4—1116no—
894C2×D4—228no—
895C2×D4—228no—
896C2×D4—228no—
897C2×D4—228no—
898C2×D4—444no—
899C2×D4—444no—
900C2×D4—444no—
901C2×D4—444no—
902C2×D4—444no—
903C2×D4—444no—
904C2×D4—444no—
905C2×D4—444no—
906C2×D4—444no—
907C2×D4—444no—
908C2×D4—444no—
909C2×D4—444no—
910C2×D4—444no—
911C2×D4—444no—
912C2×D4—444no—
913C2×D4—444no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—112no—
954C22×C4—112no—
955C22×C4—112no—
956C22×C4—112no—
957C22×C4—112no—
958C22×C4—112no—
959C22×C4—112no—
960C22×C4—228no—
961C22×C4—221no—
962C22×C4—221no—
963C22×C4—221no—
964C22×C4—221no—
965C22×C4—221no—
966C22×C4—221no—
967C22×C4—221no—
968C22×C4—221no—
969C22×C4—221no—
970C22×C4—221no—
971C22×C4—221no—
972C22×C4—221no—
973C22×C4—221no—
974C22×C4—221no—
975C22×C4—221no—
976C22×C4—221no—
977C22×C4—221no—
978C22×C4—221no—
979C22×C4—221no—
980C22×C4—221no—
981C22×C4—221no—
982C22×C4—221no—
983C22×C4—221no—
984C22×C4—221no—
985C22×C4—221no—
986C22×C4—221no—
987C22×C4—221no—
988C22×C4—221no—
989C22×C4—221no—
990C22×C4—221no—
991C22×C4—221no—
992C22×C4—221no—
993C22×C4—221no—
994C22×C4—221no—
995C22×C4—221no—
996C22×C4—444no—
997C22×C4—444no—
998C22×C4—444no—
999C22×C4—444no—
1000C22×C4—444no—
1001C22×C4—444no—
1002C22×C4—444no—
1003C22×C4—444no—
1004C22×C4—444no—
1005C22×C4—444no—
1006C22×C4—444no—
1007C22×C4—444no—
1008C22×C4—444no—
1009C22×C4—444no—
1010C22×C4—444no—
1011C22×C4—444no—
1012C22×C4—444no—
1013C22×C4—444no—
1014C22×C4—444no—
1015C22×C4—444no—
1016C22×C4C2×C4×D1112yes—
1017C22×C4C2×C4×D1112yes—
1018C22×C4D4×D1112yes—
1019C4⋊C4—228no—
1020C22⋊C4—28no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—228no—
1024C22⋊C4—444no—
1025C22⋊C4—444no—
1026C22⋊C4—444no—
1027C22⋊C4—444no—
1028C22⋊C4—444no—
1029C22⋊C4—444no—
1030C22⋊C4—444no—
1031C22⋊C4—444no—
1032C11#1441711yescharacteristic, complemented, Sylow
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—114no—
1068C23—114no—
1069C23—222no—
1070C23—222no—
1071C23—222no—
1072C23—222no—
1073C23—222no—
1074C23—222no—
1075C23—222no—
1076C23—222no—
1077C23—222no—
1078C23—222no—
1079C23—222no—
1080C23—222no—
1081C23—222no—
1082C23—222no—
1083C23—222no—
1084C23—222no—
1085C23—222no—
1086C23—222no—
1087C23—222no—
1088C23—222no—
1089C23—222no—
1090C23—222no—
1091C23—222no—
1092C23—222no—
1093C23—222no—
1094C23—222no—
1095C23—222no—
1096C23—222no—
1097C23—222no—
1098C23—222no—
1099C23—222no—
1100C23—222no—
1101C23—222no—
1102C23—222no—
1103C23—222no—
1104C23—222no—
1105C23—441no—
1106C23—441no—
1107C23—441no—
1108C23—441no—
1109C23—441no—
1110C23—441no—
1111C23—441no—
1112C23—441no—
1113C23—441no—
1114C23—441no—
1115C23—441no—
1116C23—441no—
1117C23—441no—
1118C23—441no—
1119C23—441no—
1120C23—441no—
1121C23—441no—
1122C23—441no—
1123C23—441no—
1124C23—441no—
1125C23—441no—
1126C23—441no—
1127C23—441no—
1128C23—441no—
1129C23—441no—
1130C23—441no—
1131C23—441no—
1132C23—441no—
1133C23—441no—
1134C23—441no—
1135C23—441no—
1136C23—441no—
1137C23C22⋊C4×D1114yes—
1138C23C22×C4×D1111yescharacteristic
1139C23C2×D4×D1111yescharacteristic
1140C23C2×D4×D1111yescharacteristic
1141C23C2×D4×D1111yescharacteristic
1142C23#6703711yescharacteristic
1143C23#6703711yescharacteristic
1144C23#6703711yescharacteristic
1145C23#41×D1111yescharacteristic
1146C23#41×D1111yescharacteristic
1147C23#41×D1111yescharacteristic
1148C23#6704211yescharacteristic
1149C23#6704211yescharacteristic
1150C23#6704211yescharacteristic
1151C23#6704211yescharacteristic
1152C23#6704311yescharacteristic
1153D4—4416no—
1154D4—4416no—
1155D4—4416no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—114no—
1199C2×C4—222no—
1200C2×C4—222no—
1201C2×C4—222no—
1202C2×C4—222no—
1203C2×C4—222no—
1204C2×C4—222no—
1205C2×C4—222no—
1206C2×C4—222no—
1207C2×C4—222no—
1208C2×C4—222no—
1209C2×C4—222no—
1210C2×C4—222no—
1211C2×C4—222no—
1212C2×C4—222no—
1213C2×C4—222no—
1214C2×C4—222no—
1215C2×C4—222no—
1216C2×C4—222no—
1217C2×C4—4416no—
1218C2×C4—4416no—
1219C2×C4—4416no—
1220C2×C4—441no—
1221C2×C4—441no—
1222C2×C4—441no—
1223C2×C4—441no—
1224C2×C4—441no—
1225C2×C4—441no—
1226C2×C4—441no—
1227C2×C4—441no—
1228C2×C4—441no—
1229C2×C4—441no—
1230C2×C4—441no—
1231C2×C4—441no—
1232C2×C4—441no—
1233C2×C4—441no—
1234C2×C4—441no—
1235C2×C4—441no—
1236C2×C4—441no—
1237C2×C4—441no—
1238C2×C4—441no—
1239C2×C4—441no—
1240C2×C4—441no—
1241C2×C4—441no—
1242C2×C4—441no—
1243C22—24no—
1244C22—24no—
1245C22—24no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—224no—
1259C22—224no—
1260C22—224no—
1261C22—224no—
1262C22—224no—
1263C22—224no—
1264C22—442no—
1265C22—442no—
1266C22—442no—
1267C22—442no—
1268C22—442no—
1269C22—442no—
1270C22—442no—
1271C22—442no—
1272C22—442no—
1273C22—442no—
1274C22—442no—
1275C22—442no—
1276C22—442no—
1277C22—442no—
1278C22—442no—
1279C22—442no—
1280C22—442no—
1281C22—442no—
1282C22—442no—
1283C22—442no—
1284C22—442no—
1285C22—442no—
1286C22—442no—
1287C22—442no—
1288C22C2×C22⋊C4×D1111yescharacteristic
1289C22#1062305311yescharacteristic
1290C22#1062305411yescharacteristic
1291C22C4×D4×D1111yescharacteristic
1292C22#1062307611yescharacteristic
1293C22#1062307611yescharacteristic
1294C22#1062307611yescharacteristic
1295C22#1062312011yescharacteristic
1296C22#1062312111yescharacteristic
1297C22#1062313611yescharacteristic
1298C22#1062313611yescharacteristic
1299C22#1062313911yescharacteristic
1300C22#1062314011yescharacteristic
1301C22#1062314111yescharacteristic
1302C22#1062314111yescharacteristic
1303C22#1062314611yescharacteristic
1304C22#1062315111yescharacteristic
1305C22#1062318411yescharacteristic
1306C22#1062318411yescharacteristic
1307C22#1062318511yescharacteristic
1308C22#1062318511yescharacteristic
1309C22#1062318511yescharacteristic
1310C22#1062318611yescharacteristic
1311C22#1062318611yescharacteristic
1312C22#1062319211yescharacteristic
1313C22#1062319411yescharacteristic
1314C22#1062319811yescharacteristic
1315C22#1062320711yescharacteristic
1316C22#1062320911yescharacteristic
1317C22#1062320911yescharacteristic
1318C22#1062321511yescharacteristic
1319C22#1062323511yescharacteristic
1320C22#1062323811yescharacteristic
1321C22#1062324011yescharacteristic
1322C22#1062324211yescharacteristic
1323C4—42no—
1324C4—42no—
1325C4—42no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—224no—
1330C4—442no—
1331C4—442no—
1332C4—442no—
1333C4—442no—
1334C4—881no—
1335C2—44no—
1336C2—444no—
1337C2—444no—
1338C2#1307119011yescharacteristic
1339C2#1307132011yescharacteristic
1340C2#1307137911yescharacteristic
1341C2#1307143411yescharacteristic
1342C2#1307144011yescharacteristic
1343C2#1307166011yescharacteristic
1344C2#1307176911yescharacteristic
1345C2#1307482311yescharacteristic
1346C2#1307482611yescharacteristic
1347C2#1307485111yescharacteristic
1348C2#1307485811yescharacteristic
1349C2#1307504511yescharacteristic
1350C2#1307505411yescharacteristic
1351C2#1307533311yescharacteristic
1352C2#1307534011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1440C2
socle, cosocleC24×C11C24
prime radicalC22×#66937C2
hypercenter#1440D11
hypocenterC11#14417
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
2. C2×#10622278C2semidirect
3. C2×#10622571C2semidirect
4. C2×#10622571C2semidirect
5. C2×#10622569C2semidirect
6. #13066882C2semidirect
7. #13066882C2semidirect
8. #13066864C2semidirect
9. #13066856C2semidirect
10. #13066855C2semidirect
11. #13066838C2semidirect
12. (C2×D11)⋊#95C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1440C2semidirect
37. C2×#66937C4semidirect
78. C22×C22⋊D11C2×C4semidirect
100. C22×D44C2×C4semidirect
114. C22×C4×D11C2×C4semidirect
123. C2×C11×C22⋊C4C2×C4semidirect
149. C2×(C2×D11)⋊C4C2×C4semidirect
150. C2×(C2×D11)⋊C4D4semidirect
153. C2×Dic11⋊C4C2×C4semidirect
273. C2×C22⋊D11C22⋊C4semidirect
365. #1440D11semidirect
812. C2×C22⋊C4C4×D11semidirect
1032. C11#14417semidirect

Maximal subgroups

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

subgroupindex
C22×#669372
C2×#106222782
C2×#106225712
C2×#106225692
#130668822
#130668642
#130668562
#130668552
#130668382
(C2×D11)⋊#952
C11×#14402
#1441711