Finite Group Databasebeta

← #14676911

Subgroups — #14676911

Order 2816.

2682 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66992C211yesmaximal, characteristic
2C2×#10622834C211yesmaximal, characteristic, complemented
3C2×#10622570C211yesmaximal, characteristic, complemented
4C2×#10622570C211yesmaximal, characteristic, complemented
5C2×#10622570C211yesmaximal, characteristic, complemented
6C2×#10622260C211yesmaximal, characteristic, complemented
7C2×#10622555C211yesmaximal, characteristic, complemented
8C2×#10622262C211yesmaximal, characteristic, complemented
9C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
10#13066862C211yesmaximal, characteristic, complemented
11#13066859C211yesmaximal, characteristic, complemented
12#13066855C211yesmaximal, characteristic, complemented
13#13066853C211yesmaximal, characteristic, complemented
14#13066852C211yesmaximal, characteristic, complemented
15C11×#1438C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C2×#66992—24no—
30C2×#66992—24no—
31C2×#66992C418yescomplemented
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×C4×Dic11C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47C2×C11×#95C2211yescharacteristic
48#10622834—24no—
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55#10622570—24no—
56#10622570—24no—
57#10622570—24no—
58#10622555—24no—
59C22⋊C4×Dic11—24no—
60#10622262—24no—
61#10622260—24no—
62C25×C11C2311yescharacteristic
63C25×C11C2311yescharacteristic
64C24×D11C2311yescharacteristic
65C22×D4×C11—22no—
66C22×D4×C11—22no—
67C22×D4×C11—22no—
68C22×D4×C11—22no—
69C22×D4×C11—41no—
70C22×D4×C11—41no—
71C22×D4×C11C2×C414yes—
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C22×C22⋊D11—22no—
78C22×C22⋊D11—22no—
79C22×C22⋊D11—22no—
80C22×C22⋊D11—22no—
81C22×C22⋊D11—22no—
82C22×C22⋊D11—22no—
83C22×C22⋊D11—22no—
84C22×C22⋊D11—22no—
85C22×C22⋊D11—22no—
86C22×C22⋊D11—22no—
87C22×C22⋊D11—41no—
88C22×C22⋊D11—41no—
89C22×C22⋊D11C2×C414yes—
90C22×C22⋊D11C2×C414yes—
91C23×Dic11—22no—
92C23×Dic11—22no—
93C23×Dic11—22no—
94C23×Dic11—22no—
95C23×Dic11—22no—
96C23×Dic11—22no—
97C23×Dic11C2×C414yes—
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4—22no—
108C2×C11×C22⋊C4—22no—
109C2×C11×C22⋊C4—22no—
110C2×C11×C22⋊C4—22no—
111C2×C11×C22⋊C4—22no—
112C2×C11×C22⋊C4—22no—
113C2×C11×C22⋊C4—41no—
114C2×C11×C22⋊C4—41no—
115C2×C11×C22⋊C4—41no—
116C2×C11×C22⋊C4—41no—
117C2×C22⋊Dic11—22no—
118C2×C22⋊Dic11—22no—
119C2×C22⋊Dic11—22no—
120C2×C22⋊Dic11—22no—
121C2×C22⋊Dic11—22no—
122C2×C22⋊Dic11—22no—
123C2×C22⋊Dic11—22no—
124C2×C22⋊Dic11—22no—
125C2×C22⋊Dic11—22no—
126C2×C22⋊Dic11—22no—
127C2×C22⋊Dic11—22no—
128C2×C22⋊Dic11—41no—
129C2×C22⋊Dic11—41no—
130C2×C22⋊Dic11C2×C414yes—
131C2×C22⋊Dic11D414yescomplemented
132#66992—232no—
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—22no—
140C2×(C2×D11)⋊C4—22no—
141C2×(C2×D11)⋊C4—22no—
142C2×(C2×D11)⋊C4—22no—
143C2×(C2×D11)⋊C4—41no—
144C2×(C2×D11)⋊C4—41no—
145C2×(C2×D11)⋊C4—41no—
146C2×(C2×D11)⋊C4—41no—
147C2×(C2×D11)⋊C4C2×C414yes—
148C2×C4⋊Dic11—22no—
149C2×C4⋊Dic11—22no—
150C2×C4⋊Dic11—41no—
151C2×Dic11⋊C4—22no—
152C2×Dic11⋊C4—22no—
153C2×Dic11⋊C4—22no—
154C2×Dic11⋊C4—22no—
155C2×Dic11⋊C4—22no—
156C2×Dic11⋊C4—22no—
157C2×Dic11⋊C4—22no—
158C2×Dic11⋊C4—41no—
159C2×Dic11⋊C4C2×C414yes—
160C2×Dic11⋊C4D414yes—
161C2×Dic11⋊C4D414yes—
162C2×Dic11⋊C4D414yescomplemented
163C2×C4×Dic11—22no—
164C2×C4×Dic11—22no—
165C2×C4×Dic11—22no—
166C2×C4×Dic11—22no—
167C2×C4×Dic11—22no—
168C2×C4×Dic11—22no—
169C2×C4×Dic11—22no—
170C2×C4×Dic11—22no—
171C2×C4×Dic11—22no—
172C2×C4×Dic11—41no—
173C2×C4×Dic11—41no—
174C2×C4×Dic11D414yescomplemented
175C11×#95—22no—
176C11×#95—22no—
177C11⋊#95—22no—
178C11⋊#95—22no—
179C11⋊#95—22no—
180C11⋊#95—22no—
181C11⋊#95—22no—
182C11⋊#95—22no—
183#13998—111nomaximal, Sylow
184C24×C11—21no—
185C24×C11—21no—
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—21no—
189C24×C11—21no—
190C24×C11—21no—
191C24×C11—21no—
192C24×C11—21no—
193C24×C11—21no—
194C24×C11—21no—
195C24×C11—21no—
196C24×C11—21no—
197C24×C11—21no—
198C24×C11—21no—
199C24×C11—21no—
200C24×C11—21no—
201C24×C11—21no—
202C24×C11—21no—
203C24×C11—21no—
204C24×C11—21no—
205C24×C11—21no—
206C24×C11—21no—
207C24×C11—21no—
208C24×C11—21no—
209C24×C11—21no—
210C24×C11C22×C412yes—
211C24×C11C22×C412yes—
212C24×C11C2×D412yes—
213C24×C11#4112yes—
214C24×C11C2411yescharacteristic
215C23×D11—21no—
216C23×D11—21no—
217C23×D11—21no—
218C23×D11—21no—
219C23×D11—21no—
220C23×D11—21no—
221C23×D11—21no—
222C23×D11—21no—
223C23×D11—21no—
224C23×D11—21no—
225C23×D11—21no—
226C23×D11—21no—
227C23×D11—21no—
228C23×D11—21no—
229C23×D11C22×C412yes—
230C2×D4×C11—28no—
231C2×D4×C11—28no—
232C2×D4×C11—44no—
233C2×D4×C11—44no—
234C2×D4×C11—44no—
235C2×D4×C11—44no—
236C2×D4×C11—44no—
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×C11—21no—
258C22×C4×C11—21no—
259C22×C4×C11—21no—
260C22×C4×C11—21no—
261C22×C4×C11—21no—
262C22×C4×C11—21no—
263C22×C4×C11—21no—
264C22×C4×C11—21no—
265C22×C4×C11—21no—
266C22×C4×C11C22×C412yes—
267C22×C4×C11C2×D412yes—
268C22×C4×C11C2×D412yes—
269C22×C4×C11C2×D412yes—
270C22×C4×C11C2×D412yes—
271C22×C4×C11#4112yes—
272C2×C22⋊D11—28no—
273C2×C22⋊D11—28no—
274C2×C22⋊D11—28no—
275C2×C22⋊D11—28no—
276C2×C22⋊D11—28no—
277C2×C22⋊D11—44no—
278C2×C22⋊D11—44no—
279C2×C22⋊D11—44no—
280C2×C22⋊D11—44no—
281C2×C22⋊D11—44no—
282C2×C22⋊D11—44no—
283C2×C22⋊D11—44no—
284C2×C22⋊D11—44no—
285C2×C22⋊D11—44no—
286C22×Dic11—28no—
287C22×Dic11—28no—
288C22×Dic11—28no—
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—21no—
310C22×Dic11—21no—
311C22×Dic11—21no—
312C22×Dic11—21no—
313C22×Dic11—21no—
314C22×Dic11—21no—
315C22×Dic11—21no—
316C22×Dic11—21no—
317C22×Dic11—21no—
318C22×Dic11—21no—
319C22×Dic11—21no—
320C22×Dic11—21no—
321C22×Dic11—21no—
322C22×Dic11—44no—
323C22×Dic11—44no—
324C22×Dic11—44no—
325C22×Dic11—44no—
326C22×Dic11C22×C412yes—
327C22×Dic11C22×C412yes—
328C22×Dic11C22×C412yes—
329C22×Dic11C2×D412yes—
330C22×Dic11C2×D412yes—
331C22×Dic11C2×D412yes—
332C22×Dic11C2×D412yes—
333C22×Dic11C2×D412yes—
334C22×Dic11C2×D412yes—
335C22×Dic11C2×D412yes—
336C22×Dic11C2×D412yes—
337C22×Dic11C2×D412yes—
338C22×Dic11C2×D412yes—
339C22×Dic11#4112yes—
340C22×Dic11#4112yes—
341C22×Dic11#4112yes—
342C11×C22⋊C4—28no—
343C11×C22⋊C4—44no—
344C11×C22⋊C4—44no—
345C11×C22⋊C4—44no—
346C22⋊Dic11—28no—
347C22⋊Dic11—28no—
348C22⋊Dic11—44no—
349C22⋊Dic11—44no—
350C22⋊Dic11—44no—
351(C2×D11)⋊C4—28no—
352(C2×D11)⋊C4—44no—
353(C2×D11)⋊C4—44no—
354(C2×D11)⋊C4—44no—
355(C2×D11)⋊C4—44no—
356C4⋊Dic11—44no—
357Dic11⋊C4—28no—
358Dic11⋊C4—44no—
359Dic11⋊C4—44no—
360Dic11⋊C4C22⋊C4116yescomplemented
361C4×Dic11—28no—
362C4×Dic11—44no—
363C4×Dic11—44no—
364C4×Dic11—44no—
365C22×#121—111no—
366C2×#390—111no—
367C2×#390—111no—
368C2×#390—111no—
369C2×#390—111no—
370C2×#389—111no—
371C2×#380—111no—
372C2×C4×C4⋊C4—111no—
373C2×C4×C22⋊C4—111no—
374#1439—111no—
375#1439—111no—
376#1438—111no—
377#1438D1111yescharacteristic, complemented
378#1437—111no—
379#1437—111no—
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—22no—
391C23×C11—22no—
392C23×C11—22no—
393C23×C11—22no—
394C23×C11—22no—
395C23×C11—22no—
396C23×C11—22no—
397C23×C11—22no—
398C23×C11—22no—
399C23×C11—22no—
400C23×C11—22no—
401C23×C11—22no—
402C23×C11—22no—
403C23×C11—22no—
404C23×C11—22no—
405C23×C11—41no—
406C23×C11—41no—
407C23×C11—41no—
408C23×C11—41no—
409C23×C11—41no—
410C23×C11—41no—
411C23×C11—41no—
412C23×C11—41no—
413C23×C11—41no—
414C23×C11—41no—
415C23×C11—41no—
416C23×C11—41no—
417C23×C11—41no—
418C23×C11—41no—
419C23×C11—41no—
420C23×C11—41no—
421C23×C11—41no—
422C23×C11—41no—
423C23×C11—41no—
424C23×C11—41no—
425C23×C11—41no—
426C23×C11—41no—
427C23×C11—41no—
428C23×C11—41no—
429C23×C11—41no—
430C23×C11—41no—
431C23×C11—41no—
432C23×C11—41no—
433C23×C11—41no—
434C23×C11—41no—
435C23×C11—41no—
436C23×C11—41no—
437C23×C11—41no—
438C23×C11—41no—
439C23×C11—41no—
440C23×C11—41no—
441C23×C11—41no—
442C23×C11—41no—
443C23×C11—41no—
444C23×C11—41no—
445C23×C11—41no—
446C23×C11—41no—
447C23×C11—41no—
448C23×C11—41no—
449C23×C11C4×D414yes—
450C23×C11C23×C411yescharacteristic
451C23×C11C22×D411yescharacteristic
452C23×C11C22×D411yescharacteristic
453C23×C11C22×D411yescharacteristic
454C23×C11C22×D411yescharacteristic
455C23×C11C22×D411yescharacteristic
456C23×C11C2×#4111yescharacteristic
457C23×C11C2×#4111yescharacteristic
458C23×C11C2×#4111yescharacteristic
459C23×C11C2×#4111yescharacteristic
460C23×C11C2×#4111yescharacteristic
461C23×C11H(5,𝔽2)11yescharacteristic
462C23×C11H(5,𝔽2)11yescharacteristic
463C23×C11H(5,𝔽2)11yescharacteristic
464C23×C112−1+411yescharacteristic
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
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×D11—41no—
491C22×D11—41no—
492C22×D11—41no—
493C22×D11—41no—
494C22×D11—41no—
495C22×D11—41no—
496C22×D11—41no—
497C22×D11—41no—
498C22×D11—41no—
499C22×D11—41no—
500D4×C11—416no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—22no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—22no—
509C2×C4×C11—22no—
510C2×C4×C11—22no—
511C2×C4×C11—22no—
512C2×C4×C11—22no—
513C2×C4×C11—22no—
514C2×C4×C11—22no—
515C2×C4×C11—22no—
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—
534C2×C4×C11—41no—
535C2×C4×C11C2×C22⋊C414yes—
536C22⋊D11—416no—
537C22⋊D11—416no—
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—22no—
555C2×Dic11—22no—
556C2×Dic11—22no—
557C2×Dic11—22no—
558C2×Dic11—22no—
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—416no—
572C2×Dic11—41no—
573C2×Dic11—41no—
574C2×Dic11—41no—
575C2×Dic11—41no—
576C2×Dic11—41no—
577C2×Dic11—41no—
578C2×Dic11—41no—
579C2×Dic11C2×C22⋊C414yes—
580C2×Dic11C2×C22⋊C414yes—
581C2×Dic11C4×D414yes—
582C2×Dic11C4×D414yes—
583C2×Dic11#12114yes—
584C2×Dic11#12114yes—
585C2×Dic11#12114yescomplemented
586C2×Dic11#12414yes—
587C2×Dic11#12714yes—
588C23×D4—111no—
589C23×D4—111no—
590C23×D4C2×D1111yescharacteristic
591C24×C4—111no—
592C2×#121—118no—
593C2×#121—224no—
594C2×#121—224no—
595C22×C4⋊C4—111no—
596C22×C4⋊C4—111no—
597C22×C4⋊C4—111no—
598C22×C4⋊C4—111no—
599C22×C4⋊C4—111no—
600C22×C22⋊C4—111no—
601C22×C22⋊C4—111no—
602C22×C22⋊C4—111no—
603C22×C22⋊C4—111no—
604C22×C22⋊C4—111no—
605C22×C22⋊C4—111no—
606C22×C22⋊C4—111no—
607C22×C22⋊C4—111no—
608C22×C22⋊C4—111no—
609C22×C22⋊C4—111no—
610C22×C22⋊C4C2×D1111yescharacteristic
611C22×C22⋊C4C2×D1111yescharacteristic
612C22×C22⋊C4C2×D1111yescharacteristic
613C22×C22⋊C4C2×D1111yescharacteristic
614C22×C42—111no—
615C22×C42—111no—
616C22×C42—111no—
617C22×C42—111no—
618#390—224no—
619#390—224no—
620#390—224no—
621#390—224no—
622#389—224no—
623#380—224no—
624C4×C4⋊C4—224no—
625C4×C22⋊C4—224no—
626C2×#95—111no—
627C2×#95—111no—
628C2×#95—111no—
629C2×#95—111no—
630C2×#95—111no—
631C2×#95—111no—
632C2×#95C2×D1111yescharacteristic
633C2×#95C2×D1111yescharacteristic
634C22×C11—24no—
635C22×C11—24no—
636C22×C11—24no—
637C22×C11—42no—
638C22×C11—42no—
639C22×C11—42no—
640C22×C11—42no—
641C22×C11—42no—
642C22×C11—42no—
643C22×C11—42no—
644C22×C11—42no—
645C22×C11—42no—
646C22×C11—42no—
647C22×C11—42no—
648C22×C11—42no—
649C22×C11—42no—
650C22×C11—42no—
651C22×C11—42no—
652C22×C11—42no—
653C22×C11—42no—
654C22×C11—42no—
655C22×C11—42no—
656C22×C11—81no—
657C22×C11—81no—
658C22×C11—81no—
659C22×C11—81no—
660C22×C11—81no—
661C22×C11—81no—
662C22×C11—81no—
663C22×C11—81no—
664C22×C11C22×C22⋊C411yescharacteristic
665C22×C11C2×C4×D411yescharacteristic
666C22×C11C2×C4×D411yescharacteristic
667C22×C11C2×C4×D411yescharacteristic
668C22×C11C4×#4111yescharacteristic
669C22×C11#51811yescharacteristic
670C22×C11#52011yescharacteristic
671C22×C11C2×#12111yescharacteristic
672C22×C11C2×#12111yescharacteristic
673C22×C11C2×#12111yescharacteristic
674C22×C11#52511yescharacteristic
675C22×C11C2×#12411yescharacteristic
676C22×C11#52911yescharacteristic
677C22×C11C2×#12711yescharacteristic
678C22×C11#53211yescharacteristic
679C22×C11#53511yescharacteristic
680C22×C11#53711yescharacteristic
681C22×C11#54011yescharacteristic
682C22×C11#54211yescharacteristic
683C22×C11D4211yescharacteristic
684C22×C11D4211yescharacteristic
685C22×C11D4211yescharacteristic
686C22×C11#54611yescharacteristic
687C22×C11#54611yescharacteristic
688C22×C11#54611yescharacteristic
689C22×C11#54711yescharacteristic
690C22×C11#54811yescharacteristic
691C22×C11#54811yescharacteristic
692C22×C11#54811yescharacteristic
693C22×C11#55011yescharacteristic
694C22×C11#55011yescharacteristic
695C22×C11#55011yescharacteristic
696C22×C11#55311yescharacteristic
697C22×C11#55311yescharacteristic
698C22×C11#55511yescharacteristic
699C2×D11—42no—
700C2×D11—42no—
701C2×D11—42no—
702C2×D11—42no—
703C2×D11—42no—
704C2×D11—42no—
705C2×D11—42no—
706C2×D11—81no—
707C2×D11—81no—
708C2×D11—81no—
709C2×D11—81no—
710C2×D11—81no—
711C2×D11—81no—
712C2×D11—81no—
713C2×D11—81no—
714C4×C11—24no—
715C4×C11—42no—
716C4×C11—42no—
717C4×C11—42no—
718C4×C11—81no—
719Dic11—24no—
720Dic11—24no—
721Dic11—42no—
722Dic11—42no—
723Dic11—42no—
724Dic11—81no—
725Dic11#39018yescomplemented
726C25—111no—
727C25C22×D1111yescharacteristic
728C25C22×D1111yescharacteristic
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—41no—
734C22×D4—41no—
735C22×D4—114no—
736C22×D4—114no—
737C22×D4—222no—
738C22×D4—222no—
739C22×D4—222no—
740C22×D4—222no—
741C22×D4—222no—
742C22×D4—222no—
743C22×D4—222no—
744C22×D4—222no—
745C22×D4—222no—
746C22×D4—222no—
747C22×D4—441no—
748C22×D4—441no—
749C22×D4C4×D1114yes—
750C23×C4—111no—
751C23×C4—111no—
752C23×C4—111no—
753C23×C4—114no—
754C23×C4—111no—
755C23×C4—111no—
756C23×C4—111no—
757C23×C4—111no—
758C23×C4—222no—
759C23×C4—222no—
760C23×C4—222no—
761C23×C4—222no—
762C23×C4—222no—
763C23×C4—222no—
764C23×C4C22×D1111yescharacteristic
765C23×C4C22×D1111yescharacteristic
766C23×C4C22×D1111yescharacteristic
767C23×C4C22×D1111yescharacteristic
768C23×C4C22×D1111yescharacteristic
769#121—2232no—
770C2×C4⋊C4—114no—
771C2×C4⋊C4—114no—
772C2×C4⋊C4—114no—
773C2×C4⋊C4—114no—
774C2×C4⋊C4—222no—
775C2×C4⋊C4—222no—
776C2×C4⋊C4—222no—
777C2×C4⋊C4—222no—
778C2×C4⋊C4—222no—
779C2×C4⋊C4—222no—
780C2×C4⋊C4—222no—
781C2×C4⋊C4—222no—
782C2×C4⋊C4—222no—
783C2×C4⋊C4—441no—
784C2×C4⋊C4—441no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—114no—
798C2×C22⋊C4—114no—
799C2×C22⋊C4—114no—
800C2×C22⋊C4—222no—
801C2×C22⋊C4—222no—
802C2×C22⋊C4—222no—
803C2×C22⋊C4—222no—
804C2×C22⋊C4—222no—
805C2×C22⋊C4—222no—
806C2×C22⋊C4—222no—
807C2×C22⋊C4—222no—
808C2×C22⋊C4—222no—
809C2×C22⋊C4—222no—
810C2×C22⋊C4—222no—
811C2×C22⋊C4—222no—
812C2×C22⋊C4—222no—
813C2×C22⋊C4—222no—
814C2×C22⋊C4—222no—
815C2×C22⋊C4—222no—
816C2×C22⋊C4—222no—
817C2×C22⋊C4—222no—
818C2×C22⋊C4—222no—
819C2×C22⋊C4—222no—
820C2×C22⋊C4—222no—
821C2×C22⋊C4—441no—
822C2×C22⋊C4—441no—
823C2×C22⋊C4—441no—
824C2×C22⋊C4—441no—
825C2×C22⋊C4—441no—
826C2×C22⋊C4—441no—
827C2×C42—114no—
828C2×C42—222no—
829C2×C42—222no—
830C2×C42—222no—
831C2×C42—222no—
832C2×C42—222no—
833C2×C42—222no—
834C2×C42—222no—
835C2×C42—222no—
836C2×C42—222no—
837C2×C42—441no—
838C2×C42—441no—
839#95—22no—
840#95—22no—
841#95—222no—
842#95—222no—
843#95—222no—
844#95—222no—
845#95—222no—
846#95—222no—
847C2×C11—44no—
848C2×C11—82no—
849C2×C11C2×#39011yescharacteristic
850C2×C11C4×#12111yescharacteristic
851C2×C11#232411yescharacteristic
852C2×C11D4×C22⋊C411yescharacteristic
853C2×C11#234111yescharacteristic
854C2×C11#236111yescharacteristic
855C2×C11#236311yescharacteristic
856C2×C11#241411yescharacteristic
857C2×C11#241611yescharacteristic
858C2×C11#242611yescharacteristic
859C2×C11#242811yescharacteristic
860C2×C11#249011yescharacteristic
861C2×C11#249111yescharacteristic
862C2×C11#254011yescharacteristic
863C2×C11#254111yescharacteristic
864D11—82no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—112no—
892C24—221no—
893C24—221no—
894C24—221no—
895C24—221no—
896C24—221no—
897C24—221no—
898C24—221no—
899C24—221no—
900C24—221no—
901C24—221no—
902C24—221no—
903C24—221no—
904C24—221no—
905C24—221no—
906C24C2×C4×D1112yes—
907C24C2×C4×D1112yes—
908C24D4×D1112yes—
909C24#434112yes—
910C24C23×D1111yescharacteristic
911C2×D4—28no—
912C2×D4—28no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—228no—
919C2×D4—228no—
920C2×D4—228no—
921C2×D4—228no—
922C2×D4—228no—
923C2×D4—444no—
924C2×D4—444no—
925C2×D4—444no—
926C2×D4—444no—
927C2×D4—444no—
928C2×D4—444no—
929C2×D4—444no—
930C2×D4—444no—
931C2×D4—444no—
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—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—112no—
962C22×C4—112no—
963C22×C4—112no—
964C22×C4—112no—
965C22×C4—112no—
966C22×C4—112no—
967C22×C4—112no—
968C22×C4—112no—
969C22×C4—112no—
970C22×C4—112no—
971C22×C4—112no—
972C22×C4—112no—
973C22×C4—112no—
974C22×C4—112no—
975C22×C4—112no—
976C22×C4—112no—
977C22×C4—228no—
978C22×C4—228no—
979C22×C4—228no—
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—221no—
997C22×C4—221no—
998C22×C4—221no—
999C22×C4—221no—
1000C22×C4—221no—
1001C22×C4—221no—
1002C22×C4—221no—
1003C22×C4—221no—
1004C22×C4—221no—
1005C22×C4—221no—
1006C22×C4—221no—
1007C22×C4—221no—
1008C22×C4—221no—
1009C22×C4—221no—
1010C22×C4—221no—
1011C22×C4—221no—
1012C22×C4—221no—
1013C22×C4—444no—
1014C22×C4—444no—
1015C22×C4—444no—
1016C22×C4—444no—
1017C22×C4C2×C4×D1112yes—
1018C22×C4D4×D1112yes—
1019C22×C4D4×D1112yes—
1020C22×C4D4×D1112yes—
1021C22×C4D4×D1112yes—
1022C22×C4#434112yes—
1023C4⋊C4—1116no—
1024C4⋊C4—228no—
1025C4⋊C4—444no—
1026C4⋊C4—444no—
1027C4⋊C4—444no—
1028C22⋊C4—28no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—228no—
1033C22⋊C4—228no—
1034C22⋊C4—228no—
1035C22⋊C4—444no—
1036C22⋊C4—444no—
1037C22⋊C4—444no—
1038C22⋊C4—444no—
1039C22⋊C4—444no—
1040C22⋊C4—444no—
1041C22⋊C4—444no—
1042C42—228no—
1043C42—444no—
1044C42—444no—
1045C42—444no—
1046C11#1399811yescharacteristic, complemented, Sylow
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—222no—
1117C23—222no—
1118C23—222no—
1119C23—222no—
1120C23—222no—
1121C23—222no—
1122C23—222no—
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—
1137C23—441no—
1138C23—441no—
1139C23—441no—
1140C23—441no—
1141C23—441no—
1142C23—441no—
1143C23—441no—
1144C23—441no—
1145C23—441no—
1146C23—441no—
1147C23—441no—
1148C23—441no—
1149C23—441no—
1150C23—441no—
1151C23(C22⋊D11)⋊C414yes—
1152C23C22×C4×D1111yescharacteristic
1153C23C2×D4×D1111yescharacteristic
1154C23C2×D4×D1111yescharacteristic
1155C23C2×D4×D1111yescharacteristic
1156C23C2×D4×D1111yescharacteristic
1157C23C2×D4×D1111yescharacteristic
1158C23C2×#434111yescharacteristic
1159C23C2×#434111yescharacteristic
1160C23#6703711yescharacteristic
1161C23#6703711yescharacteristic
1162C23#6703711yescharacteristic
1163C23#41×D1111yescharacteristic
1164C23#41×D1111yescharacteristic
1165C23#41×D1111yescharacteristic
1166C23#6704311yescharacteristic
1167D4—416no—
1168D4—4416no—
1169D4—4416no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
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—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—114no—
1205C2×C4—114no—
1206C2×C4—114no—
1207C2×C4—114no—
1208C2×C4—114no—
1209C2×C4—114no—
1210C2×C4—114no—
1211C2×C4—114no—
1212C2×C4—114no—
1213C2×C4—222no—
1214C2×C4—222no—
1215C2×C4—222no—
1216C2×C4—222no—
1217C2×C4—222no—
1218C2×C4—222no—
1219C2×C4—222no—
1220C2×C4—222no—
1221C2×C4—222no—
1222C2×C4—222no—
1223C2×C4—222no—
1224C2×C4—222no—
1225C2×C4—222no—
1226C2×C4—222no—
1227C2×C4—222no—
1228C2×C4—222no—
1229C2×C4—222no—
1230C2×C4—222no—
1231C2×C4—222no—
1232C2×C4—222no—
1233C2×C4—222no—
1234C2×C4—4416no—
1235C2×C4—441no—
1236C2×C4—441no—
1237C2×C4—441no—
1238C2×C4—441no—
1239C2×C4—441no—
1240C2×C4—441no—
1241C2×C4—441no—
1242C2×C4—441no—
1243C2×C4—441no—
1244C2×C4—441no—
1245C2×C4—441no—
1246C2×C4—441no—
1247C2×C4—441no—
1248C2×C4—441no—
1249C2×C4—441no—
1250C2×C4—441no—
1251C2×C4—441no—
1252C2×C4—441no—
1253C2×C4—441no—
1254C2×C4C22⋊C4×D1114yes—
1255C22—24no—
1256C22—24no—
1257C22—24no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—442no—
1286C22—442no—
1287C22—442no—
1288C22—442no—
1289C22—442no—
1290C22—442no—
1291C22—442no—
1292C22—881no—
1293C22—881no—
1294C22—881no—
1295C22—881no—
1296C22—881no—
1297C22—881no—
1298C22—881no—
1299C22—881no—
1300C22C2×C22⋊C4×D1111yescharacteristic
1301C22C2×(C22⋊D11)⋊C411yescharacteristic
1302C22#1062301711yescharacteristic
1303C22C4×#434111yescharacteristic
1304C22C4×D4×D1111yescharacteristic
1305C22C4×D4×D1111yescharacteristic
1306C22#1062307711yescharacteristic
1307C22#1062311711yescharacteristic
1308C22#1062312111yescharacteristic
1309C22#1062312111yescharacteristic
1310C22#1062312111yescharacteristic
1311C22#1062312211yescharacteristic
1312C22#1062312211yescharacteristic
1313C22#1062312211yescharacteristic
1314C22#1062312311yescharacteristic
1315C22#1062312711yescharacteristic
1316C22#1062312911yescharacteristic
1317C22#1062312911yescharacteristic
1318C22#1062313011yescharacteristic
1319C22#1062313011yescharacteristic
1320C22#1062313211yescharacteristic
1321C22D11×#12111yescharacteristic
1322C22D11×#12111yescharacteristic
1323C22D11×#12111yescharacteristic
1324C22#1062313911yescharacteristic
1325C22#1062314611yescharacteristic
1326C22#1062314711yescharacteristic
1327C22#1062318011yescharacteristic
1328C22#1062318611yescharacteristic
1329C22#1062319211yescharacteristic
1330C22#1062319311yescharacteristic
1331C22D11×#12411yescharacteristic
1332C22#1062320811yescharacteristic
1333C22D11×#12711yescharacteristic
1334C22#1062324911yescharacteristic
1335C4—24no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—81no—
1340C4—118no—
1341C4—224no—
1342C4—224no—
1343C4—442no—
1344C4—442no—
1345C4—442no—
1346C4—881no—
1347C2—44no—
1348C2—82no—
1349C2—882no—
1350C2D11×#39011yescharacteristic
1351C2#1307112611yescharacteristic
1352C2#1307130611yescharacteristic
1353C2#1307143211yescharacteristic
1354C2#1307145511yescharacteristic
1355C2#1307162711yescharacteristic
1356C2#1307165711yescharacteristic
1357C2#1307202711yescharacteristic
1358C2#1307204911yescharacteristic
1359C2#1307217511yescharacteristic
1360C2#1307219711yescharacteristic
1361C2#1307296111yescharacteristic
1362C2#1307297211yescharacteristic
1363C2#1307354911yescharacteristic
1364C2#1307355711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC22×#66992C2
hypercenter#1438D11
hypocenterC11#13998
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#10622834C2semidirect
3. C2×#10622570C2semidirect
4. C2×#10622570C2semidirect
5. C2×#10622570C2semidirect
6. C2×#10622260C2semidirect
7. C2×#10622555C2semidirect
8. C2×#10622262C2semidirect
9. C2×C22⋊C4×Dic11C2semidirect
10. #13066862C2semidirect
11. #13066859C2semidirect
12. #13066855C2semidirect
13. #13066853C2semidirect
14. #13066852C2semidirect
15. C11×#1438C2semidirect
31. C2×#66992C4semidirect
131. C2×C22⋊Dic11D4semidirect
162. C2×Dic11⋊C4D4semidirect
174. C2×C4×Dic11D4semidirect
360. Dic11⋊C4C22⋊C4semidirect
377. #1438D11semidirect
585. C2×Dic11#121semidirect
725. Dic11#390semidirect
1046. C11#13998semidirect

Maximal subgroups

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

subgroupindex
C22×#669922
C2×#106228342
C2×#106225702
C2×#106222602
C2×#106225552
C2×#106222622
C2×C22⋊C4×Dic112
#130668622
#130668592
#130668552
#130668532
#130668522
C11×#14382
#1399811