Finite Group Databasebeta

← #14676917

Subgroups — #14676917

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×#66937C211yesmaximal, characteristic
2C2×#10622552C211yesmaximal, characteristic, complemented
3C2×#10622570C211yesmaximal, characteristic, complemented
4C2×#10622570C211yesmaximal, characteristic, complemented
5C2×#10622570C211yesmaximal, characteristic, complemented
6C2×#10622260C211yesmaximal, characteristic, complemented
7C2×#10622280C211yesmaximal, characteristic, complemented
8C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
9C2×#10622279C211yesmaximal, characteristic, complemented
10#13066861C211yesmaximal, characteristic, complemented
11#13066860C211yesmaximal, characteristic, complemented
12#13066856C211yesmaximal, characteristic, complemented
13#13066855C211yesmaximal, characteristic, complemented
14#13066852C211yesmaximal, characteristic, complemented
15C11×#1437C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
35C22×C4⋊Dic11C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C22×C4×Dic11C2211yescharacteristic
43C2×#66937—24no—
44C2×#66937—24no—
45C2×#66937C418yescomplemented
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#10622570—24no—
55#10622570—24no—
56#10622570—24no—
57#10622552—24no—
58C4×Dic11⋊C4—24no—
59#10622280—24no—
60#10622279—24no—
61#10622260—24no—
62C25×C11C2311yescharacteristic
63C24×D11C2311yescharacteristic
64C24×D11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C22×C22⋊D11—22no—
72C22×C22⋊D11—22no—
73C22×C22⋊D11—22no—
74C22×C22⋊D11—22no—
75C22×C22⋊D11—22no—
76C22×C22⋊D11—22no—
77C22×C22⋊D11—22no—
78C22×C22⋊D11—22no—
79C22×C22⋊D11—22no—
80C22×C22⋊D11—22no—
81C22×C22⋊D11—41no—
82C22×C22⋊D11—41no—
83C22×C22⋊D11C2×C414yes—
84C22×C22⋊D11C2×C414yes—
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C22×D44—22no—
92C22×D44—22no—
93C22×D44—22no—
94C22×D44—22no—
95C22×D44—41no—
96C22×D44—41no—
97C22×D44C2×C414yes—
98C22×C4×D11—22no—
99C22×C4×D11—22no—
100C22×C4×D11—22no—
101C22×C4×D11—22no—
102C22×C4×D11—22no—
103C22×C4×D11—22no—
104C22×C4×D11C2×C414yes—
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—41no—
113C2×C11×C22⋊C4C2×C414yes—
114C2×C42×C11—22no—
115C2×C42×C11—22no—
116C2×C42×C11—41no—
117C2×C22⋊Dic11—22no—
118C2×C22⋊Dic11—22no—
119C2×C22⋊Dic11—22no—
120C2×C22⋊Dic11—41no—
121C2×C22⋊Dic11—41no—
122C2×C22⋊Dic11—41no—
123C2×(C2×D11)⋊C4—22no—
124C2×(C2×D11)⋊C4—22no—
125C2×(C2×D11)⋊C4—22no—
126C2×(C2×D11)⋊C4—22no—
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—22no—
140C2×(C2×D11)⋊C4—22no—
141C2×(C2×D11)⋊C4—22no—
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)⋊C4C2×C414yes—
149C2×(C2×D11)⋊C4D414yescomplemented
150C2×C4⋊Dic11—22no—
151C2×C4⋊Dic11—22no—
152C2×C4⋊Dic11—41no—
153C2×Dic11⋊C4—22no—
154C2×Dic11⋊C4—22no—
155C2×Dic11⋊C4—22no—
156C2×Dic11⋊C4—22no—
157C2×Dic11⋊C4—22no—
158C2×Dic11⋊C4—22no—
159C2×Dic11⋊C4—22no—
160C2×Dic11⋊C4—41no—
161C2×Dic11⋊C4C2×C414yes—
162C2×Dic11⋊C4D414yes—
163C2×Dic11⋊C4D414yes—
164C2×Dic11⋊C4D414yescomplemented
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×Dic11D414yescomplemented
174#66937—232no—
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×C11C22×C412yes—
199C24×C11C2411yescharacteristic
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×D11—21no—
213C23×D11—21no—
214C23×D11—21no—
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×D11C22×C412yes—
227C23×D11C22×C412yes—
228C23×D11C2×D412yes—
229C23×D11#4112yes—
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×C11—21no—
258C22×C4×C11—21no—
259C22×C4×C11—21no—
260C22×C4×C11—21no—
261C22×C4×C11—21no—
262C22×C4×C11—21no—
263C22×C4×C11C22×C412yes—
264C22×C4×C11C22×C412yes—
265C22×C4×C11C2×D412yes—
266C22×C4×C11C2×D412yes—
267C22×C4×C11C2×D412yes—
268C22×C4×C11C2×D412yes—
269C22×C4×C11C2×D412yes—
270C22×C4×C11#4112yes—
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—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—21no—
310C22×Dic11—21no—
311C22×Dic11—21no—
312C22×Dic11—21no—
313C22×Dic11—21no—
314C22×Dic11—21no—
315C22×Dic11C22×C412yes—
316C22×Dic11C22×C412yes—
317C22×Dic11C2×D412yes—
318C22×Dic11C2×D412yes—
319C22×Dic11C2×D412yes—
320C22×Dic11C2×D412yes—
321C22×Dic11C2×D412yes—
322C22×Dic11C2×D412yes—
323C22×Dic11C2×D412yes—
324C22×Dic11C2×D412yes—
325C22×Dic11C2×D412yes—
326C22×Dic11#4112yes—
327C22×Dic11#4112yes—
328C2×D44—28no—
329C2×D44—28no—
330C2×D44—44no—
331C2×D44—44no—
332C2×D44—44no—
333C2×D44—44no—
334C2×D44—44no—
335C2×C4×D11—28no—
336C2×C4×D11—28no—
337C2×C4×D11—28no—
338C2×C4×D11—44no—
339C2×C4×D11—44no—
340C2×C4×D11—44no—
341C2×C4×D11—44no—
342C11×C22⋊C4—28no—
343C11×C22⋊C4—44no—
344C11×C22⋊C4—44no—
345C42×C11—44no—
346C22⋊Dic11—44no—
347C22⋊Dic11—44no—
348(C2×D11)⋊C4—28no—
349(C2×D11)⋊C4—28no—
350(C2×D11)⋊C4—28no—
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—
356(C2×D11)⋊C4—44no—
357C4⋊Dic11—44no—
358Dic11⋊C4—28no—
359Dic11⋊C4—44no—
360Dic11⋊C4—44no—
361Dic11⋊C4C22⋊C4116yescomplemented
362C4×Dic11—28no—
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#1438—111no—
378#1437—111no—
379#1437D1111yescharacteristic, complemented
380C23×C11—22no—
381C23×C11—22no—
382C23×C11—22no—
383C23×C11—22no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—41no—
388C23×C11—41no—
389C23×C11—41no—
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×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×C11C23×C411yescharacteristic
416C23×C11C22×D411yescharacteristic
417C23×C11C22×D411yescharacteristic
418C23×C11C22×D411yescharacteristic
419C23×C11C22×D411yescharacteristic
420C23×C11C22×D411yescharacteristic
421C23×C11C2×#4111yescharacteristic
422C23×C11C2×#4111yescharacteristic
423C23×C11C2×#4111yescharacteristic
424C23×C11C2×#4111yescharacteristic
425C23×C11C2×#4111yescharacteristic
426C23×C11H(5,𝔽2)11yescharacteristic
427C23×C11H(5,𝔽2)11yescharacteristic
428C23×C11H(5,𝔽2)11yescharacteristic
429C23×C112−1+411yescharacteristic
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—41no—
456C22×D11—41no—
457C22×D11—41no—
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×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×D11C4×D414yes—
500C2×C4×C11—22no—
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—22no—
517C2×C4×C11—22no—
518C2×C4×C11—22no—
519C2×C4×C11—22no—
520C2×C4×C11—22no—
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×C11—41no—
536C2×C4×C11—41no—
537C2×C4×C11—41no—
538C2×C4×C11—41no—
539C2×C4×C11—41no—
540C2×C4×C11C2×C22⋊C414yes—
541C2×C4×C11#12114yescomplemented
542C22⋊D11—416no—
543C22⋊D11—416no—
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—41no—
572C2×Dic11—41no—
573C2×Dic11—41no—
574C2×Dic11—41no—
575C2×Dic11—41no—
576C2×Dic11—41no—
577C2×Dic11—41no—
578C2×Dic11C2×C22⋊C414yes—
579C2×Dic11C2×C22⋊C414yes—
580C2×Dic11C4×D414yes—
581C2×Dic11C4×D414yes—
582C2×Dic11#12114yes—
583C2×Dic11#12114yes—
584C2×Dic11#12414yes—
585C2×Dic11#12714yes—
586D44—416no—
587C4×D11—416no—
588C23×D4—111no—
589C23×D4—111no—
590C23×D4—111no—
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⋊C4—111no—
611C22×C22⋊C4C2×D1111yescharacteristic
612C22×C22⋊C4C2×D1111yescharacteristic
613C22×C22⋊C4C2×D1111yescharacteristic
614C22×C42—111no—
615C22×C42—111no—
616C22×C42—111no—
617C22×C42C2×D1111yescharacteristic
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×#95C2×D1111yescharacteristic
632C2×#95C2×D1111yescharacteristic
633C2×#95C2×D1111yescharacteristic
634C22×C11—42no—
635C22×C11—42no—
636C22×C11—42no—
637C22×C11—42no—
638C22×C11—42no—
639C22×C11—42no—
640C22×C11—42no—
641C22×C11—81no—
642C22×C11—81no—
643C22×C11—81no—
644C22×C11—81no—
645C22×C11—81no—
646C22×C11—81no—
647C22×C11—81no—
648C22×C11—81no—
649C22×C11C22×C22⋊C411yescharacteristic
650C22×C11C2×C4×D411yescharacteristic
651C22×C11C2×C4×D411yescharacteristic
652C22×C11C2×C4×D411yescharacteristic
653C22×C11C4×#4111yescharacteristic
654C22×C11#51811yescharacteristic
655C22×C11#52011yescharacteristic
656C22×C11C2×#12111yescharacteristic
657C22×C11C2×#12111yescharacteristic
658C22×C11C2×#12111yescharacteristic
659C22×C11#52511yescharacteristic
660C22×C11C2×#12411yescharacteristic
661C22×C11#52911yescharacteristic
662C22×C11C2×#12711yescharacteristic
663C22×C11#53211yescharacteristic
664C22×C11#53511yescharacteristic
665C22×C11#53711yescharacteristic
666C22×C11#54011yescharacteristic
667C22×C11#54211yescharacteristic
668C22×C11D4211yescharacteristic
669C22×C11D4211yescharacteristic
670C22×C11D4211yescharacteristic
671C22×C11#54611yescharacteristic
672C22×C11#54611yescharacteristic
673C22×C11#54611yescharacteristic
674C22×C11#54711yescharacteristic
675C22×C11#54811yescharacteristic
676C22×C11#54811yescharacteristic
677C22×C11#54811yescharacteristic
678C22×C11#55011yescharacteristic
679C22×C11#55011yescharacteristic
680C22×C11#55011yescharacteristic
681C22×C11#55311yescharacteristic
682C22×C11#55311yescharacteristic
683C22×C11#55511yescharacteristic
684C2×D11—24no—
685C2×D11—24no—
686C2×D11—24no—
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—
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—24no—
716C4×C11—42no—
717C4×C11—42no—
718C4×C11—42no—
719C4×C11—81no—
720Dic11—24no—
721Dic11—42no—
722Dic11—42no—
723Dic11—42no—
724Dic11—81no—
725Dic11#39018yescomplemented
726C25—111no—
727C25—111no—
728C25C22×D1111yescharacteristic
729C22×D4—114no—
730C22×D4—114no—
731C22×D4—114no—
732C22×D4—222no—
733C22×D4—222no—
734C22×D4—222no—
735C22×D4—222no—
736C22×D4—222no—
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—441no—
747C22×D4—441no—
748C22×D4—441no—
749C22×D4—441no—
750C23×C4—111no—
751C23×C4—111no—
752C23×C4—111no—
753C23×C4—111no—
754C23×C4—111no—
755C23×C4—114no—
756C23×C4—111no—
757C23×C4—222no—
758C23×C4—222no—
759C23×C4—222no—
760C23×C4—222no—
761C23×C4—222no—
762C23×C4—222no—
763C23×C4C22×D1111yescharacteristic
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—41no—
793C2×C22⋊C4—114no—
794C2×C22⋊C4—114no—
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—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—441no—
818C2×C22⋊C4—441no—
819C2×C22⋊C4—441no—
820C2×C22⋊C4—441no—
821C2×C22⋊C4—441no—
822C2×C22⋊C4—441no—
823C2×C22⋊C4—441no—
824C2×C22⋊C4—441no—
825C2×C22⋊C4—441no—
826C2×C22⋊C4C4×D1114yes—
827C2×C42—22no—
828C2×C42—22no—
829C2×C42—41no—
830C2×C42—114no—
831C2×C42—222no—
832C2×C42—222no—
833C2×C42—222no—
834C2×C42—222no—
835C2×C42—222no—
836C2×C42—222no—
837C2×C42—222no—
838C2×C42—441no—
839#95—22no—
840#95—22no—
841#95—22no—
842#95—222no—
843#95—222no—
844#95—222no—
845#95—222no—
846#95—222no—
847C2×C11—82no—
848C2×C11C2×#39011yescharacteristic
849C2×C11C4×#12111yescharacteristic
850C2×C11#232411yescharacteristic
851C2×C11D4×C22⋊C411yescharacteristic
852C2×C11#234111yescharacteristic
853C2×C11#236111yescharacteristic
854C2×C11#236311yescharacteristic
855C2×C11#241411yescharacteristic
856C2×C11#241611yescharacteristic
857C2×C11#242611yescharacteristic
858C2×C11#242811yescharacteristic
859C2×C11#249011yescharacteristic
860C2×C11#249111yescharacteristic
861C2×C11#254011yescharacteristic
862C2×C11#254111yescharacteristic
863D11—44no—
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—112no—
880C24—112no—
881C24—112no—
882C24—112no—
883C24—221no—
884C24—221no—
885C24—221no—
886C24—221no—
887C24—221no—
888C24—221no—
889C24—221no—
890C24—221no—
891C24—221no—
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—
906C24—221no—
907C24—221no—
908C24—221no—
909C24C2×C4×D1112yes—
910C24C23×D1111yescharacteristic
911C2×D4—228no—
912C2×D4—228no—
913C2×D4—228no—
914C2×D4—228no—
915C2×D4—228no—
916C2×D4—228no—
917C2×D4—228no—
918C2×D4—444no—
919C2×D4—444no—
920C2×D4—444no—
921C2×D4—444no—
922C2×D4—444no—
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—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
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—112no—
978C22×C4—228no—
979C22×C4—228no—
980C22×C4—228no—
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—444no—
1011C22×C4—444no—
1012C22×C4—444no—
1013C22×C4—444no—
1014C22×C4C2×C4×D1112yes—
1015C22×C4C2×C4×D1112yes—
1016C22×C4#433912yes—
1017C22×C4#433912yes—
1018C22×C4D4×D1112yes—
1019C22×C4D4×D1112yes—
1020C22×C4D4×D1112yes—
1021C22×C4D4×D1112yes—
1022C22×C4D4×D1112yes—
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—228no—
1032C22⋊C4—228no—
1033C22⋊C4—228no—
1034C22⋊C4—444no—
1035C22⋊C4—444no—
1036C22⋊C4—444no—
1037C22⋊C4—444no—
1038C22⋊C4—444no—
1039C22⋊C4—444no—
1040C22⋊C4—444no—
1041C22⋊C4—444no—
1042C42—44no—
1043C42—228no—
1044C42—444no—
1045C42—444no—
1046C11#1399811yescharacteristic, complemented, Sylow
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
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—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—114no—
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—222no—
1106C23—222no—
1107C23—222no—
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—
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—441no—
1152C23C22×C4×D1111yescharacteristic
1153C23C2×#433911yescharacteristic
1154C23C2×#433911yescharacteristic
1155C23C2×D4×D1111yescharacteristic
1156C23C2×D4×D1111yescharacteristic
1157C23C2×D4×D1111yescharacteristic
1158C23C2×D4×D1111yescharacteristic
1159C23C2×D4×D1111yescharacteristic
1160C23#6703711yescharacteristic
1161C23#41×D1111yescharacteristic
1162C23#41×D1111yescharacteristic
1163C23#41×D1111yescharacteristic
1164C23#6704211yescharacteristic
1165C23#6704211yescharacteristic
1166C23#6704311yescharacteristic
1167D4—4416no—
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—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
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—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—114no—
1211C2×C4—114no—
1212C2×C4—114no—
1213C2×C4—114no—
1214C2×C4—114no—
1215C2×C4—114no—
1216C2×C4—114no—
1217C2×C4—114no—
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—4416no—
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—
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×C4C22⋊C4×D1114yes—
1254C2×C4#6693714yescomplemented
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—224no—
1271C22—224no—
1272C22—224no—
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—
1288C22—442no—
1289C22—442no—
1290C22—442no—
1291C22—442no—
1292C22—881no—
1293C22—881no—
1294C22—881no—
1295C22—881no—
1296C22—881no—
1297C22—881no—
1298C22—881no—
1299C22—881no—
1300C22C4×#433911yescharacteristic
1301C22C2×C22⋊C4×D1111yescharacteristic
1302C22C2×#6693711yescharacteristic
1303C22#1062302111yescharacteristic
1304C22#1062305411yescharacteristic
1305C22#1062305911yescharacteristic
1306C22#1062306311yescharacteristic
1307C22#1062307111yescharacteristic
1308C22C4×D4×D1111yescharacteristic
1309C22C4×D4×D1111yescharacteristic
1310C22C4×D4×D1111yescharacteristic
1311C22#1062307611yescharacteristic
1312C22#1062307811yescharacteristic
1313C22#1062307911yescharacteristic
1314C22#1062308311yescharacteristic
1315C22#1062308311yescharacteristic
1316C22#1062308411yescharacteristic
1317C22#1062308411yescharacteristic
1318C22#1062308411yescharacteristic
1319C22#1062312111yescharacteristic
1320C22#1062312811yescharacteristic
1321C22D11×#12111yescharacteristic
1322C22D11×#12111yescharacteristic
1323C22#1062314011yescharacteristic
1324C22#1062314011yescharacteristic
1325C22#1062314111yescharacteristic
1326C22#1062318511yescharacteristic
1327C22#1062318611yescharacteristic
1328C22#1062319411yescharacteristic
1329C22D11×#12411yescharacteristic
1330C22#1062320511yescharacteristic
1331C22#1062320811yescharacteristic
1332C22#1062324011yescharacteristic
1333C22#1062324111yescharacteristic
1334C22D11×#12711yescharacteristic
1335C4—24no—
1336C4—24no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—81no—
1341C4—118no—
1342C4—224no—
1343C4—442no—
1344C4—442no—
1345C4—442no—
1346C4—881no—
1347C2—82no—
1348C2—444no—
1349C2—882no—
1350C2D11×#39011yescharacteristic
1351C2C4×#6693711yescharacteristic
1352C2#1307130411yescharacteristic
1353C2#1307143411yescharacteristic
1354C2#1307145611yescharacteristic
1355C2#1307162911yescharacteristic
1356C2#1307165511yescharacteristic
1357C2#1307203311yescharacteristic
1358C2#1307205511yescharacteristic
1359C2#1307218111yescharacteristic
1360C2#1307220311yescharacteristic
1361C2#1307296711yescharacteristic
1362C2#1307297811yescharacteristic
1363C2#1307355311yescharacteristic
1364C2#1307356111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1437C2
socle, cosocleC24×C11C24
prime radicalC22×#66937C2
hypercenter#1437D11
hypocenterC11#13998
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C2×#10622552C2semidirect
3. C2×#10622570C2semidirect
4. C2×#10622570C2semidirect
5. C2×#10622570C2semidirect
6. C2×#10622260C2semidirect
7. C2×#10622280C2semidirect
8. C2×C4×Dic11⋊C4C2semidirect
9. C2×#10622279C2semidirect
10. #13066861C2semidirect
11. #13066860C2semidirect
12. #13066856C2semidirect
13. #13066855C2semidirect
14. #13066852C2semidirect
15. C11×#1437C2semidirect
45. C2×#66937C4semidirect
149. C2×(C2×D11)⋊C4D4semidirect
164. C2×Dic11⋊C4D4semidirect
173. C2×C4×Dic11D4semidirect
361. Dic11⋊C4C22⋊C4semidirect
379. #1437D11semidirect
541. C2×C4×C11#121semidirect
725. Dic11#390semidirect
1046. C11#13998semidirect
1254. C2×C4#66937semidirect

Maximal subgroups

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

subgroupindex
C22×#669372
C2×#106225522
C2×#106225702
C2×#106222602
C2×#106222802
C2×C4×Dic11⋊C42
C2×#106222792
#130668612
#130668602
#130668562
#130668552
#130668522
C11×#14372
#1399811