Finite Group Databasebeta

← #14676626

Subgroups — #14676626

Order 2816.

2690 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66946C211yesmaximal, characteristic
2C2×#10622278C211yesmaximal, characteristic
3C2×#10622278C211yesmaximal, characteristic
4C2×#10622602C211yesmaximal, characteristic, complemented
5C2×#10622602C211yesmaximal, characteristic, complemented
6C2×#10622600C211yesmaximal, characteristic, complemented
7C2×D11×#95C211yesmaximal, characteristic, complemented
8#13066875C211yesmaximal, characteristic, complemented
9#13066862C211yesmaximal, characteristic, complemented
10#13066858C211yesmaximal, characteristic, complemented
11#13066850C211yesmaximal, characteristic, complemented
12#13066847C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1444C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×#66946—24no—
36C2×#66946—24no—
37C2×#66946—24no—
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#10622602—24no—
55#10622602—24no—
56#10622600—24no—
57#10622278—24no—
58#10622278C418yescomplemented
59D11×#95—24no—
60C24×D11C2311yescharacteristic
61C24×D11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C22×D44—22no—
76C22×D44—22no—
77C22×D44—22no—
78C22×D44—22no—
79C22×D44C2×C414yes—
80C22×D44D414yes—
81C22×D44Q814yes—
82C22×C4×D11—22no—
83C22×C4×D11—22no—
84C22×C4×D11—22no—
85C22×C4×D11—22no—
86C22×C4×D11—22no—
87C22×C4×D11—22no—
88C22×C4×D11—22no—
89C22×C4×D11—22no—
90C22×C4×D11—22no—
91C22×C4×D11—22no—
92C22×C4×D11—22no—
93C22×C4×D11—22no—
94C22×C4×D11—22no—
95C22×C4×D11—22no—
96C22×C4×D11—22no—
97C22×C4×D11—22no—
98C22×C4×D11—22no—
99C22×C4×D11—22no—
100C22×C4×D11—41no—
101C22×C4×D11—41no—
102C22×C4×D11—41no—
103C22×C4×D11—41no—
104C22×C4×D11—41no—
105C22×C4×D11—41no—
106C22×C4×D11—41no—
107C22×C4×D11—41no—
108C22×C4×D11C2×C414yescomplemented
109C22×C4×D11D414yes—
110C2×C11×C4⋊C4—22no—
111C2×C11×C4⋊C4—22no—
112C2×C11×C4⋊C4—22no—
113C2×C11×C4⋊C4—22no—
114C2×C11×C4⋊C4—22no—
115C2×C11×C4⋊C4—22no—
116C2×C11×C4⋊C4—41no—
117C2×C11×C4⋊C4—41no—
118C2×C11×C4⋊C4—41no—
119C2×(C2×D11)⋊C4—22no—
120C2×(C2×D11)⋊C4—22no—
121C2×(C2×D11)⋊C4—22no—
122C2×(C2×D11)⋊C4—22no—
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—41no—
136C2×(C2×D11)⋊C4—41no—
137C2×(C2×D11)⋊C4—41no—
138C2×(C2×D11)⋊C4—41no—
139C2×(C2×D11)⋊C4C2×C414yescomplemented
140C2×(C2×D11)⋊C4C2×C414yescomplemented
141C2×(C2×D11)⋊C4C2×C414yescomplemented
142C2×(C2×D11)⋊C4D414yes—
143C2×C4⋊Dic11—22no—
144C2×C4⋊Dic11—22no—
145C2×C4⋊Dic11—41no—
146C2×Dic11⋊C4—22no—
147C2×Dic11⋊C4—22no—
148C2×Dic11⋊C4—22no—
149C2×C4×Dic11—22no—
150C2×C4×Dic11—22no—
151C2×C4×Dic11—22no—
152#66946—232no—
153C11×#95—22no—
154C11×#95—22no—
155C11×#95—41no—
156C11×#95C2×C414yescomplemented
157C11⋊#95—22no—
158C11⋊#95—22no—
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⋊#95C2×C414yescomplemented
168C11⋊#95D414yescomplemented
169#13975—111nomaximal, Sylow
170C24×C11C2411yescharacteristic
171C23×D11—21no—
172C23×D11—21no—
173C23×D11—21no—
174C23×D11—21no—
175C23×D11—21no—
176C23×D11—21no—
177C23×D11—21no—
178C23×D11—21no—
179C23×D11—21no—
180C23×D11—21no—
181C23×D11—21no—
182C23×D11—21no—
183C23×D11—21no—
184C23×D11—21no—
185C23×D11—21no—
186C23×D11—21no—
187C23×D11—21no—
188C23×D11—21no—
189C23×D11—21no—
190C23×D11—21no—
191C23×D11C22×C412yes—
192C23×D11C22×C412yes—
193C23×D11C2×D412yes—
194C23×D11C2×D412yes—
195C23×D11C2×D412yes—
196C23×D11C2×D412yes—
197C23×D11C2×Q812yes—
198C23×D11C2×Q812yes—
199C23×D11#4112yes—
200C23×D11#4112yes—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
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×C11C22×C412yes—
241C22×C4×C11C22×C412yes—
242C22×C4×C11C22×C412yes—
243C22×C4×C11C2×D412yes—
244C22×C4×C11C2×D412yes—
245C22×C4×C11C2×D412yes—
246C22×C4×C11C2×D412yes—
247C22×C4×C11C2×Q812yes—
248C22×C4×C11#4112yes—
249C22×C4×C11#4112yes—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—21no—
273C22×Dic11—21no—
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×Dic11C22×C412yes—
286C22×Dic11C22×C412yes—
287C22×Dic11C2×D412yes—
288C22×Dic11C2×D412yes—
289C22×Dic11C2×D412yes—
290C22×Dic11C2×D412yes—
291C22×Dic11#4112yes—
292C2×D44—28no—
293C2×D44—28no—
294C2×D44—28no—
295C2×D44—28no—
296C2×D44—28no—
297C2×D44—28no—
298C2×D44C4⋊C4116yescomplemented
299C2×C4×D11—28no—
300C2×C4×D11—28no—
301C2×C4×D11—28no—
302C2×C4×D11—28no—
303C2×C4×D11—28no—
304C2×C4×D11—28no—
305C2×C4×D11—44no—
306C2×C4×D11—44no—
307C2×C4×D11—44no—
308C2×C4×D11—44no—
309C2×C4×D11—44no—
310C2×C4×D11—44no—
311C2×C4×D11—44no—
312C2×C4×D11—44no—
313C2×C4×D11—44no—
314C2×C4×D11—44no—
315C2×C4×D11—44no—
316C2×C4×D11—44no—
317C2×C4×D11—44no—
318C2×C4×D11—44no—
319C2×C4×D11—44no—
320C2×C4×D11—44no—
321C2×C4×D11—44no—
322C2×C4×D11—44no—
323C2×C4×D11—44no—
324C2×C4×D11—44no—
325C2×C4×D11—44no—
326C2×C4×D11—44no—
327C11×C4⋊C4—28no—
328C11×C4⋊C4—44no—
329C11×C4⋊C4—44no—
330(C2×D11)⋊C4—28no—
331(C2×D11)⋊C4—28no—
332(C2×D11)⋊C4—28no—
333(C2×D11)⋊C4—28no—
334(C2×D11)⋊C4—44no—
335(C2×D11)⋊C4—44no—
336(C2×D11)⋊C4—44no—
337(C2×D11)⋊C4—44no—
338C4⋊Dic11—44no—
339Dic11⋊C4—44no—
340C4×Dic11—28no—
341C22×C4×D4—111no—
342C2×#386—111no—
343C2×#386—111no—
344C2×#385—111no—
345C2×#385—111no—
346C2×#380—111no—
347C22×#95—111no—
348#1444D1111yescharacteristic, complemented
349#1442—111no—
350#1439—111no—
351#1439—111no—
352#1436—111no—
353#1436—111no—
354C22⋊#95—111no—
355C22⋊#95—111no—
356C23×C11C23×C411yescharacteristic
357C23×C11C22×D411yescharacteristic
358C23×C11C22×D411yescharacteristic
359C23×C11C22×D411yescharacteristic
360C23×C11C22×D411yescharacteristic
361C23×C11C22×Q811yescharacteristic
362C23×C11C2×#4111yescharacteristic
363C23×C11C2×#4111yescharacteristic
364C23×C11C2×#4111yescharacteristic
365C23×C11C2×#4111yescharacteristic
366C23×C11C2×#4111yescharacteristic
367C23×C11H(5,𝔽2)11yescharacteristic
368C23×C11H(5,𝔽2)11yescharacteristic
369C23×C11H(5,𝔽2)11yescharacteristic
370C23×C112−1+411yescharacteristic
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—22no—
384C22×D11—22no—
385C22×D11—22no—
386C22×D11—22no—
387C22×D11—22no—
388C22×D11—22no—
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—22no—
395C22×D11—22no—
396C22×D11—22no—
397C22×D11—22no—
398C22×D11—22no—
399C22×D11—22no—
400C22×D11—22no—
401C22×D11—22no—
402C22×D11—22no—
403C22×D11—22no—
404C22×D11—22no—
405C22×D11—22no—
406C22×D11—22no—
407C22×D11—22no—
408C22×D11—22no—
409C22×D11—22no—
410C22×D11—22no—
411C22×D11—22no—
412C22×D11—22no—
413C22×D11—22no—
414C22×D11—22no—
415C22×D11—22no—
416C22×D11—22no—
417C22×D11—41no—
418C22×D11—41no—
419C22×D11—41no—
420C22×D11—41no—
421C22×D11—41no—
422C22×D11—41no—
423C22×D11—41no—
424C22×D11—41no—
425C22×D11—41no—
426C22×D11—41no—
427C22×D11—41no—
428C22×D11—41no—
429C22×D11—41no—
430C22×D11—41no—
431C22×D11—41no—
432C22×D11—41no—
433C22×D11C2×C4⋊C414yes—
434C22×D11C2×C4⋊C414yes—
435C22×D11C4×D414yes—
436C22×D11C4×D414yes—
437C22×D11#12014yes—
438C22×D11C22⋊Q814yes—
439C22×D11C22⋊Q814yes—
440C22×D11#12314yes—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—22no—
457C2×C4×C11—22no—
458C2×C4×C11—22no—
459C2×C4×C11—22no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—22no—
463C2×C4×C11—22no—
464C2×C4×C11—22no—
465C2×C4×C11—41no—
466C2×C4×C11—41no—
467C2×C4×C11—41no—
468C2×C4×C11—41no—
469C2×C4×C11—41no—
470C2×C4×C11—41no—
471C2×C4×C11—41no—
472C2×C4×C11—41no—
473C2×C4×C11—41no—
474C2×C4×C11—41no—
475C2×C4×C11—41no—
476C2×C4×C11—41no—
477C2×C4×C11—41no—
478C2×C4×C11—41no—
479C2×C4×C11—41no—
480C2×C4×C11—41no—
481C2×C4×C11—41no—
482C2×C4×C11—41no—
483C2×C4×C11—41no—
484C2×C4×C11—41no—
485C2×C4×C11—41no—
486C2×C4×C11—41no—
487C2×C4×C11—41no—
488C2×C4×C11C2×C4⋊C414yes—
489C2×C4×C11C4×D414yescomplemented
490C2×Dic11—22no—
491C2×Dic11—22no—
492C2×Dic11—22no—
493C2×Dic11—22no—
494C2×Dic11—22no—
495C2×Dic11—22no—
496C2×Dic11—22no—
497C2×Dic11—22no—
498C2×Dic11—22no—
499C2×Dic11—22no—
500C2×Dic11—22no—
501C2×Dic11—22no—
502C2×Dic11—22no—
503C2×Dic11—22no—
504C2×Dic11—22no—
505C2×Dic11—22no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—41no—
509C2×Dic11—41no—
510C2×Dic11—41no—
511C2×Dic11—41no—
512C2×Dic11—41no—
513C2×Dic11—41no—
514C2×Dic11—41no—
515C2×Dic11—41no—
516C2×Dic11—41no—
517C2×Dic11—41no—
518C2×Dic11—41no—
519C2×Dic11—41no—
520C2×Dic11—41no—
521C2×Dic11—41no—
522C2×Dic11—41no—
523C2×Dic11—41no—
524C2×Dic11—41no—
525C2×Dic11—41no—
526C2×Dic11—41no—
527C2×Dic11—41no—
528C2×Dic11—41no—
529C2×Dic11—41no—
530C2×Dic11—41no—
531C2×Dic11#12114yes—
532D44—232no—
533C4×D11—416no—
534C4×D11—416no—
535C4×D11—416no—
536C4×D11—416no—
537C23×D4—111no—
538C24×C4—111no—
539C24×C4—111no—
540C24×C4—111no—
541C24×C4—111no—
542C2×C4×D4—224no—
543C2×C4×D4—224no—
544C2×C4×D4—224no—
545C22×C4⋊C4—111no—
546C22×C4⋊C4—111no—
547C22×C4⋊C4C2×D1111yescharacteristic
548C22×C4⋊C4C2×D1111yescharacteristic
549C22×C4⋊C4C2×D1111yescharacteristic
550C22×C22⋊C4—111no—
551C22×C22⋊C4—111no—
552C22×C22⋊C4—111no—
553C22×C22⋊C4—111no—
554C22×C22⋊C4—111no—
555C22×C22⋊C4—111no—
556C22×C22⋊C4—111no—
557C22×C22⋊C4—111no—
558C22×C42—111no—
559#386—118no—
560#386—224no—
561#385—224no—
562#385—224no—
563#380—224no—
564C2×#95—111no—
565C2×#95—111no—
566C2×#95—111no—
567C2×#95—111no—
568C2×#95—111no—
569C2×#95—111no—
570C2×#95—111no—
571C2×#95—111no—
572C2×#95—111no—
573C2×#95—111no—
574C2×#95—111no—
575C2×#95—111no—
576C2×#95—224no—
577C2×#95C2×D1111yescharacteristic
578C2×#95C2×D1111yescharacteristic
579C2×#95C2×D1111yescharacteristic
580C2×#95C2×D1111yescharacteristic
581C22×C11C22×C4⋊C411yescharacteristic
582C22×C11C2×C4×D411yescharacteristic
583C22×C11C2×C4×D411yescharacteristic
584C22×C11C2×C4×D411yescharacteristic
585C22×C11C4×#4111yescharacteristic
586C22×C11#51811yescharacteristic
587C22×C11#52011yescharacteristic
588C22×C11C2×#12011yescharacteristic
589C22×C11C2×#12111yescharacteristic
590C22×C11C2×C22⋊Q811yescharacteristic
591C22×C11C2×C22⋊Q811yescharacteristic
592C22×C11C2×#12311yescharacteristic
593C22×C11#52511yescharacteristic
594C22×C11#52911yescharacteristic
595C22×C11#53211yescharacteristic
596C22×C11#53411yescharacteristic
597C22×C11#53711yescharacteristic
598C22×C11#53811yescharacteristic
599C22×C11#53911yescharacteristic
600C22×C11D4211yescharacteristic
601C22×C11D4211yescharacteristic
602C22×C11#54611yescharacteristic
603C22×C11#54611yescharacteristic
604C22×C11#54611yescharacteristic
605C22×C11#54611yescharacteristic
606C22×C11#54611yescharacteristic
607C22×C11#54711yescharacteristic
608C22×C11#54711yescharacteristic
609C22×C11D4×Q811yescharacteristic
610C22×C11#55111yescharacteristic
611C22×C11#55111yescharacteristic
612C22×C11#55211yescharacteristic
613C22×C11#55411yescharacteristic
614C22×C11#55411yescharacteristic
615C22×C11#55411yescharacteristic
616C2×D11—24no—
617C2×D11—24no—
618C2×D11—24no—
619C2×D11—24no—
620C2×D11—24no—
621C2×D11—24no—
622C2×D11—24no—
623C2×D11—24no—
624C2×D11—24no—
625C2×D11—24no—
626C2×D11—24no—
627C2×D11—24no—
628C2×D11—24no—
629C2×D11—24no—
630C2×D11—24no—
631C2×D11—24no—
632C2×D11—24no—
633C2×D11—42no—
634C2×D11—42no—
635C2×D11—42no—
636C2×D11—42no—
637C2×D11—42no—
638C2×D11—42no—
639C2×D11—42no—
640C2×D11—42no—
641C2×D11—42no—
642C2×D11—42no—
643C2×D11—42no—
644C2×D11—42no—
645C2×D11#38518yescomplemented
646C4×C11—24no—
647C4×C11—24no—
648C4×C11—42no—
649C4×C11—42no—
650C4×C11—42no—
651C4×C11—42no—
652C4×C11—81no—
653Dic11—24no—
654Dic11—42no—
655Dic11—42no—
656Dic11—42no—
657Dic11—42no—
658Dic11—81no—
659C25—111no—
660C25—111no—
661C22×D4—114no—
662C22×D4—114no—
663C22×D4—114no—
664C22×D4—222no—
665C22×D4—222no—
666C22×D4—222no—
667C22×D4—222no—
668C23×C4—111no—
669C23×C4—111no—
670C23×C4—111no—
671C23×C4—111no—
672C23×C4—111no—
673C23×C4—114no—
674C23×C4—114no—
675C23×C4—111no—
676C23×C4—222no—
677C23×C4—222no—
678C23×C4—222no—
679C23×C4—222no—
680C23×C4—222no—
681C23×C4—222no—
682C23×C4—222no—
683C23×C4—222no—
684C23×C4—222no—
685C23×C4—222no—
686C23×C4—222no—
687C23×C4—222no—
688C23×C4—222no—
689C23×C4—222no—
690C23×C4—222no—
691C23×C4—222no—
692C23×C4—222no—
693C23×C4—222no—
694C23×C4—441no—
695C23×C4—441no—
696C23×C4—441no—
697C23×C4—441no—
698C23×C4—441no—
699C23×C4—441no—
700C23×C4—441no—
701C23×C4—441no—
702C23×C4C22×D1111yescharacteristic
703C23×C4C22×D1111yescharacteristic
704C23×C4C22×D1111yescharacteristic
705C23×C4C22×D1111yescharacteristic
706C23×C4C22×D1111yescharacteristic
707C23×C4C22×D1111yescharacteristic
708C23×C4C22×D1111yescharacteristic
709C4×D4—2232no—
710C2×C4⋊C4—22no—
711C2×C4⋊C4—22no—
712C2×C4⋊C4—22no—
713C2×C4⋊C4—22no—
714C2×C4⋊C4—22no—
715C2×C4⋊C4—22no—
716C2×C4⋊C4—41no—
717C2×C4⋊C4—41no—
718C2×C4⋊C4—41no—
719C2×C4⋊C4—222no—
720C2×C4⋊C4—222no—
721C2×C4⋊C4—222no—
722C2×C4⋊C4—222no—
723C2×C4⋊C4—222no—
724C2×C4⋊C4—441no—
725C2×C22⋊C4—114no—
726C2×C22⋊C4—114no—
727C2×C22⋊C4—114no—
728C2×C22⋊C4—114no—
729C2×C22⋊C4—222no—
730C2×C22⋊C4—222no—
731C2×C22⋊C4—222no—
732C2×C22⋊C4—222no—
733C2×C22⋊C4—222no—
734C2×C22⋊C4—222no—
735C2×C22⋊C4—222no—
736C2×C22⋊C4—222no—
737C2×C22⋊C4—222no—
738C2×C22⋊C4—222no—
739C2×C22⋊C4—222no—
740C2×C22⋊C4—222no—
741C2×C22⋊C4—222no—
742C2×C22⋊C4—222no—
743C2×C22⋊C4—222no—
744C2×C22⋊C4—222no—
745C2×C22⋊C4—441no—
746C2×C22⋊C4—441no—
747C2×C22⋊C4—441no—
748C2×C22⋊C4—441no—
749C2×C42—222no—
750C2×C42—222no—
751C2×C42—222no—
752#95—22no—
753#95—22no—
754#95—41no—
755#95—114no—
756#95—114no—
757#95—222no—
758#95—222no—
759#95—222no—
760#95—222no—
761#95—222no—
762#95—222no—
763#95—222no—
764#95—222no—
765#95—222no—
766#95—441no—
767#95C4×D1114yescomplemented
768C2×C11C2×#38511yescharacteristic
769C2×C11C4×#12111yescharacteristic
770C2×C11#232511yescharacteristic
771C2×C11D4×C4⋊C411yescharacteristic
772C2×C11#234911yescharacteristic
773C2×C11#235811yescharacteristic
774C2×C11#235911yescharacteristic
775C2×C11#241011yescharacteristic
776C2×C11#241711yescharacteristic
777C2×C11#241811yescharacteristic
778C2×C11#241911yescharacteristic
779C2×C11#243011yescharacteristic
780C2×C11#244911yescharacteristic
781C2×C11#245011yescharacteristic
782C2×C11#256411yescharacteristic
783D11—28no—
784D11—44no—
785C24—112no—
786C24—112no—
787C24—112no—
788C24—112no—
789C24—112no—
790C24—112no—
791C24—112no—
792C24—112no—
793C24—112no—
794C24—112no—
795C24—221no—
796C24—221no—
797C24—221no—
798C24—221no—
799C24—221no—
800C24—221no—
801C24—221no—
802C24—221no—
803C24—221no—
804C24—221no—
805C24—221no—
806C24—221no—
807C24—221no—
808C24—221no—
809C24—221no—
810C24—221no—
811C24—221no—
812C24—221no—
813C24—221no—
814C24—221no—
815C24C23×D1111yescharacteristic
816C2×D4—1116no—
817C2×D4—228no—
818C2×D4—228no—
819C2×D4—228no—
820C2×D4—228no—
821C2×D4—228no—
822C2×D4—228no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—112no—
863C22×C4—112no—
864C22×C4—112no—
865C22×C4—112no—
866C22×C4—112no—
867C22×C4—112no—
868C22×C4—112no—
869C22×C4—228no—
870C22×C4—228no—
871C22×C4—228no—
872C22×C4—228no—
873C22×C4—228no—
874C22×C4—221no—
875C22×C4—221no—
876C22×C4—221no—
877C22×C4—221no—
878C22×C4—221no—
879C22×C4—221no—
880C22×C4—221no—
881C22×C4—221no—
882C22×C4—221no—
883C22×C4—221no—
884C22×C4—221no—
885C22×C4—221no—
886C22×C4—221no—
887C22×C4—221no—
888C22×C4—221no—
889C22×C4—221no—
890C22×C4—221no—
891C22×C4—221no—
892C22×C4—221no—
893C22×C4—221no—
894C22×C4—221no—
895C22×C4—221no—
896C22×C4—221no—
897C22×C4—221no—
898C22×C4—221no—
899C22×C4—221no—
900C22×C4—221no—
901C22×C4—221no—
902C22×C4—228no—
903C22×C4—221no—
904C22×C4—221no—
905C22×C4—221no—
906C22×C4—221no—
907C22×C4—221no—
908C22×C4—221no—
909C22×C4—221no—
910C22×C4—444no—
911C22×C4—444no—
912C22×C4—444no—
913C22×C4—444no—
914C22×C4—444no—
915C22×C4—444no—
916C22×C4—444no—
917C22×C4—444no—
918C22×C4—444no—
919C22×C4—444no—
920C22×C4—444no—
921C22×C4—444no—
922C22×C4—444no—
923C22×C4—444no—
924C22×C4—444no—
925C22×C4—444no—
926C22×C4—444no—
927C22×C4—444no—
928C22×C4—444no—
929C22×C4—444no—
930C22×C4—444no—
931C22×C4—444no—
932C22×C4C2×C4×D1112yes—
933C22×C4C2×C4×D1112yes—
934C22×C4C2×C4×D1112yes—
935C22×C4D4×D1112yes—
936C22×C4D4×D1112yes—
937C22×C4D4×D1112yes—
938C22×C4D4×D1112yes—
939C22×C4Q8×D1112yes—
940C22×C4#434312yes—
941C22×C4#434312yes—
942C4⋊C4—28no—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C4⋊C4—444no—
946C4⋊C4—444no—
947C22⋊C4—228no—
948C22⋊C4—228no—
949C22⋊C4—228no—
950C22⋊C4—228no—
951C22⋊C4—444no—
952C22⋊C4—444no—
953C22⋊C4—444no—
954C22⋊C4—444no—
955C42—228no—
956C11#1397511yescharacteristic, complemented, Sylow
957C23—114no—
958C23—114no—
959C23—114no—
960C23—114no—
961C23—114no—
962C23—114no—
963C23—114no—
964C23—114no—
965C23—222no—
966C23—222no—
967C23—222no—
968C23—222no—
969C23—222no—
970C23—222no—
971C23—222no—
972C23—222no—
973C23—222no—
974C23—222no—
975C23—222no—
976C23—222no—
977C23—222no—
978C23—222no—
979C23—222no—
980C23—222no—
981C23—222no—
982C23—222no—
983C23—222no—
984C23—222no—
985C23—222no—
986C23—222no—
987C23—222no—
988C23—222no—
989C23—222no—
990C23—222no—
991C23—222no—
992C23—222no—
993C23—222no—
994C23—222no—
995C23—222no—
996C23—222no—
997C23—222no—
998C23—222no—
999C23—222no—
1000C23—222no—
1001C23—222no—
1002C23—222no—
1003C23—222no—
1004C23—222no—
1005C23—222no—
1006C23—222no—
1007C23—222no—
1008C23—222no—
1009C23—222no—
1010C23—222no—
1011C23—441no—
1012C23—441no—
1013C23—441no—
1014C23—441no—
1015C23—441no—
1016C23—441no—
1017C23—441no—
1018C23—441no—
1019C23—441no—
1020C23—441no—
1021C23—441no—
1022C23—441no—
1023C23—441no—
1024C23—441no—
1025C23—441no—
1026C23—441no—
1027C23C22×C4×D1111yescharacteristic
1028C23C2×D4×D1111yescharacteristic
1029C23C2×D4×D1111yescharacteristic
1030C23C2×D4×D1111yescharacteristic
1031C23C2×D4×D1111yescharacteristic
1032C23#6703711yescharacteristic
1033C23#6703711yescharacteristic
1034C23C2×Q8×D1111yescharacteristic
1035C23C2×#434311yescharacteristic
1036C23C2×#434311yescharacteristic
1037C23#6704011yescharacteristic
1038C23#41×D1111yescharacteristic
1039C23#41×D1111yescharacteristic
1040C23#41×D1111yescharacteristic
1041C23#6704211yescharacteristic
1042D4—2232no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—114no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—222no—
1095C2×C4—222no—
1096C2×C4—222no—
1097C2×C4—222no—
1098C2×C4—222no—
1099C2×C4—222no—
1100C2×C4—222no—
1101C2×C4—222no—
1102C2×C4—222no—
1103C2×C4—222no—
1104C2×C4—222no—
1105C2×C4—222no—
1106C2×C4—222no—
1107C2×C4—222no—
1108C2×C4—222no—
1109C2×C4—4416no—
1110C2×C4—4416no—
1111C2×C4—4416no—
1112C2×C4—4416no—
1113C2×C4—441no—
1114C2×C4—441no—
1115C2×C4—441no—
1116C2×C4—441no—
1117C2×C4—441no—
1118C2×C4—441no—
1119C2×C4—441no—
1120C2×C4—441no—
1121C2×C4—441no—
1122C2×C4—441no—
1123C2×C4—441no—
1124C2×C4—441no—
1125C2×C4—441no—
1126C2×C4—441no—
1127C2×C4—441no—
1128C2×C4—441no—
1129C2×C4—441no—
1130C2×C4—441no—
1131C2×C4—441no—
1132C2×C4—441no—
1133C2×C4—441no—
1134C2×C4—441no—
1135C2×C4—441no—
1136C2×C4C4⋊C4×D1114yes—
1137C2×C4#6694614yescomplemented
1138C22—118no—
1139C22—224no—
1140C22—224no—
1141C22—224no—
1142C22—224no—
1143C22—224no—
1144C22—224no—
1145C22—224no—
1146C22—224no—
1147C22—224no—
1148C22—224no—
1149C22—224no—
1150C22—224no—
1151C22—224no—
1152C22—224no—
1153C22—224no—
1154C22—224no—
1155C22—224no—
1156C22—442no—
1157C22—442no—
1158C22—442no—
1159C22—442no—
1160C22—442no—
1161C22—442no—
1162C22—442no—
1163C22—442no—
1164C22—442no—
1165C22—442no—
1166C22—442no—
1167C22—442no—
1168C22C2×C4⋊C4×D1111yescharacteristic
1169C22C2×#6694611yescharacteristic
1170C22#1062303511yescharacteristic
1171C22C4×D4×D1111yescharacteristic
1172C22C4×D4×D1111yescharacteristic
1173C22#1062307611yescharacteristic
1174C22C4×#434311yescharacteristic
1175C22D11×#12011yescharacteristic
1176C22#1062312011yescharacteristic
1177C22#1062312111yescharacteristic
1178C22D11×#12111yescharacteristic
1179C22#1062314111yescharacteristic
1180C22#1062314311yescharacteristic
1181C22D11×C22⋊Q811yescharacteristic
1182C22D11×C22⋊Q811yescharacteristic
1183C22#1062315811yescharacteristic
1184C22#1062316011yescharacteristic
1185C22#1062316111yescharacteristic
1186C22#1062316111yescharacteristic
1187C22#1062316811yescharacteristic
1188C22#1062316811yescharacteristic
1189C22#1062316911yescharacteristic
1190C22D11×#12311yescharacteristic
1191C22#1062318511yescharacteristic
1192C22#1062318811yescharacteristic
1193C22#1062322111yescharacteristic
1194C22#1062322211yescharacteristic
1195C22#1062322411yescharacteristic
1196C22#1062324811yescharacteristic
1197C22#1062325611yescharacteristic
1198C22#1062325711yescharacteristic
1199C22#1062325711yescharacteristic
1200C22#1062325811yescharacteristic
1201C22#1062326111yescharacteristic
1202C22#1062326111yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—81no—
1210C4—224no—
1211C4—442no—
1212C4—442no—
1213C4—442no—
1214C4—442no—
1215C4—881no—
1216C2—228no—
1217C2—444no—
1218C2D11×#38511yescharacteristic
1219C2#1307112411yescharacteristic
1220C2#1307131311yescharacteristic
1221C2#1307151611yescharacteristic
1222C2#1307152511yescharacteristic
1223C2#1307159211yescharacteristic
1224C2#1307160311yescharacteristic
1225C2#1307198311yescharacteristic
1226C2#1307206211yescharacteristic
1227C2#1307208111yescharacteristic
1228C2#1307209411yescharacteristic
1229C2#1307222711yescharacteristic
1230C2#1307241811yescharacteristic
1231C2#1307244111yescharacteristic
1232C2#1307379711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1444C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1444D11
hypocenterC11#13975
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
4. C2×#10622602C2semidirect
5. C2×#10622602C2semidirect
6. C2×#10622600C2semidirect
7. C2×D11×#95C2semidirect
8. #13066875C2semidirect
9. #13066862C2semidirect
10. #13066858C2semidirect
11. #13066850C2semidirect
12. #13066847C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1444C2semidirect
58. #10622278C4semidirect
108. C22×C4×D11C2×C4semidirect
139. C2×(C2×D11)⋊C4C2×C4semidirect
140. C2×(C2×D11)⋊C4C2×C4semidirect
141. C2×(C2×D11)⋊C4C2×C4semidirect
156. C11×#95C2×C4semidirect
167. C11⋊#95C2×C4semidirect
168. C11⋊#95D4semidirect
298. C2×D44C4⋊C4semidirect
348. #1444D11semidirect
489. C2×C4×C11C4×D4semidirect
645. C2×D11#385semidirect
767. #95C4×D11semidirect
956. C11#13975semidirect
1137. C2×C4#66946semidirect

Maximal subgroups

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

subgroupindex
C22×#669462
C2×#106222782
C2×#106226022
C2×#106226002
C2×D11×#952
#130668752
#130668622
#130668582
#130668502
#130668472
(C2×D11)⋊#952
C11×#14442
#1397511