Finite Group Databasebeta

← #14675958

Subgroups — #14675958

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×D4×Dic11C211yesmaximal, characteristic
2C2×#10622833C211yesmaximal, characteristic
3C2×#10622823C211yesmaximal, characteristic, complemented
4C2×#10622559C211yesmaximal, characteristic, complemented
5C2×#10622555C211yesmaximal, characteristic, complemented
6C22×C11⋊#95C211yesmaximal, characteristic, complemented
7#13066868C211yesmaximal, characteristic, complemented
8#13066868C211yesmaximal, characteristic, complemented
9#13066859C211yesmaximal, characteristic, complemented
10#13066859C211yesmaximal, characteristic, complemented
11Dic11⋊#95C211yesmaximal, characteristic, complemented
12#13066842C211yesmaximal, characteristic, complemented
13#13066838C211yesmaximal, characteristic, complemented
14#13066838C211yesmaximal, characteristic, complemented
15C2×C11×#386C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
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×D4×Dic11—24no—
30C2×D4×Dic11—24no—
31C2×D4×Dic11C418yescomplemented
32C22×C4⋊Dic11C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C11×#386—24no—
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41#10622833—24no—
42#10622823—24no—
43C2×C11⋊#95—24no—
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
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58#10622559—24no—
59#10622555—24no—
60C25×C11C2311yescharacteristic
61C25×C11C2311yescharacteristic
62C22×D4×C11—22no—
63C22×D4×C11—22no—
64C22×D4×C11—22no—
65C22×D4×C11—22no—
66C22×D4×C11C2×C414yes—
67C22×D4×C11D414yes—
68C22×D4×C11Q814yes—
69C23×C4×C11—22no—
70C23×C4×C11—22no—
71C23×C4×C11—22no—
72C23×C4×C11—22no—
73C23×C4×C11—22no—
74C23×C4×C11—41no—
75C23×C4×C11—41no—
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×Dic11—22no—
82C23×Dic11—22no—
83C23×Dic11—22no—
84C23×Dic11—22no—
85C23×Dic11—22no—
86C23×Dic11—22no—
87C23×Dic11—22no—
88C23×Dic11—22no—
89C23×Dic11—22no—
90C23×Dic11—22no—
91C23×Dic11—22no—
92C23×Dic11—22no—
93C23×Dic11—22no—
94C23×Dic11—41no—
95C23×Dic11—41no—
96C23×Dic11—41no—
97C23×Dic11—41no—
98C23×Dic11—41no—
99C23×Dic11—41no—
100C23×Dic11C2×C414yes—
101C23×Dic11C2×C414yescomplemented
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C2×C11×C22⋊C4—22no—
111C2×C11×C22⋊C4—22no—
112C2×C11×C22⋊C4—22no—
113C2×C11×C22⋊C4—22no—
114C2×C11×C22⋊C4—22no—
115C2×C11×C22⋊C4—22no—
116C2×C11×C22⋊C4—22no—
117C2×C11×C22⋊C4—41no—
118C2×C11×C22⋊C4—41no—
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⋊Dic11C2×C414yescomplemented
132C2×C22⋊Dic11D414yes—
133C2×C22⋊Dic11D414yes—
134D4×Dic11—232no—
135C2×C4⋊Dic11—22no—
136C2×C4⋊Dic11—22no—
137C2×C4⋊Dic11C2×C414yescomplemented
138C2×Dic11⋊C4—22no—
139C2×Dic11⋊C4—22no—
140C2×Dic11⋊C4—22no—
141C2×Dic11⋊C4—22no—
142C2×Dic11⋊C4—22no—
143C2×Dic11⋊C4—22no—
144C2×Dic11⋊C4—22no—
145C2×Dic11⋊C4—22no—
146C2×Dic11⋊C4—41no—
147C2×Dic11⋊C4—41no—
148C2×Dic11⋊C4—41no—
149C2×Dic11⋊C4—41no—
150C2×C4×Dic11—22no—
151C2×C4×Dic11—22no—
152C2×C4×Dic11C2×C414yescomplemented
153C11×#95—22no—
154C11×#95—22no—
155C11⋊#95—22no—
156C11⋊#95—22no—
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⋊#95—41no—
168C11⋊#95D414yescomplemented
169#13899—111nomaximal, Sylow
170C24×C11—21no—
171C24×C11—21no—
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×C11—21no—
185C24×C11—21no—
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—21no—
189C24×C11—21no—
190C24×C11C22×C412yes—
191C24×C11C22×C412yes—
192C24×C11C2×D412yes—
193C24×C11C2×D412yes—
194C24×C11C2×D412yes—
195C24×C11C2×D412yes—
196C24×C11C2×Q812yes—
197C24×C11C2×Q812yes—
198C24×C11#4112yes—
199C24×C11#4112yes—
200C24×C11C2411yescharacteristic
201C2×D4×C11—28no—
202C2×D4×C11—28no—
203C2×D4×C11—28no—
204C2×D4×C11—28no—
205C2×D4×C11—28no—
206C2×D4×C11—28no—
207C2×D4×C11C4⋊C4116yescomplemented
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—28no—
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—44no—
240C22×C4×C11—44no—
241C22×C4×C11—44no—
242C22×C4×C11—44no—
243C22×C4×C11—44no—
244C22×C4×C11—44no—
245C22×C4×C11C22×C412yes—
246C22×C4×C11C2×D412yes—
247C22×C4×C11C2×D412yes—
248C22×C4×C11C2×Q812yes—
249C22×C4×C11#4112yes—
250C22×Dic11—28no—
251C22×Dic11—28no—
252C22×Dic11—28no—
253C22×Dic11—28no—
254C22×Dic11—28no—
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×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—44no—
300C22×Dic11—44no—
301C22×Dic11—44no—
302C22×Dic11—44no—
303C22×Dic11—44no—
304C22×Dic11—44no—
305C22×Dic11—44no—
306C22×Dic11—44no—
307C22×Dic11—44no—
308C22×Dic11—44no—
309C22×Dic11—44no—
310C22×Dic11—44no—
311C22×Dic11—44no—
312C22×Dic11—44no—
313C22×Dic11—44no—
314C22×Dic11—44no—
315C22×Dic11C22×C412yes—
316C22×Dic11C22×C412yes—
317C22×Dic11C22×C412yes—
318C22×Dic11C22×C412yes—
319C22×Dic11C2×D412yes—
320C22×Dic11C2×D412yes—
321C22×Dic11C2×D412yes—
322C22×Dic11C2×D412yes—
323C22×Dic11C2×D412yes—
324C22×Dic11C2×D412yes—
325C22×Dic11#4112yes—
326C22×Dic11#4112yes—
327C11×C22⋊C4—44no—
328C11×C22⋊C4—44no—
329C11×C22⋊C4—44no—
330C22⋊Dic11—28no—
331C22⋊Dic11—44no—
332C22⋊Dic11—44no—
333C22⋊Dic11—44no—
334C22⋊Dic11C22⋊C4116yescomplemented
335C4⋊Dic11—28no—
336Dic11⋊C4—44no—
337Dic11⋊C4—44no—
338Dic11⋊C4—44no—
339Dic11⋊C4—44no—
340C4×Dic11—28no—
341C22×C4×D4—111no—
342C2×#386—111no—
343C2×#386D1111yescharacteristic
344C2×#385—111no—
345C2×#385—111no—
346C2×#380—111no—
347C22×#95—111no—
348#1441—111no—
349#1441—111no—
350#1439—111no—
351#1439—111no—
352C4⋊#95—111no—
353#1434—111no—
354C22⋊#95—111no—
355C22⋊#95—111no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—22no—
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—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—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×C11—41no—
416C23×C11—41no—
417C23×C11—41no—
418C23×C11C2×C22⋊C414yes—
419C23×C11C2×C4⋊C414yes—
420C23×C11C2×C4⋊C414yes—
421C23×C11#11714yes—
422C23×C11#12114yes—
423C23×C11#12114yes—
424C23×C11C22⋊Q814yes—
425C23×C11C22⋊Q814yes—
426C23×C11C23×C411yescharacteristic
427C23×C11C22×D411yescharacteristic
428C23×C11C22×D411yescharacteristic
429C23×C11C22×D411yescharacteristic
430C23×C11C22×D411yescharacteristic
431C23×C11C22×Q811yescharacteristic
432C23×C11C2×#4111yescharacteristic
433C23×C11C2×#4111yescharacteristic
434C23×C11C2×#4111yescharacteristic
435C23×C11C2×#4111yescharacteristic
436C23×C11C2×#4111yescharacteristic
437C23×C11H(5,𝔽2)11yescharacteristic
438C23×C11H(5,𝔽2)11yescharacteristic
439C23×C11H(5,𝔽2)11yescharacteristic
440C23×C112−1+411yescharacteristic
441D4×C11—232no—
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—416no—
455C2×C4×C11—41no—
456C2×C4×C11—41no—
457C2×C4×C11—41no—
458C2×C4×C11—41no—
459C2×C4×C11—41no—
460C2×C4×C11—41no—
461C2×C4×C11—41no—
462C2×C4×C11—41no—
463C2×C4×C11—41no—
464C2×C4×C11—41no—
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×C11C2×C4⋊C414yes—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—22no—
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—416no—
506C2×Dic11—416no—
507C2×Dic11—416no—
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—41no—
532C2×Dic11—41no—
533C2×Dic11—41no—
534C2×Dic11C2×C22⋊C414yes—
535C2×Dic11C2×C22⋊C414yes—
536C2×Dic11C4×D414yes—
537C23×D4C2×D1111yescharacteristic
538C24×C4—111no—
539C24×C4—111no—
540C24×C4—111no—
541C24×C4C2×D1111yescharacteristic
542C2×C4×D4—118no—
543C2×C4×D4—224no—
544C2×C4×D4—224no—
545C22×C4⋊C4—111no—
546C22×C4⋊C4—111no—
547C22×C4⋊C4—111no—
548C22×C4⋊C4—111no—
549C22×C4⋊C4—111no—
550C22×C22⋊C4—111no—
551C22×C22⋊C4—111no—
552C22×C22⋊C4—111no—
553C22×C22⋊C4—111no—
554C22×C22⋊C4—111no—
555C22×C22⋊C4C2×D1111yescharacteristic
556C22×C22⋊C4C2×D1111yescharacteristic
557C22×C22⋊C4C2×D1111yescharacteristic
558C22×C42—111no—
559#386—24no—
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—111no—
577C2×#95—111no—
578C2×#95—224no—
579C2×#95C2×D1111yescharacteristic
580C2×#95C2×D1111yescharacteristic
581C22×C11—24no—
582C22×C11—24no—
583C22×C11—24no—
584C22×C11—24no—
585C22×C11—24no—
586C22×C11—24no—
587C22×C11—24no—
588C22×C11—24no—
589C22×C11—24no—
590C22×C11—24no—
591C22×C11—24no—
592C22×C11—24no—
593C22×C11—24no—
594C22×C11—24no—
595C22×C11—24no—
596C22×C11—24no—
597C22×C11—24no—
598C22×C11—42no—
599C22×C11—42no—
600C22×C11—42no—
601C22×C11—42no—
602C22×C11—42no—
603C22×C11—42no—
604C22×C11—42no—
605C22×C11—42no—
606C22×C11—42no—
607C22×C11—42no—
608C22×C11—42no—
609C22×C11—42no—
610C22×C11#38018yescomplemented
611C22×C11C22×C22⋊C411yescharacteristic
612C22×C11C22×C4⋊C411yescharacteristic
613C22×C11C2×#11711yescharacteristic
614C22×C11C2×C4×D411yescharacteristic
615C22×C11C4×#4111yescharacteristic
616C22×C11#51811yescharacteristic
617C22×C11#52011yescharacteristic
618C22×C11C2×#12111yescharacteristic
619C22×C11C2×#12111yescharacteristic
620C22×C11C2×C22⋊Q811yescharacteristic
621C22×C11C2×C22⋊Q811yescharacteristic
622C22×C11#52511yescharacteristic
623C22×C11#52511yescharacteristic
624C22×C11#52911yescharacteristic
625C22×C11#52911yescharacteristic
626C22×C11#53811yescharacteristic
627C22×C11#53811yescharacteristic
628C22×C11#53911yescharacteristic
629C22×C11#53911yescharacteristic
630C22×C11D4211yescharacteristic
631C22×C11D4211yescharacteristic
632C22×C11D4211yescharacteristic
633C22×C11#54611yescharacteristic
634C22×C11#54611yescharacteristic
635C22×C11#54611yescharacteristic
636C22×C11#54611yescharacteristic
637C22×C11#54611yescharacteristic
638C22×C11#54611yescharacteristic
639C22×C11#54711yescharacteristic
640C22×C11#54711yescharacteristic
641C22×C11#54711yescharacteristic
642C22×C11D4×Q811yescharacteristic
643C22×C11#55411yescharacteristic
644C22×C11#55411yescharacteristic
645C22×C11#55411yescharacteristic
646C4×C11—24no—
647C4×C11—42no—
648C4×C11—42no—
649C4×C11—81no—
650C4×C11—81no—
651Dic11—24no—
652Dic11—24no—
653Dic11—24no—
654Dic11—42no—
655Dic11—42no—
656Dic11—42no—
657Dic11—81no—
658Dic11—81no—
659C25C22×D1111yescharacteristic
660C25C22×D1111yescharacteristic
661C22×D4—22no—
662C22×D4—22no—
663C22×D4—22no—
664C22×D4—22no—
665C22×D4Dic2214yes—
666C22×D4C4×D1114yes—
667C22×D4C22⋊D1114yes—
668C23×C4—22no—
669C23×C4—22no—
670C23×C4—22no—
671C23×C4—22no—
672C23×C4—22no—
673C23×C4—41no—
674C23×C4—41no—
675C23×C4—111no—
676C23×C4—111no—
677C23×C4—111no—
678C23×C4—111no—
679C23×C4—111no—
680C23×C4—111no—
681C23×C4—114no—
682C23×C4—114no—
683C23×C4—111no—
684C23×C4—111no—
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—222no—
695C23×C4—222no—
696C23×C4—222no—
697C23×C4—222no—
698C23×C4—441no—
699C23×C4—441no—
700C23×C4—441no—
701C23×C4—441no—
702C23×C4—441no—
703C23×C4—441no—
704C23×C4C22×D1111yescharacteristic
705C23×C4C22×D1111yescharacteristic
706C23×C4C22×D1111yescharacteristic
707C23×C4C22×D1111yescharacteristic
708C23×C4C22×D1111yescharacteristic
709C4×D4—2232no—
710C2×C4⋊C4—114no—
711C2×C4⋊C4—222no—
712C2×C4⋊C4—222no—
713C2×C4⋊C4—222no—
714C2×C4⋊C4—222no—
715C2×C4⋊C4—222no—
716C2×C4⋊C4—222no—
717C2×C4⋊C4—222no—
718C2×C4⋊C4—222no—
719C2×C4⋊C4—222no—
720C2×C4⋊C4—222no—
721C2×C4⋊C4—441no—
722C2×C4⋊C4—441no—
723C2×C4⋊C4—441no—
724C2×C4⋊C4—441no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—22no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—41no—
733C2×C22⋊C4—41no—
734C2×C22⋊C4—114no—
735C2×C22⋊C4—114no—
736C2×C22⋊C4—114no—
737C2×C22⋊C4—114no—
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—222no—
746C2×C22⋊C4—222no—
747C2×C22⋊C4—441no—
748C2×C22⋊C4—441no—
749C2×C42—114no—
750C2×C42—222no—
751C2×C42—222no—
752#95—22no—
753#95—22no—
754#95—114no—
755#95—222no—
756#95—222no—
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#95—441no—
768C2×C11—28no—
769C2×C11—44no—
770C2×C11C2×#38011yescharacteristic
771C2×C11#229011yescharacteristic
772C2×C11#231811yescharacteristic
773C2×C11D4×C22⋊C411yescharacteristic
774C2×C11#233911yescharacteristic
775C2×C11D4×C4⋊C411yescharacteristic
776C2×C11#234911yescharacteristic
777C2×C11#242411yescharacteristic
778C2×C11#242411yescharacteristic
779C2×C11#242511yescharacteristic
780C2×C11#242511yescharacteristic
781C2×C11#244911yescharacteristic
782C2×C11#244911yescharacteristic
783C2×C11#245011yescharacteristic
784C2×C11#245011yescharacteristic
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—21no—
799C24—21no—
800C24—21no—
801C24—21no—
802C24—21no—
803C24—21no—
804C24—21no—
805C24C2×Dic2212yes—
806C24C2×Dic2212yes—
807C24C2×C4×D1112yes—
808C24C2×C4×D1112yes—
809C24D4×D1112yes—
810C24D4×D1112yes—
811C24#434112yes—
812C24#434112yes—
813C24C2×C22⋊D1112yes—
814C24C2×C22⋊D1112yes—
815C24C23×D1111yescharacteristic
816C2×D4—28no—
817C2×D4—28no—
818C2×D4—28no—
819C2×D4—28no—
820C2×D4—28no—
821C2×D4—28no—
822C2×D4Dic11⋊C4116yescomplemented
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—28no—
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—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—112no—
861C22×C4—112no—
862C22×C4—112no—
863C22×C4—112no—
864C22×C4—112no—
865C22×C4—112no—
866C22×C4—112no—
867C22×C4—112no—
868C22×C4—112no—
869C22×C4—112no—
870C22×C4—112no—
871C22×C4—112no—
872C22×C4—228no—
873C22×C4—228no—
874C22×C4—228no—
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—228no—
888C22×C4—228no—
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—221no—
903C22×C4—221no—
904C22×C4—221no—
905C22×C4—221no—
906C22×C4—221no—
907C22×C4—221no—
908C22×C4—221no—
909C22×C4—221no—
910C22×C4—221no—
911C22×C4—221no—
912C22×C4—221no—
913C22×C4—221no—
914C22×C4—221no—
915C22×C4—221no—
916C22×C4—221no—
917C22×C4—221no—
918C22×C4—221no—
919C22×C4—221no—
920C22×C4—221no—
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×C4—444no—
933C22×C4—444no—
934C22×C4—444no—
935C22×C4—444no—
936C22×C4—444no—
937C22×C4C2×Dic2212yes—
938C22×C4C2×C4×D1112yes—
939C22×C4D4×D1112yes—
940C22×C4#434112yes—
941C22×C4C2×C22⋊D1112yes—
942C4⋊C4—228no—
943C4⋊C4—444no—
944C4⋊C4—444no—
945C4⋊C4—444no—
946C4⋊C4—444no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—1116no—
951C22⋊C4—228no—
952C22⋊C4—444no—
953C22⋊C4—444no—
954C22⋊C4—444no—
955C42—228no—
956C11#1389911yescharacteristic, complemented, Sylow
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23#6693014yes—
1020C23#6693114yes—
1021C23#6693114yes—
1022C23C22⋊C4×D1114yes—
1023C23C2×Dic11⋊C414yes—
1024C23C2×Dic11⋊C414yes—
1025C23#6699214yes—
1026C23#6699214yes—
1027C23C22×Dic2211yescharacteristic
1028C23C22×C4×D1111yescharacteristic
1029C23C2×D4×D1111yescharacteristic
1030C23C2×D4×D1111yescharacteristic
1031C23C2×D4×D1111yescharacteristic
1032C23C2×#434111yescharacteristic
1033C23C2×#434111yescharacteristic
1034C23C2×#434111yescharacteristic
1035C23#6703711yescharacteristic
1036C23#6703711yescharacteristic
1037C23#41×D1111yescharacteristic
1038C23#41×D1111yescharacteristic
1039C23#6704211yescharacteristic
1040C23#6704311yescharacteristic
1041C23C22×C22⋊D1111yescharacteristic
1042D4—232no—
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—416no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
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—114no—
1079C2×C4—114no—
1080C2×C4—114no—
1081C2×C4—222no—
1082C2×C4—222no—
1083C2×C4—222no—
1084C2×C4—222no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—222no—
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—4416no—
1109C2×C4—4416no—
1110C2×C4—4416no—
1111C2×C4—441no—
1112C2×C4—441no—
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×C4—441no—
1137C2×C4C2×Dic11⋊C414yes—
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—24no—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—24no—
1151C22—24no—
1152C22—24no—
1153C22—24no—
1154C22—24no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22#1062255518yescomplemented
1168C22C2×#6693011yescharacteristic
1169C22C2×#6693111yescharacteristic
1170C22C2×#6693111yescharacteristic
1171C22C2×C22⋊C4×D1111yescharacteristic
1172C22C4×#434111yescharacteristic
1173C22D4×Dic2211yescharacteristic
1174C22#1062307011yescharacteristic
1175C22#1062307011yescharacteristic
1176C22#1062307411yescharacteristic
1177C22C4×D4×D1111yescharacteristic
1178C22#1062307611yescharacteristic
1179C22#1062307711yescharacteristic
1180C22#1062311711yescharacteristic
1181C22#1062312111yescharacteristic
1182C22#1062312211yescharacteristic
1183C22#1062312411yescharacteristic
1184C22#1062313111yescharacteristic
1185C22#1062313311yescharacteristic
1186C22#1062313711yescharacteristic
1187C22#1062314011yescharacteristic
1188C22#1062314111yescharacteristic
1189C22#1062314111yescharacteristic
1190C22#1062314211yescharacteristic
1191C22#1062314811yescharacteristic
1192C22#1062318011yescharacteristic
1193C22#1062318511yescharacteristic
1194C22#1062318611yescharacteristic
1195C22#1062319611yescharacteristic
1196C22C22×Dic11⋊C411yescharacteristic
1197C22D4×C22⋊D1111yescharacteristic
1198C22C2×#6699211yescharacteristic
1199C22C2×#6699211yescharacteristic
1200C22#1062333711yescharacteristic
1201C22#1062335511yescharacteristic
1202C22#1062336011yescharacteristic
1203C4—24no—
1204C4—42no—
1205C4—42no—
1206C4—81no—
1207C4—81no—
1208C4—224no—
1209C4—224no—
1210C4—224no—
1211C4—442no—
1212C4—442no—
1213C4—442no—
1214C4—881no—
1215C4—881no—
1216C2—28no—
1217C2—44no—
1218C2C2×#1062255511yescharacteristic
1219C2#1307105611yescharacteristic
1220C2#1307124211yescharacteristic
1221C2#1307143411yescharacteristic
1222C2#1307144211yescharacteristic
1223C2D4×Dic11⋊C411yescharacteristic
1224C2#1307152111yescharacteristic
1225C2#1307215611yescharacteristic
1226C2#1307215811yescharacteristic
1227C2#1307217111yescharacteristic
1228C2#1307217311yescharacteristic
1229C2#1307242911yescharacteristic
1230C2#1307243111yescharacteristic
1231C2#1307244411yescharacteristic
1232C2#1307244611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#386C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#386D11
hypocenterC11#13899
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×#10622823C2semidirect
4. C2×#10622559C2semidirect
5. C2×#10622555C2semidirect
6. C22×C11⋊#95C2semidirect
7. #13066868C2semidirect
8. #13066868C2semidirect
9. #13066859C2semidirect
10. #13066859C2semidirect
11. Dic11⋊#95C2semidirect
12. #13066842C2semidirect
13. #13066838C2semidirect
14. #13066838C2semidirect
31. C2×D4×Dic11C4semidirect
101. C23×Dic11C2×C4semidirect
131. C2×C22⋊Dic11C2×C4semidirect
137. C2×C4⋊Dic11C2×C4semidirect
152. C2×C4×Dic11C2×C4semidirect
168. C11⋊#95D4semidirect
207. C2×D4×C11C4⋊C4semidirect
334. C22⋊Dic11C22⋊C4semidirect
610. C22×C11#380semidirect
822. C2×D4Dic11⋊C4semidirect
956. C11#13899semidirect
1167. C22#10622555semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
C2×#106228332
C2×#106228232
C2×#106225592
C2×#106225552
C22×C11⋊#952
#130668682
#130668592
Dic11⋊#952
#130668422
#130668382
C2×C11×#3862
#1389911