Finite Group Databasebeta

← #14677139

Subgroups — #14677139

Order 2816.

2950 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D44C211yesmaximal, characteristic
2C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
3C2×#10622278C211yesmaximal, characteristic
4C2×#10622278C211yesmaximal, characteristic
5C2×#10622281C211yesmaximal, characteristic, complemented
6C2×#10622281C211yesmaximal, characteristic, complemented
7C2×#10622602C211yesmaximal, characteristic, complemented
8#13066881C211yesmaximal, characteristic, complemented
9#13066880C211yesmaximal, characteristic, complemented
10#13066862C211yesmaximal, characteristic, complemented
11#13066860C211yesmaximal, characteristic, complemented
12#13066849C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1436C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic
23C22×(C2×D11)⋊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×C4⋊Dic11C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C22×C4⋊Dic11C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C2×C4⋊C4×D11—24no—
38C2×C4⋊C4×D11—24no—
39C2×C4⋊C4×D11—24no—
40C2×C4×D44—24no—
41C2×C4×D44—24no—
42C2×C4×D44—24no—
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
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622602—24no—
58#10622281—24no—
59#10622281—24no—
60#10622278—24no—
61#10622278C418yescomplemented
62C24×D11C2311yescharacteristic
63C24×D11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C22×D44—22no—
78C22×D44—22no—
79C22×D44—22no—
80C22×D44—22no—
81C22×D44C2×C414yes—
82C22×D44D414yes—
83C22×D44Q814yes—
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—22no—
101C22×C4×D11—22no—
102C22×C4×D11—22no—
103C22×C4×D11—22no—
104C22×C4×D11—41no—
105C22×C4×D11—41no—
106C22×C4×D11—41no—
107C22×C4×D11—41no—
108C22×C4×D11—41no—
109C22×C4×D11—41no—
110C22×C4×D11C2×C414yescomplemented
111C22×C4×D11D414yes—
112C2×C11×C4⋊C4—22no—
113C2×C11×C4⋊C4—22no—
114C2×C11×C4⋊C4D414yescomplemented
115C2×C42×C11—22no—
116C2×C42×C11—22no—
117C2×C42×C11—22no—
118C2×(C2×D11)⋊C4—22no—
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—22no—
136C2×(C2×D11)⋊C4—41no—
137C2×(C2×D11)⋊C4—41no—
138C2×(C2×D11)⋊C4C2×C414yescomplemented
139C2×(C2×D11)⋊C4C2×C414yescomplemented
140C2×(C2×D11)⋊C4C2×C414yescomplemented
141C2×(C2×D11)⋊C4D414yes—
142C2×C4⋊Dic11—22no—
143C2×C4⋊Dic11—22no—
144C2×C4⋊Dic11—22no—
145C2×C4⋊Dic11—22no—
146C2×C4⋊Dic11—22no—
147C2×C4⋊Dic11—22no—
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⋊C4D414yescomplemented
160C4⋊C4×D11—232no—
161C4×D44—232no—
162C11×#95—22no—
163C11×#95—22no—
164C11×#95—22no—
165C11×#95—22no—
166C11×#95C2×C414yescomplemented
167C11⋊#95—22no—
168C11⋊#95—22no—
169C11⋊#95—22no—
170C11⋊#95—22no—
171C11⋊#95—22no—
172C11⋊#95—22no—
173C11⋊#95—41no—
174C11⋊#95—41no—
175C11⋊#95C2×C414yescomplemented
176#14015—111nomaximal, Sylow
177C24×C11C2411yescharacteristic
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×D11—21no—
192C23×D11—21no—
193C23×D11—21no—
194C23×D11—21no—
195C23×D11—21no—
196C23×D11—21no—
197C23×D11—21no—
198C23×D11C22×C412yes—
199C23×D11C22×C412yes—
200C23×D11C2×D412yes—
201C23×D11C2×D412yes—
202C23×D11C2×D412yes—
203C23×D11C2×D412yes—
204C23×D11C2×Q812yes—
205C23×D11C2×Q812yes—
206C23×D11#4112yes—
207C23×D11#4112yes—
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×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11C22×C412yes—
246C22×C4×C11C22×C412yes—
247C22×C4×C11C22×C412yes—
248C22×C4×C11C2×D412yes—
249C22×C4×C11C2×D412yes—
250C22×C4×C11C2×D412yes—
251C22×C4×C11C2×D412yes—
252C22×C4×C11C2×D412yes—
253C22×C4×C11C2×D412yes—
254C22×C4×C11C2×D412yes—
255C22×C4×C11C2×Q812yes—
256C22×C4×C11#4112yes—
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×Dic11C22×C412yes—
293C22×Dic11C22×C412yes—
294C22×Dic11C2×D412yes—
295C22×Dic11C2×D412yes—
296C22×Dic11C2×D412yes—
297C22×Dic11C2×D412yes—
298C22×Dic11#4112yes—
299C2×D44—28no—
300C2×D44—28no—
301C2×D44—28no—
302C2×D44—28no—
303C2×D44—28no—
304C2×D44—28no—
305C2×D44C4⋊C4116yescomplemented
306C2×C4×D11—28no—
307C2×C4×D11—28no—
308C2×C4×D11—28no—
309C2×C4×D11—28no—
310C2×C4×D11—28no—
311C2×C4×D11—28no—
312C2×C4×D11—28no—
313C2×C4×D11—28no—
314C2×C4×D11—28no—
315C2×C4×D11—28no—
316C2×C4×D11—28no—
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—
327C2×C4×D11—44no—
328C2×C4×D11—44no—
329C2×C4×D11—44no—
330C2×C4×D11—44no—
331C2×C4×D11—44no—
332C2×C4×D11—44no—
333C2×C4×D11—44no—
334C11×C4⋊C4—28no—
335C42×C11—28no—
336(C2×D11)⋊C4—28no—
337(C2×D11)⋊C4—28no—
338(C2×D11)⋊C4—28no—
339(C2×D11)⋊C4—28no—
340(C2×D11)⋊C4—28no—
341(C2×D11)⋊C4—44no—
342(C2×D11)⋊C4—44no—
343(C2×D11)⋊C4—44no—
344C4⋊Dic11—28no—
345C4⋊Dic11—28no—
346C4⋊Dic11—44no—
347Dic11⋊C4—28no—
348Dic11⋊C4—28no—
349Dic11⋊C4—44no—
350C22×C4×D4—111no—
351C23×C4⋊C4—111no—
352C2×#386—111no—
353C2×#386—111no—
354C2×#385—111no—
355C2×#385—111no—
356C2×#385—111no—
357#1444—111no—
358#1444—111no—
359#1439—111no—
360#1439—111no—
361#1436—111no—
362#1436D1111yescharacteristic, complemented
363C22⋊#95—111no—
364C22⋊#95—111no—
365C23×C11C23×C411yescharacteristic
366C23×C11C22×D411yescharacteristic
367C23×C11C22×D411yescharacteristic
368C23×C11C22×D411yescharacteristic
369C23×C11C22×D411yescharacteristic
370C23×C11C22×D411yescharacteristic
371C23×C11C22×Q811yescharacteristic
372C23×C11C2×#4111yescharacteristic
373C23×C11C2×#4111yescharacteristic
374C23×C11C2×#4111yescharacteristic
375C23×C11C2×#4111yescharacteristic
376C23×C11H(5,𝔽2)11yescharacteristic
377C23×C11H(5,𝔽2)11yescharacteristic
378C23×C112−1+411yescharacteristic
379C23×C112−1+411yescharacteristic
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—22no—
418C22×D11—22no—
419C22×D11—22no—
420C22×D11—22no—
421C22×D11—22no—
422C22×D11—22no—
423C22×D11—22no—
424C22×D11—22no—
425C22×D11—22no—
426C22×D11—41no—
427C22×D11—41no—
428C22×D11—41no—
429C22×D11—41no—
430C22×D11—41no—
431C22×D11—41no—
432C22×D11—41no—
433C22×D11—41no—
434C22×D11—41no—
435C22×D11—41no—
436C22×D11—41no—
437C22×D11—41no—
438C22×D11—41no—
439C22×D11—41no—
440C22×D11—41no—
441C22×D11—41no—
442C22×D11C2×C4⋊C414yes—
443C22×D11C2×C4⋊C414yescomplemented
444C22×D11C4×D414yes—
445C22×D11C4×D414yes—
446C22×D11#12014yes—
447C22×D11C22⋊Q814yes—
448C22×D11C22⋊Q814yes—
449C22×D11#12314yes—
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—22no—
466C2×C4×C11—22no—
467C2×C4×C11—22no—
468C2×C4×C11—22no—
469C2×C4×C11—22no—
470C2×C4×C11—22no—
471C2×C4×C11—22no—
472C2×C4×C11—22no—
473C2×C4×C11—22no—
474C2×C4×C11—22no—
475C2×C4×C11—22no—
476C2×C4×C11—22no—
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×C11—41no—
489C2×C4×C11—41no—
490C2×C4×C11—41no—
491C2×C4×C11—41no—
492C2×C4×C11—41no—
493C2×C4×C11—41no—
494C2×C4×C11—41no—
495C2×C4×C11—41no—
496C2×C4×C11C2×C4⋊C414yescomplemented
497C2×C4×C11C4×D414yescomplemented
498C2×C4×C11#12014yes—
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—22no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—22no—
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×Dic11—41no—
535C2×Dic11—41no—
536C2×Dic11—41no—
537C2×Dic11—41no—
538C2×Dic11—41no—
539C2×Dic11—41no—
540C2×Dic11C4×D414yescomplemented
541D44—232no—
542C4×D11—232no—
543C4×D11—416no—
544C4×D11—416no—
545C4×D11—416no—
546C23×D4—111no—
547C24×C4—111no—
548C24×C4—111no—
549C24×C4—111no—
550C24×C4—111no—
551C2×C4×D4—224no—
552C2×C4×D4—224no—
553C2×C4×D4—224no—
554C22×C4⋊C4—111no—
555C22×C4⋊C4—111no—
556C22×C4⋊C4—111no—
557C22×C4⋊C4—111no—
558C22×C4⋊C4—111no—
559C22×C4⋊C4—111no—
560C22×C4⋊C4—224no—
561C22×C4⋊C4—224no—
562C22×C4⋊C4—224no—
563C22×C4⋊C4C2×D1111yescharacteristic
564C22×C22⋊C4—111no—
565C22×C22⋊C4—111no—
566C22×C22⋊C4—111no—
567C22×C22⋊C4—111no—
568C22×C22⋊C4—111no—
569C22×C22⋊C4—111no—
570C22×C22⋊C4—111no—
571C22×C22⋊C4—111no—
572C22×C42C2×D1111yescharacteristic
573#386—118no—
574#386—224no—
575#385—224no—
576#385—224no—
577#385—224no—
578C2×#95—111no—
579C2×#95—111no—
580C2×#95—111no—
581C2×#95—111no—
582C2×#95—111no—
583C2×#95—111no—
584C2×#95—111no—
585C2×#95—111no—
586C2×#95—111no—
587C2×#95C2×D1111yescharacteristic
588C2×#95C2×D1111yescharacteristic
589C2×#95C2×D1111yescharacteristic
590C2×#95C2×D1111yescharacteristic
591C2×#95C2×D1111yescharacteristic
592C22×C11C22×C4⋊C411yescharacteristic
593C22×C11C2×C4×D411yescharacteristic
594C22×C11C2×C4×D411yescharacteristic
595C22×C11C2×C4×D411yescharacteristic
596C22×C11C2×C4×D411yescharacteristic
597C22×C11#52011yescharacteristic
598C22×C11#52011yescharacteristic
599C22×C11C2×#12011yescharacteristic
600C22×C11C2×#12011yescharacteristic
601C22×C11C2×C22⋊Q811yescharacteristic
602C22×C11C2×C22⋊Q811yescharacteristic
603C22×C11C2×#12311yescharacteristic
604C22×C11#52511yescharacteristic
605C22×C11#52511yescharacteristic
606C22×C11#52511yescharacteristic
607C22×C11#53411yescharacteristic
608C22×C11#53611yescharacteristic
609C22×C11#53911yescharacteristic
610C22×C11#53911yescharacteristic
611C22×C11D4211yescharacteristic
612C22×C11D4211yescharacteristic
613C22×C11D4211yescharacteristic
614C22×C11D4211yescharacteristic
615C22×C11#54711yescharacteristic
616C22×C11#54711yescharacteristic
617C22×C11#54711yescharacteristic
618C22×C11#54711yescharacteristic
619C22×C11#54811yescharacteristic
620C22×C11#54811yescharacteristic
621C22×C11D4×Q811yescharacteristic
622C22×C11D4×Q811yescharacteristic
623C22×C11#55311yescharacteristic
624C22×C11#55311yescharacteristic
625C22×C11#55411yescharacteristic
626C22×C11#55411yescharacteristic
627C2×D11—24no—
628C2×D11—24no—
629C2×D11—24no—
630C2×D11—24no—
631C2×D11—24no—
632C2×D11—24no—
633C2×D11—24no—
634C2×D11—24no—
635C2×D11—24no—
636C2×D11—24no—
637C2×D11—24no—
638C2×D11—24no—
639C2×D11—24no—
640C2×D11—24no—
641C2×D11—24no—
642C2×D11—24no—
643C2×D11—24no—
644C2×D11—42no—
645C2×D11—42no—
646C2×D11—42no—
647C2×D11—42no—
648C2×D11—42no—
649C2×D11—42no—
650C2×D11—42no—
651C2×D11—42no—
652C2×D11—42no—
653C2×D11—42no—
654C2×D11—42no—
655C2×D11—42no—
656C2×D11#38518yescomplemented
657C4×C11—24no—
658C4×C11—24no—
659C4×C11—24no—
660C4×C11—42no—
661C4×C11—42no—
662C4×C11—42no—
663C4×C11—81no—
664Dic11—24no—
665Dic11—42no—
666Dic11—42no—
667Dic11—42no—
668Dic11—42no—
669Dic11—81no—
670C25—111no—
671C25—111no—
672C22×D4—114no—
673C22×D4—114no—
674C22×D4—114no—
675C22×D4—222no—
676C22×D4—222no—
677C22×D4—222no—
678C22×D4—222no—
679C23×C4—111no—
680C23×C4—111no—
681C23×C4—111no—
682C23×C4—111no—
683C23×C4—111no—
684C23×C4—114no—
685C23×C4—114no—
686C23×C4—111no—
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—222no—
699C23×C4—222no—
700C23×C4—222no—
701C23×C4—222no—
702C23×C4—222no—
703C23×C4—222no—
704C23×C4—222no—
705C23×C4—222no—
706C23×C4—222no—
707C23×C4—441no—
708C23×C4—441no—
709C23×C4—441no—
710C23×C4—441no—
711C23×C4—441no—
712C23×C4—441no—
713C23×C4C22×D1111yescharacteristic
714C23×C4C22×D1111yescharacteristic
715C23×C4C22×D1111yescharacteristic
716C23×C4C22×D1111yescharacteristic
717C23×C4C22×D1111yescharacteristic
718C23×C4C22×D1111yescharacteristic
719C23×C4C22×D1111yescharacteristic
720C4×D4—2232no—
721C2×C4⋊C4—22no—
722C2×C4⋊C4—22no—
723C2×C4⋊C4—114no—
724C2×C4⋊C4—2232no—
725C2×C4⋊C4—222no—
726C2×C4⋊C4—222no—
727C2×C4⋊C4—222no—
728C2×C4⋊C4—222no—
729C2×C4⋊C4—222no—
730C2×C4⋊C4—222no—
731C2×C4⋊C4—222no—
732C2×C4⋊C4—222no—
733C2×C4⋊C4—222no—
734C2×C4⋊C4—222no—
735C2×C4⋊C4—222no—
736C2×C4⋊C4—222no—
737C2×C4⋊C4—222no—
738C2×C4⋊C4—222no—
739C2×C4⋊C4—222no—
740C2×C4⋊C4—441no—
741C2×C4⋊C4—441no—
742C2×C4⋊C4D4414yescomplemented
743C2×C22⋊C4—114no—
744C2×C22⋊C4—114no—
745C2×C22⋊C4—114no—
746C2×C22⋊C4—114no—
747C2×C22⋊C4—222no—
748C2×C22⋊C4—222no—
749C2×C22⋊C4—222no—
750C2×C22⋊C4—222no—
751C2×C22⋊C4—222no—
752C2×C22⋊C4—222no—
753C2×C22⋊C4—222no—
754C2×C22⋊C4—222no—
755C2×C22⋊C4—222no—
756C2×C22⋊C4—222no—
757C2×C22⋊C4—222no—
758C2×C22⋊C4—222no—
759C2×C22⋊C4—222no—
760C2×C22⋊C4—222no—
761C2×C22⋊C4—222no—
762C2×C22⋊C4—222no—
763C2×C22⋊C4—222no—
764C2×C22⋊C4—222no—
765C2×C22⋊C4—441no—
766C2×C22⋊C4—441no—
767C2×C42—22no—
768C2×C42—22no—
769C2×C42—22no—
770#95—22no—
771#95—22no—
772#95—22no—
773#95—22no—
774#95—114no—
775#95—222no—
776#95—222no—
777#95—222no—
778#95—222no—
779#95—222no—
780#95—222no—
781#95—441no—
782#95—441no—
783#95C4×D1114yescomplemented
784C2×C11C2×#38511yescharacteristic
785C2×C11C4×#12011yescharacteristic
786C2×C11#232211yescharacteristic
787C2×C11D4×C4⋊C411yescharacteristic
788C2×C11D4×C4⋊C411yescharacteristic
789C2×C11#236111yescharacteristic
790C2×C11#236111yescharacteristic
791C2×C11#240311yescharacteristic
792C2×C11#240611yescharacteristic
793C2×C11#240911yescharacteristic
794C2×C11#244311yescharacteristic
795C2×C11#244311yescharacteristic
796C2×C11#244911yescharacteristic
797C2×C11#244911yescharacteristic
798C2×C11#257911yescharacteristic
799D11—28no—
800D11—44no—
801C24—112no—
802C24—112no—
803C24—112no—
804C24—112no—
805C24—112no—
806C24—112no—
807C24—112no—
808C24—112no—
809C24—112no—
810C24—112no—
811C24—221no—
812C24—221no—
813C24—221no—
814C24—221no—
815C24—221no—
816C24—221no—
817C24—221no—
818C24—221no—
819C24—221no—
820C24—221no—
821C24—221no—
822C24—221no—
823C24—221no—
824C24—221no—
825C24—221no—
826C24—221no—
827C24—221no—
828C24—221no—
829C24—221no—
830C24—221no—
831C24C23×D1111yescharacteristic
832C2×D4—1116no—
833C2×D4—228no—
834C2×D4—228no—
835C2×D4—228no—
836C2×D4—228no—
837C2×D4—228no—
838C2×D4—228no—
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—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—112no—
877C22×C4—112no—
878C22×C4—112no—
879C22×C4—112no—
880C22×C4—112no—
881C22×C4—112no—
882C22×C4—112no—
883C22×C4—228no—
884C22×C4—228no—
885C22×C4—228no—
886C22×C4—228no—
887C22×C4—228no—
888C22×C4—228no—
889C22×C4—228no—
890C22×C4—228no—
891C22×C4—228no—
892C22×C4—221no—
893C22×C4—221no—
894C22×C4—221no—
895C22×C4—221no—
896C22×C4—228no—
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—228no—
922C22×C4—221no—
923C22×C4—221no—
924C22×C4—221no—
925C22×C4—221no—
926C22×C4—221no—
927C22×C4—221no—
928C22×C4—221no—
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×C4—444no—
938C22×C4—444no—
939C22×C4—444no—
940C22×C4—444no—
941C22×C4—444no—
942C22×C4—444no—
943C22×C4—444no—
944C22×C4—444no—
945C22×C4—444no—
946C22×C4C2×C4×D1112yes—
947C22×C4C2×C4×D1112yes—
948C22×C4C2×C4×D1112yes—
949C22×C4C2×D4412yes—
950C22×C4C2×D4412yes—
951C22×C4C2×D4412yes—
952C22×C4#433912yes—
953C22×C4D4×D1112yes—
954C22×C4D4×D1112yes—
955C22×C4D4×D1112yes—
956C22×C4D4×D1112yes—
957C22×C4Q8×D1112yes—
958C4⋊C4—28no—
959C4⋊C4—228no—
960C4⋊C4—228no—
961C4⋊C4—228no—
962C4⋊C4—228no—
963C4⋊C4—444no—
964C4⋊C4—444no—
965C22⋊C4—228no—
966C22⋊C4—228no—
967C22⋊C4—228no—
968C22⋊C4—228no—
969C22⋊C4—228no—
970C22⋊C4—444no—
971C22⋊C4—444no—
972C22⋊C4—444no—
973C42—28no—
974C11#1401511yescharacteristic, complemented, Sylow
975C23—114no—
976C23—114no—
977C23—114no—
978C23—114no—
979C23—114no—
980C23—114no—
981C23—114no—
982C23—114no—
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—222no—
1012C23—222no—
1013C23—222no—
1014C23—222no—
1015C23—222no—
1016C23—222no—
1017C23—222no—
1018C23—222no—
1019C23—222no—
1020C23—222no—
1021C23—222no—
1022C23—222no—
1023C23—222no—
1024C23—222no—
1025C23—222no—
1026C23—222no—
1027C23—222no—
1028C23—222no—
1029C23—441no—
1030C23—441no—
1031C23—441no—
1032C23—441no—
1033C23—441no—
1034C23—441no—
1035C23—441no—
1036C23—441no—
1037C23—441no—
1038C23—441no—
1039C23—441no—
1040C23—441no—
1041C23—441no—
1042C23—441no—
1043C23—441no—
1044C23—441no—
1045C23C22×C4×D1111yescharacteristic
1046C23C22×D4411yescharacteristic
1047C23C2×#433911yescharacteristic
1048C23C2×D4×D1111yescharacteristic
1049C23C2×D4×D1111yescharacteristic
1050C23C2×D4×D1111yescharacteristic
1051C23C2×D4×D1111yescharacteristic
1052C23C2×Q8×D1111yescharacteristic
1053C23#6704011yescharacteristic
1054C23#41×D1111yescharacteristic
1055C23#41×D1111yescharacteristic
1056C23#41×D1111yescharacteristic
1057C23#6704211yescharacteristic
1058C23#6704211yescharacteristic
1059C23#6704311yescharacteristic
1060D4—2232no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—114no—
1108C2×C4—2232no—
1109C2×C4—222no—
1110C2×C4—222no—
1111C2×C4—222no—
1112C2×C4—222no—
1113C2×C4—222no—
1114C2×C4—222no—
1115C2×C4—222no—
1116C2×C4—222no—
1117C2×C4—222no—
1118C2×C4—222no—
1119C2×C4—222no—
1120C2×C4—222no—
1121C2×C4—222no—
1122C2×C4—222no—
1123C2×C4—222no—
1124C2×C4—222no—
1125C2×C4—222no—
1126C2×C4—222no—
1127C2×C4—4416no—
1128C2×C4—4416no—
1129C2×C4—4416no—
1130C2×C4—441no—
1131C2×C4—441no—
1132C2×C4—441no—
1133C2×C4—441no—
1134C2×C4—441no—
1135C2×C4—441no—
1136C2×C4—441no—
1137C2×C4—441no—
1138C2×C4—441no—
1139C2×C4—441no—
1140C2×C4—441no—
1141C2×C4—441no—
1142C2×C4—441no—
1143C2×C4—441no—
1144C2×C4—441no—
1145C2×C4—441no—
1146C2×C4—441no—
1147C2×C4—441no—
1148C2×C4—441no—
1149C2×C4—441no—
1150C2×C4—441no—
1151C2×C4—441no—
1152C2×C4—441no—
1153C2×C4C4×D4414yescomplemented
1154C2×C4#6693514yes—
1155C2×C4C4⋊C4×D1114yescomplemented
1156C22—118no—
1157C22—224no—
1158C22—224no—
1159C22—224no—
1160C22—224no—
1161C22—224no—
1162C22—224no—
1163C22—224no—
1164C22—224no—
1165C22—224no—
1166C22—224no—
1167C22—224no—
1168C22—224no—
1169C22—224no—
1170C22—224no—
1171C22—224no—
1172C22—224no—
1173C22—224no—
1174C22—442no—
1175C22—442no—
1176C22—442no—
1177C22—442no—
1178C22—442no—
1179C22—442no—
1180C22—442no—
1181C22—442no—
1182C22—442no—
1183C22—442no—
1184C22—442no—
1185C22—442no—
1186C22C2×C4×D4411yescharacteristic
1187C22C2×#6693511yescharacteristic
1188C22C2×C4⋊C4×D1111yescharacteristic
1189C22#1062303811yescharacteristic
1190C22#1062305411yescharacteristic
1191C22#1062305511yescharacteristic
1192C22#1062306111yescharacteristic
1193C22C4×D4×D1111yescharacteristic
1194C22C4×D4×D1111yescharacteristic
1195C22C4×D4×D1111yescharacteristic
1196C22#1062307811yescharacteristic
1197C22#1062307811yescharacteristic
1198C22D4×D4411yescharacteristic
1199C22D4×D4411yescharacteristic
1200C22#1062308211yescharacteristic
1201C22#1062310511yescharacteristic
1202C22Q8×D4411yescharacteristic
1203C22#1062310711yescharacteristic
1204C22#1062311011yescharacteristic
1205C22D11×#12011yescharacteristic
1206C22#1062314011yescharacteristic
1207C22#1062314011yescharacteristic
1208C22D11×C22⋊Q811yescharacteristic
1209C22D11×C22⋊Q811yescharacteristic
1210C22#1062315911yescharacteristic
1211C22#1062316211yescharacteristic
1212C22D11×#12311yescharacteristic
1213C22#1062318411yescharacteristic
1214C22#1062318611yescharacteristic
1215C22#1062320811yescharacteristic
1216C22#1062322111yescharacteristic
1217C22#1062322311yescharacteristic
1218C22#1062323811yescharacteristic
1219C22#1062324011yescharacteristic
1220C22#1062325811yescharacteristic
1221C4—24no—
1222C4—24no—
1223C4—24no—
1224C4—42no—
1225C4—42no—
1226C4—42no—
1227C4—81no—
1228C4—224no—
1229C4—442no—
1230C4—442no—
1231C4—442no—
1232C4—442no—
1233C4—881no—
1234C2—228no—
1235C2—444no—
1236C2D11×#38511yescharacteristic
1237C2C4×#6693511yescharacteristic
1238C2#1307128911yescharacteristic
1239C2#1307151711yescharacteristic
1240C2C4⋊C4×D4411yescharacteristic
1241C2#1307162911yescharacteristic
1242C2#1307163411yescharacteristic
1243C2#1307192811yescharacteristic
1244C2#1307194911yescharacteristic
1245C2#1307197911yescharacteristic
1246C2#1307235611yescharacteristic
1247C2#1307235811yescharacteristic
1248C2#1307243011yescharacteristic
1249C2#1307243211yescharacteristic
1250C2#1307396711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1436D11
hypocenterC11#14015
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D11C2semidirect
5. C2×#10622281C2semidirect
6. C2×#10622281C2semidirect
7. C2×#10622602C2semidirect
8. #13066881C2semidirect
9. #13066880C2semidirect
10. #13066862C2semidirect
11. #13066860C2semidirect
12. #13066849C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1436C2semidirect
61. #10622278C4semidirect
110. C22×C4×D11C2×C4semidirect
114. C2×C11×C4⋊C4D4semidirect
138. C2×(C2×D11)⋊C4C2×C4semidirect
139. C2×(C2×D11)⋊C4C2×C4semidirect
140. C2×(C2×D11)⋊C4C2×C4semidirect
159. C2×Dic11⋊C4D4semidirect
166. C11×#95C2×C4semidirect
175. C11⋊#95C2×C4semidirect
305. C2×D44C4⋊C4semidirect
362. #1436D11semidirect
443. C22×D11C2×C4⋊C4semidirect
496. C2×C4×C11C2×C4⋊C4semidirect
497. C2×C4×C11C4×D4semidirect
540. C2×Dic11C4×D4semidirect
656. C2×D11#385semidirect
742. C2×C4⋊C4D44semidirect
783. #95C4×D11semidirect
974. C11#14015semidirect
1153. C2×C4C4×D44semidirect
1155. C2×C4C4⋊C4×D11semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D442
C22×C4⋊C4×D112
C2×#106222782
C2×#106222812
C2×#106226022
#130668812
#130668802
#130668622
#130668602
#130668492
(C2×D11)⋊#952
C11×#14362
#1401511