Finite Group Databasebeta

← #14681950

Subgroups — #14681950

Order 2816.

2126 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66928C211yesmaximal, characteristic
2C2×#10622259C211yesmaximal, characteristic, complemented
3C2×#10622603C211yesmaximal, characteristic, complemented
4C2×#10622278C211yesmaximal, characteristic
5C2×#10622602C211yesmaximal, characteristic, complemented
6#13066886C211yesmaximal, characteristic, complemented
7#13066864C211yesmaximal, characteristic, complemented
8#13066860C211yesmaximal, characteristic, complemented
9#13066858C211yesmaximal, characteristic, complemented
10#13066858C211yesmaximal, characteristic, complemented
11#13066856C211yesmaximal, characteristic
12#13066852C211yesmaximal, characteristic, complemented
13#13066843C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×C4⋊#95C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×Dic22C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×#66928—24no—
36C2×#66928—24no—
37C2×#66928C418yescomplemented
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#10622603—24no—
55#10622602—24no—
56#10622278—24no—
57#10622259—24no—
58C24×D11C2311yescharacteristic
59C24×D11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C22×D44—22no—
74C22×D44—22no—
75C22×D44—22no—
76C22×D44—22no—
77C22×D44—41no—
78C22×D44—41no—
79C22×D44C2×C414yes—
80C22×C4×D11—22no—
81C22×C4×D11—22no—
82C22×C4×D11—22no—
83C22×C4×D11—41no—
84C22×C4×D11—41no—
85C22×C4×D11—41no—
86C22×C4×D11—41no—
87C22×Dic22—22no—
88C22×Dic22—22no—
89C22×Dic22—22no—
90C22×Dic22—22no—
91C22×Dic22—41no—
92C22×Dic22—41no—
93C22×Dic22C2×C414yescomplemented
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4—22no—
98C2×C11×C4⋊C4—41no—
99C2×C11×C4⋊C4—41no—
100C2×C42×C11—22no—
101C2×C42×C11—22no—
102C2×C42×C11C2×C414yescomplemented
103C2×(C2×D11)⋊C4—22no—
104C2×(C2×D11)⋊C4—22no—
105C2×(C2×D11)⋊C4—22no—
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—22no—
109C2×(C2×D11)⋊C4—22no—
110C2×(C2×D11)⋊C4—22no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4—22no—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—22no—
115C2×(C2×D11)⋊C4—22no—
116C2×(C2×D11)⋊C4—22no—
117C2×(C2×D11)⋊C4—22no—
118C2×(C2×D11)⋊C4—41no—
119C2×(C2×D11)⋊C4—41no—
120C2×(C2×D11)⋊C4—41no—
121C2×(C2×D11)⋊C4—41no—
122C2×(C2×D11)⋊C4—41no—
123C2×(C2×D11)⋊C4—41no—
124C2×(C2×D11)⋊C4—41no—
125C2×(C2×D11)⋊C4—41no—
126C2×(C2×D11)⋊C4—41no—
127C2×(C2×D11)⋊C4—41no—
128C2×(C2×D11)⋊C4—41no—
129C2×(C2×D11)⋊C4—41no—
130C2×(C2×D11)⋊C4C2×C414yes—
131C2×(C2×D11)⋊C4C2×C414yes—
132C2×(C2×D11)⋊C4C2×C414yescomplemented
133C2×(C2×D11)⋊C4C2×C414yescomplemented
134C2×(C2×D11)⋊C4D414yes—
135C2×(C2×D11)⋊C4D414yes—
136C2×Dic11⋊C4—22no—
137C2×Dic11⋊C4—22no—
138C2×Dic11⋊C4—41no—
139C2×C4×Dic11—22no—
140C2×C4×Dic11—22no—
141C2×C4×Dic11—41no—
142#66928—232no—
143C11×#95—22no—
144C11×#95—22no—
145C11×#95—41no—
146C11×#95—41no—
147C11⋊#95—22no—
148C11⋊#95—22no—
149C11⋊#95—22no—
150C11⋊#95—22no—
151C11⋊#95—22no—
152C11⋊#95—22no—
153C11⋊#95—22no—
154C11⋊#95—41no—
155C11⋊#95—41no—
156C11⋊#95—41no—
157C11⋊#95—41no—
158C11⋊#95D414yes—
159#14421—111nomaximal, Sylow
160C24×C11C2411yescharacteristic
161C23×D11—21no—
162C23×D11—21no—
163C23×D11—21no—
164C23×D11—21no—
165C23×D11—21no—
166C23×D11—21no—
167C23×D11—21no—
168C23×D11—21no—
169C23×D11—21no—
170C23×D11—21no—
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×D11C22×C412yes—
188C23×D11C22×C412yes—
189C23×D11C2×D412yes—
190C23×D11C2×D412yes—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
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×C11C22×C412yes—
232C22×C4×C11C22×C412yes—
233C22×C4×C11C22×C412yes—
234C22×C4×C11C2×D412yes—
235C22×C4×C11C2×D412yes—
236C22×C4×C11C2×D412yes—
237C22×C4×C11#4112yes—
238C22×C4×C11#4112yes—
239C22×C4×C11#4112yes—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
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×Dic11C22×C412yes—
277C22×Dic11C22×C412yes—
278C22×Dic11C2×D412yes—
279C22×Dic11C2×D412yes—
280C22×Dic11C2×D412yes—
281C22×Dic11C2×D412yes—
282C2×D44—28no—
283C2×D44—28no—
284C2×D44—44no—
285C2×D44—44no—
286C2×D44—44no—
287C2×D44—44no—
288C2×D44—44no—
289C2×C4×D11—44no—
290C2×C4×D11—44no—
291C2×C4×D11—44no—
292C2×C4×D11—44no—
293C2×C4×D11—44no—
294C2×C4×D11—44no—
295C2×C4×D11—44no—
296C2×Dic22—28no—
297C2×Dic22—28no—
298C2×Dic22—44no—
299C2×Dic22—44no—
300C2×Dic22—44no—
301C2×Dic22—44no—
302C2×Dic22—44no—
303C11×C4⋊C4—44no—
304C11×C4⋊C4—44no—
305C42×C11—28no—
306(C2×D11)⋊C4—28no—
307(C2×D11)⋊C4—28no—
308(C2×D11)⋊C4—28no—
309(C2×D11)⋊C4—44no—
310(C2×D11)⋊C4—44no—
311(C2×D11)⋊C4—44no—
312(C2×D11)⋊C4—44no—
313(C2×D11)⋊C4—44no—
314(C2×D11)⋊C4—44no—
315(C2×D11)⋊C4—44no—
316(C2×D11)⋊C4C22⋊C4116yescomplemented
317Dic11⋊C4—44no—
318C4×Dic11—44no—
319C22×#124—111no—
320C2×#391—111no—
321C2×#388—111no—
322C2×#386—111no—
323C2×#385—111no—
324#1446—111no—
325#1440—111no—
326#1439—111no—
327#1439—111no—
328#1439—111no—
329#1438—111no—
330#1437—111no—
331C4⋊#95D1111yescharacteristic, complemented
332#1434—111no—
333C22⋊#95—111no—
334C23×C11C23×C411yescharacteristic
335C23×C11C22×D411yescharacteristic
336C23×C11C22×D411yescharacteristic
337C23×C11C22×D411yescharacteristic
338C23×C11C2×#4111yescharacteristic
339C23×C11C2×#4111yescharacteristic
340C23×C11C2×#4111yescharacteristic
341C23×C11H(5,𝔽2)11yescharacteristic
342C23×C11H(5,𝔽2)11yescharacteristic
343C23×C11H(5,𝔽2)11yescharacteristic
344C23×C11H(5,𝔽2)11yescharacteristic
345C23×C11H(5,𝔽2)11yescharacteristic
346C23×C112−1+411yescharacteristic
347C23×C112−1+411yescharacteristic
348C23×C112−1+411yescharacteristic
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—41no—
375C22×D11—41no—
376C22×D11—41no—
377C22×D11—41no—
378C22×D11—41no—
379C22×D11—41no—
380C22×D11—41no—
381C22×D11—41no—
382C22×D11—41no—
383C22×D11—41no—
384C22×D11—41no—
385C22×D11—41no—
386C22×D11—41no—
387C22×D11—41no—
388C22×D11—41no—
389C22×D11—41no—
390C22×D11—41no—
391C22×D11—41no—
392C22×D11—41no—
393C22×D11—41no—
394C22×D11—41no—
395C22×D11—41no—
396C22×D11—41no—
397C22×D11—41no—
398C22×D11—41no—
399C22×D11—41no—
400C22×D11—41no—
401C22×D11—41no—
402C22×D11—41no—
403C22×D11—41no—
404C22×D11—41no—
405C22×D11—41no—
406C22×D11—41no—
407C22×D11—41no—
408C22×D11—41no—
409C22×D11—41no—
410C22×D11—41no—
411C22×D11—41no—
412C22×D11—41no—
413C22×D11—41no—
414C22×D11—41no—
415C22×D11—41no—
416C22×D11—41no—
417C22×D11—41no—
418C22×D11C2×C22⋊C414yes—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
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×C11C2×C22⋊C414yes—
467C2×C4×C11C4×D414yes—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—41no—
484C2×Dic11—41no—
485C2×Dic11—41no—
486C2×Dic11—41no—
487C2×Dic11—41no—
488C2×Dic11—41no—
489C2×Dic11—41no—
490C2×Dic11—41no—
491C2×Dic11—41no—
492C2×Dic11—41no—
493C2×Dic11—41no—
494C2×Dic11—41no—
495C2×Dic11—41no—
496C2×Dic11—41no—
497C2×Dic11—41no—
498C2×Dic11—41no—
499C2×Dic11—41no—
500C2×Dic11—41no—
501C2×Dic11—41no—
502C2×Dic11—41no—
503C2×Dic11—41no—
504C2×Dic11—41no—
505C2×Dic11—41no—
506C2×Dic11—41no—
507C2×Dic11—41no—
508C2×Dic11—41no—
509C2×Dic11C2×C22⋊C414yes—
510D44—416no—
511C4×D11—416no—
512Dic22—416no—
513C23×Q8—111no—
514C23×D4—111no—
515C24×C4—111no—
516C2×#124—118no—
517C2×#124—224no—
518C2×#124—224no—
519C22×C4⋊C4—111no—
520C22×C4⋊C4C2×D1111yescharacteristic
521C22×C4⋊C4C2×D1111yescharacteristic
522C22×C22⋊C4—111no—
523C22×C22⋊C4—111no—
524C22×C22⋊C4—111no—
525C22×C22⋊C4—111no—
526C22×C22⋊C4—111no—
527C22×C22⋊C4—111no—
528C22×C22⋊C4—111no—
529C22×C22⋊C4—111no—
530C22×C22⋊C4—111no—
531C22×C22⋊C4—111no—
532C22×C22⋊C4—111no—
533C22×C42—111no—
534C22×C42C2×D1111yescharacteristic
535#391—224no—
536#388—224no—
537#386—224no—
538#385—224no—
539C2×#95—111no—
540C2×#95—111no—
541C2×#95—111no—
542C2×#95—111no—
543C2×#95—111no—
544C2×#95—111no—
545C2×#95—111no—
546C2×#95—111no—
547C2×#95—111no—
548C2×#95—111no—
549C2×#95—111no—
550C2×#95—111no—
551C2×#95C2×D1111yescharacteristic
552C2×#95C2×D1111yescharacteristic
553C2×#95C2×D1111yescharacteristic
554C2×#95C2×D1111yescharacteristic
555C22×C11C22×C22⋊C411yescharacteristic
556C22×C11C2×C4×D411yescharacteristic
557C22×C11C4×#4111yescharacteristic
558C22×C11#51811yescharacteristic
559C22×C11#52011yescharacteristic
560C22×C11#52011yescharacteristic
561C22×C11#52011yescharacteristic
562C22×C11#53511yescharacteristic
563C22×C11#53511yescharacteristic
564C22×C11#53611yescharacteristic
565C22×C11#53611yescharacteristic
566C22×C11#53711yescharacteristic
567C22×C11#53711yescharacteristic
568C22×C11#53811yescharacteristic
569C22×C11#53811yescharacteristic
570C22×C11#54211yescharacteristic
571C22×C11#54211yescharacteristic
572C22×C11#54211yescharacteristic
573C22×C11#54211yescharacteristic
574C22×C11D4211yescharacteristic
575C22×C11D4211yescharacteristic
576C22×C11#54611yescharacteristic
577C22×C11#54611yescharacteristic
578C22×C11#54611yescharacteristic
579C22×C11#54611yescharacteristic
580C22×C11#54611yescharacteristic
581C22×C11#54711yescharacteristic
582C22×C11#54711yescharacteristic
583C22×C11#54811yescharacteristic
584C22×C11#55611yescharacteristic
585C22×C11#55911yescharacteristic
586C22×C11H(3,𝔽4)11yescharacteristic
587C22×C11#56211yescharacteristic
588C22×C11#56211yescharacteristic
589C22×C11#56311yescharacteristic
590C2×D11—24no—
591C2×D11—24no—
592C2×D11—24no—
593C2×D11—42no—
594C2×D11—42no—
595C2×D11—42no—
596C2×D11—42no—
597C2×D11—42no—
598C2×D11—42no—
599C2×D11—42no—
600C2×D11—42no—
601C2×D11—42no—
602C2×D11—42no—
603C2×D11—42no—
604C2×D11—42no—
605C2×D11—42no—
606C2×D11—42no—
607C2×D11—42no—
608C2×D11—42no—
609C2×D11—42no—
610C2×D11—42no—
611C2×D11—42no—
612C2×D11—81no—
613C2×D11—81no—
614C2×D11—81no—
615C2×D11—81no—
616C2×D11—81no—
617C2×D11—81no—
618C2×D11—81no—
619C2×D11—81no—
620C4×C11—24no—
621C4×C11—24no—
622C4×C11—42no—
623C4×C11—42no—
624C4×C11—42no—
625C4×C11—81no—
626C4×C11—81no—
627Dic11—24no—
628Dic11—42no—
629Dic11—42no—
630Dic11—42no—
631Dic11—81no—
632Dic11—81no—
633C25—111no—
634C25—111no—
635C22×Q8—114no—
636C22×Q8—222no—
637C22×Q8—222no—
638C22×Q8—222no—
639C22×Q8—222no—
640C22×Q8—441no—
641C22×Q8—441no—
642C22×D4—114no—
643C22×D4—222no—
644C22×D4—222no—
645C22×D4—222no—
646C22×D4—222no—
647C22×D4—441no—
648C22×D4—441no—
649C23×C4—111no—
650C23×C4—111no—
651C23×C4—111no—
652C23×C4—111no—
653C23×C4—111no—
654C23×C4—111no—
655C23×C4—222no—
656C23×C4—222no—
657C23×C4—222no—
658C23×C4—441no—
659C23×C4—441no—
660C23×C4—441no—
661C23×C4—441no—
662C23×C4C22×D1111yescharacteristic
663C23×C4C22×D1111yescharacteristic
664C23×C4C22×D1111yescharacteristic
665C23×C4C22×D1111yescharacteristic
666C23×C4C22×D1111yescharacteristic
667C23×C4C22×D1111yescharacteristic
668C23×C4C22×D1111yescharacteristic
669#124—2232no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—22no—
672C2×C4⋊C4—22no—
673C2×C4⋊C4—22no—
674C2×C4⋊C4—41no—
675C2×C4⋊C4—41no—
676C2×C4⋊C4—222no—
677C2×C4⋊C4—222no—
678C2×C4⋊C4—441no—
679C2×C22⋊C4—114no—
680C2×C22⋊C4—114no—
681C2×C22⋊C4—114no—
682C2×C22⋊C4—114no—
683C2×C22⋊C4—114no—
684C2×C22⋊C4—114no—
685C2×C22⋊C4—222no—
686C2×C22⋊C4—222no—
687C2×C22⋊C4—222no—
688C2×C22⋊C4—222no—
689C2×C22⋊C4—222no—
690C2×C22⋊C4—222no—
691C2×C22⋊C4—222no—
692C2×C22⋊C4—222no—
693C2×C22⋊C4—222no—
694C2×C22⋊C4—222no—
695C2×C22⋊C4—222no—
696C2×C22⋊C4—222no—
697C2×C22⋊C4—222no—
698C2×C22⋊C4—222no—
699C2×C22⋊C4—222no—
700C2×C22⋊C4—441no—
701C2×C22⋊C4—441no—
702C2×C22⋊C4—441no—
703C2×C22⋊C4—441no—
704C2×C22⋊C4—441no—
705C2×C22⋊C4—441no—
706C2×C22⋊C4—441no—
707C2×C22⋊C4—441no—
708C2×C22⋊C4—441no—
709C2×C22⋊C4—441no—
710C2×C22⋊C4—441no—
711C2×C22⋊C4—441no—
712C2×C42—22no—
713C2×C42—22no—
714C2×C42—222no—
715C2×C42—222no—
716C2×C42—441no—
717C2×C42C4×D1114yescomplemented
718#95—22no—
719#95—22no—
720#95—41no—
721#95—41no—
722#95—114no—
723#95—222no—
724#95—222no—
725#95—222no—
726#95—222no—
727#95—222no—
728#95—222no—
729#95—222no—
730#95—441no—
731#95—441no—
732#95—441no—
733#95—441no—
734C2×C11#231111yescharacteristic
735C2×C11#232611yescharacteristic
736C2×C11#233711yescharacteristic
737C2×C11D4×C22⋊C411yescharacteristic
738C2×C11#233911yescharacteristic
739C2×C11#236711yescharacteristic
740C2×C11#237911yescharacteristic
741C2×C11#267011yescharacteristic
742C2×C11#267211yescharacteristic
743C2×C11#267411yescharacteristic
744C2×C11#267611yescharacteristic
745C2×C11#270011yescharacteristic
746C2×C11#271011yescharacteristic
747C2×C11#271211yescharacteristic
748C2×C11#271511yescharacteristic
749D11—44no—
750D11—82no—
751C24—112no—
752C24—112no—
753C24—112no—
754C24—112no—
755C24—221no—
756C24—221no—
757C24—221no—
758C24—221no—
759C24—221no—
760C24—221no—
761C24—221no—
762C24—221no—
763C24—221no—
764C24—221no—
765C24—221no—
766C24—221no—
767C24—221no—
768C24—221no—
769C24—221no—
770C24—221no—
771C24—221no—
772C24—221no—
773C24—221no—
774C24—221no—
775C24—221no—
776C24—221no—
777C24—221no—
778C24—221no—
779C24—221no—
780C24—221no—
781C24C23×D1111yescharacteristic
782C2×Q8—228no—
783C2×Q8—228no—
784C2×Q8—444no—
785C2×Q8—444no—
786C2×Q8—444no—
787C2×Q8—444no—
788C2×Q8—444no—
789C2×D4—228no—
790C2×D4—228no—
791C2×D4—444no—
792C2×D4—444no—
793C2×D4—444no—
794C2×D4—444no—
795C2×D4—444no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
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—112no—
837C22×C4—112no—
838C22×C4—112no—
839C22×C4—112no—
840C22×C4—112no—
841C22×C4—112no—
842C22×C4—221no—
843C22×C4—221no—
844C22×C4—221no—
845C22×C4—221no—
846C22×C4—221no—
847C22×C4—221no—
848C22×C4—221no—
849C22×C4—221no—
850C22×C4—221no—
851C22×C4—221no—
852C22×C4—221no—
853C22×C4—221no—
854C22×C4—221no—
855C22×C4—221no—
856C22×C4—221no—
857C22×C4—221no—
858C22×C4—221no—
859C22×C4—221no—
860C22×C4—221no—
861C22×C4—221no—
862C22×C4—221no—
863C22×C4—221no—
864C22×C4—221no—
865C22×C4—221no—
866C22×C4—221no—
867C22×C4—221no—
868C22×C4—221no—
869C22×C4—221no—
870C22×C4—221no—
871C22×C4—221no—
872C22×C4—221no—
873C22×C4—221no—
874C22×C4—221no—
875C22×C4—221no—
876C22×C4—221no—
877C22×C4—221no—
878C22×C4—444no—
879C22×C4—444no—
880C22×C4—444no—
881C22×C4—444no—
882C22×C4—444no—
883C22×C4—444no—
884C22×C4—444no—
885C22×C4C2×C4×D1112yes—
886C22×C4C2×C4×D1112yes—
887C22×C4C2×C4×D1112yes—
888C22×C4#433912yes—
889C22×C4#433912yes—
890C22×C4D4×D1112yes—
891C22×C4D4×D1112yes—
892C22×C4D4×D1112yes—
893C22×C4#434312yes—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—444no—
897C22⋊C4—1116no—
898C22⋊C4—228no—
899C22⋊C4—228no—
900C22⋊C4—228no—
901C22⋊C4—444no—
902C22⋊C4—444no—
903C22⋊C4—444no—
904C22⋊C4—444no—
905C22⋊C4—444no—
906C22⋊C4—444no—
907C22⋊C4—444no—
908C42—28no—
909C42—444no—
910C11#1442111yescharacteristic, complemented, Sylow
911C23—114no—
912C23—222no—
913C23—222no—
914C23—222no—
915C23—222no—
916C23—222no—
917C23—222no—
918C23—222no—
919C23—222no—
920C23—222no—
921C23—222no—
922C23—222no—
923C23—222no—
924C23—222no—
925C23—222no—
926C23—222no—
927C23—222no—
928C23—222no—
929C23—222no—
930C23—222no—
931C23—222no—
932C23—222no—
933C23—222no—
934C23—222no—
935C23—222no—
936C23—222no—
937C23—441no—
938C23—441no—
939C23—441no—
940C23—441no—
941C23—441no—
942C23—441no—
943C23—441no—
944C23—441no—
945C23—441no—
946C23—441no—
947C23—441no—
948C23—441no—
949C23—441no—
950C23—441no—
951C23—441no—
952C23—441no—
953C23—441no—
954C23—441no—
955C23—441no—
956C23—441no—
957C23—441no—
958C23—441no—
959C23—441no—
960C23—441no—
961C23—441no—
962C23—441no—
963C23—441no—
964C23—441no—
965C23—441no—
966C23—441no—
967C23—441no—
968C23—441no—
969C23—441no—
970C23—441no—
971C23—441no—
972C23—441no—
973C23—441no—
974C23—441no—
975C23—441no—
976C23—441no—
977C23—441no—
978C23—441no—
979C23—441no—
980C23—441no—
981C23C22×C4×D1111yescharacteristic
982C23C2×#433911yescharacteristic
983C23C2×#433911yescharacteristic
984C23C2×D4×D1111yescharacteristic
985C23C2×D4×D1111yescharacteristic
986C23C2×D4×D1111yescharacteristic
987C23#6703711yescharacteristic
988C23#6703711yescharacteristic
989C23C2×#434311yescharacteristic
990C23#6704011yescharacteristic
991C23#6704011yescharacteristic
992C23#6704211yescharacteristic
993C23#6704211yescharacteristic
994C23#6704211yescharacteristic
995C23#6704311yescharacteristic
996Q8—4416no—
997D4—4416no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—114no—
1046C2×C4—222no—
1047C2×C4—222no—
1048C2×C4—222no—
1049C2×C4—222no—
1050C2×C4—222no—
1051C2×C4—222no—
1052C2×C4—222no—
1053C2×C4—222no—
1054C2×C4—222no—
1055C2×C4—222no—
1056C2×C4—222no—
1057C2×C4—222no—
1058C2×C4—222no—
1059C2×C4—222no—
1060C2×C4—222no—
1061C2×C4—4416no—
1062C2×C4—441no—
1063C2×C4—441no—
1064C2×C4—441no—
1065C2×C4—441no—
1066C2×C4—441no—
1067C2×C4—441no—
1068C2×C4—441no—
1069C2×C4—441no—
1070C2×C4—441no—
1071C2×C4—441no—
1072C2×C4—441no—
1073C2×C4—441no—
1074C2×C4—441no—
1075C2×C4—441no—
1076C2×C4—441no—
1077C2×C4—441no—
1078C2×C4—441no—
1079C2×C4—441no—
1080C2×C4—441no—
1081C2×C4—441no—
1082C2×C4—441no—
1083C2×C4—441no—
1084C2×C4—441no—
1085C2×C4—441no—
1086C2×C4—441no—
1087C2×C4—441no—
1088C2×C4C22⋊C4×D1114yes—
1089C2×C4#6694614yes—
1090C22—224no—
1091C22—224no—
1092C22—224no—
1093C22—442no—
1094C22—442no—
1095C22—442no—
1096C22—442no—
1097C22—442no—
1098C22—442no—
1099C22—442no—
1100C22—442no—
1101C22—442no—
1102C22—442no—
1103C22—442no—
1104C22—442no—
1105C22—442no—
1106C22—442no—
1107C22—442no—
1108C22—442no—
1109C22—442no—
1110C22—442no—
1111C22—442no—
1112C22—881no—
1113C22—881no—
1114C22—881no—
1115C22—881no—
1116C22—881no—
1117C22—881no—
1118C22—881no—
1119C22—881no—
1120C22C4×#433911yescharacteristic
1121C22C2×C22⋊C4×D1111yescharacteristic
1122C22#1062302111yescharacteristic
1123C22#1062302111yescharacteristic
1124C22C2×#6694611yescharacteristic
1125C22#1062303511yescharacteristic
1126C22#1062303511yescharacteristic
1127C22#1062303811yescharacteristic
1128C22#1062303811yescharacteristic
1129C22#1062305211yescharacteristic
1130C22#1062305411yescharacteristic
1131C22#1062308111yescharacteristic
1132C22#1062308311yescharacteristic
1133C22#1062309111yescharacteristic
1134C22#1062309111yescharacteristic
1135C22#1062311311yescharacteristic
1136C22#1062311311yescharacteristic
1137C22#1062311511yescharacteristic
1138C22#1062311611yescharacteristic
1139C22#1062313811yescharacteristic
1140C22#1062313911yescharacteristic
1141C22#1062314011yescharacteristic
1142C22#1062314011yescharacteristic
1143C22#1062315911yescharacteristic
1144C22#1062316011yescharacteristic
1145C22#1062316111yescharacteristic
1146C22#1062316111yescharacteristic
1147C22#1062321411yescharacteristic
1148C22#1062321511yescharacteristic
1149C22#1062323011yescharacteristic
1150C22#1062323111yescharacteristic
1151C22#1062324611yescharacteristic
1152C22#1062325511yescharacteristic
1153C22#1062326411yescharacteristic
1154C22#1062326411yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—42no—
1158C4—42no—
1159C4—42no—
1160C4—81no—
1161C4—81no—
1162C4—224no—
1163C4—442no—
1164C4—442no—
1165C4—442no—
1166C4—881no—
1167C4—881no—
1168C2—444no—
1169C2—882no—
1170C2#1307120511yescharacteristic
1171C2#1307132411yescharacteristic
1172C2#1307142911yescharacteristic
1173C2#1307143611yescharacteristic
1174C2#1307144311yescharacteristic
1175C2#1307168511yescharacteristic
1176C2#1307178711yescharacteristic
1177C2#1307483911yescharacteristic
1178C2#1307486411yescharacteristic
1179C2#1307489811yescharacteristic
1180C2#1307491411yescharacteristic
1181C2#1307521711yescharacteristic
1182C2#1307535911yescharacteristic
1183C2#1307538611yescharacteristic
1184C2#1307542811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC4⋊#95D11
hypocenterC11#14421
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622259C2semidirect
3. C2×#10622603C2semidirect
5. C2×#10622602C2semidirect
6. #13066886C2semidirect
7. #13066864C2semidirect
8. #13066860C2semidirect
9. #13066858C2semidirect
10. #13066858C2semidirect
12. #13066852C2semidirect
13. #13066843C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×C4⋊#95C2semidirect
37. C2×#66928C4semidirect
93. C22×Dic22C2×C4semidirect
102. C2×C42×C11C2×C4semidirect
132. C2×(C2×D11)⋊C4C2×C4semidirect
133. C2×(C2×D11)⋊C4C2×C4semidirect
316. (C2×D11)⋊C4C22⋊C4semidirect
331. C4⋊#95D11semidirect
717. C2×C42C4×D11semidirect
910. C11#14421semidirect

Maximal subgroups

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

subgroupindex
C22×#669282
C2×#106222592
C2×#106226032
C2×#106222782
C2×#106226022
#130668862
#130668642
#130668602
#130668582
#130668562
#130668522
#130668432
(C2×D11)⋊#952
C11×C4⋊#952
#1442111