Finite Group Databasebeta

← #14675740

Subgroups — #14675740

Order 2816.

2222 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66925C211yesmaximal, characteristic
2C2×#10622277C211yesmaximal, characteristic
3C2×#10622280C211yesmaximal, characteristic
4C2×#10622600C211yesmaximal, characteristic
5C2×D11×#95C211yesmaximal, characteristic
6#13066880C211yesmaximal, characteristic, complemented
7#13066879C211yesmaximal, characteristic, complemented
8#13066874C211yesmaximal, characteristic, complemented
9#13066871C211yesmaximal, characteristic, complemented
10#13066850C211yesmaximal, characteristic, complemented
11#13066849C211yesmaximal, characteristic, complemented
12#13066847C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic
14(C2×D11)⋊#95C211yesmaximal, characteristic
15C11×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C2×#66925—24no—
32C2×#66925—24no—
33C2×#66925—24no—
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
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#10622600—24no—
55#10622280—24no—
56#10622277—24no—
57D11×#95C418yescomplemented
58C24×D11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C22×C4×D11—22no—
74C22×C4×D11—22no—
75C22×C4×D11—22no—
76C22×C4×D11—22no—
77C22×C4×D11—22no—
78C22×C4×D11—22no—
79C22×C4×D11—22no—
80C22×C4×D11—22no—
81C22×C4×D11—22no—
82C22×C4×D11—22no—
83C22×C4×D11—22no—
84C22×C4×D11—22no—
85C22×C4×D11—41no—
86C22×C4×D11—41no—
87C22×C4×D11—41no—
88C22×C4×D11—41no—
89C22×C4×D11C2×C414yes—
90C22×C4×D11C2×C414yes—
91C22×C4×D11C2×C414yes—
92C22×C4×D11D414yes—
93C22×C4×D11Q814yes—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—41no—
97C2×C42×C11—22no—
98C2×C42×C11—22no—
99C2×C42×C11—22no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
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)⋊C4D414yes—
111C2×(C2×D11)⋊C4D414yes—
112C2×C4⋊Dic11—22no—
113C2×C4⋊Dic11—22no—
114C2×C4⋊Dic11—41no—
115C2×Dic11⋊C4—22no—
116C2×Dic11⋊C4—22no—
117C2×Dic11⋊C4—22no—
118C2×Dic11⋊C4—22no—
119C2×Dic11⋊C4—22no—
120C2×Dic11⋊C4—22no—
121C2×Dic11⋊C4—22no—
122C2×Dic11⋊C4—22no—
123C2×Dic11⋊C4—22no—
124C2×Dic11⋊C4—22no—
125C2×Dic11⋊C4—41no—
126C2×Dic11⋊C4—41no—
127C2×C4×Dic11—22no—
128C2×C4×Dic11—22no—
129C2×C4×Dic11—22no—
130#66925—232no—
131C11×#95—22no—
132C11×#95—22no—
133C11×#95—22no—
134C11×#95—41no—
135C11×#95C2×C414yes—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—22no—
139C11⋊#95—22no—
140C11⋊#95—22no—
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—22no—
145C11⋊#95—41no—
146C11⋊#95—41no—
147C11⋊#95—41no—
148C11⋊#95C2×C414yes—
149C11⋊#95C2×C414yes—
150C11⋊#95C2×C414yes—
151#13878—111nomaximal, Sylow
152C24×C11C2411yescharacteristic
153C23×D11—21no—
154C23×D11—21no—
155C23×D11—21no—
156C23×D11—21no—
157C23×D11—21no—
158C23×D11—21no—
159C23×D11—21no—
160C23×D11—21no—
161C23×D11C22×C412yes—
162C23×D11C2×D412yes—
163C23×D11C2×D412yes—
164C23×D11C2×D412yes—
165C23×D11C2×Q812yes—
166C23×D11#4112yes—
167C23×D11#4112yes—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
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×C11C22×C412yes—
209C22×C4×C11C22×C412yes—
210C22×C4×C11C22×C412yes—
211C22×C4×C11C2×D412yes—
212C22×C4×C11C2×D412yes—
213C22×C4×C11C2×D412yes—
214C22×C4×C11C2×Q812yes—
215C22×C4×C11#4112yes—
216C22×C4×C11#4112yes—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
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×Dic11C22×C412yes—
258C22×Dic11C22×C412yes—
259C22×Dic11C22×C412yes—
260C22×Dic11C2×D412yes—
261C22×Dic11C2×D412yes—
262C22×Dic11C2×D412yes—
263C22×Dic11C2×Q812yes—
264C22×Dic11#4112yes—
265C22×Dic11#4112yes—
266C2×C4×D11—28no—
267C2×C4×D11—28no—
268C2×C4×D11—28no—
269C2×C4×D11—28no—
270C2×C4×D11—28no—
271C2×C4×D11—28no—
272C2×C4×D11—28no—
273C2×C4×D11—28no—
274C2×C4×D11—28no—
275C2×C4×D11—28no—
276C2×C4×D11—44no—
277C2×C4×D11—44no—
278C2×C4×D11—44no—
279C2×C4×D11—44no—
280C2×C4×D11—44no—
281C2×C4×D11—44no—
282C2×C4×D11—44no—
283C2×C4×D11—44no—
284C2×C4×D11—44no—
285C2×C4×D11—44no—
286C2×C4×D11C4⋊C4116yescomplemented
287C11×C4⋊C4—44no—
288C42×C11—28no—
289(C2×D11)⋊C4—28no—
290(C2×D11)⋊C4—28no—
291(C2×D11)⋊C4—44no—
292(C2×D11)⋊C4—44no—
293C4⋊Dic11—44no—
294Dic11⋊C4—28no—
295Dic11⋊C4—28no—
296Dic11⋊C4—44no—
297Dic11⋊C4—44no—
298C4×Dic11—28no—
299C22×#117—111no—
300C2×#381—111no—
301C2×#380—111no—
302C2×#380—111no—
303C22×#95—111no—
304#1444—111no—
305#1444—111no—
306#1442—111no—
307#1442—111no—
308#1436—111no—
309#1436—111no—
310#1436—111no—
311#1436D1111yescharacteristic, complemented
312C22⋊#95—111no—
313C22⋊#95—111no—
314C23×C11C23×C411yescharacteristic
315C23×C11C22×D411yescharacteristic
316C23×C11C22×D411yescharacteristic
317C23×C11C22×D411yescharacteristic
318C23×C11C22×Q811yescharacteristic
319C23×C11C2×#4111yescharacteristic
320C23×C11C2×#4111yescharacteristic
321C23×C11C2×#4111yescharacteristic
322C23×C11C2×#4111yescharacteristic
323C23×C11C2×#4111yescharacteristic
324C23×C11C2×#4111yescharacteristic
325C23×C11H(5,𝔽2)11yescharacteristic
326C23×C11H(5,𝔽2)11yescharacteristic
327C23×C112−1+411yescharacteristic
328C23×C112−1+411yescharacteristic
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
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×D11C2×C4⋊C414yes—
358C22×D11C4×D414yes—
359C22×D11C4×D414yes—
360C22×D11#12014yes—
361C22×D11C22⋊Q814yes—
362C22×D11C22⋊Q814yes—
363C22×D11#12314yes—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11C2×C4⋊C414yes—
412C2×C4×C11#11714yescomplemented
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—41no—
435C2×Dic11—41no—
436C2×Dic11—41no—
437C2×Dic11—41no—
438C2×Dic11—41no—
439C2×Dic11—41no—
440C2×Dic11—41no—
441C2×Dic11—41no—
442C2×Dic11—41no—
443C2×Dic11—41no—
444C2×Dic11—41no—
445C2×Dic11—41no—
446C2×Dic11—41no—
447C2×Dic11—41no—
448C2×Dic11—41no—
449C2×Dic11—41no—
450C2×Dic11—41no—
451C2×Dic11—41no—
452C2×Dic11—41no—
453C2×Dic11—41no—
454C2×Dic11—41no—
455C2×Dic11—41no—
456C2×Dic11—41no—
457C2×Dic11—41no—
458C2×Dic11—41no—
459C2×Dic11—41no—
460C2×Dic11C2×C4⋊C414yes—
461C2×Dic11#11714yescomplemented
462C4×D11—232no—
463C4×D11—416no—
464C4×D11—416no—
465C24×C4—111no—
466C24×C4—111no—
467C24×C4—111no—
468C2×#117—224no—
469C2×#117—224no—
470C2×#117—224no—
471C22×C4⋊C4—111no—
472C22×C4⋊C4—111no—
473C22×C4⋊C4—111no—
474C22×C4⋊C4—111no—
475C22×C4⋊C4—111no—
476C22×C4⋊C4C2×D1111yescharacteristic
477C22×C22⋊C4—111no—
478C22×C22⋊C4—111no—
479C22×C22⋊C4—111no—
480C22×C22⋊C4—111no—
481C22×C42—111no—
482C22×C42C2×D1111yescharacteristic
483#381—224no—
484#380—224no—
485#380—224no—
486C2×#95—111no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—118no—
490C2×#95—111no—
491C2×#95—111no—
492C2×#95—111no—
493C2×#95—111no—
494C2×#95—111no—
495C2×#95—111no—
496C2×#95—111no—
497C2×#95—111no—
498C2×#95—111no—
499C2×#95—111no—
500C2×#95—111no—
501C2×#95—111no—
502C2×#95C2×D1111yescharacteristic
503C2×#95C2×D1111yescharacteristic
504C2×#95C2×D1111yescharacteristic
505C2×#95C2×D1111yescharacteristic
506C2×#95C2×D1111yescharacteristic
507C22×C11C22×C4⋊C411yescharacteristic
508C22×C11C2×#11711yescharacteristic
509C22×C11C2×#11711yescharacteristic
510C22×C11C2×C4×D411yescharacteristic
511C22×C11C2×C4×D411yescharacteristic
512C22×C11#51811yescharacteristic
513C22×C11#51911yescharacteristic
514C22×C11C2×#12011yescharacteristic
515C22×C11C2×C22⋊Q811yescharacteristic
516C22×C11C2×C22⋊Q811yescharacteristic
517C22×C11C2×#12311yescharacteristic
518C22×C11#53211yescharacteristic
519C22×C11#53211yescharacteristic
520C22×C11#53311yescharacteristic
521C22×C11#53311yescharacteristic
522C22×C11#53711yescharacteristic
523C22×C11#53711yescharacteristic
524C22×C11#54411yescharacteristic
525C22×C11#54411yescharacteristic
526C22×C11#54611yescharacteristic
527C22×C11#54611yescharacteristic
528C22×C11#54611yescharacteristic
529C22×C11#54611yescharacteristic
530C22×C11#54711yescharacteristic
531C22×C11#54711yescharacteristic
532C22×C11#54711yescharacteristic
533C22×C11#54711yescharacteristic
534C22×C11#55111yescharacteristic
535C22×C11#55111yescharacteristic
536C22×C11#55111yescharacteristic
537C22×C11#55111yescharacteristic
538C22×C11#55211yescharacteristic
539C22×C11#55211yescharacteristic
540C22×C11#55211yescharacteristic
541C22×C11#55211yescharacteristic
542C2×D11—24no—
543C2×D11—24no—
544C2×D11—24no—
545C2×D11—24no—
546C2×D11—24no—
547C2×D11—24no—
548C2×D11—24no—
549C2×D11—24no—
550C2×D11—24no—
551C2×D11—24no—
552C2×D11—24no—
553C2×D11—24no—
554C2×D11—24no—
555C2×D11—24no—
556C2×D11#38518yes—
557C4×C11—24no—
558C4×C11—24no—
559C4×C11—42no—
560C4×C11—42no—
561C4×C11—42no—
562C4×C11—81no—
563C4×C11—81no—
564Dic11—24no—
565Dic11—24no—
566Dic11—42no—
567Dic11—42no—
568Dic11—42no—
569Dic11—81no—
570Dic11—81no—
571C25—111no—
572C23×C4—111no—
573C23×C4—111no—
574C23×C4—114no—
575C23×C4—114no—
576C23×C4—114no—
577C23×C4—111no—
578C23×C4—111no—
579C23×C4—111no—
580C23×C4—114no—
581C23×C4—114no—
582C23×C4—111no—
583C23×C4—111no—
584C23×C4—222no—
585C23×C4—222no—
586C23×C4—222no—
587C23×C4—222no—
588C23×C4—222no—
589C23×C4—222no—
590C23×C4—222no—
591C23×C4—222no—
592C23×C4—222no—
593C23×C4—222no—
594C23×C4—222no—
595C23×C4—222no—
596C23×C4—441no—
597C23×C4—441no—
598C23×C4—441no—
599C23×C4—441no—
600C23×C4C22×D1111yescharacteristic
601C23×C4C22×D1111yescharacteristic
602C23×C4C22×D1111yescharacteristic
603C23×C4C22×D1111yescharacteristic
604C23×C4C22×D1111yescharacteristic
605C23×C4C22×D1111yescharacteristic
606C23×C4C22×D1111yescharacteristic
607#117—2232no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4—222no—
612C2×C4⋊C4—222no—
613C2×C4⋊C4—222no—
614C2×C4⋊C4—222no—
615C2×C4⋊C4—222no—
616C2×C4⋊C4—222no—
617C2×C4⋊C4—222no—
618C2×C4⋊C4—222no—
619C2×C4⋊C4—222no—
620C2×C4⋊C4—222no—
621C2×C4⋊C4—222no—
622C2×C4⋊C4—222no—
623C2×C4⋊C4—441no—
624C2×C4⋊C4—441no—
625C2×C4⋊C4—441no—
626C2×C22⋊C4—114no—
627C2×C22⋊C4—114no—
628C2×C22⋊C4—222no—
629C2×C22⋊C4—222no—
630C2×C22⋊C4—222no—
631C2×C22⋊C4—222no—
632C2×C22⋊C4—222no—
633C2×C22⋊C4—222no—
634C2×C22⋊C4—222no—
635C2×C22⋊C4—222no—
636C2×C22⋊C4—222no—
637C2×C22⋊C4—222no—
638C2×C42—22no—
639C2×C42—22no—
640C2×C42—22no—
641C2×C42—222no—
642C2×C42—222no—
643C2×C42—222no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—41no—
648#95—114no—
649#95—114no—
650#95—114no—
651#95—222no—
652#95—222no—
653#95—222no—
654#95—222no—
655#95—222no—
656#95—222no—
657#95—222no—
658#95—222no—
659#95—222no—
660#95—441no—
661#95—441no—
662#95—441no—
663#95C4×D1114yes—
664C2×C11#228511yescharacteristic
665C2×C11C2×#38511yescharacteristic
666C2×C11#231611yescharacteristic
667C2×C11#234211yescharacteristic
668C2×C11#234211yescharacteristic
669C2×C11#234411yescharacteristic
670C2×C11#234411yescharacteristic
671C2×C11#243011yescharacteristic
672C2×C11#243011yescharacteristic
673C2×C11#243811yescharacteristic
674C2×C11#243811yescharacteristic
675C2×C11#243811yescharacteristic
676C2×C11#243811yescharacteristic
677C2×C11#249811yescharacteristic
678C2×C11#249811yescharacteristic
679D11—28no—
680C24—112no—
681C24—112no—
682C24—112no—
683C24—112no—
684C24—112no—
685C24—112no—
686C24—112no—
687C24—221no—
688C24—221no—
689C24—221no—
690C24—221no—
691C24—221no—
692C24—221no—
693C24—221no—
694C24—221no—
695C24C23×D1111yescharacteristic
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—112no—
737C22×C4—112no—
738C22×C4—112no—
739C22×C4—112no—
740C22×C4—112no—
741C22×C4—112no—
742C22×C4—1116no—
743C22×C4—112no—
744C22×C4—112no—
745C22×C4—112no—
746C22×C4—228no—
747C22×C4—228no—
748C22×C4—228no—
749C22×C4—228no—
750C22×C4—228no—
751C22×C4—228no—
752C22×C4—228no—
753C22×C4—228no—
754C22×C4—228no—
755C22×C4—221no—
756C22×C4—221no—
757C22×C4—221no—
758C22×C4—221no—
759C22×C4—221no—
760C22×C4—221no—
761C22×C4—221no—
762C22×C4—221no—
763C22×C4—221no—
764C22×C4—221no—
765C22×C4—221no—
766C22×C4—221no—
767C22×C4—221no—
768C22×C4—221no—
769C22×C4—221no—
770C22×C4—221no—
771C22×C4—221no—
772C22×C4—221no—
773C22×C4—221no—
774C22×C4—221no—
775C22×C4—221no—
776C22×C4—221no—
777C22×C4—221no—
778C22×C4—221no—
779C22×C4—221no—
780C22×C4—221no—
781C22×C4—228no—
782C22×C4—221no—
783C22×C4—221no—
784C22×C4—221no—
785C22×C4—221no—
786C22×C4—221no—
787C22×C4—221no—
788C22×C4—221no—
789C22×C4—221no—
790C22×C4—221no—
791C22×C4—221no—
792C22×C4—221no—
793C22×C4—221no—
794C22×C4—221no—
795C22×C4—221no—
796C22×C4—444no—
797C22×C4—444no—
798C22×C4—444no—
799C22×C4—444no—
800C22×C4—444no—
801C22×C4—444no—
802C22×C4—444no—
803C22×C4—444no—
804C22×C4—444no—
805C22×C4—444no—
806C22×C4C2×C4×D1112yes—
807C22×C4C2×C4×D1112yes—
808C22×C4C2×C4×D1112yes—
809C22×C4#433912yes—
810C22×C4#433912yes—
811C22×C4D4×D1112yes—
812C22×C4D4×D1112yes—
813C22×C4D4×D1112yes—
814C22×C4Q8×D1112yes—
815C4⋊C4—44no—
816C4⋊C4—228no—
817C4⋊C4—228no—
818C4⋊C4—444no—
819C4⋊C4—444no—
820C4⋊C4—444no—
821C22⋊C4—228no—
822C22⋊C4—228no—
823C22⋊C4—444no—
824C22⋊C4—444no—
825C42—28no—
826C42—228no—
827C11#1387811yescharacteristic, complemented, Sylow
828C23—114no—
829C23—114no—
830C23—114no—
831C23—114no—
832C23—114no—
833C23—114no—
834C23—114no—
835C23—222no—
836C23—222no—
837C23—222no—
838C23—222no—
839C23—222no—
840C23—222no—
841C23—222no—
842C23—222no—
843C23—222no—
844C23—222no—
845C23—222no—
846C23—222no—
847C23—222no—
848C23—222no—
849C23—222no—
850C23—222no—
851C23—222no—
852C23—222no—
853C23—222no—
854C23—222no—
855C23—222no—
856C23—222no—
857C23—222no—
858C23—222no—
859C23—222no—
860C23—222no—
861C23—222no—
862C23—222no—
863C23C22×C4×D1111yescharacteristic
864C23C2×#433911yescharacteristic
865C23C2×#433911yescharacteristic
866C23C2×D4×D1111yescharacteristic
867C23C2×D4×D1111yescharacteristic
868C23C2×D4×D1111yescharacteristic
869C23#6703711yescharacteristic
870C23C2×Q8×D1111yescharacteristic
871C23#6704011yescharacteristic
872C23#41×D1111yescharacteristic
873C23#41×D1111yescharacteristic
874C23#41×D1111yescharacteristic
875C23#41×D1111yescharacteristic
876C23#6704211yescharacteristic
877C23#6704311yescharacteristic
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—114no—
926C2×C4—114no—
927C2×C4—2232no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—222no—
932C2×C4—222no—
933C2×C4—222no—
934C2×C4—222no—
935C2×C4—222no—
936C2×C4—222no—
937C2×C4—222no—
938C2×C4—222no—
939C2×C4—222no—
940C2×C4—222no—
941C2×C4—222no—
942C2×C4—222no—
943C2×C4—222no—
944C2×C4—222no—
945C2×C4—222no—
946C2×C4—222no—
947C2×C4—222no—
948C2×C4—222no—
949C2×C4—4416no—
950C2×C4—4416no—
951C2×C4—441no—
952C2×C4—441no—
953C2×C4—441no—
954C2×C4—441no—
955C2×C4—441no—
956C2×C4—441no—
957C2×C4—441no—
958C2×C4—441no—
959C2×C4—441no—
960C2×C4—441no—
961C2×C4—441no—
962C2×C4—441no—
963C2×C4—441no—
964C2×C4—441no—
965C2×C4—441no—
966C2×C4—441no—
967C2×C4—441no—
968C2×C4—441no—
969C2×C4—441no—
970C2×C4—441no—
971C2×C4—441no—
972C2×C4—441no—
973C2×C4—441no—
974C2×C4—441no—
975C2×C4—441no—
976C2×C4—441no—
977C2×C4#6692514yescomplemented
978C2×C4C4⋊C4×D1114yes—
979C22—118no—
980C22—224no—
981C22—224no—
982C22—224no—
983C22—224no—
984C22—224no—
985C22—224no—
986C22—224no—
987C22—224no—
988C22—224no—
989C22—224no—
990C22—224no—
991C22—224no—
992C22—224no—
993C22—224no—
994C22C2×#6692511yescharacteristic
995C22#1062302111yescharacteristic
996C22C2×C4⋊C4×D1111yescharacteristic
997C22#1062303811yescharacteristic
998C22D11×#11711yescharacteristic
999C22#1062305811yescharacteristic
1000C22#1062306011yescharacteristic
1001C22C4×D4×D1111yescharacteristic
1002C22C4×D4×D1111yescharacteristic
1003C22#1062307611yescharacteristic
1004C22#1062307911yescharacteristic
1005C22#1062307911yescharacteristic
1006C22#1062308111yescharacteristic
1007C22#1062308211yescharacteristic
1008C22#1062308711yescharacteristic
1009C22#1062310311yescharacteristic
1010C22#1062310911yescharacteristic
1011C22#1062310911yescharacteristic
1012C22#1062311211yescharacteristic
1013C22D11×#12011yescharacteristic
1014C22#1062313911yescharacteristic
1015C22#1062314311yescharacteristic
1016C22D11×C22⋊Q811yescharacteristic
1017C22D11×C22⋊Q811yescharacteristic
1018C22#1062316011yescharacteristic
1019C22#1062316211yescharacteristic
1020C22D11×#12311yescharacteristic
1021C22#1062318511yescharacteristic
1022C22#1062318611yescharacteristic
1023C22#1062321011yescharacteristic
1024C22#1062322011yescharacteristic
1025C22#1062322411yescharacteristic
1026C22#1062323611yescharacteristic
1027C22#1062323911yescharacteristic
1028C22#1062326011yescharacteristic
1029C4—24no—
1030C4—24no—
1031C4—42no—
1032C4—42no—
1033C4—42no—
1034C4—81no—
1035C4—81no—
1036C4—224no—
1037C4—224no—
1038C4—442no—
1039C4—442no—
1040C4—442no—
1041C4—881no—
1042C4—881no—
1043C2—228no—
1044C2#1307102011yescharacteristic
1045C2D11×#38511yescharacteristic
1046C2#1307123111yescharacteristic
1047C2#1307145911yescharacteristic
1048C2#1307146011yescharacteristic
1049C2#1307148111yescharacteristic
1050C2#1307148211yescharacteristic
1051C2#1307222311yescharacteristic
1052C2#1307222511yescharacteristic
1053C2#1307228911yescharacteristic
1054C2#1307229111yescharacteristic
1055C2#1307229711yescharacteristic
1056C2#1307229911yescharacteristic
1057C2#1307305711yescharacteristic
1058C2#1307305911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1436D11
hypocenterC11#13878
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
6. #13066880C2semidirect
7. #13066879C2semidirect
8. #13066874C2semidirect
9. #13066871C2semidirect
10. #13066850C2semidirect
11. #13066849C2semidirect
12. #13066847C2semidirect
15. C11×#1436C2semidirect
57. D11×#95C4semidirect
286. C2×C4×D11C4⋊C4semidirect
311. #1436D11semidirect
412. C2×C4×C11#117semidirect
461. C2×Dic11#117semidirect
827. C11#13878semidirect
977. C2×C4#66925semidirect

Maximal subgroups

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

subgroupindex
C22×#669252
C2×#106222772
C2×#106222802
C2×#106226002
C2×D11×#952
#130668802
#130668792
#130668742
#130668712
#130668502
#130668492
#130668472
(C2×D11)⋊#952
C11×#14362
#1387811