Finite Group Databasebeta

← #14681119

Subgroups — #14681119

Order 2816.

1910 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66949C211yesmaximal, characteristic
2C2×#10622587C211yesmaximal, characteristic, complemented
3C2×#10622594C211yesmaximal, characteristic, complemented
4C2×#10622600C211yesmaximal, characteristic
5#13066886C211yesmaximal, characteristic, complemented
6#13066870C211yesmaximal, characteristic, complemented
7#13066866C211yesmaximal, characteristic, complemented
8#13066866C211yesmaximal, characteristic, complemented
9#13066858C211yesmaximal, characteristic
10#13066858C211yesmaximal, characteristic
11#13066854C211yesmaximal, characteristic
12#13066852C211yesmaximal, characteristic
13#13066849C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic
15C2×C11×#389C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C2×#66949—24no—
34C2×#66949—24no—
35C2×#66949C418yescomplemented
36C11×#389—24no—
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
54C2×C11⋊#95C2211yescharacteristic
55#10622600—24no—
56#10622594—24no—
57#10622587—24no—
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—41no—
78C22×C4×D11—41no—
79C22×C4×D11C2×C414yes—
80C22×Dic22—22no—
81C22×Dic22—22no—
82C22×Dic22—22no—
83C22×Dic22—22no—
84C22×Dic22—41no—
85C22×Dic22—41no—
86C22×Dic22C2×C414yes—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—41no—
93C2×C11×C4⋊C4—41no—
94C2×C11×C4⋊C4—41no—
95C2×C11×C4⋊C4—41no—
96C2×C11×C4⋊C4C2×C414yes—
97C2×C11×C4⋊C4D414yes—
98C2×C11×C4⋊C4D414yes—
99C2×C42×C11—22no—
100C2×C42×C11—41no—
101C2×C42×C11—41no—
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)⋊C4—22no—
111C2×(C2×D11)⋊C4—41no—
112C2×(C2×D11)⋊C4—41no—
113C2×(C2×D11)⋊C4—41no—
114C2×(C2×D11)⋊C4—41no—
115C2×(C2×D11)⋊C4—41no—
116C2×(C2×D11)⋊C4—41no—
117C2×(C2×D11)⋊C4C2×C414yes—
118C2×(C2×D11)⋊C4C2×C414yes—
119C2×(C2×D11)⋊C4Q814yescomplemented
120C2×C4⋊Dic11—22no—
121C2×C4⋊Dic11—22no—
122C2×C4⋊Dic11—41no—
123C2×Dic11⋊C4—22no—
124C2×Dic11⋊C4—22no—
125C2×Dic11⋊C4—22no—
126C2×Dic11⋊C4—22no—
127C2×Dic11⋊C4C2×C414yes—
128C2×Dic11⋊C4C2×C414yes—
129C2×C4×Dic11—22no—
130C2×C4×Dic11—22no—
131C2×C4×Dic11—41no—
132#66949—232no—
133C11×#95—22no—
134C11×#95—22no—
135C11⋊#95—22no—
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—41no—
145C11⋊#95—41no—
146C11⋊#95—41no—
147C11⋊#95—41no—
148C11⋊#95—41no—
149C11⋊#95—41no—
150C11⋊#95D414yes—
151#14362—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×D11—21no—
162C23×D11—21no—
163C23×D11—21no—
164C23×D11—21no—
165C23×D11C22×C412yes—
166C23×D11C2×Q812yes—
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×C11C22×C412yes—
207C22×C4×C11C22×C412yes—
208C22×C4×C11C22×C412yes—
209C22×C4×C11C2×D412yes—
210C22×C4×C11C2×D412yes—
211C22×C4×C11C2×D412yes—
212C22×C4×C11C2×D412yes—
213C22×C4×C11C2×D412yes—
214C22×C4×C11C2×D412yes—
215C22×C4×C11C2×D412yes—
216C22×C4×C11C2×Q812yes—
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×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11C22×C412yes—
260C22×Dic11C22×C412yes—
261C22×Dic11C22×C412yes—
262C22×Dic11C2×D412yes—
263C22×Dic11C2×D412yes—
264C22×Dic11C2×Q812yes—
265C22×Dic11#4112yes—
266C2×C4×D11—28no—
267C2×C4×D11—28no—
268C2×C4×D11—44no—
269C2×C4×D11—44no—
270C2×C4×D11—44no—
271C2×C4×D11—44no—
272C2×C4×D11—44no—
273C2×Dic22—28no—
274C2×Dic22—28no—
275C2×Dic22—44no—
276C2×Dic22—44no—
277C2×Dic22—44no—
278C2×Dic22—44no—
279C2×Dic22—44no—
280C11×C4⋊C4—44no—
281C11×C4⋊C4—44no—
282C11×C4⋊C4—44no—
283C11×C4⋊C4C22⋊C4116yescomplemented
284C42×C11—44no—
285(C2×D11)⋊C4—28no—
286(C2×D11)⋊C4—28no—
287(C2×D11)⋊C4—44no—
288(C2×D11)⋊C4—44no—
289(C2×D11)⋊C4—44no—
290(C2×D11)⋊C4—44no—
291C4⋊Dic11—44no—
292Dic11⋊C4—28no—
293Dic11⋊C4—28no—
294C4×Dic11—44no—
295C22×C22⋊Q8—111no—
296C2×#391—111no—
297C2×#389D1111yescharacteristic, complemented
298C2×#387—111no—
299C2×#380—111no—
300#1446—111no—
301#1441—111no—
302#1441—111no—
303#1441—111no—
304#1439—111no—
305#1439—111no—
306#1437—111no—
307#1437—111no—
308#1436—111no—
309C22⋊#95—111no—
310C23×C11C23×C411yescharacteristic
311C23×C11C22×D411yescharacteristic
312C23×C11C22×D411yescharacteristic
313C23×C11C22×D411yescharacteristic
314C23×C11C22×Q811yescharacteristic
315C23×C11C2×#4111yescharacteristic
316C23×C11C2×#4111yescharacteristic
317C23×C11H(5,𝔽2)11yescharacteristic
318C23×C11H(5,𝔽2)11yescharacteristic
319C23×C11H(5,𝔽2)11yescharacteristic
320C23×C11H(5,𝔽2)11yescharacteristic
321C23×C112−1+411yescharacteristic
322C23×C112−1+411yescharacteristic
323C23×C112−1+411yescharacteristic
324C23×C112−1+411yescharacteristic
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
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—41no—
344C22×D11—41no—
345C22×D11—41no—
346C22×D11—41no—
347C22×D11—41no—
348C22×D11—41no—
349C22×D11—41no—
350C22×D11—41no—
351C22×D11—41no—
352C22×D11—41no—
353C22×D11—41no—
354C22×D11—41no—
355C22×D11—41no—
356C22×D11—41no—
357C22×D11—41no—
358C22×D11—41no—
359C22×D11C4×Q814yes—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
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—41no—
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×C11C2×C22⋊C414yes—
407C2×C4×C11C2×C22⋊C414yes—
408C2×C4×C11C2×C22⋊C414yes—
409C2×Dic11—22no—
410C2×Dic11—22no—
411C2×Dic11—22no—
412C2×Dic11—22no—
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—41no—
428C2×Dic11—41no—
429C2×Dic11—41no—
430C2×Dic11—41no—
431C2×Dic11—41no—
432C2×Dic11—41no—
433C2×Dic11—41no—
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×Dic11C4×D414yes—
458C4×D11—416no—
459Dic22—416no—
460C23×Q8—111no—
461C24×C4—111no—
462C2×C22⋊Q8—118no—
463C2×C22⋊Q8—224no—
464C2×C22⋊Q8—224no—
465C22×C4⋊C4—111no—
466C22×C4⋊C4—111no—
467C22×C4⋊C4—111no—
468C22×C4⋊C4C2×D1111yescharacteristic
469C22×C4⋊C4C2×D1111yescharacteristic
470C22×C4⋊C4C2×D1111yescharacteristic
471C22×C4⋊C4C2×D1111yescharacteristic
472C22×C22⋊C4—111no—
473C22×C22⋊C4—111no—
474C22×C22⋊C4—111no—
475C22×C22⋊C4—111no—
476C22×C22⋊C4—111no—
477C22×C22⋊C4—111no—
478C22×C42—111no—
479C22×C42C2×D1111yescharacteristic
480#391—224no—
481#389—24no—
482#387—224no—
483#380—224no—
484C2×#95—111no—
485C2×#95—111no—
486C2×#95—111no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
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×#95C2×D1111yescharacteristic
501C2×#95C2×D1111yescharacteristic
502C22×C11C22×C22⋊C411yescharacteristic
503C22×C11C2×C4×D411yescharacteristic
504C22×C11C2×C4×Q811yescharacteristic
505C22×C11#51811yescharacteristic
506C22×C11#51911yescharacteristic
507C22×C11#52011yescharacteristic
508C22×C11#52011yescharacteristic
509C22×C11#53511yescharacteristic
510C22×C11#53611yescharacteristic
511C22×C11#53611yescharacteristic
512C22×C11#53711yescharacteristic
513C22×C11#53711yescharacteristic
514C22×C11#53711yescharacteristic
515C22×C11#53811yescharacteristic
516C22×C11#53911yescharacteristic
517C22×C11#54111yescharacteristic
518C22×C11#54211yescharacteristic
519C22×C11#54311yescharacteristic
520C22×C11#54411yescharacteristic
521C22×C11D4211yescharacteristic
522C22×C11D4211yescharacteristic
523C22×C11#54611yescharacteristic
524C22×C11#54611yescharacteristic
525C22×C11#54611yescharacteristic
526C22×C11#54811yescharacteristic
527C22×C11#54811yescharacteristic
528C22×C11D4×Q811yescharacteristic
529C22×C11D4×Q811yescharacteristic
530C22×C11D4×Q811yescharacteristic
531C22×C11#55211yescharacteristic
532C22×C11#55411yescharacteristic
533C22×C11#56211yescharacteristic
534C22×C11#56211yescharacteristic
535C22×C11#56311yescharacteristic
536C22×C11#56311yescharacteristic
537C2×D11—24no—
538C2×D11—24no—
539C2×D11—24no—
540C2×D11—42no—
541C2×D11—42no—
542C2×D11—42no—
543C2×D11—42no—
544C2×D11—42no—
545C2×D11—42no—
546C2×D11—42no—
547C2×D11—42no—
548C2×D11—42no—
549C2×D11—42no—
550C2×D11—42no—
551C2×D11—42no—
552C4×C11—24no—
553C4×C11—24no—
554C4×C11—24no—
555C4×C11—42no—
556C4×C11—42no—
557C4×C11—81no—
558C4×C11—81no—
559Dic11—24no—
560Dic11—42no—
561Dic11—42no—
562Dic11—42no—
563Dic11—42no—
564Dic11—81no—
565Dic11—81no—
566C25—111no—
567C22×Q8—114no—
568C22×Q8—222no—
569C22×Q8—222no—
570C22×Q8—222no—
571C22×Q8—222no—
572C22×Q8—441no—
573C22×Q8—441no—
574C23×C4—111no—
575C23×C4—111no—
576C23×C4—111no—
577C23×C4—111no—
578C23×C4—111no—
579C23×C4—114no—
580C23×C4—111no—
581C23×C4—111no—
582C23×C4—222no—
583C23×C4—222no—
584C23×C4—222no—
585C23×C4—222no—
586C23×C4—441no—
587C23×C4—441no—
588C23×C4C22×D1111yescharacteristic
589C23×C4C22×D1111yescharacteristic
590C23×C4C22×D1111yescharacteristic
591C23×C4C22×D1111yescharacteristic
592C23×C4C22×D1111yescharacteristic
593C23×C4C22×D1111yescharacteristic
594C23×C4C22×D1111yescharacteristic
595C22⋊Q8—2232no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—114no—
606C2×C4⋊C4—114no—
607C2×C4⋊C4—222no—
608C2×C4⋊C4—222no—
609C2×C4⋊C4—222no—
610C2×C4⋊C4—222no—
611C2×C4⋊C4—222no—
612C2×C4⋊C4—222no—
613C2×C4⋊C4—441no—
614C2×C4⋊C4C4×D1114yes—
615C2×C4⋊C4D4414yes—
616C2×C4⋊C4C22⋊D1114yes—
617C2×C22⋊C4—114no—
618C2×C22⋊C4—114no—
619C2×C22⋊C4—114no—
620C2×C22⋊C4—222no—
621C2×C22⋊C4—222no—
622C2×C22⋊C4—222no—
623C2×C22⋊C4—222no—
624C2×C22⋊C4—222no—
625C2×C22⋊C4—222no—
626C2×C22⋊C4—222no—
627C2×C22⋊C4—222no—
628C2×C22⋊C4—222no—
629C2×C22⋊C4—441no—
630C2×C22⋊C4—441no—
631C2×C22⋊C4—441no—
632C2×C22⋊C4—441no—
633C2×C22⋊C4—441no—
634C2×C22⋊C4—441no—
635C2×C42—22no—
636C2×C42—41no—
637C2×C42—41no—
638C2×C42—222no—
639C2×C42—222no—
640C2×C42—441no—
641#95—22no—
642#95—22no—
643#95—114no—
644#95—222no—
645#95—222no—
646#95—222no—
647#95—222no—
648#95—222no—
649#95—222no—
650#95—222no—
651#95—222no—
652#95—222no—
653#95—441no—
654#95—441no—
655#95—441no—
656#95—441no—
657#95—441no—
658#95—441no—
659C2×C11#231111yescharacteristic
660C2×C11#232311yescharacteristic
661C2×C11#232911yescharacteristic
662C2×C11D4×C22⋊C411yescharacteristic
663C2×C11Q8×C22⋊C411yescharacteristic
664C2×C11#236011yescharacteristic
665C2×C11#237811yescharacteristic
666C2×C11#267611yescharacteristic
667C2×C11#267711yescharacteristic
668C2×C11#268111yescharacteristic
669C2×C11#268311yescharacteristic
670C2×C11#269011yescharacteristic
671C2×C11#269211yescharacteristic
672C2×C11#270211yescharacteristic
673C2×C11#270411yescharacteristic
674D11—44no—
675C24—112no—
676C24—112no—
677C24—112no—
678C24—221no—
679C24—221no—
680C24—221no—
681C24—221no—
682C24—221no—
683C24—221no—
684C24—221no—
685C24—221no—
686C24—221no—
687C24—221no—
688C24—221no—
689C24—221no—
690C24C23×D1111yescharacteristic
691C2×Q8—228no—
692C2×Q8—228no—
693C2×Q8—444no—
694C2×Q8—444no—
695C2×Q8—444no—
696C2×Q8—444no—
697C2×Q8—444no—
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—112no—
743C22×C4—228no—
744C22×C4—221no—
745C22×C4—221no—
746C22×C4—221no—
747C22×C4—221no—
748C22×C4—221no—
749C22×C4—221no—
750C22×C4—221no—
751C22×C4—221no—
752C22×C4—221no—
753C22×C4—221no—
754C22×C4—221no—
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—228no—
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—221no—
782C22×C4—221no—
783C22×C4—221no—
784C22×C4—221no—
785C22×C4—221no—
786C22×C4—221no—
787C22×C4—444no—
788C22×C4—444no—
789C22×C4—444no—
790C22×C4—444no—
791C22×C4—444no—
792C22×C4C2×C4×D1112yes—
793C22×C4C2×C4×D1112yes—
794C22×C4C2×C4×D1112yes—
795C22×C4C2×D4412yes—
796C22×C4C2×D4412yes—
797C22×C4C2×D4412yes—
798C22×C4D4×D1112yes—
799C22×C4Q8×D1112yes—
800C22×C4C2×C22⋊D1112yes—
801C22×C4C2×C22⋊D1112yes—
802C22×C4C2×C22⋊D1112yes—
803C4⋊C4—44no—
804C4⋊C4—44no—
805C4⋊C4—44no—
806C4⋊C4—228no—
807C4⋊C4—228no—
808C4⋊C4—444no—
809C4⋊C4(C2×D11)⋊C4116yescomplemented
810C22⋊C4—228no—
811C22⋊C4—228no—
812C22⋊C4—444no—
813C22⋊C4—444no—
814C22⋊C4—444no—
815C22⋊C4—444no—
816C42—44no—
817C42—444no—
818C11#1436211yescharacteristic, complemented, Sylow
819C23—114no—
820C23—222no—
821C23—222no—
822C23—222no—
823C23—222no—
824C23—222no—
825C23—222no—
826C23—222no—
827C23—222no—
828C23—222no—
829C23—222no—
830C23—222no—
831C23—222no—
832C23—222no—
833C23—222no—
834C23—222no—
835C23—222no—
836C23—222no—
837C23—222no—
838C23—441no—
839C23—441no—
840C23—441no—
841C23—441no—
842C23—441no—
843C23—441no—
844C23—441no—
845C23—441no—
846C23—441no—
847C23—441no—
848C23—441no—
849C23—441no—
850C23—441no—
851C23—441no—
852C23—441no—
853C23—441no—
854C23C22×C4×D1111yescharacteristic
855C23C22×D4411yescharacteristic
856C23C2×D4×D1111yescharacteristic
857C23#6703711yescharacteristic
858C23#6703711yescharacteristic
859C23#6703711yescharacteristic
860C23C2×Q8×D1111yescharacteristic
861C23#6704011yescharacteristic
862C23#6704011yescharacteristic
863C23#6704011yescharacteristic
864C23#41×D1111yescharacteristic
865C23#41×D1111yescharacteristic
866C23#6704211yescharacteristic
867C23#6704311yescharacteristic
868C23C22×C22⋊D1111yescharacteristic
869Q8—4416no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
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—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
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—114no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—222no—
921C2×C4—222no—
922C2×C4—222no—
923C2×C4—222no—
924C2×C4—222no—
925C2×C4—222no—
926C2×C4—222no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—222no—
932C2×C4—222no—
933C2×C4—222no—
934C2×C4—222no—
935C2×C4—4416no—
936C2×C4—441no—
937C2×C4—441no—
938C2×C4—441no—
939C2×C4—441no—
940C2×C4—441no—
941C2×C4—441no—
942C2×C4—441no—
943C2×C4—441no—
944C2×C4—441no—
945C2×C4—441no—
946C2×C4—441no—
947C2×C4—441no—
948C2×C4—441no—
949C2×C4—441no—
950C2×C4—441no—
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×C4C2×(C2×D11)⋊C414yes—
967C2×C4C2×(C2×D11)⋊C414yes—
968C2×C4C2×(C2×D11)⋊C414yes—
969C22—224no—
970C22—224no—
971C22—224no—
972C22—442no—
973C22—442no—
974C22—442no—
975C22—442no—
976C22—442no—
977C22—442no—
978C22—442no—
979C22—442no—
980C22—442no—
981C22—442no—
982C22—442no—
983C22—442no—
984C22#1062303511yescharacteristic
985C22#1062303511yescharacteristic
986C22#1062304111yescharacteristic
987C22#1062304111yescharacteristic
988C22C4×D4×D1111yescharacteristic
989C22#1062307611yescharacteristic
990C22D4×D4411yescharacteristic
991C22#1062308511yescharacteristic
992C22C4×Q8×D1111yescharacteristic
993C22#1062310311yescharacteristic
994C22Q8×D4411yescharacteristic
995C22#1062310711yescharacteristic
996C22#1062312811yescharacteristic
997C22#1062314111yescharacteristic
998C22#1062314411yescharacteristic
999C22#1062315211yescharacteristic
1000C22#1062316511yescharacteristic
1001C22#1062316711yescharacteristic
1002C22#1062317111yescharacteristic
1003C22#1062317811yescharacteristic
1004C22#1062322311yescharacteristic
1005C22#1062322411yescharacteristic
1006C22#1062322711yescharacteristic
1007C22#1062323011yescharacteristic
1008C22#1062325511yescharacteristic
1009C22#1062325811yescharacteristic
1010C22#1062326011yescharacteristic
1011C22#1062326611yescharacteristic
1012C22C22×(C2×D11)⋊C411yescharacteristic
1013C22D4×C22⋊D1111yescharacteristic
1014C22#1062333611yescharacteristic
1015C22Q8×C22⋊D1111yescharacteristic
1016C22#1062334711yescharacteristic
1017C22#1062336011yescharacteristic
1018C22#1062336211yescharacteristic
1019C4—24no—
1020C4—24no—
1021C4—24no—
1022C4—42no—
1023C4—42no—
1024C4—81no—
1025C4—81no—
1026C4—224no—
1027C4—442no—
1028C4—442no—
1029C4—442no—
1030C4—442no—
1031C4—881no—
1032C4—881no—
1033C2—444no—
1034C2#1307120911yescharacteristic
1035C2#1307129311yescharacteristic
1036C2#1307135011yescharacteristic
1037C2D4×(C2×D11)⋊C411yescharacteristic
1038C2Q8×(C2×D11)⋊C411yescharacteristic
1039C2#1307161811yescharacteristic
1040C2#1307177811yescharacteristic
1041C2#1307491111yescharacteristic
1042C2#1307492611yescharacteristic
1043C2#1307496311yescharacteristic
1044C2#1307498711yescharacteristic
1045C2#1307507611yescharacteristic
1046C2#1307510611yescharacteristic
1047C2#1307524211yescharacteristic
1048C2#1307527211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#389C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#389D11
hypocenterC11#14362
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#10622587C2semidirect
3. C2×#10622594C2semidirect
5. #13066886C2semidirect
6. #13066870C2semidirect
7. #13066866C2semidirect
8. #13066866C2semidirect
13. #13066849C2semidirect
15. C2×C11×#389C2semidirect
35. C2×#66949C4semidirect
119. C2×(C2×D11)⋊C4Q8semidirect
283. C11×C4⋊C4C22⋊C4semidirect
297. C2×#389D11semidirect
809. C4⋊C4(C2×D11)⋊C4semidirect
818. C11#14362semidirect

Maximal subgroups

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

subgroupindex
C22×#669492
C2×#106225872
C2×#106225942
C2×#106226002
#130668862
#130668702
#130668662
#130668582
#130668542
#130668522
#130668492
(C2×D11)⋊#952
C2×C11×#3892
#1436211