Finite Group Databasebeta

← #14677731

Subgroups — #14677731

Order 2816.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66925C211yesmaximal, characteristic
2C2×#10622283C211yesmaximal, characteristic
3C2×#10622266C211yesmaximal, characteristic, complemented
4C2×#10622281C211yesmaximal, characteristic
5C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
6#13066880C211yesmaximal, characteristic, complemented
7#13066868C211yesmaximal, characteristic, complemented
8#13066864C211yesmaximal, characteristic
9#13066860C211yesmaximal, characteristic
10#13066852C211yesmaximal, characteristic
11#13066851C211yesmaximal, characteristic, complemented
12#13066851C211yesmaximal, characteristic, complemented
13#13066850C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic
15C11×#1434C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C2×#66925—24no—
34C2×#66925—24no—
35C2×#66925—24no—
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
54C4×Dic11⋊C4—24no—
55#10622283—24no—
56#10622281C418yescomplemented
57#10622266—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—22no—
78C22×C4×D11—22no—
79C22×C4×D11C2×C414yes—
80C2×C42×C11—22no—
81C2×C42×C11—22no—
82C2×C42×C11D414yes—
83C2×(C2×D11)⋊C4—22no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—41no—
97C2×(C2×D11)⋊C4—41no—
98C2×(C2×D11)⋊C4C2×C414yes—
99C2×(C2×D11)⋊C4C2×C414yes—
100C2×(C2×D11)⋊C4D414yes—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11—22no—
105C2×C4⋊Dic11—41no—
106C2×C4⋊Dic11C2×C414yes—
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—22no—
111C2×Dic11⋊C4—22no—
112C2×Dic11⋊C4—22no—
113C2×Dic11⋊C4—22no—
114C2×Dic11⋊C4—22no—
115C2×Dic11⋊C4—22no—
116C2×Dic11⋊C4—22no—
117C2×Dic11⋊C4C2×C414yes—
118C2×Dic11⋊C4D414yes—
119C2×C4×Dic11—22no—
120C2×C4×Dic11—22no—
121C2×C4×Dic11—22no—
122C2×C4×Dic11—22no—
123C2×C4×Dic11—22no—
124C2×C4×Dic11—22no—
125C2×C4×Dic11—22no—
126C2×C4×Dic11—22no—
127C2×C4×Dic11—22no—
128#66925—232no—
129C11×#95—22no—
130C11×#95—22no—
131C11×#95—22no—
132C11×#95—41no—
133C11×#95—41no—
134C11×#95C2×C414yes—
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—22no—
145C11⋊#95—41no—
146C11⋊#95C2×C414yes—
147#14063—111nomaximal, Sylow
148C24×C11C2411yescharacteristic
149C23×D11—21no—
150C23×D11—21no—
151C23×D11—21no—
152C23×D11—21no—
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×D11#4112yes—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
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×C11C22×C412yes—
205C22×C4×C11C22×C412yes—
206C22×C4×C11C22×C412yes—
207C22×C4×C11C2×D412yes—
208C22×C4×C11C2×D412yes—
209C22×C4×C11C2×D412yes—
210C22×C4×C11C2×D412yes—
211C22×C4×C11C2×D412yes—
212C22×C4×C11#4112yes—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
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×Dic11C22×C412yes—
252C22×Dic11C22×C412yes—
253C22×Dic11C22×C412yes—
254C22×Dic11C2×D412yes—
255C22×Dic11C2×D412yes—
256C22×Dic11C2×D412yes—
257C22×Dic11#4112yes—
258C22×Dic11#4112yes—
259C22×Dic11#4112yes—
260C22×Dic11#4112yes—
261C22×Dic11#4112yes—
262C2×C4×D11—28no—
263C2×C4×D11—28no—
264C2×C4×D11—28no—
265C2×C4×D11—28no—
266C2×C4×D11—28no—
267C2×C4×D11—28no—
268C2×C4×D11—28no—
269C42×C11—28no—
270(C2×D11)⋊C4—28no—
271(C2×D11)⋊C4—28no—
272(C2×D11)⋊C4—28no—
273(C2×D11)⋊C4—28no—
274(C2×D11)⋊C4—44no—
275(C2×D11)⋊C4—44no—
276C4⋊Dic11—28no—
277C4⋊Dic11—44no—
278Dic11⋊C4—28no—
279Dic11⋊C4—28no—
280Dic11⋊C4—28no—
281Dic11⋊C4—28no—
282C4×Dic11—28no—
283C4×Dic11—28no—
284C4×Dic11—44no—
285C22×#117—111no—
286C2×#388—111no—
287C2×#387—111no—
288C2×#385—111no—
289C2×C4×C4⋊C4—111no—
290#1444—111no—
291#1441—111no—
292#1440—111no—
293#1439—111no—
294#1437—111no—
295#1436—111no—
296#1436—111no—
297#1436—111no—
298#1434D1111yescharacteristic, complemented
299C22⋊#95—111no—
300C23×C11C23×C411yescharacteristic
301C23×C11C22×D411yescharacteristic
302C23×C11C22×D411yescharacteristic
303C23×C11C22×D411yescharacteristic
304C23×C11C2×#4111yescharacteristic
305C23×C11C2×#4111yescharacteristic
306C23×C11C2×#4111yescharacteristic
307C23×C11C2×#4111yescharacteristic
308C23×C11C2×#4111yescharacteristic
309C23×C11C2×#4111yescharacteristic
310C23×C11C2×#4111yescharacteristic
311C23×C11H(5,𝔽2)11yescharacteristic
312C23×C112−1+411yescharacteristic
313C23×C112−1+411yescharacteristic
314C23×C112−1+411yescharacteristic
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
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—41no—
334C22×D11—41no—
335C22×D11—41no—
336C22×D11—41no—
337C22×D11—41no—
338C22×D11—41no—
339C22×D11—41no—
340C22×D11—41no—
341C22×D11—41no—
342C22×D11—41no—
343C22×D11—41no—
344C22×D11—41no—
345C22×D11—41no—
346C22×D11—41no—
347C22×D11—41no—
348C22×D11—41no—
349C22×D11C4×D414yes—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
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—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
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×C11C4×D414yes—
398C2×C4×C11#12014yes—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
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—41no—
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#11714yescomplemented
447C2×Dic11C4×D414yes—
448C4×D11—232no—
449C24×C4—111no—
450C2×#117—224no—
451C2×#117—224no—
452C2×#117—224no—
453C22×C4⋊C4—111no—
454C22×C4⋊C4—111no—
455C22×C4⋊C4—111no—
456C22×C4⋊C4—111no—
457C22×C4⋊C4—111no—
458C22×C4⋊C4—111no—
459C22×C22⋊C4—111no—
460C22×C22⋊C4—111no—
461C22×C22⋊C4—111no—
462C22×C22⋊C4—111no—
463C22×C22⋊C4—111no—
464C22×C22⋊C4—111no—
465C22×C42—111no—
466C22×C42—111no—
467C22×C42—111no—
468C22×C42C2×D1111yescharacteristic
469#388—224no—
470#387—224no—
471#385—118no—
472C4×C4⋊C4—224no—
473C2×#95—111no—
474C2×#95—111no—
475C2×#95—111no—
476C2×#95—111no—
477C2×#95—111no—
478C2×#95—111no—
479C2×#95—111no—
480C2×#95—111no—
481C2×#95—111no—
482C2×#95—111no—
483C2×#95—111no—
484C2×#95—111no—
485C2×#95C2×D1111yescharacteristic
486C2×#95C2×D1111yescharacteristic
487C2×#95C2×D1111yescharacteristic
488C2×#95C2×D1111yescharacteristic
489C2×#95C2×D1111yescharacteristic
490C2×#95C2×D1111yescharacteristic
491C22×C11C2×#11711yescharacteristic
492C22×C11C2×C4×D411yescharacteristic
493C22×C11C2×C4×D411yescharacteristic
494C22×C11C2×C4×D411yescharacteristic
495C22×C11C4×#4111yescharacteristic
496C22×C11#51911yescharacteristic
497C22×C11#52011yescharacteristic
498C22×C11C2×#12011yescharacteristic
499C22×C11#52511yescharacteristic
500C22×C11#52511yescharacteristic
501C22×C11#52511yescharacteristic
502C22×C11#52511yescharacteristic
503C22×C11#52511yescharacteristic
504C22×C11#52911yescharacteristic
505C22×C11#52911yescharacteristic
506C22×C11#53611yescharacteristic
507C22×C11#53711yescharacteristic
508C22×C11#54111yescharacteristic
509C22×C11#54211yescharacteristic
510C22×C11#54611yescharacteristic
511C22×C11#54711yescharacteristic
512C22×C11#54711yescharacteristic
513C22×C11#54711yescharacteristic
514C22×C11#54711yescharacteristic
515C22×C11#54711yescharacteristic
516C22×C11#54811yescharacteristic
517C22×C11#55011yescharacteristic
518C22×C11#55111yescharacteristic
519C22×C11#55211yescharacteristic
520C22×C11#55211yescharacteristic
521C22×C11#55211yescharacteristic
522C22×C11#55211yescharacteristic
523C22×C11#55511yescharacteristic
524C22×C11#55611yescharacteristic
525C22×C11#55611yescharacteristic
526C2×D11—24no—
527C2×D11—24no—
528C2×D11—24no—
529C2×D11—42no—
530C2×D11—42no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—42no—
539C2×D11—42no—
540C2×D11—42no—
541C4×C11—24no—
542C4×C11—24no—
543C4×C11—42no—
544C4×C11—42no—
545C4×C11—42no—
546C4×C11—81no—
547C4×C11—81no—
548Dic11—24no—
549Dic11—24no—
550Dic11—42no—
551Dic11—42no—
552Dic11—42no—
553Dic11—42no—
554Dic11—42no—
555C25—111no—
556C23×C4—111no—
557C23×C4—111no—
558C23×C4—111no—
559C23×C4—111no—
560C23×C4—111no—
561C23×C4—111no—
562C23×C4—111no—
563C23×C4—114no—
564C23×C4—222no—
565C23×C4—222no—
566C23×C4—222no—
567C23×C4—222no—
568C23×C4—222no—
569C23×C4—222no—
570C23×C4C22×D1111yescharacteristic
571C23×C4C22×D1111yescharacteristic
572C23×C4C22×D1111yescharacteristic
573C23×C4C22×D1111yescharacteristic
574C23×C4C22×D1111yescharacteristic
575C23×C4C22×D1111yescharacteristic
576C23×C4C22×D1111yescharacteristic
577#117—2232no—
578C2×C4⋊C4—114no—
579C2×C4⋊C4—114no—
580C2×C4⋊C4—114no—
581C2×C4⋊C4—222no—
582C2×C4⋊C4—222no—
583C2×C4⋊C4—222no—
584C2×C4⋊C4—222no—
585C2×C4⋊C4—222no—
586C2×C4⋊C4—222no—
587C2×C4⋊C4—222no—
588C2×C4⋊C4—222no—
589C2×C4⋊C4—222no—
590C2×C4⋊C4—222no—
591C2×C4⋊C4—222no—
592C2×C4⋊C4—222no—
593C2×C4⋊C4—222no—
594C2×C4⋊C4—222no—
595C2×C4⋊C4—441no—
596C2×C22⋊C4—114no—
597C2×C22⋊C4—114no—
598C2×C22⋊C4—114no—
599C2×C22⋊C4—222no—
600C2×C22⋊C4—222no—
601C2×C22⋊C4—222no—
602C2×C22⋊C4—222no—
603C2×C22⋊C4—222no—
604C2×C22⋊C4—222no—
605C2×C22⋊C4—222no—
606C2×C22⋊C4—222no—
607C2×C22⋊C4—222no—
608C2×C22⋊C4—222no—
609C2×C22⋊C4—222no—
610C2×C22⋊C4—222no—
611C2×C22⋊C4—222no—
612C2×C22⋊C4—441no—
613C2×C22⋊C4—441no—
614C2×C42—22no—
615C2×C42—22no—
616C2×C42—222no—
617C2×C42—222no—
618C2×C42—222no—
619C2×C42—222no—
620C2×C42—222no—
621C2×C42—222no—
622C2×C42—222no—
623C2×C42—222no—
624C2×C42—222no—
625C2×C42D4414yes—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—41no—
630#95—41no—
631#95—114no—
632#95—222no—
633#95—222no—
634#95—222no—
635#95—222no—
636#95—222no—
637#95—222no—
638#95—222no—
639#95—222no—
640#95—222no—
641#95—222no—
642#95—441no—
643#95C4×D1114yes—
644C2×C11#229011yescharacteristic
645C2×C11C4×#12011yescharacteristic
646C2×C11#232311yescharacteristic
647C2×C11#234411yescharacteristic
648C2×C11#235411yescharacteristic
649C2×C11#235911yescharacteristic
650C2×C11#236211yescharacteristic
651C2×C11#240611yescharacteristic
652C2×C11#240711yescharacteristic
653C2×C11#247411yescharacteristic
654C2×C11#247511yescharacteristic
655C2×C11#247811yescharacteristic
656C2×C11#247911yescharacteristic
657C2×C11#259911yescharacteristic
658C2×C11#260911yescharacteristic
659D11—44no—
660C24—112no—
661C24—112no—
662C24—112no—
663C24—221no—
664C24—221no—
665C24—221no—
666C24—221no—
667C24—221no—
668C24—221no—
669C24—221no—
670C24—221no—
671C24—221no—
672C24—221no—
673C24—221no—
674C24—221no—
675C24C23×D1111yescharacteristic
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
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—112no—
717C22×C4—112no—
718C22×C4—112no—
719C22×C4—112no—
720C22×C4—112no—
721C22×C4—112no—
722C22×C4—112no—
723C22×C4—112no—
724C22×C4—112no—
725C22×C4—112no—
726C22×C4—112no—
727C22×C4—228no—
728C22×C4—228no—
729C22×C4—228no—
730C22×C4—228no—
731C22×C4—228no—
732C22×C4—228no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—221no—
736C22×C4—221no—
737C22×C4—221no—
738C22×C4—221no—
739C22×C4—221no—
740C22×C4—221no—
741C22×C4—228no—
742C22×C4—221no—
743C22×C4—221no—
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×C4C2×C4×D1112yes—
773C22×C4C2×C4×D1112yes—
774C22×C4C2×C4×D1112yes—
775C22×C4C2×D4412yes—
776C22×C4C2×D4412yes—
777C22×C4C2×D4412yes—
778C22×C4#433912yes—
779C22×C4D4×D1112yes—
780C22×C4D4×D1112yes—
781C4⋊C4—228no—
782C4⋊C4—228no—
783C4⋊C4—228no—
784C4⋊C4—228no—
785C4⋊C4—228no—
786C4⋊C4—444no—
787C22⋊C4—228no—
788C22⋊C4—228no—
789C22⋊C4—228no—
790C22⋊C4—228no—
791C22⋊C4—444no—
792C22⋊C4—444no—
793C42—28no—
794C42—228no—
795C42—228no—
796C42—444no—
797C11#1406311yescharacteristic, complemented, Sylow
798C23—114no—
799C23—222no—
800C23—222no—
801C23—222no—
802C23—222no—
803C23—222no—
804C23—222no—
805C23—222no—
806C23—222no—
807C23—222no—
808C23—222no—
809C23—222no—
810C23—222no—
811C23—222no—
812C23—222no—
813C23—222no—
814C23—222no—
815C23—222no—
816C23—222no—
817C23—441no—
818C23—441no—
819C23—441no—
820C23—441no—
821C23—441no—
822C23—441no—
823C23—441no—
824C23—441no—
825C23—441no—
826C23—441no—
827C23—441no—
828C23—441no—
829C23—441no—
830C23—441no—
831C23—441no—
832C23—441no—
833C23C22×C4×D1111yescharacteristic
834C23C22×D4411yescharacteristic
835C23C2×#433911yescharacteristic
836C23C2×D4×D1111yescharacteristic
837C23C2×D4×D1111yescharacteristic
838C23#6703711yescharacteristic
839C23#6704011yescharacteristic
840C23#41×D1111yescharacteristic
841C23#41×D1111yescharacteristic
842C23#41×D1111yescharacteristic
843C23#41×D1111yescharacteristic
844C23#41×D1111yescharacteristic
845C23#41×D1111yescharacteristic
846C23#6704311yescharacteristic
847C23#6704311yescharacteristic
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—114no—
896C2×C4—114no—
897C2×C4—2232no—
898C2×C4—222no—
899C2×C4—222no—
900C2×C4—222no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—222no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—222no—
908C2×C4—222no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—222no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—222no—
916C2×C4—222no—
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—441no—
926C2×C4—441no—
927C2×C4—441no—
928C2×C4—441no—
929C2×C4—441no—
930C2×C4—441no—
931C2×C4—441no—
932C2×C4—441no—
933C2×C4—441no—
934C2×C4—441no—
935C2×C4—441no—
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×C4C4×D4414yes—
946C2×C4#6693514yes—
947C22—224no—
948C22—224no—
949C22—224no—
950C22—442no—
951C22—442no—
952C22—442no—
953C22—442no—
954C22—442no—
955C22—442no—
956C22—442no—
957C22—442no—
958C22—442no—
959C22—442no—
960C22—442no—
961C22—442no—
962C22C2×C4×D4411yescharacteristic
963C22C2×#6693511yescharacteristic
964C22#1062304111yescharacteristic
965C22D11×#11711yescharacteristic
966C22#1062305311yescharacteristic
967C22#1062305511yescharacteristic
968C22#1062305511yescharacteristic
969C22#1062305511yescharacteristic
970C22#1062305711yescharacteristic
971C22#1062305911yescharacteristic
972C22#1062305911yescharacteristic
973C22C4×D4×D1111yescharacteristic
974C22C4×D4×D1111yescharacteristic
975C22#1062307711yescharacteristic
976C22#1062307811yescharacteristic
977C22#1062307811yescharacteristic
978C22#1062309211yescharacteristic
979C22#1062310311yescharacteristic
980C22#1062311411yescharacteristic
981C22#1062313011yescharacteristic
982C22#1062314311yescharacteristic
983C22#1062316211yescharacteristic
984C22#1062316411yescharacteristic
985C22#1062318611yescharacteristic
986C22#1062318611yescharacteristic
987C22#1062318611yescharacteristic
988C22#1062318611yescharacteristic
989C22#1062320111yescharacteristic
990C22#1062321011yescharacteristic
991C22#1062322411yescharacteristic
992C22#1062322411yescharacteristic
993C22#1062323311yescharacteristic
994C22#1062323311yescharacteristic
995C22#1062323911yescharacteristic
996C22#1062323911yescharacteristic
997C4—24no—
998C4—24no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—81no—
1003C4—81no—
1004C4—224no—
1005C4—224no—
1006C4—442no—
1007C4—442no—
1008C4—442no—
1009C4—442no—
1010C4—442no—
1011C2—444no—
1012C2#1307106011yescharacteristic
1013C2C4×#6693511yescharacteristic
1014C2#1307129911yescharacteristic
1015C2#1307148211yescharacteristic
1016C2#1307156211yescharacteristic
1017C2#1307160511yescharacteristic
1018C2#1307163811yescharacteristic
1019C2#1307195311yescharacteristic
1020C2#1307196211yescharacteristic
1021C2#1307277411yescharacteristic
1022C2#1307278911yescharacteristic
1023C2#1307283411yescharacteristic
1024C2#1307284911yescharacteristic
1025C2#1307419511yescharacteristic
1026C2#1307429311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1434D11
hypocenterC11#14063
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. C2×#10622266C2semidirect
5. C2×C4×Dic11⋊C4C2semidirect
6. #13066880C2semidirect
7. #13066868C2semidirect
11. #13066851C2semidirect
12. #13066851C2semidirect
13. #13066850C2semidirect
15. C11×#1434C2semidirect
56. #10622281C4semidirect
298. #1434D11semidirect
446. C2×Dic11#117semidirect
797. C11#14063semidirect

Maximal subgroups

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

subgroupindex
C22×#669252
C2×#106222832
C2×#106222662
C2×#106222812
C2×C4×Dic11⋊C42
#130668802
#130668682
#130668642
#130668602
#130668522
#130668512
#130668502
(C2×D11)⋊#952
C11×#14342
#1406311