Finite Group Databasebeta

← #14680652

Subgroups — #14680652

Order 2816.

1506 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622607C211yesmaximal, characteristic
2C2×#10622553C211yesmaximal, characteristic
3C2×#10622603C211yesmaximal, characteristic
4C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
5#13066874C211yesmaximal, characteristic, complemented
6#13066869C211yesmaximal, characteristic, complemented
7#13066868C211yesmaximal, characteristic, complemented
8#13066867C211yesmaximal, characteristic, complemented
9#13066864C211yesmaximal, characteristic
10#13066862C211yesmaximal, characteristic
11#13066860C211yesmaximal, characteristic
12#13066852C211yesmaximal, characteristic
13#13066848C211yesmaximal, characteristic, complemented
14Dic11⋊#95C211yesmaximal, characteristic, complemented
15C2×C11×#387C211yesmaximal, characteristic, complemented
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C11×#387—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
52#10622607C418yescomplemented
53#10622603—24no—
54#10622553—24no—
55C4×C4⋊Dic11—24no—
56C24×D11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4C2×C414yes—
77C2×C42×C11—22no—
78C2×C42×C11—22no—
79C2×C42×C11D414yes—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—22no—
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—41no—
91C2×(C2×D11)⋊C4—41no—
92C2×(C2×D11)⋊C4—41no—
93C2×(C2×D11)⋊C4—41no—
94C2×(C2×D11)⋊C4—41no—
95C2×(C2×D11)⋊C4—41no—
96C2×(C2×D11)⋊C4—41no—
97C2×(C2×D11)⋊C4—41no—
98C2×(C2×D11)⋊C4C2×C414yes—
99C2×(C2×D11)⋊C4C2×C414yes—
100C2×(C2×D11)⋊C4C2×C414yes—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11—22no—
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11C2×C414yes—
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4—41no—
110C2×Dic11⋊C4—41no—
111C2×Dic11⋊C4—41no—
112C2×Dic11⋊C4—41no—
113C2×Dic11⋊C4—41no—
114C2×Dic11⋊C4—41no—
115C2×Dic11⋊C4C2×C414yes—
116C2×C4×Dic11—22no—
117C2×C4×Dic11—41no—
118C2×C4×Dic11—41no—
119C2×C4×Dic11—41no—
120C2×C4×Dic11—41no—
121C2×C4×Dic11D414yes—
122C11×#95—22no—
123C11×#95—22no—
124C11×#95—22no—
125C11×#95—22no—
126C11⋊#95—22no—
127C11⋊#95—22no—
128C11⋊#95—22no—
129C11⋊#95—22no—
130C11⋊#95—22no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—41no—
134C11⋊#95—41no—
135C11⋊#95—41no—
136C11⋊#95—41no—
137C11⋊#95—41no—
138C11⋊#95—41no—
139C11⋊#95C2×C414yes—
140#14310—111nomaximal, Sylow
141C24×C11C2411yescharacteristic
142C23×D11—21no—
143C23×D11—21no—
144C23×D11—21no—
145C23×D11—21no—
146C23×D11—21no—
147C23×D11—21no—
148C23×D11—21no—
149C23×D11—21no—
150C23×D11—21no—
151C23×D11—21no—
152C23×D11—21no—
153C23×D11—21no—
154C23×D11—21no—
155C23×D11—21no—
156C23×D11C22×C412yes—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
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×C11C22×C412yes—
198C22×C4×C11C22×C412yes—
199C22×C4×C11C22×C412yes—
200C22×C4×C11C2×D412yes—
201C22×C4×C11C2×D412yes—
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2×D412yes—
204C22×C4×C11#4112yes—
205C22×C4×C11#4112yes—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
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×Dic11C22×C412yes—
249C22×Dic11C22×C412yes—
250C22×Dic11C22×C412yes—
251C22×Dic11C2×D412yes—
252C22×Dic11C2×D412yes—
253C22×Dic11#4112yes—
254C22×Dic11#4112yes—
255C11×C4⋊C4—28no—
256C11×C4⋊C4—44no—
257C42×C11—28no—
258(C2×D11)⋊C4—28no—
259(C2×D11)⋊C4—28no—
260(C2×D11)⋊C4—44no—
261(C2×D11)⋊C4—44no—
262(C2×D11)⋊C4—44no—
263(C2×D11)⋊C4—44no—
264(C2×D11)⋊C4—44no—
265C4⋊Dic11—28no—
266C4⋊Dic11—28no—
267Dic11⋊C4—44no—
268Dic11⋊C4—44no—
269Dic11⋊C4—44no—
270C4×Dic11—44no—
271C4×Dic11—44no—
272C2×#396—111no—
273C2×#388—111no—
274C2×#388—111no—
275C2×#387D1111yescharacteristic, complemented
276C2×C4×C4⋊C4—111no—
277#1442—111no—
278#1441—111no—
279#1441—111no—
280#1441—111no—
281#1440—111no—
282#1439—111no—
283#1439—111no—
284#1437—111no—
285#1436—111no—
286C4⋊#95—111no—
287C23×C11C23×C411yescharacteristic
288C23×C11C22×D411yescharacteristic
289C23×C11C22×D411yescharacteristic
290C23×C11C2×#4111yescharacteristic
291C23×C11C2×#4111yescharacteristic
292C23×C11C2×#4111yescharacteristic
293C23×C11C2×#4111yescharacteristic
294C23×C11H(5,𝔽2)11yescharacteristic
295C23×C11H(5,𝔽2)11yescharacteristic
296C23×C11H(5,𝔽2)11yescharacteristic
297C23×C11H(5,𝔽2)11yescharacteristic
298C23×C112−1+411yescharacteristic
299C23×C112−1+411yescharacteristic
300C23×C112−1+411yescharacteristic
301C23×C112−1+411yescharacteristic
302C22×D11—22no—
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—41no—
310C22×D11—41no—
311C22×D11—41no—
312C22×D11—41no—
313C22×D11—41no—
314C22×D11—41no—
315C22×D11—41no—
316C22×D11—41no—
317C22×D11—41no—
318C22×D11—41no—
319C22×D11—41no—
320C22×D11—41no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—41no—
329C22×D11—41no—
330C22×D11—41no—
331C22×D11—41no—
332C22×D11—41no—
333C22×D11—41no—
334C22×D11—41no—
335C22×D11—41no—
336C22×D11—41no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
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—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
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×C11C4×D414yes—
385C2×C4×C11#12114yes—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—41no—
405C2×Dic11—41no—
406C2×Dic11—41no—
407C2×Dic11—41no—
408C2×Dic11—41no—
409C2×Dic11—41no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C2×Dic11—41no—
413C2×Dic11—41no—
414C2×Dic11—41no—
415C2×Dic11—41no—
416C2×Dic11—41no—
417C2×Dic11—41no—
418C2×Dic11—41no—
419C2×Dic11—41no—
420C2×Dic11—41no—
421C2×Dic11—41no—
422C2×Dic11—41no—
423C2×Dic11—41no—
424C2×Dic11—41no—
425C2×Dic11—41no—
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×Dic11C4×D414yes—
435C22×C4⋊C4—111no—
436C22×C4⋊C4—111no—
437C22×C4⋊C4—111no—
438C22×C4⋊C4—111no—
439C22×C4⋊C4—111no—
440C22×C4⋊C4C2×D1111yescharacteristic
441C22×C4⋊C4C2×D1111yescharacteristic
442C22×C22⋊C4—111no—
443C22×C22⋊C4—111no—
444C22×C22⋊C4—111no—
445C22×C22⋊C4—111no—
446C22×C22⋊C4—111no—
447C22×C22⋊C4—111no—
448C22×C22⋊C4—111no—
449C22×C42—111no—
450C22×C42—111no—
451C22×C42C2×D1111yescharacteristic
452#396—118no—
453#388—224no—
454#388—224no—
455#387—24no—
456C4×C4⋊C4—224no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95—111no—
460C2×#95—111no—
461C2×#95—111no—
462C2×#95—111no—
463C2×#95—111no—
464C2×#95—111no—
465C2×#95—111no—
466C2×#95—111no—
467C2×#95—111no—
468C2×#95—111no—
469C2×#95—111no—
470C2×#95—111no—
471C2×#95C2×D1111yescharacteristic
472C2×#95C2×D1111yescharacteristic
473C2×#95C2×D1111yescharacteristic
474C2×#95C2×D1111yescharacteristic
475C22×C11C2×C4×D411yescharacteristic
476C22×C11C2×C4×D411yescharacteristic
477C22×C11C4×#4111yescharacteristic
478C22×C11#51811yescharacteristic
479C22×C11#51911yescharacteristic
480C22×C11#52011yescharacteristic
481C22×C11#52011yescharacteristic
482C22×C11C2×#12111yescharacteristic
483C22×C11#52511yescharacteristic
484C22×C11#52911yescharacteristic
485C22×C11#53211yescharacteristic
486C22×C11#53411yescharacteristic
487C22×C11#53511yescharacteristic
488C22×C11#53611yescharacteristic
489C22×C11#53611yescharacteristic
490C22×C11#53711yescharacteristic
491C22×C11#53711yescharacteristic
492C22×C11#53711yescharacteristic
493C22×C11#53711yescharacteristic
494C22×C11#53811yescharacteristic
495C22×C11#53811yescharacteristic
496C22×C11#53911yescharacteristic
497C22×C11#53911yescharacteristic
498C22×C11#53911yescharacteristic
499C22×C11#53911yescharacteristic
500C22×C11#54011yescharacteristic
501C22×C11#54111yescharacteristic
502C22×C11#54111yescharacteristic
503C22×C11#54111yescharacteristic
504C22×C11#54211yescharacteristic
505C22×C11#54211yescharacteristic
506C22×C11#54211yescharacteristic
507C22×C11#54211yescharacteristic
508C22×C11#54211yescharacteristic
509C22×C11#54211yescharacteristic
510C2×D11—42no—
511C2×D11—42no—
512C2×D11—42no—
513C2×D11—42no—
514C2×D11—42no—
515C2×D11—42no—
516C2×D11—42no—
517C2×D11—81no—
518C2×D11—81no—
519C2×D11—81no—
520C2×D11—81no—
521C2×D11—81no—
522C2×D11—81no—
523C2×D11—81no—
524C2×D11—81no—
525C4×C11—24no—
526C4×C11—24no—
527C4×C11—42no—
528C4×C11—42no—
529C4×C11—42no—
530C4×C11—81no—
531C4×C11—81no—
532Dic11—24no—
533Dic11—42no—
534Dic11—42no—
535Dic11—42no—
536Dic11—42no—
537Dic11—81no—
538Dic11—81no—
539C25—111no—
540C23×C4—111no—
541C23×C4—111no—
542C23×C4—111no—
543C23×C4—111no—
544C23×C4—111no—
545C23×C4—111no—
546C23×C4—111no—
547C23×C4C22×D1111yescharacteristic
548C23×C4C22×D1111yescharacteristic
549C23×C4C22×D1111yescharacteristic
550C23×C4C22×D1111yescharacteristic
551C23×C4C22×D1111yescharacteristic
552C23×C4C22×D1111yescharacteristic
553C23×C4C22×D1111yescharacteristic
554C2×C4⋊C4—22no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—114no—
560C2×C4⋊C4—114no—
561C2×C4⋊C4—222no—
562C2×C4⋊C4—222no—
563C2×C4⋊C4—222no—
564C2×C4⋊C4—222no—
565C2×C4⋊C4—222no—
566C2×C4⋊C4—222no—
567C2×C4⋊C4—222no—
568C2×C4⋊C4—441no—
569C2×C4⋊C4—441no—
570C2×C4⋊C4—441no—
571C2×C4⋊C4—441no—
572C2×C4⋊C4—441no—
573C2×C4⋊C4—441no—
574C2×C4⋊C4C4×D1114yes—
575C2×C22⋊C4—114no—
576C2×C22⋊C4—114no—
577C2×C22⋊C4—114no—
578C2×C22⋊C4—222no—
579C2×C22⋊C4—222no—
580C2×C22⋊C4—222no—
581C2×C22⋊C4—222no—
582C2×C22⋊C4—222no—
583C2×C22⋊C4—222no—
584C2×C22⋊C4—222no—
585C2×C22⋊C4—222no—
586C2×C22⋊C4—222no—
587C2×C22⋊C4—222no—
588C2×C22⋊C4—441no—
589C2×C22⋊C4—441no—
590C2×C22⋊C4—441no—
591C2×C22⋊C4—441no—
592C2×C22⋊C4—441no—
593C2×C22⋊C4—441no—
594C2×C22⋊C4—441no—
595C2×C22⋊C4—441no—
596C2×C42—22no—
597C2×C42—22no—
598C2×C42—114no—
599C2×C42—222no—
600C2×C42—441no—
601C2×C42—441no—
602C2×C42—441no—
603C2×C42—441no—
604C2×C42C22⋊D1114yes—
605#95—22no—
606#95—22no—
607#95—22no—
608#95—22no—
609#95—114no—
610#95—222no—
611#95—222no—
612#95—222no—
613#95—222no—
614#95—222no—
615#95—222no—
616#95—222no—
617#95—441no—
618#95—441no—
619#95—441no—
620#95—441no—
621#95—441no—
622#95—441no—
623C2×C11C4×#12111yescharacteristic
624C2×C11#232311yescharacteristic
625C2×C11#232311yescharacteristic
626C2×C11#232411yescharacteristic
627C2×C11#232511yescharacteristic
628C2×C11#233211yescharacteristic
629C2×C11#233411yescharacteristic
630C2×C11#261811yescharacteristic
631C2×C11#262011yescharacteristic
632C2×C11#263011yescharacteristic
633C2×C11#263711yescharacteristic
634C2×C11#265011yescharacteristic
635C2×C11#265411yescharacteristic
636C2×C11#266211yescharacteristic
637C2×C11#266411yescharacteristic
638D11—82no—
639C24—112no—
640C24—221no—
641C24—221no—
642C24—221no—
643C24—221no—
644C24—221no—
645C24—221no—
646C24—221no—
647C24—221no—
648C24—221no—
649C24—221no—
650C24—221no—
651C24—221no—
652C24—221no—
653C24—221no—
654C24C23×D1111yescharacteristic
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
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—112no—
696C22×C4—112no—
697C22×C4—112no—
698C22×C4—112no—
699C22×C4—112no—
700C22×C4—112no—
701C22×C4—112no—
702C22×C4—221no—
703C22×C4—221no—
704C22×C4—221no—
705C22×C4—221no—
706C22×C4—221no—
707C22×C4—221no—
708C22×C4—221no—
709C22×C4—221no—
710C22×C4—221no—
711C22×C4—221no—
712C22×C4—221no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—221no—
726C22×C4—221no—
727C22×C4—221no—
728C22×C4—221no—
729C22×C4—221no—
730C22×C4—221no—
731C22×C4—221no—
732C22×C4—221no—
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—221no—
742C22×C4—221no—
743C22×C4—221no—
744C22×C4C2×C4×D1112yes—
745C22×C4C2×C4×D1112yes—
746C22×C4C2×C4×D1112yes—
747C22×C4#433912yes—
748C22×C4D4×D1112yes—
749C22×C4#434112yes—
750C22×C4C2×C22⋊D1112yes—
751C22×C4C2×C22⋊D1112yes—
752C22×C4C2×C22⋊D1112yes—
753C4⋊C4—28no—
754C4⋊C4—44no—
755C4⋊C4—228no—
756C4⋊C4—228no—
757C4⋊C4—444no—
758C4⋊C4—444no—
759C4⋊C4—444no—
760C22⋊C4—228no—
761C22⋊C4—228no—
762C22⋊C4—444no—
763C22⋊C4—444no—
764C22⋊C4—444no—
765C22⋊C4—444no—
766C22⋊C4—444no—
767C42—28no—
768C42—444no—
769C42—444no—
770C11#1431011yescharacteristic, complemented, Sylow
771C23—222no—
772C23—222no—
773C23—222no—
774C23—222no—
775C23—222no—
776C23—222no—
777C23—222no—
778C23—441no—
779C23—441no—
780C23—441no—
781C23—441no—
782C23—441no—
783C23—441no—
784C23—441no—
785C23—441no—
786C23—441no—
787C23—441no—
788C23—441no—
789C23—441no—
790C23—441no—
791C23—441no—
792C23—441no—
793C23—441no—
794C23—441no—
795C23—441no—
796C23—441no—
797C23—441no—
798C23—441no—
799C23—441no—
800C23—441no—
801C23—441no—
802C23—441no—
803C23—441no—
804C23—441no—
805C23—441no—
806C23C22×C4×D1111yescharacteristic
807C23C2×#433911yescharacteristic
808C23C2×D4×D1111yescharacteristic
809C23C2×#434111yescharacteristic
810C23#6704011yescharacteristic
811C23#6704011yescharacteristic
812C23#41×D1111yescharacteristic
813C23#41×D1111yescharacteristic
814C23#6704211yescharacteristic
815C23#6704211yescharacteristic
816C23#6704211yescharacteristic
817C23#6704211yescharacteristic
818C23#6704311yescharacteristic
819C23#6704311yescharacteristic
820C23C22×C22⋊D1111yescharacteristic
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—114no—
869C2×C4—222no—
870C2×C4—222no—
871C2×C4—222no—
872C2×C4—222no—
873C2×C4—222no—
874C2×C4—222no—
875C2×C4—222no—
876C2×C4—222no—
877C2×C4—222no—
878C2×C4—222no—
879C2×C4—222no—
880C2×C4—222no—
881C2×C4—222no—
882C2×C4—222no—
883C2×C4—222no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—222no—
887C2×C4—441no—
888C2×C4—441no—
889C2×C4—441no—
890C2×C4—441no—
891C2×C4—441no—
892C2×C4—441no—
893C2×C4—441no—
894C2×C4—441no—
895C2×C4—441no—
896C2×C4—441no—
897C2×C4—441no—
898C2×C4—441no—
899C2×C4—441no—
900C2×C4—441no—
901C2×C4—441no—
902C2×C4—441no—
903C2×C4—441no—
904C2×C4—441no—
905C2×C4—441no—
906C2×C4—441no—
907C2×C4—441no—
908C2×C4—441no—
909C2×C4—441no—
910C2×C4—441no—
911C2×C4—441no—
912C2×C4—441no—
913C2×C4—441no—
914C2×C4—441no—
915C2×C4—441no—
916C2×C4—441no—
917C2×C4C4×C22⋊D1114yes—
918C2×C4#6699214yes—
919C22—442no—
920C22—442no—
921C22—442no—
922C22—442no—
923C22—442no—
924C22—442no—
925C22—442no—
926C22—881no—
927C22—881no—
928C22—881no—
929C22—881no—
930C22—881no—
931C22—881no—
932C22—881no—
933C22—881no—
934C22#1062305211yescharacteristic
935C22#1062305411yescharacteristic
936C22#1062306511yescharacteristic
937C22#1062306611yescharacteristic
938C22C4×#434111yescharacteristic
939C22#1062306911yescharacteristic
940C22C4×D4×D1111yescharacteristic
941C22#1062307811yescharacteristic
942C22#1062310311yescharacteristic
943C22#1062310511yescharacteristic
944C22#1062311311yescharacteristic
945C22#1062311411yescharacteristic
946C22#1062316011yescharacteristic
947C22#1062316011yescharacteristic
948C22#1062317411yescharacteristic
949C22#1062317411yescharacteristic
950C22#1062317911yescharacteristic
951C22#1062318411yescharacteristic
952C22#1062319611yescharacteristic
953C22#1062319611yescharacteristic
954C22#1062322311yescharacteristic
955C22#1062322311yescharacteristic
956C22#1062322711yescharacteristic
957C22#1062322711yescharacteristic
958C22#1062323511yescharacteristic
959C22#1062323511yescharacteristic
960C22#1062324111yescharacteristic
961C22#1062324111yescharacteristic
962C22C2×C4×C22⋊D1111yescharacteristic
963C22C2×#6699211yescharacteristic
964C22#1062334711yescharacteristic
965C22#1062336111yescharacteristic
966C22#1062336311yescharacteristic
967C22#1062336411yescharacteristic
968C22#1062336411yescharacteristic
969C4—24no—
970C4—24no—
971C4—42no—
972C4—42no—
973C4—42no—
974C4—81no—
975C4—81no—
976C4—224no—
977C4—442no—
978C4—442no—
979C4—442no—
980C4—442no—
981C4—881no—
982C4—881no—
983C2—882no—
984C2C4×#6699211yescharacteristic
985C2#1307129211yescharacteristic
986C2#1307129711yescharacteristic
987C2#1307130911yescharacteristic
988C2#1307131511yescharacteristic
989C2#1307136811yescharacteristic
990C2#1307139611yescharacteristic
991C2#1307436211yescharacteristic
992C2#1307437811yescharacteristic
993C2#1307446511yescharacteristic
994C2#1307453011yescharacteristic
995C2#1307463611yescharacteristic
996C2#1307469411yescharacteristic
997C2#1307475611yescharacteristic
998C2#1307477711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#387C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#387D11
hypocenterC11#14310
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
4. C2×C4×C4⋊Dic11C2semidirect
5. #13066874C2semidirect
6. #13066869C2semidirect
7. #13066868C2semidirect
8. #13066867C2semidirect
13. #13066848C2semidirect
14. Dic11⋊#95C2semidirect
15. C2×C11×#387C2semidirect
52. #10622607C4semidirect
275. C2×#387D11semidirect
770. C11#14310semidirect

Maximal subgroups

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

subgroupindex
C2×#106226072
C2×#106225532
C2×#106226032
C2×C4×C4⋊Dic112
#130668742
#130668692
#130668682
#130668672
#130668642
#130668622
#130668602
#130668522
#130668482
Dic11⋊#952
C2×C11×#3872
#1431011