Finite Group Databasebeta

← #14677945

Subgroups — #14677945

Order 2816.

1578 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×#10622586C211yesmaximal, characteristic, complemented
2C2×#10622283C211yesmaximal, characteristic
3C2×#10622282C211yesmaximal, characteristic
4C2×#10622282C211yesmaximal, characteristic
5C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
6#13066877C211yesmaximal, characteristic, complemented
7#13066868C211yesmaximal, characteristic, complemented
8#13066860C211yesmaximal, characteristic
9#13066858C211yesmaximal, characteristic
10#13066854C211yesmaximal, characteristic
11#13066852C211yesmaximal, characteristic
12#13066847C211yesmaximal, characteristic, complemented
13#13066840C211yesmaximal, characteristic, complemented
14#95×Dic11C211yesmaximal, characteristic, complemented
15C11×#1436C211yesmaximal, characteristic, complemented
16C22×C11×C4⋊C4C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
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
51#10622586—24no—
52C4×Dic11⋊C4—24no—
53#10622283C418yescomplemented
54#10622282—24no—
55#10622282—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—41no—
74C2×C42×C11—22no—
75C2×C42×C11—41no—
76C2×C42×C11—41no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4—22no—
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—22no—
91C2×(C2×D11)⋊C4—41no—
92C2×(C2×D11)⋊C4—41no—
93C2×(C2×D11)⋊C4—41no—
94C2×(C2×D11)⋊C4—41no—
95C2×(C2×D11)⋊C4C2×C414yes—
96C2×(C2×D11)⋊C4C2×C414yes—
97C2×(C2×D11)⋊C4C2×C414yes—
98C2×C4⋊Dic11—22no—
99C2×C4⋊Dic11—22no—
100C2×C4⋊Dic11C2×C414yes—
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—22no—
103C2×Dic11⋊C4—22no—
104C2×Dic11⋊C4—22no—
105C2×Dic11⋊C4—22no—
106C2×Dic11⋊C4—22no—
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4D414yes—
110C2×C4×Dic11—22no—
111C2×C4×Dic11—22no—
112C2×C4×Dic11—22no—
113C2×C4×Dic11—22no—
114C2×C4×Dic11—22no—
115C2×C4×Dic11—22no—
116C2×C4×Dic11—41no—
117C2×C4×Dic11—41no—
118C2×C4×Dic11—41no—
119C2×C4×Dic11—41no—
120C2×C4×Dic11C2×C414yes—
121C2×C4×Dic11D414yes—
122C11×#95—22no—
123C11×#95—22no—
124C11×#95—22no—
125C11×#95—41no—
126C11×#95C2×C414yes—
127C11⋊#95—22no—
128C11⋊#95—22no—
129C11⋊#95—22no—
130C11⋊#95—22no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—22no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—22no—
139C11⋊#95C2×C414yes—
140#14077—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×C11#4112yes—
203C22×C4×C11#4112yes—
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×Dic11C22×C412yes—
245C22×Dic11C22×C412yes—
246C22×Dic11C22×C412yes—
247C22×Dic11C2×D412yes—
248C22×Dic11C2×D412yes—
249C22×Dic11C2×D412yes—
250C22×Dic11C2×D412yes—
251C22×Dic11#4112yes—
252C22×Dic11#4112yes—
253C22×Dic11#4112yes—
254C22×Dic11#4112yes—
255C11×C4⋊C4—44no—
256C42×C11—44no—
257(C2×D11)⋊C4—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—
264C4⋊Dic11—28no—
265Dic11⋊C4—28no—
266Dic11⋊C4—28no—
267Dic11⋊C4—44no—
268C4×Dic11—28no—
269C4×Dic11—44no—
270C4×Dic11—44no—
271C4×Dic11—44no—
272C2×#389—111no—
273C2×#388—111no—
274C2×#388—111no—
275C2×#388—111no—
276C2×C4×C4⋊C4—111no—
277#1443—111no—
278#1441—111no—
279#1439—111no—
280#1439—111no—
281#1437—111no—
282#1437—111no—
283#1436—111no—
284#1436D1111yescharacteristic, complemented
285#1434—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×C11C2×#4111yescharacteristic
295C23×C11C2×#4111yescharacteristic
296C23×C11C2×#4111yescharacteristic
297C23×C11C2×#4111yescharacteristic
298C23×C11H(5,𝔽2)11yescharacteristic
299C23×C11H(5,𝔽2)11yescharacteristic
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×C11#11714yes—
385C2×C4×C11C4×D414yes—
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—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—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×Dic11C4×D414yes—
434C2×Dic11#12114yes—
435C22×C4⋊C4—111no—
436C22×C4⋊C4—111no—
437C22×C4⋊C4—111no—
438C22×C4⋊C4—111no—
439C22×C4⋊C4C2×D1111yescharacteristic
440C22×C22⋊C4—111no—
441C22×C22⋊C4—111no—
442C22×C22⋊C4—111no—
443C22×C22⋊C4—111no—
444C22×C22⋊C4—111no—
445C22×C22⋊C4—111no—
446C22×C22⋊C4—111no—
447C22×C42—111no—
448C22×C42—111no—
449C22×C42—111no—
450C22×C42—111no—
451C22×C42C2×D1111yescharacteristic
452#389—224no—
453#388—118no—
454#388—224no—
455#388—224no—
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×#95C2×D1111yescharacteristic
471C2×#95C2×D1111yescharacteristic
472C2×#95C2×D1111yescharacteristic
473C2×#95C2×D1111yescharacteristic
474C2×#95C2×D1111yescharacteristic
475C22×C11C2×#11711yescharacteristic
476C22×C11C2×C4×D411yescharacteristic
477C22×C11C2×C4×D411yescharacteristic
478C22×C11C4×#4111yescharacteristic
479C22×C11C4×#4111yescharacteristic
480C22×C11#52011yescharacteristic
481C22×C11#52011yescharacteristic
482C22×C11C2×#12111yescharacteristic
483C22×C11#52511yescharacteristic
484C22×C11#52911yescharacteristic
485C22×C11#52911yescharacteristic
486C22×C11#52911yescharacteristic
487C22×C11#53211yescharacteristic
488C22×C11#53211yescharacteristic
489C22×C11#53211yescharacteristic
490C22×C11#53411yescharacteristic
491C22×C11#53611yescharacteristic
492C22×C11#53911yescharacteristic
493C22×C11#53911yescharacteristic
494C22×C11#54611yescharacteristic
495C22×C11#54611yescharacteristic
496C22×C11#54811yescharacteristic
497C22×C11#54811yescharacteristic
498C22×C11#55111yescharacteristic
499C22×C11#55211yescharacteristic
500C22×C11#55211yescharacteristic
501C22×C11#55311yescharacteristic
502C22×C11#55311yescharacteristic
503C22×C11#55311yescharacteristic
504C22×C11#55311yescharacteristic
505C22×C11#55611yescharacteristic
506C22×C11#55611yescharacteristic
507C22×C11#55611yescharacteristic
508C22×C11#55611yescharacteristic
509C22×C11#55911yescharacteristic
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—24no—
534Dic11—42no—
535Dic11—42no—
536Dic11—42no—
537Dic11—42no—
538Dic11—42no—
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—41no—
557C2×C4⋊C4—114no—
558C2×C4⋊C4—114no—
559C2×C4⋊C4—222no—
560C2×C4⋊C4—222no—
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—222no—
569C2×C22⋊C4—114no—
570C2×C22⋊C4—114no—
571C2×C22⋊C4—114no—
572C2×C22⋊C4—222no—
573C2×C22⋊C4—222no—
574C2×C22⋊C4—222no—
575C2×C22⋊C4—222no—
576C2×C22⋊C4—222no—
577C2×C22⋊C4—222no—
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—441no—
587C2×C22⋊C4—441no—
588C2×C22⋊C4—441no—
589C2×C22⋊C4—441no—
590C2×C42—22no—
591C2×C42—41no—
592C2×C42—41no—
593C2×C42—114no—
594C2×C42—114no—
595C2×C42—222no—
596C2×C42—222no—
597C2×C42—222no—
598C2×C42—222no—
599C2×C42—222no—
600C2×C42—222no—
601C2×C42—441no—
602C2×C42—441no—
603C2×C42—441no—
604C2×C42—441no—
605#95—22no—
606#95—22no—
607#95—22no—
608#95—41no—
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—222no—
618#95—222no—
619#95—222no—
620#95—222no—
621#95—222no—
622#95C4×D1114yes—
623C2×C11#229311yescharacteristic
624C2×C11C4×#12111yescharacteristic
625C2×C11#232211yescharacteristic
626C2×C11#234711yescharacteristic
627C2×C11#235211yescharacteristic
628C2×C11#236711yescharacteristic
629C2×C11#237311yescharacteristic
630C2×C11#254311yescharacteristic
631C2×C11#254511yescharacteristic
632C2×C11#255811yescharacteristic
633C2×C11#256011yescharacteristic
634C2×C11#259411yescharacteristic
635C2×C11#259611yescharacteristic
636C2×C11#260211yescharacteristic
637C2×C11#260411yescharacteristic
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—112no—
703C22×C4—112no—
704C22×C4—112no—
705C22×C4—112no—
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×C4#433912yes—
749C22×C4D4×D1112yes—
750C22×C4D4×D1112yes—
751C22×C4#434312yes—
752C22×C4#434312yes—
753C4⋊C4—44no—
754C4⋊C4—228no—
755C4⋊C4—228no—
756C4⋊C4—228no—
757C4⋊C4—444no—
758C22⋊C4—228no—
759C22⋊C4—228no—
760C22⋊C4—228no—
761C22⋊C4—444no—
762C22⋊C4—444no—
763C22⋊C4—444no—
764C22⋊C4—444no—
765C42—44no—
766C42—228no—
767C42—444no—
768C42—444no—
769C42—444no—
770C11#1407711yescharacteristic, 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×#433911yescharacteristic
809C23C2×D4×D1111yescharacteristic
810C23C2×D4×D1111yescharacteristic
811C23#6703711yescharacteristic
812C23#6703711yescharacteristic
813C23C2×#434311yescharacteristic
814C23C2×#434311yescharacteristic
815C23#41×D1111yescharacteristic
816C23#41×D1111yescharacteristic
817C23#41×D1111yescharacteristic
818C23#41×D1111yescharacteristic
819C23#6704311yescharacteristic
820C23#6704311yescharacteristic
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—114no—
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—222no—
888C2×C4—222no—
889C2×C4—222no—
890C2×C4—222no—
891C2×C4—222no—
892C2×C4—222no—
893C2×C4—222no—
894C2×C4—222no—
895C2×C4—222no—
896C2×C4—222no—
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×C4#6692514yes—
918C2×C4#6694614yes—
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—
934C22C2×#6692511yescharacteristic
935C22#1062302111yescharacteristic
936C22C2×#6694611yescharacteristic
937C22#1062304511yescharacteristic
938C22#1062305311yescharacteristic
939C22#1062306211yescharacteristic
940C22#1062306411yescharacteristic
941C22#1062307111yescharacteristic
942C22C4×D4×D1111yescharacteristic
943C22#1062307711yescharacteristic
944C22#1062307711yescharacteristic
945C22#1062307911yescharacteristic
946C22#1062307911yescharacteristic
947C22#1062308311yescharacteristic
948C22#1062308911yescharacteristic
949C22C4×#434311yescharacteristic
950C22#1062311111yescharacteristic
951C22#1062311111yescharacteristic
952C22#1062311511yescharacteristic
953C22#1062312011yescharacteristic
954C22D11×#12111yescharacteristic
955C22#1062314111yescharacteristic
956C22#1062315811yescharacteristic
957C22#1062316811yescharacteristic
958C22#1062317611yescharacteristic
959C22#1062317611yescharacteristic
960C22#1062317911yescharacteristic
961C22#1062319211yescharacteristic
962C22#1062319511yescharacteristic
963C22#1062320811yescharacteristic
964C22#1062322211yescharacteristic
965C22#1062322511yescharacteristic
966C22#1062323311yescharacteristic
967C22#1062323311yescharacteristic
968C22#1062325611yescharacteristic
969C4—24no—
970C4—24no—
971C4—42no—
972C4—42no—
973C4—42no—
974C4—81no—
975C4—81no—
976C4—224no—
977C4—224no—
978C4—442no—
979C4—442no—
980C4—442no—
981C4—442no—
982C4—442no—
983C2—882no—
984C2#1307107711yescharacteristic
985C2#1307112411yescharacteristic
986C2#1307128411yescharacteristic
987C2#1307150511yescharacteristic
988C2#1307153911yescharacteristic
989C2#1307168211yescharacteristic
990C2#1307174211yescharacteristic
991C2#1307357511yescharacteristic
992C2#1307359411yescharacteristic
993C2#1307373711yescharacteristic
994C2#1307376711yescharacteristic
995C2#1307412911yescharacteristic
996C2#1307415911yescharacteristic
997C2#1307423211yescharacteristic
998C2#1307425311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1436D11
hypocenterC11#14077
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
1. C2×#10622586C2semidirect
5. C2×C4×Dic11⋊C4C2semidirect
6. #13066877C2semidirect
7. #13066868C2semidirect
12. #13066847C2semidirect
13. #13066840C2semidirect
14. #95×Dic11C2semidirect
15. C11×#1436C2semidirect
53. #10622283C4semidirect
284. #1436D11semidirect
770. C11#14077semidirect

Maximal subgroups

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

subgroupindex
C2×#106225862
C2×#106222832
C2×#106222822
C2×C4×Dic11⋊C42
#130668772
#130668682
#130668602
#130668582
#130668542
#130668522
#130668472
#130668402
#95×Dic112
C11×#14362
#1407711