Finite Group Databasebeta

← C2×#13076748 #14960092

Subgroups — C2×#13076748 #14960092

Order 2816.

2434 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076748C2116yesmaximal, direct product factor
2C2×#10622562C211yesmaximal, characteristic, complemented
3C2×#10622270C211yesmaximal, characteristic, complemented
4C2×#10622565C211yesmaximal, characteristic, complemented
5C2×#10622565C211yesmaximal, characteristic, complemented
6C2×#10622561C211yesmaximal, characteristic, complemented
7C2×#10622561C211yesmaximal, characteristic, complemented
8C2×#10622835C211yesmaximal, characteristic, complemented
9C2×#10622835C211yesmaximal, characteristic, complemented
10C2×#10622835C211yesmaximal, characteristic, complemented
11C2×#10622835C211yesmaximal, characteristic, complemented
12C2×#10622835C211yesmaximal, characteristic, complemented
13C2×#10622834C211yesmaximal, characteristic, complemented
14C2×#10622564C211yesmaximal, characteristic, complemented
15C2×#10622265C211yesmaximal, characteristic, complemented
16C2×C11×#392C211yesmaximal, characteristic
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C22×C4⋊Dic11C2211yescharacteristic
36C22×C4⋊Dic11C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C11×#392C2218yes—
45C2×C11×#95C2211yescharacteristic
46#10622835C2218yescomplemented
47#10622835C2218yescomplemented
48#10622835C2218yescomplemented
49#10622835C2218yescomplemented
50#10622835C2218yescomplemented
51#10622834C2218yescomplemented
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59#10622565C2218yescomplemented
60#10622565C2218yescomplemented
61#10622564C2218yescomplemented
62#10622562C2218yescomplemented
63#10622561C2218yescomplemented
64#10622561C2218yescomplemented
65#10622270C2218yescomplemented
66#10622265C2218yescomplemented
67C25×C11C2311yescharacteristic
68C25×C11C2311yescharacteristic
69C25×C11C2311yescharacteristic
70C22×D4×C11—24no—
71C22×D4×C11—42no—
72C22×D4×C11—42no—
73C22×D4×C11—42no—
74C22×D4×C11—42no—
75C22×D4×C11—42no—
76C22×D4×C11—42no—
77C22×D4×C11—42no—
78C22×D4×C11—42no—
79C22×D4×C11C2314yes—
80C22×D4×C11C2314yes—
81C22×D4×C11C2314yes—
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C2×C11×C22⋊C4—24no—
95C2×C11×C22⋊C4—42no—
96C2×C11×C22⋊C4—42no—
97C2×C11×C22⋊C4C2314yes—
98C2×C11×C22⋊C4C2314yes—
99C2×C11×C22⋊C4C2314yes—
100C2×C22⋊Dic11—42no—
101C2×C22⋊Dic11—42no—
102C2×C22⋊Dic11—42no—
103C2×C22⋊Dic11—42no—
104C2×C22⋊Dic11—42no—
105C2×C22⋊Dic11—42no—
106C2×C22⋊Dic11—42no—
107C2×C22⋊Dic11—42no—
108C2×C22⋊Dic11—42no—
109C2×C22⋊Dic11—42no—
110C2×C22⋊Dic11—42no—
111C2×C22⋊Dic11—42no—
112C2×C22⋊Dic11C2314yes—
113C2×C22⋊Dic11C2314yes—
114C2×C22⋊Dic11C2314yes—
115C2×C22⋊Dic11C2314yes—
116C2×C22⋊Dic11C2314yes—
117C2×C22⋊Dic11C2314yes—
118C2×C22⋊Dic11C2314yes—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124C2×C4⋊Dic11—42no—
125C2×C4⋊Dic11—42no—
126C2×C4⋊Dic11C2314yes—
127C2×C4⋊Dic11C2314yes—
128C2×Dic11⋊C4—24no—
129C2×Dic11⋊C4—42no—
130C2×Dic11⋊C4—42no—
131C2×Dic11⋊C4—42no—
132C2×Dic11⋊C4—42no—
133C2×Dic11⋊C4—42no—
134C2×Dic11⋊C4C2314yes—
135C2×Dic11⋊C4C2314yes—
136C2×Dic11⋊C4C2314yes—
137C2×Dic11⋊C4C2314yes—
138C2×Dic11⋊C4C2314yes—
139C2×Dic11⋊C4C2314yes—
140C2×C4×Dic11—42no—
141C2×C4×Dic11C2314yes—
142C11×#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C2×#2829—111nomaximal, Sylow
151C24×C11—22no—
152C24×C11—22no—
153C24×C11—22no—
154C24×C11—22no—
155C24×C11—22no—
156C24×C11—22no—
157C24×C11—22no—
158C24×C11—22no—
159C24×C11—22no—
160C24×C11—22no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
165C24×C11—22no—
166C24×C11—22no—
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11—22no—
172C24×C11C2412yes—
173C24×C11C2412yes—
174C24×C11C2412yes—
175C24×C11C2411yescharacteristic
176C2×D4×C11—28no—
177C2×D4×C11—44no—
178C2×D4×C11—44no—
179C2×D4×C11—44no—
180C2×D4×C11—44no—
181C2×D4×C11—44no—
182C2×D4×C11—44no—
183C2×D4×C11—44no—
184C2×D4×C11—44no—
185C2×D4×C11—416no—
186C2×D4×C11—416no—
187C2×D4×C11—416no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11#4114yes—
200C22×C4×C11C2412yes—
201C22×C4×C11C2412yes—
202C22×C4×C11C2412yes—
203C22×C4×C11C2412yes—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11C2412yes—
229C22×Dic11C2412yes—
230C22×Dic11C2412yes—
231C22×Dic11C2412yes—
232C22×Dic11C2412yes—
233C22×Dic11C2412yes—
234C22×Dic11C2412yes—
235C22×Dic11C2412yes—
236C11×C22⋊C4—28no—
237C11×C22⋊C4—44no—
238C11×C22⋊C4—44no—
239C22⋊Dic11—44no—
240C22⋊Dic11—44no—
241C22⋊Dic11—44no—
242C22⋊Dic11—44no—
243C22⋊Dic11—44no—
244C22⋊Dic11—44no—
245C22⋊Dic11—44no—
246C22⋊Dic11—44no—
247C22⋊Dic11—44no—
248C22⋊Dic11—44no—
249C22⋊Dic11—44no—
250C22⋊Dic11—44no—
251C4⋊Dic11—44no—
252C4⋊Dic11—44no—
253Dic11⋊C4—28no—
254Dic11⋊C4—44no—
255Dic11⋊C4—44no—
256Dic11⋊C4—44no—
257Dic11⋊C4—44no—
258Dic11⋊C4—44no—
259C4×Dic11—44no—
260#2829—1116no—
261C2×#399—111no—
262C2×#398—111no—
263C2×#397—111no—
264C2×#397—111no—
265C2×#396—111no—
266C2×#396—111no—
267C2×#394—111no—
268C2×#394—111no—
269C2×#394—111no—
270C2×#394—111no—
271C2×#394—111no—
272C2×#392D1111yescharacteristic
273C2×#390—111no—
274C2×#388—111no—
275C2×#387—111no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—44no—
298C23×C11—44no—
299C23×C11—44no—
300C23×C11—44no—
301C23×C11—44no—
302C23×C11—44no—
303C23×C11—44no—
304C23×C11—44no—
305C23×C11—44no—
306C23×C11—44no—
307C23×C11—44no—
308C23×C11—44no—
309C23×C11—44no—
310C23×C11—44no—
311C23×C11—44no—
312C23×C11—44no—
313C23×C11—44no—
314C23×C11—44no—
315C23×C11—44no—
316C23×C11—44no—
317C23×C11—44no—
318C23×C11C2×#4112yes—
319C23×C11H(5,𝔽2)12yes—
320C23×C11H(5,𝔽2)12yes—
321C23×C11H(5,𝔽2)12yes—
322C23×C11H(5,𝔽2)12yes—
323C23×C11H(5,𝔽2)12yes—
324C23×C112−1+412yes—
325C23×C11C2511yescharacteristic
326D4×C11—416no—
327D4×C11—416no—
328D4×C11—416no—
329C2×C4×C11—28no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—44no—
342C2×C4×C11—44no—
343C2×C4×C11—44no—
344C2×C4×C11C2×#4114yes—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—44no—
370C2×Dic11—44no—
371C2×Dic11—44no—
372C2×Dic11—44no—
373C2×Dic11—44no—
374C2×Dic11—44no—
375C2×Dic11—44no—
376C2×Dic11—44no—
377C23×D4C2×D1111yescharacteristic
378C23×D4C2×D1111yescharacteristic
379C23×D4C2×D1111yescharacteristic
380C22×C4⋊C4—111no—
381C22×C4⋊C4—111no—
382C22×C4⋊C4—111no—
383C22×C4⋊C4—111no—
384C22×C4⋊C4—111no—
385C22×C4⋊C4—111no—
386C22×C4⋊C4—111no—
387C22×C4⋊C4—111no—
388C22×C22⋊C4—111no—
389C22×C22⋊C4—111no—
390C22×C22⋊C4—111no—
391C22×C22⋊C4—111no—
392C22×C22⋊C4—111no—
393C22×C22⋊C4—111no—
394C22×C22⋊C4—111no—
395C22×C22⋊C4—111no—
396C22×C22⋊C4—111no—
397C22×C22⋊C4—111no—
398C22×C22⋊C4—111no—
399C22×C22⋊C4—111no—
400C22×C22⋊C4C2×D1111yescharacteristic
401C22×C22⋊C4C2×D1111yescharacteristic
402C22×C22⋊C4C2×D1111yescharacteristic
403C22×C42—111no—
404#399—118no—
405#398—118no—
406#397—118no—
407#397—118no—
408#396—118no—
409#396—118no—
410#394—118no—
411#394—118no—
412#394—118no—
413#394—118no—
414#394—118no—
415#392C2×D1118yes—
416#390—118no—
417#388—118no—
418#387—118no—
419C2×#95—111no—
420C2×#95—111no—
421C2×#95—111no—
422C2×#95—111no—
423C2×#95—111no—
424C2×#95—111no—
425C2×#95—111no—
426C2×#95C2×D1111yescharacteristic
427C22×C11—42no—
428C22×C11—42no—
429C22×C11—42no—
430C22×C11—42no—
431C22×C11—42no—
432C22×C11—42no—
433C22×C11—42no—
434C22×C11—42no—
435C22×C11—42no—
436C22×C11—42no—
437C22×C11—42no—
438C22×C11—42no—
439C22×C11—42no—
440C22×C11—42no—
441C22×C11—42no—
442C22×C11—42no—
443C22×C11—42no—
444C22×C11—42no—
445C22×C11—42no—
446C22×C11—42no—
447C22×C11—42no—
448C22×C11—88no—
449C22×C11—88no—
450C22×C11—88no—
451C22×C11#53814yes—
452C22×C11#54014yes—
453C22×C11#54214yes—
454C22×C11#56014yes—
455C22×C11#56014yes—
456C22×C11#56214yes—
457C22×C11#56214yes—
458C22×C11C22×#4111yescharacteristic
459C22×C11C2×H(5,𝔽2)11yescharacteristic
460C22×C11C2×H(5,𝔽2)11yescharacteristic
461C22×C11C2×H(5,𝔽2)11yescharacteristic
462C22×C11C2×H(5,𝔽2)11yescharacteristic
463C22×C11C2×H(5,𝔽2)11yescharacteristic
464C22×C11C2×2−1+411yescharacteristic
465C4×C11—24no—
466C4×C11—42no—
467C4×C11—42no—
468C4×C11—42no—
469Dic11—42no—
470Dic11—42no—
471Dic11—42no—
472Dic11—42no—
473Dic11—42no—
474Dic11—42no—
475Dic11—42no—
476Dic11—42no—
477C25C22×D1111yescharacteristic
478C25C22×D1111yescharacteristic
479C25C22×D1111yescharacteristic
480C22×D4—24no—
481C22×D4—42no—
482C22×D4—42no—
483C22×D4—42no—
484C22×D4—42no—
485C22×D4—42no—
486C22×D4—42no—
487C22×D4—42no—
488C22×D4—42no—
489C22×D4C22×D1114yes—
490C22×D4C22×D1114yes—
491C22×D4C22×D1114yes—
492C23×C4—111no—
493C23×C4—111no—
494C23×C4—111no—
495C23×C4—111no—
496C23×C4—111no—
497C23×C4—111no—
498C23×C4—111no—
499C23×C4—111no—
500C23×C4C22×D1111yescharacteristic
501C23×C4C22×D1111yescharacteristic
502C23×C4C22×D1111yescharacteristic
503C23×C4C22×D1111yescharacteristic
504C2×C4⋊C4—114no—
505C2×C4⋊C4—114no—
506C2×C4⋊C4—114no—
507C2×C4⋊C4—114no—
508C2×C4⋊C4—114no—
509C2×C4⋊C4—114no—
510C2×C4⋊C4—114no—
511C2×C4⋊C4—114no—
512C2×C4⋊C4—224no—
513C2×C4⋊C4—442no—
514C2×C4⋊C4—442no—
515C2×C4⋊C4—442no—
516C2×C4⋊C4—442no—
517C2×C4⋊C4—442no—
518C2×C4⋊C4—442no—
519C2×C4⋊C4—442no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—114no—
524C2×C22⋊C4—114no—
525C2×C22⋊C4—114no—
526C2×C22⋊C4—114no—
527C2×C22⋊C4—114no—
528C2×C22⋊C4—114no—
529C2×C22⋊C4—114no—
530C2×C22⋊C4—114no—
531C2×C22⋊C4—114no—
532C2×C22⋊C4—114no—
533C2×C22⋊C4—114no—
534C2×C22⋊C4—114no—
535C2×C22⋊C4—442no—
536C2×C22⋊C4—442no—
537C2×C22⋊C4—442no—
538C2×C22⋊C4—442no—
539C2×C22⋊C4—442no—
540C2×C22⋊C4—442no—
541C2×C22⋊C4—442no—
542C2×C22⋊C4—442no—
543C2×C22⋊C4—442no—
544C2×C22⋊C4—442no—
545C2×C22⋊C4—442no—
546C2×C22⋊C4—442no—
547C2×C22⋊C4C22×D1114yes—
548C2×C22⋊C4C22×D1114yes—
549C2×C22⋊C4C22×D1114yes—
550C2×C42—114no—
551C2×C42—442no—
552#95—114no—
553#95—114no—
554#95—114no—
555#95—114no—
556#95—114no—
557#95—114no—
558#95—114no—
559#95C22×D1114yes—
560C2×C11—82no—
561C2×C11—82no—
562C2×C11—82no—
563C2×C11#282918yescomplemented
564C2×C11C2×#53811yescharacteristic
565C2×C11C2×#54011yescharacteristic
566C2×C11C2×#54211yescharacteristic
567C2×C11C2×#56011yescharacteristic
568C2×C11C2×#56011yescharacteristic
569C2×C11C2×#56211yescharacteristic
570C2×C11C2×#56211yescharacteristic
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24C23×D1112yes—
593C24C23×D1112yes—
594C24C23×D1112yes—
595C24C23×D1111yescharacteristic
596C2×D4—28no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4—44no—
600C2×D4—44no—
601C2×D4—44no—
602C2×D4—44no—
603C2×D4—44no—
604C2×D4—44no—
605C2×D4—416no—
606C2×D4—416no—
607C2×D4—416no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—112no—
620C22×C4—112no—
621C22×C4—112no—
622C22×C4—112no—
623C22×C4—112no—
624C22×C4—112no—
625C22×C4—112no—
626C22×C4—112no—
627C22×C4—222no—
628C22×C4—222no—
629C22×C4—222no—
630C22×C4—222no—
631C22×C4—222no—
632C22×C4—222no—
633C22×C4—222no—
634C22×C4—222no—
635C22×C4—222no—
636C22×C4—222no—
637C22×C4—222no—
638C22×C4—222no—
639C22×C4—222no—
640C22×C4—222no—
641C22×C4—222no—
642C22×C4—222no—
643C22×C4—222no—
644C22×C4—222no—
645C22×C4—222no—
646C22×C4—222no—
647C22×C4—222no—
648C22×C4—222no—
649C22×C4—222no—
650C22×C4—222no—
651C22×C4#434114yes—
652C22×C4C23×D1112yes—
653C22×C4C23×D1112yes—
654C22×C4C23×D1112yes—
655C22×C4C23×D1112yes—
656C4⋊C4—228no—
657C4⋊C4—444no—
658C4⋊C4—444no—
659C4⋊C4—444no—
660C4⋊C4—444no—
661C4⋊C4—444no—
662C4⋊C4—444no—
663C4⋊C4—444no—
664C22⋊C4—28no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—444no—
668C22⋊C4—444no—
669C22⋊C4—444no—
670C22⋊C4—444no—
671C22⋊C4—444no—
672C22⋊C4—444no—
673C22⋊C4—444no—
674C22⋊C4—444no—
675C22⋊C4—444no—
676C22⋊C4—444no—
677C22⋊C4—444no—
678C22⋊C4—444no—
679C42—444no—
680C11C2×#282911yescharacteristic, complemented, Sylow
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23C2×#434112yes—
724C23#6703712yes—
725C23#6703712yes—
726C23#6703712yes—
727C23#6703712yes—
728C23#6703712yes—
729C23#6704312yes—
730C23C24×D1111yescharacteristic
731D4—416no—
732D4—416no—
733D4—416no—
734C2×C4—28no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—222no—
767C2×C4—222no—
768C2×C4—222no—
769C2×C4—222no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—222no—
773C2×C4—444no—
774C2×C4—444no—
775C2×C4—444no—
776C2×C4—444no—
777C2×C4—444no—
778C2×C4—444no—
779C2×C4—444no—
780C2×C4—444no—
781C2×C4C2×#434114yes—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—88no—
804C22—88no—
805C22—88no—
806C22#1062312414yes—
807C22#1062312614yes—
808C22#1062312614yes—
809C22#1062313414yes—
810C22#1062315214yes—
811C22#1062315214yes—
812C22#1062325014yes—
813C22C22×#434111yescharacteristic
814C22C2×#6703711yescharacteristic
815C22C2×#6703711yescharacteristic
816C22C2×#6703711yescharacteristic
817C22C2×#6703711yescharacteristic
818C22C2×#6703711yescharacteristic
819C22C2×#6704311yescharacteristic
820C4—24no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—442no—
825C4—442no—
826C4—442no—
827C4—442no—
828C4—442no—
829C4—442no—
830C4—442no—
831C4—442no—
832C2—82no—
833C2—82no—
834C2—82no—
835C2#1307674818yesdirect product factor
836C2C2×#1062312411yescharacteristic
837C2C2×#1062325011yescharacteristic
838C2C2×#1062313411yescharacteristic
839C2C2×#1062312611yescharacteristic
840C2C2×#1062312611yescharacteristic
841C2C2×#1062315211yescharacteristic
842C2C2×#1062315211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
Fitting, prime radicalC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2829
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. #13076748C2direct (N × H)
2. C2×#10622562C2semidirect
3. C2×#10622270C2semidirect
4. C2×#10622565C2semidirect
5. C2×#10622565C2semidirect
6. C2×#10622561C2semidirect
7. C2×#10622561C2semidirect
8. C2×#10622835C2semidirect
9. C2×#10622835C2semidirect
10. C2×#10622835C2semidirect
11. C2×#10622835C2semidirect
12. C2×#10622835C2semidirect
13. C2×#10622834C2semidirect
14. C2×#10622564C2semidirect
15. C2×#10622265C2semidirect
46. #10622835C22semidirect
47. #10622835C22semidirect
48. #10622835C22semidirect
49. #10622835C22semidirect
50. #10622835C22semidirect
51. #10622834C22semidirect
59. #10622565C22semidirect
60. #10622565C22semidirect
61. #10622564C22semidirect
62. #10622562C22semidirect
63. #10622561C22semidirect
64. #10622561C22semidirect
65. #10622270C22semidirect
66. #10622265C22semidirect
563. C2×C11#2829semidirect
680. C11C2×#2829semidirect
835. C2#13076748direct (N × H)

Maximal subgroups

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

subgroupindex
#130767482
C2×#106225622
C2×#106222702
C2×#106225652
C2×#106225612
C2×#106228352
C2×#106228342
C2×#106225642
C2×#106222652
C2×C11×#3922
C2×#282911