Finite Group Databasebeta

← C2×#13073341 #14922971

Subgroups — C2×#13073341 #14922971

Order 2816.

2270 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073341C2116yesmaximal, direct product factor
2C2×#10622605C211yesmaximal, characteristic
3C2×#10622270C211yesmaximal, characteristic, complemented
4C2×#10622593C211yesmaximal, characteristic, complemented
5C2×#10622289C211yesmaximal, characteristic
6C2×#10622260C211yesmaximal, characteristic, complemented
7C2×#10622585C211yesmaximal, characteristic, complemented
8C2×#10622553C211yesmaximal, characteristic
9C2×#10622282C211yesmaximal, characteristic
10C2×#10622268C211yesmaximal, characteristic, complemented
11C2×#10622266C211yesmaximal, characteristic, complemented
12C2×#10622281C211yesmaximal, characteristic
13C2×#10622600C211yesmaximal, characteristic
14C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic
16C2×C11×#387C211yesmaximal, characteristic, complemented
17C23×C4×D11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C11×#387C2218yescomplemented
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
53#10622605C2218yes—
54#10622600C2218yes—
55#10622593C2218yescomplemented
56#10622585C2218yescomplemented
57#10622553C2218yes—
58C4×Dic11⋊C4C2218yescomplemented
59#10622289C2218yes—
60#10622282C2218yes—
61#10622281C2218yes—
62#10622279C2218yes—
63#10622270C2218yescomplemented
64#10622268C2218yescomplemented
65#10622266C2218yescomplemented
66#10622260C2218yescomplemented
67C24×D11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C22×C4×D11—24no—
83C22×C4×D11—24no—
84C22×C4×D11—42no—
85C22×C4×D11C2314yes—
86C2×C11×C4⋊C4—24no—
87C2×C11×C4⋊C4—42no—
88C2×C11×C4⋊C4C2314yes—
89C2×C11×C4⋊C4C2314yes—
90C2×C42×C11—42no—
91C2×C42×C11C2314yes—
92C2×(C2×D11)⋊C4—24no—
93C2×(C2×D11)⋊C4—24no—
94C2×(C2×D11)⋊C4—42no—
95C2×(C2×D11)⋊C4—42no—
96C2×(C2×D11)⋊C4—42no—
97C2×(C2×D11)⋊C4Q818yes—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2314yes—
100C2×(C2×D11)⋊C4C2314yes—
101C2×(C2×D11)⋊C4C2314yes—
102C2×(C2×D11)⋊C4C2314yes—
103C2×(C2×D11)⋊C4C2314yes—
104C2×C4⋊Dic11—24no—
105C2×C4⋊Dic11—42no—
106C2×C4⋊Dic11C2314yes—
107C2×C4⋊Dic11C2314yes—
108C2×Dic11⋊C4—24no—
109C2×Dic11⋊C4—24no—
110C2×Dic11⋊C4—24no—
111C2×Dic11⋊C4—24no—
112C2×Dic11⋊C4—24no—
113C2×Dic11⋊C4—42no—
114C2×Dic11⋊C4—42no—
115C2×Dic11⋊C4—42no—
116C2×Dic11⋊C4C2314yes—
117C2×Dic11⋊C4C2314yes—
118C2×Dic11⋊C4C2314yes—
119C2×Dic11⋊C4C2314yes—
120C2×Dic11⋊C4C2314yes—
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2314yes—
123C2×Dic11⋊C4C2314yes—
124C2×C4×Dic11—24no—
125C2×C4×Dic11—42no—
126C2×C4×Dic11—42no—
127C2×C4×Dic11C2314yes—
128C2×C4×Dic11C2314yes—
129C2×C4×Dic11C2314yes—
130C11×#95C2314yes—
131C11×#95C2314yes—
132C11×#95C2314yes—
133C11×#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138C11⋊#95C2314yes—
139C11⋊#95C2314yes—
140C11⋊#95C2314yes—
141C11⋊#95C2314yes—
142C2×#2522—111nomaximal, Sylow
143C24×C11C2411yescharacteristic
144C23×D11—22no—
145C23×D11—22no—
146C23×D11—22no—
147C23×D11—22no—
148C23×D11—22no—
149C23×D11—22no—
150C23×D11C2×Q814yes—
151C23×D11C2412yes—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11C2×Q814yes—
172C22×C4×C11#4114yes—
173C22×C4×C11C2412yes—
174C22×C4×C11C2412yes—
175C22×C4×C11C2412yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2412yes—
178C22×C4×C11C2412yes—
179C22×C4×C11C2412yes—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11C2×Q814yes—
198C22×Dic11#4114yes—
199C22×Dic11#4114yes—
200C22×Dic11#4114yes—
201C22×Dic11C2412yes—
202C22×Dic11C2412yes—
203C22×Dic11C2412yes—
204C22×Dic11C2412yes—
205C22×Dic11C2412yes—
206C22×Dic11C2412yes—
207C22×Dic11C2412yes—
208C2×C4×D11—28no—
209C2×C4×D11—28no—
210C2×C4×D11—44no—
211C2×C4×D11—416no—
212C11×C4⋊C4—28no—
213C11×C4⋊C4—44no—
214C42×C11—44no—
215(C2×D11)⋊C4—28no—
216(C2×D11)⋊C4—28no—
217(C2×D11)⋊C4—44no—
218(C2×D11)⋊C4—44no—
219(C2×D11)⋊C4—44no—
220(C2×D11)⋊C4C2×Q8116yes—
221C4⋊Dic11—28no—
222C4⋊Dic11—44no—
223Dic11⋊C4—28no—
224Dic11⋊C4—28no—
225Dic11⋊C4—28no—
226Dic11⋊C4—28no—
227Dic11⋊C4—28no—
228Dic11⋊C4—44no—
229Dic11⋊C4—44no—
230Dic11⋊C4—44no—
231C4×Dic11—28no—
232C4×Dic11—44no—
233C4×Dic11—44no—
234#2522—1116no—
235C2×#399—111no—
236C2×#398—111no—
237C2×#398—111no—
238C2×#396—111no—
239C2×#389—111no—
240C2×#389—111no—
241C2×#388—111no—
242C2×#388—111no—
243C2×#387—111no—
244C2×#387—111no—
245C2×#387D1111yescharacteristic, complemented
246C2×#385—111no—
247C2×#380—111no—
248C2×C4×C4⋊C4—111no—
249C2×C4×C22⋊C4—111no—
250C23×C11C22×Q812yes—
251C23×C11C2×#4112yes—
252C23×C11C2×#4112yes—
253C23×C11C2×#4112yes—
254C23×C11C2×#4112yes—
255C23×C11H(5,𝔽2)12yes—
256C23×C11H(5,𝔽2)12yes—
257C23×C11C2511yescharacteristic
258C22×D11—28no—
259C22×D11—28no—
260C22×D11—28no—
261C22×D11—22no—
262C22×D11—22no—
263C22×D11—22no—
264C22×D11—22no—
265C22×D11—22no—
266C22×D11—22no—
267C22×D11—44no—
268C22×D11—44no—
269C22×D11—44no—
270C22×D11—44no—
271C22×D11C22×Q814yes—
272C2×C4×C11—28no—
273C2×C4×C11—28no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—44no—
294C2×C4×C11—44no—
295C2×C4×C11—44no—
296C2×C4×C11—44no—
297C2×C4×C11—44no—
298C2×C4×C11C22×Q814yes—
299C2×C4×C11C2×#4114yes—
300C2×Dic11—28no—
301C2×Dic11—28no—
302C2×Dic11—28no—
303C2×Dic11—28no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—44no—
322C2×Dic11—44no—
323C2×Dic11—44no—
324C2×Dic11C22×Q814yes—
325C2×Dic11C2×#4114yes—
326C2×Dic11C2×#4114yes—
327C2×Dic11C2×#4114yes—
328C4×D11—416no—
329C24×C4—111no—
330C22×C4⋊C4—111no—
331C22×C4⋊C4—111no—
332C22×C4⋊C4—111no—
333C22×C4⋊C4—111no—
334C22×C4⋊C4—111no—
335C22×C4⋊C4—111no—
336C22×C4⋊C4—111no—
337C22×C4⋊C4—111no—
338C22×C4⋊C4—111no—
339C22×C4⋊C4—111no—
340C22×C4⋊C4C2×D1111yescharacteristic
341C22×C4⋊C4C2×D1111yescharacteristic
342C22×C22⋊C4—111no—
343C22×C22⋊C4—111no—
344C22×C22⋊C4—111no—
345C22×C22⋊C4—111no—
346C22×C22⋊C4—111no—
347C22×C22⋊C4—111no—
348C22×C42—111no—
349C22×C42—111no—
350C22×C42—111no—
351C22×C42C2×D1111yescharacteristic
352#399—118no—
353#398—118no—
354#398—118no—
355#396—118no—
356#389—118no—
357#389—118no—
358#388—118no—
359#388—118no—
360#387—118no—
361#387—118no—
362#387C2×D1118yescomplemented
363#385—118no—
364#380—118no—
365C4×C4⋊C4—118no—
366C4×C22⋊C4—118no—
367C2×#95—111no—
368C2×#95—111no—
369C2×#95—111no—
370C2×#95—111no—
371C2×#95—111no—
372C2×#95—111no—
373C2×#95—111no—
374C2×#95—111no—
375C2×#95C2×D1111yescharacteristic
376C2×#95C2×D1111yescharacteristic
377C2×#95C2×D1111yescharacteristic
378C2×#95C2×D1111yescharacteristic
379C22×C11#52914yes—
380C22×C11#53314yes—
381C22×C11#54014yes—
382C22×C11#55114yes—
383C22×C11#55314yes—
384C22×C11#55414yes—
385C22×C11#55414yes—
386C22×C11C23×Q811yescharacteristic
387C22×C11C22×#4111yescharacteristic
388C22×C11C22×#4111yescharacteristic
389C22×C11C22×#4111yescharacteristic
390C22×C11C22×#4111yescharacteristic
391C22×C11C2×H(5,𝔽2)11yescharacteristic
392C22×C11C2×H(5,𝔽2)11yescharacteristic
393C2×D11—24no—
394C2×D11—24no—
395C2×D11—24no—
396C2×D11—42no—
397C2×D11—42no—
398C2×D11—42no—
399C2×D11—42no—
400C2×D11—416no—
401C4×C11—24no—
402C4×C11—24no—
403C4×C11—42no—
404C4×C11—42no—
405C4×C11—42no—
406C4×C11—42no—
407C4×C11—42no—
408Dic11—24no—
409Dic11—24no—
410Dic11—24no—
411Dic11—24no—
412Dic11—42no—
413Dic11—42no—
414Dic11—42no—
415C25—111no—
416C23×C4—111no—
417C23×C4—111no—
418C23×C4—111no—
419C23×C4—111no—
420C23×C4—111no—
421C23×C4—111no—
422C23×C4—111no—
423C23×C4—114no—
424C23×C4—224no—
425C23×C4—224no—
426C23×C4—442no—
427C23×C4C22×D1111yescharacteristic
428C23×C4C22×D1111yescharacteristic
429C23×C4C22×D1111yescharacteristic
430C23×C4C22×D1111yescharacteristic
431C23×C4C22×D1111yescharacteristic
432C23×C4C22×D1111yescharacteristic
433C23×C4C22×D1111yescharacteristic
434C2×C4⋊C4—24no—
435C2×C4⋊C4—42no—
436C2×C4⋊C4—114no—
437C2×C4⋊C4—114no—
438C2×C4⋊C4—114no—
439C2×C4⋊C4—114no—
440C2×C4⋊C4—114no—
441C2×C4⋊C4—114no—
442C2×C4⋊C4—114no—
443C2×C4⋊C4—114no—
444C2×C4⋊C4—114no—
445C2×C4⋊C4—114no—
446C2×C4⋊C4—224no—
447C2×C4⋊C4—224no—
448C2×C4⋊C4—224no—
449C2×C4⋊C4—224no—
450C2×C4⋊C4—224no—
451C2×C4⋊C4—224no—
452C2×C4⋊C4—442no—
453C2×C4⋊C4—442no—
454C2×C4⋊C4—442no—
455C2×C4⋊C4—442no—
456C2×C4⋊C4C22×D1114yes—
457C2×C4⋊C4C22×D1114yes—
458C2×C22⋊C4—118no—
459C2×C22⋊C4—114no—
460C2×C22⋊C4—114no—
461C2×C22⋊C4—114no—
462C2×C22⋊C4—114no—
463C2×C22⋊C4—114no—
464C2×C22⋊C4—114no—
465C2×C22⋊C4—224no—
466C2×C22⋊C4—224no—
467C2×C22⋊C4—442no—
468C2×C22⋊C4—442no—
469C2×C22⋊C4—442no—
470C2×C42—42no—
471C2×C42—114no—
472C2×C42—114no—
473C2×C42—114no—
474C2×C42—224no—
475C2×C42—442no—
476C2×C42—442no—
477C2×C42C22×D1114yes—
478#95—114no—
479#95—114no—
480#95—114no—
481#95—114no—
482#95—114no—
483#95—114no—
484#95—114no—
485#95—114no—
486#95C22×D1114yes—
487#95C22×D1114yes—
488#95C22×D1114yes—
489#95C22×D1114yes—
490C2×C11#252218yescomplemented
491C2×C11C2×#52911yescharacteristic
492C2×C11C2×#53311yescharacteristic
493C2×C11C2×#54011yescharacteristic
494C2×C11C2×#55111yescharacteristic
495C2×C11C2×#55311yescharacteristic
496C2×C11C2×#55411yescharacteristic
497C2×C11C2×#55411yescharacteristic
498D11—44no—
499C24—114no—
500C24—112no—
501C24—222no—
502C24—222no—
503C24—222no—
504C24—222no—
505C24—222no—
506C24—222no—
507C24C23×D1111yescharacteristic
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—114no—
528C22×C4—114no—
529C22×C4—114no—
530C22×C4—114no—
531C22×C4—112no—
532C22×C4—112no—
533C22×C4—112no—
534C22×C4—112no—
535C22×C4—112no—
536C22×C4—112no—
537C22×C4—112no—
538C22×C4—228no—
539C22×C4—222no—
540C22×C4—222no—
541C22×C4—222no—
542C22×C4—222no—
543C22×C4—222no—
544C22×C4—222no—
545C22×C4—222no—
546C22×C4—222no—
547C22×C4—222no—
548C22×C4—222no—
549C22×C4—222no—
550C22×C4—222no—
551C22×C4—222no—
552C22×C4—222no—
553C22×C4—222no—
554C22×C4—222no—
555C22×C4—222no—
556C22×C4—228no—
557C22×C4—444no—
558C22×C4—4416no—
559C22×C4#433914yes—
560C22×C4Q8×D1114yes—
561C22×C4C23×D1112yes—
562C22×C4C23×D1112yes—
563C22×C4C23×D1112yes—
564C22×C4C23×D1112yes—
565C22×C4C23×D1112yes—
566C22×C4C23×D1112yes—
567C22×C4C23×D1112yes—
568C4⋊C4—28no—
569C4⋊C4—44no—
570C4⋊C4—228no—
571C4⋊C4—228no—
572C4⋊C4—228no—
573C4⋊C4—228no—
574C4⋊C4—228no—
575C4⋊C4—228no—
576C4⋊C4—444no—
577C4⋊C4—444no—
578C4⋊C4—444no—
579C4⋊C4—444no—
580C22⋊C4—1116no—
581C22⋊C4—228no—
582C22⋊C4—228no—
583C22⋊C4—444no—
584C22⋊C4—444no—
585C22⋊C4—444no—
586C42—44no—
587C42—228no—
588C42—444no—
589C42—444no—
590C11C2×#252211yescharacteristic, complemented, Sylow
591C23—114no—
592C23—228no—
593C23—228no—
594C23—222no—
595C23—222no—
596C23—222no—
597C23—222no—
598C23—222no—
599C23—222no—
600C23—228no—
601C23—444no—
602C23—444no—
603C23—444no—
604C23—444no—
605C23C2×#433912yes—
606C23#6703712yes—
607C23C2×Q8×D1112yes—
608C23#41×D1112yes—
609C23#41×D1112yes—
610C23#41×D1112yes—
611C23#6704212yes—
612C23C24×D1111yescharacteristic
613C2×C4—28no—
614C2×C4—28no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—44no—
635C2×C4—44no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—114no—
640C2×C4—114no—
641C2×C4—114no—
642C2×C4—114no—
643C2×C4—228no—
644C2×C4—228no—
645C2×C4—228no—
646C2×C4—222no—
647C2×C4—222no—
648C2×C4—222no—
649C2×C4—222no—
650C2×C4—222no—
651C2×C4—222no—
652C2×C4—222no—
653C2×C4—222no—
654C2×C4—228no—
655C2×C4—222no—
656C2×C4—222no—
657C2×C4—222no—
658C2×C4—222no—
659C2×C4—222no—
660C2×C4—222no—
661C2×C4—222no—
662C2×C4—222no—
663C2×C4—222no—
664C2×C4—4416no—
665C2×C4—444no—
666C2×C4—444no—
667C2×C4—444no—
668C2×C4C2×#433914yes—
669C2×C4C2×Q8×D1114yes—
670C22—224no—
671C22—224no—
672C22—224no—
673C22—442no—
674C22—442no—
675C22—442no—
676C22—4416no—
677C22—442no—
678C22#1062305814yes—
679C22#1062308914yes—
680C22#1062310914yes—
681C22#1062316714yes—
682C22#1062319414yes—
683C22#1062322114yes—
684C22#1062323714yes—
685C22C22×#433911yescharacteristic
686C22C2×#6703711yescharacteristic
687C22C22×Q8×D1111yescharacteristic
688C22C2×#41×D1111yescharacteristic
689C22C2×#41×D1111yescharacteristic
690C22C2×#41×D1111yescharacteristic
691C22C2×#6704211yescharacteristic
692C4—24no—
693C4—24no—
694C4—42no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—42no—
699C4—224no—
700C4—224no—
701C4—224no—
702C4—224no—
703C4—442no—
704C4—442no—
705C4—442no—
706C2—444no—
707C2#1307334118yesdirect product factor
708C2C2×#1062323711yescharacteristic
709C2C2×#1062310911yescharacteristic
710C2C2×#1062319411yescharacteristic
711C2C2×#1062305811yescharacteristic
712C2C2×#1062308911yescharacteristic
713C2C2×#1062316711yescharacteristic
714C2C2×#1062322111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#387C2
socleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#387D11
hypocenterC11C2×#2522
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. #13073341C2direct (N × H)
3. C2×#10622270C2semidirect
4. C2×#10622593C2semidirect
6. C2×#10622260C2semidirect
7. C2×#10622585C2semidirect
10. C2×#10622268C2semidirect
11. C2×#10622266C2semidirect
14. C2×C4×Dic11⋊C4C2semidirect
16. C2×C11×#387C2semidirect
40. C11×#387C22semidirect
55. #10622593C22semidirect
56. #10622585C22semidirect
58. C4×Dic11⋊C4C22semidirect
63. #10622270C22semidirect
64. #10622268C22semidirect
65. #10622266C22semidirect
66. #10622260C22semidirect
245. C2×#387D11semidirect
362. #387C2×D11semidirect
490. C2×C11#2522semidirect
590. C11C2×#2522semidirect
707. C2#13073341direct (N × H)

Maximal subgroups

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

subgroupindex
#130733412
C2×#106226052
C2×#106222702
C2×#106225932
C2×#106222892
C2×#106222602
C2×#106225852
C2×#106225532
C2×#106222822
C2×#106222682
C2×#106222662
C2×#106222812
C2×#106226002
C2×C4×Dic11⋊C42
C2×#106222792
C2×C11×#3872
C2×#252211