Finite Group Databasebeta

← C2×#13073120 #14922720

Subgroups — C2×#13073120 #14922720

Order 2816.

2486 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073120C2116yesmaximal, direct product factor
2C2×#10622271C211yesmaximal, characteristic, complemented
3C2×#10622271C211yesmaximal, characteristic, complemented
4C2×#10622270C211yesmaximal, characteristic, complemented
5C2×#10622585C211yesmaximal, characteristic, complemented
6C2×#10622268C211yesmaximal, characteristic, complemented
7C2×#10622266C211yesmaximal, characteristic, complemented
8C2×#10622281C211yesmaximal, characteristic
9C2×#10622281C211yesmaximal, characteristic
10C2×#10622602C211yesmaximal, characteristic
11C2×#10622602C211yesmaximal, characteristic
12C2×#10622590C211yesmaximal, characteristic, complemented
13C2×#10622280C211yesmaximal, characteristic
14C2×#10622279C211yesmaximal, characteristic
15C2×D11×#95C211yesmaximal, characteristic
16C2×C11×#400C211yesmaximal, characteristic, complemented
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊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×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C11×#400C2218yescomplemented
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
53#10622602C2218yes—
54#10622602C2218yes—
55#10622590C2218yescomplemented
56#10622585C2218yescomplemented
57#10622281C2218yes—
58#10622281C2218yes—
59#10622280C2218yes—
60#10622279C2218yes—
61D11×#95C2218yes—
62#10622271C2218yescomplemented
63#10622271C2218yescomplemented
64#10622270C2218yescomplemented
65#10622268C2218yescomplemented
66#10622266C2218yescomplemented
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—24no—
85C22×C4×D11—24no—
86C22×C4×D11—24no—
87C22×C4×D11—42no—
88C22×C4×D11—42no—
89C22×C4×D11—42no—
90C22×C4×D11—42no—
91C22×C4×D11C2314yes—
92C22×C4×D11C2314yes—
93C22×C4×D11C2314yes—
94C2×C11×C4⋊C4—42no—
95C2×C11×C4⋊C4—42no—
96C2×C11×C4⋊C4C2314yes—
97C2×C11×C4⋊C4C2314yes—
98C2×(C2×D11)⋊C4—24no—
99C2×(C2×D11)⋊C4—24no—
100C2×(C2×D11)⋊C4—24no—
101C2×(C2×D11)⋊C4Q818yes—
102C2×(C2×D11)⋊C4C2314yes—
103C2×(C2×D11)⋊C4C2314yes—
104C2×(C2×D11)⋊C4C2314yes—
105C2×(C2×D11)⋊C4C2314yes—
106C2×C4⋊Dic11—24no—
107C2×C4⋊Dic11—42no—
108C2×C4⋊Dic11C2314yes—
109C2×C4⋊Dic11C2314yes—
110C2×Dic11⋊C4—24no—
111C2×Dic11⋊C4—24no—
112C2×Dic11⋊C4—42no—
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×C4×Dic11—24no—
123C2×C4×Dic11—42no—
124C2×C4×Dic11C2314yes—
125C2×C4×Dic11C2314yes—
126C11×#95C2314yes—
127C11×#95C2314yes—
128C11×#95C2314yes—
129C11×#95C2314yes—
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×#2505—111nomaximal, Sylow
143C24×C11C2411yescharacteristic
144C23×D11—22no—
145C23×D11—22no—
146C23×D11—22no—
147C23×D11—22no—
148C23×D11C2×Q814yes—
149C23×D11#4114yes—
150C23×D11#4114yes—
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×C11—22no—
172C22×C4×C11C2×Q814yes—
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×Dic11—22no—
198C22×Dic11C2×Q814yes—
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—28no—
211C2×C4×D11—28no—
212C2×C4×D11—28no—
213C2×C4×D11—44no—
214C2×C4×D11—44no—
215C2×C4×D11—44no—
216C2×C4×D11—44no—
217C2×C4×D11—416no—
218C2×C4×D11—416no—
219C2×C4×D11—416no—
220C11×C4⋊C4—44no—
221C11×C4⋊C4—44no—
222(C2×D11)⋊C4—28no—
223(C2×D11)⋊C4—28no—
224(C2×D11)⋊C4—28no—
225(C2×D11)⋊C4C2×Q8116yes—
226C4⋊Dic11—28no—
227C4⋊Dic11—44no—
228Dic11⋊C4—28no—
229Dic11⋊C4—28no—
230Dic11⋊C4—44no—
231Dic11⋊C4—44no—
232Dic11⋊C4—44no—
233Dic11⋊C4—44no—
234C4×Dic11—28no—
235C4×Dic11—44no—
236#2505—1116no—
237C2×#400—111no—
238C2×#400—111no—
239C2×#400D1111yescharacteristic, complemented
240C2×#398—111no—
241C2×#389—111no—
242C2×#387—111no—
243C2×#387—111no—
244C2×#385—111no—
245C2×#385—111no—
246C2×#385—111no—
247C2×#385—111no—
248C2×#382—111no—
249C2×#380—111no—
250C2×C4×C22⋊C4—111no—
251C22×#95—111no—
252C23×C11C22×Q812yes—
253C23×C11C2×#4112yes—
254C23×C11C2×#4112yes—
255C23×C11C2×#4112yes—
256C23×C11C2×#4112yes—
257C23×C11H(5,𝔽2)12yes—
258C23×C11H(5,𝔽2)12yes—
259C23×C11C2511yescharacteristic
260C22×D11—28no—
261C22×D11—28no—
262C22×D11—28no—
263C22×D11—28no—
264C22×D11—28no—
265C22×D11—28no—
266C22×D11—22no—
267C22×D11—22no—
268C22×D11—22no—
269C22×D11—22no—
270C22×D11#125116yes—
271C22×D11C22×Q814yes—
272C22×D11C2×#4114yes—
273C22×D11C2×#4114yes—
274C2×C4×C11—28no—
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—22no—
294C2×C4×C11—22no—
295C2×C4×C11—44no—
296C2×C4×C11—44no—
297C2×C4×C11—44no—
298C2×C4×C11—44no—
299C2×C4×C11—44no—
300C2×C4×C11—44no—
301C2×C4×C11C22×Q814yes—
302C2×Dic11—28no—
303C2×Dic11—28no—
304C2×Dic11—28no—
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—22no—
322C2×Dic11—22no—
323C2×Dic11—44no—
324C2×Dic11—44no—
325C2×Dic11—44no—
326C2×Dic11—44no—
327C2×Dic11C22×Q814yes—
328C2×Dic11C2×#4114yes—
329C2×Dic11C2×#4114yes—
330C4×D11—416no—
331C4×D11—416no—
332C4×D11—416no—
333C24×C4—111no—
334C24×C4—111no—
335C24×C4—111no—
336C22×C4⋊C4—111no—
337C22×C4⋊C4—111no—
338C22×C4⋊C4—111no—
339C22×C4⋊C4—111no—
340C22×C4⋊C4—111no—
341C22×C4⋊C4—111no—
342C22×C4⋊C4—111no—
343C22×C4⋊C4—111no—
344C22×C4⋊C4C2×D1111yescharacteristic
345C22×C4⋊C4C2×D1111yescharacteristic
346C22×C22⋊C4—111no—
347C22×C22⋊C4—111no—
348C22×C22⋊C4—111no—
349C22×C22⋊C4—111no—
350C22×C42—111no—
351C22×C42—111no—
352#400—118no—
353#400—118no—
354#400C2×D1118yescomplemented
355#398—118no—
356#389—118no—
357#387—118no—
358#387—118no—
359#385—118no—
360#385—118no—
361#385—118no—
362#385—118no—
363#382—118no—
364#380—118no—
365C4×C22⋊C4—118no—
366C2×#95—111no—
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×#95—111no—
376C2×#95—111no—
377C2×#95—118no—
378C2×#95C2×D1111yescharacteristic
379C2×#95C2×D1111yescharacteristic
380C2×#95C2×D1111yescharacteristic
381C2×#95C2×D1111yescharacteristic
382C2×#95C2×D1111yescharacteristic
383C22×C11C2×#12514yes—
384C22×C11#52914yes—
385C22×C11#53814yes—
386C22×C11#55114yes—
387C22×C11#55114yes—
388C22×C11#55414yes—
389C22×C11#55414yes—
390C22×C11C23×Q811yescharacteristic
391C22×C11C22×#4111yescharacteristic
392C22×C11C22×#4111yescharacteristic
393C22×C11C22×#4111yescharacteristic
394C22×C11C22×#4111yescharacteristic
395C22×C11C2×H(5,𝔽2)11yescharacteristic
396C22×C11C2×H(5,𝔽2)11yescharacteristic
397C2×D11—24no—
398C2×D11—24no—
399C2×D11—24no—
400C2×D11—24no—
401C2×D11—24no—
402C2×D11—24no—
403C2×D11—232no—
404C2×D11C2×#12518yes—
405C4×C11—24no—
406C4×C11—42no—
407C4×C11—42no—
408C4×C11—42no—
409C4×C11—42no—
410C4×C11—42no—
411C4×C11—42no—
412Dic11—24no—
413Dic11—24no—
414Dic11—24no—
415Dic11—42no—
416Dic11—42no—
417Dic11—42no—
418Dic11—42no—
419C25—111no—
420C23×C4—111no—
421C23×C4—111no—
422C23×C4—111no—
423C23×C4—111no—
424C23×C4—111no—
425C23×C4—111no—
426C23×C4—111no—
427C23×C4—114no—
428C23×C4—114no—
429C23×C4—114no—
430C23×C4—224no—
431C23×C4—224no—
432C23×C4—224no—
433C23×C4—224no—
434C23×C4—224no—
435C23×C4—442no—
436C23×C4—442no—
437C23×C4—442no—
438C23×C4—442no—
439C23×C4C22×D1111yescharacteristic
440C23×C4C22×D1111yescharacteristic
441C23×C4C22×D1111yescharacteristic
442C23×C4C22×D1111yescharacteristic
443C23×C4C22×D1111yescharacteristic
444C23×C4C22×D1111yescharacteristic
445C23×C4C22×D1111yescharacteristic
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—114no—
449C2×C4⋊C4—114no—
450C2×C4⋊C4—114no—
451C2×C4⋊C4—114no—
452C2×C4⋊C4—114no—
453C2×C4⋊C4—114no—
454C2×C4⋊C4—114no—
455C2×C4⋊C4—114no—
456C2×C4⋊C4—224no—
457C2×C4⋊C4—224no—
458C2×C4⋊C4—224no—
459C2×C4⋊C4—442no—
460C2×C4⋊C4—442no—
461C2×C4⋊C4—442no—
462C2×C4⋊C4—442no—
463C2×C4⋊C4—442no—
464C2×C4⋊C4C22×D1114yes—
465C2×C4⋊C4C22×D1114yes—
466C2×C22⋊C4—118no—
467C2×C22⋊C4—114no—
468C2×C22⋊C4—114no—
469C2×C22⋊C4—114no—
470C2×C22⋊C4—114no—
471C2×C22⋊C4—224no—
472C2×C22⋊C4—224no—
473C2×C22⋊C4—224no—
474C2×C42—114no—
475C2×C42—114no—
476C2×C42—224no—
477C2×C42—442no—
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#95—114no—
487#95—114no—
488#95—114no—
489#95C22×D1114yes—
490#95C22×D1114yes—
491#95C22×D1114yes—
492#95C22×D1114yes—
493#95C22×D1114yes—
494C2×C11#250518yescomplemented
495C2×C11C22×#12511yescharacteristic
496C2×C11C2×#52911yescharacteristic
497C2×C11C2×#53811yescharacteristic
498C2×C11C2×#55111yescharacteristic
499C2×C11C2×#55111yescharacteristic
500C2×C11C2×#55411yescharacteristic
501C2×C11C2×#55411yescharacteristic
502D11—28no—
503C24—114no—
504C24—114no—
505C24—114no—
506C24—112no—
507C24—222no—
508C24—222no—
509C24—222no—
510C24—222no—
511C24C23×D1111yescharacteristic
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—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—114no—
533C22×C4—114no—
534C22×C4—114no—
535C22×C4—112no—
536C22×C4—112no—
537C22×C4—112no—
538C22×C4—112no—
539C22×C4—112no—
540C22×C4—112no—
541C22×C4—112no—
542C22×C4—228no—
543C22×C4—228no—
544C22×C4—228no—
545C22×C4—228no—
546C22×C4—228no—
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—222no—
557C22×C4—222no—
558C22×C4—222no—
559C22×C4—222no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—222no—
564C22×C4—222no—
565C22×C4—444no—
566C22×C4—444no—
567C22×C4—444no—
568C22×C4—444no—
569C22×C4—4416no—
570C22×C4—4416no—
571C22×C4—4416no—
572C22×C4Q8×D1114yes—
573C22×C4C23×D1112yes—
574C22×C4C23×D1112yes—
575C22×C4C23×D1112yes—
576C22×C4C23×D1112yes—
577C22×C4C23×D1112yes—
578C22×C4C23×D1112yes—
579C22×C4C23×D1112yes—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—228no—
583C4⋊C4—228no—
584C4⋊C4—228no—
585C4⋊C4—444no—
586C4⋊C4—444no—
587C4⋊C4—444no—
588C4⋊C4—444no—
589C4⋊C4—444no—
590C22⋊C4—1116no—
591C22⋊C4—228no—
592C22⋊C4—228no—
593C22⋊C4—228no—
594C42—228no—
595C42—444no—
596C11C2×#250511yescharacteristic, complemented, Sylow
597C23—114no—
598C23—114no—
599C23—114no—
600C23—1116no—
601C23—228no—
602C23—228no—
603C23—228no—
604C23—228no—
605C23—222no—
606C23—222no—
607C23—222no—
608C23—222no—
609C23—228no—
610C23—228no—
611C23#6703712yes—
612C23C2×Q8×D1112yes—
613C23#41×D1112yes—
614C23#41×D1112yes—
615C23#41×D1112yes—
616C23#41×D1112yes—
617C23#6704212yes—
618C23C24×D1111yescharacteristic
619C2×C4—28no—
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—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—114no—
647C2×C4—114no—
648C2×C4—114no—
649C2×C4—228no—
650C2×C4—228no—
651C2×C4—222no—
652C2×C4—222no—
653C2×C4—222no—
654C2×C4—222no—
655C2×C4—222no—
656C2×C4—222no—
657C2×C4—228no—
658C2×C4—222no—
659C2×C4—222no—
660C2×C4—222no—
661C2×C4—222no—
662C2×C4—222no—
663C2×C4—222no—
664C2×C4—222no—
665C2×C4—222no—
666C2×C4—222no—
667C2×C4—222no—
668C2×C4—222no—
669C2×C4—222no—
670C2×C4—4416no—
671C2×C4—4416no—
672C2×C4—4416no—
673C2×C4—444no—
674C2×C4—444no—
675C2×C4—444no—
676C2×C4—444no—
677C2×C4C2×Q8×D1114yes—
678C22—118no—
679C22—224no—
680C22—224no—
681C22—224no—
682C22—224no—
683C22—224no—
684C22—224no—
685C22—2232no—
686C22#1062316714yes—
687C22#1062319014yes—
688C22#1062320914yes—
689C22D11×#12514yes—
690C22#1062322114yes—
691C22#1062323614yes—
692C22#1062323714yes—
693C22C2×#6703711yescharacteristic
694C22C22×Q8×D1111yescharacteristic
695C22C2×#41×D1111yescharacteristic
696C22C2×#41×D1111yescharacteristic
697C22C2×#41×D1111yescharacteristic
698C22C2×#41×D1111yescharacteristic
699C22C2×#6704211yescharacteristic
700C4—24no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—224no—
708C4—224no—
709C4—224no—
710C4—442no—
711C4—442no—
712C4—442no—
713C4—442no—
714C2—228no—
715C2#1307312018yesdirect product factor
716C2C2×D11×#12511yescharacteristic
717C2C2×#1062323711yescharacteristic
718C2C2×#1062320911yescharacteristic
719C2C2×#1062323611yescharacteristic
720C2C2×#1062319011yescharacteristic
721C2C2×#1062316711yescharacteristic
722C2C2×#1062322111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#400C2
socleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#400D11
hypocenterC11C2×#2505
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. #13073120C2direct (N × H)
2. C2×#10622271C2semidirect
3. C2×#10622271C2semidirect
4. C2×#10622270C2semidirect
5. C2×#10622585C2semidirect
6. C2×#10622268C2semidirect
7. C2×#10622266C2semidirect
12. C2×#10622590C2semidirect
16. C2×C11×#400C2semidirect
36. C11×#400C22semidirect
55. #10622590C22semidirect
56. #10622585C22semidirect
62. #10622271C22semidirect
63. #10622271C22semidirect
64. #10622270C22semidirect
65. #10622268C22semidirect
66. #10622266C22semidirect
239. C2×#400D11semidirect
354. #400C2×D11semidirect
494. C2×C11#2505semidirect
596. C11C2×#2505semidirect
715. C2#13073120direct (N × H)

Maximal subgroups

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

subgroupindex
#130731202
C2×#106222712
C2×#106222702
C2×#106225852
C2×#106222682
C2×#106222662
C2×#106222812
C2×#106226022
C2×#106225902
C2×#106222802
C2×#106222792
C2×D11×#952
C2×C11×#4002
C2×#250511