Finite Group Databasebeta

← C2×#13074588 #14920216

Subgroups — C2×#13074588 #14920216

Order 2816.

2374 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#13074588C2116yesmaximal, direct product factor
2C2×#10622271C211yesmaximal, characteristic, complemented
3C2×#10622271C211yesmaximal, characteristic, complemented
4C2×#10622272C211yesmaximal, characteristic, complemented
5C2×#10622595C211yesmaximal, characteristic, complemented
6C2×#10622270C211yesmaximal, characteristic, complemented
7C2×#10622597C211yesmaximal, characteristic, complemented
8C2×#10622593C211yesmaximal, characteristic, complemented
9C2×#10622596C211yesmaximal, characteristic, complemented
10C2×#10622563C211yesmaximal, characteristic
11C2×#10622823C211yesmaximal, characteristic
12C2×#10622559C211yesmaximal, characteristic
13C2×#10622555C211yesmaximal, characteristic
14C2×#10622555C211yesmaximal, characteristic
15C22×C11⋊#95C211yesmaximal, characteristic
16C2×C11×#385C211yesmaximal, characteristic
17C24×C4×C11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C11×#385C2218yes—
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39#10622823C2218yes—
40C2×C11⋊#95C2218yes—
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
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55#10622597C2218yescomplemented
56#10622596C2218yescomplemented
57#10622595C2218yescomplemented
58#10622593C2218yescomplemented
59#10622563C2218yes—
60#10622559C2218yes—
61#10622555C2218yes—
62#10622555C2218yes—
63#10622272C2218yescomplemented
64#10622271C2218yescomplemented
65#10622271C2218yescomplemented
66#10622270C2218yescomplemented
67C25×C11C2311yescharacteristic
68C23×C4×C11—24no—
69C23×C4×C11—42no—
70C23×C4×C11—42no—
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2314yes—
78C23×Dic11—24no—
79C23×Dic11—42no—
80C23×Dic11—42no—
81C23×Dic11—42no—
82C23×Dic11—42no—
83C23×Dic11Q818yes—
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2314yes—
93C23×Dic11C2314yes—
94C2×C11×C4⋊C4—42no—
95C2×C11×C4⋊C4—42no—
96C2×C11×C4⋊C4C2314yes—
97C2×C11×C4⋊C4C2314yes—
98C2×C11×C22⋊C4—24no—
99C2×C11×C22⋊C4—24no—
100C2×C11×C22⋊C4C2314yes—
101C2×C11×C22⋊C4C2314yes—
102C2×C22⋊Dic11—24no—
103C2×C22⋊Dic11—24no—
104C2×C22⋊Dic11C2314yes—
105C2×C22⋊Dic11C2314yes—
106C2×C4⋊Dic11—42no—
107C2×C4⋊Dic11—42no—
108C2×C4⋊Dic11C2314yes—
109C2×C4⋊Dic11C2314yes—
110C2×Dic11⋊C4—42no—
111C2×Dic11⋊C4—42no—
112C2×Dic11⋊C4—42no—
113C2×Dic11⋊C4—42no—
114C2×Dic11⋊C4—42no—
115C2×Dic11⋊C4—42no—
116C2×Dic11⋊C4—42no—
117C2×Dic11⋊C4—42no—
118C2×Dic11⋊C4C2314yes—
119C2×Dic11⋊C4C2314yes—
120C2×Dic11⋊C4C2314yes—
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2314yes—
123C2×Dic11⋊C4C2314yes—
124C2×Dic11⋊C4C2314yes—
125C2×Dic11⋊C4C2314yes—
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×#2646—111nomaximal, Sylow
143C24×C11—22no—
144C24×C11—22no—
145C24×C11—22no—
146C24×C11—22no—
147C24×C11C2×Q814yes—
148C24×C11#4114yes—
149C24×C11#4114yes—
150C24×C11C2412yes—
151C24×C11C2411yescharacteristic
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—28no—
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—44no—
172C22×C4×C11—44no—
173C22×C4×C11—416no—
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—28no—
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×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—416no—
204C22×Dic11—44no—
205C22×Dic11—44no—
206C22×Dic11—44no—
207C22×Dic11—44no—
208C22×Dic11—416no—
209C22×Dic11C2×Q814yes—
210C22×Dic11C2×Q814yes—
211C22×Dic11C2×Q8116yes—
212C22×Dic11C2412yes—
213C22×Dic11C2412yes—
214C22×Dic11C2412yes—
215C22×Dic11C2412yes—
216C22×Dic11C2412yes—
217C22×Dic11C2412yes—
218C22×Dic11C2412yes—
219C22×Dic11C2412yes—
220C11×C4⋊C4—44no—
221C11×C4⋊C4—44no—
222C11×C22⋊C4—28no—
223C11×C22⋊C4—28no—
224C22⋊Dic11—28no—
225C22⋊Dic11—28no—
226C4⋊Dic11—44no—
227C4⋊Dic11—44no—
228Dic11⋊C4—44no—
229Dic11⋊C4—44no—
230Dic11⋊C4—44no—
231Dic11⋊C4—44no—
232Dic11⋊C4—44no—
233Dic11⋊C4—44no—
234Dic11⋊C4—44no—
235Dic11⋊C4—44no—
236#2646—1116no—
237C2×#400—111no—
238C2×#400—111no—
239C2×#400—111no—
240C2×#400—111no—
241C2×#398—111no—
242C2×#398—111no—
243C2×#398—111no—
244C2×#398—111no—
245C2×#385—111no—
246C2×#385—111no—
247C2×#385—111no—
248C2×#385D1111yescharacteristic
249C2×#380—111no—
250C2×#380—111no—
251C22×#95—111no—
252C23×C11—28no—
253C23×C11—28no—
254C23×C11—28no—
255C23×C11—28no—
256C23×C11—28no—
257C23×C11—28no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11#125116yes—
263C23×C11C22×Q814yes—
264C23×C11C22×Q812yes—
265C23×C11C2×#4114yes—
266C23×C11C2×#4112yes—
267C23×C11C2×#4114yes—
268C23×C11C2×#4112yes—
269C23×C11H(5,𝔽2)12yes—
270C23×C11H(5,𝔽2)12yes—
271C23×C11H(5,𝔽2)12yes—
272C23×C112−1+412yes—
273C23×C11C2511yescharacteristic
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—416no—
293C2×C4×C11—44no—
294C2×C4×C11—44no—
295C2×C4×C11—44no—
296C2×C4×C11—44no—
297C2×C4×C11—44no—
298C2×C4×C11—44no—
299C2×Dic11—28no—
300C2×Dic11—28no—
301C2×Dic11—22no—
302C2×Dic11—22no—
303C2×Dic11—22no—
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—22no—
322C2×Dic11—22no—
323C2×Dic11—416no—
324C2×Dic11—416no—
325C2×Dic11—44no—
326C2×Dic11—44no—
327C2×Dic11—44no—
328C2×Dic11—44no—
329C2×Dic11—44no—
330C2×Dic11—44no—
331C2×Dic11C22×Q814yes—
332C2×Dic11C22×Q814yes—
333C24×C4—111no—
334C24×C4—111no—
335C24×C4C2×D1111yescharacteristic
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⋊C4—111no—
345C22×C4⋊C4—111no—
346C22×C4⋊C4C2×D1111yescharacteristic
347C22×C4⋊C4C2×D1111yescharacteristic
348C22×C22⋊C4—111no—
349C22×C22⋊C4—111no—
350C22×C22⋊C4C2×D1111yescharacteristic
351C22×C22⋊C4C2×D1111yescharacteristic
352#400—118no—
353#400—118no—
354#400—118no—
355#400—118no—
356#398—118no—
357#398—118no—
358#398—118no—
359#398—118no—
360#385—118no—
361#385—118no—
362#385—118no—
363#385C2×D1118yes—
364#380—118no—
365#380—118no—
366C2×#95—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×#95—111no—
376C2×#95—111no—
377C2×#95—111no—
378C2×#95—111no—
379C2×#95—111no—
380C2×#95—111no—
381C2×#95C2×D1111yescharacteristic
382C2×#95C2×D1111yescharacteristic
383C22×C11—232no—
384C22×C11—24no—
385C22×C11—24no—
386C22×C11—24no—
387C22×C11—24no—
388C22×C11—24no—
389C22×C11—24no—
390C22×C11C2×#12518yes—
391C22×C11C2×#12514yes—
392C22×C11#53814yes—
393C22×C11#53814yes—
394C22×C11#53914yes—
395C22×C11#53914yes—
396C22×C11#54314yes—
397C22×C11#54414yes—
398C22×C11C23×Q811yescharacteristic
399C22×C11C22×#4111yescharacteristic
400C22×C11C22×#4111yescharacteristic
401C22×C11C2×H(5,𝔽2)11yescharacteristic
402C22×C11C2×H(5,𝔽2)11yescharacteristic
403C22×C11C2×H(5,𝔽2)11yescharacteristic
404C22×C11C2×2−1+411yescharacteristic
405C4×C11—42no—
406C4×C11—42no—
407C4×C11—42no—
408C4×C11—42no—
409C4×C11—42no—
410C4×C11—42no—
411Dic11—24no—
412Dic11—24no—
413Dic11—42no—
414Dic11—42no—
415Dic11—42no—
416Dic11—42no—
417Dic11—42no—
418Dic11—42no—
419C25C22×D1111yescharacteristic
420C23×C4—24no—
421C23×C4—42no—
422C23×C4—42no—
423C23×C4—111no—
424C23×C4—111no—
425C23×C4—118no—
426C23×C4—114no—
427C23×C4—111no—
428C23×C4—111no—
429C23×C4—111no—
430C23×C4—111no—
431C23×C4—111no—
432C23×C4—111no—
433C23×C4—114no—
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×D1114yes—
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—114no—
457C2×C4⋊C4—114no—
458C2×C4⋊C4—442no—
459C2×C4⋊C4—442no—
460C2×C4⋊C4—442no—
461C2×C4⋊C4—442no—
462C2×C4⋊C4—442no—
463C2×C4⋊C4—442no—
464C2×C4⋊C4—442no—
465C2×C4⋊C4—442no—
466C2×C4⋊C4—442no—
467C2×C4⋊C4—442no—
468C2×C4⋊C4C22×D1114yes—
469C2×C4⋊C4C22×D1114yes—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—114no—
473C2×C22⋊C4—114no—
474C2×C22⋊C4—224no—
475C2×C22⋊C4—224no—
476C2×C22⋊C4C22×D1114yes—
477C2×C22⋊C4C22×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#95—114no—
487#95—114no—
488#95—114no—
489#95—114no—
490#95—114no—
491#95—114no—
492#95C22×D1114yes—
493#95C22×D1114yes—
494C2×C11—28no—
495C2×C11#264618yescomplemented
496C2×C11C22×#12511yescharacteristic
497C2×C11C2×#53811yescharacteristic
498C2×C11C2×#53811yescharacteristic
499C2×C11C2×#53911yescharacteristic
500C2×C11C2×#53911yescharacteristic
501C2×C11C2×#54311yescharacteristic
502C2×C11C2×#54411yescharacteristic
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24#433914yes—
508C24#434114yes—
509C24Q8×D1114yes—
510C24C23×D1112yes—
511C24C23×D1111yescharacteristic
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—28no—
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—44no—
532C22×C4—44no—
533C22×C4—416no—
534C22×C4—114no—
535C22×C4—114no—
536C22×C4—112no—
537C22×C4—112no—
538C22×C4—1116no—
539C22×C4—112no—
540C22×C4—112no—
541C22×C4—112no—
542C22×C4—112no—
543C22×C4—112no—
544C22×C4—112no—
545C22×C4—222no—
546C22×C4—222no—
547C22×C4—222no—
548C22×C4—222no—
549C22×C4—222no—
550C22×C4—222no—
551C22×C4—228no—
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—222no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—4416no—
569C22×C4—444no—
570C22×C4—444no—
571C22×C4—444no—
572C22×C4—444no—
573C22×C4—4416no—
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—444no—
583C4⋊C4—444no—
584C4⋊C4—444no—
585C4⋊C4—444no—
586C4⋊C4—444no—
587C4⋊C4—444no—
588C4⋊C4—444no—
589C4⋊C4—444no—
590C4⋊C4—444no—
591C4⋊C4—444no—
592C22⋊C4—28no—
593C22⋊C4—28no—
594C22⋊C4—228no—
595C22⋊C4—228no—
596C11C2×#264611yescharacteristic, complemented, Sylow
597C23—28no—
598C23—28no—
599C23—28no—
600C23—28no—
601C23—28no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—28no—
606C23—22no—
607C23#66942116yes—
608C23C2×#433914yes—
609C23C2×#433912yes—
610C23C2×#434114yes—
611C23C2×#434112yes—
612C23#6703712yes—
613C23#6703712yes—
614C23C2×Q8×D1114yes—
615C23C2×Q8×D1112yes—
616C23#6704212yes—
617C23#6704312yes—
618C23C24×D1111yescharacteristic
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—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—416no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—114no—
645C2×C4—114no—
646C2×C4—228no—
647C2×C4—228no—
648C2×C4—222no—
649C2×C4—222no—
650C2×C4—222no—
651C2×C4—222no—
652C2×C4—222no—
653C2×C4—222no—
654C2×C4—222no—
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—222no—
665C2×C4—222no—
666C2×C4—222no—
667C2×C4—222no—
668C2×C4—222no—
669C2×C4—222no—
670C2×C4—4416no—
671C2×C4—4416no—
672C2×C4—444no—
673C2×C4—444no—
674C2×C4—444no—
675C2×C4—444no—
676C2×C4—444no—
677C2×C4—444no—
678C22—24no—
679C22—24no—
680C22—24no—
681C22—24no—
682C22—24no—
683C22—232no—
684C22—24no—
685C22C2×#6694218yes—
686C22C2×#6694214yes—
687C22#1062309114yes—
688C22#1062309514yes—
689C22#1062312414yes—
690C22#1062315414yes—
691C22#1062316514yes—
692C22#1062319614yes—
693C22C22×#433911yescharacteristic
694C22C22×#434111yescharacteristic
695C22C2×#6703711yescharacteristic
696C22C2×#6703711yescharacteristic
697C22C22×Q8×D1111yescharacteristic
698C22C2×#6704211yescharacteristic
699C22C2×#6704311yescharacteristic
700C4—42no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—224no—
707C4—224no—
708C4—442no—
709C4—442no—
710C4—442no—
711C4—442no—
712C4—442no—
713C4—442no—
714C2—28no—
715C2#1307458818yesdirect product factor
716C2C22×#6694211yescharacteristic
717C2C2×#1062309111yescharacteristic
718C2C2×#1062312411yescharacteristic
719C2C2×#1062309511yescharacteristic
720C2C2×#1062319611yescharacteristic
721C2C2×#1062316511yescharacteristic
722C2C2×#1062315411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#385C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#385D11
hypocenterC11C2×#2646
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. #13074588C2direct (N × H)
2. C2×#10622271C2semidirect
3. C2×#10622271C2semidirect
4. C2×#10622272C2semidirect
5. C2×#10622595C2semidirect
6. C2×#10622270C2semidirect
7. C2×#10622597C2semidirect
8. C2×#10622593C2semidirect
9. C2×#10622596C2semidirect
55. #10622597C22semidirect
56. #10622596C22semidirect
57. #10622595C22semidirect
58. #10622593C22semidirect
63. #10622272C22semidirect
64. #10622271C22semidirect
65. #10622271C22semidirect
66. #10622270C22semidirect
495. C2×C11#2646semidirect
596. C11C2×#2646semidirect
715. C2#13074588direct (N × H)

Maximal subgroups

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

subgroupindex
#130745882
C2×#106222712
C2×#106222722
C2×#106225952
C2×#106222702
C2×#106225972
C2×#106225932
C2×#106225962
C2×#106225632
C2×#106228232
C2×#106225592
C2×#106225552
C22×C11⋊#952
C2×C11×#3852
C2×#264611