Finite Group Databasebeta

← C2×#13069794 #14781212

Subgroups — C2×#13069794 #14781212

Order 2816.

1434 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623014C211yesmaximal, characteristic, complemented
2C22×#66870C211yesmaximal, characteristic
3C22×#66870C211yesmaximal, characteristic
4C22×#66870C211yesmaximal, characteristic
5#13069794C218yesmaximal, direct product factor
6C2×#10622164C211yesmaximal, characteristic, complemented
7C2×#10622165C211yesmaximal, characteristic, complemented
8C2×C11×#342C211yesmaximal, characteristic, complemented
9C23×C22⋊D11C2211yescharacteristic
10C22×C11×C22⋊C4C2211yescharacteristic
11C22×C11×C22⋊C4C2211yescharacteristic
12C22×C11×C22⋊C4C2211yescharacteristic
13C22×C22⋊Dic11C2211yescharacteristic
14C22×C22⋊Dic11C2211yescharacteristic
15C22×C22⋊Dic11C2211yescharacteristic
16C2×#66977—22no—
17#10623014—22no—
18#10623014—22no—
19#10623014—22no—
20#10623014C2214yescomplemented
21C2×#66931—22no—
22C2×#66931—22no—
23C2×#66870—22no—
24C2×#66870—22no—
25C2×#66870—22no—
26C2×#66870—22no—
27C2×#66870—22no—
28C2×#66870—22no—
29C2×#66870C2214yes—
30C2×#66870C2214yes—
31C2×#66870C2214yes—
32C11×#342C2214yescomplemented
33#10622165C2214yescomplemented
34#10622164C2214yescomplemented
35C25×C11C2311yescharacteristic
36C24×D11Q811yescharacteristic, complemented
37C23×C4×C11—21no—
38C23×C4×C11—21no—
39C23×C4×C11—21no—
40C22×C22⋊D11—21no—
41C22×C22⋊D11—21no—
42C22×C22⋊D11—21no—
43C22×C22⋊D11—21no—
44C22×C22⋊D11—21no—
45C22×C22⋊D11—21no—
46C22×C22⋊D11—21no—
47C22×C22⋊D11—21no—
48C22×C22⋊D11—21no—
49C22×C22⋊D11—21no—
50C22×C22⋊D11—21no—
51C22×C22⋊D11—21no—
52C22×C22⋊D11Q812yescomplemented
53C22×C22⋊D11C2312yes—
54C23×Dic11—21no—
55C23×Dic11—21no—
56C23×Dic11—21no—
57C23×Dic11Q811yescharacteristic, complemented
58C22×Dic22—22no—
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—21no—
61C2×C11×C22⋊C4—21no—
62C2×C11×C22⋊C4—21no—
63C2×C11×C22⋊C4—21no—
64C2×C11×C22⋊C4—21no—
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4D412yes—
73C2×C11×C22⋊C4D412yes—
74C2×C11×C22⋊C4C2312yes—
75C2×C11×C22⋊C4C2312yes—
76C2×C11×C22⋊C4C2312yes—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11D412yes—
89C2×C22⋊Dic11D412yes—
90C2×C22⋊Dic11D412yes—
91C2×C22⋊Dic11D412yes—
92C2×C22⋊Dic11C2312yes—
93C2×C22⋊Dic11C2312yes—
94C2×C22⋊Dic11C2312yes—
95C2×C4⋊Dic11—22no—
96#66977—28no—
97#66977—28no—
98C2×Dic11⋊C4—24no—
99#66931—28no—
100#66931—28no—
101#66931—28no—
102#66931—28no—
103#66870—28no—
104#66870—28no—
105#66870—28no—
106C2×#2032—111nomaximal, Sylow
107C24×C11—82no—
108C24×C11C2×D411yescharacteristic
109C24×C11C2×D411yescharacteristic
110C24×C11C2×D411yescharacteristic
111C24×C11C2×D411yescharacteristic
112C24×C11C2×D411yescharacteristic
113C24×C11C2×D411yescharacteristic
114C24×C11C2×Q811yescharacteristic
115C24×C11C2×Q811yescharacteristic
116C24×C11#4111yescharacteristic
117C24×C11#4111yescharacteristic
118C24×C11#4111yescharacteristic
119C24×C11#4111yescharacteristic
120C24×C11#4111yescharacteristic
121C24×C11#4111yescharacteristic
122C24×C11C2411yescharacteristic
123C23×D11—21no—
124C23×D11—21no—
125C23×D11—21no—
126C23×D11—21no—
127C23×D11—21no—
128C23×D11—21no—
129C23×D11—82no—
130C23×D11C2×Q812yescomplemented
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—41no—
137C22×C4×C11—41no—
138C22×C4×C11—41no—
139C22×C4×C11—41no—
140C22×C4×C11—82no—
141C22×C4×C11—82no—
142C22×C4×C11—82no—
143C2×C22⋊D11—22no—
144C2×C22⋊D11—22no—
145C2×C22⋊D11—22no—
146C2×C22⋊D11—22no—
147C2×C22⋊D11—22no—
148C2×C22⋊D11—22no—
149C2×C22⋊D11—22no—
150C2×C22⋊D11—22no—
151C2×C22⋊D11—22no—
152C2×C22⋊D11—22no—
153C2×C22⋊D11—22no—
154C2×C22⋊D11—22no—
155C2×C22⋊D11—41no—
156C2×C22⋊D11—41no—
157C2×C22⋊D11—41no—
158C2×C22⋊D11—41no—
159C2×C22⋊D11—41no—
160C2×C22⋊D11—41no—
161C2×C22⋊D11—41no—
162C2×C22⋊D11—41no—
163C2×C22⋊D11—41no—
164C2×C22⋊D11—41no—
165C2×C22⋊D11—41no—
166C2×C22⋊D11—41no—
167C2×C22⋊D11—41no—
168C2×C22⋊D11—41no—
169C2×C22⋊D11—41no—
170C2×C22⋊D11—41no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—41no—
185C22×Dic11—41no—
186C22×Dic11—82no—
187C22×Dic11—82no—
188C22×Dic11—82no—
189C22×Dic11C2×Q812yescomplemented
190C2×Dic22—28no—
191C2×Dic22—84no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—41no—
200C11×C22⋊C4—41no—
201C11×C22⋊C4—41no—
202C11×C22⋊C4—41no—
203C11×C22⋊C4C2×D414yes—
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—41no—
213C22⋊Dic11—41no—
214C22⋊Dic11C2×D414yes—
215C22⋊Dic11C2×D414yes—
216C4⋊Dic11—28no—
217Dic11⋊C4—216no—
218C2×#543—111no—
219C22×#99—111no—
220C22×#99—111no—
221C22×#99—111no—
222#2032—118no—
223C2×#342—111no—
224C2×#342—111no—
225C2×#342D1111yescharacteristic, complemented
226C23×C11—42no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—81no—
234C23×C11—81no—
235C23×C11—81no—
236C23×C11—81no—
237C23×C11—81no—
238C23×C11—81no—
239C23×C11—81no—
240C23×C11—81no—
241C23×C11#12011yescharacteristic
242C23×C11#12011yescharacteristic
243C23×C11#12011yescharacteristic
244C23×C11#12011yescharacteristic
245C23×C11C22⋊Q811yescharacteristic
246C23×C11C22⋊Q811yescharacteristic
247C23×C11C22⋊Q811yescharacteristic
248C23×C11C22⋊Q811yescharacteristic
249C23×C11C22⋊Q811yescharacteristic
250C23×C11C22⋊Q811yescharacteristic
251C23×C11C22⋊Q811yescharacteristic
252C23×C11C22⋊Q811yescharacteristic
253C23×C11C22⋊Q811yescharacteristic
254C23×C11C22⋊Q811yescharacteristic
255C23×C11C22⋊Q811yescharacteristic
256C23×C11C22⋊Q811yescharacteristic
257C23×C11#12411yescharacteristic
258C23×C11#12411yescharacteristic
259C23×C11#12411yescharacteristic
260C23×C11#12411yescharacteristic
261C23×C11#12411yescharacteristic
262C23×C11#12411yescharacteristic
263C23×C11#12411yescharacteristic
264C23×C11#12411yescharacteristic
265C23×C11#12411yescharacteristic
266C23×C11#12411yescharacteristic
267C23×C11#12411yescharacteristic
268C23×C11#12411yescharacteristic
269C23×C11C22×D411yescharacteristic
270C23×C11C22×D411yescharacteristic
271C23×C11C22×D411yescharacteristic
272C23×C11C22×Q811yescharacteristic
273C23×C11C2×#4111yescharacteristic
274C23×C11C2×#4111yescharacteristic
275C23×C11C2×#4111yescharacteristic
276C22×D11—22no—
277C22×D11—22no—
278C22×D11—22no—
279C22×D11—41no—
280C22×D11—41no—
281C22×D11—41no—
282C22×D11—41no—
283C22×D11—82no—
284C22×D11—82no—
285C22×D11—82no—
286C22×D11—82no—
287C22×D11—82no—
288C22×D11—82no—
289C22×D11—82no—
290C2×C4×C11—24no—
291C2×C4×C11—44no—
292C2×C4×C11—42no—
293C2×C4×C11—42no—
294C2×C4×C11—82no—
295C2×C4×C11—82no—
296C2×C4×C11—82no—
297C2×C4×C11—82no—
298C2×C4×C11—82no—
299C2×C4×C11—82no—
300C2×C4×C11—82no—
301C2×C4×C11—82no—
302C22⋊D11—42no—
303C22⋊D11—42no—
304C22⋊D11—42no—
305C22⋊D11—42no—
306C22⋊D11—42no—
307C22⋊D11—42no—
308C22⋊D11—42no—
309C22⋊D11—42no—
310C2×Dic11—24no—
311C2×Dic11—24no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—44no—
316C2×Dic11—44no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—42no—
322C2×Dic11—82no—
323C2×Dic11—82no—
324C2×Dic11—82no—
325C2×Dic11—82no—
326C2×Dic11—82no—
327C2×Dic11—82no—
328C2×Dic11—82no—
329Dic22—88no—
330C23×D4—111no—
331#543—114no—
332#543—222no—
333#543—222no—
334#543—222no—
335C2×C22⋊Q8—222no—
336C2×C22⋊Q8—222no—
337C2×C22⋊Q8—222no—
338C22×C22⋊C4—111no—
339C22×C22⋊C4—111no—
340C22×C22⋊C4—111no—
341C22×C22⋊C4C2×D1111yescharacteristic
342C22×C22⋊C4C2×D1111yescharacteristic
343C22×C22⋊C4C2×D1111yescharacteristic
344C2×#99—114no—
345C2×#99—114no—
346C2×#99—114no—
347C2×#99—222no—
348C2×#99—222no—
349C2×#99—222no—
350C2×#99—222no—
351C2×#99—222no—
352C2×#99—222no—
353#342—114no—
354#342—114no—
355#342C2×D1114yescomplemented
356C22×C11—22no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—22no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11—41no—
371C22×C11—41no—
372C22×C11—41no—
373C22×C11—41no—
374C22×C11—41no—
375C22×C11—41no—
376C22×C11—41no—
377C22×C11—41no—
378C22×C11—41no—
379C22×C11—41no—
380C22×C11—41no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11—41no—
384C22×C11—41no—
385C22×C11—41no—
386C22×C11—41no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11#39311yescharacteristic
392C22×C11#39311yescharacteristic
393C22×C11#39311yescharacteristic
394C22×C11#39311yescharacteristic
395C22×C11#39311yescharacteristic
396C22×C11#39311yescharacteristic
397C22×C11#39311yescharacteristic
398C22×C11#39311yescharacteristic
399C22×C11C2×#12011yescharacteristic
400C22×C11C2×C22⋊Q811yescharacteristic
401C22×C11C2×C22⋊Q811yescharacteristic
402C22×C11C2×C22⋊Q811yescharacteristic
403C22×C11C2×#12411yescharacteristic
404C22×C11C2×#12411yescharacteristic
405C22×C11C2×#12411yescharacteristic
406C2×D11—42no—
407C2×D11—82no—
408C2×D11—82no—
409C2×D11—82no—
410C2×D11—82no—
411C2×D11—82no—
412C2×D11—82no—
413C2×D11—82no—
414C4×C11—44no—
415C4×C11—82no—
416C4×C11—82no—
417Dic11—44no—
418Dic11—44no—
419Dic11—42no—
420Dic11—82no—
421C25—111no—
422C25C22×D1111yescharacteristic
423C22×Q8—222no—
424C22×D4—112no—
425C22×D4—112no—
426C22×D4—221no—
427C22×D4—221no—
428C22×D4—221no—
429C22×D4—221no—
430C22×D4—221no—
431C22×D4—221no—
432C22×D4—221no—
433C22×D4—221no—
434C22×D4—221no—
435C22×D4—221no—
436C22×D4—221no—
437C22×D4—221no—
438C23×C4—21no—
439C23×C4—21no—
440C23×C4—21no—
441C23×C4—111no—
442C23×C4—221no—
443C23×C4—221no—
444C23×C4—221no—
445C22⋊Q8—228no—
446C22⋊Q8—228no—
447C22⋊Q8—228no—
448C22⋊Q8—228no—
449C22⋊Q8—228no—
450C22⋊Q8—228no—
451C2×C4⋊C4—224no—
452C2×C4⋊C4—222no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—112no—
467C2×C22⋊C4—112no—
468C2×C22⋊C4—112no—
469C2×C22⋊C4—112no—
470C2×C22⋊C4—112no—
471C2×C22⋊C4—112no—
472C2×C22⋊C4—112no—
473C2×C22⋊C4—221no—
474C2×C22⋊C4—221no—
475C2×C22⋊C4—221no—
476C2×C22⋊C4—221no—
477C2×C22⋊C4—221no—
478C2×C22⋊C4—221no—
479C2×C22⋊C4—221no—
480C2×C22⋊C4—221no—
481C2×C22⋊C4—221no—
482C2×C22⋊C4—221no—
483C2×C22⋊C4—221no—
484C2×C22⋊C4D4412yes—
485C2×C22⋊C4D4412yes—
486C2×C22⋊C4C22×D1112yes—
487C2×C22⋊C4C22×D1112yes—
488C2×C22⋊C4C22×D1112yes—
489#99—228no—
490#99—228no—
491#99—228no—
492C2×C11—21no—
493C2×C11—21no—
494C2×C11—21no—
495C2×C11—21no—
496C2×C11—21no—
497C2×C11—21no—
498C2×C11—21no—
499C2×C11—21no—
500C2×C11—21no—
501C2×C11—21no—
502C2×C11—21no—
503C2×C11—21no—
504C2×C11—21no—
505C2×C11—21no—
506C2×C11#203212yescomplemented
507C2×C11C2×#39311yescharacteristic
508D11—82no—
509C24—82no—
510C24—112no—
511C24—221no—
512C24—221no—
513C24—221no—
514C24—221no—
515C24—221no—
516C24—221no—
517C24—882no—
518C24C2×D4411yescharacteristic
519C24C2×D4411yescharacteristic
520C24#433911yescharacteristic
521C24#433911yescharacteristic
522C24#433911yescharacteristic
523C24#433911yescharacteristic
524C24D4×D1111yescharacteristic
525C24D4×D1111yescharacteristic
526C24D4×D1111yescharacteristic
527C24D4×D1111yescharacteristic
528C24#434111yescharacteristic
529C24#434111yescharacteristic
530C24Q8×D1111yescharacteristic
531C24Q8×D1111yescharacteristic
532C24C23×D1111yescharacteristic
533C2×Q8—228no—
534C2×Q8—884no—
535C2×D4—222no—
536C2×D4—222no—
537C2×D4—222no—
538C2×D4—222no—
539C2×D4—222no—
540C2×D4—222no—
541C2×D4—222no—
542C2×D4—222no—
543C2×D4—222no—
544C2×D4—222no—
545C2×D4—222no—
546C2×D4—222no—
547C2×D4—441no—
548C2×D4—441no—
549C2×D4—441no—
550C2×D4—441no—
551C2×D4—441no—
552C2×D4—441no—
553C2×D4—441no—
554C2×D4—441no—
555C2×D4—441no—
556C2×D4—441no—
557C2×D4—441no—
558C2×D4—441no—
559C2×D4—441no—
560C2×D4—441no—
561C2×D4—441no—
562C2×D4—441no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—82no—
573C22×C4—82no—
574C22×C4—82no—
575C22×C4—112no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—221no—
579C22×C4—221no—
580C22×C4—221no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—441no—
590C22×C4—441no—
591C22×C4—882no—
592C22×C4—882no—
593C22×C4—882no—
594C4⋊C4—2216no—
595C4⋊C4—228no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—41no—
604C22⋊C4—41no—
605C22⋊C4—41no—
606C22⋊C4—41no—
607C22⋊C4—114no—
608C22⋊C4—114no—
609C22⋊C4—222no—
610C22⋊C4—222no—
611C22⋊C4—222no—
612C22⋊C4—222no—
613C22⋊C4—222no—
614C22⋊C4—222no—
615C22⋊C4—222no—
616C22⋊C4—222no—
617C22⋊C4—441no—
618C22⋊C4—441no—
619C22⋊C4C2×D4414yes—
620C11C2×#203211yescharacteristic, complemented, Sylow
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—81no—
629C23—81no—
630C23—81no—
631C23—81no—
632C23—81no—
633C23—81no—
634C23—81no—
635C23—81no—
636C23—222no—
637C23—222no—
638C23—222no—
639C23—441no—
640C23—441no—
641C23—441no—
642C23—441no—
643C23—882no—
644C23—882no—
645C23—882no—
646C23—882no—
647C23—882no—
648C23—882no—
649C23—882no—
650C23#6692811yescharacteristic
651C23#6692811yescharacteristic
652C23#6692811yescharacteristic
653C23#6692811yescharacteristic
654C23#6693511yescharacteristic
655C23#6693511yescharacteristic
656C23#6693511yescharacteristic
657C23#6693511yescharacteristic
658C23#6693811yescharacteristic
659C23#6693811yescharacteristic
660C23#6693811yescharacteristic
661C23#6693811yescharacteristic
662C23#6693811yescharacteristic
663C23#6693811yescharacteristic
664C23#6693811yescharacteristic
665C23#6693811yescharacteristic
666C23#6694911yescharacteristic
667C23#6694911yescharacteristic
668C23#6694911yescharacteristic
669C23#6694911yescharacteristic
670C23#6694911yescharacteristic
671C23#6694911yescharacteristic
672C23#6694911yescharacteristic
673C23#6694911yescharacteristic
674C23#6695011yescharacteristic
675C23#6695011yescharacteristic
676C23#6695011yescharacteristic
677C23#6695011yescharacteristic
678C23C22×D4411yescharacteristic
679C23C2×#433911yescharacteristic
680C23C2×#433911yescharacteristic
681C23C2×D4×D1111yescharacteristic
682C23C2×D4×D1111yescharacteristic
683C23C2×#434111yescharacteristic
684C23C2×Q8×D1111yescharacteristic
685Q8—888no—
686D4—442no—
687D4—442no—
688D4—442no—
689D4—442no—
690D4—442no—
691D4—442no—
692D4—442no—
693D4—442no—
694C2×C4—24no—
695C2×C4—44no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—82no—
699C2×C4—82no—
700C2×C4—82no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4—224no—
707C2×C4—224no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—444no—
712C2×C4—444no—
713C2×C4—441no—
714C2×C4—441no—
715C2×C4—441no—
716C2×C4—441no—
717C2×C4—442no—
718C2×C4—882no—
719C2×C4—882no—
720C2×C4—882no—
721C2×C4—882no—
722C2×C4—882no—
723C2×C4—882no—
724C2×C4—882no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—442no—
761C22—882no—
762C22—882no—
763C22—882no—
764C22—882no—
765C22—882no—
766C22—882no—
767C22—882no—
768C22#1062228611yescharacteristic
769C22#1062228611yescharacteristic
770C22#1062228611yescharacteristic
771C22#1062228611yescharacteristic
772C22#1062228611yescharacteristic
773C22#1062228611yescharacteristic
774C22#1062228611yescharacteristic
775C22#1062228611yescharacteristic
776C22C2×#6692811yescharacteristic
777C22C2×#6693511yescharacteristic
778C22C2×#6693811yescharacteristic
779C22C2×#6693811yescharacteristic
780C22C2×#6694911yescharacteristic
781C22C2×#6694911yescharacteristic
782C22C2×#6695011yescharacteristic
783C4—44no—
784C4—82no—
785C4—82no—
786C4—444no—
787C4—444no—
788C4—442no—
789C4—882no—
790C2—21no—
791C2—21no—
792C2—21no—
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—882no—
805C2#1306979412yesdirect product factor
806C2C2×#1062228611yescharacteristic
subgroupG/H
centerC22#10622286
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC2×C11×#342C2
socleC22×C11#393
prime radicalC23×C22⋊D11C22
hypercenterC2×#342D11
hypocenterC11C2×#2032
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
1. C2×#10623014C2semidirect
5. #13069794C2direct (N × H)
6. C2×#10622164C2semidirect
7. C2×#10622165C2semidirect
8. C2×C11×#342C2semidirect
20. #10623014C22semidirect
32. C11×#342C22semidirect
33. #10622165C22semidirect
34. #10622164C22semidirect
36. C24×D11Q8semidirect
52. C22×C22⋊D11Q8semidirect
57. C23×Dic11Q8semidirect
130. C23×D11C2×Q8semidirect
189. C22×Dic11C2×Q8semidirect
225. C2×#342D11semidirect
355. #342C2×D11semidirect
506. C2×C11#2032semidirect
620. C11C2×#2032semidirect
805. C2#13069794direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230142
C22×#668702
#130697942
C2×#106221642
C2×#106221652
C2×C11×#3422
C2×#203211