Finite Group Databasebeta

← C2×#13069793 #14781211

Subgroups — C2×#13069793 #14781211

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×#66898C211yesmaximal, characteristic
3C22×#66898C211yesmaximal, characteristic
4#13069793C218yesmaximal, direct product factor
5C2×#10622164C211yesmaximal, characteristic, complemented
6C2×#10622165C211yesmaximal, characteristic, complemented
7C2×#10622165C211yesmaximal, characteristic, complemented
8C22×C11×#99C211yesmaximal, characteristic
9C23×D4×C11C2211yescharacteristic
10C22×C11×C22⋊C4C2211yescharacteristic
11C22×C11×C22⋊C4C2211yescharacteristic
12C22×C22⋊Dic11C2211yescharacteristic
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×C11×#99—22no—
24C2×C11×#99—22no—
25C2×C11×#99C2214yes—
26C2×#66898—22no—
27C2×#66898—22no—
28C2×#66898—22no—
29C2×#66898—22no—
30C2×#66898C2214yes—
31C2×#66898C2214yes—
32#10622165C2214yescomplemented
33#10622165C2214yescomplemented
34#10622164C2214yescomplemented
35C25×C11Q811yescharacteristic, complemented
36C25×C11C2311yescharacteristic
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11Q812yescomplemented
50C22×D4×C11C2312yes—
51C23×C4×C11—21no—
52C23×C4×C11—21no—
53C23×C4×C11Q811yescharacteristic, complemented
54C23×Dic11—21no—
55C23×Dic11—21no—
56C23×Dic11—21no—
57C23×Dic11—21no—
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⋊C4D412yes—
68C2×C11×C22⋊C4D412yes—
69C2×C11×C22⋊C4C2312yes—
70C2×C11×C22⋊C4C2312yes—
71C2×C22⋊Dic11—21no—
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
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⋊Dic11D412yes—
88C2×C22⋊Dic11D412yes—
89C2×C22⋊Dic11D412yes—
90C2×C22⋊Dic11D412yes—
91C2×C22⋊Dic11C2312yes—
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—
103C11×#99—28no—
104#66898—28no—
105#66898—28no—
106C2×#2032—111nomaximal, Sylow
107C24×C11—21no—
108C24×C11—21no—
109C24×C11—21no—
110C24×C11—21no—
111C24×C11—21no—
112C24×C11—21no—
113C24×C11—82no—
114C24×C11—82no—
115C24×C11C2×D411yescharacteristic
116C24×C11C2×D411yescharacteristic
117C24×C11C2×D411yescharacteristic
118C24×C11C2×D411yescharacteristic
119C24×C11C2×D411yescharacteristic
120C24×C11C2×D411yescharacteristic
121C24×C11C2×Q811yescharacteristic
122C24×C11C2×Q811yescharacteristic
123C24×C11C2×Q812yescomplemented
124C24×C11#4111yescharacteristic
125C24×C11#4111yescharacteristic
126C24×C11#4111yescharacteristic
127C24×C11#4111yescharacteristic
128C24×C11#4111yescharacteristic
129C24×C11#4111yescharacteristic
130C24×C11C2411yescharacteristic
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—41no—
144C2×D4×C11—41no—
145C2×D4×C11—41no—
146C2×D4×C11—41no—
147C2×D4×C11—41no—
148C2×D4×C11—41no—
149C2×D4×C11—41no—
150C2×D4×C11—41no—
151C2×D4×C11—41no—
152C2×D4×C11—41no—
153C2×D4×C11—41no—
154C2×D4×C11—41no—
155C2×D4×C11—41no—
156C2×D4×C11—41no—
157C2×D4×C11—41no—
158C2×D4×C11—41no—
159C22×C4×C11—22no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—41no—
170C22×C4×C11—41no—
171C22×C4×C11—82no—
172C22×C4×C11—82no—
173C22×C4×C11C2×Q812yescomplemented
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—41no—
183C22×Dic11—41no—
184C22×Dic11—41no—
185C22×Dic11—41no—
186C22×Dic11—82no—
187C22×Dic11—82no—
188C22×Dic11—82no—
189C22×Dic11—82no—
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—41no—
198C11×C22⋊C4—41no—
199C11×C22⋊C4C2×D414yes—
200C22⋊Dic11—22no—
201C22⋊Dic11—22no—
202C22⋊Dic11—22no—
203C22⋊Dic11—22no—
204C22⋊Dic11—22no—
205C22⋊Dic11—22no—
206C22⋊Dic11—22no—
207C22⋊Dic11—22no—
208C22⋊Dic11—22no—
209C22⋊Dic11—22no—
210C22⋊Dic11—41no—
211C22⋊Dic11—41no—
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×#99D1111yescharacteristic
222#2032—118no—
223C2×#342—111no—
224C2×#342—111no—
225C2×#342—111no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—82no—
241C23×C11—82no—
242C23×C11—82no—
243C23×C11—81no—
244C23×C11—81no—
245C23×C11—81no—
246C23×C11—81no—
247C23×C11—81no—
248C23×C11—81no—
249C23×C11—81no—
250C23×C11—81no—
251C23×C11—82no—
252C23×C11—82no—
253C23×C11—82no—
254C23×C11—82no—
255C23×C11#12011yescharacteristic
256C23×C11#12011yescharacteristic
257C23×C11#12011yescharacteristic
258C23×C11#12011yescharacteristic
259C23×C11C22⋊Q811yescharacteristic
260C23×C11C22⋊Q811yescharacteristic
261C23×C11C22⋊Q811yescharacteristic
262C23×C11C22⋊Q811yescharacteristic
263C23×C11C22⋊Q811yescharacteristic
264C23×C11C22⋊Q811yescharacteristic
265C23×C11C22⋊Q811yescharacteristic
266C23×C11C22⋊Q811yescharacteristic
267C23×C11C22⋊Q811yescharacteristic
268C23×C11C22⋊Q811yescharacteristic
269C23×C11C22⋊Q811yescharacteristic
270C23×C11C22⋊Q811yescharacteristic
271C23×C11#12411yescharacteristic
272C23×C11#12411yescharacteristic
273C23×C11#12411yescharacteristic
274C23×C11#12411yescharacteristic
275C23×C11#12411yescharacteristic
276C23×C11#12411yescharacteristic
277C23×C11#12411yescharacteristic
278C23×C11#12411yescharacteristic
279C23×C11#12411yescharacteristic
280C23×C11#12411yescharacteristic
281C23×C11#12411yescharacteristic
282C23×C11#12411yescharacteristic
283C23×C11C22×D411yescharacteristic
284C23×C11C22×D411yescharacteristic
285C23×C11C22×D411yescharacteristic
286C23×C11C22×Q811yescharacteristic
287C23×C11C2×#4111yescharacteristic
288C23×C11C2×#4111yescharacteristic
289C23×C11C2×#4111yescharacteristic
290D4×C11—42no—
291D4×C11—42no—
292D4×C11—42no—
293D4×C11—42no—
294D4×C11—42no—
295D4×C11—42no—
296D4×C11—42no—
297D4×C11—42no—
298C2×C4×C11—24no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—44no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—42no—
308C2×C4×C11—82no—
309C2×C4×C11—82no—
310C2×C4×C11—82no—
311C2×C4×C11—82no—
312C2×C4×C11—82no—
313C2×Dic11—24no—
314C2×Dic11—24no—
315C2×Dic11—44no—
316C2×Dic11—44no—
317C2×Dic11—42no—
318C2×Dic11—42no—
319C2×Dic11—82no—
320C2×Dic11—82no—
321C2×Dic11—82no—
322C2×Dic11—82no—
323C2×Dic11—82no—
324C2×Dic11—82no—
325C2×Dic11—82no—
326C2×Dic11—82no—
327C2×Dic11—82no—
328C2×Dic11—82no—
329Dic22—88no—
330C23×D4C2×D1111yescharacteristic
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⋊C4—111no—
342C22×C22⋊C4C2×D1111yescharacteristic
343C22×C22⋊C4C2×D1111yescharacteristic
344C2×#99—22no—
345C2×#99—22no—
346C2×#99—114no—
347C2×#99—114no—
348C2×#99—222no—
349C2×#99—222no—
350C2×#99—222no—
351C2×#99—222no—
352C2×#99C2×D1114yes—
353#342—114no—
354#342—114no—
355#342—114no—
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—42no—
392C22×C11—82no—
393C22×C11—82no—
394C22×C11—82no—
395C22×C11—82no—
396C22×C11—82no—
397C22×C11—82no—
398C22×C11—82no—
399C22×C11#39311yescharacteristic
400C22×C11#39311yescharacteristic
401C22×C11#39311yescharacteristic
402C22×C11#39311yescharacteristic
403C22×C11#39311yescharacteristic
404C22×C11#39311yescharacteristic
405C22×C11#39311yescharacteristic
406C22×C11#39311yescharacteristic
407C22×C11C2×#12011yescharacteristic
408C22×C11C2×C22⋊Q811yescharacteristic
409C22×C11C2×C22⋊Q811yescharacteristic
410C22×C11C2×C22⋊Q811yescharacteristic
411C22×C11C2×#12411yescharacteristic
412C22×C11C2×#12411yescharacteristic
413C22×C11C2×#12411yescharacteristic
414C4×C11—44no—
415C4×C11—42no—
416C4×C11—82no—
417Dic11—44no—
418Dic11—44no—
419Dic11—82no—
420Dic11—82no—
421C25Dic2211yescharacteristic, complemented
422C25C22×D1111yescharacteristic
423C22×Q8—222no—
424C22×D4—21no—
425C22×D4—21no—
426C22×D4—21no—
427C22×D4—21no—
428C22×D4—21no—
429C22×D4—21no—
430C22×D4—21no—
431C22×D4—21no—
432C22×D4—21no—
433C22×D4—21no—
434C22×D4—21no—
435C22×D4—21no—
436C22×D4Dic2212yescomplemented
437C22×D4C22×D1112yes—
438C23×C4—21no—
439C23×C4—21no—
440C23×C4—221no—
441C23×C4—221no—
442C23×C4—221no—
443C23×C4—221no—
444C23×C4Dic2211yescharacteristic, complemented
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—112no—
462C2×C22⋊C4—112no—
463C2×C22⋊C4—112no—
464C2×C22⋊C4—112no—
465C2×C22⋊C4—112no—
466C2×C22⋊C4—112no—
467C2×C22⋊C4—112no—
468C2×C22⋊C4—112no—
469C2×C22⋊C4—221no—
470C2×C22⋊C4—221no—
471C2×C22⋊C4—221no—
472C2×C22⋊C4—221no—
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⋊C4—221no—
485C2×C22⋊C4C22⋊D1112yes—
486C2×C22⋊C4C22⋊D1112yes—
487C2×C22⋊C4C22×D1112yes—
488C2×C22⋊C4C22×D1112yes—
489#99—28no—
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—82no—
507C2×C11#203212yescomplemented
508C2×C11C2×#39311yescharacteristic
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—82no—
516C24—82no—
517C24C2×Dic2211yescharacteristic
518C24C2×Dic2211yescharacteristic
519C24C2×Dic2212yescomplemented
520C24#433911yescharacteristic
521C24#433911yescharacteristic
522C24D4×D1111yescharacteristic
523C24D4×D1111yescharacteristic
524C24D4×D1111yescharacteristic
525C24D4×D1111yescharacteristic
526C24#434111yescharacteristic
527C24#434111yescharacteristic
528C24#434111yescharacteristic
529C24#434111yescharacteristic
530C24C2×C22⋊D1111yescharacteristic
531C24C2×C22⋊D1111yescharacteristic
532C24C23×D1111yescharacteristic
533C2×Q8—228no—
534C2×Q8—884no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—41no—
548C2×D4—41no—
549C2×D4—41no—
550C2×D4—41no—
551C2×D4—41no—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—41no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—82no—
576C22×C4—82no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—441no—
586C22×C4—441no—
587C22×C4—441no—
588C22×C4—441no—
589C22×C4—882no—
590C22×C4—882no—
591C22×C4—882no—
592C22×C4—882no—
593C22×C4C2×Dic2212yescomplemented
594C4⋊C4—2216no—
595C4⋊C4—228no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—41no—
602C22⋊C4—41no—
603C22⋊C4—114no—
604C22⋊C4—114no—
605C22⋊C4—222no—
606C22⋊C4—222no—
607C22⋊C4—222no—
608C22⋊C4—222no—
609C22⋊C4—222no—
610C22⋊C4—222no—
611C22⋊C4—222no—
612C22⋊C4—222no—
613C22⋊C4—222no—
614C22⋊C4—222no—
615C22⋊C4—441no—
616C22⋊C4—441no—
617C22⋊C4—441no—
618C22⋊C4—441no—
619C22⋊C4C2×C22⋊D1114yes—
620C11C2×#203211yescharacteristic, complemented, Sylow
621C23—22no—
622C23—22no—
623C23—22no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—82no—
636C23—82no—
637C23—82no—
638C23—81no—
639C23—81no—
640C23—81no—
641C23—81no—
642C23—81no—
643C23—81no—
644C23—81no—
645C23—81no—
646C23—82no—
647C23—82no—
648C23—82no—
649C23—82no—
650C23#6693111yescharacteristic
651C23#6693111yescharacteristic
652C23#6693111yescharacteristic
653C23#6693111yescharacteristic
654C23#6693111yescharacteristic
655C23#6693111yescharacteristic
656C23#6693111yescharacteristic
657C23#6693111yescharacteristic
658C23#6693811yescharacteristic
659C23#6693811yescharacteristic
660C23#6693811yescharacteristic
661C23#6693811yescharacteristic
662C23#6693811yescharacteristic
663C23#6693811yescharacteristic
664C23#6693811yescharacteristic
665C23#6693811yescharacteristic
666C23#6697711yescharacteristic
667C23#6697711yescharacteristic
668C23#6697711yescharacteristic
669C23#6697711yescharacteristic
670C23#6698911yescharacteristic
671C23#6698911yescharacteristic
672C23#6698911yescharacteristic
673C23#6698911yescharacteristic
674C23#6699011yescharacteristic
675C23#6699011yescharacteristic
676C23#6699011yescharacteristic
677C23#6699011yescharacteristic
678C23C22×Dic2211yescharacteristic
679C23C2×#433911yescharacteristic
680C23C2×D4×D1111yescharacteristic
681C23C2×D4×D1111yescharacteristic
682C23C2×#434111yescharacteristic
683C23C2×#434111yescharacteristic
684C23C22×C22⋊D1111yescharacteristic
685Q8—888no—
686D4—42no—
687D4—42no—
688D4—42no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—42no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—44no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4—82no—
707C2×C4—82no—
708C2×C4—82no—
709C2×C4—224no—
710C2×C4—224no—
711C2×C4—444no—
712C2×C4—444no—
713C2×C4—442no—
714C2×C4—442no—
715C2×C4—882no—
716C2×C4—882no—
717C2×C4—882no—
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—42no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22#1062256011yescharacteristic
769C22#1062256011yescharacteristic
770C22#1062256011yescharacteristic
771C22#1062256011yescharacteristic
772C22#1062256011yescharacteristic
773C22#1062256011yescharacteristic
774C22#1062256011yescharacteristic
775C22#1062256011yescharacteristic
776C22C2×#6693111yescharacteristic
777C22C2×#6693111yescharacteristic
778C22C2×#6693811yescharacteristic
779C22C2×#6693811yescharacteristic
780C22C2×#6697711yescharacteristic
781C22C2×#6698911yescharacteristic
782C22C2×#6699011yescharacteristic
783C4—44no—
784C4—42no—
785C4—82no—
786C4—444no—
787C4—444no—
788C4—882no—
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—82no—
805C2#1306979312yesdirect product factor
806C2C2×#1062256011yescharacteristic
subgroupG/H
centerC22#10622560
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC22×C11×#99C2
socleC22×C11#393
prime radicalC23×D4×C11C22
hypercenterC22×#99D11
hypocenterC11C2×#2032
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
1. C2×#10623014C2semidirect
4. #13069793C2direct (N × H)
5. C2×#10622164C2semidirect
6. C2×#10622165C2semidirect
7. C2×#10622165C2semidirect
20. #10623014C22semidirect
32. #10622165C22semidirect
33. #10622165C22semidirect
34. #10622164C22semidirect
35. C25×C11Q8semidirect
49. C22×D4×C11Q8semidirect
53. C23×C4×C11Q8semidirect
123. C24×C11C2×Q8semidirect
173. C22×C4×C11C2×Q8semidirect
421. C25Dic22semidirect
436. C22×D4Dic22semidirect
444. C23×C4Dic22semidirect
507. C2×C11#2032semidirect
519. C24C2×Dic22semidirect
593. C22×C4C2×Dic22semidirect
620. C11C2×#2032semidirect
805. C2#13069793direct (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×#668982
#130697932
C2×#106221642
C2×#106221652
C22×C11×#992
C2×#203211