Finite Group Databasebeta

← #14660710

Subgroups — #14660710

Order 2816.

1178 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66898C211yesmaximal, characteristic
2#13071228C211yesmaximal, characteristic, complemented
3#13071194C211yesmaximal, characteristic
4C2×#10622164C211yesmaximal, characteristic, complemented
5C2×#10622165C211yesmaximal, characteristic, complemented
6C2×#10622165C211yesmaximal, characteristic, complemented
7C22×C11×#99C211yesmaximal, characteristic
8C23×D4×C11C2211yescharacteristic
9C22×C11×C22⋊C4C2211yescharacteristic
10C22×C11×C22⋊C4C2211yescharacteristic
11C22×C22⋊Dic11C2211yescharacteristic
12C22×C22⋊Dic11C2211yescharacteristic
13C22×C22⋊Dic11C2211yescharacteristic
14C22×C22⋊Dic11C2211yescharacteristic
15C2×C11×#99—22no—
16C2×C11×#99—22no—
17C2×C11×#99—22no—
18#10622860C412yescomplemented
19#10622833—22no—
20#10622833—22no—
21C2×#66898—22no—
22C2×#66898—22no—
23C2×#66898—22no—
24#10622824C412yescomplemented
25#10622823—22no—
26#10622559—22no—
27#10622555—22no—
28#10622165—22no—
29#10622165—22no—
30#10622164—22no—
31C25×C11C2×C411yescharacteristic
32C25×C11C2311yescharacteristic
33C22×D4×C11—21no—
34C22×D4×C11—21no—
35C22×D4×C11—21no—
36C22×D4×C11—21no—
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×C11D412yes—
46C22×D4×C11Q812yes—
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C23×C4×C11C2×C411yescharacteristic
50C23×Dic11—21no—
51C23×Dic11—21no—
52C23×Dic11—21no—
53C23×Dic11D412yes—
54C2×C11×C22⋊C4—21no—
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4—21no—
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⋊C4D412yes—
65C2×C11×C22⋊C4D412yes—
66C2×C22⋊Dic11—21no—
67C2×C22⋊Dic11—21no—
68C2×C22⋊Dic11—21no—
69C2×C22⋊Dic11—21no—
70C2×C22⋊Dic11—21no—
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—24no—
86C2×C22⋊Dic11C2×C412yes—
87C2×C22⋊Dic11C2×C412yes—
88C2×C22⋊Dic11D412yes—
89C2×C22⋊Dic11D412yes—
90C2×C22⋊Dic11D412yes—
91C2×Dic11⋊C4—24no—
92C11×#99—28no—
93#66898—28no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96#11046—111nomaximal, Sylow
97C24×C11—21no—
98C24×C11—21no—
99C24×C11—21no—
100C24×C11—21no—
101C24×C11—21no—
102C24×C11—21no—
103C24×C11—82no—
104C24×C11—82no—
105C24×C11C4⋊C412yescomplemented
106C24×C11C22×C411yescharacteristic
107C24×C11C2×D411yescharacteristic
108C24×C11C2×D411yescharacteristic
109C24×C11C2×D411yescharacteristic
110C24×C11C2×D411yescharacteristic
111C24×C11C2×D411yescharacteristic
112C24×C11C2×D411yescharacteristic
113C24×C11C2×D411yescharacteristic
114C24×C11C2×Q811yescharacteristic
115C24×C11#4111yescharacteristic
116C24×C11#4111yescharacteristic
117C24×C11#4111yescharacteristic
118C24×C11#4111yescharacteristic
119C24×C11#4111yescharacteristic
120C24×C11#4111yescharacteristic
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—41no—
134C2×D4×C11—41no—
135C2×D4×C11—41no—
136C2×D4×C11—41no—
137C2×D4×C11—41no—
138C2×D4×C11—41no—
139C2×D4×C11—41no—
140C2×D4×C11—41no—
141C2×D4×C11—41no—
142C2×D4×C11—41no—
143C2×D4×C11—41no—
144C2×D4×C11—41no—
145C2×D4×C11—41no—
146C2×D4×C11—41no—
147C2×D4×C11—41no—
148C2×D4×C11—41no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—41no—
158C22×C4×C11—41no—
159C22×C4×C11—41no—
160C22×C4×C11—41no—
161C22×C4×C11—82no—
162C22×C4×C11—82no—
163C22×C4×C11C4⋊C412yescomplemented
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—41no—
170C22×Dic11—41no—
171C22×Dic11—41no—
172C22×Dic11—41no—
173C22×Dic11—41no—
174C22×Dic11—41no—
175C22×Dic11—82no—
176C22×Dic11—82no—
177C22×Dic11—82no—
178C22×Dic11—82no—
179C22×Dic11C22⋊C414yes—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—41no—
185C11×C22⋊C4—41no—
186C11×C22⋊C4—41no—
187C11×C22⋊C4—41no—
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—41no—
199C22⋊Dic11—41no—
200C22⋊Dic11—41no—
201C22⋊Dic11—41no—
202C22⋊Dic11—41no—
203C22⋊Dic11—41no—
204C22⋊Dic11—84no—
205Dic11⋊C4—84no—
206C22×#99—111no—
207C22×#99D1111yescharacteristic
208#2315—111no—
209#2308—111no—
210C2×#342—111no—
211C2×#342—111no—
212C2×#342—111no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—44no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—82no—
229C23×C11—82no—
230C23×C11—81no—
231C23×C11—81no—
232C23×C11—81no—
233C23×C11—81no—
234C23×C11—81no—
235C23×C11—81no—
236C23×C11—81no—
237C23×C11—81no—
238C23×C11—82no—
239C23×C11—82no—
240C23×C11—82no—
241C23×C11—82no—
242C23×C11C2×C22⋊C411yescharacteristic
243C23×C11C2×C4⋊C411yescharacteristic
244C23×C11#11711yescharacteristic
245C23×C11C4×D411yescharacteristic
246C23×C11C4×D411yescharacteristic
247C23×C11C4×D411yescharacteristic
248C23×C11C4×D411yescharacteristic
249C23×C11#12011yescharacteristic
250C23×C11#12011yescharacteristic
251C23×C11#12011yescharacteristic
252C23×C11#12111yescharacteristic
253C23×C11#12111yescharacteristic
254C23×C11#12111yescharacteristic
255C23×C11#12111yescharacteristic
256C23×C11#12111yescharacteristic
257C23×C11#12111yescharacteristic
258C23×C11#12111yescharacteristic
259C23×C11#12111yescharacteristic
260C23×C11C22⋊Q811yescharacteristic
261C23×C11C22⋊Q811yescharacteristic
262C23×C11C22⋊Q811yescharacteristic
263C23×C11C22⋊Q811yescharacteristic
264C23×C11C22⋊Q811yescharacteristic
265C23×C11C22⋊Q811yescharacteristic
266C23×C11#12311yescharacteristic
267C23×C11#12311yescharacteristic
268C23×C11#12311yescharacteristic
269C23×C11#12311yescharacteristic
270C23×C11#12311yescharacteristic
271C23×C11#12411yescharacteristic
272C23×C11#12411yescharacteristic
273C23×C11#12411yescharacteristic
274C23×C11#12611yescharacteristic
275C23×C11#12611yescharacteristic
276C23×C11#12711yescharacteristic
277D4×C11—42no—
278D4×C11—42no—
279D4×C11—42no—
280D4×C11—42no—
281D4×C11—42no—
282D4×C11—42no—
283D4×C11—42no—
284D4×C11—42no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—44no—
293C2×C4×C11—42no—
294C2×C4×C11—42no—
295C2×C4×C11—82no—
296C2×C4×C11—82no—
297C2×C4×C11—82no—
298C2×C4×C11—82no—
299C2×C4×C11—82no—
300C2×Dic11—24no—
301C2×Dic11—44no—
302C2×Dic11—44no—
303C2×Dic11—44no—
304C2×Dic11—44no—
305C2×Dic11—42no—
306C2×Dic11—42no—
307C2×Dic11—42no—
308C2×Dic11—82no—
309C2×Dic11—82no—
310C2×Dic11—82no—
311C2×Dic11—82no—
312C2×Dic11—82no—
313C2×Dic11—82no—
314C2×Dic11—82no—
315C2×Dic11—82no—
316C23×D4C2×D1111yescharacteristic
317C22×C22⋊C4—111no—
318C22×C22⋊C4—111no—
319C22×C22⋊C4—111no—
320C22×C22⋊C4—111no—
321C22×C22⋊C4C2×D1111yescharacteristic
322C22×C22⋊C4C2×D1111yescharacteristic
323C2×#99—22no—
324C2×#99—22no—
325C2×#99—22no—
326C2×#99—222no—
327C2×#99—222no—
328C2×#99—222no—
329#386—222no—
330#386—222no—
331#385—222no—
332#385—222no—
333#381—112no—
334#380—222no—
335#379—112no—
336#342—222no—
337#342—222no—
338#342—222no—
339C22×C11—22no—
340C22×C11—22no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11—22no—
345C22×C11—22no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
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—44no—
375C22×C11—42no—
376C22×C11—82no—
377C22×C11—82no—
378C22×C11—82no—
379C22×C11—82no—
380C22×C11—82no—
381C22×C11—82no—
382C22×C11#38011yescharacteristic
383C22×C11#38511yescharacteristic
384C22×C11#38511yescharacteristic
385C22×C11#38611yescharacteristic
386C22×C11#38811yescharacteristic
387C22×C11#38811yescharacteristic
388C22×C11#39011yescharacteristic
389C22×C11#39211yescharacteristic
390C22×C11#39311yescharacteristic
391C22×C11#39411yescharacteristic
392C22×C11#39411yescharacteristic
393C22×C11#39611yescharacteristic
394C22×C11#39611yescharacteristic
395C22×C11#39711yescharacteristic
396C22×C11#39911yescharacteristic
397C4×C11—42no—
398C4×C11—82no—
399C4×C11—82no—
400Dic11—44no—
401Dic11—82no—
402Dic11—82no—
403Dic11—82no—
404C25C4×D1111yescharacteristic
405C25C22×D1111yescharacteristic
406C22×D4—21no—
407C22×D4—21no—
408C22×D4—21no—
409C22×D4—21no—
410C22×D4—21no—
411C22×D4—21no—
412C22×D4—21no—
413C22×D4—21no—
414C22×D4—21no—
415C22×D4—21no—
416C22×D4—21no—
417C22×D4—21no—
418C22×D4Dic2212yes—
419C22×D4C22⋊D1112yes—
420C23×C4—21no—
421C23×C4—21no—
422C23×C4—112no—
423C23×C4—221no—
424C23×C4—221no—
425C23×C4—221no—
426C23×C4C4×D1111yescharacteristic
427C2×C4⋊C4—224no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—112no—
439C2×C22⋊C4—112no—
440C2×C22⋊C4—112no—
441C2×C22⋊C4—112no—
442C2×C22⋊C4—112no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C22⋊C4—221no—
449C2×C22⋊C4—221no—
450C2×C22⋊C4—221no—
451C2×C22⋊C4—221no—
452C2×C22⋊C4—221no—
453C2×C22⋊C4—221no—
454C2×C22⋊C4—221no—
455C2×C22⋊C4—221no—
456C2×C22⋊C4—221no—
457C2×C22⋊C4—221no—
458C2×C22⋊C4—221no—
459C2×C22⋊C4—221no—
460C2×C22⋊C4—221no—
461C2×C22⋊C4—221no—
462C2×C22⋊C4—224no—
463C2×C22⋊C4C22⋊D1112yes—
464C2×C22⋊C4C22⋊D1112yes—
465#99—28no—
466#99—228no—
467#95—224no—
468#95—224no—
469C2×C11—21no—
470C2×C11—21no—
471C2×C11—21no—
472C2×C11—21no—
473C2×C11—21no—
474C2×C11—21no—
475C2×C11—21no—
476C2×C11—21no—
477C2×C11—21no—
478C2×C11—21no—
479C2×C11—21no—
480C2×C11—21no—
481C2×C11—21no—
482C2×C11—21no—
483C2×C11—82no—
484C2×C11#143911yescharacteristic
485C2×C11#191312yes—
486C24—21no—
487C24—21no—
488C24—21no—
489C24—21no—
490C24—21no—
491C24—21no—
492C24—82no—
493C24—82no—
494C24Dic11⋊C412yescomplemented
495C24C2×Dic2211yescharacteristic
496C24C2×C4×D1111yescharacteristic
497C24#433911yescharacteristic
498C24#433911yescharacteristic
499C24D4×D1111yescharacteristic
500C24D4×D1111yescharacteristic
501C24D4×D1111yescharacteristic
502C24D4×D1111yescharacteristic
503C24#434111yescharacteristic
504C24#434111yescharacteristic
505C24#434111yescharacteristic
506C24#434111yescharacteristic
507C24C2×C22⋊D1111yescharacteristic
508C24C2×C22⋊D1111yescharacteristic
509C24C2×C22⋊D1111yescharacteristic
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—41no—
523C2×D4—41no—
524C2×D4—41no—
525C2×D4—41no—
526C2×D4—41no—
527C2×D4—41no—
528C2×D4—41no—
529C2×D4—41no—
530C2×D4—41no—
531C2×D4—41no—
532C2×D4—41no—
533C2×D4—41no—
534C2×D4—41no—
535C2×D4—41no—
536C2×D4—41no—
537C2×D4—41no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—82no—
551C22×C4—82no—
552C22×C4—114no—
553C22×C4—222no—
554C22×C4—222no—
555C22×C4—222no—
556C22×C4—222no—
557C22×C4—222no—
558C22×C4—441no—
559C22×C4—441no—
560C22×C4—441no—
561C22×C4—441no—
562C22×C4—441no—
563C22×C4—441no—
564C22×C4—882no—
565C22×C4—882no—
566C22×C4—882no—
567C22×C4—882no—
568C22×C4Dic11⋊C412yescomplemented
569C4⋊C4—884no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C22⋊C4—41no—
578C22⋊C4—222no—
579C22⋊C4—222no—
580C22⋊C4—222no—
581C22⋊C4—222no—
582C22⋊C4—222no—
583C22⋊C4—222no—
584C22⋊C4—222no—
585C22⋊C4—222no—
586C22⋊C4—222no—
587C22⋊C4—222no—
588C22⋊C4—441no—
589C22⋊C4—441no—
590C22⋊C4—441no—
591C22⋊C4—441no—
592C22⋊C4—441no—
593C22⋊C4—441no—
594C22⋊C4—884no—
595C11#1104611yescharacteristic, complemented, Sylow
596C23—22no—
597C23—22no—
598C23—22no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—44no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—82no—
612C23—82no—
613C23—81no—
614C23—81no—
615C23—81no—
616C23—81no—
617C23—81no—
618C23—81no—
619C23—81no—
620C23—81no—
621C23—82no—
622C23—82no—
623C23—82no—
624C23—82no—
625C23#6693011yescharacteristic
626C23#6693111yescharacteristic
627C23#6693111yescharacteristic
628C23#6693111yescharacteristic
629C23#6693111yescharacteristic
630C23#6693211yescharacteristic
631C23#6693211yescharacteristic
632C23C22⋊C4×D1111yescharacteristic
633C23(C22⋊D11)⋊C411yescharacteristic
634C23(C22⋊D11)⋊C411yescharacteristic
635C23#6693611yescharacteristic
636C23#6693611yescharacteristic
637C23#6693711yescharacteristic
638C23#6693711yescharacteristic
639C23#6693811yescharacteristic
640C23#6693811yescharacteristic
641C23C2×Dic11⋊C411yescharacteristic
642C23#6697711yescharacteristic
643C23#6697711yescharacteristic
644C23C4×C22⋊D1111yescharacteristic
645C23C4×C22⋊D1111yescharacteristic
646C23#6698211yescharacteristic
647C23#6698811yescharacteristic
648C23#6698811yescharacteristic
649C23#6698911yescharacteristic
650C23#6699011yescharacteristic
651C23#6699011yescharacteristic
652C23#6699111yescharacteristic
653C23#6699111yescharacteristic
654C23#6699211yescharacteristic
655C23#6699211yescharacteristic
656C23#6699211yescharacteristic
657C23#6699211yescharacteristic
658C23#6699311yescharacteristic
659C23#6700611yescharacteristic
660D4—42no—
661D4—42no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—42no—
667D4—42no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—44no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—82no—
679C2×C4—82no—
680C2×C4—82no—
681C2×C4—82no—
682C2×C4—82no—
683C2×C4—224no—
684C2×C4—444no—
685C2×C4—444no—
686C2×C4—444no—
687C2×C4—444no—
688C2×C4—442no—
689C2×C4—442no—
690C2×C4—442no—
691C2×C4—882no—
692C2×C4—882no—
693C2×C4—882no—
694C2×C4—882no—
695C2×C4—882no—
696C2×C4—882no—
697C2×C4—882no—
698C2×C4—882no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—44no—
735C22—42no—
736C22—82no—
737C22—82no—
738C22—82no—
739C22—82no—
740C22—82no—
741C22—82no—
742C22#1062255511yescharacteristic
743C22#1062255711yescharacteristic
744C22#1062255811yescharacteristic
745C22#1062255911yescharacteristic
746C22#1062256011yescharacteristic
747C22#1062256111yescharacteristic
748C22#1062256111yescharacteristic
749C22#1062256211yescharacteristic
750C22#1062256511yescharacteristic
751C22#1062256911yescharacteristic
752C22#1062257011yescharacteristic
753C22#1062257211yescharacteristic
754C22#1062282311yescharacteristic
755C22#1062283511yescharacteristic
756C22#1062283611yescharacteristic
757C4—42no—
758C4—82no—
759C4—82no—
760C4—444no—
761C4—882no—
762C4—882no—
763C4—882no—
764C2—21no—
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—21no—
772C2—21no—
773C2—21no—
774C2—21no—
775C2—21no—
776C2—21no—
777C2—21no—
778C2—82no—
779C2#1306685911yescharacteristic
780C2#1306915512yes—
subgroupG/H
centerC22#10622569
commutatorC24×C11C22×C4
FrattiniC25C22×D11
FittingC22×C11×#99C2
socleC22×C11#386
prime radicalC23×D4×C11C22
cosocleC25×C11C23
hypercenterC22×#99D11
hypocenterC11#11046
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
2. #13071228C2semidirect
4. C2×#10622164C2semidirect
5. C2×#10622165C2semidirect
6. C2×#10622165C2semidirect
18. #10622860C4semidirect
24. #10622824C4semidirect
105. C24×C11C4⋊C4semidirect
163. C22×C4×C11C4⋊C4semidirect
494. C24Dic11⋊C4semidirect
568. C22×C4Dic11⋊C4semidirect
595. C11#11046semidirect

Maximal subgroups

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

subgroupindex
C22×#668982
#130712282
#130711942
C2×#106221642
C2×#106221652
C22×C11×#992
#1104611