Finite Group Databasebeta

← #14660711

Subgroups — #14660711

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×#66870C211yesmaximal, characteristic
2C22×#66870C211yesmaximal, characteristic
3#13071228C211yesmaximal, characteristic, complemented
4#13071191C211yesmaximal, characteristic
5C2×#10622165C211yesmaximal, characteristic, complemented
6C2×#10622165C211yesmaximal, characteristic, complemented
7C2×C11×#342C211yesmaximal, characteristic, complemented
8C23×C22⋊D11C2211yescharacteristic
9C22×C11×C22⋊C4C2211yescharacteristic
10C22×C11×C22⋊C4C2211yescharacteristic
11C22×C11×C22⋊C4C2211yescharacteristic
12C22×C22⋊Dic11C2211yescharacteristic
13C22×C22⋊Dic11C2211yescharacteristic
14C22×C22⋊Dic11C2211yescharacteristic
15#10622826—22no—
16#10622823—22no—
17#10622571—22no—
18#10622568C412yescomplemented
19C2×#66870—22no—
20C2×#66870—22no—
21C2×#66870—22no—
22C2×#66870—22no—
23C2×#66870—22no—
24C2×#66870—22no—
25#10622559—22no—
26#10622556C412yescomplemented
27#10622555—22no—
28C11×#342—22no—
29#10622165—22no—
30#10622165—22no—
31C25×C11C2311yescharacteristic
32C24×D11C2×C411yescharacteristic
33C23×C4×C11—21no—
34C23×C4×C11—21no—
35C23×C4×C11—21no—
36C22×C22⋊D11—21no—
37C22×C22⋊D11—21no—
38C22×C22⋊D11—21no—
39C22×C22⋊D11—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⋊D11D412yes—
49C22×C22⋊D11Q812yes—
50C23×Dic11—21no—
51C23×Dic11—21no—
52C23×Dic11C2×C411yescharacteristic
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⋊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⋊C4C2×C412yes—
70C2×C11×C22⋊C4D412yes—
71C2×C11×C22⋊C4D412yes—
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⋊Dic11C2×C412yes—
87C2×C22⋊Dic11D412yes—
88C2×C22⋊Dic11D412yes—
89C2×C22⋊Dic11D412yes—
90C2×(C2×D11)⋊C4—24no—
91C2×Dic11⋊C4—24no—
92C11⋊#95—24no—
93C11⋊#95—24no—
94#66870—28no—
95#66870—28no—
96#11046—111nomaximal, Sylow
97C24×C11—82no—
98C24×C11C22×C411yescharacteristic
99C24×C11C2×D411yescharacteristic
100C24×C11C2×D411yescharacteristic
101C24×C11C2×D411yescharacteristic
102C24×C11C2×D411yescharacteristic
103C24×C11C2×D411yescharacteristic
104C24×C11C2×D411yescharacteristic
105C24×C11C2×D411yescharacteristic
106C24×C11C2×Q811yescharacteristic
107C24×C11#4111yescharacteristic
108C24×C11#4111yescharacteristic
109C24×C11#4111yescharacteristic
110C24×C11#4111yescharacteristic
111C24×C11#4111yescharacteristic
112C24×C11#4111yescharacteristic
113C23×D11—21no—
114C23×D11—21no—
115C23×D11—21no—
116C23×D11—21no—
117C23×D11—21no—
118C23×D11—21no—
119C23×D11—82no—
120C23×D11C4⋊C412yescomplemented
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—41no—
125C22×C4×C11—41no—
126C22×C4×C11—41no—
127C22×C4×C11—41no—
128C22×C4×C11—41no—
129C22×C4×C11—41no—
130C22×C4×C11—82no—
131C22×C4×C11—82no—
132C22×C4×C11—82no—
133C2×C22⋊D11—22no—
134C2×C22⋊D11—22no—
135C2×C22⋊D11—22no—
136C2×C22⋊D11—22no—
137C2×C22⋊D11—22no—
138C2×C22⋊D11—22no—
139C2×C22⋊D11—22no—
140C2×C22⋊D11—22no—
141C2×C22⋊D11—22no—
142C2×C22⋊D11—22no—
143C2×C22⋊D11—22no—
144C2×C22⋊D11—22no—
145C2×C22⋊D11—41no—
146C2×C22⋊D11—41no—
147C2×C22⋊D11—41no—
148C2×C22⋊D11—41no—
149C2×C22⋊D11—41no—
150C2×C22⋊D11—41no—
151C2×C22⋊D11—41no—
152C2×C22⋊D11—41no—
153C2×C22⋊D11—41no—
154C2×C22⋊D11—41no—
155C2×C22⋊D11—41no—
156C2×C22⋊D11—41no—
157C2×C22⋊D11—41no—
158C2×C22⋊D11—41no—
159C2×C22⋊D11—41no—
160C2×C22⋊D11—41no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—41no—
172C22×Dic11—41no—
173C22×Dic11—41no—
174C22×Dic11—41no—
175C22×Dic11—82no—
176C22×Dic11—82no—
177C22×Dic11—82no—
178C22×Dic11C22⋊C414yes—
179C22×Dic11C4⋊C412yescomplemented
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—41no—
187C11×C22⋊C4—41no—
188C11×C22⋊C4—41no—
189C11×C22⋊C4—41no—
190C11×C22⋊C4—41no—
191C11×C22⋊C4—41no—
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—41no—
201C22⋊Dic11—41no—
202C22⋊Dic11—41no—
203C22⋊Dic11—41no—
204(C2×D11)⋊C4—84no—
205Dic11⋊C4—84no—
206C22×#99—111no—
207C22×#99—111no—
208#2315—111no—
209#2308—111no—
210C2×#342—111no—
211C2×#342—111no—
212C2×#342D1111yescharacteristic, complemented
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—81no—
221C23×C11—81no—
222C23×C11—81no—
223C23×C11—81no—
224C23×C11—81no—
225C23×C11—81no—
226C23×C11—81no—
227C23×C11—81no—
228C23×C11C2×C22⋊C411yescharacteristic
229C23×C11C2×C4⋊C411yescharacteristic
230C23×C11#11711yescharacteristic
231C23×C11C4×D411yescharacteristic
232C23×C11C4×D411yescharacteristic
233C23×C11C4×D411yescharacteristic
234C23×C11C4×D411yescharacteristic
235C23×C11#12011yescharacteristic
236C23×C11#12011yescharacteristic
237C23×C11#12011yescharacteristic
238C23×C11#12111yescharacteristic
239C23×C11#12111yescharacteristic
240C23×C11#12111yescharacteristic
241C23×C11#12111yescharacteristic
242C23×C11#12111yescharacteristic
243C23×C11#12111yescharacteristic
244C23×C11#12111yescharacteristic
245C23×C11#12111yescharacteristic
246C23×C11C22⋊Q811yescharacteristic
247C23×C11C22⋊Q811yescharacteristic
248C23×C11C22⋊Q811yescharacteristic
249C23×C11C22⋊Q811yescharacteristic
250C23×C11C22⋊Q811yescharacteristic
251C23×C11C22⋊Q811yescharacteristic
252C23×C11#12311yescharacteristic
253C23×C11#12311yescharacteristic
254C23×C11#12311yescharacteristic
255C23×C11#12311yescharacteristic
256C23×C11#12311yescharacteristic
257C23×C11#12411yescharacteristic
258C23×C11#12411yescharacteristic
259C23×C11#12411yescharacteristic
260C23×C11#12611yescharacteristic
261C23×C11#12611yescharacteristic
262C23×C11#12711yescharacteristic
263C22×D11—22no—
264C22×D11—22no—
265C22×D11—22no—
266C22×D11—44no—
267C22×D11—41no—
268C22×D11—41no—
269C22×D11—41no—
270C22×D11—41no—
271C22×D11—82no—
272C22×D11—82no—
273C22×D11—82no—
274C22×D11—82no—
275C22×D11—82no—
276C22×D11—82no—
277C2×C4×C11—44no—
278C2×C4×C11—44no—
279C2×C4×C11—42no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11—82no—
283C2×C4×C11—82no—
284C2×C4×C11—82no—
285C2×C4×C11—82no—
286C2×C4×C11—82no—
287C2×C4×C11—82no—
288C2×C4×C11—82no—
289C22⋊D11—42no—
290C22⋊D11—42no—
291C22⋊D11—42no—
292C22⋊D11—42no—
293C22⋊D11—42no—
294C22⋊D11—42no—
295C22⋊D11—42no—
296C22⋊D11—42no—
297C2×Dic11—22no—
298C2×Dic11—22no—
299C2×Dic11—22no—
300C2×Dic11—24no—
301C2×Dic11—44no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—44no—
307C2×Dic11—44no—
308C2×Dic11—42no—
309C2×Dic11—42no—
310C2×Dic11—82no—
311C2×Dic11—82no—
312C2×Dic11—82no—
313C2×Dic11—82no—
314C2×Dic11—82no—
315C2×Dic11—82no—
316C23×D4—111no—
317C22×C22⋊C4—111no—
318C22×C22⋊C4—111no—
319C22×C22⋊C4—111no—
320C22×C22⋊C4C2×D1111yescharacteristic
321C22×C22⋊C4C2×D1111yescharacteristic
322C22×C22⋊C4C2×D1111yescharacteristic
323C2×#99—222no—
324C2×#99—222no—
325C2×#99—222no—
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—22no—
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#38011yescharacteristic
375C22×C11#38511yescharacteristic
376C22×C11#38511yescharacteristic
377C22×C11#38611yescharacteristic
378C22×C11#38811yescharacteristic
379C22×C11#38811yescharacteristic
380C22×C11#39011yescharacteristic
381C22×C11#39211yescharacteristic
382C22×C11#39311yescharacteristic
383C22×C11#39411yescharacteristic
384C22×C11#39411yescharacteristic
385C22×C11#39611yescharacteristic
386C22×C11#39611yescharacteristic
387C22×C11#39711yescharacteristic
388C22×C11#39911yescharacteristic
389C2×D11—44no—
390C2×D11—42no—
391C2×D11—82no—
392C2×D11—82no—
393C2×D11—82no—
394C2×D11—82no—
395C2×D11—82no—
396C2×D11—82no—
397C4×C11—82no—
398C4×C11—82no—
399C4×C11—82no—
400Dic11—44no—
401Dic11—42no—
402Dic11—82no—
403Dic11—82no—
404C25—111no—
405C25C22×D1111yescharacteristic
406C22×D4—112no—
407C22×D4—112no—
408C22×D4—221no—
409C22×D4—221no—
410C22×D4—221no—
411C22×D4—221no—
412C22×D4—221no—
413C22×D4—221no—
414C22×D4—221no—
415C22×D4—221no—
416C22×D4—221no—
417C22×D4—221no—
418C22×D4—221no—
419C22×D4—221no—
420C23×C4—21no—
421C23×C4—21no—
422C23×C4—21no—
423C23×C4—111no—
424C23×C4—112no—
425C23×C4—221no—
426C23×C4—221no—
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—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—112no—
444C2×C22⋊C4—112no—
445C2×C22⋊C4—112no—
446C2×C22⋊C4—112no—
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—224no—
462C2×C22⋊C4C4×D1112yes—
463C2×C22⋊C4D4412yes—
464C2×C22⋊C4C22⋊D1112yes—
465#99—228no—
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#143911yescharacteristic
484C2×C11#191312yes—
485D11—82no—
486C24—82no—
487C24—112no—
488C24—221no—
489C24—221no—
490C24—221no—
491C24—221no—
492C24—221no—
493C24—221no—
494C24—882no—
495C24C2×C4×D1111yescharacteristic
496C24C2×D4411yescharacteristic
497C24#433911yescharacteristic
498C24#433911yescharacteristic
499C24#433911yescharacteristic
500C24#433911yescharacteristic
501C24D4×D1111yescharacteristic
502C24D4×D1111yescharacteristic
503C24D4×D1111yescharacteristic
504C24D4×D1111yescharacteristic
505C24D4×D1111yescharacteristic
506C24#434111yescharacteristic
507C24Q8×D1111yescharacteristic
508C24#434311yescharacteristic
509C24C2×C22⋊D1111yescharacteristic
510C2×D4—222no—
511C2×D4—222no—
512C2×D4—222no—
513C2×D4—222no—
514C2×D4—222no—
515C2×D4—222no—
516C2×D4—222no—
517C2×D4—222no—
518C2×D4—222no—
519C2×D4—222no—
520C2×D4—222no—
521C2×D4—222no—
522C2×D4—441no—
523C2×D4—441no—
524C2×D4—441no—
525C2×D4—441no—
526C2×D4—441no—
527C2×D4—441no—
528C2×D4—441no—
529C2×D4—441no—
530C2×D4—441no—
531C2×D4—441no—
532C2×D4—441no—
533C2×D4—441no—
534C2×D4—441no—
535C2×D4—441no—
536C2×D4—441no—
537C2×D4—441no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—82no—
548C22×C4—82no—
549C22×C4—82no—
550C22×C4—112no—
551C22×C4—114no—
552C22×C4—221no—
553C22×C4—221no—
554C22×C4—221no—
555C22×C4—221no—
556C22×C4—222no—
557C22×C4—221no—
558C22×C4—221no—
559C22×C4—222no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—441no—
563C22×C4—441no—
564C22×C4—441no—
565C22×C4—441no—
566C22×C4—882no—
567C22×C4—882no—
568C22×C4—882no—
569C4⋊C4—884no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—41no—
577C22⋊C4—41no—
578C22⋊C4—41no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—222no—
583C22⋊C4—222no—
584C22⋊C4—222no—
585C22⋊C4—222no—
586C22⋊C4—222no—
587C22⋊C4—222no—
588C22⋊C4—222no—
589C22⋊C4—222no—
590C22⋊C4—441no—
591C22⋊C4—441no—
592C22⋊C4—441no—
593C22⋊C4—441no—
594C22⋊C4—884no—
595C11#1104611yescharacteristic, complemented, Sylow
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—81no—
604C23—81no—
605C23—81no—
606C23—81no—
607C23—81no—
608C23—81no—
609C23—81no—
610C23—81no—
611C23—222no—
612C23—222no—
613C23—222no—
614C23—444no—
615C23—441no—
616C23—441no—
617C23—441no—
618C23—441no—
619C23—882no—
620C23—882no—
621C23—882no—
622C23—882no—
623C23—882no—
624C23—882no—
625C23#6692511yescharacteristic
626C23C4×D4411yescharacteristic
627C23#6692811yescharacteristic
628C23#6692911yescharacteristic
629C23C22⋊C4×D1111yescharacteristic
630C23(C22⋊D11)⋊C411yescharacteristic
631C23#6693511yescharacteristic
632C23#6693511yescharacteristic
633C23#6693611yescharacteristic
634C23#6693711yescharacteristic
635C23#6693711yescharacteristic
636C23#6693711yescharacteristic
637C23#6693711yescharacteristic
638C23#6693711yescharacteristic
639C23#6693811yescharacteristic
640C23#6693811yescharacteristic
641C23C4⋊C4×D1111yescharacteristic
642C23#6694611yescharacteristic
643C23#6694711yescharacteristic
644C23#6694711yescharacteristic
645C23#6694711yescharacteristic
646C23#6694811yescharacteristic
647C23#6694911yescharacteristic
648C23#6694911yescharacteristic
649C23#6694911yescharacteristic
650C23#6694911yescharacteristic
651C23#6695011yescharacteristic
652C23#6695111yescharacteristic
653C23C4×C22⋊D1111yescharacteristic
654C23#6698211yescharacteristic
655C23#6698311yescharacteristic
656C23#6699011yescharacteristic
657C23#6699211yescharacteristic
658C23#6699311yescharacteristic
659C23#6699911yescharacteristic
660D4—442no—
661D4—442no—
662D4—442no—
663D4—442no—
664D4—442no—
665D4—442no—
666D4—442no—
667D4—442no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—82no—
674C2×C4—82no—
675C2×C4—82no—
676C2×C4—82no—
677C2×C4—82no—
678C2×C4—82no—
679C2×C4—82no—
680C2×C4—224no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—222no—
684C2×C4—444no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4—444no—
690C2×C4—444no—
691C2×C4—442no—
692C2×C4—442no—
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—444no—
735C22—442no—
736C22—882no—
737C22—882no—
738C22—882no—
739C22—882no—
740C22—882no—
741C22—882no—
742C22#1062227811yescharacteristic
743C22#1062228011yescharacteristic
744C22#1062228111yescharacteristic
745C22#1062228211yescharacteristic
746C22#1062228511yescharacteristic
747C22#1062228611yescharacteristic
748C22#1062228811yescharacteristic
749C22#1062228911yescharacteristic
750C22#1062255311yescharacteristic
751C22#1062257011yescharacteristic
752C22#1062257211yescharacteristic
753C22#1062257311yescharacteristic
754C22#1062260211yescharacteristic
755C22#1062260511yescharacteristic
756C22#1062260711yescharacteristic
757C4—82no—
758C4—82no—
759C4—82no—
760C4—444no—
761C4—442no—
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—882no—
779C2#1306686011yescharacteristic
780C2#1306915712yes—
subgroupG/H
centerC22#10622278
commutatorC24×C11C22×C4
FrattiniC25C22×D11
FittingC2×C11×#342C2
socleC22×C11#386
prime radicalC23×C22⋊D11C22
cosocleC25×C11C23
hypercenterC2×#342D11
hypocenterC11#11046
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
3. #13071228C2semidirect
5. C2×#10622165C2semidirect
6. C2×#10622165C2semidirect
7. C2×C11×#342C2semidirect
18. #10622568C4semidirect
26. #10622556C4semidirect
120. C23×D11C4⋊C4semidirect
179. C22×Dic11C4⋊C4semidirect
212. C2×#342D11semidirect
595. C11#11046semidirect

Maximal subgroups

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

subgroupindex
C22×#668702
#130712282
#130711912
C2×#106221652
C2×C11×#3422
#1104611