Finite Group Databasebeta

← #14810973

Subgroups — #14810973

Order 2816.

1162 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622679C211yesmaximal, characteristic, complemented
2C2×D11×#102C211yesmaximal, characteristic
3#13072336C211yesmaximal, characteristic, complemented
4#13071437C211yesmaximal, characteristic
5#13070135C211yesmaximal, characteristic, complemented
6#13070000C211yesmaximal, characteristic, complemented
7#13069990C211yesmaximal, characteristic, complemented
8#13068878C211yesmaximal, characteristic, complemented
9#13068866C211yesmaximal, characteristic, complemented
10#13068805C211yesmaximal, characteristic, complemented
11#13068795C211yesmaximal, characteristic, complemented
12#13068640C211yesmaximal, characteristic, complemented
13#13068625C211yesmaximal, characteristic, complemented
14#13068545C211yesmaximal, characteristic
15C11×#2025C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C2×C11×#125C2211yescharacteristic, complemented
18C22×C8×D11C2211yescharacteristic
19C2×#66946C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C22⋊C4×D11—21no—
22C2×C4×D44C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C11×#390C2211yescharacteristic
26#10622834C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×#66882C2211yescharacteristic, complemented
33C2×Dic11⋊C8C2211yescharacteristic, complemented
34#10622679—24no—
35#10622602—21no—
36#10622600—21no—
37#10622600C2211yescharacteristic
38#10622600C2211yescharacteristic
39#10622598C2211yescharacteristic, complemented
40#10622597—21no—
41#10622595—21no—
42#10622590C2211yescharacteristic, complemented
43C2×#66873C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66872C2211yescharacteristic, complemented
46C2×#66872C2211yescharacteristic, complemented
47C2×#66871C2211yescharacteristic, complemented
48#10622569—21no—
49#10622569—21no—
50#10622568—21no—
51C4×(C2×D11)⋊C4C2211yescharacteristic
52#10622541C2211yescharacteristic, complemented
53C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
54D11×#102—24no—
55C11×#340C2211yescharacteristic, complemented
56C11×#340C2211yescharacteristic, complemented
57C11×#336C2211yescharacteristic, complemented
58#10622189C2211yescharacteristic, complemented
59#10622188C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61C24×D11—21no—
62C22×D4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C2×D4×D11—22no—
65C2×D4×D11—22no—
66C2×D4×D11—22no—
67C2×D4×D11—41no—
68C2×D4×D11—41no—
69C2×D4×D11Q814yes—
70C22×D44C2311yescharacteristic
71C22×C4×D11—21no—
72C22×C4×D11—21no—
73C22×C4×D11—21no—
74C22×C4×D11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×#125—22no—
78C11×#125—41no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C42×C11C2311yescharacteristic
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4D411yescharacteristic
94C2×(C2×D11)⋊C4D411yescharacteristic
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C2×C8×D11—22no—
105C2×C8×D11—22no—
106C2×C8×D11—41no—
107#66946—22no—
108#66946—41no—
109C4⋊C4×D11—22no—
110C4⋊C4×D11—41no—
111C22⋊C4×D11—44no—
112C4×D44—22no—
113C4×D44—41no—
114C11×#102—22no—
115C11×#102—41no—
116#66896—22no—
117#66896—41no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95D411yescharacteristic
125C11⋊#95D411yescharacteristic
126#66885—22no—
127#66885—22no—
128(C2×D11)⋊C8—22no—
129#66882—41no—
130Dic11⋊C8—41no—
131#66873—22no—
132#66873D414yes—
133#66872—22no—
134#66872—41no—
135#66871—22no—
136C4⋊(C11⋊C8)—22no—
137#25960—111nomaximal, Sylow
138C24×C11—21no—
139C23×D11—21no—
140C23×D11—24no—
141C23×D11—42no—
142C23×D11—42no—
143C23×D11—42no—
144C23×D11—42no—
145C23×D11—81no—
146C23×D11—81no—
147C23×D11C2×D411yescharacteristic
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11C2×Q812yes—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—24no—
161C2×C22⋊D11—42no—
162C2×C22⋊D11—42no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169D4×D11—28no—
170D4×D11—44no—
171D4×D11—44no—
172D4×D11—44no—
173C2×D44—21no—
174C2×D44—21no—
175C2×D44—21no—
176C2×D44C2×D412yes—
177C2×D44C2×Q812yes—
178C2×D44#4112yes—
179C2×C4×D11—21no—
180C2×C4×D11—21no—
181C2×C4×D11—21no—
182C2×C4×D11—21no—
183C2×C4×D11—42no—
184C2×C4×D11—42no—
185C2×C4×D11—42no—
186C2×C4×D11—42no—
187C2×C4×D11—42no—
188C2×C4×D11—42no—
189C2×C4×D11—81no—
190C2×C4×D11—81no—
191C2×C4×D11—81no—
192C2×C4×D11C2×Q812yes—
193C2×C4×D11#4112yes—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—42no—
206C11×C4⋊C4—42no—
207C11×C4⋊C4C2×D412yes—
208C11×C22⋊C4—42no—
209C11×C22⋊C4—81no—
210C42×C11—21no—
211C42×C11—21no—
212C22⋊Dic11—42no—
213C22⋊Dic11—81no—
214(C2×D11)⋊C4—22no—
215(C2×D11)⋊C4—22no—
216(C2×D11)⋊C4—42no—
217(C2×D11)⋊C4—42no—
218(C2×D11)⋊C4—42no—
219(C2×D11)⋊C4—42no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—81no—
227Dic11⋊C4—42no—
228Dic11⋊C4—81no—
229C4×Dic11—21no—
230C4×Dic11—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8C2×D412yes—
237C8×D11—44no—
238C2×#478—111no—
239C22×#102—111no—
240#2442—111no—
241D4×C22⋊C4—111no—
242#2092—111no—
243#2067—111no—
244#2065—111no—
245#2025D1111yescharacteristic, complemented
246#1864—111no—
247#1862—111no—
248#1852—111no—
249#1850—111no—
250#1807—111no—
251#1804—111no—
252#1786—111no—
253C23×C11—22no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11C22×D411yescharacteristic
261C22×D11—21no—
262C22×D11—21no—
263C22×D11—21no—
264C22×D11—21no—
265C22×D11—22no—
266C22×D11—22no—
267C22×D11—22no—
268C22×D11—48no—
269C22×D11—41no—
270C22×D11—41no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—48no—
274C22×D11—84no—
275C22×D11—84no—
276C22×D11—84no—
277C22×D11—84no—
278C22×D11—84no—
279C22×D11C22⋊Q812yes—
280C22×D11#13512yes—
281C22×D11AGL(1,ℤ/8)12yes—
282D4×C11—22no—
283D4×C11—22no—
284D4×C11—41no—
285D4×C11—41no—
286C2×C4×C11—22no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11C22×D411yescharacteristic
302C2×C4×C11C22×Q811yescharacteristic
303C2×C4×C11C2×#4111yescharacteristic
304C2×C4×C11C2×#4111yescharacteristic
305C2×C4×C11H(5,𝔽2)11yescharacteristic
306C2×C4×C11H(5,𝔽2)11yescharacteristic
307C22⋊D11—48no—
308C2×Dic11—21no—
309C2×Dic11—21no—
310C2×Dic11—21no—
311C2×Dic11—21no—
312C2×Dic11—21no—
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11C22⋊Q812yes—
326D44—22no—
327D44—22no—
328D44—22no—
329D44C22⋊Q814yes—
330C4×D11—22no—
331C4×D11—22no—
332C4×D11—22no—
333C4×D11—22no—
334C4×D11—84no—
335C4×D11—84no—
336C4×D11—84no—
337C8×C11—41no—
338C8×C11—41no—
339C11⋊C8—22no—
340C11⋊C8—41no—
341C23×D4—111no—
342C23×C8—111no—
343C2×#125C2×D1111yescharacteristic, complemented
344C2×C4×D4—111no—
345C2×C4×D4—111no—
346C22×C4⋊C4—111no—
347C22×C22⋊C4—221no—
348#478—224no—
349C2×#107—111no—
350C2×#107—111no—
351C2×#106—111no—
352C2×#106—111no—
353C2×C4⋊C8—111no—
354C2×C4⋊C8—111no—
355C2×#102—111no—
356C2×#102—111no—
357C2×#102—111no—
358C2×#102—111no—
359C2×#102—111no—
360C2×#102—111no—
361C2×#102—224no—
362C2×#102C2×D1111yescharacteristic
363C2×#102C2×D1111yescharacteristic
364C2×C22⋊C8—111no—
365#400—221no—
366#398—221no—
367#390—111no—
368#390C2×D1111yescharacteristic
369#389—111no—
370#389—111no—
371#386—221no—
372#386—221no—
373#385—221no—
374#382—111no—
375#380—111no—
376#380—111no—
377#380—221no—
378#379—221no—
379C4×C22⋊C4—111no—
380#340—111no—
381#340—111no—
382#340C2×D1111yescharacteristic, complemented
383#340C2×D1111yescharacteristic, complemented
384#336—111no—
385#336C2×D1111yescharacteristic, complemented
386C22×C11—42no—
387C22×C11—42no—
388C22×C11—42no—
389C22×C11—81no—
390C22×C11—81no—
391C22×C11—81no—
392C22×C11—81no—
393C22×C11C2×C22⋊Q811yescharacteristic
394C22×C11D4211yescharacteristic
395C22×C11#54611yescharacteristic
396C22×C11C2×#13511yescharacteristic
397C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
398C22×C11#57611yescharacteristic
399C22×C11#57711yescharacteristic
400C2×D11—22no—
401C2×D11—22no—
402C2×D11—22no—
403C2×D11—22no—
404C2×D11—22no—
405C2×D11—22no—
406C2×D11—24no—
407C2×D11—42no—
408C2×D11—42no—
409C2×D11—42no—
410C2×D11—42no—
411C2×D11—42no—
412C2×D11—42no—
413C2×D11—816no—
414C2×D11#47814yescomplemented
415C4×C11—41no—
416C4×C11—42no—
417C4×C11—41no—
418C4×C11—81no—
419C4×C11—81no—
420C4×C11C2×C22⋊Q811yescharacteristic
421C4×C11#54311yescharacteristic
422C4×C11#54611yescharacteristic
423C4×C11#55111yescharacteristic
424Dic11—22no—
425Dic11—41no—
426Dic11—41no—
427Dic11—81no—
428Dic11—81no—
429Dic11—81no—
430C25—221no—
431C22×D4—114no—
432C22×D4—111no—
433C22×D4—222no—
434C22×D4—221no—
435C22×D4—222no—
436C22×D4—222no—
437C22×D4—441no—
438C22×D4—441no—
439C22×D4C22×D1111yescharacteristic
440C23×C4—111no—
441C23×C4—221no—
442C23×C4—221no—
443C23×C4—221no—
444C22×C8—111no—
445C22×C8—111no—
446C22×C8—222no—
447C22×C8—222no—
448C22×C8—441no—
449C22×C8C22×D1111yescharacteristic
450C22×C8C22×D1111yescharacteristic
451#125—22no—
452#125—41no—
453C4×D4—222no—
454C4×D4—222no—
455C4×D4—441no—
456C4×D4—441no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—111no—
460C2×C4⋊C4—111no—
461C2×C4⋊C4—111no—
462C2×C4⋊C4—222no—
463C2×C4⋊C4—221no—
464C2×C4⋊C4—221no—
465C2×C4⋊C4—221no—
466C2×C4⋊C4—441no—
467C2×C4⋊C4C22×D1111yescharacteristic
468C2×C4⋊C4C22×D1111yescharacteristic
469C2×C4⋊C4C22×D1111yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—111no—
473C2×C22⋊C4—111no—
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—444no—
481C2×C42—111no—
482C2×C42C22×D1111yescharacteristic
483#107—222no—
484#107—441no—
485#106—222no—
486#106—441no—
487C4⋊C8—222no—
488C4⋊C8—441no—
489#102—22no—
490#102—41no—
491#102—114no—
492#102—222no—
493#102—222no—
494#102—222no—
495#102—222no—
496#102—441no—
497C22⋊C8—222no—
498#95—111no—
499#95—111no—
500#95—221no—
501#95—221no—
502#95—221no—
503#95—221no—
504#95—221no—
505#95—221no—
506C2×C11—82no—
507C2×C11#243711yescharacteristic
508C2×C11C2×#47811yescharacteristic
509C2×C11#308111yescharacteristic
510C2×C11#326411yescharacteristic
511C2×C11#328211yescharacteristic
512C2×C11#329711yescharacteristic
513C2×C11#331011yescharacteristic
514D11—24no—
515D11—44no—
516C24—21no—
517C24—111no—
518C24—224no—
519C24—221no—
520C24—442no—
521C24—442no—
522C24—442no—
523C24—442no—
524C24—881no—
525C24—881no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—112no—
532C2×D4—112no—
533C2×D4—112no—
534C2×D4—224no—
535C2×D4—228no—
536C2×D4—221no—
537C2×D4—221no—
538C2×D4—221no—
539C2×D4—444no—
540C2×D4—444no—
541C2×D4—444no—
542C2×D4—442no—
543C2×D4—442no—
544C2×D4Q8×D1112yes—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—111no—
549C22×C4—112no—
550C22×C4—112no—
551C22×C4—111no—
552C22×C4—111no—
553C22×C4—221no—
554C22×C4—221no—
555C22×C4—221no—
556C22×C4—221no—
557C22×C4—221no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—442no—
561C22×C4—442no—
562C22×C4—442no—
563C22×C4—442no—
564C22×C4—442no—
565C22×C4—442no—
566C22×C4—881no—
567C22×C4—881no—
568C22×C4—881no—
569C22×C4D4×D1111yescharacteristic
570C22×C4D4×D1111yescharacteristic
571C22×C4C23×D1111yescharacteristic
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—112no—
579C2×C8—221no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—444no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—221no—
593C4⋊C4—221no—
594C4⋊C4—221no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4—442no—
599C4⋊C4—881no—
600C4⋊C4—881no—
601C4⋊C4D4×D1112yes—
602C22⋊C4—42no—
603C22⋊C4—81no—
604C22⋊C4—222no—
605C22⋊C4—222no—
606C22⋊C4—442no—
607C22⋊C4—442no—
608C22⋊C4—442no—
609C22⋊C4—442no—
610C22⋊C4—442no—
611C22⋊C4—881no—
612C42—21no—
613C42—21no—
614C42—221no—
615C42—221no—
616C11#2596011yescharacteristic, complemented, Sylow
617C23—22no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—112no—
625C23—112no—
626C23—112no—
627C23—221no—
628C23—221no—
629C23—221no—
630C23—221no—
631C23—222no—
632C23—222no—
633C23—222no—
634C23—448no—
635C23—448no—
636C23—441no—
637C23—441no—
638C23—441no—
639C23—441no—
640C23—884no—
641C23—884no—
642C23—884no—
643C23—884no—
644C23—884no—
645C23C2×D4×D1111yescharacteristic
646D4—22no—
647D4—22no—
648D4—41no—
649D4—41no—
650D4—114no—
651D4—222no—
652D4—222no—
653D4—222no—
654D4—448no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—112no—
671C2×C4—221no—
672C2×C4—221no—
673C2×C4—222no—
674C2×C4—222no—
675C2×C4—222no—
676C2×C4—222no—
677C2×C4—221no—
678C2×C4—221no—
679C2×C4—221no—
680C2×C4—221no—
681C2×C4—221no—
682C2×C4—221no—
683C2×C4—441no—
684C2×C4—441no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4—441no—
690C2×C4—441no—
691C2×C4—441no—
692C2×C4—884no—
693C2×C4—884no—
694C2×C4—884no—
695C2×C4C2×D4×D1111yescharacteristic
696C2×C4#6703711yescharacteristic
697C2×C4C2×Q8×D1111yescharacteristic
698C2×C4#41×D1111yescharacteristic
699C2×C4#41×D1111yescharacteristic
700C2×C4#6704211yescharacteristic
701C8—41no—
702C8—41no—
703C8—222no—
704C8—441no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—114no—
713C22—222no—
714C22—222no—
715C22—222no—
716C22—222no—
717C22—222no—
718C22—222no—
719C22—224no—
720C22—442no—
721C22—442no—
722C22—442no—
723C22—442no—
724C22—442no—
725C22—442no—
726C22—8816no—
727C22#1062312111yescharacteristic
728C22D11×C22⋊Q811yescharacteristic
729C22#1062320711yescharacteristic
730C22D11×#13511yescharacteristic
731C22#1062330011yescharacteristic
732C22D11×AGL(1,ℤ/8)11yescharacteristic
733C22#1062330611yescharacteristic
734C4—41no—
735C4—41no—
736C4—42no—
737C4—81no—
738C4—81no—
739C4—222no—
740C4—441no—
741C4—441no—
742C4—881no—
743C4—881no—
744C4—881no—
745C4D11×C22⋊Q811yescharacteristic
746C4#1062316511yescharacteristic
747C4#1062320711yescharacteristic
748C4#1062321011yescharacteristic
749C2—82no—
750C2—224no—
751C2—444no—
752C2#1307227611yescharacteristic
753C2D11×#47811yescharacteristic
754C2#1307844411yescharacteristic
755C2#1308009911yescharacteristic
756C2#1308032611yescharacteristic
757C2#1308046511yescharacteristic
758C2#1308063611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2025C2
socleC23×C11C22×D4
prime radicalC22×D4×D11C22
hypercenter#2025D11
hypocenterC11#25960
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2025

Complements

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

NH ≅ G/Ntype
1. C2×#10622679C2semidirect
3. #13072336C2semidirect
5. #13070135C2semidirect
6. #13070000C2semidirect
7. #13069990C2semidirect
8. #13068878C2semidirect
9. #13068866C2semidirect
10. #13068805C2semidirect
11. #13068795C2semidirect
12. #13068640C2semidirect
13. #13068625C2semidirect
15. C11×#2025C2semidirect
17. C2×C11×#125C22semidirect
32. C2×#66882C22semidirect
33. C2×Dic11⋊C8C22semidirect
39. #10622598C22semidirect
42. #10622590C22semidirect
45. C2×#66872C22semidirect
46. C2×#66872C22semidirect
47. C2×#66871C22semidirect
52. #10622541C22semidirect
53. C2×C4⋊(C11⋊C8)C22semidirect
55. C11×#340C22semidirect
56. C11×#340C22semidirect
57. C11×#336C22semidirect
58. #10622189C22semidirect
59. #10622188C22semidirect
60. #10622167C22semidirect
245. #2025D11semidirect
343. C2×#125C2×D11semidirect
382. #340C2×D11semidirect
383. #340C2×D11semidirect
385. #336C2×D11semidirect
414. C2×D11#478semidirect
616. C11#25960semidirect

Maximal subgroups

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

subgroupindex
C2×#106226792
C2×D11×#1022
#130723362
#130714372
#130701352
#130700002
#130699902
#130688782
#130688662
#130688052
#130687952
#130686402
#130686252
#130685452
C11×#20252
#2596011