Finite Group Databasebeta

← #14814974

Subgroups — #14814974

Order 2816.

970 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622647C211yesmaximal, characteristic, complemented
2C2×#10622656C211yesmaximal, characteristic, complemented
3D4×C4⋊Dic11C211yesmaximal, characteristic, complemented
4#13069816C211yesmaximal, characteristic, complemented
5#13069809C211yesmaximal, characteristic, complemented
6#13069802C211yesmaximal, characteristic, complemented
7#13069795C211yesmaximal, characteristic, complemented
8#13069549C211yesmaximal, characteristic, complemented
9#13069433C211yesmaximal, characteristic, complemented
10#13069415C211yesmaximal, characteristic, complemented
11#13069379C211yesmaximal, characteristic, complemented
12#13068934C211yesmaximal, characteristic, complemented
13#13068924C211yesmaximal, characteristic, complemented
14#13068514C211yesmaximal, characteristic, complemented
15C11×#2540C211yesmaximal, characteristic
16C2×C11×#124C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×D4×Dic11—21no—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C11×#399—21no—
26C11×#392—21no—
27C11×#390—21no—
28C11×#390—21no—
29C4×C11×C4⋊C4C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38#10622825C2211yescharacteristic
39#10622825C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44#10622656—24no—
45#10622647—24no—
46#10622598—21no—
47C2×#66872C2211yescharacteristic
48C2×#66872C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×#66871C2211yescharacteristic
51#10622563—21no—
52#10622563—21no—
53#10622548C2211yescharacteristic
54C4×C4⋊Dic11C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×#66867C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11—21no—
64C22×D4×C11D411yescharacteristic
65C22×D4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×Dic11—21no—
69C23×Dic11—21no—
70C11×#124—22no—
71C11×#124—22no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—41no—
75C11×C22⋊Q8—41no—
76C11×#121—22no—
77C11×#121—22no—
78C11×#121—41no—
79C11×#121—41no—
80C4×D4×C11—22no—
81C4×D4×C11—22no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C11×C22⋊C4D411yescharacteristic
95C2×C42×C11—21no—
96C2×C42×C11C2311yescharacteristic
97C2×C22⋊Dic11—21no—
98C2×C22⋊Dic11—21no—
99D4×Dic11—44no—
100C2×C4⋊Dic11—22no—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11—21no—
106C2×C4⋊Dic11—41no—
107C2×C4⋊Dic11—41no—
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4×Dic11—21no—
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C11×#95—21no—
118#66899—22no—
119#66899—22no—
120#66899—41no—
121#66899—41no—
122#66896—22no—
123#66896—22no—
124#66896—41no—
125#66896—41no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C22⋊(C11⋊C8)—22no—
130C22⋊(C11⋊C8)—22no—
131C22⋊(C11⋊C8)—41no—
132C22⋊(C11⋊C8)—41no—
133#66872—22no—
134#66872—22no—
135#66872D414yescomplemented
136#66871—22no—
137C4⋊(C11⋊C8)—22no—
138#66867—22no—
139#26242—111nomaximal, Sylow
140C24×C11—21no—
141C24×C11C2×D411yescharacteristic
142C24×C11C2×D411yescharacteristic
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—42no—
159C2×D4×C11—42no—
160C2×D4×C11—42no—
161C2×D4×C11—42no—
162C2×D4×C11—81no—
163C2×D4×C11—81no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2411yescharacteristic
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—42no—
189C22×Dic11—42no—
190C22×Dic11—42no—
191C22×Dic11—42no—
192C22×Dic11—81no—
193C22×Dic11—81no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—42no—
198C11×C4⋊C4—42no—
199C11×C4⋊C4C2×D412yes—
200C11×C4⋊C4#4112yes—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—42no—
204C11×C22⋊C4—42no—
205C11×C22⋊C4—42no—
206C11×C22⋊C4—42no—
207C11×C22⋊C4—42no—
208C11×C22⋊C4—42no—
209C42×C11—81no—
210C42×C11#4112yes—
211C42×C11#4112yes—
212C22⋊Dic11—42no—
213C22⋊Dic11—42no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220C4⋊Dic11—21no—
221C4⋊Dic11—42no—
222C4⋊Dic11—42no—
223C4⋊Dic11—42no—
224C4⋊Dic11—81no—
225C4⋊Dic11C2×D412yes—
226C4×Dic11—42no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8C2×D412yes—
239C2×#481—111no—
240C2×#483—111no—
241#2540D1111yescharacteristic
242D4×C4⋊C4—111no—
243#2036—111no—
244#2035—111no—
245#2034—111no—
246#2033—111no—
247#1983—111no—
248#1959—111no—
249#1955—111no—
250#1948—111no—
251#1874—111no—
252#1872—111no—
253#1776—111no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11AGL(1,ℤ/8)12yes—
274C23×C11#13712yes—
275C23×C11C22×D411yescharacteristic
276Q8×C11—41no—
277Q8×C11—41no—
278Q8×C11—41no—
279Q8×C11—41no—
280D4×C11—28no—
281D4×C11—41no—
282D4×C11—41no—
283D4×C11—41no—
284D4×C11—41no—
285D4×C11—84no—
286D4×C11—84no—
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—21no—
294C2×C4×C11—21no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11#12312yes—
315C2×C4×C11#12312yes—
316C2×C4×C11C22×D411yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11C2×#4111yescharacteristic
319C2×C4×C11C2×#4111yescharacteristic
320C2×C4×C11H(5,𝔽2)11yescharacteristic
321C2×C4×C11H(5,𝔽2)11yescharacteristic
322C2×Dic11—22no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—84no—
335C2×Dic11—84no—
336C11⋊C8—22no—
337C11⋊C8—41no—
338C11⋊C8—41no—
339C11⋊C8—41no—
340C2×#124C2×D1111yescharacteristic
341C2×C22⋊Q8C2×D1111yescharacteristic
342C2×C22⋊Q8C2×D1111yescharacteristic
343C2×#121C2×D1111yescharacteristic
344C2×#121C2×D1111yescharacteristic
345C2×C4×D4—221no—
346C2×C4×D4C2×D1111yescharacteristic
347C22×C4⋊C4—111no—
348C22×C4⋊C4—111no—
349#483—224no—
350#481—224no—
351C2×#107—111no—
352C2×#106—111no—
353C2×#106—111no—
354C2×#106—111no—
355C2×C4⋊C8—111no—
356C2×#103—111no—
357C2×#103—111no—
358C2×#103—111no—
359C2×#103—111no—
360C2×#102—111no—
361C2×#102—111no—
362C2×#102—111no—
363C2×#102—111no—
364C2×C22⋊C8—111no—
365C2×C22⋊C8—111no—
366C2×C22⋊C8—111no—
367C2×C22⋊C8—111no—
368C2×#97—111no—
369#399—21no—
370#392—21no—
371#390—21no—
372#390—21no—
373#389—221no—
374#385—221no—
375#385—221no—
376#384—111no—
377#380—111no—
378#380—111no—
379C4×C4⋊C4—111no—
380C4×C4⋊C4C2×D1111yescharacteristic
381#340—111no—
382#340—111no—
383#340—111no—
384#340—111no—
385C22×C11—22no—
386C22×C11—22no—
387C22×C11—22no—
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—81no—
400C22×C11—81no—
401C22×C11—81no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11—81no—
405C22×C11—81no—
406C22×C11C2×#12311yescharacteristic
407C22×C11D4211yescharacteristic
408C22×C11#54611yescharacteristic
409C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
410C22×C11C2×#13711yescharacteristic
411C22×C11#57711yescharacteristic
412C22×C11#57711yescharacteristic
413C4×C11—22no—
414C4×C11—22no—
415C4×C11—41no—
416C4×C11—41no—
417C4×C11—42no—
418C4×C11—42no—
419C4×C11—81no—
420C4×C11#53211yescharacteristic
421C4×C11#54011yescharacteristic
422C4×C11#55011yescharacteristic
423C4×C11#55911yescharacteristic
424Dic11—42no—
425Dic11—81no—
426Dic11—81no—
427Dic11—81no—
428C22×Q8C22×D1111yescharacteristic
429C22×D4—21no—
430C22×D4—21no—
431C22×D4C22⋊D1111yescharacteristic
432C22×D4C22×D1111yescharacteristic
433C23×C4—221no—
434C23×C4—221no—
435C23×C4C22×D1111yescharacteristic
436C23×C4C22×D1111yescharacteristic
437C22×C8—111no—
438C22×C8—111no—
439C22×C8—111no—
440C22×C8—111no—
441#124—22no—
442#124—22no—
443C22⋊Q8—22no—
444C22⋊Q8—22no—
445C22⋊Q8—41no—
446C22⋊Q8—41no—
447#121—22no—
448#121—22no—
449#121—41no—
450#121—41no—
451C4×D4—22no—
452C4×D4—22no—
453C4×D4—444no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—111no—
457C2×C4⋊C4—111no—
458C2×C4⋊C4—111no—
459C2×C4⋊C4—111no—
460C2×C4⋊C4—222no—
461C2×C4⋊C4—222no—
462C2×C4⋊C4—221no—
463C2×C4⋊C4—221no—
464C2×C4⋊C4—221no—
465C2×C4⋊C4—221no—
466C2×C4⋊C4—441no—
467C2×C4⋊C4—441no—
468C2×C4⋊C4C22⋊D1111yescharacteristic
469C2×C4⋊C4C22×D1111yescharacteristic
470C2×C4⋊C4C22×D1111yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—221no—
478C2×C22⋊C4—221no—
479C2×C22⋊C4C22⋊D1111yescharacteristic
480C2×C22⋊C4C22⋊D1111yescharacteristic
481C2×C42—21no—
482C2×C42—221no—
483C2×C42C22×D1111yescharacteristic
484#107—222no—
485#106—114no—
486#106—222no—
487#106—222no—
488C4⋊C8—222no—
489#103—222no—
490#103—222no—
491#103—441no—
492#103—441no—
493#102—222no—
494#102—222no—
495#102—441no—
496#102—441no—
497C22⋊C8—222no—
498C22⋊C8—222no—
499C22⋊C8—441no—
500C22⋊C8—441no—
501#97—222no—
502#95—21no—
503#95—221no—
504#95—221no—
505#95—221no—
506C2×C11—42no—
507C2×C11—42no—
508C2×C11—161no—
509C2×C11#244511yescharacteristic
510C2×C11#309211yescharacteristic
511C2×C11#309911yescharacteristic
512C2×C11#326511yescharacteristic
513C2×C11#326611yescharacteristic
514C2×C11#330611yescharacteristic
515C2×C11#331611yescharacteristic
516C24—21no—
517C24C2×C22⋊D1111yescharacteristic
518C24C2×C22⋊D1111yescharacteristic
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—81no—
539C2×D4—81no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—221no—
556C22×C4—221no—
557C22×C4—221no—
558C22×C4—221no—
559C22×C4—442no—
560C22×C4—442no—
561C22×C4—442no—
562C22×C4—442no—
563C22×C4—881no—
564C22×C4—881no—
565C22×C4C2×C22⋊D1111yescharacteristic
566C22×C4C2×C22⋊D1111yescharacteristic
567C22×C4C2×C22⋊D1111yescharacteristic
568C22×C4C2×C22⋊D1111yescharacteristic
569C22×C4C23×D1111yescharacteristic
570C2×C8—112no—
571C2×C8—221no—
572C2×C8—221no—
573C2×C8—221no—
574C2×C8—221no—
575C2×C8—221no—
576C2×C8—221no—
577C2×C8—221no—
578C2×C8—221no—
579C2×C8—221no—
580C2×C8—221no—
581C2×C8—221no—
582C4⋊C4—22no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—112no—
588C4⋊C4—221no—
589C4⋊C4—221no—
590C4⋊C4—221no—
591C4⋊C4—221no—
592C4⋊C4—221no—
593C4⋊C4—221no—
594C4⋊C4—221no—
595C4⋊C4—442no—
596C4⋊C4—442no—
597C4⋊C4—442no—
598C4⋊C4—881no—
599C4⋊C4D4×D1112yes—
600C4⋊C4#434112yes—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—442no—
610C22⋊C4—442no—
611C42—81no—
612C42—442no—
613C42#434112yes—
614C42#434112yes—
615C11#2624211yescharacteristic, complemented, Sylow
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23#6700212yes—
636C23#6700412yes—
637C23C22×C22⋊D1111yescharacteristic
638Q8—41no—
639Q8—41no—
640Q8—41no—
641Q8—41no—
642D4—28no—
643D4—41no—
644D4—41no—
645D4—41no—
646D4—41no—
647D4—84no—
648D4—84no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—41no—
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—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—222no—
677C2×C4—441no—
678C2×C4—441no—
679C2×C4—441no—
680C2×C4—441no—
681C2×C4—441no—
682C2×C4—441no—
683C2×C4—441no—
684C2×C4—441no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—884no—
689C2×C4—884no—
690C2×C4#6698812yes—
691C2×C4#6698812yes—
692C2×C4C2×D4×D1111yescharacteristic
693C2×C4C2×#434111yescharacteristic
694C2×C4C2×#434111yescharacteristic
695C2×C4C2×#434111yescharacteristic
696C2×C4#6703711yescharacteristic
697C2×C4#6703711yescharacteristic
698C8—222no—
699C8—441no—
700C8—441no—
701C8—441no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22C2×#6698811yescharacteristic
724C22D4×C22⋊D1111yescharacteristic
725C22#1062333711yescharacteristic
726C22C2×#6700211yescharacteristic
727C22C2×#6700411yescharacteristic
728C22#1062336711yescharacteristic
729C22#1062336811yescharacteristic
730C4—22no—
731C4—22no—
732C4—42no—
733C4—42no—
734C4—41no—
735C4—41no—
736C4—81no—
737C4—442no—
738C4—881no—
739C4—881no—
740C4—881no—
741C4#1062324411yescharacteristic
742C4#1062324711yescharacteristic
743C4#1062324911yescharacteristic
744C4#1062325011yescharacteristic
745C2—42no—
746C2—42no—
747C2—161no—
748C2#1307237711yescharacteristic
749C2#1307853611yescharacteristic
750C2#1307860111yescharacteristic
751C2#1308011211yescharacteristic
752C2#1308012211yescharacteristic
753C2#1308057711yescharacteristic
754C2#1308072711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2540C2
socleC23×C11C22×D4
hypercenter#2540D11
hypocenterC11#26242
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2540

Complements

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

NH ≅ G/Ntype
1. C2×#10622647C2semidirect
2. C2×#10622656C2semidirect
3. D4×C4⋊Dic11C2semidirect
4. #13069816C2semidirect
5. #13069809C2semidirect
6. #13069802C2semidirect
7. #13069795C2semidirect
8. #13069549C2semidirect
9. #13069433C2semidirect
10. #13069415C2semidirect
11. #13069379C2semidirect
12. #13068934C2semidirect
13. #13068924C2semidirect
14. #13068514C2semidirect
135. #66872D4semidirect
615. C11#26242semidirect

Maximal subgroups

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

subgroupindex
C2×#106226472
C2×#106226562
D4×C4⋊Dic112
#130698162
#130698092
#130698022
#130697952
#130695492
#130694332
#130694152
#130693792
#130689342
#130689242
#130685142
C11×#25402
#2624211