Finite Group Databasebeta

← #14796185

Subgroups — #14796185

Order 2816.

1026 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622662C211yesmaximal, characteristic, complemented
2C2×#10622662C211yesmaximal, characteristic, complemented
3C2×#10622625C211yesmaximal, characteristic, complemented
4C2×#10622608C211yesmaximal, characteristic, complemented
5#13072056C211yesmaximal, characteristic
6#13070001C211yesmaximal, characteristic, complemented
7#13069997C211yesmaximal, characteristic, complemented
8#13069816C211yesmaximal, characteristic, complemented
9#13069805C211yesmaximal, characteristic, complemented
10#13069473C211yesmaximal, characteristic, complemented
11#13069346C211yesmaximal, characteristic, complemented
12#13068938C211yesmaximal, characteristic, complemented
13#13068924C211yesmaximal, characteristic, complemented
14#13068647C211yesmaximal, characteristic, complemented
15C11×#2415C211yesmaximal, characteristic, complemented
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C2×#66992—21no—
22C2×#66983C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26C22×#4318C2211yescharacteristic
27C11×#397—21no—
28C11×#394—21no—
29C11×#391C2211yescharacteristic
30C11×#389—21no—
31C11×#389C2211yescharacteristic
32C11×#388—21no—
33C11×#380C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37#10622825C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40#10622662—24no—
41#10622662—24no—
42#10622625—24no—
43#10622608—24no—
44#10622607—21no—
45C2×#66873C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66872C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×#66871C2211yescharacteristic
51C2×#66871C2211yescharacteristic
52C2×#66871C2211yescharacteristic
53#10622574—21no—
54#10622571—21no—
55#10622552C2211yescharacteristic
56#10622541C2211yescharacteristic
57C2×C4⋊(C11⋊C8)C2211yescharacteristic
58C2×C4×C11⋊C8C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11D411yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—21no—
68C22×C22⋊D11—21no—
69C23×Dic11—21no—
70C22×D44C2311yescharacteristic
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—41no—
75C4×D4×C11—22no—
76C4×D4×C11—22no—
77C11×#117—22no—
78C11×#117—41no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4D411yescharacteristic
91C2×C11×C22⋊C4D411yescharacteristic
92C2×C42×C11—21no—
93C2×C42×C11C2311yescharacteristic
94C2×C22⋊Dic11—21no—
95C2×#4325—22no—
96C2×#4325—22no—
97C2×#4325—22no—
98#66992—44no—
99#66983—22no—
100#66983—22no—
101#66983—22no—
102#66983—41no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×C4⋊Dic11—22no—
108C2×C4⋊Dic11—21no—
109C2×C4⋊Dic11—41no—
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4⋊Dic11C2311yescharacteristic
113C2×Dic11⋊C4—21no—
114C2×#4318—22no—
115C2×#4318—22no—
116C2×#4318—22no—
117C2×#4318—22no—
118C2×#4318—22no—
119C2×#4318D414yescomplemented
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124C11×#95—21no—
125C11×#95—21no—
126C11×#95—21no—
127C11×#95—21no—
128#66899—22no—
129#66899—22no—
130#66899—41no—
131C11⋊#95—21no—
132C11⋊#95—21no—
133C22⋊(C11⋊C8)—22no—
134C22⋊(C11⋊C8)—22no—
135#66873—22no—
136#66873—22no—
137#66873—41no—
138#66872—22no—
139#66872—22no—
140#66871—22no—
141#66871—22no—
142#66871D414yescomplemented
143C4⋊(C11⋊C8)—22no—
144C4×C11⋊C8—22no—
145#24794—111nomaximal, Sylow
146C24×C11C2×D411yescharacteristic
147C24×C11C2×D411yescharacteristic
148C23×D11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×D4×C11—22no—
156C2×D4×C11—22no—
157C2×D4×C11—41no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
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—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D412yes—
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11#4112yes—
178C22×C4×C11C2411yescharacteristic
179C2×C22⋊D11—42no—
180C2×C22⋊D11—42no—
181C2×C22⋊D11—42no—
182C2×C22⋊D11—42no—
183C2×C22⋊D11—42no—
184C2×C22⋊D11—81no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—42no—
189C22×Dic11—42no—
190C22×Dic11—81no—
191C2×D44—21no—
192C2×D44—21no—
193C2×D44—21no—
194C2×D44—21no—
195C2×D44—21no—
196C2×D44—21no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—42no—
204C11×C4⋊C4—42no—
205C11×C4⋊C4—42no—
206C11×C4⋊C4C2×D412yes—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—42no—
210C11×C22⋊C4—42no—
211C11×C22⋊C4—42no—
212C11×C22⋊C4—42no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—42no—
216C22⋊Dic11—42no—
217#4325—44no—
218(C2×D11)⋊C4—42no—
219(C2×D11)⋊C4—42no—
220(C2×D11)⋊C4—42no—
221(C2×D11)⋊C4—81no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—42no—
228C4⋊Dic11C2×D412yes—
229Dic11⋊C4—42no—
230#4318—28no—
231#4318—44no—
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⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8C2×D412yes—
241C2×C11⋊C8C2×D412yes—
242C2×C11⋊C8C2×D412yes—
243C2×C11⋊C8#4112yes—
244C2×#468—111no—
245C2×#468—111no—
246C2×#436—111no—
247C2×#428—111no—
248#2416—111no—
249#2415D1111yescharacteristic, complemented
250#2067—111no—
251#2066—111no—
252#2036—111no—
253#2034—111no—
254#1968—111no—
255#1942—111no—
256#1875—111no—
257#1872—111no—
258#1809—111no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11#12112yes—
273C23×C11C22×D411yescharacteristic
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—41no—
279C22×D11—41no—
280C22×D11—41no—
281Q8×C11—41no—
282Q8×C11—41no—
283Q8×C11—41no—
284Q8×C11—41no—
285D4×C11—44no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—22no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
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—41no—
315C2×C4×C11—41no—
316C2×C4×C11#12112yes—
317C2×C4×C11AGL(1,ℤ/8)12yes—
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11C22×D411yescharacteristic
320C2×C4×C11C2×#4111yescharacteristic
321C2×C4×C11C2×#4111yescharacteristic
322C2×C4×C11H(5,𝔽2)11yescharacteristic
323C2×C4×C112−1+411yescharacteristic
324C22⋊D11—84no—
325C22⋊D11—84no—
326C2×Dic11—22no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—84no—
336D44—41no—
337D44—41no—
338D44—41no—
339D44—41no—
340C11⋊C8—22no—
341C11⋊C8—41no—
342C11⋊C8—41no—
343C11⋊C8#12114yescomplemented
344C22×SD16—111no—
345C22×M16—111no—
346C22×M16—111no—
347C2×C22⋊Q8C2×D1111yescharacteristic
348C2×C22⋊Q8C2×D1111yescharacteristic
349C2×#121—111no—
350C2×#121—111no—
351C2×#121—221no—
352C2×C4×D4C2×D1111yescharacteristic
353C2×#117C2×D1111yescharacteristic
354C22×C4⋊C4—111no—
355#468—224no—
356#468—224no—
357#436—224no—
358#428—224no—
359C2×#107—111no—
360C2×#107—111no—
361C2×#107—111no—
362C2×#106—111no—
363C2×#106—111no—
364C2×C4⋊C8—111no—
365C2×#103—111no—
366C2×#103—111no—
367C2×#103—111no—
368C2×#102—111no—
369C2×#102—111no—
370C2×#102—111no—
371C2×C22⋊C8—111no—
372C2×C22⋊C8—111no—
373C2×C4×C8—111no—
374#397—21no—
375#396—221no—
376#394—21no—
377#394—221no—
378#391C2×D1111yescharacteristic
379#390—111no—
380#389—21no—
381#389—111no—
382#389C2×D1111yescharacteristic
383#388—21no—
384#386—221no—
385#380—111no—
386#380C2×D1111yescharacteristic
387#340—111no—
388#340—111no—
389#340—111no—
390#340—111no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11C2×#12111yescharacteristic
406C22×C11D4211yescharacteristic
407C22×C11#54711yescharacteristic
408C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C11#57511yescharacteristic
410C22×C11#57711yescharacteristic
411C22×C11#57811yescharacteristic
412C2×D11—81no—
413C2×D11—81no—
414C2×D11—81no—
415C2×D11—81no—
416C2×D11—81no—
417C2×D11—81no—
418C2×D11—81no—
419C4×C11—22no—
420C4×C11—22no—
421C4×C11—41no—
422C4×C11—42no—
423C4×C11—41no—
424C4×C11—81no—
425C4×C11—81no—
426C4×C11—81no—
427C4×C11C2×#12111yescharacteristic
428C4×C11#53711yescharacteristic
429C4×C11#54811yescharacteristic
430C4×C11#55311yescharacteristic
431Dic11—42no—
432Dic11—81no—
433Dic11—81no—
434C22×Q8C22×D1111yescharacteristic
435C22×D4—111no—
436C22×D4—221no—
437C22×D4—221no—
438C22×D4C22⋊D1111yescharacteristic
439C23×C4—221no—
440C23×C4C22×D1111yescharacteristic
441C23×C4C22×D1111yescharacteristic
442C2×SD16—222no—
443C2×SD16—222no—
444C2×SD16—222no—
445C2×M16—114no—
446C2×M16—222no—
447C2×M16—222no—
448C2×M16—222no—
449C2×M16—222no—
450C2×M16—222no—
451C22×C8—111no—
452C22×C8—111no—
453C22×C8—111no—
454C22×C8—111no—
455C22⋊Q8—22no—
456C22⋊Q8—22no—
457C22⋊Q8—22no—
458C22⋊Q8—41no—
459#121—222no—
460#121—222no—
461#121—222no—
462#121—441no—
463#121—444no—
464C4×D4—22no—
465C4×D4—22no—
466#117—22no—
467#117—41no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—111no—
472C2×C4⋊C4—111no—
473C2×C4⋊C4—111no—
474C2×C4⋊C4—222no—
475C2×C4⋊C4—221no—
476C2×C4⋊C4—221no—
477C2×C4⋊C4—441no—
478C2×C4⋊C4C22⋊D1111yescharacteristic
479C2×C4⋊C4C22×D1111yescharacteristic
480C2×C4⋊C4C22×D1111yescharacteristic
481C2×C4⋊C4C22×D1111yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—221no—
487C2×C22⋊C4—221no—
488C2×C22⋊C4—221no—
489C2×C22⋊C4—221no—
490C2×C22⋊C4—221no—
491C2×C22⋊C4C22⋊D1111yescharacteristic
492C2×C22⋊C4C22⋊D1111yescharacteristic
493C2×C42—21no—
494C2×C42C22×D1111yescharacteristic
495#107—114no—
496#107—222no—
497#107—222no—
498#106—222no—
499#106—222no—
500C4⋊C8—222no—
501#103—222no—
502#103—222no—
503#103—441no—
504#102—222no—
505#102—222no—
506#102—441no—
507C22⋊C8—222no—
508C22⋊C8—222no—
509C4×C8—222no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—221no—
515#95—221no—
516C2×C11—42no—
517C2×C11—81no—
518C2×C11#241611yescharacteristic
519C2×C11#305511yescharacteristic
520C2×C11#306311yescharacteristic
521C2×C11#327211yescharacteristic
522C2×C11#327711yescharacteristic
523C2×C11#335111yescharacteristic
524C2×C11#335311yescharacteristic
525D11—161no—
526C24—221no—
527C24C2×C22⋊D1111yescharacteristic
528C24C2×C22⋊D1111yescharacteristic
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—41no—
538C2×D4—221no—
539C2×D4—221no—
540C2×D4—221no—
541C2×D4—221no—
542C2×D4—221no—
543C2×D4—221no—
544C2×D4—442no—
545C2×D4—442no—
546C2×D4—442no—
547C2×D4—442no—
548C2×D4—442no—
549C2×D4—881no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—442no—
568C22×C4—442no—
569C22×C4—881no—
570C22×C4D4×D1112yes—
571C22×C4#434112yes—
572C22×C4C2×C22⋊D1111yescharacteristic
573C22×C4C2×C22⋊D1111yescharacteristic
574C22×C4C2×C22⋊D1111yescharacteristic
575C22×C4C2×C22⋊D1111yescharacteristic
576C22×C4C23×D1111yescharacteristic
577SD16—444no—
578M16—228no—
579M16—444no—
580C2×C8—112no—
581C2×C8—112no—
582C2×C8—112no—
583C2×C8—112no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8—221no—
587C2×C8—221no—
588C2×C8—221no—
589C2×C8—221no—
590C2×C8—221no—
591C2×C8—221no—
592C4⋊C4—22no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—112no—
602C4⋊C4—221no—
603C4⋊C4—221no—
604C4⋊C4—221no—
605C4⋊C4—221no—
606C4⋊C4—221no—
607C4⋊C4—442no—
608C4⋊C4—442no—
609C4⋊C4D4×D1112yes—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—442no—
617C22⋊C4—442no—
618C22⋊C4—442no—
619C22⋊C4—442no—
620C22⋊C4—881no—
621C42—21no—
622C42—21no—
623C42—42no—
624C11#2479411yescharacteristic, complemented, Sylow
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—441no—
639C23—441no—
640C23—441no—
641C23—441no—
642C23—441no—
643C23—441no—
644C23—441no—
645C23#6699212yes—
646C23C22×C22⋊D1111yescharacteristic
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651D4—44no—
652D4—441no—
653D4—441no—
654D4—441no—
655D4—441no—
656D4—884no—
657D4—884no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—222no—
689C2×C4—441no—
690C2×C4—441no—
691C2×C4—441no—
692C2×C4—441no—
693C2×C4—441no—
694C2×C4—441no—
695C2×C4—441no—
696C2×C4—441no—
697C2×C4—884no—
698C2×C4#6699212yes—
699C2×C4#6700212yes—
700C2×C4C2×D4×D1111yescharacteristic
701C2×C4C2×D4×D1111yescharacteristic
702C2×C4C2×#434111yescharacteristic
703C2×C4#6703711yescharacteristic
704C2×C4#41×D1111yescharacteristic
705C2×C4#6704311yescharacteristic
706C8—114no—
707C8—222no—
708C8—441no—
709C8—441no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—881no—
725C22—881no—
726C22—881no—
727C22—881no—
728C22—881no—
729C22—881no—
730C22—881no—
731C22D4×C22⋊D1111yescharacteristic
732C22C2×#6699211yescharacteristic
733C22C2×#6700211yescharacteristic
734C22#1062335311yescharacteristic
735C22#1062335511yescharacteristic
736C22#1062336811yescharacteristic
737C22#1062336911yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—42no—
742C4—41no—
743C4—81no—
744C4—81no—
745C4—81no—
746C4—442no—
747C4—881no—
748C4—881no—
749C4#1062312811yescharacteristic
750C4#1062312911yescharacteristic
751C4#1062313211yescharacteristic
752C4D11×#12111yescharacteristic
753C2—42no—
754C2—81no—
755C2—1761no—
756C2#1307205311yescharacteristic
757C2#1307823711yescharacteristic
758C2#1307830311yescharacteristic
759C2#1308021611yescharacteristic
760C2#1308026911yescharacteristic
761C2#1308117611yescharacteristic
762C2#1308119411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2415C2
socleC23×C11C22×D4
prime radical#13072056C2
hypercenter#2415D11
hypocenterC11#24794
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2415

Complements

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

NH ≅ G/Ntype
1. C2×#10622662C2semidirect
2. C2×#10622662C2semidirect
3. C2×#10622625C2semidirect
4. C2×#10622608C2semidirect
6. #13070001C2semidirect
7. #13069997C2semidirect
8. #13069816C2semidirect
9. #13069805C2semidirect
10. #13069473C2semidirect
11. #13069346C2semidirect
12. #13068938C2semidirect
13. #13068924C2semidirect
14. #13068647C2semidirect
15. C11×#2415C2semidirect
119. C2×#4318D4semidirect
142. #66871D4semidirect
249. #2415D11semidirect
343. C11⋊C8#121semidirect
624. C11#24794semidirect

Maximal subgroups

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

subgroupindex
C2×#106226622
C2×#106226252
C2×#106226082
#130720562
#130700012
#130699972
#130698162
#130698052
#130694732
#130693462
#130689382
#130689242
#130686472
C11×#24152
#2479411