Finite Group Databasebeta

← #14804383

Subgroups — #14804383

Order 2816.

1022 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622699C211yesmaximal, characteristic, complemented
2C2×#10622641C211yesmaximal, characteristic, complemented
3C2×#10622640C211yesmaximal, characteristic
4C2×#10622696C211yesmaximal, characteristic, complemented
5#13073587C211yesmaximal, characteristic
6#13069938C211yesmaximal, characteristic, complemented
7#13069931C211yesmaximal, characteristic, complemented
8#13069709C211yesmaximal, characteristic, complemented
9#13069703C211yesmaximal, characteristic
10#13069548C211yesmaximal, characteristic, complemented
11#13069340C211yesmaximal, characteristic, complemented
12#13068971C211yesmaximal, characteristic, complemented
13#13068957C211yesmaximal, characteristic, complemented
14#13068444C211yesmaximal, characteristic, complemented
15C11×#2365C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C22×#4325C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C22×#4325C2211yescharacteristic
24C22×#4325C2211yescharacteristic
25C2×#66928C2211yescharacteristic
26C2×#66928C2211yescharacteristic
27C2×#66927C2211yescharacteristic
28C2×C4×D44C2211yescharacteristic
29C11×#391C2211yescharacteristic
30C11×#391C2211yescharacteristic
31C11×#389—21no—
32C11×#387—21no—
33C11×#387—21no—
34C4×C11×C4⋊C4—21no—
35C4×C11×C4⋊C4C2211yescharacteristic
36C4×C11×C4⋊C4C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39#10622699—24no—
40#10622696—24no—
41#10622641—24no—
42#10622640—24no—
43#10622604—21no—
44#10622604—21no—
45C2×#66874C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66873C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51#10622552C2211yescharacteristic
52#10622542C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×#66867C2211yescharacteristic
57#10622278—21no—
58#10622278—21no—
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×D44—21no—
66C22×D44—21no—
67C22×D44C2311yescharacteristic
68C22×D44C2311yescharacteristic
69C22×C4×D11—21no—
70C22×Dic22C2311yescharacteristic
71C11×C4⋊Q8—22no—
72C11×C4⋊Q8D414yescomplemented
73C4×Q8×C11—22no—
74C4×Q8×C11—22no—
75C4×Q8×C11—41no—
76C4×Q8×C11—41no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C42×C11—21no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×#4326—22no—
92C2×#4326—22no—
93C2×#4326—22no—
94C2×#4326—22no—
95C2×#4326—41no—
96C2×#4326—41no—
97C2×#4325—22no—
98C2×#4325—22no—
99C2×#4325—22no—
100C2×#4325—22no—
101C2×#4325—22no—
102C2×#4325—22no—
103C2×#4325—22no—
104C2×#4325—22no—
105C2×#4325—41no—
106C2×#4325—41no—
107C2×#4325—41no—
108C2×#4325—41no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×C4⋊Dic11C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121#66928—22no—
122#66928—22no—
123#66928—22no—
124#66928—41no—
125#66927—22no—
126#66927—41no—
127C4×D44—22no—
128C4×D44—22no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95D411yescharacteristic
135C11×#95D411yescharacteristic
136#66899—22no—
137#66899—22no—
138C11⋊#95—21no—
139C11⋊#95—21no—
140#66874—22no—
141#66874—41no—
142#66873—22no—
143#66873—22no—
144#66873—41no—
145#66873D414yes—
146C4⋊(C11⋊C8)—22no—
147C4⋊(C11⋊C8)—22no—
148C4⋊(C11⋊C8)—22no—
149#66867—22no—
150#25377—111nomaximal, Sylow
151C23×D11—21no—
152C23×D11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11C2×D412yes—
164C2×Q8×C11C2×D412yes—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2411yescharacteristic
176C22×Dic11—21no—
177C22×Dic11—21no—
178C2×D44—21no—
179C2×D44—21no—
180C2×D44—21no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44—21no—
185C2×D44—21no—
186C2×D44—21no—
187C2×D44—21no—
188C2×D44—21no—
189C2×D44—42no—
190C2×D44—42no—
191C2×D44—42no—
192C2×D44—42no—
193C2×D44—81no—
194C2×D44—81no—
195C2×D44C2×D412yes—
196C2×C4×D11—42no—
197C2×C4×D11—81no—
198C2×C4×D11—81no—
199C2×Dic22—21no—
200C2×Dic22—21no—
201C2×Dic22—21no—
202C2×Dic22—21no—
203C2×Dic22—21no—
204C2×Dic22—21no—
205C11×C4⋊C4—24no—
206C11×C4⋊C4—24no—
207C11×C4⋊C4—22no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—41no—
212C11×C4⋊C4—42no—
213C11×C4⋊C4—42no—
214C11×C4⋊C4C2×D412yes—
215C42×C11—21no—
216C42×C11—21no—
217C42×C11—21no—
218C42×C11—21no—
219C42×C11—42no—
220C42×C11—42no—
221C42×C11—42no—
222C42×C11C2×D412yes—
223C42×C11#4112yes—
224#4326—44no—
225#4326—44no—
226#4325—44no—
227#4325—44no—
228#4325—44no—
229#4325—44no—
230(C2×D11)⋊C4—42no—
231(C2×D11)⋊C4—42no—
232(C2×D11)⋊C4—42no—
233(C2×D11)⋊C4—42no—
234(C2×D11)⋊C4—42no—
235(C2×D11)⋊C4—81no—
236(C2×D11)⋊C4—81no—
237C4⋊Dic11—21no—
238C4⋊Dic11—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8C2×D412yes—
250C2×C11⋊C8#4112yes—
251C2×#497—111no—
252C2×#464—111no—
253C2×#460—111no—
254C2×#461—111no—
255#2544—111no—
256#2365D1111yescharacteristic, complemented
257#2056—111no—
258#2055—111no—
259#2015—111no—
260#2014—111no—
261#1983—111no—
262#1940—111no—
263#1880—111no—
264#1878—111no—
265#1762—111no—
266C23×C11C22×D411yescharacteristic
267C22×D11—22no—
268C22×D11—41no—
269C22×D11—41no—
270C22×D11—41no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—41no—
279C22×D11—41no—
280C22×D11—41no—
281Q8×C11—22no—
282Q8×C11—22no—
283Q8×C11—22no—
284Q8×C11—22no—
285Q8×C11—41no—
286Q8×C11—41no—
287Q8×C11—41no—
288Q8×C11—41no—
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—21no—
300C2×C4×C11—22no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
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×C11#12112yes—
318C2×C4×C11#13712yes—
319C2×C4×C11C22×D411yescharacteristic
320C2×C4×C11C22×D411yescharacteristic
321C2×C4×C11C2×#4111yescharacteristic
322C2×C4×C11C2×#4111yescharacteristic
323C2×C4×C11H(5,𝔽2)11yescharacteristic
324C2×C4×C11H(5,𝔽2)11yescharacteristic
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331D44—22no—
332D44—22no—
333D44—41no—
334D44—41no—
335D44—41no—
336D44—41no—
337D44—41no—
338D44—41no—
339D44—84no—
340D44—84no—
341C4×D11—84no—
342Dic22—41no—
343Dic22—41no—
344Dic22—41no—
345Dic22—41no—
346C11⋊C8—22no—
347C11⋊C8—22no—
348C11⋊C8—41no—
349C11⋊C8—41no—
350C22×Q16—111no—
351C22×Q16—111no—
352C22×SD16—111no—
353C22×SD16—111no—
354C22×SD16—111no—
355C22×SD16—111no—
356C2×C4⋊Q8C2×D1111yescharacteristic
357C2×#127—111no—
358C2×#124—111no—
359C2×#124—111no—
360C2×C4×Q8C2×D1111yescharacteristic
361C2×C4×Q8C2×D1111yescharacteristic
362C2×C4×D4—111no—
363#497—224no—
364#464—224no—
365#461—224no—
366#460—224no—
367C2×C4⋊C8—111no—
368C2×C4⋊C8—111no—
369C2×C4⋊C8—111no—
370C2×#103—111no—
371C2×#103—111no—
372C2×#103—111no—
373C2×#103—111no—
374C2×#102—111no—
375C2×#102—111no—
376C2×#102—111no—
377C2×#102—111no—
378C2×#97—111no—
379#394—221no—
380#394—221no—
381#391—111no—
382#391C2×D1111yescharacteristic
383#391C2×D1111yescharacteristic
384#390—111no—
385#389—21no—
386#387—21no—
387#387—21no—
388#386—221no—
389#386—221no—
390C4×C4⋊C4—21no—
391C4×C4⋊C4C2×D1111yescharacteristic
392C4×C4⋊C4C2×D1111yescharacteristic
393#340—111no—
394#340—111no—
395#336—111no—
396#336—111no—
397C22×C11C2×#12111yescharacteristic
398C22×C11D4211yescharacteristic
399C22×C11#55011yescharacteristic
400C22×C11C2×#13711yescharacteristic
401C22×C11#57511yescharacteristic
402C22×C11#57711yescharacteristic
403C22×C11#57711yescharacteristic
404C2×D11—42no—
405C2×D11—42no—
406C2×D11—42no—
407C2×D11—81no—
408C2×D11—81no—
409C2×D11—81no—
410C2×D11—81no—
411C2×D11—81no—
412C2×D11—81no—
413C2×D11—81no—
414C2×D11—81no—
415C2×D11—81no—
416C2×D11—81no—
417C2×D11—81no—
418C4×C11—22no—
419C4×C11—22no—
420C4×C11—22no—
421C4×C11—42no—
422C4×C11—42no—
423C4×C11—41no—
424C4×C11—41no—
425C4×C11—41no—
426C4×C11—42no—
427C4×C11—81no—
428C4×C11#53211yescharacteristic
429C4×C11#54011yescharacteristic
430C4×C11D4211yescharacteristic
431C4×C11#54611yescharacteristic
432Dic11—81no—
433Dic11—81no—
434C22×Q8—111no—
435C22×Q8C22×D1111yescharacteristic
436C22×Q8C22×D1111yescharacteristic
437C22×D4—111no—
438C22×D4—111no—
439C22×D4—221no—
440C22×D4—221no—
441C23×C4—221no—
442C2×Q16—222no—
443C2×Q16—222no—
444C2×Q16—222no—
445C2×Q16—222no—
446C2×Q16—441no—
447C2×Q16—441no—
448C2×SD16—222no—
449C2×SD16—222no—
450C2×SD16—222no—
451C2×SD16—222no—
452C2×SD16—222no—
453C2×SD16—222no—
454C2×SD16—222no—
455C2×SD16—222no—
456C2×SD16—441no—
457C2×SD16—441no—
458C2×SD16—441no—
459C2×SD16—441no—
460C22×C8—111no—
461C22×C8—111no—
462C22×C8—111no—
463C22×C8—111no—
464C4⋊Q8—22no—
465C4⋊Q8D4414yescomplemented
466#127—222no—
467#127—441no—
468#124—222no—
469#124—222no—
470#124—222no—
471#124—441no—
472C4×Q8—22no—
473C4×Q8—22no—
474C4×Q8—41no—
475C4×Q8—41no—
476C4×D4—222no—
477C4×D4—222no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—111no—
483C2×C4⋊C4C22⋊D1111yescharacteristic
484C2×C4⋊C4C22⋊D1111yescharacteristic
485C2×C4⋊C4C22×D1111yescharacteristic
486C2×C4⋊C4C22×D1111yescharacteristic
487C2×C22⋊C4—221no—
488C2×C22⋊C4—221no—
489C2×C22⋊C4—221no—
490C2×C22⋊C4—221no—
491C2×C22⋊C4—221no—
492C2×C22⋊C4—221no—
493C2×C22⋊C4—221no—
494C2×C42—21no—
495C2×C42—21no—
496C2×C42—21no—
497C2×C42C22×D1111yescharacteristic
498C2×C42C22×D1111yescharacteristic
499C2×C42C22×D1111yescharacteristic
500C4⋊C8—222no—
501C4⋊C8—222no—
502C4⋊C8—222no—
503#103—222no—
504#103—222no—
505#103—222no—
506#103—441no—
507#102—114no—
508#102—222no—
509#102—222no—
510#102—441no—
511#97—222no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—221no—
518#95—221no—
519#95C22⋊D1111yescharacteristic
520#95C22⋊D1111yescharacteristic
521C2×C11#242811yescharacteristic
522C2×C11#303711yescharacteristic
523C2×C11#304311yescharacteristic
524C2×C11#326611yescharacteristic
525C2×C11#326711yescharacteristic
526C2×C11#340011yescharacteristic
527C2×C11#340111yescharacteristic
528D11—82no—
529D11—161no—
530C24—221no—
531C24—221no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—221no—
543C2×Q8—221no—
544C2×Q8—221no—
545C2×Q8—221no—
546C2×Q8—221no—
547C2×Q8—221no—
548C2×Q8C2×D4412yes—
549C2×Q8C2×D4412yes—
550C2×D4—112no—
551C2×D4—221no—
552C2×D4—221no—
553C2×D4—221no—
554C2×D4—221no—
555C2×D4—221no—
556C2×D4—221no—
557C2×D4—221no—
558C2×D4—221no—
559C2×D4—221no—
560C2×D4—221no—
561C2×D4—221no—
562C2×D4—442no—
563C2×D4—442no—
564C2×D4—442no—
565C2×D4—442no—
566C2×D4—881no—
567C2×D4—881no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—442no—
575C22×C4—881no—
576C22×C4—881no—
577C22×C4C2×C22⋊D1111yescharacteristic
578C22×C4C2×C22⋊D1111yescharacteristic
579C22×C4C2×C22⋊D1111yescharacteristic
580C22×C4C2×C22⋊D1111yescharacteristic
581C22×C4C2×C22⋊D1111yescharacteristic
582C22×C4C2×C22⋊D1111yescharacteristic
583C22×C4C23×D1111yescharacteristic
584Q16—444no—
585Q16—444no—
586SD16—444no—
587SD16—444no—
588SD16—444no—
589SD16—444no—
590C2×C8—112no—
591C2×C8—112no—
592C2×C8—221no—
593C2×C8—221no—
594C2×C8—221no—
595C2×C8—221no—
596C2×C8—221no—
597C2×C8—221no—
598C2×C8—221no—
599C2×C8—221no—
600C2×C8—221no—
601C2×C8—221no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—22no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—41no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—221no—
612C4⋊C4—221no—
613C4⋊C4D4×D1112yes—
614C22⋊C4—442no—
615C22⋊C4—442no—
616C22⋊C4—442no—
617C22⋊C4—442no—
618C22⋊C4—442no—
619C22⋊C4—881no—
620C22⋊C4—881no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42—42no—
626C42—42no—
627C42—42no—
628C42C2×D4412yes—
629C42#433912yes—
630C11#2537711yescharacteristic, complemented, Sylow
631C23—222no—
632C23—441no—
633C23—441no—
634C23—441no—
635C23—441no—
636C23—441no—
637C23—441no—
638C23—441no—
639C23—441no—
640C23—441no—
641C23—441no—
642C23—441no—
643C23—441no—
644C23—441no—
645C23C22×C22⋊D1111yescharacteristic
646Q8—22no—
647Q8—22no—
648Q8—22no—
649Q8—22no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653Q8—41no—
654Q8—441no—
655Q8—441no—
656Q8—441no—
657Q8—441no—
658D4—222no—
659D4—222no—
660D4—441no—
661D4—441no—
662D4—441no—
663D4—441no—
664D4—441no—
665D4—441no—
666D4—884no—
667D4—884no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—441no—
696C2×C4—441no—
697C2×C4—441no—
698C2×C4—441no—
699C2×C4—441no—
700C2×C4—441no—
701C2×C4—884no—
702C2×C4#6698312yes—
703C2×C4#6698312yes—
704C2×C4#6699512yes—
705C2×C4C22×D4411yescharacteristic
706C2×C4C2×#433911yescharacteristic
707C2×C4C2×D4×D1111yescharacteristic
708C2×C4#6703711yescharacteristic
709C2×C4#41×D1111yescharacteristic
710C2×C4#6704211yescharacteristic
711C8—222no—
712C8—222no—
713C8—441no—
714C8—441no—
715C22—442no—
716C22—442no—
717C22—442no—
718C22—881no—
719C22—881no—
720C22—881no—
721C22—881no—
722C22—881no—
723C22—881no—
724C22—881no—
725C22—881no—
726C22—881no—
727C22—881no—
728C22—881no—
729C22C2×#6698311yescharacteristic
730C22D4×C22⋊D1111yescharacteristic
731C22C2×#6699511yescharacteristic
732C22#1062335311yescharacteristic
733C22#1062336511yescharacteristic
734C22#1062336811yescharacteristic
735C22#1062336811yescharacteristic
736C4—22no—
737C4—22no—
738C4—22no—
739C4—41no—
740C4—42no—
741C4—42no—
742C4—41no—
743C4—41no—
744C4—42no—
745C4—81no—
746C4—881no—
747C4—881no—
748C4#1062307911yescharacteristic
749C4D4×D4411yescharacteristic
750C4#1062308511yescharacteristic
751C4#1062309311yescharacteristic
752C2—882no—
753C2—1761no—
754C2#1307219811yescharacteristic
755C2#1307808811yescharacteristic
756C2#1307813711yescharacteristic
757C2#1308012711yescharacteristic
758C2#1308014211yescharacteristic
759C2#1308166511yescharacteristic
760C2#1308168211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2365C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenter#2365D11
hypocenterC11#25377
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2365

Complements

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

NH ≅ G/Ntype
1. C2×#10622699C2semidirect
2. C2×#10622641C2semidirect
4. C2×#10622696C2semidirect
6. #13069938C2semidirect
7. #13069931C2semidirect
8. #13069709C2semidirect
10. #13069548C2semidirect
11. #13069340C2semidirect
12. #13068971C2semidirect
13. #13068957C2semidirect
14. #13068444C2semidirect
15. C11×#2365C2semidirect
72. C11×C4⋊Q8D4semidirect
256. #2365D11semidirect
465. C4⋊Q8D44semidirect
630. C11#25377semidirect

Maximal subgroups

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

subgroupindex
C2×#106226992
C2×#106226412
C2×#106226402
C2×#106226962
#130735872
#130699382
#130699312
#130697092
#130697032
#130695482
#130693402
#130689712
#130689572
#130684442
C11×#23652
#2537711