Finite Group Databasebeta

← #14774078

Subgroups — #14774078

Order 2816.

1146 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622771C211yesmaximal, characteristic
2C2×#10622631C211yesmaximal, characteristic, complemented
3C2×#10622385C211yesmaximal, characteristic, complemented
4#13071650C211yesmaximal, characteristic, complemented
5#13071455C211yesmaximal, characteristic, complemented
6#13069493C211yesmaximal, characteristic, complemented
7#13069316C211yesmaximal, characteristic, complemented
8#13069239C211yesmaximal, characteristic, complemented
9#13069041C211yesmaximal, characteristic, complemented
10#13068968C211yesmaximal, characteristic, complemented
11#13068887C211yesmaximal, characteristic, complemented
12#13068816C211yesmaximal, characteristic, complemented
13#13068445C211yesmaximal, characteristic, complemented
14#13068391C211yesmaximal, characteristic, complemented
15C11×#1879C211yesmaximal, characteristic, complemented
16C22×#4341C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66991C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22C2×#66945C2211yescharacteristic
23C2×#66940C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C11×#390C2211yescharacteristic
28#10622834C2211yescharacteristic
29#10622834C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33#10622826—21no—
34C4×C22⋊Dic11—21no—
35#10622771C418yescomplemented
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×#66881C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39C2×#66880C2211yescharacteristic
40C2×#66879C2211yescharacteristic
41#10622631—24no—
42#10622600C2211yescharacteristic
43C4⋊C4×Dic11C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622570—21no—
47#10622570—21no—
48#10622570—21no—
49#10622557—21no—
50#10622555—21no—
51C22⋊C4×Dic11—21no—
52C4×(C2×D11)⋊C4C2211yescharacteristic
53#10622541C2211yescharacteristic
54C2×#66867C2211yescharacteristic
55#10622385—24no—
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C22×C22⋊D11—21no—
66C22×C22⋊D11—21no—
67C23×Dic11—21no—
68C2×#4341—22no—
69C2×#4341—22no—
70C2×#4341—22no—
71C2×#4341—41no—
72C2×#4341—41no—
73C2×#4341C2×C414yescomplemented
74C22×C4×D11C2311yescharacteristic
75C22×Dic22C2311yescharacteristic
76C2×C11×D8—41no—
77C2×C11×D8—41no—
78C2×C11×D8C2×C414yes—
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C4×D4×C11—22no—
82C4×D4×C11—41no—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11—21no—
90C2×C22⋊Dic11—21no—
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—21no—
93C2×C22⋊Dic11—21no—
94#66991—22no—
95#66991C2×C414yes—
96C2×#4324—22no—
97C2×#4324—22no—
98C2×#4324C2×C414yes—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4D411yescharacteristic
102C2×(C2×D11)⋊C4D411yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4—21no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11—21no—
113C2×C4×Dic11C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C2×C8×D11—22no—
117C2×C8×D11—22no—
118C2×C8×D11—41no—
119#66945—22no—
120#66945—41no—
121#66940—22no—
122#66940—41no—
123C4×Dic22—22no—
124C4×Dic22—41no—
125C11×#102—22no—
126C11×#102—41no—
127#66896—22no—
128#66896—22no—
129#66896C2×C414yescomplemented
130C11⋊#95—21no—
131C11⋊#95—21no—
132C11⋊#95—21no—
133C11⋊#95D411yescharacteristic
134C11⋊#95D411yescharacteristic
135(C2×D11)⋊C8C2×C414yescomplemented
136#66881—41no—
137#66880—22no—
138#66880C2×C414yescomplemented
139#66879—41no—
140#66874D414yescomplemented
141#66871—22no—
142#66867—22no—
143#22857—111nomaximal, Sylow
144C24×C11—21no—
145C24×C11—21no—
146C23×D11C2×D411yescharacteristic
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11C22×C412yes—
158C2×D4×C11C22×C412yes—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—42no—
162C22×C4×C11—42no—
163C22×C4×C11—81no—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2411yescharacteristic
167C2×C22⋊D11—24no—
168C2×C22⋊D11—24no—
169C2×C22⋊D11—42no—
170C2×C22⋊D11—42no—
171C2×C22⋊D11—81no—
172C2×C22⋊D11—81no—
173C22×Dic11—24no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—42no—
179C22×Dic11—42no—
180C22×Dic11C2×D411yescharacteristic
181C22×Dic11C2×D411yescharacteristic
182C22×Dic11C2×D411yescharacteristic
183#4341—28no—
184#4341—44no—
185#4341—44no—
186#4341—44no—
187C2×C4×D11—21no—
188C2×C4×D11—21no—
189C2×C4×D11—21no—
190C2×C4×D11—21no—
191C2×C4×D11C22×C412yes—
192C2×C4×D11#4112yes—
193C2×Dic22—21no—
194C2×Dic22—21no—
195C2×Dic22—21no—
196C2×Dic22C22×C412yes—
197C2×Dic22C2×D412yes—
198C2×Dic22#4112yes—
199C11×D8—44no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11C22×C412yes—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4C2×D412yes—
210C11×C22⋊C4—42no—
211C11×C22⋊C4—42no—
212C11×C22⋊C4—81no—
213C42×C11—21no—
214C42×C11—21no—
215C22⋊Dic11—24no—
216C22⋊Dic11—42no—
217C22⋊Dic11—42no—
218C22⋊Dic11—81no—
219C22⋊Dic11—81no—
220#4324—28no—
221(C2×D11)⋊C4—41no—
222(C2×D11)⋊C4—41no—
223(C2×D11)⋊C4—42no—
224(C2×D11)⋊C4—81no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11C22×C412yes—
231Dic11⋊C4—42no—
232Dic11⋊C4—42no—
233Dic11⋊C4—81no—
234C4×Dic11—21no—
235C4×Dic11—21no—
236C4×Dic11—42no—
237C4×Dic11—42no—
238C4×Dic11—42no—
239C4×Dic11—81no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8C22×C412yes—
245C2×C11⋊C8C2×D412yes—
246C8×D11—44no—
247C2×#449—111no—
248C2×#440—111no—
249C2×#416—111no—
250#2363—111no—
251#2341—111no—
252#1972—111no—
253#1936—111no—
254#1925—111no—
255#1893—111no—
256#1880—111no—
257#1879D1111yescharacteristic, complemented
258#1865—111no—
259#1854—111no—
260#1763—111no—
261#1752—111no—
262C23×C11—22no—
263C23×C11—22no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11C22×D411yescharacteristic
277C22×D11—21no—
278C22×D11—21no—
279C22×D11—21no—
280C22×D11—21no—
281C22×D11—21no—
282C22×D11—21no—
283C22×D11C4×D412yes—
284D4×C11—22no—
285D4×C11—22no—
286D4×C11—22no—
287D4×C11—22no—
288D4×C11—41no—
289D4×C11—41no—
290D4×C11—41no—
291D4×C11—41no—
292C2×C4×C11—21no—
293C2×C4×C11—22no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
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—84no—
305C2×C4×C11C23×C411yescharacteristic
306C2×C4×C11C22×D411yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11H(5,𝔽2)11yescharacteristic
310C2×C4×C11H(5,𝔽2)11yescharacteristic
311C22⋊D11—48no—
312C22⋊D11—84no—
313C2×Dic11—22no—
314C2×Dic11—21no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—21no—
318C2×Dic11—22no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—48no—
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×Dic11C4×D412yes—
335C4×D11—22no—
336C4×D11—22no—
337C4×D11—22no—
338C4×D11—22no—
339Dic22—22no—
340Dic22—22no—
341Dic22—22no—
342Dic22C4×D414yes—
343C8×C11—22no—
344C8×C11—41no—
345C11⋊C8—22no—
346C11⋊C8—22no—
347C22×#41—111no—
348C22×SD16—111no—
349C22×D8C2×D1111yescharacteristic
350C23×C8—111no—
351C2×#121—111no—
352C2×C4×Q8—111no—
353C2×C4×Q8—111no—
354C2×C4×D4C2×D1111yescharacteristic
355C2×#117—111no—
356#449—118no—
357#440—224no—
358C2×#107—111no—
359C2×#106—111no—
360#416—224no—
361C2×#103—111no—
362C2×#103—111no—
363C2×#103—111no—
364C2×#102—111no—
365C2×#102—111no—
366C2×#102—111no—
367C2×#102C2×D1111yescharacteristic
368C2×#102C2×D1111yescharacteristic
369C2×C22⋊C8—111no—
370C2×#97—111no—
371C2×#97—111no—
372#390—111no—
373#390—111no—
374#390—221no—
375#390—221no—
376#390—221no—
377#390C2×D1111yescharacteristic
378#389—111no—
379#388—221no—
380#386—221no—
381#380—111no—
382#380—221no—
383C4×C4⋊C4—111no—
384C4×C22⋊C4—111no—
385C4×C22⋊C4—221no—
386C4×C22⋊C4—221no—
387#340—111no—
388#340—111no—
389#340—111no—
390#340C2×D1111yescharacteristic
391#336—111no—
392#336C2×D1111yescharacteristic
393C22×C11—42no—
394C22×C11—42no—
395C22×C11—42no—
396C22×C11—42no—
397C22×C11—42no—
398C22×C11—42no—
399C22×C11—81no—
400C22×C11—81no—
401C22×C11—81no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11—81no—
405C22×C11—81no—
406C22×C11—81no—
407C22×C11C2×C4×D411yescharacteristic
408C22×C11D4211yescharacteristic
409C22×C11#54611yescharacteristic
410C22×C11#57511yescharacteristic
411C22×C11#57511yescharacteristic
412C22×C11#57611yescharacteristic
413C22×C11#57711yescharacteristic
414C2×D11—22no—
415C2×D11—22no—
416C2×D11—22no—
417C2×D11—41no—
418C2×D11—41no—
419C2×D11—41no—
420C2×D11—41no—
421C4×C11—41no—
422C4×C11—42no—
423C4×C11—41no—
424C4×C11—81no—
425C4×C11C2×C4×D411yescharacteristic
426C4×C11#51811yescharacteristic
427C4×C11#54611yescharacteristic
428C4×C11#55111yescharacteristic
429Dic11—24no—
430Dic11—22no—
431Dic11—42no—
432Dic11—41no—
433Dic11—41no—
434Dic11—81no—
435Dic11—81no—
436C2×#41—114no—
437C2×#41—222no—
438C2×#41—222no—
439C2×#41—222no—
440C2×#41—441no—
441C2×#41—441no—
442C22×Q8—111no—
443C22×D4—221no—
444C22×D4—221no—
445C22×D4C22×D1111yescharacteristic
446C22×D4C22×D1111yescharacteristic
447C23×C4—21no—
448C23×C4—111no—
449C23×C4—221no—
450C2×SD16—114no—
451C2×SD16—222no—
452C2×SD16—222no—
453C2×D8—41no—
454C2×D8—41no—
455C2×D8C4×D1114yes—
456C22×C8—111no—
457C22×C8—111no—
458C22×C8—222no—
459C22×C8—222no—
460C22×C8—441no—
461C22×C8C22×D1111yescharacteristic
462C22×C8C22×D1111yescharacteristic
463#121—114no—
464#121—222no—
465C4×Q8—222no—
466C4×Q8—222no—
467C4×Q8—441no—
468C4×Q8—441no—
469C4×D4—22no—
470C4×D4—41no—
471#117—222no—
472#117—441no—
473C2×C4⋊C4—111no—
474C2×C4⋊C4—111no—
475C2×C4⋊C4—111no—
476C2×C4⋊C4—221no—
477C2×C4⋊C4—221no—
478C2×C4⋊C4—221no—
479C2×C4⋊C4C22×D1111yescharacteristic
480C2×C4⋊C4C22×D1111yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—111no—
485C2×C22⋊C4—111no—
486C2×C22⋊C4—221no—
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×C42—111no—
494C2×C42—221no—
495C2×C42—221no—
496C2×C42—221no—
497C2×C42—221no—
498C2×C42C22×D1111yescharacteristic
499#107—222no—
500#106—441no—
501#103—114no—
502#103—114no—
503#103—222no—
504#102—22no—
505#102—41no—
506#102—114no—
507#102—222no—
508#102—222no—
509C22⋊C8—114no—
510#97—222no—
511#97—441no—
512#95—111no—
513#95—111no—
514#95—221no—
515#95—221no—
516#95—221no—
517C2×C11—82no—
518C2×C11—82no—
519C2×C11#235811yescharacteristic
520C2×C11#294311yescharacteristic
521C2×C11#294611yescharacteristic
522C2×C11#326811yescharacteristic
523C2×C11#327111yescharacteristic
524C2×C11#330911yescharacteristic
525C2×C11#332111yescharacteristic
526D11—42no—
527C24—21no—
528C24—21no—
529C24—111no—
530#41—228no—
531#41—444no—
532#41—444no—
533#41—444no—
534C2×Q8—112no—
535C2×Q8—112no—
536C2×Q8—112no—
537C2×Q8—221no—
538C2×Q8—221no—
539C2×Q8—221no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—224no—
551C2×D4—224no—
552C2×D4—442no—
553C2×D4—442no—
554C2×D4—881no—
555C2×D4—881no—
556C2×D4C2×C4×D1112yes—
557C2×D4C2×C4×D1112yes—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—81no—
563C22×C4—111no—
564C22×C4—112no—
565C22×C4—112no—
566C22×C4—111no—
567C22×C4—111no—
568C22×C4—224no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—221no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—221no—
576C22×C4—221no—
577C22×C4—442no—
578C22×C4—442no—
579C22×C4D4×D1111yescharacteristic
580C22×C4D4×D1111yescharacteristic
581C22×C4C23×D1111yescharacteristic
582SD16—228no—
583D8—44no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—112no—
590C2×C8—112no—
591C2×C8—221no—
592C2×C8—221no—
593C2×C8—221no—
594C2×C8—221no—
595C2×C8—444no—
596C2×C8C2×C4×D1112yes—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—112no—
601C4⋊C4—221no—
602C4⋊C4—221no—
603C4⋊C4—221no—
604C4⋊C4—221no—
605C4⋊C4—221no—
606C4⋊C4—442no—
607C4⋊C4—442no—
608C4⋊C4—881no—
609C4⋊C4D4×D1112yes—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—81no—
613C22⋊C4—224no—
614C22⋊C4—441no—
615C22⋊C4—441no—
616C22⋊C4—442no—
617C22⋊C4—442no—
618C22⋊C4—442no—
619C22⋊C4—881no—
620C22⋊C4—881no—
621C22⋊C4—881no—
622C42—21no—
623C42—21no—
624C42—221no—
625C42—221no—
626C42—442no—
627C42—442no—
628C42—442no—
629C42—881no—
630C11#2285711yescharacteristic, complemented, Sylow
631C23—22no—
632C23—22no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—112no—
646C23—221no—
647C23—221no—
648C23—221no—
649C23—221no—
650C23—221no—
651C23—221no—
652C23C2×D4×D1111yescharacteristic
653Q8—114no—
654Q8—222no—
655Q8—222no—
656Q8—222no—
657D4—22no—
658D4—22no—
659D4—22no—
660D4—22no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—448no—
666D4—884no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—84no—
680C2×C4—112no—
681C2×C4—222no—
682C2×C4—221no—
683C2×C4—222no—
684C2×C4—222no—
685C2×C4—221no—
686C2×C4—222no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—221no—
691C2×C4—221no—
692C2×C4—221no—
693C2×C4—221no—
694C2×C4—222no—
695C2×C4—221no—
696C2×C4—221no—
697C2×C4—448no—
698C2×C4—441no—
699C2×C4—441no—
700C2×C4—441no—
701C2×C4—441no—
702C2×C4—441no—
703C2×C4—441no—
704C2×C4—441no—
705C2×C4—441no—
706C2×C4C22×C4×D1111yescharacteristic
707C2×C4C2×D4×D1111yescharacteristic
708C2×C4#6703711yescharacteristic
709C2×C4#6703711yescharacteristic
710C2×C4#41×D1111yescharacteristic
711C2×C4#41×D1111yescharacteristic
712C8—22no—
713C8—41no—
714C8—222no—
715C8—222no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—222no—
731C22—222no—
732C22—222no—
733C22—441no—
734C22—441no—
735C22—441no—
736C22—441no—
737C22C4×D4×D1111yescharacteristic
738C22#1062312111yescharacteristic
739C22#1062314311yescharacteristic
740C22#1062328811yescharacteristic
741C22#1062330111yescharacteristic
742C22#1062330411yescharacteristic
743C22#1062330411yescharacteristic
744C4—41no—
745C4—42no—
746C4—41no—
747C4—81no—
748C4—222no—
749C4—224no—
750C4—441no—
751C4—442no—
752C4—441no—
753C4—881no—
754C4—881no—
755C4#1062301711yescharacteristic
756C4C4×D4×D1111yescharacteristic
757C4#1062314311yescharacteristic
758C4#1062319011yescharacteristic
759C2—82no—
760C2—82no—
761C2—442no—
762C2#1307159911yescharacteristic
763C2#1307741311yescharacteristic
764C2#1307744111yescharacteristic
765C2#1308015411yescharacteristic
766C2#1308019911yescharacteristic
767C2#1308062911yescharacteristic
768C2#1308080911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1879C2
socleC23×C11C22×D4
prime radicalC2×#10622771C2
cosocleC22×C4×C11C24
hypercenter#1879D11
hypocenterC11#22857
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
2. C2×#10622631C2semidirect
3. C2×#10622385C2semidirect
4. #13071650C2semidirect
5. #13071455C2semidirect
6. #13069493C2semidirect
7. #13069316C2semidirect
8. #13069239C2semidirect
9. #13069041C2semidirect
10. #13068968C2semidirect
11. #13068887C2semidirect
12. #13068816C2semidirect
13. #13068445C2semidirect
14. #13068391C2semidirect
15. C11×#1879C2semidirect
35. #10622771C4semidirect
73. C2×#4341C2×C4semidirect
129. #66896C2×C4semidirect
135. (C2×D11)⋊C8C2×C4semidirect
138. #66880C2×C4semidirect
140. #66874D4semidirect
257. #1879D11semidirect
630. C11#22857semidirect

Maximal subgroups

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

subgroupindex
C2×#106227712
C2×#106226312
C2×#106223852
#130716502
#130714552
#130694932
#130693162
#130692392
#130690412
#130689682
#130688872
#130688162
#130684452
#130683912
C11×#18792
#2285711