Finite Group Databasebeta

← #14774164

Subgroups — #14774164

Order 2816.

1190 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622771C211yesmaximal, characteristic
2C2×#10622370C211yesmaximal, characteristic, complemented
3C2×#10622384C211yesmaximal, characteristic, complemented
4#13071637C211yesmaximal, characteristic, complemented
5#13071455C211yesmaximal, characteristic, complemented
6#13069310C211yesmaximal, characteristic, complemented
7#13069233C211yesmaximal, characteristic, complemented
8#13069051C211yesmaximal, characteristic, complemented
9#13068974C211yesmaximal, characteristic, complemented
10#13068966C211yesmaximal, characteristic, complemented
11#13068867C211yesmaximal, characteristic, complemented
12#13068802C211yesmaximal, characteristic, complemented
13C4×#66880C211yesmaximal, characteristic, complemented
14#13068399C211yesmaximal, characteristic, complemented
15C11×#1970C211yesmaximal, characteristic, complemented
16C22×#4341C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×#66991C2211yescharacteristic
19C2×D4×Dic11C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C22×#4313C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×#66940C2211yescharacteristic
24C2×(C22⋊D11)⋊C4—21no—
25C2×C4×Dic22C2211yescharacteristic
26C2×C11×#107C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C4×C8×C11C2211yescharacteristic
30C11×#390C2211yescharacteristic
31C11×#390C2211yescharacteristic
32#10622834C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36#10622771C418yescomplemented
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39C2×#66880C2211yescharacteristic
40C2×#66879C2211yescharacteristic
41#10622600C2211yescharacteristic
42#10622586C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622570—21no—
46#10622570—21no—
47#10622569—21no—
48#10622559—21no—
49#10622557—21no—
50#10622555—21no—
51C22⋊C4×Dic11—21no—
52C4×(C2×D11)⋊C4C2211yescharacteristic
53C4×C4⋊Dic11C2211yescharacteristic
54#10622384—24no—
55#10622370—24no—
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C22×C22⋊D11—21no—
65C22×C22⋊D11—21no—
66C23×Dic11—21no—
67C23×Dic11—21no—
68C2×#4341—22no—
69C2×#4341—22no—
70C2×#4341—22no—
71C2×#4341—41no—
72C2×#4341—41no—
73C2×#4341C2×C414yescomplemented
74C22×C4×D11—21no—
75C22×C4×D11C2311yescharacteristic
76C22×Dic22C2311yescharacteristic
77C2×C11×D8—41no—
78C2×C11×D8—41no—
79C2×C11×D8C2×C414yescomplemented
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—21no—
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—
93#66991—22no—
94#66991C2×C414yes—
95D4×Dic11—22no—
96D4×Dic11—41no—
97C2×#4324—22no—
98C2×#4324—22no—
99C2×#4324C2×C414yescomplemented
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×Dic11⋊C4—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11—21no—
113C2×C4×Dic11C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C2×#4313—22no—
117C2×#4313—22no—
118C2×#4313—41no—
119C4⋊C4×D11—22no—
120C4⋊C4×D11—41no—
121#66940—22no—
122#66940—41no—
123(C22⋊D11)⋊C4—44no—
124C4×Dic22—22no—
125C4×Dic22—41no—
126C11×#107—41no—
127C11×#102—22no—
128C11×#102—22no—
129C4×C8×C11—41no—
130#66896—22no—
131#66896—41no—
132#66896C2×C414yescomplemented
133C11⋊#95—21no—
134C11⋊#95—21no—
135C11⋊#95—21no—
136C11⋊#95D411yescharacteristic
137C11⋊#95D411yescharacteristic
138(C2×D11)⋊C8C2×C414yescomplemented
139#66880C2×C414yescomplemented
140#66880D414yescomplemented
141#66879—22no—
142#66874—22no—
143#66871—22no—
144#22863—111nomaximal, Sylow
145C24×C11—21no—
146C24×C11—21no—
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×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11C22×C412yes—
159C2×D4×C11C22×C412yes—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2411yescharacteristic
165C2×C22⋊D11—24no—
166C2×C22⋊D11—24no—
167C2×C22⋊D11—42no—
168C2×C22⋊D11—42no—
169C2×C22⋊D11—42no—
170C2×C22⋊D11—42no—
171C22×Dic11—24no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—42no—
177C22×Dic11—42no—
178C22×Dic11—42no—
179C22×Dic11—42no—
180C22×Dic11—81no—
181C22×Dic11C2×D411yescharacteristic
182C22×Dic11C2×D411yescharacteristic
183C22×Dic11C2×D411yescharacteristic
184#4341—28no—
185#4341—44no—
186#4341—44no—
187#4341—44no—
188C2×C4×D11—21no—
189C2×C4×D11—21no—
190C2×C4×D11—21no—
191C2×C4×D11—21no—
192C2×C4×D11—42no—
193C2×C4×D11—42no—
194C2×C4×D11—81no—
195C2×C4×D11C22×C412yes—
196C2×C4×D11#4112yes—
197C2×Dic22—21no—
198C2×Dic22—21no—
199C2×Dic22—21no—
200C2×Dic22C22×C412yes—
201C2×Dic22C2×D412yes—
202C2×Dic22#4112yes—
203C11×D8—44no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11C22×C412yes—
209C2×C8×C11C2×D412yes—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—81no—
217C11×C22⋊C4—81no—
218C42×C11—21no—
219C42×C11—21no—
220C22⋊Dic11—24no—
221C22⋊Dic11—42no—
222C22⋊Dic11—42no—
223C22⋊Dic11—81no—
224#4324—28no—
225(C2×D11)⋊C4—22no—
226(C2×D11)⋊C4—41no—
227(C2×D11)⋊C4—81no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11C22×C412yes—
233C4⋊Dic11C2×D412yes—
234Dic11⋊C4—42no—
235Dic11⋊C4—42no—
236Dic11⋊C4—42no—
237Dic11⋊C4—42no—
238C4×Dic11—21no—
239C4×Dic11—21no—
240C4×Dic11—42no—
241C4×Dic11—42no—
242C4×Dic11—42no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8C22×C412yes—
249#4313—44no—
250C2×#449—111no—
251C2×#440—111no—
252C2×#417—111no—
253#2361—111no—
254#2341—111no—
255#1970D1111yescharacteristic, complemented
256#1936—111no—
257#1925—111no—
258#1895—111no—
259#1880—111no—
260#1879—111no—
261#1863—111no—
262#1852—111no—
263C4×#103—111no—
264#1753—111no—
265C23×C11—22no—
266C23×C11—22no—
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×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11C22×D411yescharacteristic
280C22×D11—21no—
281C22×D11—21no—
282C22×D11—21no—
283C22×D11—21no—
284C22×D11—21no—
285C22×D11—21no—
286C22×D11C4×D412yes—
287D4×C11—22no—
288D4×C11—22no—
289D4×C11—22no—
290D4×C11—22no—
291D4×C11—41no—
292D4×C11—41no—
293D4×C11—41no—
294D4×C11—41no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
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×C11AGL(1,ℤ/8)12yes—
307C2×C4×C11C23×C411yescharacteristic
308C2×C4×C11C22×D411yescharacteristic
309C2×C4×C11C2×#4111yescharacteristic
310C2×C4×C11C2×#4111yescharacteristic
311C2×C4×C11H(5,𝔽2)11yescharacteristic
312C2×C4×C11H(5,𝔽2)11yescharacteristic
313C22⋊D11—48no—
314C22⋊D11—48no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—21no—
318C2×Dic11—22no—
319C2×Dic11—21no—
320C2×Dic11—22no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—22no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—21no—
327C2×Dic11—21no—
328C2×Dic11—48no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—84no—
337C2×Dic11C4×D412yes—
338C4×D11—22no—
339C4×D11—22no—
340C4×D11—22no—
341C4×D11—22no—
342C4×D11—84no—
343Dic22—22no—
344Dic22—22no—
345Dic22—22no—
346Dic22C4×D414yescomplemented
347C8×C11—22no—
348C8×C11—22no—
349C11⋊C8—22no—
350C11⋊C8—41no—
351C22×#41—111no—
352C22×SD16—111no—
353C22×D8C2×D1111yescharacteristic
354C22×M16—111no—
355C2×#121—111no—
356C2×C4×Q8—111no—
357C2×C4×Q8—111no—
358C2×C4×D4—111no—
359C2×C4×D4—221no—
360C22×C4⋊C4—111no—
361#449—118no—
362#440—224no—
363C2×#107—111no—
364C2×#107C2×D1111yescharacteristic
365#417—224no—
366C2×#103—111no—
367C2×#103—111no—
368C2×#103—111no—
369C2×#102—111no—
370C2×#102—111no—
371C2×#102—111no—
372C2×#102C2×D1111yescharacteristic
373C2×#102C2×D1111yescharacteristic
374C2×C22⋊C8—111no—
375C2×#97—111no—
376C2×C4×C8C2×D1111yescharacteristic
377#390—111no—
378#390—221no—
379#390—221no—
380#390C2×D1111yescharacteristic
381#390C2×D1111yescharacteristic
382#389—111no—
383#388—221no—
384#386—221no—
385#385—221no—
386#380—111no—
387#380—221no—
388C4×C4⋊C4—111no—
389C4×C22⋊C4—111no—
390C4×C22⋊C4—221no—
391#340—111no—
392#340—111no—
393#340—111no—
394#340—111no—
395#336—111no—
396#336—111no—
397C22×C11—42no—
398C22×C11—42no—
399C22×C11—42no—
400C22×C11—42no—
401C22×C11—42no—
402C22×C11—42no—
403C22×C11—81no—
404C22×C11—81no—
405C22×C11—81no—
406C22×C11—81no—
407C22×C11—81no—
408C22×C11—81no—
409C22×C11—81no—
410C22×C11—81no—
411C22×C11C2×C4×D411yescharacteristic
412C22×C11D4211yescharacteristic
413C22×C11#54611yescharacteristic
414C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
415C22×C11#57511yescharacteristic
416C22×C11#57611yescharacteristic
417C22×C11#57811yescharacteristic
418C2×D11—22no—
419C2×D11—22no—
420C2×D11—22no—
421C2×D11—41no—
422C2×D11—41no—
423C2×D11—41no—
424C2×D11—41no—
425C4×C11—22no—
426C4×C11—41no—
427C4×C11—81no—
428C4×C11—81no—
429C4×C11C2×C4×D411yescharacteristic
430C4×C11#51811yescharacteristic
431C4×C11#54611yescharacteristic
432C4×C11#55111yescharacteristic
433Dic11—24no—
434Dic11—22no—
435Dic11—42no—
436Dic11—42no—
437Dic11—41no—
438Dic11—41no—
439Dic11—81no—
440C2×#41—114no—
441C2×#41—222no—
442C2×#41—222no—
443C2×#41—222no—
444C2×#41—441no—
445C2×#41—441no—
446C22×Q8—111no—
447C22×D4—221no—
448C22×D4—221no—
449C22×D4C22×D1111yescharacteristic
450C22×D4C22×D1111yescharacteristic
451C23×C4—111no—
452C23×C4—221no—
453C23×C4—221no—
454C23×C4—221no—
455C2×SD16—114no—
456C2×SD16—222no—
457C2×SD16—222no—
458C2×D8—41no—
459C2×D8—41no—
460C2×D8C4×D1114yescomplemented
461C2×M16—222no—
462C2×M16—222no—
463C2×M16—441no—
464C22×C8—111no—
465C22×C8—111no—
466C22×C8C22×D1111yescharacteristic
467C22×C8C22×D1111yescharacteristic
468#121—114no—
469#121—222no—
470C4×Q8—222no—
471C4×Q8—222no—
472C4×Q8—441no—
473C4×Q8—441no—
474C4×D4—222no—
475C4×D4—441no—
476C4×D4—444no—
477C2×C4⋊C4—111no—
478C2×C4⋊C4—111no—
479C2×C4⋊C4—111no—
480C2×C4⋊C4—222no—
481C2×C4⋊C4—221no—
482C2×C4⋊C4—221no—
483C2×C4⋊C4—221no—
484C2×C4⋊C4—221no—
485C2×C4⋊C4—441no—
486C2×C4⋊C4C22×D1111yescharacteristic
487C2×C4⋊C4C22×D1111yescharacteristic
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—111no—
493C2×C22⋊C4—111no—
494C2×C22⋊C4—221no—
495C2×C22⋊C4—221no—
496C2×C22⋊C4—221no—
497C2×C22⋊C4—221no—
498C2×C22⋊C4—221no—
499C2×C42—111no—
500C2×C42—221no—
501C2×C42—221no—
502C2×C42—221no—
503C2×C42C22×D1111yescharacteristic
504#107—41no—
505#107—222no—
506#103—114no—
507#103—114no—
508#103—222no—
509#102—22no—
510#102—22no—
511#102—114no—
512#102—222no—
513#102—441no—
514C22⋊C8—114no—
515#97—222no—
516C4×C8—41no—
517#95—111no—
518#95—111no—
519#95—221no—
520#95—221no—
521#95—221no—
522C2×C11—82no—
523C2×C11—82no—
524C2×C11#235811yescharacteristic
525C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
526C2×C11#295111yescharacteristic
527C2×C11#327411yescharacteristic
528C2×C11#327711yescharacteristic
529C2×C11#330811yescharacteristic
530C2×C11#330911yescharacteristic
531D11—42no—
532C24—21no—
533C24—21no—
534C24—111no—
535#41—228no—
536#41—444no—
537#41—444no—
538#41—444no—
539C2×Q8—112no—
540C2×Q8—112no—
541C2×Q8—112no—
542C2×Q8—221no—
543C2×Q8—221no—
544C2×Q8—221no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—224no—
556C2×D4—224no—
557C2×D4—442no—
558C2×D4—442no—
559C2×D4—442no—
560C2×D4—442no—
561C2×D4C2×C4×D1112yes—
562C2×D4C2×C4×D1112yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—111no—
566C22×C4—112no—
567C22×C4—112no—
568C22×C4—111no—
569C22×C4—111no—
570C22×C4—224no—
571C22×C4—221no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—221no—
576C22×C4—221no—
577C22×C4—221no—
578C22×C4—221no—
579C22×C4—442no—
580C22×C4—442no—
581C22×C4—442no—
582C22×C4—442no—
583C22×C4—442no—
584C22×C4—442no—
585C22×C4—881no—
586C22×C4—881no—
587C22×C4D4×D1111yescharacteristic
588C22×C4D4×D1111yescharacteristic
589C22×C4C23×D1111yescharacteristic
590SD16—228no—
591D8—44no—
592M16—444no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—112no—
598C2×C8—221no—
599C2×C8—221no—
600C2×C8—221no—
601C2×C8—221no—
602C2×C8—221no—
603C2×C8C2×C4×D1112yes—
604C2×C8D4×D1112yes—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—112no—
610C4⋊C4—112no—
611C4⋊C4—221no—
612C4⋊C4—221no—
613C4⋊C4—221no—
614C4⋊C4—221no—
615C4⋊C4—442no—
616C4⋊C4—442no—
617C4⋊C4—442no—
618C4⋊C4—442no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—81no—
622C22⋊C4—81no—
623C22⋊C4—224no—
624C22⋊C4—222no—
625C22⋊C4—441no—
626C22⋊C4—442no—
627C22⋊C4—442no—
628C22⋊C4—881no—
629C22⋊C4—881no—
630C42—21no—
631C42—21no—
632C42—221no—
633C42—221no—
634C42—442no—
635C42—442no—
636C42—442no—
637C11#2286311yescharacteristic, complemented, Sylow
638C23—22no—
639C23—22no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—112no—
653C23—221no—
654C23—221no—
655C23—221no—
656C23—221no—
657C23—221no—
658C23—221no—
659C23C2×D4×D1111yescharacteristic
660Q8—114no—
661Q8—222no—
662Q8—222no—
663Q8—222no—
664D4—22no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—448no—
673D4—448no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—112no—
686C2×C4—222no—
687C2×C4—221no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—221no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—221no—
696C2×C4—221no—
697C2×C4—222no—
698C2×C4—221no—
699C2×C4—221no—
700C2×C4—221no—
701C2×C4—221no—
702C2×C4—222no—
703C2×C4—448no—
704C2×C4—441no—
705C2×C4—441no—
706C2×C4—441no—
707C2×C4—441no—
708C2×C4—441no—
709C2×C4—441no—
710C2×C4—441no—
711C2×C4—884no—
712C2×C4—884no—
713C2×C4#6696412yes—
714C2×C4C22×C4×D1111yescharacteristic
715C2×C4C2×D4×D1111yescharacteristic
716C2×C4#6703711yescharacteristic
717C2×C4#6703711yescharacteristic
718C2×C4#41×D1111yescharacteristic
719C2×C4#41×D1111yescharacteristic
720C8—22no—
721C8—22no—
722C8—222no—
723C8—441no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—222no—
739C22—222no—
740C22—222no—
741C22—441no—
742C22—441no—
743C22—441no—
744C22—441no—
745C22C4×D4×D1111yescharacteristic
746C22#1062314111yescharacteristic
747C22#1062324811yescharacteristic
748C22C2×#6696411yescharacteristic
749C22#1062328811yescharacteristic
750C22#1062329911yescharacteristic
751C22#1062330211yescharacteristic
752C4—22no—
753C4—41no—
754C4—81no—
755C4—81no—
756C4—222no—
757C4—224no—
758C4—442no—
759C4—441no—
760C4—442no—
761C4—441no—
762C4—881no—
763C4#1062301711yescharacteristic
764C4C4×D4×D1111yescharacteristic
765C4#1062314111yescharacteristic
766C4#1062321011yescharacteristic
767C2—82no—
768C2—82no—
769C2—442no—
770C2#1307159711yescharacteristic
771C2C4×#6696411yescharacteristic
772C2#1307748611yescharacteristic
773C2#1308023511yescharacteristic
774C2#1308027111yescharacteristic
775C2#1308061311yescharacteristic
776C2#1308062811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1970C2
socleC23×C11C22×D4
prime radicalC2×#10622771C2
cosocleC22×C4×C11C24
hypercenter#1970D11
hypocenterC11#22863
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1970

Complements

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

NH ≅ G/Ntype
2. C2×#10622370C2semidirect
3. C2×#10622384C2semidirect
4. #13071637C2semidirect
5. #13071455C2semidirect
6. #13069310C2semidirect
7. #13069233C2semidirect
8. #13069051C2semidirect
9. #13068974C2semidirect
10. #13068966C2semidirect
11. #13068867C2semidirect
12. #13068802C2semidirect
13. C4×#66880C2semidirect
14. #13068399C2semidirect
15. C11×#1970C2semidirect
36. #10622771C4semidirect
73. C2×#4341C2×C4semidirect
79. C2×C11×D8C2×C4semidirect
99. C2×#4324C2×C4semidirect
132. #66896C2×C4semidirect
138. (C2×D11)⋊C8C2×C4semidirect
139. #66880C2×C4semidirect
140. #66880D4semidirect
255. #1970D11semidirect
346. Dic22C4×D4semidirect
460. C2×D8C4×D11semidirect
637. C11#22863semidirect

Maximal subgroups

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

subgroupindex
C2×#106227712
C2×#106223702
C2×#106223842
#130716372
#130714552
#130693102
#130692332
#130690512
#130689742
#130689662
#130688672
#130688022
C4×#668802
#130683992
C11×#19702
#2286311