Finite Group Databasebeta

← #14774160

Subgroups — #14774160

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×#10622394C211yesmaximal, characteristic
2C2×#10622502C211yesmaximal, characteristic, complemented
3C2×#10622384C211yesmaximal, characteristic, complemented
4#13071634C211yesmaximal, characteristic, complemented
5#13071455C211yesmaximal, characteristic, complemented
6#13069481C211yesmaximal, characteristic, complemented
7#13069315C211yesmaximal, characteristic, complemented
8#13069053C211yesmaximal, characteristic, complemented
9#13068970C211yesmaximal, characteristic, complemented
10#13068961C211yesmaximal, characteristic, complemented
11#13068871C211yesmaximal, characteristic, complemented
12#13068802C211yesmaximal, characteristic, complemented
13C4×#66874C211yesmaximal, characteristic, complemented
14#13068396C211yesmaximal, characteristic, complemented
15C11×#1925C211yesmaximal, characteristic, complemented
16C22×#4341C2211yescharacteristic
17C22×#4323C2211yescharacteristic
18C22×#4314C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20C2×#66948C2211yescharacteristic
21C2×#66946C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×#66940C2211yescharacteristic
24C2×C4×D44—21no—
25C2×C4×Dic22C2211yescharacteristic
26C2×C11×#107C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C11×#390C2211yescharacteristic
30C4×C11×C4⋊C4C2211yescharacteristic
31#10622834C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37#10622600C2211yescharacteristic
38#10622598C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43#10622570—21no—
44#10622570—21no—
45#10622555—21no—
46C22⋊C4×Dic11—21no—
47#10622553—21no—
48#10622552C2211yescharacteristic
49C4×(C2×D11)⋊C4C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622502—24no—
52#10622394C418yescomplemented
53#10622384—24no—
54#10622281—21no—
55#10622278—21no—
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C23×Dic11—21no—
65C2×#4341—22no—
66C2×#4341—22no—
67C2×#4341—22no—
68C2×#4341—41no—
69C2×#4341—41no—
70C2×#4341C2×C414yescomplemented
71C22×D44—21no—
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×C4×D11—21no—
75C22×C4×D11C2311yescharacteristic
76C22×Dic22C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C42×C11—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×#4323—41no—
89C2×#4323—41no—
90C2×#4323C2×C414yescomplemented
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4D411yescharacteristic
97C2×(C2×D11)⋊C4D411yescharacteristic
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C2×#4314—22no—
110C2×#4314—22no—
111C2×#4314C2×C414yescomplemented
112C2×#4313—22no—
113C2×#4313—22no—
114C2×#4313—41no—
115#66948—22no—
116#66948C2×C414yes—
117#66946—22no—
118#66946—41no—
119C4⋊C4×D11—22no—
120C4⋊C4×D11—41no—
121#66940—22no—
122#66940—41no—
123C4×D44—44no—
124C4×Dic22—22no—
125C4×Dic22—41no—
126C11×#107—22no—
127C11×#102—22no—
128C11×#102C2×C414yescomplemented
129C11×#95—21no—
130#66896—22no—
131C11⋊#95—21no—
132C11⋊#95—21no—
133C11⋊#95D411yescharacteristic
134C11⋊#95D411yescharacteristic
135#66885—41no—
136(C2×D11)⋊C8C2×C414yescomplemented
137#66880—22no—
138#66879—22no—
139#66874C2×C414yescomplemented
140#66874D414yescomplemented
141#66873—22no—
142#66871—41no—
143C4×C11⋊C8—41no—
144#22863—111nomaximal, Sylow
145C24×C11—21no—
146C23×D11—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×C11C22×C412yes—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—24no—
161C2×C22⋊D11—42no—
162C2×C22⋊D11—42no—
163C22×Dic11—24no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—42no—
168C22×Dic11—42no—
169C22×Dic11C2×D411yescharacteristic
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172#4341—28no—
173#4341—44no—
174#4341—44no—
175#4341—44no—
176C2×D44—24no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—21no—
180C2×D44—21no—
181C2×D44—21no—
182C2×D44—42no—
183C2×D44—42no—
184C2×D44C22×C412yes—
185C2×C4×D11—21no—
186C2×C4×D11—21no—
187C2×C4×D11—21no—
188C2×C4×D11—21no—
189C2×C4×D11—42no—
190C2×C4×D11—42no—
191C2×C4×D11—42no—
192C2×C4×D11—42no—
193C2×C4×D11—81no—
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—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11C22×C412yes—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4C22×C412yes—
214C11×C4⋊C4C2×D412yes—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—81no—
217C42×C11—21no—
218C42×C11—21no—
219C42×C11—42no—
220C22⋊Dic11—42no—
221C22⋊Dic11—81no—
222#4323—44no—
223(C2×D11)⋊C4—24no—
224(C2×D11)⋊C4—22no—
225(C2×D11)⋊C4—41no—
226(C2×D11)⋊C4—42no—
227(C2×D11)⋊C4—42no—
228(C2×D11)⋊C4—81no—
229(C2×D11)⋊C4—81no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11—21no—
233C4⋊Dic11—21no—
234C4⋊Dic11—42no—
235Dic11⋊C4—42no—
236Dic11⋊C4—42no—
237Dic11⋊C4—42no—
238C4×Dic11—21no—
239C4×Dic11—21no—
240C4×Dic11—42no—
241C4×Dic11—42no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8C22×C412yes—
247C2×C11⋊C8C2×D412yes—
248#4314—28no—
249#4313—44no—
250C2×#449—111no—
251C2×#440—111no—
252C2×#417—111no—
253#2361—111no—
254#2341—111no—
255#1970—111no—
256#1936—111no—
257#1925D1111yescharacteristic, complemented
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—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11C22×D411yescharacteristic
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—21no—
276C22×D11—21no—
277C22×D11—21no—
278C22×D11—21no—
279C22×D11—22no—
280C22×D11—41no—
281C22×D11—41no—
282C22×D11—41no—
283C22×D11—41no—
284C22×D11—41no—
285C22×D11—41no—
286C22×D11C4×D412yes—
287D4×C11—22no—
288D4×C11—22no—
289D4×C11—41no—
290D4×C11—41no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—41no—
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×C11AGL(1,ℤ/8)12yes—
306C2×C4×C11C23×C411yescharacteristic
307C2×C4×C11C22×D411yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11C2×#4111yescharacteristic
310C2×C4×C11H(5,𝔽2)11yescharacteristic
311C2×C4×C11H(5,𝔽2)11yescharacteristic
312C22⋊D11—48no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—21no—
316C2×Dic11—22no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—48no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11C4×D412yes—
332D44—22no—
333D44—22no—
334D44—48no—
335D44—41no—
336D44—41no—
337C4×D11—22no—
338C4×D11—22no—
339C4×D11—22no—
340C4×D11—22no—
341C4×D11—84no—
342C4×D11—84no—
343Dic22—22no—
344Dic22—22no—
345Dic22—22no—
346Dic22C4×D414yescomplemented
347C8×C11—22no—
348C8×C11—41no—
349C11⋊C8—22no—
350C11⋊C8—22no—
351C22×#41—111no—
352C22×SD16—111no—
353C22×D8—111no—
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×C8—111no—
377#390—111no—
378#390—111no—
379#390—221no—
380#390—221no—
381#390C2×D1111yescharacteristic
382#389—111no—
383#388—221no—
384#386—221no—
385#385—221no—
386#380—111no—
387#380—221no—
388C4×C4⋊C4C2×D1111yescharacteristic
389C4×C22⋊C4—111no—
390C4×C22⋊C4—221no—
391#340—111no—
392#340—111no—
393#340—111no—
394#340C2×D1111yescharacteristic
395#336—111no—
396#336C2×D1111yescharacteristic
397C22×C11—42no—
398C22×C11—42no—
399C22×C11—42no—
400C22×C11—81no—
401C22×C11—81no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11C2×C4×D411yescharacteristic
405C22×C11D4211yescharacteristic
406C22×C11#54611yescharacteristic
407C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
408C22×C11#57511yescharacteristic
409C22×C11#57611yescharacteristic
410C22×C11#57811yescharacteristic
411C2×D11—22no—
412C2×D11—22no—
413C2×D11—22no—
414C2×D11—41no—
415C2×D11—41no—
416C2×D11—41no—
417C2×D11—41no—
418C2×D11—42no—
419C2×D11—42no—
420C2×D11—42no—
421C2×D11—81no—
422C2×D11—81no—
423C2×D11—81no—
424C2×D11—81no—
425C4×C11—22no—
426C4×C11—42no—
427C4×C11—42no—
428C4×C11—41no—
429C4×C11—81no—
430C4×C11C2×C4×D411yescharacteristic
431C4×C11#51811yescharacteristic
432C4×C11#54611yescharacteristic
433C4×C11#55111yescharacteristic
434Dic11—24no—
435Dic11—22no—
436Dic11—41no—
437Dic11—41no—
438Dic11—81no—
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—111no—
448C22×D4—221no—
449C22×D4—221no—
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—114no—
459C2×D8—441no—
460C2×D8—441no—
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—444no—
476C4×D4—441no—
477C2×C4⋊C4—111no—
478C2×C4⋊C4—111no—
479C2×C4⋊C4—222no—
480C2×C4⋊C4—221no—
481C2×C4⋊C4—221no—
482C2×C4⋊C4—221no—
483C2×C4⋊C4—221no—
484C2×C4⋊C4—441no—
485C2×C4⋊C4C22×D1111yescharacteristic
486C2×C4⋊C4C22×D1111yescharacteristic
487C2×C4⋊C4C22×D1111yescharacteristic
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—111no—
491C2×C22⋊C4—111no—
492C2×C22⋊C4—221no—
493C2×C22⋊C4—221no—
494C2×C22⋊C4—221no—
495C2×C22⋊C4—221no—
496C2×C22⋊C4—221no—
497C2×C22⋊C4—221no—
498C2×C22⋊C4—221no—
499C2×C42—21no—
500C2×C42—111no—
501C2×C42—221no—
502C2×C42—221no—
503C2×C42C22×D1111yescharacteristic
504#107—22no—
505#107—441no—
506#103—114no—
507#103—114no—
508#103—222no—
509#102—22no—
510#102—222no—
511#102—222no—
512#102—441no—
513#102C4×D1114yescomplemented
514C22⋊C8—114no—
515#97—222no—
516C4×C8—441no—
517#95—21no—
518#95—111no—
519#95—111no—
520#95—221no—
521#95—221no—
522C2×C11—82no—
523C2×C11#235811yescharacteristic
524C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
525C2×C11#295111yescharacteristic
526C2×C11#327411yescharacteristic
527C2×C11#327711yescharacteristic
528C2×C11#330811yescharacteristic
529C2×C11#330911yescharacteristic
530D11—42no—
531D11—82no—
532C24—21no—
533C24—111no—
534C24—221no—
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—112no—
551C2×D4—224no—
552C2×D4—224no—
553C2×D4—221no—
554C2×D4—221no—
555C2×D4—221no—
556C2×D4—221no—
557C2×D4—221no—
558C2×D4—442no—
559C2×D4—442no—
560C2×D4—442no—
561C2×D4—442no—
562C2×D4C2×C4×D1112yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—111no—
567C22×C4—112no—
568C22×C4—112no—
569C22×C4—111no—
570C22×C4—111no—
571C22×C4—224no—
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—444no—
592M16—444no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—112no—
599C2×C8—112no—
600C2×C8—221no—
601C2×C8—221no—
602C2×C8—221no—
603C2×C8—221no—
604C2×C8C2×C4×D1112yes—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—221no—
610C4⋊C4—221no—
611C4⋊C4—221no—
612C4⋊C4—221no—
613C4⋊C4—442no—
614C4⋊C4—442no—
615C4⋊C4—442no—
616C4⋊C4—442no—
617C4⋊C4C2×C4×D1112yes—
618C4⋊C4D4×D1112yes—
619C22⋊C4—42no—
620C22⋊C4—81no—
621C22⋊C4—224no—
622C22⋊C4—222no—
623C22⋊C4—441no—
624C22⋊C4—442no—
625C22⋊C4—442no—
626C22⋊C4—442no—
627C22⋊C4—881no—
628C22⋊C4—881no—
629C22⋊C4—881no—
630C42—21no—
631C42—21no—
632C42—42no—
633C42—221no—
634C42—221no—
635C42—442no—
636C42—442no—
637C11#2286311yescharacteristic, complemented, Sylow
638C23—22no—
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—
652C23—222no—
653C23—441no—
654C23—441no—
655C23—441no—
656C23—441no—
657C23—441no—
658C23—441no—
659C23C2×D4×D1111yescharacteristic
660Q8—114no—
661Q8—222no—
662Q8—222no—
663Q8—222no—
664D4—22no—
665D4—22no—
666D4—41no—
667D4—41no—
668D4—222no—
669D4—222no—
670D4—448no—
671D4—448no—
672D4—441no—
673D4—441no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—112no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—221no—
692C2×C4—222no—
693C2×C4—221no—
694C2×C4—222no—
695C2×C4—222no—
696C2×C4—222no—
697C2×C4—222no—
698C2×C4—221no—
699C2×C4—221no—
700C2×C4—221no—
701C2×C4—221no—
702C2×C4—221no—
703C2×C4—221no—
704C2×C4—448no—
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#41×D1111yescharacteristic
717C2×C4#41×D1111yescharacteristic
718C2×C4#6704211yescharacteristic
719C2×C4#6704211yescharacteristic
720C8—22no—
721C8—41no—
722C8—222no—
723C8—222no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—222no—
732C22—222no—
733C22—222no—
734C22—441no—
735C22—441no—
736C22—441no—
737C22—441no—
738C22—442no—
739C22—442no—
740C22—442no—
741C22—881no—
742C22—881no—
743C22—881no—
744C22—881no—
745C22C4×D4×D1111yescharacteristic
746C22#1062314011yescharacteristic
747C22#1062318511yescharacteristic
748C22C2×#6696411yescharacteristic
749C22#1062329911yescharacteristic
750C22#1062330511yescharacteristic
751C22#1062331011yescharacteristic
752C4—22no—
753C4—41no—
754C4—42no—
755C4—42no—
756C4—81no—
757C4—222no—
758C4—224no—
759C4—441no—
760C4—441no—
761C4—881no—
762C4—881no—
763C4#1062305211yescharacteristic
764C4C4×D4×D1111yescharacteristic
765C4#1062320711yescharacteristic
766C4#1062323611yescharacteristic
767C2—82no—
768C2—442no—
769C2—882no—
770C2#1307159411yescharacteristic
771C2C4×#6696411yescharacteristic
772C2#1307748811yescharacteristic
773C2#1308023911yescharacteristic
774C2#1308026811yescharacteristic
775C2#1308060511yescharacteristic
776C2#1308062011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1925C2
socleC23×C11C22×D4
prime radicalC2×#10622394C2
cosocleC22×C4×C11C24
hypercenter#1925D11
hypocenterC11#22863
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1925

Complements

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

NH ≅ G/Ntype
2. C2×#10622502C2semidirect
3. C2×#10622384C2semidirect
4. #13071634C2semidirect
5. #13071455C2semidirect
6. #13069481C2semidirect
7. #13069315C2semidirect
8. #13069053C2semidirect
9. #13068970C2semidirect
10. #13068961C2semidirect
11. #13068871C2semidirect
12. #13068802C2semidirect
13. C4×#66874C2semidirect
14. #13068396C2semidirect
15. C11×#1925C2semidirect
52. #10622394C4semidirect
70. C2×#4341C2×C4semidirect
90. C2×#4323C2×C4semidirect
111. C2×#4314C2×C4semidirect
128. C11×#102C2×C4semidirect
136. (C2×D11)⋊C8C2×C4semidirect
139. #66874C2×C4semidirect
140. #66874D4semidirect
257. #1925D11semidirect
346. Dic22C4×D4semidirect
513. #102C4×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×#106223942
C2×#106225022
C2×#106223842
#130716342
#130714552
#130694812
#130693152
#130690532
#130689702
#130689612
#130688712
#130688022
C4×#668742
#130683962
C11×#19252
#2286311