Finite Group Databasebeta

← #14764945

Subgroups — #14764945

Order 2816.

1224 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622389C211yesmaximal, characteristic
2C4×#66950C211yesmaximal, characteristic, complemented
3D11×#390C211yesmaximal, characteristic
4#13069471C211yesmaximal, characteristic, complemented
5#13069468C211yesmaximal, characteristic, complemented
6#13069301C211yesmaximal, characteristic, complemented
7#13069300C211yesmaximal, characteristic, complemented
8#13069243C211yesmaximal, characteristic, complemented
9#13068974C211yesmaximal, characteristic, complemented
10#13068970C211yesmaximal, characteristic, complemented
11#13068922C211yesmaximal, characteristic, complemented
12#13068807C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic
14#13068373C211yesmaximal, characteristic, complemented
15C11×#1926C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C22×#4324C2211yescharacteristic
18C22×#4314C2211yescharacteristic
19C2×#66950C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C22⋊C4×D11—21no—
22C2×C22⋊C4×D11—21no—
23C2×C42×D11C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic, complemented
25C2×C11×#106C2211yescharacteristic, complemented
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C11×#390C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic, complemented
30#10622834C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×#66880C2211yescharacteristic, complemented
36C2×C8×Dic11C2211yescharacteristic, complemented
37C2×C8×Dic11C2211yescharacteristic, complemented
38#10622601C2211yescharacteristic
39#10622600C2211yescharacteristic
40#10622598C2211yescharacteristic, complemented
41#10622587C2211yescharacteristic, complemented
42C2×#66874C2211yescharacteristic, complemented
43C2×#66873C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66872C2211yescharacteristic, complemented
46#10622570—21no—
47#10622570—21no—
48#10622552C2211yescharacteristic
49C4×(C2×D11)⋊C4—21no—
50C4×C4⋊Dic11—21no—
51#10622389C418yescomplemented
52#10622281—21no—
53#10622266—21no—
54C11×#340C2211yescharacteristic, complemented
55C11×#336C2211yescharacteristic, complemented
56#10622189C2211yescharacteristic, complemented
57#10622167C2211yescharacteristic, complemented
58#10622167C2211yescharacteristic, complemented
59#10622162C2211yescharacteristic, complemented
60C24×D11—21no—
61C22×D4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C2×D4×D11—22no—
64C2×D4×D11—41no—
65C2×D4×D11—41no—
66C2×D4×D11—41no—
67C2×D4×D11—41no—
68C2×D4×D11C2×C414yes—
69C22×D44C2311yescharacteristic
70C22×C4×D11—21no—
71C22×C4×D11D411yescharacteristic
72C22×C4×D11D411yescharacteristic
73C22×C4×D11C2311yescharacteristic
74C22×Dic22C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×#4324—41no—
87C2×#4324—41no—
88C2×#4324C2×C414yescomplemented
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11D411yescharacteristic
103C2×C4×Dic11D411yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C2×#4314—41no—
108C2×#4314—41no—
109C2×#4314C2×C414yescomplemented
110#66950—22no—
111#66950C2×C414yes—
112C4⋊C4×D11—41no—
113C4⋊C4×D11—41no—
114C22⋊C4×D11—44no—
115C22⋊C4×D11—44no—
116C42×D11—41no—
117C42×D11—41no—
118C4×Dic22—41no—
119C4×Dic22—41no—
120C11×#106—41no—
121C11×#102—41no—
122C11×#102C2×C414yescomplemented
123C11×#95—21no—
124#66896—41no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129#66885—41no—
130(C2×D11)⋊C8—22no—
131(C2×D11)⋊C8C2×C414yes—
132#66880—41no—
133C8×Dic11—41no—
134C8×Dic11—41no—
135#66874—41no—
136#66873—41no—
137#66873C2×C414yescomplemented
138#66872—41no—
139#22043—111nomaximal, Sylow
140C24×C11—21no—
141C23×D11—21no—
142C23×D11—24no—
143C23×D11—42no—
144C23×D11—42no—
145C23×D11—42no—
146C23×D11—42no—
147C23×D11—42no—
148C23×D11—42no—
149C23×D11C2×D411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11C22×C412yes—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2411yescharacteristic
162C2×C22⋊D11—24no—
163C2×C22⋊D11—42no—
164C2×C22⋊D11—42no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D411yescharacteristic
170C22×Dic11C2×D411yescharacteristic
171D4×D11—44no—
172D4×D11—44no—
173D4×D11—44no—
174D4×D11—44no—
175C2×D44—21no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—21no—
180C2×D44C22×C412yes—
181C2×C4×D11—22no—
182C2×C4×D11—22no—
183C2×C4×D11—21no—
184C2×C4×D11—21no—
185C2×C4×D11—21no—
186C2×C4×D11—21no—
187C2×C4×D11—41no—
188C2×C4×D11—41no—
189C2×C4×D11—41no—
190C2×C4×D11—42no—
191C2×C4×D11—42no—
192C2×C4×D11—42no—
193C2×C4×D11SD1614yescomplemented
194C2×C4×D11C22×C412yes—
195C2×C4×D11#4112yes—
196C2×Dic22—21no—
197C2×Dic22—21no—
198C2×Dic22—21no—
199C2×Dic22—21no—
200C2×Dic22—21no—
201C2×Dic22C22×C412yes—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11C22×C412yes—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4C22×C412yes—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—42no—
216C42×C11—21no—
217C42×C11—21no—
218C42×C11—42no—
219C22⋊Dic11—42no—
220C22⋊Dic11—42no—
221#4324—44no—
222(C2×D11)⋊C4—24no—
223(C2×D11)⋊C4—42no—
224(C2×D11)⋊C4—42no—
225(C2×D11)⋊C4—42no—
226(C2×D11)⋊C4—42no—
227(C2×D11)⋊C4—42no—
228C4⋊Dic11—24no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11—21no—
233C4⋊Dic11—42no—
234Dic11⋊C4—42no—
235Dic11⋊C4—42no—
236C4×Dic11—21no—
237C4×Dic11—21no—
238C4×Dic11—41no—
239C4×Dic11—41no—
240C4×Dic11—42no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8C22×C412yes—
247#4314—44no—
248C2×#450—111no—
249C4×C22⋊Q8—111no—
250C2×#390—111no—
251#1968—111no—
252#1968—111no—
253#1934—111no—
254#1934—111no—
255#1926—111no—
256#1926D1111yescharacteristic, complemented
257#1880—111no—
258#1880—111no—
259#1872—111no—
260#1853—111no—
261#1786—111no—
262C4×C22⋊C8—111no—
263C23×C11—22no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11C22×D411yescharacteristic
271C22×D11—21no—
272C22×D11—21no—
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—22no—
276C22×D11—48no—
277C22×D11—48no—
278C22×D11—41no—
279C22×D11—41no—
280C22×D11—41no—
281C22×D11—41no—
282C22×D11—41no—
283C22×D11—41no—
284C22×D11—48no—
285C22×D11—84no—
286C22×D11—84no—
287C22×D11—84no—
288C22×D11—84no—
289C22×D11C4×D412yes—
290C22×D11C2×SD1612yes—
291C22×D11#13512yes—
292D4×C11—22no—
293D4×C11—22no—
294D4×C11—41no—
295D4×C11—41no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—22no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
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×C11C2×SD1612yes—
311C2×C4×C11C23×C411yescharacteristic
312C2×C4×C11C2×#4111yescharacteristic
313C2×C4×C11H(5,𝔽2)11yescharacteristic
314C2×C4×C11H(5,𝔽2)11yescharacteristic
315C2×C4×C11H(5,𝔽2)11yescharacteristic
316C2×C4×C11H(5,𝔽2)11yescharacteristic
317C22⋊D11—48no—
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—22no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11C4×D412yes—
334C2×Dic11C2×SD1612yes—
335C2×Dic11AGL(1,ℤ/8)12yes—
336D44—22no—
337D44—22no—
338D44—41no—
339D44—41no—
340C4×D11—22no—
341C4×D11—22no—
342C4×D11—22no—
343C4×D11—22no—
344C4×D11—44no—
345C4×D11—44no—
346C4×D11—84no—
347Dic22—22no—
348Dic22—22no—
349Dic22—41no—
350Dic22—41no—
351C8×C11—22no—
352C8×C11—41no—
353C11⋊C8—22no—
354C11⋊C8—41no—
355C23×D4—111no—
356C22×SD16—111no—
357C22×SD16—111no—
358C2×C22⋊Q8—111no—
359C2×C4×Q8—111no—
360C22×C4⋊C4—111no—
361C22×C22⋊C4—221no—
362C22×C22⋊C4—221no—
363C22×C42—111no—
364#450—118no—
365C2×#106—111no—
366C2×#106C2×D1111yescharacteristic, complemented
367C2×#103—111no—
368C2×#103—111no—
369C2×#102—111no—
370C2×#102—111no—
371C2×#102—111no—
372C2×#102—111no—
373C2×#102C2×D1111yescharacteristic
374C2×#102C2×D1111yescharacteristic
375C2×C22⋊C8—111no—
376C2×C22⋊C8—111no—
377C2×C4×C8—111no—
378C2×C4×C8—111no—
379#391—111no—
380#390—111no—
381#390—111no—
382#390—111no—
383#390—221no—
384#390—221no—
385#390C2×D1111yescharacteristic
386#389—111no—
387#387—221no—
388#385—221no—
389#380—111no—
390C4×C4⋊C4—221no—
391C4×C4⋊C4C2×D1111yescharacteristic, complemented
392C4×C22⋊C4—221no—
393#340—111no—
394#340—111no—
395#340—111no—
396#340C2×D1111yescharacteristic, complemented
397#336—111no—
398#336C2×D1111yescharacteristic, complemented
399C22×C11—42no—
400C22×C11—42no—
401C22×C11—42no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11—81no—
405C22×C11—81no—
406C22×C11C2×C4×D411yescharacteristic
407C22×C11#53411yescharacteristic
408C22×C11#53511yescharacteristic
409C22×C11C22×SD1611yescharacteristic
410C22×C11C2×#13511yescharacteristic
411C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
412C22×C11#57511yescharacteristic
413C2×D11—22no—
414C2×D11—22no—
415C2×D11—22no—
416C2×D11—22no—
417C2×D11—22no—
418C2×D11—22no—
419C2×D11—42no—
420C2×D11—42no—
421C2×D11—42no—
422C2×D11—816no—
423C2×D11—81no—
424C2×D11—81no—
425C2×D11—81no—
426C2×D11—81no—
427C2×D11C4×SD1614yes—
428C4×C11—22no—
429C4×C11—41no—
430C4×C11—42no—
431C4×C11—81no—
432C4×C11—81no—
433C4×C11#51811yescharacteristic
434C4×C11#51811yescharacteristic
435C4×C11#53811yescharacteristic
436C4×C11#53811yescharacteristic
437Dic11—22no—
438Dic11—22no—
439Dic11—22no—
440Dic11—42no—
441Dic11—81no—
442Dic11—81no—
443C25—221no—
444C22×Q8—111no—
445C22×D4—114no—
446C22×D4—111no—
447C22×D4—222no—
448C22×D4—221no—
449C22×D4—441no—
450C22×D4—441no—
451C22×D4—441no—
452C22×D4—441no—
453C22×D4C22×D1111yescharacteristic
454C23×C4—111no—
455C23×C4—111no—
456C23×C4—111no—
457C23×C4—221no—
458C2×SD16—114no—
459C2×SD16—114no—
460C2×SD16—441no—
461C2×SD16—441no—
462C2×SD16—441no—
463C2×SD16—441no—
464C22×C8—111no—
465C22×C8—111no—
466C22×C8C22×D1111yescharacteristic
467C22×C8C22×D1111yescharacteristic
468C22⋊Q8—114no—
469C22⋊Q8—222no—
470C4×Q8—441no—
471C4×Q8—441no—
472C2×C4⋊C4—111no—
473C2×C4⋊C4—111no—
474C2×C4⋊C4—221no—
475C2×C4⋊C4—221no—
476C2×C4⋊C4—221no—
477C2×C4⋊C4—221no—
478C2×C4⋊C4—441no—
479C2×C4⋊C4—441no—
480C2×C4⋊C4C22×D1111yescharacteristic
481C2×C4⋊C4C22×D1111yescharacteristic
482C2×C4⋊C4C22×D1111yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—221no—
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×C22⋊C4—444no—
494C2×C22⋊C4—444no—
495C2×C42—21no—
496C2×C42—111no—
497C2×C42—111no—
498C2×C42—111no—
499C2×C42—221no—
500C2×C42—441no—
501C2×C42—441no—
502C2×C42C22×D1111yescharacteristic
503#106—41no—
504#106—441no—
505#103—441no—
506#103—441no—
507#102—41no—
508#102—114no—
509#102—441no—
510#102—441no—
511#102—441no—
512#102C4×D1114yescomplemented
513C22⋊C8—114no—
514C22⋊C8—222no—
515C4×C8—441no—
516C4×C8—441no—
517#95—21no—
518#95—221no—
519#95—221no—
520#95—221no—
521#95—221no—
522C2×C11—82no—
523C2×C11#232111yescharacteristic
524C2×C11C2×C4×SD1611yescharacteristic
525C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
526C2×C11#318711yescharacteristic
527C2×C11#318811yescharacteristic
528C2×C11#320811yescharacteristic
529C2×C11#321111yescharacteristic
530D11—24no—
531D11—82no—
532C24—21no—
533C24—111no—
534C24—224no—
535C24—221no—
536C24—442no—
537C24—442no—
538C24—442no—
539C24—442no—
540C24—442no—
541C24—442no—
542C2×Q8—112no—
543C2×Q8—221no—
544C2×Q8—221no—
545C2×Q8—221no—
546C2×Q8—221no—
547C2×Q8—221no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—112no—
554C2×D4—224no—
555C2×D4—221no—
556C2×D4—221no—
557C2×D4—221no—
558C2×D4—221no—
559C2×D4—221no—
560C2×D4—444no—
561C2×D4—444no—
562C2×D4—444no—
563C2×D4—444no—
564C2×D4—442no—
565C2×D4—442no—
566C2×D4C2×C4×D1112yes—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—111no—
571C22×C4—111no—
572C22×C4—111no—
573C22×C4—112no—
574C22×C4—112no—
575C22×C4—114no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—221no—
579C22×C4—221no—
580C22×C4—221no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4—441no—
586C22×C4—441no—
587C22×C4—441no—
588C22×C4—442no—
589C22×C4—442no—
590C22×C4—442no—
591C22×C4D4×D1111yescharacteristic
592C22×C4D4×D1111yescharacteristic
593C22×C4C23×D1111yescharacteristic
594SD16—444no—
595SD16—444no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—112no—
602C2×C8—221no—
603C2×C8—221no—
604C2×C8—221no—
605C2×C8—221no—
606C2×C8—221no—
607C2×C8C2×C4×D1112yes—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—224no—
614C4⋊C4—221no—
615C4⋊C4—221no—
616C4⋊C4—221no—
617C4⋊C4—221no—
618C4⋊C4—442no—
619C4⋊C4—442no—
620C4⋊C4—442no—
621C4⋊C4C2×C4×D1112yes—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—224no—
625C22⋊C4—442no—
626C22⋊C4—442no—
627C22⋊C4—442no—
628C22⋊C4—442no—
629C22⋊C4—442no—
630C22⋊C4—442no—
631C22⋊C4—442no—
632C42—21no—
633C42—21no—
634C42—42no—
635C42—221no—
636C42—221no—
637C42—441no—
638C42—441no—
639C42—442no—
640C11#2204311yescharacteristic, complemented, Sylow
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—112no—
649C23—112no—
650C23—112no—
651C23—221no—
652C23—221no—
653C23—221no—
654C23—221no—
655C23—222no—
656C23—448no—
657C23—448no—
658C23—448no—
659C23—441no—
660C23—441no—
661C23—441no—
662C23—441no—
663C23—441no—
664C23—441no—
665C23—884no—
666C23—884no—
667C23—884no—
668C23—884no—
669C23C2×D4×D1111yescharacteristic
670Q8—222no—
671Q8—222no—
672Q8—441no—
673Q8—441no—
674D4—22no—
675D4—22no—
676D4—41no—
677D4—41no—
678D4—222no—
679D4—222no—
680D4—448no—
681D4—441no—
682D4—441no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—112no—
698C2×C4—112no—
699C2×C4—112no—
700C2×C4—221no—
701C2×C4—221no—
702C2×C4—221no—
703C2×C4—221no—
704C2×C4—221no—
705C2×C4—221no—
706C2×C4—222no—
707C2×C4—222no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—444no—
712C2×C4—444no—
713C2×C4—441no—
714C2×C4—441no—
715C2×C4—441no—
716C2×C4—441no—
717C2×C4—441no—
718C2×C4—441no—
719C2×C4—441no—
720C2×C4—441no—
721C2×C4—884no—
722C2×C4SD16×D1112yes—
723C2×C4C22×C4×D1111yescharacteristic
724C2×C4#6703711yescharacteristic
725C2×C4#41×D1111yescharacteristic
726C2×C4#6704211yescharacteristic
727C2×C4#6704211yescharacteristic
728C2×C4#6704211yescharacteristic
729C8—22no—
730C8—41no—
731C8—222no—
732C8—441no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—114no—
741C22—222no—
742C22—222no—
743C22—222no—
744C22—222no—
745C22—222no—
746C22—222no—
747C22—442no—
748C22—442no—
749C22—442no—
750C22—8816no—
751C22—881no—
752C22—881no—
753C22—881no—
754C22—881no—
755C22C4×D4×D1111yescharacteristic
756C22#1062313811yescharacteristic
757C22#1062318411yescharacteristic
758C22C2×SD16×D1111yescharacteristic
759C22D11×#13511yescharacteristic
760C22D11×AGL(1,ℤ/8)11yescharacteristic
761C22#1062330411yescharacteristic
762C4—22no—
763C4—41no—
764C4—42no—
765C4—81no—
766C4—81no—
767C4—222no—
768C4—222no—
769C4—222no—
770C4—442no—
771C4—881no—
772C4—881no—
773C4#1062305211yescharacteristic
774C4#1062307611yescharacteristic
775C4#1062320911yescharacteristic
776C4#1062323511yescharacteristic
777C2—82no—
778C2—224no—
779C2—882no—
780C2#1307127811yescharacteristic
781C2C4×SD16×D1111yescharacteristic
782C2#1307742711yescharacteristic
783C2#1307937511yescharacteristic
784C2#1307938511yescharacteristic
785C2#1307955611yescharacteristic
786C2#1307957911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1926C2
socleC23×C11C22×D4
prime radicalC22×D4×D11C22
cosocleC22×C4×C11C24
hypercenter#1926D11
hypocenterC11#22043
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1926

Complements

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

NH ≅ G/Ntype
2. C4×#66950C2semidirect
4. #13069471C2semidirect
5. #13069468C2semidirect
6. #13069301C2semidirect
7. #13069300C2semidirect
8. #13069243C2semidirect
9. #13068974C2semidirect
10. #13068970C2semidirect
11. #13068922C2semidirect
12. #13068807C2semidirect
14. #13068373C2semidirect
15. C11×#1926C2semidirect
24. C2×C4×Dic22C22semidirect
25. C2×C11×#106C22semidirect
29. C4×C11×C4⋊C4C22semidirect
35. C2×#66880C22semidirect
36. C2×C8×Dic11C22semidirect
37. C2×C8×Dic11C22semidirect
40. #10622598C22semidirect
41. #10622587C22semidirect
42. C2×#66874C22semidirect
45. C2×#66872C22semidirect
51. #10622389C4semidirect
54. C11×#340C22semidirect
55. C11×#336C22semidirect
56. #10622189C22semidirect
57. #10622167C22semidirect
58. #10622167C22semidirect
59. #10622162C22semidirect
88. C2×#4324C2×C4semidirect
109. C2×#4314C2×C4semidirect
122. C11×#102C2×C4semidirect
137. #66873C2×C4semidirect
193. C2×C4×D11SD16semidirect
256. #1926D11semidirect
366. C2×#106C2×D11semidirect
391. C4×C4⋊C4C2×D11semidirect
396. #340C2×D11semidirect
398. #336C2×D11semidirect
512. #102C4×D11semidirect
640. C11#22043semidirect

Maximal subgroups

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

subgroupindex
C2×#106223892
C4×#669502
D11×#3902
#130694712
#130694682
#130693012
#130693002
#130692432
#130689742
#130689702
#130689222
#130688072
#130685452
#130683732
C11×#19262
#2204311