Finite Group Databasebeta

← #14795070

Subgroups — #14795070

Order 2816.

912 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622372C211yesmaximal, characteristic, complemented
2C2×#10622332C211yesmaximal, characteristic, complemented
3#13076966C211yesmaximal, characteristic, complemented
4#121×Dic11C211yesmaximal, characteristic
5#13070047C211yesmaximal, characteristic, complemented
6#13070044C211yesmaximal, characteristic, complemented
7#13069802C211yesmaximal, characteristic
8#13069566C211yesmaximal, characteristic, complemented
9#13069376C211yesmaximal, characteristic, complemented
10#13069360C211yesmaximal, characteristic, complemented
11#13069358C211yesmaximal, characteristic, complemented
12#13069315C211yesmaximal, characteristic, complemented
13#13069310C211yesmaximal, characteristic, complemented
14#13068614C211yesmaximal, characteristic, complemented
15C11×#2034C211yesmaximal, characteristic
16C2×C11×#121C2211yescharacteristic
17C2×D4×Dic11—21no—
18C2×D4×Dic11C2211yescharacteristic
19C22×C4×Dic11C2211yescharacteristic
20C2×#66941C2211yescharacteristic
21C2×#66931—21no—
22C2×C11×#106C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C11×#380C2211yescharacteristic
27#10622834C2211yescharacteristic
28#10622833—21no—
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31#10622825C2211yescharacteristic
32#10622825C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×#66879C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39#10622598C2211yescharacteristic
40#10622598C2211yescharacteristic
41#10622589C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43#10622586C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622564—21no—
47#10622555—21no—
48C22⋊C4×Dic11—21no—
49#10622372—24no—
50#10622332—24no—
51#10622260—21no—
52#10622259—21no—
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11—21no—
65C23×Dic11D411yescharacteristic
66C23×Dic11D411yescharacteristic
67C22×Dic22—21no—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×#121—22no—
71C11×#121—22no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82D4×Dic11—22no—
83D4×Dic11—22no—
84D4×Dic11—44no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—22no—
96C2×C4×Dic11—22no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11D411yescharacteristic
99C2×C4×Dic11D411yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104#66941—22no—
105#66941—22no—
106#66931—44no—
107C11×#106—22no—
108C11×#102—22no—
109C11×#102—22no—
110C11×C22⋊C8—22no—
111C11×#95—21no—
112#66896—22no—
113#66896—22no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C22⋊(C11⋊C8)—22no—
121#66882—22no—
122#66879—22no—
123#66879—22no—
124Dic11⋊C8—22no—
125Dic11⋊C8D414yescomplemented
126#66872—22no—
127#66871—22no—
128#24709—111nomaximal, Sylow
129C24×C11—21no—
130C24×C11C2×D411yescharacteristic
131C2×D4×C11—24no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—42no—
138C2×D4×C11—42no—
139C2×D4×C11#4112yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—41no—
161C22×Dic11—42no—
162C22×Dic11—42no—
163C22×Dic11—42no—
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C2×Dic22—42no—
169C2×Dic22—42no—
170C2×Dic22—42no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11C2×D412yes—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4#4112yes—
183C11×C22⋊C4—24no—
184C11×C22⋊C4—42no—
185C22⋊Dic11—42no—
186C22⋊Dic11—42no—
187C22⋊Dic11—42no—
188C22⋊Dic11—42no—
189C22⋊Dic11—42no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—42no—
199C4⋊Dic11—42no—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204C4×Dic11—22no—
205C4×Dic11—22no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—42no—
209C4×Dic11C2×D412yes—
210C4×Dic11#4112yes—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8C2×D412yes—
217C2×#474—111no—
218C2×#432—111no—
219#2857—111no—
220C4×#121—111no—
221#2076—111no—
222#2076—111no—
223#2034—111no—
224#2034D1111yescharacteristic
225#1988—111no—
226#1948—111no—
227#1944—111no—
228#1944—111no—
229#1936—111no—
230#1936—111no—
231#1802—111no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—22no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11#13712yes—
246C23×C11C22×D411yescharacteristic
247D4×C11—22no—
248D4×C11—22no—
249D4×C11—48no—
250D4×C11—41no—
251D4×C11—41no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—21no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C112−1+411yescharacteristic
273C2×C4×C112−1+411yescharacteristic
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—44no—
283C2×Dic11—44no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—84no—
297C2×Dic11#12112yes—
298C2×Dic11#12112yes—
299C2×Dic11AGL(1,ℤ/8)12yes—
300C2×Dic11AGL(1,ℤ/8)12yes—
301Dic22—84no—
302C8×C11—22no—
303C8×C11—41no—
304C11⋊C8—22no—
305C11⋊C8—41no—
306C2×C4⋊Q8—111no—
307C2×C22⋊Q8—221no—
308C2×#121C2×D1111yescharacteristic
309C2×C4×D4—111no—
310C2×C4×D4—221no—
311C22×C42—111no—
312#474—224no—
313#432—224no—
314C2×#107—111no—
315C2×#107—111no—
316C2×#106—111no—
317C2×#106C2×D1111yescharacteristic
318C2×C4⋊C8—111no—
319C2×C4⋊C8—111no—
320C2×#102—111no—
321C2×#102—111no—
322C2×#102C2×D1111yescharacteristic
323C2×#102C2×D1111yescharacteristic
324C2×C22⋊C8—111no—
325C2×C22⋊C8C2×D1111yescharacteristic
326C2×#97—111no—
327C2×#97—111no—
328#391—221no—
329#390—111no—
330#389—111no—
331#389—111no—
332#389—111no—
333#389—221no—
334#388—221no—
335#386—221no—
336#384—111no—
337#380—111no—
338#380—111no—
339#380—221no—
340#380C2×D1111yescharacteristic
341C4×C4⋊C4—111no—
342C4×C22⋊C4—221no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340C2×D1111yescharacteristic
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—42no—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—81no—
362C22×C11—81no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11C2×#12111yescharacteristic
366C22×C11#52511yescharacteristic
367C22×C11#53611yescharacteristic
368C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
369C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C11C2×#13711yescharacteristic
371C22×C11#57511yescharacteristic
372C4×C11—42no—
373C4×C11—41no—
374C4×C11—81no—
375C4×C11—81no—
376C4×C11#54711yescharacteristic
377C4×C11#54811yescharacteristic
378C4×C11#55211yescharacteristic
379C4×C11#55611yescharacteristic
380Dic11—22no—
381Dic11—41no—
382Dic11—41no—
383Dic11—81no—
384Dic11—81no—
385Dic11—81no—
386Dic11—81no—
387Dic11#46914yes—
388C22×Q8—221no—
389C22×D4—21no—
390C22×D4C22×D1111yescharacteristic
391C23×C4—111no—
392C23×C4—111no—
393C23×C4—221no—
394C23×C4C22×D1111yescharacteristic
395C22×C8—111no—
396C22×C8—111no—
397C22×C8C22×D1111yescharacteristic
398C22×C8C22×D1111yescharacteristic
399C4⋊Q8—222no—
400C4⋊Q8—222no—
401C22⋊Q8—444no—
402#121—22no—
403#121—22no—
404C4×D4—222no—
405C4×D4—222no—
406C4×D4—444no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C42—111no—
428C2×C42—111no—
429C2×C42—111no—
430C2×C42—111no—
431C2×C42—222no—
432C2×C42—222no—
433C2×C42—221no—
434#107—222no—
435#107—222no—
436#106—22no—
437#106—222no—
438C4⋊C8—114no—
439C4⋊C8—222no—
440#102—22no—
441#102—22no—
442#102—222no—
443#102—222no—
444C22⋊C8—22no—
445C22⋊C8—222no—
446#97—222no—
447#97—222no—
448#95—21no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455C2×C11—42no—
456C2×C11—82no—
457C2×C11#241511yescharacteristic
458C2×C11C2×#46911yescharacteristic
459C2×C11#305611yescharacteristic
460C2×C11#311011yescharacteristic
461C2×C11#311511yescharacteristic
462C2×C11#323511yescharacteristic
463C2×C11#323911yescharacteristic
464C24—21no—
465C24D4×D1111yescharacteristic
466C2×Q8—442no—
467C2×Q8—442no—
468C2×Q8—442no—
469C2×D4—24no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4#434112yes—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—111no—
488C22×C4—111no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4—222no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—442no—
501C22×C4—442no—
502C22×C4—442no—
503C22×C4—441no—
504C22×C4D4×D1111yescharacteristic
505C22×C4C23×D1111yescharacteristic
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—112no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8D4×D1112yes—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—442no—
532C4⋊C4—442no—
533C4⋊C4—442no—
534C4⋊C4—442no—
535C4⋊C4—442no—
536C4⋊C4—442no—
537C4⋊C4#434112yes—
538C22⋊C4—24no—
539C22⋊C4—42no—
540C22⋊C4—442no—
541C22⋊C4—442no—
542C22⋊C4—442no—
543C22⋊C4—442no—
544C22⋊C4—442no—
545C42—112no—
546C42—112no—
547C42—222no—
548C42—222no—
549C42—221no—
550C42—221no—
551C42—442no—
552C11#2470911yescharacteristic, complemented, Sylow
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—22no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23#6696812yes—
567C23C2×D4×D1111yescharacteristic
568Q8—884no—
569D4—22no—
570D4—22no—
571D4—48no—
572D4—41no—
573D4—41no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—112no—
591C2×C4—112no—
592C2×C4—112no—
593C2×C4—112no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—444no—
603C2×C4—444no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—884no—
617C2×C4C2×D4×D1111yescharacteristic
618C2×C4C2×#434111yescharacteristic
619C2×C4C2×#434111yescharacteristic
620C2×C4#41×D1111yescharacteristic
621C2×C4#6704311yescharacteristic
622C2×C4#6704311yescharacteristic
623C8—22no—
624C8—41no—
625C8—222no—
626C8—441no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22#1062311711yescharacteristic
642C22D11×#12111yescharacteristic
643C22#1062317911yescharacteristic
644C22C2×#6696811yescharacteristic
645C22#1062329911yescharacteristic
646C22D11×AGL(1,ℤ/8)11yescharacteristic
647C22D11×AGL(1,ℤ/8)11yescharacteristic
648C4—41no—
649C4—42no—
650C4—81no—
651C4—81no—
652C4—114no—
653C4—222no—
654C4—441no—
655C4—441no—
656C4—881no—
657C4—881no—
658C4—881no—
659C4—881no—
660C4#1062312911yescharacteristic
661C4#1062314211yescharacteristic
662C4#1062318111yescharacteristic
663C4#1062320211yescharacteristic
664C2—42no—
665C2—82no—
666C2#1307203811yescharacteristic
667C2D11×#46911yescharacteristic
668C2#1307823911yescharacteristic
669C2#1307871011yescharacteristic
670C2#1307876011yescharacteristic
671C2#1307981111yescharacteristic
672C2#1307984411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2034C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#2034D11
hypocenterC11#24709
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2034

Complements

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

NH ≅ G/Ntype
1. C2×#10622372C2semidirect
2. C2×#10622332C2semidirect
3. #13076966C2semidirect
5. #13070047C2semidirect
6. #13070044C2semidirect
8. #13069566C2semidirect
9. #13069376C2semidirect
10. #13069360C2semidirect
11. #13069358C2semidirect
12. #13069315C2semidirect
13. #13069310C2semidirect
14. #13068614C2semidirect
125. Dic11⋊C8D4semidirect
552. C11#24709semidirect

Maximal subgroups

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

subgroupindex
C2×#106223722
C2×#106223322
#130769662
#121×Dic112
#130700472
#130700442
#130698022
#130695662
#130693762
#130693602
#130693582
#130693152
#130693102
#130686142
C11×#20342
#2470911