Finite Group Databasebeta

← #14816700

Subgroups — #14816700

Order 2816.

896 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622379C211yesmaximal, characteristic, complemented
2C2×#10622734C211yesmaximal, characteristic, complemented
3#13072330C211yesmaximal, characteristic, complemented
4#13071636C211yesmaximal, characteristic
5#13070147C211yesmaximal, characteristic, complemented
6#13070116C211yesmaximal, characteristic, complemented
7#13070002C211yesmaximal, characteristic, complemented
8#13069957C211yesmaximal, characteristic, complemented
9#13069378C211yesmaximal, characteristic, complemented
10#13069186C211yesmaximal, characteristic, complemented
11#13068939C211yesmaximal, characteristic
12#13068879C211yesmaximal, characteristic, complemented
13#13068808C211yesmaximal, characteristic, complemented
14#13068799C211yesmaximal, characteristic, complemented
15C11×#1895C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×D4×Dic11—21no—
19C2×D4×Dic11C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C2×#66943C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C11×#380C2211yescharacteristic
26#10622834C2211yescharacteristic
27#10622833—21no—
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C4×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32#10622734—24no—
33C2×#66882C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36C2×#66881C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39#10622598C2211yescharacteristic
40#10622598C2211yescharacteristic
41#10622589C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43#10622586C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46#10622564—21no—
47#10622563—21no—
48#10622562—21no—
49#10622561—21no—
50#10622379—24no—
51#10622268—21no—
52#10622260—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11—21no—
65C23×Dic11—21no—
66C2×C11×M16—22no—
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C11×#121—22no—
72C11×#121Q814yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11D411yescharacteristic
83C2×C22⋊Dic11D411yescharacteristic
84D4×Dic11—22no—
85D4×Dic11—41no—
86D4×Dic11—44no—
87#66979—22no—
88#66979—41no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—41no—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109#66943—22no—
110#66943—41no—
111C11×#102—22no—
112C11×#102—22no—
113C11×#95—21no—
114#66896—22no—
115#66896—41no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95D411yescharacteristic
121C11⋊#95D411yescharacteristic
122C22⋊(C11⋊C8)—22no—
123#66882—22no—
124#66882D414yescomplemented
125#66881—22no—
126#66881—22no—
127Dic11⋊C8—22no—
128Dic11⋊C8—22no—
129#66872—22no—
130#66872—41no—
131#26366—111nomaximal, Sylow
132C24×C11—21no—
133C24×C11C2×D411yescharacteristic
134C2×D4×C11—24no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—42no—
141C2×D4×C11—42no—
142C2×D4×C11C2×Q812yes—
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×C11—21no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×Q812yes—
152C22×C4×C11#4112yes—
153C22×C4×C11C2411yescharacteristic
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—42no—
159C22×Dic11—42no—
160C22×Dic11—42no—
161C22×Dic11—42no—
162C22×Dic11—81no—
163C22×Dic11—81no—
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C11×M16—28no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11C2×D412yes—
174C2×C8×C11#4112yes—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4C2×Q812yes—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—81no—
183C22⋊Dic11—22no—
184C22⋊Dic11—41no—
185C22⋊Dic11—42no—
186C22⋊Dic11—42no—
187C22⋊Dic11—42no—
188C22⋊Dic11—81no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—42no—
196C4⋊Dic11—42no—
197C4⋊Dic11—42no—
198C4⋊Dic11—81no—
199C4⋊Dic11C2×D412yes—
200C4⋊Dic11C2×D412yes—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204Dic11⋊C4—81no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—42no—
210C4×Dic11—42no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×#478—111no—
218C2×#428—111no—
219#2441—111no—
220#2361—111no—
221#2094—111no—
222#2088—111no—
223#2067—111no—
224#2059—111no—
225#1948—111no—
226#1918—111no—
227#1895D1111yescharacteristic
228#1875—111no—
229#1864—111no—
230#1853—111no—
231#1851—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×C11C22⋊Q812yes—
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—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
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×C11C22⋊Q812yes—
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×Q811yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11H(5,𝔽2)11yescharacteristic
273C2×C4×C112−1+411yescharacteristic
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
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—41no—
297C2×Dic11—84no—
298C2×Dic11—84no—
299C2×Dic11AGL(1,ℤ/8)12yes—
300C8×C11—22no—
301C8×C11—22no—
302C11⋊C8—41no—
303C11⋊C8—41no—
304C22×M16C2×D1111yescharacteristic
305C2×#125—111no—
306C2×#121C2×D1111yescharacteristic
307C2×C4×D4—111no—
308C2×C4×D4—221no—
309C2×#117—111no—
310C22×C4⋊C4—111no—
311#478—224no—
312#428—224no—
313C2×#107—111no—
314C2×#107—111no—
315C2×#106—111no—
316C2×#106—111no—
317C2×#106—111no—
318C2×#106—111no—
319C2×C4⋊C8—111no—
320C2×C4⋊C8—111no—
321C2×#102—111no—
322C2×#102—111no—
323C2×#102C2×D1111yescharacteristic
324C2×#102C2×D1111yescharacteristic
325C2×C22⋊C8—111no—
326#399—221no—
327#396—221no—
328#390—111no—
329#389—111no—
330#389—111no—
331#389—111no—
332#389—221no—
333#388—221no—
334#387—221no—
335#386—221no—
336#385—221no—
337#384—111no—
338#380C2×D1111yescharacteristic
339C4×C4⋊C4—111no—
340C4×C22⋊C4—111no—
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340C2×D1111yescharacteristic
346#340C2×D1111yescharacteristic
347#336—111no—
348#336—111no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—42no—
357C22×C11—42no—
358C22×C11—42no—
359C22×C11—81no—
360C22×C11—81no—
361C22×C11—81no—
362C22×C11—81no—
363C22×C11C2×C22⋊Q811yescharacteristic
364C22×C11D4211yescharacteristic
365C22×C11#54711yescharacteristic
366C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C11#57511yescharacteristic
368C22×C11#57711yescharacteristic
369C22×C11#57711yescharacteristic
370C4×C11—22no—
371C4×C11—42no—
372C4×C11—81no—
373C4×C11—81no—
374C4×C11#52511yescharacteristic
375C4×C11#53911yescharacteristic
376C4×C11D4×Q811yescharacteristic
377C4×C11#55411yescharacteristic
378Dic11—22no—
379Dic11—41no—
380Dic11—41no—
381Dic11—41no—
382Dic11—42no—
383Dic11—42no—
384Dic11—81no—
385Dic11—81no—
386C22×D4—21no—
387C22×D4C22×D1111yescharacteristic
388C23×C4—221no—
389C23×C4—221no—
390C23×C4C22×D1111yescharacteristic
391C2×M16—22no—
392C2×M16—22no—
393C2×M16—22no—
394C22×C8—111no—
395C22×C8—111no—
396C22×C8C22×D1111yescharacteristic
397C22×C8C22×D1111yescharacteristic
398#125—222no—
399#125—441no—
400#121—22no—
401#121Dic2214yes—
402C4×D4—222no—
403C4×D4—441no—
404C4×D4—444no—
405#117—222no—
406#117—441no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—222no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—441no—
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—111no—
427C2×C22⋊C4—111no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C42—111no—
433C2×C42—111no—
434C2×C42—221no—
435C2×C42—221no—
436#107—114no—
437#107—222no—
438#106—222no—
439#106—222no—
440#106—222no—
441#106—441no—
442C4⋊C8—222no—
443C4⋊C8—222no—
444#102—22no—
445#102—22no—
446#102—222no—
447#102—441no—
448C22⋊C8—222no—
449#95—21no—
450#95—111no—
451#95—111no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456C2×C11—42no—
457C2×C11—82no—
458C2×C11#244911yescharacteristic
459C2×C11#307711yescharacteristic
460C2×C11#308411yescharacteristic
461C2×C11#327111yescharacteristic
462C2×C11#327211yescharacteristic
463C2×C11#334511yescharacteristic
464C2×C11#335111yescharacteristic
465C24—21no—
466C24D4×D1111yescharacteristic
467C2×D4—24no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4C2×Dic2212yes—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—111no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—442no—
492C22×C4—442no—
493C22×C4—442no—
494C22×C4—442no—
495C22×C4—881no—
496C22×C4—881no—
497C22×C4C2×Dic2212yes—
498C22×C4D4×D1111yescharacteristic
499C22×C4#434112yes—
500C22×C4C23×D1111yescharacteristic
501M16—28no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8D4×D1112yes—
513C2×C8#434112yes—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—112no—
520C4⋊C4—112no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—442no—
528C4⋊C4—442no—
529C4⋊C4—442no—
530C4⋊C4—442no—
531C4⋊C4—442no—
532C4⋊C4—442no—
533C4⋊C4—881no—
534C4⋊C4—881no—
535C4⋊C4C2×Dic2212yes—
536C22⋊C4—24no—
537C22⋊C4—81no—
538C22⋊C4—222no—
539C22⋊C4—442no—
540C22⋊C4—441no—
541C22⋊C4—442no—
542C22⋊C4—442no—
543C22⋊C4—881no—
544C42—221no—
545C42—221no—
546C42—221no—
547C42—221no—
548C42—442no—
549C42—442no—
550C11#2636611yescharacteristic, complemented, Sylow
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—22no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23#6693112yes—
565C23C2×D4×D1111yescharacteristic
566D4—22no—
567D4—22no—
568D4—48no—
569D4—41no—
570D4—41no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
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—112no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—221no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—884no—
611C2×C4—884no—
612C2×C4#6693112yes—
613C2×C4C22×Dic2211yescharacteristic
614C2×C4C2×D4×D1111yescharacteristic
615C2×C4C2×#434111yescharacteristic
616C2×C4C2×#434111yescharacteristic
617C2×C4#6704211yescharacteristic
618C2×C4#6704311yescharacteristic
619C8—22no—
620C8—22no—
621C8—441no—
622C8—441no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22C2×#6693111yescharacteristic
638C22#1062314011yescharacteristic
639C22#1062314211yescharacteristic
640C22D11×AGL(1,ℤ/8)11yescharacteristic
641C22#1062330411yescharacteristic
642C22#1062330611yescharacteristic
643C22#1062330911yescharacteristic
644C4—22no—
645C4—42no—
646C4—81no—
647C4—81no—
648C4—222no—
649C4—441no—
650C4—441no—
651C4—441no—
652C4—442no—
653C4—442no—
654C4—881no—
655C4—881no—
656C4D4×Dic2211yescharacteristic
657C4#1062307411yescharacteristic
658C4#1062311711yescharacteristic
659C4#1062319611yescharacteristic
660C2—42no—
661C2—82no—
662C2#1307243111yescharacteristic
663C2#1307841011yescharacteristic
664C2#1307848211yescharacteristic
665C2#1308020811yescharacteristic
666C2#1308021311yescharacteristic
667C2#1308108111yescharacteristic
668C2#1308117111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1895C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#1895D11
hypocenterC11#26366
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1895

Complements

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

NH ≅ G/Ntype
1. C2×#10622379C2semidirect
2. C2×#10622734C2semidirect
3. #13072330C2semidirect
5. #13070147C2semidirect
6. #13070116C2semidirect
7. #13070002C2semidirect
8. #13069957C2semidirect
9. #13069378C2semidirect
10. #13069186C2semidirect
12. #13068879C2semidirect
13. #13068808C2semidirect
14. #13068799C2semidirect
124. #66882D4semidirect
550. C11#26366semidirect

Maximal subgroups

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

subgroupindex
C2×#106223792
C2×#106227342
#130723302
#130716362
#130701472
#130701162
#130700022
#130699572
#130693782
#130691862
#130689392
#130688792
#130688082
#130687992
C11×#18952
#2636611