Finite Group Databasebeta

← #14808000

Subgroups — #14808000

Order 2816.

984 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079016C211yesmaximal, characteristic, complemented
2#13078438C211yesmaximal, characteristic, complemented
3#13076976C211yesmaximal, characteristic, complemented
4#13069842C212yesmaximal, complemented
5#13069837C212yesmaximal, complemented
6#13069610C211yesmaximal, characteristic, complemented
7#13069445C211yesmaximal, characteristic, complemented
8#13068849C212yesmaximal, complemented
9#13068842C212yesmaximal, complemented
10C4×#66901C211yesmaximal, characteristic, complemented
11C11×#3512C211yesmaximal, characteristic
12C11×#553—22no—
13C11×#553—24no—
14C11×#552—22no—
15C11×#541—21no—
16C11×#540—21no—
17C11×#537C2212yes—
18C11×#532C2211yescharacteristic
19C11×#529—22no—
20C2×C11×#125C2211yescharacteristic
21C11×#520C2212yes—
22C4×C11×#41C2211yescharacteristic
23C2×#66923C2211yescharacteristic
24C2×#66901C2211yescharacteristic
25C2×#66901C2212yes—
26C2×#66901C2211yescharacteristic
27C2×#66901C2212yes—
28#10622845C2212yes—
29#10622845C2212yes—
30#10622845C2212yes—
31#10622695—21no—
32#10622684—21no—
33#10622669—22no—
34#10622635—22no—
35#10622622—22no—
36#10622608C2212yes—
37#10622590C2212yes—
38#10622589C2212yes—
39#10622585—24no—
40C42×Dic11C2211yescharacteristic
41#10622537C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622170C2211yescharacteristic
44#10622170C2211yescharacteristic
45#10622168C2212yes—
46#10622168C2212yes—
47C2×C11×#41C2311yescharacteristic
48C2×C11×#41C2312yes—
49C11×C4⋊Q8D411yescharacteristic
50C11×#127D411yescharacteristic
51C11×#126—24no—
52C11×#126—24no—
53C11×#125—24no—
54C11×#125—21no—
55C11×#125—21no—
56C11×#125—22no—
57C11×#124D412yes—
58C11×#123—24no—
59C11×#123—24no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—22no—
62C11×#121—24no—
63C11×#121—22no—
64C11×#121—22no—
65C11×#121—22no—
66C11×#121—24no—
67C4×Q8×C11—22no—
68C4×Q8×C11D412yes—
69C4×D4×C11—24no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11—24no—
73C4×D4×C11—22no—
74C4×D4×C11D412yes—
75C11×#117—24no—
76C11×#117—22no—
77C11×#117—21no—
78C11×#117C2311yescharacteristic
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4D414yes—
81C2×C11×C4⋊C4C2312yes—
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C4⋊Dic11C2312yes—
85C2×Dic11⋊C4—22no—
86C2×Dic11⋊C4—24no—
87C2×C4×Dic11—22no—
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C2×#4318C2311yescharacteristic
91C2×#4318C2311yescharacteristic
92C2×#4318C2312yes—
93#66923—22no—
94#66923—21no—
95#66923—21no—
96#66901—22no—
97#66901—24no—
98#66901—22no—
99#66901—24no—
100#66899—22no—
101#66899—22no—
102#66899—22no—
103#66896—22no—
104#66896—22no—
105#66896—22no—
106C11⋊#95—24no—
107#66872—22no—
108#66871—22no—
109C4⋊(C11⋊C8)—22no—
110#66867—21no—
111C4×C11⋊C8—21no—
112#25668—111nomaximal, Sylow
113C11×#41—22no—
114C11×#41—22no—
115C11×#41—21no—
116C11×#41—21no—
117C11×#41—22no—
118C11×#41—22no—
119C11×#41—21no—
120C11×#41—21no—
121C2×Q8×C11C2×D412yes—
122C2×Q8×C11C2×D411yescharacteristic
123C2×D4×C11—21no—
124C2×D4×C11—22no—
125C2×D4×C11—24no—
126C2×D4×C11—22no—
127C2×D4×C11C2×D412yes—
128C2×D4×C11C2×D411yescharacteristic
129C22×C4×C11—24no—
130C22×C4×C11—21no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11C2×D414yes—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2411yescharacteristic
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—22no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4C2×D412yes—
148C11×C22⋊C4—24no—
149C11×C22⋊C4—24no—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—21no—
152C11×C22⋊C4—22no—
153C11×C22⋊C4—22no—
154C11×C22⋊C4—22no—
155C42×C11—24no—
156C42×C11—22no—
157C42×C11—21no—
158C42×C11C2×D411yescharacteristic
159C42×C11C2×D411yescharacteristic
160C42×C11C2×D412yes—
161C4⋊Dic11—22no—
162C4⋊Dic11—22no—
163Dic11⋊C4—48no—
164Dic11⋊C4—42no—
165Dic11⋊C4—42no—
166C4×Dic11—21no—
167C4×Dic11—21no—
168C4×Dic11—44no—
169C4×Dic11#4112yes—
170C4×Dic11#4112yes—
171#4318—22no—
172#4318—22no—
173#4318—21no—
174#4318—21no—
175#4318—21no—
176#4318—21no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—22no—
180#3512D1111yescharacteristic
181#3142—111no—
182#3080—111no—
183#2859—111no—
184#2040—112no—
185#2039—112no—
186#1998—111no—
187#1962—111no—
188#1860—112no—
189#1859—112no—
190C4×#104—111no—
191C23×C11—22no—
192C23×C11—21no—
193C23×C11C22×D411yescharacteristic
194Q8×C11—21no—
195Q8×C11—21no—
196Q8×C11—22no—
197Q8×C11—22no—
198D4×C11—21no—
199D4×C11—21no—
200D4×C11—22no—
201D4×C11—22no—
202D4×C11—42no—
203D4×C11—42no—
204D4×C11—41no—
205D4×C11—41no—
206D4×C11—82no—
207D4×C11—84no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—21no—
211C2×C4×C11—24no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—44no—
218C2×C4×C11—82no—
219C2×C4×C11—84no—
220C2×C4×C11#12012yes—
221C2×C4×C11#12012yes—
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C112−1+411yescharacteristic
227C2×C4×C112−1+411yescharacteristic
228C2×Dic11—24no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—42no—
232C2×Dic11—44no—
233C2×Dic11—42no—
234C11⋊C8—42no—
235C11⋊C8—41no—
236C11⋊C8—41no—
237#553—22no—
238#553—24no—
239#552—22no—
240#541—21no—
241#540—21no—
242#537C2×D1112yes—
243#532C2×D1111yescharacteristic
244#529—22no—
245C2×#125—111no—
246C2×#125C2×D1111yescharacteristic
247#520C2×D1112yes—
248C4×#41C2×D1111yescharacteristic
249#491—221no—
250#490—221no—
251#488—222no—
252#479—222no—
253#478—222no—
254#428—112no—
255#423—111no—
256C2×#104—112no—
257C2×#104—112no—
258C2×#104—111no—
259C2×#104—111no—
260#417—112no—
261#417—112no—
262#417—112no—
263C4×M16—111no—
264#389—224no—
265#384—112no—
266#382—112no—
267C43—111no—
268#343—112no—
269#343—112no—
270#339—111no—
271#339—111no—
272C22×C11—22no—
273C22×C11—42no—
274C22×C11—41no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11C2×#12011yescharacteristic
279C22×C11#54811yescharacteristic
280C22×C11#54811yescharacteristic
281C4×C11—22no—
282C4×C11—22no—
283C4×C11—42no—
284C4×C11—41no—
285C4×C11—44no—
286C4×C11—42no—
287C4×C11#53211yescharacteristic
288C4×C11#53611yescharacteristic
289C4×C11#54711yescharacteristic
290C4×C11#54711yescharacteristic
291Dic11—24no—
292Dic11—42no—
293Dic11—82no—
294C2×#41C22×D1111yescharacteristic
295C2×#41C22×D1112yes—
296C2×M16—111no—
297C2×M16—111no—
298C2×M16—112no—
299C4⋊Q8C22⋊D1111yescharacteristic
300#127C22⋊D1111yescharacteristic
301#126—24no—
302#126—24no—
303#125—24no—
304#125—21no—
305#125—21no—
306#125—22no—
307#125—222no—
308#125—221no—
309#125—221no—
310#124C22⋊D1112yes—
311#123—24no—
312#123—24no—
313C22⋊Q8—22no—
314C22⋊Q8—22no—
315#121—24no—
316#121—22no—
317#121—22no—
318#121—22no—
319#121—24no—
320C4×Q8—22no—
321C4×Q8C22⋊D1112yes—
322C4×D4—24no—
323C4×D4—22no—
324C4×D4—22no—
325C4×D4—24no—
326C4×D4—22no—
327C4×D4C22⋊D1112yes—
328#117—24no—
329#117—22no—
330#117—21no—
331#117C22×D1111yescharacteristic
332C2×C4⋊C4—22no—
333C2×C4⋊C4—112no—
334C2×C4⋊C4—222no—
335C2×C4⋊C4—224no—
336C2×C4⋊C4C22⋊D1114yes—
337C2×C4⋊C4C22×D1112yes—
338C2×C42—21no—
339C2×C42—111no—
340C2×C42—111no—
341C2×C42—222no—
342C2×C42C22×D1111yescharacteristic
343#107—222no—
344#106—222no—
345C4⋊C8—222no—
346#104—224no—
347#104—224no—
348#104—222no—
349#104—222no—
350#103—222no—
351#103—222no—
352#103—222no—
353#102—222no—
354#102—222no—
355#102—222no—
356#97—221no—
357C4×C8—221no—
358#95—224no—
359C2×C11—21no—
360C2×C11—21no—
361C2×C11—82no—
362C2×C11—81no—
363C2×C11#243211yescharacteristic
364C2×C11#301812yes—
365#41—21no—
366#41—21no—
367#41—22no—
368#41—22no—
369#41—21no—
370#41—21no—
371#41—22no—
372#41—22no—
373C2×Q8C2×C22⋊D1112yes—
374C2×Q8C2×C22⋊D1111yescharacteristic
375C2×D4—21no—
376C2×D4—22no—
377C2×D4—24no—
378C2×D4—22no—
379C2×D4C2×C22⋊D1112yes—
380C2×D4C2×C22⋊D1111yescharacteristic
381C22×C4—24no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—221no—
386C22×C4—221no—
387C22×C4—222no—
388C22×C4C2×C22⋊D1114yes—
389C22×C4C2×C22⋊D1112yes—
390C22×C4C23×D1111yescharacteristic
391M16—221no—
392M16—221no—
393M16—222no—
394M16—222no—
395M16—221no—
396M16—221no—
397C2×C8—221no—
398C2×C8—221no—
399C2×C8—222no—
400C4⋊C4—24no—
401C4⋊C4—24no—
402C4⋊C4—24no—
403C4⋊C4—24no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—222no—
409C4⋊C4—222no—
410C4⋊C4—448no—
411C4⋊C4—442no—
412C4⋊C4—442no—
413C4⋊C4C2×C22⋊D1112yes—
414C22⋊C4—24no—
415C22⋊C4—24no—
416C22⋊C4—24no—
417C22⋊C4—21no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C42—24no—
422C42—22no—
423C42—21no—
424C42—112no—
425C42—112no—
426C42—221no—
427C42—221no—
428C42—444no—
429C42C2×C22⋊D1111yescharacteristic
430C42C2×C22⋊D1111yescharacteristic
431C42C2×C22⋊D1112yes—
432C11#2566811yescharacteristic, complemented, Sylow
433C23—22no—
434C23—21no—
435C23C22×C22⋊D1111yescharacteristic
436Q8—22no—
437Q8—22no—
438Q8—21no—
439Q8—21no—
440D4—22no—
441D4—22no—
442D4—21no—
443D4—21no—
444D4—41no—
445D4—41no—
446D4—42no—
447D4—42no—
448D4—82no—
449D4—84no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—21no—
453C2×C4—24no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—44no—
460C2×C4—82no—
461C2×C4—84no—
462C2×C4—224no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4—442no—
466C2×C4—444no—
467C2×C4—442no—
468C2×C4#6700612yes—
469C2×C4#6700612yes—
470C2×C4#41×D1111yescharacteristic
471C2×C4#41×D1111yescharacteristic
472C2×C4#6704311yescharacteristic
473C2×C4#6704311yescharacteristic
474C2×C4C22×C22⋊D1111yescharacteristic
475C2×C4C22×C22⋊D1111yescharacteristic
476C8—441no—
477C8—441no—
478C8—442no—
479C22—22no—
480C22—41no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22#1062336211yescharacteristic
486C22#1062336211yescharacteristic
487C22C2×#6700611yescharacteristic
488C4—22no—
489C4—22no—
490C4—41no—
491C4—42no—
492C4—44no—
493C4—42no—
494C4—224no—
495C4—442no—
496C4—882no—
497C4#1062335511yescharacteristic
498C4#1062335511yescharacteristic
499C4#1062335611yescharacteristic
500C4#1062336311yescharacteristic
501C2—21no—
502C2—21no—
503C2—82no—
504C2—81no—
505C2#1307224011yescharacteristic
506C2#1307796512yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3512C2
socleC22×C11C2×#120
hypercenter#3512D11
hypocenterC11#25668
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3512

Complements

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

NH ≅ G/Ntype
1. #13079016C2semidirect
2. #13078438C2semidirect
3. #13076976C2semidirect
4. #13069842C2semidirect
5. #13069837C2semidirect
6. #13069610C2semidirect
7. #13069445C2semidirect
8. #13068849C2semidirect
9. #13068842C2semidirect
10. C4×#66901C2semidirect
432. C11#25668semidirect

Maximal subgroups

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

subgroupindex
#130790162
#130784382
#130769762
#130698422
#130698372
#130696102
#130694452
#130688492
#130688422
C4×#669012
C11×#35122
#2566811