Finite Group Databasebeta

← #14739021

Subgroups — #14739021

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079764C211yesmaximal, characteristic, complemented
2#13078409C211yesmaximal, characteristic
3C2×#10622455C211yesmaximal, characteristic
4#13077639C211yesmaximal, characteristic
5#13068066C214yesmaximal, complemented
6#13068014C214yesmaximal, complemented
7#13067390C211yesmaximal, characteristic, complemented
8#13067296C211yesmaximal, characteristic, complemented
9C11×#1542C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11C2×C4×D44C2211yescharacteristic
12C2×#66922C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×#66885—21no—
16C2×#66881—21no—
17#10622700C2212yes—
18#10622697C2212yes—
19#10622694C2212yescomplemented
20#10622691C2212yescomplemented
21#10622679—22no—
22#10622657—22no—
23#10622634—22no—
24#10622614—21no—
25#10622608—21no—
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622455—22no—
29#10622455C2214yes—
30#10622447C2214yes—
31D11×C22⋊C8—22no—
32C8×D44—22no—
33C11×#333C2212yescomplemented
34C11×#332C2212yescomplemented
35#10622119C2214yescomplemented
36#10622117C2214yescomplemented
37C22×D44D411yescharacteristic
38C22×C4×D11—21no—
39C22×Dic22—21no—
40C22×C8×C11—21no—
41C11×C4⋊Q8C2311yescharacteristic
42C11×C4⋊Q8C2311yescharacteristic
43C11×#125—21no—
44C11×C22⋊Q8—21no—
45C11×C22⋊Q8—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C11×#117—21no—
49C2×C42×C11C2311yescharacteristic
50C2×(C2×D11)⋊C4—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11D411yescharacteristic
54C2×#4318—21no—
55C2×C8×D11—24no—
56C4×D44—21no—
57C4×D44—21no—
58C4×D44D412yes—
59C4×D44C2312yes—
60#66922—21no—
61#66922—21no—
62#66922—21no—
63#66922C2312yes—
64C11×C4⋊C8—21no—
65C11×C4⋊C8C2312yes—
66C11×C4⋊C8C2312yes—
67C11×C22⋊C8—21no—
68C4×C8×C11—21no—
69#66899—24no—
70C22⋊(C11⋊C8)D412yes—
71#66885—24no—
72(C2×D11)⋊C8—24no—
73#66881—24no—
74#66873—22no—
75#66873—22no—
76#66872—22no—
77#66871—22no—
78#66871—24no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)D412yes—
81C4⋊(C11⋊C8)C2312yes—
82C4×C11⋊C8C2312yes—
83#19393—111nomaximal, Sylow
84C23×D11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×Dic11—21no—
91C22×Dic11—41no—
92C2×D44—21no—
93C2×D44—22no—
94C2×D44Q1614yes—
95C2×D44C2×D412yes—
96C2×C4×D11—22no—
97C2×C4×D11—22no—
98C2×C4×D11—82no—
99C2×Dic22—22no—
100C2×Dic22—41no—
101C2×Dic22—82no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—42no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C22⋊C4—41no—
112C42×C11—41no—
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11#4111yescharacteristic
116C42×C11C2411yescharacteristic
117(C2×D11)⋊C4—22no—
118(C2×D11)⋊C4—22no—
119C4⋊Dic11—21no—
120C4⋊Dic11—22no—
121C4⋊Dic11—22no—
122C4⋊Dic11—41no—
123C4⋊Dic11—41no—
124C4⋊Dic11C2×D412yes—
125#4318—42no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8C2×D414yes—
128C8×D11—84no—
129#3230—111no—
130#3077—111no—
131C2×#476—111no—
132#2972—111no—
133#1683—114no—
134#1675—114no—
135#1571—111no—
136#1548—111no—
137#1542D1111yescharacteristic, complemented
138C23×C11#12111yescharacteristic
139C22×D11—22no—
140C22×D11—24no—
141C22×D11—81no—
142C22×D11—81no—
143Q8×C11—42no—
144Q8×C11—81no—
145C2×C4×C11—22no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11C2×Q1612yes—
153C2×C4×C11#13512yes—
154C2×C4×C11C22×D411yescharacteristic
155C2×C4×C11C22×D411yescharacteristic
156C2×C4×C11C2×#4111yescharacteristic
157C2×Dic11—22no—
158C2×Dic11—42no—
159C2×Dic11—81no—
160C2×Dic11—82no—
161D44—22no—
162D44—24no—
163D44C2×Q1614yes—
164C4×D11—44no—
165C4×D11—82no—
166Dic22—82no—
167Dic22—82no—
168C8×C11—42no—
169C8×C11—42no—
170C11⋊C8—24no—
171C11⋊C8—42no—
172#533C2×D1111yescharacteristic
173C2×C4⋊Q8—111no—
174C2×C4×D4—111no—
175#500—112no—
176#487—112no—
177#484—222no—
178#478—222no—
179#477—222no—
180#476—112no—
181#476—114no—
182#476—222no—
183#474—112no—
184C8×D4—114no—
185C8×D4—222no—
186#431—111no—
187#431C2×D1111yescharacteristic
188#428—221no—
189C2×#106—221no—
190#423—111no—
191C2×C4⋊C8C2×D1111yescharacteristic
192#418—221no—
193C2×#102—221no—
194C2×C22⋊C8—222no—
195#335—114no—
196#333—114no—
197#333C2×D1112yescomplemented
198#332C2×D1112yescomplemented
199C22×C11—21no—
200C22×C11—21no—
201C22×C11#46712yes—
202C22×C11C2×#12111yescharacteristic
203C2×D11—24no—
204C2×D11—42no—
205C2×D11—42no—
206C2×D11—84no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—81no—
211C4×C11—81no—
212C4×C11#46712yes—
213C4×C11C22×Q1611yescharacteristic
214C4×C11C2×#13511yescharacteristic
215C4×C11#57712yes—
216Dic11—42no—
217Dic11—82no—
218C22×Q8—221no—
219C22×D4—111no—
220C23×C4—221no—
221C2×M16—221no—
222C22×C8—21no—
223C22×C8—224no—
224C4⋊Q8—112no—
225C4⋊Q8—221no—
226C4⋊Q8—221no—
227C4⋊Q8—221no—
228C4⋊Q8C22×D1111yescharacteristic
229C4⋊Q8C22×D1111yescharacteristic
230#125—21no—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×D4—112no—
236C4×D4—112no—
237C4×D4—221no—
238C4×D4—221no—
239#117—21no—
240C2×C4⋊C4—111no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4—221no—
243C2×C22⋊C4—221no—
244C2×C42C22×D1111yescharacteristic
245#107—222no—
246#107—224no—
247#106—222no—
248#106—224no—
249C4⋊C8—21no—
250C4⋊C8—112no—
251C4⋊C8—112no—
252C4⋊C8—221no—
253C4⋊C8C22×D1112yes—
254C4⋊C8C22×D1112yes—
255#103—224no—
256#102—222no—
257#102—222no—
258#102—224no—
259C22⋊C8—21no—
260C22⋊C8—112no—
261C22⋊C8—224no—
262C4×C8—21no—
263C4×C8—112no—
264C2×C11—22no—
265C2×C11#304211yescharacteristic
266C2×C11C2×#46711yescharacteristic
267C2×C11#306811yescharacteristic
268D11—44no—
269C24—221no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—222no—
273C2×Q8—441no—
274C2×Q8—882no—
275C2×D4—114no—
276C2×D4—112no—
277C2×D4—221no—
278C2×D4—222no—
279C22×C4—221no—
280C22×C4—222no—
281C22×C4—222no—
282C22×C4—441no—
283C22×C4—882no—
284C22×C4#433911yescharacteristic
285C22×C4D4×D1111yescharacteristic
286C22×C4D4×D1111yescharacteristic
287M16—442no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—42no—
291C2×C8—114no—
292C2×C8—222no—
293C2×C8—884no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—112no—
301C4⋊C4—221no—
302C4⋊C4—222no—
303C4⋊C4—222no—
304C4⋊C4—441no—
305C4⋊C4—441no—
306C22⋊C4—41no—
307C22⋊C4—222no—
308C22⋊C4—222no—
309C42—41no—
310C42#433911yescharacteristic
311C42D4×D1111yescharacteristic
312C42D4×D1111yescharacteristic
313C42C23×D1111yescharacteristic
314C11#1939311yescharacteristic, complemented, Sylow
315C23—222no—
316C23—224no—
317C23—881no—
318C23—881no—
319C23#6693711yescharacteristic
320Q8—42no—
321Q8—81no—
322Q8—882no—
323Q8—882no—
324D4—114no—
325D4—222no—
326D4—224no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—222no—
332C2×C4—444no—
333C2×C4—442no—
334C2×C4—882no—
335C2×C4—881no—
336C2×C4—882no—
337C2×C4#6693711yescharacteristic
338C2×C4#6693711yescharacteristic
339C2×C4#6693711yescharacteristic
340C2×C4#6696912yes—
341C2×C4Q16×D1112yes—
342C2×C4C2×#433911yescharacteristic
343C2×C4C2×D4×D1111yescharacteristic
344C2×C4C2×D4×D1111yescharacteristic
345C8—42no—
346C8—42no—
347C8—224no—
348C8—442no—
349C22—21no—
350C22—21no—
351C22—224no—
352C22—442no—
353C22—442no—
354C22—884no—
355C22#1062242612yes—
356C22C2×#6693711yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—81no—
361C4—81no—
362C4—442no—
363C4—882no—
364C4#1062242612yes—
365C4C2×#6696911yescharacteristic
366C4C2×Q16×D1111yescharacteristic
367C4#1062330112yes—
368C2—22no—
369C2—444no—
370C2#1307813111yescharacteristic
371C2C2×#1062242611yescharacteristic
372C2#1307834711yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1542C2
socleC22×C11C2×#121
prime radicalC22×D44D4
hypercenter#1542D11
hypocenterC11#19393
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
1. #13079764C2semidirect
5. #13068066C2semidirect
6. #13068014C2semidirect
7. #13067390C2semidirect
8. #13067296C2semidirect
9. C11×#1542C2semidirect
19. #10622694C22semidirect
20. #10622691C22semidirect
33. C11×#333C22semidirect
34. C11×#332C22semidirect
35. #10622119C22semidirect
36. #10622117C22semidirect
137. #1542D11semidirect
197. #333C2×D11semidirect
198. #332C2×D11semidirect
314. C11#19393semidirect

Maximal subgroups

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

subgroupindex
#130797642
#130784092
C2×#106224552
#130776392
#130680662
#130680142
#130673902
#130672962
C11×#15422
#1939311