Finite Group Databasebeta

← #14651304

Subgroups — #14651304

Order 2816.

436 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078991C211yesmaximal, characteristic
2#13077721C211yesmaximal, characteristic, complemented
3#13067329C211yesmaximal, characteristic
4#13067329C211yesmaximal, characteristic
5#13067253C211yesmaximal, characteristic, complemented
6#13066488C211yesmaximal, characteristic, complemented
7C11×#1291C211yesmaximal, characteristic, complemented
8C2×#66927C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#432C2211yescharacteristic
12C4×C11×M16C2211yescharacteristic
13#10622744—22no—
14#10622539C2211yescharacteristic
15#10622539C2211yescharacteristic
16#10622441—22no—
17#10622333—22no—
18#10622326—22no—
19#10622314—22no—
20#10622307C412yes—
21#10622307C412yes—
22#10622123—22no—
23#10622123—22no—
24#10622103—22no—
25C22×D44—21no—
26C22×D44—21no—
27C22×D44—21no—
28C2×C11×M16—21no—
29C2×C42×C11C2311yescharacteristic
30#66979D412yes—
31#66977—21no—
32#66977—21no—
33#66927—21no—
34#66927—21no—
35#66927—21no—
36#66927C2×C412yes—
37#66923D412yes—
38#66922C2×C411yescharacteristic
39#66922C2×C411yescharacteristic
40C4×Dic22—21no—
41C4×Dic22—21no—
42C11×C4⋊C8—21no—
43C11×C4⋊C8D412yes—
44C11×C22⋊C8—21no—
45C11×C22⋊C8—21no—
46C11×#97—21no—
47C11×#97—21no—
48C11×#97—21no—
49C4×C8×C11C2×C412yes—
50C22⋊(C11⋊C8)—21no—
51C22⋊(C11⋊C8)—21no—
52#66885—24no—
53#66885—24no—
54#66879—22no—
55Dic11⋊C8—24no—
56C8×Dic11—22no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)D412yes—
59#66867—21no—
60#66867—21no—
61#9424—111nomaximal, Sylow
62C23×D11—41no—
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11#4111yescharacteristic
65C22×C4×C11#4111yescharacteristic
66C2×D44—22no—
67C2×D44—22no—
68C2×D44—22no—
69C2×D44—44no—
70C2×D44—41no—
71C2×D44—41no—
72C2×D44—41no—
73C2×D44—82no—
74C2×D44—82no—
75C2×Dic22—21no—
76C2×Dic22—21no—
77C11×M16—42no—
78C2×C8×C11—22no—
79C2×C8×C11—22no—
80C2×C8×C11—41no—
81C42×C11C22×C411yescharacteristic
82C42×C11C2×D411yescharacteristic
83C42×C11C2×D411yescharacteristic
84C42×C11C2×D411yescharacteristic
85C22⋊Dic11—22no—
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11C22⋊C412yes—
89C4⋊Dic11C22⋊C412yes—
90Dic11⋊C4—22no—
91Dic11⋊C4—22no—
92C4×Dic11—22no—
93C2×C11⋊C8—22no—
94C2×C11⋊C8—41no—
95#3138—111no—
96#2987—111no—
97#1555—111no—
98#1555—111no—
99#1537—111no—
100#1291—111no—
101#1291D1111yescharacteristic, complemented
102C23×C11#12311yescharacteristic
103C22×D11—42no—
104C22×D11—82no—
105C22×D11—82no—
106C22×D11—82no—
107C2×C4×C11—22no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11C2×C22⋊C411yescharacteristic
111C2×C4×C11C4×D411yescharacteristic
112C2×C4×C11C4×D411yescharacteristic
113C2×C4×C11#12011yescharacteristic
114C2×C4×C11#12111yescharacteristic
115C2×C4×C11#12111yescharacteristic
116C2×Dic11—22no—
117C2×Dic11—22no—
118D44—44no—
119D44—82no—
120D44—82no—
121D44—82no—
122D44—82no—
123D44—82no—
124Dic22—81no—
125Dic22—81no—
126C8×C11—42no—
127C8×C11—42no—
128C8×C11—81no—
129C11⋊C8—42no—
130C11⋊C8—81no—
131#533—111no—
132C2×#127—111no—
133#490—222no—
134#486—112no—
135#486—112no—
136#446—222no—
137#446—222no—
138#433—222no—
139#432—111no—
140#432—111no—
141#432C2×D1111yescharacteristic
142#432C2×D1111yescharacteristic
143#418—222no—
144C4×M16C2×D1111yescharacteristic
145#331—222no—
146#331—222no—
147#330—222no—
148C22×C11—21no—
149C22×C11—21no—
150C22×C11—21no—
151C22×C11#38611yescharacteristic
152C2×D11—82no—
153C2×D11—82no—
154C2×D11—82no—
155C2×D11—164no—
156C4×C11—21no—
157C4×C11—21no—
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—21no—
161C4×C11#45412yes—
162Dic11—42no—
163Dic11—42no—
164C22×D4—221no—
165C22×D4—221no—
166C22×D4—221no—
167C2×M16—21no—
168C4⋊Q8—111no—
169C4⋊Q8—111no—
170#127—112no—
171#127—221no—
172#127—221no—
173#127—221no—
174#125—112no—
175C22⋊Q8—221no—
176C22⋊Q8—221no—
177C4×Q8—221no—
178C4×Q8—221no—
179#117—112no—
180C2×C42C22×D1111yescharacteristic
181C4⋊C8—21no—
182C4⋊C8—112no—
183C4⋊C8—224no—
184C4⋊C8—221no—
185C4⋊C8D4412yes—
186#102—224no—
187#102—224no—
188C22⋊C8—21no—
189C22⋊C8—21no—
190C22⋊C8—221no—
191C22⋊C8—221no—
192#97—21no—
193#97—21no—
194#97—21no—
195#97—222no—
196#97—221no—
197#97—221no—
198C4×C8—222no—
199C4×C8C4×D1112yes—
200C2×C11—41no—
201C2×C11#188811yescharacteristic
202C2×C11#190311yescharacteristic
203C2×C11#190311yescharacteristic
204D11—162no—
205C24—441no—
206C2×Q8—221no—
207C2×Q8—221no—
208C2×D4—222no—
209C2×D4—222no—
210C2×D4—222no—
211C2×D4—444no—
212C2×D4—441no—
213C2×D4—441no—
214C2×D4—441no—
215C2×D4—882no—
216C2×D4—882no—
217C22×C4#433911yescharacteristic
218C22×C4D4×D1111yescharacteristic
219C22×C4#434311yescharacteristic
220M16—42no—
221C2×C8—22no—
222C2×C8—22no—
223C2×C8—41no—
224C2×C8—222no—
225C2×C8—441no—
226C4⋊C4—112no—
227C4⋊C4—112no—
228C4⋊C4—221no—
229C4⋊C4—222no—
230C4⋊C4—221no—
231C4⋊C4—222no—
232C22⋊C4—222no—
233C42—222no—
234C42C2×C4×D1111yescharacteristic
235C42C2×D4411yescharacteristic
236C42D4×D1111yescharacteristic
237C42D4×D1111yescharacteristic
238C11#942411yescharacteristic, complemented, Sylow
239C23—442no—
240C23—882no—
241C23—882no—
242C23—882no—
243C23#6694711yescharacteristic
244Q8—881no—
245Q8—881no—
246D4—444no—
247D4—882no—
248D4—882no—
249D4—882no—
250D4—882no—
251D4—882no—
252C2×C4—22no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—222no—
256C2×C4—222no—
257C2×C4C4×D4411yescharacteristic
258C2×C4C22⋊C4×D1111yescharacteristic
259C2×C4#6693511yescharacteristic
260C2×C4#6693711yescharacteristic
261C2×C4#6694611yescharacteristic
262C2×C4#6694811yescharacteristic
263C8—42no—
264C8—42no—
265C8—81no—
266C8—442no—
267C8—881no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—882no—
272C22—882no—
273C22—882no—
274C22—1764no—
275C22#1062227811yescharacteristic
276C4—21no—
277C4—21no—
278C4—21no—
279C4—21no—
280C4—21no—
281C4—442no—
282C4—442no—
283C4#1062244012yes—
284C2—41no—
285C2—1762no—
286C2#1306901811yescharacteristic
287C2#1306909511yescharacteristic
288C2#1306909711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1291C2
socleC22×C11#386
prime radicalC2×#66927C22
cosocleC2×C42×C11C23
hypercenter#1291D11
hypocenterC11#9424
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1291

Complements

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

NH ≅ G/Ntype
2. #13077721C2semidirect
5. #13067253C2semidirect
6. #13066488C2semidirect
7. C11×#1291C2semidirect
101. #1291D11semidirect
238. C11#9424semidirect

Maximal subgroups

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

subgroupindex
#130789912
#130777212
#130673292
#130672532
#130664882
C11×#12912
#942411