Finite Group Databasebeta

← #14654739

Subgroups — #14654739

Order 2816.

636 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079062C211yesmaximal, characteristic, complemented
2#13078616C212yesmaximal, complemented
3#13067014C212yesmaximal, complemented
4#13066447C211yesmaximal, characteristic, complemented
5C11×#1955C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66957—22no—
8#10623008C2212yes—
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C11×C22⋊C8—22no—
11C2×C11×#97C2211yescharacteristic
12#10622830—22no—
13#10622628—22no—
14C4×#4323—24no—
15#10622620—22no—
16#10622580—22no—
17#10622538C2212yes—
18#10622328—22no—
19#10622325—22no—
20#10622121—24no—
21C22×D4×C11D411yescharacteristic
22C23×C4×C11—21no—
23C2×#4339—22no—
24C22×C8×C11—21no—
25C22×C8×C11D412yes—
26C4×D4×C11—22no—
27C4×D4×C11—22no—
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C22⋊C4—21no—
30C2×C42×C11C2311yescharacteristic
31C2×#4323—24no—
32#66983—22no—
33#66983—22no—
34C2×Dic44—22no—
35#66957—44no—
36#66957—44no—
37C2×D88—22no—
38C2×#4314—24no—
39#66928—22no—
40#66927D412yes—
41C4×D44—22no—
42C4×D44—22no—
43#66922D412yes—
44C11×C4⋊C8—22no—
45C11×C22⋊C8—44no—
46C11×#97—22no—
47#66896—24no—
48C22⋊(C11⋊C8)—22no—
49#66873—24no—
50#66871—24no—
51C4⋊(C11⋊C8)—22no—
52C4×C11⋊C8D414yes—
53#10032—111nomaximal, Sylow
54C24×C11—21no—
55C2×D4×C11—22no—
56C2×D4×C11—42no—
57C22×C4×C11—21no—
58C22×C4×C11—41no—
59C22×C4×C11—41no—
60C22×C4×C11—42no—
61C22×C4×C11—42no—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11#4111yescharacteristic
65C2×C22⋊D11—42no—
66#4339—44no—
67#4339—44no—
68C2×D44—22no—
69C2×D44—22no—
70C2×D44—22no—
71C2×C4×D11—42no—
72C2×Dic22—22no—
73C2×C8×C11—22no—
74C2×C8×C11—22no—
75C2×C8×C11—41no—
76C2×C8×C11—42no—
77C2×C8×C11D814yescomplemented
78C11×C4⋊C4—22no—
79C11×C22⋊C4—42no—
80C42×C11C2×D412yes—
81C42×C11C2×D412yes—
82#4323—48no—
83(C2×D11)⋊C4—42no—
84(C2×D11)⋊C4—42no—
85C4⋊Dic11—22no—
86C4⋊Dic11—22no—
87C2×C11⋊C8—24no—
88Dic44—44no—
89D88—44no—
90#4314—48no—
91#3150—111no—
92#3100—112no—
93#1955D1111yescharacteristic, complemented
94#1480—112no—
95#1275—111no—
96C23×C11—22no—
97C23×C11—41no—
98C23×C11—42no—
99C23×C11—41no—
100C23×C11—42no—
101C23×C11#12111yescharacteristic
102C22×D11—42no—
103D4×C11—24no—
104D4×C11—42no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—42no—
109C2×C4×C11—82no—
110C2×C4×C11—81no—
111C2×C4×C11—81no—
112C2×C4×C11#12012yes—
113C2×C4×C11#12011yescharacteristic
114C2×C4×C11#12112yes—
115C2×C4×C11#12711yescharacteristic
116C2×C4×C11C2×D812yes—
117C2×C4×C11AGL(1,ℤ/8)12yes—
118C22⋊D11—84no—
119C2×Dic11—42no—
120D44—44no—
121D44—44no—
122D44—44no—
123C4×D11—82no—
124C4×D11—82no—
125Dic22—44no—
126C8×C11—24no—
127C8×C11—81no—
128C11⋊C8—44no—
129C2×#135—222no—
130#532—112no—
131C2×C4×D4C2×D1111yescharacteristic
132#497—222no—
133#496—222no—
134#480—222no—
135#474—222no—
136#459—222no—
137#447—222no—
138C4×D8—224no—
139#431—112no—
140C2×C4⋊C8C2×D1111yescharacteristic
141C2×C22⋊C8—22no—
142C2×#97C2×D1111yescharacteristic
143D4⋊C8—224no—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11—44no—
147C22×C11—42no—
148C22×C11—82no—
149C22×C11—81no—
150C22×C11—81no—
151C22×C11#39211yescharacteristic
152C22×C11#45912yes—
153C2×D11—82no—
154C2×D11—82no—
155C2×D11—82no—
156C4×C11—22no—
157C4×C11—22no—
158C4×C11—81no—
159C4×C11#44712yes—
160C4×C11#49311yescharacteristic
161C4×C11#49611yescharacteristic
162Dic11—82no—
163C2×#41—222no—
164C22×D4D4411yescharacteristic
165C23×C4—21no—
166#135—444no—
167#135—444no—
168C2×Q16—222no—
169C2×SD16—224no—
170C2×D8—222no—
171C2×D8—224no—
172C22×C8—21no—
173C22×C8C22⋊D1112yes—
174C4⋊Q8—112no—
175#127—112no—
176#124—222no—
177#121—222no—
178#121—222no—
179C4×D4—22no—
180C4×D4—22no—
181C4×D4—222no—
182C4×D4—222no—
183C2×C4⋊C4D4411yescharacteristic
184C2×C22⋊C4—21no—
185C2×C42C22×D1111yescharacteristic
186#107—224no—
187C4⋊C8—22no—
188C4⋊C8—222no—
189#102—224no—
190#102—224no—
191C22⋊C8—44no—
192C22⋊C8—222no—
193#97—22no—
194C4×C8—114no—
195C2×C11—22no—
196C2×C11—82no—
197C2×C11#201011yescharacteristic
198C2×C11#201111yescharacteristic
199C2×C11#201711yescharacteristic
200D11—162no—
201C24—21no—
202#41—444no—
203#41—444no—
204C2×Q8—222no—
205C2×D4—22no—
206C2×D4—42no—
207C2×D4—222no—
208C2×D4—222no—
209C2×D4—222no—
210C2×D4—442no—
211C22×C4—21no—
212C22×C4—42no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—42no—
216C22×C4—442no—
217C22×C4C2×D4411yescharacteristic
218C22×C4#433911yescharacteristic
219C22×C4C2×C22⋊D1111yescharacteristic
220Q16—444no—
221SD16—448no—
222D8—444no—
223D8—448no—
224C2×C8—22no—
225C2×C8—22no—
226C2×C8—42no—
227C2×C8—41no—
228C2×C8—224no—
229C2×C8#432314yescomplemented
230C4⋊C4—22no—
231C4⋊C4—222no—
232C4⋊C4—222no—
233C22⋊C4—42no—
234C22⋊C4—442no—
235C22⋊C4—442no—
236C42D4×D1112yes—
237C42D4×D1112yes—
238C11#1003211yescharacteristic, complemented, Sylow
239C23—22no—
240C23—41no—
241C23—42no—
242C23—41no—
243C23—42no—
244C23—442no—
245C23#6698311yescharacteristic
246Q8—444no—
247D4—24no—
248D4—42no—
249D4—444no—
250D4—444no—
251D4—444no—
252D4—884no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—82no—
258C2×C4—81no—
259C2×C4—81no—
260C2×C4—442no—
261C2×C4—882no—
262C2×C4—882no—
263C2×C4#6693512yes—
264C2×C4#6693712yes—
265C2×C4C2×#432312yes—
266C2×C4#6699011yescharacteristic
267C2×C4#6699311yescharacteristic
268C2×C4#6700212yes—
269C8—24no—
270C8—81no—
271C8—444no—
272C22—21no—
273C22—21no—
274C22—44no—
275C22—42no—
276C22—82no—
277C22—81no—
278C22—81no—
279C22—882no—
280C22—882no—
281C22—882no—
282C22#1062257311yescharacteristic
283C22#1062262812yes—
284C4—22no—
285C4—22no—
286C4—81no—
287C4—882no—
288C4#1062264912yes—
289C4#1062267111yescharacteristic
290C4#1062268611yescharacteristic
291C2—22no—
292C2—82no—
293C2—1762no—
294C2#1306968311yescharacteristic
295C2#1306968611yescharacteristic
296C2#1306972011yescharacteristic
subgroupG/H
centerC2×C4#66993
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1955C2
socleC22×C11#392
hypercenter#1955D11
hypocenterC11#10032
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1955

Complements

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

NH ≅ G/Ntype
1. #13079062C2semidirect
2. #13078616C2semidirect
3. #13067014C2semidirect
4. #13066447C2semidirect
5. C11×#1955C2semidirect
77. C2×C8×C11D8semidirect
93. #1955D11semidirect
229. C2×C8#4323semidirect
238. C11#10032semidirect

Maximal subgroups

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

subgroupindex
#130790622
#130786162
#130670142
#130664472
C11×#19552
#1003211