Finite Group Databasebeta

← #13073555

Subgroups — #13073555

Order 1408.

760 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C2×C4×D4×C11C211yesmaximal, characteristic, complemented
2C2×#66983C212yesmaximal, complemented
3C2×#66977C212yesmaximal, complemented
4C2×#66928C211yesmaximal, characteristic, complemented
5#10622836C212yesmaximal, complemented
6#10622605C212yesmaximal, complemented
7#10622570C214yesmaximal, complemented
8C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
9C22×D4×C11C2211yescharacteristic
10C23×C4×C11C2212yes—
11C22×C22⋊D11C2214yes—
12C22×D44C2211yescharacteristic
13C22×Dic22C2211yescharacteristic
14C4×D4×C11—24no—
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C22⋊C4C2212yes—
17C2×C42×C11C2211yescharacteristic
18C2×C22⋊Dic11C2214yes—
19#66983—28no—
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2214yes—
23C2×C4⋊Dic11C2212yes—
24#66977—28no—
25C2×Dic11⋊C4C2214yes—
26C2×C4×Dic11C2212yes—
27#66928—24no—
28C11⋊#95C2212yes—
29C24×C11C2312yes—
30C23×D11C2312yes—
31C2×D4×C11—24no—
32C2×D4×C11—22no—
33C22×C4×C11—24no—
34C22×C4×C11—24no—
35C22×C4×C11—24no—
36C22×C4×C11C2312yes—
37C22×C4×C11C2311yescharacteristic
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2311yescharacteristic
40C2×C22⋊D11—28no—
41C2×C22⋊D11—28no—
42C2×C22⋊D11—44no—
43C22×Dic11C2312yes—
44C22×Dic11C2314yes—
45C2×D44—22no—
46C2×D44—24no—
47C2×Dic22—22no—
48C2×Dic22—24no—
49C11×C4⋊C4—22no—
50C11×C22⋊C4—24no—
51C42×C11D414yescomplemented
52C22⋊Dic11—28no—
53(C2×D11)⋊C4—28no—
54(C2×D11)⋊C4—24no—
55(C2×D11)⋊C4—24no—
56C4⋊Dic11D418yescomplemented
57Dic11⋊C4—28no—
58C4×Dic11—42no—
59#2540—111nomaximal, Sylow
60C23×C11—22no—
61C23×C11—22no—
62C23×C11—22no—
63C23×C11—22no—
64C23×C11—22no—
65C23×C11—22no—
66C23×C11#4114yes—
67C23×C11C2411yescharacteristic
68C22×D11—22no—
69C22×D11—24no—
70C22×D11—24no—
71C22×D11—22no—
72C22×D11—22no—
73D4×C11—28no—
74C2×C4×C11—22no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—48no—
81C2×C4×C11C2×D414yes—
82C2×C4×C11C2×D412yes—
83C2×C4×C11C2×D412yes—
84C2×C4×C11C2×D412yes—
85C22⋊D11—416no—
86C2×Dic11—24no—
87C2×Dic11—24no—
88C2×Dic11—24no—
89C2×Dic11—22no—
90C2×Dic11C2×D418yes—
91D44—44no—
92Dic22—44no—
93C2×#124—111no—
94C2×C22⋊Q8—112no—
95C2×#121—112no—
96C2×C4×D4D1111yescharacteristic, complemented
97#399—112no—
98#392—112no—
99#390—114no—
100C4×C4⋊C4—111no—
101C22×C11—24no—
102C22×C11—24no—
103C22×C11—24no—
104C22×C11—42no—
105C22×C11—42no—
106C22×C11—42no—
107C22×C11—42no—
108C22×C11C22×D412yes—
109C22×C11C22×D411yescharacteristic
110C22×C11C2×#4112yes—
111C22×C11H(5,𝔽2)11yescharacteristic
112C22×C112−1+411yescharacteristic
113C2×D11—42no—
114C2×D11—42no—
115C2×D11—42no—
116C2×D11—44no—
117C2×D11—44no—
118C4×C11—22no—
119C4×C11—22no—
120C4×C11—42no—
121C4×C11#12714yes—
122Dic11—28no—
123Dic11—42no—
124C22×Q8—111no—
125C22×D4—114no—
126C22×D4—111no—
127C22×D4C2×D1111yescharacteristic
128C23×C4C2×D1112yes—
129#124—224no—
130C22⋊Q8—228no—
131#121—228no—
132C4×D4—24no—
133C2×C4⋊C4—112no—
134C2×C4⋊C4—114no—
135C2×C4⋊C4C2×D1111yescharacteristic
136C2×C22⋊C4—114no—
137C2×C22⋊C4—114no—
138C2×C22⋊C4—112no—
139C2×C22⋊C4—112no—
140C2×C22⋊C4C2×D1112yes—
141C2×C42—112no—
142C2×C42C2×D1111yescharacteristic
143#95—112no—
144C2×C11—44no—
145C2×C11#52511yescharacteristic
146C2×C11C2×#12711yescharacteristic
147C2×C11#53711yescharacteristic
148C2×C11#54612yes—
149C2×C11#54812yes—
150D11—82no—
151C24—112no—
152C24C22×D1112yes—
153C2×Q8—224no—
154C2×Q8—222no—
155C2×D4—24no—
156C2×D4—22no—
157C2×D4—228no—
158C2×D4—228no—
159C2×D4—224no—
160C2×D4—222no—
161C2×D4—444no—
162C22×C4—24no—
163C22×C4—24no—
164C22×C4—24no—
165C22×C4—114no—
166C22×C4—112no—
167C22×C4C22×D1112yes—
168C22×C4C22×D1111yescharacteristic
169C22×C4C22×D1111yescharacteristic
170C22×C4C22×D1111yescharacteristic
171C4⋊C4—22no—
172C4⋊C4—118no—
173C4⋊C4—228no—
174C22⋊C4—24no—
175C22⋊C4—228no—
176C22⋊C4—228no—
177C22⋊C4—224no—
178C22⋊C4—224no—
179C42—442no—
180C42C22⋊D1114yescomplemented
181C11#254011yescharacteristic, complemented, Sylow
182C23—22no—
183C23—22no—
184C23—22no—
185C23—22no—
186C23—22no—
187C23—22no—
188C23—224no—
189C23—224no—
190C23—222no—
191C23—222no—
192C23—222no—
193C23#433914yes—
194C23C23×D1111yescharacteristic
195Q8—444no—
196D4—28no—
197D4—4416no—
198D4—444no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—48no—
206C2×C4—118no—
207C2×C4—224no—
208C2×C4—224no—
209C2×C4—224no—
210C2×C4—222no—
211C2×C4D4×D1114yes—
212C2×C4C2×C22⋊D1112yes—
213C2×C4C2×C22⋊D1112yes—
214C2×C4C2×C22⋊D1112yes—
215C22—24no—
216C22—24no—
217C22—24no—
218C22—42no—
219C22—42no—
220C22—42no—
221C22—42no—
222C22—442no—
223C22—442no—
224C22—444no—
225C22—444no—
226C22—442no—
227C22C2×#433912yes—
228C22C2×D4×D1112yes—
229C22#6704211yescharacteristic
230C22#6704311yescharacteristic
231C22C22×C22⋊D1111yescharacteristic
232C4—22no—
233C4—22no—
234C4—42no—
235C4—228no—
236C4—442no—
237C4#6699314yes—
238C2—44no—
239C2—882no—
240C2#1062308112yes—
241C2#1062308312yes—
242C2#1062332211yescharacteristic
243C2C2×#6699311yescharacteristic
244C2#1062336411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C4×D4×C11C2
hypercenterC2×C4×D4D11
hypocenterC11#2540
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C4×D4×C11C2semidirect
2. C2×#66983C2semidirect
3. C2×#66977C2semidirect
4. C2×#66928C2semidirect
5. #10622836C2semidirect
6. #10622605C2semidirect
7. #10622570C2semidirect
8. C4×C4⋊Dic11C2semidirect
51. C42×C11D4semidirect
56. C4⋊Dic11D4semidirect
96. C2×C4×D4D11semidirect
180. C42C22⋊D11semidirect
181. C11#2540semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C112
C2×#669832
C2×#669772
C2×#669282
#106228362
#106226052
#106225702
C4×C4⋊Dic112
#254011