Finite Group Databasebeta

← #13073822

Subgroups — #13073822

Order 1408.

500 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 177 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×#66941C211yesmaximal, characteristic
2C2×#66940C211yesmaximal, characteristic
3C11×#384C211yesmaximal, characteristic
4#10622592C214yesmaximal
5#10622589C211yesmaximal, characteristic
6#10622587C211yesmaximal, characteristic
7#10622585C214yesmaximal
8C4×Dic11⋊C4C211yesmaximal, characteristic
9#10622542C211yesmaximal, characteristic
10C22×Dic22C2211yescharacteristic
11C22×Dic22C2212yes—
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2214yes—
15C2×C42×C11C2211yescharacteristic
16C2×C4⋊Dic11C2211yescharacteristic
17C2×Dic11⋊C4C2212yes—
18C2×Dic11⋊C4C2212yes—
19C2×Dic11⋊C4C2214yes—
20C2×Dic11⋊C4C2212yes—
21C2×C4×Dic11C2212yes—
22C2×C4×Dic11C2211yescharacteristic
23C2×C4×Dic11C2211yescharacteristic
24#66941—24no—
25#66940—24no—
26C11⋊#95C2214yes—
27C11⋊#95C2212yes—
28C11⋊#95C2214yes—
29C22×C4×C11C2312yes—
30C22×C4×C11C2312yes—
31C22×C4×C11C2312yes—
32C22×C4×C11C2311yescharacteristic
33C22×Dic11C2312yes—
34C22×Dic11C2311yescharacteristic
35C22×Dic11C2312yes—
36C22×Dic11C2312yes—
37C22×Dic11C2311yescharacteristic
38C2×Dic22—24no—
39C2×Dic22—22no—
40C2×Dic22—22no—
41C2×Dic22—44no—
42C2×Dic22Q814yescomplemented
43C11×C4⋊C4—22no—
44C11×C4⋊C4—22no—
45C11×C4⋊C4—44no—
46C42×C11—22no—
47C4⋊Dic11—22no—
48Dic11⋊C4—24no—
49Dic11⋊C4—24no—
50Dic11⋊C4—44no—
51Dic11⋊C4Q818yescomplemented
52C4×Dic11—24no—
53C4×Dic11—22no—
54C4×Dic11D414yes—
55#2567—111nomaximal, Sylow
56C23×C11C2411yescharacteristic
57C2×C4×C11—22no—
58C2×C4×C11—22no—
59C2×C4×C11—22no—
60C2×C4×C11—22no—
61C2×C4×C11—24no—
62C2×C4×C11—24no—
63C2×C4×C11C2×D412yes—
64C2×C4×C11C2×Q814yes—
65C2×C4×C11C2×Q812yes—
66C2×C4×C11#4112yes—
67C2×Dic11—22no—
68C2×Dic11—22no—
69C2×Dic11—22no—
70C2×Dic11—22no—
71C2×Dic11—22no—
72C2×Dic11—22no—
73C2×Dic11—24no—
74C2×Dic11C2×D412yes—
75C2×Dic11C2×D412yes—
76C2×Dic11C2×Q814yes—
77C2×Dic11C2×Q814yes—
78C2×Dic11C2×Q814yes—
79Dic22—28no—
80Dic22—48no—
81C2×C4⋊Q8—111no—
82C2×C4×Q8—111no—
83#395—114no—
84#391—111no—
85#391—111no—
86#389—114no—
87#384—111no—
88#384D1111yescharacteristic
89C4×C4⋊C4—111no—
90C22×C11C22×D411yescharacteristic
91C22×C11C22×Q811yescharacteristic
92C22×C11C22×Q812yes—
93C22×C11C2×#4111yescharacteristic
94C22×C11H(5,𝔽2)12yes—
95C4×C11—24no—
96C4×C11—42no—
97C4×C11—42no—
98C4×C11C22⋊Q814yes—
99Dic11—24no—
100Dic11—22no—
101Dic11—24no—
102Dic11—42no—
103Dic11C4⋊Q814yes—
104C22×Q8—111no—
105C22×Q8—112no—
106C4⋊Q8—224no—
107C4×Q8—224no—
108C2×C4⋊C4—112no—
109C2×C4⋊C4—112no—
110C2×C4⋊C4—111no—
111C2×C4⋊C4—112no—
112C2×C4⋊C4—114no—
113C2×C4⋊C4C2×D1111yescharacteristic
114C2×C4⋊C4C2×D1111yescharacteristic
115C2×C4⋊C4C2×D1114yes—
116C2×C42—111no—
117C2×C42—112no—
118C2×C42—111no—
119C2×C42C2×D1111yescharacteristic
120#95—112no—
121#95—114no—
122#95—114no—
123C2×C11C2×C22⋊Q811yescharacteristic
124C2×C11C2×C4⋊Q811yescharacteristic
125C2×C11#53511yescharacteristic
126C2×C11#55412yes—
127C2×C11Q8212yes—
128C2×Q8—114no—
129C2×Q8—224no—
130C2×Q8—222no—
131C2×Q8—222no—
132C2×Q8—444no—
133C22×C4—111no—
134C22×C4—112no—
135C22×C4—112no—
136C22×C4—111no—
137C22×C4—112no—
138C22×C4C22×D1112yes—
139C22×C4C22×D1112yes—
140C22×C4C22×D1112yes—
141C22×C4C22×D1111yescharacteristic
142C4⋊C4—22no—
143C4⋊C4—22no—
144C4⋊C4—44no—
145C4⋊C4—118no—
146C4⋊C4—224no—
147C4⋊C4—224no—
148C4⋊C4—222no—
149C4⋊C4—444no—
150C42—22no—
151C42—114no—
152C42—224no—
153C42—222no—
154C11#256711yescharacteristic, complemented, Sylow
155C23C23×D1111yescharacteristic
156Q8—228no—
157Q8—448no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—24no—
163C2×C4—24no—
164C2×C4—112no—
165C2×C4—114no—
166C2×C4—112no—
167C2×C4—114no—
168C2×C4—114no—
169C2×C4—222no—
170C2×C4—222no—
171C2×C4—222no—
172C2×C4—222no—
173C2×C4—222no—
174C2×C4—222no—
175C2×C4—224no—
176C2×C4#433912yes—
177C2×C4D4×D1112yes—
178C2×C4Q8×D1114yes—
179C2×C4Q8×D1112yes—
180C22C2×#433911yescharacteristic
181C22C2×D4×D1111yescharacteristic
182C22#6703712yes—
183C22C2×Q8×D1111yescharacteristic
184C22C2×Q8×D1112yes—
185C4—24no—
186C4—42no—
187C4—42no—
188C4—114no—
189C4—222no—
190C4—224no—
191C4—224no—
192C4—442no—
193C4#6694914yes—
194C2C2×#6694911yescharacteristic
195C2#1062304212yes—
196C2#1062324611yescharacteristic
197C2#1062325312yes—
198C2D11×C4⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#384C2
hypercenter#384D11
hypocenterC11#2567
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
42. C2×Dic22Q8semidirect
51. Dic11⋊C4Q8semidirect
154. C11#2567semidirect

Maximal subgroups

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

subgroupindex
C2×#669412
C2×#669402
C11×#3842
#106225922
#106225892
#106225872
#106225852
C4×Dic11⋊C42
#106225422
#256711