Finite Group Databasebeta

← #13076643

Subgroups — #13076643

Order 1408.

528 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 133 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×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#66983C211yesmaximal, characteristic
3#10622844C212yesmaximal, complemented
4#10622824C211yesmaximal, characteristic, complemented
5#10622605C212yesmaximal, complemented
6#10622604C212yesmaximal, complemented
7#10622596C212yesmaximal, complemented
8#10622572C214yesmaximal, complemented
9C22×Q8×C11C2211yescharacteristic
10C23×C4×C11C2211yescharacteristic
11C22×C22⋊D11C2212yes—
12C22×D44C2211yescharacteristic
13C11×C22⋊Q8—24no—
14C2×C11×C4⋊C4C2212yes—
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C22⋊C4C2212yes—
17C2×C22⋊Dic11C2212yes—
18#66983—24no—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2214yes—
21C2×(C2×D11)⋊C4C2214yes—
22C2×C4⋊Dic11C2211yescharacteristic
23C2×Dic11⋊C4C2214yes—
24C11⋊#95C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2214yes—
27C24×C11C2311yescharacteristic
28C23×D11C2312yes—
29C2×Q8×C11—22no—
30C2×Q8×C11—42no—
31C22×C4×C11—42no—
32C22×C4×C11D414yes—
33C22×C4×C11C2312yes—
34C22×C4×C11C2312yes—
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2311yescharacteristic
37C2×C22⋊D11—24no—
38C2×C22⋊D11—44no—
39C22×Dic11C2314yes—
40C22×Dic11C2312yes—
41C2×D44—22no—
42C2×D44—42no—
43C11×C4⋊C4—22no—
44C11×C4⋊C4—24no—
45C11×C22⋊C4—24no—
46C22⋊Dic11—42no—
47(C2×D11)⋊C4—24no—
48(C2×D11)⋊C4—44no—
49(C2×D11)⋊C4—44no—
50C4⋊Dic11—22no—
51Dic11⋊C4—44no—
52#2816—111nomaximal, Sylow
53C23×C11—22no—
54C23×C11—22no—
55C23×C11—22no—
56C23×C11C2×D412yes—
57C23×C11C2411yescharacteristic
58C22×D11—22no—
59C22×D11—24no—
60C22×D11—24no—
61C22×D11—24no—
62Q8×C11—44no—
63C2×C4×C11—22no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—22no—
68C2×C4×C11—22no—
69C2×C4×C11—24no—
70C2×C4×C11—44no—
71C2×C4×C11C2×D412yes—
72C2×C4×C11C2×D412yes—
73C22⋊D11—48no—
74C2×Dic11—22no—
75C2×Dic11—24no—
76C2×Dic11—24no—
77C2×Dic11—24no—
78C2×Dic11—24no—
79D44—44no—
80C2×C22⋊Q8D1111yescharacteristic, complemented
81C2×#121—111no—
82#399—112no—
83#398—112no—
84#394—112no—
85#394—114no—
86#393—112no—
87#381—111no—
88C22×C11—22no—
89C22×C11—22no—
90C22×C11—22no—
91C22×C11—44no—
92C22×C11C22×D411yescharacteristic
93C22×C11H(5,𝔽2)12yes—
94C22×C11H(5,𝔽2)12yes—
95C22×C112−1+412yes—
96C2×D11—42no—
97C2×D11—42no—
98C2×D11—42no—
99C2×D11—48no—
100C4×C11—22no—
101C4×C11—22no—
102C4×C11—42no—
103C4×C11—42no—
104Dic11—42no—
105Dic11—44no—
106C22×Q8C2×D1111yescharacteristic
107C22×D4—112no—
108C22×D4—111no—
109C23×C4C2×D1111yescharacteristic
110C22⋊Q8—24no—
111#121—224no—
112C2×C4⋊C4—111no—
113C2×C4⋊C4—114no—
114C2×C4⋊C4C2×D1112yes—
115C2×C4⋊C4C2×D1111yescharacteristic
116C2×C22⋊C4—112no—
117C2×C22⋊C4—112no—
118C2×C22⋊C4—114no—
119C2×C22⋊C4—114no—
120C2×C22⋊C4C2×D1112yes—
121#95—112no—
122#95—112no—
123#95—114no—
124C2×C11—42no—
125C2×C11#53411yescharacteristic
126C2×C11#53511yescharacteristic
127C2×C11#53611yescharacteristic
128C2×C11#56214yes—
129D11—82no—
130C24—112no—
131C24C22×D1111yescharacteristic
132C2×Q8—22no—
133C2×Q8—42no—
134C2×D4—224no—
135C2×D4—222no—
136C2×D4—442no—
137C2×D4—444no—
138C22×C4—42no—
139C22×C4—114no—
140C22×C4—112no—
141C22×C4C22⋊D1114yes—
142C22×C4C22×D1112yes—
143C22×C4C22×D1112yes—
144C22×C4C22×D1111yescharacteristic
145C22×C4C22×D1111yescharacteristic
146C4⋊C4—22no—
147C4⋊C4—24no—
148C4⋊C4—222no—
149C4⋊C4—444no—
150C22⋊C4—24no—
151C22⋊C4—224no—
152C22⋊C4—444no—
153C22⋊C4—444no—
154C22⋊C4—442no—
155C11#281611yescharacteristic, complemented, Sylow
156C23—22no—
157C23—22no—
158C23—22no—
159C23—224no—
160C23—224no—
161C23—224no—
162C23—222no—
163C23C2×C22⋊D1112yes—
164C23C23×D1111yescharacteristic
165Q8—44no—
166D4—444no—
167D4—448no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—44no—
176C2×C4—224no—
177C2×C4—224no—
178C2×C4—224no—
179C2×C4—224no—
180C2×C4—222no—
181C2×C4C2×C22⋊D1112yes—
182C2×C4C2×C22⋊D1112yes—
183C22—22no—
184C22—22no—
185C22—22no—
186C22—44no—
187C22—442no—
188C22—442no—
189C22—442no—
190C22—448no—
191C22#6703712yes—
192C22#6704012yes—
193C22#6704212yes—
194C22C22×C22⋊D1111yescharacteristic
195C4—22no—
196C4—22no—
197C4—42no—
198C4—42no—
199C4—442no—
200C4—444no—
201C2—42no—
202C2—882no—
203C2#1062317814yes—
204C2#1062333511yescharacteristic
205C2#1062334711yescharacteristic
206C2#1062336111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×C22⋊Q8C2
prime radicalC2×#66983C2
hypercenterC2×C22⋊Q8D11
hypocenterC11#2816
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C11×C22⋊Q8C2semidirect
3. #10622844C2semidirect
4. #10622824C2semidirect
5. #10622605C2semidirect
6. #10622604C2semidirect
7. #10622596C2semidirect
8. #10622572C2semidirect
80. C2×C22⋊Q8D11semidirect
155. C11#2816semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C22⋊Q82
C2×#669832
#106228442
#106228242
#106226052
#106226042
#106225962
#106225722
#281611