Finite Group Databasebeta

← #13073777

Subgroups — #13073777

Order 1408.

532 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 153 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×D44C211yesmaximal, characteristic
2C2×#66923C211yesmaximal, characteristic, complemented
3C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
4#10622600C212yesmaximal, complemented
5#10622600C212yesmaximal, complemented
6#10622553C214yesmaximal, complemented
7#10622285C212yesmaximal
8#10622272C212yesmaximal, complemented
9C22×D44C2211yescharacteristic
10C22×C4×D11C2212yes—
11C2×C11×C4⋊C4C2212yes—
12C2×C42×C11C2212yes—
13C2×C42×C11C2211yescharacteristic
14C2×(C2×D11)⋊C4C2212yes—
15C2×(C2×D11)⋊C4C2214yes—
16C2×(C2×D11)⋊C4C2214yes—
17C2×C4⋊Dic11C2211yescharacteristic
18C2×C4⋊Dic11C2211yescharacteristic
19C2×C4⋊Dic11C2211yescharacteristic
20C2×Dic11⋊C4C2212yes—
21C2×Dic11⋊C4C2212yes—
22C4×D44—24no—
23#66923—24no—
24C11×#95C2212yes—
25C11⋊#95C2214yes—
26C11⋊#95C2214yes—
27C23×D11C2312yes—
28C22×C4×C11C2314yes—
29C22×C4×C11C2311yescharacteristic
30C22×C4×C11C2311yescharacteristic
31C22×C4×C11C2311yescharacteristic
32C22×Dic11C2312yes—
33C22×Dic11C2312yes—
34C22×Dic11C2312yes—
35C2×D44—24no—
36C2×D44—22no—
37C2×C4×D11—24no—
38C2×C4×D11—24no—
39C2×C4×D11—24no—
40C11×C4⋊C4—24no—
41C42×C11—42no—
42C42×C11D414yes—
43(C2×D11)⋊C4—28no—
44(C2×D11)⋊C4—24no—
45(C2×D11)⋊C4—44no—
46C4⋊Dic11—22no—
47C4⋊Dic11—22no—
48C4⋊Dic11—22no—
49Dic11⋊C4—24no—
50Dic11⋊C4—24no—
51#2562—111nomaximal, Sylow
52C23×C11C2411yescharacteristic
53C22×D11—22no—
54C22×D11—22no—
55C22×D11—22no—
56C22×D11—22no—
57C22×D11—22no—
58C22×D11—22no—
59C22×D11#4114yes—
60C2×C4×C11—22no—
61C2×C4×C11—21no—
62C2×C4×C11—21no—
63C2×C4×C11—24no—
64C2×C4×C11—24no—
65C2×C4×C11—24no—
66C2×C4×C11C2×D412yes—
67C2×C4×C11C2×D412yes—
68C2×C4×C11C2×D412yes—
69C2×C4×C11#4114yes—
70C2×Dic11—22no—
71C2×Dic11—22no—
72C2×Dic11—22no—
73C2×Dic11—24no—
74C2×Dic11—22no—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78D44—28no—
79C4×D11—48no—
80C2×#125—111no—
81C2×C4×D4—111no—
82#400—112no—
83#394—112no—
84#388—114no—
85#380—112no—
86#380—112no—
87C4×C4⋊C4D1111yescharacteristic, complemented
88C22×C11C22×D411yescharacteristic
89C22×C11C2×#4112yes—
90C22×C11C2×#4112yes—
91C22×C11H(5,𝔽2)11yescharacteristic
92C22×C112−1+411yescharacteristic
93C2×D11—24no—
94C2×D11—24no—
95C2×D11—24no—
96C2×D11—42no—
97C2×D11—42no—
98C2×D11—42no—
99C2×D11—42no—
100C4×C11—22no—
101C4×C11—22no—
102C4×C11—44no—
103C4×C11#12414yes—
104Dic11—42no—
105Dic11—42no—
106Dic11—42no—
107C22×D4—111no—
108C23×C4—112no—
109#125—224no—
110C4×D4—224no—
111C2×C4⋊C4—111no—
112C2×C4⋊C4—111no—
113C2×C4⋊C4—111no—
114C2×C4⋊C4—112no—
115C2×C4⋊C4—112no—
116C2×C4⋊C4C2×D1112yes—
117C2×C22⋊C4—112no—
118C2×C22⋊C4—114no—
119C2×C22⋊C4—114no—
120C2×C42C2×D1112yes—
121C2×C42C2×D1111yescharacteristic
122#95—114no—
123#95—114no—
124#95C2×D1112yes—
125C2×C11#52511yescharacteristic
126C2×C11C2×#12411yescharacteristic
127C2×C11#53711yescharacteristic
128C2×C11#55212yes—
129C2×C11#55312yes—
130D11—44no—
131C24—112no—
132C2×D4—224no—
133C2×D4—222no—
134C22×C4—112no—
135C22×C4—112no—
136C22×C4—112no—
137C22×C4—224no—
138C22×C4—224no—
139C22×C4—224no—
140C22×C4C22×D1114yes—
141C22×C4C22×D1111yescharacteristic
142C22×C4C22×D1111yescharacteristic
143C22×C4C22×D1111yescharacteristic
144C4⋊C4—24no—
145C4⋊C4—222no—
146C4⋊C4—224no—
147C4⋊C4—224no—
148C4⋊C4—222no—
149C4⋊C4—222no—
150C22⋊C4—228no—
151C22⋊C4—224no—
152C22⋊C4—444no—
153C42—42no—
154C42D4414yes—
155C11#256211yescharacteristic, complemented, Sylow
156C23—114no—
157C23—222no—
158C23—222no—
159C23—222no—
160C23—222no—
161C23—222no—
162C23—222no—
163C23C23×D1111yescharacteristic
164D4—228no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—24no—
169C2×C4—24no—
170C2×C4—24no—
171C2×C4—222no—
172C2×C4—222no—
173C2×C4—222no—
174C2×C4—222no—
175C2×C4—222no—
176C2×C4—222no—
177C2×C4—222no—
178C2×C4—224no—
179C2×C4—448no—
180C2×C4C2×D4412yes—
181C2×C4C2×D4412yes—
182C2×C4C2×D4412yes—
183C2×C4#433914yes—
184C22—224no—
185C22—224no—
186C22—224no—
187C22—442no—
188C22—442no—
189C22—442no—
190C22—442no—
191C22C22×D4411yescharacteristic
192C22C2×#433912yes—
193C22#6703711yescharacteristic
194C22#6704011yescharacteristic
195C22#41×D1112yes—
196C4—22no—
197C4—22no—
198C4—44no—
199C4—442no—
200C4—442no—
201C4—442no—
202C4#6692814yes—
203C2—444no—
204C2C2×#6692811yescharacteristic
205C2#1062304111yescharacteristic
206C2#1062305511yescharacteristic
207C2#1062308912yes—
208C2#1062311212yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC4×C11×C4⋊C4C2
prime radicalC22×D44C22
hypercenterC4×C4⋊C4D11
hypocenterC11#2562
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#66923C2semidirect
3. C4×C11×C4⋊C4C2semidirect
4. #10622600C2semidirect
5. #10622600C2semidirect
6. #10622553C2semidirect
8. #10622272C2semidirect
87. C4×C4⋊C4D11semidirect
155. C11#2562semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D442
C2×#669232
C4×C11×C4⋊C42
#106226002
#106225532
#106222852
#106222722
#256211