Finite Group Databasebeta

← #13076955

Subgroups — #13076955

Order 1408.

564 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 189 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
1C22×C42×C11C211yesmaximal, characteristic
2C2×#66977C211yesmaximal, characteristic
3#10622825C211yesmaximal, characteristic
4#10622824C212yesmaximal
5#10622823C212yesmaximal
6#10622546C214yesmaximal, complemented
7#10622542C212yesmaximal, complemented
8#10622541C212yesmaximal, complemented
9C23×C4×C11C2211yescharacteristic
10C23×C4×C11C2211yescharacteristic
11C23×C4×C11C2211yescharacteristic
12C22×Dic22C2211yescharacteristic
13C2×C42×C11—24no—
14C2×C42×C11C2212yes—
15C2×C42×C11C2212yes—
16C2×C22⋊Dic11C2212yes—
17C2×C22⋊Dic11C2212yes—
18C2×C4⋊Dic11C2211yescharacteristic
19C2×C4⋊Dic11C2212yes—
20#66977—24no—
21C2×Dic11⋊C4C2214yes—
22C2×Dic11⋊C4C2212yes—
23C11⋊#95C2214yes—
24C11⋊#95C2214yes—
25C11⋊#95C2214yes—
26C11⋊#95C2212yes—
27C24×C11C2311yescharacteristic
28C22×C4×C11—22no—
29C22×C4×C11—22no—
30C22×C4×C11—22no—
31C22×C4×C11—24no—
32C22×C4×C11—24no—
33C22×C4×C11D414yes—
34C22×C4×C11Q814yescomplemented
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2312yes—
37C22×C4×C11C2312yes—
38C22×C4×C11C2311yescharacteristic
39C22×Dic11C2314yes—
40C22×Dic11C2312yes—
41C22×Dic11C2312yes—
42C2×Dic22—22no—
43C2×Dic22—24no—
44C42×C11—24no—
45C42×C11—24no—
46C22⋊Dic11—24no—
47C22⋊Dic11—24no—
48C4⋊Dic11—22no—
49C4⋊Dic11—24no—
50Dic11⋊C4—24no—
51Dic11⋊C4—28no—
52#2855—111nomaximal, Sylow
53C23×C11—22no—
54C23×C11—22no—
55C23×C11C2×D412yes—
56C23×C11C2×Q812yes—
57C23×C11#4112yes—
58C23×C11C2411yescharacteristic
59C2×C4×C11—28no—
60C2×C4×C11—28no—
61C2×C4×C11—22no—
62C2×C4×C11—22no—
63C2×C4×C11—22no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—28no—
67C2×C4×C11C2×D412yes—
68C2×C4×C11C2×D412yes—
69C2×C4×C11C2×Q814yes—
70C2×C4×C11#4114yes—
71C2×C4×C11#4114yes—
72C2×Dic11—22no—
73C2×Dic11—22no—
74C2×Dic11—24no—
75C2×Dic11—24no—
76C2×Dic11—24no—
77C2×Dic11—24no—
78C2×Dic11—24no—
79Dic22—44no—
80C2×C22⋊Q8—111no—
81C22×C42D1111yescharacteristic
82#391—112no—
83#389—112no—
84#387—114no—
85#385—112no—
86#381—112no—
87#380—111no—
88C22×C11—22no—
89C22×C11—22no—
90C22×C11—24no—
91C22×C11—24no—
92C22×C11C22⋊Q814yes—
93C22×C11C22×D411yescharacteristic
94C22×C11C22×Q811yescharacteristic
95C22×C11C2×#4111yescharacteristic
96C22×C11C2×#4112yes—
97C22×C11C2×#4112yes—
98C4×C11—24no—
99C4×C11—22no—
100C4×C11—24no—
101C4×C11#12314yes—
102Dic11—42no—
103Dic11—42no—
104Dic11—44no—
105C22×Q8—111no—
106C23×C4C2×D1111yescharacteristic
107C23×C4C2×D1111yescharacteristic
108C23×C4C2×D1111yescharacteristic
109C22⋊Q8—224no—
110C2×C4⋊C4—112no—
111C2×C4⋊C4—111no—
112C2×C4⋊C4—112no—
113C2×C4⋊C4—114no—
114C2×C22⋊C4—112no—
115C2×C22⋊C4—112no—
116C2×C42—24no—
117C2×C42C2×D1112yes—
118C2×C42C2×D1112yes—
119#95—112no—
120#95—114no—
121#95—114no—
122#95—114no—
123C2×C11—24no—
124C2×C11C2×C22⋊Q811yescharacteristic
125C2×C11C2×#12311yescharacteristic
126C2×C11#52511yescharacteristic
127C2×C11#52912yes—
128C2×C11#53312yes—
129C24C22×D1111yescharacteristic
130C2×Q8—224no—
131C2×Q8—222no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—24no—
136C22×C4—24no—
137C22×C4—114no—
138C22×C4—112no—
139C22×C4—112no—
140C22×C4Dic2214yescomplemented
141C22×C4C22⋊D1114yes—
142C22×C4C22×D1112yes—
143C22×C4C22×D1112yes—
144C22×C4C22×D1111yescharacteristic
145C22×C4C22×D1111yescharacteristic
146C4⋊C4—228no—
147C4⋊C4—224no—
148C4⋊C4—224no—
149C4⋊C4—222no—
150C22⋊C4—224no—
151C22⋊C4—224no—
152C42—24no—
153C42—24no—
154C11#285511yescharacteristic, complemented, Sylow
155C23—22no—
156C23—22no—
157C23C2×Dic2212yes—
158C23#433912yes—
159C23C2×C22⋊D1112yes—
160C23C23×D1111yescharacteristic
161Q8—444no—
162C2×C4—28no—
163C2×C4—28no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—28no—
170C2×C4—224no—
171C2×C4—224no—
172C2×C4—224no—
173C2×C4—224no—
174C2×C4—224no—
175C2×C4—222no—
176C2×C4—222no—
177C2×C4C2×Dic2214yes—
178C2×C4#433914yes—
179C2×C4#433914yes—
180C2×C4C2×C22⋊D1112yes—
181C2×C4C2×C22⋊D1112yes—
182C22—24no—
183C22—24no—
184C22—22no—
185C22—22no—
186C22#6697714yes—
187C22C22×Dic2211yescharacteristic
188C22C2×#433912yes—
189C22C2×#433912yes—
190C22C2×#433911yescharacteristic
191C22C22×C22⋊D1111yescharacteristic
192C4—24no—
193C4—22no—
194C4—24no—
195C4—444no—
196C4—442no—
197C4—442no—
198C4#6698214yes—
199C2—24no—
200C2#1062300112yes—
201C2#1062301012yes—
202C2C2×#6697711yescharacteristic
203C2C2×#6698211yescharacteristic
204C2#1062332211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC22×C42×C11C2
prime radicalC24×C11C23
hypercenterC22×C42D11
hypocenterC11#2855
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
6. #10622546C2semidirect
7. #10622542C2semidirect
8. #10622541C2semidirect
34. C22×C4×C11Q8semidirect
140. C22×C4Dic22semidirect
154. C11#2855semidirect

Maximal subgroups

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

subgroupindex
C22×C42×C112
C2×#669772
#106228252
#106228242
#106228232
#106225462
#106225422
#106225412
#285511