Finite Group Databasebeta

← #13073970

Subgroups — #13073970

Order 1408.

564 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 169 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
2C2×C4×Dic22C211yesmaximal, characteristic, complemented
3#10622834C212yesmaximal
4#10622823C214yesmaximal, complemented
5#10622586C212yesmaximal, complemented
6#10622562C212yesmaximal, complemented
7#10622560C212yesmaximal, complemented
8#10622549C211yesmaximal, characteristic, complemented
9C22×D4×C11C2211yescharacteristic
10C23×C4×C11C2212yes—
11C22×Dic22C2211yescharacteristic
12C4×D4×C11—24no—
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C22⋊C4C2212yes—
15C2×C42×C11C2211yescharacteristic
16C2×C22⋊Dic11C2214yes—
17C2×C22⋊Dic11C2214yes—
18C2×C4⋊Dic11C2211yescharacteristic
19C2×C4⋊Dic11C2212yes—
20C2×Dic11⋊C4C2212yes—
21C2×Dic11⋊C4C2214yes—
22C2×C4×Dic11C2212yes—
23C4×Dic22—24no—
24C11⋊#95C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2214yes—
27C24×C11C2312yes—
28C2×D4×C11—22no—
29C2×D4×C11—22no—
30C2×D4×C11Q814yescomplemented
31C22×C4×C11—24no—
32C22×C4×C11—44no—
33C22×C4×C11C2312yes—
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2311yescharacteristic
37C22×Dic11C2314yes—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C2×Dic22—24no—
41C2×Dic22—22no—
42C11×C4⋊C4—22no—
43C11×C22⋊C4—24no—
44C42×C11D414yes—
45C22⋊Dic11—28no—
46C22⋊Dic11—44no—
47C4⋊Dic11—22no—
48C4⋊Dic11—24no—
49Dic11⋊C4—24no—
50Dic11⋊C4—44no—
51C4×Dic11—24no—
52#2580—111nomaximal, Sylow
53C23×C11—22no—
54C23×C11—24no—
55C23×C11—22no—
56C23×C11—24no—
57C23×C11C2×Q814yes—
58C23×C11C2411yescharacteristic
59D4×C11—28no—
60C2×C4×C11—22no—
61C2×C4×C11—22no—
62C2×C4×C11—22no—
63C2×C4×C11—24no—
64C2×C4×C11—48no—
65C2×C4×C11C2×D412yes—
66C2×C4×C11C2×D412yes—
67C2×C4×C11C2×D412yes—
68C2×C4×C11C2×Q812yes—
69C2×C4×C11#4112yes—
70C2×Dic11—22no—
71C2×Dic11—22no—
72C2×Dic11—22no—
73C2×Dic11—24no—
74C2×Dic11—24no—
75C2×Dic11—22no—
76C2×Dic11—24no—
77C2×Dic11—22no—
78C2×Dic11#4114yes—
79Dic22—28no—
80C2×C4×Q8—111no—
81C2×C4×D4D1111yescharacteristic
82#399—112no—
83#393—112no—
84#390—112no—
85#389—112no—
86#385—114no—
87#382—111no—
88C22×C11—24no—
89C22×C11—28no—
90C22×C11—42no—
91C22×C11—42no—
92C22×C11—44no—
93C22×C11C22×D411yescharacteristic
94C22×C11C22×Q811yescharacteristic
95C22×C11C2×#4111yescharacteristic
96C22×C11C2×#4112yes—
97C22×C11H(5,𝔽2)12yes—
98C4×C11—22no—
99C4×C11—22no—
100C4×C11—42no—
101C4×C11C22⋊Q814yes—
102Dic11—24no—
103Dic11—42no—
104Dic11—44no—
105C22×Q8—111no—
106C22×D4C2×D1111yescharacteristic
107C23×C4C2×D1112yes—
108C4×Q8—224no—
109C4×D4—24no—
110C2×C4⋊C4—112no—
111C2×C4⋊C4—111no—
112C2×C4⋊C4—112no—
113C2×C4⋊C4—114no—
114C2×C4⋊C4C2×D1111yescharacteristic
115C2×C22⋊C4—114no—
116C2×C22⋊C4—114no—
117C2×C22⋊C4C2×D1112yes—
118C2×C42—112no—
119C2×C42C2×D1111yescharacteristic
120#95—112no—
121#95—112no—
122#95—114no—
123C2×C11—44no—
124C2×C11C2×C22⋊Q811yescharacteristic
125C2×C11#52511yescharacteristic
126C2×C11#53511yescharacteristic
127C2×C11#55412yes—
128C2×C11#55912yes—
129C24C22×D1112yes—
130C2×Q8—224no—
131C2×Q8—222no—
132C2×D4—22no—
133C2×D4—22no—
134C2×D4Dic2214yescomplemented
135C22×C4—24no—
136C22×C4—44no—
137C22×C4—112no—
138C22×C4—114no—
139C22×C4—112no—
140C22×C4C22×D1112yes—
141C22×C4C22×D1111yescharacteristic
142C22×C4C22×D1111yescharacteristic
143C22×C4C22×D1111yescharacteristic
144C4⋊C4—22no—
145C4⋊C4—224no—
146C4⋊C4—224no—
147C4⋊C4—222no—
148C4⋊C4—444no—
149C22⋊C4—24no—
150C22⋊C4—228no—
151C22⋊C4—444no—
152C42—224no—
153C42C22⋊D1114yes—
154C11#258011yescharacteristic, complemented, Sylow
155C23—22no—
156C23—24no—
157C23—24no—
158C23—22no—
159C23C2×Dic2214yes—
160C23C23×D1111yescharacteristic
161Q8—228no—
162D4—28no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—24no—
166C2×C4—22no—
167C2×C4—48no—
168C2×C4—114no—
169C2×C4—222no—
170C2×C4—222no—
171C2×C4—224no—
172C2×C4—222no—
173C2×C4—224no—
174C2×C4—222no—
175C2×C4—224no—
176C2×C4—222no—
177C2×C4C2×Dic2212yes—
178C2×C4#433912yes—
179C2×C4C2×C22⋊D1112yes—
180C2×C4C2×C22⋊D1112yes—
181C2×C4C2×C22⋊D1112yes—
182C22—24no—
183C22—28no—
184C22—42no—
185C22—44no—
186C22—42no—
187C22C22×Dic2211yescharacteristic
188C22C2×#433911yescharacteristic
189C22#6703712yes—
190C22#41×D1112yes—
191C22C22×C22⋊D1111yescharacteristic
192C4—22no—
193C4—22no—
194C4—42no—
195C4—224no—
196C4—442no—
197C4—444no—
198C4#6697714yes—
199C2—44no—
200C2#1062307012yes—
201C2#1062309012yes—
202C2C2×#6697711yescharacteristic
203C2#1062333611yescharacteristic
204C2#1062335911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C4×D4×C11C2
prime radicalC22×D4×C11C22
hypercenterC2×C4×D4D11
hypocenterC11#2580
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic22C2semidirect
4. #10622823C2semidirect
5. #10622586C2semidirect
6. #10622562C2semidirect
7. #10622560C2semidirect
8. #10622549C2semidirect
30. C2×D4×C11Q8semidirect
134. C2×D4Dic22semidirect
154. C11#2580semidirect

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×C4×Dic222
#106228342
#106228232
#106225862
#106225622
#106225602
#106225492
#258011