Finite Group Databasebeta

← #15671860

Subgroups — #15671860

Order 2944.

216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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
1#13092951C211yesmaximal, characteristic
2#13092470C211yesmaximal, characteristic, complemented
3#13092147C212yesmaximal, complemented
4#13092144C212yesmaximal, complemented
5C23×#423C211yesmaximal, characteristic, complemented
6C2×M16×C23—21no—
7C2×C42×C23C2211yescharacteristic
8#10625101C411yescharacteristic
9#10625100—21no—
10C4×C22⋊D23—21no—
11#10625095C411yescharacteristic
12#10625047—21no—
13#10625046C411yescharacteristic
14C4×D92C2211yescharacteristic
15#10625043—21no—
16#10625041C411yescharacteristic
17C4×Dic46C2211yescharacteristic
18C23×C4⋊C8—21no—
19C23×C4⋊C8C2212yes—
20C22⋊(C23⋊C8)—21no—
21C4⋊(C23⋊C8)—21no—
22C4×C23⋊C8C2212yes—
23C22×C4×C23C2×C411yescharacteristic
24C22×C4×C23D411yescharacteristic
25C22×C4×C23D411yescharacteristic
26C2×C22⋊D23—21no—
27C2×D92C2×C411yescharacteristic
28C2×C4×D23—21no—
29C2×Dic46C2×C411yescharacteristic
30M16×C23—42no—
31C2×C8×C23—22no—
32C42×C23C2×C411yescharacteristic
33C42×C23D411yescharacteristic
34C42×C23D411yescharacteristic
35C42×C23C2311yescharacteristic
36C22⋊Dic23—21no—
37(C2×D23)⋊C4—21no—
38(C2×D23)⋊C4—21no—
39(C2×D23)⋊C4—21no—
40(C2×D23)⋊C4—21no—
41C4⋊Dic23C2×C411yescharacteristic
42C4⋊Dic23C2×C411yescharacteristic
43Dic23⋊C4—21no—
44Dic23⋊C4—21no—
45Dic23⋊C4—21no—
46Dic23⋊C4—21no—
47C4×Dic23—21no—
48C2×C23⋊C8—22no—
49C23×C23C22⋊C411yescharacteristic
50C22×D23—21no—
51C2×C4×C23—22no—
52C2×C4×C23—21no—
53C2×C4×C23—21no—
54C2×C4×C23—41no—
55C2×C4×C23C22⋊C411yescharacteristic
56C2×C4×C23C22⋊C411yescharacteristic
57C2×C4×C23C22⋊C411yescharacteristic
58C2×C4×C23C22×C411yescharacteristic
59C2×C4×C23C2×D411yescharacteristic
60C2×C4×C23C2×D411yescharacteristic
61C22⋊D23—42no—
62C2×Dic23—21no—
63C2×Dic23—21no—
64C2×Dic23—21no—
65D92—22no—
66C4×D23—41no—
67C4×D23—41no—
68Dic46—22no—
69C8×C23—42no—
70C23⋊C8—42no—
71#1495—231nomaximal, Sylow
72C22×C23—21no—
73C22×C23—21no—
74C22×C23—21no—
75C22×C23C2×C22⋊C411yescharacteristic
76C2×D23—41no—
77C2×D23—41no—
78C2×D23—41no—
79C4×C23—21no—
80C4×C23—21no—
81C4×C23—21no—
82C4×C23—21no—
83C4×C23#13112yes—
84C4×C23AGL(1,ℤ/8)11yescharacteristic
85C4×C23#13711yescharacteristic
86Dic23—41no—
87Dic23—41no—
88Dic23—41no—
89#529—231no—
90#431—231no—
91#423D2311yescharacteristic, complemented
92Q8⋊C8—232no—
93D4⋊C8—232no—
94C2×C23—41no—
95C2×C23#40811yescharacteristic
96C2×C23#41711yescharacteristic
97C2×C23#42111yescharacteristic
98D23—81no—
99C2×M16—21no—
100#126—461no—
101#125—231no—
102#124—231no—
103#123—461no—
104C22⋊Q8—231no—
105#121—231no—
106C4×Q8—231no—
107C4×D4—231no—
108C4×D4—461no—
109#117—461no—
110C2×C42C2×D2311yescharacteristic
111C4⋊C8—21no—
112C4⋊C8—461no—
113C4⋊C8C2×D2312yes—
114C22⋊C8—461no—
115C4×C8—232no—
116C23#149511yescharacteristic, complemented, Sylow
117C2×Q8—231no—
118C2×D4—231no—
119C2×D4—461no—
120C22×C4—461no—
121C22×C4C4×D2311yescharacteristic
122C22×C4D9211yescharacteristic
123C22×C4C22⋊D2311yescharacteristic
124M16—42no—
125C2×C8—22no—
126C2×C8—462no—
127C4⋊C4—231no—
128C4⋊C4—231no—
129C4⋊C4—461no—
130C4⋊C4—461no—
131C4⋊C4—461no—
132C4⋊C4—461no—
133C22⋊C4—461no—
134C22⋊C4—461no—
135C22⋊C4—461no—
136C22⋊C4—461no—
137C22⋊C4—461no—
138C42—461no—
139C42C4×D2311yescharacteristic
140C42D9211yescharacteristic
141C42C22⋊D2311yescharacteristic
142C42C22×D2311yescharacteristic
143C23—461no—
144C23(C2×D23)⋊C411yescharacteristic
145Q8—462no—
146D4—462no—
147D4—922no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—461no—
153C2×C4—461no—
154C2×C4—461no—
155C2×C4—921no—
156C2×C4—921no—
157C2×C4(C2×D23)⋊C411yescharacteristic
158C2×C4(C2×D23)⋊C411yescharacteristic
159C2×C4(C2×D23)⋊C411yescharacteristic
160C2×C4C2×C4×D2311yescharacteristic
161C2×C4C2×D9211yescharacteristic
162C2×C4C2×C22⋊D2311yescharacteristic
163C8—42no—
164C8—922no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—921no—
169C22—921no—
170C22—921no—
171C22C2×(C2×D23)⋊C411yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—921no—
177C4—921no—
178C4—921no—
179C4#1062507812yes—
180C4#1062510311yescharacteristic
181C4#1062511311yescharacteristic
182C2—41no—
183C2—1841no—
184C2#1309238511yescharacteristic
185C2#1309241611yescharacteristic
186C2#1309243311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D23
commutatorC2×C4×C23C22×C4
FrattiniC42C22×D23
FittingC23×#423C2
socleC22×C23C2×C22⋊C4
prime radical#10625101C4
cosocleC42×C23C23
hypercenter#423D23
hypocenterC23#1495
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
2. #13092470C2semidirect
3. #13092147C2semidirect
4. #13092144C2semidirect
5. C23×#423C2semidirect
91. #423D23semidirect
116. C23#1495semidirect

Maximal subgroups

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

subgroupindex
#130929512
#130924702
#130921472
#130921442
C23×#4232
#149523