Finite Group Databasebeta

← #15672015

Subgroups — #15672015

Order 2944.

218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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#13092474C211yesmaximal, characteristic, complemented
3#13092158C212yesmaximal, complemented
4#13092156C212yesmaximal, complemented
5C2×C23×#97C211yesmaximal, characteristic, complemented
6C22×C8×C23—21no—
7C2×C42×C23C2211yescharacteristic
8#10625101C411yescharacteristic
9#10625100—21no—
10C4×C22⋊D23—21no—
11#10625095C411yescharacteristic
12#10625047—21no—
13#10625046C2211yescharacteristic
14C4×D92C411yescharacteristic
15#10625043—21no—
16#10625041C2211yescharacteristic
17C4×Dic46C411yescharacteristic
18C23×#97—21no—
19C23×#97C2212yes—
20C22⋊(C23⋊C8)—21no—
21C4⋊(C23⋊C8)—21no—
22#10624985C2212yes—
23C22×C4×C23C2×C411yescharacteristic
24C22×C4×C23D411yescharacteristic
25C22×C4×C23D411yescharacteristic
26C2×C22⋊D23—21no—
27C2×D92C2×C411yescharacteristic
28C2×C4×D23—21no—
29C2×Dic46C2×C411yescharacteristic
30C2×C8×C23—24no—
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—41no—
53C2×C4×C23—41no—
54C2×C4×C23C22⋊C411yescharacteristic
55C2×C4×C23C22⋊C411yescharacteristic
56C2×C4×C23C22⋊C411yescharacteristic
57C2×C4×C23C22×C411yescharacteristic
58C2×C4×C23C2×D411yescharacteristic
59C2×C4×C23C2×D411yescharacteristic
60C22⋊D23—42no—
61C2×Dic23—21no—
62C2×Dic23—21no—
63C2×Dic23—21no—
64D92—41no—
65C4×D23—42no—
66Dic46—41no—
67C8×C23—24no—
68C23⋊C8—42no—
69#1532—231nomaximal, Sylow
70C22×C23—21no—
71C22×C23—21no—
72C22×C23#10412yes—
73C22×C23C2×C22⋊C411yescharacteristic
74C2×D23—41no—
75C2×D23—41no—
76C2×D23—41no—
77C4×C23—21no—
78C4×C23—21no—
79C4×C23—21no—
80C4×C23—21no—
81C4×C23—21no—
82C4×C23—21no—
83Dic23—41no—
84Dic23—41no—
85Dic23—41no—
86#529—231no—
87#432—231no—
88C2×#97D2311yescharacteristic, complemented
89#330—232no—
90#329—232no—
91C2×C23—22no—
92C2×C23#41311yescharacteristic
93C2×C23C2×#10411yescharacteristic
94C2×C23#42111yescharacteristic
95D23—81no—
96C22×C8—21no—
97#126—461no—
98#125—231no—
99#124—231no—
100#123—461no—
101C22⋊Q8—231no—
102#121—231no—
103C4×Q8—231no—
104C4×D4—231no—
105C4×D4—461no—
106#117—461no—
107C2×C42C2×D2311yescharacteristic
108C4⋊C8—461no—
109C22⋊C8—461no—
110#97—21no—
111#97—232no—
112#97C2×D2312yes—
113C23#153211yescharacteristic, complemented, Sylow
114C2×Q8—231no—
115C2×D4—231no—
116C2×D4—461no—
117C22×C4—461no—
118C22×C4C4×D2311yescharacteristic
119C22×C4D9211yescharacteristic
120C22×C4C22⋊D2311yescharacteristic
121C2×C8—24no—
122C2×C8—22no—
123C2×C8—462no—
124C4⋊C4—231no—
125C4⋊C4—231no—
126C4⋊C4—461no—
127C4⋊C4—461no—
128C4⋊C4—461no—
129C4⋊C4—461no—
130C22⋊C4—461no—
131C22⋊C4—461no—
132C22⋊C4—461no—
133C22⋊C4—461no—
134C22⋊C4—461no—
135C42—461no—
136C42C4×D2311yescharacteristic
137C42D9211yescharacteristic
138C42C22⋊D2311yescharacteristic
139C42C22×D2311yescharacteristic
140C23—461no—
141C23(C2×D23)⋊C411yescharacteristic
142Q8—921no—
143D4—921no—
144D4—922no—
145C2×C4—22no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—461no—
149C2×C4—461no—
150C2×C4—461no—
151C2×C4—922no—
152C2×C4(C2×D23)⋊C411yescharacteristic
153C2×C4(C2×D23)⋊C411yescharacteristic
154C2×C4(C2×D23)⋊C411yescharacteristic
155C2×C4C2×C4×D2311yescharacteristic
156C2×C4C2×D9211yescharacteristic
157C2×C4C2×C22⋊D2311yescharacteristic
158C8—24no—
159C8—922no—
160C22—21no—
161C22—21no—
162C22—921no—
163C22—921no—
164C22—921no—
165C22#1062498712yes—
166C22C2×(C2×D23)⋊C411yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—921no—
174C4—921no—
175C4—921no—
176C2—22no—
177C2—1841no—
178C2#1309239911yescharacteristic
179C2C2×#1062498711yescharacteristic
180C2#1309243311yescharacteristic
subgroupG/H
centerC22C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C4
FrattiniC42C22×D23
FittingC2×C23×#97C2
socleC22×C23C2×C22⋊C4
prime radical#10625101C4
cosocleC42×C23C23
hypercenterC2×#97D23
hypocenterC23#1532
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
2. #13092474C2semidirect
3. #13092158C2semidirect
4. #13092156C2semidirect
5. C2×C23×#97C2semidirect
88. C2×#97D23semidirect
113. C23#1532semidirect

Maximal subgroups

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

subgroupindex
#130929512
#130924742
#130921582
#130921562
C2×C23×#972
#153223