Finite Group Databasebeta

← #15675090

Subgroups — #15675090

Order 2944.

230 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 55 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#13092992C211yesmaximal, characteristic
2#13092400C212yesmaximal
3#13092216C211yesmaximal, characteristic, complemented
4#13092215C212yesmaximal, complemented
5C23×#356C211yesmaximal, characteristic, complemented
6C2×#67292C2211yescharacteristic
7C2×Q8×D23C411yescharacteristic
8C23×C4⋊Q8C2211yescharacteristic
9#10625118C411yescharacteristic
10#10625115C2211yescharacteristic
11M16×D23—22no—
12#10625067—22no—
13#10625065—22no—
14#10625046C411yescharacteristic
15#10625043C411yescharacteristic
16C23×#101C2212yes—
17#10625018C2212yes—
18#10625005—22no—
19C2×Q8×C23C2×C411yescharacteristic
20C2×Q8×C23C2311yescharacteristic
21#67292—42no—
22Q8×D23—42no—
23C2×D92C2×C411yescharacteristic
24C2×D92D412yes—
25C2×C4×D23—21no—
26C2×C4×D23C2×C411yescharacteristic
27C2×C4×D23D412yes—
28C2×Dic46—21no—
29C2×Dic46C2×C411yescharacteristic
30M16×C23—22no—
31C4⋊C4×C23—22no—
32C42×C23C2×C411yescharacteristic
33(C2×D23)⋊C4—21no—
34(C2×D23)⋊C4—22no—
35(C2×D23)⋊C4—22no—
36Dic23⋊C4—22no—
37Dic23⋊C4—21no—
38C4×Dic23C2×C411yescharacteristic
39#67267—22no—
40#67262—42no—
41C8×D23—42no—
42C22×D23C22⋊C412yes—
43C22×D23C22⋊C411yescharacteristic
44Q8×C23—41no—
45Q8×C23—41no—
46C2×C4×C23—21no—
47C2×C4×C23—21no—
48C2×C4×C23C22×C411yescharacteristic
49C2×C4×C23C2×D412yes—
50C2×Dic23—21no—
51C2×Dic23—21no—
52C2×Dic23C22⋊C411yescharacteristic
53D92—41no—
54D92—42no—
55C4×D23—22no—
56C4×D23—22no—
57C4×D23—22no—
58C4×D23—42no—
59Dic46—42no—
60Dic46—41no—
61C8×C23—42no—
62C23⋊C8—42no—
63#2135—231nomaximal, Sylow
64C22×C23C2×C22⋊C411yescharacteristic
65C2×D23—21no—
66C2×D23—22no—
67C2×D23—42no—
68C2×D23—41no—
69C4×C23—22no—
70C4×C23—21no—
71C4×C23—41no—
72C4×C23—41no—
73Dic23—41no—
74Dic23—41no—
75Dic23#9912yes—
76#536—231no—
77#413—232no—
78#356—231no—
79#356—232no—
80#356D2311yescharacteristic, complemented
81C2×C23—21no—
82C2×C23C2×#9911yescharacteristic
83D23—41no—
84D23—42no—
85C2×#41—231no—
86C22×Q8—231no—
87C2×M16—462no—
88C4⋊Q8—231no—
89C4⋊Q8C2×D2311yescharacteristic
90#124—231no—
91#124—231no—
92#123—462no—
93C22⋊Q8—462no—
94#117—231no—
95#101—232no—
96#101C2×D2312yes—
97#100—462no—
98C23#213511yescharacteristic, complemented, Sylow
99#41—922no—
100C2×Q8—231no—
101C2×Q8—461no—
102C2×Q8—922no—
103C2×Q8C4×D2311yescharacteristic
104C2×Q8C22×D2311yescharacteristic
105C2×D4—231no—
106C2×D4—232no—
107C22×C4—231no—
108C22×C4—232no—
109C22×C4—461no—
110M16—22no—
111M16—462no—
112M16—922no—
113C2×C8—922no—
114C4⋊C4—22no—
115C4⋊C4—461no—
116C4⋊C4—462no—
117C22⋊C4—461no—
118C22⋊C4—462no—
119C22⋊C4—462no—
120C42—231no—
121C42C4×D2311yescharacteristic
122C23—232no—
123C23—231no—
124Q8—41no—
125Q8—41no—
126Q8—921no—
127Q8—922no—
128D4—922no—
129D4—921no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—231no—
133C2×C4—462no—
134C2×C4—462no—
135C2×C4—462no—
136C2×C4—461no—
137C2×C4—461no—
138C2×C4—922no—
139C2×C4C2×C4×D2311yescharacteristic
140C2×C4D4×D2312yes—
141C8—42no—
142C8—922no—
143C22—461no—
144C22—462no—
145C22—922no—
146C22—921no—
147C22C22⋊C4×D2311yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—41no—
152C4—232no—
153C4—921no—
154C4—921no—
155C2—21no—
156C2—921no—
157C2—922no—
158C2#99×D2311yescharacteristic
subgroupG/H
centerC2#99×D23
commutatorC2×C4×C23C22×C4
FrattiniC2×Q8C22×D23
FittingC23×#356C2
socleC2×C23C2×#99
prime radicalC2×#67292C22
cosocleC2×Q8×C23C23
hypercenter#356D23
hypocenterC23#2135
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
3. #13092216C2semidirect
4. #13092215C2semidirect
5. C23×#356C2semidirect
80. #356D23semidirect
98. C23#2135semidirect

Maximal subgroups

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

subgroupindex
#130929922
#130924002
#130922162
#130922152
C23×#3562
#213523