Finite Group Databasebeta

← #15675091

Subgroups — #15675091

Order 2944.

230 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 65 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#13092988C211yesmaximal, characteristic
2#13092401C211yesmaximal, characteristic
3#13092215C214yesmaximal, complemented
4C23×#413C211yesmaximal, characteristic
5C2×#41×C23C2211yescharacteristic
6C22×Dic46C411yescharacteristic
7C2×M16×C23—21no—
8#10625115C2212yes—
9#10625107C412yes—
10#10625106—21no—
11#10625106—21no—
12#10625097C411yescharacteristic
13#10625095—21no—
14#10625095—21no—
15C2×#67267—21no—
16C23×#101C2212yes—
17C23×#100—21no—
18#10625018C2212yes—
19#10625015—21no—
20#41×C23—41no—
21#41×C23—41no—
22C2×Q8×C23C2311yescharacteristic
23C2×D4×C23C2×C411yescharacteristic
24C2×D4×C23D411yescharacteristic
25C2×D4×C23D411yescharacteristic
26C22×C4×C23C2×C411yescharacteristic
27C22×C4×C23D411yescharacteristic
28C22×C4×C23D411yescharacteristic
29C22×Dic23—21no—
30C2×Dic46—21no—
31C2×Dic46—41no—
32C2×Dic46—41no—
33C2×Dic46C2×C412yes—
34M16×C23—22no—
35M16×C23—41no—
36C2×C8×C23—41no—
37C22⋊Dic23—22no—
38C22⋊Dic23—22no—
39C22⋊Dic23—21no—
40C4⋊Dic23—21no—
41Dic23⋊C4—22no—
42Dic23⋊C4—22no—
43C4×Dic23C2×C412yes—
44#67267—22no—
45#67267—41no—
46C2×C23⋊C8—41no—
47C23×C23C22⋊C411yescharacteristic
48C23×C23C22⋊C411yescharacteristic
49C23×C23C22⋊C411yescharacteristic
50Q8×C23—41no—
51D4×C23—41no—
52D4×C23—41no—
53D4×C23—41no—
54C2×C4×C23—21no—
55C2×C4×C23—21no—
56C2×C4×C23—21no—
57C2×C4×C23—21no—
58C2×C4×C23—21no—
59C2×C4×C23—21no—
60C2×C4×C23C22⋊C411yescharacteristic
61C2×C4×C23C22×C411yescharacteristic
62C2×C4×C23C2×D411yescharacteristic
63C2×C4×C23C2×D411yescharacteristic
64C2×Dic23—22no—
65C2×Dic23—22no—
66C2×Dic23—42no—
67Dic46—41no—
68Dic46—41no—
69Dic46—42no—
70C8×C23—42no—
71C23⋊C8—42no—
72#2135—231nomaximal, Sylow
73C22×C23—21no—
74C22×C23—21no—
75C22×C23—21no—
76C22×C23—41no—
77C22×C23—41no—
78C22×C23—41no—
79C22×C23C2×C22⋊C411yescharacteristic
80C4×C23—21no—
81C4×C23—21no—
82C4×C23—21no—
83C4×C23#9911yescharacteristic
84C4×C23#9911yescharacteristic
85Dic23—42no—
86Dic23—42no—
87#536—231no—
88#413—231no—
89#413D2311yescharacteristic
90#356—234no—
91C2×C23—21no—
92C2×C23—41no—
93C2×C23—41no—
94C2×C23—41no—
95C2×C23C2×#9911yescharacteristic
96C2×#41C2×D2311yescharacteristic
97C22×Q8—231no—
98C2×M16—21no—
99C2×M16—461no—
100C4⋊Q8—232no—
101#124—232no—
102#123—461no—
103#123—461no—
104C22⋊Q8—461no—
105C22⋊Q8—461no—
106#117—231no—
107#101—232no—
108#101C2×D2312yes—
109#100—21no—
110#100—461no—
111C23#213511yescharacteristic, complemented, Sylow
112#41—41no—
113#41—41no—
114C2×Q8—232no—
115C2×Q8—461no—
116C2×Q8—921no—
117C2×Q8—921no—
118C2×Q8C22×D2311yescharacteristic
119C2×D4C4×D2311yescharacteristic
120C2×D4D9211yescharacteristic
121C2×D4C22⋊D2311yescharacteristic
122C22×C4—461no—
123C22×C4C4×D2311yescharacteristic
124C22×C4D9211yescharacteristic
125C22×C4C22⋊D2311yescharacteristic
126M16—22no—
127M16—41no—
128M16—462no—
129M16—921no—
130C2×C8—41no—
131C2×C8—921no—
132C4⋊C4—461no—
133C4⋊C4—462no—
134C4⋊C4—462no—
135C22⋊C4—461no—
136C22⋊C4—462no—
137C22⋊C4—462no—
138C42—232no—
139C23(C2×D23)⋊C411yescharacteristic
140C23(C2×D23)⋊C411yescharacteristic
141C23(C2×D23)⋊C411yescharacteristic
142Q8—41no—
143Q8—922no—
144Q8—921no—
145Q8—921no—
146D4—41no—
147D4—41no—
148D4—41no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—462no—
156C2×C4—462no—
157C2×C4—922no—
158C2×C4(C2×D23)⋊C411yescharacteristic
159C2×C4C2×C4×D2311yescharacteristic
160C2×C4C2×D9211yescharacteristic
161C2×C4C2×C22⋊D2311yescharacteristic
162C8—42no—
163C8—922no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22C2×(C2×D23)⋊C411yescharacteristic
171C4—21no—
172C4—21no—
173C4—21no—
174C4—922no—
175C4—922no—
176C4#1062498811yescharacteristic
177C4#1062498811yescharacteristic
178C2—21no—
179C2—41no—
180C2—41no—
181C2—41no—
182C2C2×#1062498811yescharacteristic
subgroupG/H
centerC2C2×#10624988
commutatorC2×C4×C23C22×C4
FrattiniC2×Q8C22×D23
FittingC23×#413C2
socleC2×C23C2×#99
prime radicalC2×#41×C23C22
cosocleC2×Q8×C23C23
hypercenter#413D23
hypocenterC23#2135
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
3. #13092215C2semidirect
111. C23#2135semidirect

Maximal subgroups

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

subgroupindex
#130929882
#130924012
#130922152
C23×#4132
#213523