Finite Group Databasebeta

← #15675087

Subgroups — #15675087

Order 2944.

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

normal subgroups only

This group has 262 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#13092985C211yesmaximal, characteristic
2#13092400C212yesmaximal, complemented
3#13092214C211yesmaximal, characteristic, complemented
4#13092213C212yesmaximal, complemented
5C23×#355C211yesmaximal, characteristic, complemented
6C2×#67292C2211yescharacteristic
7C2×D4×D23C411yescharacteristic
8C23×#124C2211yescharacteristic
9#10625118C2211yescharacteristic
10#10625111C411yescharacteristic
11M16×D23—22no—
12#10625055—22no—
13#10625053—22no—
14#10625045C411yescharacteristic
15#10625043C411yescharacteristic
16C23×#101C2212yescomplemented
17#10625018C2212yescomplemented
18#10625005—22no—
19C23×D23—21no—
20C2×Q8×C23C2311yescharacteristic
21C2×D4×C23C2×C411yescharacteristic
22C2×C22⋊D23—22no—
23C2×C22⋊D23—21no—
24#67292—42no—
25D4×D23—42no—
26C2×D92—22no—
27C2×D92C2×C411yescharacteristic
28C2×D92C2×C411yescharacteristic
29C2×D92D412yes—
30C2×C4×D23C2×C411yescharacteristic
31C2×C4×D23D412yes—
32M16×C23—22no—
33C22⋊C4×C23—22no—
34C42×C23C2×C411yescharacteristic
35(C2×D23)⋊C4—21no—
36(C2×D23)⋊C4—22no—
37Dic23⋊C4—21no—
38C4×Dic23C2×C411yescharacteristic
39#67267—22no—
40#67262—42no—
41C8×D23—42no—
42C23×C23—21no—
43C22×D23—21no—
44C22×D23—42no—
45C22×D23—82no—
46C22×D23C22⋊C411yescharacteristic
47C22×D23C22⋊C412yes—
48Q8×C23—41no—
49D4×C23—41no—
50C2×C4×C23—21no—
51C2×C4×C23C22×C411yescharacteristic
52C2×C4×C23C2×D412yes—
53C22⋊D23—42no—
54C22⋊D23—82no—
55C2×Dic23—21no—
56C2×Dic23C22⋊C411yescharacteristic
57D92—41no—
58D92—42no—
59D92—41no—
60D92—82no—
61C4×D23—22no—
62C4×D23—22no—
63C4×D23—22no—
64C8×C23—42no—
65C23⋊C8—42no—
66#2134—231nomaximal, Sylow
67C22×C23—42no—
68C22×C23—41no—
69C22×C23C2×C22⋊C411yescharacteristic
70C2×D23—21no—
71C2×D23—22no—
72C2×D23—42no—
73C2×D23—41no—
74C2×D23—42no—
75C2×D23—41no—
76C2×D23—84no—
77C4×C23—22no—
78C4×C23—21no—
79C4×C23—41no—
80Dic23—41no—
81Dic23#9912yes—
82#535—231no—
83#413—232no—
84#355—231no—
85#355—232no—
86#355D2311yescharacteristic, complemented
87C2×C23—21no—
88C2×C23—81no—
89C2×C23C2×#9911yescharacteristic
90D23—42no—
91D23—41no—
92D23—81no—
93C2×#41—231no—
94C22×D4—231no—
95C2×M16—462no—
96#127—231no—
97#127—231no—
98#124—231no—
99#124C2×D2311yescharacteristic
100#121—462no—
101#120—462no—
102#117—231no—
103#101—232no—
104#101C2×D2312yescomplemented
105#100—462no—
106C23#213411yescharacteristic, complemented, Sylow
107C24—461no—
108#41—922no—
109C2×Q8C22×D2311yescharacteristic
110C2×D4—231no—
111C2×D4—231no—
112C2×D4—232no—
113C2×D4—462no—
114C2×D4—461no—
115C2×D4—462no—
116C2×D4—922no—
117C2×D4C4×D2311yescharacteristic
118C22×C4—231no—
119C22×C4—232no—
120M16—22no—
121M16—462no—
122M16—922no—
123C2×C8—922no—
124C4⋊C4—461no—
125C22⋊C4—22no—
126C22⋊C4—461no—
127C22⋊C4—462no—
128C42—231no—
129C42C4×D2311yescharacteristic
130C23—21no—
131C23—231no—
132C23—232no—
133C23—461no—
134C23—922no—
135C23—1842no—
136Q8—41no—
137D4—41no—
138D4—922no—
139D4—921no—
140D4—921no—
141D4—922no—
142D4—1842no—
143D4—1842no—
144C2×C4—21no—
145C2×C4—231no—
146C2×C4—462no—
147C2×C4—462no—
148C2×C4—462no—
149C2×C4—461no—
150C2×C4C2×C4×D2311yescharacteristic
151C2×C4D4×D2312yes—
152C8—42no—
153C8—922no—
154C22—42no—
155C22—41no—
156C22—461no—
157C22—462no—
158C22—922no—
159C22—921no—
160C22—922no—
161C22—921no—
162C22—1844no—
163C22C22⋊C4×D2311yescharacteristic
164C4—22no—
165C4—21no—
166C4—41no—
167C4—232no—
168C4—921no—
169C2—21no—
170C2—81no—
171C2—921no—
172C2—922no—
173C2—1841no—
174C2#99×D2311yescharacteristic
subgroupG/H
centerC2#99×D23
commutatorC2×C4×C23C22×C4
FrattiniC2×Q8C22×D23
FittingC23×#355C2
socleC2×C23C2×#99
prime radical#13092985C2
cosocleC2×Q8×C23C23
hypercenter#355D23
hypocenterC23#2134
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #13092400C2semidirect
3. #13092214C2semidirect
4. #13092213C2semidirect
5. C23×#355C2semidirect
16. C23×#101C22semidirect
17. #10625018C22semidirect
86. #355D23semidirect
104. #101C2×D23semidirect
106. C23#2134semidirect

Maximal subgroups

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

subgroupindex
#130929852
#130924002
#130922142
#130922132
C23×#3552
#213423