Finite Group Databasebeta

← #15671986

Subgroups — #15671986

Order 2944.

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

normal subgroups only

This group has 234 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
2C2×#10624985C211yesmaximal, characteristic, complemented
3#13092158C212yesmaximal, complemented
4#13092156C212yesmaximal, complemented
5C4×M16×C23C211yesmaximal, characteristic, complemented
6C2×M16×C23—21no—
7C2×C42×C23C2211yescharacteristic
8#10625101C411yescharacteristic
9#10625100—21no—
10C4×C22⋊D23—21no—
11#10625095C411yescharacteristic
12C22×C23⋊C8—21no—
13#10625047—21no—
14#10625046C2211yescharacteristic
15C4×D92C411yescharacteristic
16#10625043—21no—
17#10625041C2211yescharacteristic
18C4×Dic46C411yescharacteristic
19C23×#97C2212yes—
20C4×C8×C23—21no—
21#10624985—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
30M16×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—24no—
49C2×C23⋊C8—22no—
50C23×C23C22⋊C411yescharacteristic
51C22×D23—21no—
52C2×C4×C23—22no—
53C2×C4×C23—22no—
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—41no—
66C4×D23—42no—
67Dic46—41no—
68C8×C23—24no—
69C23⋊C8—24no—
70#1524—231nomaximal, Sylow
71C22×C23—21no—
72C22×C23—21no—
73C22×C23#10412yes—
74C22×C23C2×C22⋊C411yescharacteristic
75C2×D23—41no—
76C2×D23—41no—
77C2×D23—41no—
78C4×C23—21no—
79C4×C23—21no—
80C4×C23—21no—
81C4×C23—21no—
82C4×C23—21no—
83C4×C23#10412yes—
84Dic23—41no—
85Dic23—41no—
86Dic23—41no—
87#529—231no—
88C4×M16D2311yescharacteristic, complemented
89C2×#97—231no—
90#330—232no—
91#329—232no—
92C2×C23—22no—
93C2×C23#41311yescharacteristic
94C2×C23C2×#10411yescharacteristic
95C2×C23C2×#10411yescharacteristic
96D23—81no—
97C2×M16—21no—
98C22×C8—461no—
99#126—461no—
100#125—231no—
101#124—231no—
102#123—461no—
103C22⋊Q8—231no—
104#121—231no—
105C4×Q8—231no—
106C4×D4—231no—
107C4×D4—461no—
108#117—461no—
109C2×C42C2×D2311yescharacteristic
110#97—232no—
111#97—461no—
112#97C2×D2312yes—
113C4×C8—21no—
114C23#152411yescharacteristic, complemented, Sylow
115C2×Q8—231no—
116C2×D4—231no—
117C2×D4—461no—
118C22×C4—461no—
119C22×C4C4×D2311yescharacteristic
120C22×C4D9211yescharacteristic
121C22×C4C22⋊D2311yescharacteristic
122M16—24no—
123C2×C8—22no—
124C2×C8—464no—
125C2×C8—462no—
126C4⋊C4—231no—
127C4⋊C4—231no—
128C4⋊C4—461no—
129C4⋊C4—461no—
130C4⋊C4—461no—
131C4⋊C4—461no—
132C22⋊C4—461no—
133C22⋊C4—461no—
134C22⋊C4—461no—
135C22⋊C4—461no—
136C22⋊C4—461no—
137C42—461no—
138C42C4×D2311yescharacteristic
139C42D9211yescharacteristic
140C42C22⋊D2311yescharacteristic
141C42C22×D2311yescharacteristic
142C23—461no—
143C23(C2×D23)⋊C411yescharacteristic
144Q8—921no—
145D4—921no—
146D4—922no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—41no—
150C2×C4—461no—
151C2×C4—461no—
152C2×C4—461no—
153C2×C4—922no—
154C2×C4(C2×D23)⋊C411yescharacteristic
155C2×C4(C2×D23)⋊C411yescharacteristic
156C2×C4(C2×D23)⋊C411yescharacteristic
157C2×C4C2×C4×D2311yescharacteristic
158C2×C4C2×D9211yescharacteristic
159C2×C4C2×C22⋊D2311yescharacteristic
160C8—24no—
161C8—464no—
162C22—21no—
163C22—21no—
164C22—921no—
165C22—921no—
166C22—921no—
167C22#1062498712yes—
168C22C2×(C2×D23)⋊C411yescharacteristic
169C4—21no—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—921no—
175C4—921no—
176C4—921no—
177C4#1062500712yes—
178C2—22no—
179C2—1841no—
180C2#1309239911yescharacteristic
181C2C2×#1062500711yescharacteristic
182C2C2×#1062498711yescharacteristic
subgroupG/H
centerC2×C4(C2×D23)⋊C4
commutatorC2×C4×C23C22×C4
FrattiniC42C22×D23
FittingC4×M16×C23C2
socleC22×C23C2×C22⋊C4
prime radical#10625101C4
cosocleC42×C23C23
hypercenterC4×M16D23
hypocenterC23#1524
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. C2×#10624985C2semidirect
3. #13092158C2semidirect
4. #13092156C2semidirect
5. C4×M16×C23C2semidirect
88. C4×M16D23semidirect
114. C23#1524semidirect

Maximal subgroups

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

subgroupindex
#130929512
C2×#106249852
#130921582
#130921562
C4×M16×C232
#152423