Finite Group Databasebeta

← #15673787

Subgroups — #15673787

Order 2944.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#10625115C211yesmaximal, characteristic
2#13092894C211yesmaximal, characteristic
3#13092426C211yesmaximal, characteristic
4C2×#10625006C211yesmaximal, characteristic
5#13092178C211yesmaximal, characteristic
6#13092176C211yesmaximal, characteristic
7C23×#419C211yesmaximal, characteristic
8C22×Q8×C23C2211yescharacteristic
9C22×Dic46C2211yescharacteristic
10C2×M16×C23C2211yescharacteristic
11C23×#117C2211yescharacteristic
12#10625115—22no—
13#10625115C414yescomplemented
14#10625097C2211yescharacteristic
15C2×Dic23⋊C4—22no—
16C2×C4×Dic23C2211yescharacteristic
17C2×#67267C2211yescharacteristic
18#10625058—22no—
19#10625048—22no—
20C4×Dic46—22no—
21C23×#103—22no—
22#10625017—22no—
23#10625006—22no—
24C2×Q8×C23—21no—
25C2×Q8×C23—21no—
26C2×Q8×C23—21no—
27C2×Q8×C23—21no—
28C2×Q8×C23—21no—
29C2×Q8×C23C2×C412yes—
30C22×C4×C23—21no—
31C22×C4×C23C2311yescharacteristic
32C22×Dic23—21no—
33C22×Dic23D412yes—
34C2×Dic46—21no—
35C2×Dic46—21no—
36C2×Dic46—21no—
37C2×Dic46—21no—
38C2×Dic46C2×C412yes—
39C2×Dic46D412yes—
40M16×C23—21no—
41M16×C23—21no—
42C2×C8×C23—21no—
43C4⋊C4×C23D412yes—
44C22⋊C4×C23—21no—
45C42×C23—21no—
46C22⋊Dic23—21no—
47C4⋊Dic23D412yes—
48Dic23⋊C4—24no—
49Dic23⋊C4—28no—
50C4×Dic23—24no—
51C4×Dic23—21no—
52C4×Dic23—21no—
53C4×Dic23C2×C412yes—
54#67267—21no—
55#67267—21no—
56C2×C23⋊C8—21no—
57C23×C23C2×D411yescharacteristic
58Q8×C23—22no—
59Q8×C23—22no—
60Q8×C23—41no—
61Q8×C23—41no—
62C2×C4×C23—22no—
63C2×C4×C23—22no—
64C2×C4×C23—41no—
65C2×C4×C23—41no—
66C2×C4×C23C22×C411yescharacteristic
67C2×C4×C23C2×D411yescharacteristic
68C2×C4×C23C2×D411yescharacteristic
69C2×C4×C23C2×D411yescharacteristic
70C2×C4×C23#4111yescharacteristic
71C2×C4×C23#4111yescharacteristic
72C2×Dic23—24no—
73C2×Dic23—22no—
74C2×Dic23—22no—
75C2×Dic23—22no—
76C2×Dic23—22no—
77C2×Dic23C22⋊C414yes—
78Dic46—22no—
79Dic46—22no—
80Dic46—22no—
81Dic46—22no—
82C8×C23—41no—
83C23⋊C8—41no—
84#1886—231nomaximal, Sylow
85C22×C23—22no—
86C22×C23C2×C22⋊C411yescharacteristic
87C22×C23#12011yescharacteristic
88C22×C23#12311yescharacteristic
89C4×C23—42no—
90C4×C23—42no—
91C4×C23C4×D411yescharacteristic
92C4×C23C4×D411yescharacteristic
93C4×C23#12111yescharacteristic
94C4×C23#12111yescharacteristic
95Dic23—24no—
96Dic23—24no—
97Dic23—42no—
98C2×C4⋊Q8—231no—
99#519—231no—
100#419—231no—
101#419D2311yescharacteristic
102C2×#101—231no—
103#339—231no—
104#339—231no—
105C2×C23—21no—
106C2×C23—21no—
107C2×C23#38611yescharacteristic
108C2×C23#45612yes—
109C22×Q8—231no—
110C22×Q8C2×D2311yescharacteristic
111C2×M16—231no—
112C2×M16C2×D2311yescharacteristic
113C4⋊Q8—234no—
114C4⋊Q8—462no—
115C4×Q8—462no—
116C4×Q8—462no—
117#117—231no—
118#117—462no—
119#117C2×D2311yescharacteristic
120C2×C4⋊C4—462no—
121C2×C42—231no—
122#103—22no—
123#103—462no—
124#101—462no—
125C23#188611yescharacteristic, complemented, Sylow
126C2×Q8—21no—
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—232no—
132C2×Q8—232no—
133C2×Q8—461no—
134C2×Q8—461no—
135C2×Q8—461no—
136C2×Q8—461no—
137C2×Q8C4×D2312yes—
138C22×C4—21no—
139C22×C4—232no—
140C22×C4—461no—
141C22×C4C22×D2311yescharacteristic
142M16—21no—
143M16—21no—
144M16—461no—
145M16—461no—
146C2×C8—21no—
147C2×C8—461no—
148C4⋊C4—232no—
149C4⋊C4—468no—
150C4⋊C4—464no—
151C4⋊C4C22⋊D2312yes—
152C22⋊C4—21no—
153C22⋊C4—461no—
154C42—21no—
155C42—232no—
156C42—464no—
157C42—461no—
158C42—461no—
159C23D4×D2311yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—41no—
163Q8—41no—
164Q8—462no—
165Q8—462no—
166Q8—462no—
167Q8—462no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—234no—
173C2×C4—464no—
174C2×C4—462no—
175C2×C4—462no—
176C2×C4—462no—
177C2×C4—462no—
178C2×C4C2×C4×D2311yescharacteristic
179C2×C4#6728811yescharacteristic
180C2×C4D4×D2311yescharacteristic
181C2×C4D4×D2311yescharacteristic
182C2×C4#6729011yescharacteristic
183C2×C4C2×C22⋊D2311yescharacteristic
184C8—41no—
185C8—921no—
186C22—22no—
187C22C22⋊C4×D2311yescharacteristic
188C22#1062505411yescharacteristic
189C22#1062510811yescharacteristic
190C4—42no—
191C4—42no—
192C4—464no—
193C4—464no—
194C4—922no—
195C4(C22⋊D23)⋊C411yescharacteristic
196C4#1062505511yescharacteristic
197C4C4×C22⋊D2311yescharacteristic
198C4#1062510911yescharacteristic
199C2—21no—
200C2—21no—
201C2#1309229311yescharacteristic
202C2#1309259812yes—
subgroupG/H
centerC22#10625108
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#419C2
socleC22×C23#120
prime radicalC23×C23C2×D4
cosocleC22×C4×C23C23
hypercenter#419D23
hypocenterC23#1886
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
13. #10625115C4semidirect
125. C23#1886semidirect

Maximal subgroups

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

subgroupindex
C2×#106251152
#130928942
#130924262
C2×#106250062
#130921782
#130921762
C23×#4192
#188623