Finite Group Databasebeta

← #15672406

Subgroups — #15672406

Order 2944.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#13093046C211yesmaximal, characteristic
2#13092748C211yesmaximal, characteristic
3#13092745C211yesmaximal, characteristic
4#13092349C211yesmaximal, characteristic
5#13092153C211yesmaximal, characteristic
6#13092142C211yesmaximal, characteristic
7C23×#328C211yesmaximal, characteristic
8C23×C22⋊Q8C2211yescharacteristic
9#10625115—21no—
10C2×C4⋊Dic23—21no—
11C2×C4⋊Dic23C2211yescharacteristic
12#10625095C2211yescharacteristic
13C2×Dic23⋊C4C2211yescharacteristic
14#10625060—21no—
15#10625060—21no—
16#10625059—21no—
17#10625049—21no—
18#10625048—21no—
19C23×C22⋊C8C2211yescharacteristic
20C23×#95C2211yescharacteristic
21#10625017—21no—
22C23⋊#95—21no—
23C22⋊(C23⋊C8)C2211yescharacteristic
24#10624999—21no—
25#10624998—21no—
26#10624990—21no—
27C2×Q8×C23D411yescharacteristic
28C22×C4×C23—21no—
29C22×C4×C23C2311yescharacteristic
30C22×Dic23—21no—
31C22×Dic23D411yescharacteristic
32C22×Dic23D411yescharacteristic
33C2×Dic46—21no—
34C2×Dic46D411yescharacteristic
35C2×C8×C23—21no—
36C4⋊C4×C23—21no—
37C4⋊C4×C23D411yescharacteristic
38C22⋊C4×C23—21no—
39C22⋊Dic23—21no—
40C4⋊Dic23—21no—
41C4⋊Dic23—21no—
42C4⋊Dic23—21no—
43C4⋊Dic23—42no—
44C4⋊Dic23D411yescharacteristic
45Dic23⋊C4—21no—
46Dic23⋊C4—21no—
47Dic23⋊C4—21no—
48Dic23⋊C4—21no—
49Dic23⋊C4—21no—
50Dic23⋊C4—21no—
51Dic23⋊C4—21no—
52C4×Dic23—21no—
53C4×Dic23—21no—
54C2×C23⋊C8—21no—
55C23×C23C2×D411yescharacteristic
56Q8×C23—41no—
57C2×C4×C23—22no—
58C2×C4×C23—21no—
59C2×C4×C23—21no—
60C2×C4×C23—41no—
61C2×C4×C23—41no—
62C2×C4×C23—41no—
63C2×C4×C23C2×D411yescharacteristic
64C2×C4×C23C2×D411yescharacteristic
65C2×Dic23—21no—
66C2×Dic23—21no—
67C2×Dic23—21no—
68C2×Dic23—21no—
69C2×Dic23—21no—
70C2×Dic23—41no—
71C2×Dic23—41no—
72C2×Dic23—41no—
73C2×Dic23—41no—
74C2×Dic23SD1612yes—
75Dic46—41no—
76Dic46—81no—
77C8×C23—41no—
78C23⋊C8—41no—
79#1611—231nomaximal, Sylow
80C22×C23—21no—
81C22×C23—21no—
82C22×C23#12011yescharacteristic
83C22×C23C2×SD1611yescharacteristic
84C22×C23#13711yescharacteristic
85C4×C23—21no—
86C4×C23—21no—
87C4×C23—42no—
88C4×C23—41no—
89C4×C23—41no—
90Dic23—22no—
91Dic23—41no—
92Dic23—41no—
93Dic23—41no—
94Dic23—81no—
95#544—231no—
96#483—231no—
97#483—231no—
98#398—231no—
99#328—231no—
100#328D2311yescharacteristic
101#324—231no—
102C2×C23—21no—
103C2×C23—21no—
104C2×C23#44811yescharacteristic
105C2×C23#45611yescharacteristic
106C2×C23#45811yescharacteristic
107C4⋊Q8—461no—
108C4⋊Q8—461no—
109#125—461no—
110#125—461no—
111C22⋊Q8—231no—
112C22⋊Q8—461no—
113C22⋊Q8C2×D2311yescharacteristic
114#117—461no—
115C2×C4⋊C4—231no—
116C2×C4⋊C4—231no—
117C2×C4⋊C4—461no—
118#106—461no—
119#106—461no—
120#103—461no—
121#103—461no—
122C22⋊C8—231no—
123C22⋊C8C2×D2311yescharacteristic
124#95—461no—
125#95C2×D2311yescharacteristic
126C23#161111yescharacteristic, complemented, Sylow
127C2×Q8—231no—
128C2×Q8—461no—
129C2×Q8D9211yescharacteristic
130C22×C4—21no—
131C22×C4—231no—
132C22×C4—231no—
133C22×C4—461no—
134C22×C4C22×D2311yescharacteristic
135C2×C8—21no—
136C2×C8—461no—
137C4⋊C4—21no—
138C4⋊C4—231no—
139C4⋊C4—461no—
140C4⋊C4—461no—
141C4⋊C4—461no—
142C4⋊C4—461no—
143C4⋊C4—461no—
144C4⋊C4—461no—
145C4⋊C4—461no—
146C4⋊C4—461no—
147C4⋊C4—461no—
148C4⋊C4—461no—
149C4⋊C4—922no—
150C4⋊C4D9211yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—461no—
153C42—461no—
154C42—461no—
155C23D4×D2311yescharacteristic
156Q8—41no—
157Q8—921no—
158Q8—1841no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—232no—
166C2×C4—461no—
167C2×C4—461no—
168C2×C4—461no—
169C2×C4—461no—
170C2×C4—461no—
171C2×C4—921no—
172C2×C4—921no—
173C2×C4—921no—
174C2×C4—921no—
175C2×C4C2×D9211yescharacteristic
176C2×C4D4×D2311yescharacteristic
177C8—41no—
178C8—921no—
179C22—21no—
180C22—21no—
181C22#1062505311yescharacteristic
182C22SD16×D2311yescharacteristic
183C22#1062508911yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—462no—
190C4—921no—
191C4—921no—
192C4—921no—
193C4—1841no—
194C2—21no—
195C2—21no—
196C2#1309255711yescharacteristic
197C2#1309260111yescharacteristic
198C2#1309260811yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#328C2
socleC22×C23#120
prime radicalC23×C23C2×D4
hypercenter#328D23
hypocenterC23#1611
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
126. C23#1611semidirect

Maximal subgroups

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

subgroupindex
#130930462
#130927482
#130927452
#130923492
#130921532
#130921422
C23×#3282
#161123