Finite Group Databasebeta

← #15672397

Subgroups — #15672397

Order 2944.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#13093016C211yesmaximal, characteristic
2#13092745C211yesmaximal, characteristic, complemented
3#13092731C211yesmaximal, characteristic
4#13092349C211yesmaximal, characteristic, complemented
5#13092150C211yesmaximal, characteristic
6#13092142C211yesmaximal, characteristic, complemented
7C23×#328C211yesmaximal, characteristic, complemented
8C23×C22⋊Q8C2211yescharacteristic
9#10625117—21no—
10#10625101C2211yescharacteristic
11C2×C4⋊Dic23—21no—
12C2×C4⋊Dic23C2211yescharacteristic
13C2×Dic23⋊C4C2211yescharacteristic
14#10625069—21no—
15#10625065—21no—
16#10625061—21no—
17#10625057—21no—
18(C22⋊D23)⋊C4—21no—
19C23×C22⋊C8C2211yescharacteristic
20C23×#95C2211yescharacteristic
21#10625017—21no—
22C23⋊#95—21no—
23C22⋊(C23⋊C8)C2211yescharacteristic
24#10625003—21no—
25#10625000—21no—
26#10624990—21no—
27C2×Q8×C23D411yescharacteristic
28C22×C4×C23—21no—
29C22×C4×C23C2311yescharacteristic
30C2×C22⋊D23—21no—
31C22×Dic23—21no—
32C22×Dic23D411yescharacteristic
33C22×Dic23D411yescharacteristic
34C2×D92D411yescharacteristic
35C2×C4×D23—21no—
36C2×C8×C23—21no—
37C4⋊C4×C23—21no—
38C4⋊C4×C23D411yescharacteristic
39C22⋊C4×C23—21no—
40(C2×D23)⋊C4—21no—
41(C2×D23)⋊C4—21no—
42(C2×D23)⋊C4—21no—
43(C2×D23)⋊C4—21no—
44C4⋊Dic23—21no—
45C4⋊Dic23—21no—
46C4⋊Dic23—21no—
47C4⋊Dic23—21no—
48C4⋊Dic23—42no—
49C4⋊Dic23D411yescharacteristic
50Dic23⋊C4—21no—
51Dic23⋊C4—21no—
52Dic23⋊C4—21no—
53C4×Dic23—21no—
54C2×C23⋊C8—21no—
55C23×C23C2×D411yescharacteristic
56C22×D23—21no—
57Q8×C23—41no—
58C2×C4×C23—22no—
59C2×C4×C23—21no—
60C2×C4×C23—21no—
61C2×C4×C23—41no—
62C2×C4×C23—41no—
63C2×C4×C23—41no—
64C2×C4×C23C2×D411yescharacteristic
65C2×C4×C23C2×D411yescharacteristic
66C22⋊D23—41no—
67C22⋊D23—41no—
68C2×Dic23—21no—
69C2×Dic23—21no—
70C2×Dic23—21no—
71C2×Dic23—21no—
72C2×Dic23—21no—
73C2×Dic23—41no—
74C2×Dic23—41no—
75C2×Dic23—41no—
76C2×Dic23—41no—
77D92—41no—
78C4×D23—81no—
79C8×C23—41no—
80C23⋊C8—41no—
81#1609—231nomaximal, Sylow
82C22×C23—21no—
83C22×C23—21no—
84C22×C23#12011yescharacteristic
85C22×C23#13511yescharacteristic
86C22×C23AGL(1,ℤ/8)11yescharacteristic
87C2×D23—41no—
88C2×D23—41no—
89C2×D23—41no—
90C4×C23—21no—
91C4×C23—21no—
92C4×C23—42no—
93C4×C23—41no—
94C4×C23—41no—
95Dic23—41no—
96Dic23—41no—
97Dic23—41no—
98Dic23—81no—
99#539—231no—
100#483—231no—
101#480—231no—
102#398—231no—
103#328D2311yescharacteristic, complemented
104#327—231no—
105#324—231no—
106C2×C23—21no—
107C2×C23—21no—
108C2×C23#44911yescharacteristic
109C2×C23#45611yescharacteristic
110C2×C23#45811yescharacteristic
111D23—81no—
112#126—461no—
113#125—461no—
114#123—461no—
115#123—461no—
116C22⋊Q8—461no—
117C22⋊Q8C2×D2311yescharacteristic
118#121—231no—
119C4×D4—461no—
120C2×C4⋊C4—231no—
121C2×C4⋊C4—231no—
122C2×C4⋊C4—461no—
123#107—461no—
124#106—461no—
125#103—461no—
126#102—461no—
127C22⋊C8—231no—
128C22⋊C8C2×D2311yescharacteristic
129#95—461no—
130#95C2×D2311yescharacteristic
131C23#160911yescharacteristic, complemented, Sylow
132C2×Q8D9211yescharacteristic
133C2×D4—231no—
134C2×D4—461no—
135C22×C4—21no—
136C22×C4—231no—
137C22×C4—231no—
138C22×C4—461no—
139C22×C4—461no—
140C22×C4C22×D2311yescharacteristic
141C2×C8—21no—
142C2×C8—461no—
143C4⋊C4—21no—
144C4⋊C4—231no—
145C4⋊C4—461no—
146C4⋊C4—461no—
147C4⋊C4—461no—
148C4⋊C4—461no—
149C4⋊C4—461no—
150C4⋊C4—461no—
151C4⋊C4—461no—
152C4⋊C4—922no—
153C4⋊C4D9211yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—461no—
156C22⋊C4—461no—
157C22⋊C4—461no—
158C22⋊C4—461no—
159C42—461no—
160C23—461no—
161C23D4×D2311yescharacteristic
162Q8—41no—
163D4—921no—
164D4—921no—
165D4—921no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—461no—
173C2×C4—461no—
174C2×C4—461no—
175C2×C4—461no—
176C2×C4—461no—
177C2×C4—921no—
178C2×C4—921no—
179C2×C4—921no—
180C2×C4—921no—
181C2×C4—1841no—
182C2×C4C2×D9211yescharacteristic
183C2×C4D4×D2311yescharacteristic
184C8—41no—
185C8—921no—
186C22—21no—
187C22—21no—
188C22—921no—
189C22—921no—
190C22—921no—
191C22#1062505311yescharacteristic
192C22#1062508511yescharacteristic
193C22#1062509011yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—41no—
199C4—921no—
200C4—921no—
201C4—921no—
202C4—1841no—
203C2—21no—
204C2—21no—
205C2—1841no—
206C2#1309256511yescharacteristic
207C2#1309260111yescharacteristic
208C2#1309260811yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#328C2
socleC22×C23#120
prime radical#10625101C22
hypercenter#328D23
hypocenterC23#1609
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
2. #13092745C2semidirect
4. #13092349C2semidirect
6. #13092142C2semidirect
7. C23×#328C2semidirect
103. #328D23semidirect
131. C23#1609semidirect

Maximal subgroups

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

subgroupindex
#130930162
#130927452
#130927312
#130923492
#130921502
#130921422
C23×#3282
#160923