Finite Group Databasebeta

← #15672396

Subgroups — #15672396

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#13093014C211yesmaximal, characteristic
2#13092748C211yesmaximal, characteristic, complemented
3#13092731C211yesmaximal, characteristic
4#13092347C211yesmaximal, characteristic, complemented
5#13092155C211yesmaximal, characteristic, complemented
6#13092152C211yesmaximal, characteristic
7C23×#324C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×C23C2211yescharacteristic
9#10625101C2211yescharacteristic
10#10625100—21no—
11C4×C22⋊D23—21no—
12C2×C4⋊Dic23C2211yescharacteristic
13#10625095C2211yescharacteristic
14C2×Dic23⋊C4—21no—
15#10625069—21no—
16#10625067—21no—
17#10625065—21no—
18#10625060—21no—
19C23×C22⋊C8C2211yescharacteristic
20C23×C22⋊C8C2211yescharacteristic
21C23⋊#95—21no—
22C23⋊#95C2211yescharacteristic
23#10625003—21no—
24#10625000—21no—
25#10624999—21no—
26#10624998—21no—
27C22×C4×C23D411yescharacteristic
28C22×C4×C23D411yescharacteristic
29C22×C4×C23C2311yescharacteristic
30C2×C22⋊D23—21no—
31C22×Dic23—21no—
32C22×Dic23—21no—
33C2×D92D411yescharacteristic
34C2×C4×D23—21no—
35C2×Dic46D411yescharacteristic
36C2×C8×C23—21no—
37C2×C8×C23—21no—
38C4⋊C4×C23—21no—
39C4⋊C4×C23—21no—
40C22⋊Dic23—21no—
41(C2×D23)⋊C4—21no—
42(C2×D23)⋊C4—21no—
43(C2×D23)⋊C4—21no—
44(C2×D23)⋊C4—21no—
45C4⋊Dic23—21no—
46C4⋊Dic23—21no—
47C4⋊Dic23D411yescharacteristic
48C4⋊Dic23D411yescharacteristic
49Dic23⋊C4—21no—
50Dic23⋊C4—21no—
51Dic23⋊C4—21no—
52Dic23⋊C4—21no—
53Dic23⋊C4—42no—
54C4×Dic23—21no—
55C23×C23C2×D411yescharacteristic
56C22×D23—21no—
57C2×C4×C23—21no—
58C2×C4×C23—21no—
59C2×C4×C23—21no—
60C2×C4×C23—21no—
61C2×C4×C23—41no—
62C2×C4×C23—41no—
63C2×C4×C23C2×D411yescharacteristic
64C2×C4×C23C2×D411yescharacteristic
65C22⋊D23—41no—
66C22⋊D23—41no—
67C2×Dic23—22no—
68C2×Dic23—21no—
69C2×Dic23—21no—
70C2×Dic23—21no—
71C2×Dic23—41no—
72C2×Dic23—41no—
73C2×Dic23—41no—
74C2×Dic23—41no—
75C2×Dic23—41no—
76D92—41no—
77C4×D23—81no—
78Dic46—41no—
79C8×C23—41no—
80C8×C23—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—41no—
93C4×C23—41no—
94Dic23—42no—
95Dic23—41no—
96Dic23—41no—
97Dic23—41no—
98Dic23—81no—
99#539—231no—
100#483—231no—
101#480—231no—
102#398—231no—
103#328—231no—
104#327—231no—
105#324D2311yescharacteristic, complemented
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—231no—
117C22⋊Q8—461no—
118#121—231no—
119C4×D4—461no—
120C2×C4⋊C4—231no—
121C2×C4⋊C4—461no—
122C2×C4⋊C4C2×D2311yescharacteristic
123#107—461no—
124#106—461no—
125#103—461no—
126#102—461no—
127C22⋊C8C2×D2311yescharacteristic
128C22⋊C8C2×D2311yescharacteristic
129#95—231no—
130#95—461no—
131C23#160911yescharacteristic, complemented, Sylow
132C2×Q8—231no—
133C2×D4—231no—
134C2×D4—461no—
135C22×C4—461no—
136C22×C4—461no—
137C22×C4—461no—
138C22×C4D9211yescharacteristic
139C22×C4D9211yescharacteristic
140C22×C4C22×D2311yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—231no—
146C4⋊C4—231no—
147C4⋊C4—461no—
148C4⋊C4—461no—
149C4⋊C4—461no—
150C4⋊C4—461no—
151C4⋊C4—461no—
152C4⋊C4—461no—
153C4⋊C4—922no—
154C22⋊C4—461no—
155C22⋊C4—461no—
156C22⋊C4—461no—
157C22⋊C4—461no—
158C22⋊C4—461no—
159C42—461no—
160C23—461no—
161C23C2×D9211yescharacteristic
162Q8—921no—
163D4—921no—
164D4—921no—
165D4—921no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—462no—
173C2×C4—461no—
174C2×C4—461no—
175C2×C4—461no—
176C2×C4—921no—
177C2×C4—921no—
178C2×C4—921no—
179C2×C4—921no—
180C2×C4—921no—
181C2×C4—1841no—
182C2×C4D4×D2311yescharacteristic
183C2×C4D4×D2311yescharacteristic
184C8—41no—
185C8—41no—
186C22—21no—
187C22—21no—
188C22—921no—
189C22—921no—
190C22—921no—
191C22#1062505311yescharacteristic
192C22#1062507511yescharacteristic
193C22#1062507911yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—41no—
198C4—922no—
199C4—921no—
200C4—921no—
201C4—921no—
202C4—1841no—
203C2—21no—
204C2—21no—
205C2—1841no—
206C2#1309256411yescharacteristic
207C2#1309260211yescharacteristic
208C2#1309260811yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#324C2
socleC22×C23#120
prime radical#10625101C22
hypercenter#324D23
hypocenterC23#1609
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #13092748C2semidirect
4. #13092347C2semidirect
5. #13092155C2semidirect
7. C23×#324C2semidirect
105. #324D23semidirect
131. C23#1609semidirect

Maximal subgroups

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

subgroupindex
#130930142
#130927482
#130927312
#130923472
#130921552
#130921522
C23×#3242
#160923