Finite Group Databasebeta

← #15672419

Subgroups — #15672419

Order 2944.

288 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 53 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#13092979C211yesmaximal, characteristic
2#13092736C212yesmaximal, complemented
3#13092353C211yesmaximal, characteristic, complemented
4#13092152C212yesmaximal, complemented
5C23×#323C211yesmaximal, characteristic, complemented
6C22×C22⋊D23—21no—
7C2×C22⋊C4×C23C2211yescharacteristic
8C2×C22⋊Dic23—21no—
9#10625101—21no—
10#10625101C2212yes—
11C2×C4⋊Dic23C2211yescharacteristic, complemented
12C2×Dic23⋊C4—21no—
13#10625057—22no—
14#10625053—22no—
15C23×C22⋊C8C2212yescomplemented
16C23⋊#95C2211yescharacteristic, complemented
17#10625003—22no—
18#10624999—22no—
19C24×C23D411yescharacteristic
20C23×D23—21no—
21C22×C4×C23D411yescharacteristic
22C22×C4×C23C2311yescharacteristic
23C2×C22⋊D23—22no—
24C2×C22⋊D23—22no—
25C2×C22⋊D23—42no—
26C2×C22⋊D23—42no—
27C22×Dic23—21no—
28C22×Dic23—21no—
29C22×Dic23—21no—
30C2×D92—21no—
31C2×D92D412yes—
32C2×C8×C23—22no—
33C22⋊C4×C23—22no—
34C22⋊Dic23—42no—
35(C2×D23)⋊C4—22no—
36(C2×D23)⋊C4—22no—
37C4⋊Dic23—21no—
38C4⋊Dic23—22no—
39C4⋊Dic23D412yes—
40Dic23⋊C4—42no—
41C23×C23—21no—
42C23×C23—21no—
43C23×C23—41no—
44C23×C23—41no—
45C23×C23SD1612yes—
46C23×C23C2×D411yescharacteristic
47C22×D23—22no—
48C22×D23—42no—
49C22×D23—81no—
50C22×D23—81no—
51C2×C4×C23—21no—
52C2×C4×C23—41no—
53C2×C4×C23—41no—
54C2×C4×C23C2×D412yes—
55C22⋊D23—44no—
56C22⋊D23—42no—
57C22⋊D23—42no—
58C2×Dic23—22no—
59C2×Dic23—22no—
60C2×Dic23—41no—
61C2×Dic23—42no—
62C2×Dic23—41no—
63C2×Dic23—41no—
64C2×Dic23—41no—
65C2×Dic23—41no—
66D92—42no—
67D92—81no—
68C8×C23—42no—
69#1613—231nomaximal, Sylow
70C22×C23—21no—
71C22×C23—21no—
72C22×C23—22no—
73C22×C23—42no—
74C22×C23—41no—
75C22×C23—41no—
76C22×C23—81no—
77C22×C23#12011yescharacteristic
78C22×C23C2×SD1611yescharacteristic
79C22×C23AGL(1,ℤ/8)11yescharacteristic
80C2×D23—42no—
81C2×D23—42no—
82C2×D23—42no—
83C2×D23—84no—
84C4×C23—22no—
85C4×C23—41no—
86Dic23—42no—
87Dic23—42no—
88Dic23—81no—
89#534—231no—
90#481—232no—
91#399—231no—
92#327—232no—
93#323D2311yescharacteristic, complemented
94C2×C23—21no—
95C2×C23—21no—
96C2×C23—42no—
97C2×C23#45011yescharacteristic
98C2×C23#45311yescharacteristic
99C2×C23#45811yescharacteristic
100D23—82no—
101C22×D4—461no—
102#123—462no—
103#121—232no—
104#121—461no—
105#120—462no—
106C2×C4⋊C4—231no—
107C2×C4⋊C4—461no—
108C2×C22⋊C4—461no—
109C2×C22⋊C4C2×D2311yescharacteristic
110#106—462no—
111#102—462no—
112C22⋊C8C2×D2312yescomplemented
113#95—231no—
114C23#161311yescharacteristic, complemented, Sylow
115C24—461no—
116C24D9211yescharacteristic
117C2×D4—232no—
118C2×D4—461no—
119C2×D4—462no—
120C2×D4—462no—
121C2×D4—922no—
122C2×D4—922no—
123C22×C4—461no—
124C22×C4—461no—
125C22×C4—461no—
126C22×C4D9211yescharacteristic
127C22×C4C22×D2311yescharacteristic
128C2×C8—22no—
129C4⋊C4—232no—
130C4⋊C4—461no—
131C4⋊C4—462no—
132C4⋊C4—922no—
133C22⋊C4—22no—
134C22⋊C4—462no—
135C22⋊C4—462no—
136C22⋊C4—922no—
137C23—21no—
138C23—21no—
139C23—41no—
140C23—41no—
141C23—462no—
142C23—922no—
143C23—1841no—
144C23—1841no—
145C23#6726312yes—
146C23C2×D9211yescharacteristic
147D4—922no—
148D4—924no—
149D4—922no—
150D4—922no—
151D4—1841no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—462no—
156C2×C4—462no—
157C2×C4—922no—
158C2×C4—921no—
159C2×C4—921no—
160C2×C4—921no—
161C2×C4—921no—
162C2×C4—921no—
163C2×C4D4×D2312yes—
164C8—42no—
165C22—21no—
166C22—21no—
167C22—22no—
168C22—42no—
169C22—41no—
170C22—41no—
171C22—81no—
172C22—922no—
173C22—922no—
174C22—922no—
175C22—1844no—
176C22#1062505311yescharacteristic
177C22C2×#6726311yescharacteristic
178C22#1062507911yescharacteristic
179C4—22no—
180C4—41no—
181C4—922no—
182C4—922no—
183C4—1841no—
184C2—21no—
185C2—21no—
186C2—42no—
187C2—1842no—
188C2#1309257011yescharacteristic
189C2#1309258711yescharacteristic
190C2#1309260811yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#323C2
socleC22×C23#120
prime radical#13092979C2
hypercenter#323D23
hypocenterC23#1613
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #13092736C2semidirect
3. #13092353C2semidirect
4. #13092152C2semidirect
5. C23×#323C2semidirect
11. C2×C4⋊Dic23C22semidirect
15. C23×C22⋊C8C22semidirect
16. C23⋊#95C22semidirect
93. #323D23semidirect
112. C22⋊C8C2×D23semidirect
114. C23#1613semidirect

Maximal subgroups

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

subgroupindex
#130929792
#130927362
#130923532
#130921522
C23×#3232
#161323