Finite Group Databasebeta

← #15672433

Subgroups — #15672433

Order 2944.

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

normal subgroups only

This group has 246 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#13092998C211yesmaximal, characteristic
2#13092735C212yesmaximal, complemented
3#13092150C212yesmaximal, complemented
4#13092143C211yesmaximal, characteristic, complemented
5C23×#400C211yesmaximal, characteristic, complemented
6C2×#67288—21no—
7C2×C4⋊C4×C23C2211yescharacteristic
8C2×C4⋊C4×C23C2211yescharacteristic
9#10625101—21no—
10#10625101C2212yes—
11#10625068—22no—
12#10625066—22no—
13C23×#95—21no—
14C23×#95—21no—
15C23×#95C2211yescharacteristic
16C22⋊(C23⋊C8)C2212yes—
17#10624991—22no—
18#10624990—22no—
19C22×C4×C23—21no—
20C22×C4×C23—21no—
21C22×C4×C23D411yescharacteristic
22C22×C4×C23D411yescharacteristic
23C22×C4×C23C2311yescharacteristic
24C2×C22⋊D23—22no—
25#67288—42no—
26#67288—42no—
27C2×D92—21no—
28C2×D92—21no—
29C2×D92D412yes—
30C2×C4×D23—22no—
31C2×Dic46—21no—
32C4⋊C4×C23—22no—
33C4⋊C4×C23—22no—
34(C2×D23)⋊C4—22no—
35(C2×D23)⋊C4—22no—
36C4⋊Dic23—21no—
37C4⋊Dic23D412yes—
38C2×C23⋊C8—22no—
39C23×C23C2×D411yescharacteristic
40C22×D23—22no—
41C2×C4×C23—21no—
42C2×C4×C23—21no—
43C2×C4×C23—21no—
44C2×C4×C23—41no—
45C2×C4×C23—41no—
46C2×C4×C23—41no—
47C2×C4×C23—41no—
48C2×C4×C23—42no—
49C2×C4×C23—41no—
50C2×C4×C23—41no—
51C2×C4×C23SD1612yes—
52C2×C4×C23C2×D412yes—
53C22⋊D23—42no—
54C22⋊D23—42no—
55C2×Dic23—22no—
56D92—42no—
57D92—42no—
58D92—81no—
59C4×D23—44no—
60Dic46—42no—
61C23⋊C8—42no—
62#1616—231nomaximal, Sylow
63C22×C23—21no—
64C22×C23—21no—
65C22×C23#12011yescharacteristic
66C22×C23C2×SD1611yescharacteristic
67C22×C23AGL(1,ℤ/8)11yescharacteristic
68C2×D23—42no—
69C2×D23—42no—
70C2×D23—42no—
71C4×C23—22no—
72C4×C23—22no—
73C4×C23—41no—
74C4×C23—81no—
75C4×C23—81no—
76Dic23—42no—
77#537—231no—
78#481—232no—
79#400D2311yescharacteristic, complemented
80#327—232no—
81#324—231no—
82C2×C23—21no—
83C2×C23—21no—
84C2×C23#45011yescharacteristic
85C2×C23#45411yescharacteristic
86C2×C23#45811yescharacteristic
87D23—82no—
88C2×#41—461no—
89C22⋊Q8—462no—
90#121—232no—
91#121—462no—
92#121—461no—
93C2×C4⋊C4C2×D2311yescharacteristic
94C2×C4⋊C4C2×D2311yescharacteristic
95#106—462no—
96#102—462no—
97C22⋊C8—232no—
98#95—21no—
99#95—21no—
100#95C2×D2311yescharacteristic
101C23#161611yescharacteristic, complemented, Sylow
102#41—922no—
103#41—922no—
104C2×Q8—461no—
105C2×D4—232no—
106C2×D4—461no—
107C2×D4—461no—
108C2×D4—462no—
109C22×C4—21no—
110C22×C4—21no—
111C22×C4—462no—
112C22×C4C22⋊D2311yescharacteristic
113C22×C4C22⋊D2311yescharacteristic
114C22×C4C22×D2311yescharacteristic
115C2×C8—462no—
116C4⋊C4—22no—
117C4⋊C4—22no—
118C4⋊C4—232no—
119C4⋊C4—461no—
120C22⋊C4—462no—
121C22⋊C4—462no—
122C23—462no—
123C23C2×C22⋊D2311yescharacteristic
124Q8—922no—
125D4—922no—
126D4—922no—
127D4—922no—
128D4—922no—
129D4—1841no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—462no—
141C2×C4—924no—
142C2×C4#6727412yes—
143C2×C4D4×D2312yes—
144C8—922no—
145C22—21no—
146C22—21no—
147C22—922no—
148C22—922no—
149C22—922no—
150C22#1062510811yescharacteristic
151C22C2×#6727411yescharacteristic
152C22#1062512011yescharacteristic
153C4—22no—
154C4—22no—
155C4—41no—
156C4—81no—
157C4—81no—
158C4—922no—
159C2—21no—
160C2—21no—
161C2—1842no—
162C2#1309256711yescharacteristic
163C2#1309258911yescharacteristic
164C2#1309260611yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#400C2
socleC22×C23#120
prime radical#13092998C2
hypercenter#400D23
hypocenterC23#1616
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
2. #13092735C2semidirect
3. #13092150C2semidirect
4. #13092143C2semidirect
5. C23×#400C2semidirect
79. #400D23semidirect
101. C23#1616semidirect

Maximal subgroups

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

subgroupindex
#130929982
#130927352
#130921502
#130921432
C23×#4002
#161623