Finite Group Databasebeta

← #15672422

Subgroups — #15672422

Order 2944.

236 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 57 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#13092750C212yesmaximal, complemented
2#13092353C211yesmaximal, characteristic
3#13092154C212yesmaximal, complemented
4#13092141C211yesmaximal, characteristic
5C23×#543C211yesmaximal, characteristic
6C23×C22⋊Q8—22no—
7C23×C22⋊Q8—21no—
8C23×C22⋊Q8—22no—
9C23×C22⋊Q8C2212yes—
10C2×C22⋊C4×C23—21no—
11C2×C22⋊C4×C23C2211yescharacteristic
12C2×C22⋊Dic23—21no—
13C2×C4⋊Dic23C2211yescharacteristic
14C2×Dic23⋊C4—21no—
15#10625017—22no—
16C23⋊#95C2211yescharacteristic
17C22⋊(C23⋊C8)C2212yes—
18#10624989—22no—
19C24×C23D411yescharacteristic
20C2×Q8×C23—21no—
21C2×Q8×C23D412yes—
22C22×C4×C23—21no—
23C22×C4×C23—21no—
24C22×C4×C23D411yescharacteristic
25C22×C4×C23C2311yescharacteristic
26C22×Dic23—21no—
27C22×Dic23—21no—
28C4⋊C4×C23—21no—
29C4⋊C4×C23—22no—
30C4⋊C4×C23—22no—
31C4⋊C4×C23D412yes—
32C22⋊C4×C23—22no—
33C22⋊C4×C23—22no—
34C22⋊C4×C23—22no—
35C22⋊Dic23—42no—
36C4⋊Dic23—22no—
37Dic23⋊C4—42no—
38C2×C23⋊C8—22no—
39C23×C23—21no—
40C23×C23—21no—
41C23×C23—41no—
42C23×C23—41no—
43C23×C23Q1612yes—
44C23×C23C2×D411yescharacteristic
45Q8×C23—42no—
46Q8×C23—81no—
47C2×C4×C23—22no—
48C2×C4×C23—21no—
49C2×C4×C23—22no—
50C2×C4×C23—41no—
51C2×C4×C23—41no—
52C2×C4×C23—81no—
53C2×C4×C23—81no—
54C2×C4×C23C2×D412yes—
55C2×Dic23—22no—
56C2×Dic23—41no—
57C2×Dic23—41no—
58C2×Dic23—41no—
59C2×Dic23—41no—
60C2×Dic23—41no—
61C23⋊C8—42no—
62#1614—231nomaximal, Sylow
63C22×C23—21no—
64C22×C23—21no—
65C22×C23—22no—
66C22×C23—42no—
67C22×C23—41no—
68C22×C23—41no—
69C22×C23—81no—
70C22×C23#12011yescharacteristic
71C22×C23C2×Q1611yescharacteristic
72C22×C23#13711yescharacteristic
73C4×C23—22no—
74C4×C23—41no—
75C4×C23—42no—
76C4×C23—42no—
77Dic23—42no—
78Dic23—81no—
79#543D2311yescharacteristic
80#484—232no—
81#399—231no—
82#328—232no—
83#323—231no—
84C2×C23—21no—
85C2×C23—21no—
86C2×C23—42no—
87C2×C23#45111yescharacteristic
88C2×C23#45311yescharacteristic
89C2×C23#45811yescharacteristic
90C22⋊Q8—22no—
91C22⋊Q8—21no—
92C22⋊Q8—22no—
93C22⋊Q8C2×D2312yes—
94C2×C4⋊C4—231no—
95C2×C4⋊C4—461no—
96C2×C22⋊C4—21no—
97C2×C22⋊C4—461no—
98C2×C22⋊C4C2×D2311yescharacteristic
99#107—462no—
100#103—462no—
101C22⋊C8—232no—
102#95—231no—
103C23#161411yescharacteristic, complemented, Sylow
104C24C22⋊D2311yescharacteristic
105C2×Q8—21no—
106C2×Q8C22⋊D2312yes—
107C22×C4—21no—
108C22×C4—21no—
109C22×C4—461no—
110C22×C4—461no—
111C22×C4C22⋊D2311yescharacteristic
112C22×C4C22×D2311yescharacteristic
113C2×C8—462no—
114C4⋊C4—21no—
115C4⋊C4—22no—
116C4⋊C4—22no—
117C4⋊C4—462no—
118C4⋊C4—922no—
119C4⋊C4C22⋊D2312yes—
120C22⋊C4—22no—
121C22⋊C4—22no—
122C22⋊C4—22no—
123C22⋊C4—922no—
124C23—21no—
125C23—21no—
126C23—41no—
127C23—41no—
128C23#6727512yes—
129C23C2×C22⋊D2311yescharacteristic
130Q8—42no—
131Q8—81no—
132C2×C4—22no—
133C2×C4—21no—
134C2×C4—22no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—81no—
138C2×C4—81no—
139C2×C4—462no—
140C2×C4—921no—
141C2×C4—921no—
142C2×C4—921no—
143C2×C4—921no—
144C2×C4—921no—
145C2×C4C2×C22⋊D2312yes—
146C8—922no—
147C22—21no—
148C22—21no—
149C22—22no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22—81no—
154C22#1062511311yescharacteristic
155C22C2×#6727511yescharacteristic
156C22#1062512411yescharacteristic
157C4—22no—
158C4—41no—
159C4—42no—
160C4—42no—
161C4—922no—
162C4—1841no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2#1309257311yescharacteristic
167C2#1309258511yescharacteristic
168C2#1309260711yescharacteristic
subgroupG/H
centerC22#10625124
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#543C2
socleC22×C23#120
prime radicalC24×C23D4
hypercenter#543D23
hypocenterC23#1614
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #543

Complements

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

NH ≅ G/Ntype
1. #13092750C2semidirect
3. #13092154C2semidirect
103. C23#1614semidirect

Maximal subgroups

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

subgroupindex
#130927502
#130923532
#130921542
#130921412
C23×#5432
#161423