Finite Group Databasebeta

← #15674618

Subgroups — #15674618

Order 2944.

306 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C2×#10625019C212yesmaximal, complemented
2#13092418C212yesmaximal, complemented
3#13092286C211yesmaximal, characteristic, complemented
4#13092186C211yesmaximal, characteristic, complemented
5C23×#537C211yesmaximal, characteristic
6C2×#41×C23C2212yes—
7C23×C22⋊Q8—22no—
8C23×#121—22no—
9C23×#121—22no—
10C2×C4⋊C4×C23C2211yescharacteristic
11C2×C4⋊Dic23C2211yescharacteristic
12C2×Dic23⋊C4—22no—
13C2×C4×Dic23C2211yescharacteristic
14C2×#67267C2212yes—
15#10625019—24no—
16#10625017—22no—
17#10625014—22no—
18#41×C23—22no—
19#41×C23—22no—
20#41×C23—22no—
21#41×C23—22no—
22C2×Q8×C23D412yes—
23C2×D4×C23—22no—
24C2×D4×C23—22no—
25C2×D4×C23D412yes—
26C22×C4×C23—22no—
27C22×C4×C23D412yes—
28C22×C4×C23C2311yescharacteristic
29C22×Dic23—21no—
30C22×Dic23—21no—
31C4⋊C4×C23—22no—
32C4⋊C4×C23—22no—
33C22⋊C4×C23—24no—
34C4⋊Dic23—22no—
35Dic23⋊C4—44no—
36C4×Dic23—21no—
37C4×Dic23D412yescomplemented
38#67267—22no—
39#67267—22no—
40C2×C23⋊C8—22no—
41C23×C23—22no—
42C23×C23C2×D411yescharacteristic
43Q8×C23—22no—
44Q8×C23—22no—
45D4×C23—22no—
46D4×C23—22no—
47D4×C23—42no—
48D4×C23—42no—
49D4×C23—82no—
50C2×C4×C23—22no—
51C2×C4×C23—22no—
52C2×C4×C23—42no—
53C2×C4×C23—42no—
54C2×C4×C23—42no—
55C2×C4×C23C2×D411yescharacteristic
56C2×C4×C23C2×D412yes—
57C2×C4×C23#4112yes—
58C2×C4×C23#4111yescharacteristic
59C2×Dic23—22no—
60C2×Dic23—22no—
61C2×Dic23—22no—
62C2×Dic23—42no—
63C2×Dic23—41no—
64C23⋊C8—42no—
65#2039—231nomaximal, Sylow
66C22×C23—21no—
67C22×C23—21no—
68C22×C23—42no—
69C22×C23—42no—
70C22×C23—42no—
71C22×C23#12011yescharacteristic
72C22×C23#12111yescharacteristic
73C22×C23#12411yescharacteristic
74C4×C23—42no—
75C4×C23—42no—
76C4×C23#12112yes—
77C4×C23#12312yes—
78Dic23—24no—
79Dic23—81no—
80#537D2311yescharacteristic
81C2×#104—232no—
82#417—232no—
83#384—231no—
84#343—231no—
85C2×C23—21no—
86C2×C23—21no—
87C2×C23—82no—
88C2×C23#39411yescharacteristic
89C2×C23#45311yescharacteristic
90C2×C23#45611yescharacteristic
91C2×#41C2×D2312yes—
92C2×M16—232no—
93C22⋊Q8—22no—
94#121—22no—
95#121—22no—
96C2×C4⋊C4—231no—
97C2×C4⋊C4—462no—
98C2×C4⋊C4C2×D2311yescharacteristic
99C2×C42—231no—
100#104—464no—
101#103—462no—
102#102—462no—
103C23#203911yescharacteristic, complemented, Sylow
104#41—22no—
105#41—22no—
106#41—22no—
107#41—22no—
108C2×Q8C22⋊D2312yes—
109C2×D4—22no—
110C2×D4—22no—
111C2×D4C22⋊D2312yes—
112C22×C4—22no—
113C22×C4—461no—
114C22×C4—461no—
115C22×C4C22⋊D2312yes—
116C22×C4C22×D2311yescharacteristic
117M16—462no—
118M16—462no—
119C2×C8—462no—
120C4⋊C4—22no—
121C4⋊C4—22no—
122C4⋊C4—462no—
123C4⋊C4—924no—
124C22⋊C4—24no—
125C42—232no—
126C42—461no—
127C23—22no—
128C23C2×C22⋊D2311yescharacteristic
129Q8—22no—
130Q8—22no—
131D4—22no—
132D4—22no—
133D4—42no—
134D4—42no—
135D4—82no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—42no—
140C2×C4—42no—
141C2×C4—462no—
142C2×C4—462no—
143C2×C4—462no—
144C2×C4—922no—
145C2×C4—921no—
146C2×C4D4×D2311yescharacteristic
147C2×C4#6729011yescharacteristic
148C2×C4#6729012yes—
149C2×C4C2×C22⋊D2312yes—
150C8—922no—
151C22—21no—
152C22—21no—
153C22—42no—
154C22—42no—
155C22—42no—
156C22#1062510711yescharacteristic
157C22#1062510911yescharacteristic
158C22#1062512411yescharacteristic
159C4—42no—
160C4—42no—
161C4—464no—
162C4—1841no—
163C4#1062510612yes—
164C4#1062511012yes—
165C2—21no—
166C2—21no—
167C2—82no—
168C2#1309233111yescharacteristic
169C2#1309258511yescharacteristic
170C2#1309260011yescharacteristic
subgroupG/H
centerC22#10625124
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
Fitting, prime radicalC23×#537C2
socleC22×C23#120
hypercenter#537D23
hypocenterC23#2039
LCSG ▷ C22×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#10625019C2semidirect
2. #13092418C2semidirect
3. #13092286C2semidirect
4. #13092186C2semidirect
37. C4×Dic23D4semidirect
103. C23#2039semidirect

Maximal subgroups

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

subgroupindex
C2×#106250192
#130924182
#130922862
#130921862
C23×#5372
#203923