Finite Group Databasebeta

← #15674622

Subgroups — #15674622

Order 2944.

306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 67 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
2C2×#10625007C212yesmaximal, complemented
3#13092419C212yesmaximal, complemented
4#13092286C211yesmaximal, characteristic, complemented
5C23×#343C211yesmaximal, characteristic, complemented
6C2×#67288C2212yes—
7C2×M16×C23C2212yes—
8C2×C4⋊C4×C23C2211yescharacteristic
9#10625101—22no—
10C2×C4⋊Dic23C2211yescharacteristic
11C2×Dic23⋊C4—22no—
12C2×C4×Dic23C2211yescharacteristic
13#10625068—22no—
14#10625066—22no—
15#10625007—24no—
16#10625003—22no—
17#10624998—22no—
18C22×C4×C23D412yes—
19C22×C4×C23C2311yescharacteristic
20C2×C22⋊D23—22no—
21C22×Dic23—21no—
22C22×Dic23—21no—
23#67288—22no—
24#67288—22no—
25#67288—22no—
26#67288—22no—
27C2×D92—22no—
28C2×D92D412yes—
29C2×C4×D23—22no—
30C2×Dic46D412yes—
31M16×C23—22no—
32M16×C23—22no—
33C2×C8×C23—22no—
34C4⋊C4×C23—22no—
35(C2×D23)⋊C4—24no—
36C4⋊Dic23—22no—
37C4⋊Dic23—22no—
38Dic23⋊C4—44no—
39C4×Dic23—21no—
40C4×Dic23D412yescomplemented
41C23×C23C2×D411yescharacteristic
42C22×D23—22no—
43C2×C4×C23—22no—
44C2×C4×C23—42no—
45C2×C4×C23C2×D411yescharacteristic
46C2×C4×C23C2×D412yes—
47C2×C4×C23#4112yes—
48C2×C4×C23#4111yescharacteristic
49C22⋊D23—42no—
50C22⋊D23—42no—
51C2×Dic23—22no—
52C2×Dic23—22no—
53C2×Dic23—22no—
54C2×Dic23—22no—
55C2×Dic23—42no—
56C2×Dic23—41no—
57D92—22no—
58D92—22no—
59D92—82no—
60C4×D23—42no—
61C4×D23—42no—
62Dic46—22no—
63Dic46—22no—
64C8×C23—42no—
65#2039—231nomaximal, Sylow
66C22×C23—21no—
67C22×C23—21no—
68C22×C23#12011yescharacteristic
69C22×C23#12111yescharacteristic
70C22×C23#12411yescharacteristic
71C2×D23—42no—
72C2×D23—42no—
73C2×D23—42no—
74C4×C23—42no—
75C4×C23#12112yes—
76C4×C23#12312yes—
77Dic23—24no—
78Dic23—42no—
79Dic23—81no—
80#537—231no—
81C2×#104—232no—
82#417—232no—
83#384—231no—
84#343D2311yescharacteristic, complemented
85C2×C23—21no—
86C2×C23—21no—
87C2×C23#39411yescharacteristic
88C2×C23#45311yescharacteristic
89C2×C23#45611yescharacteristic
90D23—82no—
91C2×#41—232no—
92C2×M16C2×D2312yes—
93C22⋊Q8—462no—
94#121—462no—
95#121—462no—
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—462no—
105#41—462no—
106#41—462no—
107#41—462no—
108C2×Q8—232no—
109C2×D4—232no—
110C2×D4—462no—
111C2×D4—462no—
112C22×C4—461no—
113C22×C4—462no—
114C22×C4—461no—
115C22×C4D9212yes—
116C22×C4C22×D2311yescharacteristic
117M16—22no—
118M16—22no—
119C2×C8—22no—
120C4⋊C4—22no—
121C4⋊C4—462no—
122C4⋊C4—462no—
123C4⋊C4—924no—
124C22⋊C4—464no—
125C42—232no—
126C42—461no—
127C23—462no—
128C23C2×D9211yescharacteristic
129Q8—462no—
130Q8—462no—
131D4—462no—
132D4—462no—
133D4—922no—
134D4—922no—
135D4—1842no—
136C2×C4—22no—
137C2×C4—42no—
138C2×C4—462no—
139C2×C4—462no—
140C2×C4—462no—
141C2×C4—462no—
142C2×C4—922no—
143C2×C4—922no—
144C2×C4—922no—
145C2×C4—921no—
146C2×C4#6728812yes—
147C2×C4D4×D2311yescharacteristic
148C2×C4D4×D2312yes—
149C2×C4#6729211yescharacteristic
150C8—42no—
151C22—21no—
152C22—21no—
153C22—922no—
154C22—922no—
155C22—922no—
156C22#1062504611yescharacteristic
157C22#1062505311yescharacteristic
158C22#1062506611yescharacteristic
159C4—42no—
160C4—464no—
161C4—922no—
162C4—1841no—
163C4#1062505512yes—
164C4#1062506512yes—
165C2—21no—
166C2—21no—
167C2—1842no—
168C2#1309233511yescharacteristic
169C2#1309258711yescharacteristic
170C2#1309260211yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#343C2
socleC22×C23#120
prime radical#13092998C2
hypercenter#343D23
hypocenterC23#2039
LCSG ▷ C22×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
2. C2×#10625007C2semidirect
3. #13092419C2semidirect
4. #13092286C2semidirect
5. C23×#343C2semidirect
40. C4×Dic23D4semidirect
84. #343D23semidirect
103. C23#2039semidirect

Maximal subgroups

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

subgroupindex
#130929982
C2×#106250072
#130924192
#130922862
C23×#3432
#203923