Finite Group Databasebeta

← #15672695

Subgroups — #15672695

Order 2944.

206 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 49 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#13092807C211yesmaximal, characteristic
2#13092783C212yesmaximal, complemented
3#13092159C212yesmaximal, complemented
4#13092157C211yesmaximal, characteristic, complemented
5C23×#563C211yesmaximal, characteristic, complemented
6C23×C4⋊Q8—21no—
7C23×#126—22no—
8C23×#125C2212yes—
9C23×#124C2211yescharacteristic
10C23×#123—21no—
11C23×C22⋊Q8—22no—
12C2×#67274—21no—
13C2×#67272—21no—
14#10625045C2211yescharacteristic
15#10624991—22no—
16#10624991—22no—
17#10624985C2212yes—
18#10624985C2211yescharacteristic
19C2×Q8×C23—21no—
20C2×Q8×C23D411yescharacteristic
21C2×D4×C23D411yescharacteristic
22C22×C4×C23—21no—
23C2×D92—21no—
24C2×D92—22no—
25C4⋊C4×C23—22no—
26C4⋊C4×C23—22no—
27C4⋊C4×C23—22no—
28C4⋊C4×C23D412yes—
29C4⋊C4×C23D412yes—
30C22⋊C4×C23—22no—
31C22⋊C4×C23—21no—
32C22⋊C4×C23—22no—
33C42×C23—21no—
34C42×C23C2311yescharacteristic
35#67274—42no—
36#67272—42no—
37C2×C23⋊C8—21no—
38C2×C23⋊C8—22no—
39C23×C23—21no—
40C22×D23—41no—
41Q8×C23—41no—
42Q8×C23—81no—
43D4×C23—41no—
44C2×C4×C23—22no—
45C2×C4×C23—21no—
46C2×C4×C23—22no—
47C2×C4×C23—81no—
48C2×C4×C23C2×D412yes—
49C2×C4×C23C2×D411yescharacteristic
50D92—41no—
51D92—41no—
52D92—44no—
53C23⋊C8—22no—
54C23⋊C8—42no—
55#1657—231nomaximal, Sylow
56C22×C23—41no—
57C22×C23—42no—
58C22×C23#12011yescharacteristic
59C2×D23—81no—
60C2×D23—82no—
61C4×C23—21no—
62C4×C23—22no—
63C4×C23—42no—
64C4×C23—41no—
65C4×C23—42no—
66#563D2311yescharacteristic, complemented
67#496—231no—
68#490—232no—
69#330—232no—
70#329—231no—
71C2×C23—81no—
72C2×C23#45311yescharacteristic
73C2×C23#45412yes—
74D23—161no—
75C2×SD16—461no—
76C2×D8—461no—
77C4⋊Q8—21no—
78#127—231no—
79#126—22no—
80#125C2×D2312yes—
81#124C2×D2311yescharacteristic
82#123—21no—
83C22⋊Q8—22no—
84#102—462no—
85#102—462no—
86#97—232no—
87#97—231no—
88C23#165711yescharacteristic, complemented, Sylow
89C2×Q8—21no—
90C2×Q8C22⋊D2311yescharacteristic
91C2×D4—462no—
92C2×D4—461no—
93C2×D4C22⋊D2311yescharacteristic
94C22×C4—21no—
95SD16—922no—
96D8—922no—
97C2×C8—461no—
98C2×C8—462no—
99C4⋊C4—22no—
100C4⋊C4—22no—
101C4⋊C4—22no—
102C4⋊C4C22⋊D2312yes—
103C4⋊C4C22⋊D2312yes—
104C22⋊C4—22no—
105C22⋊C4—21no—
106C22⋊C4—22no—
107C42—21no—
108C42C22×D2311yescharacteristic
109C23—21no—
110C23—921no—
111Q8—41no—
112Q8—81no—
113D4—41no—
114D4—921no—
115D4—921no—
116D4—924no—
117C2×C4—22no—
118C2×C4—21no—
119C2×C4—22no—
120C2×C4—81no—
121C2×C4C2×C22⋊D2312yes—
122C2×C4C2×C22⋊D2311yescharacteristic
123C8—462no—
124C8—922no—
125C22—41no—
126C22—42no—
127C22—1841no—
128C22—1842no—
129C22#1062512411yescharacteristic
130C4—21no—
131C4—22no—
132C4—42no—
133C4—41no—
134C4—42no—
135C2—81no—
136C2—3681no—
137C2#1309258511yescharacteristic
138C2#1309259012yes—
subgroupG/H
centerC22#10625124
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#563C2
socleC22×C23#120
prime radical#13092807C2
hypercenter#563D23
hypocenterC23#1657
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
2. #13092783C2semidirect
3. #13092159C2semidirect
4. #13092157C2semidirect
5. C23×#563C2semidirect
66. #563D23semidirect
88. C23#1657semidirect

Maximal subgroups

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

subgroupindex
#130928072
#130927832
#130921592
#130921572
C23×#5632
#165723