Finite Group Databasebeta

← #15675409

Subgroups — #15675409

Order 2944.

226 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 41 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#13093167C211yesmaximal, characteristic, complemented
2#13092607C212yesmaximal
3#13092212C211yesmaximal, characteristic, complemented
4#13092208C212yesmaximal, complemented
5C23×#455C211yesmaximal, characteristic
6C23×H(5,𝔽2)C2211yescharacteristic
7C23×#137—21no—
8C23×#124C2211yescharacteristic
9#10625115—21no—
10#10625106—22no—
11#10625106C2212yes—
12#10625050—22no—
13#10625049—22no—
14#10625041—21no—
15C23×#104—21no—
16C23×#100C2211yescharacteristic
17#10625016—22no—
18#10625016C2212yes—
19#41×C23—21no—
20#41×C23—41no—
21C2×Q8×C23D411yescharacteristic
22C2×D4×C23—22no—
23C2×D4×C23—41no—
24C2×D4×C23C2311yescharacteristic
25C22×Dic23D412yes—
26C2×Dic46—21no—
27Q16×C23—41no—
28SD16×C23—41no—
29M16×C23—21no—
30C22⋊C4×C23—22no—
31C42×C23D411yescharacteristic
32C22⋊Dic23—22no—
33C22⋊Dic23—22no—
34C22⋊Dic23—42no—
35C22⋊Dic23D412yes—
36C4⋊Dic23—21no—
37C4⋊Dic23—21no—
38Dic23⋊C4—22no—
39Dic23⋊C4—22no—
40Dic23⋊C4—22no—
41Dic23⋊C4—42no—
42C4×Dic23—21no—
43C23×C23—22no—
44C23×C23C2×D412yes—
45Q8×C23—21no—
46Q8×C23—41no—
47D4×C23—21no—
48D4×C23—41no—
49D4×C23—42no—
50D4×C23—41no—
51C2×C4×C23—22no—
52C2×C4×C23—21no—
53C2×C4×C23—21no—
54C2×C4×C23—41no—
55C2×C4×C23C2×D411yescharacteristic
56C2×Dic23—22no—
57C2×Dic23—22no—
58C2×Dic23—42no—
59C2×Dic23—42no—
60Dic46—81no—
61C8×C23—41no—
62#2201—231nomaximal, Sylow
63C22×C23—22no—
64C22×C23—42no—
65C22×C23—41no—
66C22×C23—82no—
67C22×C23#12011yescharacteristic
68C4×C23—21no—
69C4×C23—41no—
70C4×C23—41no—
71C4×C23—41no—
72Dic23—42no—
73Dic23—42no—
74Dic23—82no—
75#563—231no—
76#458—232no—
77#455D2311yescharacteristic
78#354—231no—
79#352—232no—
80C2×C23—21no—
81C2×C23—42no—
82C2×C23—81no—
83C2×C23B(4,𝔽2)11yescharacteristic
84H(5,𝔽2)C2×D2311yescharacteristic
85#137—21no—
86C4⋊Q8—461no—
87#126—462no—
88#125—461no—
89#124C2×D2311yescharacteristic
90#123—232no—
91#123—462no—
92C22⋊Q8—462no—
93#104—21no—
94#100C2×D2311yescharacteristic
95#99—232no—
96#99—462no—
97C23#220111yescharacteristic, complemented, Sylow
98#41—21no—
99#41—41no—
100C2×Q8—461no—
101C2×Q8C22⋊D2311yescharacteristic
102C2×D4—22no—
103C2×D4—41no—
104C2×D4C22×D2311yescharacteristic
105C22×C4—232no—
106Q16—41no—
107SD16—41no—
108M16—21no—
109C4⋊C4—461no—
110C4⋊C4—462no—
111C4⋊C4—462no—
112C4⋊C4—461no—
113C4⋊C4—462no—
114C4⋊C4—922no—
115C22⋊C4—22no—
116C22⋊C4—232no—
117C22⋊C4—462no—
118C22⋊C4—462no—
119C22⋊C4—922no—
120C42—461no—
121C42C22⋊D2311yescharacteristic
122C23—22no—
123C23D4×D2312yes—
124Q8—21no—
125Q8—41no—
126Q8—1841no—
127D4—21no—
128D4—41no—
129D4—42no—
130D4—41no—
131C2×C4—22no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—41no—
135C2×C4—462no—
136C2×C4—462no—
137C2×C4—922no—
138C2×C4—922no—
139C2×C4C2×C22⋊D2311yescharacteristic
140C8—41no—
141C22—22no—
142C22—42no—
143C22—41no—
144C22—82no—
145C22#1062510811yescharacteristic
146C4—21no—
147C4—41no—
148C4—41no—
149C4—41no—
150C4—922no—
151C4—922no—
152C4—1842no—
153C2—21no—
154C2—42no—
155C2—81no—
156C2#1309260311yescharacteristic
subgroupG/H
centerC2#13092603
commutator, cosocleC2×D4×C23C23
FrattiniC2×D4C22×D23
FittingC23×#455C2
socleC2×C23B(4,𝔽2)
prime radicalC23×H(5,𝔽2)C22
hypercenter#455D23
hypocenterC23#2201
LCSG ▷ C2×D4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #13093167C2semidirect
3. #13092212C2semidirect
4. #13092208C2semidirect
97. C23#2201semidirect

Maximal subgroups

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

subgroupindex
#130931672
#130926072
#130922122
#130922082
C23×#4552
#220123