Finite Group Databasebeta

← #15675397

Subgroups — #15675397

Order 2944.

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

normal subgroups only

This group has 270 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#13093159C211yesmaximal, characteristic, complemented
2#13092604C212yesmaximal, complemented
3#13092212C211yesmaximal, characteristic, complemented
4#13092205C212yesmaximal, complemented
5C23×#455C211yesmaximal, characteristic, complemented
6C23×H(5,𝔽2)C2211yescharacteristic
7C23×#137—21no—
8C23×#124C2211yescharacteristic
9#10625118—21no—
10#10625108—22no—
11#10625108C2212yes—
12#10625056—22no—
13#10625053—22no—
14#10625046—21no—
15C23×#104—21no—
16C23×#100C2211yescharacteristic
17#10625016—22no—
18#10625016C2212yes—
19C23×D23D412yescomplemented
20#41×C23—21no—
21#41×C23—41no—
22C2×Q8×C23D411yescharacteristic, complemented
23C2×D4×C23—22no—
24C2×D4×C23—41no—
25C2×D4×C23C2311yescharacteristic
26C2×C22⋊D23—22no—
27C2×C22⋊D23—42no—
28C2×D92—21no—
29C2×D92—21no—
30C2×Dic46—21no—
31Q16×C23—41no—
32SD16×C23—41no—
33M16×C23—21no—
34C22⋊C4×C23—22no—
35C42×C23D411yescharacteristic, complemented
36C22⋊Dic23—22no—
37C22⋊Dic23D412yescomplemented
38(C2×D23)⋊C4—22no—
39(C2×D23)⋊C4—22no—
40(C2×D23)⋊C4—22no—
41(C2×D23)⋊C4—42no—
42C4×Dic23—21no—
43C23×C23—22no—
44C23×C23C2×D412yes—
45C22×D23—22no—
46C22×D23—42no—
47C22×D23—82no—
48Q8×C23—21no—
49Q8×C23—41no—
50D4×C23—21no—
51D4×C23—41no—
52D4×C23—42no—
53D4×C23—41no—
54C2×C4×C23—22no—
55C2×C4×C23—21no—
56C2×C4×C23—21no—
57C2×C4×C23—41no—
58C2×C4×C23C2×D411yescharacteristic
59C22⋊D23—82no—
60C22⋊D23—84no—
61C2×Dic23—22no—
62C2×Dic23—42no—
63D92—81no—
64D92—81no—
65Dic46—81no—
66C8×C23—41no—
67#2199—231nomaximal, Sylow
68C22×C23—22no—
69C22×C23—42no—
70C22×C23—41no—
71C22×C23—82no—
72C22×C23#12011yescharacteristic
73C2×D23—42no—
74C2×D23—42no—
75C2×D23—44no—
76C2×D23—42no—
77C2×D23—82no—
78C4×C23—21no—
79C4×C23—41no—
80C4×C23—41no—
81C4×C23—41no—
82Dic23—42no—
83Dic23—82no—
84H(3,𝔽4)—231no—
85B(4,𝔽2)—232no—
86#455D2311yescharacteristic, complemented
87#354—231no—
88AΣL(1,𝔽16)—232no—
89C2×C23—21no—
90C2×C23—42no—
91C2×C23—81no—
92C2×C23B(4,𝔽2)11yescharacteristic
93D23—82no—
94H(5,𝔽2)C2×D2311yescharacteristic
95#137—21no—
96#124—462no—
97#124—461no—
98#124—461no—
99#124C2×D2311yescharacteristic
100#120—232no—
101#120—462no—
102#120—462no—
103#104—21no—
104#100C2×D2311yescharacteristic
105#99—232no—
106#99—462no—
107C23#219911yescharacteristic, complemented, Sylow
108C24—232no—
109#41—21no—
110#41—41no—
111C2×Q8—461no—
112C2×Q8C22⋊D2311yescharacteristic, complemented
113C2×D4—22no—
114C2×D4—41no—
115C2×D4—461no—
116C2×D4—461no—
117C2×D4—462no—
118C2×D4—922no—
119C2×D4C22×D2311yescharacteristic
120Q16—41no—
121SD16—41no—
122M16—21no—
123C22⋊C4—22no—
124C22⋊C4—232no—
125C22⋊C4—462no—
126C22⋊C4—462no—
127C22⋊C4—462no—
128C22⋊C4—462no—
129C22⋊C4—922no—
130C42—461no—
131C42C22⋊D2311yescharacteristic, complemented
132C23—22no—
133C23—462no—
134C23—922no—
135C23—1842no—
136C23D4×D2312yes—
137Q8—21no—
138Q8—41no—
139Q8—1841no—
140D4—21no—
141D4—41no—
142D4—42no—
143D4—41no—
144D4—1841no—
145D4—1841no—
146D4—1842no—
147D4—1844no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—462no—
153C2×C4—922no—
154C2×C4C2×C22⋊D2311yescharacteristic
155C8—41no—
156C22—22no—
157C22—42no—
158C22—41no—
159C22—82no—
160C22—922no—
161C22—922no—
162C22—924no—
163C22—922no—
164C22—1842no—
165C22#1062510811yescharacteristic
166C4—21no—
167C4—41no—
168C4—41no—
169C4—41no—
170C4—922no—
171C4—1842no—
172C2—21no—
173C2—42no—
174C2—81no—
175C2—1842no—
176C2#1309260311yescharacteristic
subgroupG/H
centerC2#13092603
commutator, cosocleC2×D4×C23C23
FrattiniC2×D4C22×D23
FittingC23×#455C2
socleC2×C23B(4,𝔽2)
hypercenter#455D23
hypocenterC23#2199
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. #13093159C2semidirect
2. #13092604C2semidirect
3. #13092212C2semidirect
4. #13092205C2semidirect
5. C23×#455C2semidirect
19. C23×D23D4semidirect
22. C2×Q8×C23D4semidirect
35. C42×C23D4semidirect
37. C22⋊Dic23D4semidirect
86. #455D23semidirect
107. C23#2199semidirect
112. C2×Q8C22⋊D23semidirect
131. C42C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
#130931592
#130926042
#130922122
#130922052
C23×#4552
#219923