Finite Group Databasebeta

← #15675353

Subgroups — #15675353

Order 2944.

220 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 47 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#13093218C211yesmaximal, characteristic, complemented
2#13092853C211yesmaximal, characteristic, complemented
3#13092684C211yesmaximal, characteristic, complemented
4#13092230C211yesmaximal, characteristic, complemented
5#13092225C211yesmaximal, characteristic, complemented
6#13092200C211yesmaximal, characteristic, complemented
7C2×C23×D16C211yesmaximal, characteristic, complemented
8#10625155—21no—
9C2×D8×C23C2211yescharacteristic
10C2×D8×C23C2211yescharacteristic, complemented
11#10625103—21no—
12#10625103—21no—
13#10625083—21no—
14#10625082—22no—
15D8×D23—21no—
16#10625075C2211yescharacteristic
17#10625072C2211yescharacteristic
18C23×D16—22no—
19C2×C16×C23C2211yescharacteristic, complemented
20#10625015—21no—
21#10625009—21no—
22#10625008—21no—
23#10625001C2211yescharacteristic, complemented
24#10624994C2211yescharacteristic, complemented
25C2×D4×C23—21no—
26C2×D4×C23—21no—
27C2×C22⋊D23—42no—
28#67290—22no—
29#67290—41no—
30D4×D23—22no—
31D4×D23—41no—
32#67288—21no—
33#67288D411yescharacteristic
34D8×C23—21no—
35D8×C23—21no—
36D8×C23—21no—
37D8×C23D412yes—
38C2×C8×C23C2311yescharacteristic
39#67273—22no—
40#67273—41no—
41#67272—22no—
42#67272—41no—
43#67267—21no—
44#67267D411yescharacteristic
45Dic92D411yescharacteristic
46D184D411yescharacteristic
47#67263—21no—
48#67262—21no—
49C8×D23—21no—
50C16×C23—21no—
51C23⋊C16—21no—
52C23×C23—41no—
53C23×C23—41no—
54C22×D23—42no—
55D4×C23—22no—
56D4×C23—41no—
57D4×C23—41no—
58D4×C23—41no—
59C2×C4×C23C2×D411yescharacteristic
60C22⋊D23—21no—
61C22⋊D23—42no—
62C22⋊D23—42no—
63C22⋊D23—41no—
64C2×Dic23—42no—
65D92—21no—
66D92D811yescharacteristic
67C4×D23—21no—
68C4×D23—41no—
69Dic46—21no—
70Dic46D811yescharacteristic
71C8×C23C2×D411yescharacteristic
72C8×C23C2×D411yescharacteristic
73C23⋊C8—21no—
74C23⋊C8—41no—
75#2192—231nomaximal, Sylow
76C22×C23—42no—
77C22×C23—81no—
78C22×C23—161no—
79C22×C23—161no—
80C22×C23AGL(1,ℤ/8)11yescharacteristic
81C2×D23—21no—
82C2×D23—41no—
83C2×D23—162no—
84C4×C23#12011yescharacteristic
85C4×C23C2×D811yescharacteristic
86Dic23—21no—
87Dic23—41no—
88#576—231no—
89#509—231no—
90C2×D16D2311yescharacteristic, complemented
91#472—231no—
92#361—231no—
93#359—231no—
94#350—231no—
95C2×C23—21no—
96C2×C23—82no—
97C2×C23—161no—
98C2×C23#44711yescharacteristic
99D23—41no—
100D23—81no—
101H(5,𝔽2)—461no—
102AGL(1,ℤ/8)—461no—
103AGL(1,ℤ/8)—462no—
104AGL(1,ℤ/8)—461no—
105#135—231no—
106#135—461no—
107C2×D8—461no—
108C2×D8C2×D2311yescharacteristic
109C2×D8C2×D2311yescharacteristic, complemented
110#131—231no—
111SD32—461no—
112D16—22no—
113D16—461no—
114M32—231no—
115C2×C16C2×D2311yescharacteristic, complemented
116#108—231no—
117#100—461no—
118C23#219211yescharacteristic, complemented, Sylow
119#41—231no—
120#41—462no—
121#41—461no—
122#41—921no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—462no—
126C2×D4—921no—
127C2×D4—922no—
128Q16—231no—
129SD16—462no—
130SD16—461no—
131SD16—921no—
132D8—21no—
133D8—21no—
134D8—21no—
135D8—231no—
136D8—462no—
137D8—921no—
138D8C22⋊D2312yes—
139M16—231no—
140M16—461no—
141M16—461no—
142C2×C8—461no—
143C2×C8C22×D2311yescharacteristic
144C16—21no—
145C16—461no—
146C23—41no—
147C23—41no—
148C23—922no—
149Q8—231no—
150Q8—461no—
151D4—22no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—231no—
156D4—461no—
157D4—461no—
158D4—922no—
159D4—922no—
160D4—921no—
161C2×C4—461no—
162C2×C4—922no—
163C2×C4—921no—
164C2×C4D4×D2311yescharacteristic
165C8—461no—
166C8—921no—
167C8D4×D2311yescharacteristic
168C8C2×C22⋊D2311yescharacteristic
169C22—42no—
170C22—81no—
171C22—161no—
172C22—161no—
173C22—461no—
174C22—921no—
175C22—3682no—
176C22#1062508211yescharacteristic
177C4—461no—
178C4—921no—
179C4D8×D2311yescharacteristic
180C4#1062510811yescharacteristic
181C2—21no—
182C2—82no—
183C2—161no—
184C2—921no—
185C2—1841no—
186C2#1309254911yescharacteristic
subgroupG/H
centerC2#13092549
commutator, cosocleC2×C8×C23C23
FrattiniC2×C8C22×D23
FittingC2×C23×D16C2
socleC2×C23#447
hypercenterC2×D16D23
hypocenterC23#2192
LCSG ▷ C2×C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. #13093218C2semidirect
2. #13092853C2semidirect
3. #13092684C2semidirect
4. #13092230C2semidirect
5. #13092225C2semidirect
6. #13092200C2semidirect
7. C2×C23×D16C2semidirect
10. C2×D8×C23C22semidirect
19. C2×C16×C23C22semidirect
23. #10625001C22semidirect
24. #10624994C22semidirect
90. C2×D16D23semidirect
109. C2×D8C2×D23semidirect
115. C2×C16C2×D23semidirect
118. C23#2192semidirect

Maximal subgroups

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

subgroupindex
#130932182
#130928532
#130926842
#130922302
#130922252
#130922002
C2×C23×D162
#219223