Finite Group Databasebeta

← #15675367

Subgroups — #15675367

Order 2944.

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

normal subgroups only

This group has 216 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
2#13092858C211yesmaximal, characteristic, complemented
3#13092689C211yesmaximal, characteristic, complemented
4#13092230C211yesmaximal, characteristic, complemented
5#13092225C211yesmaximal, characteristic, complemented
6#13092200C211yesmaximal, characteristic, complemented
7C2×C23×SD32C211yesmaximal, characteristic, complemented
8#10625155—21no—
9C2×Q16×C23C2211yescharacteristic, complemented
10C2×D8×C23C2211yescharacteristic
11#10625113—21no—
12#10625103—21no—
13#10625083—21no—
14#10625082—22no—
15D8×D23—21no—
16#10625075C2211yescharacteristic
17#10625072C2211yescharacteristic
18C23×SD32—22no—
19C2×C16×C23C2211yescharacteristic, complemented
20#10625018—21no—
21#10625011—21no—
22#10625010—21no—
23#10625001C2211yescharacteristic, complemented
24#10624994C2211yescharacteristic, complemented
25C2×Q8×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
34Q16×C23—21no—
35Q16×C23—21no—
36D8×C23—21no—
37D8×C23D412yes—
38C2×C8×C23C2311yescharacteristic
39#67275—41no—
40#67274—41no—
41#67273—22no—
42#67272—22no—
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—
53C22×D23—42no—
54Q8×C23—41no—
55Q8×C23—41no—
56D4×C23—22no—
57D4×C23—41no—
58C2×C4×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#2194—231nomaximal, Sylow
76C22×C23—42no—
77C22×C23—161no—
78C22×C23AGL(1,ℤ/8)11yescharacteristic
79C2×D23—21no—
80C2×D23—41no—
81C2×D23—162no—
82C4×C23—81no—
83C4×C23#12011yescharacteristic
84C4×C23C2×D811yescharacteristic
85Dic23—21no—
86Dic23—41no—
87#576—231no—
88#510—231no—
89C2×SD32D2311yescharacteristic, complemented
90#473—231no—
91#361—231no—
92#359—231no—
93#350—231no—
94C2×C23—21no—
95C2×C23—82no—
96C2×C23#44711yescharacteristic
97D23—41no—
98D23—81no—
99H(5,𝔽2)—461no—
100#137—461no—
101AGL(1,ℤ/8)—461no—
102AGL(1,ℤ/8)—462no—
103#135—231no—
104#135—461no—
105C2×Q16C2×D2311yescharacteristic, complemented
106C2×D8—461no—
107C2×D8C2×D2311yescharacteristic
108#131—231no—
109Q32—461no—
110SD32—22no—
111SD32—461no—
112M32—231no—
113C2×C16C2×D2311yescharacteristic, complemented
114#108—231no—
115#101—461no—
116C23#219411yescharacteristic, complemented, Sylow
117#41—231no—
118#41—462no—
119#41—461no—
120#41—921no—
121C2×Q8—21no—
122C2×D4—21no—
123C2×D4—462no—
124C2×D4—921no—
125C2×D4—922no—
126Q16—21no—
127Q16—21no—
128Q16—231no—
129Q16—921no—
130SD16—462no—
131SD16—461no—
132SD16—921no—
133D8—21no—
134D8—231no—
135D8—462no—
136D8C22⋊D2312yes—
137M16—231no—
138M16—461no—
139M16—461no—
140C2×C8—461no—
141C2×C8C22×D2311yescharacteristic
142C16—21no—
143C16—461no—
144C23—41no—
145C23—922no—
146Q8—41no—
147Q8—41no—
148Q8—231no—
149Q8—461no—
150D4—22no—
151D4—41no—
152D4—231no—
153D4—461no—
154D4—461no—
155D4—922no—
156D4—922no—
157D4—921no—
158C2×C4—41no—
159C2×C4—461no—
160C2×C4—922no—
161C2×C4—921no—
162C2×C4D4×D2311yescharacteristic
163C8—461no—
164C8—921no—
165C8D4×D2311yescharacteristic
166C8C2×C22⋊D2311yescharacteristic
167C22—42no—
168C22—161no—
169C22—461no—
170C22—921no—
171C22—3682no—
172C22#1062508211yescharacteristic
173C4—81no—
174C4—461no—
175C4—921no—
176C4D8×D2311yescharacteristic
177C4#1062510811yescharacteristic
178C2—21no—
179C2—82no—
180C2—921no—
181C2—1841no—
182C2#1309254911yescharacteristic
subgroupG/H
centerC2#13092549
commutator, cosocleC2×C8×C23C23
FrattiniC2×C8C22×D23
FittingC2×C23×SD32C2
socleC2×C23#447
prime radical#13093218C2
hypercenterC2×SD32D23
hypocenterC23#2194
LCSG ▷ C2×C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
2. #13092858C2semidirect
3. #13092689C2semidirect
4. #13092230C2semidirect
5. #13092225C2semidirect
6. #13092200C2semidirect
7. C2×C23×SD32C2semidirect
9. C2×Q16×C23C22semidirect
19. C2×C16×C23C22semidirect
23. #10625001C22semidirect
24. #10624994C22semidirect
89. C2×SD32D23semidirect
105. C2×Q16C2×D23semidirect
113. C2×C16C2×D23semidirect
116. C23#2194semidirect

Maximal subgroups

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

subgroupindex
#130932182
#130928582
#130926892
#130922302
#130922252
#130922002
C2×C23×SD322
#219423