Finite Group Databasebeta

← #16818615

Subgroups — #16818615

Order 3712.

218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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#14271898C211yesmaximal, characteristic
2#14271536C211yesmaximal, characteristic
3#14271459C211yesmaximal, characteristic, complemented
4#14271458C211yesmaximal, characteristic, complemented
5#14270906C211yesmaximal, characteristic
6#14270895C211yesmaximal, characteristic, complemented
7C29×Q8⋊C8C211yesmaximal, characteristic, complemented
8C4×Q8×C29C2211yescharacteristic
9#11745309—21no—
10C2×#90773—22no—
11#11745256—22no—
12#11745255—21no—
13#11745237—21no—
14#11745236C2211yescharacteristic
15C4×D116—21no—
16#11745231C2211yescharacteristic
17C4×Dic58C2211yescharacteristic
18C29×C4⋊C8C2211yescharacteristic
19C4×C8×C29C2211yescharacteristic
20#11745183—21no—
21#11745166—21no—
22#11745164—21no—
23#11745155—21no—
24C4⋊#6597C2211yescharacteristic
25C2×Q8×C29D411yescharacteristic
26C2×D116—21no—
27C2×D116—21no—
28C2×D116D412yes—
29C2×C4×D29—22no—
30C2×Dic58—21no—
31C2×Dic58D411yescharacteristic
32C2×C8×C29—21no—
33C2×C8×C29—21no—
34C4⋊C4×C29—21no—
35C4⋊C4×C29D411yescharacteristic
36C42×C29—21no—
37C42×C29C2311yescharacteristic
38#90781—22no—
39#90781—22no—
40#90781—22no—
41C4⋊Dic29—21no—
42C4⋊Dic29—21no—
43C4⋊Dic29D411yescharacteristic
44#90779—21no—
45C4×Dic29—21no—
46C2×#6597—21no—
47#90773—44no—
48C22×D29—22no—
49Q8×C29—21no—
50Q8×C29—21no—
51C2×C4×C29—21no—
52C2×C4×C29—21no—
53C2×C4×C29C2×D411yescharacteristic
54C2×C4×C29C2×D411yescharacteristic
55C2×C4×C29C2×D411yescharacteristic
56C2×Dic29—21no—
57C2×Dic29—21no—
58C2×Dic29—41no—
59D116—42no—
60D116—41no—
61D116—41no—
62D116—41no—
63D116—41no—
64C4×D29—82no—
65Dic58—21no—
66Dic58—21no—
67Dic58—42no—
68C8×C29—22no—
69C8×C29—41no—
70#6597—41no—
71#1630—291nomaximal, Sylow
72C22×C29#12011yescharacteristic
73C2×D29—42no—
74C2×D29—42no—
75C2×D29—42no—
76C4×C29—21no—
77C4×C29—41no—
78C4×C29—41no—
79C4×C29#13511yescharacteristic
80C4×C29#13511yescharacteristic
81C4×C29#13711yescharacteristic
82C4×C29#13711yescharacteristic
83Dic29—41no—
84Dic29—41no—
85Dic29—81no—
86#559—291no—
87#492—291no—
88#477—291no—
89#477—291no—
90#331—291no—
91Q8⋊C8—291no—
92Q8⋊C8D2911yescharacteristic, complemented
93C2×C29#45211yescharacteristic
94C2×C29#45211yescharacteristic
95C2×C29#45311yescharacteristic
96D29—82no—
97C2×SD16—582no—
98C4⋊Q8—291no—
99#127—291no—
100#124—581no—
101#124—581no—
102#123—582no—
103C4×Q8—291no—
104C4×Q8C2×D2911yescharacteristic
105C4×D4—581no—
106C4×D4—581no—
107#107—581no—
108#107—581no—
109C4⋊C8—291no—
110C4⋊C8C2×D2911yescharacteristic
111#103—581no—
112#103—581no—
113C4×C8C2×D2911yescharacteristic
114C29#163011yescharacteristic, complemented, Sylow
115C2×Q8—291no—
116C2×Q8—581no—
117C2×Q8D11611yescharacteristic
118C2×D4—292no—
119C2×D4—581no—
120C2×D4—581no—
121C22×C4—582no—
122SD16—1164no—
123C2×C8—21no—
124C2×C8—21no—
125C2×C8—581no—
126C4⋊C4—21no—
127C4⋊C4—291no—
128C4⋊C4—581no—
129C4⋊C4—581no—
130C4⋊C4—581no—
131C4⋊C4D11611yescharacteristic
132C22⋊C4—582no—
133C22⋊C4—582no—
134C22⋊C4—582no—
135C42—21no—
136C42—581no—
137C42C22×D2911yescharacteristic
138C23—582no—
139Q8—21no—
140Q8—21no—
141Q8—581no—
142Q8—581no—
143Q8—1162no—
144D4—1162no—
145D4—1161no—
146D4—1161no—
147D4—1161no—
148D4—1161no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—581no—
152C2×C4—581no—
153C2×C4—1161no—
154C2×C4—2322no—
155C2×C4C2×D11611yescharacteristic
156C2×C4D4×D2911yescharacteristic
157C2×C4D4×D2911yescharacteristic
158C8—22no—
159C8—41no—
160C8—1161no—
161C22—1162no—
162C22—1162no—
163C22—1162no—
164C22#1174524411yescharacteristic
165C4—21no—
166C4—41no—
167C4—41no—
168C4—1161no—
169C4—1161no—
170C4—2321no—
171C4#1174526611yescharacteristic
172C4#1174527111yescharacteristic
173C4#1174527811yescharacteristic
174C4#1174528011yescharacteristic
175C2—2322no—
176C2#1427132711yescharacteristic
177C2#1427132811yescharacteristic
178C2#1427133211yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×Q8⋊C8C2
socleC22×C29#120
prime radical#11745236C22
hypercenterQ8⋊C8D29
hypocenterC29#1630
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
3. #14271459C2semidirect
4. #14271458C2semidirect
6. #14270895C2semidirect
7. C29×Q8⋊C8C2semidirect
92. Q8⋊C8D29semidirect
114. C29#1630semidirect

Maximal subgroups

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

subgroupindex
#142718982
#142715362
#142714592
#142714582
#142709062
#142708952
C29×Q8⋊C82
#163029