Finite Group Databasebeta

← #16818829

Subgroups — #16818829

Order 3712.

184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 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#14271913C211yesmaximal, characteristic
2#14271572C211yesmaximal, characteristic, complemented
3#14271532C211yesmaximal, characteristic, complemented
4#14271522C211yesmaximal, characteristic
5#14270904C211yesmaximal, characteristic, complemented
6#14270904C211yesmaximal, characteristic, complemented
7C29×#329C211yesmaximal, characteristic
8C29×#124C2211yescharacteristic
9#11745306—21no—
10#11745297—21no—
11#11745241—21no—
12#11745241—21no—
13#11745240—21no—
14#11745240—21no—
15#11745232C2211yescharacteristic
16#11745232C2211yescharacteristic
17#11745231C2211yescharacteristic
18C29×#97C2211yescharacteristic
19C29×#97C2211yescharacteristic
20#11745183—21no—
21#11745180—21no—
22#11745166—21no—
23#11745165—21no—
24#11745164—21no—
25#11745164—21no—
26#11745151C2211yescharacteristic
27C2×Q8×C29D411yescharacteristic
28C2×D4×C29D411yescharacteristic
29C22×Dic29—21no—
30C2×Dic58—21no—
31C2×Dic58—21no—
32C2×C8×C29—21no—
33C2×C8×C29—21no—
34C22⋊C4×C29—21no—
35C22⋊C4×C29—21no—
36C42×C29C2311yescharacteristic
37C22⋊Dic29—21no—
38C22⋊Dic29—21no—
39C22⋊Dic29—21no—
40C4⋊Dic29—21no—
41C4⋊Dic29—21no—
42C4⋊Dic29D411yescharacteristic
43C4⋊Dic29D411yescharacteristic
44C4⋊Dic29D411yescharacteristic
45C4⋊Dic29D411yescharacteristic
46#90779—21no—
47#90779—21no—
48#90779—21no—
49#90779—21no—
50#90779—21no—
51#90779—21no—
52C4×Dic29—21no—
53C2×#6597—21no—
54C23×C29—21no—
55Q8×C29—41no—
56D4×C29—41no—
57C2×C4×C29—21no—
58C2×C4×C29C2×D411yescharacteristic
59C2×C4×C29C2×D411yescharacteristic
60C2×C4×C29C2×D411yescharacteristic
61C2×Dic29—21no—
62C2×Dic29—21no—
63C2×Dic29—21no—
64C2×Dic29—21no—
65C2×Dic29—41no—
66C2×Dic29—81no—
67Dic58—42no—
68Dic58—81no—
69C8×C29—22no—
70C8×C29—41no—
71#6597—41no—
72#1664—291nomaximal, Sylow
73C22×C29—41no—
74C22×C29—41no—
75C22×C29—41no—
76C22×C29#12011yescharacteristic
77C4×C29—21no—
78C4×C29—21no—
79C4×C29—21no—
80C4×C29—41no—
81Dic29—41no—
82Dic29—41no—
83Dic29—41no—
84Dic29—41no—
85Dic29—81no—
86#563—291no—
87#501—291no—
88#491—291no—
89#489—291no—
90#330—291no—
91#330—291no—
92#329D2911yescharacteristic
93C2×C29—81no—
94C2×C29#45411yescharacteristic
95C2×C29#45511yescharacteristic
96C2×C29#45611yescharacteristic
97C4⋊Q8—291no—
98C4⋊Q8—581no—
99#126—581no—
100#126—581no—
101#125—291no—
102#125—291no—
103#124C2×D2911yescharacteristic
104#123—581no—
105C22⋊Q8—581no—
106C22⋊Q8—581no—
107#107—581no—
108#106—581no—
109#103—581no—
110#103—581no—
111#103—581no—
112#102—581no—
113#97—291no—
114#97C2×D2911yescharacteristic
115#97C2×D2911yescharacteristic
116C29#166411yescharacteristic, complemented, Sylow
117C2×Q8—581no—
118C2×Q8—581no—
119C2×Q8D11611yescharacteristic
120C2×D4D11611yescharacteristic
121C22×C4—581no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—581no—
125C4⋊C4—291no—
126C4⋊C4—291no—
127C4⋊C4—291no—
128C4⋊C4—291no—
129C4⋊C4—581no—
130C4⋊C4—581no—
131C4⋊C4—581no—
132C4⋊C4—581no—
133C4⋊C4—581no—
134C4⋊C4—581no—
135C4⋊C4—581no—
136C4⋊C4—581no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—581no—
140C22⋊C4—581no—
141C22⋊C4—581no—
142C42—581no—
143C42C22×D2911yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—1162no—
147Q8—2321no—
148D4—41no—
149C2×C4—21no—
150C2×C4—581no—
151C2×C4—581no—
152C2×C4—581no—
153C2×C4—581no—
154C2×C4—1161no—
155C2×C4—2321no—
156C2×C4C2×D11611yescharacteristic
157C2×C4D4×D2911yescharacteristic
158C2×C4D4×D2911yescharacteristic
159C8—22no—
160C8—41no—
161C8—1161no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#1174524411yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—1161no—
171C4—1161no—
172C4—1161no—
173C4—1161no—
174C4—2321no—
175C2—81no—
176C2#1427133711yescharacteristic
177C2#1427134311yescharacteristic
178C2#1427134711yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#329C2
socleC22×C29#120
prime radicalC2×D4×C29D4
hypercenter#329D29
hypocenterC29#1664
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #14271572C2semidirect
3. #14271532C2semidirect
5. #14270904C2semidirect
6. #14270904C2semidirect
116. C29#1664semidirect

Maximal subgroups

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

subgroupindex
#142719132
#142715722
#142715322
#142715222
#142709042
C29×#3292
#166429