Finite Group Databasebeta

← #16818826

Subgroups — #16818826

Order 3712.

184 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 49 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#14271573C211yesmaximal, characteristic, complemented
2#14271533C211yesmaximal, characteristic, complemented
3#14271522C211yesmaximal, characteristic
4#14270905C211yesmaximal, characteristic, complemented
5#14270905C211yesmaximal, characteristic, complemented
6#14270903C211yesmaximal, characteristic
7C29×#563C211yesmaximal, characteristic
8C29×C4⋊Q8—21no—
9C29×#126—21no—
10C29×#126—21no—
11C29×#125C2211yescharacteristic
12C29×#125C2211yescharacteristic
13C29×#124C2211yescharacteristic
14C29×#123—21no—
15C29×C22⋊Q8—21no—
16C29×C22⋊Q8—21no—
17#11745231C2211yescharacteristic
18#11745183—21no—
19#11745180—21no—
20#11745158—21no—
21#11745158—21no—
22#11745156—21no—
23#11745155—21no—
24#11745151C2211yescharacteristic
25#11745151C2211yescharacteristic
26#11745151C2211yescharacteristic
27C2×Q8×C29—21no—
28C2×Q8×C29D411yescharacteristic
29C2×D4×C29D411yescharacteristic
30C22×C4×C29—21no—
31C2×Dic58—21no—
32C4⋊C4×C29—21no—
33C4⋊C4×C29—21no—
34C4⋊C4×C29—21no—
35C4⋊C4×C29—21no—
36C4⋊C4×C29—21no—
37C4⋊C4×C29—21no—
38C4⋊C4×C29D411yescharacteristic
39C4⋊C4×C29D411yescharacteristic
40C4⋊C4×C29D411yescharacteristic
41C4⋊C4×C29D411yescharacteristic
42C22⋊C4×C29—21no—
43C22⋊C4×C29—21no—
44C22⋊C4×C29—21no—
45C22⋊C4×C29—21no—
46C22⋊C4×C29—21no—
47C42×C29—21no—
48C42×C29C2311yescharacteristic
49C4⋊Dic29—21no—
50C4⋊Dic29—21no—
51C2×#6597—21no—
52C2×#6597—21no—
53C2×#6597—21no—
54C23×C29—21no—
55Q8×C29—41no—
56Q8×C29—81no—
57D4×C29—41no—
58C2×C4×C29—21no—
59C2×C4×C29—21no—
60C2×C4×C29—21no—
61C2×C4×C29—21no—
62C2×C4×C29—21no—
63C2×C4×C29—81no—
64C2×C4×C29C2×D411yescharacteristic
65C2×C4×C29C2×D411yescharacteristic
66C2×C4×C29C2×D411yescharacteristic
67C2×Dic29—41no—
68Dic58—42no—
69#6597—22no—
70#6597—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—
81C4×C29—41no—
82C4×C29—41no—
83C4×C29—41no—
84C4×C29—41no—
85Dic29—81no—
86#563D2911yescharacteristic
87#501—291no—
88#491—291no—
89#489—291no—
90#330—291no—
91#330—291no—
92#329—291no—
93C2×C29—81no—
94C2×C29#45411yescharacteristic
95C2×C29#45511yescharacteristic
96C2×C29#45611yescharacteristic
97C4⋊Q8—21no—
98C4⋊Q8—291no—
99#126—21no—
100#126—21no—
101#125C2×D2911yescharacteristic
102#125C2×D2911yescharacteristic
103#124C2×D2911yescharacteristic
104#123—21no—
105C22⋊Q8—21no—
106C22⋊Q8—21no—
107#107—581no—
108#106—581no—
109#103—581no—
110#103—581no—
111#103—581no—
112#102—581no—
113#97—291no—
114#97—291no—
115#97—291no—
116C29#166411yescharacteristic, complemented, Sylow
117C2×Q8—21no—
118C2×Q8—581no—
119C2×Q8C22⋊D2911yescharacteristic
120C2×D4C22⋊D2911yescharacteristic
121C22×C4—21no—
122C2×C8—581no—
123C2×C8—581no—
124C2×C8—581no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—581no—
132C4⋊C4—581no—
133C4⋊C4C22⋊D2911yescharacteristic
134C4⋊C4C22⋊D2911yescharacteristic
135C4⋊C4C22⋊D2911yescharacteristic
136C4⋊C4C22⋊D2911yescharacteristic
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C22⋊C4—21no—
141C22⋊C4—21no—
142C42—21no—
143C42C22×D2911yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—81no—
147Q8—1162no—
148D4—41no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—81no—
155C2×C4—1161no—
156C2×C4C2×C22⋊D2911yescharacteristic
157C2×C4C2×C22⋊D2911yescharacteristic
158C2×C4C2×C22⋊D2911yescharacteristic
159C8—582no—
160C8—1161no—
161C8—1161no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#1174531511yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—41no—
172C4—41no—
173C4—41no—
174C4—2321no—
175C2—81no—
176C2#1427133611yescharacteristic
177C2#1427134111yescharacteristic
178C2#1427134611yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#563C2
socleC22×C29#120
prime radicalC2×D4×C29D4
hypercenter#563D29
hypocenterC29#1664
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
1. #14271573C2semidirect
2. #14271533C2semidirect
4. #14270905C2semidirect
5. #14270905C2semidirect
116. C29#1664semidirect

Maximal subgroups

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

subgroupindex
#142715732
#142715332
#142715222
#142709052
#142709032
C29×#5632
#166429