Finite Group Databasebeta

← #16818535

Subgroups — #16818535

Order 3712.

202 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 51 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#14271792C211yesmaximal, characteristic
2#14271499C211yesmaximal, characteristic
3#14271496C211yesmaximal, characteristic
4#14271103C211yesmaximal, characteristic
5#14270899C211yesmaximal, characteristic
6#14270888C211yesmaximal, characteristic
7C29×#328C211yesmaximal, characteristic
8C29×C22⋊Q8C2211yescharacteristic
9#11745306—21no—
10C2×C4⋊Dic29C2211yescharacteristic
11#11745286C2211yescharacteristic
12C2×#90779C2211yescharacteristic
13#11745251—21no—
14#11745251—21no—
15#11745250—21no—
16#11745240—21no—
17#11745239—21no—
18C29×C22⋊C8C2211yescharacteristic
19C29×#95C2211yescharacteristic
20#11745183—21no—
21#11745179—21no—
22#11745179—21no—
23C22⋊#6597C2211yescharacteristic
24#11745166—21no—
25#11745164—21no—
26#11745155—21no—
27C2×Q8×C29D411yescharacteristic
28C22×C4×C29—21no—
29C22×C4×C29C2311yescharacteristic
30C22×Dic29—21no—
31C22×Dic29D411yescharacteristic
32C22×Dic29D411yescharacteristic
33C2×Dic58—21no—
34C2×Dic58D411yescharacteristic
35C2×C8×C29—21no—
36C4⋊C4×C29—21no—
37C4⋊C4×C29D411yescharacteristic
38C22⋊C4×C29—21no—
39C22⋊Dic29—21no—
40C4⋊Dic29—21no—
41C4⋊Dic29—21no—
42C4⋊Dic29—21no—
43C4⋊Dic29D411yescharacteristic
44#90779—21no—
45#90779—21no—
46#90779—21no—
47#90779—21no—
48#90779—21no—
49#90779—21no—
50#90779—21no—
51C4×Dic29—21no—
52C4×Dic29—21no—
53C2×#6597—21no—
54C23×C29C2×D411yescharacteristic
55Q8×C29—41no—
56C2×C4×C29—21no—
57C2×C4×C29—21no—
58C2×C4×C29—41no—
59C2×C4×C29—41no—
60C2×C4×C29—41no—
61C2×C4×C29—41no—
62C2×C4×C29C2×D411yescharacteristic
63C2×C4×C29C2×D411yescharacteristic
64C2×Dic29—21no—
65C2×Dic29—21no—
66C2×Dic29—21no—
67C2×Dic29—21no—
68C2×Dic29—21no—
69C2×Dic29—41no—
70C2×Dic29—42no—
71C2×Dic29—41no—
72C2×Dic29Q1612yes—
73Dic58—41no—
74Dic58—81no—
75C8×C29—41no—
76#6597—41no—
77#1617—291nomaximal, Sylow
78C22×C29—21no—
79C22×C29—21no—
80C22×C29#12011yescharacteristic
81C22×C29C2×Q1611yescharacteristic
82C22×C29#13711yescharacteristic
83C4×C29—21no—
84C4×C29—21no—
85C4×C29—41no—
86C4×C29—41no—
87C4×C29—81no—
88Dic29—22no—
89Dic29—41no—
90Dic29—41no—
91Dic29—41no—
92Dic29—81no—
93#544—291no—
94#484—291no—
95#484—291no—
96#400—291no—
97#328—291no—
98#328D2911yescharacteristic
99#324—291no—
100C2×C29—21no—
101C2×C29—21no—
102C2×C29#45111yescharacteristic
103C2×C29#45411yescharacteristic
104C2×C29#45811yescharacteristic
105C4⋊Q8—581no—
106C4⋊Q8—581no—
107#125—581no—
108#125—581no—
109C22⋊Q8—291no—
110C22⋊Q8—581no—
111C22⋊Q8C2×D2911yescharacteristic
112#117—581no—
113C2×C4⋊C4—291no—
114C2×C4⋊C4—291no—
115#107—581no—
116#107—581no—
117#103—581no—
118#103—581no—
119C22⋊C8—291no—
120C22⋊C8C2×D2911yescharacteristic
121#95—581no—
122#95—581no—
123#95C2×D2911yescharacteristic
124C29#161711yescharacteristic, complemented, Sylow
125C2×Q8—291no—
126C2×Q8—581no—
127C2×Q8D11611yescharacteristic
128C22×C4—21no—
129C22×C4—291no—
130C22×C4—291no—
131C22×C4—581no—
132C22×C4C22×D2911yescharacteristic
133C2×C8—21no—
134C2×C8—581no—
135C4⋊C4—21no—
136C4⋊C4—291no—
137C4⋊C4—581no—
138C4⋊C4—581no—
139C4⋊C4—581no—
140C4⋊C4—581no—
141C4⋊C4—581no—
142C4⋊C4—581no—
143C4⋊C4—581no—
144C4⋊C4—581no—
145C4⋊C4—581no—
146C4⋊C4—581no—
147C4⋊C4D11611yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—581no—
150C42—581no—
151C42—581no—
152C23D4×D2911yescharacteristic
153Q8—41no—
154Q8—1161no—
155Q8—2321no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—292no—
163C2×C4—581no—
164C2×C4—581no—
165C2×C4—581no—
166C2×C4—581no—
167C2×C4—581no—
168C2×C4—1161no—
169C2×C4—1162no—
170C2×C4—1161no—
171C2×C4C2×D11611yescharacteristic
172C2×C4D4×D2911yescharacteristic
173C8—41no—
174C8—1161no—
175C22—21no—
176C22—21no—
177C22#1174524411yescharacteristic
178C22#1174527711yescharacteristic
179C22Q16×D2911yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—582no—
186C4—1161no—
187C4—1161no—
188C4—1161no—
189C4—2321no—
190C2—21no—
191C2—21no—
192C2#1427132011yescharacteristic
193C2#1427133711yescharacteristic
194C2#1427135411yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#328C2
socleC22×C29#120
prime radicalC23×C29C2×D4
hypercenter#328D29
hypocenterC29#1617
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
124. C29#1617semidirect

Maximal subgroups

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

subgroupindex
#142717922
#142714992
#142714962
#142711032
#142708992
#142708882
C29×#3282
#161729