Finite Group Databasebeta

← #16818523

Subgroups — #16818523

Order 3712.

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

normal subgroups only

This group has 208 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#14271496C211yesmaximal, characteristic, complemented
2#14271479C211yesmaximal, characteristic
3#14271102C211yesmaximal, characteristic, complemented
4#14270900C211yesmaximal, characteristic, complemented
5#14270897C211yesmaximal, characteristic
6#14270889C211yesmaximal, characteristic, complemented
7C29×#539C211yesmaximal, characteristic
8C29×#126—21no—
9C29×#125—21no—
10C29×#123—21no—
11C29×#123—21no—
12C29×C22⋊Q8—21no—
13C29×C22⋊Q8C2211yescharacteristic
14C29×#121C2211yescharacteristic
15C4×D4×C29—21no—
16C2×C4⋊C4×C29C2211yescharacteristic
17C2×C4⋊Dic29C2211yescharacteristic
18#11745183—21no—
19#11745180—21no—
20#11745179—21no—
21#11745179—21no—
22#11745179C2211yescharacteristic
23C22⋊#6597C2211yescharacteristic
24C22⋊#6597C2211yescharacteristic
25#11745156—21no—
26#11745155—21no—
27C2×Q8×C29D411yescharacteristic
28C2×D4×C29—21no—
29C2×D4×C29D411yescharacteristic
30C22×C4×C29—21no—
31C22×C4×C29D411yescharacteristic
32C22×C4×C29D411yescharacteristic
33C22×C4×C29C2311yescharacteristic
34C22×Dic29—21no—
35C22×Dic29—21no—
36C4⋊C4×C29—21no—
37C4⋊C4×C29—21no—
38C4⋊C4×C29—21no—
39C4⋊C4×C29—21no—
40C4⋊C4×C29—21no—
41C4⋊C4×C29—21no—
42C4⋊C4×C29D411yescharacteristic
43C4⋊C4×C29D411yescharacteristic
44C22⋊C4×C29—21no—
45C22⋊C4×C29—21no—
46C22⋊C4×C29—21no—
47C22⋊C4×C29—21no—
48C22⋊C4×C29—21no—
49C42×C29—21no—
50C4⋊Dic29—21no—
51C4⋊Dic29—21no—
52C2×#6597—21no—
53C2×#6597—21no—
54C23×C29—21no—
55C23×C29C2×D411yescharacteristic
56Q8×C29—41no—
57D4×C29—41no—
58D4×C29—41no—
59D4×C29—41no—
60C2×C4×C29—21no—
61C2×C4×C29—21no—
62C2×C4×C29—21no—
63C2×C4×C29—21no—
64C2×C4×C29—21no—
65C2×C4×C29—21no—
66C2×C4×C29—21no—
67C2×C4×C29—41no—
68C2×C4×C29—41no—
69C2×C4×C29—81no—
70C2×C4×C29C2×D411yescharacteristic
71C2×C4×C29C2×D411yescharacteristic
72C2×Dic29—41no—
73C2×Dic29—41no—
74C2×Dic29—42no—
75C2×Dic29—41no—
76C2×Dic29—41no—
77#6597—41no—
78#6597—41no—
79#1615—291nomaximal, Sylow
80C22×C29—21no—
81C22×C29—21no—
82C22×C29—41no—
83C22×C29—41no—
84C22×C29—41no—
85C22×C29#12011yescharacteristic
86C22×C29#13511yescharacteristic
87C22×C29#13711yescharacteristic
88C4×C29—21no—
89C4×C29—21no—
90C4×C29—41no—
91C4×C29—41no—
92C4×C29—41no—
93C4×C29—41no—
94C4×C29—41no—
95Dic29—81no—
96Dic29—81no—
97#539D2911yescharacteristic
98#484—291no—
99#481—291no—
100#400—291no—
101#328—291no—
102#327—291no—
103#324—291no—
104C2×C29—21no—
105C2×C29—21no—
106C2×C29—81no—
107C2×C29#45211yescharacteristic
108C2×C29#45411yescharacteristic
109C2×C29#45811yescharacteristic
110#126—21no—
111#125—21no—
112#123—21no—
113#123—21no—
114C22⋊Q8—21no—
115C22⋊Q8C2×D2911yescharacteristic
116#121C2×D2911yescharacteristic
117C4×D4—21no—
118C2×C4⋊C4—291no—
119C2×C4⋊C4C2×D2911yescharacteristic
120#107—581no—
121#106—581no—
122#103—581no—
123#102—581no—
124C22⋊C8—291no—
125C22⋊C8—291no—
126#95—291no—
127#95—581no—
128#95—581no—
129C29#161511yescharacteristic, complemented, Sylow
130C2×Q8C22⋊D2911yescharacteristic
131C2×D4—21no—
132C2×D4C22⋊D2911yescharacteristic
133C22×C4—21no—
134C22×C4—581no—
135C22×C4—581no—
136C22×C4C22⋊D2911yescharacteristic
137C22×C4C22⋊D2911yescharacteristic
138C22×C4C22×D2911yescharacteristic
139C2×C8—581no—
140C2×C8—581no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—581no—
148C4⋊C4—581no—
149C4⋊C4C22⋊D2911yescharacteristic
150C4⋊C4C22⋊D2911yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—21no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C22⋊C4—21no—
156C42—21no—
157C23—21no—
158C23C2×C22⋊D2911yescharacteristic
159Q8—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—81no—
173C2×C4—1161no—
174C2×C4—1161no—
175C2×C4—1162no—
176C2×C4—1161no—
177C2×C4—1161no—
178C2×C4C2×C22⋊D2911yescharacteristic
179C2×C4C2×C22⋊D2911yescharacteristic
180C8—1161no—
181C8—1161no—
182C22—21no—
183C22—21no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22#1174531211yescharacteristic
188C22#1174531311yescharacteristic
189C22#1174531511yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—41no—
195C4—41no—
196C4—41no—
197C4—2321no—
198C4—2321no—
199C2—21no—
200C2—21no—
201C2—81no—
202C2#1427132511yescharacteristic
203C2#1427133611yescharacteristic
204C2#1427135311yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#539C2
socleC22×C29#120
prime radicalC29×#121C22
hypercenter#539D29
hypocenterC29#1615
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #539

Complements

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

NH ≅ G/Ntype
1. #14271496C2semidirect
3. #14271102C2semidirect
4. #14270900C2semidirect
6. #14270889C2semidirect
129. C29#1615semidirect

Maximal subgroups

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

subgroupindex
#142714962
#142714792
#142711022
#142709002
#142708972
#142708892
C29×#5392
#161529