Finite Group Databasebeta

← #16818489

Subgroups — #16818489

Order 3712.

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

normal subgroups only

This group has 216 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#14271491C211yesmaximal, characteristic, complemented
2#14271474C211yesmaximal, characteristic
3#14271093C211yesmaximal, 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
18C2×#90779—21no—
19#11745183—21no—
20#11745180—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—
52#90779—42no—
53C2×#6597—21no—
54C2×#6597—21no—
55C23×C29—21no—
56C23×C29C2×D411yescharacteristic
57Q8×C29—41no—
58D4×C29—41no—
59D4×C29—41no—
60D4×C29—41no—
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—21no—
68C2×C4×C29—41no—
69C2×C4×C29—41no—
70C2×C4×C29—81no—
71C2×C4×C29C2×D411yescharacteristic
72C2×C4×C29C2×D411yescharacteristic
73C2×Dic29—22no—
74C2×Dic29—41no—
75C2×Dic29—41no—
76C2×Dic29—41no—
77C2×Dic29—41no—
78C2×Dic29—41no—
79#6597—41no—
80#6597—41no—
81#1609—291nomaximal, Sylow
82C22×C29—21no—
83C22×C29—21no—
84C22×C29—41no—
85C22×C29—41no—
86C22×C29—41no—
87C22×C29#12011yescharacteristic
88C22×C29#13511yescharacteristic
89C22×C29AGL(1,ℤ/8)11yescharacteristic
90C4×C29—21no—
91C4×C29—21no—
92C4×C29—41no—
93C4×C29—41no—
94C4×C29—41no—
95C4×C29—41no—
96C4×C29—41no—
97Dic29—42no—
98Dic29—81no—
99#539D2911yescharacteristic
100#483—291no—
101#480—291no—
102#398—291no—
103#328—291no—
104#327—291no—
105#324—291no—
106C2×C29—21no—
107C2×C29—21no—
108C2×C29—81no—
109C2×C29#44911yescharacteristic
110C2×C29#45611yescharacteristic
111C2×C29#45811yescharacteristic
112#126—21no—
113#125—21no—
114#123—21no—
115#123—21no—
116C22⋊Q8—21no—
117C22⋊Q8C2×D2911yescharacteristic
118#121C2×D2911yescharacteristic
119C4×D4—21no—
120C2×C4⋊C4—291no—
121C2×C4⋊C4—581no—
122C2×C4⋊C4C2×D2911yescharacteristic
123#107—581no—
124#106—581no—
125#103—581no—
126#102—581no—
127C22⋊C8—291no—
128C22⋊C8—291no—
129#95—291no—
130#95—581no—
131C29#160911yescharacteristic, complemented, Sylow
132C2×Q8C22⋊D2911yescharacteristic
133C2×D4—21no—
134C2×D4C22⋊D2911yescharacteristic
135C22×C4—21no—
136C22×C4—581no—
137C22×C4—581no—
138C22×C4C22⋊D2911yescharacteristic
139C22×C4C22⋊D2911yescharacteristic
140C22×C4C22×D2911yescharacteristic
141C2×C8—581no—
142C2×C8—581no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—581no—
150C4⋊C4—581no—
151C4⋊C4—1162no—
152C4⋊C4C22⋊D2911yescharacteristic
153C4⋊C4C22⋊D2911yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—21no—
156C22⋊C4—21no—
157C22⋊C4—21no—
158C22⋊C4—21no—
159C42—21no—
160C23—21no—
161C23C2×C22⋊D2911yescharacteristic
162Q8—41no—
163D4—41no—
164D4—41no—
165D4—41no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—81no—
176C2×C4—582no—
177C2×C4—1161no—
178C2×C4—1161no—
179C2×C4—1161no—
180C2×C4—1161no—
181C2×C4—1161no—
182C2×C4C2×C22⋊D2911yescharacteristic
183C2×C4C2×C22⋊D2911yescharacteristic
184C8—1161no—
185C8—1161no—
186C22—21no—
187C22—21no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22#1174531111yescharacteristic
192C22#1174531211yescharacteristic
193C22#1174531511yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—41no—
198C4—41no—
199C4—41no—
200C4—41no—
201C4—1162no—
202C4—2321no—
203C2—21no—
204C2—21no—
205C2—81no—
206C2#1427130811yescharacteristic
207C2#1427134611yescharacteristic
208C2#1427135311yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#539C2
socleC22×C29#120
prime radicalC29×#121C22
hypercenter#539D29
hypocenterC29#1609
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. #14271491C2semidirect
3. #14271093C2semidirect
4. #14270900C2semidirect
6. #14270889C2semidirect
131. C29#1609semidirect

Maximal subgroups

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

subgroupindex
#142714912
#142714742
#142710932
#142709002
#142708972
#142708892
C29×#5392
#160929