Finite Group Databasebeta

← #16818490

Subgroups — #16818490

Order 3712.

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

normal subgroups only

This group has 216 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#14271758C211yesmaximal, characteristic
2#14271494C211yesmaximal, characteristic, complemented
3#14271474C211yesmaximal, characteristic
4#14271095C211yesmaximal, characteristic, complemented
5#14270899C211yesmaximal, characteristic, complemented
6#14270888C211yesmaximal, characteristic, complemented
7C29×#327C211yesmaximal, characteristic
8C29×#121C2211yescharacteristic
9#11745297—21no—
10#11745297—21no—
11D4×Dic29—21no—
12C2×C4⋊Dic29—21no—
13C2×C4⋊Dic29C2211yescharacteristic
14#11745286C2211yescharacteristic
15C2×#90779C2211yescharacteristic
16#11745251—21no—
17#11745241—21no—
18#11745240—21no—
19C29×C22⋊C8C2211yescharacteristic
20C29×#95C2211yescharacteristic
21#11745180—21no—
22#11745179—21no—
23C22⋊#6597C2211yescharacteristic
24#11745165—21no—
25#11745164—21no—
26#11745155—21no—
27C2×D4×C29—21no—
28C2×D4×C29D411yescharacteristic
29C22×C4×C29—21no—
30C22×C4×C29C2311yescharacteristic
31C22×Dic29—21no—
32C22×Dic29—21no—
33C22×Dic29D411yescharacteristic
34C22×Dic29D411yescharacteristic
35C2×Dic58D411yescharacteristic
36C2×C8×C29—21no—
37C4⋊C4×C29D411yescharacteristic
38C22⋊C4×C29—21no—
39C22⋊Dic29—21no—
40C22⋊Dic29—21no—
41C22⋊Dic29—21no—
42C22⋊Dic29—21no—
43C4⋊Dic29—21no—
44C4⋊Dic29—21no—
45C4⋊Dic29—21no—
46C4⋊Dic29—42no—
47C4⋊Dic29D411yescharacteristic
48#90779—21no—
49#90779—21no—
50#90779—21no—
51#90779—21no—
52#90779—21no—
53C4×Dic29—21no—
54C2×#6597—21no—
55C23×C29—21no—
56C23×C29C2×D411yescharacteristic
57D4×C29—41no—
58D4×C29—41no—
59D4×C29—41no—
60C2×C4×C29—22no—
61C2×C4×C29—21no—
62C2×C4×C29—41no—
63C2×C4×C29—41no—
64C2×C4×C29—41no—
65C2×C4×C29C2×D411yescharacteristic
66C2×C4×C29C2×D411yescharacteristic
67C2×Dic29—21no—
68C2×Dic29—21no—
69C2×Dic29—21no—
70C2×Dic29—21no—
71C2×Dic29—21no—
72C2×Dic29—21no—
73C2×Dic29—41no—
74C2×Dic29—41no—
75C2×Dic29—41no—
76C2×Dic29—41no—
77C2×Dic29—81no—
78Dic58—41no—
79C8×C29—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—42no—
93C4×C29—41no—
94Dic29—41no—
95Dic29—41no—
96Dic29—41no—
97Dic29—41no—
98Dic29—81no—
99#539—291no—
100#483—291no—
101#480—291no—
102#398—291no—
103#328—291no—
104#327D2911yescharacteristic
105#324—291no—
106C2×C29—21no—
107C2×C29—21no—
108C2×C29—81no—
109C2×C29#44911yescharacteristic
110C2×C29#45611yescharacteristic
111C2×C29#45811yescharacteristic
112#126—581no—
113#125—581no—
114#123—581no—
115#123—581no—
116C22⋊Q8—291no—
117C22⋊Q8—581no—
118#121C2×D2911yescharacteristic
119C4×D4—581no—
120C2×C4⋊C4—291no—
121C2×C4⋊C4—291no—
122C2×C4⋊C4—581no—
123#107—581no—
124#106—581no—
125#103—581no—
126#102—581no—
127C22⋊C8—291no—
128C22⋊C8C2×D2911yescharacteristic
129#95—581no—
130#95C2×D2911yescharacteristic
131C29#160911yescharacteristic, complemented, Sylow
132C2×Q8—291no—
133C2×D4—21no—
134C2×D4D11611yescharacteristic
135C22×C4—21no—
136C22×C4—291no—
137C22×C4—291no—
138C22×C4—581no—
139C22×C4—581no—
140C22×C4C22×D2911yescharacteristic
141C2×C8—21no—
142C2×C8—581no—
143C4⋊C4—291no—
144C4⋊C4—581no—
145C4⋊C4—581no—
146C4⋊C4—581no—
147C4⋊C4—581no—
148C4⋊C4—581no—
149C4⋊C4—581no—
150C4⋊C4—581no—
151C4⋊C4—581no—
152C4⋊C4—1162no—
153C4⋊C4D11611yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—581no—
156C22⋊C4—581no—
157C22⋊C4—581no—
158C22⋊C4—581no—
159C42—581no—
160C23—21no—
161C23D4×D2911yescharacteristic
162Q8—1161no—
163D4—41no—
164D4—41no—
165D4—41no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—581no—
172C2×C4—581no—
173C2×C4—581no—
174C2×C4—581no—
175C2×C4—581no—
176C2×C4—581no—
177C2×C4—1161no—
178C2×C4—1161no—
179C2×C4—1161no—
180C2×C4—1161no—
181C2×C4—2321no—
182C2×C4C2×D11611yescharacteristic
183C2×C4D4×D2911yescharacteristic
184C8—41no—
185C8—1161no—
186C22—21no—
187C22—21no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22#1174524411yescharacteristic
192C22#1174527311yescharacteristic
193C22#1174527811yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—1161no—
199C4—1161no—
200C4—1161no—
201C4—1161no—
202C4—2321no—
203C2—21no—
204C2—21no—
205C2—81no—
206C2#1427130911yescharacteristic
207C2#1427134711yescharacteristic
208C2#1427135411yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#327C2
socleC22×C29#120
prime radicalC29×#121C22
hypercenter#327D29
hypocenterC29#1609
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #14271494C2semidirect
4. #14271095C2semidirect
5. #14270899C2semidirect
6. #14270888C2semidirect
131. C29#1609semidirect

Maximal subgroups

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

subgroupindex
#142717582
#142714942
#142714742
#142710952
#142708992
#142708882
C29×#3272
#160929