Finite Group Databasebeta

← #16820651

Subgroups — #16820651

Order 3712.

246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 69 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#14271791C211yesmaximal, characteristic
2#14271172C211yesmaximal, characteristic
3#14271070C211yesmaximal, characteristic
4#14270931C211yesmaximal, characteristic
5#14270924C211yesmaximal, characteristic
6#14270922C211yesmaximal, characteristic
7C29×#419C211yesmaximal, characteristic
8C22×Q8×C29C2211yescharacteristic
9C2×M16×C29C2211yescharacteristic
10C29×#117C2211yescharacteristic
11#11745288C2211yescharacteristic
12C2×C4⋊Dic29C2211yescharacteristic
13C2×C4×Dic29C2211yescharacteristic
14C2×#90777C2211yescharacteristic
15#11745252—21no—
16#11745250—21no—
17#11745240—22no—
18#11745232—21no—
19#11745231—21no—
20C29×#103—21no—
21C29×#103—21no—
22#11745183—21no—
23#11745183—21no—
24#11745179—22no—
25C2×Q8×C29—21no—
26C2×Q8×C29—21no—
27C2×Q8×C29—21no—
28C2×Q8×C29—21no—
29C2×Q8×C29—21no—
30C2×Q8×C29Q812yescomplemented
31C22×C4×C29—21no—
32C22×C4×C29C2311yescharacteristic
33C22×Dic29—21no—
34C22×Dic29D412yes—
35C2×Dic58—22no—
36M16×C29—21no—
37M16×C29—21no—
38C2×C8×C29—21no—
39C4⋊C4×C29D411yescharacteristic
40C4⋊C4×C29D411yescharacteristic
41C22⋊C4×C29—21no—
42C42×C29—21no—
43C22⋊Dic29—21no—
44C4⋊Dic29—22no—
45C4⋊Dic29—21no—
46C4⋊Dic29—21no—
47C4⋊Dic29D411yescharacteristic
48C4⋊Dic29D411yescharacteristic
49#90779—22no—
50#90779—22no—
51C4×Dic29—21no—
52C4×Dic29—21no—
53C4×Dic29—21no—
54#90777—21no—
55#90777—21no—
56C2×#6597—21no—
57C23×C29C2×D411yescharacteristic
58Q8×C29—22no—
59Q8×C29—22no—
60Q8×C29—41no—
61Q8×C29—41no—
62C2×C4×C29—21no—
63C2×C4×C29—21no—
64C2×C4×C29—22no—
65C2×C4×C29—41no—
66C2×C4×C29—41no—
67C2×C4×C29C2×D411yescharacteristic
68C2×C4×C29C2×D411yescharacteristic
69C2×C4×C29C2×Q811yescharacteristic
70C2×C4×C29#4111yescharacteristic
71C2×C4×C29#4111yescharacteristic
72C2×C4×C29#4111yescharacteristic
73C2×Dic29—22no—
74C2×Dic29—21no—
75C2×Dic29—21no—
76C2×Dic29—22no—
77C2×Dic29—41no—
78C2×Dic29—41no—
79C2×Dic29—42no—
80Dic58—82no—
81C8×C29—41no—
82#6597—41no—
83#2028—291nomaximal, Sylow
84C22×C29—21no—
85C22×C29—21no—
86C22×C29#12011yescharacteristic
87C22×C29C22⋊Q811yescharacteristic
88C22×C29#12411yescharacteristic
89C4×C29—42no—
90C4×C29—41no—
91C4×C29—41no—
92C4×C29C22⋊Q811yescharacteristic
93C4×C29C22⋊Q811yescharacteristic
94C4×C29#12411yescharacteristic
95C4×C29#12411yescharacteristic
96Dic29—42no—
97Dic29—41no—
98Dic29—42no—
99Dic29—41no—
100#544—291no—
101#419—291no—
102#419D2911yescharacteristic
103#391—291no—
104#343—291no—
105#339—291no—
106#339—291no—
107C2×C29—21no—
108C2×C29—21no—
109C2×C29#39311yescharacteristic
110C2×C29#45511yescharacteristic
111C2×C29#45611yescharacteristic
112C22×Q8C2×D2911yescharacteristic
113C2×M16—291no—
114C2×M16C2×D2911yescharacteristic
115C4⋊Q8—581no—
116C4⋊Q8—581no—
117#125—581no—
118#125—581no—
119C22⋊Q8—582no—
120#117—291no—
121#117C2×D2911yescharacteristic
122C2×C4⋊C4—291no—
123C2×C42—291no—
124#103—21no—
125#103—21no—
126#103—581no—
127#103—581no—
128#95—582no—
129C29#202811yescharacteristic, complemented, Sylow
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—582no—
136C2×Q8Dic5812yescomplemented
137C22×C4—21no—
138C22×C4—292no—
139C22×C4—581no—
140C22×C4C22×D2911yescharacteristic
141M16—21no—
142M16—21no—
143M16—581no—
144M16—581no—
145C2×C8—21no—
146C2×C8—581no—
147C4⋊C4—291no—
148C4⋊C4—291no—
149C4⋊C4—582no—
150C4⋊C4—582no—
151C4⋊C4—582no—
152C4⋊C4—581no—
153C4⋊C4—581no—
154C4⋊C4C22⋊D2911yescharacteristic
155C4⋊C4C22⋊D2911yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—581no—
158C42—21no—
159C42—581no—
160C42—581no—
161C42—581no—
162C23D4×D2911yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—41no—
166Q8—41no—
167Q8—2322no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—582no—
174C2×C4—581no—
175C2×C4—581no—
176C2×C4—582no—
177C2×C4—1161no—
178C2×C4—1161no—
179C2×C4—1162no—
180C2×C4C2×Dic5811yescharacteristic
181C2×C4#9080511yescharacteristic
182C2×C4D4×D2911yescharacteristic
183C2×C4#9080711yescharacteristic
184C2×C4#9080711yescharacteristic
185C2×C4C2×C22⋊D2911yescharacteristic
186C8—41no—
187C8—1161no—
188C22—21no—
189C22—21no—
190C22#1174524011yescharacteristic
191C22#1174524711yescharacteristic
192C22#1174529911yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—1162no—
197C4—1162no—
198C4—1161no—
199C4—1161no—
200C4#1174524011yescharacteristic
201C4#1174524711yescharacteristic
202C4#1174528611yescharacteristic
203C4#1174529811yescharacteristic
204C2—21no—
205C2—21no—
206C2#1427107511yescharacteristic
207C2#1427133911yescharacteristic
208C2#1427134411yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#419C2
socleC22×C29#120
prime radicalC23×C29C2×D4
hypercenter#419D29
hypocenterC29#2028
LCSG ▷ C22×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
30. C2×Q8×C29Q8semidirect
129. C29#2028semidirect
136. C2×Q8Dic58semidirect

Maximal subgroups

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

subgroupindex
#142717912
#142711722
#142710702
#142709312
#142709242
#142709222
C29×#4192
#202829