Finite Group Databasebeta

← #16819941

Subgroups — #16819941

Order 3712.

358 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#11745288C211yesmaximal, characteristic, complemented
2C2×#11745185C212yesmaximal, complemented
3#14271127C211yesmaximal, characteristic, complemented
4#14270922C212yesmaximal, complemented
5C29×#525C211yesmaximal, characteristic
6C2×#41×C29C2211yescharacteristic
7C23×C4×C29C2211yescharacteristic
8C29×#123—21no—
9C29×C22⋊Q8C412yescomplemented
10C29×#121C412yescomplemented
11C29×#120—21no—
12C4×D4×C29—22no—
13C29×#117C2211yescharacteristic
14C2×C22⋊Dic29—21no—
15#11745288—24no—
16C2×C4⋊Dic29—21no—
17C2×C4×Dic29C2212yes—
18C2×#90777C2212yes—
19#11745185—24no—
20C22⋊#6597—22no—
21C24×C29D411yescharacteristic
22#41×C29—22no—
23#41×C29—22no—
24C2×Q8×C29C2×C411yescharacteristic
25C2×D4×C29—22no—
26C2×D4×C29—21no—
27C2×D4×C29C2×C411yescharacteristic
28C22×C4×C29—22no—
29C22×C4×C29—22no—
30C22×C4×C29—21no—
31C22×C4×C29C2×C412yes—
32C22×C4×C29D411yescharacteristic
33C22×C4×C29D412yes—
34C22×C4×C29C2311yescharacteristic
35C22×Dic29—22no—
36C4⋊C4×C29—22no—
37C4⋊C4×C29C2×C412yes—
38C22⋊C4×C29—22no—
39C22⋊C4×C29—21no—
40C22⋊C4×C29—22no—
41C42×C29—21no—
42C22⋊Dic29—24no—
43C4⋊Dic29—24no—
44C4×Dic29—22no—
45C4×Dic29D414yescomplemented
46#90777—22no—
47#90777—22no—
48C2×#6597—22no—
49C23×C29—21no—
50C23×C29—21no—
51C23×C29—21no—
52C23×C29—42no—
53C23×C29C22⋊C412yes—
54C23×C29C2×D411yescharacteristic
55Q8×C29—22no—
56D4×C29—22no—
57D4×C29—44no—
58D4×C29—41no—
59D4×C29—41no—
60C2×C4×C29—21no—
61C2×C4×C29—21no—
62C2×C4×C29—24no—
63C2×C4×C29—24no—
64C2×C4×C29—22no—
65C2×C4×C29—21no—
66C2×C4×C29—42no—
67C2×C4×C29C22⋊C412yes—
68C2×C4×C29C22×C411yescharacteristic
69C2×C4×C29C2×D412yes—
70C2×C4×C29C2×D411yescharacteristic
71C2×C4×C29#4112yes—
72C2×Dic29—24no—
73C2×Dic29—44no—
74#6597—42no—
75#1897—291nomaximal, Sylow
76C22×C29—22no—
77C22×C29—22no—
78C22×C29—22no—
79C22×C29—22no—
80C22×C29—42no—
81C22×C29—42no—
82C22×C29—41no—
83C22×C29—42no—
84C22×C29C2×C22⋊C411yescharacteristic
85C22×C29#12011yescharacteristic
86C22×C29#12311yescharacteristic
87C4×C29—22no—
88C4×C29—41no—
89C4×C29—42no—
90C4×C29C4×D412yes—
91C4×C29#12112yes—
92Dic29—44no—
93#525D2911yescharacteristic
94C2×#117—291no—
95C2×#104—292no—
96#407—291no—
97#339—292no—
98C2×C29—21no—
99C2×C29—21no—
100C2×C29—42no—
101C2×C29—81no—
102C2×C29#38611yescharacteristic
103C2×C29#42112yes—
104C2×#41C2×D2911yescharacteristic
105C23×C4C2×D2911yescharacteristic
106C2×M16—292no—
107#123—21no—
108C22⋊Q8Dic2912yescomplemented
109#121Dic2912yescomplemented
110#120—21no—
111C4×D4—22no—
112#117—584no—
113#117C2×D2911yescharacteristic
114C2×C4⋊C4—581no—
115C2×C22⋊C4—581no—
116C2×C42—292no—
117#104—584no—
118C22⋊C8—582no—
119C29#189711yescharacteristic, complemented, Sylow
120C24C22⋊D2911yescharacteristic
121#41—22no—
122#41—22no—
123C2×Q8C2×Dic2911yescharacteristic
124C2×D4—22no—
125C2×D4—21no—
126C2×D4C2×Dic2911yescharacteristic
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—21no—
130C22×C4—582no—
131C22×C4C2×Dic2912yes—
132C22×C4C22⋊D2911yescharacteristic
133C22×C4C22⋊D2912yes—
134C22×C4C22×D2911yescharacteristic
135M16—582no—
136M16—582no—
137C2×C8—582no—
138C4⋊C4—22no—
139C4⋊C4—584no—
140C4⋊C4C2×Dic2912yes—
141C22⋊C4—22no—
142C22⋊C4—21no—
143C22⋊C4—22no—
144C22⋊C4—584no—
145C42—21no—
146C42—294no—
147C42—582no—
148C23—21no—
149C23—21no—
150C23—21no—
151C23—42no—
152C23C22⋊Dic2912yes—
153C23C2×C22⋊D2911yescharacteristic
154Q8—22no—
155D4—22no—
156D4—44no—
157D4—41no—
158D4—41no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—42no—
166C2×C4—584no—
167C2×C4—1164no—
168C2×C4C22⋊Dic2912yes—
169C2×C4D4×D2912yes—
170C2×C4#9080712yes—
171C2×C4C22×Dic2911yescharacteristic
172C2×C4C2×C22⋊D2911yescharacteristic
173C8—1162no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—41no—
181C22—42no—
182C22#1174529711yescharacteristic
183C22#1174529911yescharacteristic
184C22C2×C22⋊Dic2911yescharacteristic
185C4—22no—
186C4—41no—
187C4—42no—
188C4—1164no—
189C4D4×Dic2912yes—
190C4#1174530112yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—81no—
195C2#1427104311yescharacteristic
196C2#1427118012yes—
subgroupG/H
centerC2×C4C2×C22⋊D29
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
Fitting, prime radicalC29×#525C2
socleC22×C29C2×C22⋊C4
cosocleC22×C4×C29C23
hypercenter#525D29
hypocenterC29#1897
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#11745288C2semidirect
2. C2×#11745185C2semidirect
3. #14271127C2semidirect
4. #14270922C2semidirect
9. C29×C22⋊Q8C4semidirect
10. C29×#121C4semidirect
45. C4×Dic29D4semidirect
108. C22⋊Q8Dic29semidirect
109. #121Dic29semidirect
119. C29#1897semidirect

Maximal subgroups

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

subgroupindex
C2×#117452882
C2×#117451852
#142711272
#142709222
C29×#5252
#189729