Finite Group Databasebeta

← #16821161

Subgroups — #16821161

Order 3712.

286 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 73 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×#11745182C212yesmaximal, complemented
2#14270958C212yesmaximal, complemented
3#14270956C212yesmaximal, complemented
4C29×#535C211yesmaximal, characteristic
5C2×#41×C29C411yescharacteristic, complemented
6C22×D4×C29C2211yescharacteristic
7C29×#127C411yescharacteristic, complemented
8C29×#127C2211yescharacteristic
9C29×#124C411yescharacteristic, complemented
10C29×#124C2211yescharacteristic
11C29×#121—22no—
12C29×#120—22no—
13C29×#117C411yescharacteristic, complemented
14C2×C22⋊Dic29—22no—
15#11745182—22no—
16#11745182C2214yes—
17C24×C29D412yes—
18#41×C29—42no—
19C2×Q8×C29C2×C411yescharacteristic, complemented
20C2×D4×C29—21no—
21C2×D4×C29—22no—
22C2×D4×C29—22no—
23C2×D4×C29—42no—
24C2×D4×C29C2×C411yescharacteristic
25C2×D4×C29C2×C411yescharacteristic, complemented
26C2×D4×C29D412yes—
27C2×D4×C29C2311yescharacteristic
28C22×C4×C29—21no—
29C22×C4×C29C2×C411yescharacteristic
30C22×Dic29—42no—
31C4⋊C4×C29—21no—
32C22⋊C4×C29—21no—
33C22⋊C4×C29—22no—
34C22⋊C4×C29—22no—
35C42×C29C2×C411yescharacteristic, complemented
36C42×C29C2×C411yescharacteristic, complemented
37C22⋊Dic29—24no—
38C22⋊Dic29—42no—
39C23×C29—22no—
40C23×C29—22no—
41C23×C29—21no—
42C23×C29—82no—
43C23×C29C22⋊C412yes—
44C23×C29C22⋊C411yescharacteristic
45C23×C29C2×D412yes—
46Q8×C29—41no—
47D4×C29—41no—
48D4×C29—42no—
49D4×C29—41no—
50D4×C29—41no—
51D4×C29—42no—
52D4×C29—82no—
53D4×C29—82no—
54C2×C4×C29—22no—
55C2×C4×C29—21no—
56C2×C4×C29—21no—
57C2×C4×C29—21no—
58C2×C4×C29—42no—
59C2×C4×C29C22⋊C411yescharacteristic
60C2×C4×C29C22×C411yescharacteristic
61C2×Dic29—44no—
62C2×Dic29—84no—
63#2127—291nomaximal, Sylow
64C22×C29—22no—
65C22×C29—22no—
66C22×C29—41no—
67C22×C29—42no—
68C22×C29—42no—
69C22×C29—44no—
70C22×C29—42no—
71C22×C29—41no—
72C22×C29—82no—
73C22×C29#9912yes—
74C22×C29C2×C22⋊C411yescharacteristic
75C4×C29—21no—
76C4×C29—21no—
77C4×C29—41no—
78C4×C29—41no—
79C4×C29—41no—
80Dic29—84no—
81#535D2911yescharacteristic
82C2×#99—292no—
83#354—292no—
84#353—292no—
85C2×C29—21no—
86C2×C29—22no—
87C2×C29—42no—
88C2×C29—42no—
89C2×C29—81no—
90C2×C29C2×#9911yescharacteristic
91C2×#41Dic2911yescharacteristic, complemented
92C22×D4C2×D2911yescharacteristic
93#127Dic2911yescharacteristic, complemented
94#127C2×D2911yescharacteristic
95#124Dic2911yescharacteristic, complemented
96#124C2×D2911yescharacteristic
97#121—22no—
98#120—22no—
99#117Dic2911yescharacteristic, complemented
100C2×C22⋊C4—582no—
101#99—294no—
102#99—582no—
103C29#212711yescharacteristic, complemented, Sylow
104C24C22⋊D2912yes—
105#41—42no—
106C2×Q8C2×Dic2911yescharacteristic, complemented
107C2×D4—21no—
108C2×D4—22no—
109C2×D4—22no—
110C2×D4—42no—
111C2×D4C2×Dic2911yescharacteristic
112C2×D4C2×Dic2911yescharacteristic, complemented
113C2×D4C22⋊D2912yes—
114C2×D4C22×D2911yescharacteristic
115C22×C4—21no—
116C22×C4—1162no—
117C22×C4C2×Dic2911yescharacteristic
118C4⋊C4—21no—
119C22⋊C4—22no—
120C22⋊C4—21no—
121C22⋊C4—22no—
122C22⋊C4—584no—
123C22⋊C4—1162no—
124C42C2×Dic2911yescharacteristic, complemented
125C42C2×Dic2911yescharacteristic, complemented
126C23—22no—
127C23—22no—
128C23—21no—
129C23—82no—
130C23C22⋊Dic2912yes—
131C23C22⋊Dic2911yescharacteristic
132C23C2×C22⋊D2912yes—
133Q8—41no—
134D4—41no—
135D4—42no—
136D4—41no—
137D4—41no—
138D4—42no—
139D4—82no—
140D4—82no—
141C2×C4—22no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—42no—
146C2×C4—1164no—
147C2×C4—2324no—
148C2×C4C22⋊Dic2911yescharacteristic
149C2×C4C22×Dic2911yescharacteristic
150C22—22no—
151C22—22no—
152C22—41no—
153C22—42no—
154C22—42no—
155C22—44no—
156C22—42no—
157C22—41no—
158C22—82no—
159C22#1174518212yes—
160C22C2×C22⋊Dic2911yescharacteristic
161C4—21no—
162C4—21no—
163C4—41no—
164C4—41no—
165C4—41no—
166C4—2324no—
167C2—21no—
168C2—22no—
169C2—42no—
170C2—42no—
171C2—81no—
172C2C2×#1174518211yescharacteristic
subgroupG/H
centerC2C2×#11745182
commutatorC2×C4×C29C22×C4
FrattiniC2×D4C22×D29
Fitting, prime radicalC29×#535C2
socleC2×C29C2×#99
cosocleC2×D4×C29C23
hypercenter#535D29
hypocenterC29#2127
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#11745182C2semidirect
2. #14270958C2semidirect
3. #14270956C2semidirect
5. C2×#41×C29C4semidirect
7. C29×#127C4semidirect
9. C29×#124C4semidirect
13. C29×#117C4semidirect
19. C2×Q8×C29C2×C4semidirect
25. C2×D4×C29C2×C4semidirect
35. C42×C29C2×C4semidirect
36. C42×C29C2×C4semidirect
91. C2×#41Dic29semidirect
93. #127Dic29semidirect
95. #124Dic29semidirect
99. #117Dic29semidirect
103. C29#2127semidirect
106. C2×Q8C2×Dic29semidirect
112. C2×D4C2×Dic29semidirect
124. C42C2×Dic29semidirect
125. C42C2×Dic29semidirect

Maximal subgroups

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

subgroupindex
C2×#117451822
#142709582
#142709562
C29×#5352
#212729