Finite Group Databasebeta

← #16821158

Subgroups — #16821158

Order 3712.

286 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 55 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#14271726C211yesmaximal, characteristic
2#99×D29C212yesmaximal, complemented
3#14270957C212yesmaximal, complemented
4#14270956C211yesmaximal, characteristic, complemented
5C29×#353C211yesmaximal, characteristic, complemented
6C2×#90807C411yescharacteristic, complemented
7C2×D4×D29C2211yescharacteristic
8C29×#127C2211yescharacteristic
9#11745302C411yescharacteristic, complemented
10#11745301—22no—
11#11745299—22no—
12#11745298C2211yescharacteristic
13C22⋊C4×D29—22no—
14#11745237C411yescharacteristic, complemented
15#11745234C411yescharacteristic, complemented
16C29×#99C2212yes—
17#11745182C2212yes—
18#11745154—22no—
19C23×D29D412yes—
20C2×D4×C29—22no—
21C2×D4×C29C2×C411yescharacteristic, complemented
22C2×D4×C29C2311yescharacteristic
23C2×C22⋊D29—21no—
24C2×C22⋊D29—22no—
25C2×C22⋊D29D412yes—
26C22×Dic29—21no—
27#90807—42no—
28D4×D29—42no—
29C2×D116C2×C411yescharacteristic
30C2×C4×D29—42no—
31C2×C4×D29C2×C411yescharacteristic
32C2×Dic58C2×C411yescharacteristic, complemented
33C22⋊C4×C29—22no—
34C42×C29C2×C411yescharacteristic, complemented
35C22⋊Dic29—22no—
36C22⋊Dic29—22no—
37#90781—21no—
38#90781—22no—
39#90781—42no—
40#90779—21no—
41C4×Dic29C2×C411yescharacteristic, complemented
42C23×C29—21no—
43C23×C29C2×D412yes—
44C22×D29—22no—
45C22×D29—22no—
46C22×D29—82no—
47C22×D29C22⋊C412yes—
48C22×D29C22⋊C411yescharacteristic
49D4×C29—41no—
50D4×C29—41no—
51D4×C29—82no—
52C2×C4×C29—21no—
53C2×C4×C29—42no—
54C2×C4×C29C22×C411yescharacteristic
55C22⋊D29—42no—
56C22⋊D29—42no—
57C22⋊D29—82no—
58C2×Dic29—21no—
59C2×Dic29—21no—
60C2×Dic29—42no—
61C2×Dic29—42no—
62C2×Dic29C22⋊C411yescharacteristic
63D116—41no—
64C4×D29—22no—
65C4×D29—84no—
66Dic58—41no—
67#2127—291nomaximal, Sylow
68C22×C29—22no—
69C22×C29—42no—
70C22×C29—42no—
71C22×C29—41no—
72C22×C29C2×C22⋊C411yescharacteristic
73C2×D29—22no—
74C2×D29—41no—
75C2×D29—44no—
76C2×D29—42no—
77C2×D29—82no—
78C2×D29#9912yes—
79C4×C29—21no—
80C4×C29—41no—
81C4×C29—82no—
82Dic29—21no—
83Dic29—41no—
84Dic29—41no—
85Dic29—82no—
86#535—291no—
87C2×#99—292no—
88#354—292no—
89#353—291no—
90#353D2911yescharacteristic, complemented
91C2×C29—21no—
92C2×C29—42no—
93C2×C29—81no—
94C2×C29C2×#9911yescharacteristic
95D29—22no—
96D29—42no—
97C2×#41—291no—
98C22×D4—291no—
99#127—291no—
100#127C2×D2911yescharacteristic
101#124—291no—
102#124—291no—
103#121—582no—
104#120—582no—
105#117—291no—
106C2×C22⋊C4—582no—
107#99—292no—
108#99—582no—
109#99C2×D2912yes—
110C29#212711yescharacteristic, complemented, Sylow
111C24—292no—
112#41—1162no—
113C2×Q8—291no—
114C2×D4—22no—
115C2×D4—292no—
116C2×D4—291no—
117C2×D4—581no—
118C2×D4—582no—
119C2×D4—1162no—
120C2×D4C4×D2911yescharacteristic, complemented
121C2×D4C22×D2911yescharacteristic
122C22×C4—291no—
123C22×C4—581no—
124C22×C4—1162no—
125C4⋊C4—581no—
126C22⋊C4—22no—
127C22⋊C4—581no—
128C22⋊C4—582no—
129C22⋊C4—582no—
130C22⋊C4—582no—
131C22⋊C4—1162no—
132C42—291no—
133C42C4×D2911yescharacteristic, complemented
134C23—21no—
135C23—291no—
136C23—292no—
137C23—582no—
138C23—582no—
139C23—2322no—
140C23D4×D2912yes—
141Q8—1161no—
142D4—41no—
143D4—41no—
144D4—82no—
145D4—1161no—
146D4—1162no—
147D4—1162no—
148D4—2322no—
149C2×C4—21no—
150C2×C4—42no—
151C2×C4—291no—
152C2×C4—582no—
153C2×C4—581no—
154C2×C4—581no—
155C2×C4—1162no—
156C2×C4—1162no—
157C2×C4—2324no—
158C2×C4C2×C4×D2911yescharacteristic
159C22—22no—
160C22—42no—
161C22—42no—
162C22—41no—
163C22—292no—
164C22—582no—
165C22—1161no—
166C22—1162no—
167C22—1164no—
168C22—2322no—
169C22C22⋊C4×D2911yescharacteristic
170C4—21no—
171C4—41no—
172C4—82no—
173C4—581no—
174C4—1161no—
175C4—1161no—
176C4—2322no—
177C2—21no—
178C2—42no—
179C2—81no—
180C2—582no—
181C2—1162no—
182C2#99×D2911yescharacteristic
subgroupG/H
centerC2#99×D29
commutatorC2×C4×C29C22×C4
FrattiniC2×D4C22×D29
FittingC29×#353C2
socleC2×C29C2×#99
prime radical#14271726C2
cosocleC2×D4×C29C23
hypercenter#353D29
hypocenterC29#2127
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #99×D29C2semidirect
3. #14270957C2semidirect
4. #14270956C2semidirect
5. C29×#353C2semidirect
6. C2×#90807C4semidirect
9. #11745302C4semidirect
14. #11745237C4semidirect
15. #11745234C4semidirect
21. C2×D4×C29C2×C4semidirect
32. C2×Dic58C2×C4semidirect
34. C42×C29C2×C4semidirect
41. C4×Dic29C2×C4semidirect
90. #353D29semidirect
110. C29#2127semidirect
120. C2×D4C4×D29semidirect
133. C42C4×D29semidirect

Maximal subgroups

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

subgroupindex
#142717262
#99×D292
#142709572
#142709562
C29×#3532
#212729