Finite Group Databasebeta

← #16821154

Subgroups — #16821154

Order 3712.

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

normal subgroups only

This group has 258 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#14271711C211yesmaximal, characteristic
2#14271135C212yesmaximal, complemented
3#14270957C212yesmaximal, complemented
4#14270956C211yesmaximal, characteristic, complemented
5C29×#353C211yesmaximal, characteristic, complemented
6C2×#90807C411yescharacteristic, complemented
7C2×#90807C2211yescharacteristic
8C29×#127C2211yescharacteristic
9#11745300—22no—
10#11745298C411yescharacteristic, complemented
11#11745298C2211yescharacteristic
12D4×Dic29—22no—
13#11745239—22no—
14C42×D29C411yescharacteristic, complemented
15#11745231C411yescharacteristic, complemented
16C29×#99C2212yes—
17#11745182C2212yes—
18#11745154—22no—
19C2×D4×C29—22no—
20C2×D4×C29C2×C411yescharacteristic
21C2×D4×C29C2311yescharacteristic
22C2×C22⋊D29—21no—
23C2×C22⋊D29D412yes—
24C22×Dic29—21no—
25C22×Dic29D412yes—
26#90807—41no—
27#90807—41no—
28#90807—41no—
29#90807—41no—
30C2×C4×D29—21no—
31C2×C4×D29C2×C411yescharacteristic
32C2×Dic58C2×C411yescharacteristic
33C2×Dic58C2×C411yescharacteristic
34C22⋊C4×C29—22no—
35C42×C29C2×C411yescharacteristic
36C22⋊Dic29—22no—
37C22⋊Dic29—22no—
38C22⋊Dic29—22no—
39C4⋊Dic29—22no—
40#90779—42no—
41C4×Dic29—21no—
42C4×Dic29—42no—
43C4×Dic29C2×C411yescharacteristic
44C23×C29—21no—
45C23×C29C2×D412yes—
46C22×D29C22⋊C411yescharacteristic
47D4×C29—41no—
48D4×C29—41no—
49D4×C29—44no—
50C2×C4×C29—21no—
51C2×C4×C29—42no—
52C2×C4×C29C22×C411yescharacteristic
53C22⋊D29—42no—
54C22⋊D29—42no—
55C2×Dic29—22no—
56C2×Dic29—22no—
57C2×Dic29—21no—
58C2×Dic29—21no—
59C2×Dic29—41no—
60C2×Dic29—41no—
61C2×Dic29—42no—
62C2×Dic29C22⋊C412yes—
63C2×Dic29C22⋊C411yescharacteristic
64C4×D29—21no—
65C4×D29—21no—
66C4×D29—42no—
67Dic58—41no—
68Dic58—41no—
69#2126—291nomaximal, Sylow
70C22×C29—22no—
71C22×C29—42no—
72C22×C29—42no—
73C22×C29—41no—
74C22×C29C2×C22⋊C411yescharacteristic
75C2×D29—21no—
76C2×D29—41no—
77C4×C29—22no—
78C4×C29—21no—
79C4×C29—82no—
80Dic29—22no—
81Dic29—41no—
82Dic29—41no—
83Dic29—82no—
84Dic29#9911yescharacteristic
85Dic29#9911yescharacteristic
86#532—291no—
87#410—292no—
88#354—292no—
89#353—291no—
90#353D2911yescharacteristic, complemented
91C2×C29—21no—
92C2×C29—42no—
93C2×C29—81no—
94C2×C29C2×#9911yescharacteristic
95D29—41no—
96C2×#41—291no—
97C2×#41—291no—
98C4⋊Q8—291no—
99#127C2×D2911yescharacteristic
100#124—291no—
101#124—291no—
102#121—582no—
103C4×D4—582no—
104#117—582no—
105C2×C42—291no—
106#99—292no—
107#99—582no—
108#99C2×D2912yes—
109C29#212611yescharacteristic, complemented, Sylow
110#41—1161no—
111#41—1161no—
112#41—1161no—
113#41—1161no—
114C2×Q8—291no—
115C2×Q8—291no—
116C2×D4—22no—
117C2×D4—292no—
118C2×D4—581no—
119C2×D4C4×D2911yescharacteristic
120C2×D4C22×D2911yescharacteristic
121C22×C4—292no—
122C22×C4—291no—
123C22×C4—581no—
124C22×C4—581no—
125C4⋊C4—582no—
126C4⋊C4—1162no—
127C22⋊C4—22no—
128C22⋊C4—582no—
129C22⋊C4—582no—
130C22⋊C4—582no—
131C42—291no—
132C42—581no—
133C42—1162no—
134C42C4×D2911yescharacteristic
135C23—21no—
136C23—291no—
137C23D4×D2912yes—
138Q8—1161no—
139Q8—1161no—
140D4—41no—
141D4—41no—
142D4—44no—
143D4—1162no—
144D4—1162no—
145C2×C4—21no—
146C2×C4—42no—
147C2×C4—291no—
148C2×C4—292no—
149C2×C4—581no—
150C2×C4—581no—
151C2×C4—582no—
152C2×C4—582no—
153C2×C4—581no—
154C2×C4—581no—
155C2×C4—1162no—
156C2×C4—1161no—
157C2×C4—1161no—
158C2×C4—1162no—
159C2×C4C2×C4×D2911yescharacteristic
160C22—22no—
161C22—42no—
162C22—42no—
163C22—41no—
164C22—581no—
165C22—1161no—
166C22C22⋊C4×D2911yescharacteristic
167C4—22no—
168C4—21no—
169C4—82no—
170C4—291no—
171C4—291no—
172C4—582no—
173C4—1161no—
174C4—1161no—
175C4—2322no—
176C2—21no—
177C2—42no—
178C2—81no—
179C2—1161no—
180C2#99×D2911yescharacteristic
subgroupG/H
centerC2#99×D29
commutatorC2×C4×C29C22×C4
FrattiniC2×D4C22×D29
FittingC29×#353C2
socleC2×C29C2×#99
prime radical#14271711C2
cosocleC2×D4×C29C23
hypercenter#353D29
hypocenterC29#2126
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. #14271135C2semidirect
3. #14270957C2semidirect
4. #14270956C2semidirect
5. C29×#353C2semidirect
6. C2×#90807C4semidirect
10. #11745298C4semidirect
14. C42×D29C4semidirect
15. #11745231C4semidirect
90. #353D29semidirect
109. C29#2126semidirect

Maximal subgroups

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

subgroupindex
#142717112
#142711352
#142709572
#142709562
C29×#3532
#212629