Finite Group Databasebeta

← #16821165

Subgroups — #16821165

Order 3712.

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

normal subgroups only

This group has 238 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#14271733C211yesmaximal, characteristic
2#14271135C212yesmaximal
3#14270958C211yesmaximal, characteristic, complemented
4#14270957C212yesmaximal, complemented
5C29×#354C211yesmaximal, characteristic, complemented
6C2×Q8×D29C411yescharacteristic, complemented
7C2×#90807C2211yescharacteristic
8C29×#124C2211yescharacteristic
9#11745306C411yescharacteristic, complemented
10#11745298C2211yescharacteristic
11#11745245—22no—
12#11745240—22no—
13#11745239—22no—
14#11745234C411yescharacteristic, complemented
15#11745231C411yescharacteristic, complemented
16C29×#99C2212yes—
17#11745182C2212yes—
18#11745154—22no—
19C2×Q8×C29C2×C411yescharacteristic
20C2×D4×C29C2311yescharacteristic
21C2×C22⋊D29D412yes—
22C22×Dic29D412yes—
23Q8×D29—42no—
24#90807—42no—
25C2×C4×D29—21no—
26C2×C4×D29C2×C411yescharacteristic
27C2×Dic58—21no—
28C2×Dic58C2×C411yescharacteristic
29C2×Dic58C2×C411yescharacteristic
30C22⋊C4×C29—22no—
31C22⋊C4×C29—22no—
32C42×C29C2×C411yescharacteristic
33C22⋊Dic29—22no—
34C22⋊Dic29—22no—
35#90781—21no—
36C4⋊Dic29—22no—
37#90779—22no—
38#90779—21no—
39#90779—42no—
40C4×Dic29—42no—
41C4×Dic29C2×C411yescharacteristic
42C23×C29C2×D412yes—
43C22×D29C22⋊C411yescharacteristic
44Q8×C29—41no—
45D4×C29—41no—
46C2×C4×C29—21no—
47C2×C4×C29—21no—
48C2×C4×C29—42no—
49C2×C4×C29C22×C411yescharacteristic
50C22⋊D29—42no—
51C2×Dic29—22no—
52C2×Dic29—22no—
53C2×Dic29—21no—
54C2×Dic29—21no—
55C2×Dic29—42no—
56C2×Dic29C22⋊C412yes—
57C2×Dic29C22⋊C411yescharacteristic
58C4×D29—22no—
59C4×D29—42no—
60Dic58—41no—
61Dic58—42no—
62Dic58—41no—
63#2129—291nomaximal, Sylow
64C22×C29—22no—
65C22×C29—42no—
66C22×C29C2×C22⋊C411yescharacteristic
67C2×D29—21no—
68C2×D29—41no—
69C4×C29—21no—
70C4×C29—41no—
71C4×C29—41no—
72C4×C29—82no—
73Dic29—22no—
74Dic29—41no—
75Dic29—41no—
76Dic29—82no—
77Dic29#9912yes—
78#536—291no—
79#410—292no—
80#354—291no—
81#354—292no—
82#354D2911yescharacteristic, complemented
83C2×C29—21no—
84C2×C29—42no—
85C2×C29C2×#9911yescharacteristic
86D29—41no—
87C2×#41—291no—
88C22×Q8—291no—
89C4⋊Q8—291no—
90C4⋊Q8—291no—
91#124—291no—
92#124C2×D2911yescharacteristic
93#123—582no—
94C22⋊Q8—582no—
95#117—291no—
96#117—582no—
97#99—292no—
98#99—582no—
99#99C2×D2912yes—
100C29#212911yescharacteristic, complemented, Sylow
101#41—1162no—
102C2×Q8—291no—
103C2×Q8—291no—
104C2×Q8—581no—
105C2×Q8—1162no—
106C2×Q8C4×D2911yescharacteristic
107C2×D4—292no—
108C2×D4C22×D2911yescharacteristic
109C22×C4—292no—
110C22×C4—291no—
111C22×C4—581no—
112C4⋊C4—581no—
113C4⋊C4—582no—
114C4⋊C4—582no—
115C4⋊C4—1162no—
116C22⋊C4—22no—
117C22⋊C4—22no—
118C22⋊C4—581no—
119C22⋊C4—582no—
120C22⋊C4—582no—
121C42—291no—
122C42—1162no—
123C42C4×D2911yescharacteristic
124C23—291no—
125C23D4×D2912yes—
126Q8—41no—
127Q8—1161no—
128Q8—1161no—
129Q8—1162no—
130D4—41no—
131D4—1162no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—42no—
135C2×C4—291no—
136C2×C4—292no—
137C2×C4—582no—
138C2×C4—582no—
139C2×C4—582no—
140C2×C4—581no—
141C2×C4—581no—
142C2×C4—1162no—
143C2×C4—1162no—
144C2×C4C2×C4×D2911yescharacteristic
145C22—22no—
146C22—42no—
147C22—581no—
148C22—1161no—
149C22C22⋊C4×D2911yescharacteristic
150C4—21no—
151C4—41no—
152C4—41no—
153C4—82no—
154C4—292no—
155C4—582no—
156C4—1161no—
157C4—1161no—
158C4—2322no—
159C2—21no—
160C2—42no—
161C2—1161no—
162C2#99×D2911yescharacteristic
subgroupG/H
centerC2#99×D29
commutatorC2×C4×C29C22×C4
FrattiniC2×D4C22×D29
FittingC29×#354C2
socleC2×C29C2×#99
prime radicalC2×#90807C22
cosocleC2×D4×C29C23
hypercenter#354D29
hypocenterC29#2129
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #14270958C2semidirect
4. #14270957C2semidirect
5. C29×#354C2semidirect
6. C2×Q8×D29C4semidirect
9. #11745306C4semidirect
14. #11745234C4semidirect
15. #11745231C4semidirect
82. #354D29semidirect
100. C29#2129semidirect

Maximal subgroups

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

subgroupindex
#142717332
#142711352
#142709582
#142709572
C29×#3542
#212929