Finite Group Databasebeta

← #16821176

Subgroups — #16821176

Order 3712.

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

normal subgroups only

This group has 250 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#14271714C211yesmaximal, characteristic
2#14271146C212yesmaximal, complemented
3#14270962C211yesmaximal, characteristic, complemented
4#14270959C212yesmaximal, complemented
5C29×#356C211yesmaximal, characteristic, complemented
6C2×#90809C411yescharacteristic
7C2×#90809C2211yescharacteristic
8C29×C4⋊Q8C2211yescharacteristic
9#11745309C411yescharacteristic
10#11745309C2211yescharacteristic
11M16×D29—22no—
12#11745257—22no—
13#11745255—22no—
14#11745236C411yescharacteristic
15C42×D29C411yescharacteristic
16C29×#101C2212yes—
17#11745184C2212yes—
18#11745171—22no—
19C2×Q8×C29C2×C411yescharacteristic
20C2×Q8×C29C2311yescharacteristic
21#90809—41no—
22#90809—41no—
23#90809—41no—
24#90809—41no—
25C2×D116—21no—
26C2×D116—22no—
27C2×D116C2×C411yescharacteristic
28C2×D116C2×C411yescharacteristic
29C2×D116D412yes—
30C2×C4×D29—21no—
31C2×C4×D29—21no—
32C2×C4×D29C2×C411yescharacteristic
33C2×C4×D29D412yes—
34M16×C29—22no—
35C4⋊C4×C29—22no—
36C42×C29C2×C411yescharacteristic
37#90781—22no—
38#90781—22no—
39C4×Dic29—21no—
40C4×Dic29C2×C411yescharacteristic
41#90777—22no—
42#90772—42no—
43C8×D29—42no—
44C22×D29—21no—
45C22×D29C22⋊C412yes—
46C22×D29C22⋊C411yescharacteristic
47Q8×C29—41no—
48Q8×C29—41no—
49C2×C4×C29—21no—
50C2×C4×C29—21no—
51C2×C4×C29C22×C411yescharacteristic
52C2×C4×C29C2×D412yes—
53C2×Dic29—21no—
54C2×Dic29C22⋊C411yescharacteristic
55D116—41no—
56D116—42no—
57D116—41no—
58D116—44no—
59D116—42no—
60C4×D29—22no—
61C4×D29—22no—
62C4×D29—21no—
63C4×D29—21no—
64C4×D29—42no—
65C4×D29—41no—
66C4×D29—41no—
67C8×C29—42no—
68#6597—42no—
69#2132—291nomaximal, Sylow
70C22×C29C2×C22⋊C411yescharacteristic
71C2×D29—21no—
72C2×D29—22no—
73C2×D29—41no—
74C2×D29—42no—
75C2×D29—42no—
76C2×D29—41no—
77C4×C29—22no—
78C4×C29—22no—
79C4×C29—21no—
80C4×C29—41no—
81Dic29—41no—
82Dic29#9911yescharacteristic
83Dic29#9911yescharacteristic
84#532—291no—
85#413—292no—
86#356—291no—
87#356D2911yescharacteristic, complemented
88#355—292no—
89C2×C29—21no—
90C2×C29C2×#9911yescharacteristic
91D29—41no—
92D29—42no—
93D29—81no—
94C2×#41—291no—
95C2×#41—291no—
96C2×M16—582no—
97C4⋊Q8C2×D2911yescharacteristic
98#127—291no—
99#124—291no—
100#124—291no—
101#121—582no—
102C4×D4—582no—
103C2×C42—291no—
104#101—292no—
105#101C2×D2912yes—
106#100—582no—
107C29#213211yescharacteristic, complemented, Sylow
108#41—1161no—
109#41—1161no—
110#41—1161no—
111#41—1161no—
112C2×Q8C4×D2911yescharacteristic
113C2×Q8C22×D2911yescharacteristic
114C2×D4—291no—
115C2×D4—291no—
116C2×D4—292no—
117C2×D4—582no—
118C2×D4—581no—
119C22×C4—291no—
120C22×C4—292no—
121C22×C4—581no—
122C22×C4—581no—
123M16—22no—
124M16—582no—
125M16—1162no—
126C2×C8—1162no—
127C4⋊C4—22no—
128C22⋊C4—582no—
129C22⋊C4—582no—
130C42—291no—
131C42—581no—
132C42C4×D2911yescharacteristic
133C23—292no—
134C23—291no—
135C23—581no—
136Q8—41no—
137Q8—41no—
138D4—1162no—
139D4—1161no—
140D4—1161no—
141D4—1164no—
142D4—1162no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—291no—
146C2×C4—582no—
147C2×C4—582no—
148C2×C4—581no—
149C2×C4—581no—
150C2×C4—581no—
151C2×C4—1162no—
152C2×C4—1161no—
153C2×C4—1161no—
154C2×C4C2×C4×D2911yescharacteristic
155C2×C4D4×D2912yes—
156C8—42no—
157C8—1162no—
158C22—581no—
159C22—582no—
160C22—1161no—
161C22—1162no—
162C22—1162no—
163C22—1161no—
164C22C22⋊C4×D2911yescharacteristic
165C4—22no—
166C4—22no—
167C4—21no—
168C4—41no—
169C4—291no—
170C4—291no—
171C4—1161no—
172C2—21no—
173C2—1161no—
174C2—1162no—
175C2—2321no—
176C2#99×D2911yescharacteristic
subgroupG/H
centerC2#99×D29
commutatorC2×C4×C29C22×C4
FrattiniC2×Q8C22×D29
FittingC29×#356C2
socleC2×C29C2×#99
prime radical#14271714C2
cosocleC2×Q8×C29C23
hypercenter#356D29
hypocenterC29#2132
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
2. #14271146C2semidirect
3. #14270962C2semidirect
4. #14270959C2semidirect
5. C29×#356C2semidirect
87. #356D29semidirect
107. C29#2132semidirect

Maximal subgroups

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

subgroupindex
#142717142
#142711462
#142709622
#142709592
C29×#3562
#213229