Finite Group Databasebeta

← #16821180

Subgroups — #16821180

Order 3712.

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

normal subgroups only

This group has 230 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#14271738C211yesmaximal, characteristic
2#101×D29C212yesmaximal, complemented
3#14270962C211yesmaximal, characteristic, complemented
4#14270959C212yesmaximal, complemented
5C29×#356C211yesmaximal, characteristic, complemented
6C2×#90809C411yescharacteristic
7C2×Q8×D29C2211yescharacteristic
8C29×C4⋊Q8C2211yescharacteristic
9#11745309C2211yescharacteristic
10#11745306C411yescharacteristic
11M16×D29—22no—
12#11745258—22no—
13#11745256—22no—
14#11745237C411yescharacteristic
15#11745234C411yescharacteristic
16C29×#101C2212yes—
17#11745184C2212yes—
18#11745172—22no—
19C2×Q8×C29C2×C411yescharacteristic
20C2×Q8×C29C2311yescharacteristic
21#90809—42no—
22Q8×D29—42no—
23C2×D116—21no—
24C2×D116C2×C411yescharacteristic
25C2×C4×D29—21no—
26C2×C4×D29C2×C411yescharacteristic
27C2×C4×D29D412yes—
28C2×Dic58C2×C411yescharacteristic
29C2×Dic58D412yes—
30M16×C29—22no—
31C4⋊C4×C29—22no—
32C42×C29C2×C411yescharacteristic
33#90781—21no—
34#90781—22no—
35#90781—22no—
36#90779—22no—
37#90779—21no—
38C4×Dic29C2×C411yescharacteristic
39#90777—22no—
40#90772—42no—
41C8×D29—42no—
42C22×D29—21no—
43C22×D29C22⋊C411yescharacteristic
44Q8×C29—41no—
45Q8×C29—41no—
46C2×C4×C29—21no—
47C2×C4×C29—21no—
48C2×C4×C29C22×C411yescharacteristic
49C2×C4×C29C2×D412yes—
50C2×Dic29—21no—
51C2×Dic29C22⋊C412yes—
52C2×Dic29C22⋊C411yescharacteristic
53D116—41no—
54D116—42no—
55C4×D29—22no—
56C4×D29—22no—
57C4×D29—22no—
58C4×D29—42no—
59Dic58—41no—
60Dic58—42no—
61C8×C29—42no—
62#6597—42no—
63#2133—291nomaximal, Sylow
64C22×C29C2×C22⋊C411yescharacteristic
65C2×D29—41no—
66C2×D29—42no—
67C2×D29—41no—
68C2×D29#9912yes—
69C4×C29—22no—
70C4×C29—21no—
71C4×C29—41no—
72C4×C29—41no—
73Dic29—21no—
74Dic29—22no—
75Dic29—41no—
76#536—291no—
77C2×#101—292no—
78#356—291no—
79#356D2911yescharacteristic, complemented
80#355—292no—
81C2×C29—21no—
82C2×C29C2×#9911yescharacteristic
83D29—22no—
84D29—81no—
85C2×#41—291no—
86C22×Q8—291no—
87C2×M16—582no—
88C4⋊Q8—291no—
89C4⋊Q8C2×D2911yescharacteristic
90#124—291no—
91#124—291no—
92#123—582no—
93C22⋊Q8—582no—
94#117—291no—
95#101—292no—
96#101—582no—
97#101C2×D2912yes—
98C29#213311yescharacteristic, complemented, Sylow
99#41—1162no—
100C2×Q8—291no—
101C2×Q8—292no—
102C2×Q8—1162no—
103C2×Q8C4×D2911yescharacteristic
104C2×Q8C22×D2911yescharacteristic
105C2×D4—291no—
106C2×D4—581no—
107C22×C4—291no—
108C22×C4—292no—
109C22×C4—581no—
110M16—22no—
111M16—582no—
112M16—1162no—
113C2×C8—1162no—
114C4⋊C4—22no—
115C4⋊C4—581no—
116C4⋊C4—582no—
117C22⋊C4—582no—
118C22⋊C4—581no—
119C22⋊C4—582no—
120C42—291no—
121C42C4×D2911yescharacteristic
122C23—291no—
123C23—581no—
124Q8—41no—
125Q8—41no—
126Q8—1162no—
127Q8—1161no—
128D4—1161no—
129D4—1162no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—292no—
133C2×C4—291no—
134C2×C4—582no—
135C2×C4—582no—
136C2×C4—582no—
137C2×C4—581no—
138C2×C4—1162no—
139C2×C4C2×C4×D2911yescharacteristic
140C2×C4D4×D2912yes—
141C8—42no—
142C8—1162no—
143C22—292no—
144C22—1161no—
145C22—1162no—
146C22—1161no—
147C22C22⋊C4×D2911yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—41no—
152C4—581no—
153C4—582no—
154C4—1161no—
155C2—21no—
156C2—582no—
157C2—2321no—
158C2#99×D2911yescharacteristic
subgroupG/H
centerC2#99×D29
commutatorC2×C4×C29C22×C4
FrattiniC2×Q8C22×D29
FittingC29×#356C2
socleC2×C29C2×#99
prime radicalC2×#90809C4
cosocleC2×Q8×C29C23
hypercenter#356D29
hypocenterC29#2133
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. #101×D29C2semidirect
3. #14270962C2semidirect
4. #14270959C2semidirect
5. C29×#356C2semidirect
79. #356D29semidirect
98. C29#2133semidirect

Maximal subgroups

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

subgroupindex
#142717382
#101×D292
#142709622
#142709592
C29×#3562
#213329