Finite Group Databasebeta

← #16835802

Subgroups — #16835802

Order 3712.

220 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 64 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
1D29⋊M32C211yesmaximal, characteristic
2#14272173C211yesmaximal, characteristic
3#14272076C214yesmaximal, complemented
4C2×Q16×D29C211yesmaximal, characteristic
5C2×Q8×D29—21no—
6#11745345—21no—
7C2×Q16×C29C411yescharacteristic, complemented
8C2×#90785—21no—
9Q16×D29—21no—
10Q16×D29—21no—
11Q16×D29C412yescomplemented
12Q16×D29C2212yes—
13C2×Dic116C411yescharacteristic, complemented
14C2×C8×D29C2211yescharacteristic
15#11745214—21no—
16#11745210C2212yes—
17#11745209—21no—
18#11745206—21no—
19D29⋊C16C2212yes—
20C2×Q8×C29—21no—
21Q8×D29—22no—
22Q8×D29—22no—
23Q8×D29—41no—
24Q8×D29—41no—
25C2×C4×D29—41no—
26C2×C4×D29D411yescharacteristic
27C2×Dic58—21no—
28C2×Dic58—41no—
29C22⋊#1181—41no—
30C4⋊#1181—22no—
31C4×#1181—41no—
32Q16×C29—21no—
33Q16×C29C2×C412yes—
34C2×C8×C29C2×C411yescharacteristic
35#90785—22no—
36#90785—22no—
37C2×#6597D411yescharacteristic
38Dic116—21no—
39Dic116C2×C412yes—
40C8×D29C2×C411yescharacteristic
41C8×D29D411yescharacteristic
42C8×D29D411yescharacteristic
43C8×D29C2311yescharacteristic
44#90770—22no—
45C22×D29D811yescharacteristic
46C2×#1181—42no—
47Q8×C29—22no—
48Q8×C29—41no—
49C2×C4×C29—41no—
50C2×C4×C29C22⋊C411yescharacteristic
51C2×Dic29—41no—
52C2×Dic29SD1611yescharacteristic
53C4×D29—42no—
54C4×D29—42no—
55C4×D29C22⋊C411yescharacteristic
56C4×D29D811yescharacteristic
57C4×D29SD1611yescharacteristic
58C4×D29C2×D411yescharacteristic
59Dic58—22no—
60Dic58—41no—
61Dic58—42no—
62Dic58—42no—
63C8×C29C22⋊C411yescharacteristic
64C8×C29C22×C411yescharacteristic
65#6597C22⋊C411yescharacteristic
66#6597C2×D411yescharacteristic
67#2141—291nomaximal, Sylow
68C22×C29#10211yescharacteristic
69C2×D29—22no—
70C2×D29#10211yescharacteristic
71C2×D29C2×D811yescharacteristic
72#1181—82no—
73C4×C29—42no—
74C4×C29#10211yescharacteristic
75C4×C29C2×C22⋊C411yescharacteristic
76Dic29—42no—
77Dic29#10211yescharacteristic
78Dic29C2×SD1611yescharacteristic
79C22×Q16—291no—
80C2×M32—291no—
81#427—291no—
82#358—294no—
83C2×C29—21no—
84C2×C29C2×#10211yescharacteristic
85D29—21no—
86D29#51012yes—
87C22×Q8—581no—
88C2×Q16—292no—
89C2×Q16—292no—
90C2×Q16—291no—
91C2×Q16—581no—
92C2×Q16—581no—
93C2×Q16—581no—
94C2×Q16#118111yescharacteristic, complemented
95C22×C8—291no—
96#117—581no—
97M32—581no—
98M32—581no—
99C2×C16—292no—
100#107—292no—
101#106—581no—
102C29#214111yescharacteristic, complemented, Sylow
103C2×Q8—21no—
104C2×Q8—582no—
105C2×Q8—582no—
106C2×Q8—581no—
107C2×Q8—1161no—
108C2×Q8—1161no—
109C2×Q8—1161no—
110C22×C4—291no—
111C22×C4—1161no—
112Q16—21no—
113Q16—292no—
114Q16—582no—
115Q16—582no—
116Q16—581no—
117Q16C2×#118112yes—
118C2×C8—291no—
119C2×C8—291no—
120C2×C8—291no—
121C2×C8—291no—
122C2×C8—291no—
123C2×C8C2×#118111yescharacteristic
124C4⋊C4—582no—
125C22⋊C4—1161no—
126C42—1161no—
127C16—582no—
128C23—291no—
129Q8—22no—
130Q8—41no—
131Q8—582no—
132Q8—1162no—
133Q8—1162no—
134Q8—1161no—
135C2×C4—41no—
136C2×C4—291no—
137C2×C4—291no—
138C2×C4—291no—
139C2×C4—291no—
140C2×C4—291no—
141C2×C4—1162no—
142C2×C4—1162no—
143C2×C4—1161no—
144C2×C4—1162no—
145C2×C4C22⋊#118111yescharacteristic
146C8—291no—
147C8—291no—
148C8C22⋊#118111yescharacteristic
149C8C22×#118111yescharacteristic
150C22—291no—
151C22—291no—
152C22—582no—
153C22#1174522311yescharacteristic
154C4—42no—
155C4—291no—
156C4—291no—
157C4—1162no—
158C4—2322no—
159C4#1174522311yescharacteristic
160C4C2×C22⋊#118111yescharacteristic
161C2—21no—
162C2—292no—
163C2—581no—
164C2C2×#1174522311yescharacteristic
subgroupG/H
centerC2C2×#11745223
commutatorC8×C29C22×C4
FrattiniC8C22×#1181
FittingC2×Q16×C29C4
socleC2×C29C2×#102
prime radicalC22×D29D8
cosocleC8×D29C23
hypercenterC2×Q16#1181
hypocenterC29#2141
LCSG ▷ C8×C29 ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
3. #14272076C2semidirect
7. C2×Q16×C29C4semidirect
11. Q16×D29C4semidirect
13. C2×Dic116C4semidirect
94. C2×Q16#1181semidirect
102. C29#2141semidirect

Maximal subgroups

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

subgroupindex
D29⋊M322
#142721732
#142720762
C2×Q16×D292
#214129