Finite Group Databasebeta

← #49158029

Subgroups — #49158029

Order 37504.

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

normal subgroups only

This group has 194 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#34036857C211yesmaximal, characteristic
2#34036534C211yesmaximal, characteristic
3#34036415C211yesmaximal, characteristic
4#34036339C211yesmaximal, characteristic
5#34035874C211yesmaximal, characteristic
6#34035861C211yesmaximal, characteristic
7Q8⋊C8×C293C211yesmaximal, characteristic
8C2×#17989792—21no—
9#22627624C2211yescharacteristic
10#22627624C2211yescharacteristic
11#22627622—21no—
12#22627616—21no—
13#22627614—22no—
14C4×Dic586—21no—
15C4×Dic586C2211yescharacteristic
16#22627589—21no—
17#22627558—22no—
18#22627556—21no—
19C4⋊#14556873C2211yescharacteristic
20#22627549—21no—
21#22627547—21no—
22C4×Q8×C293C2211yescharacteristic
23C4⋊C8×C293C2211yescharacteristic
24C4×C8×C293C2211yescharacteristic
25C2×Dic586—21no—
26C2×Dic586—21no—
27C2×Dic586D411yescharacteristic
28#17989792—42no—
29C2×#14556873—21no—
30C4⋊Dic293—21no—
31C4⋊Dic293—21no—
32C4⋊Dic293—21no—
33C4⋊Dic293D411yescharacteristic
34C4⋊Dic293D412yes—
35#17989781—22no—
36#17989781—22no—
37#17989781—22no—
38#17989781—21no—
39C4×Dic293—22no—
40C4×Dic293—21no—
41C2×Q8×C293D411yescharacteristic
42C2×C8×C293—21no—
43C2×C8×C293—21no—
44C4⋊C4×C293—21no—
45C4⋊C4×C293D411yescharacteristic
46C42×C293—21no—
47C42×C293C2311yescharacteristic
48Dic586—21no—
49Dic586—41no—
50Dic586—41no—
51Dic586—41no—
52Dic586—41no—
53Dic586Q1612yescomplemented
54C2×Dic293—21no—
55C2×Dic293—21no—
56C2×Dic293—22no—
57C2×Dic293—41no—
58#14556873—41no—
59Q8×C293—21no—
60Q8×C293—21no—
61C2×C4×C293—21no—
62C2×C4×C293—21no—
63C2×C4×C293C2×D411yescharacteristic
64C2×C4×C293C2×D411yescharacteristic
65C2×C4×C293C2×D411yescharacteristic
66C8×C293—22no—
67C8×C293—41no—
68C22×C293#12011yescharacteristic
69C4×C293—21no—
70C4×C293—41no—
71C4×C293—41no—
72C4×C293C2×Q1611yescharacteristic
73C4×C293#13511yescharacteristic
74C4×C293AGL(1,ℤ/8)11yescharacteristic
75C4×C293#13711yescharacteristic
76Dic293—22no—
77Dic293—42no—
78Dic293—41no—
79Dic293—81no—
80C2×C293#44911yescharacteristic
81C2×C293#45111yescharacteristic
82C2×C293#45611yescharacteristic
83C293#164811yescharacteristic, complemented, Sylow
84#1648—2931nomaximal, Sylow
85#557—2931no—
86#500—2931no—
87#475—2931no—
88#462—2931no—
89#332—2931no—
90Q8⋊C8—2931no—
91Q8⋊C8D29311yescharacteristic
92C2×Q16—5861no—
93C4⋊Q8—2931no—
94C4⋊Q8—2931no—
95C4⋊Q8—5861no—
96#125—5861no—
97#125—5862no—
98C4×Q8—2931no—
99C4×Q8—5861no—
100C4×Q8—5861no—
101C4×Q8C2×D29311yescharacteristic
102#107—5862no—
103#106—5861no—
104C4⋊C8—2931no—
105C4⋊C8C2×D29311yescharacteristic
106#103—5861no—
107#103—5861no—
108C4×C8C2×D29311yescharacteristic
109C2×Q8—2931no—
110C2×Q8—5861no—
111C2×Q8—5861no—
112C2×Q8D117211yescharacteristic
113Q16—11722no—
114C2×C8—21no—
115C2×C8—21no—
116C2×C8—5861no—
117C4⋊C4—21no—
118C4⋊C4—2931no—
119C4⋊C4—2932no—
120C4⋊C4—5862no—
121C4⋊C4—5862no—
122C4⋊C4—5862no—
123C4⋊C4—5861no—
124C4⋊C4—5861no—
125C4⋊C4—5861no—
126C4⋊C4—5861no—
127C4⋊C4D117211yescharacteristic
128C42—21no—
129C42—5862no—
130C42—5861no—
131C42C22×D29311yescharacteristic
132Q8—21no—
133Q8—21no—
134Q8—2932no—
135Q8—5861no—
136Q8—11721no—
137Q8—11721no—
138Q8—11721no—
139Q8—11721no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—5861no—
143C2×C4—5861no—
144C2×C4—5862no—
145C2×C4—11721no—
146C2×C4D4×D29311yescharacteristic
147C2×C4D4×D29311yescharacteristic
148C2×C4C2×D117211yescharacteristic
149C8—22no—
150C8—41no—
151C8—11721no—
152C22#2262759411yescharacteristic
153C4—21no—
154C4—41no—
155C4—41no—
156C4—23441no—
157C4—5862no—
158C4—11722no—
159C4—11721no—
160C4Q16×D29311yescharacteristic
161C4#2262764611yescharacteristic
162C4#2262765211yescharacteristic
163C4#2262765311yescharacteristic
164C2#3403627611yescharacteristic
165C2#3403628611yescharacteristic
166C2#3403631311yescharacteristic
subgroupG/H
centerC22#22627594
commutator, cosocleC42×C293C23
FrattiniC42C22×D293
FittingQ8⋊C8×C293C2
socle, prime radicalC22×C293#120
hypercenterQ8⋊C8D293
hypocenterC293#1648
LCSG ▷ C42×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
53. Dic586Q16semidirect
83. C293#1648semidirect

Maximal subgroups

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

subgroupindex
#340368572
#340365342
#340364152
#340363392
#340358742
#340358612
Q8⋊C8×C2932
#1648293