Finite Group Databasebeta

← #49158028

Subgroups — #49158028

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#34036854C211yesmaximal, characteristic
2#34036532C211yesmaximal, characteristic
3#34036415C211yesmaximal, characteristic
4#34036340C211yesmaximal, characteristic
5#34035859C211yesmaximal, characteristic
6#34035859C211yesmaximal, characteristic
7#332×C293C211yesmaximal, characteristic
8C2×Dic1172—21no—
9#22627624C2211yescharacteristic
10#22627622—21no—
11#22627615—21no—
12#22627614—22no—
13Q8×Dic293—21no—
14C4×Dic586C2211yescharacteristic
15C4×Dic586C2211yescharacteristic
16#22627589—21no—
17#22627557—22no—
18#22627556—21no—
19#22627549—21no—
20#22627549—21no—
21C4×#14556873C2211yescharacteristic
22C4⋊Q8×C293C2211yescharacteristic
23C4⋊C8×C293C2211yescharacteristic
24C4⋊C8×C293C2211yescharacteristic
25C2×Dic586—21no—
26C2×Dic586D411yescharacteristic
27C2×Dic586D411yescharacteristic
28Dic1172—42no—
29C2×#14556873—21no—
30C4⋊Dic293—22no—
31C4⋊Dic293—21no—
32C4⋊Dic293—21no—
33C4⋊Dic293D411yescharacteristic
34C4⋊Dic293D411yescharacteristic
35#17989781—22no—
36#17989781—22no—
37#17989781—21no—
38#17989781—21no—
39C4×Dic293—22no—
40C4×Dic293—21no—
41C4×Dic293—21no—
42C2×Q8×C293—21no—
43C2×C8×C293—21no—
44C2×C8×C293—21no—
45C4⋊C4×C293—21no—
46C4⋊C4×C293D412yes—
47C42×C293C2311yescharacteristic
48Dic586—21no—
49Dic586—21no—
50Dic586—21no—
51Dic586—41no—
52Dic586—41no—
53Dic586Q1612yescomplemented
54C2×Dic293—21no—
55C2×Dic293—21no—
56C2×Dic293—21no—
57C2×Dic293—21no—
58C2×Dic293—41no—
59#14556873—22no—
60Q8×C293—41no—
61Q8×C293—41no—
62C2×C4×C293—22no—
63C2×C4×C293C2×D411yescharacteristic
64C2×C4×C293C2×D411yescharacteristic
65C2×C4×C293C2×D411yescharacteristic
66C8×C293—41no—
67C8×C293—41no—
68C22×C293#12011yescharacteristic
69C4×C293—21no—
70C4×C293—42no—
71C4×C293C2×Q1611yescharacteristic
72C4×C293#13511yescharacteristic
73C4×C293AGL(1,ℤ/8)11yescharacteristic
74C4×C293#13711yescharacteristic
75Dic293—22no—
76Dic293—41no—
77Dic293—41no—
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#332D29311yescharacteristic
90Q8⋊C8—2931no—
91Q8⋊C8—2931no—
92C2×Q16—5861no—
93C4⋊Q8—2931no—
94C4⋊Q8—5861no—
95C4⋊Q8C2×D29311yescharacteristic
96#125—5861no—
97#125—5862no—
98C4×Q8—2931no—
99C4×Q8—2931no—
100C4×Q8—5861no—
101C4×Q8—5861no—
102#107—5862no—
103#106—5861no—
104C4⋊C8C2×D29311yescharacteristic
105C4⋊C8C2×D29311yescharacteristic
106#103—5861no—
107#103—5861no—
108C4×C8—2931no—
109C2×Q8—21no—
110C2×Q8—2931no—
111C2×Q8—2931no—
112C2×Q8—5861no—
113Q16—11722no—
114C2×C8—21no—
115C2×C8—21no—
116C2×C8—5861no—
117C4⋊C4—21no—
118C4⋊C4—2931no—
119C4⋊C4—2931no—
120C4⋊C4—5862no—
121C4⋊C4—5862no—
122C4⋊C4—5862no—
123C4⋊C4—5861no—
124C4⋊C4—5861no—
125C4⋊C4—5861no—
126C4⋊C4—5861no—
127C4⋊C4D117212yes—
128C42—5862no—
129C42—5861no—
130C42—5861no—
131C42C22×D29311yescharacteristic
132Q8—41no—
133Q8—41no—
134Q8—2932no—
135Q8—5861no—
136Q8—5861no—
137Q8—5861no—
138Q8—11721no—
139Q8—11721no—
140C2×C4—22no—
141C2×C4—5861no—
142C2×C4—5861no—
143C2×C4—5861no—
144C2×C4—5861no—
145C2×C4—11721no—
146C2×C4D4×D29311yescharacteristic
147C2×C4D4×D29311yescharacteristic
148C2×C4C2×D117211yescharacteristic
149C8—41no—
150C8—41no—
151C8—5862no—
152C22#2262759411yescharacteristic
153C4—21no—
154C4—42no—
155C4—23441no—
156C4—5862no—
157C4—11721no—
158C4—11721no—
159C4—11721no—
160C4Q16×D29311yescharacteristic
161C4#2262764511yescharacteristic
162C4#2262764811yescharacteristic
163C4#2262765311yescharacteristic
164C2#3403627511yescharacteristic
165C2#3403628611yescharacteristic
166C2#3403631411yescharacteristic
subgroupG/H
centerC22#22627594
commutator, cosocleC42×C293C23
FrattiniC42C22×D293
Fitting#332×C293C2
socle, prime radicalC22×C293#120
hypercenter#332D293
hypocenterC293#1648
LCSG ▷ C42×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #332

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
#340368542
#340365322
#340364152
#340363402
#340358592
#332×C2932
#1648293