Finite Group Databasebeta

← #49157996

Subgroups — #49157996

Order 37504.

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

normal subgroups only

This group has 208 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#34036840C211yesmaximal, characteristic
2#34036406C211yesmaximal, characteristic
3#34036336C211yesmaximal, characteristic, complemented
4#34035878C211yesmaximal, characteristic, complemented
5#34035861C211yesmaximal, characteristic, complemented
6#34035858C211yesmaximal, characteristic
7#487×C293C211yesmaximal, characteristic, complemented
8C2×#17989792—21no—
9#22627615—21no—
10#22627604—21no—
11#22627600—22no—
12C4×Dic586C2211yescharacteristic
13C4×D1172C2211yescharacteristic
14#22627586—21no—
15C4⋊C4×D293—21no—
16#22627557—21no—
17C4⋊#14556873C2211yescharacteristic
18C4⋊#14556873C2211yescharacteristic
19#22627548—21no—
20#22627544—21no—
21C4⋊Q8×C293C2211yescharacteristic
22C4⋊Q8×C293C2211yescharacteristic
23#103×C293—22no—
24C4×C8×C293C2211yescharacteristic
25C2×Dic586D411yescharacteristic
26C2×D1172D411yescharacteristic
27C2×C4×D293—22no—
28C2×C4×D293—21no—
29#17989792—42no—
30C2×#14556873—21no—
31C2×#14556873—21no—
32C4⋊Dic293—22no—
33C4⋊Dic293D411yescharacteristic
34C4⋊Dic293D411yescharacteristic
35#17989781—22no—
36#17989781—21no—
37#17989779—22no—
38#17989779—21no—
39C4×Dic293—21no—
40C2×Q8×C293—21no—
41C2×Q8×C293D412yes—
42C2×C8×C293—21no—
43C4⋊C4×C293—21no—
44C4⋊C4×C293—21no—
45C4⋊C4×C293—21no—
46C4⋊C4×C293—21no—
47C42×C293C2311yescharacteristic
48C22×D293—21no—
49Dic586—21no—
50Dic586—21no—
51D1172—21no—
52D1172Q1612yescomplemented
53C2×Dic293—21no—
54C2×Dic293—21no—
55C2×Dic293—21no—
56C4×D293—41no—
57C4×D293—41no—
58C4×D293—82no—
59#14556873—41no—
60#14556873—41no—
61Q8×C293—42no—
62Q8×C293—41no—
63Q8×C293—41no—
64C2×C4×C293—22no—
65C2×C4×C293—41no—
66C2×C4×C293C2×D411yescharacteristic
67C2×C4×C293C2×D411yescharacteristic
68C2×C4×C293C2×D411yescharacteristic
69C8×C293—41no—
70C22×C293#12011yescharacteristic
71C2×D293—22no—
72C2×D293—41no—
73C2×D293—41no—
74C4×C293—21no—
75C4×C293—42no—
76C4×C293—81no—
77C4×C293C2×Q1611yescharacteristic
78C4×C293#13511yescharacteristic
79C4×C293AGL(1,ℤ/8)11yescharacteristic
80C4×C293#13711yescharacteristic
81Dic293—41no—
82Dic293—41no—
83Dic293—41no—
84C2×C293#44911yescharacteristic
85C2×C293#45111yescharacteristic
86C2×C293#45511yescharacteristic
87D293—42no—
88C293#164411yescharacteristic, complemented, Sylow
89#1644—2931nomaximal, Sylow
90#554—2931no—
91#487D29311yescharacteristic, complemented
92#474—2931no—
93#462—2931no—
94#333—2931no—
95Q8⋊C8—2931no—
96D4⋊C8—2931no—
97C2×Q16—5861no—
98C4⋊Q8C2×D29311yescharacteristic
99C4⋊Q8C2×D29311yescharacteristic
100#125—5861no—
101C22⋊Q8—5861no—
102C22⋊Q8—5862no—
103C4×Q8—2931no—
104C4×D4—2931no—
105C4×D4—5861no—
106C2×C4⋊C4—5861no—
107#107—5861no—
108C4⋊C8—2931no—
109C4⋊C8—2931no—
110#103—22no—
111#103—5861no—
112#102—5861no—
113C4×C8C2×D29311yescharacteristic
114C2×Q8—21no—
115C2×Q8—2931no—
116C2×Q8C22⋊D29312yes—
117C2×D4—2931no—
118C22×C4—5862no—
119C22×C4—5861no—
120Q16—11722no—
121C2×C8—21no—
122C2×C8—5861no—
123C2×C8—5861no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—2931no—
129C4⋊C4—2931no—
130C4⋊C4—5862no—
131C4⋊C4—5862no—
132C4⋊C4—5861no—
133C22⋊C4—5862no—
134C22⋊C4—5861no—
135C42—5861no—
136C42C22×D29311yescharacteristic
137C23—5861no—
138Q8—42no—
139Q8—41no—
140Q8—41no—
141Q8—5861no—
142Q8—5861no—
143D4—2932no—
144D4—5861no—
145C2×C4—22no—
146C2×C4—41no—
147C2×C4—23442no—
148C2×C4—5861no—
149C2×C4—5861no—
150C2×C4—5861no—
151C2×C4—11721no—
152C2×C4—11721no—
153C2×C4D4×D29311yescharacteristic
154C2×C4D4×D29311yescharacteristic
155C2×C4C2×C22⋊D29311yescharacteristic
156C8—41no—
157C8—11721no—
158C8—11721no—
159C22—5862no—
160C22—11721no—
161C22—11721no—
162C22#2262759211yescharacteristic
163C4—21no—
164C4—42no—
165C4—81no—
166C4—11721no—
167C4—11721no—
168C4—11721no—
169C4Q16×D29311yescharacteristic
170C4#2262764511yescharacteristic
171C4#2262765111yescharacteristic
172C4#2262765611yescharacteristic
173C2—11722no—
174C2#3403627311yescharacteristic
175C2#3403628311yescharacteristic
176C2#3403630611yescharacteristic
subgroupG/H
centerC22#22627592
commutator, cosocleC42×C293C23
FrattiniC42C22×D293
Fitting#487×C293C2
socleC22×C293#120
prime radicalC2×D1172D4
hypercenter#487D293
hypocenterC293#1644
LCSG ▷ C42×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #34036336C2semidirect
4. #34035878C2semidirect
5. #34035861C2semidirect
7. #487×C293C2semidirect
52. D1172Q16semidirect
88. C293#1644semidirect
91. #487D293semidirect

Maximal subgroups

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

subgroupindex
#340368402
#340364062
#340363362
#340358782
#340358612
#340358582
#487×C2932
#1644293