Finite Group Databasebeta

← #49157892

Subgroups — #49157892

Order 37504.

216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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#34036853C211yesmaximal, characteristic, complemented
2#34036326C211yesmaximal, characteristic, complemented
3#34036321C211yesmaximal, characteristic
4#34035875C211yesmaximal, characteristic, complemented
5#34035861C211yesmaximal, characteristic, complemented
6#34035858C211yesmaximal, characteristic, complemented
7#486×C293C211yesmaximal, characteristic, complemented
8C2×#17989790—21no—
9C2×#17989787—21no—
10#22627619—22no—
11#22627613—21no—
12#22627604—21no—
13Q8×Dic293—21no—
14C4×Dic586C2211yescharacteristic
15C4×D1172C2211yescharacteristic
16#22627582—21no—
17C4⋊#14556873C2211yescharacteristic
18C4⋊#14556873C2211yescharacteristic
19#22627545—21no—
20#22627545—21no—
21C4⋊Q8×C293C2211yescharacteristic
22#127×C293C2211yescharacteristic
23#102×C293—22no—
24C4×C8×C293C2211yescharacteristic
25C2×Dic586D411yescharacteristic
26C2×D1172D411yescharacteristic
27C2×C4×D293—21no—
28#17989790—42no—
29#17989787—42no—
30C2×#14556873—21no—
31C2×#14556873—21no—
32C4⋊Dic293—22no—
33C4⋊Dic293D411yescharacteristic
34C4⋊Dic293D411yescharacteristic
35#17989781—21no—
36#17989779—22no—
37#17989779—22no—
38#17989779—21no—
39C4×Dic293—22no—
40C4×Dic293—21no—
41C2×Q8×C293—21no—
42C2×D4×C293—21no—
43C2×D4×C293—21no—
44C2×D4×C293—21no—
45C2×C8×C293—21no—
46C4⋊C4×C293—21no—
47C4⋊C4×C293D412yes—
48C42×C293C2311yescharacteristic
49C22×D293—21no—
50Dic586—21no—
51Dic586—21no—
52D1172—21no—
53D1172—21no—
54C2×Dic293—21no—
55C2×Dic293—21no—
56C2×Dic293—21no—
57C4×D293—41no—
58C4×D293—41no—
59#14556873—41no—
60#14556873—41no—
61C23×C293—41no—
62Q8×C293—41no—
63Q8×C293—41no—
64D4×C293—42no—
65D4×C293—41no—
66D4×C293—41no—
67D4×C293—41no—
68D4×C293—41no—
69C2×C4×C293—22no—
70C2×C4×C293C2×D411yescharacteristic
71C2×C4×C293C2×D411yescharacteristic
72C2×C4×C293C2×D411yescharacteristic
73C8×C293—41no—
74C22×C293—81no—
75C22×C293—81no—
76C22×C293—81no—
77C22×C293#12011yescharacteristic
78C2×D293—41no—
79C2×D293—41no—
80C2×D293—41no—
81C4×C293—21no—
82C4×C293—42no—
83C4×C293#13511yescharacteristic
84C4×C293#13511yescharacteristic
85C4×C293AGL(1,ℤ/8)11yescharacteristic
86C4×C293AGL(1,ℤ/8)11yescharacteristic
87Dic293—41no—
88Dic293—41no—
89Dic293—41no—
90C2×C293—161no—
91C2×C293#44911yescharacteristic
92C2×C293#44911yescharacteristic
93C2×C293#45411yescharacteristic
94D293—81no—
95C293#162811yescharacteristic, complemented, Sylow
96#1628—2931nomaximal, Sylow
97#556—2931no—
98#486D29311yescharacteristic, complemented
99#460—2931no—
100#459—2931no—
101#332—2931no—
102Q8⋊C8—2931no—
103D4⋊C8—2931no—
104C2×SD16—5861no—
105C2×D8—5861no—
106C4⋊Q8C2×D29311yescharacteristic
107#127C2×D29311yescharacteristic
108#126—5862no—
109#124—5861no—
110C22⋊Q8—5861no—
111C4×Q8—2931no—
112C4×Q8—5861no—
113C4×D4—2931no—
114#117—5861no—
115C4⋊C8—2931no—
116C4⋊C8—2931no—
117#102—22no—
118#102—5861no—
119#102—5861no—
120C4×C8C2×D29311yescharacteristic
121C2×Q8—21no—
122C2×Q8—2931no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—2931no—
127C22×C4—5861no—
128SD16—11722no—
129D8—11722no—
130C2×C8—21no—
131C2×C8—5861no—
132C2×C8—5861no—
133C4⋊C4—21no—
134C4⋊C4—2931no—
135C4⋊C4—2931no—
136C4⋊C4—5862no—
137C4⋊C4—5861no—
138C4⋊C4C22⋊D29312yes—
139C22⋊C4—5862no—
140C22⋊C4—5862no—
141C22⋊C4—5861no—
142C42—5862no—
143C42—5861no—
144C42C22×D29311yescharacteristic
145C23—41no—
146C23—5861no—
147Q8—41no—
148Q8—41no—
149Q8—5861no—
150Q8—5861no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—5861no—
157D4—5861no—
158C2×C4—22no—
159C2×C4—5861no—
160C2×C4—5861no—
161C2×C4—5861no—
162C2×C4—11721no—
163C2×C4—11721no—
164C2×C4D4×D29311yescharacteristic
165C2×C4D4×D29311yescharacteristic
166C2×C4C2×C22⋊D29311yescharacteristic
167C8—41no—
168C8—11721no—
169C8—11721no—
170C22—81no—
171C22—81no—
172C22—81no—
173C22—11721no—
174C22—11721no—
175C22—11721no—
176C22#2262759211yescharacteristic
177C4—21no—
178C4—42no—
179C4—11721no—
180C4—11721no—
181C4—11721no—
182C4#2262764311yescharacteristic
183C4#2262764511yescharacteristic
184C4#2262764811yescharacteristic
185C4#2262765111yescharacteristic
186C2—161no—
187C2—23441no—
188C2#3403627111yescharacteristic
189C2#3403627311yescharacteristic
190C2#3403630111yescharacteristic
subgroupG/H
centerC22#22627592
commutator, cosocleC42×C293C23
FrattiniC42C22×D293
Fitting#486×C293C2
socleC22×C293#120
prime radical#34036321C2
hypercenter#486D293
hypocenterC293#1628
LCSG ▷ C42×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #34036853C2semidirect
2. #34036326C2semidirect
4. #34035875C2semidirect
5. #34035861C2semidirect
6. #34035858C2semidirect
7. #486×C293C2semidirect
95. C293#1628semidirect
98. #486D293semidirect

Maximal subgroups

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

subgroupindex
#340368532
#340363262
#340363212
#340358752
#340358612
#340358582
#486×C2932
#1628293