Finite Group Databasebeta

← #49157955

Subgroups — #49157955

Order 37504.

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

normal subgroups only

This group has 194 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#34036849C211yesmaximal, characteristic
2#34036479C211yesmaximal, characteristic, complemented
3#34036421C211yesmaximal, characteristic, complemented
4#34035876C211yesmaximal, characteristic, complemented
5#34035859C211yesmaximal, characteristic, complemented
6D4⋊#14556873C211yesmaximal, characteristic
7#476×C293C211yesmaximal, characteristic
8#22627624C2211yescharacteristic
9#22627617—22no—
10#22627611—21no—
11#22627603—21no—
12C4×Dic586C2211yescharacteristic
13#22627589—21no—
14#22627583—21no—
15#22627557—21no—
16C4⋊#14556873C2211yescharacteristic
17#22627548—22no—
18#22627547—21no—
19C4×#14556873C2211yescharacteristic
20C4⋊Q8×C293C2211yescharacteristic
21C4×D4×C293C2211yescharacteristic
22#106×C293—21no—
23C4⋊C8×C293C2211yescharacteristic
24#102×C293—21no—
25C2×Dic586—21no—
26C2×Dic586D411yescharacteristic
27C2×#14556873—21no—
28C2×#14556873—21no—
29C4⋊Dic293—21no—
30C4⋊Dic293D411yescharacteristic
31C4⋊Dic293D412yes—
32#17989781—22no—
33#17989781—21no—
34C22⋊Dic293—22no—
35C22⋊Dic293—22no—
36C4×Dic293—22no—
37C4×Dic293—21no—
38C2×Q8×C293—21no—
39C2×D4×C293D411yescharacteristic
40C22×C4×C293—21no—
41C2×C8×C293—21no—
42C4⋊C4×C293—21no—
43C4⋊C4×C293—21no—
44C4⋊C4×C293D411yescharacteristic
45C22⋊C4×C293—21no—
46C42×C293C2311yescharacteristic
47Dic586—21no—
48Dic586—21no—
49Dic586—41no—
50Dic586—41no—
51C2×Dic293—21no—
52C2×Dic293—21no—
53C2×Dic293—22no—
54#14556873—41no—
55#14556873—41no—
56C23×C293—21no—
57Q8×C293—42no—
58D4×C293—21no—
59D4×C293—21no—
60C2×C4×C293—21no—
61C2×C4×C293—41no—
62C2×C4×C293—41no—
63C2×C4×C293—41no—
64C2×C4×C293C2×D411yescharacteristic
65C2×C4×C293C2×D411yescharacteristic
66C2×C4×C293C2×D411yescharacteristic
67C8×C293—41no—
68C22×C293—41no—
69C22×C293—41no—
70C22×C293—41no—
71C22×C293#12011yescharacteristic
72C4×C293—21no—
73C4×C293—41no—
74C4×C293—81no—
75C4×C293#13511yescharacteristic
76C4×C293#13511yescharacteristic
77C4×C293#13711yescharacteristic
78C4×C293#13711yescharacteristic
79Dic293—41no—
80Dic293—42no—
81Dic293—41no—
82C2×C293—81no—
83C2×C293#45211yescharacteristic
84C2×C293#45211yescharacteristic
85C2×C293#45411yescharacteristic
86C293#163811yescharacteristic, complemented, Sylow
87#1638—2931nomaximal, Sylow
88#556—2931no—
89#487—2931no—
90#477—2931no—
91#476D29311yescharacteristic
92#332—2931no—
93Q8⋊C8—2931no—
94D4⋊C8—2931no—
95C4⋊Q8—2931no—
96C4⋊Q8C2×D29311yescharacteristic
97#126—5862no—
98#124—5861no—
99C22⋊Q8—5861no—
100C4×Q8—2931no—
101C4×Q8—5861no—
102C4×D4C2×D29311yescharacteristic
103#117—5861no—
104#107—5861no—
105#106—21no—
106C4⋊C8—2931no—
107C4⋊C8C2×D29311yescharacteristic
108#103—5861no—
109#103—5862no—
110#102—21no—
111C4×C8—2931no—
112C2×Q8—21no—
113C2×Q8—2931no—
114C2×Q8—5861no—
115C2×D4C22⋊D29311yescharacteristic
116C22×C4—21no—
117C2×C8—21no—
118C2×C8—5861no—
119C2×C8—5861no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—2932no—
123C4⋊C4—2931no—
124C4⋊C4—5862no—
125C4⋊C4—5861no—
126C4⋊C4—5861no—
127C4⋊C4C22⋊D29311yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—5862no—
130C22⋊C4—5862no—
131C42—5862no—
132C42—5861no—
133C42C22×D29311yescharacteristic
134C23—21no—
135Q8—42no—
136Q8—5861no—
137Q8—5861no—
138Q8—11721no—
139Q8—11721no—
140D4—21no—
141D4—21no—
142C2×C4—21no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—5861no—
147C2×C4—5862no—
148C2×C4—5861no—
149C2×C4D4×D29311yescharacteristic
150C2×C4D4×D29311yescharacteristic
151C2×C4C2×C22⋊D29311yescharacteristic
152C8—41no—
153C8—11721no—
154C8—11721no—
155C22—41no—
156C22—41no—
157C22—41no—
158C22#2262759211yescharacteristic
159C4—21no—
160C4—41no—
161C4—81no—
162C4—11721no—
163C4—11722no—
164C4—11721no—
165C4#2262764411yescharacteristic
166C4#2262764511yescharacteristic
167C4#2262765311yescharacteristic
168C4#2262765511yescharacteristic
169C2—81no—
170C2#3403628811yescharacteristic
171C2#3403628911yescharacteristic
172C2#3403630011yescharacteristic
subgroupG/H
centerC22#22627592
commutator, cosocleC42×C293C23
FrattiniC42C22×D293
Fitting#476×C293C2
socleC22×C293#120
prime radicalC2×D4×C293D4
hypercenter#476D293
hypocenterC293#1638
LCSG ▷ C42×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #34036479C2semidirect
3. #34036421C2semidirect
4. #34035876C2semidirect
5. #34035859C2semidirect
86. C293#1638semidirect

Maximal subgroups

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

subgroupindex
#340368492
#340364792
#340364212
#340358762
#340358592
D4⋊#145568732
#476×C2932
#1638293