Finite Group Databasebeta

← #49174307

Subgroups — #49174307

Order 37504.

208 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 60 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#34037152C211yesmaximal, characteristic
2D293⋊(C4⋊C8)C211yesmaximal, characteristic
3#34036988C212yesmaximal, complemented
4#34036988C212yesmaximal, complemented
5#34036685C211yesmaximal, characteristic
6C2×D293⋊C8—21no—
7#22627691C2212yes—
8#22627691C2212yes—
9C4⋊#14556880—21no—
10#22627681—21no—
11#22627679—21no—
12#22627623C2211yescharacteristic
13#22627623C2211yescharacteristic
14#22627616C411yescharacteristic
15#22627602—21no—
16#22627602—21no—
17#22627589—21no—
18#22627589—21no—
19#22627582C411yescharacteristic
20#22627582C411yescharacteristic
21C42×D293C2211yescharacteristic
22#125×C293C411yescharacteristic
23D293⋊C8—42no—
24C2×#14556880—22no—
25C2×#14556880—22no—
26C2×Dic586—21no—
27C2×Dic586—21no—
28C2×C4×D293C2×C411yescharacteristic
29C2×C4×D293D411yescharacteristic
30C2×C4×D293D411yescharacteristic
31C4⋊Dic293C2×C411yescharacteristic
32C4⋊Dic293C2×C411yescharacteristic
33#17989781—21no—
34#17989781—21no—
35#17989781—21no—
36#17989781—21no—
37#17989779—21no—
38#17989779—21no—
39C4×Dic293—21no—
40C4×Dic293—21no—
41C4×Dic293D411yescharacteristic
42C4×Dic293D411yescharacteristic
43C4×Dic293C2311yescharacteristic
44C4⋊C4×C293—21no—
45C4⋊C4×C293—21no—
46C4⋊C4×C293C2×C411yescharacteristic
47C4⋊C4×C293C2×C411yescharacteristic
48C42×C293C2×C411yescharacteristic
49#14556880—42no—
50#14556880—42no—
51C22×D293C22⋊C411yescharacteristic
52Dic586—42no—
53Dic586—41no—
54Dic586—41no—
55C2×Dic293—21no—
56C2×Dic293—21no—
57C2×Dic293C22⋊C411yescharacteristic
58C2×Dic293C2×D411yescharacteristic
59C2×Dic293C2×D411yescharacteristic
60C4×D293—22no—
61C4×D293—22no—
62C4×D293—21no—
63C4×D293—21no—
64C2×C4×C293—21no—
65C2×C4×C293—21no—
66C2×C4×C293C22⋊C411yescharacteristic
67C2×C4×C293C22⋊C411yescharacteristic
68C2×C4×C293C22×C411yescharacteristic
69C22×C293C2×C22⋊C411yescharacteristic
70C2×D293—21no—
71C2×D293—21no—
72C2×D293#10112yes—
73C4×C293—21no—
74C4×C293—21no—
75C4×C293—21no—
76C4×C293—41no—
77C4×C293—41no—
78Dic293—21no—
79Dic293—41no—
80Dic293—41no—
81Dic293#13512yes—
82Dic293AGL(1,ℤ/8)11yescharacteristic
83Dic293#13711yescharacteristic
84C2×C293C2×#10111yescharacteristic
85C2×C293#41611yescharacteristic
86C2×C293#41711yescharacteristic
87D293—22no—
88C293#155211yescharacteristic, complemented, Sylow
89#1552—2931nomaximal, Sylow
90#533—2931no—
91#432—2931no—
92C2×C4⋊C8—2931no—
93#332—2932no—
94#332—2932no—
95C22×C8—5861no—
96C4⋊Q8—2931no—
97C4⋊Q8—2931no—
98#125—2931no—
99#125#1192407811yescharacteristic
100C22⋊Q8—5861no—
101C22⋊Q8—5861no—
102C4×Q8—5861no—
103C4×Q8—5861no—
104#117—2931no—
105#117—2931no—
106C2×C42—2931no—
107C4⋊C8—2932no—
108C4⋊C8—2932no—
109C4⋊C8—5861no—
110C22⋊C8—5861no—
111#97—5861no—
112C2×Q8—5861no—
113C2×Q8—5861no—
114C22×C4—2931no—
115C22×C4—2931no—
116C22×C4—2931no—
117C2×C8—5862no—
118C2×C8—5862no—
119C2×C8—11722no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—2931no—
123C4⋊C4—2931no—
124C4⋊C4—5861no—
125C4⋊C4—5861no—
126C4⋊C4—5861no—
127C4⋊C4—5861no—
128C4⋊C4C2×#1192407811yescharacteristic
129C4⋊C4C2×#1192407811yescharacteristic
130C22⋊C4—5861no—
131C22⋊C4—5861no—
132C42—2931no—
133C42—2931no—
134C42—2931no—
135C42—5861no—
136C42—5861no—
137C42C2×#1192407811yescharacteristic
138C23—2931no—
139Q8—11722no—
140Q8—11721no—
141Q8—11721no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—2931no—
145C2×C4—2931no—
146C2×C4—2931no—
147C2×C4—5861no—
148C2×C4—5862no—
149C2×C4—5861no—
150C2×C4—5862no—
151C2×C4—5861no—
152C2×C4—5861no—
153C2×C4C22⋊#1192407811yescharacteristic
154C2×C4C22⋊#1192407811yescharacteristic
155C2×C4C22×#1192407811yescharacteristic
156C8—11722no—
157C8—11722no—
158C22—2932no—
159C22—5861no—
160C22—5861no—
161C22C2×C22⋊#1192407811yescharacteristic
162C4—21no—
163C4—21no—
164C4—21no—
165C4—41no—
166C4—41no—
167C4—2932no—
168C4—2931no—
169C4—2931no—
170C4—5861no—
171C4—11721no—
172C4—11721no—
173C2—5862no—
174C2D293⋊#10111yescharacteristic
175C2#3403711911yescharacteristic
176C2#3403712011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
Fitting#125×C293C4
socleC22×C293C2×C22⋊C4
prime radicalC22×D293C22⋊C4
cosocleC4×Dic293C23
hypercenter#125#11924078
hypocenterC293#1552
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. #34036988C2semidirect
4. #34036988C2semidirect
88. C293#1552semidirect

Maximal subgroups

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

subgroupindex
#340371522
D293⋊(C4⋊C8)2
#340369882
#340366852
#1552293