Finite Group Databasebeta

← #49174209

Subgroups — #49174209

Order 37504.

208 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 56 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
2#34037074C211yesmaximal, characteristic
3#34036983C214yesmaximal
4#34036684C211yesmaximal, characteristic
5#22627691—21no—
6#22627681C2212yes—
7#22627679—21no—
8(C2×#11924078)⋊C4—21no—
9(C2×#11924078)⋊C4—21no—
10(C2×#11924078)⋊C4C2212yes—
11#22627624C411yescharacteristic, complemented
12#22627615—21no—
13#22627604—21no—
14#22627600C2212yes—
15Q8×Dic293C412yescomplemented
16#22627589—21no—
17#22627582—21no—
18C42×D293C2211yescharacteristic
19C4⋊Q8×C293C411yescharacteristic, complemented
20C22×#11924078—22no—
21C2×#14556880—22no—
22C2×Dic586—21no—
23C2×C4×D293D411yescharacteristic
24C2×C4×D293D411yescharacteristic
25C2×C4×D293C2311yescharacteristic
26C4⋊Dic293—22no—
27C4⋊Dic293—21no—
28C4⋊Dic293C2×C412yes—
29#17989781—22no—
30#17989779—22no—
31C4×Dic293—22no—
32C4×Dic293C2×C411yescharacteristic
33C4×Dic293D411yescharacteristic
34C4×Dic293D411yescharacteristic
35C2×Q8×C293C2×C412yes—
36C4⋊C4×C293—21no—
37C4⋊C4×C293—21no—
38C42×C293C2×C411yescharacteristic
39C2×#11924078—42no—
40C2×#11924078—42no—
41C2×#11924078—42no—
42#14556880—42no—
43C22×D293C2×D411yescharacteristic
44Dic586—42no—
45C2×Dic293—22no—
46C2×Dic293C22⋊C411yescharacteristic
47C2×Dic293C22⋊C411yescharacteristic
48C2×Dic293C2×D411yescharacteristic
49C4×D293—22no—
50C4×D293—41no—
51C4×D293—41no—
52Q8×C293—42no—
53C2×C4×C293—22no—
54C2×C4×C293C22⋊C411yescharacteristic
55C2×C4×C293C22⋊C411yescharacteristic
56C2×C4×C293C22×C411yescharacteristic
57C22×C293C2×C22⋊C411yescharacteristic
58C2×D293—21no—
59C2×D293—21no—
60C2×D293#13712yes—
61#11924078—82no—
62C4×C293—21no—
63C4×C293—21no—
64C4×C293—21no—
65C4×C293—42no—
66Dic293—21no—
67Dic293—21no—
68Dic293—21no—
69Dic293—42no—
70C2×C293#41011yescharacteristic
71C2×C293#41911yescharacteristic
72C2×C293#42111yescharacteristic
73D293—22no—
74C293#151511yescharacteristic, complemented, Sylow
75#1515—2931nomaximal, Sylow
76#533—2931no—
77#432—2931no—
78#383—2931no—
79#328—2934no—
80C4⋊Q8—2931no—
81C4⋊Q8#1192407811yescharacteristic, complemented
82#125—5861no—
83C22⋊Q8—2932no—
84C22⋊Q8—5861no—
85C4×Q8—2932no—
86C4×Q8—5861no—
87#117—5861no—
88C2×C42—2931no—
89C4⋊C8—5861no—
90C22⋊C8—2932no—
91#97—5861no—
92#95—2932no—
93#95—5861no—
94#95—5861no—
95C2×Q8—5861no—
96C2×Q8C2×#1192407812yes—
97C22×C4—2931no—
98C22×C4—2931no—
99C22×C4—2931no—
100C22×C4—5862no—
101C2×C8—5862no—
102C4⋊C4—21no—
103C4⋊C4—21no—
104C4⋊C4—2932no—
105C4⋊C4—5862no—
106C4⋊C4—5862no—
107C4⋊C4—5861no—
108C22⋊C4—5862no—
109C42—2931no—
110C42—2931no—
111C42—2931no—
112C42—5862no—
113C42C2×#1192407811yescharacteristic
114C23—2931no—
115Q8—42no—
116Q8—11722no—
117C2×C4—22no—
118C2×C4—2931no—
119C2×C4—2931no—
120C2×C4—2931no—
121C2×C4—5862no—
122C2×C4—5862no—
123C2×C4—11721no—
124C2×C4—11721no—
125C2×C4—11722no—
126C2×C4—11722no—
127C2×C4—11722no—
128C2×C4C22⋊#1192407811yescharacteristic
129C2×C4C22⋊#1192407811yescharacteristic
130C2×C4C22×#1192407811yescharacteristic
131C8—11722no—
132C22—2932no—
133C22—5861no—
134C22—5861no—
135C22C2×C22⋊#1192407811yescharacteristic
136C4—21no—
137C4—21no—
138C4—21no—
139C4—42no—
140C4—23442no—
141C4—5861no—
142C4—5861no—
143C4—5861no—
144C4—11722no—
145C2—5862no—
146C2#3403710911yescharacteristic
147C2#3403712211yescharacteristic
148C2#3403712811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
FittingC4⋊Q8×C293C4
socleC22×C293C2×C22⋊C4
prime radicalC22×D293C2×D4
cosocleC2×C4×D293C23
hypercenterC4⋊Q8#11924078
hypocenterC293#1515
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
11. #22627624C4semidirect
15. Q8×Dic293C4semidirect
19. C4⋊Q8×C293C4semidirect
74. C293#1515semidirect
81. C4⋊Q8#11924078semidirect

Maximal subgroups

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

subgroupindex
#340371522
#340370742
#340369832
#340366842
#1515293