Finite Group Databasebeta

← #49174177

Subgroups — #49174177

Order 37504.

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

normal subgroups only

This group has 228 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#34037151C211yesmaximal, characteristic
2#34037065C211yesmaximal, characteristic
3#34036982C214yesmaximal
4#34036684C211yesmaximal, characteristic
5C2×C4×#11924078—21no—
6C4⋊#14556880—21no—
7#22627681C2212yes—
8#22627679—21no—
9(C2×#11924078)⋊C4—21no—
10(C2×#11924078)⋊C4C2212yes—
11#22627624C411yescharacteristic, complemented
12#22627615—21no—
13#22627604C2212yes—
14#22627600—21no—
15Q8×Dic293—21no—
16#22627589C412yescomplemented
17#22627582—21no—
18C42×D293C2211yescharacteristic
19C4⋊Q8×C293C411yescharacteristic, complemented
20C22×#11924078—22no—
21C2×#14556880—22no—
22C4×#11924078—24no—
23C2×Dic586C2×C412yes—
24C2×C4×D293D411yescharacteristic
25C2×C4×D293D411yescharacteristic
26C2×C4×D293C2311yescharacteristic
27C4⋊Dic293—22no—
28C4⋊Dic293—21no—
29C4⋊Dic293—21no—
30#17989781—22no—
31#17989779—22no—
32C4×Dic293—22no—
33C4×Dic293C2×C411yescharacteristic
34C4×Dic293D411yescharacteristic
35C4×Dic293D411yescharacteristic
36C2×Q8×C293—21no—
37C4⋊C4×C293—21no—
38C4⋊C4×C293C2×C412yes—
39C42×C293C2×C411yescharacteristic
40C2×#11924078—24no—
41C2×#11924078—42no—
42C2×#11924078—42no—
43#14556880—42no—
44C22×D293C2×D411yescharacteristic
45Dic586—42no—
46C2×Dic293—22no—
47C2×Dic293C22⋊C411yescharacteristic
48C2×Dic293C22⋊C411yescharacteristic
49C2×Dic293C2×D411yescharacteristic
50C4×D293—22no—
51C4×D293—22no—
52C4×D293—41no—
53Q8×C293—42no—
54C2×C4×C293—22no—
55C2×C4×C293C22⋊C411yescharacteristic
56C2×C4×C293C22⋊C411yescharacteristic
57C2×C4×C293C22×C411yescharacteristic
58C22×C293C2×C22⋊C411yescharacteristic
59C2×D293—21no—
60C2×D293—21no—
61C2×D293#13712yes—
62#11924078—44no—
63C4×C293—21no—
64C4×C293—21no—
65C4×C293—42no—
66C4×C293#10412yes—
67Dic293—21no—
68Dic293—21no—
69Dic293—21no—
70Dic293—42no—
71C2×C293#41011yescharacteristic
72C2×C293#41911yescharacteristic
73C2×C293C2×#10411yescharacteristic
74D293—22no—
75C293#150611yescharacteristic, complemented, Sylow
76#1506—2931nomaximal, Sylow
77#533—2931no—
78#432—2931no—
79#376—2931no—
80#328—2934no—
81C4⋊Q8—2931no—
82C4⋊Q8#1192407811yescharacteristic, complemented
83#125—5861no—
84C22⋊Q8—2932no—
85C22⋊Q8—5861no—
86C4×Q8—2932no—
87C4×Q8—5861no—
88#117—5861no—
89C2×C42—2931no—
90C2×C42—5861no—
91C4⋊C8—5861no—
92C22⋊C8—2932no—
93#97—5861no—
94#95—2932no—
95#95—5861no—
96C2×Q8—21no—
97C2×Q8—2932no—
98C22×C4—2931no—
99C22×C4—2931no—
100C22×C4—2931no—
101C22×C4—5862no—
102C2×C8—5862no—
103C4⋊C4—21no—
104C4⋊C4—5862no—
105C4⋊C4—5862no—
106C4⋊C4—5861no—
107C4⋊C4—5861no—
108C4⋊C4C2×#1192407812yes—
109C22⋊C4—5862no—
110C42—2931no—
111C42—2931no—
112C42—2931no—
113C42—5862no—
114C42—5864no—
115C42C2×#1192407811yescharacteristic
116C23—2931no—
117Q8—42no—
118Q8—11722no—
119C2×C4—22no—
120C2×C4—2931no—
121C2×C4—2931no—
122C2×C4—2931no—
123C2×C4—5862no—
124C2×C4—5862no—
125C2×C4—5864no—
126C2×C4—5862no—
127C2×C4—11721no—
128C2×C4—11722no—
129C2×C4—11722no—
130C2×C4C22⋊#1192407811yescharacteristic
131C2×C4C22⋊#1192407811yescharacteristic
132C2×C4C22×#1192407811yescharacteristic
133C8—11722no—
134C22—2932no—
135C22—5861no—
136C22—5861no—
137C22C2×C22⋊#1192407811yescharacteristic
138C4—21no—
139C4—21no—
140C4—42no—
141C4—5861no—
142C4—5861no—
143C4—5861no—
144C4—11724no—
145C4—11722no—
146C4#2262768812yes—
147C2—5862no—
148C2#3403711011yescharacteristic
149C2#3403712211yescharacteristic
150C2C2×#2262768811yescharacteristic
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#1506
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
16. #22627589C4semidirect
19. C4⋊Q8×C293C4semidirect
75. C293#1506semidirect
82. C4⋊Q8#11924078semidirect

Maximal subgroups

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

subgroupindex
#340371512
#340370652
#340369822
#340366842
#1506293