Finite Group Databasebeta

← #49174176

Subgroups — #49174176

Order 37504.

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

normal subgroups only

This group has 272 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, complemented
2#34037065C211yesmaximal, characteristic, complemented
3#34036981C214yesmaximal, complemented
4#34036680C211yesmaximal, characteristic
5C2×C4×#11924078—21no—
6C4⋊#14556880—21no—
7#22627681C2212yes—
8#22627679—21no—
9(C2×#11924078)⋊C4—21no—
10(C2×#11924078)⋊C4C2212yes—
11C2×#17989803—21no—
12#22627621C411yescharacteristic, complemented
13#22627613—21no—
14#22627599—21no—
15#22627599C2212yes—
16#22627586—21no—
17#22627586C412yescomplemented
18C42×D293C2211yescharacteristic
19C4⋊Q8×C293C411yescharacteristic, complemented
20C22×#11924078—22no—
21C2×#14556880—22no—
22C4×#11924078—24no—
23#17989803—44no—
24C2×D1172—22no—
25C2×D1172—21no—
26C2×D1172—21no—
27C2×D1172C2×C412yes—
28C2×C4×D293—22no—
29C2×C4×D293D411yescharacteristic
30C2×C4×D293D411yescharacteristic
31C2×C4×D293C2311yescharacteristic
32#17989779—22no—
33#17989779—22no—
34C4×Dic293C2×C411yescharacteristic
35C4×Dic293D411yescharacteristic
36C4×Dic293D411yescharacteristic
37C2×Q8×C293—21no—
38C4⋊C4×C293—21no—
39C4⋊C4×C293C2×C412yes—
40C42×C293C2×C411yescharacteristic
41C2×#11924078—24no—
42C2×#11924078—42no—
43C2×#11924078—42no—
44#14556880—42no—
45C22×D293—22no—
46C22×D293C2×D411yescharacteristic
47D1172—42no—
48D1172—42no—
49D1172—44no—
50D1172—42no—
51C2×Dic293C22⋊C411yescharacteristic
52C2×Dic293C22⋊C411yescharacteristic
53C2×Dic293C2×D411yescharacteristic
54C4×D293—22no—
55C4×D293—22no—
56C4×D293—41no—
57C4×D293—44no—
58Q8×C293—42no—
59C2×C4×C293—22no—
60C2×C4×C293C22⋊C411yescharacteristic
61C2×C4×C293C22⋊C411yescharacteristic
62C2×C4×C293C22×C411yescharacteristic
63C22×C293C2×C22⋊C411yescharacteristic
64C2×D293—21no—
65C2×D293—21no—
66C2×D293—42no—
67C2×D293—42no—
68C2×D293—42no—
69C2×D293AGL(1,ℤ/8)12yes—
70#11924078—44no—
71C4×C293—21no—
72C4×C293—21no—
73C4×C293—42no—
74C4×C293#10412yes—
75Dic293—21no—
76Dic293—21no—
77Dic293—21no—
78C2×C293#41011yescharacteristic
79C2×C293#41811yescharacteristic
80C2×C293C2×#10411yescharacteristic
81D293—22no—
82D293—82no—
83C293#150511yescharacteristic, complemented, Sylow
84#1505—2931nomaximal, Sylow
85#532—2931no—
86#432—2931no—
87#376—2931no—
88#327—2934no—
89C2×#41—5861no—
90C4⋊Q8#1192407811yescharacteristic, complemented
91#127—2931no—
92#124—5861no—
93#121—2932no—
94#121—5861no—
95C4×D4—2932no—
96C4×D4—5861no—
97C2×C42—2931no—
98C2×C42—5861no—
99C4⋊C8—5861no—
100C22⋊C8—2932no—
101#97—5861no—
102#95—2932no—
103#95—5861no—
104#41—11724no—
105C2×Q8—21no—
106C2×D4—2932no—
107C2×D4—5862no—
108C2×D4—5861no—
109C2×D4—5861no—
110C22×C4—2931no—
111C22×C4—2931no—
112C22×C4—2931no—
113C22×C4—5862no—
114C22×C4—5862no—
115C2×C8—5862no—
116C4⋊C4—21no—
117C4⋊C4C2×#1192407812yes—
118C22⋊C4—5862no—
119C22⋊C4—5862no—
120C42—2931no—
121C42—2931no—
122C42—2931no—
123C42—5864no—
124C42C2×#1192407811yescharacteristic
125C23—2931no—
126C23—5862no—
127Q8—42no—
128D4—11722no—
129D4—11722no—
130D4—11724no—
131D4—11722no—
132C2×C4—22no—
133C2×C4—2931no—
134C2×C4—2931no—
135C2×C4—2931no—
136C2×C4—5862no—
137C2×C4—5862no—
138C2×C4—5864no—
139C2×C4—11721no—
140C2×C4—11724no—
141C2×C4—11722no—
142C2×C4—11722no—
143C2×C4C22⋊#1192407811yescharacteristic
144C2×C4C22⋊#1192407811yescharacteristic
145C2×C4C22×#1192407811yescharacteristic
146C8—11722no—
147C22—2932no—
148C22—5861no—
149C22—5861no—
150C22—11722no—
151C22—11722no—
152C22—11722no—
153C22C2×C22⋊#1192407811yescharacteristic
154C4—21no—
155C4—21no—
156C4—42no—
157C4—5861no—
158C4—5861no—
159C4—5861no—
160C4—11724no—
161C4#2262768912yes—
162C2—23442no—
163C2—5862no—
164C2#3403711011yescharacteristic
165C2#3403712111yescharacteristic
166C2C2×#2262768911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
FittingC4⋊Q8×C293C4
socleC22×C293C2×C22⋊C4
prime radical#34036680C2
cosocleC2×C4×D293C23
hypercenterC4⋊Q8#11924078
hypocenterC293#1505
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
1. #34037151C2semidirect
2. #34037065C2semidirect
3. #34036981C2semidirect
12. #22627621C4semidirect
17. #22627586C4semidirect
19. C4⋊Q8×C293C4semidirect
83. C293#1505semidirect
90. 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
#340369812
#340366802
#1505293