Finite Group Databasebeta

← #49174166

Subgroups — #49174166

Order 37504.

284 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 70 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#34037148C211yesmaximal, characteristic, complemented
2C4×C4⋊#11924078C211yesmaximal, characteristic, complemented
3#34036981C214yesmaximal, complemented
4#34036680C211yesmaximal, characteristic
5C2×C4⋊#11924078—21no—
6C2×C4×#11924078—21no—
7C4⋊#14556880—21no—
8#22627681C2212yes—
9C4×#14556880—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—
23C4×#11924078—42no—
24#17989803—42no—
25#17989803—42no—
26C2×D1172—22no—
27C2×D1172—21no—
28C2×D1172—21no—
29C2×D1172C2×C412yes—
30C2×C4×D293—22no—
31C2×C4×D293D411yescharacteristic
32C2×C4×D293D411yescharacteristic
33C2×C4×D293C2311yescharacteristic
34#17989779—22no—
35#17989779—22no—
36C4×Dic293C2×C411yescharacteristic
37C4×Dic293D411yescharacteristic
38C4×Dic293D411yescharacteristic
39C2×Q8×C293—21no—
40C4⋊C4×C293—21no—
41C4⋊C4×C293C2×C412yes—
42C42×C293C2×C411yescharacteristic
43C2×#11924078—24no—
44C2×#11924078—42no—
45C2×#11924078—42no—
46#14556880—42no—
47C22×D293—22no—
48C22×D293C2×D411yescharacteristic
49D1172—42no—
50D1172—42no—
51D1172—42no—
52D1172—42no—
53D1172—42no—
54C2×Dic293C22⋊C411yescharacteristic
55C2×Dic293C22⋊C411yescharacteristic
56C2×Dic293C2×D411yescharacteristic
57C4×D293—22no—
58C4×D293—41no—
59C4×D293—44no—
60C4×D293D812yes—
61C4×D293SD1612yes—
62Q8×C293—42no—
63C2×C4×C293—22no—
64C2×C4×C293C22⋊C411yescharacteristic
65C2×C4×C293C22⋊C411yescharacteristic
66C2×C4×C293C22×C411yescharacteristic
67C22×C293C2×C22⋊C411yescharacteristic
68C2×D293—21no—
69C2×D293—21no—
70C2×D293—42no—
71C2×D293—42no—
72C2×D293—42no—
73C2×D293C2×D811yescharacteristic
74C2×D293C2×SD1611yescharacteristic
75#11924078—44no—
76C4×C293—21no—
77C4×C293—42no—
78C4×C293#10212yes—
79C4×C293#10412yes—
80Dic293—21no—
81Dic293—21no—
82Dic293#10212yes—
83C2×C293#41011yescharacteristic
84C2×C293C2×#10211yescharacteristic
85C2×C293C2×#10411yescharacteristic
86D293—21no—
87D293—21no—
88D293—82no—
89C293#150211yescharacteristic, complemented, Sylow
90#1502—2931nomaximal, Sylow
91#532—2931no—
92#431—2931no—
93C4×C4⋊C4—2931no—
94#327—2934no—
95C2×#41—5861no—
96C4⋊Q8#1192407811yescharacteristic, complemented
97#127—2931no—
98#124—5861no—
99#121—2932no—
100#121—5861no—
101C4×D4—2932no—
102C4×D4—5861no—
103C2×C4⋊C4—5861no—
104C2×C42—2931no—
105C2×C42—5861no—
106C4⋊C8—5861no—
107C22⋊C8—2932no—
108C4×C8—5861no—
109#95—2932no—
110#41—11722no—
111#41—11722no—
112C2×Q8—21no—
113C2×D4—2932no—
114C2×D4—5862no—
115C2×D4—5861no—
116C2×D4—5861no—
117C22×C4—2931no—
118C22×C4—2931no—
119C22×C4—2931no—
120C22×C4—5862no—
121C22×C4—5862no—
122C2×C8—5862no—
123C4⋊C4—21no—
124C4⋊C4—5864no—
125C4⋊C4C2×#1192407812yes—
126C22⋊C4—5862no—
127C22⋊C4—5862no—
128C42—2931no—
129C42—2931no—
130C42—2931no—
131C42—11722no—
132C42C2×#1192407811yescharacteristic
133C23—2931no—
134C23—5862no—
135Q8—42no—
136D4—11722no—
137D4—11722no—
138D4—11722no—
139D4—11722no—
140D4—11722no—
141C2×C4—22no—
142C2×C4—2931no—
143C2×C4—2932no—
144C2×C4—2932no—
145C2×C4—2931no—
146C2×C4—2931no—
147C2×C4—5862no—
148C2×C4—5864no—
149C2×C4—11721no—
150C2×C4—11724no—
151C2×C4—11722no—
152C2×C4—11722no—
153C2×C4C22⋊#1192407811yescharacteristic
154C2×C4C22⋊#1192407811yescharacteristic
155C2×C4C22×#1192407811yescharacteristic
156C8—11722no—
157C22—2931no—
158C22—2931no—
159C22—5861no—
160C22—5861no—
161C22—11722no—
162C22—11722no—
163C22—11722no—
164C22C2×C22⋊#1192407811yescharacteristic
165C4—21no—
166C4—42no—
167C4—2932no—
168C4—5861no—
169C4—5861no—
170C4—11724no—
171C4#2262768612yes—
172C4#2262768912yes—
173C2—23442no—
174C2—5861no—
175C2—5861no—
176C2#3403711011yescharacteristic
177C2C2×#2262768611yescharacteristic
178C2C2×#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#1502
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. #34037148C2semidirect
2. C4×C4⋊#11924078C2semidirect
3. #34036981C2semidirect
12. #22627621C4semidirect
17. #22627586C4semidirect
19. C4⋊Q8×C293C4semidirect
89. C293#1502semidirect
96. C4⋊Q8#11924078semidirect

Maximal subgroups

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

subgroupindex
#340371482
C4×C4⋊#119240782
#340369812
#340366802
#1502293