Finite Group Databasebeta

← #49174192

Subgroups — #49174192

Order 37504.

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

normal subgroups only

This group has 326 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#34037101C211yesmaximal, characteristic, complemented
2#34037072C211yesmaximal, characteristic, complemented
3#34036981C214yesmaximal, complemented
4C2×#22627599C211yesmaximal, characteristic
5C2×#17989811—21no—
6C2×C22⋊#11924078—21no—
7#22627681—21no—
8#22627681C2212yescomplemented
9(C2×#11924078)⋊C4—21no—
10(C2×#11924078)⋊C4C2212yescomplemented
11C22×D1172—21no—
12C22×D1172C411yescharacteristic, complemented
13C22×C4×D293C2211yescharacteristic
14#22627599—21no—
15#22627599—21no—
16#22627599C412yescomplemented
17#22627599C2212yes—
18C2×#17989779—21no—
19C2×C4⋊C4×C293C411yescharacteristic, complemented
20C22×#11924078—22no—
21#17989811—42no—
22C2×#14556880—22no—
23C22⋊#11924078—42no—
24C23×D293—21no—
25C23×D293D411yescharacteristic
26C2×D1172—22no—
27C2×D1172—22no—
28C2×D1172—21no—
29C2×D1172—42no—
30C2×D1172—44no—
31C2×D1172C2×C412yes—
32C22×Dic293D411yescharacteristic
33C2×C4×D293—42no—
34C2×C4×D293C2×C411yescharacteristic
35C2×C4×D293D411yescharacteristic
36C2×C4×D293D411yescharacteristic
37C2×C4×D293C2311yescharacteristic
38#17989779—22no—
39#17989779—22no—
40C22×C4×C293—21no—
41C22×C4×C293C2×C411yescharacteristic
42C4⋊C4×C293—21no—
43C4⋊C4×C293C2×C412yes—
44C2×#11924078—42no—
45C2×#11924078—42no—
46C2×#11924078—42no—
47#14556880—42no—
48C22×D293—22no—
49C22×D293—22no—
50C22×D293—22no—
51C22×D293—41no—
52C22×D293—42no—
53C22×D293—42no—
54C22×D293—42no—
55C22×D293C22⋊C411yescharacteristic
56C22×D293C2×D411yescharacteristic
57D1172—42no—
58D1172—42no—
59D1172—44no—
60D1172—44no—
61C2×Dic293—22no—
62C2×Dic293C22⋊C411yescharacteristic
63C2×Dic293C2×D411yescharacteristic
64C4×D293—41no—
65C4×D293—41no—
66C4×D293—41no—
67C4×D293—41no—
68C23×C293C22⋊C411yescharacteristic
69C2×C4×C293—22no—
70C2×C4×C293—22no—
71C2×C4×C293—42no—
72C2×C4×C293C22⋊C411yescharacteristic
73C2×C4×C293C22×C411yescharacteristic
74C22×C293—21no—
75C22×C293—21no—
76C22×C293#9912yes—
77C22×C293C2×C22⋊C411yescharacteristic
78C2×D293—21no—
79C2×D293—21no—
80C2×D293—21no—
81C2×D293—21no—
82C2×D293—21no—
83C2×D293—44no—
84C2×D293—42no—
85C2×D293—42no—
86C2×D293—42no—
87C2×D293—84no—
88C2×D293AGL(1,ℤ/8)12yes—
89#11924078—82no—
90C4×C293—21no—
91C4×C293—21no—
92C4×C293—42no—
93Dic293—21no—
94Dic293—21no—
95C2×C293—22no—
96C2×C293C2×#9911yescharacteristic
97C2×C293#41811yescharacteristic
98C2×C293#42111yescharacteristic
99D293—22no—
100D293—41no—
101D293—82no—
102C293#151011yescharacteristic, complemented, Sylow
103#1510—2931nomaximal, Sylow
104C2×#121—2931no—
105#407—2931no—
106#381—2931no—
107#327—2934no—
108C22×D4—2931no—
109C22×D4—5861no—
110C23×C4—2931no—
111C2×M16—5861no—
112#121—2932no—
113#121—2932no—
114#121—5861no—
115#121—5861no—
116C2×C4⋊C4#1192407811yescharacteristic, complemented
117C2×C22⋊C4—5861no—
118C2×C22⋊C4—5861no—
119C22⋊C8—2932no—
120C22⋊C8—5861no—
121#95—2932no—
122#95—5861no—
123C24—2931no—
124C24—5861no—
125C2×D4—2932no—
126C2×D4—5862no—
127C2×D4—5862no—
128C2×D4—5861no—
129C2×D4—11722no—
130C2×D4—11724no—
131C22×C4—21no—
132C22×C4—2931no—
133C22×C4—2931no—
134C22×C4—2931no—
135C22×C4—2931no—
136C22×C4—2931no—
137C22×C4—5862no—
138C22×C4—11722no—
139C22×C4C2×#1192407811yescharacteristic
140M16—11722no—
141C2×C8—5862no—
142C4⋊C4—21no—
143C4⋊C4C2×#1192407812yes—
144C22⋊C4—5862no—
145C22⋊C4—5862no—
146C22⋊C4—11722no—
147C23—2931no—
148C23—2931no—
149C23—5862no—
150C23—5862no—
151C23—5862no—
152C23—11722no—
153C23—11722no—
154C23—11721no—
155C23—11722no—
156C23C22⋊#1192407811yescharacteristic
157D4—11722no—
158D4—11722no—
159D4—11724no—
160D4—11724no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—42no—
164C2×C4—2931no—
165C2×C4—2931no—
166C2×C4—5862no—
167C2×C4—11721no—
168C2×C4—11721no—
169C2×C4—11721no—
170C2×C4—11721no—
171C2×C4—11722no—
172C2×C4—11722no—
173C2×C4—11722no—
174C2×C4C22⋊#1192407811yescharacteristic
175C2×C4C22×#1192407811yescharacteristic
176C8—11722no—
177C22—21no—
178C22—21no—
179C22—2932no—
180C22—23444no—
181C22—5861no—
182C22—5861no—
183C22—5861no—
184C22—5861no—
185C22—5861no—
186C22—11724no—
187C22—11722no—
188C22—11722no—
189C22—11722no—
190C22#2262768312yes—
191C22C2×C22⋊#1192407811yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—23442no—
196C4—5861no—
197C4—5861no—
198C2—22no—
199C2—23442no—
200C2—5862no—
201C2—11721no—
202C2C2×#2262768311yescharacteristic
203C2#3403712111yescharacteristic
204C2#3403712811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
FittingC2×C4⋊C4×C293C4
socleC22×C293C2×C22⋊C4
prime radicalC2×#22627599C2
cosocleC2×C4×D293C23
hypercenterC2×C4⋊C4#11924078
hypocenterC293#1510
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #34037101C2semidirect
2. #34037072C2semidirect
3. #34036981C2semidirect
8. #22627681C22semidirect
10. (C2×#11924078)⋊C4C22semidirect
12. C22×D1172C4semidirect
16. #22627599C4semidirect
19. C2×C4⋊C4×C293C4semidirect
102. C293#1510semidirect
116. C2×C4⋊C4#11924078semidirect

Maximal subgroups

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

subgroupindex
#340371012
#340370722
#340369812
C2×#226275992
#1510293