Finite Group Databasebeta

← #49174182

Subgroups — #49174182

Order 37504.

346 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 64 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#34037100C211yesmaximal, characteristic, complemented
2C4×C22⋊#11924078C211yesmaximal, characteristic, complemented
3#34036981C214yesmaximal, complemented
4C2×#22627599C211yesmaximal, characteristic
5C2×#17989812—21no—
6C2×C22⋊#11924078—21no—
7C2×C4×#11924078—21no—
8#22627681C2212yescomplemented
9C22⋊#14556880—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#17989812—42no—
22C2×#14556880—22no—
23C22⋊#11924078—24no—
24C4×#11924078—42no—
25C23×D293—21no—
26C23×D293D411yescharacteristic
27C2×D1172—22no—
28C2×D1172—22no—
29C2×D1172—21no—
30C2×D1172—42no—
31C2×D1172—44no—
32C2×D1172C2×C412yes—
33C22×Dic293D411yescharacteristic
34C2×C4×D293—42no—
35C2×C4×D293C2×C411yescharacteristic
36C2×C4×D293D411yescharacteristic
37C2×C4×D293D411yescharacteristic
38C2×C4×D293C2311yescharacteristic
39#17989779—22no—
40#17989779—22no—
41C22×C4×C293—21no—
42C22×C4×C293C2×C411yescharacteristic
43C4⋊C4×C293—21no—
44C4⋊C4×C293C2×C412yes—
45C2×#11924078—24no—
46C2×#11924078—42no—
47C2×#11924078—42no—
48#14556880—42no—
49C22×D293—22no—
50C22×D293—22no—
51C22×D293—22no—
52C22×D293—41no—
53C22×D293—42no—
54C22×D293—42no—
55C22×D293—42no—
56C22×D293C22⋊C411yescharacteristic
57C22×D293C2×D411yescharacteristic
58D1172—42no—
59D1172—44no—
60D1172—44no—
61D1172—42no—
62C2×Dic293—41no—
63C2×Dic293C22⋊C411yescharacteristic
64C2×Dic293C2×D411yescharacteristic
65C4×D293—22no—
66C4×D293—22no—
67C4×D293—41no—
68C4×D293—41no—
69C23×C293C22⋊C411yescharacteristic
70C2×C4×C293—22no—
71C2×C4×C293—22no—
72C2×C4×C293—42no—
73C2×C4×C293C22⋊C411yescharacteristic
74C2×C4×C293C22×C411yescharacteristic
75C22×C293—21no—
76C22×C293—21no—
77C22×C293#10412yes—
78C22×C293C2×C22⋊C411yescharacteristic
79C2×D293—21no—
80C2×D293—21no—
81C2×D293—21no—
82C2×D293—21no—
83C2×D293—21no—
84C2×D293—44no—
85C2×D293—42no—
86C2×D293—42no—
87C2×D293—42no—
88C2×D293—84no—
89C2×D293AGL(1,ℤ/8)12yes—
90#11924078—44no—
91C4×C293—21no—
92C4×C293—42no—
93C4×C293#9912yes—
94Dic293—21no—
95Dic293—21no—
96C2×C293—22no—
97C2×C293C2×#9911yescharacteristic
98C2×C293#41811yescharacteristic
99C2×C293C2×#10411yescharacteristic
100D293—22no—
101D293—41no—
102D293—82no—
103C293#150711yescharacteristic, complemented, Sylow
104#1507—2931nomaximal, Sylow
105C2×#121—2931no—
106#407—2931no—
107C4×C22⋊C4—2931no—
108#327—2934no—
109C22×D4—2931no—
110C22×D4—5861no—
111C23×C4—2931no—
112C2×M16—5861no—
113#121—2932no—
114#121—2932no—
115#121—5861no—
116#121—5861no—
117C2×C4⋊C4#1192407811yescharacteristic, complemented
118C2×C22⋊C4—5861no—
119C2×C22⋊C4—5861no—
120C2×C42—5861no—
121C22⋊C8—2932no—
122C22⋊C8—5861no—
123#95—2932no—
124C24—2931no—
125C24—5861no—
126C2×D4—2932no—
127C2×D4—5862no—
128C2×D4—5862no—
129C2×D4—5861no—
130C2×D4—11722no—
131C2×D4—11724no—
132C22×C4—21no—
133C22×C4—2931no—
134C22×C4—2931no—
135C22×C4—2931no—
136C22×C4—2931no—
137C22×C4—2931no—
138C22×C4—5862no—
139C22×C4—11722no—
140C22×C4C2×#1192407811yescharacteristic
141M16—11722no—
142C2×C8—5862no—
143C4⋊C4—21no—
144C4⋊C4C2×#1192407812yes—
145C22⋊C4—5862no—
146C22⋊C4—5862no—
147C22⋊C4—5864no—
148C42—11722no—
149C23—2931no—
150C23—2931no—
151C23—5862no—
152C23—5862no—
153C23—5862no—
154C23—11722no—
155C23—11722no—
156C23—11721no—
157C23—11722no—
158C23C22⋊#1192407811yescharacteristic
159D4—11722no—
160D4—11724no—
161D4—11724no—
162D4—11722no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—42no—
166C2×C4—2931no—
167C2×C4—2931no—
168C2×C4—5862no—
169C2×C4—5862no—
170C2×C4—5864no—
171C2×C4—11721no—
172C2×C4—11721no—
173C2×C4—11721no—
174C2×C4—11722no—
175C2×C4—11722no—
176C2×C4C22⋊#1192407811yescharacteristic
177C2×C4C22×#1192407811yescharacteristic
178C8—11722no—
179C22—21no—
180C22—21no—
181C22—2932no—
182C22—23444no—
183C22—5861no—
184C22—5861no—
185C22—5861no—
186C22—5861no—
187C22—5861no—
188C22—11724no—
189C22—11722no—
190C22—11722no—
191C22—11722no—
192C22#2262768912yes—
193C22C2×C22⋊#1192407811yescharacteristic
194C4—21no—
195C4—42no—
196C4—5861no—
197C4—5861no—
198C4—11724no—
199C4#2262768312yes—
200C2—22no—
201C2—23442no—
202C2—5862no—
203C2—11721no—
204C2C2×#2262768311yescharacteristic
205C2#3403712111yescharacteristic
206C2C2×#2262768911yescharacteristic
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#1507
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. #34037100C2semidirect
2. C4×C22⋊#11924078C2semidirect
3. #34036981C2semidirect
8. #22627681C22semidirect
10. (C2×#11924078)⋊C4C22semidirect
12. C22×D1172C4semidirect
16. #22627599C4semidirect
19. C2×C4⋊C4×C293C4semidirect
103. C293#1507semidirect
117. C2×C4⋊C4#11924078semidirect

Maximal subgroups

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

subgroupindex
#340371002
C4×C22⋊#119240782
#340369812
C2×#226275992
#1507293