Finite Group Databasebeta

← #49174186

Subgroups — #49174186

Order 37504.

242 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 58 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#34037152C211yesmaximal, characteristic, complemented
2C4×C4⋊#11924078C211yesmaximal, characteristic, complemented
3#34036983C212yesmaximal, complemented
4#34036980C212yesmaximal
5#34036658C211yesmaximal, characteristic
6C2×C4⋊#11924078—21no—
7C2×C4×#11924078—21no—
8#22627691—21no—
9#22627681C2212yes—
10#22627679—21no—
11(C2×#11924078)⋊C4C2212yes—
12#22627617—21no—
13#22627616C411yescharacteristic, complemented
14#22627606—21no—
15#22627600C2211yescharacteristic
16#22627595C2211yescharacteristic
17Q8×Dic293C411yescharacteristic, complemented
18D4×Dic293C411yescharacteristic, complemented
19#22627584—21no—
20#22627580—21no—
21C42×D293C2211yescharacteristic
22#124×C293C411yescharacteristic, complemented
23C22×#11924078—22no—
24C2×#14556880—22no—
25C4⋊#11924078—24no—
26C4×#11924078—42no—
27C2×C22⋊D293—21no—
28C22×Dic293—21no—
29C2×C4×D293D411yescharacteristic
30C2×C4×D293D411yescharacteristic
31C2×C4×D293C2311yescharacteristic
32C4⋊Dic293—21no—
33C4⋊Dic293C2×C411yescharacteristic
34C4⋊Dic293C2×C411yescharacteristic
35#17989781—21no—
36#17989781—21no—
37#17989781—21no—
38C22⋊Dic293—21no—
39C22⋊Dic293—21no—
40#17989779—21no—
41C4×Dic293—21no—
42C4×Dic293C2×C411yescharacteristic
43C4×Dic293D411yescharacteristic
44C4×Dic293D411yescharacteristic
45C2×Q8×C293C2×C411yescharacteristic
46C2×D4×C293C2×C411yescharacteristic
47C22⋊C4×C293—21no—
48C22⋊C4×C293—21no—
49C42×C293C2×C411yescharacteristic
50C2×#11924078—24no—
51C2×#11924078—42no—
52C2×#11924078—42no—
53#14556880—42no—
54C22×D293C2×D411yescharacteristic
55C22⋊D293—41no—
56C22⋊D293—41no—
57C2×Dic293—21no—
58C2×Dic293—21no—
59C2×Dic293—42no—
60C2×Dic293C22⋊C411yescharacteristic
61C2×Dic293C22⋊C411yescharacteristic
62C2×Dic293C2×D411yescharacteristic
63C4×D293—21no—
64C4×D293—21no—
65C4×D293—22no—
66C4×D293—41no—
67C23×C293—21no—
68Q8×C293—41no—
69D4×C293—41no—
70C2×C4×C293—21no—
71C2×C4×C293C22⋊C411yescharacteristic
72C2×C4×C293C22⋊C411yescharacteristic
73C2×C4×C293C22×C411yescharacteristic
74C22×C293—41no—
75C22×C293—41no—
76C22×C293—41no—
77C22×C293C2×C22⋊C411yescharacteristic
78C2×D293—21no—
79C2×D293—21no—
80C2×D293AGL(1,ℤ/8)11yescharacteristic
81C2×D293#13711yescharacteristic
82#11924078—44no—
83C4×C293—21no—
84C4×C293—21no—
85C4×C293—21no—
86C4×C293—41no—
87Dic293—21no—
88Dic293—21no—
89Dic293—41no—
90Dic293—41no—
91Dic293#10412yes—
92C2×C293—81no—
93C2×C293#41011yescharacteristic
94C2×C293#41711yescharacteristic
95C2×C293C2×#10411yescharacteristic
96D293—21no—
97D293—21no—
98C293#150911yescharacteristic, complemented, Sylow
99#1509—2931nomaximal, Sylow
100#529—2931no—
101#432—2931no—
102C4×C4⋊C4—2931no—
103#328—2932no—
104#327—2932no—
105#126—5861no—
106#125—2931no—
107#124#1192407811yescharacteristic, complemented
108#123—5861no—
109C22⋊Q8—2931no—
110#121—2931no—
111C4×Q8—2931no—
112C4×D4—2931no—
113C4×D4—5861no—
114#117—5861no—
115C2×C4⋊C4—5861no—
116C2×C42—2931no—
117C2×C42—5861no—
118C4⋊C8—5861no—
119C22⋊C8—2932no—
120#97—5861no—
121#95—2932no—
122C2×Q8C2×#1192407811yescharacteristic
123C2×D4—5861no—
124C2×D4C2×#1192407811yescharacteristic
125C22×C4—2931no—
126C22×C4—2931no—
127C22×C4—2931no—
128C22×C4—5861no—
129C22×C4—5862no—
130C2×C8—5862no—
131C4⋊C4—2931no—
132C4⋊C4—2931no—
133C4⋊C4—5861no—
134C4⋊C4—5861no—
135C4⋊C4—5864no—
136C4⋊C4—5861no—
137C4⋊C4—5861no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C22⋊C4—5861no—
141C22⋊C4—5861no—
142C22⋊C4—5861no—
143C42—2931no—
144C42—2931no—
145C42—2931no—
146C42—5861no—
147C42—11722no—
148C42C2×#1192407811yescharacteristic
149C23—21no—
150C23—2931no—
151Q8—41no—
152D4—41no—
153D4—11721no—
154D4—11721no—
155C2×C4—21no—
156C2×C4—2931no—
157C2×C4—2931no—
158C2×C4—2931no—
159C2×C4—5862no—
160C2×C4—5861no—
161C2×C4—5861no—
162C2×C4—5864no—
163C2×C4—5861no—
164C2×C4—5861no—
165C2×C4—11721no—
166C2×C4—11722no—
167C2×C4—11722no—
168C2×C4—11722no—
169C2×C4C22⋊#1192407811yescharacteristic
170C2×C4C22⋊#1192407811yescharacteristic
171C2×C4C22×#1192407811yescharacteristic
172C8—11722no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—2931no—
177C22—2931no—
178C22—5861no—
179C22—5861no—
180C22C2×C22⋊#1192407811yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—2932no—
186C4—5861no—
187C4—5861no—
188C4—11724no—
189C4—11721no—
190C4—11721no—
191C2—81no—
192C2—5861no—
193C2—5861no—
194C2#3403710911yescharacteristic
195C2#3403712011yescharacteristic
196C2D293⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
Fitting#124×C293C4
socleC22×C293C2×C22⋊C4
prime radical#22627595C22
cosocleC2×C4×D293C23
hypercenter#124#11924078
hypocenterC293#1509
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #34037152C2semidirect
2. C4×C4⋊#11924078C2semidirect
3. #34036983C2semidirect
13. #22627616C4semidirect
17. Q8×Dic293C4semidirect
18. D4×Dic293C4semidirect
22. #124×C293C4semidirect
98. C293#1509semidirect
107. #124#11924078semidirect

Maximal subgroups

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

subgroupindex
#340371522
C4×C4⋊#119240782
#340369832
#340369802
#340366582
#1509293