Finite Group Databasebeta

← #49174198

Subgroups — #49174198

Order 37504.

222 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 56 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
2#34037073C211yesmaximal, characteristic, complemented
3#34036983C212yesmaximal, complemented
4#34036981C212yesmaximal
5#34036666C211yesmaximal, characteristic
6C2×C4⋊#11924078—21no—
7#22627691—21no—
8#22627681C2212yes—
9#22627679—21no—
10(C2×#11924078)⋊C4—21no—
11(C2×#11924078)⋊C4C2212yes—
12#22627619—21no—
13#22627615C411yescharacteristic, complemented
14#22627613C411yescharacteristic, complemented
15#22627609—21no—
16#22627600C2211yescharacteristic
17#22627599C2211yescharacteristic
18C4×D1172—21no—
19C4×D1172C411yescharacteristic, complemented
20#22627581—21no—
21C42×D293C2211yescharacteristic
22C4×Q8×C293C411yescharacteristic, complemented
23C22×#11924078—22no—
24C2×#14556880—22no—
25C4⋊#11924078—42no—
26C2×D1172—21no—
27C2×D1172C2×C411yescharacteristic
28C2×C4×D293—21no—
29C2×C4×D293D411yescharacteristic
30C2×C4×D293D411yescharacteristic
31C2×C4×D293C2311yescharacteristic
32C4⋊Dic293—21no—
33C4⋊Dic293C2×C411yescharacteristic
34#17989781—21no—
35#17989781—21no—
36#17989779—21no—
37#17989779—21no—
38#17989779—21no—
39#17989779—21no—
40#17989779—21no—
41C4×Dic293C2×C411yescharacteristic
42C4×Dic293D411yescharacteristic
43C4×Dic293D411yescharacteristic
44C2×Q8×C293C2×C411yescharacteristic
45C4⋊C4×C293—21no—
46C4⋊C4×C293C2×C411yescharacteristic
47C42×C293—21no—
48C42×C293C2×C411yescharacteristic
49C2×#11924078—42no—
50C2×#11924078—42no—
51C2×#11924078—42no—
52#14556880—42no—
53C22×D293—21no—
54C22×D293C2×D411yescharacteristic
55D1172—41no—
56D1172—41no—
57D1172—41no—
58C2×Dic293—21no—
59C2×Dic293C22⋊C411yescharacteristic
60C2×Dic293C22⋊C411yescharacteristic
61C2×Dic293C2×D411yescharacteristic
62C4×D293—21no—
63C4×D293—21no—
64C4×D293—41no—
65C4×D293—41no—
66C4×D293—42no—
67Q8×C293—41no—
68C2×C4×C293—21no—
69C2×C4×C293—21no—
70C2×C4×C293C22⋊C411yescharacteristic
71C2×C4×C293C22⋊C411yescharacteristic
72C2×C4×C293C22×C411yescharacteristic
73C22×C293C2×C22⋊C411yescharacteristic
74C2×D293—21no—
75C2×D293—21no—
76C2×D293—41no—
77C2×D293—41no—
78C2×D293—41no—
79C2×D293AGL(1,ℤ/8)11yescharacteristic
80C2×D293#13711yescharacteristic
81#11924078—82no—
82C4×C293—21no—
83C4×C293—21no—
84C4×C293—21no—
85C4×C293—41no—
86C4×C293—41no—
87Dic293—21no—
88Dic293—21no—
89Dic293—21no—
90Dic293—41no—
91C2×C293#41011yescharacteristic
92C2×C293#41711yescharacteristic
93C2×C293#42111yescharacteristic
94D293—21no—
95D293—21no—
96D293—81no—
97C293#151211yescharacteristic, complemented, Sylow
98#1512—2931nomaximal, Sylow
99#529—2931no—
100#432—2931no—
101#382—2931no—
102#328—2932no—
103#327—2932no—
104#126—5861no—
105#125—2931no—
106#124—2931no—
107#123—5861no—
108C22⋊Q8—2931no—
109#121—2931no—
110C4×Q8#1192407811yescharacteristic, complemented
111C4×D4—2931no—
112C4×D4—5861no—
113#117—5861no—
114C2×C4⋊C4—5861no—
115C2×C42—2931no—
116C4⋊C8—5861no—
117C22⋊C8—2932no—
118#97—5861no—
119#95—2932no—
120#95—5861no—
121C2×Q8C2×#1192407811yescharacteristic
122C2×D4—2931no—
123C2×D4—5861no—
124C22×C4—2931no—
125C22×C4—2931no—
126C22×C4—2931no—
127C22×C4—5861no—
128C22×C4—5862no—
129C2×C8—5862no—
130C4⋊C4—21no—
131C4⋊C4—2931no—
132C4⋊C4—5861no—
133C4⋊C4—5861no—
134C4⋊C4—5861no—
135C4⋊C4—11722no—
136C4⋊C4C2×#1192407811yescharacteristic
137C22⋊C4—5861no—
138C22⋊C4—5861no—
139C22⋊C4—5861no—
140C22⋊C4—5861no—
141C22⋊C4—5861no—
142C42—21no—
143C42—2931no—
144C42—2931no—
145C42—2931no—
146C42C2×#1192407811yescharacteristic
147C23—2931no—
148C23—5861no—
149Q8—41no—
150D4—11721no—
151D4—11721no—
152D4—11721no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—2931no—
156C2×C4—2931no—
157C2×C4—2931no—
158C2×C4—5861no—
159C2×C4—5861no—
160C2×C4—5861no—
161C2×C4—11721no—
162C2×C4—11721no—
163C2×C4—11722no—
164C2×C4—11722no—
165C2×C4—11722no—
166C2×C4—11722no—
167C2×C4C22⋊#1192407811yescharacteristic
168C2×C4C22⋊#1192407811yescharacteristic
169C2×C4C22×#1192407811yescharacteristic
170C8—11722no—
171C22—2931no—
172C22—2931no—
173C22—5861no—
174C22—5861no—
175C22—11721no—
176C22—11721no—
177C22—11721no—
178C22C2×C22⋊#1192407811yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—23442no—
185C4—5861no—
186C4—5861no—
187C4—5861no—
188C4—11721no—
189C2—23441no—
190C2—5861no—
191C2—5861no—
192C2#3403710811yescharacteristic
193C2#3403712011yescharacteristic
194C2#3403712811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
FittingC4×Q8×C293C4
socleC22×C293C2×C22⋊C4
prime radical#22627599C22
cosocleC2×C4×D293C23
hypercenterC4×Q8#11924078
hypocenterC293#1512
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. #34037152C2semidirect
2. #34037073C2semidirect
3. #34036983C2semidirect
13. #22627615C4semidirect
14. #22627613C4semidirect
19. C4×D1172C4semidirect
22. C4×Q8×C293C4semidirect
97. C293#1512semidirect
110. C4×Q8#11924078semidirect

Maximal subgroups

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

subgroupindex
#340371522
#340370732
#340369832
#340369812
#340366662
#1512293