Finite Group Databasebeta

← #49174218

Subgroups — #49174218

Order 37504.

220 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 66 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
2#34037073C211yesmaximal, characteristic
3#34036983C212yesmaximal
4#34036982C212yesmaximal
5#34036683C211yesmaximal, characteristic
6C2×C4⋊#11924078—21no—
7C4⋊#14556880—21no—
8#22627681C2212yes—
9C4×#14556880—21no—
10(C2×#11924078)⋊C4—21no—
11(C2×#11924078)⋊C4C2212yes—
12#22627623C411yescharacteristic, complemented
13#22627622C411yescharacteristic, complemented
14#22627614—21no—
15#22627604C2211yescharacteristic
16#22627602—21no—
17#22627600C2211yescharacteristic
18C4×Dic586—21no—
19C4×Dic586C411yescharacteristic, complemented
20#22627581—21no—
21C42×D293C2211yescharacteristic
22C4×Q8×C293C411yescharacteristic, complemented
23C22×#11924078—22no—
24C2×#14556880—22no—
25C4⋊#11924078—42no—
26C2×Dic586—21no—
27C2×Dic586C2×C411yescharacteristic
28C2×C4×D293D411yescharacteristic
29C2×C4×D293D411yescharacteristic
30C2×C4×D293C2311yescharacteristic
31C4⋊Dic293—21no—
32C4⋊Dic293C2×C411yescharacteristic
33#17989781—21no—
34#17989781—21no—
35#17989781—21no—
36#17989781—21no—
37#17989781—21no—
38#17989779—21no—
39#17989779—21no—
40C4×Dic293—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×D293C2×D411yescharacteristic
54Dic586—42no—
55Dic586—41no—
56C2×Dic293—21no—
57C2×Dic293—21no—
58C2×Dic293C22⋊C411yescharacteristic
59C2×Dic293C22⋊C411yescharacteristic
60C2×Dic293C2×D411yescharacteristic
61C4×D293—41no—
62C4×D293—41no—
63C4×D293SD1612yes—
64C4×D293Q1612yes—
65Q8×C293—41no—
66C2×C4×C293—21no—
67C2×C4×C293—21no—
68C2×C4×C293C22⋊C411yescharacteristic
69C2×C4×C293C22⋊C411yescharacteristic
70C2×C4×C293C22×C411yescharacteristic
71C22×C293C2×C22⋊C411yescharacteristic
72C2×D293—21no—
73C2×D293—21no—
74C2×D293C2×SD1611yescharacteristic
75C2×D293C2×Q1611yescharacteristic
76#11924078—82no—
77C4×C293—21no—
78C4×C293—21no—
79C4×C293—41no—
80C4×C293—41no—
81C4×C293#10312yes—
82Dic293—21no—
83Dic293—21no—
84Dic293—41no—
85Dic293—41no—
86Dic293#10312yes—
87C2×C293#41011yescharacteristic
88C2×C293C2×#10311yescharacteristic
89C2×C293#42111yescharacteristic
90D293—21no—
91D293—21no—
92C293#151811yescharacteristic, complemented, Sylow
93#1518—2931nomaximal, Sylow
94#533—2931no—
95#431—2931no—
96#382—2931no—
97#328—2932no—
98#328—2932no—
99C4⋊Q8—2931no—
100C4⋊Q8—2931no—
101#125—5861no—
102C22⋊Q8—2931no—
103C22⋊Q8—2931no—
104C22⋊Q8—5861no—
105C4×Q8—2931no—
106C4×Q8—5861no—
107C4×Q8#1192407811yescharacteristic, complemented
108#117—5861no—
109C2×C4⋊C4—5861no—
110C2×C42—2931no—
111C4⋊C8—5861no—
112C22⋊C8—2932no—
113C4×C8—5861no—
114#95—2932no—
115#95—5861no—
116C2×Q8—2931no—
117C2×Q8—5861no—
118C2×Q8C2×#1192407811yescharacteristic
119C22×C4—2931no—
120C22×C4—2931no—
121C22×C4—2931no—
122C22×C4—5862no—
123C2×C8—5862no—
124C4⋊C4—21no—
125C4⋊C4—2931no—
126C4⋊C4—5861no—
127C4⋊C4—5861no—
128C4⋊C4—5861no—
129C4⋊C4—5861no—
130C4⋊C4—5861no—
131C4⋊C4—5861no—
132C4⋊C4—11722no—
133C4⋊C4C2×#1192407811yescharacteristic
134C22⋊C4—5861no—
135C22⋊C4—5861no—
136C42—21no—
137C42—2931no—
138C42—2931no—
139C42—2931no—
140C42—5861no—
141C42C2×#1192407811yescharacteristic
142C23—2931no—
143Q8—41no—
144Q8—11721no—
145Q8—11722no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—2931no—
149C2×C4—2932no—
150C2×C4—2932no—
151C2×C4—2931no—
152C2×C4—2931no—
153C2×C4—5861no—
154C2×C4—5861no—
155C2×C4—11721no—
156C2×C4—11721no—
157C2×C4—11722no—
158C2×C4—11722no—
159C2×C4—11722no—
160C2×C4C22⋊#1192407811yescharacteristic
161C2×C4C22⋊#1192407811yescharacteristic
162C2×C4C22×#1192407811yescharacteristic
163C8—11722no—
164C22—2931no—
165C22—2931no—
166C22—5861no—
167C22—5861no—
168C22C2×C22⋊#1192407811yescharacteristic
169C4—21no—
170C4—21no—
171C4—41no—
172C4—41no—
173C4—2932no—
174C4—23442no—
175C4—5861no—
176C4—5861no—
177C4—11721no—
178C4—11721no—
179C4#2262768712yes—
180C2—5861no—
181C2—5861no—
182C2#3403710811yescharacteristic
183C2C2×#2262768711yescharacteristic
184C2#3403712611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
FittingC4×Q8×C293C4
socleC22×C293C2×C22⋊C4
prime radicalC22×D293C2×D4
cosocleC2×C4×D293C23
hypercenterC4×Q8#11924078
hypocenterC293#1518
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
12. #22627623C4semidirect
13. #22627622C4semidirect
19. C4×Dic586C4semidirect
22. C4×Q8×C293C4semidirect
92. C293#1518semidirect
107. C4×Q8#11924078semidirect

Maximal subgroups

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

subgroupindex
#340371482
#340370732
#340369832
#340369822
#340366832
#1518293