Finite Group Databasebeta

← #49174178

Subgroups — #49174178

Order 37504.

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

normal subgroups only

This group has 228 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
2#34037065C211yesmaximal, characteristic
3#34036983C212yesmaximal
4#34036982C212yesmaximal
5#34036683C211yesmaximal, characteristic
6C2×C4×#11924078—21no—
7#22627691—21no—
8#22627681C2212yes—
9#22627679—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—24no—
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—24no—
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—22no—
62C4×D293—22no—
63C4×D293—41no—
64Q8×C293—41no—
65C2×C4×C293—21no—
66C2×C4×C293—21no—
67C2×C4×C293C22⋊C411yescharacteristic
68C2×C4×C293C22⋊C411yescharacteristic
69C2×C4×C293C22×C411yescharacteristic
70C22×C293C2×C22⋊C411yescharacteristic
71C2×D293—21no—
72C2×D293—21no—
73C2×D293#13712yes—
74#11924078—44no—
75C4×C293—21no—
76C4×C293—21no—
77C4×C293—21no—
78C4×C293—41no—
79C4×C293—41no—
80Dic293—21no—
81Dic293—21no—
82Dic293—41no—
83Dic293—41no—
84Dic293#10412yes—
85C2×C293#41011yescharacteristic
86C2×C293#41911yescharacteristic
87C2×C293C2×#10411yescharacteristic
88D293—22no—
89C293#150611yescharacteristic, complemented, Sylow
90#1506—2931nomaximal, Sylow
91#533—2931no—
92#432—2931no—
93#376—2931no—
94#328—2932no—
95#328—2932no—
96C4⋊Q8—2931no—
97C4⋊Q8—2931no—
98#125—5861no—
99C22⋊Q8—2931no—
100C22⋊Q8—2931no—
101C22⋊Q8—5861no—
102C4×Q8—2931no—
103C4×Q8—5861no—
104C4×Q8#1192407811yescharacteristic, complemented
105#117—5861no—
106C2×C42—2931no—
107C2×C42—5861no—
108C4⋊C8—5861no—
109C22⋊C8—2932no—
110#97—5861no—
111#95—2932no—
112#95—5861no—
113C2×Q8—2931no—
114C2×Q8—5861no—
115C2×Q8C2×#1192407811yescharacteristic
116C22×C4—2931no—
117C22×C4—2931no—
118C22×C4—2931no—
119C22×C4—5862no—
120C2×C8—5862no—
121C4⋊C4—21no—
122C4⋊C4—2931no—
123C4⋊C4—5861no—
124C4⋊C4—5861no—
125C4⋊C4—5861no—
126C4⋊C4—5861no—
127C4⋊C4—5861no—
128C4⋊C4—5861no—
129C4⋊C4C2×#1192407811yescharacteristic
130C22⋊C4—5861no—
131C22⋊C4—5861no—
132C42—21no—
133C42—2931no—
134C42—2931no—
135C42—2931no—
136C42—5864no—
137C42—5861no—
138C42C2×#1192407811yescharacteristic
139C23—2931no—
140Q8—41no—
141Q8—11721no—
142Q8—11722no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—2931no—
146C2×C4—2931no—
147C2×C4—2931no—
148C2×C4—5862no—
149C2×C4—5862no—
150C2×C4—5864no—
151C2×C4—5861no—
152C2×C4—5861no—
153C2×C4—11721no—
154C2×C4—11722no—
155C2×C4—11722no—
156C2×C4C22⋊#1192407811yescharacteristic
157C2×C4C22⋊#1192407811yescharacteristic
158C2×C4C22×#1192407811yescharacteristic
159C8—11722no—
160C22—2932no—
161C22—5861no—
162C22—5861no—
163C22C2×C22⋊#1192407811yescharacteristic
164C4—21no—
165C4—21no—
166C4—21no—
167C4—41no—
168C4—41no—
169C4—2932no—
170C4—5861no—
171C4—5861no—
172C4—11724no—
173C4—11721no—
174C4—11721no—
175C2—5862no—
176C2#3403710811yescharacteristic
177C2#3403712211yescharacteristic
178C2D293⋊#10411yescharacteristic
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#1506
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
89. C293#1506semidirect
104. C4×Q8#11924078semidirect

Maximal subgroups

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

subgroupindex
#340371522
#340370652
#340369832
#340369822
#340366832
#1506293