Finite Group Databasebeta

← #49174306

Subgroups — #49174306

Order 37504.

208 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 62 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#34037149C211yesmaximal, characteristic
2C2×#22627691C211yesmaximal, characteristic
3#34036988C212yesmaximal, complemented
4#34036988C212yesmaximal, complemented
5#34036682C211yesmaximal, characteristic
6C22×#14556880—21no—
7#22627691—21no—
8#22627691C2212yes—
9#22627691C2212yes—
10C22⋊#14556880—21no—
11#22627679—21no—
12#22627623C2211yescharacteristic
13#22627623C2211yescharacteristic
14#22627615C411yescharacteristic
15#22627615C411yescharacteristic
16#22627601—21no—
17#22627601—21no—
18C4×Dic586—21no—
19C4×Dic586—21no—
20#22627583C411yescharacteristic
21C2×C4×Dic293C2211yescharacteristic
22#117×C293C411yescharacteristic
23C2×#14556880—22no—
24C2×#14556880—22no—
25C2×#14556880—42no—
26C2×Dic586—21no—
27C2×Dic586—21no—
28C22×Dic293D411yescharacteristic
29C22×Dic293D411yescharacteristic
30C4⋊Dic293—21no—
31C4⋊Dic293—21no—
32C4⋊Dic293C2×C411yescharacteristic
33C4⋊Dic293C2×C411yescharacteristic
34#17989781—21no—
35#17989781—21no—
36#17989781—21no—
37#17989781—21no—
38C22⋊Dic293—21no—
39C4×Dic293—21no—
40C4×Dic293C2×C411yescharacteristic
41C4×Dic293D411yescharacteristic
42C4×Dic293D411yescharacteristic
43C4×Dic293C2311yescharacteristic
44C22×C4×C293C2×C411yescharacteristic
45C4⋊C4×C293C2×C411yescharacteristic
46C4⋊C4×C293C2×C411yescharacteristic
47C22⋊C4×C293—21no—
48C42×C293—21no—
49#14556880—42no—
50#14556880—42no—
51Dic586—42no—
52Dic586—41no—
53Dic586—41no—
54C2×Dic293—22no—
55C2×Dic293—21no—
56C2×Dic293—21no—
57C2×Dic293—21no—
58C2×Dic293—21no—
59C2×Dic293C22⋊C411yescharacteristic
60C2×Dic293C22⋊C411yescharacteristic
61C2×Dic293C2×D411yescharacteristic
62C2×Dic293C2×D411yescharacteristic
63C23×C293C22⋊C411yescharacteristic
64C2×C4×C293—22no—
65C2×C4×C293—21no—
66C2×C4×C293—21no—
67C2×C4×C293C22⋊C411yescharacteristic
68C2×C4×C293C22×C411yescharacteristic
69C22×C293—21no—
70C22×C293—21no—
71C22×C293#10112yes—
72C22×C293C2×C22⋊C411yescharacteristic
73C4×C293—21no—
74C4×C293—21no—
75C4×C293—41no—
76C4×C293—41no—
77Dic293—21no—
78Dic293—21no—
79Dic293—41no—
80Dic293—41no—
81Dic293#13512yes—
82Dic293AGL(1,ℤ/8)11yescharacteristic
83Dic293#13711yescharacteristic
84C2×C293—22no—
85C2×C293C2×#10111yescharacteristic
86C2×C293#41611yescharacteristic
87C2×C293#41711yescharacteristic
88C293#155211yescharacteristic, complemented, Sylow
89#1552—2931nomaximal, Sylow
90#533—2931no—
91#432—2931no—
92C2×C4⋊C8—2931no—
93#332—2932no—
94#332—2932no—
95C22×C8—5861no—
96C4⋊Q8—2931no—
97C4⋊Q8—2931no—
98#125—2931no—
99#125—2931no—
100C22⋊Q8—5861no—
101C22⋊Q8—5861no—
102C4×Q8—5861no—
103C4×Q8—5861no—
104#117—2931no—
105#117#1192407811yescharacteristic
106C2×C42—2931no—
107C4⋊C8—2932no—
108C4⋊C8—2932no—
109C4⋊C8—5861no—
110C22⋊C8—5861no—
111#97—5861no—
112C2×Q8—5861no—
113C2×Q8—5861no—
114C22×C4—2931no—
115C22×C4—2931no—
116C22×C4C2×#1192407811yescharacteristic
117C2×C8—5862no—
118C2×C8—5862no—
119C2×C8—11722no—
120C4⋊C4—2931no—
121C4⋊C4—2931no—
122C4⋊C4—5861no—
123C4⋊C4—5861no—
124C4⋊C4—5861no—
125C4⋊C4—5861no—
126C4⋊C4—5861no—
127C4⋊C4—5861no—
128C4⋊C4C2×#1192407811yescharacteristic
129C4⋊C4C2×#1192407811yescharacteristic
130C22⋊C4—21no—
131C22⋊C4—5861no—
132C42—21no—
133C42—2931no—
134C42—2931no—
135C42—2931no—
136C42—2931no—
137C42—5861no—
138C23C22⋊#1192407811yescharacteristic
139Q8—11722no—
140Q8—11721no—
141Q8—11721no—
142C2×C4—22no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—2931no—
146C2×C4—2931no—
147C2×C4—2931no—
148C2×C4—2931no—
149C2×C4—5861no—
150C2×C4—5862no—
151C2×C4—5861no—
152C2×C4—5861no—
153C2×C4—5861no—
154C2×C4C22⋊#1192407811yescharacteristic
155C2×C4C22×#1192407811yescharacteristic
156C8—11722no—
157C8—11722no—
158C22—21no—
159C22—21no—
160C22#2262768512yes—
161C22C2×C22⋊#1192407811yescharacteristic
162C4—21no—
163C4—21no—
164C4—41no—
165C4—41no—
166C4—2932no—
167C4—2931no—
168C4—2931no—
169C4—5861no—
170C4—5861no—
171C4—11721no—
172C4—11721no—
173C2—22no—
174C2C2×#2262768511yescharacteristic
175C2#3403711911yescharacteristic
176C2#3403712011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
Fitting#117×C293C4
socleC22×C293C2×C22⋊C4
prime radicalC23×C293C22⋊C4
cosocleC4×Dic293C23
hypercenter#117#11924078
hypocenterC293#1552
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #34036988C2semidirect
4. #34036988C2semidirect
88. C293#1552semidirect

Maximal subgroups

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

subgroupindex
#340371492
C2×#226276912
#340369882
#340366822
#1552293