Finite Group Databasebeta

← #49174287

Subgroups — #49174287

Order 37504.

212 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 68 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#34037146C211yesmaximal, characteristic
2C2×#22627691C211yesmaximal, characteristic
3#34036989C212yesmaximal, complemented
4#34036988C212yesmaximal, complemented
5#34036681C211yesmaximal, characteristic
6C22×#14556880—21no—
7#22627691—21no—
8#22627691C2212yes—
9#22627691C2212yes—
10C22⋊#14556880—21no—
11C4×#14556880—21no—
12#22627623C2211yescharacteristic
13#22627622C2211yescharacteristic
14#22627614—21no—
15#22627603C411yescharacteristic
16#22627601—21no—
17Q8×Dic293C411yescharacteristic
18#22627589—21no—
19#22627589C411yescharacteristic
20#22627580—21no—
21C2×C4×Dic293C2211yescharacteristic
22C22⋊Q8×C293C411yescharacteristic
23C2×#14556880—22no—
24C2×#14556880—22no—
25C2×#14556880—42no—
26C2×Dic586—21no—
27C2×Dic586C2×C411yescharacteristic
28C22×Dic293D411yescharacteristic
29C22×Dic293D411yescharacteristic
30C4⋊Dic293—21no—
31C4⋊Dic293C2×C411yescharacteristic
32#17989781—21no—
33#17989781—21no—
34#17989781—21no—
35#17989781—21no—
36#17989781—21no—
37C22⋊Dic293—21no—
38C4×Dic293—21no—
39C4×Dic293—21no—
40C4×Dic293C2×C411yescharacteristic
41C4×Dic293D411yescharacteristic
42C4×Dic293D411yescharacteristic
43C4×Dic293C2311yescharacteristic
44C2×Q8×C293C2×C411yescharacteristic
45C22×C4×C293C2×C411yescharacteristic
46C4⋊C4×C293—21no—
47C4⋊C4×C293C2×C411yescharacteristic
48C22⋊C4×C293—21no—
49#14556880—42no—
50#14556880—42no—
51Dic586—42no—
52Dic586—41no—
53C2×Dic293—22no—
54C2×Dic293—21no—
55C2×Dic293—21no—
56C2×Dic293C22⋊C411yescharacteristic
57C2×Dic293C22⋊C411yescharacteristic
58C2×Dic293SD1612yes—
59C2×Dic293Q1612yes—
60C2×Dic293C2×D411yescharacteristic
61C2×Dic293C2×D411yescharacteristic
62C23×C293C22⋊C411yescharacteristic
63Q8×C293—41no—
64C2×C4×C293—21no—
65C2×C4×C293—21no—
66C2×C4×C293—41no—
67C2×C4×C293C22⋊C411yescharacteristic
68C2×C4×C293C22×C411yescharacteristic
69C22×C293—21no—
70C22×C293—21no—
71C22×C293#10312yes—
72C22×C293C2×C22⋊C411yescharacteristic
73C4×C293—21no—
74C4×C293—21no—
75C4×C293—41no—
76C4×C293—41no—
77Dic293—21no—
78Dic293—41no—
79Dic293—41no—
80Dic293#10312yes—
81Dic293C2×SD1611yescharacteristic
82Dic293C2×Q1611yescharacteristic
83Dic293#13512yes—
84C2×C293—22no—
85C2×C293#41311yescharacteristic
86C2×C293C2×#10311yescharacteristic
87C2×C293#41611yescharacteristic
88C293#154211yescharacteristic, complemented, Sylow
89#1542—2931nomaximal, Sylow
90#533—2931no—
91#431—2931no—
92C2×C4⋊C8—2931no—
93#333—2932no—
94#332—2932no—
95C22×C8—5861no—
96C4⋊Q8—2931no—
97C4⋊Q8—2931no—
98#125—5861no—
99C22⋊Q8—2931no—
100C22⋊Q8—5861no—
101C22⋊Q8#1192407811yescharacteristic
102C4×Q8—2931no—
103C4×Q8—2931no—
104C4×Q8—5861no—
105#117—5861no—
106C2×C42—2931no—
107C4⋊C8—2932no—
108C4⋊C8—2932no—
109C4⋊C8—5861no—
110C22⋊C8—5861no—
111C4×C8—5861no—
112C2×Q8—2931no—
113C2×Q8—5861no—
114C2×Q8C2×#1192407811yescharacteristic
115C22×C4—2931no—
116C22×C4—2931no—
117C22×C4C2×#1192407811yescharacteristic
118C2×C8—5862no—
119C2×C8—5862no—
120C2×C8—11722no—
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—21no—
131C22⋊C4—5861no—
132C42—2931no—
133C42—2931no—
134C42—2931no—
135C42—2931no—
136C42—5861no—
137C42—5861no—
138C23C22⋊#1192407811yescharacteristic
139Q8—41no—
140Q8—11721no—
141Q8—11722no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—2932no—
146C2×C4—2932no—
147C2×C4—2931no—
148C2×C4—2931no—
149C2×C4—2931no—
150C2×C4—2931no—
151C2×C4—5862no—
152C2×C4—5861no—
153C2×C4—5861no—
154C2×C4C22⋊#1192407811yescharacteristic
155C2×C4C22×#1192407811yescharacteristic
156C8—11722no—
157C8—11722no—
158C22—21no—
159C22—21no—
160C22#2262768712yes—
161C22C2×C22⋊#1192407811yescharacteristic
162C4—21no—
163C4—21no—
164C4—41no—
165C4—41no—
166C4—2931no—
167C4—2932no—
168C4—2931no—
169C4—2932no—
170C4—5861no—
171C4—11721no—
172C4—11721no—
173C2—22no—
174C2#3403711611yescharacteristic
175C2C2×#2262768711yescharacteristic
176C2#3403711911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
FittingC22⋊Q8×C293C4
socleC22×C293C2×C22⋊C4
prime radicalC23×C293C22⋊C4
cosocleC4×Dic293C23
hypercenterC22⋊Q8#11924078
hypocenterC293#1542
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #34036989C2semidirect
4. #34036988C2semidirect
88. C293#1542semidirect

Maximal subgroups

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

subgroupindex
#340371462
C2×#226276912
#340369892
#340369882
#340366812
#1542293