Finite Group Databasebeta

← #49174265

Subgroups — #49174265

Order 37504.

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

normal subgroups only

This group has 248 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#34037151C212yesmaximal, complemented
2#34036985C212yesmaximal, complemented
3#34036984C212yesmaximal, complemented
4#124×D293C211yesmaximal, characteristic
5C4⋊#14556880—22no—
6#22627681—22no—
7#22627679C2214yescomplemented
8C2×Q8×D293C411yescharacteristic
9C2×D4×D293C411yescharacteristic
10#22627613C2211yescharacteristic
11#22627612C411yescharacteristic
12#22627611C2211yescharacteristic
13#22627610—22no—
14C22⋊C4×D293—22no—
15C42×D293C2211yescharacteristic
16#124×C293C411yescharacteristic
17C2×#14556880—24no—
18C23×D293—21no—
19C2×Dic586—21no—
20C2×Dic586C2×C411yescharacteristic
21Q8×D293—42no—
22C2×D1172C2×C411yescharacteristic
23C2×C22⋊D293—21no—
24D4×D293—42no—
25C2×C4×D293—21no—
26C2×C4×D293C2×C411yescharacteristic
27C2×C4×D293D412yes—
28C22⋊Dic293—22no—
29#17989779—22no—
30#17989779—22no—
31C4×Dic293D412yes—
32C4×Dic293C2311yescharacteristic
33C2×Q8×C293C2×C411yescharacteristic
34C2×D4×C293C2×C411yescharacteristic
35C22⋊C4×C293—22no—
36C42×C293C2×C411yescharacteristic
37#14556880—44no—
38C22×D293—21no—
39C22×D293—44no—
40C22×D293—42no—
41C22×D293C22⋊C411yescharacteristic
42Dic586—42no—
43Dic586—41no—
44D1172—41no—
45C22⋊D293—42no—
46C2×Dic293—21no—
47C2×Dic293C22⋊C411yescharacteristic
48C2×Dic293C2×D412yes—
49C4×D293—22no—
50C4×D293—42no—
51C4×D293—42no—
52C23×C293—21no—
53Q8×C293—41no—
54D4×C293—41no—
55C2×C4×C293—21no—
56C2×C4×C293C22⋊C412yes—
57C2×C4×C293C22×C411yescharacteristic
58C22×C293—41no—
59C22×C293—42no—
60C22×C293C2×C22⋊C411yescharacteristic
61C2×D293—22no—
62C2×D293—41no—
63C2×D293—42no—
64C2×D293—84no—
65C2×D293#10012yes—
66C4×C293—21no—
67C4×C293—22no—
68C4×C293—41no—
69Dic293—21no—
70Dic293—22no—
71Dic293—41no—
72C2×C293—81no—
73C2×C293C2×#10011yescharacteristic
74C2×C293#42112yes—
75D293—22no—
76D293—81no—
77C293#153311yescharacteristic, complemented, Sylow
78#1533—2931nomaximal, Sylow
79C2×#124—2931no—
80#432—2932no—
81#329—2932no—
82#329—2932no—
83C22×Q8—2931no—
84C22×D4—2931no—
85#124—2931no—
86#124—2931no—
87#124—2931no—
88#124—5862no—
89#124#1192407811yescharacteristic
90C2×C22⋊C4—5862no—
91C2×C42—2931no—
92C4⋊C8—5862no—
93C22⋊C8—5862no—
94#97—2934no—
95C24—5861no—
96C2×Q8—2931no—
97C2×Q8—5861no—
98C2×Q8—11722no—
99C2×Q8C2×#1192407811yescharacteristic
100C2×D4—2931no—
101C2×D4—5861no—
102C2×D4—11722no—
103C2×D4C2×#1192407811yescharacteristic
104C22×C4—2931no—
105C22×C4—2932no—
106C22×C4—5861no—
107C2×C8—5864no—
108C22⋊C4—22no—
109C22⋊C4—5862no—
110C22⋊C4—5862no—
111C22⋊C4—5862no—
112C42—2932no—
113C42—2931no—
114C42C2×#1192407811yescharacteristic
115C23—21no—
116C23—2931no—
117C23—5861no—
118C23—11722no—
119C23—11724no—
120Q8—41no—
121Q8—11721no—
122Q8—11722no—
123D4—41no—
124D4—11721no—
125D4—11722no—
126C2×C4—21no—
127C2×C4—2932no—
128C2×C4—2931no—
129C2×C4—5862no—
130C2×C4—5861no—
131C2×C4—11722no—
132C2×C4—11722no—
133C2×C4C22⋊#1192407812yes—
134C2×C4C22×#1192407811yescharacteristic
135C8—11724no—
136C22—41no—
137C22—42no—
138C22—2932no—
139C22—23444no—
140C22—5862no—
141C22—11721no—
142C22—11722no—
143C22C2×C22⋊#1192407811yescharacteristic
144C4—21no—
145C4—22no—
146C4—41no—
147C4—5861no—
148C4—5862no—
149C4—11721no—
150C2—81no—
151C2—23441no—
152C2—5862no—
153C2D293⋊#10011yescharacteristic
154C2#3403712612yes—
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
Fitting#124×C293C4
socleC22×C293C2×C22⋊C4
prime radicalC2×D4×D293C4
cosocleC4×Dic293C23
hypercenter#124#11924078
hypocenterC293#1533
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #34037151C2semidirect
2. #34036985C2semidirect
3. #34036984C2semidirect
7. #22627679C22semidirect
77. C293#1533semidirect

Maximal subgroups

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

subgroupindex
#340371512
#340369852
#340369842
#124×D2932
#1533293