Finite Group Databasebeta

← #49174289

Subgroups — #49174289

Order 37504.

246 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 60 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#34037147C212yesmaximal, complemented
2#34036989C212yesmaximal, complemented
3#34036987C212yesmaximal, complemented
4#34036678C211yesmaximal, characteristic
5#22627691C2214yes—
6#22627681—22no—
7C4×#14556880—22no—
8C2×#17989803C411yescharacteristic
9C2×#17989801C411yescharacteristic
10#22627622C2211yescharacteristic
11#22627620C2211yescharacteristic
12#22627612C411yescharacteristic
13#22627597—22no—
14#22627584—22no—
15C42×D293C2211yescharacteristic
16#124×C293C411yescharacteristic
17C2×#14556880—24no—
18#17989803—42no—
19#17989801—42no—
20C2×Dic586C2×C411yescharacteristic
21C2×D1172—21no—
22C2×D1172C2×C411yescharacteristic
23C2×C22⋊D293—21no—
24C2×C22⋊D293—22no—
25C22×Dic293—21no—
26C2×C4×D293—21no—
27C2×C4×D293C2×C411yescharacteristic
28C2×C4×D293D412yes—
29#17989781—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×D293C22⋊C411yescharacteristic
40Dic586—41no—
41D1172—41no—
42D1172—42no—
43C22⋊D293—42no—
44C22⋊D293—44no—
45C2×Dic293—21no—
46C2×Dic293—42no—
47C2×Dic293C22⋊C411yescharacteristic
48C2×Dic293C2×D412yes—
49C4×D293—22no—
50C4×D293—24no—
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—21no—
62C2×D293—22no—
63C2×D293—41no—
64C2×D293—42no—
65C4×C293—21no—
66C4×C293—22no—
67C4×C293—41no—
68Dic293—41no—
69Dic293#10012yes—
70Dic293#13514yes—
71C2×C293—81no—
72C2×C293C2×#10011yescharacteristic
73C2×C293#41612yes—
74D293—41no—
75D293—81no—
76C293#154311yescharacteristic, complemented, Sylow
77#1543—2931nomaximal, Sylow
78#532—2931no—
79#431—2932no—
80#333—2932no—
81#331—2932no—
82C2×#41—2931no—
83C2×#41—2931no—
84C4⋊Q8—2931no—
85#127—2931no—
86#124—2931no—
87#124#1192407811yescharacteristic
88#121—5862no—
89C4×D4—5862no—
90C2×C42—2931no—
91C4⋊C8—2934no—
92C22⋊C8—5862no—
93C4×C8—5862no—
94#41—11722no—
95#41—11722no—
96C2×Q8—2931no—
97C2×Q8C2×#1192407811yescharacteristic
98C2×D4—2931no—
99C2×D4—5861no—
100C2×D4—5862no—
101C2×D4—5861no—
102C2×D4C2×#1192407811yescharacteristic
103C22×C4—2932no—
104C22×C4—2931no—
105C22×C4—5861no—
106C22×C4—5861no—
107C2×C8—5864no—
108C4⋊C4—5862no—
109C22⋊C4—22no—
110C22⋊C4—5862no—
111C42—2932no—
112C42—2931no—
113C42C2×#1192407811yescharacteristic
114C23—21no—
115C23—2931no—
116C23—5861no—
117Q8—41no—
118Q8—11721no—
119D4—41no—
120D4—11721no—
121D4—11722no—
122D4—11724no—
123D4—11722no—
124C2×C4—21no—
125C2×C4—2932no—
126C2×C4—2931no—
127C2×C4—5862no—
128C2×C4—5864no—
129C2×C4—5861no—
130C2×C4—11722no—
131C2×C4—11722no—
132C2×C4C22⋊#1192407812yes—
133C2×C4C22×#1192407811yescharacteristic
134C8—11724no—
135C22—41no—
136C22—42no—
137C22—5861no—
138C22—5862no—
139C22—11721no—
140C22—11722no—
141C22C2×C22⋊#1192407811yescharacteristic
142C4—21no—
143C4—22no—
144C4—41no—
145C4—2932no—
146C4—2934no—
147C4—11721no—
148C2—81no—
149C2—23441no—
150C2—11721no—
151C2D293⋊#10011yescharacteristic
152C2#3403711912yes—
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
Fitting#124×C293C4
socleC22×C293C2×C22⋊C4
prime radical#34036678C2
cosocleC4×Dic293C23
hypercenter#124#11924078
hypocenterC293#1543
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. #34037147C2semidirect
2. #34036989C2semidirect
3. #34036987C2semidirect
76. C293#1543semidirect

Maximal subgroups

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

subgroupindex
#340371472
#340369892
#340369872
#340366782
#1543293