Finite Group Databasebeta

← #49160011

Subgroups — #49160011

Order 37504.

290 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C2×#22627551C212yesmaximal, complemented
2#34036130C212yesmaximal, complemented
3#34035994C211yesmaximal, characteristic, complemented
4#34035898C211yesmaximal, characteristic, complemented
5#537×C293C211yesmaximal, characteristic
6C2×#17989786C2212yes—
7C2×C4⋊Dic293C2211yescharacteristic
8C2×C4×Dic293C2211yescharacteristic
9#22627551—24no—
10#22627548—22no—
11#22627545—22no—
12#22627531—22no—
13C2×#41×C293C2212yes—
14C22⋊Q8×C293—22no—
15#121×C293—22no—
16#121×C293—22no—
17C2×C4⋊C4×C293C2211yescharacteristic
18C22×Dic293—21no—
19C22×Dic293—21no—
20#17989786—22no—
21#17989786—22no—
22C2×#14556873—22no—
23C4⋊Dic293—22no—
24C4×Dic293—21no—
25C4×Dic293D412yescomplemented
26#41×C293—22no—
27#41×C293—22no—
28#41×C293—22no—
29#41×C293—22no—
30C2×Q8×C293D412yes—
31C2×D4×C293—22no—
32C2×D4×C293—22no—
33C2×D4×C293D412yes—
34C22×C4×C293—22no—
35C22×C4×C293D412yes—
36C22×C4×C293C2311yescharacteristic
37C4⋊C4×C293—22no—
38C4⋊C4×C293—22no—
39C22⋊C4×C293—24no—
40C2×Dic293—22no—
41C2×Dic293—41no—
42C2×Dic293—41no—
43C2×Dic293—42no—
44C2×Dic293—41no—
45#14556873—42no—
46C23×C293—22no—
47C23×C293C2×D411yescharacteristic
48Q8×C293—22no—
49Q8×C293—22no—
50D4×C293—22no—
51D4×C293—22no—
52D4×C293—42no—
53D4×C293—42no—
54D4×C293—82no—
55C2×C4×C293—22no—
56C2×C4×C293—22no—
57C2×C4×C293—42no—
58C2×C4×C293—42no—
59C2×C4×C293—42no—
60C2×C4×C293C2×D411yescharacteristic
61C2×C4×C293C2×D412yes—
62C2×C4×C293#4112yes—
63C2×C4×C293#4111yescharacteristic
64C22×C293—21no—
65C22×C293—21no—
66C22×C293—42no—
67C22×C293—42no—
68C22×C293—42no—
69C22×C293#12011yescharacteristic
70C22×C293#12111yescharacteristic
71C22×C293#12411yescharacteristic
72C4×C293—42no—
73C4×C293—42no—
74C4×C293#12112yes—
75C4×C293#12312yes—
76Dic293—42no—
77Dic293—81no—
78C2×C293—21no—
79C2×C293—21no—
80C2×C293—82no—
81C2×C293#39411yescharacteristic
82C2×C293#45411yescharacteristic
83C2×C293#45511yescharacteristic
84C293#204011yescharacteristic, complemented, Sylow
85#2040—2931nomaximal, Sylow
86#537D29311yescharacteristic
87C2×#104—2932no—
88#417—2932no—
89#382—2931no—
90#343—2931no—
91C2×#41C2×D29312yes—
92C2×M16—2932no—
93C22⋊Q8—22no—
94#121—22no—
95#121—22no—
96C2×C4⋊C4—2931no—
97C2×C4⋊C4C2×D29311yescharacteristic
98C2×C42—2931no—
99#104—5864no—
100#103—5862no—
101#102—5862no—
102#95—5862no—
103#41—22no—
104#41—22no—
105#41—22no—
106#41—22no—
107C2×Q8C22⋊D29312yes—
108C2×D4—22no—
109C2×D4—22no—
110C2×D4C22⋊D29312yes—
111C22×C4—22no—
112C22×C4—5861no—
113C22×C4—5861no—
114C22×C4C22⋊D29312yes—
115C22×C4C22×D29311yescharacteristic
116M16—5862no—
117M16—5862no—
118C2×C8—5862no—
119C4⋊C4—22no—
120C4⋊C4—22no—
121C4⋊C4—5862no—
122C22⋊C4—24no—
123C42—2932no—
124C42—5861no—
125C23—22no—
126C23C2×C22⋊D29311yescharacteristic
127Q8—22no—
128Q8—22no—
129D4—22no—
130D4—22no—
131D4—42no—
132D4—42no—
133D4—82no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—42no—
137C2×C4—42no—
138C2×C4—42no—
139C2×C4—5862no—
140C2×C4—11722no—
141C2×C4—11721no—
142C2×C4—11721no—
143C2×C4—11721no—
144C2×C4D4×D29311yescharacteristic
145C2×C4C2×C22⋊D29312yes—
146C2×C4#1798980112yes—
147C2×C4#1798980111yescharacteristic
148C8—11722no—
149C22—21no—
150C22—21no—
151C22—42no—
152C22—42no—
153C22—42no—
154C22#2262759311yescharacteristic
155C22#2262759511yescharacteristic
156C22#2262761111yescharacteristic
157C4—42no—
158C4—42no—
159C4—23441no—
160C4—11722no—
161C4#2262759612yes—
162C4#2262760512yes—
163C2—21no—
164C2—21no—
165C2—82no—
166C2#3403604311yescharacteristic
167C2#3403630211yescharacteristic
168C2#3403630711yescharacteristic
subgroupG/H
centerC22#22627593
commutator, cosocleC22×C4×C293C23
FrattiniC22×C4C22×D293
Fitting, prime radical#537×C293C2
socleC22×C293#120
hypercenter#537D293
hypocenterC293#2040
LCSG ▷ C22×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#22627551C2semidirect
2. #34036130C2semidirect
3. #34035994C2semidirect
4. #34035898C2semidirect
25. C4×Dic293D4semidirect
84. C293#2040semidirect

Maximal subgroups

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

subgroupindex
C2×#226275512
#340361302
#340359942
#340358982
#537×C2932
#2040293