Finite Group Databasebeta

← #49160010

Subgroups — #49160010

Order 37504.

306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 67 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#34036710C211yesmaximal, characteristic
2C2×#22627550C212yesmaximal, complemented
3#34036131C212yesmaximal, complemented
4#34035998C211yesmaximal, characteristic, complemented
5#343×C293C211yesmaximal, characteristic, complemented
6C2×#17989802C2212yes—
7#22627604—22no—
8#22627599—22no—
9#22627598—22no—
10C2×C4⋊Dic293C2211yescharacteristic
11C2×#17989781—22no—
12C2×C4×Dic293C2211yescharacteristic
13#22627550—24no—
14#22627549—22no—
15#22627546—22no—
16C2×M16×C293C2212yes—
17C2×C4⋊C4×C293C2211yescharacteristic
18#17989802—22no—
19#17989802—22no—
20#17989802—22no—
21#17989802—22no—
22C2×Dic586D412yes—
23C2×D1172—22no—
24C2×D1172D412yes—
25C2×C22⋊D293—22no—
26C22×Dic293—21no—
27C22×Dic293—21no—
28C2×C4×D293—22no—
29C4⋊Dic293—22no—
30C4⋊Dic293—22no—
31#17989781—44no—
32#17989779—24no—
33C4×Dic293—21no—
34C4×Dic293D412yescomplemented
35C22×C4×C293D412yes—
36C22×C4×C293C2311yescharacteristic
37M16×C293—22no—
38M16×C293—22no—
39C2×C8×C293—22no—
40C4⋊C4×C293—22no—
41C22×D293—22no—
42Dic586—22no—
43Dic586—22no—
44D1172—22no—
45D1172—22no—
46D1172—82no—
47C22⋊D293—42no—
48C22⋊D293—42no—
49C2×Dic293—22no—
50C2×Dic293—22no—
51C2×Dic293—22no—
52C2×Dic293—22no—
53C2×Dic293—42no—
54C2×Dic293—41no—
55C4×D293—42no—
56C4×D293—42no—
57C23×C293C2×D411yescharacteristic
58C2×C4×C293—22no—
59C2×C4×C293—42no—
60C2×C4×C293C2×D411yescharacteristic
61C2×C4×C293C2×D412yes—
62C2×C4×C293#4112yes—
63C2×C4×C293#4111yescharacteristic
64C8×C293—42no—
65C22×C293—21no—
66C22×C293—21no—
67C22×C293#12011yescharacteristic
68C22×C293#12111yescharacteristic
69C22×C293#12411yescharacteristic
70C2×D293—42no—
71C2×D293—42no—
72C2×D293—42no—
73C4×C293—42no—
74C4×C293#12112yes—
75C4×C293#12312yes—
76Dic293—24no—
77Dic293—42no—
78Dic293—81no—
79C2×C293—21no—
80C2×C293—21no—
81C2×C293#39411yescharacteristic
82C2×C293#45311yescharacteristic
83C2×C293#45611yescharacteristic
84D293—82no—
85C293#203911yescharacteristic, complemented, Sylow
86#2039—2931nomaximal, Sylow
87#537—2931no—
88C2×#104—2932no—
89#417—2932no—
90#384—2931no—
91#343D29311yescharacteristic, complemented
92C2×#41—2932no—
93C2×M16C2×D29312yes—
94C22⋊Q8—5862no—
95#121—5862no—
96#121—5862no—
97C2×C4⋊C4—2931no—
98C2×C4⋊C4—5862no—
99C2×C4⋊C4C2×D29311yescharacteristic
100C2×C42—2931no—
101#104—5864no—
102#103—5862no—
103#102—5862no—
104#41—5862no—
105#41—5862no—
106#41—5862no—
107#41—5862no—
108C2×Q8—2932no—
109C2×D4—2932no—
110C2×D4—5862no—
111C2×D4—5862no—
112C22×C4—5861no—
113C22×C4—5862no—
114C22×C4—5861no—
115C22×C4D117212yes—
116C22×C4C22×D29311yescharacteristic
117M16—22no—
118M16—22no—
119C2×C8—22no—
120C4⋊C4—22no—
121C4⋊C4—5862no—
122C4⋊C4—5862no—
123C4⋊C4—11724no—
124C22⋊C4—5864no—
125C42—2932no—
126C42—5861no—
127C23—5862no—
128C23C2×D117211yescharacteristic
129Q8—5862no—
130Q8—5862no—
131D4—23442no—
132D4—5862no—
133D4—5862no—
134D4—11722no—
135D4—11722no—
136C2×C4—22no—
137C2×C4—42no—
138C2×C4—5862no—
139C2×C4—5862no—
140C2×C4—5862no—
141C2×C4—5862no—
142C2×C4—11722no—
143C2×C4—11721no—
144C2×C4—11722no—
145C2×C4—11722no—
146C2×C4D4×D29311yescharacteristic
147C2×C4D4×D29312yes—
148C2×C4#1798980212yes—
149C2×C4#1798980311yescharacteristic
150C8—42no—
151C22—21no—
152C22—21no—
153C22—11722no—
154C22—11722no—
155C22—11722no—
156C22#2262759411yescharacteristic
157C22#2262759911yescharacteristic
158C22#2262761211yescharacteristic
159C4—42no—
160C4—23441no—
161C4—5864no—
162C4—11722no—
163C4#2262759712yes—
164C4#2262760912yes—
165C2—21no—
166C2—21no—
167C2—23442no—
168C2#3403604711yescharacteristic
169C2#3403629911yescharacteristic
170C2#3403631411yescharacteristic
subgroupG/H
centerC22#22627594
commutator, cosocleC22×C4×C293C23
FrattiniC22×C4C22×D293
Fitting#343×C293C2
socleC22×C293#120
prime radical#34036710C2
hypercenter#343D293
hypocenterC293#2039
LCSG ▷ C22×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
2. C2×#22627550C2semidirect
3. #34036131C2semidirect
4. #34035998C2semidirect
5. #343×C293C2semidirect
34. C4×Dic293D4semidirect
85. C293#2039semidirect
91. #343D293semidirect

Maximal subgroups

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

subgroupindex
#340367102
C2×#226275502
#340361312
#340359982
#343×C2932
#2039293