Finite Group Databasebeta

← #49160451

Subgroups — #49160451

Order 37504.

286 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 55 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#34036692C211yesmaximal, characteristic
2#99×D293C212yesmaximal, complemented
3#34035923C212yesmaximal, complemented
4#34035922C211yesmaximal, characteristic, complemented
5#353×C293C211yesmaximal, characteristic, complemented
6C2×#17989801C411yescharacteristic, complemented
7C2×D4×D293C2211yescharacteristic
8#22627620C411yescharacteristic, complemented
9#22627612C411yescharacteristic, complemented
10#22627611C2211yescharacteristic
11#22627596—22no—
12#22627592—22no—
13#22627581C411yescharacteristic, complemented
14C22⋊C4×D293—22no—
15#22627539C2212yes—
16#22627538—22no—
17#127×C293C2211yescharacteristic
18#99×C293C2212yes—
19C23×D293D412yes—
20#17989801—42no—
21C2×Dic586C2×C411yescharacteristic, complemented
22C2×D1172C2×C411yescharacteristic
23C2×C22⋊D293—21no—
24C2×C22⋊D293—22no—
25C2×C22⋊D293D412yes—
26D4×D293—42no—
27C22×Dic293—21no—
28C2×C4×D293—42no—
29C2×C4×D293C2×C411yescharacteristic
30#17989781—21no—
31C22⋊Dic293—22no—
32C22⋊Dic293—22no—
33#17989779—21no—
34#17989779—22no—
35#17989779—42no—
36C4×Dic293C2×C411yescharacteristic, complemented
37C2×D4×C293—22no—
38C2×D4×C293C2×C411yescharacteristic, complemented
39C2×D4×C293C2311yescharacteristic
40C22⋊C4×C293—22no—
41C42×C293C2×C411yescharacteristic, complemented
42C22×D293—22no—
43C22×D293—22no—
44C22×D293—82no—
45C22×D293C22⋊C412yes—
46C22×D293C22⋊C411yescharacteristic
47Dic586—41no—
48D1172—41no—
49C22⋊D293—42no—
50C22⋊D293—42no—
51C22⋊D293—82no—
52C2×Dic293—21no—
53C2×Dic293—21no—
54C2×Dic293—42no—
55C2×Dic293—42no—
56C2×Dic293C22⋊C411yescharacteristic
57C4×D293—22no—
58C4×D293—84no—
59C23×C293—21no—
60C23×C293C2×D412yes—
61D4×C293—41no—
62D4×C293—41no—
63D4×C293—82no—
64C2×C4×C293—21no—
65C2×C4×C293—42no—
66C2×C4×C293C22×C411yescharacteristic
67C22×C293—22no—
68C22×C293—42no—
69C22×C293—42no—
70C22×C293—41no—
71C22×C293C2×C22⋊C411yescharacteristic
72C2×D293—22no—
73C2×D293—41no—
74C2×D293—44no—
75C2×D293—42no—
76C2×D293—82no—
77C2×D293#9912yes—
78C4×C293—21no—
79C4×C293—41no—
80C4×C293—82no—
81Dic293—21no—
82Dic293—41no—
83Dic293—41no—
84Dic293—82no—
85C2×C293—21no—
86C2×C293—42no—
87C2×C293—81no—
88C2×C293C2×#9911yescharacteristic
89D293—22no—
90D293—42no—
91C293#212711yescharacteristic, complemented, Sylow
92#2127—2931nomaximal, Sylow
93#535—2931no—
94C2×#99—2932no—
95#354—2932no—
96#353—2931no—
97#353D29311yescharacteristic, complemented
98C2×#41—2931no—
99C22×D4—2931no—
100#127—2931no—
101#127C2×D29311yescharacteristic
102#124—2931no—
103#124—2931no—
104#121—5862no—
105#120—5862no—
106#117—2931no—
107C2×C22⋊C4—5862no—
108#99—2932no—
109#99—5862no—
110#99C2×D29312yes—
111C24—2932no—
112#41—11722no—
113C2×Q8—2931no—
114C2×D4—22no—
115C2×D4—2932no—
116C2×D4—2931no—
117C2×D4—5862no—
118C2×D4—5861no—
119C2×D4—11722no—
120C2×D4C4×D29311yescharacteristic, complemented
121C2×D4C22×D29311yescharacteristic
122C22×C4—2931no—
123C22×C4—5861no—
124C22×C4—11722no—
125C4⋊C4—5861no—
126C22⋊C4—22no—
127C22⋊C4—5861no—
128C22⋊C4—5862no—
129C22⋊C4—5862no—
130C22⋊C4—5862no—
131C22⋊C4—11722no—
132C42—2931no—
133C42C4×D29311yescharacteristic, complemented
134C23—21no—
135C23—2931no—
136C23—2932no—
137C23—23442no—
138C23—5862no—
139C23—5862no—
140C23D4×D29312yes—
141Q8—11721no—
142D4—41no—
143D4—41no—
144D4—82no—
145D4—23442no—
146D4—11721no—
147D4—11722no—
148D4—11722no—
149C2×C4—21no—
150C2×C4—42no—
151C2×C4—2931no—
152C2×C4—23444no—
153C2×C4—5862no—
154C2×C4—5861no—
155C2×C4—5861no—
156C2×C4—11722no—
157C2×C4—11722no—
158C2×C4C2×C4×D29311yescharacteristic
159C22—22no—
160C22—42no—
161C22—42no—
162C22—41no—
163C22—2932no—
164C22—23442no—
165C22—5862no—
166C22—11721no—
167C22—11722no—
168C22—11724no—
169C22C22⋊C4×D29311yescharacteristic
170C4—21no—
171C4—41no—
172C4—82no—
173C4—23442no—
174C4—5861no—
175C4—11721no—
176C4—11721no—
177C2—21no—
178C2—42no—
179C2—81no—
180C2—5862no—
181C2—11722no—
182C2#99×D29311yescharacteristic
subgroupG/H
centerC2#99×D293
commutatorC2×C4×C293C22×C4
FrattiniC2×D4C22×D293
Fitting#353×C293C2
socleC2×C293C2×#99
prime radical#34036692C2
cosocleC2×D4×C293C23
hypercenter#353D293
hypocenterC293#2127
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #99×D293C2semidirect
3. #34035923C2semidirect
4. #34035922C2semidirect
5. #353×C293C2semidirect
6. C2×#17989801C4semidirect
8. #22627620C4semidirect
9. #22627612C4semidirect
13. #22627581C4semidirect
21. C2×Dic586C2×C4semidirect
36. C4×Dic293C2×C4semidirect
38. C2×D4×C293C2×C4semidirect
41. C42×C293C2×C4semidirect
91. C293#2127semidirect
97. #353D293semidirect
120. C2×D4C4×D293semidirect
133. C42C4×D293semidirect

Maximal subgroups

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

subgroupindex
#340366922
#99×D2932
#340359232
#340359222
#353×C2932
#2127293