Finite Group Databasebeta

← #49157113

Subgroups — #49157113

Order 37504.

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

normal subgroups only

This group has 312 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×C4⋊C4×D293C211yesmaximal, characteristic
2#34036091C212yesmaximal
3#34035855C211yesmaximal, characteristic, complemented
4#34035854C212yesmaximal, complemented
5#324×C293C211yesmaximal, characteristic, complemented
6C22×C4×D293C411yescharacteristic
7C22×C4×D293C411yescharacteristic
8C22×C4×D293C2211yescharacteristic
9C2×#17989785—22no—
10C2×C4⋊Dic293C411yescharacteristic
11C2×#17989781C411yescharacteristic
12C2×#17989781C2211yescharacteristic
13C4⋊C4×D293—22no—
14C4⋊C4×D293—22no—
15C22⋊#14556873C2212yes—
16#22627536—22no—
17C2×C4⋊C4×C293C2211yescharacteristic
18C22⋊C8×C293C2212yes—
19C23×D293C2×C411yescharacteristic
20C22×Dic293C2×C411yescharacteristic
21C22×Dic293C2×C411yescharacteristic
22C22×Dic293C2×C411yescharacteristic
23C2×C4×D293—21no—
24C2×C4×D293—21no—
25C2×C4×D293—22no—
26C2×C4×D293—21no—
27C2×C4×D293—21no—
28C2×C4×D293—22no—
29C2×C4×D293—42no—
30C2×C4×D293—42no—
31C2×C4×D293D412yes—
32C2×C4×D293D412yes—
33#17989785—44no—
34C2×#14556873—22no—
35C4⋊Dic293—22no—
36#17989781—22no—
37#17989781—22no—
38C22×C4×C293C2×C411yescharacteristic
39C22×C4×C293C2×C411yescharacteristic
40C22×C4×C293C2311yescharacteristic
41C2×C8×C293—22no—
42C4⋊C4×C293—22no—
43C22×D293—21no—
44C22×D293—21no—
45C22×D293—22no—
46C22×D293—22no—
47C22×D293C22⋊C411yescharacteristic
48C22×D293C22⋊C411yescharacteristic
49C2×Dic293—21no—
50C2×Dic293—21no—
51C2×Dic293—21no—
52C2×Dic293—41no—
53C2×Dic293—41no—
54C2×Dic293C22⋊C412yes—
55C2×Dic293M1612yescomplemented
56C4×D293—24no—
57C4×D293—24no—
58C4×D293—24no—
59C4×D293—42no—
60C4×D293—42no—
61C4×D293—42no—
62#14556873—42no—
63C23×C293C22×C411yescharacteristic
64C2×C4×C293—21no—
65C2×C4×C293—21no—
66C2×C4×C293—21no—
67C2×C4×C293—41no—
68C2×C4×C293—41no—
69C2×C4×C293M1612yescomplemented
70C2×C4×C293C2×D412yes—
71C8×C293—42no—
72C22×C293—21no—
73C22×C293—21no—
74C22×C293C2×C22⋊C411yescharacteristic
75C22×C293C2×M1611yescharacteristic
76C22×C293C2×M1611yescharacteristic
77C2×D293—24no—
78C2×D293—24no—
79C2×D293—21no—
80C2×D293—21no—
81C2×D293—21no—
82C2×D293—21no—
83C2×D293#9912yes—
84C2×D293#10112yes—
85C4×C293—22no—
86C4×C293—22no—
87C4×C293—41no—
88Dic293—22no—
89Dic293—22no—
90Dic293—41no—
91C2×C293—21no—
92C2×C293—21no—
93C2×C293#40711yescharacteristic
94C2×C293C2×#9911yescharacteristic
95C2×C293C2×#10111yescharacteristic
96D293—22no—
97D293—22no—
98C293#146311yescharacteristic, complemented, Sylow
99#1463—2931nomaximal, Sylow
100C22×C4⋊C4—2931no—
101#407—2932no—
102#324—2931no—
103#324—2932no—
104#324D29311yescharacteristic, complemented
105C23×C4—2931no—
106C23×C4—2931no—
107C23×C4—2931no—
108C2×M16—5862no—
109C2×C4⋊C4—2931no—
110C2×C4⋊C4—2931no—
111C2×C4⋊C4—2931no—
112C2×C4⋊C4—5862no—
113C2×C4⋊C4—5862no—
114C2×C4⋊C4C2×D29311yescharacteristic
115C22⋊C8—2932no—
116C22⋊C8—5862no—
117C22⋊C8C2×D29312yes—
118C24—2931no—
119C22×C4—2931no—
120C22×C4—2931no—
121C22×C4—2932no—
122C22×C4—2932no—
123C22×C4—2931no—
124C22×C4—5862no—
125C22×C4—5861no—
126C22×C4—5861no—
127C22×C4—5861no—
128C22×C4—5861no—
129C22×C4—5862no—
130C22×C4—11722no—
131C22×C4—11722no—
132C22×C4C4×D29311yescharacteristic
133C22×C4C4×D29311yescharacteristic
134C22×C4C22×D29311yescharacteristic
135M16—11724no—
136C2×C8—22no—
137C2×C8—5862no—
138C4⋊C4—22no—
139C4⋊C4—5862no—
140C4⋊C4—5862no—
141C4⋊C4—5862no—
142C23—2931no—
143C23—2931no—
144C23—5862no—
145C23—5862no—
146C23—5861no—
147C23—5861no—
148C23C2×C4×D29311yescharacteristic
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—2932no—
155C2×C4—2932no—
156C2×C4—5864no—
157C2×C4—5864no—
158C2×C4—5864no—
159C2×C4—5861no—
160C2×C4—5861no—
161C2×C4—5861no—
162C2×C4—11722no—
163C2×C4—11722no—
164C2×C4—11722no—
165C2×C4—11721no—
166C2×C4—11721no—
167C2×C4#1798978512yescomplemented
168C2×C4D4×D29312yes—
169C8—42no—
170C8—11722no—
171C22—21no—
172C22—21no—
173C22—2932no—
174C22—2932no—
175C22—5864no—
176C22—5864no—
177C22—5861no—
178C22—5861no—
179C22—5861no—
180C22—5861no—
181C22C22⋊C4×D29311yescharacteristic
182C22M16×D29311yescharacteristic
183C22C2×#1798978511yescharacteristic
184C4—22no—
185C4—22no—
186C4—41no—
187C4—5862no—
188C4—5862no—
189C4—11721no—
190C2—21no—
191C2—21no—
192C2—5862no—
193C2—5862no—
194C2#3403609111yescharacteristic
195C2#99×D29311yescharacteristic
196C2#101×D29311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D293
commutatorC23×C293C22×C4
FrattiniC22×C4C22×D293
Fitting#324×C293C2
socleC22×C293C2×C22⋊C4
prime radicalC23×D293C2×C4
cosocleC22×C4×C293C23
hypercenter#324D293
hypocenterC293#1463
LCSG ▷ C23×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
3. #34035855C2semidirect
4. #34035854C2semidirect
5. #324×C293C2semidirect
55. C2×Dic293M16semidirect
69. C2×C4×C293M16semidirect
98. C293#1463semidirect
104. #324D293semidirect
167. C2×C4#17989785semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D2932
#340360912
#340358552
#340358542
#324×C2932
#1463293