Finite Group Databasebeta

← #49161964

Subgroups — #49161964

Order 37504.

424 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 173 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×#22627622C211yesmaximal, characteristic
2#34036036C211yesmaximal, characteristic
3#34036033C212yesmaximal
4#34036016C212yesmaximal
5#34036013C212yesmaximal
6#34036011C212yesmaximal
7#34036010C212yesmaximal
8#34035996C212yesmaximal
9#391×C293C211yesmaximal, characteristic
10C22×Dic586C2211yescharacteristic
11#22627622C418yescomplemented
12C2×C4⋊Dic293C2211yescharacteristic
13C2×#17989781C2212yes—
14C2×#17989781C2212yes—
15C2×#17989781C2212yes—
16C2×C4×Dic293C2212yes—
17C2×C4×Dic293C2211yescharacteristic
18C2×C4×Dic293C2211yescharacteristic
19#22627531C2212yes—
20#22627531C2212yes—
21#22627531C2212yes—
22#22627531C2212yes—
23#22627531C2212yes—
24#22627531C2212yes—
25#22627531C2212yes—
26#22627531C2212yes—
27C22×Q8×C293C2211yescharacteristic
28C2×C4⋊C4×C293C2211yescharacteristic
29C2×C42×C293C2211yescharacteristic
30#95×C293C2212yes—
31#95×C293C2212yes—
32C2×Dic586—41no—
33C2×Dic586—41no—
34C2×Dic586C2×C414yes—
35C22×Dic293C2312yes—
36C22×Dic293C2312yes—
37C22×Dic293C2312yes—
38C22×Dic293C2312yes—
39C4⋊Dic293—41no—
40#17989781—42no—
41#17989781C2×C418yes—
42#17989781C2×C418yes—
43C4×Dic293—41no—
44C4×Dic293—42no—
45C4×Dic293C2×C414yes—
46C2×Q8×C293—41no—
47C2×Q8×C293—41no—
48C2×Q8×C293C2×C414yes—
49C22×C4×C293C2312yes—
50C22×C4×C293C2312yes—
51C22×C4×C293C2311yescharacteristic
52C22×C4×C293C2311yescharacteristic
53C22×C4×C293C2311yescharacteristic
54C4⋊C4×C293—41no—
55C42×C293—41no—
56Dic586—44no—
57C2×Dic293—22no—
58C2×Dic293—22no—
59C2×Dic293—22no—
60C2×Dic293—22no—
61C2×Dic293—22no—
62C2×Dic293—22no—
63C2×Dic293—22no—
64C2×Dic293—22no—
65C2×Dic293—24no—
66C2×Dic293C22×C414yes—
67C2×Dic293C22×C414yes—
68C23×C293C2411yescharacteristic
69Q8×C293—44no—
70C2×C4×C293—21no—
71C2×C4×C293—21no—
72C2×C4×C293—21no—
73C2×C4×C293—21no—
74C2×C4×C293—21no—
75C2×C4×C293—21no—
76C2×C4×C293—22no—
77C2×C4×C293—22no—
78C2×C4×C293—22no—
79C2×C4×C293—24no—
80C2×C4×C293—22no—
81C2×C4×C293C22×C412yes—
82C2×C4×C293C22×C412yes—
83C2×C4×C293C22×C412yes—
84C22×C293C23×C411yescharacteristic
85C22×C293H(5,𝔽2)11yescharacteristic
86C22×C293H(5,𝔽2)11yescharacteristic
87C22×C2932−1+412yes—
88C22×C2932−1+412yes—
89C4×C293—22no—
90C4×C293—22no—
91C4×C293—22no—
92C4×C293—42no—
93C4×C293—42no—
94Dic293—24no—
95Dic293—24no—
96Dic293—42no—
97Dic293—42no—
98C2×C293#51811yescharacteristic
99C2×C293#51912yes—
100C2×C293#56311yescharacteristic
101C2×C293#56311yescharacteristic
102C2×C293#56312yes—
103C293#238111yescharacteristic, complemented, Sylow
104#2381—2931nomaximal, Sylow
105C2×C4⋊Q8—2931no—
106#391—2931no—
107#391—2932no—
108#391D29311yescharacteristic
109#387—2932no—
110#387—2932no—
111#387—2932no—
112#387—2932no—
113#383—2932no—
114C22×Q8—2931no—
115C22×Q8C2×D29311yescharacteristic
116C4⋊Q8—2938no—
117C2×C4⋊C4—2932no—
118C2×C4⋊C4—2932no—
119C2×C4⋊C4—2932no—
120C2×C4⋊C4—2931no—
121C2×C4⋊C4C2×D29311yescharacteristic
122C2×C42—2931no—
123C2×C42—2932no—
124C2×C42—2931no—
125C2×C42C2×D29311yescharacteristic
126#95—2932no—
127#95—2932no—
128#95—2932no—
129#95—2932no—
130#95—2932no—
131#95—2932no—
132#95—2932no—
133#95—2932no—
134#95C2×D29312yes—
135#95C2×D29312yes—
136C2×Q8—41no—
137C2×Q8—41no—
138C2×Q8—2934no—
139C2×Q8—11721no—
140C2×Q8—11721no—
141C2×Q8C4×D29314yes—
142C22×C4—2932no—
143C22×C4—2932no—
144C22×C4—2932no—
145C22×C4—2932no—
146C22×C4C22×D29312yes—
147C22×C4C22×D29312yes—
148C22×C4C22×D29311yescharacteristic
149C22×C4C22×D29311yescharacteristic
150C22×C4C22×D29311yescharacteristic
151C4⋊C4—41no—
152C4⋊C4—2938no—
153C4⋊C4—2938no—
154C4⋊C4—11722no—
155C4⋊C4—11721no—
156C42—41no—
157C42—2934no—
158C42—11721no—
159C42—11722no—
160C23C23×D29311yescharacteristic
161Q8—44no—
162Q8—11724no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—2934no—
175C2×C4—2934no—
176C2×C4—5862no—
177C2×C4—5862no—
178C2×C4—5862no—
179C2×C4—5862no—
180C2×C4—5862no—
181C2×C4—5862no—
182C2×C4—5862no—
183C2×C4—5864no—
184C2×C4—5862no—
185C2×C4C2×C4×D29312yes—
186C2×C4C2×C4×D29312yes—
187C2×C4C2×C4×D29312yes—
188C22C22×C4×D29311yescharacteristic
189C22#2262766911yescharacteristic
190C22#2262766911yescharacteristic
191C22#2262767112yes—
192C22#2262767212yes—
193C4—22no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—42no—
198C4—5864no—
199C4—5864no—
200C4—11722no—
201C4—11722no—
202C2#3403660211yescharacteristic
203C2#3403660512yes—
204C2#3403687811yescharacteristic
205C2#3403687911yescharacteristic
206C2#3403688012yes—
subgroupG/H
center, FrattiniC23C23×D293
commutatorC22×C293C23×C4
Fitting#391×C293C2
socle, prime radical, cosocleC23×C293C24
hypercenter#391D293
hypocenterC293#2381
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
11. #22627622C4semidirect
103. C293#2381semidirect

Maximal subgroups

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

subgroupindex
C2×#226276222
#340360362
#340360332
#340360162
#340360132
#340360112
#340360102
#340359962
#391×C2932
#2381293