Finite Group Databasebeta

← #16847725

Subgroups — #16847725

Order 3968.

226 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 41 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#14521802C211yesmaximal, characteristic, complemented
2#14521240C211yesmaximal, characteristic
3#14521238C211yesmaximal, characteristic
4#14521229C211yesmaximal, characteristic
5#14520843C211yesmaximal, characteristic, complemented
6#14520840C211yesmaximal, characteristic, complemented
7C31×#352C211yesmaximal, characteristic, complemented
8#11758561C2211yescharacteristic
9C31×#123C2211yescharacteristic
10#11758513C2211yescharacteristic
11#11758512C2211yescharacteristic
12#11758506—21no—
13#11758501—21no—
14#11758486—21no—
15#11758466—21no—
16#11758465—21no—
17#11758463—21no—
18#11758456—21no—
19#11758456—21no—
20#11758455—21no—
21C31×#100C2211yescharacteristic
22C31×#99C2211yescharacteristic
23#11758422C2211yescharacteristic
24#11758413—21no—
25#11758394—21no—
26#11758394—21no—
27C2×D4×C31C2311yescharacteristic
28C22×C4×C31D411yescharacteristic
29C2×C22⋊D31—21no—
30C2×C22⋊D31—21no—
31C22×Dic31D411yescharacteristic
32#92497—41no—
33D4×D31—41no—
34#92495—21no—
35C2×Dic62—21no—
36C2×Dic62D411yescharacteristic
37M16×C31—21no—
38C4⋊C4×C31—21no—
39C22⋊C4×C31—21no—
40C22⋊C4×C31—21no—
41C22⋊C4×C31D411yescharacteristic
42C22⋊Dic31—21no—
43C22⋊Dic31—21no—
44C22⋊Dic31—21no—
45C22⋊Dic31—21no—
46C22⋊Dic31D411yescharacteristic
47(C2×D31)⋊C4—41no—
48(C2×D31)⋊C4—41no—
49C4⋊Dic31—21no—
50C4⋊Dic31—21no—
51C4⋊Dic31—41no—
52Dic31⋊C4—21no—
53Dic31⋊C4—21no—
54Dic31⋊C4—21no—
55Dic31⋊C4—21no—
56Dic31⋊C4—21no—
57Dic31⋊C4—41no—
58C4×Dic31—21no—
59C4×Dic31D411yescharacteristic
60Dic124—41no—
61#92470—41no—
62C23×C31C2×D411yescharacteristic
63C23×C31C2×D411yescharacteristic
64C22×D31—21no—
65C22×D31—21no—
66D4×C31—41no—
67C2×C4×C31—21no—
68C2×C4×C31—21no—
69C2×C4×C31—41no—
70C2×C4×C31—41no—
71C2×C4×C31C2×D411yescharacteristic
72C22⋊D31—41no—
73C22⋊D31—41no—
74C22⋊D31—41no—
75C2×Dic31—21no—
76C2×Dic31—21no—
77C2×Dic31—21no—
78C2×Dic31—21no—
79C2×Dic31—21no—
80C2×Dic31—21no—
81C2×Dic31—41no—
82C2×Dic31—41no—
83D124—21no—
84C4×D31—41no—
85Dic62—21no—
86Dic62—41no—
87Dic62—81no—
88C8×C31—41no—
89#2201—311nomaximal, Sylow
90C22×C31—21no—
91C22×C31—21no—
92C22×C31—41no—
93C22×C31—41no—
94C22×C31#12011yescharacteristic
95C2×D31—41no—
96C2×D31—81no—
97C2×D31—81no—
98C4×C31—21no—
99C4×C31—41no—
100C4×C31—41no—
101C4×C31—81no—
102Dic31—41no—
103Dic31—41no—
104Dic31—41no—
105Dic31—41no—
106Dic31—41no—
107Dic31—81no—
108#563—311no—
109#458—311no—
110#458—311no—
111#455—311no—
112#354—311no—
113#352—311no—
114#352D3111yescharacteristic, complemented
115C2×C31—21no—
116C2×C31—41no—
117C2×C31—41no—
118C2×C31B(4,𝔽2)11yescharacteristic
119D31—81no—
120H(5,𝔽2)—311no—
121#137—621no—
122C4⋊Q8—621no—
123#126—621no—
124#126—621no—
125#125—621no—
126#124—311no—
127#123—311no—
128#123—621no—
129#123—621no—
130#123C2×D3111yescharacteristic
131C22⋊Q8—621no—
132C22⋊Q8—621no—
133#104—621no—
134#100C2×D3111yescharacteristic
135#99—311no—
136#99—621no—
137#99—621no—
138#99C2×D3111yescharacteristic
139C31#220111yescharacteristic, complemented, Sylow
140#41—621no—
141#41—1241no—
142C2×Q8—311no—
143C2×Q8—621no—
144C2×D4—621no—
145C2×D4—621no—
146C2×D4—1241no—
147C2×D4C22×D3111yescharacteristic
148C22×C4—311no—
149C22×C4D12411yescharacteristic
150Q16—1241no—
151SD16—1241no—
152M16—21no—
153C4⋊C4—21no—
154C4⋊C4—621no—
155C4⋊C4—621no—
156C4⋊C4—621no—
157C4⋊C4—621no—
158C4⋊C4—621no—
159C4⋊C4—621no—
160C4⋊C4—621no—
161C4⋊C4—1241no—
162C4⋊C4—1241no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—311no—
166C22⋊C4—621no—
167C22⋊C4—621no—
168C22⋊C4—621no—
169C22⋊C4—621no—
170C22⋊C4—1241no—
171C22⋊C4—1241no—
172C22⋊C4D12411yescharacteristic
173C42—311no—
174C42—621no—
175C23—621no—
176C23—621no—
177C23C2×D12411yescharacteristic
178C23D4×D3111yescharacteristic
179Q8—621no—
180Q8—1241no—
181Q8—2481no—
182D4—41no—
183D4—621no—
184D4—1241no—
185D4—1241no—
186D4—1241no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—621no—
192C2×C4—621no—
193C2×C4—621no—
194C2×C4—621no—
195C2×C4—621no—
196C2×C4—621no—
197C2×C4—1241no—
198C2×C4—1241no—
199C2×C4—1241no—
200C2×C4D4×D3111yescharacteristic
201C8—41no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—1241no—
207C22—2481no—
208C22—2481no—
209C22#1175845911yescharacteristic
210C4—21no—
211C4—41no—
212C4—41no—
213C4—81no—
214C4—1241no—
215C4—1241no—
216C4—1241no—
217C4—1241no—
218C4—1241no—
219C4—2481no—
220C2—21no—
221C2—41no—
222C2—41no—
223C2—2481no—
224C2#1452123711yescharacteristic
subgroupG/H
centerC2#14521237
commutator, cosocleC2×D4×C31C23
FrattiniC2×D4C22×D31
FittingC31×#352C2
socleC2×C31B(4,𝔽2)
prime radical#11758561C22
hypercenter#352D31
hypocenterC31#2201
LCSG ▷ C2×D4×C31 ▷ C22×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
1. #14521802C2semidirect
5. #14520843C2semidirect
6. #14520840C2semidirect
7. C31×#352C2semidirect
114. #352D31semidirect
139. C31#2201semidirect

Maximal subgroups

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

subgroupindex
#145218022
#145212402
#145212382
#145212292
#145208432
#145208402
C31×#3522
#220131