Finite Group Databasebeta

← #16844749

Subgroups — #16844749

Order 3968.

246 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 51 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#14521626C211yesmaximal, characteristic
2#14521368C211yesmaximal, characteristic, complemented
3#14521365C211yesmaximal, characteristic, complemented
4#14520989C211yesmaximal, characteristic, complemented
5#14520782C211yesmaximal, characteristic, complemented
6#14520774C211yesmaximal, characteristic, complemented
7C31×#327C211yesmaximal, characteristic, complemented
8C2×#92497—21no—
9C31×#121C2211yescharacteristic
10#11758516—21no—
11#11758516—21no—
12#11758507C2211yescharacteristic
13C2×C4⋊Dic31C2211yescharacteristic
14C2×Dic31⋊C4C2211yescharacteristic
15#11758473—21no—
16#11758461—21no—
17#11758455—21no—
18C31×C22⋊C8C2211yescharacteristic
19C31×#95C2211yescharacteristic
20#11758420—21no—
21C31⋊#95—21no—
22C31⋊#95—21no—
23C22⋊(C31⋊C8)C2211yescharacteristic
24#11758409—21no—
25#11758405—21no—
26#11758396—21no—
27C2×D4×C31—21no—
28C2×D4×C31D411yescharacteristic
29C22×C4×C31—21no—
30C22×C4×C31C2311yescharacteristic
31C2×C22⋊D31—21no—
32C2×C22⋊D31—21no—
33C2×C22⋊D31—21no—
34C22×Dic31—21no—
35C22×Dic31—21no—
36C22×Dic31D411yescharacteristic
37C22×Dic31D411yescharacteristic
38#92497—42no—
39#92497—42no—
40C2×D124D411yescharacteristic
41C2×C4×D31—21no—
42C2×Dic62—21no—
43C2×C8×C31—21no—
44C4⋊C4×C31D411yescharacteristic
45C22⋊C4×C31—21no—
46C22⋊Dic31—21no—
47(C2×D31)⋊C4—21no—
48(C2×D31)⋊C4—21no—
49C4⋊Dic31—21no—
50C4⋊Dic31—21no—
51C4⋊Dic31D411yescharacteristic
52Dic31⋊C4—21no—
53Dic31⋊C4—21no—
54Dic31⋊C4—21no—
55C2×C31⋊C8—21no—
56C23×C31—21no—
57C23×C31C2×D411yescharacteristic
58C22×D31—21no—
59D4×C31—41no—
60D4×C31—41no—
61D4×C31—41no—
62C2×C4×C31—21no—
63C2×C4×C31—41no—
64C2×C4×C31—41no—
65C2×C4×C31—41no—
66C2×C4×C31—41no—
67C2×C4×C31C2×D411yescharacteristic
68C2×C4×C31C2×D411yescharacteristic
69C22⋊D31—42no—
70C22⋊D31—41no—
71C22⋊D31—41no—
72C22⋊D31—81no—
73C2×Dic31—21no—
74C2×Dic31—21no—
75C2×Dic31—21no—
76C2×Dic31—21no—
77C2×Dic31—42no—
78C2×Dic31—41no—
79C2×Dic31—42no—
80C2×Dic31—41no—
81C2×Dic31SD1612yes—
82D124—41no—
83C4×D31—42no—
84Dic62—42no—
85C8×C31—41no—
86C31⋊C8—41no—
87#1616—311nomaximal, Sylow
88C22×C31—21no—
89C22×C31—21no—
90C22×C31—41no—
91C22×C31—41no—
92C22×C31—41no—
93C22×C31#12011yescharacteristic
94C22×C31C2×SD1611yescharacteristic
95C22×C31AGL(1,ℤ/8)11yescharacteristic
96C2×D31—41no—
97C2×D31—41no—
98C2×D31—41no—
99C4×C31—21no—
100C4×C31—21no—
101C4×C31—41no—
102C4×C31—81no—
103Dic31—22no—
104Dic31—41no—
105Dic31—41no—
106Dic31—81no—
107#537—311no—
108#481—311no—
109#481—311no—
110#400—311no—
111#327—311no—
112#327D3111yescharacteristic, complemented
113#324—311no—
114C2×C31—21no—
115C2×C31—21no—
116C2×C31—81no—
117C2×C31#45011yescharacteristic
118C2×C31#45411yescharacteristic
119C2×C31#45811yescharacteristic
120D31—81no—
121C2×#41—621no—
122C22⋊Q8—621no—
123C22⋊Q8—621no—
124#121—311no—
125#121—621no—
126#121—621no—
127#121—621no—
128#121C2×D3111yescharacteristic
129C2×C4⋊C4—311no—
130C2×C4⋊C4—311no—
131#106—621no—
132#106—621no—
133#102—621no—
134#102—621no—
135C22⋊C8—311no—
136C22⋊C8C2×D3111yescharacteristic
137#95—621no—
138#95—621no—
139#95C2×D3111yescharacteristic
140C31#161611yescharacteristic, complemented, Sylow
141#41—1242no—
142#41—1242no—
143C2×Q8—621no—
144C2×D4—21no—
145C2×D4—311no—
146C2×D4—621no—
147C2×D4—621no—
148C2×D4—621no—
149C2×D4D12411yescharacteristic
150C22×C4—21no—
151C22×C4—311no—
152C22×C4—311no—
153C22×C4—621no—
154C22×C4—621no—
155C22×C4—621no—
156C22×C4C22×D3111yescharacteristic
157C2×C8—21no—
158C2×C8—621no—
159C4⋊C4—311no—
160C4⋊C4—621no—
161C4⋊C4—621no—
162C4⋊C4—621no—
163C4⋊C4—621no—
164C4⋊C4—621no—
165C4⋊C4D12411yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—621no—
168C22⋊C4—621no—
169C22⋊C4—621no—
170C23—21no—
171C23—621no—
172C23D4×D3111yescharacteristic
173Q8—1242no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—1241no—
178D4—1242no—
179D4—1241no—
180D4—1241no—
181D4—2481no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—312no—
188C2×C4—621no—
189C2×C4—621no—
190C2×C4—621no—
191C2×C4—621no—
192C2×C4—1242no—
193C2×C4—1242no—
194C2×C4—1241no—
195C2×C4—1242no—
196C2×C4—1241no—
197C2×C4C2×D12411yescharacteristic
198C2×C4D4×D3111yescharacteristic
199C8—41no—
200C8—1241no—
201C22—21no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—1241no—
207C22—1241no—
208C22—1241no—
209C22#1175845911yescharacteristic
210C22#1175848811yescharacteristic
211C22SD16×D3111yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—622no—
217C4—1241no—
218C4—1241no—
219C4—2481no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—2481no—
224C2#1452120111yescharacteristic
225C2#1452122311yescharacteristic
226C2#1452124011yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#327C2
socleC22×C31#120
prime radical#14521626C2
hypercenter#327D31
hypocenterC31#1616
LCSG ▷ C22×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #14521368C2semidirect
3. #14521365C2semidirect
4. #14520989C2semidirect
5. #14520782C2semidirect
6. #14520774C2semidirect
7. C31×#327C2semidirect
112. #327D31semidirect
140. C31#1616semidirect

Maximal subgroups

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

subgroupindex
#145216262
#145213682
#145213652
#145209892
#145207822
#145207742
C31×#3272
#161631