Finite Group Databasebeta

← #16844266

Subgroups — #16844266

Order 3968.

284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 63 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#14521562C211yesmaximal, characteristic
2C22⋊C8×D31C211yesmaximal, characteristic, complemented
3#14520911C211yesmaximal, characteristic, complemented
4#14520786C211yesmaximal, characteristic, complemented
5#14520784C211yesmaximal, characteristic, complemented
6#14520782C211yesmaximal, characteristic, complemented
7C31×#328C211yesmaximal, characteristic, complemented
8C2×#92499C411yescharacteristic, complemented
9C22×C4×D31C2211yescharacteristic
10C31×C22⋊Q8C2211yescharacteristic
11#11758523C411yescharacteristic, complemented
12#11758507C2211yescharacteristic
13C2×(C2×D31)⋊C4—21no—
14C2×C8×D31—21no—
15#11758472C411yescharacteristic, complemented
16#11758471—21no—
17#11758470—21no—
18#11758469C411yescharacteristic, complemented
19#11758459—21no—
20(C22⋊D31)⋊C4—21no—
21C31×C22⋊C8C2211yescharacteristic
22C31×#95C2211yescharacteristic
23C31⋊#95—21no—
24C31⋊#95C2211yescharacteristic
25C22⋊(C31⋊C8)C2211yescharacteristic
26(C2×D31)⋊C8—21no—
27C23×D31D411yescharacteristic
28C2×Q8×C31C2×C411yescharacteristic
29C22×C4×C31—21no—
30C22×C4×C31C2311yescharacteristic
31C2×C22⋊D31—21no—
32C22×Dic31—21no—
33C22×Dic31D411yescharacteristic
34#92499—42no—
35C2×D124—21no—
36C2×D124—21no—
37C2×D124C2×C411yescharacteristic
38C2×C4×D31—21no—
39C2×C4×D31—42no—
40C2×C4×D31C2×C411yescharacteristic
41C2×C4×D31C2×C411yescharacteristic
42C2×C4×D31D411yescharacteristic
43C2×C4×D31D411yescharacteristic
44C2×C8×C31—21no—
45C4⋊C4×C31—21no—
46C4⋊C4×C31C2×C411yescharacteristic
47C22⋊C4×C31—21no—
48(C2×D31)⋊C4—21no—
49(C2×D31)⋊C4—21no—
50(C2×D31)⋊C4—21no—
51(C2×D31)⋊C4—21no—
52(C2×D31)⋊C4—42no—
53C4⋊Dic31C2×C411yescharacteristic
54Dic31⋊C4—21no—
55C4×Dic31—21no—
56C2×C31⋊C8—21no—
57C8×D31—42no—
58C23×C31C2×D411yescharacteristic
59C22×D31—21no—
60C22×D31—21no—
61C22×D31—22no—
62C22×D31—21no—
63C22×D31—41no—
64C22×D31C22⋊C411yescharacteristic
65C22×D31C22⋊C411yescharacteristic
66Q8×C31—41no—
67C2×C4×C31—21no—
68C2×C4×C31—21no—
69C2×C4×C31—41no—
70C2×C4×C31—41no—
71C2×C4×C31—41no—
72C2×C4×C31—41no—
73C2×C4×C31C22×C411yescharacteristic
74C2×C4×C31C2×D411yescharacteristic
75C22⋊D31—41no—
76C22⋊D31—41no—
77C2×Dic31—21no—
78C2×Dic31—41no—
79C2×Dic31—41no—
80C2×Dic31—41no—
81C2×Dic31—41no—
82C2×Dic31C22⋊C411yescharacteristic
83C2×Dic31C22⋊C411yescharacteristic
84D124—41no—
85D124—42no—
86D124—42no—
87C4×D31—22no—
88C4×D31—22no—
89C4×D31—41no—
90C4×D31—41no—
91C4×D31—42no—
92C8×C31—41no—
93C31⋊C8—41no—
94#1516—311nomaximal, Sylow
95C22×C31—21no—
96C22×C31—21no—
97C22×C31C2×C22⋊C411yescharacteristic
98C22×C31#13511yescharacteristic
99C22×C31#13511yescharacteristic
100C2×D31—21no—
101C2×D31—21no—
102C2×D31—21no—
103C2×D31—21no—
104C2×D31—21no—
105C2×D31—42no—
106C2×D31—42no—
107C2×D31—41no—
108C2×D31—41no—
109C2×D31—41no—
110C2×D31#9912yes—
111C4×C31—21no—
112C4×C31—21no—
113C4×C31—41no—
114C4×C31—41no—
115C4×C31—81no—
116Dic31—21no—
117Dic31—21no—
118Dic31—41no—
119Dic31—81no—
120#525—311no—
121C2×C22⋊C8—311no—
122#381—311no—
123#328—311no—
124#328D3111yescharacteristic, complemented
125#327—311no—
126#327—311no—
127C2×C31—21no—
128C2×C31—21no—
129C2×C31C2×#9911yescharacteristic
130C2×C31#41611yescharacteristic
131C2×C31#42111yescharacteristic
132D31—22no—
133D31—41no—
134D31—81no—
135C2×#41—311no—
136C23×C4—311no—
137C22×C8—621no—
138#123—621no—
139C22⋊Q8—311no—
140C22⋊Q8C2×D3111yescharacteristic
141#121—311no—
142#121—311no—
143#120—621no—
144C4×D4—621no—
145C4×D4—621no—
146#117—311no—
147C2×C22⋊C4—621no—
148C22⋊C8—311no—
149C22⋊C8—621no—
150C22⋊C8C2×D3111yescharacteristic
151#95—311no—
152#95—621no—
153#95C2×D3111yescharacteristic
154C31#151611yescharacteristic, complemented, Sylow
155C24—311no—
156#41—1242no—
157C2×Q8C4×D3111yescharacteristic
158C2×D4—311no—
159C2×D4—621no—
160C2×D4—621no—
161C2×D4—621no—
162C22×C4—21no—
163C22×C4—311no—
164C22×C4—311no—
165C22×C4—311no—
166C22×C4—311no—
167C22×C4—311no—
168C22×C4—621no—
169C22×C4—621no—
170C22×C4—1242no—
171C22×C4C22×D3111yescharacteristic
172C2×C8—21no—
173C2×C8—621no—
174C2×C8—1242no—
175C4⋊C4—21no—
176C4⋊C4—311no—
177C4⋊C4—621no—
178C4⋊C4C4×D3111yescharacteristic
179C22⋊C4—21no—
180C22⋊C4—621no—
181C22⋊C4—621no—
182C22⋊C4—621no—
183C22⋊C4—621no—
184C22⋊C4—1242no—
185C42—621no—
186C23—311no—
187C23—311no—
188C23—622no—
189C23—621no—
190C23—621no—
191C23—621no—
192C23—1241no—
193C23D4×D3111yescharacteristic
194Q8—41no—
195D4—1241no—
196D4—1242no—
197D4—1242no—
198D4—1241no—
199D4—1241no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—311no—
207C2×C4—311no—
208C2×C4—622no—
209C2×C4—622no—
210C2×C4—621no—
211C2×C4—1241no—
212C2×C4—1241no—
213C2×C4—1242no—
214C2×C4—1241no—
215C2×C4—1241no—
216C2×C4—1241no—
217C2×C4—1241no—
218C2×C4C2×C4×D3111yescharacteristic
219C2×C4D4×D3111yescharacteristic
220C8—41no—
221C8—1241no—
222C22—21no—
223C22—21no—
224C22—312no—
225C22—621no—
226C22—621no—
227C22—621no—
228C22—621no—
229C22—621no—
230C22—1242no—
231C22—1242no—
232C22—1241no—
233C22—1241no—
234C22—1241no—
235C22C22⋊C4×D3111yescharacteristic
236C22#1175849311yescharacteristic
237C22#1175849611yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—41no—
242C4—81no—
243C4—621no—
244C4—621no—
245C4—1241no—
246C4—2481no—
247C2—21no—
248C2—21no—
249C2—622no—
250C2—1241no—
251C2—2481no—
252C2#99×D3111yescharacteristic
253C2#1452104411yescharacteristic
254C2#1452106411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#328C2
socleC22×C31C2×C22⋊C4
prime radical#14521562C2
cosocleC22×C4×C31C23
hypercenter#328D31
hypocenterC31#1516
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D31C2semidirect
3. #14520911C2semidirect
4. #14520786C2semidirect
5. #14520784C2semidirect
6. #14520782C2semidirect
7. C31×#328C2semidirect
8. C2×#92499C4semidirect
11. #11758523C4semidirect
15. #11758472C4semidirect
18. #11758469C4semidirect
124. #328D31semidirect
154. C31#1516semidirect

Maximal subgroups

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

subgroupindex
#145215622
C22⋊C8×D312
#145209112
#145207862
#145207842
#145207822
C31×#3282
#151631