Finite Group Databasebeta

← #68338

Subgroups — #68338

Order 384.

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#5627C211yesmaximal, characteristic
2D3×C22⋊C8C211yesmaximal, characteristic, complemented
3#4664C211yesmaximal, characteristic, complemented
4C3×#328C211yesmaximal, characteristic, complemented
5#4538C211yesmaximal, characteristic, complemented
6#4470C211yesmaximal, characteristic, complemented
7#4451C211yesmaximal, characteristic, complemented
8#1516—31nomaximal, Sylow
9C2×#239C411yescharacteristic, complemented
10C22×C4×D3C2211yescharacteristic
11C3×C22⋊Q8C2211yescharacteristic
12#946C411yescharacteristic, complemented
13#930C2211yescharacteristic
14C2×(C2×D3)⋊C4—21no—
15C2×D3×C8—21no—
16#895C411yescharacteristic, complemented
17#894—21no—
18#893—21no—
19#892C411yescharacteristic, complemented
20#882—21no—
21#67⋊C4—21no—
22C3×C22⋊C8C2211yescharacteristic
23C3×#95C2211yescharacteristic
24C3⋊#95—21no—
25C3⋊#95C2211yescharacteristic
26#830C2211yescharacteristic
27(C2×D3)⋊C8—21no—
28#525—31no—
29C2×C22⋊C8—31no—
30#381—31no—
31#328—31no—
32#328D311yescharacteristic, complemented
33#327—31no—
34#327—31no—
35C23×D3D411yescharacteristic
36C2×C3×Q8C2×C411yescharacteristic
37C22×C3×C4—21no—
38C22×C3×C4C2311yescharacteristic
39C2×#67—21no—
40C22×Dic3—21no—
41C22×Dic3D411yescharacteristic
42#239—42no—
43C2×D12—21no—
44C2×D12—21no—
45C2×D12C2×C411yescharacteristic
46C2×C4×D3—21no—
47C2×C4×D3—42no—
48C2×C4×D3C2×C411yescharacteristic
49C2×C4×D3C2×C411yescharacteristic
50C2×C4×D3D411yescharacteristic
51C2×C4×D3D411yescharacteristic
52C2×C3×C8—21no—
53C3×C4⋊C4—21no—
54C3×C4⋊C4C2×C411yescharacteristic
55C3×C22⋊C4—21no—
56(C2×D3)⋊C4—21no—
57(C2×D3)⋊C4—21no—
58(C2×D3)⋊C4—21no—
59(C2×D3)⋊C4—21no—
60(C2×D3)⋊C4—42no—
61C4⋊Dic3C2×C411yescharacteristic
62Dic3⋊C4—21no—
63C4×Dic3—21no—
64C2×C3⋊C8—21no—
65D3×C8—42no—
66C2×#41—31no—
67C23×C4—31no—
68C22×C8—61no—
69#123—61no—
70C22⋊Q8—31no—
71C22⋊Q8C2×D311yescharacteristic
72#121—31no—
73#121—31no—
74#120—61no—
75C4×D4—61no—
76C4×D4—61no—
77#117—31no—
78C2×C22⋊C4—61no—
79C22⋊C8—31no—
80C22⋊C8—61no—
81C22⋊C8C2×D311yescharacteristic
82#95—31no—
83#95—61no—
84#95C2×D311yescharacteristic
85C23×C3C2×D411yescharacteristic
86C22×D3—21no—
87C22×D3—21no—
88C22×D3—22no—
89C22×D3—21no—
90C22×D3—41no—
91C22×D3C22⋊C411yescharacteristic
92C22×D3C22⋊C411yescharacteristic
93C3×Q8—41no—
94C2×C3×C4—21no—
95C2×C3×C4—21no—
96C2×C3×C4—41no—
97C2×C3×C4—41no—
98C2×C3×C4—41no—
99C2×C3×C4—41no—
100C2×C3×C4C22×C411yescharacteristic
101C2×C3×C4C2×D411yescharacteristic
102#67—41no—
103#67—41no—
104C2×Dic3—21no—
105C2×Dic3—41no—
106C2×Dic3—41no—
107C2×Dic3—41no—
108C2×Dic3—41no—
109C2×Dic3C22⋊C411yescharacteristic
110C2×Dic3C22⋊C411yescharacteristic
111D12—41no—
112D12—42no—
113D12—42no—
114C4×D3—22no—
115C4×D3—22no—
116C4×D3—41no—
117C4×D3—41no—
118C4×D3—42no—
119C3×C8—41no—
120C3⋊C8—41no—
121C24—31no—
122#41—122no—
123C2×Q8C4×D311yescharacteristic
124C2×D4—31no—
125C2×D4—61no—
126C2×D4—61no—
127C2×D4—61no—
128C22×C4—21no—
129C22×C4—31no—
130C22×C4—31no—
131C22×C4—31no—
132C22×C4—31no—
133C22×C4—31no—
134C22×C4—61no—
135C22×C4—61no—
136C22×C4—122no—
137C22×C4C22×D311yescharacteristic
138C2×C8—21no—
139C2×C8—61no—
140C2×C8—122no—
141C4⋊C4—21no—
142C4⋊C4—31no—
143C4⋊C4—61no—
144C4⋊C4C4×D311yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—61no—
147C22⋊C4—61no—
148C22⋊C4—61no—
149C22⋊C4—61no—
150C22⋊C4—122no—
151C42—61no—
152C22×C3—21no—
153C22×C3—21no—
154C22×C3C2×C22⋊C411yescharacteristic
155C22×C3#13511yescharacteristic
156C22×C3#13511yescharacteristic
157C2×D3—21no—
158C2×D3—21no—
159C2×D3—21no—
160C2×D3—21no—
161C2×D3—21no—
162C2×D3—42no—
163C2×D3—42no—
164C2×D3—41no—
165C2×D3—41no—
166C2×D3—41no—
167C2×D3#9912yes—
168C3×C4—21no—
169C3×C4—21no—
170C3×C4—41no—
171C3×C4—41no—
172C3×C4—81no—
173Dic3—21no—
174Dic3—21no—
175Dic3—41no—
176Dic3—81no—
177C23—31no—
178C23—31no—
179C23—62no—
180C23—61no—
181C23—61no—
182C23—61no—
183C23—121no—
184C23D3×D411yescharacteristic
185Q8—41no—
186D4—121no—
187D4—122no—
188D4—122no—
189D4—121no—
190D4—121no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—31no—
194C2×C4—31no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—62no—
200C2×C4—62no—
201C2×C4—61no—
202C2×C4—121no—
203C2×C4—121no—
204C2×C4—122no—
205C2×C4—121no—
206C2×C4—121no—
207C2×C4—121no—
208C2×C4—121no—
209C2×C4C2×C4×D311yescharacteristic
210C2×C4D3×D411yescharacteristic
211C8—41no—
212C8—121no—
213C2×C3—21no—
214C2×C3—21no—
215C2×C3C2×#9911yescharacteristic
216C2×C3#41611yescharacteristic
217C2×C3#42111yescharacteristic
218D3—22no—
219D3—41no—
220D3—81no—
221C22—21no—
222C22—21no—
223C22—32no—
224C22—61no—
225C22—61no—
226C22—61no—
227C22—61no—
228C22—61no—
229C22—122no—
230C22—122no—
231C22—121no—
232C22—121no—
233C22—121no—
234C22D3×C22⋊C411yescharacteristic
235C22#91611yescharacteristic
236C22#91911yescharacteristic
237C4—21no—
238C4—21no—
239C4—41no—
240C4—41no—
241C4—61no—
242C4—61no—
243C4—81no—
244C4—121no—
245C4—241no—
246C3#151611yescharacteristic, complemented, Sylow
247C2—21no—
248C2—21no—
249C2—62no—
250C2—121no—
251C2—241no—
252C2D3×#9911yescharacteristic
253C2#480411yescharacteristic
254C2#482111yescharacteristic
subgroupG/H
centerC22D3×C22⋊C4
commutatorC2×C3×C4C22×C4
FrattiniC22×C4C22×D3
FittingC3×#328C2
socleC22×C3C2×C22⋊C4
prime radical#5627C2
cosocleC22×C3×C4C23
hypercenter#328D3
hypocenterC3#1516
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. D3×C22⋊C8C2semidirect
3. #4664C2semidirect
4. C3×#328C2semidirect
5. #4538C2semidirect
6. #4470C2semidirect
7. #4451C2semidirect
9. C2×#239C4semidirect
12. #946C4semidirect
16. #895C4semidirect
19. #892C4semidirect
32. #328D3semidirect
246. C3#1516semidirect

Maximal subgroups

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

subgroupindex
#56272
D3×C22⋊C82
#46642
C3×#3282
#45382
#44702
#44512
#15163