Finite Group Databasebeta

← #80408

Subgroups — #80408

Order 384.

448 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 127 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#5728C211yesmaximal, characteristic, complemented
2C4×D3×D4C211yesmaximal, characteristic
3C3×#461C211yesmaximal, characteristic, complemented
4#5169C212yesmaximal
5Dic3×SD16C212yesmaximal, complemented
6#5083C211yesmaximal, characteristic, complemented
7#5008C211yesmaximal, characteristic, complemented
8#4842C211yesmaximal, characteristic, complemented
9#4833C211yesmaximal, characteristic, complemented
10#4805C212yesmaximal, complemented
11#4788C212yesmaximal, complemented
12#3101—31nomaximal, Sylow
13C2×D3×D4C2211yescharacteristic
14C22×C4×D3—21no—
15C2×C3×SD16C2212yes—
16C3×C4⋊Q8C2211yescharacteristic, complemented
17C3×C4×D4C2211yescharacteristic
18#946C2212yes—
19Q8×Dic3C2212yescomplemented
20C2×#215C2212yes—
21D4×Dic3C2211yescharacteristic
22C4×#67—21no—
23#897—21no—
24#893C2211yescharacteristic
25#892—21no—
26D3×C4⋊C4C2211yescharacteristic
27#890—21no—
28#887—21no—
29#67⋊C4—21no—
30D3×C22⋊C4—21no—
31C4×D12C2211yescharacteristic
32C42×D3C2211yescharacteristic
33#869C2211yescharacteristic, complemented
34C3×C4⋊C8C2211yescharacteristic, complemented
35C3×#103C2212yescomplemented
36#835C2212yescomplemented
37#832C2212yes—
38#821C2212yes—
39(C2×D3)⋊C8C2212yes—
40#817C2212yescomplemented
41C8×Dic3C2212yescomplemented
42#808C2212yescomplemented
43C4⋊(C3⋊C8)C2211yescharacteristic, complemented
44#533—31no—
45C2×C4×D4—31no—
46#483—32no—
47#476—31no—
48#476—31no—
49#461—31no—
50#461D311yescharacteristic, complemented
51#450—32no—
52C4×SD16—32no—
53C4×SD16—32no—
54#431—31no—
55C23×D3—21no—
56C2×C3×Q8C2312yes—
57C2×C3×D4C2311yescharacteristic
58C22×C3×C4—21no—
59C2×#67—21no—
60C22×Dic3—21no—
61D3×D4—22no—
62D3×D4—22no—
63C2×D12C2311yescharacteristic
64C2×C4×D3—21no—
65C2×C4×D3—21no—
66C2×C4×D3—21no—
67C2×C4×D3—44no—
68C2×C4×D3D411yescharacteristic
69C2×C4×D3D411yescharacteristic
70C2×C4×D3C2311yescharacteristic
71C2×Dic6—21no—
72C3×SD16—24no—
73C2×C3×C8C2312yes—
74C3×C4⋊C4—21no—
75C3×C4⋊C4—21no—
76C3×C4⋊C4C2311yescharacteristic
77C3×C22⋊C4—21no—
78C3×C42C2311yescharacteristic
79#217—21no—
80#215—24no—
81(C2×D3)⋊C4—22no—
82(C2×D3)⋊C4—21no—
83(C2×D3)⋊C4—21no—
84C4⋊Dic3—21no—
85C4⋊Dic3—22no—
86C4⋊Dic3C2312yes—
87C4⋊Dic3C2311yescharacteristic
88Dic3⋊C4—21no—
89Dic3⋊C4—22no—
90C4×Dic3—22no—
91C4×Dic3D411yescharacteristic
92C4×Dic3D411yescharacteristic
93C4×Dic3C2311yescharacteristic
94C2×C3⋊C8C2312yes—
95C22×D4—31no—
96C23×C4—61no—
97C2×SD16—32no—
98C2×SD16C2×D312yes—
99C4⋊Q8—31no—
100C4⋊Q8C2×D311yescharacteristic, complemented
101#125—61no—
102C22⋊Q8—32no—
103C22⋊Q8—61no—
104C4×Q8—32no—
105C4×Q8—61no—
106C4×D4—31no—
107C4×D4—31no—
108C4×D4—31no—
109C4×D4—61no—
110C4×D4—61no—
111C4×D4C2×D311yescharacteristic
112#117—61no—
113C2×C4⋊C4—31no—
114C2×C22⋊C4—61no—
115C2×C42—31no—
116#106—32no—
117#106—32no—
118C4⋊C8—31no—
119C4⋊C8C2×D311yescharacteristic, complemented
120#103—32no—
121#103C2×D312yescomplemented
122#102—32no—
123#102—32no—
124C22⋊C8—32no—
125C4×C8—32no—
126C23×C3—21no—
127C22×D3—24no—
128C22×D3—21no—
129C22×D3—42no—
130C22×D3—42no—
131C22×D3C2×D411yescharacteristic
132C3×Q8—22no—
133C3×Q8—22no—
134C3×D4—21no—
135C3×D4#4112yes—
136C2×C3×C4—22no—
137C2×C3×C4—21no—
138C2×C3×C4—42no—
139C2×C3×C4C2×D411yescharacteristic
140C2×C3×C4C2×D411yescharacteristic
141C2×C3×C4C2411yescharacteristic
142#67—24no—
143C2×Dic3—22no—
144C2×Dic3—21no—
145C2×Dic3—42no—
146C2×Dic3C2×D411yescharacteristic
147C2×Dic3C2×D411yescharacteristic
148C2×Dic3C2×D411yescharacteristic
149D12—21no—
150D12#4112yes—
151C4×D3—21no—
152C4×D3—21no—
153C4×D3—41no—
154C4×D3—42no—
155C4×D3—42no—
156C4×D3—42no—
157C4×D3SD1614yescomplemented
158Dic6—42no—
159C3×C8—22no—
160C3⋊C8—22no—
161C24—61no—
162C2×Q8—61no—
163C2×Q8C22×D312yes—
164C2×D4—31no—
165C2×D4—61no—
166C2×D4—62no—
167C2×D4—62no—
168C2×D4C22×D311yescharacteristic
169C22×C4—21no—
170C22×C4—31no—
171C22×C4—31no—
172C22×C4—31no—
173C22×C4—61no—
174C22×C4—61no—
175C22×C4—61no—
176C22×C4—61no—
177C22×C4—124no—
178SD16—24no—
179SD16—64no—
180C2×C8—32no—
181C2×C8C22×D312yes—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—32no—
185C4⋊C4—31no—
186C4⋊C4—61no—
187C4⋊C4—62no—
188C4⋊C4—62no—
189C4⋊C4—61no—
190C4⋊C4C22×D311yescharacteristic
191C22⋊C4—21no—
192C22⋊C4—61no—
193C22⋊C4—62no—
194C22⋊C4—61no—
195C22⋊C4—61no—
196C42—31no—
197C42—31no—
198C42—31no—
199C42—62no—
200C42C22×D311yescharacteristic
201C22×C3—22no—
202C22×C3—41no—
203C22×C3—41no—
204C22×C3C22×D411yescharacteristic
205C2×D3—21no—
206C2×D3—21no—
207C2×D3—22no—
208C2×D3—48no—
209C2×D3—41no—
210C2×D3—41no—
211C2×D3C2×SD1612yes—
212C3×C4—21no—
213C3×C4—42no—
214C3×C4—41no—
215C3×C4C2×SD1612yes—
216C3×C4C2×#4111yescharacteristic
217C3×C4C2×#4111yescharacteristic
218Dic3—21no—
219Dic3—21no—
220Dic3—41no—
221Dic3—42no—
222Dic3C2×SD1612yes—
223C23—21no—
224C23—31no—
225C23—64no—
226C23—61no—
227C23—122no—
228C23—122no—
229Q8—22no—
230Q8—22no—
231Q8—122no—
232D4—21no—
233D4—32no—
234D4—64no—
235D4—61no—
236D4#23712yes—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—31no—
240C2×C4—34no—
241C2×C4—31no—
242C2×C4—31no—
243C2×C4—42no—
244C2×C4—61no—
245C2×C4—61no—
246C2×C4—62no—
247C2×C4—61no—
248C2×C4—121no—
249C2×C4—122no—
250C2×C4—122no—
251C2×C4—122no—
252C2×C4—122no—
253C2×C4D3×D411yescharacteristic
254C2×C4D3×D411yescharacteristic
255C2×C4C23×D311yescharacteristic
256C8—22no—
257C8—62no—
258C2×C3—42no—
259C2×C3#52511yescharacteristic
260C2×C3C22×SD1611yescharacteristic
261C2×C3#57511yescharacteristic
262D3—22no—
263D3—42no—
264C22—22no—
265C22—32no—
266C22—41no—
267C22—41no—
268C22—61no—
269C22—61no—
270C22—62no—
271C22—128no—
272C22—121no—
273C22—121no—
274C22C2×D3×D411yescharacteristic
275C4—21no—
276C4—32no—
277C4—41no—
278C4—42no—
279C4—61no—
280C4—61no—
281C4—121no—
282C4—122no—
283C4D3×SD1612yes—
284C4C2×#23711yescharacteristic
285C4D3×#4111yescharacteristic
286C3#310111yescharacteristic, complemented, Sylow
287C2—42no—
288C2—62no—
289C2—122no—
290C2#560611yescharacteristic
291C2C2×D3×SD1611yescharacteristic
292C2#577711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#461C2
socleC22×C3C22×D4
prime radicalC2×D3×D4C22
hypercenter#461D3
hypocenterC3#3101
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #5728C2semidirect
3. C3×#461C2semidirect
5. Dic3×SD16C2semidirect
6. #5083C2semidirect
7. #5008C2semidirect
8. #4842C2semidirect
9. #4833C2semidirect
10. #4805C2semidirect
11. #4788C2semidirect
16. C3×C4⋊Q8C22semidirect
19. Q8×Dic3C22semidirect
33. #869C22semidirect
34. C3×C4⋊C8C22semidirect
35. C3×#103C22semidirect
36. #835C22semidirect
40. #817C22semidirect
41. C8×Dic3C22semidirect
42. #808C22semidirect
43. C4⋊(C3⋊C8)C22semidirect
50. #461D3semidirect
100. C4⋊Q8C2×D3semidirect
119. C4⋊C8C2×D3semidirect
121. #103C2×D3semidirect
157. C4×D3SD16semidirect
286. C3#3101semidirect

Maximal subgroups

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

subgroupindex
#57282
C4×D3×D42
C3×#4612
#51692
Dic3×SD162
#50832
#50082
#48422
#48332
#48052
#47882
#31013