Finite Group Databasebeta

← #80951

Subgroups — #80951

Order 384.

430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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#5725C211yesmaximal, characteristic, complemented
2C4×#237C211yesmaximal, characteristic, complemented
3C3×#474C211yesmaximal, characteristic, complemented
4#5094C211yesmaximal, characteristic, complemented
5#5015C211yesmaximal, characteristic, complemented
6#4889C212yesmaximal, complemented
7#4885C212yesmaximal, complemented
8#4848C211yesmaximal, characteristic, complemented
9#4835C211yesmaximal, characteristic, complemented
10#4785C212yesmaximal, complemented
11#4781C212yesmaximal, complemented
12#3115—31nomaximal, Sylow
13C2×#239—21no—
14C2×#237C2211yescharacteristic
15C3×C4⋊Q8C2211yescharacteristic
16C3×C4×D4C2211yescharacteristic
17#947—21no—
18D4×Dic3C2211yescharacteristic
19C2×#213C2212yes—
20C4×#67—21no—
21C2×C4×Dic3—21no—
22C2×#204C2212yes—
23#895—21no—
24#895C2212yes—
25#893—21no—
26#893C2212yes—
27#892C2211yescharacteristic
28#887C2211yescharacteristic
29#67⋊C4—21no—
30#877—21no—
31#874C2211yescharacteristic
32C42×D3C2211yescharacteristic
33C4×Dic6C2211yescharacteristic
34C3×#107C2212yes—
35C3×C4⋊C8C2211yescharacteristic
36C3×#102C2212yes—
37#821C2212yes—
38(C2×D3)⋊C8C2212yes—
39#815C2212yes—
40#810C2212yes—
41#809C2212yes—
42#808C2212yes—
43C4⋊(C3⋊C8)C2211yescharacteristic
44#532—31no—
45C4×#41—31no—
46#482—32no—
47#475—31no—
48#474D311yescharacteristic, complemented
49#460—31no—
50#459—31no—
51#449—32no—
52#442—32no—
53#440—32no—
54#432—31no—
55C2×C3×Q8—21no—
56C2×C3×D4C2311yescharacteristic
57C22×C3×C4—21no—
58C2×#67—21no—
59C22×Dic3—21no—
60C22×Dic3—21no—
61#239—44no—
62#237—22no—
63#237—22no—
64C2×D12—22no—
65C2×D12—21no—
66C2×D12—21no—
67C2×D12C2312yes—
68C2×C4×D3—22no—
69C2×C4×D3D411yescharacteristic
70C2×C4×D3D411yescharacteristic
71C2×C4×D3C2311yescharacteristic
72C2×Dic6C2311yescharacteristic
73C2×C3×C8C2312yes—
74C3×C4⋊C4—21no—
75C3×C4⋊C4C2312yes—
76C3×C4⋊C4C2311yescharacteristic
77C3×C22⋊C4—21no—
78C3×C42C2311yescharacteristic
79#217—21no—
80#213—24no—
81(C2×D3)⋊C4—21no—
82(C2×D3)⋊C4—22no—
83(C2×D3)⋊C4—22no—
84C4⋊Dic3C2311yescharacteristic
85Dic3⋊C4—21no—
86Dic3⋊C4—21no—
87C4×Dic3—21no—
88C4×Dic3—21no—
89C4×Dic3—21no—
90C4×Dic3D411yescharacteristic
91C4×Dic3D411yescharacteristic
92C4×Dic3C2311yescharacteristic
93C2×C3⋊C8C2312yes—
94#204—24no—
95C2×#41—31no—
96C2×#41—61no—
97C2×SD16—32no—
98C2×D8—32no—
99C4⋊Q8C2×D311yescharacteristic
100#127—31no—
101#124—61no—
102#121—32no—
103#121—61no—
104C4×Q8—31no—
105C4×Q8—31no—
106C4×D4—31no—
107C4×D4—32no—
108C4×D4—61no—
109C4×D4—61no—
110C4×D4—61no—
111C4×D4C2×D311yescharacteristic
112#117—31no—
113#117—61no—
114C2×C42—31no—
115C2×C42—61no—
116#107C2×D312yes—
117#106—32no—
118C4⋊C8—31no—
119C4⋊C8C2×D311yescharacteristic
120#103—32no—
121#102—32no—
122#102—32no—
123#102C2×D312yes—
124C22⋊C8—32no—
125#97—32no—
126C23×C3—21no—
127C22×D3—22no—
128C22×D3C2×D411yescharacteristic
129C3×Q8—42no—
130C3×D4—21no—
131C3×D4#4112yescomplemented
132C2×C3×C4—21no—
133C2×C3×C4—22no—
134C2×C3×C4—42no—
135C2×C3×C4C2×D411yescharacteristic
136C2×C3×C4C2×D411yescharacteristic
137C2×C3×C4C2411yescharacteristic
138#67—24no—
139C2×Dic3—24no—
140C2×Dic3—21no—
141C2×Dic3—21no—
142C2×Dic3—42no—
143C2×Dic3C2×D411yescharacteristic
144C2×Dic3C2×D411yescharacteristic
145C2×Dic3C2×D411yescharacteristic
146D12—22no—
147D12—22no—
148D12—42no—
149D12—44no—
150D12—42no—
151C4×D3—22no—
152C4×D3—21no—
153C4×D3—21no—
154C4×D3—41no—
155C4×D3—44no—
156Dic6—21no—
157Dic6#4112yescomplemented
158C3×C8—22no—
159C3⋊C8—22no—
160#41—62no—
161#41—62no—
162#41—124no—
163C2×Q8—21no—
164C2×Q8—31no—
165C2×D4—32no—
166C2×D4—62no—
167C2×D4—61no—
168C2×D4—61no—
169C2×D4—61no—
170C2×D4C22×D311yescharacteristic
171C22×C4—21no—
172C22×C4—31no—
173C22×C4—31no—
174C22×C4—31no—
175C22×C4—62no—
176C22×C4—61no—
177C22×C4—61no—
178SD16—64no—
179D8—64no—
180C2×C8—32no—
181C2×C8C22×D312yes—
182C4⋊C4—21no—
183C4⋊C4—31no—
184C4⋊C4—61no—
185C4⋊C4—61no—
186C4⋊C4C22×D311yescharacteristic
187C4⋊C4C22×D312yes—
188C22⋊C4—21no—
189C22⋊C4—62no—
190C22⋊C4—62no—
191C22⋊C4—61no—
192C22⋊C4—61no—
193C42—31no—
194C42—31no—
195C42—31no—
196C42—61no—
197C42—61no—
198C42—61no—
199C42C22×D311yescharacteristic
200C22×C3—22no—
201C22×C3—41no—
202C22×C3—41no—
203C22×C3C22×D411yescharacteristic
204C2×D3—21no—
205C2×D3—21no—
206C2×D3—21no—
207C2×D3—42no—
208C2×D3—42no—
209C2×D3—42no—
210C3×C4—21no—
211C3×C4—42no—
212C3×C4—41no—
213C3×C4AGL(1,ℤ/8)12yes—
214C3×C4C2×#4111yescharacteristic
215C3×C4C2×#4111yescharacteristic
216Dic3—22no—
217Dic3—21no—
218Dic3—21no—
219Dic3—21no—
220Dic3—41no—
221C23—21no—
222C23—31no—
223C23—62no—
224Q8—32no—
225Q8—42no—
226Q8—61no—
227D4—21no—
228D4—64no—
229D4—62no—
230D4—62no—
231D4—122no—
232D4—124no—
233D4—122no—
234D4#23912yescomplemented
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—31no—
238C2×C4—31no—
239C2×C4—31no—
240C2×C4—42no—
241C2×C4—64no—
242C2×C4—61no—
243C2×C4—62no—
244C2×C4—61no—
245C2×C4—61no—
246C2×C4—61no—
247C2×C4—121no—
248C2×C4—124no—
249C2×C4—122no—
250C2×C4D3×D411yescharacteristic
251C2×C4D3×D411yescharacteristic
252C2×C4C23×D311yescharacteristic
253C8—22no—
254C8—62no—
255C2×C3—42no—
256C2×C3#52511yescharacteristic
257C2×C3C2×AGL(1,ℤ/8)11yescharacteristic
258C2×C3#57511yescharacteristic
259D3—41no—
260D3—82no—
261C22—22no—
262C22—41no—
263C22—41no—
264C22—61no—
265C22—61no—
266C22—61no—
267C22—122no—
268C22—122no—
269C22—122no—
270C22C2×D3×D411yescharacteristic
271C4—21no—
272C4—41no—
273C4—42no—
274C4—61no—
275C4—61no—
276C4—61no—
277C4—62no—
278C4—121no—
279C4#91112yes—
280C4C2×#23911yescharacteristic
281C4D3×#4111yescharacteristic
282C3#311511yescharacteristic, complemented, Sylow
283C2—42no—
284C2—121no—
285C2—242no—
286C2#562711yescharacteristic
287C2C2×#91111yescharacteristic
288C2#577711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#474C2
socleC22×C3C22×D4
hypercenter#474D3
hypocenterC3#3115
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #5725C2semidirect
2. C4×#237C2semidirect
3. C3×#474C2semidirect
4. #5094C2semidirect
5. #5015C2semidirect
6. #4889C2semidirect
7. #4885C2semidirect
8. #4848C2semidirect
9. #4835C2semidirect
10. #4785C2semidirect
11. #4781C2semidirect
48. #474D3semidirect
131. C3×D4#41semidirect
157. Dic6#41semidirect
234. D4#239semidirect
282. C3#3115semidirect

Maximal subgroups

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

subgroupindex
#57252
C4×#2372
C3×#4742
#50942
#50152
#48892
#48852
#48482
#48352
#47852
#47812
#31153