Finite Group Databasebeta

← #79218

Subgroups — #79218

Order 384.

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

normal subgroups only

This group has 410 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
1D3×#117C211yesmaximal, characteristic
2C2×#897C211yesmaximal, characteristic
3C3×#428C211yesmaximal, characteristic, complemented
4#5126C211yesmaximal, characteristic
5#5120C211yesmaximal, characteristic, complemented
6#5004C211yesmaximal, characteristic, complemented
7#4964C211yesmaximal, characteristic, complemented
8#4888C212yesmaximal, complemented
9#4884C212yesmaximal, complemented
10#4868C212yesmaximal, complemented
11#4862C212yesmaximal, complemented
12#3095—31nomaximal, Sylow
13C22×C4×D3C2211yescharacteristic
14C22×Dic6C2211yescharacteristic
15C2×C3×M16C2211yescharacteristic
16C3×#117C2211yescharacteristic
17C2×C3×C4⋊C4C2211yescharacteristic
18C2×(C2×D3)⋊C4—21no—
19#926C2211yescharacteristic
20C2×C4⋊Dic3—21no—
21C2×#208C2211yescharacteristic
22#897—21no—
23#897—21no—
24#897C2212yes—
25#897C2212yes—
26#892C2211yescharacteristic
27#892C2211yescharacteristic
28D3×C4⋊C4C2211yescharacteristic
29D3×C4⋊C4C2211yescharacteristic
30D3×C22⋊C4—21no—
31#877—21no—
32#872—21no—
33C42×D3—21no—
34C3×#107C2212yescomplemented
35C3×#106C2212yescomplemented
36(C2×D3)⋊C8C2212yes—
37(C2×D3)⋊C8C2212yes—
38#816C2212yescomplemented
39#816C2212yescomplemented
40#810C2212yescomplemented
41#810C2212yescomplemented
42#808C2212yescomplemented
43#807C2212yescomplemented
44C2×C22⋊Q8—31no—
45C2×#117—31no—
46#485—32no—
47#485—32no—
48#484—32no—
49#483—32no—
50#428—31no—
51#428D311yescharacteristic, complemented
52#419—31no—
53#419—31no—
54#407—31no—
55C23×D3D411yescharacteristic
56C22×C3×C4—21no—
57C22×C3×C4C2311yescharacteristic
58C22×Dic3—21no—
59C22×Dic3D411yescharacteristic
60C2×C4×D3—22no—
61C2×C4×D3—22no—
62C2×C4×D3—21no—
63C2×C4×D3—21no—
64C2×C4×D3D411yescharacteristic
65C2×C4×D3D411yescharacteristic
66C2×C4×D3C2311yescharacteristic
67C2×C4×D3C2311yescharacteristic
68C2×Dic6—22no—
69C2×Dic6—22no—
70C2×Dic6—21no—
71C2×Dic6C2312yes—
72C3×M16—22no—
73C2×C3×C8C2312yes—
74C3×C4⋊C4—21no—
75C3×C4⋊C4C2312yes—
76C3×C4⋊C4C2311yescharacteristic
77C3×C4⋊C4C2311yescharacteristic
78C3×C22⋊C4—21no—
79C3×C42—21no—
80#217—21no—
81(C2×D3)⋊C4—21no—
82(C2×D3)⋊C4—21no—
83(C2×D3)⋊C4—22no—
84(C2×D3)⋊C4—22no—
85C4⋊Dic3—22no—
86C4⋊Dic3—22no—
87C4⋊Dic3C2311yescharacteristic
88C4⋊Dic3C2311yescharacteristic
89Dic3⋊C4—21no—
90Dic3⋊C4—21no—
91C4×Dic3—21no—
92C4×Dic3—21no—
93C4×Dic3—21no—
94#208—22no—
95C2×C3⋊C8C2312yes—
96C22×Q8—31no—
97C23×C4—31no—
98C2×M16—31no—
99C2×M16C2×D311yescharacteristic
100C22⋊Q8—32no—
101C22⋊Q8—32no—
102C22⋊Q8—61no—
103C22⋊Q8—61no—
104#117—31no—
105#117—31no—
106#117—31no—
107#117—61no—
108#117—61no—
109#117C2×D311yescharacteristic
110C2×C4⋊C4—31no—
111C2×C4⋊C4—31no—
112C2×C4⋊C4—61no—
113C2×C4⋊C4C2×D311yescharacteristic
114C2×C22⋊C4—61no—
115C2×C22⋊C4—61no—
116C2×C42—61no—
117#107—32no—
118#107C2×D312yescomplemented
119#106—32no—
120#106C2×D312yescomplemented
121#103—32no—
122#103—32no—
123#103—32no—
124#103—32no—
125C22⋊C8—32no—
126C22⋊C8—32no—
127C23×C3C2×D411yescharacteristic
128C22×D3—22no—
129C22×D3—22no—
130C22×D3—41no—
131C22×D3C2×D411yescharacteristic
132C22×D3C2×D411yescharacteristic
133C2×C3×C4—21no—
134C2×C3×C4—21no—
135C2×C3×C4—22no—
136C2×C3×C4—42no—
137C2×C3×C4C2×D411yescharacteristic
138C2×C3×C4#4112yes—
139C2×C3×C4#4112yes—
140C2×C3×C4C2411yescharacteristic
141C2×Dic3—22no—
142C2×Dic3—21no—
143C2×Dic3—21no—
144C2×Dic3—22no—
145C2×Dic3—42no—
146C2×Dic3C2×D411yescharacteristic
147C2×Dic3C2×D411yescharacteristic
148C4×D3—22no—
149C4×D3—22no—
150C4×D3—21no—
151C4×D3—21no—
152C4×D3—21no—
153C4×D3—21no—
154C4×D3—42no—
155C4×D3—42no—
156Dic6—22no—
157Dic6—22no—
158Dic6—42no—
159C3×C8—22no—
160C3⋊C8—22no—
161C24—31no—
162C2×Q8—32no—
163C2×Q8—61no—
164C2×Q8—62no—
165C2×Q8—62no—
166C22×C4—21no—
167C22×C4—31no—
168C22×C4—31no—
169C22×C4—31no—
170C22×C4—31no—
171C22×C4—31no—
172C22×C4—61no—
173C22×C4—61no—
174C22×C4—62no—
175C22×C4—62no—
176C22×C4—61no—
177C22×C4C22×D311yescharacteristic
178M16—22no—
179M16—62no—
180C2×C8—32no—
181C2×C8C22×D312yes—
182C4⋊C4—21no—
183C4⋊C4—31no—
184C4⋊C4—31no—
185C4⋊C4—61no—
186C4⋊C4—61no—
187C4⋊C4—62no—
188C4⋊C4—62no—
189C4⋊C4C22×D311yescharacteristic
190C4⋊C4C22×D311yescharacteristic
191C4⋊C4C22×D312yes—
192C22⋊C4—21no—
193C22⋊C4—61no—
194C22⋊C4—61no—
195C22⋊C4—62no—
196C22⋊C4—62no—
197C22⋊C4—61no—
198C42—21no—
199C42—61no—
200C42—61no—
201C42—61no—
202C22×C3—21no—
203C22×C3—21no—
204C22×C3#12312yes—
205C22×C3C22×D411yescharacteristic
206C2×D3—21no—
207C2×D3—21no—
208C2×D3—21no—
209C2×D3—21no—
210C2×D3—21no—
211C2×D3—44no—
212C2×D3#13712yes—
213C3×C4—41no—
214C3×C4—41no—
215C3×C4—42no—
216C3×C4#12312yes—
217C3×C4C2×#4111yescharacteristic
218C3×C4C2×#4111yescharacteristic
219Dic3—21no—
220Dic3—21no—
221Dic3—42no—
222Dic3—41no—
223Dic3—41no—
224C23—31no—
225C23—31no—
226C23—62no—
227C23—62no—
228C23—121no—
229C23D3×D411yescharacteristic
230Q8—62no—
231Q8—62no—
232Q8—122no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—31no—
237C2×C4—31no—
238C2×C4—42no—
239C2×C4—62no—
240C2×C4—62no—
241C2×C4—62no—
242C2×C4—61no—
243C2×C4—61no—
244C2×C4—61no—
245C2×C4—61no—
246C2×C4—61no—
247C2×C4—61no—
248C2×C4—62no—
249C2×C4—122no—
250C2×C4—122no—
251C2×C4—122no—
252C2×C4#23512yes—
253C2×C4D3×D411yescharacteristic
254C2×C4#23912yes—
255C2×C4C23×D311yescharacteristic
256C8—22no—
257C8—62no—
258C2×C3—22no—
259C2×C3C2×#12311yescharacteristic
260C2×C3C2×#13711yescharacteristic
261C2×C3#57511yescharacteristic
262D3—22no—
263D3—41no—
264C22—21no—
265C22—21no—
266C22—32no—
267C22—61no—
268C22—61no—
269C22—61no—
270C22—61no—
271C22—61no—
272C22—124no—
273C22#89412yes—
274C22C2×D3×D411yescharacteristic
275C4—42no—
276C4—41no—
277C4—41no—
278C4—61no—
279C4—61no—
280C4—122no—
281C4—121no—
282C4—121no—
283C4#89412yes—
284C4C2×#23511yescharacteristic
285C4C2×#23911yescharacteristic
286C3#309511yescharacteristic, complemented, Sylow
287C2—22no—
288C2—62no—
289C2—121no—
290C2C2×#89411yescharacteristic
291C2#577311yescharacteristic
292C2D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#428C2
socleC22×C3C22×D4
prime radicalC23×D3D4
hypercenter#428D3
hypocenterC3#3095
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. C3×#428C2semidirect
5. #5120C2semidirect
6. #5004C2semidirect
7. #4964C2semidirect
8. #4888C2semidirect
9. #4884C2semidirect
10. #4868C2semidirect
11. #4862C2semidirect
34. C3×#107C22semidirect
35. C3×#106C22semidirect
38. #816C22semidirect
39. #816C22semidirect
40. #810C22semidirect
41. #810C22semidirect
42. #808C22semidirect
43. #807C22semidirect
51. #428D3semidirect
118. #107C2×D3semidirect
120. #106C2×D3semidirect
286. C3#3095semidirect

Maximal subgroups

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

subgroupindex
D3×#1172
C2×#8972
C3×#4282
#51262
#51202
#50042
#49642
#48882
#48842
#48682
#48622
#30953