Finite Group Databasebeta

← #78911

Subgroups — #78911

Order 384.

504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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#5830C211yesmaximal, characteristic, complemented
2C2×#950C211yesmaximal, characteristic, complemented
3C2×#908C211yesmaximal, characteristic, complemented
4#5504C211yesmaximal, characteristic, complemented
5C3×#417C211yesmaximal, characteristic, complemented
6#5119C211yesmaximal, characteristic, complemented
7C2×#809C211yesmaximal, characteristic, complemented
8#4819C212yesmaximal, complemented
9#4798C212yesmaximal, complemented
10#4786C212yesmaximal, complemented
11#4762C212yesmaximal, complemented
12#3045—31nomaximal, Sylow
13C2×C3×#41C2211yescharacteristic
14C2×#235C2211yescharacteristic
15C22×D12C2211yescharacteristic
16C2×C3×M16C2211yescharacteristic
17C2×C3×C4⋊C4C2211yescharacteristic
18#950—24no—
19#947C2212yes—
20C2×#216C2211yescharacteristic, complemented
21C2×#215C2211yescharacteristic, complemented
22#940C2212yes—
23#937—22no—
24C2×#214C2211yescharacteristic, complemented
25C2×#213C2211yescharacteristic, complemented
26#930—21no—
27#930—21no—
28C4×#67—22no—
29#926C2211yescharacteristic
30C22×C3⋊C8C2211yescharacteristic
31#908—24no—
32C2×D24C2212yes—
33C2×#204C2212yes—
34#893C2212yescomplemented
35#892—21no—
36D3×C4⋊C4—21no—
37#887C2212yescomplemented
38C3×#103C2212yescomplemented
39C3×#102C2212yescomplemented
40Dic3⋊C8C2212yescomplemented
41Dic3⋊C8C2212yescomplemented
42#809C2212yes—
43#809C2212yes—
44C2×AGL(1,ℤ/8)—31no—
45C2×#135—31no—
46#535—31no—
47#520—31no—
48#464—32no—
49#463—32no—
50#460—32no—
51#459—32no—
52#424—31no—
53#417D311yescharacteristic, complemented
54C2×#102—31no—
55C23×D3—21no—
56C3×#41—22no—
57C3×#41—22no—
58C2×C3×Q8C2311yescharacteristic
59C2×C3×D4—21no—
60C2×C3×D4C2311yescharacteristic
61C22×C3×C4—21no—
62C22×C3×C4—21no—
63C22×C3×C4C2311yescharacteristic
64C2×#67—21no—
65C2×#67—22no—
66C2×#67—22no—
67#235—22no—
68#235D414yescomplemented
69C2×D12—22no—
70C2×D12—22no—
71C2×D12—21no—
72C2×D12C2312yes—
73C2×D12C2311yescharacteristic
74C2×C4×D3—21no—
75C2×C4×D3—22no—
76C2×Dic6C2311yescharacteristic
77C3×M16—22no—
78C2×C3×C8C2312yes—
79C3×C4⋊C4—21no—
80C3×C4⋊C4C2312yes—
81#217D412yes—
82#216—22no—
83#215—22no—
84#214—22no—
85#213—22no—
86(C2×D3)⋊C4—22no—
87(C2×D3)⋊C4—22no—
88(C2×D3)⋊C4—22no—
89C4⋊Dic3D411yescharacteristic
90C4⋊Dic3D411yescharacteristic
91Dic3⋊C4—22no—
92C4×Dic3—22no—
93C4×Dic3C2312yes—
94C2×C3⋊C8—22no—
95C2×C3⋊C8C2311yescharacteristic
96C2×C3⋊C8C2311yescharacteristic
97D24—24no—
98#204—24no—
99C2×#41—31no—
100C2×#41C2×D311yescharacteristic
101C22×D4—31no—
102AGL(1,ℤ/8)—64no—
103#135—64no—
104C2×Q16—31no—
105C2×SD16—31no—
106C2×SD16—31no—
107C2×SD16—32no—
108C2×D8—31no—
109C2×D8—32no—
110C2×M16C2×D311yescharacteristic
111C22×C8—31no—
112#127—32no—
113#124—32no—
114#121—61no—
115#121—61no—
116#120—62no—
117C4×Q8—32no—
118C4×D4—32no—
119C4×D4—62no—
120#117—31no—
121#117—61no—
122C2×C4⋊C4—61no—
123C2×C4⋊C4C2×D311yescharacteristic
124C4⋊C8—32no—
125C4⋊C8—32no—
126#103C2×D312yescomplemented
127#102—32no—
128#102—32no—
129#102C2×D312yescomplemented
130C23×C3—21no—
131C23×C3C2×D411yescharacteristic
132C22×D3—21no—
133C22×D3—22no—
134C22×D3—42no—
135C22×D3—81no—
136C22×D3—81no—
137C3×Q8—21no—
138C3×Q8—21no—
139C3×D4—21no—
140C3×D4—21no—
141C3×D4—42no—
142C2×C3×C4—22no—
143C2×C3×C4—21no—
144C2×C3×C4—42no—
145C2×C3×C4—81no—
146C2×C3×C4C2×D411yescharacteristic
147C2×C3×C4C2×D412yes—
148C2×C3×C4#4112yes—
149C2×C3×C4C2411yescharacteristic
150#67—24no—
151#67—82no—
152#67—82no—
153C2×Dic3—21no—
154C2×Dic3C2×D412yes—
155C2×Dic3C2×D412yes—
156D12—22no—
157D12—21no—
158D12—22no—
159D12—42no—
160D12C2×D412yes—
161C4×D3—24no—
162C4×D3—82no—
163Dic6—21no—
164Dic6C2×D412yes—
165C3×C8—22no—
166C3⋊C8—21no—
167C3⋊C8—21no—
168C24—61no—
169#41—22no—
170#41—22no—
171#41—34no—
172#41—62no—
173C2×Q8—31no—
174C2×Q8C22×D311yescharacteristic
175C2×D4—21no—
176C2×D4—31no—
177C2×D4—32no—
178C2×D4—62no—
179C2×D4—62no—
180C2×D4—61no—
181C2×D4—62no—
182C2×D4—62no—
183C2×D4—61no—
184C2×D4C22×D311yescharacteristic
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—62no—
188C22×C4—61no—
189C22×C4C22×D311yescharacteristic
190Q16—62no—
191SD16—64no—
192SD16—62no—
193SD16—62no—
194D8—64no—
195D8—62no—
196M16—22no—
197C2×C8—31no—
198C2×C8—31no—
199C2×C8—62no—
200C2×C8C22×D312yes—
201C4⋊C4—21no—
202C4⋊C4—31no—
203C4⋊C4—31no—
204C4⋊C4—62no—
205C4⋊C4C22×D312yes—
206C22⋊C4—32no—
207C22⋊C4—62no—
208C22⋊C4—62no—
209C22⋊C4—62no—
210C42—32no—
211C42—62no—
212C22×C3—21no—
213C22×C3—21no—
214C22×C3—41no—
215C22×C3—41no—
216C22×C3—41no—
217C22×C3#12112yes—
218C22×C3C22×D411yescharacteristic
219C2×D3—22no—
220C2×D3—41no—
221C2×D3—41no—
222C2×D3—42no—
223C2×D3—42no—
224C2×D3—42no—
225C2×D3—84no—
226C3×C4—41no—
227C3×C4—42no—
228C3×C4#12112yes—
229C3×C4C22×D411yescharacteristic
230C3×C4C2×#4111yescharacteristic
231Dic3—22no—
232Dic3—22no—
233Dic3—22no—
234C23—21no—
235C23—61no—
236C23—62no—
237C23—122no—
238C23—241no—
239C23—241no—
240C23D3×D411yescharacteristic
241Q8—21no—
242Q8—21no—
243Q8—32no—
244Q8—61no—
245D4—21no—
246D4—21no—
247D4—32no—
248D4—42no—
249D4—64no—
250D4—61no—
251D4—62no—
252D4—62no—
253D4—122no—
254D4—242no—
255D4—242no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—32no—
259C2×C4—32no—
260C2×C4—42no—
261C2×C4—61no—
262C2×C4—64no—
263C2×C4—81no—
264C2×C4—242no—
265C2×C4#23512yes—
266C2×C4D3×D411yescharacteristic
267C2×C4D3×D412yes—
268C2×C4C23×D311yescharacteristic
269C8—22no—
270C8—61no—
271C8—61no—
272C2×C3—22no—
273C2×C3—81no—
274C2×C3C2×#12111yescharacteristic
275C2×C3#57611yescharacteristic
276C2×C3#57711yescharacteristic
277D3—42no—
278D3—82no—
279C22—21no—
280C22—21no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—62no—
285C22—121no—
286C22—121no—
287C22—122no—
288C22—122no—
289C22—122no—
290C22—244no—
291C22#88412yes—
292C22C2×D3×D411yescharacteristic
293C4—41no—
294C4—42no—
295C4—62no—
296C4—62no—
297C4—62no—
298C4#88412yes—
299C4C2×#23511yescharacteristic
300C4C2×D3×D411yescharacteristic
301C3#304511yescharacteristic, complemented, Sylow
302C2—22no—
303C2—81no—
304C2—122no—
305C2—242no—
306C2C2×#88411yescharacteristic
307C2#577411yescharacteristic
308C2#577811yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#417C2
socleC22×C3C22×D4
hypercenter#417D3
hypocenterC3#3045
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #5830C2semidirect
2. C2×#950C2semidirect
3. C2×#908C2semidirect
4. #5504C2semidirect
5. C3×#417C2semidirect
6. #5119C2semidirect
7. C2×#809C2semidirect
8. #4819C2semidirect
9. #4798C2semidirect
10. #4786C2semidirect
11. #4762C2semidirect
20. C2×#216C22semidirect
21. C2×#215C22semidirect
24. C2×#214C22semidirect
25. C2×#213C22semidirect
34. #893C22semidirect
37. #887C22semidirect
38. C3×#103C22semidirect
39. C3×#102C22semidirect
40. Dic3⋊C8C22semidirect
41. Dic3⋊C8C22semidirect
53. #417D3semidirect
68. #235D4semidirect
126. #103C2×D3semidirect
129. #102C2×D3semidirect
301. C3#3045semidirect

Maximal subgroups

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

subgroupindex
#58302
C2×#9502
C2×#9082
#55042
C3×#4172
#51192
C2×#8092
#48192
#47982
#47862
#47622
#30453