Finite Group Databasebeta

← #80965

Subgroups — #80965

Order 384.

440 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 131 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×#474C211yesmaximal, characteristic, complemented
4#5087C211yesmaximal, characteristic, complemented
5#5008C211yesmaximal, characteristic, complemented
6#4891C212yesmaximal, complemented
7#4881C212yesmaximal, complemented
8#4842C211yesmaximal, characteristic, complemented
9#4837C211yesmaximal, characteristic, complemented
10#4770C212yesmaximal
11#4763C212yesmaximal, complemented
12#3077—31nomaximal, Sylow
13C2×D3×D4C2211yescharacteristic
14C22×C4×D3—21no—
15C3×C4⋊Q8C2211yescharacteristic, complemented
16C3×C4×D4C2211yescharacteristic
17#946—21no—
18Q8×Dic3—21no—
19D4×Dic3C2211yescharacteristic
20C4×#67—21no—
21C2×ΓL(1,𝔽25)C2212yes—
22#897—21no—
23#893C2211yescharacteristic
24#892C2212yes—
25D3×C4⋊C4C2211yescharacteristic
26#890C2212yescomplemented
27#887—21no—
28#67⋊C4—21no—
29D3×C22⋊C4—21no—
30C4×D12C2211yescharacteristic
31C42×D3C2211yescharacteristic
32#869C2211yescharacteristic, complemented
33C3×#107C2212yescomplemented
34C3×C4⋊C8C2211yescharacteristic, complemented
35C3×#102C2212yes—
36#832C2212yes—
37#821C2212yes—
38#817C2212yescomplemented
39Dic3⋊C8C2212yescomplemented
40#809C2212yes—
41#808C2212yescomplemented
42#807C2212yescomplemented
43C4⋊(C3⋊C8)C2211yescharacteristic, complemented
44#533—31no—
45C2×C4×D4—31no—
46#478—32no—
47#478—32no—
48#476—31no—
49#476—31no—
50#474—31no—
51#474D311yescharacteristic, complemented
52#428—32no—
53#423—31no—
54#418—32no—
55C23×D3—21no—
56C2×C3×Q8—21no—
57C2×C3×D4C2311yescharacteristic
58C22×C3×C4—21no—
59C2×#67—21no—
60C22×Dic3—21no—
61D3×D4—22no—
62D3×D4Q814yescomplemented
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—
72C2×C3×C8C2312yes—
73C3×C4⋊C4—21no—
74C3×C4⋊C4C2312yes—
75C3×C4⋊C4C2311yescharacteristic
76C3×C22⋊C4—21no—
77C3×C42C2311yescharacteristic
78#217—21no—
79(C2×D3)⋊C4—22no—
80(C2×D3)⋊C4—21no—
81(C2×D3)⋊C4—21no—
82C4⋊Dic3—21no—
83C4⋊Dic3—22no—
84C4⋊Dic3C2311yescharacteristic
85C4⋊Dic3C2312yes—
86Dic3⋊C4—21no—
87Dic3⋊C4—22no—
88C4×Dic3—22no—
89C4×Dic3D411yescharacteristic
90C4×Dic3D411yescharacteristic
91C4×Dic3C2311yescharacteristic
92C2×C3⋊C8C2312yes—
93ΓL(1,𝔽25)—24no—
94C22×D4—31no—
95C23×C4—61no—
96C2×M16—32no—
97C4⋊Q8—31no—
98C4⋊Q8C2×D311yescharacteristic, complemented
99#125—32no—
100C22⋊Q8—61no—
101C22⋊Q8—61no—
102C4×Q8—61no—
103C4×Q8—61no—
104C4×D4—31no—
105C4×D4—31no—
106C4×D4—31no—
107C4×D4—61no—
108C4×D4—61no—
109C4×D4C2×D311yescharacteristic
110#117—32no—
111C2×C4⋊C4—31no—
112C2×C22⋊C4—61no—
113C2×C42—31no—
114#107—32no—
115#107C2×D312yescomplemented
116#106—32no—
117#106—32no—
118C4⋊C8—32no—
119C4⋊C8—31no—
120C4⋊C8C2×D311yescharacteristic, complemented
121#102—32no—
122#102—32no—
123#102—32no—
124#102C2×D312yes—
125C23×C3—21no—
126C22×D3—21no—
127C22×D3—24no—
128C22×D3—42no—
129C22×D3—42no—
130C22×D3C2×D411yescharacteristic
131C3×Q8—42no—
132C3×D4—21no—
133C3×D4C2×Q812yes—
134C2×C3×C4—22no—
135C2×C3×C4—21no—
136C2×C3×C4—42no—
137C2×C3×C4C2×D411yescharacteristic
138C2×C3×C4C2×D411yescharacteristic
139C2×C3×C4C2411yescharacteristic
140#67—24no—
141C2×Dic3—22no—
142C2×Dic3—21no—
143C2×Dic3—42no—
144C2×Dic3C2×D411yescharacteristic
145C2×Dic3C2×D411yescharacteristic
146C2×Dic3C2×D411yescharacteristic
147D12—21no—
148D12C2×Q812yes—
149C4×D3—22no—
150C4×D3—41no—
151C4×D3—42no—
152C4×D3—42no—
153C4×D3—42no—
154C4×D3C2×Q812yes—
155C4×D3#4112yes—
156Dic6—42no—
157C3×C8—22no—
158C3⋊C8—22no—
159C24—61no—
160C2×Q8—21no—
161C2×Q8—61no—
162C2×D4—34no—
163C2×D4—31no—
164C2×D4—62no—
165C2×D4—61no—
166C2×D4C22×D311yescharacteristic
167C22×C4—21no—
168C22×C4—31no—
169C22×C4—31no—
170C22×C4—31no—
171C22×C4—61no—
172C22×C4—61no—
173C22×C4—61no—
174C22×C4—61no—
175C22×C4—124no—
176M16—64no—
177C2×C8—32no—
178C2×C8C22×D312yes—
179C4⋊C4—21no—
180C4⋊C4—32no—
181C4⋊C4—31no—
182C4⋊C4—61no—
183C4⋊C4—62no—
184C4⋊C4—62no—
185C4⋊C4—61no—
186C4⋊C4C22×D312yes—
187C4⋊C4C22×D311yescharacteristic
188C22⋊C4—21no—
189C22⋊C4—61no—
190C22⋊C4—62no—
191C22⋊C4—61no—
192C22⋊C4—61no—
193C42—31no—
194C42—31no—
195C42—31no—
196C42—62no—
197C42C22×D311yescharacteristic
198C22×C3—22no—
199C22×C3—41no—
200C22×C3—41no—
201C22×C3C22×D411yescharacteristic
202C2×D3—21no—
203C2×D3—21no—
204C2×D3—22no—
205C2×D3—48no—
206C2×D3—41no—
207C2×D3—41no—
208C2×D3C22⋊Q812yes—
209C3×C4—21no—
210C3×C4—41no—
211C3×C4—42no—
212C3×C4AGL(1,ℤ/8)12yes—
213C3×C4C22×Q811yescharacteristic
214C3×C4C2×#4111yescharacteristic
215Dic3—21no—
216Dic3—21no—
217Dic3—41no—
218Dic3—42no—
219Dic3C22⋊Q812yes—
220C23—21no—
221C23—31no—
222C23—64no—
223C23—61no—
224C23—122no—
225C23—122no—
226Q8—42no—
227Q8—122no—
228D4—21no—
229D4—32no—
230D4—64no—
231D4—61no—
232D4D3×Q812yes—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—31no—
236C2×C4—32no—
237C2×C4—32no—
238C2×C4—31no—
239C2×C4—31no—
240C2×C4—42no—
241C2×C4—62no—
242C2×C4—62no—
243C2×C4—61no—
244C2×C4—121no—
245C2×C4—122no—
246C2×C4—122no—
247C2×C4—122no—
248C2×C4—122no—
249C2×C4D3×D411yescharacteristic
250C2×C4D3×D411yescharacteristic
251C2×C4C23×D311yescharacteristic
252C8—22no—
253C8—62no—
254C2×C3—42no—
255C2×C3C2×C22⋊Q811yescharacteristic
256C2×C3C2×AGL(1,ℤ/8)11yescharacteristic
257C2×C3#57511yescharacteristic
258D3—22no—
259D3—42no—
260C22—22no—
261C22—32no—
262C22—41no—
263C22—41no—
264C22—61no—
265C22—61no—
266C22—62no—
267C22—128no—
268C22—121no—
269C22—121no—
270C22C2×D3×D411yescharacteristic
271C4—21no—
272C4—32no—
273C4—41no—
274C4—42no—
275C4—61no—
276C4—61no—
277C4—121no—
278C4—122no—
279C4#91112yes—
280C4C2×D3×Q811yescharacteristic
281C4D3×#4111yescharacteristic
282C3#307711yescharacteristic, complemented, Sylow
283C2—42no—
284C2—62no—
285C2—122no—
286C2D3×C22⋊Q811yescharacteristic
287C2C2×#91111yescharacteristic
288C2#577711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#474C2
socleC22×C3C22×D4
prime radicalC2×D3×D4C22
hypercenter#474D3
hypocenterC3#3077
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. #5728C2semidirect
3. C3×#474C2semidirect
4. #5087C2semidirect
5. #5008C2semidirect
6. #4891C2semidirect
7. #4881C2semidirect
8. #4842C2semidirect
9. #4837C2semidirect
11. #4763C2semidirect
15. C3×C4⋊Q8C22semidirect
26. #890C22semidirect
32. #869C22semidirect
33. C3×#107C22semidirect
34. C3×C4⋊C8C22semidirect
38. #817C22semidirect
39. Dic3⋊C8C22semidirect
41. #808C22semidirect
42. #807C22semidirect
43. C4⋊(C3⋊C8)C22semidirect
51. #474D3semidirect
62. D3×D4Q8semidirect
98. C4⋊Q8C2×D3semidirect
115. #107C2×D3semidirect
120. C4⋊C8C2×D3semidirect
282. C3#3077semidirect

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×#4742
#50872
#50082
#48912
#48812
#48422
#48372
#47702
#47632
#30773