Finite Group Databasebeta

← #80964

Subgroups — #80964

Order 384.

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

normal subgroups only

This group has 388 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×#237C211yesmaximal, characteristic
3C3×#474C211yesmaximal, characteristic, complemented
4#5094C211yesmaximal, characteristic, complemented
5#5008C211yesmaximal, characteristic, complemented
6#4880C212yesmaximal, complemented
7#4877C212yesmaximal, complemented
8#4850C211yesmaximal, characteristic, complemented
9D3×C4⋊C8C211yesmaximal, characteristic, complemented
10#4772C212yesmaximal
11#4766C212yesmaximal, complemented
12#3076—31nomaximal, Sylow
13C2×#237C2211yescharacteristic
14C3×C4⋊Q8C2211yescharacteristic
15C3×C4×D4C2211yescharacteristic
16#946—21no—
17Q8×Dic3—21no—
18D4×Dic3C2211yescharacteristic
19C4×#67—21no—
20C2×C4×Dic3—21no—
21C2×D3×C8C2212yes—
22#897—21no—
23#892C2211yescharacteristic
24#892C2212yes—
25#890C2212yes—
26#887—21no—
27#887C2211yescharacteristic
28#67⋊C4—21no—
29#877—21no—
30C42×D3C2211yescharacteristic
31#869C2211yescharacteristic
32C4×Dic6C2211yescharacteristic
33C3×#107C2212yes—
34C3×C4⋊C8C2211yescharacteristic
35C3×#102C2212yes—
36#832C2212yes—
37#818C2212yes—
38#816C2212yes—
39Dic3⋊C8C2212yes—
40#810C2212yes—
41#808C2212yes—
42#808C2212yes—
43C4⋊(C3⋊C8)C2211yescharacteristic
44#533—31no—
45C4×#41—31no—
46#479—32no—
47#478—32no—
48#477—31no—
49#476—31no—
50#475—31no—
51#474D311yescharacteristic, complemented
52#427—32no—
53C2×C4⋊C8—31no—
54#416—32no—
55C2×C3×Q8—21no—
56C2×C3×D4C2311yescharacteristic
57C22×C3×C4—21no—
58C2×#67—21no—
59C22×Dic3—21no—
60C22×Dic3—21no—
61#237—22no—
62#237Q814yescomplemented
63C2×C4×D3D411yescharacteristic
64C2×C4×D3D411yescharacteristic
65C2×C4×D3C2311yescharacteristic
66C2×Dic6—21no—
67C2×Dic6C2311yescharacteristic
68C2×C3×C8C2312yes—
69C3×C4⋊C4—21no—
70C3×C4⋊C4C2311yescharacteristic
71C3×C4⋊C4C2312yes—
72C3×C22⋊C4—21no—
73C3×C42C2311yescharacteristic
74#217—21no—
75(C2×D3)⋊C4—21no—
76(C2×D3)⋊C4—22no—
77C4⋊Dic3—21no—
78C4⋊Dic3—22no—
79C4⋊Dic3C2311yescharacteristic
80C4⋊Dic3C2312yes—
81Dic3⋊C4—21no—
82Dic3⋊C4—21no—
83Dic3⋊C4—22no—
84C4×Dic3—21no—
85C4×Dic3—21no—
86C4×Dic3—21no—
87C4×Dic3—22no—
88C4×Dic3D411yescharacteristic
89C4×Dic3D411yescharacteristic
90C4×Dic3C2311yescharacteristic
91C2×C3⋊C8C2312yes—
92D3×C8—24no—
93C2×#41—31no—
94C22×C8—32no—
95C4⋊Q8—31no—
96C4⋊Q8C2×D311yescharacteristic
97#125—32no—
98C22⋊Q8—61no—
99C22⋊Q8—61no—
100C4×Q8—31no—
101C4×Q8—31no—
102C4×Q8—61no—
103C4×Q8—61no—
104C4×D4—31no—
105C4×D4—61no—
106C4×D4—61no—
107C4×D4C2×D311yescharacteristic
108#117—31no—
109#117—32no—
110#117—61no—
111C2×C42—31no—
112C2×C42—61no—
113#107—32no—
114#107C2×D312yes—
115#106—32no—
116#106—32no—
117C4⋊C8—32no—
118C4⋊C8—31no—
119C4⋊C8C2×D311yescharacteristic
120#103—32no—
121#103—32no—
122#102—32no—
123#102C2×D312yes—
124C23×C3—21no—
125C22×D3C2×D411yescharacteristic
126C3×Q8—42no—
127C3×D4—21no—
128C3×D4C2×Q812yes—
129C2×C3×C4—21no—
130C2×C3×C4—22no—
131C2×C3×C4—42no—
132C2×C3×C4C2×D411yescharacteristic
133C2×C3×C4C2×D411yescharacteristic
134C2×C3×C4C2411yescharacteristic
135#67—24no—
136C2×Dic3—21no—
137C2×Dic3—24no—
138C2×Dic3—21no—
139C2×Dic3—22no—
140C2×Dic3—42no—
141C2×Dic3C2×D411yescharacteristic
142C2×Dic3C2×D411yescharacteristic
143C2×Dic3C2×D411yescharacteristic
144C4×D3—22no—
145C4×D3—41no—
146C4×D3C2×Q812yes—
147C4×D3#4112yes—
148Dic6—21no—
149Dic6—42no—
150Dic6C2×Q812yes—
151C3×C8—22no—
152C3⋊C8—22no—
153#41—34no—
154#41—62no—
155C2×Q8—21no—
156C2×Q8—31no—
157C2×Q8—61no—
158C2×D4—61no—
159C2×D4C22×D311yescharacteristic
160C22×C4—21no—
161C22×C4—31no—
162C22×C4—31no—
163C22×C4—31no—
164C22×C4—61no—
165C22×C4—61no—
166C2×C8—32no—
167C2×C8—64no—
168C2×C8C22×D312yes—
169C4⋊C4—21no—
170C4⋊C4—32no—
171C4⋊C4—31no—
172C4⋊C4—61no—
173C4⋊C4—62no—
174C4⋊C4—62no—
175C4⋊C4—61no—
176C4⋊C4—61no—
177C4⋊C4C22×D312yes—
178C4⋊C4C22×D311yescharacteristic
179C22⋊C4—21no—
180C22⋊C4—61no—
181C22⋊C4—62no—
182C22⋊C4—61no—
183C42—31no—
184C42—31no—
185C42—31no—
186C42—61no—
187C42—61no—
188C42—62no—
189C42—61no—
190C42C22×D311yescharacteristic
191C22×C3—22no—
192C22×C3—41no—
193C22×C3—41no—
194C22×C3C22×D411yescharacteristic
195C2×D3—21no—
196C2×D3—21no—
197C2×D3C22⋊Q812yes—
198C3×C4—21no—
199C3×C4—41no—
200C3×C4—42no—
201C3×C4#13512yes—
202C3×C4C22×Q811yescharacteristic
203C3×C4C2×#4111yescharacteristic
204Dic3—22no—
205Dic3—21no—
206Dic3—21no—
207Dic3—42no—
208Dic3—41no—
209Dic3C22⋊Q812yes—
210C23—21no—
211C23—31no—
212Q8—32no—
213Q8—42no—
214Q8—61no—
215Q8—122no—
216D4—21no—
217D4—64no—
218D4D3×Q812yes—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—31no—
222C2×C4—32no—
223C2×C4—32no—
224C2×C4—31no—
225C2×C4—31no—
226C2×C4—42no—
227C2×C4—64no—
228C2×C4—61no—
229C2×C4—62no—
230C2×C4—61no—
231C2×C4—62no—
232C2×C4—121no—
233C2×C4—122no—
234C2×C4D3×D411yescharacteristic
235C2×C4D3×D411yescharacteristic
236C2×C4C23×D311yescharacteristic
237C8—22no—
238C8—62no—
239C2×C3—42no—
240C2×C3C2×C22⋊Q811yescharacteristic
241C2×C3C2×#13511yescharacteristic
242C2×C3#57511yescharacteristic
243D3—22no—
244C22—22no—
245C22—32no—
246C22—41no—
247C22—41no—
248C22—61no—
249C22—61no—
250C22C2×D3×D411yescharacteristic
251C4—21no—
252C4—32no—
253C4—41no—
254C4—42no—
255C4—61no—
256C4—61no—
257C4—62no—
258C4—121no—
259C4—122no—
260C4#91212yes—
261C4C2×D3×Q811yescharacteristic
262C4D3×#4111yescharacteristic
263C3#307611yescharacteristic, complemented, Sylow
264C2—42no—
265C2—62no—
266C2D3×C22⋊Q811yescharacteristic
267C2C2×#91211yescharacteristic
268C2#577711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#474C2
socleC22×C3C22×D4
prime radicalC2×#237C22
hypercenter#474D3
hypocenterC3#3076
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. #5094C2semidirect
5. #5008C2semidirect
6. #4880C2semidirect
7. #4877C2semidirect
8. #4850C2semidirect
9. D3×C4⋊C8C2semidirect
11. #4766C2semidirect
51. #474D3semidirect
62. #237Q8semidirect
263. C3#3076semidirect

Maximal subgroups

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

subgroupindex
#57282
C4×#2372
C3×#4742
#50942
#50082
#48802
#48772
#48502
D3×C4⋊C82
#47722
#47662
#30763