Finite Group Databasebeta

← #79130

Subgroups — #79130

Order 384.

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

normal subgroups only

This group has 376 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#5504C211yesmaximal, characteristic
2#5500C211yesmaximal, characteristic, complemented
3C2×C3×#106C211yesmaximal, characteristic, complemented
4#5113C211yesmaximal, characteristic
5#5102C211yesmaximal, characteristic, complemented
6#4966C211yesmaximal, characteristic
7#4964C211yesmaximal, characteristic, complemented
8#4871C212yesmaximal, complemented
9#4870C212yesmaximal, complemented
10#4857C212yesmaximal, complemented
11#4854C212yesmaximal, complemented
12#3084—31nomaximal, Sylow
13C2×#235C2211yescharacteristic
14C22×C3×C8C2211yescharacteristic
15C2×C3×C4⋊C4C2211yescharacteristic
16C2×C3×C4⋊C4C2211yescharacteristic
17C4×#67—22no—
18#926C2211yescharacteristic
19#926C2211yescharacteristic
20#924—22no—
21C2×#208C2211yescharacteristic
22#893C2212yes—
23#892—21no—
24D3×C4⋊C4—21no—
25#890—21no—
26#890C2212yes—
27#888—21no—
28#888C2212yes—
29#887C2212yes—
30C3×#106C2212yes—
31C3×#106C2212yes—
32#821C2211yescharacteristic
33#821C2211yescharacteristic
34#816C2211yescharacteristic
35#816C2211yescharacteristic
36Dic3⋊C8C2212yes—
37Dic3⋊C8C2212yes—
38#810C2212yes—
39#809C2212yes—
40#808C2212yes—
41#807C2212yes—
42#544—31no—
43#520—31no—
44#479—32no—
45#478—32no—
46#476—32no—
47#475—32no—
48#428—31no—
49C2×#106D311yescharacteristic, complemented
50#424—31no—
51#417—31no—
52#416—31no—
53C22×C3×C4—21no—
54C22×C3×C4—21no—
55C22×C3×C4C2311yescharacteristic
56C2×#67—21no—
57#235—22no—
58#235Q814yescomplemented
59C2×D12C2311yescharacteristic
60C2×C4×D3—21no—
61C2×C4×D3—22no—
62C2×Dic6—22no—
63C2×Dic6C2311yescharacteristic
64C2×C3×C8—22no—
65C2×C3×C8C2311yescharacteristic
66C2×C3×C8C2311yescharacteristic
67C3×C4⋊C4—21no—
68C3×C4⋊C4—21no—
69C3×C4⋊C4C2312yes—
70C3×C4⋊C4C2312yes—
71#217—21no—
72#217D412yes—
73(C2×D3)⋊C4—22no—
74C4⋊Dic3—22no—
75C4⋊Dic3D411yescharacteristic
76C4⋊Dic3D411yescharacteristic
77C4⋊Dic3C2311yescharacteristic
78C4⋊Dic3C2311yescharacteristic
79Dic3⋊C4—22no—
80Dic3⋊C4—22no—
81Dic3⋊C4—22no—
82C4×Dic3—21no—
83C4×Dic3—22no—
84C4×Dic3C2312yes—
85#208—22no—
86C2×C3⋊C8C2312yes—
87C2×#41—31no—
88C2×M16—31no—
89C22×C8C2×D311yescharacteristic
90C4⋊Q8—32no—
91C4⋊Q8—61no—
92#125—32no—
93#125—61no—
94C22⋊Q8—62no—
95C4×Q8—32no—
96C4×D4—32no—
97C4×D4—62no—
98#117—31no—
99#117—31no—
100#117—61no—
101C2×C4⋊C4—61no—
102C2×C4⋊C4C2×D311yescharacteristic
103C2×C4⋊C4C2×D311yescharacteristic
104#107—32no—
105#106—32no—
106#106C2×D312yes—
107#106C2×D312yes—
108C4⋊C8—32no—
109C4⋊C8—32no—
110#103—31no—
111#103—31no—
112#103—32no—
113#102—31no—
114#102—31no—
115#102—32no—
116C23×C3C2×D411yescharacteristic
117C22×D3—21no—
118C2×C3×C4—22no—
119C2×C3×C4—22no—
120C2×C3×C4—81no—
121C2×C3×C4—81no—
122C2×C3×C4C2×D411yescharacteristic
123C2×C3×C4C2×Q812yes—
124C2×C3×C4#4112yes—
125C2×C3×C4C2411yescharacteristic
126#67—24no—
127C2×Dic3—21no—
128C2×Dic3—21no—
129C2×Dic3—21no—
130C2×Dic3C2×D412yes—
131C2×Dic3C2×D412yes—
132D12—21no—
133D12C2×Q812yes—
134C4×D3—24no—
135C4×D3—82no—
136Dic6—21no—
137Dic6—82no—
138Dic6C2×Q812yes—
139C3×C8—21no—
140C3×C8—21no—
141C3⋊C8—22no—
142#41—34no—
143#41—62no—
144C2×Q8—31no—
145C2×Q8—62no—
146C2×D4—31no—
147C2×D4—61no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—62no—
151C22×C4—61no—
152C22×C4C22×D311yescharacteristic
153M16—62no—
154C2×C8—22no—
155C2×C8—32no—
156C2×C8C22×D311yescharacteristic
157C2×C8C22×D311yescharacteristic
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—31no—
161C4⋊C4—31no—
162C4⋊C4—31no—
163C4⋊C4—31no—
164C4⋊C4—62no—
165C4⋊C4—62no—
166C4⋊C4—62no—
167C4⋊C4—62no—
168C4⋊C4C22×D312yes—
169C4⋊C4C22×D312yes—
170C22⋊C4—32no—
171C22⋊C4—62no—
172C22⋊C4—61no—
173C42—32no—
174C42—62no—
175C42—61no—
176C22×C3—21no—
177C22×C3—21no—
178C22×C3C22⋊Q812yes—
179C22×C3C22×D411yescharacteristic
180C2×D3—22no—
181C2×D3—41no—
182C2×D3—41no—
183C3×C4—42no—
184C3×C4—42no—
185C3×C4C22⋊Q812yes—
186C3×C4C22×Q811yescharacteristic
187C3×C4C2×#4111yescharacteristic
188Dic3—22no—
189Dic3—22no—
190Dic3—22no—
191Dic3—41no—
192Dic3—41no—
193C23—61no—
194C23D3×D411yescharacteristic
195Q8—32no—
196Q8—61no—
197Q8—242no—
198D4—32no—
199D4—64no—
200D4—61no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—32no—
204C2×C4—32no—
205C2×C4—61no—
206C2×C4—64no—
207C2×C4—61no—
208C2×C4—61no—
209C2×C4—81no—
210C2×C4—81no—
211C2×C4—242no—
212C2×C4#23512yes—
213C2×C4D3×D411yescharacteristic
214C2×C4D3×Q812yes—
215C2×C4C23×D311yescharacteristic
216C8—21no—
217C8—21no—
218C8—62no—
219C2×C3—22no—
220C2×C3C2×C22⋊Q811yescharacteristic
221C2×C3#57711yescharacteristic
222C2×C3#57711yescharacteristic
223D3—42no—
224C22—21no—
225C22—21no—
226C22—62no—
227C22—121no—
228C22—121no—
229C22#89612yes—
230C22C2×D3×D411yescharacteristic
231C4—42no—
232C4—42no—
233C4—62no—
234C4—62no—
235C4—62no—
236C4—121no—
237C4—121no—
238C4#89612yes—
239C4C2×#23511yescharacteristic
240C4C2×D3×Q811yescharacteristic
241C3#308411yescharacteristic, complemented, Sylow
242C2—22no—
243C2—122no—
244C2C2×#89611yescharacteristic
245C2#576211yescharacteristic
246C2#576211yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC2×C3×#106C2
socleC22×C3C22×D4
prime radicalC2×#235C22
hypercenterC2×#106D3
hypocenterC3#3084
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. #5500C2semidirect
3. C2×C3×#106C2semidirect
5. #5102C2semidirect
7. #4964C2semidirect
8. #4871C2semidirect
9. #4870C2semidirect
10. #4857C2semidirect
11. #4854C2semidirect
49. C2×#106D3semidirect
58. #235Q8semidirect
241. C3#3084semidirect

Maximal subgroups

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

subgroupindex
#55042
#55002
C2×C3×#1062
#51132
#51022
#49662
#49642
#48712
#48702
#48572
#48542
#30843