Finite Group Databasebeta

← #81876

Subgroups — #81876

Order 384.

386 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 113 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×C4⋊Q8C211yesmaximal, characteristic, complemented
2#5680C211yesmaximal, characteristic
3C3×#497C211yesmaximal, characteristic, complemented
4#5186C212yesmaximal, complemented
5#5182C212yesmaximal, complemented
6#5170C212yesmaximal
7#5162C212yesmaximal, complemented
8#5082C211yesmaximal, characteristic, complemented
9#5060C211yesmaximal, characteristic, complemented
10#4705C211yesmaximal, characteristic, complemented
11#4703C211yesmaximal, characteristic, complemented
12#3218—31nomaximal, Sylow
13C2×D3×Q8C2212yes—
14C2×C3×Q16C2212yes—
15C2×C3×SD16C2212yes—
16C3×C4⋊Q8C2211yescharacteristic
17C3×#124C2211yescharacteristic
18#946C2211yescharacteristic
19Q8×Dic3C2211yescharacteristic
20#944C2212yes—
21C2×#216C2212yes—
22#938C2211yescharacteristic
23D4×Dic3C2211yescharacteristic
24C2×#214C2212yes—
25D3×C4⋊C4—21no—
26D3×C4⋊C4—21no—
27#888—21no—
28#888—21no—
29#883—21no—
30#67⋊C4—21no—
31#879—21no—
32#877—21no—
33C42×D3C2211yescharacteristic
34#870C2211yescharacteristic
35#869C2211yescharacteristic
36C3×#97C2211yescharacteristic
37#835C2212yes—
38#835C2212yes—
39(C2×D3)⋊C8C2212yes—
40#816C2212yes—
41#816C2212yes—
42Dic3⋊C8C2212yes—
43#803C2211yescharacteristic
44C2×C4⋊Q8—31no—
45#529—31no—
46#497—31no—
47#497D311yescharacteristic, complemented
48#491—31no—
49#491—31no—
50#462—32no—
51#461—32no—
52#451—32no—
53#448—32no—
54#432—31no—
55C2×C3×Q8C2312yes—
56C2×C3×Q8C2311yescharacteristic
57C2×C3×D4C2311yescharacteristic
58C2×#67—21no—
59C22×Dic3—21no—
60D3×Q8—42no—
61D3×Q8—42no—
62C2×C4×D3—22no—
63C2×C4×D3D411yescharacteristic
64C2×C4×D3D411yescharacteristic
65C2×C4×D3C2311yescharacteristic
66C2×Dic6—22no—
67C2×Dic6C2312yes—
68C3×Q16—42no—
69C3×SD16—42no—
70C2×C3×C8C2312yes—
71C3×C4⋊C4—21no—
72C3×C4⋊C4—21no—
73C3×C22⋊C4—21no—
74C3×C22⋊C4—21no—
75C3×C42C2311yescharacteristic
76#217—21no—
77#217—21no—
78#216—42no—
79#214—42no—
80(C2×D3)⋊C4—21no—
81C4⋊Dic3—21no—
82C4⋊Dic3—21no—
83C4⋊Dic3—21no—
84C4⋊Dic3C2311yescharacteristic
85C4⋊Dic3C2311yescharacteristic
86Dic3⋊C4—21no—
87Dic3⋊C4—21no—
88Dic3⋊C4—21no—
89Dic3⋊C4—22no—
90Dic3⋊C4—22no—
91C4×Dic3—21no—
92C4×Dic3D411yescharacteristic
93C4×Dic3D411yescharacteristic
94C4×Dic3C2311yescharacteristic
95C2×C3⋊C8C2312yes—
96C22×Q8—32no—
97C2×Q16—32no—
98C2×Q16C2×D312yes—
99C2×SD16—32no—
100C2×SD16C2×D312yes—
101C4⋊Q8—32no—
102C4⋊Q8—31no—
103C4⋊Q8—61no—
104C4⋊Q8—61no—
105C4⋊Q8C2×D311yescharacteristic
106#126—61no—
107#125—31no—
108#124C2×D311yescharacteristic
109#123—61no—
110C22⋊Q8—31no—
111#121—31no—
112C4×Q8—31no—
113C4×D4—31no—
114C4×D4—61no—
115#117—61no—
116C2×C4⋊C4—61no—
117C2×C4⋊C4—61no—
118C2×C42—31no—
119C4⋊C8—32no—
120#103—32no—
121#103—32no—
122#103—32no—
123#103—32no—
124C22⋊C8—32no—
125#97—31no—
126#97C2×D311yescharacteristic
127C23×C3—21no—
128C22×D3C2×D411yescharacteristic
129C3×Q8—22no—
130C3×Q8—22no—
131C3×Q8—22no—
132C3×D4—22no—
133C2×C3×C4—21no—
134C2×C3×C4—22no—
135C2×C3×C4C2×D411yescharacteristic
136C2×C3×C4C2×D411yescharacteristic
137C2×C3×C4C2411yescharacteristic
138#67—42no—
139C2×Dic3—21no—
140C2×Dic3—21no—
141C2×Dic3—22no—
142C2×Dic3—42no—
143C2×Dic3C2×D411yescharacteristic
144C2×Dic3C2×D411yescharacteristic
145C2×Dic3C2×D411yescharacteristic
146C4×D3—22no—
147C4×D3—22no—
148C4×D3—22no—
149C4×D3—44no—
150Dic6—22no—
151Dic6—22no—
152Dic6—44no—
153C3×C8—22no—
154C3⋊C8—22no—
155C2×Q8—32no—
156C2×Q8—62no—
157C2×Q8—122no—
158C2×Q8—122no—
159C2×Q8C22×D312yes—
160C2×Q8C22×D311yescharacteristic
161C2×D4—61no—
162C2×D4C22×D311yescharacteristic
163C22×C4—31no—
164C22×C4—31no—
165C22×C4—31no—
166C22×C4—62no—
167C22×C4—61no—
168Q16—42no—
169Q16—122no—
170SD16—42no—
171SD16—122no—
172C2×C8—32no—
173C2×C8C22×D312yes—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—31no—
177C4⋊C4—31no—
178C4⋊C4—62no—
179C4⋊C4—62no—
180C4⋊C4—61no—
181C4⋊C4—61no—
182C4⋊C4—61no—
183C4⋊C4—61no—
184C4⋊C4—61no—
185C4⋊C4—61no—
186C22⋊C4—21no—
187C22⋊C4—21no—
188C22⋊C4—61no—
189C22⋊C4—61no—
190C22⋊C4—61no—
191C42—31no—
192C42—31no—
193C42—31no—
194C42—61no—
195C42C22×D311yescharacteristic
196C22×C3—41no—
197C22×C3—41no—
198C22×C3—41no—
199C22×C3C22×D411yescharacteristic
200C2×D3—21no—
201C2×D3—21no—
202C2×D3#13712yes—
203C3×C4—21no—
204C3×C4—21no—
205C3×C4—42no—
206C3×C4—41no—
207C3×C4H(5,𝔽2)12yes—
208Dic3—21no—
209Dic3—21no—
210Dic3—42no—
211Dic3—41no—
212Dic3—41no—
213Dic3#13712yes—
214C23—21no—
215C23—31no—
216Q8—22no—
217Q8—22no—
218Q8—22no—
219Q8—62no—
220Q8—62no—
221Q8—124no—
222D4—22no—
223D4—122no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—31no—
227C2×C4—31no—
228C2×C4—31no—
229C2×C4—62no—
230C2×C4—62no—
231C2×C4—62no—
232C2×C4—61no—
233C2×C4—61no—
234C2×C4—62no—
235C2×C4—122no—
236C2×C4—124no—
237C2×C4D3×D411yescharacteristic
238C2×C4D3×D411yescharacteristic
239C2×C4C23×D311yescharacteristic
240C8—22no—
241C8—62no—
242C2×C3—81no—
243C2×C3#53511yescharacteristic
244C2×C3C2×#13711yescharacteristic
245C2×C3C2×#13711yescharacteristic
246D3—22no—
247C22—32no—
248C22—41no—
249C22—41no—
250C22—41no—
251C22—61no—
252C22—61no—
253C22C2×D3×D411yescharacteristic
254C4—21no—
255C4—21no—
256C4—32no—
257C4—42no—
258C4—41no—
259C4—61no—
260C4—61no—
261C4—122no—
262C4—121no—
263C4—121no—
264C4#100412yes—
265C3#321811yescharacteristic, complemented, Sylow
266C2—62no—
267C2—81no—
268C2#571511yescharacteristic
269C2D3×#13711yescharacteristic
270C2D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#497C2
socleC22×C3C22×D4
prime radical#938C22
hypercenter#497D3
hypocenterC3#3218
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. D3×C4⋊Q8C2semidirect
3. C3×#497C2semidirect
4. #5186C2semidirect
5. #5182C2semidirect
7. #5162C2semidirect
8. #5082C2semidirect
9. #5060C2semidirect
10. #4705C2semidirect
11. #4703C2semidirect
47. #497D3semidirect
265. C3#3218semidirect

Maximal subgroups

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

subgroupindex
D3×C4⋊Q82
#56802
C3×#4972
#51862
#51822
#51702
#51622
#50822
#50602
#47052
#47032
#32183