Finite Group Databasebeta

← #80179

Subgroups — #80179

Order 384.

386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C2×#944C211yesmaximal, characteristic, complemented
2#5624C211yesmaximal, characteristic
3C3×#451C211yesmaximal, characteristic, complemented
4#5227C211yesmaximal, characteristic
5#5190C212yesmaximal, complemented
6#5182C212yesmaximal, complemented
7#5050C211yesmaximal, characteristic, complemented
8#4818C212yesmaximal, complemented
9#4797C212yesmaximal, complemented
10#4738C211yesmaximal, characteristic
11#4719C211yesmaximal, characteristic, complemented
12#3218—31nomaximal, Sylow
13C22×C3×Q8C2211yescharacteristic
14C22×Dic6C2211yescharacteristic
15C2×C3×Q16C2212yes—
16C3×C22⋊Q8C2211yescharacteristic
17#947C2211yescharacteristic
18Q8×Dic3C2211yescharacteristic
19#944—21no—
20#944—21no—
21#944C2212yes—
22#944C2212yes—
23C2×#216C2212yes—
24C2×#215C2212yes—
25#930C2211yescharacteristic
26C2×Dic3⋊C4—21no—
27C2×Dic3⋊C4—21no—
28C2×C4×Dic3C2211yescharacteristic
29C2×#204C2212yes—
30#898—21no—
31#893C2211yescharacteristic
32#892—21no—
33#890C2211yescharacteristic
34#886—21no—
35#67⋊C4—21no—
36C3×#103C2212yes—
37C3×C22⋊C8C2211yescharacteristic
38#835C2212yes—
39#830C2211yescharacteristic
40#816C2212yes—
41#815C2212yes—
42Dic3⋊C8C2212yes—
43#810C2212yes—
44C2×C4⋊Q8—31no—
45#529—31no—
46#497—32no—
47#491—32no—
48#462—32no—
49#461—32no—
50#451—31no—
51#451D311yescharacteristic, complemented
52#448—31no—
53#448—31no—
54#432—31no—
55C2×C3×Q8—21no—
56C2×C3×Q8—42no—
57C2×C3×Q8C2312yes—
58C2×C3×Q8C2311yescharacteristic
59C22×C3×C4—21no—
60C22×C3×C4C2311yescharacteristic
61C2×#67—21no—
62C22×Dic3—21no—
63C22×Dic3D411yescharacteristic
64C22×Dic3D411yescharacteristic
65C2×D12C2311yescharacteristic
66C2×C4×D3—21no—
67C2×Dic6—21no—
68C2×Dic6—42no—
69C2×Dic6C2312yes—
70C3×Q16—42no—
71C2×C3×C8C2312yes—
72C3×C4⋊C4—21no—
73C3×C4⋊C4C2311yescharacteristic
74C3×C22⋊C4—21no—
75#216—42no—
76#215—42no—
77(C2×D3)⋊C4—21no—
78(C2×D3)⋊C4—21no—
79(C2×D3)⋊C4—21no—
80(C2×D3)⋊C4—21no—
81C4⋊Dic3—21no—
82C4⋊Dic3—21no—
83C4⋊Dic3C2311yescharacteristic
84Dic3⋊C4—21no—
85Dic3⋊C4—22no—
86Dic3⋊C4—22no—
87Dic3⋊C4—22no—
88Dic3⋊C4—22no—
89C4×Dic3—21no—
90C4×Dic3D411yescharacteristic
91C4×Dic3D411yescharacteristic
92C4×Dic3C2311yescharacteristic
93C4×Dic3C2311yescharacteristic
94C2×C3⋊C8C2312yes—
95#204—42no—
96C22×Q8—31no—
97C22×Q8C2×D311yescharacteristic
98C2×Q16—32no—
99C2×Q16C2×D312yes—
100C2×SD16—32no—
101C2×SD16—32no—
102C4⋊Q8—32no—
103C4⋊Q8—32no—
104C4⋊Q8—61no—
105C4⋊Q8—61no—
106#126—61no—
107#125—31no—
108#124—31no—
109#123—61no—
110C22⋊Q8C2×D311yescharacteristic
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#103C2×D312yes—
124C22⋊C8—31no—
125C22⋊C8C2×D311yescharacteristic
126#97—32no—
127C23×C3C2×D411yescharacteristic
128C22×D3—21no—
129C3×Q8—22no—
130C3×Q8—22no—
131C3×Q8—22no—
132C3×Q8—42no—
133C2×C3×C4—22no—
134C2×C3×C4—21no—
135C2×C3×C4—22no—
136C2×C3×C4—21no—
137C2×C3×C4—42no—
138C2×C3×C4C2×D411yescharacteristic
139C2×C3×C4C2411yescharacteristic
140#67—42no—
141C2×Dic3—22no—
142C2×Dic3—22no—
143C2×Dic3—21no—
144C2×Dic3—22no—
145C2×Dic3—42no—
146C2×Dic3C2×D411yescharacteristic
147C2×Dic3C2×D411yescharacteristic
148C2×Dic3C2×D411yescharacteristic
149C2×Dic3C2×D411yescharacteristic
150D12—22no—
151C4×D3—42no—
152Dic6—22no—
153Dic6—22no—
154Dic6—42no—
155C3×C8—22no—
156C3⋊C8—22no—
157C2×Q8—21no—
158C2×Q8—32no—
159C2×Q8—42no—
160C2×Q8—61no—
161C2×Q8—122no—
162C2×Q8C22×D312yes—
163C2×Q8C22×D311yescharacteristic
164C2×D4—31no—
165C2×D4—61no—
166C22×C4—21no—
167C22×C4—31no—
168C22×C4—31no—
169C22×C4—61no—
170C22×C4—61no—
171C22×C4C22×D311yescharacteristic
172Q16—42no—
173Q16—122no—
174SD16—122no—
175SD16—122no—
176C2×C8—32no—
177C2×C8C22×D312yes—
178C4⋊C4—21no—
179C4⋊C4—31no—
180C4⋊C4—62no—
181C4⋊C4—62no—
182C4⋊C4—62no—
183C4⋊C4—62no—
184C4⋊C4—61no—
185C4⋊C4—61no—
186C4⋊C4—61no—
187C4⋊C4C22×D311yescharacteristic
188C22⋊C4—21no—
189C22⋊C4—61no—
190C22⋊C4—61no—
191C22⋊C4—61no—
192C22⋊C4—61no—
193C42—31no—
194C42—31no—
195C42—31no—
196C42—31no—
197C42—61no—
198C22×C3—21no—
199C22×C3—21no—
200C22×C3#13712yes—
201C22×C3C22×D411yescharacteristic
202C2×D3—41no—
203C2×D3—41no—
204C2×D3—41no—
205C3×C4—21no—
206C3×C4—42no—
207C3×C4—41no—
208C3×C4—41no—
209C3×C4H(5,𝔽2)12yes—
210Dic3—21no—
211Dic3—21no—
212Dic3—21no—
213Dic3—42no—
214Dic3—41no—
215Dic3#13712yes—
216C23—61no—
217C23D3×D411yescharacteristic
218Q8—22no—
219Q8—22no—
220Q8—22no—
221Q8—42no—
222Q8—62no—
223Q8—62no—
224Q8—122no—
225D4—62no—
226D4—122no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—31no—
232C2×C4—31no—
233C2×C4—31no—
234C2×C4—31no—
235C2×C4—42no—
236C2×C4—62no—
237C2×C4—62no—
238C2×C4—61no—
239C2×C4—62no—
240C2×C4—122no—
241C2×C4—122no—
242C2×C4D3×D411yescharacteristic
243C2×C4C23×D311yescharacteristic
244C8—22no—
245C8—62no—
246C2×C3—22no—
247C2×C3#53511yescharacteristic
248C2×C3C2×#13711yescharacteristic
249C2×C3C2×#13711yescharacteristic
250D3—81no—
251C22—21no—
252C22—21no—
253C22—121no—
254C22—121no—
255C22—121no—
256C22#91812yes—
257C22C2×D3×D411yescharacteristic
258C4—21no—
259C4—32no—
260C4—41no—
261C4—42no—
262C4—41no—
263C4—61no—
264C4—61no—
265C4—61no—
266C4—121no—
267C4—122no—
268C4#100412yes—
269C3#321811yescharacteristic, complemented, Sylow
270C2—22no—
271C2—241no—
272C2#559211yescharacteristic
273C2C2×#91811yescharacteristic
274C2D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#451C2
socleC22×C3C22×D4
prime radical#930C22
hypercenter#451D3
hypocenterC3#3218
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. C2×#944C2semidirect
3. C3×#451C2semidirect
5. #5190C2semidirect
6. #5182C2semidirect
7. #5050C2semidirect
8. #4818C2semidirect
9. #4797C2semidirect
11. #4719C2semidirect
51. #451D3semidirect
269. C3#3218semidirect

Maximal subgroups

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

subgroupindex
C2×#9442
#56242
C3×#4512
#52272
#51902
#51822
#50502
#48182
#47972
#47382
#47192
#32183