Finite Group Databasebeta

← #80632

Subgroups — #80632

Order 384.

412 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5622C211yesmaximal, characteristic, complemented
2#5596C211yesmaximal, characteristic
3C3×#465C211yesmaximal, characteristic, complemented
4#5175C211yesmaximal, characteristic, complemented
5Dic3×SD16C211yesmaximal, characteristic, complemented
6#5114C211yesmaximal, characteristic, complemented
7C2×C8×Dic3C211yesmaximal, characteristic, complemented
8#5048C211yesmaximal, characteristic, complemented
9#5041C211yesmaximal, characteristic, complemented
10#4855C211yesmaximal, characteristic, complemented
11#4852C211yesmaximal, characteristic, complemented
12#4792C211yesmaximal, characteristic, complemented
13#4788C211yesmaximal, characteristic, complemented
14#4760C211yesmaximal, characteristic, complemented
15#4758C211yesmaximal, characteristic, complemented
16#3167—31nomaximal, Sylow
17C2×#237—21no—
18C2×C3×SD16C2211yescharacteristic
19C22×C3×C8C2211yescharacteristic
20C3×C22⋊Q8C2211yescharacteristic
21C3×#121C2211yescharacteristic
22Q8×Dic3C2211yescharacteristic
23#944C2211yescharacteristic
24C2×#215C2211yescharacteristic
25#940C2211yescharacteristic
26#939—21no—
27D4×Dic3C2211yescharacteristic
28C2×#214C2211yescharacteristic
29#930C2211yescharacteristic
30#924C2211yescharacteristic
31C2×C4×Dic3C2211yescharacteristic
32C22×C3⋊C8C2211yescharacteristic
33C2×#204C2211yescharacteristic
34#893C2211yescharacteristic
35#889—21no—
36#888C2211yescharacteristic
37#888C2211yescharacteristic
38#887—21no—
39#887C2211yescharacteristic
40#885—21no—
41#67⋊C4—21no—
42#878—21no—
43#877—21no—
44C3×#106C2211yescharacteristic
45C3×#103C2211yescharacteristic
46C3×#102C2211yescharacteristic
47#835C2211yescharacteristic
48#832C2211yescharacteristic
49#821C2211yescharacteristic
50#817C2211yescharacteristic
51#816C2211yescharacteristic
52C8×Dic3C2211yescharacteristic
53C8×Dic3C2211yescharacteristic
54C8×Dic3C2211yescharacteristic
55C8×Dic3C2211yescharacteristic
56#810C2211yescharacteristic
57#809C2211yescharacteristic
58#808C2211yescharacteristic
59#808C2211yescharacteristic
60#533—31no—
61#532—31no—
62#498—31no—
63#492—31no—
64#487—31no—
65#486—31no—
66#465—31no—
67#465—31no—
68#465—31no—
69#465D311yescharacteristic, complemented
70C4×SD16—31no—
71C4×SD16—31no—
72C4×SD16—31no—
73C4×SD16—31no—
74C2×C4×C8—31no—
75C2×C3×Q8C2311yescharacteristic
76C2×C3×D4—21no—
77C2×C3×D4C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C2×#67—21no—
80C2×#67—21no—
81C2×#67—21no—
82C22×Dic3—21no—
83C22×Dic3D411yescharacteristic
84C22×Dic3D411yescharacteristic
85#237—44no—
86C2×D12C2311yescharacteristic
87C2×C4×D3—21no—
88C2×Dic6—21no—
89C2×Dic6—21no—
90C2×Dic6C2311yescharacteristic
91C3×SD16—22no—
92C2×C3×C8—22no—
93C2×C3×C8C2311yescharacteristic
94C2×C3×C8C2311yescharacteristic
95C3×C4⋊C4—21no—
96C3×C4⋊C4C2311yescharacteristic
97C3×C4⋊C4C2311yescharacteristic
98C3×C22⋊C4—21no—
99C3×C22⋊C4—21no—
100#217—21no—
101#217—21no—
102#215—22no—
103#214—22no—
104(C2×D3)⋊C4—21no—
105(C2×D3)⋊C4—21no—
106C4⋊Dic3—21no—
107C4⋊Dic3C2311yescharacteristic
108C4⋊Dic3C2311yescharacteristic
109Dic3⋊C4—21no—
110Dic3⋊C4—21no—
111Dic3⋊C4—21no—
112Dic3⋊C4—21no—
113Dic3⋊C4—21no—
114Dic3⋊C4—21no—
115C4×Dic3—21no—
116C4×Dic3—21no—
117C4×Dic3D411yescharacteristic
118C4×Dic3D411yescharacteristic
119C4×Dic3C2311yescharacteristic
120C4×Dic3C2311yescharacteristic
121C2×C3⋊C8—22no—
122C2×C3⋊C8C2311yescharacteristic
123C2×C3⋊C8C2311yescharacteristic
124#204—22no—
125C2×#41—61no—
126C2×SD16—31no—
127C2×SD16—31no—
128C2×SD16—31no—
129C2×SD16C2×D311yescharacteristic
130C22×C8—31no—
131C22×C8C2×D311yescharacteristic
132C4⋊Q8—31no—
133C4⋊Q8—31no—
134C4⋊Q8—31no—
135#127—31no—
136#125—61no—
137#124—61no—
138C22⋊Q8—31no—
139C22⋊Q8—61no—
140C22⋊Q8C2×D311yescharacteristic
141#121—31no—
142#121—61no—
143#121C2×D311yescharacteristic
144C4×Q8—31no—
145C4×Q8—31no—
146C4×Q8—61no—
147C4×D4—31no—
148C4×D4—31no—
149C4×D4—61no—
150#117—61no—
151C2×C42—31no—
152#106—31no—
153#106—31no—
154#106—31no—
155#106C2×D311yescharacteristic
156#103—31no—
157#103—31no—
158#103—31no—
159#103C2×D311yescharacteristic
160#102—31no—
161#102—31no—
162#102—31no—
163#102C2×D311yescharacteristic
164C4×C8—31no—
165C4×C8—31no—
166C4×C8—31no—
167C4×C8—31no—
168C23×C3—21no—
169C23×C3C2×D411yescharacteristic
170C22×D3—21no—
171C3×Q8—21no—
172C3×Q8—21no—
173C3×D4—21no—
174C3×D4—21no—
175C3×D4—42no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4C2×D411yescharacteristic
182C2×C3×C4C2411yescharacteristic
183#67—42no—
184#67—42no—
185#67—42no—
186C2×Dic3—22no—
187C2×Dic3—21no—
188C2×Dic3—21no—
189C2×Dic3—21no—
190C2×Dic3—42no—
191C2×Dic3SD1614yescomplemented
192C2×Dic3C2×D411yescharacteristic
193C2×Dic3C2×D411yescharacteristic
194C2×Dic3C2×D411yescharacteristic
195C2×Dic3C2×D411yescharacteristic
196D12—21no—
197D12—21no—
198C4×D3—42no—
199Dic6—21no—
200Dic6—21no—
201Dic6—42no—
202Dic6—42no—
203C3×C8—21no—
204C3×C8#4112yescomplemented
205C3⋊C8—21no—
206C3⋊C8#4112yescomplemented
207#41—124no—
208C2×Q8—31no—
209C2×Q8—61no—
210C2×Q8—61no—
211C2×Q8C22×D311yescharacteristic
212C2×D4—21no—
213C2×D4—31no—
214C2×D4—61no—
215C2×D4—61no—
216C2×D4—61no—
217C2×D4C22×D311yescharacteristic
218C22×C4—31no—
219C22×C4—31no—
220C22×C4—61no—
221C22×C4—61no—
222C22×C4C22×D311yescharacteristic
223SD16—22no—
224SD16—62no—
225SD16—62no—
226SD16—62no—
227C2×C8—22no—
228C2×C8—31no—
229C2×C8—31no—
230C2×C8—62no—
231C2×C8C22×D311yescharacteristic
232C2×C8C22×D311yescharacteristic
233C4⋊C4—21no—
234C4⋊C4—31no—
235C4⋊C4—31no—
236C4⋊C4—61no—
237C4⋊C4—61no—
238C4⋊C4—61no—
239C4⋊C4—61no—
240C4⋊C4—61no—
241C4⋊C4—61no—
242C4⋊C4—61no—
243C4⋊C4C22×D311yescharacteristic
244C4⋊C4C22×D311yescharacteristic
245C22⋊C4—21no—
246C22⋊C4—21no—
247C22⋊C4—61no—
248C22⋊C4—61no—
249C22⋊C4—61no—
250C22⋊C4—61no—
251C42—31no—
252C42—31no—
253C42—31no—
254C42—31no—
255C42—61no—
256C42—61no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—41no—
260C22×C3—41no—
261C22×C3—41no—
262C22×C3C2×SD1612yes—
263C22×C3C22×D411yescharacteristic
264C2×D3—41no—
265C2×D3—41no—
266C2×D3—41no—
267C3×C4—21no—
268C3×C4—41no—
269C3×C4—41no—
270C3×C4—41no—
271C3×C4C2×#4111yescharacteristic
272C3×C4C2×#4111yescharacteristic
273Dic3—21no—
274Dic3—41no—
275Dic3—41no—
276Dic3—41no—
277Dic3C2×SD1612yes—
278Dic3C2×SD1612yes—
279Dic3#13512yes—
280C23—21no—
281C23—61no—
282C23D3×D411yescharacteristic
283Q8—21no—
284Q8—21no—
285Q8—61no—
286Q8—61no—
287Q8—122no—
288Q8—122no—
289D4—21no—
290D4—21no—
291D4—42no—
292D4—61no—
293D4—61no—
294D4—122no—
295D4—122no—
296D4—122no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—34no—
303C2×C4—31no—
304C2×C4—31no—
305C2×C4—31no—
306C2×C4—31no—
307C2×C4—62no—
308C2×C4—61no—
309C2×C4—61no—
310C2×C4—61no—
311C2×C4—122no—
312C2×C4—122no—
313C2×C4D3×D411yescharacteristic
314C2×C4C23×D311yescharacteristic
315C8—21no—
316C8—32no—
317C8—61no—
318C8#23712yescomplemented
319C2×C3—22no—
320C2×C3—81no—
321C2×C3#53211yescharacteristic
322C2×C3C22×SD1611yescharacteristic
323C2×C3C2×#13511yescharacteristic
324D3—81no—
325C22—21no—
326C22—21no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—121no—
331C22—121no—
332C22—121no—
333C22D3×SD1612yes—
334C22C2×D3×D411yescharacteristic
335C4—21no—
336C4—32no—
337C4—32no—
338C4—32no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—61no—
343C4—121no—
344C4—121no—
345C4—121no—
346C4C2×#23711yescharacteristic
347C4D3×#4111yescharacteristic
348C3#316711yescharacteristic, complemented, Sylow
349C2—22no—
350C2—81no—
351C2—241no—
352C2#559611yescharacteristic
353C2C2×D3×SD1611yescharacteristic
354C2D3×#13511yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#465C2
socleC22×C3C22×D4
prime radical#5596C2
hypercenter#465D3
hypocenterC3#3167
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #5622C2semidirect
3. C3×#465C2semidirect
4. #5175C2semidirect
5. Dic3×SD16C2semidirect
6. #5114C2semidirect
7. C2×C8×Dic3C2semidirect
8. #5048C2semidirect
9. #5041C2semidirect
10. #4855C2semidirect
11. #4852C2semidirect
12. #4792C2semidirect
13. #4788C2semidirect
14. #4760C2semidirect
15. #4758C2semidirect
69. #465D3semidirect
191. C2×Dic3SD16semidirect
204. C3×C8#41semidirect
206. C3⋊C8#41semidirect
318. C8#237semidirect
348. C3#3167semidirect

Maximal subgroups

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

subgroupindex
#56222
#55962
C3×#4652
#51752
Dic3×SD162
#51142
C2×C8×Dic32
#50482
#50412
#48552
#48522
#47922
#47882
#47602
#47582
#31673