Finite Group Databasebeta

← #80247

Subgroups — #80247

Order 384.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5831C211yesmaximal, characteristic
2#5639C211yesmaximal, characteristic, complemented
3C3×#452C211yesmaximal, characteristic, complemented
4#5233C211yesmaximal, characteristic, complemented
5#5186C211yesmaximal, characteristic, complemented
6Dic3×Q16C211yesmaximal, characteristic, complemented
7#5171C211yesmaximal, characteristic, complemented
8#5166C211yesmaximal, characteristic, complemented
9#5051C211yesmaximal, characteristic, complemented
10D3×#103C211yesmaximal, characteristic, complemented
11#4799C211yesmaximal, characteristic, complemented
12#4774C211yesmaximal, characteristic, complemented
13#4768C211yesmaximal, characteristic, complemented
14#67⋊C8C211yesmaximal, characteristic, complemented
15#4723C211yesmaximal, characteristic, complemented
16#3300—31nomaximal, Sylow
17C2×C3×#41C2211yescharacteristic
18C2×D3×Q8C2211yescharacteristic
19C2×C3×Q16C2211yescharacteristic
20C2×C3×SD16C2211yescharacteristic
21C3×C22⋊Q8C2211yescharacteristic
22#946C2211yescharacteristic
23Q8×Dic3C2211yescharacteristic
24Q8×Dic3C2211yescharacteristic
25C2×#216C2211yescharacteristic
26#938—21no—
27#938C2211yescharacteristic
28#936—21no—
29#936C2211yescharacteristic
30C4×#67—21no—
31C4×#67C2211yescharacteristic
32#926C2211yescharacteristic
33#924—21no—
34#924C2211yescharacteristic
35C22×C3⋊C8C2211yescharacteristic
36C2×D3×C8C2211yescharacteristic
37#892—21no—
38D3×C4⋊C4C2211yescharacteristic
39#890C2211yescharacteristic
40#889—21no—
41#883—21no—
42#879—21no—
43C3×#103C2211yescharacteristic
44C3×#102C2211yescharacteristic
45C3×C22⋊C8C2211yescharacteristic
46#835C2211yescharacteristic
47#835C2211yescharacteristic
48#835C2211yescharacteristic
49#832C2211yescharacteristic
50#832C2211yescharacteristic
51(C2×D3)⋊C8C2211yescharacteristic
52#818C2211yescharacteristic
53#817C2211yescharacteristic
54#816C2211yescharacteristic
55#816C2211yescharacteristic
56Dic3⋊C8C2211yescharacteristic
57C8×Dic3C2211yescharacteristic
58#810C2211yescharacteristic
59#807C2211yescharacteristic
60#552—31no—
61#548—31no—
62#488—31no—
63#485—31no—
64#480—31no—
65#479—31no—
66#467—31no—
67#465—31no—
68#464—31no—
69#452D311yescharacteristic, complemented
70#451—31no—
71C4×Q16—31no—
72C8×D4—31no—
73#416—31no—
74C2×#103—31no—
75C3×#41—22no—
76C3×#41—41no—
77C2×C3×Q8C2311yescharacteristic
78C2×C3×Q8C2311yescharacteristic
79C2×C3×D4—21no—
80C2×C3×D4C2311yescharacteristic
81C22×C3×C4—21no—
82C22×C3×C4C2311yescharacteristic
83C2×#67—21no—
84C2×#67D411yescharacteristic
85D3×Q8—22no—
86D3×Q8—41no—
87C2×C4×D3—21no—
88C2×C4×D3—21no—
89C2×C4×D3C2311yescharacteristic
90C2×Dic6—21no—
91C2×Dic6C2311yescharacteristic
92C3×Q16—22no—
93C3×SD16—41no—
94C2×C3×C8C2311yescharacteristic
95C2×C3×C8C2311yescharacteristic
96C3×C4⋊C4—21no—
97C3×C4⋊C4C2311yescharacteristic
98C3×C22⋊C4—21no—
99#217—21no—
100#217—21no—
101#217—21no—
102#217—21no—
103#217—21no—
104#217D411yescharacteristic
105#216—41no—
106(C2×D3)⋊C4—21no—
107(C2×D3)⋊C4D411yescharacteristic
108C4⋊Dic3—21no—
109C4⋊Dic3—21no—
110C4⋊Dic3—21no—
111C4⋊Dic3C2311yescharacteristic
112C4⋊Dic3C2311yescharacteristic
113C4⋊Dic3C2311yescharacteristic
114Dic3⋊C4—21no—
115Dic3⋊C4—21no—
116Dic3⋊C4—21no—
117Dic3⋊C4—21no—
118Dic3⋊C4D411yescharacteristic
119C4×Dic3—21no—
120C4×Dic3—21no—
121C4×Dic3—21no—
122C4×Dic3C2311yescharacteristic
123C2×C3⋊C8—41no—
124C2×C3⋊C8C2311yescharacteristic
125C2×C3⋊C8C2311yescharacteristic
126D3×C8—41no—
127C2×#41C2×D311yescharacteristic
128C22×Q8—31no—
129C2×Q16—31no—
130C2×Q16C2×D311yescharacteristic
131C2×SD16C2×D311yescharacteristic
132C22×C8—31no—
133C22×C8—31no—
134#126—61no—
135#125—31no—
136#125—61no—
137#124—31no—
138#124—61no—
139#123—61no—
140C22⋊Q8—31no—
141C22⋊Q8—31no—
142C22⋊Q8—61no—
143C22⋊Q8C2×D311yescharacteristic
144#121—31no—
145#121—61no—
146C4×Q8—31no—
147C4×Q8—31no—
148C4×D4—31no—
149C4×D4—61no—
150#117—31no—
151#117—61no—
152C2×C4⋊C4—31no—
153#107—31no—
154#107—31no—
155#106—31no—
156C4⋊C8—31no—
157#103—31no—
158#103—31no—
159#103—31no—
160#103—31no—
161#103—31no—
162#103—31no—
163#103C2×D311yescharacteristic
164#102—31no—
165#102—31no—
166#102C2×D311yescharacteristic
167C22⋊C8—31no—
168C22⋊C8C2×D311yescharacteristic
169C4×C8—31no—
170C23×C3—21no—
171C23×C3C2×D411yescharacteristic
172C22×D3C2×D411yescharacteristic
173C3×Q8—21no—
174C3×Q8—21no—
175C3×Q8—21no—
176C3×Q8#4112yes—
177C3×D4—21no—
178C3×D4—21no—
179C3×D4—42no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—42no—
186C2×C3×C4C2×D411yescharacteristic
187C2×C3×C4C2411yescharacteristic
188#67—22no—
189#67—42no—
190C2×Dic3—21no—
191C2×Dic3—21no—
192C2×Dic3—21no—
193C2×Dic3—21no—
194C2×Dic3C2×D411yescharacteristic
195C2×Dic3C2×D411yescharacteristic
196C2×Dic3C2×D411yescharacteristic
197C4×D3—21no—
198C4×D3—21no—
199C4×D3—42no—
200C4×D3—42no—
201Dic6—21no—
202Dic6—21no—
203Dic6—42no—
204C3×C8—21no—
205C3×C8—21no—
206C3⋊C8—21no—
207C3⋊C8—21no—
208#41—22no—
209#41—41no—
210C2×Q8—31no—
211C2×Q8—61no—
212C2×Q8—62no—
213C2×Q8—121no—
214C2×Q8C22×D311yescharacteristic
215C2×Q8C22×D311yescharacteristic
216C2×D4—21no—
217C2×D4—31no—
218C2×D4—61no—
219C2×D4C22×D311yescharacteristic
220C22×C4—21no—
221C22×C4—31no—
222C22×C4—61no—
223C22×C4—61no—
224C22×C4C22×D311yescharacteristic
225Q16—22no—
226Q16—121no—
227SD16—41no—
228C2×C8—31no—
229C2×C8—31no—
230C2×C8—121no—
231C2×C8—121no—
232C2×C8C22×D311yescharacteristic
233C2×C8C22×D311yescharacteristic
234C4⋊C4—21no—
235C4⋊C4—31no—
236C4⋊C4—31no—
237C4⋊C4—31no—
238C4⋊C4—31no—
239C4⋊C4—61no—
240C4⋊C4—61no—
241C4⋊C4—61no—
242C4⋊C4—61no—
243C4⋊C4—61no—
244C4⋊C4—61no—
245C4⋊C4—61no—
246C4⋊C4C22×D311yescharacteristic
247C22⋊C4—21no—
248C22⋊C4—31no—
249C22⋊C4—31no—
250C22⋊C4—61no—
251C22⋊C4—61no—
252C22⋊C4—61no—
253C22⋊C4—61no—
254C22⋊C4—61no—
255C22⋊C4—61no—
256C42—31no—
257C42—61no—
258C42—61no—
259C42—61no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—41no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3C22×D411yescharacteristic
267C2×D3—21no—
268C2×D3—21no—
269C2×D3#13512yes—
270C3×C4—22no—
271C3×C4—21no—
272C3×C4—41no—
273C3×C4—41no—
274C3×C4C2×#4111yescharacteristic
275C3×C4H(5,𝔽2)11yescharacteristic
276Dic3—21no—
277Dic3—21no—
278Dic3—21no—
279Dic3—41no—
280Dic3—41no—
281Dic3—41no—
282Dic3—41no—
283C23—21no—
284C23—31no—
285C23D3×D411yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—61no—
290Q8—61no—
291Q8—122no—
292Q8#23712yes—
293D4—21no—
294D4—21no—
295D4—42no—
296D4—62no—
297D4—122no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—31no—
304C2×C4—31no—
305C2×C4—31no—
306C2×C4—42no—
307C2×C4—61no—
308C2×C4—61no—
309C2×C4—61no—
310C2×C4—61no—
311C2×C4—61no—
312C2×C4—61no—
313C2×C4—122no—
314C2×C4—122no—
315C2×C4D3×D411yescharacteristic
316C2×C4C23×D311yescharacteristic
317C8—21no—
318C8—21no—
319C8—61no—
320C8—61no—
321C2×C3—41no—
322C2×C3—81no—
323C2×C3#54611yescharacteristic
324C2×C3C2×#13511yescharacteristic
325C2×C3#57811yescharacteristic
326D3—22no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—32no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—61no—
335C22—61no—
336C22C2×D3×D411yescharacteristic
337C4—21no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—61no—
342C4—61no—
343C4—61no—
344C4—121no—
345C4—121no—
346C4—121no—
347C4—121no—
348C4C2×#23711yescharacteristic
349C4#100411yescharacteristic
350C3#330011yescharacteristic, complemented, Sylow
351C2—41no—
352C2—62no—
353C2—81no—
354C2#559111yescharacteristic
355C2D3×#13511yescharacteristic
356C2#577911yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#452C2
socleC22×C3C22×D4
prime radical#5831C2
hypercenter#452D3
hypocenterC3#3300
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. #5639C2semidirect
3. C3×#452C2semidirect
4. #5233C2semidirect
5. #5186C2semidirect
6. Dic3×Q16C2semidirect
7. #5171C2semidirect
8. #5166C2semidirect
9. #5051C2semidirect
10. D3×#103C2semidirect
11. #4799C2semidirect
12. #4774C2semidirect
13. #4768C2semidirect
14. #67⋊C8C2semidirect
15. #4723C2semidirect
69. #452D3semidirect
350. C3#3300semidirect

Maximal subgroups

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

subgroupindex
#58312
#56392
C3×#4522
#52332
#51862
Dic3×Q162
#51712
#51662
#50512
D3×#1032
#47992
#47742
#47682
#67⋊C82
#47232
#33003