Finite Group Databasebeta

← #81518

Subgroups — #81518

Order 384.

386 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5628C211yesmaximal, characteristic
2#5523C211yesmaximal, characteristic
3C3×#485C211yesmaximal, characteristic, complemented
4#5044C211yesmaximal, characteristic, complemented
5#4996C211yesmaximal, characteristic, complemented
6#4884C211yesmaximal, characteristic, complemented
7#4881C211yesmaximal, characteristic, complemented
8#4868C211yesmaximal, characteristic, complemented
9#4860C211yesmaximal, characteristic, complemented
10#4815C211yesmaximal, characteristic, complemented
11#4805C211yesmaximal, characteristic, complemented
12#4802C211yesmaximal, characteristic, complemented
13D3×#103C211yesmaximal, characteristic, complemented
14#4727C211yesmaximal, characteristic
15#4721C211yesmaximal, characteristic, complemented
16#3097—31nomaximal, Sylow
17C2×D3×Q8C2211yescharacteristic
18C2×#235C2211yescharacteristic
19C3×C22⋊Q8C2211yescharacteristic
20C3×#117C2211yescharacteristic
21#946C2211yescharacteristic
22C2×C4⋊Dic3C2211yescharacteristic
23#924C2211yescharacteristic
24C2×ΓL(1,𝔽25)C2211yescharacteristic
25C2×D3×C8C2211yescharacteristic
26#897C2211yescharacteristic
27#894—21no—
28#892C2211yescharacteristic
29#892C2211yescharacteristic
30#892C2211yescharacteristic
31D3×C4⋊C4C2211yescharacteristic
32D3×C4⋊C4C2211yescharacteristic
33#888—21no—
34#885—21no—
35#883—21no—
36#67⋊C4—21no—
37#67⋊C4—21no—
38C4×D12—21no—
39C4×Dic6—21no—
40C3×#107C2211yescharacteristic
41C3×#106C2211yescharacteristic
42C3×#103C2211yescharacteristic
43C3×#103C2211yescharacteristic
44C3×C22⋊C8C2211yescharacteristic
45#835C2211yescharacteristic
46#835C2211yescharacteristic
47#830C2211yescharacteristic
48(C2×D3)⋊C8C2211yescharacteristic
49(C2×D3)⋊C8C2211yescharacteristic
50#817C2211yescharacteristic
51#817C2211yescharacteristic
52#816C2211yescharacteristic
53#816C2211yescharacteristic
54#810C2211yescharacteristic
55#810C2211yescharacteristic
56#808C2211yescharacteristic
57#807C2211yescharacteristic
58#807C2211yescharacteristic
59#807C2211yescharacteristic
60#536—31no—
61#520—31no—
62#485—31no—
63#485—31no—
64#485—31no—
65#485D311yescharacteristic, complemented
66#484—31no—
67#484—31no—
68#483—31no—
69#483—31no—
70#428—31no—
71#427—31no—
72#419—31no—
73C2×#103—31no—
74#408—31no—
75C2×C3×Q8C2311yescharacteristic
76C22×C3×C4C2311yescharacteristic
77C2×#67D411yescharacteristic
78C2×#67D411yescharacteristic
79C22×Dic3—21no—
80D3×Q8—22no—
81D3×Q8—22no—
82#235—22no—
83#235—22no—
84C2×D12D411yescharacteristic
85C2×C4×D3—21no—
86C2×C4×D3—21no—
87C2×C4×D3—21no—
88C2×C4×D3C2311yescharacteristic
89C2×C4×D3C2311yescharacteristic
90C2×Dic6—21no—
91C2×Dic6D411yescharacteristic
92C2×Dic6C2311yescharacteristic
93C2×C3×C8C2311yescharacteristic
94C2×C3×C8C2311yescharacteristic
95C3×C4⋊C4—21no—
96C3×C4⋊C4C2311yescharacteristic
97C3×C4⋊C4C2311yescharacteristic
98C3×C4⋊C4C2311yescharacteristic
99C3×C22⋊C4—21no—
100C3×C22⋊C4—21no—
101C3×C42—21no—
102#217—21no—
103(C2×D3)⋊C4—21no—
104(C2×D3)⋊C4—21no—
105(C2×D3)⋊C4—21no—
106(C2×D3)⋊C4—21no—
107(C2×D3)⋊C4—21no—
108C4⋊Dic3—21no—
109C4⋊Dic3—21no—
110C4⋊Dic3C2311yescharacteristic
111C4⋊Dic3C2311yescharacteristic
112C4⋊Dic3C2311yescharacteristic
113Dic3⋊C4—21no—
114Dic3⋊C4—21no—
115Dic3⋊C4—21no—
116Dic3⋊C4—21no—
117C4×Dic3—21no—
118C4×Dic3—21no—
119C4×Dic3—21no—
120C2×C3⋊C8C2311yescharacteristic
121C2×C3⋊C8C2311yescharacteristic
122ΓL(1,𝔽25)—22no—
123D3×C8—22no—
124C2×#41—31no—
125C22×Q8—31no—
126C2×M16—31no—
127C22×C8—31no—
128C4⋊Q8—61no—
129#124—61no—
130#123—61no—
131#123—61no—
132C22⋊Q8—31no—
133C22⋊Q8—31no—
134C22⋊Q8—31no—
135C22⋊Q8C2×D311yescharacteristic
136C4×Q8—61no—
137C4×D4—61no—
138C4×D4—61no—
139C4×D4—61no—
140#117—31no—
141#117—31no—
142#117—31no—
143#117C2×D311yescharacteristic
144C2×C4⋊C4—31no—
145C2×C4⋊C4—31no—
146C2×C4⋊C4—31no—
147#107—31no—
148#107—31no—
149#107—31no—
150#107C2×D311yescharacteristic
151#106—31no—
152#106—31no—
153#106—31no—
154#106C2×D311yescharacteristic
155#103—31no—
156#103—31no—
157#103—31no—
158#103—31no—
159#103—31no—
160#103—31no—
161#103C2×D311yescharacteristic
162#103C2×D311yescharacteristic
163C22⋊C8—31no—
164C22⋊C8—31no—
165C22⋊C8—31no—
166C22⋊C8C2×D311yescharacteristic
167C23×C3C2×D411yescharacteristic
168C22×D3C2×D411yescharacteristic
169C22×D3C2×D411yescharacteristic
170C3×Q8—21no—
171C3×Q8—21no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4C2×D411yescharacteristic
179C2×C3×C4C2411yescharacteristic
180#67—22no—
181#67—22no—
182C2×Dic3—21no—
183C2×Dic3—21no—
184C2×Dic3—21no—
185C2×Dic3—21no—
186C2×Dic3—81no—
187C2×Dic3C2×D411yescharacteristic
188C2×Dic3C2×D411yescharacteristic
189D12—22no—
190C4×D3—21no—
191C4×D3—21no—
192C4×D3—42no—
193C4×D3—81no—
194C4×D3—81no—
195C4×D3#4112yes—
196C4×D3#4112yes—
197Dic6—22no—
198Dic6—21no—
199Dic6—21no—
200Dic6—42no—
201C3×C8—21no—
202C3×C8—21no—
203C3⋊C8—21no—
204C3⋊C8—21no—
205#41—62no—
206#41—62no—
207C2×Q8—31no—
208C2×Q8—31no—
209C2×Q8—61no—
210C2×Q8—62no—
211C2×Q8—62no—
212C2×Q8C22×D311yescharacteristic
213C2×D4—31no—
214C2×D4—31no—
215C2×D4—31no—
216C22×C4—31no—
217C22×C4—31no—
218C22×C4—61no—
219C22×C4—61no—
220C22×C4—61no—
221C22×C4—61no—
222C22×C4C22×D311yescharacteristic
223M16—62no—
224C2×C8—31no—
225C2×C8—31no—
226C2×C8—62no—
227C2×C8C22×D311yescharacteristic
228C2×C8C22×D311yescharacteristic
229C4⋊C4—21no—
230C4⋊C4—31no—
231C4⋊C4—31no—
232C4⋊C4—31no—
233C4⋊C4—61no—
234C4⋊C4—61no—
235C4⋊C4—61no—
236C4⋊C4—61no—
237C4⋊C4—61no—
238C4⋊C4—61no—
239C4⋊C4C22×D311yescharacteristic
240C4⋊C4C22×D311yescharacteristic
241C4⋊C4C22×D311yescharacteristic
242C22⋊C4—21no—
243C22⋊C4—21no—
244C22⋊C4—61no—
245C22⋊C4—61no—
246C22⋊C4—61no—
247C22⋊C4—61no—
248C22⋊C4—61no—
249C22⋊C4—61no—
250C42—21no—
251C42—61no—
252C42—61no—
253C42—61no—
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3C22×D411yescharacteristic
258C2×D3—21no—
259C2×D3—21no—
260C2×D3—21no—
261C2×D3—21no—
262C2×D3—21no—
263C2×D3#12312yes—
264C3×C4—21no—
265C3×C4—41no—
266C3×C4—41no—
267C3×C4—41no—
268C3×C4—41no—
269C3×C4C2×#4111yescharacteristic
270C3×C4C2×#4111yescharacteristic
271Dic3—21no—
272Dic3—41no—
273Dic3—41no—
274Dic3—41no—
275Dic3—41no—
276Dic3#12312yes—
277C23—31no—
278C23—31no—
279C23D3×D411yescharacteristic
280Q8—21no—
281Q8—21no—
282Q8—62no—
283Q8—61no—
284Q8—61no—
285Q8—122no—
286D4—62no—
287D4—62no—
288D4—62no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—31no—
296C2×C4—32no—
297C2×C4—32no—
298C2×C4—31no—
299C2×C4—61no—
300C2×C4—61no—
301C2×C4—61no—
302C2×C4—61no—
303C2×C4—61no—
304C2×C4—61no—
305C2×C4—122no—
306C2×C4—241no—
307C2×C4—241no—
308C2×C4—241no—
309C2×C4D3×D411yescharacteristic
310C2×C4C23×D311yescharacteristic
311C8—21no—
312C8—21no—
313C8—61no—
314C8—61no—
315C2×C3—41no—
316C2×C3C2×#12311yescharacteristic
317C2×C3#57711yescharacteristic
318C2×C3#57811yescharacteristic
319D3—22no—
320D3—41no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—32no—
325C22—61no—
326C22—61no—
327C22—61no—
328C22—61no—
329C22—61no—
330C22C2×D3×D411yescharacteristic
331C4—21no—
332C4—32no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—61no—
338C4—121no—
339C4—121no—
340C4—121no—
341C4—121no—
342C4D3×#4111yescharacteristic
343C4D3×#4111yescharacteristic
344C3#309711yescharacteristic, complemented, Sylow
345C2—41no—
346C2—62no—
347C2—121no—
348C2D3×#12311yescharacteristic
349C2#577011yescharacteristic
350C2#577911yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#485C2
socleC22×C3C22×D4
prime radicalC2×#235C22
hypercenter#485D3
hypocenterC3#3097
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. C3×#485C2semidirect
4. #5044C2semidirect
5. #4996C2semidirect
6. #4884C2semidirect
7. #4881C2semidirect
8. #4868C2semidirect
9. #4860C2semidirect
10. #4815C2semidirect
11. #4805C2semidirect
12. #4802C2semidirect
13. D3×#103C2semidirect
15. #4721C2semidirect
65. #485D3semidirect
344. C3#3097semidirect

Maximal subgroups

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

subgroupindex
#56282
#55232
C3×#4852
#50442
#49962
#48842
#48812
#48682
#48602
#48152
#48052
#48022
D3×#1032
#47272
#47212
#30973