Finite Group Databasebeta

← #81062

Subgroups — #81062

Order 384.

398 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5729C211yesmaximal, characteristic, complemented
2#5545C211yesmaximal, characteristic
3C3×#476C211yesmaximal, characteristic, complemented
4#5087C211yesmaximal, characteristic, complemented
5#5009C211yesmaximal, characteristic, complemented
6#4871C211yesmaximal, characteristic, complemented
7#4870C211yesmaximal, characteristic, complemented
8#4861C211yesmaximal, characteristic, complemented
9#4860C211yesmaximal, characteristic, complemented
10#4847C211yesmaximal, characteristic, complemented
11#4839C211yesmaximal, characteristic, complemented
12#4770C211yesmaximal, characteristic
13D3×#102C211yesmaximal, characteristic
14#4763C211yesmaximal, characteristic, complemented
15#4759C211yesmaximal, characteristic, complemented
16#3081—31nomaximal, Sylow
17C2×D3×D4C2211yescharacteristic
18C3×C4⋊Q8C2211yescharacteristic, complemented
19C3×C4×D4C2211yescharacteristic
20#946—21no—
21#944—21no—
22D4×Dic3C2211yescharacteristic
23C4×#67—21no—
24C2×(C2×D3)⋊C4—21no—
25C2×ΓL(1,𝔽25)C2211yescharacteristic
26C2×D3×C8C2211yescharacteristic
27#896—21no—
28#893C2211yescharacteristic
29#892C2211yescharacteristic
30#892C2211yescharacteristic
31D3×C4⋊C4C2211yescharacteristic
32#890C2211yescharacteristic, complemented
33#889—21no—
34#888C2211yescharacteristic, complemented
35#67⋊C4—21no—
36D3×C22⋊C4—21no—
37C4×D12C2211yescharacteristic
38#872C2211yescharacteristic
39#870C2211yescharacteristic, complemented
40C3×#106C2211yescharacteristic, complemented
41C3×#106C2211yescharacteristic, complemented
42C3×C4⋊C8C2211yescharacteristic, complemented
43C3×#102C2211yescharacteristic
44C3×#102C2211yescharacteristic
45#832C2211yescharacteristic
46#832C2211yescharacteristic
47#821C2211yescharacteristic
48#821C2211yescharacteristic
49#818C2211yescharacteristic, complemented
50#817C2211yescharacteristic, complemented
51Dic3⋊C8C2211yescharacteristic, complemented
52Dic3⋊C8C2211yescharacteristic, complemented
53#809C2211yescharacteristic
54#809C2211yescharacteristic
55#808C2211yescharacteristic, complemented
56#807C2211yescharacteristic, complemented
57#807C2211yescharacteristic, complemented
58#807C2211yescharacteristic, complemented
59C4⋊(C3⋊C8)C2211yescharacteristic, complemented
60#544—31no—
61#518—31no—
62#478—31no—
63#478—31no—
64#478—31no—
65#478—31no—
66#476—31no—
67#476D311yescharacteristic, complemented
68#474—31no—
69#474—31no—
70#428—31no—
71#427—31no—
72#424—31no—
73#418—31no—
74C2×#102—31no—
75C23×D3—21no—
76C2×C3×Q8—21no—
77C2×C3×D4C2311yescharacteristic
78C22×C3×C4—21no—
79C2×#67—21no—
80C22×Dic3—21no—
81D3×D4—22no—
82D3×D4Q814yescomplemented
83C2×D12C2311yescharacteristic
84C2×C4×D3—21no—
85C2×C4×D3—21no—
86C2×C4×D3—21no—
87C2×C4×D3C2311yescharacteristic
88C2×Dic6—21no—
89C2×C3×C8C2311yescharacteristic
90C2×C3×C8C2311yescharacteristic
91C3×C4⋊C4—21no—
92C3×C4⋊C4C2311yescharacteristic
93C3×C4⋊C4C2311yescharacteristic
94C3×C4⋊C4C2311yescharacteristic
95C3×C22⋊C4—21no—
96C3×C42C2311yescharacteristic
97#217—21no—
98(C2×D3)⋊C4—21no—
99(C2×D3)⋊C4—21no—
100(C2×D3)⋊C4—21no—
101(C2×D3)⋊C4—21no—
102(C2×D3)⋊C4D411yescharacteristic
103(C2×D3)⋊C4D411yescharacteristic
104C4⋊Dic3—21no—
105C4⋊Dic3C2311yescharacteristic
106C4⋊Dic3C2311yescharacteristic
107C4⋊Dic3C2311yescharacteristic
108Dic3⋊C4—21no—
109Dic3⋊C4—21no—
110Dic3⋊C4—21no—
111Dic3⋊C4—21no—
112Dic3⋊C4—21no—
113Dic3⋊C4D411yescharacteristic
114Dic3⋊C4D411yescharacteristic
115C4×Dic3—21no—
116C4×Dic3—21no—
117C4×Dic3C2311yescharacteristic
118C2×C3⋊C8C2311yescharacteristic
119C2×C3⋊C8C2311yescharacteristic
120ΓL(1,𝔽25)—22no—
121D3×C8—22no—
122C22×D4—31no—
123C2×M16—31no—
124C22×C8—31no—
125C4⋊Q8—31no—
126C4⋊Q8—61no—
127C4⋊Q8C2×D311yescharacteristic, complemented
128#125—31no—
129#125—31no—
130#125—61no—
131C22⋊Q8—61no—
132C22⋊Q8—61no—
133C4×D4—31no—
134C4×D4—31no—
135C4×D4—31no—
136C4×D4—61no—
137C4×D4—61no—
138C4×D4C2×D311yescharacteristic
139#117—31no—
140#117—31no—
141#117—31no—
142C2×C4⋊C4—31no—
143C2×C22⋊C4—61no—
144C2×C22⋊C4—61no—
145#107—31no—
146#107—31no—
147#107—31no—
148#107—31no—
149#106—31no—
150#106—31no—
151#106C2×D311yescharacteristic, complemented
152#106C2×D311yescharacteristic, complemented
153C4⋊C8—31no—
154C4⋊C8—31no—
155C4⋊C8—31no—
156C4⋊C8C2×D311yescharacteristic, complemented
157#102—31no—
158#102—31no—
159#102—31no—
160#102—31no—
161#102—31no—
162#102—31no—
163#102C2×D311yescharacteristic
164#102C2×D311yescharacteristic
165C23×C3—21no—
166C22×D3—21no—
167C22×D3—24no—
168C22×D3—81no—
169C22×D3—81no—
170C22×D3C2×D411yescharacteristic
171C3×Q8—81no—
172C3×D4—21no—
173C3×D4C2×Q812yes—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—81no—
178C2×C3×C4C2×D411yescharacteristic
179C2×C3×C4C2×D411yescharacteristic
180C2×C3×C4C2411yescharacteristic
181#67—24no—
182C2×Dic3—21no—
183C2×Dic3—21no—
184C2×Dic3—21no—
185C2×Dic3—81no—
186C2×Dic3C2×D411yescharacteristic
187C2×Dic3C2×D411yescharacteristic
188C2×Dic3C2×D411yescharacteristic
189D12—21no—
190D12C2×Q812yes—
191C4×D3—81no—
192C4×D3—81no—
193C4×D3—81no—
194C4×D3C2×Q812yes—
195C4×D3#4112yes—
196Dic6—81no—
197C3×C8—21no—
198C3×C8—21no—
199C3⋊C8—21no—
200C3⋊C8—21no—
201C24—61no—
202C2×Q8—21no—
203C2×Q8—61no—
204C2×D4—34no—
205C2×D4—31no—
206C2×D4—62no—
207C2×D4—61no—
208C2×D4C22×D311yescharacteristic
209C22×C4—21no—
210C22×C4—31no—
211C22×C4—61no—
212C22×C4—61no—
213C22×C4—61no—
214C22×C4—61no—
215M16—62no—
216C2×C8—31no—
217C2×C8—31no—
218C2×C8—62no—
219C2×C8C22×D311yescharacteristic
220C2×C8C22×D311yescharacteristic
221C4⋊C4—21no—
222C4⋊C4—31no—
223C4⋊C4—31no—
224C4⋊C4—31no—
225C4⋊C4—31no—
226C4⋊C4—31no—
227C4⋊C4—61no—
228C4⋊C4—61no—
229C4⋊C4—61no—
230C4⋊C4—61no—
231C4⋊C4—61no—
232C4⋊C4—61no—
233C4⋊C4C22×D311yescharacteristic
234C4⋊C4C22×D311yescharacteristic
235C4⋊C4C22×D311yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—31no—
238C22⋊C4—31no—
239C22⋊C4—61no—
240C22⋊C4—61no—
241C22⋊C4—61no—
242C22⋊C4—61no—
243C22⋊C4—61no—
244C42—31no—
245C42—61no—
246C42—61no—
247C42C22×D311yescharacteristic
248C22×C3—22no—
249C22×C3—41no—
250C22×C3—41no—
251C22×C3C22×D411yescharacteristic
252C2×D3—21no—
253C2×D3—21no—
254C2×D3—22no—
255C2×D3—41no—
256C2×D3—41no—
257C2×D3—84no—
258C2×D3C22⋊Q812yes—
259C3×C4—21no—
260C3×C4—21no—
261C3×C4—41no—
262C3×C4—41no—
263C3×C4—41no—
264C3×C4C22×Q811yescharacteristic
265C3×C4C2×#4111yescharacteristic
266Dic3—21no—
267Dic3—21no—
268Dic3—41no—
269Dic3—41no—
270Dic3—41no—
271Dic3C22⋊Q812yes—
272C23—21no—
273C23—31no—
274C23—64no—
275C23—61no—
276C23—241no—
277C23—241no—
278Q8—81no—
279Q8—241no—
280D4—21no—
281D4—32no—
282D4—64no—
283D4—61no—
284D4D3×Q812yes—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—31no—
289C2×C4—32no—
290C2×C4—32no—
291C2×C4—31no—
292C2×C4—31no—
293C2×C4—61no—
294C2×C4—61no—
295C2×C4—61no—
296C2×C4—81no—
297C2×C4—241no—
298C2×C4—241no—
299C2×C4—241no—
300C2×C4—241no—
301C2×C4D3×D411yescharacteristic
302C2×C4D3×D411yescharacteristic
303C2×C4C23×D311yescharacteristic
304C8—21no—
305C8—21no—
306C8—61no—
307C8—61no—
308C2×C3—42no—
309C2×C3C2×C22⋊Q811yescharacteristic
310C2×C3#57611yescharacteristic
311C2×C3#57711yescharacteristic
312D3—22no—
313D3—42no—
314C22—22no—
315C22—32no—
316C22—41no—
317C22—41no—
318C22—61no—
319C22—61no—
320C22—62no—
321C22—121no—
322C22—121no—
323C22—244no—
324C22C2×D3×D411yescharacteristic
325C4—21no—
326C4—21no—
327C4—32no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—61no—
332C4—61no—
333C4—121no—
334C4—121no—
335C4—121no—
336C4C2×D3×Q811yescharacteristic
337C4D3×#4111yescharacteristic
338C3#308111yescharacteristic, complemented, Sylow
339C2—42no—
340C2—62no—
341C2—122no—
342C2D3×C22⋊Q811yescharacteristic
343C2#576211yescharacteristic
344C2#577411yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#476C2
socleC22×C3C22×D4
prime radicalC2×D3×D4C22
hypercenter#476D3
hypocenterC3#3081
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #5729C2semidirect
3. C3×#476C2semidirect
4. #5087C2semidirect
5. #5009C2semidirect
6. #4871C2semidirect
7. #4870C2semidirect
8. #4861C2semidirect
9. #4860C2semidirect
10. #4847C2semidirect
11. #4839C2semidirect
14. #4763C2semidirect
15. #4759C2semidirect
18. C3×C4⋊Q8C22semidirect
32. #890C22semidirect
34. #888C22semidirect
39. #870C22semidirect
40. C3×#106C22semidirect
41. C3×#106C22semidirect
42. C3×C4⋊C8C22semidirect
49. #818C22semidirect
50. #817C22semidirect
51. Dic3⋊C8C22semidirect
52. Dic3⋊C8C22semidirect
55. #808C22semidirect
56. #807C22semidirect
57. #807C22semidirect
58. #807C22semidirect
59. C4⋊(C3⋊C8)C22semidirect
67. #476D3semidirect
82. D3×D4Q8semidirect
127. C4⋊Q8C2×D3semidirect
151. #106C2×D3semidirect
152. #106C2×D3semidirect
156. C4⋊C8C2×D3semidirect
338. C3#3081semidirect

Maximal subgroups

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

subgroupindex
#57292
#55452
C3×#4762
#50872
#50092
#48712
#48702
#48612
#48602
#48472
#48392
#47702
D3×#1022
#47632
#47592
#30813