Finite Group Databasebeta

← D47×#1331 #26126007

Subgroups — D47×#1331 #26126007

Order 12032.

470 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
1C4×D8×D47C211yesmaximal, characteristic
2C4×C16×D47C211yesmaximal, characteristic, complemented
3#335×D47C211yesmaximal, characteristic, complemented
4#20241350C211yesmaximal, characteristic, complemented
5#20241349C211yesmaximal, characteristic, complemented
6#20241348C211yesmaximal, characteristic, complemented
7C47×#1331C211yesmaximal, characteristic, complemented
8C2×D8×D47C411yescharacteristic
9C4×D4×D47—21no—
10C2×C16×D47—21no—
11C4×D376C2211yescharacteristic
12D8×Dic47C411yescharacteristic
13#15689205C411yescharacteristic
14C4×#10625334—21no—
15#15689203—21no—
16#107×D47C411yescharacteristic
17C4⋊C8×D47—21no—
18#102×D47—21no—
19C4×C8×D47C2211yescharacteristic
20C4×C47⋊C16C2211yescharacteristic, complemented
21C16×Dic47—21no—
22#15688876C2211yescharacteristic, complemented
23#15688875—21no—
24C4×D8×C47C2211yescharacteristic
25C4×C16×C47C2211yescharacteristic, complemented
26C47×#335C2211yescharacteristic, complemented
27C2×D4×D47—21no—
28C22×C4×D47—41no—
29C2×D376C2×C411yescharacteristic
30C2×#10625334—21no—
31D8×D47—22no—
32D8×D47C814yescomplemented
33C2×C8×D47—41no—
34C2×C8×D47C2×C411yescharacteristic
35C2×C8×D47D411yescharacteristic
36C4×D188—21no—
37D4×Dic47—21no—
38#13093986—21no—
39C4×C22⋊D47—41no—
40(C22⋊D47)⋊C4—41no—
41C4⋊C4×D47—21no—
42C22⋊C4×D47—41no—
43C42×D47D411yescharacteristic
44C2×C47⋊C16—21no—
45C16×D47—24no—
46#13093958C2×C411yescharacteristic
47#13093957—21no—
48C4⋊(C47⋊C8)—21no—
49Dic47⋊C8—41no—
50#13093946—21no—
51#13093945—21no—
52#13093944—21no—
53C4×C47⋊C8D411yescharacteristic
54C8×Dic47C2×C411yescharacteristic
55C8×Dic47D411yescharacteristic
56C2×D8×C47C2×C411yescharacteristic
57C4×D4×C47—21no—
58C2×C16×C47—21no—
59#107×C47C2×C411yescharacteristic
60C4⋊C8×C47—21no—
61#102×C47—21no—
62C4×C8×C47C2311yescharacteristic
63C23×D47—41no—
64C2×D4×C47—21no—
65C22×C4×C47—41no—
66C2×C22⋊D47—41no—
67C22×Dic47—41no—
68D4×D47—24no—
69D4×D47—42no—
70C2×D188—21no—
71C2×C4×D47—41no—
72C2×C4×D47—41no—
73C2×C4×D47—41no—
74C2×C4×D47—82no—
75C2×C4×D47—82no—
76C2×C4×D47C22⋊C411yescharacteristic
77C2×C4×D47D811yescharacteristic
78C2×C4×D47SD1611yescharacteristic
79D8×C47—21no—
80D8×C47C2×C812yescomplemented
81C2×C8×C47—41no—
82C2×C8×C47C22×C411yescharacteristic
83C2×C8×C47C2×D411yescharacteristic
84C4⋊C4×C47—21no—
85C22⋊C4×C47—41no—
86C42×C47C2×D411yescharacteristic
87C22⋊Dic47—41no—
88#10625334—24no—
89(C2×D47)⋊C4—41no—
90(C2×D47)⋊C4—41no—
91C4⋊Dic47—21no—
92Dic47⋊C4—41no—
93C4×Dic47C22⋊C411yescharacteristic
94C4×Dic47D811yescharacteristic
95C4×Dic47SD1611yescharacteristic
96C2×C47⋊C8—41no—
97C2×C47⋊C8C22⋊C411yescharacteristic
98C2×C47⋊C8C22⋊C411yescharacteristic
99D376—21no—
100D376C2×C812yescomplemented
101C8×D47—22no—
102C8×D47—82no—
103C8×D47C2×C812yes—
104C8×D47M1612yes—
105C16×C47—22no—
106C47⋊C16—22no—
107C23×C47—41no—
108C22×D47—41no—
109C22×D47—44no—
110C22×D47—82no—
111C22×D47—82no—
112C22×D47#10211yescharacteristic
113D4×C47—22no—
114D4×C47—41no—
115C2×C4×C47—41no—
116C2×C4×C47—81no—
117C2×C4×C47—81no—
118C2×C4×C47C2×C22⋊C411yescharacteristic
119C2×C4×C47C2×D811yescharacteristic
120C2×C4×C47C2×SD1611yescharacteristic
121C22⋊D47—44no—
122C2×Dic47—41no—
123C2×Dic47—82no—
124C2×Dic47#10211yescharacteristic
125C2×Dic47#10211yescharacteristic
126C2×Dic47#10211yescharacteristic
127D188—22no—
128D188—41no—
129C4×D47—22no—
130C4×D47—82no—
131C4×D47—81no—
132C4×D47—81no—
133C4×D47—82no—
134C4×D47C22⋊C812yes—
135C4×D47#10412yes—
136C4×D47D1612yes—
137C4×D47SD3212yes—
138C8×C47—21no—
139C8×C47—81no—
140C8×C47C22×C811yescharacteristic
141C8×C47C2×M1611yescharacteristic
142C47⋊C8—21no—
143C47⋊C8—81no—
144C47⋊C8C22⋊C812yes—
145C2×#1331—471nomaximal, Sylow
146C22×C47—42no—
147C22×C47—81no—
148C22×C47—81no—
149C22×C47C2×#10211yescharacteristic
150C2×D47—42no—
151C2×D47—81no—
152C2×D47—81no—
153C2×D47—88no—
154C2×D47D4⋊C812yes—
155C2×D47#35712yes—
156C2×D47#35912yes—
157C4×C47—21no—
158C4×C47—81no—
159C4×C47C2×C22⋊C811yescharacteristic
160C4×C47C2×#10411yescharacteristic
161C4×C47C2×D1611yescharacteristic
162C4×C47C2×SD3211yescharacteristic
163Dic47—21no—
164Dic47—81no—
165Dic47D4⋊C812yes—
166Dic47#35712yes—
167C2×C4×D8—471no—
168C2×C4×C16—471no—
169C2×#335—471no—
170#1331—471no—
171#1331—471no—
172#1331—471no—
173#1331D4711yescharacteristic, direct product factor
174C2×C47—82no—
175C2×C47C2×D4⋊C811yescharacteristic
176C2×C47C2×#35711yescharacteristic
177C2×C47C2×#35911yescharacteristic
178D47—82no—
179D47#133114yesdirect product factor
180C22×D8—471no—
181C2×C4×D4—941no—
182C22×C16—941no—
183C4×D8—471no—
184C4×D8—471no—
185C4×D8—471no—
186C4×D8—941no—
187C4×D8—941no—
188C4×D8C2×D4711yescharacteristic
189C2×#107—471no—
190C2×C4⋊C8—941no—
191C2×#102—941no—
192C2×C4×C8—471no—
193C4×C16—471no—
194C4×C16—941no—
195C4×C16C2×D4711yescharacteristic, complemented
196#335—471no—
197#335—941no—
198#335C2×D4711yescharacteristic, complemented
199C47C2×#133111yescharacteristic, complemented, Sylow
200C22×D4—941no—
201C23×C4—1881no—
202C2×D8—474no—
203C2×D8—471no—
204C2×D8—942no—
205C2×D8—941no—
206C2×D8C4×D4711yescharacteristic
207C22×C8—471no—
208C22×C8—471no—
209C22×C8—1881no—
210C4×D4—21no—
211C4×D4—941no—
212C4×D4—941no—
213C4×D4—941no—
214C4×D4—1881no—
215C4×D4—1881no—
216C2×C4⋊C4—941no—
217C2×C22⋊C4—1881no—
218C2×C42—471no—
219C2×C16—21no—
220C2×C16—944no—
221C2×C16—941no—
222#107—471no—
223#107—941no—
224#107C4×D4711yescharacteristic
225C4⋊C8—21no—
226C4⋊C8—941no—
227C4⋊C8—1881no—
228#102—21no—
229#102—941no—
230#102—941no—
231#102—941no—
232C4×C8—471no—
233C4×C8—471no—
234C4×C8—471no—
235C4×C8C22×D4711yescharacteristic
236C24—1881no—
237C2×D4—21no—
238C2×D4—944no—
239C2×D4—941no—
240C2×D4—1882no—
241C2×D4—1881no—
242C22×C4—41no—
243C22×C4—471no—
244C22×C4—471no—
245C22×C4—471no—
246C22×C4—3762no—
247C22×C4—3762no—
248C22×C4—1881no—
249C22×C4—1881no—
250C22×C4—1881no—
251C22×C4—1881no—
252D8—21no—
253D8—472no—
254D8—944no—
255D8—941no—
256D8C8×D4712yescomplemented
257C2×C8—41no—
258C2×C8—471no—
259C2×C8—472no—
260C2×C8—472no—
261C2×C8—471no—
262C2×C8—942no—
263C2×C8—3762no—
264C2×C8—1881no—
265C2×C8C2×C4×D4711yescharacteristic
266C2×C8D4×D4711yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—941no—
269C4⋊C4—1881no—
270C22⋊C4—41no—
271C22⋊C4—1881no—
272C22⋊C4—1881no—
273C22⋊C4—1881no—
274C42—471no—
275C42—471no—
276C42—471no—
277C42D4×D4711yescharacteristic
278C16—22no—
279C16—942no—
280C23—41no—
281C23—471no—
282C23—3762no—
283C23—3762no—
284C23—1884no—
285C23—1881no—
286D4—22no—
287D4—41no—
288D4—942no—
289D4—1884no—
290D4—1881no—
291C2×C4—41no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—471no—
295C2×C4—471no—
296C2×C4—472no—
297C2×C4—472no—
298C2×C4—472no—
299C2×C4—472no—
300C2×C4—471no—
301C2×C4—942no—
302C2×C4—3762no—
303C2×C4—3762no—
304C2×C4—3762no—
305C2×C4—3761no—
306C2×C4—3761no—
307C2×C4—1881no—
308C2×C4C22⋊C4×D4711yescharacteristic
309C2×C4D8×D4711yescharacteristic
310C2×C4SD16×D4711yescharacteristic
311C8—21no—
312C8—81no—
313C8—472no—
314C8—941no—
315C8—3761no—
316C8C2×C8×D4711yescharacteristic
317C8M16×D4711yescharacteristic
318C22—42no—
319C22—81no—
320C22—81no—
321C22—472no—
322C22—472no—
323C22—472no—
324C22—3768no—
325C22—3761no—
326C22—3761no—
327C22—1882no—
328C22#102×D4711yescharacteristic
329C4—21no—
330C4—81no—
331C4—472no—
332C4—472no—
333C4—941no—
334C4—3761no—
335C4C22⋊C8×D4711yescharacteristic
336C4#104×D4711yescharacteristic
337C4D16×D4711yescharacteristic
338C4SD32×D4711yescharacteristic
339C2—82no—
340C2—474no—
341C2—3762no—
342C2D4⋊C8×D4711yescharacteristic
343C2#357×D4711yescharacteristic
344C2#359×D4711yescharacteristic
subgroupG/H
centerC2×C4D8×D47
commutatorC8×C47C22×C8
FrattiniC4×C8C22×D47
FittingC47×#1331C2
socleC22×C47C2×#102
prime radicalC2×D8×D47C4
cosocleC4×C8×C47C23
hypercenter#1331D47
hypocenterC47C2×#1331
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #1331

Complements

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

NH ≅ G/Ntype
2. C4×C16×D47C2semidirect
3. #335×D47C2semidirect
4. #20241350C2semidirect
5. #20241349C2semidirect
6. #20241348C2semidirect
7. C47×#1331C2semidirect
20. C4×C47⋊C16C22semidirect
22. #15688876C22semidirect
25. C4×C16×C47C22semidirect
26. C47×#335C22semidirect
32. D8×D47C8semidirect
80. D8×C47C2×C8semidirect
100. D376C2×C8semidirect
173. #1331D47direct (N × H)
179. D47#1331direct (N × H)
195. C4×C16C2×D47semidirect
198. #335C2×D47semidirect
199. C47C2×#1331semidirect
256. D8C8×D47semidirect

Maximal subgroups

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

subgroupindex
C4×D8×D472
C4×C16×D472
#335×D472
#202413502
#202413492
#202413482
C47×#13312
C2×#133147