Finite Group Databasebeta

← C47×#3118 #20240728

Subgroups — C47×#3118 #20240728

Order 6016.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#542C211yesmaximal, characteristic, complemented
2C47×#518C211yesmaximal, characteristic, complemented
3C47×#485C211yesmaximal, characteristic, complemented
4C47×#482C211yesmaximal, characteristic, complemented
5C47×#476C211yesmaximal, characteristic, complemented
6C47×#474C211yesmaximal, characteristic, complemented
7C47×#463C211yesmaximal, characteristic, complemented
8C47×#463C211yesmaximal, characteristic, complemented
9C47×#450C211yesmaximal, characteristic, complemented
10C47×#447C211yesmaximal, characteristic
11C47×#442C211yesmaximal, characteristic, complemented
12C47×#440C211yesmaximal, characteristic, complemented
13C4×SD16×C47C211yesmaximal, characteristic, complemented
14C4×D8×C47C211yesmaximal, characteristic, complemented
15C47×#433C211yesmaximal, characteristic, complemented
16C22×D4×C47C2211yescharacteristic
17C2×SD16×C47C2211yescharacteristic
18C2×SD16×C47C2211yescharacteristic
19C2×D8×C47C2211yescharacteristic
20C2×D8×C47C2211yescharacteristic
21C4⋊Q8×C47C2211yescharacteristic, complemented
22#126×C47—21no—
23#124×C47—21no—
24#124×C47C2211yescharacteristic, complemented
25#123×C47—21no—
26C22⋊Q8×C47—21no—
27C22⋊Q8×C47C2211yescharacteristic
28#121×C47C2211yescharacteristic
29C4×Q8×C47C2211yescharacteristic, complemented
30C4×D4×C47—21no—
31C4×D4×C47—21no—
32C4×D4×C47C2211yescharacteristic
33C4×D4×C47C2211yescharacteristic
34C4×D4×C47C2211yescharacteristic
35C4×D4×C47C2211yescharacteristic
36C4×D4×C47C2211yescharacteristic, complemented
37#117×C47C2211yescharacteristic
38#117×C47C2211yescharacteristic
39C2×C22⋊C4×C47—21no—
40C2×C22⋊C4×C47—21no—
41#107×C47C2211yescharacteristic, complemented
42#107×C47C2211yescharacteristic, complemented
43#106×C47C2211yescharacteristic, complemented
44#106×C47C2211yescharacteristic, complemented
45C4⋊C8×C47C2211yescharacteristic, complemented
46C4⋊C8×C47C2211yescharacteristic, complemented
47#103×C47C2211yescharacteristic, complemented
48#103×C47C2211yescharacteristic, complemented
49#102×C47C2211yescharacteristic
50#102×C47C2211yescharacteristic
51#102×C47C2211yescharacteristic
52#102×C47C2211yescharacteristic
53#102×C47C2211yescharacteristic, complemented
54#102×C47C2211yescharacteristic, complemented
55C22⋊C8×C47C2211yescharacteristic
56C22⋊C8×C47C2211yescharacteristic
57#97×C47C2211yescharacteristic, complemented
58C4×C8×C47C2211yescharacteristic, complemented
59C24×C47—21no—
60C2×Q8×C47—21no—
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47—22no—
63C2×D4×C47—22no—
64C2×D4×C47—21no—
65C2×D4×C47—21no—
66C2×D4×C47C2311yescharacteristic
67C2×D4×C47C2311yescharacteristic
68C2×D4×C47C2311yescharacteristic
69C22×C4×C47—21no—
70C22×C4×C47—21no—
71C22×C4×C47—21no—
72C22×C4×C47—21no—
73C22×C4×C47—21no—
74C22×C4×C47C2311yescharacteristic
75SD16×C47—22no—
76SD16×C47—22no—
77D8×C47—22no—
78D8×C47—22no—
79C2×C8×C47C2311yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C2×C8×C47C2311yescharacteristic
82C2×C8×C47C2311yescharacteristic
83C4⋊C4×C47—21no—
84C4⋊C4×C47—21no—
85C4⋊C4×C47—21no—
86C4⋊C4×C47D411yescharacteristic
87C4⋊C4×C47D411yescharacteristic
88C4⋊C4×C47C2311yescharacteristic
89C4⋊C4×C47C2311yescharacteristic
90C4⋊C4×C47C2311yescharacteristic
91C4⋊C4×C47C2311yescharacteristic
92C22⋊C4×C47—21no—
93C22⋊C4×C47—21no—
94C22⋊C4×C47—21no—
95C22⋊C4×C47—21no—
96C22⋊C4×C47—21no—
97C22⋊C4×C47—21no—
98C22⋊C4×C47—21no—
99C22⋊C4×C47—21no—
100C22⋊C4×C47—21no—
101C22⋊C4×C47—21no—
102C22⋊C4×C47D411yescharacteristic
103C22⋊C4×C47D411yescharacteristic
104C42×C47—21no—
105C42×C47—21no—
106C42×C47C2311yescharacteristic
107C42×C47C2311yescharacteristic
108C23×C47—24no—
109C23×C47—21no—
110C23×C47—21no—
111C23×C47—21no—
112C23×C47—81no—
113C23×C47—81no—
114C23×C47C2×D411yescharacteristic
115Q8×C47—21no—
116Q8×C47—21no—
117Q8×C47—81no—
118D4×C47—24no—
119D4×C47—21no—
120D4×C47—21no—
121D4×C47—21no—
122D4×C47—21no—
123D4×C47—81no—
124D4×C47#4112yes—
125D4×C47#4112yes—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—81no—
134C2×C4×C47—81no—
135C2×C4×C47—81no—
136C2×C4×C47—81no—
137C2×C4×C47—81no—
138C2×C4×C47C2×D411yescharacteristic
139C2×C4×C47C2×D411yescharacteristic
140C2×C4×C47C2×D411yescharacteristic
141C2×C4×C47C2×D411yescharacteristic
142C2×C4×C47C2×D411yescharacteristic
143C2×C4×C47C2411yescharacteristic
144C8×C47—21no—
145C8×C47—21no—
146C8×C47—21no—
147C8×C47—21no—
148C22×C47—21no—
149C22×C47—22no—
150C22×C47—22no—
151C22×C47—21no—
152C22×C47—21no—
153C22×C47—41no—
154C22×C47—41no—
155C22×C47—41no—
156C22×C47—41no—
157C22×C47—41no—
158C22×C47—41no—
159C22×C47—41no—
160C22×C47—84no—
161C22×C47C22×D411yescharacteristic
162C4×C47—21no—
163C4×C47—21no—
164C4×C47—21no—
165C4×C47—21no—
166C4×C47—21no—
167C4×C47—41no—
168C4×C47—41no—
169C4×C47—41no—
170C4×C47—41no—
171C4×C47—41no—
172C4×C47C2×#4111yescharacteristic
173C4×C47C2×#4111yescharacteristic
174#3118C4711yesmaximal, characteristic, direct product factor, Sylow
175C2×C47—41no—
176C2×C47—42no—
177C2×C47—42no—
178C2×C47—81no—
179C2×C47#52511yescharacteristic
180C2×C47#57611yescharacteristic
181C2×C47#57711yescharacteristic
182#542C2×C4711yescharacteristic, complemented
183#518C2×C4711yescharacteristic, complemented
184#485C2×C4711yescharacteristic, complemented
185#482C2×C4711yescharacteristic, complemented
186#476C2×C4711yescharacteristic, complemented
187#474C2×C4711yescharacteristic, complemented
188#463C2×C4711yescharacteristic, complemented
189#463C2×C4711yescharacteristic, complemented
190#450C2×C4711yescharacteristic, complemented
191#447C2×C4711yescharacteristic
192#442C2×C4711yescharacteristic, complemented
193#440C2×C4711yescharacteristic, complemented
194C4×SD16C2×C4711yescharacteristic, complemented
195C4×D8C2×C4711yescharacteristic, complemented
196#433C2×C4711yescharacteristic, complemented
197C47#311811yescharacteristic, direct product factor, Sylow
198C22×D4C22×C4711yescharacteristic
199C2×SD16C22×C4711yescharacteristic
200C2×SD16C22×C4711yescharacteristic
201C2×D8C22×C4711yescharacteristic
202C2×D8C22×C4711yescharacteristic
203C4⋊Q8C22×C4711yescharacteristic, complemented
204#126—21no—
205#124—21no—
206#124C22×C4711yescharacteristic, complemented
207#123—21no—
208C22⋊Q8—21no—
209C22⋊Q8C22×C4711yescharacteristic
210#121C22×C4711yescharacteristic
211C4×Q8C22×C4711yescharacteristic, complemented
212C4×D4—21no—
213C4×D4—21no—
214C4×D4C22×C4711yescharacteristic
215C4×D4C22×C4711yescharacteristic
216C4×D4C22×C4711yescharacteristic
217C4×D4C22×C4711yescharacteristic
218C4×D4C22×C4711yescharacteristic, complemented
219#117C22×C4711yescharacteristic
220#117C22×C4711yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223#107C22×C4711yescharacteristic, complemented
224#107C22×C4711yescharacteristic, complemented
225#106C22×C4711yescharacteristic, complemented
226#106C22×C4711yescharacteristic, complemented
227C4⋊C8C22×C4711yescharacteristic, complemented
228C4⋊C8C22×C4711yescharacteristic, complemented
229#103C22×C4711yescharacteristic, complemented
230#103C22×C4711yescharacteristic, complemented
231#102C22×C4711yescharacteristic
232#102C22×C4711yescharacteristic
233#102C22×C4711yescharacteristic
234#102C22×C4711yescharacteristic
235#102C22×C4711yescharacteristic, complemented
236#102C22×C4711yescharacteristic, complemented
237C22⋊C8C22×C4711yescharacteristic
238C22⋊C8C22×C4711yescharacteristic
239#97C22×C4711yescharacteristic, complemented
240C4×C8C22×C4711yescharacteristic, complemented
241C24—21no—
242C2×Q8—21no—
243C2×Q8C23×C4711yescharacteristic
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4C23×C4711yescharacteristic
249C2×D4C23×C4711yescharacteristic
250C2×D4C23×C4711yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4C23×C4711yescharacteristic
257SD16—22no—
258SD16—22no—
259D8—22no—
260D8—22no—
261C2×C8C23×C4711yescharacteristic
262C2×C8C23×C4711yescharacteristic
263C2×C8C23×C4711yescharacteristic
264C2×C8C23×C4711yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4D4×C4711yescharacteristic
269C4⋊C4D4×C4711yescharacteristic
270C4⋊C4C23×C4711yescharacteristic
271C4⋊C4C23×C4711yescharacteristic
272C4⋊C4C23×C4711yescharacteristic
273C4⋊C4C23×C4711yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4D4×C4711yescharacteristic
285C22⋊C4D4×C4711yescharacteristic
286C42—21no—
287C42—21no—
288C42C23×C4711yescharacteristic
289C42C23×C4711yescharacteristic
290C23—24no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—81no—
295C23—81no—
296C23C2×D4×C4711yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—81no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—21no—
305D4—81no—
306D4#41×C4712yes—
307D4#41×C4712yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4C2×D4×C4711yescharacteristic
321C2×C4C2×D4×C4711yescharacteristic
322C2×C4C2×D4×C4711yescharacteristic
323C2×C4C2×D4×C4711yescharacteristic
324C2×C4C2×D4×C4711yescharacteristic
325C2×C4C24×C4711yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—84no—
343C22C22×D4×C4711yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4C2×#41×C4711yescharacteristic
355C4C2×#41×C4711yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—81no—
360C2C47×#52511yescharacteristic
361C2C47×#57611yescharacteristic
362C2C47×#57711yescharacteristic
subgroupG/H
center, socleC22×C47C22×D4
commutator, Frattini, cosocleC2×C4C24×C47
prime radicalC47×#447C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ #117×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#542C2semidirect
2. C47×#518C2semidirect
3. C47×#485C2semidirect
4. C47×#482C2semidirect
5. C47×#476C2semidirect
6. C47×#474C2semidirect
7. C47×#463C2semidirect
8. C47×#463C2semidirect
9. C47×#450C2semidirect
11. C47×#442C2semidirect
12. C47×#440C2semidirect
13. C4×SD16×C47C2semidirect
14. C4×D8×C47C2semidirect
15. C47×#433C2semidirect
21. C4⋊Q8×C47C22semidirect
24. #124×C47C22semidirect
29. C4×Q8×C47C22semidirect
36. C4×D4×C47C22semidirect
41. #107×C47C22semidirect
42. #107×C47C22semidirect
43. #106×C47C22semidirect
44. #106×C47C22semidirect
45. C4⋊C8×C47C22semidirect
46. C4⋊C8×C47C22semidirect
47. #103×C47C22semidirect
48. #103×C47C22semidirect
53. #102×C47C22semidirect
54. #102×C47C22semidirect
57. #97×C47C22semidirect
58. C4×C8×C47C22semidirect
174. #3118C47direct (N × H)
182. #542C2×C47semidirect
183. #518C2×C47semidirect
184. #485C2×C47semidirect
185. #482C2×C47semidirect
186. #476C2×C47semidirect
187. #474C2×C47semidirect
188. #463C2×C47semidirect
189. #463C2×C47semidirect
190. #450C2×C47semidirect
192. #442C2×C47semidirect
193. #440C2×C47semidirect
194. C4×SD16C2×C47semidirect
195. C4×D8C2×C47semidirect
196. #433C2×C47semidirect
197. C47#3118direct (N × H)
203. C4⋊Q8C22×C47semidirect
206. #124C22×C47semidirect
211. C4×Q8C22×C47semidirect
218. C4×D4C22×C47semidirect
223. #107C22×C47semidirect
224. #107C22×C47semidirect
225. #106C22×C47semidirect
226. #106C22×C47semidirect
227. C4⋊C8C22×C47semidirect
228. C4⋊C8C22×C47semidirect
229. #103C22×C47semidirect
230. #103C22×C47semidirect
235. #102C22×C47semidirect
236. #102C22×C47semidirect
239. #97C22×C47semidirect
240. C4×C8C22×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#5422
C47×#5182
C47×#4852
C47×#4822
C47×#4762
C47×#4742
C47×#4632
C47×#4502
C47×#4472
C47×#4422
C47×#4402
C4×SD16×C472
C4×D8×C472
C47×#4332
#311847