Finite Group Databasebeta

← C47×#3401 #20241011

Subgroups — C47×#3401 #20241011

Order 6016.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#559C211yesmaximal, characteristic, complemented
2C47×#556C211yesmaximal, characteristic, complemented
3C47×#497C211yesmaximal, characteristic, complemented
4C47×#496C211yesmaximal, characteristic
5C47×#495C211yesmaximal, characteristic, complemented
6C47×#464C211yesmaximal, characteristic, complemented
7C47×#464C211yesmaximal, characteristic, complemented
8C47×#463C211yesmaximal, characteristic, complemented
9C47×#463C211yesmaximal, characteristic, complemented
10C47×#461C211yesmaximal, characteristic, complemented
11C47×#460C211yesmaximal, characteristic, complemented
12C47×#446C211yesmaximal, characteristic, complemented
13C47×#442C211yesmaximal, characteristic, complemented
14C47×#441C211yesmaximal, characteristic, complemented
15C4×SD16×C47C211yesmaximal, characteristic, complemented
16C2×Q16×C47C2211yescharacteristic
17C2×Q16×C47C2211yescharacteristic
18C2×SD16×C47C2211yescharacteristic
19C2×SD16×C47C2211yescharacteristic
20C2×SD16×C47C2211yescharacteristic
21C2×SD16×C47C2211yescharacteristic
22C2×SD16×C47C2211yescharacteristic
23C2×D8×C47C2211yescharacteristic
24C2×D8×C47C2211yescharacteristic
25C4⋊Q8×C47C2211yescharacteristic
26#127×C47C2211yescharacteristic
27#126×C47—21no—
28#126×C47—21no—
29#124×C47—21no—
30#124×C47C2211yescharacteristic
31#124×C47C2211yescharacteristic
32#124×C47C2211yescharacteristic
33#124×C47C2211yescharacteristic
34#123×C47—21no—
35#123×C47—21no—
36C22⋊Q8×C47—21no—
37C4×Q8×C47C2211yescharacteristic
38C4×Q8×C47C2211yescharacteristic
39C4×Q8×C47C2211yescharacteristic
40C4×Q8×C47C2211yescharacteristic
41C4×D4×C47—21no—
42C4×D4×C47C2211yescharacteristic
43C4×D4×C47C2211yescharacteristic
44C4×D4×C47C2211yescharacteristic
45#117×C47—21no—
46#106×C47C2211yescharacteristic
47C4⋊C8×C47C2211yescharacteristic
48C4⋊C8×C47C2211yescharacteristic
49C4⋊C8×C47C2211yescharacteristic
50#103×C47C2211yescharacteristic
51#103×C47C2211yescharacteristic
52#103×C47C2211yescharacteristic
53#102×C47C2211yescharacteristic
54#102×C47C2211yescharacteristic
55#102×C47C2211yescharacteristic
56#97×C47C2211yescharacteristic
57#97×C47C2211yescharacteristic
58C4×C8×C47C2211yescharacteristic
59C2×Q8×C47D411yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C2×Q8×C47C2311yescharacteristic
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47—21no—
64C2×D4×C47—21no—
65C2×D4×C47C2311yescharacteristic
66C2×D4×C47C2311yescharacteristic
67C2×D4×C47C2311yescharacteristic
68C22×C4×C47—21no—
69C22×C4×C47—21no—
70C22×C4×C47—21no—
71Q16×C47—22no—
72Q16×C47—41no—
73SD16×C47—22no—
74SD16×C47—41no—
75SD16×C47—41no—
76SD16×C47—41no—
77SD16×C47—41no—
78D8×C47—22no—
79D8×C47—41no—
80C2×C8×C47C2311yescharacteristic
81C2×C8×C47C2311yescharacteristic
82C2×C8×C47C2311yescharacteristic
83C2×C8×C47C2311yescharacteristic
84C4⋊C4×C47—21no—
85C4⋊C4×C47—21no—
86C4⋊C4×C47—21no—
87C4⋊C4×C47—21no—
88C4⋊C4×C47—21no—
89C4⋊C4×C47D411yescharacteristic
90C4⋊C4×C47D411yescharacteristic
91C4⋊C4×C47D411yescharacteristic
92C4⋊C4×C47C2311yescharacteristic
93C4⋊C4×C47C2311yescharacteristic
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×C47—21no—
103C22⋊C4×C47—21no—
104C22⋊C4×C47—21no—
105C42×C47—21no—
106C42×C47—21no—
107C42×C47—21no—
108C42×C47C2311yescharacteristic
109C42×C47C2311yescharacteristic
110C42×C47C2311yescharacteristic
111C23×C47—21no—
112C23×C47—21no—
113C23×C47—21no—
114Q8×C47—21no—
115Q8×C47—21no—
116Q8×C47—21no—
117Q8×C47—21no—
118Q8×C47—21no—
119Q8×C47—21no—
120Q8×C47—41no—
121D4×C47—21no—
122D4×C47—21no—
123D4×C47—21no—
124D4×C47—21no—
125D4×C47—21no—
126D4×C47—21no—
127D4×C47—42no—
128D4×C47—81no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—42no—
135C2×C4×C47—81no—
136C2×C4×C47—81no—
137C2×C4×C47C2×D411yescharacteristic
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#4112yes—
148C22×C47—41no—
149C22×C47—41no—
150C22×C47—41no—
151C22×C47—41no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47—41no—
155C22×C47—41no—
156C22×C47—41no—
157C22×C47C22×D411yescharacteristic
158C4×C47—21no—
159C4×C47—21no—
160C4×C47—21no—
161C4×C47—21no—
162C4×C47—21no—
163C4×C47—21no—
164C4×C47—41no—
165C4×C47—41no—
166C4×C47—41no—
167C4×C47—41no—
168C4×C47—41no—
169C4×C47C2×#4111yescharacteristic
170C4×C47H(5,𝔽2)11yescharacteristic
171#3401C4711yesmaximal, characteristic, direct product factor, Sylow
172C2×C47—81no—
173C2×C47—81no—
174C2×C47—81no—
175C2×C47#55011yescharacteristic
176C2×C47#57511yescharacteristic
177C2×C47#57711yescharacteristic
178#559C2×C4711yescharacteristic, complemented
179#556C2×C4711yescharacteristic, complemented
180#497C2×C4711yescharacteristic, complemented
181#496C2×C4711yescharacteristic
182#495C2×C4711yescharacteristic, complemented
183#464C2×C4711yescharacteristic, complemented
184#464C2×C4711yescharacteristic, complemented
185#463C2×C4711yescharacteristic, complemented
186#463C2×C4711yescharacteristic, complemented
187#461C2×C4711yescharacteristic, complemented
188#460C2×C4711yescharacteristic, complemented
189#446C2×C4711yescharacteristic, complemented
190#442C2×C4711yescharacteristic, complemented
191#441C2×C4711yescharacteristic, complemented
192C4×SD16C2×C4711yescharacteristic, complemented
193C47#340111yescharacteristic, direct product factor, Sylow
194C2×Q16C22×C4711yescharacteristic
195C2×Q16C22×C4711yescharacteristic
196C2×SD16C22×C4711yescharacteristic
197C2×SD16C22×C4711yescharacteristic
198C2×SD16C22×C4711yescharacteristic
199C2×SD16C22×C4711yescharacteristic
200C2×SD16C22×C4711yescharacteristic
201C2×D8C22×C4711yescharacteristic
202C2×D8C22×C4711yescharacteristic
203C4⋊Q8C22×C4711yescharacteristic
204#127C22×C4711yescharacteristic
205#126—21no—
206#126—21no—
207#124—21no—
208#124C22×C4711yescharacteristic
209#124C22×C4711yescharacteristic
210#124C22×C4711yescharacteristic
211#124C22×C4711yescharacteristic
212#123—21no—
213#123—21no—
214C22⋊Q8—21no—
215C4×Q8C22×C4711yescharacteristic
216C4×Q8C22×C4711yescharacteristic
217C4×Q8C22×C4711yescharacteristic
218C4×Q8C22×C4711yescharacteristic
219C4×D4—21no—
220C4×D4C22×C4711yescharacteristic
221C4×D4C22×C4711yescharacteristic
222C4×D4C22×C4711yescharacteristic
223#117—21no—
224#106C22×C4711yescharacteristic
225C4⋊C8C22×C4711yescharacteristic
226C4⋊C8C22×C4711yescharacteristic
227C4⋊C8C22×C4711yescharacteristic
228#103C22×C4711yescharacteristic
229#103C22×C4711yescharacteristic
230#103C22×C4711yescharacteristic
231#102C22×C4711yescharacteristic
232#102C22×C4711yescharacteristic
233#102C22×C4711yescharacteristic
234#97C22×C4711yescharacteristic
235#97C22×C4711yescharacteristic
236C4×C8C22×C4711yescharacteristic
237C2×Q8D4×C4711yescharacteristic
238C2×Q8C23×C4711yescharacteristic
239C2×Q8C23×C4711yescharacteristic
240C2×Q8C23×C4711yescharacteristic
241C2×D4—21no—
242C2×D4—21no—
243C2×D4C23×C4711yescharacteristic
244C2×D4C23×C4711yescharacteristic
245C2×D4C23×C4711yescharacteristic
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249Q16—22no—
250Q16—41no—
251SD16—22no—
252SD16—41no—
253SD16—41no—
254SD16—41no—
255SD16—41no—
256D8—22no—
257D8—41no—
258C2×C8C23×C4711yescharacteristic
259C2×C8C23×C4711yescharacteristic
260C2×C8C23×C4711yescharacteristic
261C2×C8C23×C4711yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4D4×C4711yescharacteristic
268C4⋊C4D4×C4711yescharacteristic
269C4⋊C4D4×C4711yescharacteristic
270C4⋊C4C23×C4711yescharacteristic
271C4⋊C4C23×C4711yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
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—
283C42—21no—
284C42—21no—
285C42—21no—
286C42C23×C4711yescharacteristic
287C42C23×C4711yescharacteristic
288C42C23×C4711yescharacteristic
289C23—21no—
290C23—21no—
291C23—21no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—41no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—21no—
305D4—42no—
306D4—81no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4C2×D4×C4711yescharacteristic
316C2×C4C2×D4×C4711yescharacteristic
317C2×C4C2×D4×C4711yescharacteristic
318C2×C4C2×D4×C4711yescharacteristic
319C2×C4C2×D4×C4711yescharacteristic
320C2×C4C2×D4×C4711yescharacteristic
321C2×C4C24×C4711yescharacteristic
322C8—21no—
323C8—21no—
324C8—21no—
325C8#41×C4712yes—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22C22×D4×C4711yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4C2×#41×C4711yescharacteristic
348C4H(5,𝔽2)×C4711yescharacteristic
349C2—81no—
350C2—81no—
351C2—81no—
352C2C47×#55011yescharacteristic
353C2C47×#57511yescharacteristic
354C2C47×#57711yescharacteristic
subgroupG/H
center, socleC22×C47C22×D4
commutator, Frattini, cosocleC2×C4C24×C47
prime radicalC47×#496C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C4×Q8×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#559C2semidirect
2. C47×#556C2semidirect
3. C47×#497C2semidirect
5. C47×#495C2semidirect
6. C47×#464C2semidirect
7. C47×#464C2semidirect
8. C47×#463C2semidirect
9. C47×#463C2semidirect
10. C47×#461C2semidirect
11. C47×#460C2semidirect
12. C47×#446C2semidirect
13. C47×#442C2semidirect
14. C47×#441C2semidirect
15. C4×SD16×C47C2semidirect
171. #3401C47direct (N × H)
178. #559C2×C47semidirect
179. #556C2×C47semidirect
180. #497C2×C47semidirect
182. #495C2×C47semidirect
183. #464C2×C47semidirect
184. #464C2×C47semidirect
185. #463C2×C47semidirect
186. #463C2×C47semidirect
187. #461C2×C47semidirect
188. #460C2×C47semidirect
189. #446C2×C47semidirect
190. #442C2×C47semidirect
191. #441C2×C47semidirect
192. C4×SD16C2×C47semidirect
193. C47#3401direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#5592
C47×#5562
C47×#4972
C47×#4962
C47×#4952
C47×#4642
C47×#4632
C47×#4612
C47×#4602
C47×#4462
C47×#4422
C47×#4412
C4×SD16×C472
#340147