Finite Group Databasebeta

← C47×#3317 #20240927

Subgroups — C47×#3317 #20240927

Order 6016.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#552C211yesmaximal, characteristic, complemented
2C47×#550C211yesmaximal, characteristic
3C47×#490C211yesmaximal, characteristic, complemented
4C47×#482C211yesmaximal, characteristic, complemented
5C47×#481C211yesmaximal, characteristic, complemented
6C47×#479C211yesmaximal, characteristic, complemented
7C47×#468C211yesmaximal, characteristic, complemented
8C47×#465C211yesmaximal, characteristic, complemented
9C47×#460C211yesmaximal, characteristic, complemented
10C47×#452C211yesmaximal, characteristic, complemented
11C47×#452C211yesmaximal, characteristic, complemented
12C47×#441C211yesmaximal, characteristic, complemented
13C47×#435C211yesmaximal, characteristic, complemented
14C47×#417C211yesmaximal, characteristic, complemented
15C47×#416C211yesmaximal, characteristic, complemented
16C2×#41×C47C2211yescharacteristic
17C2×#41×C47C2211yescharacteristic
18C2×Q16×C47C2211yescharacteristic
19C2×SD16×C47C2211yescharacteristic
20C2×SD16×C47C2211yescharacteristic
21C2×M16×C47C2211yescharacteristic
22C22×C8×C47C2211yescharacteristic
23#127×C47—21no—
24#127×C47C2211yescharacteristic
25#126×C47—21no—
26#125×C47—21no—
27#125×C47C2211yescharacteristic
28#123×C47—21no—
29C22⋊Q8×C47C2211yescharacteristic
30C22⋊Q8×C47C2211yescharacteristic
31#121×C47—21no—
32#121×C47—21no—
33#121×C47C2211yescharacteristic
34#121×C47C2211yescharacteristic
35C4×Q8×C47C2211yescharacteristic
36C4×Q8×C47C2211yescharacteristic
37C4×D4×C47—21no—
38C4×D4×C47C2211yescharacteristic
39#117×C47—21no—
40#117×C47C2211yescharacteristic
41C2×C4⋊C4×C47C2211yescharacteristic
42#107×C47C2211yescharacteristic
43#106×C47C2211yescharacteristic
44#106×C47C2211yescharacteristic
45C4⋊C8×C47C2211yescharacteristic
46#103×C47C2211yescharacteristic
47#103×C47C2211yescharacteristic
48#103×C47C2211yescharacteristic
49#103×C47C2211yescharacteristic
50#102×C47C2211yescharacteristic
51#102×C47C2211yescharacteristic
52#102×C47C2211yescharacteristic
53#102×C47C2211yescharacteristic
54#102×C47C2211yescharacteristic
55#102×C47C2211yescharacteristic
56C22⋊C8×C47C2211yescharacteristic
57C22⋊C8×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59#41×C47—22no—
60#41×C47—22no—
61#41×C47—41no—
62#41×C47—41no—
63C2×Q8×C47C2311yescharacteristic
64C2×Q8×C47C2311yescharacteristic
65C2×D4×C47—21no—
66C2×D4×C47—21no—
67C2×D4×C47—21no—
68C2×D4×C47—21no—
69C2×D4×C47—21no—
70C2×D4×C47—21no—
71C2×D4×C47D411yescharacteristic
72C2×D4×C47C2311yescharacteristic
73C2×D4×C47C2311yescharacteristic
74C22×C4×C47—21no—
75C22×C4×C47—21no—
76C22×C4×C47—21no—
77C22×C4×C47C2311yescharacteristic
78C22×C4×C47C2311yescharacteristic
79Q16×C47—22no—
80SD16×C47—41no—
81SD16×C47—41no—
82M16×C47—41no—
83C2×C8×C47—41no—
84C2×C8×C47C2311yescharacteristic
85C2×C8×C47C2311yescharacteristic
86C2×C8×C47C2311yescharacteristic
87C2×C8×C47C2311yescharacteristic
88C4⋊C4×C47—21no—
89C4⋊C4×C47—21no—
90C4⋊C4×C47—21no—
91C4⋊C4×C47—21no—
92C4⋊C4×C47—21no—
93C4⋊C4×C47—21no—
94C4⋊C4×C47—21no—
95C4⋊C4×C47D411yescharacteristic
96C4⋊C4×C47C2311yescharacteristic
97C4⋊C4×C47C2311yescharacteristic
98C4⋊C4×C47C2311yescharacteristic
99C4⋊C4×C47C2311yescharacteristic
100C22⋊C4×C47—21no—
101C22⋊C4×C47—21no—
102C22⋊C4×C47—21no—
103C22⋊C4×C47—21no—
104C22⋊C4×C47—21no—
105C22⋊C4×C47D411yescharacteristic
106C22⋊C4×C47D411yescharacteristic
107C42×C47—21no—
108C42×C47—21no—
109C42×C47—21no—
110C42×C47C2311yescharacteristic
111C23×C47—21no—
112C23×C47—21no—
113C23×C47C2×D411yescharacteristic
114C23×C47C2×D411yescharacteristic
115Q8×C47—21no—
116Q8×C47—21no—
117Q8×C47—21no—
118Q8×C47#4112yes—
119D4×C47—21no—
120D4×C47—21no—
121D4×C47—21no—
122D4×C47—21no—
123D4×C47—41no—
124D4×C47—42no—
125D4×C47—42no—
126D4×C47—42no—
127D4×C47—81no—
128D4×C47—81no—
129D4×C47—81no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—42no—
141C2×C4×C47—42no—
142C2×C4×C47—42no—
143C2×C4×C47C2×D411yescharacteristic
144C2×C4×C47C2×D411yescharacteristic
145C2×C4×C47C2×D411yescharacteristic
146C2×C4×C47C2×D411yescharacteristic
147C2×C4×C47C2411yescharacteristic
148C8×C47—21no—
149C8×C47—21no—
150C8×C47—21no—
151C8×C47—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—21no—
158C22×C47—41no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47—41no—
164C22×C47C22×D411yescharacteristic
165C4×C47—21no—
166C4×C47—21no—
167C4×C47—22no—
168C4×C47—21no—
169C4×C47—21no—
170C4×C47—41no—
171C4×C47—41no—
172C4×C47—41no—
173C4×C47—41no—
174C4×C47—41no—
175C4×C47C2×#4111yescharacteristic
176C4×C47H(5,𝔽2)11yescharacteristic
177#3317C4711yesmaximal, characteristic, direct product factor, Sylow
178C2×C47—41no—
179C2×C47—41no—
180C2×C47—81no—
181C2×C47—81no—
182C2×C47#54611yescharacteristic
183C2×C47#57511yescharacteristic
184C2×C47#57711yescharacteristic
185#552C2×C4711yescharacteristic, complemented
186#550C2×C4711yescharacteristic
187#490C2×C4711yescharacteristic, complemented
188#482C2×C4711yescharacteristic, complemented
189#481C2×C4711yescharacteristic, complemented
190#479C2×C4711yescharacteristic, complemented
191#468C2×C4711yescharacteristic, complemented
192#465C2×C4711yescharacteristic, complemented
193#460C2×C4711yescharacteristic, complemented
194#452C2×C4711yescharacteristic, complemented
195#452C2×C4711yescharacteristic, complemented
196#441C2×C4711yescharacteristic, complemented
197#435C2×C4711yescharacteristic, complemented
198#417C2×C4711yescharacteristic, complemented
199#416C2×C4711yescharacteristic, complemented
200C47#331711yescharacteristic, direct product factor, Sylow
201C2×#41C22×C4711yescharacteristic
202C2×#41C22×C4711yescharacteristic
203C2×Q16C22×C4711yescharacteristic
204C2×SD16C22×C4711yescharacteristic
205C2×SD16C22×C4711yescharacteristic
206C2×M16C22×C4711yescharacteristic
207C22×C8C22×C4711yescharacteristic
208#127—21no—
209#127C22×C4711yescharacteristic
210#126—21no—
211#125—21no—
212#125C22×C4711yescharacteristic
213#123—21no—
214C22⋊Q8C22×C4711yescharacteristic
215C22⋊Q8C22×C4711yescharacteristic
216#121—21no—
217#121—21no—
218#121C22×C4711yescharacteristic
219#121C22×C4711yescharacteristic
220C4×Q8C22×C4711yescharacteristic
221C4×Q8C22×C4711yescharacteristic
222C4×D4—21no—
223C4×D4C22×C4711yescharacteristic
224#117—21no—
225#117C22×C4711yescharacteristic
226C2×C4⋊C4C22×C4711yescharacteristic
227#107C22×C4711yescharacteristic
228#106C22×C4711yescharacteristic
229#106C22×C4711yescharacteristic
230C4⋊C8C22×C4711yescharacteristic
231#103C22×C4711yescharacteristic
232#103C22×C4711yescharacteristic
233#103C22×C4711yescharacteristic
234#103C22×C4711yescharacteristic
235#102C22×C4711yescharacteristic
236#102C22×C4711yescharacteristic
237#102C22×C4711yescharacteristic
238#102C22×C4711yescharacteristic
239#102C22×C4711yescharacteristic
240#102C22×C4711yescharacteristic
241C22⋊C8C22×C4711yescharacteristic
242C22⋊C8C22×C4711yescharacteristic
243#97C22×C4711yescharacteristic
244#41—22no—
245#41—22no—
246#41—41no—
247#41—41no—
248C2×Q8C23×C4711yescharacteristic
249C2×Q8C23×C4711yescharacteristic
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4D4×C4711yescharacteristic
257C2×D4C23×C4711yescharacteristic
258C2×D4C23×C4711yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4C23×C4711yescharacteristic
263C22×C4C23×C4711yescharacteristic
264Q16—22no—
265SD16—41no—
266SD16—41no—
267M16—41no—
268C2×C8—41no—
269C2×C8C23×C4711yescharacteristic
270C2×C8C23×C4711yescharacteristic
271C2×C8C23×C4711yescharacteristic
272C2×C8C23×C4711yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4D4×C4711yescharacteristic
281C4⋊C4C23×C4711yescharacteristic
282C4⋊C4C23×C4711yescharacteristic
283C4⋊C4C23×C4711yescharacteristic
284C4⋊C4C23×C4711yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4D4×C4711yescharacteristic
291C22⋊C4D4×C4711yescharacteristic
292C42—21no—
293C42—21no—
294C42—21no—
295C42C23×C4711yescharacteristic
296C23—21no—
297C23—21no—
298C23C2×D4×C4711yescharacteristic
299C23C2×D4×C4711yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8#41×C4712yes—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—41no—
309D4—42no—
310D4—42no—
311D4—42no—
312D4—81no—
313D4—81no—
314D4—81no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4C2×D4×C4711yescharacteristic
329C2×C4C2×D4×C4711yescharacteristic
330C2×C4C2×D4×C4711yescharacteristic
331C2×C4C2×D4×C4711yescharacteristic
332C2×C4C24×C4711yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22C22×D4×C4711yescharacteristic
350C4—21no—
351C4—21no—
352C4—22no—
353C4—21no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4C2×#41×C4711yescharacteristic
361C4H(5,𝔽2)×C4711yescharacteristic
362C2—41no—
363C2—41no—
364C2—81no—
365C2—81no—
366C2C47×#54611yescharacteristic
367C2C47×#57511yescharacteristic
368C2C47×#57711yescharacteristic
subgroupG/H
center, socleC22×C47C22×D4
commutator, Frattini, cosocleC2×C4C24×C47
prime radicalC47×#550C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C4×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#552C2semidirect
3. C47×#490C2semidirect
4. C47×#482C2semidirect
5. C47×#481C2semidirect
6. C47×#479C2semidirect
7. C47×#468C2semidirect
8. C47×#465C2semidirect
9. C47×#460C2semidirect
10. C47×#452C2semidirect
11. C47×#452C2semidirect
12. C47×#441C2semidirect
13. C47×#435C2semidirect
14. C47×#417C2semidirect
15. C47×#416C2semidirect
177. #3317C47direct (N × H)
185. #552C2×C47semidirect
187. #490C2×C47semidirect
188. #482C2×C47semidirect
189. #481C2×C47semidirect
190. #479C2×C47semidirect
191. #468C2×C47semidirect
192. #465C2×C47semidirect
193. #460C2×C47semidirect
194. #452C2×C47semidirect
195. #452C2×C47semidirect
196. #441C2×C47semidirect
197. #435C2×C47semidirect
198. #417C2×C47semidirect
199. #416C2×C47semidirect
200. C47#3317direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#5522
C47×#5502
C47×#4902
C47×#4822
C47×#4812
C47×#4792
C47×#4682
C47×#4652
C47×#4602
C47×#4522
C47×#4412
C47×#4352
C47×#4172
C47×#4162
#331747