Finite Group Databasebeta

← C47×#3312 #20240922

Subgroups — C47×#3312 #20240922

Order 6016.

376 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#552C211yesmaximal, characteristic
2D4×Q8×C47C211yesmaximal, characteristic
3C47×#491C211yesmaximal, characteristic, complemented
4C47×#485C211yesmaximal, characteristic, complemented
5C47×#483C211yesmaximal, characteristic, complemented
6C47×#479C211yesmaximal, characteristic, complemented
7C47×#470C211yesmaximal, characteristic, complemented
8C47×#467C211yesmaximal, characteristic, complemented
9C47×#462C211yesmaximal, characteristic, complemented
10C47×#451C211yesmaximal, characteristic, complemented
11C47×#451C211yesmaximal, characteristic, complemented
12C47×#441C211yesmaximal, characteristic, complemented
13C47×#435C211yesmaximal, characteristic
14C47×#419C211yesmaximal, characteristic, complemented
15C2×#103×C47C211yesmaximal, characteristic, complemented
16C22×Q8×C47C2211yescharacteristic
17C22×Q8×C47C2211yescharacteristic
18C2×Q16×C47C2211yescharacteristic
19C2×Q16×C47C2211yescharacteristic
20C2×Q16×C47C2211yescharacteristic
21C2×M16×C47C2211yescharacteristic
22C22×C8×C47C2211yescharacteristic
23C4⋊Q8×C47—21no—
24C4⋊Q8×C47C2211yescharacteristic
25#126×C47—21no—
26#125×C47—21no—
27#125×C47C2211yescharacteristic
28#123×C47—21no—
29C22⋊Q8×C47—21no—
30C22⋊Q8×C47—21no—
31C22⋊Q8×C47C2211yescharacteristic
32C22⋊Q8×C47C2211yescharacteristic
33C22⋊Q8×C47C2211yescharacteristic
34C22⋊Q8×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#103×C47C2211yescharacteristic
51#103×C47C2211yescharacteristic
52#103×C47C2211yescharacteristic
53#103×C47C2211yescharacteristic
54#103×C47C2211yescharacteristic
55#103×C47C2211yescharacteristic
56C22⋊C8×C47C2211yescharacteristic
57C22⋊C8×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47—21no—
61C2×Q8×C47—22no—
62C2×Q8×C47—22no—
63C2×Q8×C47—41no—
64C2×Q8×C47—41no—
65C2×Q8×C47C2311yescharacteristic
66C2×Q8×C47C2311yescharacteristic
67C2×Q8×C47C2311yescharacteristic
68C2×Q8×C47C2311yescharacteristic
69C2×D4×C47D411yescharacteristic
70C22×C4×C47—21no—
71C22×C4×C47—21no—
72C22×C4×C47—21no—
73C22×C4×C47C2311yescharacteristic
74C22×C4×C47C2311yescharacteristic
75Q16×C47—22no—
76Q16×C47—41no—
77Q16×C47—41no—
78M16×C47—41no—
79C2×C8×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×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×C47C2×D411yescharacteristic
112C23×C47C2×D411yescharacteristic
113Q8×C47—21no—
114Q8×C47—21no—
115Q8×C47—21no—
116Q8×C47—21no—
117Q8×C47—21no—
118Q8×C47—21no—
119Q8×C47—21no—
120Q8×C47—42no—
121Q8×C47—42no—
122Q8×C47#4112yes—
123D4×C47—22no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
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—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—42no—
137C2×C4×C47—42no—
138C2×C4×C47—42no—
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—21no—
150C22×C47—21no—
151C22×C47—21no—
152C22×C47—21no—
153C22×C47#13712yes—
154C22×C47C22×D411yescharacteristic
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—22no—
158C4×C47—21no—
159C4×C47—21no—
160C4×C47—41no—
161C4×C47—41no—
162C4×C47—41no—
163C4×C47—41no—
164C4×C47—41no—
165C4×C47—41no—
166C4×C47—41no—
167C4×C47C2×#4111yescharacteristic
168C4×C47H(5,𝔽2)11yescharacteristic
169#3312C4711yesmaximal, characteristic, direct product factor, Sylow
170C2×C47—22no—
171C2×C47—41no—
172C2×C47#54611yescharacteristic
173C2×C47C2×#13711yescharacteristic
174C2×C47#57811yescharacteristic
175#552C2×C4711yescharacteristic
176D4×Q8C2×C4711yescharacteristic
177#491C2×C4711yescharacteristic, complemented
178#485C2×C4711yescharacteristic, complemented
179#483C2×C4711yescharacteristic, complemented
180#479C2×C4711yescharacteristic, complemented
181#470C2×C4711yescharacteristic, complemented
182#467C2×C4711yescharacteristic, complemented
183#462C2×C4711yescharacteristic, complemented
184#451C2×C4711yescharacteristic, complemented
185#451C2×C4711yescharacteristic, complemented
186#441C2×C4711yescharacteristic, complemented
187#435C2×C4711yescharacteristic
188#419C2×C4711yescharacteristic, complemented
189C2×#103C2×C4711yescharacteristic, complemented
190C47#331211yescharacteristic, direct product factor, Sylow
191C22×Q8C22×C4711yescharacteristic
192C22×Q8C22×C4711yescharacteristic
193C2×Q16C22×C4711yescharacteristic
194C2×Q16C22×C4711yescharacteristic
195C2×Q16C22×C4711yescharacteristic
196C2×M16C22×C4711yescharacteristic
197C22×C8C22×C4711yescharacteristic
198C4⋊Q8—21no—
199C4⋊Q8C22×C4711yescharacteristic
200#126—21no—
201#125—21no—
202#125C22×C4711yescharacteristic
203#123—21no—
204C22⋊Q8—21no—
205C22⋊Q8—21no—
206C22⋊Q8C22×C4711yescharacteristic
207C22⋊Q8C22×C4711yescharacteristic
208C22⋊Q8C22×C4711yescharacteristic
209C22⋊Q8C22×C4711yescharacteristic
210C4×Q8C22×C4711yescharacteristic
211C4×Q8C22×C4711yescharacteristic
212C4×D4—21no—
213C4×D4C22×C4711yescharacteristic
214#117—21no—
215#117C22×C4711yescharacteristic
216C2×C4⋊C4C22×C4711yescharacteristic
217#107C22×C4711yescharacteristic
218#106C22×C4711yescharacteristic
219#106C22×C4711yescharacteristic
220C4⋊C8C22×C4711yescharacteristic
221#103C22×C4711yescharacteristic
222#103C22×C4711yescharacteristic
223#103C22×C4711yescharacteristic
224#103C22×C4711yescharacteristic
225#103C22×C4711yescharacteristic
226#103C22×C4711yescharacteristic
227#103C22×C4711yescharacteristic
228#103C22×C4711yescharacteristic
229#103C22×C4711yescharacteristic
230#103C22×C4711yescharacteristic
231C22⋊C8C22×C4711yescharacteristic
232C22⋊C8C22×C4711yescharacteristic
233#97C22×C4711yescharacteristic
234C2×Q8—21no—
235C2×Q8—21no—
236C2×Q8—22no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8C23×C4711yescharacteristic
241C2×Q8C23×C4711yescharacteristic
242C2×Q8C23×C4711yescharacteristic
243C2×Q8C23×C4711yescharacteristic
244C2×D4D4×C4711yescharacteristic
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4C23×C4711yescharacteristic
249C22×C4C23×C4711yescharacteristic
250Q16—22no—
251Q16—41no—
252Q16—41no—
253M16—41no—
254C2×C8—41no—
255C2×C8C23×C4711yescharacteristic
256C2×C8C23×C4711yescharacteristic
257C2×C8C23×C4711yescharacteristic
258C2×C8C23×C4711yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4D4×C4711yescharacteristic
271C4⋊C4C23×C4711yescharacteristic
272C4⋊C4C23×C4711yescharacteristic
273C4⋊C4C23×C4711yescharacteristic
274C4⋊C4C23×C4711yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4D4×C4711yescharacteristic
281C22⋊C4D4×C4711yescharacteristic
282C42—21no—
283C42—21no—
284C42—21no—
285C42C23×C4711yescharacteristic
286C23C2×D4×C4711yescharacteristic
287C23C2×D4×C4711yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—42no—
296Q8—42no—
297Q8#41×C4712yes—
298D4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4C2×D4×C4711yescharacteristic
315C2×C4C2×D4×C4711yescharacteristic
316C2×C4C2×D4×C4711yescharacteristic
317C2×C4C2×D4×C4711yescharacteristic
318C2×C4C24×C4711yescharacteristic
319C8—21no—
320C8—21no—
321C8—21no—
322C8—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22#137×C4712yes—
329C22C22×D4×C4711yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4C2×#41×C4711yescharacteristic
343C4H(5,𝔽2)×C4711yescharacteristic
344C2—22no—
345C2—41no—
346C2C47×#54611yescharacteristic
347C2C2×#137×C4711yescharacteristic
348C2C47×#57811yescharacteristic
subgroupG/H
center, socleC22×C47C22×D4
commutator, Frattini, cosocleC2×C4C24×C47
prime radicalC2×D4×C47D4
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
3. C47×#491C2semidirect
4. C47×#485C2semidirect
5. C47×#483C2semidirect
6. C47×#479C2semidirect
7. C47×#470C2semidirect
8. C47×#467C2semidirect
9. C47×#462C2semidirect
10. C47×#451C2semidirect
11. C47×#451C2semidirect
12. C47×#441C2semidirect
14. C47×#419C2semidirect
15. C2×#103×C47C2semidirect
169. #3312C47direct (N × H)
177. #491C2×C47semidirect
178. #485C2×C47semidirect
179. #483C2×C47semidirect
180. #479C2×C47semidirect
181. #470C2×C47semidirect
182. #467C2×C47semidirect
183. #462C2×C47semidirect
184. #451C2×C47semidirect
185. #451C2×C47semidirect
186. #441C2×C47semidirect
188. #419C2×C47semidirect
189. C2×#103C2×C47semidirect
190. C47#3312direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#5522
D4×Q8×C472
C47×#4912
C47×#4852
C47×#4832
C47×#4792
C47×#4702
C47×#4672
C47×#4622
C47×#4512
C47×#4412
C47×#4352
C47×#4192
C2×#103×C472
#331247