Finite Group Databasebeta

← C47×#9282 #26048980

Subgroups — C47×#9282 #26048980

Order 12032.

416 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3210C211yesmaximal, characteristic
2C47×#2985C211yesmaximal, characteristic, complemented
3C47×#1506C211yesmaximal, characteristic, complemented
4C47×#1505C211yesmaximal, characteristic
5C47×#1496C211yesmaximal, characteristic
6C47×#1287C211yesmaximal, characteristic, complemented
7C47×#1274C211yesmaximal, characteristic, complemented
8C47×#533C2211yescharacteristic
9C47×#532C2211yescharacteristic
10C47×#494C411yescharacteristic, complemented
11C47×#492C411yescharacteristic, complemented
12C47×#487C411yescharacteristic, complemented
13C47×#486C411yescharacteristic, complemented
14C47×#464—22no—
15C47×#452—22no—
16C47×#446—21no—
17C47×#446—22no—
18C8×Q8×C47—21no—
19C47×#433—22no—
20C47×#432C2211yescharacteristic
21C47×#432C2211yescharacteristic
22C47×#431C2211yescharacteristic
23C47×#431C2211yescharacteristic
24C47×#376C2211yescharacteristic
25C47×#328—22no—
26C47×#327—22no—
27C47×D4⋊C8—21no—
28C47×D4⋊C8—21no—
29C2×#41×C47—21no—
30C2×Q16×C47—22no—
31C2×SD16×C47—22no—
32C4⋊Q8×C47C2×C411yescharacteristic
33C4⋊Q8×C47C2×C411yescharacteristic
34C4⋊Q8×C47C2×C411yescharacteristic
35#127×C47C2×C411yescharacteristic
36#125×C47—21no—
37#124×C47—21no—
38C22⋊Q8×C47—21no—
39C22⋊Q8×C47D412yes—
40#121×C47—21no—
41#121×C47—21no—
42C4×Q8×C47—21no—
43C4×Q8×C47D412yes—
44C4×D4×C47—21no—
45C4×D4×C47—21no—
46#117×C47—21no—
47C2×C42×C47—21no—
48C2×C42×C47C2311yescharacteristic
49C4⋊C8×C47—22no—
50C4⋊C8×C47—22no—
51C4⋊C8×C47—21no—
52C4⋊C8×C47—21no—
53C4⋊C8×C47—21no—
54C4⋊C8×C47—21no—
55#103×C47—22no—
56#102×C47—22no—
57C22⋊C8×C47—21no—
58C22⋊C8×C47—21no—
59C22⋊C8×C47—21no—
60C22⋊C8×C47D412yes—
61#97×C47—22no—
62#97×C47—21no—
63#97×C47—21no—
64C4×C8×C47—22no—
65C4×C8×C47C2×C411yescharacteristic
66C4×C8×C47C2×C411yescharacteristic
67C4×C8×C47D411yescharacteristic
68C4×C8×C47D411yescharacteristic
69#95×C47—21no—
70#95×C47—21no—
71#41×C47—82no—
72C2×Q8×C47—21no—
73C2×Q8×C47—21no—
74C2×Q8×C47C22⋊C412yes—
75C2×D4×C47—21no—
76C2×D4×C47—21no—
77C2×D4×C47—21no—
78C2×D4×C47—41no—
79C22×C4×C47—41no—
80C22×C4×C47—41no—
81C22×C4×C47C2×D411yescharacteristic
82C22×C4×C47C2×D411yescharacteristic
83C22×C4×C47#4111yescharacteristic
84Q16×C47—82no—
85SD16×C47—82no—
86C2×C8×C47—21no—
87C2×C8×C47—21no—
88C2×C8×C47—21no—
89C2×C8×C47—22no—
90C2×C8×C47—21no—
91C2×C8×C47—41no—
92C4⋊C4×C47—21no—
93C4⋊C4×C47—21no—
94C4⋊C4×C47—21no—
95C4⋊C4×C47—22no—
96C4⋊C4×C47—22no—
97C4⋊C4×C47—21no—
98C4⋊C4×C47—21no—
99C4⋊C4×C47C22⋊C412yes—
100C22⋊C4×C47—22no—
101C22⋊C4×C47—41no—
102C22⋊C4×C47—41no—
103C42×C47—22no—
104C42×C47—22no—
105C42×C47—41no—
106C42×C47C22×C411yescharacteristic
107C42×C47C2×D411yescharacteristic
108C42×C47C2×D411yescharacteristic
109C42×C47#4111yescharacteristic
110C23×C47—41no—
111C23×C47#12111yescharacteristic
112Q8×C47—42no—
113Q8×C47—42no—
114Q8×C47—41no—
115Q8×C47—41no—
116D4×C47—42no—
117D4×C47—41no—
118D4×C47—41no—
119D4×C47—81no—
120D4×C47—82no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—22no—
124C2×C4×C47—22no—
125C2×C4×C47—41no—
126C2×C4×C47—41no—
127C2×C4×C47—42no—
128C2×C4×C47—41no—
129C2×C4×C47—82no—
130C2×C4×C47—81no—
131C2×C4×C47—81no—
132C2×C4×C47C2×C22⋊C411yescharacteristic
133C2×C4×C47C4×D411yescharacteristic
134C2×C4×C47C4×D411yescharacteristic
135C2×C4×C47#12011yescharacteristic
136C2×C4×C47#12111yescharacteristic
137C2×C4×C47#12311yescharacteristic
138C8×C47—41no—
139C8×C47—42no—
140C8×C47—41no—
141C8×C47—41no—
142C8×C47—41no—
143C8×C47—81no—
144#9282C4711yesmaximal, characteristic, direct product factor, Sylow
145C22×C47—21no—
146C22×C47—21no—
147C22×C47—21no—
148C22×C47—81no—
149C22×C47—81no—
150C22×C47—81no—
151C22×C47#38611yescharacteristic
152C4×C47—21no—
153C4×C47—21no—
154C4×C47—21no—
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—42no—
158C4×C47—42no—
159C4×C47—82no—
160C4×C47—81no—
161C4×C47#44311yescharacteristic
162C4×C47#44411yescharacteristic
163#3210C2×C4711yescharacteristic
164#2985C2×C4711yescharacteristic, complemented
165#1506C2×C4711yescharacteristic, complemented
166#1505C2×C4711yescharacteristic
167#1496C2×C4711yescharacteristic
168#1287C2×C4711yescharacteristic, complemented
169#1274C2×C4711yescharacteristic, complemented
170C2×C47—41no—
171C2×C47—161no—
172C2×C47#187611yescharacteristic
173C2×C47#190511yescharacteristic
174C2×C47#191011yescharacteristic
175#533C22×C4711yescharacteristic
176#532C22×C4711yescharacteristic
177#494C4×C4711yescharacteristic, complemented
178#492C4×C4711yescharacteristic, complemented
179#487C4×C4711yescharacteristic, complemented
180#486C4×C4711yescharacteristic, complemented
181#464—22no—
182#452—22no—
183#446—22no—
184#446—21no—
185C8×Q8—21no—
186#433—22no—
187#432C22×C4711yescharacteristic
188#432C22×C4711yescharacteristic
189#431C22×C4711yescharacteristic
190#431C22×C4711yescharacteristic
191#376C22×C4711yescharacteristic
192#328—22no—
193#327—22no—
194D4⋊C8—21no—
195D4⋊C8—21no—
196C47#928211yescharacteristic, direct product factor, Sylow
197C2×#41—21no—
198C2×Q16—22no—
199C2×SD16—22no—
200C4⋊Q8C2×C4×C4711yescharacteristic
201C4⋊Q8C2×C4×C4711yescharacteristic
202C4⋊Q8C2×C4×C4711yescharacteristic
203#127C2×C4×C4711yescharacteristic
204#125—21no—
205#124—21no—
206C22⋊Q8—21no—
207C22⋊Q8D4×C4712yes—
208#121—21no—
209#121—21no—
210C4×Q8—21no—
211C4×Q8D4×C4712yes—
212C4×D4—21no—
213C4×D4—21no—
214#117—21no—
215C2×C42—21no—
216C2×C42C23×C4711yescharacteristic
217C4⋊C8—22no—
218C4⋊C8—22no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223#103—22no—
224#102—22no—
225C22⋊C8—21no—
226C22⋊C8—21no—
227C22⋊C8—21no—
228C22⋊C8D4×C4712yes—
229#97—22no—
230#97—21no—
231#97—21no—
232C4×C8—22no—
233C4×C8C2×C4×C4711yescharacteristic
234C4×C8C2×C4×C4711yescharacteristic
235C4×C8D4×C4711yescharacteristic
236C4×C8D4×C4711yescharacteristic
237#95—21no—
238#95—21no—
239#41—82no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8C22⋊C4×C4712yes—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4C2×D4×C4711yescharacteristic
250C22×C4C2×D4×C4711yescharacteristic
251C22×C4#41×C4711yescharacteristic
252Q16—82no—
253SD16—82no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—22no—
258C2×C8—21no—
259C2×C8—41no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4C22⋊C4×C4712yes—
268C22⋊C4—22no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C42—22no—
272C42—22no—
273C42—41no—
274C42C22×C4×C4711yescharacteristic
275C42C2×D4×C4711yescharacteristic
276C42C2×D4×C4711yescharacteristic
277C42#41×C4711yescharacteristic
278C23—41no—
279C23#121×C4711yescharacteristic
280Q8—42no—
281Q8—42no—
282Q8—41no—
283Q8—41no—
284D4—42no—
285D4—41no—
286D4—41no—
287D4—81no—
288D4—82no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—82no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4C2×C22⋊C4×C4711yescharacteristic
301C2×C4C4×D4×C4711yescharacteristic
302C2×C4C4×D4×C4711yescharacteristic
303C2×C4#120×C4711yescharacteristic
304C2×C4#121×C4711yescharacteristic
305C2×C4#123×C4711yescharacteristic
306C8—41no—
307C8—42no—
308C8—41no—
309C8—41no—
310C8—41no—
311C8—81no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—81no—
316C22—81no—
317C22—81no—
318C22C47×#38611yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—42no—
325C4—42no—
326C4—82no—
327C4—81no—
328C4C47×#44311yescharacteristic
329C4C47×#44411yescharacteristic
330C2—41no—
331C2—161no—
332C2C47×#187611yescharacteristic
333C2C47×#190511yescharacteristic
334C2C47×#191011yescharacteristic
subgroupG/H
center, socleC22×C47#386
commutatorC42C22×C4×C47
Frattini, cosocleC2×C42C23×C47
prime radicalC47×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2985C2semidirect
3. C47×#1506C2semidirect
6. C47×#1287C2semidirect
7. C47×#1274C2semidirect
10. C47×#494C4semidirect
11. C47×#492C4semidirect
12. C47×#487C4semidirect
13. C47×#486C4semidirect
144. #9282C47direct (N × H)
164. #2985C2×C47semidirect
165. #1506C2×C47semidirect
168. #1287C2×C47semidirect
169. #1274C2×C47semidirect
177. #494C4×C47semidirect
178. #492C4×C47semidirect
179. #487C4×C47semidirect
180. #486C4×C47semidirect
196. C47#9282direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#32102
C47×#29852
C47×#15062
C47×#15052
C47×#14962
C47×#12872
C47×#12742
#928247