Finite Group Databasebeta

← C47×#34056 #26073754

Subgroups — C47×#34056 #26073754

Order 12032.

2358 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#41×C47C211yesmaximal, characteristic
2C47×#2320C214yesmaximal, complemented
3C47×#2319C214yesmaximal, complemented
4C47×#2318C218yesmaximal, complemented
5C47×#2298C214yesmaximal, complemented
6C47×#2297C212yesmaximal
7C47×#2296C212yesmaximal, complemented
8C47×#2283C214yesmaximal, complemented
9C4×#117×C47C211yesmaximal, characteristic, complemented
10C2×C47×#376C211yesmaximal, characteristic, complemented
11C22×#41×C47C2211yescharacteristic
12C4×#41×C47C4116yescomplemented
13C2×C4×Q8×C47C2212yes—
14C2×C4×D4×C47C2214yes—
15C2×C4×D4×C47C2212yes—
16C2×#117×C47C2212yes—
17C2×#117×C47C2211yescharacteristic
18C2×#117×C47C2212yes—
19C22×C42×C47C2212yes—
20C22×C42×C47C2211yescharacteristic
21C22×C42×C47C2212yes—
22C47×#391C2214yes—
23C47×#390C2214yes—
24C47×#389C2218yes—
25C47×#388C22116yes—
26C47×#387C22116yes—
27C47×#386C2218yes—
28C47×#385C2218yes—
29C47×#383C2218yes—
30C47×#382C2218yes—
31C47×#381C2218yes—
32C47×#380C2218yes—
33C4×C4⋊C4×C47C2214yes—
34C4×C4⋊C4×C47C2218yes—
35C4×C22⋊C4×C47C2214yes—
36C4×C22⋊C4×C47C2218yes—
37C47×#376C2212yes—
38C47×#376C2212yes—
39C47×#376C2214yes—
40C47×#376C2212yes—
41C2×#95×C47C2214yes—
42C43×C47C2212yes—
43C2×#41×C47—28no—
44C2×#41×C47C2×C418yes—
45C22×Q8×C47C2311yescharacteristic
46C22×D4×C47C2312yes—
47C22×D4×C47C2311yescharacteristic
48C23×C4×C47C2312yes—
49C23×C4×C47C2314yes—
50C23×C4×C47C2312yes—
51C23×C4×C47C2314yes—
52C23×C4×C47C2311yescharacteristic
53C4×Q8×C47C2×C4116yescomplemented
54C4×D4×C47C2×C4132yes—
55C4×D4×C47C2×C4116yescomplemented
56#117×C47—28no—
57#117×C47C2×C418yes—
58#117×C47C2×C4116yescomplemented
59C2×C4⋊C4×C47C2314yes—
60C2×C4⋊C4×C47C23116yes—
61C2×C4⋊C4×C47C2314yes—
62C2×C4⋊C4×C47C2312yes—
63C2×C22⋊C4×C47C2314yes—
64C2×C22⋊C4×C47C23116yes—
65C2×C22⋊C4×C47C2312yes—
66C2×C22⋊C4×C47C2314yes—
67C2×C42×C47—28no—
68C2×C42×C47C2×C418yes—
69C2×C42×C47C2×C4116yescomplemented
70C2×C42×C47C2314yes—
71C2×C42×C47C2314yes—
72C2×C42×C47C2314yes—
73C2×C42×C47C2318yes—
74C2×C42×C47C2312yes—
75C2×C42×C47C2314yes—
76C2×C42×C47C2311yescharacteristic
77C2×C42×C47C2311yescharacteristic
78C2×C42×C47C2312yes—
79#95×C47C2314yes—
80#95×C47C2314yes—
81#95×C47C2318yes—
82#95×C47C2318yes—
83#95×C47C23116yes—
84#95×C47C23116yes—
85C24×C47C2412yes—
86C24×C47C2411yescharacteristic
87#41×C47—232no—
88C2×Q8×C47—24no—
89C2×Q8×C47C22×C414yes—
90C2×D4×C47—28no—
91C2×D4×C47—24no—
92C2×D4×C47C22×C418yes—
93C2×D4×C47C22×C414yes—
94C22×C4×C47—28no—
95C22×C4×C47—28no—
96C22×C4×C47—44no—
97C22×C4×C47—48no—
98C22×C4×C47—48no—
99C22×C4×C47C22×C418yes—
100C22×C4×C47C22×C418yes—
101C22×C4×C47C22×C4116yes—
102C22×C4×C47C22×C414yes—
103C22×C4×C47#4118yes—
104C22×C4×C47C2418yes—
105C22×C4×C47C2418yes—
106C22×C4×C47C2412yes—
107C22×C4×C47C2412yes—
108C22×C4×C47C2414yes—
109C22×C4×C47C2412yes—
110C22×C4×C47C2411yescharacteristic
111C22×C4×C47C2411yescharacteristic
112C4⋊C4×C47—28no—
113C4⋊C4×C47—416no—
114C4⋊C4×C47C22×C418yes—
115C4⋊C4×C47C22×C4116yes—
116C22⋊C4×C47—28no—
117C22⋊C4×C47—416no—
118C22⋊C4×C47C22×C418yes—
119C22⋊C4×C47C22×C4116yes—
120C42×C47—28no—
121C42×C47—28no—
122C42×C47—28no—
123C42×C47—48no—
124C42×C47C22×C414yes—
125C42×C47C22×C414yes—
126C42×C47C22×C418yes—
127C42×C47C22×C418yes—
128C42×C47C22×C4116yes—
129C23×C47—24no—
130C23×C47—24no—
131C23×C47—28no—
132C23×C47C23×C414yes—
133C23×C47C23×C412yes—
134C23×C47C2×#4114yes—
135C23×C47C2511yescharacteristic
136Q8×C47—28no—
137D4×C47—216no—
138D4×C47—28no—
139C2×C4×C47—24no—
140C2×C4×C47—24no—
141C2×C4×C47—28no—
142C2×C4×C47—24no—
143C2×C4×C47—216no—
144C2×C4×C47—28no—
145C2×C4×C47—28no—
146C2×C4×C47—216no—
147C2×C4×C47—28no—
148C2×C4×C47—28no—
149C2×C4×C47—48no—
150C2×C4×C47—416no—
151C2×C4×C47—416no—
152C2×C4×C47#117116yes—
153C2×C4×C47C23×C414yes—
154C2×C4×C47C23×C414yes—
155C2×C4×C47C23×C418yes—
156C2×C4×C47C23×C414yes—
157C2×C4×C47C23×C412yes—
158C2×C4×C47C23×C412yes—
159C2×C4×C47C2×#4114yes—
160C2×C4×C47C2×#4114yes—
161#34056C4711yesmaximal, characteristic, direct product factor, Sylow
162C22×C47—24no—
163C22×C47—28no—
164C22×C47—24no—
165C22×C47—28no—
166C22×C47—48no—
167C22×C47C2×#11714yes—
168C22×C47C24×C411yescharacteristic
169C22×C47C22×#4112yes—
170C22×C47#58514yes—
171C4×C47—24no—
172C4×C47—24no—
173C4×C47—24no—
174C4×C47—28no—
175C4×C47—48no—
176C4×C47—48no—
177C4×C47C2×#11714yes—
178C4×C47C2×#11714yes—
179C2×C4×#41C2×C4711yescharacteristic
180#2320C2×C4714yescomplemented
181#2319C2×C4714yescomplemented
182#2318C2×C4718yescomplemented
183#2298C2×C4714yescomplemented
184#2297C2×C4712yes—
185#2296C2×C4712yescomplemented
186#2283C2×C4714yescomplemented
187C4×#117C2×C4711yescharacteristic, complemented
188C2×#376C2×C4711yescharacteristic, complemented
189C2×C47—24no—
190C2×C47—44no—
191C2×C47C22×#11711yescharacteristic
192C2×C47#342812yes—
193C2×C47#345514yes—
194C22×#41C22×C4711yescharacteristic
195C4×#41C4×C47116yescomplemented
196C2×C4×Q8C22×C4712yes—
197C2×C4×D4C22×C4714yes—
198C2×C4×D4C22×C4712yes—
199C2×#117C22×C4712yes—
200C2×#117C22×C4711yescharacteristic
201C2×#117C22×C4712yes—
202C22×C42C22×C4712yes—
203C22×C42C22×C4711yescharacteristic
204C22×C42C22×C4712yes—
205#391C22×C4714yes—
206#390C22×C4714yes—
207#389C22×C4718yes—
208#388C22×C47116yes—
209#387C22×C47116yes—
210#386C22×C4718yes—
211#385C22×C4718yes—
212#383C22×C4718yes—
213#382C22×C4718yes—
214#381C22×C4718yes—
215#380C22×C4718yes—
216C4×C4⋊C4C22×C4714yes—
217C4×C4⋊C4C22×C4718yes—
218C4×C22⋊C4C22×C4714yes—
219C4×C22⋊C4C22×C4718yes—
220#376C22×C4714yes—
221#376C22×C4712yes—
222#376C22×C4712yes—
223#376C22×C4712yes—
224C2×#95C22×C4714yes—
225C43C22×C4712yes—
226C47#3405611yescharacteristic, direct product factor, Sylow
227C2×#41—28no—
228C2×#41C2×C4×C4718yes—
229C22×Q8C23×C4711yescharacteristic
230C22×D4C23×C4712yes—
231C22×D4C23×C4711yescharacteristic
232C23×C4C23×C4712yes—
233C23×C4C23×C4714yes—
234C23×C4C23×C4712yes—
235C23×C4C23×C4714yes—
236C23×C4C23×C4711yescharacteristic
237C4×Q8C2×C4×C47116yescomplemented
238C4×D4C2×C4×C47132yes—
239C4×D4C2×C4×C47116yescomplemented
240#117—28no—
241#117C2×C4×C4718yes—
242#117C2×C4×C47116yescomplemented
243C2×C4⋊C4C23×C4714yes—
244C2×C4⋊C4C23×C47116yes—
245C2×C4⋊C4C23×C4714yes—
246C2×C4⋊C4C23×C4712yes—
247C2×C22⋊C4C23×C4714yes—
248C2×C22⋊C4C23×C47116yes—
249C2×C22⋊C4C23×C4712yes—
250C2×C22⋊C4C23×C4714yes—
251C2×C42—28no—
252C2×C42C2×C4×C4718yes—
253C2×C42C2×C4×C47116yescomplemented
254C2×C42C23×C4714yes—
255C2×C42C23×C4714yes—
256C2×C42C23×C4714yes—
257C2×C42C23×C4718yes—
258C2×C42C23×C4711yescharacteristic
259C2×C42C23×C4712yes—
260C2×C42C23×C4712yes—
261C2×C42C23×C4714yes—
262C2×C42C23×C4711yescharacteristic
263#95C23×C4714yes—
264#95C23×C4714yes—
265#95C23×C4718yes—
266#95C23×C4718yes—
267#95C23×C47116yes—
268#95C23×C47116yes—
269C24C24×C4712yes—
270C24C24×C4711yescharacteristic
271#41—232no—
272C2×Q8—24no—
273C2×Q8C22×C4×C4714yes—
274C2×D4—28no—
275C2×D4—24no—
276C2×D4C22×C4×C4718yes—
277C2×D4C22×C4×C4714yes—
278C22×C4—28no—
279C22×C4—28no—
280C22×C4—44no—
281C22×C4—48no—
282C22×C4—48no—
283C22×C4C22×C4×C4718yes—
284C22×C4C22×C4×C4718yes—
285C22×C4C22×C4×C47116yes—
286C22×C4C22×C4×C4714yes—
287C22×C4#41×C4718yes—
288C22×C4C24×C4718yes—
289C22×C4C24×C4718yes—
290C22×C4C24×C4712yes—
291C22×C4C24×C4712yes—
292C22×C4C24×C4712yes—
293C22×C4C24×C4714yes—
294C22×C4C24×C4711yescharacteristic
295C22×C4C24×C4711yescharacteristic
296C4⋊C4—28no—
297C4⋊C4—416no—
298C4⋊C4C22×C4×C4718yes—
299C4⋊C4C22×C4×C47116yes—
300C22⋊C4—28no—
301C22⋊C4—416no—
302C22⋊C4C22×C4×C4718yes—
303C22⋊C4C22×C4×C47116yes—
304C42—28no—
305C42—28no—
306C42—28no—
307C42—48no—
308C42C22×C4×C4714yes—
309C42C22×C4×C4714yes—
310C42C22×C4×C4718yes—
311C42C22×C4×C4718yes—
312C42C22×C4×C47116yes—
313C23—24no—
314C23—24no—
315C23—28no—
316C23C23×C4×C4714yes—
317C23C23×C4×C4712yes—
318C23C2×#41×C4714yes—
319C23C25×C4711yescharacteristic
320Q8—28no—
321D4—216no—
322D4—28no—
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—28no—
326C2×C4—24no—
327C2×C4—216no—
328C2×C4—28no—
329C2×C4—28no—
330C2×C4—216no—
331C2×C4—28no—
332C2×C4—28no—
333C2×C4—48no—
334C2×C4—416no—
335C2×C4—416no—
336C2×C4#117×C47116yes—
337C2×C4C23×C4×C4714yes—
338C2×C4C23×C4×C4714yes—
339C2×C4C23×C4×C4718yes—
340C2×C4C23×C4×C4714yes—
341C2×C4C23×C4×C4712yes—
342C2×C4C23×C4×C4712yes—
343C2×C4C2×#41×C4714yes—
344C2×C4C2×#41×C4714yes—
345C22—24no—
346C22—28no—
347C22—24no—
348C22—28no—
349C22—48no—
350C22C2×#117×C4714yes—
351C22C24×C4×C4711yescharacteristic
352C22C22×#41×C4712yes—
353C22C47×#58514yes—
354C4—24no—
355C4—24no—
356C4—24no—
357C4—28no—
358C4—48no—
359C4—48no—
360C4C2×#117×C4714yes—
361C4C2×#117×C4714yes—
362C2—24no—
363C2—44no—
364C2C22×#117×C4711yescharacteristic
365C2C47×#342812yes—
366C2C47×#345514yes—
subgroupG/H
centerC22×C4×C47C24
commutatorC22C24×C4×C47
Frattini, cosocleC23C25×C47
socleC23×C47C25
prime radicalC22×#41×C47C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2320C2semidirect
3. C47×#2319C2semidirect
4. C47×#2318C2semidirect
5. C47×#2298C2semidirect
7. C47×#2296C2semidirect
8. C47×#2283C2semidirect
9. C4×#117×C47C2semidirect
10. C2×C47×#376C2semidirect
12. C4×#41×C47C4semidirect
53. C4×Q8×C47C2×C4semidirect
55. C4×D4×C47C2×C4semidirect
58. #117×C47C2×C4semidirect
69. C2×C42×C47C2×C4semidirect
161. #34056C47direct (N × H)
180. #2320C2×C47semidirect
181. #2319C2×C47semidirect
182. #2318C2×C47semidirect
183. #2298C2×C47semidirect
185. #2296C2×C47semidirect
186. #2283C2×C47semidirect
187. C4×#117C2×C47semidirect
188. C2×#376C2×C47semidirect
195. C4×#41C4×C47semidirect
226. C47#34056direct (N × H)
237. C4×Q8C2×C4×C47semidirect
239. C4×D4C2×C4×C47semidirect
242. #117C2×C4×C47semidirect
253. C2×C42C2×C4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#41×C472
C47×#23202
C47×#23192
C47×#23182
C47×#22982
C47×#22972
C47×#22962
C47×#22832
C4×#117×C472
C2×C47×#3762
#3405647