Finite Group Databasebeta

← C47×#34547 #26074245

Subgroups — C47×#34547 #26074245

Order 12032.

2938 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#41×C47C212yesmaximal, complemented
2C47×#2399C211yesmaximal, characteristic, complemented
3C47×#2398C212yesmaximal, complemented
4C47×#2397C211yesmaximal, characteristic, complemented
5C47×#2396C214yesmaximal, complemented
6C47×#2395C214yesmaximal, complemented
7C47×#2392C214yesmaximal, complemented
8C47×#2392C214yesmaximal, complemented
9C47×#2388C214yesmaximal, complemented
10C42×D4×C47C214yesmaximal, complemented
11C4×#117×C47C211yesmaximal, characteristic, complemented
12C22×#41×C47C2212yes—
13C4×#41×C47—216no—
14C2×C4×Q8×C47C2212yes—
15C2×C4×Q8×C47C2212yes—
16C2×C4×D4×C47C2218yes—
17C2×C4×D4×C47C2214yes—
18C2×C4×D4×C47C2214yes—
19C2×C4×D4×C47C2214yes—
20C2×C4×D4×C47C2212yes—
21C2×C4×D4×C47C2212yes—
22C2×#117×C47C2212yes—
23C2×#117×C47C2214yes—
24C2×#117×C47C2212yes—
25C22×C42×C47C2214yes—
26C22×C42×C47C2211yescharacteristic
27C47×#400C2214yes—
28C47×#399C2214yes—
29C47×#398C2214yes—
30C47×#398C2214yes—
31C47×#397C2214yes—
32C47×#397C2214yes—
33C47×#396C2218yes—
34C47×#395C2214yes—
35C47×#394C2218yes—
36C47×#394C2214yes—
37C47×#394C2214yes—
38C47×#393C2214yes—
39C47×#392C2214yes—
40C47×#392C2214yes—
41C4×C4⋊C4×C47C2214yes—
42C4×C4⋊C4×C47C2214yes—
43C4×C4⋊C4×C47C2218yes—
44C4×C22⋊C4×C47C2214yes—
45C4×C22⋊C4×C47C2218yes—
46C4×C22⋊C4×C47C2218yes—
47C4×C22⋊C4×C47C2218yes—
48C47×#376C2211yescharacteristic
49C47×#376C2211yescharacteristic
50C43×C47C2212yes—
51C2×#41×C47—28no—
52C2×#41×C47—216no—
53C22×Q8×C47C2312yes—
54C22×D4×C47C2314yes—
55C22×D4×C47C2312yes—
56C22×D4×C47C2314yes—
57C23×C4×C47C2314yes—
58C23×C4×C47C2314yes—
59C23×C4×C47C2311yescharacteristic
60C23×C4×C47C2312yes—
61C23×C4×C47C2314yes—
62C4×Q8×C47—28no—
63C4×Q8×C47—28no—
64C4×D4×C47—216no—
65C4×D4×C47—216no—
66C4×D4×C47—232no—
67C4×D4×C47—28no—
68C4×D4×C47—28no—
69C4×D4×C47—216no—
70#117×C47—28no—
71#117×C47—216no—
72#117×C47—28no—
73C2×C4⋊C4×C47C2314yes—
74C2×C4⋊C4×C47C2314yes—
75C2×C4⋊C4×C47C2312yes—
76C2×C4⋊C4×C47C2312yes—
77C2×C4⋊C4×C47C2314yes—
78C2×C4⋊C4×C47C2318yes—
79C2×C4⋊C4×C47C2314yes—
80C2×C22⋊C4×C47C2314yes—
81C2×C22⋊C4×C47C2314yes—
82C2×C22⋊C4×C47C2314yes—
83C2×C22⋊C4×C47C2314yes—
84C2×C22⋊C4×C47C2318yes—
85C2×C22⋊C4×C47C2318yes—
86C2×C22⋊C4×C47C2318yes—
87C2×C42×C47—216no—
88C2×C42×C47D418yescomplemented
89C2×C42×C47C2314yes—
90C2×C42×C47C2314yes—
91C2×C42×C47C2314yes—
92C2×C42×C47C2312yes—
93C2×C42×C47C2318yes—
94C2×C42×C47C2312yes—
95C2×C42×C47C2311yescharacteristic
96C2×C42×C47C2312yes—
97C2×C42×C47C2311yescharacteristic
98#95×C47C2314yes—
99#95×C47C2314yes—
100#95×C47C2314yes—
101#95×C47C2318yes—
102#95×C47C2314yes—
103#95×C47C2318yes—
104C24×C47C2411yescharacteristic
105C24×C47C2414yes—
106#41×C47—264no—
107C2×Q8×C47—24no—
108C2×Q8×C47—28no—
109C2×D4×C47—28no—
110C2×D4×C47—216no—
111C2×D4×C47—28no—
112C2×D4×C47—28no—
113C2×D4×C47—24no—
114C2×D4×C47—28no—
115C2×D4×C47—28no—
116C22×C4×C47—28no—
117C22×C4×C47—24no—
118C22×C4×C47—28no—
119C22×C4×C47—28no—
120C22×C4×C47—28no—
121C22×C4×C47—28no—
122C22×C4×C47—216no—
123C22×C4×C47—216no—
124C22×C4×C47C2×D418yes—
125C22×C4×C47C2×D414yes—
126C22×C4×C47#41116yescomplemented
127C22×C4×C47C2414yes—
128C22×C4×C47C2414yes—
129C22×C4×C47C2414yes—
130C22×C4×C47C2411yescharacteristic
131C22×C4×C47C2412yes—
132C22×C4×C47C2414yes—
133C22×C4×C47C2414yes—
134C22×C4×C47C2412yes—
135C22×C4×C47C2411yescharacteristic
136C4⋊C4×C47—28no—
137C4⋊C4×C47—28no—
138C4⋊C4×C47—24no—
139C4⋊C4×C47—24no—
140C4⋊C4×C47—28no—
141C4⋊C4×C47—216no—
142C4⋊C4×C47—28no—
143C22⋊C4×C47—28no—
144C22⋊C4×C47—216no—
145C22⋊C4×C47—28no—
146C22⋊C4×C47—28no—
147C22⋊C4×C47—28no—
148C22⋊C4×C47—216no—
149C22⋊C4×C47—216no—
150C42×C47—28no—
151C42×C47—28no—
152C42×C47—28no—
153C42×C47—24no—
154C42×C47—216no—
155C42×C47C2×D414yes—
156C42×C47C2×D418yes—
157C42×C47C2×D414yes—
158C42×C47#4118yescomplemented
159C23×C47—24no—
160C23×C47—22no—
161C23×C47—28no—
162C23×C47—28no—
163C23×C47—24no—
164C23×C47—24no—
165C23×C47C22×D412yes—
166C23×C47C2×#4118yes—
167C23×C47C2511yescharacteristic
168Q8×C47—216no—
169D4×C47—232no—
170D4×C47—216no—
171D4×C47—232no—
172C2×C4×C47—24no—
173C2×C4×C47—28no—
174C2×C4×C47—22no—
175C2×C4×C47—24no—
176C2×C4×C47—24no—
177C2×C4×C47—216no—
178C2×C4×C47—232no—
179C2×C4×C47—28no—
180C2×C4×C47—24no—
181C2×C4×C47—24no—
182C2×C4×C47—28no—
183C2×C4×C47—24no—
184C2×C4×C47—28no—
185C2×C4×C47—28no—
186C2×C4×C47—416no—
187C2×C4×C47—416no—
188C2×C4×C47C22×D412yes—
189C2×C4×C47C22×D414yes—
190C2×C4×C47C22×D414yes—
191C2×C4×C47C22×D412yes—
192C2×C4×C47C2×#4118yes—
193C2×C4×C47C2×#4118yes—
194C2×C4×C47C2×#4118yes—
195C2×C4×C47C2×#4114yes—
196#34547C4711yesmaximal, characteristic, direct product factor, Sylow
197C22×C47—24no—
198C22×C47—28no—
199C22×C47—22no—
200C22×C47—216no—
201C22×C47—44no—
202C22×C47—44no—
203C22×C47—44no—
204C22×C47—48no—
205C22×C47C23×D411yescharacteristic
206C22×C47C22×#4114yes—
207C22×C47C22×#4112yes—
208C4×C47—24no—
209C4×C47—28no—
210C4×C47—22no—
211C4×C47—28no—
212C4×C47—44no—
213C4×C47—44no—
214C4×C47—44no—
215C4×C47#52518yes—
216C4×C47#53214yes—
217C2×C4×#41C2×C4712yescomplemented
218#2399C2×C4711yescharacteristic, complemented
219#2398C2×C4712yescomplemented
220#2397C2×C4711yescharacteristic, complemented
221#2396C2×C4714yescomplemented
222#2395C2×C4714yescomplemented
223#2392C2×C4714yescomplemented
224#2392C2×C4714yescomplemented
225#2388C2×C4714yescomplemented
226C42×D4C2×C4714yescomplemented
227C4×#117C2×C4711yescharacteristic, complemented
228C2×C47—42no—
229C2×C47—48no—
230C2×C47C2×#52512yes—
231C2×C47C2×#53211yescharacteristic
232C2×C47#344414yes—
233C22×#41C22×C4712yes—
234C4×#41—216no—
235C2×C4×Q8C22×C4712yes—
236C2×C4×Q8C22×C4712yes—
237C2×C4×D4C22×C4718yes—
238C2×C4×D4C22×C4714yes—
239C2×C4×D4C22×C4714yes—
240C2×C4×D4C22×C4712yes—
241C2×C4×D4C22×C4714yes—
242C2×C4×D4C22×C4712yes—
243C2×#117C22×C4712yes—
244C2×#117C22×C4714yes—
245C2×#117C22×C4712yes—
246C22×C42C22×C4714yes—
247C22×C42C22×C4711yescharacteristic
248#400C22×C4714yes—
249#399C22×C4714yes—
250#398C22×C4714yes—
251#398C22×C4714yes—
252#397C22×C4714yes—
253#397C22×C4714yes—
254#396C22×C4718yes—
255#395C22×C4714yes—
256#394C22×C4718yes—
257#394C22×C4714yes—
258#394C22×C4714yes—
259#393C22×C4714yes—
260#392C22×C4714yes—
261#392C22×C4714yes—
262C4×C4⋊C4C22×C4714yes—
263C4×C4⋊C4C22×C4714yes—
264C4×C4⋊C4C22×C4718yes—
265C4×C22⋊C4C22×C4714yes—
266C4×C22⋊C4C22×C4718yes—
267C4×C22⋊C4C22×C4718yes—
268C4×C22⋊C4C22×C4718yes—
269#376C22×C4711yescharacteristic
270#376C22×C4711yescharacteristic
271C43C22×C4712yes—
272C47#3454711yescharacteristic, direct product factor, Sylow
273C2×#41—28no—
274C2×#41—216no—
275C22×Q8C23×C4712yes—
276C22×D4C23×C4714yes—
277C22×D4C23×C4712yes—
278C22×D4C23×C4714yes—
279C23×C4C23×C4714yes—
280C23×C4C23×C4714yes—
281C23×C4C23×C4711yescharacteristic
282C23×C4C23×C4712yes—
283C23×C4C23×C4714yes—
284C4×Q8—28no—
285C4×Q8—28no—
286C4×D4—216no—
287C4×D4—216no—
288C4×D4—232no—
289C4×D4—28no—
290C4×D4—28no—
291C4×D4—216no—
292#117—28no—
293#117—216no—
294#117—28no—
295C2×C4⋊C4C23×C4714yes—
296C2×C4⋊C4C23×C4714yes—
297C2×C4⋊C4C23×C4712yes—
298C2×C4⋊C4C23×C4712yes—
299C2×C4⋊C4C23×C4714yes—
300C2×C4⋊C4C23×C4718yes—
301C2×C4⋊C4C23×C4714yes—
302C2×C22⋊C4C23×C4714yes—
303C2×C22⋊C4C23×C4714yes—
304C2×C22⋊C4C23×C4714yes—
305C2×C22⋊C4C23×C4714yes—
306C2×C22⋊C4C23×C4718yes—
307C2×C22⋊C4C23×C4718yes—
308C2×C22⋊C4C23×C4718yes—
309C2×C42—216no—
310C2×C42D4×C4718yescomplemented
311C2×C42C23×C4714yes—
312C2×C42C23×C4712yes—
313C2×C42C23×C4714yes—
314C2×C42C23×C4714yes—
315C2×C42C23×C4718yes—
316C2×C42C23×C4712yes—
317C2×C42C23×C4711yescharacteristic
318C2×C42C23×C4711yescharacteristic
319C2×C42C23×C4712yes—
320#95C23×C4714yes—
321#95C23×C4714yes—
322#95C23×C4714yes—
323#95C23×C4718yes—
324#95C23×C4714yes—
325#95C23×C4718yes—
326C24C24×C4711yescharacteristic
327C24C24×C4714yes—
328#41—264no—
329C2×Q8—24no—
330C2×Q8—28no—
331C2×D4—28no—
332C2×D4—216no—
333C2×D4—28no—
334C2×D4—28no—
335C2×D4—24no—
336C2×D4—28no—
337C2×D4—28no—
338C22×C4—28no—
339C22×C4—24no—
340C22×C4—28no—
341C22×C4—28no—
342C22×C4—28no—
343C22×C4—28no—
344C22×C4—216no—
345C22×C4—216no—
346C22×C4C2×D4×C4718yes—
347C22×C4C2×D4×C4714yes—
348C22×C4#41×C47116yescomplemented
349C22×C4C24×C4714yes—
350C22×C4C24×C4714yes—
351C22×C4C24×C4714yes—
352C22×C4C24×C4712yes—
353C22×C4C24×C4711yescharacteristic
354C22×C4C24×C4714yes—
355C22×C4C24×C4714yes—
356C22×C4C24×C4712yes—
357C22×C4C24×C4711yescharacteristic
358C4⋊C4—28no—
359C4⋊C4—28no—
360C4⋊C4—24no—
361C4⋊C4—24no—
362C4⋊C4—28no—
363C4⋊C4—216no—
364C4⋊C4—28no—
365C22⋊C4—28no—
366C22⋊C4—216no—
367C22⋊C4—28no—
368C22⋊C4—28no—
369C22⋊C4—28no—
370C22⋊C4—216no—
371C22⋊C4—216no—
372C42—28no—
373C42—28no—
374C42—28no—
375C42—24no—
376C42—216no—
377C42C2×D4×C4714yes—
378C42C2×D4×C4718yes—
379C42C2×D4×C4714yes—
380C42#41×C4718yescomplemented
381C23—24no—
382C23—22no—
383C23—28no—
384C23—28no—
385C23—24no—
386C23—24no—
387C23C22×D4×C4712yes—
388C23C2×#41×C4718yes—
389C23C25×C4711yescharacteristic
390Q8—216no—
391D4—232no—
392D4—216no—
393D4—232no—
394C2×C4—24no—
395C2×C4—28no—
396C2×C4—22no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—216no—
400C2×C4—232no—
401C2×C4—28no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—28no—
405C2×C4—24no—
406C2×C4—28no—
407C2×C4—28no—
408C2×C4—416no—
409C2×C4—416no—
410C2×C4C22×D4×C4712yes—
411C2×C4C22×D4×C4714yes—
412C2×C4C22×D4×C4714yes—
413C2×C4C22×D4×C4712yes—
414C2×C4C2×#41×C4718yes—
415C2×C4C2×#41×C4718yes—
416C2×C4C2×#41×C4718yes—
417C2×C4C2×#41×C4714yes—
418C22—24no—
419C22—28no—
420C22—22no—
421C22—216no—
422C22—44no—
423C22—44no—
424C22—44no—
425C22—48no—
426C22C23×D4×C4711yescharacteristic
427C22C22×#41×C4714yes—
428C22C22×#41×C4712yes—
429C4—24no—
430C4—28no—
431C4—22no—
432C4—28no—
433C4—44no—
434C4—44no—
435C4—44no—
436C4C47×#52518yes—
437C4C47×#53214yes—
438C2—42no—
439C2—48no—
440C2C2×C47×#52512yes—
441C2C2×C47×#53211yescharacteristic
442C2C47×#344414yes—
subgroupG/H
centerC2×C42×C47C23
commutator, Frattini, cosocleC23C25×C47
socleC23×C47C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C4×#41×C47C2semidirect
2. C47×#2399C2semidirect
3. C47×#2398C2semidirect
4. C47×#2397C2semidirect
5. C47×#2396C2semidirect
6. C47×#2395C2semidirect
7. C47×#2392C2semidirect
8. C47×#2392C2semidirect
9. C47×#2388C2semidirect
10. C42×D4×C47C2semidirect
11. C4×#117×C47C2semidirect
88. C2×C42×C47D4semidirect
126. C22×C4×C47#41semidirect
158. C42×C47#41semidirect
196. #34547C47direct (N × H)
217. C2×C4×#41C2×C47semidirect
218. #2399C2×C47semidirect
219. #2398C2×C47semidirect
220. #2397C2×C47semidirect
221. #2396C2×C47semidirect
222. #2395C2×C47semidirect
223. #2392C2×C47semidirect
224. #2392C2×C47semidirect
225. #2388C2×C47semidirect
226. C42×D4C2×C47semidirect
227. C4×#117C2×C47semidirect
272. C47#34547direct (N × H)
310. C2×C42D4×C47semidirect
348. C22×C4#41×C47semidirect
380. C42#41×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×#23992
C47×#23982
C47×#23972
C47×#23962
C47×#23952
C47×#23922
C47×#23882
C42×D4×C472
C4×#117×C472
#3454747