Finite Group Databasebeta

← C47×#34402 #26074100

Subgroups — C47×#34402 #26074100

Order 12032.

2410 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#532C211yesmaximal, characteristic
2C47×#2377C214yesmaximal, complemented
3C47×#2367C214yesmaximal, complemented
4C47×#2353C214yesmaximal, complemented
5C47×#2341C212yesmaximal, complemented
6C47×#2339C212yesmaximal, complemented
7C47×#2333C214yesmaximal, complemented
8C47×#2328C212yesmaximal, complemented
9C47×#2327C212yesmaximal, complemented
10C47×#2318C214yesmaximal, complemented
11C47×#2283C211yesmaximal, characteristic, complemented
12C47×#2283C211yesmaximal, characteristic, complemented
13C22×#41×C47C2212yes—
14C47×#532C4116yescomplemented
15C2×C4⋊Q8×C47C2211yescharacteristic
16C2×#127×C47C2211yescharacteristic
17C2×#124×C47C2212yes—
18C2×#121×C47C2212yes—
19C2×#121×C47C2212yes—
20C2×C4×Q8×C47C2214yes—
21C2×C4×D4×C47C2214yes—
22C2×C4×D4×C47C2212yes—
23C2×C4×D4×C47C2212yes—
24C22×C42×C47C2211yescharacteristic
25C47×#391C2214yes—
26C47×#390C2214yes—
27C47×#390C2218yes—
28C47×#388C2218yes—
29C47×#388C2218yes—
30C47×#387C2218yes—
31C47×#387C2218yes—
32C47×#386C2218yes—
33C47×#386C2218yes—
34C47×#386C2218yes—
35C47×#385C2218yes—
36C47×#383C2212yes—
37C47×#383C2212yes—
38C47×#382C2212yes—
39C47×#382C2212yes—
40C47×#381C2212yes—
41C47×#381C2212yes—
42C47×#381C2214yes—
43C47×#380C2212yes—
44C47×#380C2212yes—
45C47×#380C2214yes—
46C4×C4⋊C4×C47C2212yes—
47C4×C4⋊C4×C47C2212yes—
48C4×C22⋊C4×C47C2212yes—
49C4×C22⋊C4×C47C2211yescharacteristic
50C4×C22⋊C4×C47C2211yescharacteristic
51C4×C22⋊C4×C47C2214yes—
52C4×C22⋊C4×C47C2218yes—
53C47×#376C2212yes—
54C47×#376C2212yes—
55C2×#95×C47C2214yes—
56C2×#41×C47—48no—
57C2×#41×C47C2×C4116yescomplemented
58C22×Q8×C47C2312yes—
59C22×D4×C47C2312yes—
60C22×D4×C47C2312yes—
61C22×D4×C47C2312yes—
62C22×D4×C47C2314yes—
63C23×C4×C47C2311yescharacteristic
64C23×C4×C47C2318yes—
65C23×C4×C47C2311yescharacteristic
66C23×C4×C47C2311yescharacteristic
67C23×C4×C47C2314yes—
68C4⋊Q8×C47C2×C418yescomplemented
69#127×C47C2×C418yes—
70#124×C47C2×C4116yescomplemented
71#121×C47C2×C4116yescomplemented
72#121×C47C2×C4116yescomplemented
73C4×Q8×C47—48no—
74C4×D4×C47—48no—
75C4×D4×C47C2×C4116yescomplemented
76C4×D4×C47C2×C4116yescomplemented
77C2×C4⋊C4×C47C2314yes—
78C2×C4⋊C4×C47C2318yes—
79C2×C4⋊C4×C47C2314yes—
80C2×C4⋊C4×C47C2312yes—
81C2×C4⋊C4×C47C2312yes—
82C2×C22⋊C4×C47C2318yes—
83C2×C22⋊C4×C47C2312yes—
84C2×C22⋊C4×C47C2314yes—
85C2×C22⋊C4×C47C2312yes—
86C2×C22⋊C4×C47C2318yes—
87C2×C22⋊C4×C47C2318yes—
88C2×C22⋊C4×C47C2314yes—
89C2×C22⋊C4×C47C2314yes—
90C2×C42×C47C2×C418yescomplemented
91C2×C42×C47C2312yes—
92C2×C42×C47C2312yes—
93C2×C42×C47C2318yes—
94C2×C42×C47C2314yes—
95C2×C42×C47C2311yescharacteristic
96C2×C42×C47C2311yescharacteristic
97C2×C42×C47C2311yescharacteristic
98C2×C42×C47C2311yescharacteristic
99#95×C47C2312yes—
100#95×C47C2314yes—
101#95×C47C2318yes—
102#95×C47C2314yes—
103#95×C47C2314yes—
104#95×C47C2314yes—
105#95×C47C2312yes—
106#95×C47C2314yes—
107#95×C47C2318yes—
108#95×C47C2314yes—
109#95×C47C2314yes—
110C24×C47C2414yes—
111C24×C47C2411yescharacteristic
112#41×C47—432no—
113C2×Q8×C47—28no—
114C2×Q8×C47C22×C418yes—
115C2×D4×C47—28no—
116C2×D4×C47—44no—
117C2×D4×C47—44no—
118C2×D4×C47—48no—
119C2×D4×C47C22×C418yes—
120C2×D4×C47C22×C418yes—
121C2×D4×C47C22×C418yes—
122C2×D4×C47C22×C4116yes—
123C22×C4×C47—24no—
124C22×C4×C47—42no—
125C22×C4×C47—42no—
126C22×C4×C47—48no—
127C22×C4×C47—48no—
128C22×C4×C47—48no—
129C22×C4×C47—48no—
130C22×C4×C47C22×C414yes—
131C22×C4×C47C22×C414yes—
132C22×C4×C47C22×C414yes—
133C22×C4×C47C22×C4116yes—
134C22×C4×C47C2414yes—
135C22×C4×C47C2418yes—
136C22×C4×C47C2414yes—
137C22×C4×C47C2411yescharacteristic
138C22×C4×C47C2411yescharacteristic
139C22×C4×C47C2414yes—
140C22×C4×C47C2411yescharacteristic
141C22×C4×C47C2411yescharacteristic
142C22×C4×C47C2411yescharacteristic
143C22×C4×C47C2411yescharacteristic
144C4⋊C4×C47—28no—
145C4⋊C4×C47—44no—
146C4⋊C4×C47—48no—
147C4⋊C4×C47C22×C418yes—
148C4⋊C4×C47C22×C418yes—
149C22⋊C4×C47—48no—
150C22⋊C4×C47—42no—
151C22⋊C4×C47—48no—
152C22⋊C4×C47—44no—
153C22⋊C4×C47—42no—
154C22⋊C4×C47—48no—
155C22⋊C4×C47C22×C4116yes—
156C22⋊C4×C47C22×C4116yes—
157C42×C47—24no—
158C42×C47—24no—
159C42×C47—44no—
160C42×C47—48no—
161C42×C47C22×C414yes—
162C42×C47C22×C414yes—
163C42×C47C22×C414yes—
164C42×C47C22×C414yes—
165C23×C47—28no—
166C23×C47—22no—
167C23×C47—22no—
168C23×C47—22no—
169C23×C47—24no—
170C23×C47—28no—
171C23×C47—24no—
172C23×C47C23×C418yes—
173C23×C47C23×C412yes—
174C23×C47C2511yescharacteristic
175Q8×C47—216no—
176D4×C47—216no—
177D4×C47—48no—
178D4×C47—48no—
179D4×C47—416no—
180C2×C4×C47—28no—
181C2×C4×C47—22no—
182C2×C4×C47—22no—
183C2×C4×C47—22no—
184C2×C4×C47—22no—
185C2×C4×C47—22no—
186C2×C4×C47—28no—
187C2×C4×C47—24no—
188C2×C4×C47—24no—
189C2×C4×C47—28no—
190C2×C4×C47—28no—
191C2×C4×C47—24no—
192C2×C4×C47—24no—
193C2×C4×C47—28no—
194C2×C4×C47—24no—
195C2×C4×C47—24no—
196C2×C4×C47—44no—
197C2×C4×C47—44no—
198C2×C4×C47—416no—
199C2×C4×C47—816no—
200C2×C4×C47C23×C412yes—
201C2×C4×C47C23×C412yes—
202C2×C4×C47C23×C412yes—
203C2×C4×C47C23×C412yes—
204C2×C4×C47C23×C412yes—
205C2×C4×C47C23×C418yes—
206C2×C4×C47C23×C412yes—
207C2×C4×C47H(5,𝔽2)14yes—
208#34402C4711yesmaximal, characteristic, direct product factor, Sylow
209C22×C47—22no—
210C22×C47—28no—
211C22×C47—22no—
212C22×C47—22no—
213C22×C47—28no—
214C22×C47—28no—
215C22×C47—48no—
216C22×C47—48no—
217C22×C47—44no—
218C22×C47C24×C411yescharacteristic
219C22×C47C2×H(5,𝔽2)12yes—
220C22×C47#58512yes—
221C22×C47#58512yes—
222C4×C47—22no—
223C4×C47—28no—
224C4×C47—22no—
225C4×C47—22no—
226C4×C47—22no—
227C4×C47—22no—
228C4×C47—44no—
229C4×C47—48no—
230C4×C47—44no—
231C4×C47#51814yes—
232C2×#532C2×C4711yescharacteristic
233#2377C2×C4714yescomplemented
234#2367C2×C4714yescomplemented
235#2353C2×C4714yescomplemented
236#2341C2×C4712yescomplemented
237#2339C2×C4712yescomplemented
238#2333C2×C4714yescomplemented
239#2328C2×C4712yescomplemented
240#2327C2×C4712yescomplemented
241#2318C2×C4714yescomplemented
242#2283C2×C4711yescharacteristic, complemented
243#2283C2×C4711yescharacteristic, complemented
244C2×C47—42no—
245C2×C47—48no—
246C2×C47C2×#51811yescharacteristic
247C2×C47#342811yescharacteristic
248C2×C47#342811yescharacteristic
249C2×C47#356214yes—
250C22×#41C22×C4712yes—
251#532C4×C47116yescomplemented
252C2×C4⋊Q8C22×C4711yescharacteristic
253C2×#127C22×C4711yescharacteristic
254C2×#124C22×C4712yes—
255C2×#121C22×C4712yes—
256C2×#121C22×C4712yes—
257C2×C4×Q8C22×C4714yes—
258C2×C4×D4C22×C4714yes—
259C2×C4×D4C22×C4712yes—
260C2×C4×D4C22×C4712yes—
261C22×C42C22×C4711yescharacteristic
262#391C22×C4714yes—
263#390C22×C4714yes—
264#390C22×C4718yes—
265#388C22×C4718yes—
266#388C22×C4718yes—
267#387C22×C4718yes—
268#387C22×C4718yes—
269#386C22×C4718yes—
270#386C22×C4718yes—
271#386C22×C4718yes—
272#385C22×C4718yes—
273#383C22×C4712yes—
274#383C22×C4712yes—
275#382C22×C4712yes—
276#382C22×C4712yes—
277#381C22×C4714yes—
278#381C22×C4712yes—
279#381C22×C4712yes—
280#380C22×C4714yes—
281#380C22×C4712yes—
282#380C22×C4712yes—
283C4×C4⋊C4C22×C4712yes—
284C4×C4⋊C4C22×C4712yes—
285C4×C22⋊C4C22×C4714yes—
286C4×C22⋊C4C22×C4712yes—
287C4×C22⋊C4C22×C4718yes—
288C4×C22⋊C4C22×C4711yescharacteristic
289C4×C22⋊C4C22×C4711yescharacteristic
290#376C22×C4712yes—
291#376C22×C4712yes—
292C2×#95C22×C4714yes—
293C47#3440211yescharacteristic, direct product factor, Sylow
294C2×#41—48no—
295C2×#41C2×C4×C47116yescomplemented
296C22×Q8C23×C4712yes—
297C22×D4C23×C4712yes—
298C22×D4C23×C4712yes—
299C22×D4C23×C4712yes—
300C22×D4C23×C4714yes—
301C23×C4C23×C4711yescharacteristic
302C23×C4C23×C4718yes—
303C23×C4C23×C4714yes—
304C23×C4C23×C4711yescharacteristic
305C23×C4C23×C4711yescharacteristic
306C4⋊Q8C2×C4×C4718yescomplemented
307#127C2×C4×C4718yes—
308#124C2×C4×C47116yescomplemented
309#121C2×C4×C47116yescomplemented
310#121C2×C4×C47116yescomplemented
311C4×Q8—48no—
312C4×D4—48no—
313C4×D4C2×C4×C47116yescomplemented
314C4×D4C2×C4×C47116yescomplemented
315C2×C4⋊C4C23×C4714yes—
316C2×C4⋊C4C23×C4718yes—
317C2×C4⋊C4C23×C4714yes—
318C2×C4⋊C4C23×C4712yes—
319C2×C4⋊C4C23×C4712yes—
320C2×C22⋊C4C23×C4718yes—
321C2×C22⋊C4C23×C4712yes—
322C2×C22⋊C4C23×C4714yes—
323C2×C22⋊C4C23×C4712yes—
324C2×C22⋊C4C23×C4718yes—
325C2×C22⋊C4C23×C4718yes—
326C2×C22⋊C4C23×C4714yes—
327C2×C22⋊C4C23×C4714yes—
328C2×C42C2×C4×C4718yescomplemented
329C2×C42C23×C4712yes—
330C2×C42C23×C4712yes—
331C2×C42C23×C4718yes—
332C2×C42C23×C4714yes—
333C2×C42C23×C4711yescharacteristic
334C2×C42C23×C4711yescharacteristic
335C2×C42C23×C4711yescharacteristic
336C2×C42C23×C4711yescharacteristic
337#95C23×C4712yes—
338#95C23×C4714yes—
339#95C23×C4718yes—
340#95C23×C4714yes—
341#95C23×C4714yes—
342#95C23×C4714yes—
343#95C23×C4712yes—
344#95C23×C4714yes—
345#95C23×C4718yes—
346#95C23×C4714yes—
347#95C23×C4714yes—
348C24C24×C4714yes—
349C24C24×C4711yescharacteristic
350#41—432no—
351C2×Q8—28no—
352C2×Q8C22×C4×C4718yes—
353C2×D4—28no—
354C2×D4—44no—
355C2×D4—44no—
356C2×D4—48no—
357C2×D4C22×C4×C4718yes—
358C2×D4C22×C4×C4718yes—
359C2×D4C22×C4×C4718yes—
360C2×D4C22×C4×C47116yes—
361C22×C4—24no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—48no—
365C22×C4—48no—
366C22×C4—48no—
367C22×C4—48no—
368C22×C4C22×C4×C4714yes—
369C22×C4C22×C4×C4714yes—
370C22×C4C22×C4×C4714yes—
371C22×C4C22×C4×C47116yes—
372C22×C4C24×C4714yes—
373C22×C4C24×C4718yes—
374C22×C4C24×C4714yes—
375C22×C4C24×C4711yescharacteristic
376C22×C4C24×C4711yescharacteristic
377C22×C4C24×C4711yescharacteristic
378C22×C4C24×C4711yescharacteristic
379C22×C4C24×C4711yescharacteristic
380C22×C4C24×C4714yes—
381C22×C4C24×C4711yescharacteristic
382C4⋊C4—28no—
383C4⋊C4—44no—
384C4⋊C4—48no—
385C4⋊C4C22×C4×C4718yes—
386C4⋊C4C22×C4×C4718yes—
387C22⋊C4—48no—
388C22⋊C4—42no—
389C22⋊C4—48no—
390C22⋊C4—44no—
391C22⋊C4—42no—
392C22⋊C4—48no—
393C22⋊C4C22×C4×C47116yes—
394C22⋊C4C22×C4×C47116yes—
395C42—24no—
396C42—24no—
397C42—44no—
398C42—48no—
399C42C22×C4×C4714yes—
400C42C22×C4×C4714yes—
401C42C22×C4×C4714yes—
402C42C22×C4×C4714yes—
403C23—28no—
404C23—22no—
405C23—22no—
406C23—22no—
407C23—24no—
408C23—28no—
409C23—24no—
410C23C23×C4×C4718yes—
411C23C23×C4×C4712yes—
412C23C25×C4711yescharacteristic
413Q8—216no—
414D4—216no—
415D4—48no—
416D4—48no—
417D4—416no—
418C2×C4—28no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—28no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—28no—
428C2×C4—28no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—28no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—44no—
435C2×C4—44no—
436C2×C4—416no—
437C2×C4—816no—
438C2×C4C23×C4×C4712yes—
439C2×C4C23×C4×C4712yes—
440C2×C4C23×C4×C4712yes—
441C2×C4C23×C4×C4712yes—
442C2×C4C23×C4×C4712yes—
443C2×C4C23×C4×C4718yes—
444C2×C4C23×C4×C4712yes—
445C2×C4H(5,𝔽2)×C4714yes—
446C22—22no—
447C22—28no—
448C22—22no—
449C22—22no—
450C22—28no—
451C22—28no—
452C22—48no—
453C22—48no—
454C22—44no—
455C22C24×C4×C4711yescharacteristic
456C22C2×H(5,𝔽2)×C4712yes—
457C22C47×#58512yes—
458C22C47×#58512yes—
459C4—22no—
460C4—28no—
461C4—22no—
462C4—22no—
463C4—22no—
464C4—22no—
465C4—44no—
466C4—48no—
467C4—44no—
468C4C47×#51814yes—
469C2—42no—
470C2—48no—
471C2C2×C47×#51811yescharacteristic
472C2C47×#342811yescharacteristic
473C2C47×#342811yescharacteristic
474C2C47×#356214yes—
subgroupG/H
center, socleC23×C47C25
commutatorC22C24×C4×C47
Frattini, cosocleC23C25×C47
prime radicalC2×C47×#532C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2377C2semidirect
3. C47×#2367C2semidirect
4. C47×#2353C2semidirect
5. C47×#2341C2semidirect
6. C47×#2339C2semidirect
7. C47×#2333C2semidirect
8. C47×#2328C2semidirect
9. C47×#2327C2semidirect
10. C47×#2318C2semidirect
11. C47×#2283C2semidirect
12. C47×#2283C2semidirect
14. C47×#532C4semidirect
57. C2×#41×C47C2×C4semidirect
68. C4⋊Q8×C47C2×C4semidirect
70. #124×C47C2×C4semidirect
71. #121×C47C2×C4semidirect
72. #121×C47C2×C4semidirect
75. C4×D4×C47C2×C4semidirect
76. C4×D4×C47C2×C4semidirect
90. C2×C42×C47C2×C4semidirect
208. #34402C47direct (N × H)
233. #2377C2×C47semidirect
234. #2367C2×C47semidirect
235. #2353C2×C47semidirect
236. #2341C2×C47semidirect
237. #2339C2×C47semidirect
238. #2333C2×C47semidirect
239. #2328C2×C47semidirect
240. #2327C2×C47semidirect
241. #2318C2×C47semidirect
242. #2283C2×C47semidirect
243. #2283C2×C47semidirect
251. #532C4×C47semidirect
293. C47#34402direct (N × H)
295. C2×#41C2×C4×C47semidirect
306. C4⋊Q8C2×C4×C47semidirect
308. #124C2×C4×C47semidirect
309. #121C2×C4×C47semidirect
310. #121C2×C4×C47semidirect
313. C4×D4C2×C4×C47semidirect
314. C4×D4C2×C4×C47semidirect
328. 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×C47×#5322
C47×#23772
C47×#23672
C47×#23532
C47×#23412
C47×#23392
C47×#23332
C47×#23282
C47×#23272
C47×#23182
C47×#22832
#3440247