Finite Group Databasebeta

← C47×#19219 #26058917

Subgroups — C47×#19219 #26058917

Order 12032.

630 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3212C212yesmaximal, complemented
2C47×#3169C211yesmaximal, characteristic, complemented
3C47×#2966C211yesmaximal, characteristic, complemented
4C47×#1702C212yesmaximal, complemented
5C47×#1701C212yesmaximal, complemented
6C47×#1674C211yesmaximal, characteristic, complemented
7C47×#1673C211yesmaximal, characteristic, complemented
8C47×#1668C211yesmaximal, characteristic, complemented
9C47×#1667C211yesmaximal, characteristic, complemented
10C47×#1564C211yesmaximal, characteristic, complemented
11C47×#1553C212yesmaximal, complemented
12C47×#532C2212yes—
13C47×#529C2211yescharacteristic
14C47×#500C2211yescharacteristic
15C47×#495—22no—
16C47×#493C2211yescharacteristic
17C47×#488—22no—
18C47×#486C2212yes—
19C47×#466—21no—
20C47×#466—21no—
21C47×#462C2212yes—
22C47×#461C2212yes—
23C47×#460C2212yes—
24C47×#459C2212yes—
25C47×#452—22no—
26C47×#449—22no—
27C47×#446C2211yescharacteristic
28C8×Q8×C47C2211yescharacteristic
29C4×D8×C47—21no—
30C4×D8×C47—21no—
31C47×#436C2211yescharacteristic
32C47×#435—21no—
33C8×D4×C47—21no—
34C8×D4×C47C2211yescharacteristic
35C47×#433—21no—
36C47×#432C2211yescharacteristic
37C47×#431C2212yes—
38C47×#405—21no—
39C2×C4×C8×C47C2211yescharacteristic
40C47×#335C2211yescharacteristic
41C47×#335C2211yescharacteristic
42C47×#334C2212yes—
43C47×#332C2212yes—
44C47×#332C2212yes—
45C47×#331C2212yes—
46C47×#331C2212yes—
47C2×#41×C47—22no—
48C2×Q16×C47—22no—
49C2×SD16×C47—22no—
50C2×SD16×C47—22no—
51C2×D8×C47—22no—
52C2×D8×C47—21no—
53C2×D8×C47—21no—
54C2×M16×C47—21no—
55C22×C8×C47—21no—
56C22×C8×C47D411yescharacteristic
57C22×C8×C47D411yescharacteristic
58C4⋊Q8×C47C2312yes—
59#127×C47C2312yes—
60#126×C47—21no—
61#125×C47D411yescharacteristic
62#124×C47—22no—
63#124×C47D411yescharacteristic
64#123×C47—21no—
65C22⋊Q8×C47D411yescharacteristic
66#121×C47—22no—
67#121×C47—22no—
68#121×C47D411yescharacteristic
69C4×Q8×C47C2311yescharacteristic
70C4×D4×C47—21no—
71C4×D4×C47—22no—
72C4×D4×C47—22no—
73C4×D4×C47C2311yescharacteristic
74#117×C47—21no—
75C2×C42×C47C2311yescharacteristic
76#107×C47—21no—
77#107×C47—21no—
78C4⋊C8×C47—21no—
79C4⋊C8×C47—21no—
80C4⋊C8×C47C2312yes—
81C4⋊C8×C47C2312yes—
82C4⋊C8×C47C2311yescharacteristic
83C4⋊C8×C47C2311yescharacteristic
84#103×C47—22no—
85#103×C47—22no—
86#102×C47—22no—
87#102×C47—22no—
88#102×C47—22no—
89#102×C47—22no—
90C22⋊C8×C47—22no—
91C22⋊C8×C47—21no—
92C22⋊C8×C47—21no—
93C22⋊C8×C47—21no—
94#97×C47—21no—
95#97×C47—21no—
96C4×C8×C47—21no—
97C4×C8×C47—22no—
98C4×C8×C47D411yescharacteristic
99C4×C8×C47D411yescharacteristic
100C4×C8×C47C2311yescharacteristic
101C4×C8×C47C2311yescharacteristic
102#41×C47—82no—
103#41×C47—82no—
104C2×Q8×C47—22no—
105C2×Q8×C47C2×D411yescharacteristic
106C2×D4×C47—21no—
107C2×D4×C47—22no—
108C2×D4×C47—22no—
109C2×D4×C47—22no—
110C2×D4×C47—42no—
111C2×D4×C47C2×D411yescharacteristic
112C22×C4×C47—21no—
113C22×C4×C47—42no—
114C22×C4×C47C2×D411yescharacteristic
115C22×C4×C47C2×D411yescharacteristic
116C22×C4×C47#4111yescharacteristic
117Q16×C47—82no—
118SD16×C47—82no—
119SD16×C47—82no—
120D8×C47—42no—
121D8×C47—42no—
122D8×C47—82no—
123M16×C47—42no—
124C2×C8×C47—22no—
125C2×C8×C47—22no—
126C2×C8×C47—22no—
127C2×C8×C47—21no—
128C2×C8×C47—21no—
129C2×C8×C47—41no—
130C2×C8×C47—42no—
131C2×C8×C47C2×D411yescharacteristic
132C2×C8×C47C2×D411yescharacteristic
133C2×C8×C47C2×D411yescharacteristic
134C2×C8×C47C2×D411yescharacteristic
135C4⋊C4×C47—21no—
136C4⋊C4×C47—21no—
137C4⋊C4×C47—21no—
138C4⋊C4×C47—21no—
139C4⋊C4×C47—22no—
140C4⋊C4×C47—22no—
141C4⋊C4×C47C2×D411yescharacteristic
142C4⋊C4×C47C2×D411yescharacteristic
143C22⋊C4×C47—21no—
144C22⋊C4×C47—21no—
145C22⋊C4×C47—21no—
146C22⋊C4×C47—21no—
147C22⋊C4×C47—21no—
148C22⋊C4×C47—42no—
149C22⋊C4×C47—42no—
150C42×C47—21no—
151C42×C47C2×D411yescharacteristic
152C42×C47C2×D411yescharacteristic
153C42×C47#4111yescharacteristic
154C42×C47C2411yescharacteristic
155C23×C47—21no—
156C23×C47—42no—
157C23×C47#12111yescharacteristic
158Q8×C47—21no—
159Q8×C47—21no—
160Q8×C47—42no—
161Q8×C47—42no—
162D4×C47—21no—
163D4×C47—21no—
164D4×C47—42no—
165D4×C47—42no—
166D4×C47—42no—
167D4×C47—42no—
168D4×C47—42no—
169D4×C47—82no—
170D4×C47—84no—
171C2×C4×C47—21no—
172C2×C4×C47—21no—
173C2×C4×C47—21no—
174C2×C4×C47—21no—
175C2×C4×C47—21no—
176C2×C4×C47—21no—
177C2×C4×C47—21no—
178C2×C4×C47—41no—
179C2×C4×C47—41no—
180C2×C4×C47—41no—
181C2×C4×C47—42no—
182C2×C4×C47—84no—
183C2×C4×C47#12111yescharacteristic
184C2×C4×C47#12111yescharacteristic
185C2×C4×C47#12111yescharacteristic
186C2×C4×C47C22×D411yescharacteristic
187C2×C4×C47C22×D411yescharacteristic
188C2×C4×C47C2×#4111yescharacteristic
189C8×C47—21no—
190C8×C47—21no—
191C8×C47—21no—
192C8×C47—41no—
193C8×C47—41no—
194C8×C47—42no—
195C8×C47—42no—
196C8×C47#13512yes—
197#19219C4711yesmaximal, characteristic, direct product factor, Sylow
198C22×C47—21no—
199C22×C47—21no—
200C22×C47—21no—
201C22×C47—41no—
202C22×C47—41no—
203C22×C47—41no—
204C22×C47—82no—
205C22×C47—82no—
206C22×C47—82no—
207C22×C47C2×#12111yescharacteristic
208C4×C47—21no—
209C4×C47—21no—
210C4×C47—21no—
211C4×C47—21no—
212C4×C47—41no—
213C4×C47—41no—
214C4×C47—41no—
215C4×C47—82no—
216C4×C47C2×#13511yescharacteristic
217C4×C47#57511yescharacteristic
218C4×C47#57611yescharacteristic
219C4×C47#57611yescharacteristic
220#3212C2×C4712yescomplemented
221#3169C2×C4711yescharacteristic, complemented
222#2966C2×C4711yescharacteristic, complemented
223#1702C2×C4712yescomplemented
224#1701C2×C4712yescomplemented
225#1674C2×C4711yescharacteristic, complemented
226#1673C2×C4711yescharacteristic, complemented
227#1668C2×C4711yescharacteristic, complemented
228#1667C2×C4711yescharacteristic, complemented
229#1564C2×C4711yescharacteristic, complemented
230#1553C2×C4712yescomplemented
231C2×C47—41no—
232C2×C47—81no—
233C2×C47—162no—
234C2×C47#303511yescharacteristic
235C2×C47#305811yescharacteristic
236C2×C47#306711yescharacteristic
237#532C22×C4712yes—
238#529C22×C4711yescharacteristic
239#500C22×C4711yescharacteristic
240#495—22no—
241#493C22×C4711yescharacteristic
242#488—22no—
243#486C22×C4712yes—
244#466—21no—
245#466—21no—
246#462C22×C4712yes—
247#461C22×C4712yes—
248#460C22×C4712yes—
249#459C22×C4712yes—
250#452—22no—
251#449—22no—
252#446C22×C4711yescharacteristic
253C8×Q8C22×C4711yescharacteristic
254C4×D8—21no—
255C4×D8—21no—
256#436C22×C4711yescharacteristic
257#435—21no—
258C8×D4—21no—
259C8×D4C22×C4711yescharacteristic
260#433—21no—
261#432C22×C4711yescharacteristic
262#431C22×C4712yes—
263#405—21no—
264C2×C4×C8C22×C4711yescharacteristic
265#335C22×C4711yescharacteristic
266#335C22×C4711yescharacteristic
267#334C22×C4712yes—
268#332C22×C4712yes—
269#332C22×C4712yes—
270#331C22×C4712yes—
271#331C22×C4712yes—
272C47#1921911yescharacteristic, direct product factor, Sylow
273C2×#41—22no—
274C2×Q16—22no—
275C2×SD16—22no—
276C2×SD16—22no—
277C2×D8—22no—
278C2×D8—21no—
279C2×D8—21no—
280C2×M16—21no—
281C22×C8—21no—
282C22×C8D4×C4711yescharacteristic
283C22×C8D4×C4711yescharacteristic
284C4⋊Q8C23×C4712yes—
285#127C23×C4712yes—
286#126—21no—
287#125D4×C4711yescharacteristic
288#124—22no—
289#124D4×C4711yescharacteristic
290#123—21no—
291C22⋊Q8D4×C4711yescharacteristic
292#121—22no—
293#121—22no—
294#121D4×C4711yescharacteristic
295C4×Q8C23×C4711yescharacteristic
296C4×D4—21no—
297C4×D4—22no—
298C4×D4—22no—
299C4×D4C23×C4711yescharacteristic
300#117—21no—
301C2×C42C23×C4711yescharacteristic
302#107—21no—
303#107—21no—
304C4⋊C8—21no—
305C4⋊C8—21no—
306C4⋊C8C23×C4711yescharacteristic
307C4⋊C8C23×C4711yescharacteristic
308C4⋊C8C23×C4712yes—
309C4⋊C8C23×C4712yes—
310#103—22no—
311#103—22no—
312#102—22no—
313#102—22no—
314#102—22no—
315#102—22no—
316C22⋊C8—22no—
317C22⋊C8—21no—
318C22⋊C8—21no—
319C22⋊C8—21no—
320#97—21no—
321#97—21no—
322C4×C8—21no—
323C4×C8—22no—
324C4×C8D4×C4711yescharacteristic
325C4×C8D4×C4711yescharacteristic
326C4×C8C23×C4711yescharacteristic
327C4×C8C23×C4711yescharacteristic
328#41—82no—
329#41—82no—
330C2×Q8—22no—
331C2×Q8C2×D4×C4711yescharacteristic
332C2×D4—21no—
333C2×D4—22no—
334C2×D4—22no—
335C2×D4—22no—
336C2×D4—42no—
337C2×D4C2×D4×C4711yescharacteristic
338C22×C4—21no—
339C22×C4—42no—
340C22×C4C2×D4×C4711yescharacteristic
341C22×C4C2×D4×C4711yescharacteristic
342C22×C4#41×C4711yescharacteristic
343Q16—82no—
344SD16—82no—
345SD16—82no—
346D8—42no—
347D8—42no—
348D8—82no—
349M16—42no—
350C2×C8—22no—
351C2×C8—21no—
352C2×C8—22no—
353C2×C8—22no—
354C2×C8—21no—
355C2×C8—41no—
356C2×C8—42no—
357C2×C8C2×D4×C4711yescharacteristic
358C2×C8C2×D4×C4711yescharacteristic
359C2×C8C2×D4×C4711yescharacteristic
360C2×C8C2×D4×C4711yescharacteristic
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4C2×D4×C4711yescharacteristic
368C4⋊C4C2×D4×C4711yescharacteristic
369C22⋊C4—21no—
370C22⋊C4—21no—
371C22⋊C4—21no—
372C22⋊C4—21no—
373C22⋊C4—21no—
374C22⋊C4—42no—
375C22⋊C4—42no—
376C42—21no—
377C42C2×D4×C4711yescharacteristic
378C42C2×D4×C4711yescharacteristic
379C42#41×C4711yescharacteristic
380C42C24×C4711yescharacteristic
381C23—21no—
382C23—42no—
383C23#121×C4711yescharacteristic
384Q8—21no—
385Q8—21no—
386Q8—42no—
387Q8—42no—
388D4—21no—
389D4—21no—
390D4—42no—
391D4—42no—
392D4—42no—
393D4—42no—
394D4—42no—
395D4—82no—
396D4—84no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—84no—
409C2×C4#121×C4711yescharacteristic
410C2×C4#121×C4711yescharacteristic
411C2×C4#121×C4711yescharacteristic
412C2×C4C22×D4×C4711yescharacteristic
413C2×C4C22×D4×C4711yescharacteristic
414C2×C4C2×#41×C4711yescharacteristic
415C8—21no—
416C8—21no—
417C8—21no—
418C8—41no—
419C8—41no—
420C8—42no—
421C8—42no—
422C8#135×C4712yes—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—41no—
427C22—41no—
428C22—41no—
429C22—82no—
430C22—82no—
431C22—82no—
432C22C2×#121×C4711yescharacteristic
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—41no—
438C4—41no—
439C4—41no—
440C4—82no—
441C4C2×#135×C4711yescharacteristic
442C4C47×#57511yescharacteristic
443C4C47×#57611yescharacteristic
444C4C47×#57611yescharacteristic
445C2—41no—
446C2—81no—
447C2—162no—
448C2C47×#303511yescharacteristic
449C2C47×#305811yescharacteristic
450C2C47×#306711yescharacteristic
subgroupG/H
center, socleC22×C47C2×#121
commutator, Frattini, cosocleC42C24×C47
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
1. C47×#3212C2semidirect
2. C47×#3169C2semidirect
3. C47×#2966C2semidirect
4. C47×#1702C2semidirect
5. C47×#1701C2semidirect
6. C47×#1674C2semidirect
7. C47×#1673C2semidirect
8. C47×#1668C2semidirect
9. C47×#1667C2semidirect
10. C47×#1564C2semidirect
11. C47×#1553C2semidirect
197. #19219C47direct (N × H)
220. #3212C2×C47semidirect
221. #3169C2×C47semidirect
222. #2966C2×C47semidirect
223. #1702C2×C47semidirect
224. #1701C2×C47semidirect
225. #1674C2×C47semidirect
226. #1673C2×C47semidirect
227. #1668C2×C47semidirect
228. #1667C2×C47semidirect
229. #1564C2×C47semidirect
230. #1553C2×C47semidirect
272. C47#19219direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#32122
C47×#31692
C47×#29662
C47×#17022
C47×#17012
C47×#16742
C47×#16732
C47×#16682
C47×#16672
C47×#15642
C47×#15532
#1921947