Finite Group Databasebeta

← C47×#19223 #26058921

Subgroups — C47×#19223 #26058921

Order 12032.

584 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3248C212yesmaximal
2C47×#3170C211yesmaximal, characteristic, complemented
3C47×#2966C211yesmaximal, characteristic
4C47×#1700C212yesmaximal, complemented
5C47×#1699C212yesmaximal, complemented
6C47×#1674C211yesmaximal, characteristic, complemented
7C47×#1673C211yesmaximal, characteristic, complemented
8C47×#1670C211yesmaximal, characteristic, complemented
9C47×#1669C211yesmaximal, characteristic, complemented
10C2×C47×#335C211yesmaximal, characteristic, complemented
11C47×#1552C212yesmaximal, complemented
12C47×#533C2212yes—
13C47×#529C2211yescharacteristic
14C47×#500C2211yescharacteristic
15C47×#494C2211yescharacteristic
16C47×#487C2212yes—
17C47×#479—22no—
18C47×#475C2212yes—
19C47×#474C2212yes—
20C47×#467—21no—
21C47×#467—21no—
22C47×#467—22no—
23C47×#465—22no—
24C47×#464—22no—
25C47×#462C2212yes—
26C47×#461C2212yes—
27C47×#446C2211yescharacteristic
28C8×Q8×C47C2211yescharacteristic
29C4×Q16×C47—21no—
30C4×Q16×C47—21no—
31C47×#436C2211yescharacteristic
32C47×#435—21no—
33C8×D4×C47—21no—
34C8×D4×C47C2211yescharacteristic
35C47×#433—21no—
36C47×#432C2211yescharacteristic
37C2×C4⋊C8×C47C2212yes—
38C47×#405—21no—
39C2×C4×C8×C47C2211yescharacteristic
40C47×#335C2211yescharacteristic
41C47×#335C2211yescharacteristic
42C47×#335C2212yes—
43C47×#332C2212yes—
44C47×#332C2212yes—
45C47×#332C2212yes—
46C47×#332C2212yes—
47C2×Q16×C47—22no—
48C2×Q16×C47—21no—
49C2×Q16×C47—21no—
50C2×SD16×C47—22no—
51C2×M16×C47—21no—
52C22×C8×C47—22no—
53C22×C8×C47—21no—
54C22×C8×C47D411yescharacteristic
55C22×C8×C47D411yescharacteristic
56C4⋊Q8×C47C2312yes—
57C4⋊Q8×C47C2312yes—
58#126×C47—21no—
59#125×C47—22no—
60#125×C47D411yescharacteristic
61#124×C47D411yescharacteristic
62#123×C47—21no—
63C22⋊Q8×C47—22no—
64C22⋊Q8×C47—22no—
65C22⋊Q8×C47D411yescharacteristic
66#121×C47D411yescharacteristic
67C4×Q8×C47—22no—
68C4×Q8×C47—22no—
69C4×Q8×C47C2311yescharacteristic
70C4×D4×C47—21no—
71C4×D4×C47C2311yescharacteristic
72#117×C47—21no—
73#117×C47—22no—
74C2×C42×C47C2311yescharacteristic
75#107×C47—21no—
76#107×C47—21no—
77#107×C47—22no—
78#106×C47—22no—
79C4⋊C8×C47—21no—
80C4⋊C8×C47—21no—
81C4⋊C8×C47—22no—
82C4⋊C8×C47C2312yes—
83C4⋊C8×C47C2312yes—
84C4⋊C8×C47C2311yescharacteristic
85C4⋊C8×C47C2311yescharacteristic
86#103×C47—22no—
87#103×C47—22no—
88#103×C47—22no—
89#103×C47—22no—
90#103×C47—22no—
91#102×C47—22no—
92C22⋊C8×C47—21no—
93C22⋊C8×C47—21no—
94C22⋊C8×C47—21no—
95#97×C47—21no—
96#97×C47—21no—
97C4×C8×C47—21no—
98C4×C8×C47D411yescharacteristic
99C4×C8×C47D411yescharacteristic
100C4×C8×C47C2311yescharacteristic
101C4×C8×C47C2311yescharacteristic
102C2×Q8×C47—22no—
103C2×Q8×C47—22no—
104C2×Q8×C47C2×D411yescharacteristic
105C2×D4×C47—21no—
106C2×D4×C47C2×D411yescharacteristic
107C22×C4×C47—21no—
108C22×C4×C47C2×D411yescharacteristic
109C22×C4×C47C2×D411yescharacteristic
110C22×C4×C47#4111yescharacteristic
111Q16×C47—42no—
112Q16×C47—42no—
113Q16×C47—82no—
114SD16×C47—82no—
115M16×C47—42no—
116C2×C8×C47—22no—
117C2×C8×C47—22no—
118C2×C8×C47—22no—
119C2×C8×C47—21no—
120C2×C8×C47—21no—
121C2×C8×C47—41no—
122C2×C8×C47—42no—
123C2×C8×C47—82no—
124C2×C8×C47C2×D411yescharacteristic
125C2×C8×C47C2×D411yescharacteristic
126C2×C8×C47C2×D411yescharacteristic
127C2×C8×C47C2×D411yescharacteristic
128C4⋊C4×C47—21no—
129C4⋊C4×C47—21no—
130C4⋊C4×C47—21no—
131C4⋊C4×C47—21no—
132C4⋊C4×C47—22no—
133C4⋊C4×C47—22no—
134C4⋊C4×C47—22no—
135C4⋊C4×C47—22no—
136C4⋊C4×C47—42no—
137C4⋊C4×C47—42no—
138C4⋊C4×C47C2×D411yescharacteristic
139C4⋊C4×C47C2×D411yescharacteristic
140C22⋊C4×C47—21no—
141C22⋊C4×C47—21no—
142C22⋊C4×C47—21no—
143C22⋊C4×C47—21no—
144C22⋊C4×C47—21no—
145C22⋊C4×C47—42no—
146C42×C47—21no—
147C42×C47—42no—
148C42×C47C2×D411yescharacteristic
149C42×C47C2×D411yescharacteristic
150C42×C47#4111yescharacteristic
151C42×C47C2411yescharacteristic
152C23×C47—21no—
153C23×C47#12111yescharacteristic
154Q8×C47—21no—
155Q8×C47—21no—
156Q8×C47—42no—
157Q8×C47—42no—
158Q8×C47—42no—
159Q8×C47—42no—
160D4×C47—21no—
161D4×C47—21no—
162D4×C47—42no—
163C2×C4×C47—22no—
164C2×C4×C47—21no—
165C2×C4×C47—21no—
166C2×C4×C47—21no—
167C2×C4×C47—21no—
168C2×C4×C47—21no—
169C2×C4×C47—21no—
170C2×C4×C47—21no—
171C2×C4×C47—41no—
172C2×C4×C47—41no—
173C2×C4×C47—42no—
174C2×C4×C47—42no—
175C2×C4×C47#12111yescharacteristic
176C2×C4×C47#12111yescharacteristic
177C2×C4×C47#12111yescharacteristic
178C2×C4×C47C22×D411yescharacteristic
179C2×C4×C47C22×D411yescharacteristic
180C2×C4×C47C2×#4111yescharacteristic
181C8×C47—21no—
182C8×C47—21no—
183C8×C47—21no—
184C8×C47—41no—
185C8×C47—41no—
186C8×C47—42no—
187C8×C47—42no—
188C8×C47#13512yes—
189#19223C4711yesmaximal, characteristic, direct product factor, Sylow
190C22×C47—21no—
191C22×C47—21no—
192C22×C47—41no—
193C22×C47—41no—
194C22×C47—41no—
195C22×C47#47312yes—
196C22×C47C2×#12111yescharacteristic
197C4×C47—21no—
198C4×C47—21no—
199C4×C47—21no—
200C4×C47—21no—
201C4×C47—41no—
202C4×C47—41no—
203C4×C47—41no—
204C4×C47—82no—
205C4×C47—82no—
206C4×C47C2×#13511yescharacteristic
207C4×C47#57511yescharacteristic
208C4×C47#57611yescharacteristic
209C4×C47#57811yescharacteristic
210#3248C2×C4712yes—
211#3170C2×C4711yescharacteristic, complemented
212#2966C2×C4711yescharacteristic
213#1700C2×C4712yescomplemented
214#1699C2×C4712yescomplemented
215#1674C2×C4711yescharacteristic, complemented
216#1673C2×C4711yescharacteristic, complemented
217#1670C2×C4711yescharacteristic, complemented
218#1669C2×C4711yescharacteristic, complemented
219C2×#335C2×C4711yescharacteristic, complemented
220#1552C2×C4712yescomplemented
221C2×C47—22no—
222C2×C47—81no—
223C2×C47#303511yescharacteristic
224C2×C47#306111yescharacteristic
225C2×C47C2×#47311yescharacteristic
226#533C22×C4712yes—
227#529C22×C4711yescharacteristic
228#500C22×C4711yescharacteristic
229#494C22×C4711yescharacteristic
230#487C22×C4712yes—
231#479—22no—
232#475C22×C4712yes—
233#474C22×C4712yes—
234#467—21no—
235#467—21no—
236#467—22no—
237#465—22no—
238#464—22no—
239#462C22×C4712yes—
240#461C22×C4712yes—
241#446C22×C4711yescharacteristic
242C8×Q8C22×C4711yescharacteristic
243C4×Q16—21no—
244C4×Q16—21no—
245#436C22×C4711yescharacteristic
246#435—21no—
247C8×D4—21no—
248C8×D4C22×C4711yescharacteristic
249#433—21no—
250#432C22×C4711yescharacteristic
251C2×C4⋊C8C22×C4712yes—
252#405—21no—
253C2×C4×C8C22×C4711yescharacteristic
254#335C22×C4711yescharacteristic
255#335C22×C4711yescharacteristic
256#335C22×C4712yes—
257#332C22×C4712yes—
258#332C22×C4712yes—
259#332C22×C4712yes—
260#332C22×C4712yes—
261C47#1922311yescharacteristic, direct product factor, Sylow
262C2×Q16—22no—
263C2×Q16—21no—
264C2×Q16—21no—
265C2×SD16—22no—
266C2×M16—21no—
267C22×C8—22no—
268C22×C8—21no—
269C22×C8D4×C4711yescharacteristic
270C22×C8D4×C4711yescharacteristic
271C4⋊Q8C23×C4712yes—
272C4⋊Q8C23×C4712yes—
273#126—21no—
274#125—22no—
275#125D4×C4711yescharacteristic
276#124D4×C4711yescharacteristic
277#123—21no—
278C22⋊Q8—22no—
279C22⋊Q8—22no—
280C22⋊Q8D4×C4711yescharacteristic
281#121D4×C4711yescharacteristic
282C4×Q8—22no—
283C4×Q8—22no—
284C4×Q8C23×C4711yescharacteristic
285C4×D4—21no—
286C4×D4C23×C4711yescharacteristic
287#117—21no—
288#117—22no—
289C2×C42C23×C4711yescharacteristic
290#107—21no—
291#107—21no—
292#107—22no—
293#106—22no—
294C4⋊C8—21no—
295C4⋊C8—21no—
296C4⋊C8—22no—
297C4⋊C8C23×C4711yescharacteristic
298C4⋊C8C23×C4711yescharacteristic
299C4⋊C8C23×C4712yes—
300C4⋊C8C23×C4712yes—
301#103—22no—
302#103—22no—
303#103—22no—
304#103—22no—
305#103—22no—
306#102—22no—
307C22⋊C8—21no—
308C22⋊C8—21no—
309C22⋊C8—21no—
310#97—21no—
311#97—21no—
312C4×C8—21no—
313C4×C8D4×C4711yescharacteristic
314C4×C8D4×C4711yescharacteristic
315C4×C8C23×C4711yescharacteristic
316C4×C8C23×C4711yescharacteristic
317C2×Q8—22no—
318C2×Q8—22no—
319C2×Q8C2×D4×C4711yescharacteristic
320C2×D4—21no—
321C2×D4C2×D4×C4711yescharacteristic
322C22×C4—21no—
323C22×C4C2×D4×C4711yescharacteristic
324C22×C4C2×D4×C4711yescharacteristic
325C22×C4#41×C4711yescharacteristic
326Q16—42no—
327Q16—42no—
328Q16—82no—
329SD16—82no—
330M16—42no—
331C2×C8—22no—
332C2×C8—21no—
333C2×C8—21no—
334C2×C8—22no—
335C2×C8—22no—
336C2×C8—41no—
337C2×C8—42no—
338C2×C8—82no—
339C2×C8C2×D4×C4711yescharacteristic
340C2×C8C2×D4×C4711yescharacteristic
341C2×C8C2×D4×C4711yescharacteristic
342C2×C8C2×D4×C4711yescharacteristic
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—42no—
352C4⋊C4—42no—
353C4⋊C4C2×D4×C4711yescharacteristic
354C4⋊C4C2×D4×C4711yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—21no—
357C22⋊C4—21no—
358C22⋊C4—21no—
359C22⋊C4—21no—
360C22⋊C4—42no—
361C42—21no—
362C42—42no—
363C42C2×D4×C4711yescharacteristic
364C42C2×D4×C4711yescharacteristic
365C42#41×C4711yescharacteristic
366C42C24×C4711yescharacteristic
367C23—21no—
368C23#121×C4711yescharacteristic
369Q8—21no—
370Q8—21no—
371Q8—42no—
372Q8—42no—
373Q8—42no—
374Q8—42no—
375D4—21no—
376D4—21no—
377D4—42no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4#121×C4711yescharacteristic
391C2×C4#121×C4711yescharacteristic
392C2×C4#121×C4711yescharacteristic
393C2×C4C22×D4×C4711yescharacteristic
394C2×C4C22×D4×C4711yescharacteristic
395C2×C4C2×#41×C4711yescharacteristic
396C8—21no—
397C8—21no—
398C8—21no—
399C8—41no—
400C8—41no—
401C8—42no—
402C8—42no—
403C8#135×C4712yes—
404C22—21no—
405C22—21no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22C47×#47312yes—
410C22C2×#121×C4711yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—41no—
416C4—41no—
417C4—41no—
418C4—82no—
419C4—82no—
420C4C2×#135×C4711yescharacteristic
421C4C47×#57511yescharacteristic
422C4C47×#57611yescharacteristic
423C4C47×#57811yescharacteristic
424C2—22no—
425C2—81no—
426C2C47×#303511yescharacteristic
427C2C47×#306111yescharacteristic
428C2C2×C47×#47311yescharacteristic
subgroupG/H
center, socleC22×C47C2×#121
commutator, Frattini, cosocleC42C24×C47
prime radical#121×C47D4
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×#3170C2semidirect
4. C47×#1700C2semidirect
5. C47×#1699C2semidirect
6. C47×#1674C2semidirect
7. C47×#1673C2semidirect
8. C47×#1670C2semidirect
9. C47×#1669C2semidirect
10. C2×C47×#335C2semidirect
11. C47×#1552C2semidirect
189. #19223C47direct (N × H)
211. #3170C2×C47semidirect
213. #1700C2×C47semidirect
214. #1699C2×C47semidirect
215. #1674C2×C47semidirect
216. #1673C2×C47semidirect
217. #1670C2×C47semidirect
218. #1669C2×C47semidirect
219. C2×#335C2×C47semidirect
220. #1552C2×C47semidirect
261. C47#19223direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#32482
C47×#31702
C47×#29662
C47×#17002
C47×#16992
C47×#16742
C47×#16732
C47×#16702
C47×#16692
C2×C47×#3352
C47×#15522
#1922347