Finite Group Databasebeta

← C47×#19235 #26058933

Subgroups — C47×#19235 #26058933

Order 12032.

640 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3246C211yesmaximal, characteristic
2C47×#3226C211yesmaximal, characteristic
3C47×#3139C211yesmaximal, characteristic, complemented
4C47×#2935C211yesmaximal, characteristic
5C47×#1703C212yesmaximal, complemented
6C47×#1699C212yesmaximal, complemented
7C47×#1683C212yesmaximal, complemented
8C47×#1679C212yesmaximal, complemented
9C47×#1565C211yesmaximal, characteristic, complemented
10C47×#1542C211yesmaximal, characteristic, complemented
11C2×C47×#332C211yesmaximal, characteristic, complemented
12C2×#131×C47—21no—
13C47×#533C2211yescharacteristic
14C47×#532C2211yescharacteristic
15C2×C4⋊Q8×C47C2211yescharacteristic
16C47×#500—21no—
17C47×#491—22no—
18C47×#487C2212yes—
19C47×#487C2212yes—
20C47×#486—21no—
21C47×#480—22no—
22C47×#476C2212yes—
23C47×#475—21no—
24C47×#474C2212yes—
25C47×#474C2212yes—
26C47×#465—22no—
27C47×#461C2212yes—
28C47×#460—21no—
29C47×#436C2212yes—
30C47×#435—22no—
31C8×D4×C47C2212yes—
32C47×#431C2211yescharacteristic
33C2×C4⋊C8×C47C2211yescharacteristic
34C2×C4⋊C8×C47C2211yescharacteristic
35C47×#419—21no—
36C47×#419—21no—
37C47×#408—21no—
38C4×M16×C47C2211yescharacteristic
39C47×#335C2212yes—
40C47×#334C2212yes—
41C47×#333C2211yescharacteristic
42C47×#333C2211yescharacteristic
43C47×#332C2212yes—
44C47×#332C2212yes—
45C47×#332C2211yescharacteristic
46C47×#332C2211yescharacteristic
47C2×#41×C47—21no—
48C22×Q8×C47—21no—
49C2×SD16×C47—22no—
50#131×C47—44no—
51C2×M16×C47—22no—
52C2×M16×C47D411yescharacteristic
53C2×M16×C47D411yescharacteristic
54C22×C8×C47—21no—
55C22×C8×C47—21no—
56C22×C8×C47—22no—
57C4⋊Q8×C47—21no—
58C4⋊Q8×C47—21no—
59C4⋊Q8×C47—21no—
60C4⋊Q8×C47D411yescharacteristic
61C4⋊Q8×C47C2311yescharacteristic
62C4⋊Q8×C47C2312yes—
63C4⋊Q8×C47C2311yescharacteristic
64#127×C47D411yescharacteristic
65#125×C47—21no—
66#124×C47—21no—
67C22⋊Q8×C47—21no—
68C22⋊Q8×C47—21no—
69#121×C47—21no—
70#121×C47D412yes—
71C4×Q8×C47—21no—
72C4×Q8×C47—21no—
73C4×D4×C47—21no—
74C4×D4×C47C2312yes—
75#117×C47—21no—
76C2×C4⋊C4×C47—21no—
77C2×C4⋊C4×C47—21no—
78C2×C42×C47C2311yescharacteristic
79#107×C47—22no—
80#107×C47—22no—
81#106×C47—22no—
82C4⋊C8×C47—21no—
83C4⋊C8×C47—21no—
84C4⋊C8×C47C2312yes—
85C4⋊C8×C47C2311yescharacteristic
86C4⋊C8×C47C2311yescharacteristic
87C4⋊C8×C47C2311yescharacteristic
88C4⋊C8×C47C2311yescharacteristic
89#103×C47—22no—
90#103×C47—22no—
91#103×C47—22no—
92#103×C47—22no—
93#103×C47—22no—
94#102×C47—22no—
95#102×C47—22no—
96#102×C47—22no—
97C22⋊C8×C47—21no—
98C22⋊C8×C47—22no—
99C22⋊C8×C47—22no—
100#97×C47D412yes—
101C4×C8×C47—21no—
102C4×C8×C47C2312yes—
103#41×C47—42no—
104#41×C47—42no—
105C2×Q8×C47—21no—
106C2×Q8×C47—22no—
107C2×Q8×C47—21no—
108C2×Q8×C47—21no—
109C2×Q8×C47—41no—
110C2×Q8×C47—42no—
111C2×Q8×C47—42no—
112C2×D4×C47—22no—
113C2×D4×C47—21no—
114C2×D4×C47—21no—
115C2×D4×C47C2×D412yes—
116C22×C4×C47—22no—
117C22×C4×C47—41no—
118C22×C4×C47C2×D411yescharacteristic
119C22×C4×C47C2×D411yescharacteristic
120C22×C4×C47#4111yescharacteristic
121SD16×C47—82no—
122M16×C47—22no—
123M16×C47—22no—
124M16×C47—44no—
125C2×C8×C47—22no—
126C2×C8×C47—21no—
127C2×C8×C47—21no—
128C2×C8×C47—21no—
129C2×C8×C47—21no—
130C2×C8×C47—44no—
131C2×C8×C47—42no—
132C2×C8×C47—81no—
133C2×C8×C47C2×D412yes—
134C2×C8×C47C2×D412yes—
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×C47—21no—
142C4⋊C4×C47—41no—
143C4⋊C4×C47—41no—
144C4⋊C4×C47—41no—
145C4⋊C4×C47—41no—
146C4⋊C4×C47C2×D412yes—
147C22⋊C4×C47—22no—
148C22⋊C4×C47—22no—
149C22⋊C4×C47—41no—
150C42×C47—41no—
151C42×C47C2×D411yescharacteristic
152C42×C47C2×D411yescharacteristic
153C42×C47#4111yescharacteristic
154C42×C47C2411yescharacteristic
155C23×C47—22no—
156C23×C47#12111yescharacteristic
157Q8×C47—42no—
158Q8×C47—42no—
159Q8×C47—42no—
160Q8×C47—41no—
161Q8×C47—41no—
162Q8×C47—81no—
163Q8×C47—82no—
164D4×C47—22no—
165D4×C47—22no—
166D4×C47—44no—
167D4×C47—42no—
168D4×C47—81no—
169C2×C4×C47—21no—
170C2×C4×C47—21no—
171C2×C4×C47—22no—
172C2×C4×C47—41no—
173C2×C4×C47—42no—
174C2×C4×C47—42no—
175C2×C4×C47—41no—
176C2×C4×C47—41no—
177C2×C4×C47—42no—
178C2×C4×C47—82no—
179C2×C4×C47#12111yescharacteristic
180C2×C4×C47#12111yescharacteristic
181C2×C4×C47#12111yescharacteristic
182C2×C4×C47#13512yes—
183C2×C4×C47AGL(1,ℤ/8)12yes—
184C2×C4×C47C22×D411yescharacteristic
185C2×C4×C47C22×D411yescharacteristic
186C2×C4×C47C2×#4111yescharacteristic
187C8×C47—22no—
188C8×C47—22no—
189C8×C47—41no—
190C8×C47—41no—
191C8×C47—41no—
192C8×C47—42no—
193C8×C47—41no—
194#19235C4711yesmaximal, characteristic, direct product factor, Sylow
195C22×C47—21no—
196C22×C47—21no—
197C22×C47—42no—
198C22×C47—42no—
199C22×C47—42no—
200C22×C47#46312yes—
201C22×C47C2×#12111yescharacteristic
202C4×C47—21no—
203C4×C47—21no—
204C4×C47—21no—
205C4×C47—42no—
206C4×C47—82no—
207C4×C47—81no—
208C4×C47—81no—
209C4×C47#46312yes—
210C4×C47C2×#13511yescharacteristic
211C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
212C4×C47#57711yescharacteristic
213C4×C47#57811yescharacteristic
214#3246C2×C4711yescharacteristic
215#3226C2×C4711yescharacteristic
216#3139C2×C4711yescharacteristic, complemented
217#2935C2×C4711yescharacteristic
218#1703C2×C4712yescomplemented
219#1699C2×C4712yescomplemented
220#1683C2×C4712yescomplemented
221#1679C2×C4712yescomplemented
222#1565C2×C4711yescharacteristic, complemented
223#1542C2×C4711yescharacteristic, complemented
224C2×#332C2×C4711yescharacteristic, complemented
225C2×C47—22no—
226C2×C47—82no—
227C2×C47C2×#46311yescharacteristic
228C2×C47#306311yescharacteristic
229C2×C47#306911yescharacteristic
230C2×#131—21no—
231#533C22×C4711yescharacteristic
232#532C22×C4711yescharacteristic
233C2×C4⋊Q8C22×C4711yescharacteristic
234#500—21no—
235#491—22no—
236#487C22×C4712yes—
237#487C22×C4712yes—
238#486—21no—
239#480—22no—
240#476C22×C4712yes—
241#475—21no—
242#474C22×C4712yes—
243#474C22×C4712yes—
244#465—22no—
245#461C22×C4712yes—
246#460—21no—
247#436C22×C4712yes—
248#435—22no—
249C8×D4C22×C4712yes—
250#431C22×C4711yescharacteristic
251C2×C4⋊C8C22×C4711yescharacteristic
252C2×C4⋊C8C22×C4711yescharacteristic
253#419—21no—
254#419—21no—
255#408—21no—
256C4×M16C22×C4711yescharacteristic
257#335C22×C4712yes—
258#334C22×C4712yes—
259#333C22×C4711yescharacteristic
260#333C22×C4711yescharacteristic
261#332C22×C4712yes—
262#332C22×C4712yes—
263#332C22×C4711yescharacteristic
264#332C22×C4711yescharacteristic
265C47#1923511yescharacteristic, direct product factor, Sylow
266C2×#41—21no—
267C22×Q8—21no—
268C2×SD16—22no—
269#131—44no—
270C2×M16—22no—
271C2×M16D4×C4711yescharacteristic
272C2×M16D4×C4711yescharacteristic
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—22no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8—21no—
279C4⋊Q8D4×C4711yescharacteristic
280C4⋊Q8C23×C4712yes—
281C4⋊Q8C23×C4711yescharacteristic
282C4⋊Q8C23×C4711yescharacteristic
283#127D4×C4711yescharacteristic
284#125—21no—
285#124—21no—
286C22⋊Q8—21no—
287C22⋊Q8—21no—
288#121—21no—
289#121D4×C4712yes—
290C4×Q8—21no—
291C4×Q8—21no—
292C4×D4—21no—
293C4×D4C23×C4712yes—
294#117—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C42C23×C4711yescharacteristic
298#107—22no—
299#107—22no—
300#106—22no—
301C4⋊C8—21no—
302C4⋊C8—21no—
303C4⋊C8C23×C4711yescharacteristic
304C4⋊C8C23×C4711yescharacteristic
305C4⋊C8C23×C4712yes—
306C4⋊C8C23×C4711yescharacteristic
307C4⋊C8C23×C4711yescharacteristic
308#103—22no—
309#103—22no—
310#103—22no—
311#103—22no—
312#103—22no—
313#102—22no—
314#102—22no—
315#102—22no—
316C22⋊C8—21no—
317C22⋊C8—22no—
318C22⋊C8—22no—
319#97D4×C4712yes—
320C4×C8—21no—
321C4×C8C23×C4712yes—
322#41—42no—
323#41—42no—
324C2×Q8—21no—
325C2×Q8—22no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8—41no—
329C2×Q8—42no—
330C2×Q8—42no—
331C2×D4—22no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4C2×D4×C4712yes—
335C22×C4—22no—
336C22×C4—41no—
337C22×C4C2×D4×C4711yescharacteristic
338C22×C4C2×D4×C4711yescharacteristic
339C22×C4#41×C4711yescharacteristic
340SD16—82no—
341M16—22no—
342M16—22no—
343M16—44no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—22no—
349C2×C8—44no—
350C2×C8—42no—
351C2×C8—81no—
352C2×C8C2×D4×C4712yes—
353C2×C8C2×D4×C4712yes—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—22no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—22no—
360C4⋊C4—21no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4C2×D4×C4712yes—
366C22⋊C4—22no—
367C22⋊C4—22no—
368C22⋊C4—41no—
369C42—41no—
370C42C2×D4×C4711yescharacteristic
371C42C2×D4×C4711yescharacteristic
372C42#41×C4711yescharacteristic
373C42C24×C4711yescharacteristic
374C23—22no—
375C23#121×C4711yescharacteristic
376Q8—42no—
377Q8—42no—
378Q8—42no—
379Q8—41no—
380Q8—41no—
381Q8—81no—
382Q8—82no—
383D4—22no—
384D4—22no—
385D4—44no—
386D4—42no—
387D4—81no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—22no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—82no—
398C2×C4#121×C4711yescharacteristic
399C2×C4#121×C4711yescharacteristic
400C2×C4#121×C4711yescharacteristic
401C2×C4#135×C4712yes—
402C2×C4AGL(1,ℤ/8)×C4712yes—
403C2×C4C22×D4×C4711yescharacteristic
404C2×C4C22×D4×C4711yescharacteristic
405C2×C4C2×#41×C4711yescharacteristic
406C8—22no—
407C8—22no—
408C8—41no—
409C8—41no—
410C8—41no—
411C8—42no—
412C8—41no—
413C22—21no—
414C22—21no—
415C22—42no—
416C22—42no—
417C22—42no—
418C22C47×#46312yes—
419C22C2×#121×C4711yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—42no—
424C4—82no—
425C4—81no—
426C4—81no—
427C4C47×#46312yes—
428C4C2×#135×C4711yescharacteristic
429C4C2×AGL(1,ℤ/8)×C4711yescharacteristic
430C4C47×#57711yescharacteristic
431C4C47×#57811yescharacteristic
432C2—22no—
433C2—82no—
434C2C2×C47×#46311yescharacteristic
435C2C47×#306311yescharacteristic
436C2C47×#306911yescharacteristic
subgroupG/H
center, socleC22×C47C2×#121
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#532C22
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
3. C47×#3139C2semidirect
5. C47×#1703C2semidirect
6. C47×#1699C2semidirect
7. C47×#1683C2semidirect
8. C47×#1679C2semidirect
9. C47×#1565C2semidirect
10. C47×#1542C2semidirect
11. C2×C47×#332C2semidirect
194. #19235C47direct (N × H)
216. #3139C2×C47semidirect
218. #1703C2×C47semidirect
219. #1699C2×C47semidirect
220. #1683C2×C47semidirect
221. #1679C2×C47semidirect
222. #1565C2×C47semidirect
223. #1542C2×C47semidirect
224. C2×#332C2×C47semidirect
265. C47#19235direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#32462
C47×#32262
C47×#31392
C47×#29352
C47×#17032
C47×#16992
C47×#16832
C47×#16792
C47×#15652
C47×#15422
C2×C47×#3322
#1923547