Finite Group Databasebeta

← C47×#19245 #26058943

Subgroups — C47×#19245 #26058943

Order 12032.

606 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×#3209C211yesmaximal, characteristic, complemented
3C47×#3141C211yesmaximal, characteristic
4C47×#2962C211yesmaximal, characteristic, complemented
5C47×#1702C212yesmaximal, complemented
6C47×#1700C212yesmaximal, complemented
7C47×#1682C212yesmaximal, complemented
8C47×#1680C212yesmaximal, complemented
9C47×#1565C211yesmaximal, characteristic, complemented
10C47×#1540C211yesmaximal, characteristic
11C2×C47×#332C211yesmaximal, characteristic, complemented
12C47×#533C2211yescharacteristic
13C47×#532C2211yescharacteristic
14C2×C4⋊Q8×C47C2211yescharacteristic
15C47×#494—21no—
16C47×#489—22no—
17C47×#487—21no—
18C47×#487C2212yes—
19C47×#486C2212yes—
20C47×#476—21no—
21C47×#475C2212yes—
22C47×#465—22no—
23C47×#462C2212yes—
24C47×#462C2212yes—
25C47×#461—21no—
26C47×#460C2212yes—
27C47×#451—22no—
28C47×#446—22no—
29C47×#446C2212yes—
30C8×Q8×C47C2212yes—
31C47×#431C2211yescharacteristic
32C47×#424—21no—
33C2×C4⋊C8×C47C2211yescharacteristic
34C2×C4⋊C8×C47C2211yescharacteristic
35C47×#417—21no—
36C47×#417—21no—
37C47×#405—21no—
38C4×M16×C47C2211yescharacteristic
39C47×#335C2212yes—
40C47×#334C2212yes—
41C47×#332C2212yes—
42C47×#332C2212yes—
43C47×#332C2211yescharacteristic
44C47×#332C2211yescharacteristic
45C47×#331C2211yescharacteristic
46C47×#331C2211yescharacteristic
47C2×#41×C47—21no—
48C22×Q8×C47—21no—
49C2×Q16×C47—22no—
50C2×Q16×C47—22no—
51C2×SD16×C47—22no—
52C2×M16×C47D411yescharacteristic
53C2×M16×C47D411yescharacteristic
54C22×C8×C47—21no—
55C22×C8×C47—21no—
56C4⋊Q8×C47—21no—
57C4⋊Q8×C47—21no—
58C4⋊Q8×C47—21no—
59C4⋊Q8×C47D411yescharacteristic
60C4⋊Q8×C47D411yescharacteristic
61C4⋊Q8×C47C2312yes—
62C4⋊Q8×C47C2311yescharacteristic
63#127×C47C2311yescharacteristic
64#125×C47—21no—
65#124×C47—21no—
66C22⋊Q8×C47—21no—
67C22⋊Q8×C47D412yes—
68#121×C47—21no—
69#121×C47—21no—
70C4×Q8×C47—21no—
71C4×Q8×C47C2312yes—
72C4×D4×C47—21no—
73C4×D4×C47—21no—
74#117×C47—21no—
75C2×C4⋊C4×C47—21no—
76C2×C4⋊C4×C47—21no—
77C2×C42×C47C2311yescharacteristic
78#106×C47—22no—
79C4⋊C8×C47—22no—
80C4⋊C8×C47—22no—
81C4⋊C8×C47—21no—
82C4⋊C8×C47—21no—
83C4⋊C8×C47C2312yes—
84C4⋊C8×C47C2311yescharacteristic
85C4⋊C8×C47C2311yescharacteristic
86C4⋊C8×C47C2311yescharacteristic
87C4⋊C8×C47C2311yescharacteristic
88#103×C47—22no—
89#103×C47—22no—
90#103×C47—22no—
91#103×C47—22no—
92#103×C47—22no—
93#102×C47—22no—
94#102×C47—22no—
95#102×C47—22no—
96C22⋊C8×C47—21no—
97#97×C47—22no—
98#97×C47D412yes—
99C4×C8×C47—22no—
100C4×C8×C47—21no—
101C4×C8×C47C2312yes—
102#41×C47—42no—
103#41×C47—42no—
104C2×Q8×C47—21no—
105C2×Q8×C47—21no—
106C2×Q8×C47—22no—
107C2×Q8×C47—41no—
108C2×Q8×C47—81no—
109C2×Q8×C47—81no—
110C2×Q8×C47C2×D412yes—
111C2×D4×C47—21no—
112C2×D4×C47—21no—
113C2×D4×C47—21no—
114C2×D4×C47—41no—
115C22×C4×C47—41no—
116C22×C4×C47—41no—
117C22×C4×C47C2×D411yescharacteristic
118C22×C4×C47C2×D411yescharacteristic
119C22×C4×C47#4111yescharacteristic
120Q16×C47—82no—
121Q16×C47—82no—
122SD16×C47—82no—
123M16×C47—22no—
124M16×C47—22no—
125C2×C8×C47—21no—
126C2×C8×C47—21no—
127C2×C8×C47—22no—
128C2×C8×C47—21no—
129C2×C8×C47—21no—
130C2×C8×C47—42no—
131C2×C8×C47—81no—
132C2×C8×C47C2×D412yes—
133C2×C8×C47C2×D412yes—
134C4⋊C4×C47—21no—
135C4⋊C4×C47—21no—
136C4⋊C4×C47—21no—
137C4⋊C4×C47—22no—
138C4⋊C4×C47—22no—
139C4⋊C4×C47—21no—
140C4⋊C4×C47—22no—
141C4⋊C4×C47—22no—
142C4⋊C4×C47—21no—
143C4⋊C4×C47—41no—
144C4⋊C4×C47—41no—
145C4⋊C4×C47C2×D412yes—
146C22⋊C4×C47—22no—
147C22⋊C4×C47—41no—
148C22⋊C4×C47—41no—
149C42×C47—22no—
150C42×C47C2×D411yescharacteristic
151C42×C47C2×D411yescharacteristic
152C42×C47#4111yescharacteristic
153C42×C47C2411yescharacteristic
154C23×C47—41no—
155C23×C47#12111yescharacteristic
156Q8×C47—22no—
157Q8×C47—22no—
158Q8×C47—41no—
159Q8×C47—41no—
160Q8×C47—42no—
161Q8×C47—42no—
162Q8×C47—81no—
163Q8×C47—82no—
164D4×C47—41no—
165D4×C47—41no—
166D4×C47—41no—
167D4×C47—41no—
168D4×C47—81no—
169D4×C47—82no—
170C2×C4×C47—21no—
171C2×C4×C47—21no—
172C2×C4×C47—22no—
173C2×C4×C47—22no—
174C2×C4×C47—41no—
175C2×C4×C47—41no—
176C2×C4×C47—42no—
177C2×C4×C47—82no—
178C2×C4×C47—82no—
179C2×C4×C47#12111yescharacteristic
180C2×C4×C47#12111yescharacteristic
181C2×C4×C47#12111yescharacteristic
182C2×C4×C47#13512yes—
183C2×C4×C47#13712yes—
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—42no—
192C8×C47—41no—
193C8×C47—41no—
194#19245C4711yesmaximal, characteristic, direct product factor, Sylow
195C22×C47—21no—
196C22×C47—21no—
197C22×C47—81no—
198C22×C47—81no—
199C22×C47—81no—
200C22×C47#46412yes—
201C22×C47C2×#12111yescharacteristic
202C4×C47—21no—
203C4×C47—21no—
204C4×C47—21no—
205C4×C47—42no—
206C4×C47—42no—
207C4×C47—81no—
208C4×C47—82no—
209C4×C47#46412yes—
210C4×C47C2×#13511yescharacteristic
211C4×C47C2×#13711yescharacteristic
212C4×C47#57611yescharacteristic
213C4×C47#57711yescharacteristic
214#3246C2×C4711yescharacteristic
215#3209C2×C4711yescharacteristic, complemented
216#3141C2×C4711yescharacteristic
217#2962C2×C4711yescharacteristic, complemented
218#1702C2×C4712yescomplemented
219#1700C2×C4712yescomplemented
220#1682C2×C4712yescomplemented
221#1680C2×C4712yescomplemented
222#1565C2×C4711yescharacteristic, complemented
223#1540C2×C4711yescharacteristic
224C2×#332C2×C4711yescharacteristic, complemented
225C2×C47—22no—
226C2×C47—161no—
227C2×C47C2×#46411yescharacteristic
228C2×C47#306211yescharacteristic
229C2×C47#306911yescharacteristic
230#533C22×C4711yescharacteristic
231#532C22×C4711yescharacteristic
232C2×C4⋊Q8C22×C4711yescharacteristic
233#494—21no—
234#489—22no—
235#487—21no—
236#487C22×C4712yes—
237#486C22×C4712yes—
238#476—21no—
239#475C22×C4712yes—
240#465—22no—
241#462C22×C4712yes—
242#462C22×C4712yes—
243#461—21no—
244#460C22×C4712yes—
245#451—22no—
246#446—22no—
247#446C22×C4712yes—
248C8×Q8C22×C4712yes—
249#431C22×C4711yescharacteristic
250#424—21no—
251C2×C4⋊C8C22×C4711yescharacteristic
252C2×C4⋊C8C22×C4711yescharacteristic
253#417—21no—
254#417—21no—
255#405—21no—
256C4×M16C22×C4711yescharacteristic
257#335C22×C4712yes—
258#334C22×C4712yes—
259#332C22×C4712yes—
260#332C22×C4712yes—
261#332C22×C4711yescharacteristic
262#332C22×C4711yescharacteristic
263#331C22×C4711yescharacteristic
264#331C22×C4711yescharacteristic
265C47#1924511yescharacteristic, direct product factor, Sylow
266C2×#41—21no—
267C22×Q8—21no—
268C2×Q16—22no—
269C2×Q16—22no—
270C2×SD16—22no—
271C2×M16D4×C4711yescharacteristic
272C2×M16D4×C4711yescharacteristic
273C22×C8—21no—
274C22×C8—21no—
275C4⋊Q8—21no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8D4×C4711yescharacteristic
279C4⋊Q8D4×C4711yescharacteristic
280C4⋊Q8C23×C4712yes—
281C4⋊Q8C23×C4711yescharacteristic
282#127C23×C4711yescharacteristic
283#125—21no—
284#124—21no—
285C22⋊Q8—21no—
286C22⋊Q8D4×C4712yes—
287#121—21no—
288#121—21no—
289C4×Q8—21no—
290C4×Q8C23×C4712yes—
291C4×D4—21no—
292C4×D4—21no—
293#117—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C42C23×C4711yescharacteristic
297#106—22no—
298C4⋊C8—22no—
299C4⋊C8—22no—
300C4⋊C8—21no—
301C4⋊C8—21no—
302C4⋊C8C23×C4711yescharacteristic
303C4⋊C8C23×C4711yescharacteristic
304C4⋊C8C23×C4711yescharacteristic
305C4⋊C8C23×C4711yescharacteristic
306C4⋊C8C23×C4712yes—
307#103—22no—
308#103—22no—
309#103—22no—
310#103—22no—
311#103—22no—
312#102—22no—
313#102—22no—
314#102—22no—
315C22⋊C8—21no—
316#97—22no—
317#97D4×C4712yes—
318C4×C8—22no—
319C4×C8—21no—
320C4×C8C23×C4712yes—
321#41—42no—
322#41—42no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×Q8—22no—
326C2×Q8—41no—
327C2×Q8—81no—
328C2×Q8—81no—
329C2×Q8C2×D4×C4712yes—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4C2×D4×C4711yescharacteristic
337C22×C4C2×D4×C4711yescharacteristic
338C22×C4#41×C4711yescharacteristic
339Q16—82no—
340Q16—82no—
341SD16—82no—
342M16—22no—
343M16—22no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—22no—
349C2×C8—42no—
350C2×C8—81no—
351C2×C8C2×D4×C4712yes—
352C2×C8C2×D4×C4712yes—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—21no—
360C4⋊C4—22no—
361C4⋊C4—21no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4C2×D4×C4712yes—
365C22⋊C4—22no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C42—22no—
369C42C2×D4×C4711yescharacteristic
370C42C2×D4×C4711yescharacteristic
371C42#41×C4711yescharacteristic
372C42C24×C4711yescharacteristic
373C23—41no—
374C23#121×C4711yescharacteristic
375Q8—22no—
376Q8—22no—
377Q8—41no—
378Q8—41no—
379Q8—42no—
380Q8—42no—
381Q8—81no—
382Q8—82no—
383D4—41no—
384D4—41no—
385D4—41no—
386D4—41no—
387D4—81no—
388D4—82no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—82no—
397C2×C4—82no—
398C2×C4#121×C4711yescharacteristic
399C2×C4#121×C4711yescharacteristic
400C2×C4#121×C4711yescharacteristic
401C2×C4#135×C4712yes—
402C2×C4#137×C4712yes—
403C2×C4C22×D4×C4711yescharacteristic
404C2×C4C22×D4×C4711yescharacteristic
405C2×C4C2×#41×C4711yescharacteristic
406C8—22no—
407C8—22no—
408C8—41no—
409C8—41no—
410C8—42no—
411C8—41no—
412C8—41no—
413C22—21no—
414C22—21no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22C47×#46412yes—
419C22C2×#121×C4711yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—42no—
424C4—42no—
425C4—81no—
426C4—82no—
427C4C47×#46412yes—
428C4C2×#135×C4711yescharacteristic
429C4C2×#137×C4711yescharacteristic
430C4C47×#57611yescharacteristic
431C4C47×#57711yescharacteristic
432C2—22no—
433C2—161no—
434C2C2×C47×#46411yescharacteristic
435C2C47×#306211yescharacteristic
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
2. C47×#3209C2semidirect
4. C47×#2962C2semidirect
5. C47×#1702C2semidirect
6. C47×#1700C2semidirect
7. C47×#1682C2semidirect
8. C47×#1680C2semidirect
9. C47×#1565C2semidirect
11. C2×C47×#332C2semidirect
194. #19245C47direct (N × H)
215. #3209C2×C47semidirect
217. #2962C2×C47semidirect
218. #1702C2×C47semidirect
219. #1700C2×C47semidirect
220. #1682C2×C47semidirect
221. #1680C2×C47semidirect
222. #1565C2×C47semidirect
224. C2×#332C2×C47semidirect
265. C47#19245direct (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×#32092
C47×#31412
C47×#29622
C47×#17022
C47×#17002
C47×#16822
C47×#16802
C47×#15652
C47×#15402
C2×C47×#3322
#1924547