Finite Group Databasebeta

← #26120747

Subgroups — #26120747

Order 12032.

442 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20248424C211yesmaximal, characteristic
2#20244149C211yesmaximal, characteristic
3#20244144C211yesmaximal, characteristic
4#20241271C211yesmaximal, characteristic
5#20241228C211yesmaximal, characteristic
6#20241228C211yesmaximal, characteristic
7C47×#1845C211yesmaximal, characteristic
8C2×#13094015—21no—
9C2×#13093957—21no—
10C2×#13093955—21no—
11C2×C4⋊(C47⋊C8)C2211yescharacteristic
12C2×C4⋊(C47⋊C8)C2211yescharacteristic
13#15689056—22no—
14#15689022—21no—
15#15689019—21no—
16#15688992—21no—
17C4×C4⋊Dic47C2211yescharacteristic
18C4×C4⋊Dic47C2211yescharacteristic
19#15688885—21no—
20#15688885—21no—
21C2×#107×C47—22no—
22C2×C4×C8×C47C2211yescharacteristic
23C47×#384C2211yescharacteristic
24C47×#384C2211yescharacteristic
25C22×C47⋊C8—21no—
26C22×C47⋊C8—21no—
27#13094015—42no—
28#13094015—42no—
29C2×C4⋊Dic47—22no—
30C2×C4⋊Dic47D411yescharacteristic
31C2×C4⋊Dic47D411yescharacteristic
32C2×C4⋊Dic47D411yescharacteristic
33C2×C4⋊Dic47D411yescharacteristic
34C2×Dic47⋊C4—22no—
35C2×Dic47⋊C4—22no—
36C2×C4×Dic47—21no—
37C2×C4×Dic47—21no—
38#13093957—42no—
39#13093955—42no—
40C4⋊(C47⋊C8)—21no—
41C4⋊(C47⋊C8)—21no—
42C4⋊(C47⋊C8)Q812yes—
43C4⋊(C47⋊C8)Q812yes—
44C47⋊#95—22no—
45C47⋊#95—21no—
46C47⋊#95—21no—
47C22×C8×C47—21no—
48C2×C4⋊C4×C47—21no—
49C2×C4⋊C4×C47—21no—
50C2×C4⋊C4×C47—21no—
51C2×C4⋊C4×C47—21no—
52C2×C4⋊C4×C47—21no—
53C2×C4⋊C4×C47D412yes—
54C2×C42×C47C2311yescharacteristic
55#107×C47—44no—
56C4×C8×C47—21no—
57C4×C8×C47Q812yes—
58C22×C4×C47—22no—
59C22×C4×C47—41no—
60C22×C4×C47C2×D411yescharacteristic
61C22×C4×C47C2×D411yescharacteristic
62C22×C4×C47C2×D411yescharacteristic
63C22×Dic47—21no—
64C22×Dic47—21no—
65C22×Dic47—21no—
66C22×Dic47—21no—
67C2×C8×C47—22no—
68C2×C8×C47—22no—
69C2×C8×C47—22no—
70C4⋊C4×C47—42no—
71C4⋊C4×C47—42no—
72C4⋊C4×C47—41no—
73C4⋊C4×C47—41no—
74C4⋊C4×C47—41no—
75C4⋊C4×C47—41no—
76C4⋊C4×C47—41no—
77C4⋊C4×C47—41no—
78C4⋊C4×C47—41no—
79C4⋊C4×C47—41no—
80C42×C47C2×Q811yescharacteristic
81C42×C47C2×Q811yescharacteristic
82C42×C47C2×Q811yescharacteristic
83C42×C47#4111yescharacteristic
84C4⋊Dic47—21no—
85C4⋊Dic47—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47—44no—
91C4⋊Dic47D812yes—
92C4⋊Dic47Q1612yes—
93Dic47⋊C4—44no—
94Dic47⋊C4—82no—
95C4×Dic47—41no—
96C4×Dic47—41no—
97C4×Dic47—41no—
98C4×Dic47—41no—
99C2×C47⋊C8—22no—
100C2×C47⋊C8—22no—
101C2×C47⋊C8—41no—
102C2×C47⋊C8—41no—
103C2×C47⋊C8—41no—
104C2×C47⋊C8—41no—
105C23×C47#12011yescharacteristic
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—42no—
109C2×C4×C47—42no—
110C2×C4×C47—42no—
111C2×C4×C47—81no—
112C2×C4×C47—81no—
113C2×C4×C47—81no—
114C2×C4×C47C22⋊Q811yescharacteristic
115C2×C4×C47C22⋊Q811yescharacteristic
116C2×C4×C47C22⋊Q811yescharacteristic
117C2×C4×C47C4⋊Q811yescharacteristic
118C2×C4×C47C4⋊Q811yescharacteristic
119C2×C4×C47C4⋊Q811yescharacteristic
120C2×C4×C47C2×D811yescharacteristic
121C2×C4×C47C2×Q1611yescharacteristic
122C2×C4×C47#13511yescharacteristic
123C2×C4×C47#13511yescharacteristic
124C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C47#13711yescharacteristic
127C2×C4×C47#13711yescharacteristic
128C2×Dic47—22no—
129C2×Dic47—22no—
130C2×Dic47—41no—
131C2×Dic47—41no—
132C2×Dic47—41no—
133C2×Dic47—41no—
134C2×Dic47—41no—
135C2×Dic47—41no—
136C2×Dic47—41no—
137C2×Dic47—41no—
138C2×Dic47—41no—
139C2×Dic47—41no—
140C8×C47—24no—
141C47⋊C8—42no—
142C47⋊C8—42no—
143#10579—471nomaximal, Sylow
144C22×C47#39511yescharacteristic
145C22×C47#44711yescharacteristic
146C22×C47#44911yescharacteristic
147C22×C47#45111yescharacteristic
148C22×C47#45211yescharacteristic
149C22×C47#45311yescharacteristic
150C22×C47#45611yescharacteristic
151C4×C47—21no—
152C4×C47—21no—
153C4×C47—82no—
154C4×C47—161no—
155C4×C47#47411yescharacteristic
156C4×C47#47711yescharacteristic
157C4×C47#47811yescharacteristic
158C4×C47#47911yescharacteristic
159C4×C47#49911yescharacteristic
160C4×C47#50011yescharacteristic
161C4×C47#50111yescharacteristic
162C4×C47#50111yescharacteristic
163Dic47—42no—
164Dic47—42no—
165Dic47—81no—
166Dic47—81no—
167#2552—471no—
168#1948—471no—
169#1947—471no—
170#1845D4711yescharacteristic
171#1296—471no—
172#1279—471no—
173#1279—471no—
174C2×C47#162111yescharacteristic
175C2×C47#163211yescharacteristic
176C2×C47#164711yescharacteristic
177C2×C47#164811yescharacteristic
178C2×C47#205711yescharacteristic
179C2×C47#205911yescharacteristic
180C2×C47#206011yescharacteristic
181C2×#125—941no—
182C2×#107—22no—
183C2×#107—941no—
184C2×#106—941no—
185C2×C4⋊C8—471no—
186C2×C4⋊C8—471no—
187C2×C4×C8C2×D4711yescharacteristic
188#398—942no—
189#389—941no—
190#389—941no—
191#384—941no—
192#384C2×D4711yescharacteristic
193#384C2×D4711yescharacteristic
194C4×C4⋊C4—471no—
195C4×C4⋊C4—471no—
196#340—941no—
197#340—941no—
198C47#1057911yescharacteristic, complemented, Sylow
199C22×C8—21no—
200C22×C8—941no—
201C22×C8—941no—
202#125—1882no—
203#125—1882no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—471no—
210C2×C4⋊C4—471no—
211C2×C4⋊C4—471no—
212C2×C4⋊C4—471no—
213C2×C4⋊C4—942no—
214C2×C4⋊C4—942no—
215C2×C4⋊C4—942no—
216C2×C4⋊C4C22⋊D4712yes—
217C2×C42—941no—
218C2×C42—941no—
219C2×C42C22×D4711yescharacteristic
220#107—44no—
221#107—1882no—
222#106—1882no—
223C4⋊C8—472no—
224C4⋊C8—472no—
225C4⋊C8—941no—
226C4⋊C8—941no—
227C4×C8—21no—
228C4×C8Dic9412yes—
229#95—942no—
230#95—941no—
231#95—941no—
232C22×C4—22no—
233C22×C4—41no—
234C22×C4—941no—
235C22×C4—941no—
236C22×C4—941no—
237C22×C4—941no—
238C22×C4D4×D4711yescharacteristic
239C22×C4D4×D4711yescharacteristic
240C22×C4C2×C22⋊D4711yescharacteristic
241C2×C8—22no—
242C2×C8—22no—
243C2×C8—22no—
244C2×C8—942no—
245C2×C8—942no—
246C2×C8—1881no—
247C2×C8—1881no—
248C2×C8—1881no—
249C2×C8—1881no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—472no—
261C4⋊C4—472no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4—3762no—
269C4⋊C4—1884no—
270C4⋊C4—1884no—
271C42—1881no—
272C42—1881no—
273C42—1881no—
274C42—1881no—
275C42C2×Dic9411yescharacteristic
276C42#1062535011yescharacteristic
277C42Q8×D4711yescharacteristic
278C42Q8×D4711yescharacteristic
279C23#1309399211yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—942no—
289C2×C4—942no—
290C2×C4—1881no—
291C2×C4—1881no—
292C2×C4—1881no—
293C2×C4—1881no—
294C2×C4—1881no—
295C2×C4—1881no—
296C2×C4—1881no—
297C2×C4—1881no—
298C2×C4—1881no—
299C2×C4—1881no—
300C2×C4#1309400211yescharacteristic
301C2×C4#1309400211yescharacteristic
302C2×C4#1309400311yescharacteristic
303C2×C4#1309402211yescharacteristic
304C2×C4#1309402311yescharacteristic
305C2×C4#1309402311yescharacteristic
306C2×C4D8×D4711yescharacteristic
307C2×C4Q16×D4711yescharacteristic
308C2×C4#1309404311yescharacteristic
309C2×C4#1309404711yescharacteristic
310C2×C4#1309404811yescharacteristic
311C2×C4#1309404811yescharacteristic
312C2×C4#1309405611yescharacteristic
313C2×C4#1309405611yescharacteristic
314C8—24no—
315C8—1882no—
316C8—1882no—
317C22#1568904311yescharacteristic
318C22#1568925511yescharacteristic
319C22#1568926511yescharacteristic
320C22#1568927711yescharacteristic
321C22#1568928411yescharacteristic
322C22#1568929011yescharacteristic
323C22#1568930511yescharacteristic
324C4—21no—
325C4—21no—
326C4—82no—
327C4—161no—
328C4—3761no—
329C4—3761no—
330C4—1882no—
331C4—1882no—
332C4#1568940211yescharacteristic
333C4#1568941711yescharacteristic
334C4#1568942611yescharacteristic
335C4#1568942911yescharacteristic
336C4#1568952411yescharacteristic
337C4#1568952711yescharacteristic
338C4#1568953111yescharacteristic
339C4#1568953111yescharacteristic
340C2#2024245011yescharacteristic
341C2#2024251911yescharacteristic
342C2#2024262011yescharacteristic
343C2#2024262711yescharacteristic
344C2#2024471411yescharacteristic
345C2#2024472411yescharacteristic
346C2#2024473311yescharacteristic
subgroupG/H
centerC23#13093992
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1845C2
socle, prime radicalC23×C47#120
hypercenter#1845D47
hypocenterC47#10579
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1845

Complements

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

NH ≅ G/Ntype
198. C47#10579semidirect

Maximal subgroups

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

subgroupindex
#202484242
#202441492
#202441442
#202412712
#202412282
C47×#18452
#1057947