Finite Group Databasebeta

← #26116397

Subgroups — #26116397

Order 12032.

430 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#20251749C211yesmaximal, characteristic
2#20243504C211yesmaximal, characteristic
3C4⋊C8×Dic47C211yesmaximal, characteristic
4#20241272C211yesmaximal, characteristic
5#20241272C211yesmaximal, characteristic
6#20241271C211yesmaximal, characteristic
7C47×#1296C211yesmaximal, characteristic
8C2×#13094015—21no—
9C2×C4⋊(C47⋊C8)C2211yescharacteristic
10C2×C4⋊(C47⋊C8)C2211yescharacteristic
11C2×C8×Dic47—21no—
12#15689022—21no—
13#15689022C412yes—
14#15689019—21no—
15#15689019C412yes—
16#15688993C2211yescharacteristic
17#15688988—21no—
18C42×Dic47C2211yescharacteristic
19#15688877—21no—
20#15688877—21no—
21#15688877—21no—
22C2×C4⋊C8×C47C2211yescharacteristic
23C2×C4⋊C8×C47C2211yescharacteristic
24C47×#384C2211yescharacteristic
25C22×C47⋊C8—21no—
26C22×C47⋊C8—21no—
27#13094015—42no—
28#13094015—42no—
29C2×C4⋊Dic47—21no—
30C2×C4⋊Dic47—21no—
31C2×C4⋊Dic47—22no—
32C2×C4⋊Dic47C2×C412yes—
33C2×Dic47⋊C4—22no—
34C2×C4×Dic47C2×C411yescharacteristic
35C2×C4×Dic47C2×C411yescharacteristic
36C2×C4×Dic47D411yescharacteristic
37C2×C4×Dic47D411yescharacteristic
38C2×C4×Dic47D411yescharacteristic
39C2×C4×Dic47D411yescharacteristic
40C4⋊(C47⋊C8)—21no—
41C4⋊(C47⋊C8)—21no—
42C4⋊(C47⋊C8)—21no—
43C4⋊(C47⋊C8)Q812yes—
44C8×Dic47—42no—
45C47⋊#95—22no—
46C47⋊#95—22no—
47C22×C8×C47—21no—
48C22×C8×C47—21no—
49C2×C4⋊C4×C47—21no—
50C2×C4⋊C4×C47—21no—
51C2×C4⋊C4×C47C2×C412yes—
52C2×C42×C47C2311yescharacteristic
53C4⋊C8×C47—21no—
54C4⋊C8×C47—21no—
55C4⋊C8×C47—21no—
56C4⋊C8×C47Q812yes—
57C22×C4×C47—22no—
58C22×C4×C47C22×C411yescharacteristic
59C22×C4×C47C2×D411yescharacteristic
60C22×C4×C47C2×D411yescharacteristic
61C22×Dic47—22no—
62C22×Dic47C22⋊C411yescharacteristic
63C22×Dic47C22⋊C411yescharacteristic
64C22×Dic47C22⋊C411yescharacteristic
65C22×Dic47C22⋊C411yescharacteristic
66C2×C8×C47—22no—
67C2×C8×C47—41no—
68C2×C8×C47—41no—
69C2×C8×C47—41no—
70C2×C8×C47—41no—
71C2×C8×C47—41no—
72C4⋊C4×C47—42no—
73C4⋊C4×C47—41no—
74C4⋊C4×C47—41no—
75C4⋊C4×C47—41no—
76C4⋊C4×C47—41no—
77C42×C47C2×Q811yescharacteristic
78C42×C47C2×Q811yescharacteristic
79C42×C47#4111yescharacteristic
80C42×C47#4111yescharacteristic
81C4⋊Dic47—44no—
82C4⋊Dic47—41no—
83C4⋊Dic47—41no—
84C4⋊Dic47—41no—
85C4⋊Dic47—41no—
86C4⋊Dic47—42no—
87Dic47⋊C4—44no—
88C4×Dic47—21no—
89C4×Dic47—21no—
90C4×Dic47—21no—
91C4×Dic47—21no—
92C4×Dic47—21no—
93C4×Dic47—21no—
94C4×Dic47—41no—
95C4×Dic47—41no—
96C4×Dic47SD1612yes—
97C4×Dic47Q1612yes—
98C2×C47⋊C8—22no—
99C2×C47⋊C8—41no—
100C2×C47⋊C8—41no—
101C2×C47⋊C8—41no—
102C2×C47⋊C8—41no—
103C2×C47⋊C8—41no—
104C23×C47C2×C22⋊C411yescharacteristic
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—42no—
108C2×C4×C47—42no—
109C2×C4×C47—42no—
110C2×C4×C47C4×Q811yescharacteristic
111C2×C4×C47C4×Q811yescharacteristic
112C2×C4×C47C22⋊Q811yescharacteristic
113C2×C4×C47C22⋊Q811yescharacteristic
114C2×C4×C47#12411yescharacteristic
115C2×C4×C47C4⋊Q811yescharacteristic
116C2×C4×C47C2×SD1611yescharacteristic
117C2×C4×C47C2×Q1611yescharacteristic
118C2×C4×C47#13511yescharacteristic
119C2×C4×C47#13511yescharacteristic
120C2×C4×C47#13511yescharacteristic
121C2×C4×C47#13511yescharacteristic
122C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—42no—
135C2×Dic47—42no—
136C2×Dic47—42no—
137C2×Dic47#10312yes—
138C2×Dic47#10312yes—
139C8×C47—42no—
140C8×C47—81no—
141C47⋊C8—42no—
142C47⋊C8—81no—
143#9897—471nomaximal, Sylow
144C22×C47#39111yescharacteristic
145C22×C47#41311yescharacteristic
146C22×C47#41311yescharacteristic
147C22×C47C2×#10311yescharacteristic
148C22×C47#41611yescharacteristic
149C22×C47#41611yescharacteristic
150C22×C47#41811yescharacteristic
151C4×C47—21no—
152C4×C47—21no—
153C4×C47—82no—
154C4×C47#47611yescharacteristic
155C4×C47#47611yescharacteristic
156C4×C47#47711yescharacteristic
157C4×C47#47711yescharacteristic
158C4×C47#48811yescharacteristic
159C4×C47#48811yescharacteristic
160C4×C47#49911yescharacteristic
161C4×C47#49911yescharacteristic
162Dic47—22no—
163Dic47—22no—
164Dic47—41no—
165Dic47—41no—
166Dic47—82no—
167#2859—471no—
168#1831—471no—
169C4×C4⋊C8—471no—
170#1296—471no—
171#1296—471no—
172#1296—471no—
173#1296D4711yescharacteristic
174C2×C47#154211yescharacteristic
175C2×C47#154211yescharacteristic
176C2×C47#155311yescharacteristic
177C2×C47#155311yescharacteristic
178C2×C47#198711yescharacteristic
179C2×C47#199111yescharacteristic
180C2×C47#199811yescharacteristic
181C2×#125—941no—
182C2×C4⋊C8—471no—
183C2×C4⋊C8—471no—
184C2×C4⋊C8C2×D4711yescharacteristic
185C2×C4⋊C8C2×D4711yescharacteristic
186C2×C4×C8—941no—
187#389—472no—
188#389—472no—
189#389—941no—
190#389—941no—
191#384—471no—
192#384C2×D4711yescharacteristic
193#382—941no—
194C43—471no—
195#336—941no—
196#336—941no—
197#336—941no—
198C47#989711yescharacteristic, complemented, Sylow
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—941no—
202C22×C8—941no—
203#125—1882no—
204#125—1882no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—472no—
208C2×C4⋊C4—942no—
209C2×C4⋊C4—942no—
210C2×C4⋊C4—941no—
211C2×C4⋊C4—941no—
212C2×C4⋊C4C4×D4712yes—
213C2×C42—471no—
214C2×C42—471no—
215C2×C42—471no—
216C2×C42—471no—
217C2×C42—471no—
218C2×C42—471no—
219C2×C42C22×D4711yescharacteristic
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—472no—
224C4⋊C8—941no—
225C4⋊C8—941no—
226C4⋊C8—941no—
227C4⋊C8Dic9412yes—
228C4×C8—1882no—
229#95—942no—
230#95—942no—
231C22×C4—22no—
232C22×C4—471no—
233C22×C4—471no—
234C22×C4—471no—
235C22×C4—471no—
236C22×C4—942no—
237C22×C4C2×C4×D4711yescharacteristic
238C22×C4D4×D4711yescharacteristic
239C22×C4D4×D4711yescharacteristic
240C2×C8—22no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—942no—
247C2×C8—1881no—
248C2×C8—1881no—
249C2×C8—1881no—
250C2×C8—1881no—
251C2×C8—1881no—
252C4⋊C4—42no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—1882no—
258C4⋊C4—1884no—
259C4⋊C4—1884no—
260C4⋊C4—1881no—
261C4⋊C4—1881no—
262C4⋊C4—1881no—
263C4⋊C4—1881no—
264C42—472no—
265C42—472no—
266C42—941no—
267C42—941no—
268C42—941no—
269C42—941no—
270C42—941no—
271C42—941no—
272C42—1881no—
273C42—1881no—
274C42C2×Dic9411yescharacteristic
275C42#1062535011yescharacteristic
276C42#1062535211yescharacteristic
277C42Q8×D4711yescharacteristic
278C23C22⋊C4×D4711yescharacteristic
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—472no—
285C2×C4—472no—
286C2×C4—941no—
287C2×C4—941no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—941no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—1882no—
297C2×C4—1882no—
298C2×C4—1882no—
299C2×C4#1309398911yescharacteristic
300C2×C4C4×Dic9411yescharacteristic
301C2×C4#1309400111yescharacteristic
302C2×C4#1309400211yescharacteristic
303C2×C4#1309401011yescharacteristic
304C2×C4#1309402311yescharacteristic
305C2×C4SD16×D4711yescharacteristic
306C2×C4Q16×D4711yescharacteristic
307C2×C4#1309404311yescharacteristic
308C2×C4#1309404511yescharacteristic
309C2×C4#1309404511yescharacteristic
310C2×C4#1309404711yescharacteristic
311C2×C4#1309404811yescharacteristic
312C2×C4#1309405111yescharacteristic
313C8—42no—
314C8—81no—
315C8—3761no—
316C8—1882no—
317C22#1568902711yescharacteristic
318C22#1568910411yescharacteristic
319C22#1568910611yescharacteristic
320C22#103×D4711yescharacteristic
321C22#1568911611yescharacteristic
322C22#1568911811yescharacteristic
323C22#1568912611yescharacteristic
324C4—21no—
325C4—21no—
326C4—82no—
327C4—942no—
328C4—942no—
329C4—3762no—
330C4—1881no—
331C4—1881no—
332C4#1568941111yescharacteristic
333C4#1568941211yescharacteristic
334C4#1568941611yescharacteristic
335C4#1568941711yescharacteristic
336C4#1568947611yescharacteristic
337C4#1568947911yescharacteristic
338C4#1568952311yescharacteristic
339C4#1568952411yescharacteristic
340C2#2024204211yescharacteristic
341C2#2024204411yescharacteristic
342C2#2024209011yescharacteristic
343C2#2024209211yescharacteristic
344C2#2024433411yescharacteristic
345C2#2024435111yescharacteristic
346C2#2024437911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1296C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1296D47
hypocenterC47#9897
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
198. C47#9897semidirect

Maximal subgroups

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

subgroupindex
#202517492
#202435042
C4⋊C8×Dic472
#202412722
#202412712
C47×#12962
#989747