Finite Group Databasebeta

← #26104540

Subgroups — #26104540

Order 12032.

436 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20245947C211yesmaximal, characteristic
2#20243240C211yesmaximal, characteristic
3#20243240C211yesmaximal, characteristic
4#20241212C211yesmaximal, characteristic
5#20241211C211yesmaximal, characteristic
6#20241210C211yesmaximal, characteristic
7C47×#1271C211yesmaximal, characteristic
8C2×#13094015C411yescharacteristic
9C2×Dic47⋊C8—21no—
10C2×Dic47⋊C8—21no—
11C2×#13093934—21no—
12C2×#13093934—21no—
13#15689021C2211yescharacteristic
14#15689008—21no—
15#15689004—21no—
16#15688988C411yescharacteristic
17C4⋊C4×Dic47—21no—
18C4⋊C4×Dic47C411yescharacteristic
19C4⋊C4×Dic47C411yescharacteristic
20#15688974—21no—
21C42×Dic47C2211yescharacteristic
22#15688878C2211yescharacteristic
23#15688878C2211yescharacteristic
24C47×#389C2211yescharacteristic
25C47×#336C2211yescharacteristic
26C47×#336C2211yescharacteristic
27C22×C47⋊C8—21no—
28C22×C47⋊C8—21no—
29#13094015—22no—
30#13094015—22no—
31C2×C4⋊Dic47—21no—
32C2×C4⋊Dic47C2×C411yescharacteristic
33C2×C4⋊Dic47C2×C411yescharacteristic
34C2×Dic47⋊C4—21no—
35C2×Dic47⋊C4—21no—
36C2×C4×Dic47—21no—
37C2×C4×Dic47—21no—
38C2×C4×Dic47C2×C411yescharacteristic
39C2×C4×Dic47C2×C411yescharacteristic
40C2×C4×Dic47D411yescharacteristic
41C2×C4×Dic47D411yescharacteristic
42C2×C4×Dic47D411yescharacteristic
43C2×C4×Dic47D411yescharacteristic
44Dic47⋊C8—24no—
45Dic47⋊C8—24no—
46#13093934—42no—
47#13093934—42no—
48C47⋊#95—21no—
49C47⋊#95—21no—
50C47⋊#95—21no—
51C47⋊#95—21no—
52C47⋊#95—21no—
53C22×C8×C47—21no—
54C22×C8×C47—21no—
55C2×C4⋊C4×C47—21no—
56C2×C4⋊C4×C47C2×C411yescharacteristic
57C2×C4⋊C4×C47C2×C411yescharacteristic
58C2×C42×C47C2311yescharacteristic
59#95×C47—21no—
60C22×C4×C47—21no—
61C22×C4×C47—21no—
62C22×C4×C47C22×C411yescharacteristic
63C22×C4×C47C2×D411yescharacteristic
64C22×C4×C47C2×D411yescharacteristic
65C22×Dic47—21no—
66C22×Dic47—21no—
67C22×Dic47C22⋊C411yescharacteristic
68C22×Dic47C22⋊C411yescharacteristic
69C22×Dic47C22⋊C411yescharacteristic
70C22×Dic47C22⋊C411yescharacteristic
71C2×C8×C47—22no—
72C2×C8×C47—22no—
73C2×C8×C47—41no—
74C2×C8×C47—41no—
75C2×C8×C47—41no—
76C2×C8×C47—41no—
77C4⋊C4×C47—21no—
78C4⋊C4×C47—41no—
79C4⋊C4×C47—41no—
80C4⋊C4×C47—41no—
81C4⋊C4×C47M1612yes—
82C42×C47—41no—
83C4⋊Dic47—24no—
84C4⋊Dic47—21no—
85C4⋊Dic47—41no—
86C4⋊Dic47M1612yes—
87Dic47⋊C4—24no—
88Dic47⋊C4—41no—
89Dic47⋊C4—41no—
90C4×Dic47—21no—
91C4×Dic47—21no—
92C4×Dic47—21no—
93C4×Dic47—21no—
94C4×Dic47—21no—
95C4×Dic47—21no—
96C4×Dic47—22no—
97C4×Dic47—22no—
98C4×Dic47—22no—
99C4×Dic47—42no—
100C4×Dic47—42no—
101C2×C47⋊C8—22no—
102C2×C47⋊C8—22no—
103C2×C47⋊C8—41no—
104C2×C47⋊C8—41no—
105C2×C47⋊C8—41no—
106C2×C47⋊C8—41no—
107C23×C47C2×C22⋊C411yescharacteristic
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—22no—
115C2×C4×C47—41no—
116C2×C4×C47—41no—
117C2×C4×C47—41no—
118C2×C4×C47—41no—
119C2×C4×C47—41no—
120C2×C4×C47C2×M1611yescharacteristic
121C2×C4×C47C2×M1611yescharacteristic
122C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C47#13711yescharacteristic
125C2×C4×C47#13711yescharacteristic
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—22no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—41no—
137C2×Dic47—41no—
138C2×Dic47—41no—
139C2×Dic47—41no—
140C2×Dic47—41no—
141C2×Dic47#10112yes—
142C2×Dic47#10412yes—
143C2×Dic47#10412yes—
144C8×C47—42no—
145C8×C47—42no—
146C47⋊C8—42no—
147C47⋊C8—42no—
148#7636—471nomaximal, Sylow
149C22×C47#40711yescharacteristic
150C22×C47#41011yescharacteristic
151C22×C47C2×#10111yescharacteristic
152C22×C47#41711yescharacteristic
153C22×C47#41711yescharacteristic
154C22×C47C2×#10411yescharacteristic
155C22×C47C2×#10411yescharacteristic
156C4×C47—21no—
157C4×C47—21no—
158C4×C47—21no—
159C4×C47—21no—
160C4×C47—21no—
161C4×C47—21no—
162C4×C47—42no—
163C4×C47—81no—
164Dic47—41no—
165Dic47—41no—
166Dic47—41no—
167Dic47—42no—
168Dic47—81no—
169Dic47#33014yes—
170C4×#125—471no—
171#1767—471no—
172#1767—471no—
173#1271—471no—
174#1271—471no—
175#1271—471no—
176#1271D4711yescharacteristic
177C2×C47#146711yescharacteristic
178C2×C47#148911yescharacteristic
179C2×C47#148911yescharacteristic
180C2×C47#150911yescharacteristic
181C2×C47#150911yescharacteristic
182C2×C47C2×#33011yescharacteristic
183C2×C47#156111yescharacteristic
184C2×#125—471no—
185C2×C4⋊C8—941no—
186C2×C4⋊C8—941no—
187C2×#97—941no—
188C2×#97—941no—
189#389—471no—
190#389C2×D4711yescharacteristic
191#387—941no—
192#387—941no—
193#382—471no—
194C4×C4⋊C4—471no—
195C4×C4⋊C4—471no—
196C4×C4⋊C4—941no—
197C4×C4⋊C4—941no—
198C43—471no—
199#336—471no—
200#336—471no—
201#336C2×D4711yescharacteristic
202#336C2×D4711yescharacteristic
203C47#763611yescharacteristic, complemented, Sylow
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—941no—
207C22×C8—941no—
208#125—942no—
209#125—942no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—471no—
212C2×C4⋊C4—471no—
213C2×C4⋊C4—941no—
214C2×C4⋊C4—941no—
215C2×C4⋊C4—941no—
216C2×C4⋊C4C4×D4711yescharacteristic
217C2×C4⋊C4C4×D4711yescharacteristic
218C2×C42—471no—
219C2×C42—471no—
220C2×C42—471no—
221C2×C42—471no—
222C2×C42—471no—
223C2×C42—471no—
224C2×C42—941no—
225C2×C42—941no—
226C2×C42C22×D4711yescharacteristic
227C4⋊C8—944no—
228C4⋊C8—944no—
229#97—1882no—
230#97—1882no—
231#95—21no—
232#95—941no—
233#95—941no—
234#95—941no—
235#95—941no—
236#95—941no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—471no—
240C22×C4—471no—
241C22×C4—471no—
242C22×C4—471no—
243C22×C4—941no—
244C22×C4—941no—
245C22×C4C2×C4×D4711yescharacteristic
246C22×C4D4×D4711yescharacteristic
247C22×C4D4×D4711yescharacteristic
248C2×C8—22no—
249C2×C8—22no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—942no—
255C2×C8—942no—
256C2×C8—1881no—
257C2×C8—1881no—
258C2×C8—1881no—
259C2×C8—1881no—
260C4⋊C4—21no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—472no—
265C4⋊C4—944no—
266C4⋊C4—944no—
267C4⋊C4—941no—
268C4⋊C4—1881no—
269C4⋊C4—1881no—
270C4⋊C4—1881no—
271C4⋊C4#1062532412yes—
272C42—41no—
273C42—942no—
274C42—942no—
275C42—942no—
276C42—941no—
277C42—941no—
278C42—941no—
279C42—941no—
280C42—941no—
281C42—941no—
282C42—1882no—
283C42—1882no—
284C23C22⋊C4×D4711yescharacteristic
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—472no—
298C2×C4—472no—
299C2×C4—472no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—942no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—941no—
310C2×C4—1881no—
311C2×C4—1881no—
312C2×C4—1881no—
313C2×C4—1881no—
314C2×C4—1881no—
315C2×C4M16×D4711yescharacteristic
316C2×C4C2×#1062532411yescharacteristic
317C2×C4#1309404811yescharacteristic
318C2×C4#1309405111yescharacteristic
319C2×C4#1309405311yescharacteristic
320C2×C4#1309405611yescharacteristic
321C8—42no—
322C8—42no—
323C8—1882no—
324C8—1882no—
325C22#1568908511yescharacteristic
326C22#1568909511yescharacteristic
327C22#101×D4711yescharacteristic
328C22#1568912111yescharacteristic
329C22#1568912311yescharacteristic
330C22#104×D4711yescharacteristic
331C22#104×D4711yescharacteristic
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—42no—
339C4—81no—
340C4—474no—
341C4—3761no—
342C4—1881no—
343C4—1881no—
344C4—1882no—
345C4—1881no—
346C2#2024173011yescharacteristic
347C2#2024182411yescharacteristic
348C2#2024182611yescharacteristic
349C2#2024191011yescharacteristic
350C2#2024191211yescharacteristic
351C2#330×D4711yescharacteristic
352C2#2024212411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1271C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1271D47
hypocenterC47#7636
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
203. C47#7636semidirect

Maximal subgroups

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

subgroupindex
#202459472
#202432402
#202412122
#202412112
#202412102
C47×#12712
#763647