Finite Group Databasebeta

← #26104622

Subgroups — #26104622

Order 12032.

370 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 95 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#20251774C211yesmaximal, characteristic
2#20243530C211yesmaximal, characteristic
3#20243132C211yesmaximal, characteristic
4#20241212C211yesmaximal, characteristic
5#20241211C211yesmaximal, characteristic
6#20241210C211yesmaximal, characteristic
7C47×#1271C211yesmaximal, characteristic
8C2×C8×Dic47—21no—
9#15689022C411yescharacteristic
10#15689021C2211yescharacteristic
11#15689019C411yescharacteristic
12#15689009—21no—
13#15689008—21no—
14#15689005—21no—
15#15689004—21no—
16#15688988C411yescharacteristic
17#15688988C411yescharacteristic
18C42×Dic47C2211yescharacteristic
19#15688878C2211yescharacteristic
20#15688878C2211yescharacteristic
21#15688877—21no—
22#15688877—21no—
23#15688877—21no—
24C47×#389C2211yescharacteristic
25C47×#336C2211yescharacteristic
26C47×#336C2211yescharacteristic
27C22×C47⋊C8—21no—
28C22×C47⋊C8—21no—
29C2×C4⋊Dic47—21no—
30C2×C4⋊Dic47C2×C411yescharacteristic
31C2×C4⋊Dic47C2×C411yescharacteristic
32C2×Dic47⋊C4—21no—
33C2×Dic47⋊C4—21no—
34C2×C4×Dic47C2×C411yescharacteristic
35C2×C4×Dic47C2×C411yescharacteristic
36C2×C4×Dic47D411yescharacteristic
37C2×C4×Dic47D411yescharacteristic
38C2×C4×Dic47D411yescharacteristic
39C2×C4×Dic47D411yescharacteristic
40C8×Dic47—24no—
41C47⋊#95—21no—
42C47⋊#95—21no—
43C47⋊#95—21no—
44C47⋊#95—21no—
45C47⋊#95—21no—
46C47⋊#95—21no—
47C47⋊#95—21no—
48C22×C8×C47—21no—
49C22×C8×C47—21no—
50C2×C4⋊C4×C47—21no—
51C2×C4⋊C4×C47C2×C411yescharacteristic
52C2×C4⋊C4×C47C2×C411yescharacteristic
53C2×C42×C47C2311yescharacteristic
54#95×C47—21no—
55C22×C4×C47—21no—
56C22×C4×C47—21no—
57C22×C4×C47C22×C411yescharacteristic
58C22×C4×C47C2×D411yescharacteristic
59C22×C4×C47C2×D411yescharacteristic
60C22×Dic47—21no—
61C22×Dic47—21no—
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—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47—41no—
75C4⋊C4×C47—41no—
76C4⋊C4×C47—41no—
77C42×C47—41no—
78C4⋊Dic47—21no—
79C4⋊Dic47—21no—
80C4⋊Dic47—42no—
81C4⋊Dic47—41no—
82Dic47⋊C4—41no—
83Dic47⋊C4—41no—
84Dic47⋊C4—42no—
85C4×Dic47—21no—
86C4×Dic47—21no—
87C4×Dic47—21no—
88C4×Dic47—21no—
89C4×Dic47—21no—
90C4×Dic47—21no—
91C4×Dic47—22no—
92C4×Dic47—22no—
93C4×Dic47—41no—
94C2×C47⋊C8—22no—
95C2×C47⋊C8—41no—
96C2×C47⋊C8—41no—
97C2×C47⋊C8—41no—
98C2×C47⋊C8—41no—
99C2×C47⋊C8—41no—
100C23×C47C2×C22⋊C411yescharacteristic
101C2×C4×C47—21no—
102C2×C4×C47—21no—
103C2×C4×C47—21no—
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—41no—
108C2×C4×C47—41no—
109C2×C4×C47—41no—
110C2×C4×C47—41no—
111C2×C4×C47—41no—
112C2×C4×C47—41no—
113C2×C4×C47#13111yescharacteristic
114C2×C4×C47#13111yescharacteristic
115C2×C4×C47#13511yescharacteristic
116C2×C4×C47#13511yescharacteristic
117C2×C4×C47#13511yescharacteristic
118C2×C4×C47#13511yescharacteristic
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—41no—
130C2×Dic47—41no—
131C2×Dic47—41no—
132C2×Dic47—41no—
133C2×Dic47—41no—
134C2×Dic47—41no—
135C2×Dic47#10112yes—
136C2×Dic47#10412yes—
137C8×C47—42no—
138C8×C47—81no—
139C47⋊C8—42no—
140C47⋊C8—81no—
141#7657—471nomaximal, Sylow
142C22×C47#40811yescharacteristic
143C22×C47#41011yescharacteristic
144C22×C47C2×#10111yescharacteristic
145C22×C47#41611yescharacteristic
146C22×C47#41611yescharacteristic
147C22×C47C2×#10411yescharacteristic
148C22×C47#42111yescharacteristic
149C4×C47—21no—
150C4×C47—21no—
151C4×C47—21no—
152C4×C47—21no—
153C4×C47—21no—
154C4×C47—21no—
155C4×C47—81no—
156C4×C47—81no—
157Dic47—22no—
158Dic47—22no—
159Dic47—41no—
160Dic47—41no—
161Dic47—81no—
162Dic47—81no—
163#2864—471no—
164#1839—471no—
165#1744—471no—
166#1271—471no—
167#1271—471no—
168#1271—471no—
169#1271D4711yescharacteristic
170C2×C47#147011yescharacteristic
171C2×C47#148211yescharacteristic
172C2×C47#149411yescharacteristic
173C2×C47#150011yescharacteristic
174C2×C47#152111yescharacteristic
175C2×C47#153111yescharacteristic
176C2×C47#154411yescharacteristic
177C2×C4×C8—941no—
178#389—471no—
179#389—471no—
180#389—471no—
181#389C2×D4711yescharacteristic
182#387—941no—
183#387—941no—
184#387—941no—
185#387—941no—
186#382—471no—
187#382—471no—
188C43—471no—
189#336—471no—
190#336—471no—
191#336—941no—
192#336—941no—
193#336—941no—
194#336C2×D4711yescharacteristic
195#336C2×D4711yescharacteristic
196C47#765711yescharacteristic, complemented, Sylow
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—941no—
200C22×C8—941no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—471no—
203C2×C4⋊C4—471no—
204C2×C4⋊C4—941no—
205C2×C4⋊C4—941no—
206C2×C4⋊C4—941no—
207C2×C4⋊C4C4×D4711yescharacteristic
208C2×C4⋊C4C4×D4711yescharacteristic
209C2×C42—471no—
210C2×C42—471no—
211C2×C42—471no—
212C2×C42—471no—
213C2×C42—471no—
214C2×C42—471no—
215C2×C42C22×D4711yescharacteristic
216C4×C8—944no—
217#95—21no—
218#95—941no—
219#95—941no—
220#95—941no—
221#95—941no—
222#95—941no—
223#95—941no—
224#95—941no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—471no—
228C22×C4—471no—
229C22×C4—471no—
230C22×C4—471no—
231C22×C4—941no—
232C22×C4—941no—
233C22×C4C2×C4×D4711yescharacteristic
234C22×C4D4×D4711yescharacteristic
235C22×C4D4×D4711yescharacteristic
236C2×C8—22no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—942no—
243C2×C8—1881no—
244C2×C8—1881no—
245C2×C8—1881no—
246C2×C8—1881no—
247C2×C8—1881no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—1881no—
256C4⋊C4—1882no—
257C4⋊C4—1882no—
258C4⋊C4—1881no—
259C4⋊C4—1881no—
260C42—41no—
261C42—942no—
262C42—942no—
263C42—941no—
264C42—941no—
265C42—941no—
266C42—941no—
267C42—941no—
268C42—941no—
269C42—1881no—
270C23C22⋊C4×D4711yescharacteristic
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—472no—
284C2×C4—472no—
285C2×C4—941no—
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—1881no—
296C2×C4—1881no—
297C2×C4—1881no—
298C2×C4—1881no—
299C2×C4—1881no—
300C2×C4—1881no—
301C2×C4#1309403011yescharacteristic
302C2×C4#1309403211yescharacteristic
303C2×C4#1309404311yescharacteristic
304C2×C4#1309404511yescharacteristic
305C2×C4#1309404511yescharacteristic
306C2×C4#1309404711yescharacteristic
307C8—42no—
308C8—81no—
309C8—3761no—
310C8—1882no—
311C22#1568908811yescharacteristic
312C22#1568909511yescharacteristic
313C22#101×D4711yescharacteristic
314C22#1568911611yescharacteristic
315C22#1568911811yescharacteristic
316C22#104×D4711yescharacteristic
317C22#1568913811yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—81no—
325C4—81no—
326C4—942no—
327C4—942no—
328C4—3761no—
329C4—3761no—
330C4—1881no—
331C4—1881no—
332C2#2024174211yescharacteristic
333C2#2024179511yescharacteristic
334C2#2024184511yescharacteristic
335C2#2024187311yescharacteristic
336C2#2024196211yescharacteristic
337C2#2024200111yescharacteristic
338C2#2024205111yescharacteristic
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#7657
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
196. C47#7657semidirect

Maximal subgroups

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

subgroupindex
#202517742
#202435302
#202431322
#202412122
#202412112
#202412102
C47×#12712
#765747