Finite Group Databasebeta

← #26105415

Subgroups — #26105415

Order 12032.

338 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 83 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#20244946C211yesmaximal, characteristic
2#20244864C211yesmaximal, characteristic
3#20244859C211yesmaximal, characteristic
4#20241211C211yesmaximal, characteristic
5#20241211C211yesmaximal, characteristic
6#20241211C211yesmaximal, characteristic
7C47×#2810C211yesmaximal, characteristic
8C2×#13093957—21no—
9C2×#13093955—21no—
10#15688993C2211yescharacteristic
11#15688885—21no—
12#15688885—21no—
13#15688885—21no—
14#15688885—21no—
15#15688878C2211yescharacteristic
16#15688878C2211yescharacteristic
17#15688878C2211yescharacteristic
18C47×#400—21no—
19C47×#400—21no—
20C47×#400—21no—
21C47×#389C2211yescharacteristic
22C47×#389C2211yescharacteristic
23C47×#389C2211yescharacteristic
24C47×#387—21no—
25C47×#387—21no—
26C47×#387—21no—
27C22×C47⋊C8—21no—
28C22×C47⋊C8—21no—
29C22×C47⋊C8—21no—
30C2×C4⋊Dic47—21no—
31C2×C4⋊Dic47—21no—
32C2×C4⋊Dic47—21no—
33#13093957—42no—
34#13093955—42no—
35C2×C4⋊C4×C47—21no—
36C2×C4⋊C4×C47—21no—
37C2×C4⋊C4×C47—21no—
38C2×C4⋊C4×C47D411yescharacteristic
39C2×C4⋊C4×C47D411yescharacteristic
40C2×C4⋊C4×C47D411yescharacteristic
41C2×C4⋊C4×C47D411yescharacteristic
42C2×C4⋊C4×C47D411yescharacteristic
43C2×C4⋊C4×C47D411yescharacteristic
44C2×C42×C47—21no—
45C2×C42×C47C2311yescharacteristic
46#95×C47—21no—
47#95×C47—21no—
48#95×C47—21no—
49#95×C47—21no—
50#95×C47—21no—
51#95×C47—21no—
52#95×C47—21no—
53#95×C47—21no—
54#95×C47—21no—
55#95×C47—21no—
56C22×C4×C47—21no—
57C22×C4×C47—21no—
58C22×C4×C47—21no—
59C22×C4×C47—21no—
60C22×C4×C47—21no—
61C22×C4×C47—21no—
62C22×C4×C47C2×D411yescharacteristic
63C22×C4×C47C2×D411yescharacteristic
64C22×C4×C47C2×D411yescharacteristic
65C22×Dic47—41no—
66C4⋊C4×C47—21no—
67C4⋊C4×C47—21no—
68C4⋊C4×C47—21no—
69C4⋊C4×C47—21no—
70C4⋊C4×C47—21no—
71C4⋊C4×C47—21no—
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—
80C4⋊C4×C47—41no—
81C42×C47—41no—
82C42×C47—81no—
83C4⋊Dic47—42no—
84C4⋊Dic47—41no—
85C4⋊Dic47—41no—
86C4⋊Dic47—41no—
87C4⋊Dic47—41no—
88C2×C47⋊C8—22no—
89C2×C47⋊C8—22no—
90C2×C47⋊C8—41no—
91C2×C47⋊C8—41no—
92C2×C47⋊C8—41no—
93C2×C47⋊C8—41no—
94C2×C47⋊C8—41no—
95C2×C47⋊C8—41no—
96C2×C47⋊C8—41no—
97C23×C47#12011yescharacteristic
98C2×C4×C47—21no—
99C2×C4×C47—21no—
100C2×C4×C47—21no—
101C2×C4×C47—21no—
102C2×C4×C47—21no—
103C2×C4×C47—21no—
104C2×C4×C47—41no—
105C2×C4×C47—41no—
106C2×C4×C47—41no—
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—41no—
114C2×C4×C47—41no—
115C2×C4×C47—41no—
116C2×C4×C47—41no—
117C2×C4×C47—41no—
118C2×C4×C47—41no—
119C2×C4×C47—41no—
120C2×C4×C47—41no—
121C2×C4×C47—41no—
122C2×C4×C47#13511yescharacteristic
123C2×C4×C47#13511yescharacteristic
124C2×C4×C47#13511yescharacteristic
125C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C47#13711yescharacteristic
128C2×Dic47—81no—
129C2×Dic47—81no—
130C2×Dic47—81no—
131C47⋊C8—42no—
132C47⋊C8—42no—
133C47⋊C8—81no—
134#7803—471nomaximal, Sylow
135C22×C47#44911yescharacteristic
136C22×C47#44911yescharacteristic
137C22×C47#45211yescharacteristic
138C22×C47#45411yescharacteristic
139C22×C47#45611yescharacteristic
140C22×C47#45611yescharacteristic
141C22×C47#45811yescharacteristic
142C4×C47—21no—
143C4×C47—21no—
144C4×C47—21no—
145C4×C47—21no—
146C4×C47—21no—
147C4×C47—21no—
148C4×C47—81no—
149C4×C47—81no—
150C4×C47—81no—
151C4×C47—81no—
152C4×C47—81no—
153C4×C47—81no—
154Dic47—161no—
155#2810D4711yescharacteristic
156#2099—471no—
157#2084—471no—
158#2083—471no—
159#1271—471no—
160#1271—471no—
161#1271—471no—
162C2×C47#160911yescharacteristic
163C2×C47#160911yescharacteristic
164C2×C47#161511yescharacteristic
165C2×C47#162811yescharacteristic
166C2×C47#165011yescharacteristic
167C2×C47#165211yescharacteristic
168C2×C47#166311yescharacteristic
169C2×#107—941no—
170C2×#106—941no—
171#400—21no—
172#400—21no—
173#400—21no—
174#389C2×D4711yescharacteristic
175#389C2×D4711yescharacteristic
176#389C2×D4711yescharacteristic
177#387—21no—
178#387—21no—
179#387—21no—
180#384—471no—
181#340—941no—
182#340—941no—
183#340—941no—
184#340—941no—
185#336—471no—
186#336—471no—
187#336—471no—
188C47#780311yescharacteristic, complemented, Sylow
189C22×C8—941no—
190C22×C8—941no—
191C22×C8—941no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—941no—
196C2×C4⋊C4—941no—
197C2×C4⋊C4—941no—
198C2×C4⋊C4C22⋊D4711yescharacteristic
199C2×C4⋊C4C22⋊D4711yescharacteristic
200C2×C4⋊C4C22⋊D4711yescharacteristic
201C2×C4⋊C4C22⋊D4711yescharacteristic
202C2×C4⋊C4C22⋊D4711yescharacteristic
203C2×C4⋊C4C22⋊D4711yescharacteristic
204C2×C42—21no—
205C2×C42C22×D4711yescharacteristic
206#107—1882no—
207#106—1882no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—1881no—
225C22×C4C2×C22⋊D4711yescharacteristic
226C22×C4C2×C22⋊D4711yescharacteristic
227C22×C4C2×C22⋊D4711yescharacteristic
228C2×C8—942no—
229C2×C8—942no—
230C2×C8—1881no—
231C2×C8—1881no—
232C2×C8—1881no—
233C2×C8—1881no—
234C2×C8—1881no—
235C2×C8—1881no—
236C2×C8—1881no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—1882no—
253C4⋊C4—1881no—
254C4⋊C4—1881no—
255C4⋊C4—1881no—
256C4⋊C4—1881no—
257C42—41no—
258C42—81no—
259C23#1309399311yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—3761no—
285C2×C4—3761no—
286C2×C4—3761no—
287C2×C4#1309404411yescharacteristic
288C2×C4#1309404411yescharacteristic
289C2×C4#1309404411yescharacteristic
290C2×C4#1309404911yescharacteristic
291C2×C4#1309404911yescharacteristic
292C2×C4#1309405411yescharacteristic
293C8—3761no—
294C8—1882no—
295C8—1882no—
296C22#1568926811yescharacteristic
297C22#1568926811yescharacteristic
298C22#1568928511yescharacteristic
299C22#1568929611yescharacteristic
300C22#1568930611yescharacteristic
301C22#1568930611yescharacteristic
302C22#1568931311yescharacteristic
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—81no—
310C4—81no—
311C4—81no—
312C4—81no—
313C4—81no—
314C4—81no—
315C4—7521no—
316C2#2024238511yescharacteristic
317C2#2024238511yescharacteristic
318C2#2024241911yescharacteristic
319C2#2024249811yescharacteristic
320C2#2024264411yescharacteristic
321C2#2024265811yescharacteristic
322C2#2024271611yescharacteristic
subgroupG/H
centerC23#13093993
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#2810C2
socle, prime radicalC23×C47#120
hypercenter#2810D47
hypocenterC47#7803
LCSG ▷ C2×C42×C47 ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2810

Complements

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

NH ≅ G/Ntype
188. C47#7803semidirect

Maximal subgroups

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

subgroupindex
#202449462
#202448642
#202448592
#202412112
C47×#28102
#780347