Finite Group Databasebeta

← #26105413

Subgroups — #26105413

Order 12032.

338 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 79 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#20251379C211yesmaximal, characteristic
2#20244945C211yesmaximal, characteristic
3#20244865C211yesmaximal, characteristic
4#20241212C211yesmaximal, characteristic
5#20241211C211yesmaximal, characteristic
6#20241210C211yesmaximal, characteristic
7C47×#2083C211yesmaximal, characteristic
8C2×#13093955—21no—
9#15689063—21no—
10#15689062—21no—
11#15689061—21no—
12#15689021C2211yescharacteristic
13#15689021C2211yescharacteristic
14#15689010—21no—
15#15689009—21no—
16#15689004—21no—
17#15688885—21no—
18#15688885—21no—
19#15688885—21no—
20#15688878C2211yescharacteristic
21#15688878C2211yescharacteristic
22C2×#107×C47—21no—
23C47×#389C2211yescharacteristic
24C47×#384C2211yescharacteristic
25C47×#340—21no—
26C47×#336C2211yescharacteristic
27C22×C47⋊C8—21no—
28C22×C47⋊C8—21no—
29C2×C4⋊Dic47D411yescharacteristic
30C2×C4⋊Dic47D411yescharacteristic
31C2×C4⋊Dic47D411yescharacteristic
32C2×C4⋊Dic47D411yescharacteristic
33C2×Dic47⋊C4—21no—
34C2×Dic47⋊C4—21no—
35C2×C4×Dic47—21no—
36#13093955—42no—
37C47⋊#95—21no—
38C47⋊#95—21no—
39C47⋊#95—21no—
40C47⋊#95—21no—
41C47⋊#95—21no—
42C47⋊#95—21no—
43C47⋊#95—21no—
44C47⋊#95—21no—
45C47⋊#95—21no—
46C22×C8×C47—21no—
47C2×C4⋊C4×C47—21no—
48C2×C4⋊C4×C47—21no—
49C2×C4⋊C4×C47—21no—
50C2×C4⋊C4×C47—21no—
51C2×C4⋊C4×C47D411yescharacteristic
52C2×C4⋊C4×C47D411yescharacteristic
53C2×C42×C47C2311yescharacteristic
54#107×C47—42no—
55#95×C47—21no—
56C22×C4×C47—21no—
57C22×C4×C47—21no—
58C22×C4×C47—41no—
59C22×C4×C47C2×D411yescharacteristic
60C22×C4×C47C2×D411yescharacteristic
61C22×C4×C47C2×D411yescharacteristic
62C22×Dic47—21no—
63C22×Dic47—21no—
64C22×Dic47—21no—
65C22×Dic47—21no—
66C2×C8×C47—22no—
67C2×C8×C47—41no—
68C2×C8×C47—41no—
69C4⋊C4×C47—21no—
70C4⋊C4×C47—21no—
71C4⋊C4×C47—41no—
72C4⋊C4×C47—42no—
73C4⋊C4×C47—41no—
74C4⋊C4×C47—41no—
75C4⋊C4×C47—41no—
76C4⋊C4×C47—41no—
77C4⋊C4×C47—41no—
78C4⋊C4×C47—41no—
79C42×C47—41no—
80C4⋊Dic47—21no—
81C4⋊Dic47—21no—
82C4⋊Dic47—21no—
83C4⋊Dic47—21no—
84C4⋊Dic47—41no—
85C4⋊Dic47—41no—
86Dic47⋊C4—41no—
87Dic47⋊C4—41no—
88Dic47⋊C4—41no—
89Dic47⋊C4—41no—
90C4×Dic47—81no—
91C2×C47⋊C8—22no—
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—81no—
111C2×C4×C47—81no—
112C2×C4×C47—81no—
113C2×C4×C47#13511yescharacteristic
114C2×C4×C47#13511yescharacteristic
115C2×C4×C47#13511yescharacteristic
116C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C47#13711yescharacteristic
119C2×Dic47—41no—
120C2×Dic47—41no—
121C2×Dic47—41no—
122C2×Dic47—41no—
123C2×Dic47—41no—
124C2×Dic47—41no—
125C2×Dic47—41no—
126C2×Dic47—41no—
127C2×Dic47—41no—
128C2×Dic47—41no—
129C2×Dic47—41no—
130C2×Dic47—41no—
131C8×C47—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—161no—
151Dic47—81no—
152Dic47—81no—
153Dic47—81no—
154Dic47—81no—
155#2810—471no—
156#2099—471no—
157#2084—471no—
158#2083D4711yescharacteristic
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—21no—
170C2×#106—941no—
171#400—941no—
172#400—941no—
173#400—941no—
174#389—471no—
175#389—471no—
176#389C2×D4711yescharacteristic
177#387—941no—
178#387—941no—
179#387—941no—
180#384C2×D4711yescharacteristic
181#340—21no—
182#340—941no—
183#340—941no—
184#340—941no—
185#336—471no—
186#336—471no—
187#336C2×D4711yescharacteristic
188C47#780311yescharacteristic, complemented, Sylow
189C22×C8—21no—
190C22×C8—941no—
191C22×C8—941no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—471no—
197C2×C4⋊C4—471no—
198C2×C4⋊C4—471no—
199C2×C4⋊C4—471no—
200C2×C4⋊C4—941no—
201C2×C4⋊C4—941no—
202C2×C4⋊C4C22⋊D4711yescharacteristic
203C2×C4⋊C4C22⋊D4711yescharacteristic
204C2×C42—941no—
205C2×C42C22×D4711yescharacteristic
206#107—42no—
207#106—1882no—
208#95—21no—
209#95—941no—
210#95—941no—
211#95—941no—
212#95—941no—
213#95—941no—
214#95—941no—
215#95—941no—
216#95—941no—
217#95—941no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—41no—
221C22×C4—941no—
222C22×C4—941no—
223C22×C4—941no—
224C22×C4—941no—
225C22×C4D4×D4711yescharacteristic
226C22×C4D4×D4711yescharacteristic
227C22×C4C2×C22⋊D4711yescharacteristic
228C2×C8—22no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—942no—
232C2×C8—1881no—
233C2×C8—1881no—
234C2×C8—1881no—
235C2×C8—1881no—
236C2×C8—1881no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—941no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4—1881no—
252C4⋊C4—1881no—
253C4⋊C4—1881no—
254C4⋊C4—1881no—
255C4⋊C4—1881no—
256C4⋊C4—1881no—
257C42—41no—
258C42—3761no—
259C23#1309399211yescharacteristic
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—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—1881no—
276C2×C4—1881no—
277C2×C4—1881no—
278C2×C4—1881no—
279C2×C4—1881no—
280C2×C4—1881no—
281C2×C4—1881no—
282C2×C4—1881no—
283C2×C4—1881no—
284C2×C4—1881no—
285C2×C4—1881no—
286C2×C4—1881no—
287C2×C4#1309404311yescharacteristic
288C2×C4#1309404411yescharacteristic
289C2×C4#1309404711yescharacteristic
290C2×C4#1309404811yescharacteristic
291C2×C4#1309405011yescharacteristic
292C2×C4#1309405611yescharacteristic
293C8—42no—
294C8—3761no—
295C8—1882no—
296C22#1568926511yescharacteristic
297C22#1568926611yescharacteristic
298C22#1568928411yescharacteristic
299C22#1568929411yescharacteristic
300C22#1568930411yescharacteristic
301C22#1568930511yescharacteristic
302C22#1568931211yescharacteristic
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—81no—
310C4—81no—
311C4—161no—
312C4—3761no—
313C4—3761no—
314C4—3761no—
315C4—3761no—
316C2#2024238211yescharacteristic
317C2#2024238311yescharacteristic
318C2#2024241811yescharacteristic
319C2#2024249611yescharacteristic
320C2#2024264111yescharacteristic
321C2#2024265611yescharacteristic
322C2#2024271511yescharacteristic
subgroupG/H
centerC23#13093992
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#2083C2
socle, prime radicalC23×C47#120
hypercenter#2083D47
hypocenterC47#7803
LCSG ▷ C2×C42×C47 ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2083

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
#202513792
#202449452
#202448652
#202412122
#202412112
#202412102
C47×#20832
#780347