Finite Group Databasebeta

← #26105586

Subgroups — #26105586

Order 12032.

350 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 81 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#20251373C211yesmaximal, characteristic
2#20244950C211yesmaximal, characteristic
3#20244927C211yesmaximal, characteristic
4#20241213C211yesmaximal, characteristic
5#20241212C211yesmaximal, characteristic
6#20241211C211yesmaximal, characteristic
7C47×#2100C211yesmaximal, characteristic
8C2×#13093957—21no—
9C2×#13093947—21no—
10#15689065—21no—
11#15689054—21no—
12#15689053—21no—
13#15689029C2211yescharacteristic
14#15689027—21no—
15#15689021C2211yescharacteristic
16#15689009—21no—
17#15689004—21no—
18#15688885—21no—
19#15688885—21no—
20#15688878C2211yescharacteristic
21#15688878C2211yescharacteristic
22C47×#389C2211yescharacteristic
23C47×#384C2211yescharacteristic
24C47×#340—21no—
25C47×#340—21no—
26C47×#336C2211yescharacteristic
27C22×Dic94D411yescharacteristic
28C22×C47⋊C8—21no—
29C22×C47⋊C8—21no—
30C2×C4⋊Dic47D411yescharacteristic
31C2×C4⋊Dic47D411yescharacteristic
32C2×C4⋊Dic47D411yescharacteristic
33C2×Dic47⋊C4—21no—
34C2×Dic47⋊C4—21no—
35C2×Dic47⋊C4—21no—
36C2×C4×Dic47—21no—
37#13093957—42no—
38#13093947—42no—
39C47⋊#95—21no—
40C47⋊#95—21no—
41C47⋊#95—21no—
42C47⋊#95—21no—
43C47⋊#95—21no—
44C47⋊#95—21no—
45C47⋊#95—21no—
46C47⋊#95—21no—
47C22×C8×C47—21no—
48C2×C4⋊C4×C47—21no—
49C2×C4⋊C4×C47—21no—
50C2×C4⋊C4×C47—21no—
51C2×C4⋊C4×C47—21no—
52C2×C4⋊C4×C47D411yescharacteristic
53C2×C4⋊C4×C47D411yescharacteristic
54C2×C42×C47C2311yescharacteristic
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×Dic94—21no—
67C2×Dic94—41no—
68C2×Dic94—41no—
69C2×Dic94Q1612yes—
70C2×C8×C47—41no—
71C2×C8×C47—41no—
72C2×C8×C47—41no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47—21no—
75C4⋊C4×C47—41no—
76C4⋊C4×C47—42no—
77C4⋊C4×C47—42no—
78C4⋊C4×C47—41no—
79C4⋊C4×C47—41no—
80C4⋊C4×C47—41no—
81C4⋊C4×C47—41no—
82C42×C47—41no—
83C4⋊Dic47—21no—
84C4⋊Dic47—21no—
85C4⋊Dic47—41no—
86C4⋊Dic47—41no—
87Dic47⋊C4—41no—
88Dic47⋊C4—41no—
89Dic47⋊C4—81no—
90Dic47⋊C4—81no—
91C4×Dic47—81no—
92C2×C47⋊C8—22no—
93C2×C47⋊C8—41no—
94C2×C47⋊C8—41no—
95C2×C47⋊C8—41no—
96C2×C47⋊C8—41no—
97C2×C47⋊C8—41no—
98C23×C47#12011yescharacteristic
99C2×C4×C47—21no—
100C2×C4×C47—21no—
101C2×C4×C47—21no—
102C2×C4×C47—21no—
103C2×C4×C47—21no—
104C2×C4×C47—21no—
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—81no—
112C2×C4×C47—81no—
113C2×C4×C47—81no—
114C2×C4×C47C2×Q1611yescharacteristic
115C2×C4×C47#13511yescharacteristic
116C2×C4×C47#13511yescharacteristic
117C2×C4×C47#13711yescharacteristic
118C2×C4×C47#13711yescharacteristic
119C2×C4×C47#13711yescharacteristic
120C2×Dic47—22no—
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—
131C2×Dic47—41no—
132Dic94—42no—
133Dic94—81no—
134C8×C47—81no—
135C47⋊C8—42no—
136C47⋊C8—81no—
137#7831—471nomaximal, Sylow
138C22×C47#45111yescharacteristic
139C22×C47#45211yescharacteristic
140C22×C47#45211yescharacteristic
141C22×C47#45311yescharacteristic
142C22×C47#45411yescharacteristic
143C22×C47#45411yescharacteristic
144C22×C47#45811yescharacteristic
145C4×C47—21no—
146C4×C47—21no—
147C4×C47—21no—
148C4×C47—21no—
149C4×C47—21no—
150C4×C47—21no—
151C4×C47—81no—
152C4×C47—81no—
153C4×C47—161no—
154Dic47—42no—
155Dic47—81no—
156Dic47—81no—
157Dic47—81no—
158#2809—471no—
159#2100—471no—
160#2100D4711yescharacteristic
161#2095—471no—
162#1272—471no—
163#1271—471no—
164#1271—471no—
165C2×C47#161411yescharacteristic
166C2×C47#161511yescharacteristic
167C2×C47#161511yescharacteristic
168C2×C47#163411yescharacteristic
169C2×C47#163611yescharacteristic
170C2×C47#163611yescharacteristic
171C2×C47#165711yescharacteristic
172C2×#107—941no—
173C2×#103—941no—
174#400—941no—
175#398—941no—
176#398—941no—
177#391—471no—
178#391—941no—
179#389—471no—
180#389C2×D4711yescharacteristic
181#387—941no—
182#387—941no—
183#384C2×D4711yescharacteristic
184#340—21no—
185#340—21no—
186#340—941no—
187#340—941no—
188#336—471no—
189#336—471no—
190#336C2×D4711yescharacteristic
191C47#783111yescharacteristic, complemented, Sylow
192C22×Q8—471no—
193C22×C8—21no—
194C22×C8—941no—
195C22×C8—941no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—471no—
201C2×C4⋊C4—471no—
202C2×C4⋊C4—471no—
203C2×C4⋊C4—941no—
204C2×C4⋊C4—941no—
205C2×C4⋊C4—941no—
206C2×C4⋊C4C22⋊D4711yescharacteristic
207C2×C4⋊C4C22⋊D4711yescharacteristic
208C2×C42—941no—
209C2×C42C22×D4711yescharacteristic
210#107—1882no—
211#103—1882no—
212#95—21no—
213#95—941no—
214#95—941no—
215#95—941no—
216#95—941no—
217#95—941no—
218#95—941no—
219#95—941no—
220#95—941no—
221C2×Q8—472no—
222C2×Q8—941no—
223C2×Q8—1881no—
224C2×Q8—1881no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—41no—
228C22×C4—941no—
229C22×C4—941no—
230C22×C4—941no—
231C22×C4—941no—
232C22×C4D4×D4711yescharacteristic
233C22×C4D4×D4711yescharacteristic
234C22×C4C2×C22⋊D4711yescharacteristic
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—942no—
239C2×C8—1881no—
240C2×C8—1881no—
241C2×C8—1881no—
242C2×C8—1881no—
243C2×C8—1881no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—3761no—
256C4⋊C4—3761no—
257C4⋊C4—1881no—
258C4⋊C4—1881no—
259C4⋊C4—1881no—
260C4⋊C4—1881no—
261C42—41no—
262C42—3761no—
263C23#1309399211yescharacteristic
264Q8—3761no—
265Q8—1882no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—942no—
282C2×C4—1881no—
283C2×C4—1881no—
284C2×C4—1881no—
285C2×C4—1881no—
286C2×C4—1881no—
287C2×C4—1881no—
288C2×C4—1881no—
289C2×C4—1881no—
290C2×C4—1881no—
291C2×C4—1881no—
292C2×C4—1881no—
293C2×C4Q16×D4711yescharacteristic
294C2×C4#1309404411yescharacteristic
295C2×C4#1309404511yescharacteristic
296C2×C4#1309405311yescharacteristic
297C2×C4#1309405511yescharacteristic
298C2×C4#1309405611yescharacteristic
299C8—81no—
300C8—3761no—
301C8—1882no—
302C22#1568927711yescharacteristic
303C22#1568928211yescharacteristic
304C22#1568928311yescharacteristic
305C22#1568928911yescharacteristic
306C22#1568929411yescharacteristic
307C22#1568929511yescharacteristic
308C22#1568931211yescharacteristic
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—81no—
316C4—81no—
317C4—161no—
318C4—3761no—
319C4—3761no—
320C4—3761no—
321C4—1882no—
322C2#2024241111yescharacteristic
323C2#2024241611yescharacteristic
324C2#2024241711yescharacteristic
325C2#2024253211yescharacteristic
326C2#2024254311yescharacteristic
327C2#2024254411yescharacteristic
328C2#2024268511yescharacteristic
subgroupG/H
centerC23#13093992
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#2100C2
socle, prime radicalC23×C47#120
hypercenter#2100D47
hypocenterC47#7831
LCSG ▷ C2×C42×C47 ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2100

Complements

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

NH ≅ G/Ntype
191. C47#7831semidirect

Maximal subgroups

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

subgroupindex
#202513732
#202449502
#202449272
#202412132
#202412122
#202412112
C47×#21002
#783147