Finite Group Databasebeta

← #26120784

Subgroups — #26120784

Order 12032.

382 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 97 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#20251663C211yesmaximal, characteristic
2#20243557C211yesmaximal, characteristic
3#20243556C211yesmaximal, characteristic
4#20243522C211yesmaximal, characteristic
5#20241270C211yesmaximal, characteristic
6#20241270C211yesmaximal, characteristic
7C47×#1295C211yesmaximal, characteristic
8C2×#13093958—21no—
9C2×#13093957—21no—
10C2×#13093956—21no—
11C2×#13093955—21no—
12C2×#13093935C2211yescharacteristic
13#15689057—21no—
14#15689057—21no—
15#15689056—21no—
16#15689056—21no—
17#15689055—21no—
18#15689055—21no—
19#15688993C2211yescharacteristic
20#15688989C2211yescharacteristic
21#15688989C2211yescharacteristic
22#15688886—21no—
23#15688886—21no—
24C2×#97×C47C2211yescharacteristic
25C2×#97×C47C2211yescharacteristic
26C47×#382C2211yescharacteristic
27C22×C47⋊C8—21no—
28C2×C4⋊Dic47—21no—
29C2×C4⋊Dic47—21no—
30C2×C4⋊Dic47—21no—
31C2×C4⋊Dic47—21no—
32C2×C4⋊Dic47—21no—
33C2×C4⋊Dic47D411yescharacteristic
34C2×C4⋊Dic47D411yescharacteristic
35C2×C4⋊Dic47D411yescharacteristic
36C2×C4⋊Dic47D411yescharacteristic
37C2×Dic47⋊C4—21no—
38C2×Dic47⋊C4—21no—
39C2×Dic47⋊C4—21no—
40C2×Dic47⋊C4—21no—
41#13093958—42no—
42#13093957—42no—
43#13093956—42no—
44#13093955—42no—
45#13093935—21no—
46#13093935Q812yes—
47C47⋊#95—21no—
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×C47D411yescharacteristic
56C2×C4⋊C4×C47D411yescharacteristic
57C2×C42×C47C2311yescharacteristic
58#97×C47—21no—
59#97×C47—21no—
60#97×C47Q812yes—
61#97×C47Q812yes—
62#95×C47—21no—
63#95×C47—21no—
64C22×C4×C47—21no—
65C22×C4×C47—21no—
66C22×C4×C47C2×D411yescharacteristic
67C22×C4×C47C2×D411yescharacteristic
68C22×C4×C47C2×D411yescharacteristic
69C22×Dic47—21no—
70C22×Dic47—21no—
71C22×Dic47—21no—
72C22×Dic47—21no—
73C22×Dic47—41no—
74C2×C8×C47—22no—
75C2×C8×C47—22no—
76C2×C8×C47—22no—
77C2×C8×C47—22no—
78C2×C8×C47—41no—
79C2×C8×C47—41no—
80C4⋊C4×C47—41no—
81C4⋊C4×C47—41no—
82C42×C47C2×Q811yescharacteristic
83C42×C47C2×Q811yescharacteristic
84C42×C47C2×Q811yescharacteristic
85C42×C47#4111yescharacteristic
86C4⋊Dic47—41no—
87C4⋊Dic47—41no—
88C4⋊Dic47—41no—
89C4⋊Dic47—41no—
90C4⋊Dic47—41no—
91C4⋊Dic47—41no—
92C4⋊Dic47—41no—
93C4⋊Dic47—41no—
94C4⋊Dic47—42no—
95C4⋊Dic47—81no—
96C4⋊Dic47—81no—
97Dic47⋊C4—81no—
98Dic47⋊C4—81no—
99Dic47⋊C4—81no—
100Dic47⋊C4—81no—
101C2×C47⋊C8—22no—
102C2×C47⋊C8—22no—
103C2×C47⋊C8—22no—
104C23×C47#12011yescharacteristic
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
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×C47C22⋊Q811yescharacteristic
118C2×C4×C47C22⋊Q811yescharacteristic
119C2×C4×C47C22⋊Q811yescharacteristic
120C2×C4×C47C4⋊Q811yescharacteristic
121C2×C4×C47C4⋊Q811yescharacteristic
122C2×C4×C47C4⋊Q811yescharacteristic
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—
132C2×Dic47—41no—
133C2×Dic47—41no—
134C2×Dic47—41no—
135C2×Dic47—81no—
136C2×Dic47—81no—
137C2×Dic47—81no—
138C8×C47—24no—
139C8×C47—42no—
140C47⋊C8—24no—
141#10585—471nomaximal, Sylow
142C22×C47#39511yescharacteristic
143C22×C47#45311yescharacteristic
144C22×C47#45311yescharacteristic
145C22×C47#45411yescharacteristic
146C22×C47#45511yescharacteristic
147C22×C47#45611yescharacteristic
148C22×C47#45611yescharacteristic
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—81no—
158Dic47—81no—
159Dic47—81no—
160Dic47—81no—
161Dic47—161no—
162#2845—471no—
163#1847—471no—
164#1847—471no—
165#1836—471no—
166#1295—471no—
167#1295—471no—
168#1295D4711yescharacteristic
169C2×C47#165611yescharacteristic
170C2×C47#166111yescharacteristic
171C2×C47#166111yescharacteristic
172C2×C47#166311yescharacteristic
173C2×C47#206011yescharacteristic
174C2×C47#206011yescharacteristic
175C2×C47#206111yescharacteristic
176C2×#107—941no—
177C2×#107—941no—
178C2×#106—941no—
179C2×#106—941no—
180C2×#97—471no—
181C2×#97C2×D4711yescharacteristic
182C2×#97C2×D4711yescharacteristic
183#398—941no—
184#398—941no—
185#398—941no—
186#398—941no—
187#398—941no—
188#398—941no—
189#384—471no—
190#382—471no—
191#382—471no—
192#382C2×D4711yescharacteristic
193#340—941no—
194#340—941no—
195C47#1058511yescharacteristic, complemented, Sylow
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—941no—
199C2×C4⋊C4—471no—
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⋊C4—941no—
207C2×C4⋊C4—941no—
208C2×C4⋊C4—941no—
209C2×C4⋊C4—941no—
210C2×C4⋊C4—941no—
211C2×C4⋊C4—941no—
212C2×C4⋊C4D18811yescharacteristic
213C2×C4⋊C4D18811yescharacteristic
214C2×C42C22×D4711yescharacteristic
215#107—1882no—
216#107—1882no—
217#106—1882no—
218#106—1882no—
219#97—21no—
220#97—21no—
221#97—472no—
222#97—941no—
223#97Dic9412yes—
224#97Dic9412yes—
225#95—21no—
226#95—21no—
227#95—941no—
228#95—941no—
229#95—941no—
230#95—941no—
231#95—941no—
232#95—941no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—941no—
236C22×C4—941no—
237C22×C4—941no—
238C22×C4—941no—
239C22×C4—1881no—
240C22×C4C2×D18811yescharacteristic
241C22×C4D4×D4711yescharacteristic
242C22×C4D4×D4711yescharacteristic
243C2×C8—22no—
244C2×C8—22no—
245C2×C8—22no—
246C2×C8—22no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—942no—
250C2×C8—942no—
251C2×C8—942no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—3761no—
255C4⋊C4—3761no—
256C4⋊C4—3761no—
257C4⋊C4—3761no—
258C4⋊C4—3761no—
259C4⋊C4—3761no—
260C4⋊C4—1881no—
261C4⋊C4—1881no—
262C4⋊C4—1881no—
263C4⋊C4—1881no—
264C4⋊C4—1882no—
265C4⋊C4—1881no—
266C4⋊C4—1881no—
267C4⋊C4—1881no—
268C4⋊C4—1881no—
269C42C2×Dic9411yescharacteristic
270C42C2×Dic9411yescharacteristic
271C42#1062535211yescharacteristic
272C42Q8×D4711yescharacteristic
273C23#1309399411yescharacteristic
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—3761no—
287C2×C4—3761no—
288C2×C4—3761no—
289C2×C4—1881no—
290C2×C4—1881no—
291C2×C4—1881no—
292C2×C4—1881no—
293C2×C4—1881no—
294C2×C4—1881no—
295C2×C4—1881no—
296C2×C4—1881no—
297C2×C4—1881no—
298C2×C4—1881no—
299C2×C4—1881no—
300C2×C4—1881no—
301C2×C4#1309400111yescharacteristic
302C2×C4#1309400111yescharacteristic
303C2×C4#1309400411yescharacteristic
304C2×C4#1309402311yescharacteristic
305C2×C4#1309402311yescharacteristic
306C2×C4#1309402411yescharacteristic
307C8—24no—
308C8—42no—
309C8—944no—
310C22#1568904411yescharacteristic
311C22#1568929211yescharacteristic
312C22#1568929311yescharacteristic
313C22#1568929711yescharacteristic
314C22#1568930211yescharacteristic
315C22#1568930711yescharacteristic
316C22#1568930811yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—81no—
324C4—81no—
325C4—3761no—
326C4—3761no—
327C4—3761no—
328C4—3761no—
329C4—7521no—
330C2#2024268211yescharacteristic
331C2#2024270611yescharacteristic
332C2#2024270711yescharacteristic
333C2#2024271811yescharacteristic
334C2#2024473211yescharacteristic
335C2#2024473411yescharacteristic
336C2#2024473711yescharacteristic
subgroupG/H
centerC23#13093994
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1295C2
socle, prime radicalC23×C47#120
hypercenter#1295D47
hypocenterC47#10585
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
195. C47#10585semidirect

Maximal subgroups

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

subgroupindex
#202516632
#202435572
#202435562
#202435222
#202412702
C47×#12952
#1058547