Finite Group Databasebeta

← #26114811

Subgroups — #26114811

Order 12032.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20244163C211yesmaximal, characteristic, complemented
2#20242037C211yesmaximal, characteristic
3#20241839C211yesmaximal, characteristic
4#20241675C211yesmaximal, characteristic, complemented
5#20241291C211yesmaximal, characteristic, complemented
6#20241229C211yesmaximal, characteristic, complemented
7C47×#1980C211yesmaximal, characteristic
8#15689176C2211yescharacteristic
9C2×#13093959—21no—
10#15689147C2211yescharacteristic
11C2×C4⋊(C47⋊C8)C2211yescharacteristic
12C2×C4×C47⋊C8C2211yescharacteristic
13#15688887—21no—
14#15688869C411yescharacteristic, complemented
15#15688869C411yescharacteristic, complemented
16#15688867C411yescharacteristic, complemented
17#15688867C411yescharacteristic, complemented
18D4⋊(C47⋊C8)—21no—
19D4⋊(C47⋊C8)—21no—
20#15688845—21no—
21#15688845—21no—
22C47×#532C2211yescharacteristic
23C2×#104×C47—21no—
24C2×#104×C47—21no—
25C4×M16×C47C2211yescharacteristic
26C4×C4⋊C4×C47C2211yescharacteristic
27C2×#10625329—21no—
28C22×C47⋊C8—21no—
29C22×C47⋊C8—21no—
30#13093959—42no—
31C4⋊(C47⋊C8)—21no—
32C4⋊(C47⋊C8)—21no—
33C4⋊(C47⋊C8)—21no—
34C4⋊(C47⋊C8)C2×C411yescharacteristic
35C4⋊(C47⋊C8)C2×C411yescharacteristic
36C4⋊(C47⋊C8)C2×C411yescharacteristic
37C4⋊(C47⋊C8)C2×C411yescharacteristic
38C22⋊(C47⋊C8)—21no—
39C4×C47⋊C8—21no—
40C4×C47⋊C8—21no—
41C4×C47⋊C8D411yescharacteristic
42C4×C47⋊C8D411yescharacteristic
43C2×#41×C47—21no—
44C2×M16×C47D411yescharacteristic
45C2×M16×C47D411yescharacteristic
46C4⋊Q8×C47C2×C411yescharacteristic
47#127×C47C2×C411yescharacteristic
48#124×C47—21no—
49#121×C47—21no—
50#121×C47—21no—
51C4×D4×C47—21no—
52C4×D4×C47—21no—
53C2×C4⋊C4×C47—21no—
54C2×C42×C47—21no—
55C2×C42×C47C2311yescharacteristic
56#104×C47—42no—
57#104×C47—42no—
58#97×C47—21no—
59C4×C8×C47—21no—
60#95×C47—21no—
61#41×C47—41no—
62#41×C47—41no—
63#41×C47—41no—
64#41×C47—41no—
65C2×Q8×C47—21no—
66C2×D4×C47—21no—
67C2×D4×C47—21no—
68C2×D4×C47—21no—
69C2×D4×C47—41no—
70C22×C4×C47—41no—
71C22×C4×C47—41no—
72C22×C4×C47C2×D411yescharacteristic
73C22×C4×C47#4111yescharacteristic
74C22×C4×C47#4111yescharacteristic
75M16×C47—21no—
76M16×C47—21no—
77M16×C47—21no—
78M16×C47—21no—
79C2×C8×C47—21no—
80C2×C8×C47—21no—
81C4⋊C4×C47—22no—
82C4⋊C4×C47—21no—
83C4⋊C4×C47—21no—
84C4⋊C4×C47—41no—
85C22⋊C4×C47—41no—
86C22⋊C4×C47—41no—
87C42×C47—41no—
88C42×C47—41no—
89C42×C47C22×C411yescharacteristic
90C42×C47C2×D411yescharacteristic
91C42×C47#4111yescharacteristic
92C42×C47#4111yescharacteristic
93#10625329—41no—
94#10625329—41no—
95C2×C47⋊C8—21no—
96C2×C47⋊C8—21no—
97C2×C47⋊C8—21no—
98C2×C47⋊C8—21no—
99C2×C47⋊C8—21no—
100C2×C47⋊C8—21no—
101C2×C47⋊C8—42no—
102C2×C47⋊C8—41no—
103C2×C47⋊C8—41no—
104C2×C47⋊C8—41no—
105C23×C47—41no—
106C23×C47#12411yescharacteristic
107Q8×C47—41no—
108Q8×C47—41no—
109D4×C47—41no—
110D4×C47—41no—
111D4×C47—41no—
112D4×C47—41no—
113D4×C47—81no—
114D4×C47—81no—
115D4×C47—81no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—41no—
119C2×C4×C47—42no—
120C2×C4×C47—41no—
121C2×C4×C47—81no—
122C2×C4×C47—81no—
123C2×C4×C47—81no—
124C2×C4×C47—81no—
125C2×C4×C47#11711yescharacteristic
126C2×C4×C47C4×D411yescharacteristic
127C2×C4×C47C4×D411yescharacteristic
128C2×C4×C47#12111yescharacteristic
129C2×C4×C47#12311yescharacteristic
130C2×C4×C47#12611yescharacteristic
131C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C47#13711yescharacteristic
135C8×C47—41no—
136C8×C47—41no—
137C47⋊C8—22no—
138C47⋊C8—41no—
139C47⋊C8—41no—
140C47⋊C8—41no—
141C47⋊C8—41no—
142C47⋊C8—41no—
143C47⋊C8—81no—
144#9592—471nomaximal, Sylow
145C22×C47—21no—
146C22×C47—21no—
147C22×C47—81no—
148C22×C47—81no—
149C22×C47—81no—
150C22×C47#38811yescharacteristic
151C22×C47#48911yescharacteristic
152C22×C47#49011yescharacteristic
153C4×C47—21no—
154C4×C47—21no—
155C4×C47—21no—
156C4×C47—82no—
157C4×C47—81no—
158C4×C47#44011yescharacteristic
159C4×C47#44211yescharacteristic
160C4×C47#44311yescharacteristic
161C4×C47#44411yescharacteristic
162C4×C47#46811yescharacteristic
163C4×C47#46911yescharacteristic
164#1980D4711yescharacteristic
165#1950—471no—
166#1540—471no—
167#1492—471no—
168#1451—471no—
169#1303—471no—
170#1279—471no—
171C2×C47—21no—
172C2×C47—21no—
173C2×C47—161no—
174C2×C47#192911yescharacteristic
175C2×C47#193211yescharacteristic
176C2×C47#193611yescharacteristic
177#532C2×D4711yescharacteristic
178#431—471no—
179C2×#108—941no—
180#423—471no—
181C2×C4⋊C8—471no—
182C2×#104—21no—
183C2×#104—21no—
184C4×M16C2×D4711yescharacteristic
185C2×C4×C8—471no—
186C4×C4⋊C4C2×D4711yescharacteristic
187#341—941no—
188#332—471no—
189#332—471no—
190#331—471no—
191#331—471no—
192D4⋊C8—941no—
193D4⋊C8—941no—
194#322—941no—
195#322—941no—
196C47#959211yescharacteristic, complemented, Sylow
197C2×#41—21no—
198C2×M16—941no—
199C2×M16C22⋊D4711yescharacteristic
200C2×M16C22⋊D4711yescharacteristic
201C22×C8—941no—
202C22×C8—941no—
203C4⋊Q8C4×D4711yescharacteristic
204#127C4×D4711yescharacteristic
205#124—21no—
206#121—21no—
207#121—21no—
208C4×D4—21no—
209C4×D4—21no—
210C2×C4⋊C4—21no—
211C2×C42—21no—
212C2×C42C22×D4711yescharacteristic
213#108—1882no—
214C4⋊C8—471no—
215C4⋊C8—471no—
216C4⋊C8—471no—
217C4⋊C8—471no—
218C4⋊C8—941no—
219C4⋊C8—941no—
220C4⋊C8—941no—
221#104—42no—
222#104—42no—
223C22⋊C8—941no—
224#97—21no—
225C4×C8—21no—
226C4×C8—471no—
227C4×C8—471no—
228C4×C8—941no—
229C4×C8—941no—
230#95—21no—
231#41—41no—
232#41—41no—
233#41—41no—
234#41—41no—
235C2×Q8—21no—
236C2×D4—21no—
237C2×D4—21no—
238C2×D4—21no—
239C2×D4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4#1062535211yescharacteristic
243C22×C4#1062535211yescharacteristic
244C22×C4C2×C22⋊D4711yescharacteristic
245M16—21no—
246M16—21no—
247M16—21no—
248M16—21no—
249M16—1881no—
250M16—1881no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—941no—
254C2×C8—941no—
255C2×C8—941no—
256C2×C8—941no—
257C2×C8—941no—
258C2×C8—941no—
259C2×C8—1882no—
260C2×C8—1881no—
261C2×C8—1881no—
262C2×C8—1881no—
263C4⋊C4—22no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C42—41no—
270C42—41no—
271C42C2×C4×D4711yescharacteristic
272C42#1062535011yescharacteristic
273C42D4×D4711yescharacteristic
274C42#1062535211yescharacteristic
275C23—41no—
276C23#1309401111yescharacteristic
277Q8—41no—
278Q8—41no—
279D4—41no—
280D4—41no—
281D4—41no—
282D4—41no—
283D4—81no—
284D4—81no—
285D4—81no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4#1309398011yescharacteristic
296C2×C4(C22⋊D47)⋊C411yescharacteristic
297C2×C4C4×C22⋊D4711yescharacteristic
298C2×C4#1309399611yescharacteristic
299C2×C4#1309400611yescharacteristic
300C2×C4#1309401711yescharacteristic
301C2×C4#1309404911yescharacteristic
302C2×C4#1309405011yescharacteristic
303C2×C4#1309405011yescharacteristic
304C2×C4#1309405411yescharacteristic
305C8—41no—
306C8—41no—
307C8—942no—
308C8—3761no—
309C8—1881no—
310C8—1881no—
311C8—1881no—
312C8—1881no—
313C8—1881no—
314C22—21no—
315C22—21no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22#1568901711yescharacteristic
320C22#1568948211yescharacteristic
321C22#1568948711yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—82no—
326C4—81no—
327C4#1568922311yescharacteristic
328C4#1568923311yescharacteristic
329C4#1568923711yescharacteristic
330C4#1568924211yescharacteristic
331C4#1568936711yescharacteristic
332C4#1568937411yescharacteristic
333C2—21no—
334C2—21no—
335C2—161no—
336C2#2024403911yescharacteristic
337C2#2024406011yescharacteristic
338C2#2024408811yescharacteristic
subgroupG/H
centerC2×C4#13093996
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1980C2
socleC22×C47#388
prime radicalC47×#532C22
cosocleC2×C42×C47C23
hypercenter#1980D47
hypocenterC47#9592
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1980

Complements

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

NH ≅ G/Ntype
1. #20244163C2semidirect
4. #20241675C2semidirect
5. #20241291C2semidirect
6. #20241229C2semidirect
14. #15688869C4semidirect
15. #15688869C4semidirect
16. #15688867C4semidirect
17. #15688867C4semidirect
196. C47#9592semidirect

Maximal subgroups

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

subgroupindex
#202441632
#202420372
#202418392
#202416752
#202412912
#202412292
C47×#19802
#959247