Finite Group Databasebeta

← #26114805

Subgroups — #26114805

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#20244308C211yesmaximal, characteristic
2#20244161C211yesmaximal, characteristic, complemented
3#20242037C211yesmaximal, characteristic
4#20241677C211yesmaximal, characteristic, complemented
5#20241289C211yesmaximal, characteristic, complemented
6#20241228C211yesmaximal, characteristic, complemented
7C47×#1492C211yesmaximal, characteristic
8#15689176C2211yescharacteristic
9C2×#13093959—21no—
10C2×C4⋊(C47⋊C8)C2211yescharacteristic
11C2×#13093951—21no—
12C2×#13093951—21no—
13C4×#10625329C2211yescharacteristic
14C4×C4⋊Dic47C2211yescharacteristic
15#15688887—21no—
16#15688869C411yescharacteristic, complemented
17#15688869C411yescharacteristic, complemented
18#15688867C411yescharacteristic, complemented
19#15688867C411yescharacteristic, complemented
20#15688845—21no—
21#15688844—21no—
22C47×#532C2211yescharacteristic
23C47×#423C2211yescharacteristic
24C2×C4×C8×C47C2211yescharacteristic
25C47×D4⋊C8—21no—
26C47×D4⋊C8—21no—
27C2×#10625329D411yescharacteristic
28C2×#10625329D411yescharacteristic
29C22×C47⋊C8—21no—
30C2×C4⋊Dic47—21no—
31C2×C4×Dic47—21no—
32#13093959—42no—
33C4⋊(C47⋊C8)—21no—
34C4⋊(C47⋊C8)C2×C411yescharacteristic
35C4⋊(C47⋊C8)C2×C411yescharacteristic
36C4⋊(C47⋊C8)C2×C411yescharacteristic
37C4⋊(C47⋊C8)C2×C411yescharacteristic
38#13093951—42no—
39#13093951—42no—
40C22⋊(C47⋊C8)—21no—
41#13093935—21no—
42C4×C47⋊C8—21no—
43C4×C47⋊C8—21no—
44C47⋊#95—21no—
45C2×#41×C47—21no—
46C2×M16×C47—21no—
47C22×C8×C47—21no—
48C4⋊Q8×C47C2×C411yescharacteristic
49#127×C47C2×C411yescharacteristic
50#124×C47—21no—
51#121×C47—21no—
52#121×C47—21no—
53C4×D4×C47—21no—
54C4×D4×C47—21no—
55C2×C42×C47C2311yescharacteristic
56C4⋊C8×C47—21no—
57C4⋊C8×C47—21no—
58C4×C8×C47—21no—
59C4×C8×C47D411yescharacteristic
60C4×C8×C47D411yescharacteristic
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×C47C2×D411yescharacteristic
72C22×C4×C47#4111yescharacteristic
73C22×C4×C47#4111yescharacteristic
74C22×Dic47—41no—
75M16×C47—41no—
76M16×C47—41no—
77C2×C8×C47—21no—
78C2×C8×C47—21no—
79C2×C8×C47—42no—
80C2×C8×C47—41no—
81C4⋊C4×C47—21no—
82C4⋊C4×C47—21no—
83C22⋊C4×C47—41no—
84C22⋊C4×C47—41no—
85C42×C47C22×C411yescharacteristic
86C42×C47C2×D411yescharacteristic
87C42×C47#4111yescharacteristic
88C42×C47#4111yescharacteristic
89C4⋊Dic47—22no—
90C4⋊Dic47—41no—
91C4×Dic47—41no—
92C4×Dic47—41no—
93#10625329—21no—
94#10625329—21no—
95#10625329—21no—
96#10625329—21no—
97C2×C47⋊C8—21no—
98C2×C47⋊C8—21no—
99C2×C47⋊C8—21no—
100C2×C47⋊C8—21no—
101C2×C47⋊C8—21no—
102C2×C47⋊C8—21no—
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—41no—
120C2×C4×C47—81no—
121C2×C4×C47—81no—
122C2×C4×C47#11711yescharacteristic
123C2×C4×C47C4×D411yescharacteristic
124C2×C4×C47C4×D411yescharacteristic
125C2×C4×C47#12111yescharacteristic
126C2×C4×C47#12311yescharacteristic
127C2×C4×C47#12611yescharacteristic
128C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C47#13711yescharacteristic
132C2×Dic47—42no—
133C2×Dic47—81no—
134C2×Dic47—81no—
135C8×C47—22no—
136C8×C47—41no—
137C8×C47—81no—
138C47⋊C8—41no—
139C47⋊C8—41no—
140C47⋊C8—41no—
141C47⋊C8—41no—
142C47⋊C8—41no—
143C47⋊C8—41no—
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—81no—
157C4×C47#44011yescharacteristic
158C4×C47#44211yescharacteristic
159C4×C47#44311yescharacteristic
160C4×C47#44411yescharacteristic
161C4×C47#46811yescharacteristic
162C4×C47#46911yescharacteristic
163Dic47—82no—
164#1980—471no—
165#1950—471no—
166#1540—471no—
167#1492D4711yescharacteristic
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#423C2×D4711yescharacteristic
181C2×C4⋊C8—471no—
182C2×#104—941no—
183C2×#104—941no—
184C4×M16—471no—
185C2×C4×C8C2×D4711yescharacteristic
186C4×C4⋊C4—471no—
187#341—941no—
188#332—471no—
189#332—471no—
190#331—471no—
191#331—471no—
192D4⋊C8—21no—
193D4⋊C8—21no—
194#322—941no—
195#322—941no—
196C47#959211yescharacteristic, complemented, Sylow
197C2×#41—21no—
198C2×M16—21no—
199C2×M16—471no—
200C2×M16—471no—
201C22×C8—21no—
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—941no—
211C2×C42—941no—
212C2×C42C22×D4711yescharacteristic
213#108—1882no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—471no—
217C4⋊C8—471no—
218C4⋊C8—471no—
219C4⋊C8—471no—
220C4⋊C8—941no—
221#104—1882no—
222#104—1882no—
223C22⋊C8—941no—
224#97—941no—
225C4×C8—21no—
226C4×C8—941no—
227C4×C8—941no—
228C4×C8C22⋊D4711yescharacteristic
229C4×C8C22⋊D4711yescharacteristic
230#95—941no—
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—1881no—
242C22×C4#1062535011yescharacteristic
243C22×C4D4×D4711yescharacteristic
244C22×C4#1062535211yescharacteristic
245M16—41no—
246M16—41no—
247M16—941no—
248M16—941no—
249M16—941no—
250M16—941no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—42no—
254C2×C8—41no—
255C2×C8—941no—
256C2×C8—941no—
257C2×C8—941no—
258C2×C8—941no—
259C2×C8—941no—
260C2×C8—941no—
261C2×C8—1881no—
262C2×C8—1881no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—942no—
266C4⋊C4—1881no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C42—1881no—
270C42—1881no—
271C42C2×C4×D4711yescharacteristic
272C42#1062535211yescharacteristic
273C42#1062535211yescharacteristic
274C42C2×C22⋊D4711yescharacteristic
275C23—41no—
276C23#1309401011yescharacteristic
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—41no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—3761no—
293C2×C4—3761no—
294C2×C4—1882no—
295C2×C4#1309398011yescharacteristic
296C2×C4(C22⋊D47)⋊C411yescharacteristic
297C2×C4C4×C22⋊D4711yescharacteristic
298C2×C4#1309399511yescharacteristic
299C2×C4#1309400511yescharacteristic
300C2×C4#1309401711yescharacteristic
301C2×C4#1309404811yescharacteristic
302C2×C4#1309404811yescharacteristic
303C2×C4#1309405111yescharacteristic
304C2×C4#1309405311yescharacteristic
305C8—22no—
306C8—41no—
307C8—81no—
308C8—1881no—
309C8—1881no—
310C8—1881no—
311C8—1881no—
312C8—1881no—
313C8—1881no—
314C22—21no—
315C22—21no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22#1568901111yescharacteristic
320C22#1568948111yescharacteristic
321C22#1568948611yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—81no—
326C4—3762no—
327C4#1568922011yescharacteristic
328C4#1568923211yescharacteristic
329C4#1568923811yescharacteristic
330C4#1568924311yescharacteristic
331C4#1568936611yescharacteristic
332C4#1568937311yescharacteristic
333C2—21no—
334C2—21no—
335C2—161no—
336C2#2024403311yescharacteristic
337C2#2024405411yescharacteristic
338C2#2024408211yescharacteristic
subgroupG/H
centerC2×C4#13093995
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1492C2
socleC22×C47#388
prime radicalC47×#532C22
cosocleC2×C42×C47C23
hypercenter#1492D47
hypocenterC47#9592
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
2. #20244161C2semidirect
4. #20241677C2semidirect
5. #20241289C2semidirect
6. #20241228C2semidirect
16. #15688869C4semidirect
17. #15688869C4semidirect
18. #15688867C4semidirect
19. #15688867C4semidirect
196. C47#9592semidirect

Maximal subgroups

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

subgroupindex
#202443082
#202441612
#202420372
#202416772
#202412892
#202412282
C47×#14922
#959247