Finite Group Databasebeta

← #26134019

Subgroups — #26134019

Order 12032.

326 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15688943C211yesmaximal, characteristic, complemented
2C2×#15688908C211yesmaximal, characteristic
3#20245001C211yesmaximal, characteristic
4#20243227C211yesmaximal, characteristic
5#20241477C211yesmaximal, characteristic, complemented
6#20241465C211yesmaximal, characteristic, complemented
7C47×#2108C211yesmaximal, characteristic, complemented
8C2×#13094030C2211yescharacteristic
9C2×#13093964C2211yescharacteristic
10C22×C47⋊C16C2211yescharacteristic
11C2×#13093950C411yescharacteristic
12#15689117C411yescharacteristic
13C2×C8×Dic47C2211yescharacteristic
14#15688943—22no—
15#15688908—22no—
16(C2×D47)⋊C16—21no—
17(C2×D47)⋊C16—21no—
18#15688887C411yescharacteristic
19#15688882C411yescharacteristic
20C2×M32×C47C2211yescharacteristic
21C22×C16×C47C2211yescharacteristic
22C47×#405C2211yescharacteristic
23C47×#346—21no—
24C4×C16×C47—21no—
25C2×#10625350C2×C411yescharacteristic
26#13094030—21no—
27#13094030—21no—
28#13094030—21no—
29#13094030—21no—
30C2×#10625329C2×C411yescharacteristic
31C2×#10625324—21no—
32C22×C47⋊C8C2×C411yescharacteristic
33C2×C8×D47—21no—
34C2×C4×Dic47C2×C411yescharacteristic
35#13093964—21no—
36#13093964—21no—
37C2×C47⋊C16—21no—
38C2×C47⋊C16—21no—
39C2×C47⋊C16—21no—
40C2×C47⋊C16—21no—
41#13093950—22no—
42#13093947C811yescharacteristic
43#13093947C811yescharacteristic
44#13093944C811yescharacteristic
45#13093944C811yescharacteristic
46C8×Dic47—21no—
47C8×Dic47—21no—
48C2×M16×C47C2×C411yescharacteristic
49C22×C8×C47C2311yescharacteristic
50#117×C47C2×C411yescharacteristic
51M32×C47—21no—
52M32×C47D412yes—
53C2×C16×C47—21no—
54C2×C16×C47—21no—
55C2×C16×C47—21no—
56C2×C16×C47D411yescharacteristic
57C2×C16×C47D411yescharacteristic
58#97×C47—21no—
59C4×C8×C47—21no—
60C22×C4×C47C22×C411yescharacteristic
61C2×C22⋊D47—21no—
62C22×Dic47—21no—
63#10625350—21no—
64#10625350—21no—
65#10625350—21no—
66#10625350—21no—
67C2×D188C2×C811yescharacteristic
68C2×C4×D47—21no—
69C2×Dic94C2×C811yescharacteristic
70M16×C47—21no—
71M16×C47M1612yes—
72C2×C8×C47—21no—
73C2×C8×C47C2×D411yescharacteristic
74C2×C8×C47C2×D411yescharacteristic
75C2×C8×C47#4111yescharacteristic
76C2×C8×C47#4111yescharacteristic
77C2×C8×C47#4111yescharacteristic
78C2×C8×C47#4111yescharacteristic
79C4⋊C4×C47C2×C811yescharacteristic
80C4⋊C4×C47C2×C811yescharacteristic
81C22⋊C4×C47—21no—
82C42×C47—21no—
83C4×Dic47—21no—
84C4×Dic47—21no—
85#10625329—21no—
86#10625329—21no—
87C2×C47⋊C8—21no—
88C2×C47⋊C8—21no—
89C2×C47⋊C8—21no—
90C2×C47⋊C8C2×C811yescharacteristic
91C2×C47⋊C8C2×C811yescharacteristic
92#10625324—41no—
93#10625324—41no—
94C8×D47—41no—
95C8×D47—41no—
96C16×C47—22no—
97C16×C47—21no—
98C16×C47—21no—
99C47⋊C16—41no—
100C47⋊C16—41no—
101C23×C47#13111yescharacteristic
102C22×D47—21no—
103C2×C4×C47—21no—
104C2×C4×C47—21no—
105C2×C4×C47#11711yescharacteristic
106C2×C4×C47C4×D411yescharacteristic
107C2×C4×C47C4×D411yescharacteristic
108C2×C4×C47C22×C811yescharacteristic
109C2×C4×C47C2×M1611yescharacteristic
110C2×C4×C47#13111yescharacteristic
111C22⋊D47—41no—
112C22⋊D47—41no—
113C2×Dic47—22no—
114C2×Dic47—21no—
115C2×Dic47—41no—
116C2×Dic47—41no—
117D188—21no—
118D188—21no—
119C4×D47—41no—
120C4×D47—41no—
121Dic94—21no—
122Dic94—21no—
123C8×C47—22no—
124C8×C47#12111yescharacteristic
125C8×C47#12311yescharacteristic
126C8×C47#12411yescharacteristic
127C8×C47#12611yescharacteristic
128C47⋊C8—21no—
129C47⋊C8—21no—
130C47⋊C8—41no—
131#13122—471nomaximal, Sylow
132C22×C47—21no—
133C22×C47—21no—
134C22×C47#43311yescharacteristic
135C22×C47C8×D411yescharacteristic
136C22×C47#43611yescharacteristic
137C2×D47—41no—
138C2×D47—41no—
139C2×D47—41no—
140C4×C47—41no—
141C4×C47—41no—
142C4×C47#38811yescharacteristic
143C4×C47#43111yescharacteristic
144C4×C47C8×D411yescharacteristic
145C4×C47#43511yescharacteristic
146Dic47—42no—
147Dic47—41no—
148C2×#364—471no—
149C2×#350—471no—
150#2113—471no—
151#2108D4711yescharacteristic, complemented
152#1764—471no—
153#1379—471no—
154#1374—471no—
155C2×C47—21no—
156C2×C47—21no—
157C2×C47#192311yescharacteristic
158C2×C47#217011yescharacteristic
159C2×C47#217111yescharacteristic
160D47—81no—
161C2×#131—471no—
162C2×M32—471no—
163C2×M32C2×D4711yescharacteristic
164C22×C16—471no—
165C22×C16C2×D4711yescharacteristic
166C2×#104—471no—
167#416—471no—
168#405C2×D4711yescharacteristic
169C2×C4×C8—471no—
170#364—942no—
171#350—942no—
172C22⋊C16—941no—
173C22⋊C16—941no—
174#346—21no—
175C4×C16—21no—
176#341—471no—
177#339—471no—
178C47#1312211yescharacteristic, complemented, Sylow
179C2×#41—471no—
180#131—941no—
181#131—941no—
182#131—941no—
183#131—941no—
184C2×M16—471no—
185C2×M16—941no—
186C2×M16C4×D4711yescharacteristic
187C22×C8—471no—
188C22×C8—941no—
189C22×C8C22×D4711yescharacteristic
190#117C4×D4711yescharacteristic
191C2×C42—471no—
192M32—21no—
193M32—941no—
194M32—941no—
195M32D18812yes—
196C2×C16—21no—
197C2×C16—21no—
198C2×C16—21no—
199C2×C16—941no—
200C2×C16—941no—
201C2×C16—941no—
202C2×C16—941no—
203C2×C16C22⋊D4711yescharacteristic
204C2×C16C22⋊D4711yescharacteristic
205#104—942no—
206#103—471no—
207#103—471no—
208#102—471no—
209#102—471no—
210#97—21no—
211C4×C8—21no—
212C4×C8—941no—
213C4×C8—941no—
214#41—941no—
215#41—941no—
216#41—941no—
217#41—941no—
218C2×Q8—471no—
219C2×D4—471no—
220C2×D4—941no—
221C22×C4—941no—
222C22×C4—941no—
223C22×C4C2×C4×D4711yescharacteristic
224M16—21no—
225M16—941no—
226M16—941no—
227M16—1881no—
228M16—1881no—
229M16#1062532412yes—
230C2×C8—21no—
231C2×C8—471no—
232C2×C8—471no—
233C2×C8—941no—
234C2×C8—941no—
235C2×C8—941no—
236C2×C8—1881no—
237C2×C8—1881no—
238C2×C8C2×D18811yescharacteristic
239C2×C8#1062535011yescharacteristic
240C2×C8#1062535011yescharacteristic
241C2×C8#1062535011yescharacteristic
242C2×C8#1062535011yescharacteristic
243C2×C8C2×C22⋊D4711yescharacteristic
244C4⋊C4C8×D4711yescharacteristic
245C4⋊C4C8×D4711yescharacteristic
246C22⋊C4—21no—
247C42—21no—
248C42—941no—
249C42—941no—
250C16—22no—
251C16—21no—
252C16—21no—
253C16—1881no—
254C16—1881no—
255C23—941no—
256C23#1309403011yescharacteristic
257Q8—941no—
258Q8—941no—
259D4—941no—
260D4—941no—
261D4—1881no—
262D4—1881no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—942no—
266C2×C4—941no—
267C2×C4—1881no—
268C2×C4—1881no—
269C2×C4—1881no—
270C2×C4—1881no—
271C2×C4#1309398111yescharacteristic
272C2×C4C4×C22⋊D4711yescharacteristic
273C2×C4C4×D18811yescharacteristic
274C2×C4C2×C8×D4711yescharacteristic
275C2×C4C2×#1062532411yescharacteristic
276C2×C4#1309403011yescharacteristic
277C8—22no—
278C8—941no—
279C8—941no—
280C8—1881no—
281C8#1309399811yescharacteristic
282C8#1309400711yescharacteristic
283C8#1309401211yescharacteristic
284C8#1309401811yescharacteristic
285C22—21no—
286C22—21no—
287C22—1881no—
288C22—1881no—
289C22—1881no—
290C22#1568918211yescharacteristic
291C22C8×C22⋊D4711yescharacteristic
292C22#1568920211yescharacteristic
293C4—41no—
294C4—41no—
295C4—1882no—
296C4—1881no—
297C4#1568901411yescharacteristic
298C4#1568917411yescharacteristic
299C4C8×D18811yescharacteristic
300C4#1568919411yescharacteristic
301C2—21no—
302C2—21no—
303C2—3761no—
304C2#2024399411yescharacteristic
305C2#2024522311yescharacteristic
306C2#2024522811yescharacteristic
subgroupG/H
centerC2×C8C2×C22⋊D47
commutatorC2×C4×C47C22×C8
FrattiniC22×C8C22×D47
FittingC47×#2108C2
socleC22×C47C8×D4
prime radicalC2×#10625350C2×C4
cosocleC22×C8×C47C23
hypercenter#2108D47
hypocenterC47#13122
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C22×C16 ◁ #2108

Complements

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

NH ≅ G/Ntype
1. C2×#15688943C2semidirect
5. #20241477C2semidirect
6. #20241465C2semidirect
7. C47×#2108C2semidirect
151. #2108D47semidirect
178. C47#13122semidirect

Maximal subgroups

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

subgroupindex
C2×#156889432
C2×#156889082
#202450012
#202432272
#202414772
#202414652
C47×#21082
#1312247