Finite Group Databasebeta

← #26136046

Subgroups — #26136046

Order 12032.

382 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15688950C211yesmaximal, characteristic, complemented
2C2×Dic47⋊C16C211yesmaximal, characteristic, complemented
3C2×#15688925C211yesmaximal, characteristic
4C2×#15688923C211yesmaximal, characteristic
5#20244252C211yesmaximal, characteristic
6#20244119C211yesmaximal, characteristic, complemented
7C47×#1380C211yesmaximal, characteristic, complemented
8C22×D376C2211yescharacteristic
9C22×C47⋊C16C2211yescharacteristic
10C2×#13093958C2211yescharacteristic
11C2×#13093944—21no—
12C2×C8×Dic47C2211yescharacteristic
13#15689024—21no—
14#15689019—21no—
15#15688950—22no—
16Dic47⋊C16—22no—
17#15688925—22no—
18#15688923—22no—
19#15688885—21no—
20C22×C16×C47C2211yescharacteristic
21C2×#107×C47C2211yescharacteristic
22C2×#107×C47C2211yescharacteristic
23C22×D188—21no—
24C2×D376—21no—
25C2×D376—21no—
26C2×D376—21no—
27C2×D376—21no—
28C2×D376—21no—
29C2×D376Q812yes—
30C22×C47⋊C8D411yescharacteristic
31C2×C4⋊Dic47—21no—
32C2×Dic47⋊C4—41no—
33C2×(C2×D47)⋊C4—41no—
34C2×(C2×D47)⋊C4—41no—
35C2×C4×Dic47D411yescharacteristic
36C2×C47⋊C16—21no—
37C2×C47⋊C16—21no—
38C2×C47⋊C16D412yes—
39#13093958—21no—
40#13093958D412yes—
41#13093944—42no—
42C8×Dic47—21no—
43C8×Dic47—21no—
44C47⋊#95—41no—
45C22×C8×C47C2311yescharacteristic
46C2×C4⋊C4×C47—21no—
47C2×C4⋊C4×C47—21no—
48C2×C16×C47—21no—
49C2×C16×C47—21no—
50C2×C16×C47—21no—
51#107×C47—21no—
52#107×C47—21no—
53#107×C47—21no—
54#107×C47—21no—
55C23×D47—41no—
56C22×C4×C47—41no—
57C22×C4×C47—41no—
58C22×C4×C47C2×D411yescharacteristic
59C22×Dic47—41no—
60C22×Dic47D811yescharacteristic
61C22×Dic47D811yescharacteristic
62C2×D188—22no—
63C2×D188—41no—
64C2×D188—41no—
65C2×D188—41no—
66C2×D188—41no—
67C2×D188—41no—
68C2×C8×C47C2×D411yescharacteristic
69C2×C8×C47C2×D411yescharacteristic
70C2×C8×C47C2×Q811yescharacteristic
71C2×C8×C47#4111yescharacteristic
72C2×C8×C47#4111yescharacteristic
73C2×C8×C47#4111yescharacteristic
74C4⋊C4×C47—41no—
75C4⋊C4×C47—41no—
76C4⋊C4×C47—41no—
77C4⋊C4×C47—41no—
78(C2×D47)⋊C4—82no—
79(C2×D47)⋊C4—82no—
80C4⋊Dic47—22no—
81C4⋊Dic47—41no—
82Dic47⋊C4—82no—
83C4×Dic47—21no—
84C4×Dic47—21no—
85C2×C47⋊C8—21no—
86C2×C47⋊C8—21no—
87C2×C47⋊C8—21no—
88D376—22no—
89D376—22no—
90D376—41no—
91D376—41no—
92C16×C47—41no—
93C47⋊C16—22no—
94C23×C47C2×D811yescharacteristic
95C22×D47—42no—
96C22×D47—81no—
97C22×D47—81no—
98C22×D47—81no—
99C22×D47—81no—
100C22×D47—81no—
101C22×D47—81no—
102C2×C4×C47—81no—
103C2×C4×C47—81no—
104C2×C4×C47—81no—
105C2×C4×C47—81no—
106C2×C4×C47—81no—
107C2×C4×C47—81no—
108C2×C4×C47#12111yescharacteristic
109C2×C4×C47#12111yescharacteristic
110C2×C4×C47C22⋊Q811yescharacteristic
111C2×C4×C47#13511yescharacteristic
112C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
113C2×C4×C47#13711yescharacteristic
114C2×Dic47—21no—
115C2×Dic47—21no—
116C2×Dic47—21no—
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47—42no—
120C2×Dic47—81no—
121C2×Dic47—81no—
122C2×Dic47SD3212yes—
123D188—42no—
124D188—42no—
125D188—81no—
126D188—81no—
127C8×C47#12111yescharacteristic
128C8×C47C22⋊Q811yescharacteristic
129C8×C47C22⋊Q811yescharacteristic
130C8×C47#12611yescharacteristic
131C47⋊C8—41no—
132#13476—471nomaximal, Sylow
133C22×C47#45911yescharacteristic
134C22×C47#46611yescharacteristic
135C22×C47#47411yescharacteristic
136C22×C47C2×SD3211yescharacteristic
137C22×C47#50811yescharacteristic
138C22×C47#50911yescharacteristic
139C22×C47#50911yescharacteristic
140C2×D47—82no—
141C2×D47—82no—
142C2×D47—82no—
143C2×D47—161no—
144C2×D47—161no—
145C2×D47—161no—
146C2×D47—161no—
147C4×C47—161no—
148C4×C47—161no—
149C4×C47#39611yescharacteristic
150C4×C47#46411yescharacteristic
151C4×C47#46811yescharacteristic
152C4×C47#47811yescharacteristic
153Dic47—22no—
154Dic47—41no—
155Dic47—82no—
156C2×#367—471no—
157C2×C4⋊C16—471no—
158C2×#357—471no—
159C2×#357—471no—
160#1970—471no—
161#1942—471no—
162#1380D4711yescharacteristic, complemented
163C2×C47#206711yescharacteristic
164C2×C47#220711yescharacteristic
165C2×C47#221011yescharacteristic
166C2×C47#221711yescharacteristic
167C2×C47#221811yescharacteristic
168C2×C47#222611yescharacteristic
169C2×C47#222811yescharacteristic
170D47—162no—
171C22×D8—471no—
172C22×C16—471no—
173C22×C16C2×D4711yescharacteristic
174C2×#107—471no—
175C2×#107C2×D4711yescharacteristic
176C2×#107C2×D4711yescharacteristic
177C2×#102—941no—
178C2×C4×C8—471no—
179#390—941no—
180#389—941no—
181#367—942no—
182C4⋊C16—942no—
183#357—942no—
184#357—942no—
185#340—941no—
186C47#1347611yescharacteristic, complemented, Sylow
187C22×D4—941no—
188C2×D8—472no—
189C2×D8—941no—
190C2×D8—941no—
191C2×D8—941no—
192C2×D8—941no—
193C2×D8—941no—
194C22×C8—471no—
195C22×C8C22×D4711yescharacteristic
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—941no—
199C2×C4⋊C4—1881no—
200C2×C22⋊C4—1881no—
201C2×C22⋊C4—1881no—
202C2×C42—471no—
203C2×C16—21no—
204C2×C16—21no—
205C2×C16—21no—
206C2×C16—472no—
207C2×C16—941no—
208C2×C16—941no—
209#107—21no—
210#107—21no—
211#107—21no—
212#107—21no—
213#107—472no—
214#107—941no—
215#102—1882no—
216C4×C8—941no—
217C4×C8—941no—
218#95—1881no—
219C24—1881no—
220C2×D4—942no—
221C2×D4—1881no—
222C2×D4—1881no—
223C2×D4—1881no—
224C2×D4—1881no—
225C2×D4—1881no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—471no—
229C22×C4—471no—
230C22×C4—1881no—
231C22×C4D4×D4711yescharacteristic
232D8—942no—
233D8—942no—
234D8—1881no—
235D8—1881no—
236C2×C8—941no—
237C2×C8—941no—
238C2×C8—941no—
239C2×C8#1062535011yescharacteristic
240C2×C8#1062535011yescharacteristic
241C2×C8#1062535011yescharacteristic
242C2×C8D4×D4711yescharacteristic
243C2×C8D4×D4711yescharacteristic
244C2×C8Q8×D4711yescharacteristic
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—942no—
250C4⋊C4—3762no—
251C4⋊C4—1881no—
252C22⋊C4—3762no—
253C22⋊C4—3762no—
254C42—941no—
255C42—941no—
256C16—41no—
257C16—942no—
258C23—3761no—
259C23—3761no—
260C23—3761no—
261C23—3761no—
262C23—3761no—
263C23—3761no—
264C23—1882no—
265C23D8×D4711yescharacteristic
266D4—3761no—
267D4—3761no—
268D4—1882no—
269D4—1882no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—472no—
277C2×C4—941no—
278C2×C4—941no—
279C2×C4—941no—
280C2×C4—941no—
281C2×C4—941no—
282C2×C4—3761no—
283C2×C4—3761no—
284C2×C4—1882no—
285C2×C4#1309399711yescharacteristic
286C2×C4#1309399711yescharacteristic
287C2×C4#1309400211yescharacteristic
288C2×C4#1309404511yescharacteristic
289C2×C4#1309405111yescharacteristic
290C2×C4#1309405611yescharacteristic
291C8—1881no—
292C8#1309399711yescharacteristic
293C8#1309400211yescharacteristic
294C8#1309400211yescharacteristic
295C8#1309401811yescharacteristic
296C22—3762no—
297C22—3762no—
298C22—3762no—
299C22—7521no—
300C22—7521no—
301C22—7521no—
302C22—7521no—
303C22#1568931711yescharacteristic
304C22#1568935811yescharacteristic
305C22#1568940211yescharacteristic
306C22SD32×D4711yescharacteristic
307C22#1568955611yescharacteristic
308C22#1568955711yescharacteristic
309C22#1568956011yescharacteristic
310C4—161no—
311C4—161no—
312C4—942no—
313C4—3762no—
314C4—1881no—
315C4#1568904711yescharacteristic
316C4#1568934811yescharacteristic
317C4#1568937211yescharacteristic
318C4#1568942211yescharacteristic
319C2—7522no—
320C2#2024477711yescharacteristic
321C2#2024542711yescharacteristic
322C2#2024544611yescharacteristic
323C2#2024548711yescharacteristic
324C2#2024549011yescharacteristic
325C2#2024553411yescharacteristic
326C2#2024554811yescharacteristic
subgroupG/H
centerC23D8×D47
commutator, cosocleC22×C8×C47C23
FrattiniC22×C8C22×D47
FittingC47×#1380C2
socleC23×C47C2×D8
prime radicalC22×D376C22
hypercenter#1380D47
hypocenterC47#13476
LCSG ▷ C22×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
1. C2×#15688950C2semidirect
2. C2×Dic47⋊C16C2semidirect
6. #20244119C2semidirect
7. C47×#1380C2semidirect
162. #1380D47semidirect
186. C47#13476semidirect

Maximal subgroups

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

subgroupindex
C2×#156889502
C2×Dic47⋊C162
C2×#156889252
C2×#156889232
#202442522
#202441192
C47×#13802
#1347647