Finite Group Databasebeta

← #26103241

Subgroups — #26103241

Order 12032.

462 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15688849C212yesmaximal
2C47×C4⋊#95C211yesmaximal, characteristic
3C2×C22⋊(C47⋊C8)—22no—
4#15688849—22no—
5#15688849C414yescomplemented
6C22×C4⋊C4×C47C411yescharacteristic
7C22×C4⋊C4×C47C2211yescharacteristic
8C22×C42×C47C411yescharacteristic
9C2×#95×C47—22no—
10C22×C47⋊C8—42no—
11C22⋊(C47⋊C8)—24no—
12C22⋊(C47⋊C8)—42no—
13C23×C4×C47—21no—
14C23×C4×C47—21no—
15C23×C4×C47C2×C411yescharacteristic
16C23×C4×C47D412yes—
17C2×C4⋊C4×C47—21no—
18C2×C4⋊C4×C47—41no—
19C2×C4⋊C4×C47—41no—
20C2×C4⋊C4×C47—41no—
21C2×C4⋊C4×C47—41no—
22C2×C4⋊C4×C47C812yescomplemented
23C2×C4⋊C4×C47C2×C412yes—
24C2×C4⋊C4×C47D411yescharacteristic
25C2×C4⋊C4×C47Q811yescharacteristic
26C2×C42×C47—21no—
27C2×C42×C47—41no—
28C2×C42×C47—41no—
29C2×C42×C47C812yescomplemented
30#95×C47—44no—
31C24×C47C22⋊C411yescharacteristic
32C22×C4×C47—21no—
33C22×C4×C47—21no—
34C22×C4×C47—21no—
35C22×C4×C47—21no—
36C22×C4×C47—22no—
37C22×C4×C47—22no—
38C22×C4×C47—22no—
39C22×C4×C47—22no—
40C22×C4×C47—22no—
41C22×C4×C47—22no—
42C22×C4×C47—41no—
43C22×C4×C47—41no—
44C22×C4×C47—41no—
45C22×C4×C47—41no—
46C22×C4×C47—42no—
47C22×C4×C47—42no—
48C22×C4×C47—42no—
49C22×C4×C47—42no—
50C22×C4×C47—41no—
51C22×C4×C47—41no—
52C22×C4×C47C4211yescharacteristic
53C22×C4×C47C22⋊C412yes—
54C22×C4×C47C4⋊C411yescharacteristic
55C22×C4×C47C4⋊C412yes—
56C22×C4×C47C2×C811yescharacteristic
57C22×C4×C47C2×C811yescharacteristic
58C22×C4×C47M1611yescharacteristic
59C22×C4×C47M1611yescharacteristic
60C4⋊C4×C47—42no—
61C4⋊C4×C47—41no—
62C4⋊C4×C47—41no—
63C4⋊C4×C47—42no—
64C4⋊C4×C47—42no—
65C42×C47—42no—
66C42×C47—42no—
67C2×C47⋊C8—44no—
68C2×C47⋊C8—82no—
69C2×C47⋊C8—82no—
70C23×C47—21no—
71C23×C47—21no—
72C23×C47—21no—
73C23×C47—21no—
74C23×C47#9511yescharacteristic
75C23×C47C22⋊C811yescharacteristic
76C23×C47C22⋊C811yescharacteristic
77C23×C47#9911yescharacteristic
78C23×C47#9911yescharacteristic
79C23×C47#10011yescharacteristic
80C23×C47#10111yescharacteristic
81C2×C4×C47—21no—
82C2×C4×C47—21no—
83C2×C4×C47—21no—
84C2×C4×C47—21no—
85C2×C4×C47—21no—
86C2×C4×C47—21no—
87C2×C4×C47—21no—
88C2×C4×C47—21no—
89C2×C4×C47—21no—
90C2×C4×C47—21no—
91C2×C4×C47—21no—
92C2×C4×C47—21no—
93C2×C4×C47—24no—
94C2×C4×C47—22no—
95C2×C4×C47—22no—
96C2×C4×C47—42no—
97C2×C4×C47—42no—
98C2×C4×C47—42no—
99C2×C4×C47—42no—
100C2×C4×C47—42no—
101C2×C4×C47—42no—
102C2×C4×C47—42no—
103C2×C4×C47—42no—
104C2×C4×C47—42no—
105C2×C4×C47—42no—
106C2×C4×C47—44no—
107C2×C4×C47—42no—
108C2×C4×C47—82no—
109C2×C4×C47—82no—
110C2×C4×C47—81no—
111C2×C4×C47—81no—
112C2×C4×C47C4×C811yescharacteristic
113C2×C4×C47#9711yescharacteristic
114C2×C4×C47C4⋊C811yescharacteristic
115C2×C4×C47C4⋊C811yescharacteristic
116C47⋊C8—84no—
117#7189—471nomaximal, Sylow
118C22×C47—21no—
119C22×C47—21no—
120C22×C47—21no—
121C22×C47—21no—
122C22×C47—21no—
123C22×C47—21no—
124C22×C47—21no—
125C22×C47—21no—
126C22×C47—21no—
127C22×C47—21no—
128C22×C47—21no—
129C22×C47—21no—
130C22×C47#32311yescharacteristic
131C22×C47#32311yescharacteristic
132C22×C47#32411yescharacteristic
133C22×C47#32411yescharacteristic
134C22×C47#33611yescharacteristic
135C22×C47#34211yescharacteristic
136C22×C47#34311yescharacteristic
137C22×C47#35311yescharacteristic
138C22×C47#35411yescharacteristic
139C22×C47#35511yescharacteristic
140C22×C47#35611yescharacteristic
141C4×C47—21no—
142C4×C47—21no—
143C4×C47—21no—
144C4×C47—21no—
145C4×C47—44no—
146C4×C47—42no—
147C4×C47—42no—
148C4×C47—82no—
149C2×#324—472no—
150C4⋊#95D4711yescharacteristic
151C2×C47—21no—
152C2×C47—21no—
153C2×C47—21no—
154C2×C47—21no—
155C2×C47#128011yescharacteristic
156C2×C47#131811yescharacteristic
157C2×C47#131911yescharacteristic
158C2×C47#132411yescharacteristic
159C2×C47#132511yescharacteristic
160C2×C47#139311yescharacteristic
161C2×C47#139411yescharacteristic
162C22×C4⋊C4Dic4711yescharacteristic
163C22×C4⋊C4C2×D4711yescharacteristic
164C22×C42Dic4711yescharacteristic
165C2×C22⋊C8—942no—
166C2×#95—22no—
167#324—474no—
168#324—942no—
169C47#718911yescharacteristic, complemented, Sylow
170C23×C4—21no—
171C23×C4—21no—
172C23×C4C2×Dic4711yescharacteristic
173C23×C4C22⋊D4712yes—
174C22×C8—1882no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—41no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4C47⋊C812yescomplemented
181C2×C4⋊C4Dic9411yescharacteristic
182C2×C4⋊C4C4×D4712yes—
183C2×C4⋊C4D18811yescharacteristic
184C2×C42—21no—
185C2×C42—41no—
186C2×C42—41no—
187C2×C42C47⋊C812yescomplemented
188C22⋊C8—944no—
189C22⋊C8—1882no—
190#95—44no—
191C24C22⋊Dic4711yescharacteristic
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4C2×C47⋊C811yescharacteristic
213C22×C4C2×C47⋊C811yescharacteristic
214C22×C4#1062532911yescharacteristic
215C22×C4#1062532911yescharacteristic
216C22×C4C4×Dic4711yescharacteristic
217C22×C4Dic47⋊C412yes—
218C22×C4C4⋊Dic4711yescharacteristic
219C22×C4(C2×D47)⋊C412yes—
220C2×C8—3762no—
221C2×C8—3762no—
222C2×C8—1884no—
223C4⋊C4—41no—
224C4⋊C4—42no—
225C4⋊C4—41no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C42—42no—
229C42—42no—
230C23—21no—
231C23—21no—
232C23—21no—
233C23—21no—
234C23C47⋊#9511yescharacteristic
235C23C22⋊(C47⋊C8)11yescharacteristic
236C23C22⋊(C47⋊C8)11yescharacteristic
237C23#1309393911yescharacteristic
238C23#1309393911yescharacteristic
239C23#1309394111yescharacteristic
240C23#1309394311yescharacteristic
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—24no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—44no—
267C2×C4—42no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4C4×C47⋊C811yescharacteristic
273C2×C4#1309393511yescharacteristic
274C2×C4C4⋊(C47⋊C8)11yescharacteristic
275C2×C4C4⋊(C47⋊C8)11yescharacteristic
276C8—3764no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22#1568884711yescharacteristic
290C22#1568884711yescharacteristic
291C22#1568884911yescharacteristic
292C22#1568884911yescharacteristic
293C22#1568887811yescharacteristic
294C22#1568889011yescharacteristic
295C22#1568889211yescharacteristic
296C22#1568891611yescharacteristic
297C22#1568891811yescharacteristic
298C22#1568892011yescharacteristic
299C22#1568892211yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—44no—
305C4—42no—
306C4—42no—
307C4—82no—
308C2—21no—
309C2—21no—
310C2—21no—
311C2—21no—
312C2#2024123111yescharacteristic
313C2#2024132011yescharacteristic
314C2#2024132211yescharacteristic
315C2#2024133211yescharacteristic
316C2#2024133411yescharacteristic
317C2#2024151311yescharacteristic
318C2#2024151511yescharacteristic
subgroupG/H
centerC23#13093939
commutatorC2×C4×C47C4×C8
FrattiniC22×C4⋊C4C2×D47
FittingC47×C4⋊#95C2
socleC23×C47#99
prime radicalC24×C47C22⋊C4
cosocleC22×C4⋊C4×C47C22
hypercenterC4⋊#95D47
hypocenterC47#7189
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C24 ◁ C22×C4⋊C4 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
5. #15688849C4semidirect
22. C2×C4⋊C4×C47C8semidirect
29. C2×C42×C47C8semidirect
169. C47#7189semidirect
180. C2×C4⋊C4C47⋊C8semidirect
187. C2×C42C47⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×#156888492
C47×C4⋊#952
#718947