Finite Group Databasebeta

← #26104558

Subgroups — #26104558

Order 12032.

582 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20243368C211yesmaximal, characteristic
2#20243368C211yesmaximal, characteristic
3#20241211C214yesmaximal, complemented
4C2×C47×#389C211yesmaximal, characteristic
5C2×C4⋊(C47⋊C8)—21no—
6C2×C4⋊(C47⋊C8)—21no—
7C2×C22⋊(C47⋊C8)—21no—
8C2×C22⋊(C47⋊C8)—21no—
9#15688878C2212yes—
10#15688878C2212yes—
11C22×C4⋊C4×C47—21no—
12C22×C4⋊C4×C47C411yescharacteristic
13C22×C4⋊C4×C47C411yescharacteristic
14C22×C42×C47C2211yescharacteristic
15C47×#389—21no—
16C47×#389—21no—
17C47×#389C412yes—
18C47×#389C2212yes—
19C2×#95×C47—21no—
20C22×C47⋊C8—22no—
21C22×C47⋊C8—22no—
22C4⋊(C47⋊C8)—42no—
23C4⋊(C47⋊C8)—42no—
24C22⋊(C47⋊C8)—42no—
25C22⋊(C47⋊C8)—42no—
26C23×C4×C47—21no—
27C23×C4×C47—21no—
28C23×C4×C47C2×C411yescharacteristic
29C23×C4×C47D411yescharacteristic
30C23×C4×C47D411yescharacteristic
31C2×C4⋊C4×C47—21no—
32C2×C4⋊C4×C47—24no—
33C2×C4⋊C4×C47—22no—
34C2×C4⋊C4×C47—21no—
35C2×C4⋊C4×C47—22no—
36C2×C4⋊C4×C47—42no—
37C2×C4⋊C4×C47—42no—
38C2×C4⋊C4×C47—42no—
39C2×C4⋊C4×C47C2×C412yes—
40C2×C4⋊C4×C47C2×C412yes—
41C2×C42×C47—42no—
42C2×C42×C47C2×C411yescharacteristic
43C2×C42×C47D411yescharacteristic
44C2×C42×C47D411yescharacteristic
45C2×C42×C47C2311yescharacteristic
46#95×C47—22no—
47#95×C47—22no—
48C24×C47C22⋊C411yescharacteristic
49C22×C4×C47—22no—
50C22×C4×C47—22no—
51C22×C4×C47—22no—
52C22×C4×C47—24no—
53C22×C4×C47—22no—
54C22×C4×C47—22no—
55C22×C4×C47—41no—
56C22×C4×C47—41no—
57C22×C4×C47—41no—
58C22×C4×C47—41no—
59C22×C4×C47—42no—
60C22×C4×C47—42no—
61C22×C4×C47—42no—
62C22×C4×C47—42no—
63C22×C4×C47—42no—
64C22×C4×C47C22⋊C411yescharacteristic
65C22×C4×C47C22⋊C411yescharacteristic
66C22×C4×C47C22⋊C411yescharacteristic
67C22×C4×C47D812yes—
68C22×C4×C47SD1612yes—
69C22×C4×C47SD1612yes—
70C22×C4×C47Q1612yes—
71C22×C4×C47C22×C411yescharacteristic
72C22×C4×C47C2×D411yescharacteristic
73C22×C4×C47C2×D411yescharacteristic
74C4⋊C4×C47—24no—
75C4⋊C4×C47—22no—
76C4⋊C4×C47—42no—
77C4⋊C4×C47—42no—
78C4⋊C4×C47—44no—
79C4⋊C4×C47—42no—
80C4⋊C4×C47—42no—
81C4⋊C4×C47M1614yes—
82C42×C47—22no—
83C42×C47—22no—
84C42×C47—41no—
85C42×C47—41no—
86C2×C47⋊C8—42no—
87C2×C47⋊C8—42no—
88C2×C47⋊C8—42no—
89C2×C47⋊C8—42no—
90C2×C47⋊C8—42no—
91C2×C47⋊C8—42no—
92C23×C47—21no—
93C23×C47—21no—
94C23×C47—21no—
95C23×C47—21no—
96C23×C47#10112yes—
97C23×C47#10212yes—
98C23×C47#10312yes—
99C23×C47C2×C22⋊C411yescharacteristic
100C2×C4×C47—28no—
101C2×C4×C47—21no—
102C2×C4×C47—21no—
103C2×C4×C47—21no—
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—24no—
114C2×C4×C47—42no—
115C2×C4×C47—42no—
116C2×C4×C47—42no—
117C2×C4×C47—42no—
118C2×C4×C47—48no—
119C2×C4×C47—42no—
120C2×C4×C47—42no—
121C2×C4×C47—42no—
122C2×C4×C47—42no—
123C2×C4×C47—42no—
124C2×C4×C47—84no—
125C2×C4×C47#9912yes—
126C2×C4×C47#10212yes—
127C2×C4×C47#10312yes—
128C2×C4×C47C2×M1612yes—
129C2×C4×C47C2×D811yescharacteristic
130C2×C4×C47C2×SD1611yescharacteristic
131C2×C4×C47C2×SD1611yescharacteristic
132C2×C4×C47C2×Q1611yescharacteristic
133C47⋊C8—82no—
134C47⋊C8—82no—
135#7641—471nomaximal, Sylow
136C22×C47—22no—
137C22×C47—22no—
138C22×C47—22no—
139C22×C47—22no—
140C22×C47—22no—
141C22×C47—22no—
142C22×C47#33214yes—
143C22×C47#40711yescharacteristic
144C22×C47C2×#9911yescharacteristic
145C22×C47C2×#10111yescharacteristic
146C22×C47C2×#10211yescharacteristic
147C22×C47C2×#10311yescharacteristic
148C22×C47#42111yescharacteristic
149C22×C47#42111yescharacteristic
150C4×C47—22no—
151C4×C47—22no—
152C4×C47—21no—
153C4×C47—22no—
154C4×C47—21no—
155C4×C47—21no—
156C4×C47—22no—
157C4×C47—21no—
158C4×C47—44no—
159C4×C47—82no—
160C2×#389D4711yescharacteristic
161#1797—471no—
162#1797—471no—
163#1271—474no—
164C2×C47—24no—
165C2×C47#146311yescharacteristic
166C2×C47#148611yescharacteristic
167C2×C47#148711yescharacteristic
168C2×C47#151911yescharacteristic
169C2×C47#152011yescharacteristic
170C2×C47#153411yescharacteristic
171C2×C47C2×#33211yescharacteristic
172C22×C4⋊C4—21no—
173C22×C4⋊C4Dic4711yescharacteristic
174C22×C4⋊C4Dic4711yescharacteristic
175C22×C42C2×D4711yescharacteristic
176C2×C4⋊C8—941no—
177C2×C4⋊C8—941no—
178C2×C22⋊C8—941no—
179C2×C22⋊C8—941no—
180#389—21no—
181#389—21no—
182#389Dic4712yes—
183#389C2×D4712yes—
184C2×#95—21no—
185#336—472no—
186#336—472no—
187C47#764111yescharacteristic, complemented, Sylow
188C23×C4—21no—
189C23×C4—21no—
190C23×C4C2×Dic4711yescharacteristic
191C23×C4C22⋊D4711yescharacteristic
192C23×C4C22⋊D4711yescharacteristic
193C22×C8—942no—
194C22×C8—942no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—24no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—42no—
201C2×C4⋊C4—42no—
202C2×C4⋊C4—42no—
203C2×C4⋊C4C2×Dic4712yes—
204C2×C4⋊C4C2×Dic4712yes—
205C2×C42—42no—
206C2×C42C2×Dic4711yescharacteristic
207C2×C42C22⋊D4711yescharacteristic
208C2×C42C22⋊D4711yescharacteristic
209C2×C42C22×D4711yescharacteristic
210C4⋊C8—1882no—
211C4⋊C8—1882no—
212C22⋊C8—1882no—
213C22⋊C8—1882no—
214#95—22no—
215#95—22no—
216C24C22⋊Dic4711yescharacteristic
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—24no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4#1062533412yes—
233C22×C4#1062533512yes—
234C22×C4#1062533612yes—
235C22×C4#1062533712yes—
236C22×C4C22⋊Dic4711yescharacteristic
237C22×C4C22⋊Dic4711yescharacteristic
238C22×C4C22⋊Dic4711yescharacteristic
239C22×C4C22×Dic4711yescharacteristic
240C22×C4C2×C22⋊D4711yescharacteristic
241C22×C4C2×C22⋊D4711yescharacteristic
242C2×C8—1882no—
243C2×C8—1882no—
244C2×C8—1882no—
245C2×C8—1882no—
246C2×C8—1882no—
247C2×C8—1882no—
248C4⋊C4—24no—
249C4⋊C4—22no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—44no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4#1062532914yes—
256C42—22no—
257C42—22no—
258C42—41no—
259C42—41no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23#1309394312yes—
265C23#1309394512yes—
266C23#1309394812yes—
267C23C2×C22⋊Dic4711yescharacteristic
268C2×C4—28no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—24no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—48no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—84no—
293C2×C4#1309393912yes—
294C2×C4#1309394512yes—
295C2×C4#1309394812yes—
296C2×C4C2×#1062532912yes—
297C2×C4C2×#1062533411yescharacteristic
298C2×C4C2×#1062533611yescharacteristic
299C2×C4C2×#1062533511yescharacteristic
300C2×C4C2×#1062533711yescharacteristic
301C8—3762no—
302C8—3762no—
303C22—22no—
304C22—22no—
305C22—22no—
306C22—22no—
307C22—22no—
308C22—22no—
309C22#1568886914yes—
310C22#1568908711yescharacteristic
311C22C2×#1309393911yescharacteristic
312C22C2×#1309394311yescharacteristic
313C22C2×#1309394511yescharacteristic
314C22C2×#1309394811yescharacteristic
315C22#1568914011yescharacteristic
316C22#1568914011yescharacteristic
317C4—21no—
318C4—22no—
319C4—21no—
320C4—21no—
321C4—22no—
322C4—21no—
323C4—22no—
324C4—22no—
325C4—44no—
326C4—82no—
327C2—24no—
328C2#2024171811yescharacteristic
329C2#2024181311yescharacteristic
330C2#2024181711yescharacteristic
331C2#2024195611yescharacteristic
332C2#2024196011yescharacteristic
333C2#2024201511yescharacteristic
334C2C2×#1568886911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC2×C47×#389C2
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C22⋊C4
cosocleC2×C42×C47C23
hypercenterC2×#389D47
hypocenterC47#7641
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. #20241211C2semidirect
187. C47#7641semidirect

Maximal subgroups

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

subgroupindex
#202433682
#202412112
C2×C47×#3892
#764147