Finite Group Databasebeta

← #26104395

Subgroups — #26104395

Order 12032.

408 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13094016C211yesmaximal, characteristic
2#20243505C211yesmaximal, characteristic
3#20241212C212yesmaximal
4#20241210C212yesmaximal
5C47×#1831C211yesmaximal, characteristic
6C2×#13094016C411yescharacteristic
7C2×C4⋊(C47⋊C8)—21no—
8#15689021C2211yescharacteristic
9#15689021C2211yescharacteristic
10#15689007—21no—
11#15689007—21no—
12#15688989C411yescharacteristic
13C4×Dic47⋊C4—21no—
14C4×Dic47⋊C4—21no—
15C4×C4⋊Dic47C411yescharacteristic
16C4×C4⋊Dic47C411yescharacteristic
17#15688878—21no—
18#15688878C2212yes—
19C2×C4⋊C8×C47—21no—
20C43×C47C2211yescharacteristic
21C47×#336—21no—
22C47×#336C2212yes—
23C22×C47⋊C8—22no—
24#13094016—22no—
25#13094016C814yescomplemented
26C2×C4⋊Dic47C2×C411yescharacteristic
27C2×C4⋊Dic47C2×C411yescharacteristic
28C2×C4⋊Dic47C2×C411yescharacteristic
29C2×C4⋊Dic47C2×C411yescharacteristic
30C2×Dic47⋊C4—21no—
31C2×Dic47⋊C4—21no—
32C2×Dic47⋊C4—21no—
33C2×Dic47⋊C4—21no—
34C2×C4×Dic47—21no—
35C2×C4×Dic47—21no—
36C4⋊(C47⋊C8)—42no—
37C47⋊#95—21no—
38C47⋊#95—21no—
39C47⋊#95—21no—
40C47⋊#95—21no—
41C47⋊#95—21no—
42C47⋊#95—21no—
43C22×C8×C47—22no—
44C2×C42×C47C2×C411yescharacteristic
45C2×C42×C47C2×C411yescharacteristic
46C2×C42×C47D411yescharacteristic
47C2×C42×C47D411yescharacteristic
48C2×C42×C47D411yescharacteristic
49C2×C42×C47D411yescharacteristic
50C2×C42×C47C2311yescharacteristic
51C4⋊C8×C47—42no—
52C22×C4×C47C22⋊C411yescharacteristic
53C22×C4×C47C22⋊C411yescharacteristic
54C22×C4×C47C22⋊C411yescharacteristic
55C22×C4×C47C22⋊C411yescharacteristic
56C22×C4×C47C22×C411yescharacteristic
57C22×C4×C47C2×D411yescharacteristic
58C22×C4×C47C2×D411yescharacteristic
59C22×Dic47—21no—
60C22×Dic47—21no—
61C22×Dic47—21no—
62C22×Dic47—21no—
63C2×C8×C47—42no—
64C2×C8×C47—42no—
65C2×C8×C47—42no—
66C42×C47—22no—
67C42×C47—21no—
68C42×C47—21no—
69C42×C47—21no—
70C42×C47—21no—
71C42×C47—41no—
72C42×C47—41no—
73C42×C47—41no—
74C42×C47C2×C812yes—
75C42×C47M1612yes—
76C4⋊Dic47—21no—
77C4⋊Dic47—21no—
78C4⋊Dic47—41no—
79C4⋊Dic47—41no—
80C4⋊Dic47C2×C812yes—
81C4⋊Dic47C2×C812yes—
82Dic47⋊C4—24no—
83Dic47⋊C4—24no—
84Dic47⋊C4—41no—
85Dic47⋊C4—41no—
86Dic47⋊C4—41no—
87Dic47⋊C4—41no—
88C4×Dic47—42no—
89C4×Dic47—42no—
90C2×C47⋊C8—42no—
91C2×C47⋊C8—42no—
92C2×C47⋊C8—42no—
93C23×C47C2×C22⋊C411yescharacteristic
94C2×C4×C47—21no—
95C2×C4×C47—21no—
96C2×C4×C47—21no—
97C2×C4×C47—21no—
98C2×C4×C47—21no—
99C2×C4×C47—21no—
100C2×C4×C47—21no—
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×C47C22⋊C812yes—
110C2×C4×C47C22⋊C812yes—
111C2×C4×C47#10112yes—
112C2×C4×C47C22×C811yescharacteristic
113C2×C4×C47C2×M1611yescharacteristic
114C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
115C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
116C2×C4×C47#13711yescharacteristic
117C2×C4×C47#13711yescharacteristic
118C2×Dic47—22no—
119C2×Dic47—22no—
120C2×Dic47—41no—
121C2×Dic47—41no—
122C2×Dic47—41no—
123C2×Dic47—41no—
124C2×Dic47—41no—
125C2×Dic47—41no—
126C2×Dic47—41no—
127C2×Dic47—41no—
128C2×Dic47—41no—
129C2×Dic47—41no—
130C8×C47—82no—
131C47⋊C8—82no—
132#7602—471nomaximal, Sylow
133C22×C47C2×C22⋊C811yescharacteristic
134C22×C47#41011yescharacteristic
135C22×C47C2×#10111yescharacteristic
136C22×C47#41711yescharacteristic
137C22×C47#41711yescharacteristic
138C22×C47#42111yescharacteristic
139C22×C47#42111yescharacteristic
140C4×C47—21no—
141C4×C47—21no—
142C4×C47—22no—
143C4×C47—22no—
144C4×C47—21no—
145C4×C47—21no—
146C4×C47—21no—
147C4×C47—21no—
148C4×C47—22no—
149C4×C47—41no—
150Dic47—42no—
151Dic47—42no—
152Dic47—81no—
153Dic47—81no—
154C4×#125—471no—
155#1831—471no—
156#1831D4711yescharacteristic
157#1271—472no—
158#1271—472no—
159C2×C47#146111yescharacteristic
160C2×C47#147711yescharacteristic
161C2×C47#147711yescharacteristic
162C2×C47#151211yescharacteristic
163C2×C47#151211yescharacteristic
164C2×C47#153411yescharacteristic
165C2×C47#156111yescharacteristic
166C2×#125—471no—
167C2×C4⋊C8—21no—
168C2×C4⋊C8—941no—
169#389—471no—
170#389—471no—
171#387—941no—
172#387—941no—
173#382—471no—
174C4×C4⋊C4—471no—
175C4×C4⋊C4—471no—
176C4×C4⋊C4—941no—
177C4×C4⋊C4—941no—
178C43C2×D4711yescharacteristic
179#336—21no—
180#336—472no—
181#336—941no—
182#336C2×D4712yes—
183C47#760211yescharacteristic, complemented, Sylow
184C22×C8—22no—
185C22×C8—942no—
186#125—474no—
187#125—942no—
188C2×C4⋊C4—471no—
189C2×C4⋊C4—471no—
190C2×C4⋊C4—471no—
191C2×C4⋊C4—471no—
192C2×C4⋊C4—941no—
193C2×C4⋊C4—941no—
194C2×C4⋊C4—941no—
195C2×C4⋊C4—941no—
196C2×C42—941no—
197C2×C42—941no—
198C2×C42C4×D4711yescharacteristic
199C2×C42C4×D4711yescharacteristic
200C2×C42D18811yescharacteristic
201C2×C42D18811yescharacteristic
202C2×C42C22⋊D4711yescharacteristic
203C2×C42C22⋊D4711yescharacteristic
204C2×C42C22×D4711yescharacteristic
205C4⋊C8—42no—
206C4⋊C8—1882no—
207#95—941no—
208#95—941no—
209#95—941no—
210#95—941no—
211#95—941no—
212#95—941no—
213C22×C4—941no—
214C22×C4—941no—
215C22×C4—941no—
216C22×C4—941no—
217C22×C4(C2×D47)⋊C411yescharacteristic
218C22×C4(C2×D47)⋊C411yescharacteristic
219C22×C4(C2×D47)⋊C411yescharacteristic
220C22×C4(C2×D47)⋊C411yescharacteristic
221C22×C4C2×C4×D4711yescharacteristic
222C22×C4C2×D18811yescharacteristic
223C22×C4C2×C22⋊D4711yescharacteristic
224C2×C8—42no—
225C2×C8—42no—
226C2×C8—42no—
227C2×C8—1882no—
228C2×C8—1882no—
229C2×C8—1882no—
230C4⋊C4—472no—
231C4⋊C4—472no—
232C4⋊C4—944no—
233C4⋊C4—944no—
234C4⋊C4—941no—
235C4⋊C4—941no—
236C4⋊C4—1881no—
237C4⋊C4—1881no—
238C4⋊C4—1881no—
239C4⋊C4—1881no—
240C4⋊C4—1881no—
241C4⋊C4—1881no—
242C42—22no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—41no—
248C42—41no—
249C42—41no—
250C42—1882no—
251C42—1882no—
252C42C8×D4712yes—
253C42#1062532412yes—
254C23C2×(C2×D47)⋊C411yescharacteristic
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—942no—
271C2×C4—942no—
272C2×C4—1881no—
273C2×C4—1881no—
274C2×C4—1881no—
275C2×C4—1881no—
276C2×C4—1881no—
277C2×C4—1881no—
278C2×C4—1881no—
279C2×C4—1881no—
280C2×C4—1881no—
281C2×C4—1881no—
282C2×C4(C2×D47)⋊C812yes—
283C2×C4(C2×D47)⋊C812yes—
284C2×C4#1309394212yes—
285C2×C4C2×C8×D4711yescharacteristic
286C2×C4C2×#1062532411yescharacteristic
287C2×C4#1309405011yescharacteristic
288C2×C4#1309405211yescharacteristic
289C2×C4#1309405511yescharacteristic
290C2×C4#1309405711yescharacteristic
291C8—82no—
292C8—3762no—
293C22C2×(C2×D47)⋊C811yescharacteristic
294C22#1568909611yescharacteristic
295C22C2×#1309394211yescharacteristic
296C22#1568912211yescharacteristic
297C22#1568912511yescharacteristic
298C22#1568913911yescharacteristic
299C22#1568914111yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—21no—
306C4—22no—
307C4—22no—
308C4—22no—
309C4—41no—
310C4—3761no—
311C4—3761no—
312C4—1882no—
313C4—1882no—
314C2#2024171111yescharacteristic
315C2#2024177311yescharacteristic
316C2#2024177611yescharacteristic
317C2#2024192411yescharacteristic
318C2#2024192711yescharacteristic
319C2#2024201411yescharacteristic
320C2#2024212511yescharacteristic
subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutatorC2×C4×C47C22×C8
FrattiniC2×C42C22×D47
FittingC47×#1831C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1831D47
hypocenterC47#7602
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C43 ◁ #1831

Complements

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

NH ≅ G/Ntype
25. #13094016C8semidirect
183. C47#7602semidirect

Maximal subgroups

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

subgroupindex
C4×#130940162
#202435052
#202412122
#202412102
C47×#18312
#760247