Finite Group Databasebeta

← #26132453

Subgroups — #26132453

Order 12032.

418 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
1C22×#13093963C211yesmaximal, characteristic
2C2×#15688950C211yesmaximal, characteristic, complemented
3C2×#15688948C211yesmaximal, characteristic, complemented
4#20243414C211yesmaximal, characteristic
5#20243414C211yesmaximal, characteristic
6#20241480C211yesmaximal, characteristic, complemented
7C47×#1380C211yesmaximal, characteristic, complemented
8C22×C8×D47C2211yescharacteristic
9C2×#13093963—22no—
10C2×#13093963—22no—
11C2×#13093963C414yescomplemented
12C22×C47⋊C16C2211yescharacteristic
13C2×#13093958C2211yescharacteristic
14C2×#13093958C2211yescharacteristic
15#15688980—21no—
16#15688980—21no—
17#15688950—22no—
18#15688948—22no—
19#15688885—21no—
20#15688885—21no—
21C22×C16×C47C2211yescharacteristic
22C2×#107×C47C2211yescharacteristic
23C2×#107×C47C2211yescharacteristic
24C22×C4×D47D411yescharacteristic
25C22×C47⋊C8D411yescharacteristic
26C2×C8×D47—21no—
27C2×C8×D47—21no—
28C2×C8×D47—21no—
29C2×C8×D47—21no—
30C2×C8×D47C2×C412yes—
31C2×C8×D47Q812yes—
32C2×C4⋊Dic47—21no—
33C2×C4⋊Dic47—21no—
34C2×(C2×D47)⋊C4—41no—
35C2×(C2×D47)⋊C4—41no—
36#13093963—28no—
37C2×C47⋊C16C2×C412yes—
38C2×C47⋊C16D412yes—
39C2×C47⋊C16D412yes—
40#13093958—21no—
41#13093958—21no—
42#13093958—21no—
43#13093958—21no—
44C47⋊#95—41no—
45C47⋊#95—41no—
46C22×C8×C47C2311yescharacteristic
47C2×C4⋊C4×C47—21no—
48C2×C4⋊C4×C47—21no—
49C2×C16×C47—21no—
50C2×C16×C47—21no—
51C2×C16×C47C2×C412yes—
52#107×C47—21no—
53#107×C47—21no—
54#107×C47—21no—
55#107×C47—21no—
56C23×D47D811yescharacteristic
57C22×C4×C47—41no—
58C22×C4×C47—41no—
59C22×C4×C47C2×D411yescharacteristic
60C22×Dic47—41no—
61C22×Dic47—41no—
62C22×Dic47D811yescharacteristic
63C2×C4×D47—21no—
64C2×C4×D47—21no—
65C2×C4×D47—21no—
66C2×C4×D47—21no—
67C2×C4×D47C4⋊C412yes—
68C2×C4×D47Q1612yes—
69C2×C8×C47C22×C411yescharacteristic
70C2×C8×C47C2×D411yescharacteristic
71C2×C8×C47C2×D411yescharacteristic
72C2×C8×C47C2×Q811yescharacteristic
73C2×C8×C47#4111yescharacteristic
74C2×C8×C47#4111yescharacteristic
75C4⋊C4×C47—41no—
76C4⋊C4×C47—41no—
77C4⋊C4×C47—41no—
78C4⋊C4×C47—41no—
79(C2×D47)⋊C4—82no—
80(C2×D47)⋊C4—82no—
81C4⋊Dic47—41no—
82C4⋊Dic47—41no—
83C4⋊Dic47—41no—
84C4⋊Dic47—41no—
85C2×C47⋊C8—21no—
86C2×C47⋊C8—21no—
87C2×C47⋊C8C4⋊C412yes—
88C8×D47—22no—
89C8×D47—22no—
90C8×D47—22no—
91C8×D47—22no—
92C16×C47—22no—
93C47⋊C16C22⋊C414yescomplemented
94C23×C47C2×D811yescharacteristic
95C22×D47—21no—
96C22×D47—21no—
97C22×D47—21no—
98C22×D47—21no—
99C22×D47—21no—
100C22×D47—21no—
101C22×D47#10712yes—
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×C47C2×C4⋊C411yescharacteristic
109C2×C4×C47#12111yescharacteristic
110C2×C4×C47#12111yescharacteristic
111C2×C4×C47C2×Q1611yescharacteristic
112C2×C4×C47#13511yescharacteristic
113C2×C4×C47#13511yescharacteristic
114C2×Dic47—21no—
115C2×Dic47—21no—
116C2×Dic47—81no—
117C2×Dic47—81no—
118C2×Dic47—81no—
119C2×Dic47—81no—
120C2×Dic47—81no—
121C2×Dic47—81no—
122C2×Dic47#10712yes—
123C4×D47—22no—
124C4×D47—22no—
125C4×D47—22no—
126C4×D47—22no—
127C8×C47C2×C22⋊C411yescharacteristic
128C8×C47#11711yescharacteristic
129C8×C47C22⋊Q811yescharacteristic
130C8×C47C22⋊Q811yescharacteristic
131C47⋊C8—22no—
132#12836—471nomaximal, Sylow
133C22×C47C2×#10711yescharacteristic
134C22×C47#46611yescharacteristic
135C22×C47#46611yescharacteristic
136C22×C47#50911yescharacteristic
137C22×C47#50911yescharacteristic
138C22×C47#51011yescharacteristic
139C22×C47#51011yescharacteristic
140C2×D47—22no—
141C2×D47—22no—
142C2×D47—22no—
143C2×D47—41no—
144C2×D47—41no—
145C2×D47—41no—
146C2×D47—41no—
147C4×C47—161no—
148C4×C47—161no—
149C4×C47#38011yescharacteristic
150C4×C47#42711yescharacteristic
151C4×C47#46711yescharacteristic
152C4×C47#46711yescharacteristic
153Dic47—22no—
154Dic47—161no—
155Dic47—161no—
156C22×M32—471no—
157C2×#367—471no—
158C2×#366—471no—
159#1808—471no—
160#1808—471no—
161#1380—471no—
162#1380D4711yescharacteristic, complemented
163C2×C47#180811yescharacteristic
164C2×C47#215911yescharacteristic
165C2×C47#215911yescharacteristic
166C2×C47#221811yescharacteristic
167C2×C47#221911yescharacteristic
168C2×C47#222011yescharacteristic
169C2×C47#222011yescharacteristic
170D47—42no—
171C23×C8—471no—
172C2×M32—474no—
173C2×M32—942no—
174C2×M32—942no—
175C22×C16—471no—
176C22×C16C2×D4711yescharacteristic
177C2×#107—471no—
178C2×#107—471no—
179C2×#107C2×D4711yescharacteristic
180C2×#107C2×D4711yescharacteristic
181#380—941no—
182#380—941no—
183#367—942no—
184#366—942no—
185#340—941no—
186#340—941no—
187C47#1283611yescharacteristic, complemented, Sylow
188C23×C4—471no—
189C22×C8—471no—
190C22×C8—472no—
191C22×C8—472no—
192C22×C8—941no—
193C22×C8—941no—
194C22×C8—941no—
195C22×C8—941no—
196C22×C8C22×D4711yescharacteristic
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—941no—
200C2×C4⋊C4—941no—
201C2×C22⋊C4—1881no—
202C2×C22⋊C4—1881no—
203M32—948no—
204C2×C16—21no—
205C2×C16—21no—
206C2×C16—472no—
207C2×C16—472no—
208C2×C16—472no—
209C2×C16C4×D4712yes—
210#107—21no—
211#107—21no—
212#107—21no—
213#107—21no—
214#107—941no—
215#107—941no—
216#107—941no—
217#107—941no—
218#95—1881no—
219#95—1881no—
220C24—471no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—471no—
224C22×C4—472no—
225C22×C4—472no—
226C22×C4—941no—
227C22×C4—941no—
228C22×C4—941no—
229C22×C4—941no—
230C22×C4—1881no—
231C22×C4—1881no—
232C22×C4D4×D4711yescharacteristic
233C2×C8—472no—
234C2×C8—941no—
235C2×C8—941no—
236C2×C8—942no—
237C2×C8—942no—
238C2×C8—942no—
239C2×C8—942no—
240C2×C8C2×C4×D4711yescharacteristic
241C2×C8#1062535011yescharacteristic
242C2×C8#1062535011yescharacteristic
243C2×C8D4×D4711yescharacteristic
244C2×C8D4×D4711yescharacteristic
245C2×C8Q8×D4711yescharacteristic
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—1881no—
251C4⋊C4—1881no—
252C4⋊C4—1881no—
253C4⋊C4—1881no—
254C22⋊C4—3762no—
255C22⋊C4—3762no—
256C16—22no—
257C16—474no—
258C23—472no—
259C23—941no—
260C23—941no—
261C23—941no—
262C23—941no—
263C23—941no—
264C23—941no—
265C23D8×D4711yescharacteristic
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—472no—
273C2×C4—941no—
274C2×C4—941no—
275C2×C4—942no—
276C2×C4—942no—
277C2×C4—942no—
278C2×C4—942no—
279C2×C4—3761no—
280C2×C4—3761no—
281C2×C4—3761no—
282C2×C4—3761no—
283C2×C4—3761no—
284C2×C4—3761no—
285C2×C4C4⋊C4×D4711yescharacteristic
286C2×C4#1309399711yescharacteristic
287C2×C4#1309399711yescharacteristic
288C2×C4Q16×D4711yescharacteristic
289C2×C4#1309404511yescharacteristic
290C2×C4#1309404511yescharacteristic
291C8—942no—
292C8C22⋊C4×D4711yescharacteristic
293C8#1309398111yescharacteristic
294C8#1309400211yescharacteristic
295C8#1309400211yescharacteristic
296C22—942no—
297C22—942no—
298C22—942no—
299C22—1881no—
300C22—1881no—
301C22—1881no—
302C22—1881no—
303C22#107×D4711yescharacteristic
304C22#1568935811yescharacteristic
305C22#1568935811yescharacteristic
306C22#1568955711yescharacteristic
307C22#1568956011yescharacteristic
308C22#1568956211yescharacteristic
309C22#1568956511yescharacteristic
310C4—161no—
311C4—161no—
312C4—942no—
313C4—7521no—
314C4—7521no—
315C4#1568898211yescharacteristic
316C4#1568915811yescharacteristic
317C4#1568936311yescharacteristic
318C4#1568936311yescharacteristic
319C2—1882no—
320C2#2024341611yescharacteristic
321C2#2024517311yescharacteristic
322C2#2024517511yescharacteristic
323C2#2024549011yescharacteristic
324C2#2024549511yescharacteristic
325C2#2024550011yescharacteristic
326C2#2024550411yescharacteristic
subgroupG/H
centerC23D8×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC47×#1380C2
socleC23×C47C2×D8
prime radicalC23×D47D8
cosocleC22×C8×C47C23
hypercenter#1380D47
hypocenterC47#12836
LCSG ▷ C2×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
2. C2×#15688950C2semidirect
3. C2×#15688948C2semidirect
6. #20241480C2semidirect
7. C47×#1380C2semidirect
11. C2×#13093963C4semidirect
93. C47⋊C16C22⋊C4semidirect
162. #1380D47semidirect
187. C47#12836semidirect

Maximal subgroups

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

subgroupindex
C22×#130939632
C2×#156889502
C2×#156889482
#202434142
#202414802
C47×#13802
#1283647