Finite Group Databasebeta

← #26114812

Subgroups — #26114812

Order 12032.

398 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
1#20244106C211yesmaximal, characteristic
2C4×#13093955C211yesmaximal, characteristic
3C2×#15688873C211yesmaximal, characteristic
4C2×C8×C47⋊C8C211yesmaximal, characteristic
5#20241229C211yesmaximal, characteristic
6#20241227C211yesmaximal, characteristic
7C47×#1939C211yesmaximal, characteristic
8C2×#13093955C411yescharacteristic
9C2×#13093955C411yescharacteristic
10C2×C4⋊(C47⋊C8)C2211yescharacteristic
11C2×Dic47⋊C8—21no—
12C2×C4×C47⋊C8C2211yescharacteristic
13C2×C4×C47⋊C8C2211yescharacteristic
14C4×C4⋊Dic47C2211yescharacteristic
15#15688885C411yescharacteristic
16#15688885C411yescharacteristic
17#15688877—21no—
18#15688873—22no—
19C8×C47⋊C8—22no—
20C2×C4⋊C8×C47—21no—
21C2×C4⋊C8×C47C2211yescharacteristic
22C2×C4×C8×C47C2211yescharacteristic
23C4×C4⋊C4×C47C2211yescharacteristic
24C47×#336—21no—
25C22×C47⋊C8—21no—
26C22×C47⋊C8—21no—
27C22×C47⋊C8C2×C411yescharacteristic
28C22×C47⋊C8C2×C411yescharacteristic
29C2×C4⋊Dic47C2×C411yescharacteristic
30C2×C4⋊Dic47C2×C411yescharacteristic
31C2×C4×Dic47—21no—
32#13093955—22no—
33#13093955C814yescomplemented
34C4⋊(C47⋊C8)—21no—
35C4⋊(C47⋊C8)—21no—
36Dic47⋊C8—42no—
37C4×C47⋊C8—21no—
38C4×C47⋊C8D412yes—
39C4×C47⋊C8Q812yes—
40C4×C47⋊C8Q812yes—
41C47⋊#95—21no—
42C22×C8×C47—21no—
43C22×C8×C47D411yescharacteristic
44C22×C8×C47D411yescharacteristic
45C2×C4⋊C4×C47C2×C411yescharacteristic
46C2×C4⋊C4×C47C2×C411yescharacteristic
47C2×C42×C47—21no—
48C2×C42×C47C2311yescharacteristic
49C4⋊C8×C47—21no—
50C4⋊C8×C47—21no—
51C4⋊C8×C47—42no—
52C4×C8×C47—21no—
53C4×C8×C47—21no—
54#95×C47—21no—
55C22×C4×C47—21no—
56C22×C4×C47—21no—
57C22×C4×C47C22×C411yescharacteristic
58C22×C4×C47C2×D411yescharacteristic
59C22×C4×C47#4111yescharacteristic
60C22×Dic47—21no—
61C22×Dic47—21no—
62C2×C8×C47—21no—
63C2×C8×C47—21no—
64C2×C8×C47—21no—
65C2×C8×C47—21no—
66C2×C8×C47—41no—
67C2×C8×C47—41no—
68C2×C8×C47—41no—
69C2×C8×C47SD1612yes—
70C2×C8×C47SD1612yes—
71C4⋊C4×C47—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47C2×C812yes—
75C42×C47—41no—
76C42×C47—41no—
77C42×C47C2×D411yescharacteristic
78C42×C47C2×Q811yescharacteristic
79C42×C47C2×Q811yescharacteristic
80C42×C47#4111yescharacteristic
81C4⋊Dic47—21no—
82C4⋊Dic47—21no—
83C4⋊Dic47—21no—
84C4⋊Dic47C2×C812yes—
85C4×Dic47—41no—
86C4×Dic47—41no—
87C2×C47⋊C8—22no—
88C2×C47⋊C8—22no—
89C2×C47⋊C8—22no—
90C2×C47⋊C8—21no—
91C2×C47⋊C8—21no—
92C2×C47⋊C8—41no—
93C2×C47⋊C8—41no—
94C2×C47⋊C8—41no—
95C2×C47⋊C8C4⋊C412yes—
96C2×C47⋊C8C4⋊C412yes—
97C2×C47⋊C8C2×C812yes—
98C2×C47⋊C8M1612yes—
99C23×C47C4×D411yescharacteristic
100C2×C4×C47—21no—
101C2×C4×C47—21no—
102C2×C4×C47—22no—
103C2×C4×C47—41no—
104C2×C4×C47—41no—
105C2×C4×C47—41no—
106C2×C4×C47—41no—
107C2×C4×C47—41no—
108C2×C4×C47C2×C4⋊C411yescharacteristic
109C2×C4×C47C4×Q811yescharacteristic
110C2×C4×C47#12111yescharacteristic
111C2×C4×C47C22⋊Q811yescharacteristic
112C2×C4×C47#12511yescharacteristic
113C2×C4×C47C4⋊Q811yescharacteristic
114C2×C4×C47C22×C811yescharacteristic
115C2×C4×C47C2×M1611yescharacteristic
116C2×C4×C47#13111yescharacteristic
117C2×C4×C47#13111yescharacteristic
118C2×C4×C47C2×SD1611yescharacteristic
119C2×C4×C47C2×SD1611yescharacteristic
120C2×C4×C47#13511yescharacteristic
121C2×C4×C47#13511yescharacteristic
122C2×Dic47—22no—
123C2×Dic47—41no—
124C2×Dic47—41no—
125C2×Dic47—41no—
126C2×Dic47—41no—
127C2×Dic47—41no—
128C8×C47—22no—
129C8×C47—22no—
130C8×C47—81no—
131C47⋊C8—24no—
132C47⋊C8—22no—
133C47⋊C8—81no—
134C47⋊C8C4⋊C814yescomplemented
135#9593—471nomaximal, Sylow
136C22×C47#38911yescharacteristic
137C22×C47C8×D411yescharacteristic
138C22×C47#43611yescharacteristic
139C22×C47C4×SD1611yescharacteristic
140C22×C47C4×SD1611yescharacteristic
141C22×C47#44311yescharacteristic
142C22×C47#44311yescharacteristic
143C4×C47—21no—
144C4×C47—21no—
145C4×C47—42no—
146C4×C47—81no—
147C4×C47C2×C4⋊C811yescharacteristic
148C4×C47#42411yescharacteristic
149C4×C47C8×Q811yescharacteristic
150C4×C47#44611yescharacteristic
151C4×C47#46511yescharacteristic
152C4×C47#46511yescharacteristic
153C4×C47#49811yescharacteristic
154C4×C47#49911yescharacteristic
155Dic47—42no—
156Dic47—81no—
157#1939—471no—
158#1939D4711yescharacteristic
159C4×#106—471no—
160C2×#334—471no—
161C2×C82—471no—
162#1279—471no—
163#1279—471no—
164C2×C47C8×SD1611yescharacteristic
165C2×C47C8×SD1611yescharacteristic
166C2×C47#159011yescharacteristic
167C2×C47#159011yescharacteristic
168C2×C47#193911yescharacteristic
169C2×C47#194111yescharacteristic
170C2×C47#194511yescharacteristic
171C2×#106—471no—
172C2×#106—471no—
173C2×C4⋊C8—21no—
174C2×C4⋊C8—471no—
175C2×C4⋊C8—941no—
176C2×C4⋊C8C2×D4711yescharacteristic
177C2×C4×C8—471no—
178C2×C4×C8—471no—
179C2×C4×C8C2×D4711yescharacteristic
180C4×C4⋊C4—471no—
181C4×C4⋊C4C2×D4711yescharacteristic
182#340—471no—
183#340—471no—
184#336—21no—
185#336—941no—
186#334—942no—
187C82—942no—
188C47#959311yescharacteristic, complemented, Sylow
189C22×C8—21no—
190C22×C8—471no—
191C22×C8—471no—
192C22×C8—941no—
193C22×C8—941no—
194C22×C8C22⋊D4711yescharacteristic
195C22×C8C22⋊D4711yescharacteristic
196C2×C4⋊C4—471no—
197C2×C4⋊C4—471no—
198C2×C4⋊C4C4×D4711yescharacteristic
199C2×C4⋊C4C4×D4711yescharacteristic
200C2×C42—21no—
201C2×C42—941no—
202C2×C42C22×D4711yescharacteristic
203#106—474no—
204#106—942no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—42no—
208C4⋊C8—941no—
209C4⋊C8—941no—
210C4⋊C8—1882no—
211C4×C8—21no—
212C4×C8—21no—
213C4×C8—472no—
214C4×C8—472no—
215C4×C8—472no—
216C4×C8—941no—
217#95—21no—
218#95—941no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—941no—
222C22×C4—941no—
223C22×C4C2×C4×D4711yescharacteristic
224C22×C4#1062535011yescharacteristic
225C22×C4C2×C22⋊D4711yescharacteristic
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—472no—
234C2×C8—472no—
235C2×C8—472no—
236C2×C8—472no—
237C2×C8—942no—
238C2×C8—942no—
239C2×C8—942no—
240C2×C8—941no—
241C2×C8—941no—
242C2×C8—1881no—
243C2×C8—1881no—
244C2×C8—1881no—
245C2×C8#1062533512yes—
246C2×C8#1062533612yes—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—472no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4C8×D4712yes—
255C42—41no—
256C42—41no—
257C42—1881no—
258C42—1881no—
259C42D4×D4711yescharacteristic
260C42#1062535211yescharacteristic
261C42Q8×D4711yescharacteristic
262C42Q8×D4711yescharacteristic
263C23C4×C22⋊D4711yescharacteristic
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—942no—
273C2×C4—1881no—
274C2×C4—1881no—
275C2×C4—1881no—
276C2×C4—1881no—
277C2×C4—1881no—
278C2×C4C4⋊C4×D4711yescharacteristic
279C2×C4#1309398911yescharacteristic
280C2×C4#1309399611yescharacteristic
281C2×C4#1309400211yescharacteristic
282C2×C4#1309401411yescharacteristic
283C2×C4#1309402211yescharacteristic
284C2×C4C2×C8×D4711yescharacteristic
285C2×C4M16×D4711yescharacteristic
286C2×C4#1309403011yescharacteristic
287C2×C4#1309403211yescharacteristic
288C2×C4C2×#1062533611yescharacteristic
289C2×C4C2×#1062533511yescharacteristic
290C2×C4#1309404411yescharacteristic
291C2×C4#1309404411yescharacteristic
292C8—22no—
293C8—22no—
294C8—81no—
295C8—474no—
296C8—944no—
297C8—942no—
298C8—3761no—
299C22#1568901811yescharacteristic
300C22C8×C22⋊D4711yescharacteristic
301C22#1568919911yescharacteristic
302C22C4×#1062533511yescharacteristic
303C22C4×#1062533611yescharacteristic
304C22#1568923811yescharacteristic
305C22#1568923811yescharacteristic
306C4—21no—
307C4—21no—
308C4—42no—
309C4—81no—
310C4—3761no—
311C4—1882no—
312C4C4⋊C8×D4711yescharacteristic
313C4#1568914811yescharacteristic
314C4#1568924711yescharacteristic
315C4#1568925211yescharacteristic
316C4#1568935011yescharacteristic
317C4#1568935411yescharacteristic
318C4#1568951911yescharacteristic
319C4#1568952211yescharacteristic
320C2C8×#1062533511yescharacteristic
321C2C8×#1062533611yescharacteristic
322C2#2024227611yescharacteristic
323C2#2024227811yescharacteristic
324C2#2024410311yescharacteristic
325C2#2024411311yescharacteristic
326C2#2024413311yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D47
commutatorC2×C4×C47C22×C8
FrattiniC2×C42C22×D47
FittingC47×#1939C2
socle, prime radicalC23×C47C4×D4
cosocleC2×C42×C47C23
hypercenter#1939D47
hypocenterC47#9593
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1939

Complements

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

NH ≅ G/Ntype
33. #13093955C8semidirect
134. C47⋊C8C4⋊C8semidirect
188. C47#9593semidirect

Maximal subgroups

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

subgroupindex
#202441062
C4×#130939552
C2×#156888732
C2×C8×C47⋊C82
#202412292
#202412272
C47×#19392
#959347