Finite Group Databasebeta

← #26109042

Subgroups — #26109042

Order 12032.

456 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
1C4×#13094016C211yesmaximal, characteristic
2#20243241C211yesmaximal, characteristic
3C2×#15688864C212yesmaximal
4#20241270C212yesmaximal
5C47×#1767C211yesmaximal, characteristic
6C2×#13094016C2211yescharacteristic
7C2×C4⋊(C47⋊C8)—21no—
8C2×#13093935C2212yes—
9#15689021C411yescharacteristic
10#15689021C411yescharacteristic
11#15689007—21no—
12#15689007—21no—
13#15688989C2211yescharacteristic
14C4×Dic47⋊C4—21no—
15C4×Dic47⋊C4—21no—
16C4×C4⋊Dic47C411yescharacteristic
17C4×C4⋊Dic47C411yescharacteristic
18#15688878—21no—
19#15688864—24no—
20C2×C4⋊C8×C47—21no—
21C2×#97×C47C2212yes—
22C43×C47C2211yescharacteristic
23C47×#336—21no—
24C22×C47⋊C8—22no—
25#13094016—21no—
26#13094016—21no—
27#13094016D412yes—
28#13094016Q812yes—
29C2×C4⋊Dic47C2×C411yescharacteristic
30C2×C4⋊Dic47C2×C411yescharacteristic
31C2×C4⋊Dic47C2×C411yescharacteristic
32C2×C4⋊Dic47C2×C411yescharacteristic
33C2×Dic47⋊C4—21no—
34C2×Dic47⋊C4—21no—
35C2×Dic47⋊C4—21no—
36C2×Dic47⋊C4—21no—
37C2×C4×Dic47—21no—
38C2×C4×Dic47—21no—
39C4⋊(C47⋊C8)—24no—
40#13093935—22no—
41#13093935—22no—
42C47⋊#95—21no—
43C47⋊#95—21no—
44C47⋊#95—21no—
45C47⋊#95—21no—
46C47⋊#95—21no—
47C47⋊#95—21no—
48C22×C8×C47—22no—
49C2×C42×C47C2×C411yescharacteristic
50C2×C42×C47C2×C411yescharacteristic
51C2×C42×C47D411yescharacteristic
52C2×C42×C47D411yescharacteristic
53C2×C42×C47D411yescharacteristic
54C2×C42×C47D411yescharacteristic
55C2×C42×C47C2311yescharacteristic
56C4⋊C8×C47—24no—
57#97×C47—22no—
58#97×C47—22no—
59C22×C4×C47C22⋊C411yescharacteristic
60C22×C4×C47C22⋊C411yescharacteristic
61C22×C4×C47C22⋊C411yescharacteristic
62C22×C4×C47C22⋊C411yescharacteristic
63C22×C4×C47C22×C411yescharacteristic
64C22×C4×C47C2×D411yescharacteristic
65C22×C4×C47C2×D411yescharacteristic
66C22×Dic47—21no—
67C22×Dic47—21no—
68C22×Dic47—21no—
69C22×Dic47—21no—
70C2×C8×C47—24no—
71C2×C8×C47—42no—
72C2×C8×C47—42no—
73C42×C47—22no—
74C42×C47—22no—
75C42×C47—22no—
76C42×C47—41no—
77C42×C47—41no—
78C42×C47—41no—
79C42×C47C2×D411yescharacteristic
80C42×C47C2×Q811yescharacteristic
81C42×C47#4111yescharacteristic
82C42×C47#4111yescharacteristic
83C4⋊Dic47—21no—
84C4⋊Dic47—21no—
85C4⋊Dic47—41no—
86C4⋊Dic47—41no—
87C4⋊Dic47C4⋊C412yes—
88C4⋊Dic47C4⋊C412yes—
89Dic47⋊C4—22no—
90Dic47⋊C4—22no—
91Dic47⋊C4—22no—
92Dic47⋊C4—22no—
93Dic47⋊C4—42no—
94Dic47⋊C4—42no—
95C4×Dic47—42no—
96C4×Dic47—42no—
97C2×C47⋊C8—24no—
98C2×C47⋊C8—42no—
99C2×C47⋊C8—42no—
100C23×C47C2×C22⋊C411yescharacteristic
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—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47#10112yes—
117C2×C4×C47#10412yes—
118C2×C4×C47#10412yes—
119C2×C4×C47C2×C4⋊C411yescharacteristic
120C2×C4×C47#11711yescharacteristic
121C2×C4×C47#12111yescharacteristic
122C2×C4×C47#12111yescharacteristic
123C2×C4×C47C22⋊Q811yescharacteristic
124C2×C4×C47C22⋊Q811yescharacteristic
125C2×Dic47—22no—
126C2×Dic47—22no—
127C2×Dic47—41no—
128C2×Dic47—41no—
129C2×Dic47—41no—
130C2×Dic47—41no—
131C2×Dic47—41no—
132C2×Dic47—41no—
133C2×Dic47—41no—
134C2×Dic47—41no—
135C2×Dic47—41no—
136C2×Dic47—41no—
137C8×C47—44no—
138C47⋊C8—44no—
139#8580—471nomaximal, Sylow
140C22×C47#38011yescharacteristic
141C22×C47C2×#10111yescharacteristic
142C22×C47#41311yescharacteristic
143C22×C47C2×#10411yescharacteristic
144C22×C47C2×#10411yescharacteristic
145C22×C47#42111yescharacteristic
146C22×C47#42111yescharacteristic
147C4×C47—21no—
148C4×C47—21no—
149C4×C47—21no—
150C4×C47—21no—
151C4×C47—21no—
152C4×C47—21no—
153C4×C47—41no—
154C4×C47—41no—
155C4×C47—41no—
156C4×C47#33014yescomplemented
157Dic47—42no—
158Dic47—42no—
159Dic47—81no—
160Dic47—81no—
161C4×#125—471no—
162#1767—471no—
163#1767D4711yescharacteristic
164C2×#330—472no—
165#1295—472no—
166C2×C47C2×#33011yescharacteristic
167C2×C47#152911yescharacteristic
168C2×C47#152911yescharacteristic
169C2×C47#153711yescharacteristic
170C2×C47#180111yescharacteristic
171C2×C47#180611yescharacteristic
172C2×C47#180611yescharacteristic
173C2×#125—471no—
174C2×C4⋊C8—21no—
175C2×C4⋊C8—941no—
176C2×#97—472no—
177C2×#97C2×D4712yes—
178#389—471no—
179#389—471no—
180#387—941no—
181#387—941no—
182#382—471no—
183C4×C4⋊C4—471no—
184C4×C4⋊C4—471no—
185C4×C4⋊C4—941no—
186C4×C4⋊C4—941no—
187C43C2×D4711yescharacteristic
188#336—21no—
189#336—941no—
190#330—944no—
191C47#858011yescharacteristic, complemented, Sylow
192C22×C8—22no—
193C22×C8—942no—
194#125—472no—
195#125—472no—
196#125—941no—
197#125—941no—
198C2×C4⋊C4—471no—
199C2×C4⋊C4—471no—
200C2×C4⋊C4—471no—
201C2×C4⋊C4—471no—
202C2×C4⋊C4—941no—
203C2×C4⋊C4—941no—
204C2×C4⋊C4—941no—
205C2×C4⋊C4—941no—
206C2×C42—941no—
207C2×C42—941no—
208C2×C42C4×D4711yescharacteristic
209C2×C42C4×D4711yescharacteristic
210C2×C42D18811yescharacteristic
211C2×C42D18811yescharacteristic
212C2×C42C22⋊D4711yescharacteristic
213C2×C42C22⋊D4711yescharacteristic
214C2×C42C22×D4711yescharacteristic
215C4⋊C8—24no—
216C4⋊C8—944no—
217#97—22no—
218#97—22no—
219#97—942no—
220#97—942no—
221#95—941no—
222#95—941no—
223#95—941no—
224#95—941no—
225#95—941no—
226#95—941no—
227C22×C4—941no—
228C22×C4—941no—
229C22×C4—941no—
230C22×C4—941no—
231C22×C4(C2×D47)⋊C411yescharacteristic
232C22×C4(C2×D47)⋊C411yescharacteristic
233C22×C4(C2×D47)⋊C411yescharacteristic
234C22×C4(C2×D47)⋊C411yescharacteristic
235C22×C4C2×C4×D4711yescharacteristic
236C22×C4C2×D18811yescharacteristic
237C22×C4C2×C22⋊D4711yescharacteristic
238C2×C8—24no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—944no—
242C2×C8—1882no—
243C2×C8—1882no—
244C4⋊C4—472no—
245C4⋊C4—472no—
246C4⋊C4—941no—
247C4⋊C4—941no—
248C4⋊C4—942no—
249C4⋊C4—942no—
250C4⋊C4—942no—
251C4⋊C4—942no—
252C4⋊C4—1881no—
253C4⋊C4—1881no—
254C4⋊C4—1882no—
255C4⋊C4—1882no—
256C42—22no—
257C42—22no—
258C42—22no—
259C42—41no—
260C42—41no—
261C42—41no—
262C42—1882no—
263C42—1882no—
264C42D4×D4711yescharacteristic
265C42#1062535211yescharacteristic
266C42Q8×D4711yescharacteristic
267C42#1062535411yescharacteristic
268C23C2×(C2×D47)⋊C411yescharacteristic
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—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—942no—
285C2×C4—942no—
286C2×C4—1881no—
287C2×C4—1881no—
288C2×C4—1881no—
289C2×C4—1881no—
290C2×C4—1881no—
291C2×C4—1881no—
292C2×C4—1881no—
293C2×C4—1881no—
294C2×C4—1881no—
295C2×C4—1881no—
296C2×C4#1309394212yes—
297C2×C4#1309395012yes—
298C2×C4#1309395212yes—
299C2×C4C4⋊C4×D4711yescharacteristic
300C2×C4#1309398211yescharacteristic
301C2×C4#1309399511yescharacteristic
302C2×C4#1309399911yescharacteristic
303C2×C4#1309400011yescharacteristic
304C2×C4#1309400411yescharacteristic
305C8—44no—
306C8—1884no—
307C22#1568898011yescharacteristic
308C22C2×#1309394211yescharacteristic
309C22#1568910511yescharacteristic
310C22C2×#1309395011yescharacteristic
311C22C2×#1309395211yescharacteristic
312C22#1568913911yescharacteristic
313C22#1568914111yescharacteristic
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—3761no—
324C4—3761no—
325C4—1882no—
326C4—1882no—
327C4#1568886414yescomplemented
328C2C2×#1568886411yescharacteristic
329C2#2024199311yescharacteristic
330C2#2024199611yescharacteristic
331C2#2024202511yescharacteristic
332C2#2024338111yescharacteristic
333C2#2024340511yescharacteristic
334C2#2024340911yescharacteristic
subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1767C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1767D47
hypocenterC47#8580
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
156. C4×C47#330semidirect
191. C47#8580semidirect
327. C4#15688864semidirect

Maximal subgroups

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

subgroupindex
C4×#130940162
#202432412
C2×#156888642
#202412702
C47×#17672
#858047