Finite Group Databasebeta

← #26104665

Subgroups — #26104665

Order 12032.

438 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251755C211yesmaximal, characteristic
2#20243134C211yesmaximal, characteristic, complemented
3#20241212C212yesmaximal, complemented
4#20241208C212yesmaximal
5C47×#1831C211yesmaximal, characteristic, complemented
6C2×#13094018—21no—
7C2×C4×C47⋊C8—21no—
8#15689025C411yescharacteristic
9#15689025C411yescharacteristic
10#15689025C2211yescharacteristic
11#15689021C411yescharacteristic
12#15689021C411yescharacteristic
13#15689021C2211yescharacteristic
14#15689014—21no—
15#15689014—21no—
16#15689014—21no—
17#15688878—21no—
18#15688878C2212yes—
19C2×C4⋊C8×C47—21no—
20C43×C47C2211yescharacteristic
21C47×#336—21no—
22C47×#336C2212yes—
23C22×D188C2×C411yescharacteristic
24C22×C47⋊C8—22no—
25#13094018—42no—
26#13094018—42no—
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×(C2×D47)⋊C4—21no—
34C2×(C2×D47)⋊C4—21no—
35C2×(C2×D47)⋊C4—21no—
36C2×(C2×D47)⋊C4—21no—
37C2×(C2×D47)⋊C4—21no—
38C2×(C2×D47)⋊C4—21no—
39C4×C47⋊C8—24no—
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—
52C23×D47—21no—
53C22×C4×C47C22⋊C411yescharacteristic
54C22×C4×C47C22⋊C411yescharacteristic
55C22×C4×C47C22⋊C411yescharacteristic
56C22×C4×C47C22⋊C411yescharacteristic
57C22×C4×C47C22×C411yescharacteristic
58C22×C4×C47C2×D411yescharacteristic
59C22×C4×C47C2×D411yescharacteristic
60C22×Dic47—21no—
61C22×Dic47—21no—
62C22×Dic47—21no—
63C2×D188—22no—
64C2×D188—41no—
65C2×D188—41no—
66C2×C8×C47—42no—
67C2×C8×C47—42no—
68C2×C8×C47—42no—
69C42×C47—22no—
70C42×C47—22no—
71C42×C47—22no—
72C42×C47—41no—
73C42×C47—41no—
74C42×C47—41no—
75C42×C47D812yes—
76C42×C47SD1612yes—
77(C2×D47)⋊C4—42no—
78(C2×D47)⋊C4—42no—
79(C2×D47)⋊C4—42no—
80(C2×D47)⋊C4—42no—
81(C2×D47)⋊C4—41no—
82(C2×D47)⋊C4—41no—
83(C2×D47)⋊C4—42no—
84C4⋊Dic47—22no—
85C4⋊Dic47—41no—
86C4⋊Dic47—41no—
87Dic47⋊C4—42no—
88Dic47⋊C4—42no—
89Dic47⋊C4—41no—
90Dic47⋊C4—41no—
91C2×C47⋊C8—24no—
92C2×C47⋊C8—42no—
93C2×C47⋊C8—42no—
94C23×C47C2×C22⋊C411yescharacteristic
95C22×D47—41no—
96C22×D47—41no—
97C22×D47—41no—
98C22×D47—41no—
99C22×D47—41no—
100C22×D47—41no—
101C22×D47—41no—
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—21no—
117C2×C4×C47#10212yes—
118C2×C4×C47#10212yes—
119C2×C4×C47#10412yes—
120C2×C4×C47#13112yes—
121C2×C4×C47C2×D811yescharacteristic
122C2×C4×C47C2×SD1611yescharacteristic
123C2×C4×C47#13512yes—
124C2×Dic47—41no—
125C2×Dic47—41no—
126C2×Dic47—41no—
127C2×Dic47—41no—
128C2×Dic47—41no—
129C2×Dic47—41no—
130C2×Dic47—41no—
131C2×Dic47—41no—
132C2×Dic47—41no—
133D188—82no—
134C8×C47—82no—
135C47⋊C8—44no—
136#7666—471nomaximal, Sylow
137C22×C47#40811yescharacteristic
138C22×C47#41011yescharacteristic
139C22×C47#41311yescharacteristic
140C22×C47C2×#10211yescharacteristic
141C22×C47#41611yescharacteristic
142C22×C47C2×#10411yescharacteristic
143C22×C47#42111yescharacteristic
144C2×D47—81no—
145C2×D47—81no—
146C2×D47—81no—
147C2×D47—81no—
148C2×D47—81no—
149C2×D47—81no—
150C2×D47—81no—
151C4×C47—22no—
152C4×C47—22no—
153C4×C47—22no—
154C4×C47—22no—
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—22no—
158C4×C47—41no—
159Dic47—81no—
160Dic47—81no—
161Dic47—81no—
162#2860—471no—
163#1831D4711yescharacteristic, complemented
164#1744—471no—
165#1271—472no—
166#1270—472no—
167C2×C47#147311yescharacteristic
168C2×C47#148211yescharacteristic
169C2×C47#149211yescharacteristic
170C2×C47#150011yescharacteristic
171C2×C47#151711yescharacteristic
172C2×C47#153211yescharacteristic
173C2×C47#154011yescharacteristic
174D47—161no—
175C2×#126—941no—
176C2×C4⋊C8—21no—
177C2×C4×C8—941no—
178#390—471no—
179#390—471no—
180#390—471no—
181#389—471no—
182#389—471no—
183#389—471no—
184#388—941no—
185#388—941no—
186#388—941no—
187C43C2×D4711yescharacteristic
188#336—21no—
189#336—472no—
190#336—941no—
191#336C2×D4712yes—
192C47#766611yescharacteristic, complemented, Sylow
193C22×D4—471no—
194C22×C8—22no—
195C22×C8—942no—
196#126—1882no—
197#126—1882no—
198C2×C4⋊C4—471no—
199C2×C4⋊C4—471no—
200C2×C4⋊C4—471no—
201C2×C4⋊C4—941no—
202C2×C4⋊C4—941no—
203C2×C4⋊C4—941no—
204C2×C22⋊C4—941no—
205C2×C22⋊C4—941no—
206C2×C22⋊C4—941no—
207C2×C22⋊C4—941no—
208C2×C22⋊C4—941no—
209C2×C22⋊C4—941no—
210C2×C42C4×D4711yescharacteristic
211C2×C42C4×D4711yescharacteristic
212C2×C42D18811yescharacteristic
213C2×C42D18811yescharacteristic
214C2×C42C22⋊D4711yescharacteristic
215C2×C42C22⋊D4711yescharacteristic
216C2×C42C22×D4711yescharacteristic
217C4⋊C8—42no—
218C4×C8—944no—
219#95—941no—
220#95—941no—
221#95—941no—
222C24—941no—
223C2×D4—942no—
224C2×D4—1881no—
225C2×D4—1881no—
226C22×C4—941no—
227C22×C4—941no—
228C22×C4—941no—
229C22×C4(C2×D47)⋊C411yescharacteristic
230C22×C4(C2×D47)⋊C411yescharacteristic
231C22×C4(C2×D47)⋊C411yescharacteristic
232C22×C4(C2×D47)⋊C411yescharacteristic
233C22×C4C2×C4×D4711yescharacteristic
234C22×C4C2×D18811yescharacteristic
235C22×C4C2×C22⋊D4711yescharacteristic
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—944no—
240C2×C8—1882no—
241C2×C8—1882no—
242C4⋊C4—942no—
243C4⋊C4—1881no—
244C4⋊C4—1881no—
245C4⋊C4—1882no—
246C4⋊C4—1882no—
247C4⋊C4—1881no—
248C4⋊C4—1881no—
249C22⋊C4—1882no—
250C22⋊C4—1882no—
251C22⋊C4—1882no—
252C22⋊C4—1882no—
253C22⋊C4—1881no—
254C22⋊C4—1881no—
255C22⋊C4—1882no—
256C42—22no—
257C42—22no—
258C42—22no—
259C42—41no—
260C42—41no—
261C42—41no—
262C42#1062533412yes—
263C42#1062533612yes—
264C23—1881no—
265C23—1881no—
266C23—1881no—
267C23—1881no—
268C23—1881no—
269C23—1881no—
270C23—1881no—
271C23C2×(C2×D47)⋊C411yescharacteristic
272D4—3762no—
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—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
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—1881no—
297C2×C4#1309394412yes—
298C2×C4#1309394412yes—
299C2×C4#1309395012yes—
300C2×C4#1309403212yes—
301C2×C4C2×#1062533411yescharacteristic
302C2×C4C2×#1062533611yescharacteristic
303C2×C4#1309404612yes—
304C8—82no—
305C8—1884no—
306C22—3761no—
307C22—3761no—
308C22—3761no—
309C22—3761no—
310C22—3761no—
311C22—3761no—
312C22—3761no—
313C22#1568909111yescharacteristic
314C22#1568909611yescharacteristic
315C22#1568910511yescharacteristic
316C22C2×#1309394411yescharacteristic
317C22#1568912011yescharacteristic
318C22C2×#1309395011yescharacteristic
319C22#1568914111yescharacteristic
320C4—21no—
321C4—21no—
322C4—22no—
323C4—22no—
324C4—22no—
325C4—22no—
326C4—22no—
327C4—41no—
328C4—3761no—
329C4—3761no—
330C4—3761no—
331C2—7521no—
332C2#2024175811yescharacteristic
333C2#2024179711yescharacteristic
334C2#2024183811yescharacteristic
335C2#2024187511yescharacteristic
336C2#2024194711yescharacteristic
337C2#2024200911yescharacteristic
338C2#2024203811yescharacteristic
subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1831C2
socleC23×C47C2×C22⋊C4
prime radicalC22×D188C2×C4
cosocleC2×C42×C47C23
hypercenter#1831D47
hypocenterC47#7666
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C43 ◁ #1831

Complements

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

NH ≅ G/Ntype
2. #20243134C2semidirect
3. #20241212C2semidirect
5. C47×#1831C2semidirect
163. #1831D47semidirect
192. C47#7666semidirect

Maximal subgroups

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

subgroupindex
#202517552
#202431342
#202412122
#202412082
C47×#18312
#766647