Finite Group Databasebeta

← #26316619

Subgroups — #26316619

Order 12032.

590 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#20249363C211yesmaximal, characteristic
2#20244884C212yesmaximal
3#20244879C212yesmaximal
4#20244358C211yesmaximal, characteristic
5#20244354C211yesmaximal, characteristic
6#20243980C212yesmaximal
7#20243959C212yesmaximal
8#20243547C211yesmaximal, characteristic
9#20243523C211yesmaximal, characteristic
10#20243245C211yesmaximal, characteristic
11C47×#2330C211yesmaximal, characteristic
12C2×#13093957C2212yes—
13C2×#13093957C2212yes—
14C2×C4⋊(C47⋊C8)C2211yescharacteristic
15C2×C4⋊(C47⋊C8)C2211yescharacteristic
16C2×#13093935C2211yescharacteristic
17C2×C4×C47⋊C8C2211yescharacteristic
18#15689065—22no—
19#15689057—22no—
20#15689021C2212yes—
21#15689021C2212yes—
22#15688993C2211yescharacteristic
23#15688989C2211yescharacteristic
24#15688885C2212yes—
25#15688885C2212yes—
26#15688885C2212yes—
27#15688885C2212yes—
28#15688885C2212yes—
29#15688885C2212yes—
30#15688878C2211yescharacteristic
31#15688878C2211yescharacteristic
32C2×#125×C47C2211yescharacteristic
33C47×#389—22no—
34C47×#389C2212yes—
35C47×#387—22no—
36C47×#384C2211yescharacteristic
37C4×C4⋊C4×C47C2212yes—
38C47×#376C2211yescharacteristic
39C22×C47⋊C8C2311yescharacteristic
40C22×C47⋊C8C2311yescharacteristic
41C22×C47⋊C8C2311yescharacteristic
42C22×C47⋊C8C2311yescharacteristic
43C2×C4⋊Dic47—22no—
44C2×C4⋊Dic47C2312yes—
45C2×C4⋊Dic47C2312yes—
46C2×Dic47⋊C4—22no—
47C2×Dic47⋊C4—22no—
48#13093957—24no—
49#13093957—24no—
50C4⋊(C47⋊C8)—22no—
51C4⋊(C47⋊C8)—22no—
52#13093935—22no—
53C4×C47⋊C8—22no—
54C47⋊#95—22no—
55C47⋊#95—22no—
56C47⋊#95—22no—
57#125×C47—22no—
58#125×C47Q814yes—
59C2×C4⋊C4×C47—22no—
60C2×C4⋊C4×C47—22no—
61C2×C4⋊C4×C47—22no—
62C2×C4⋊C4×C47C2312yes—
63C2×C4⋊C4×C47C2312yes—
64C2×C42×C47—22no—
65C2×C42×C47C2311yescharacteristic
66C2×C42×C47C2311yescharacteristic
67C2×C42×C47C2311yescharacteristic
68#95×C47—22no—
69#95×C47—22no—
70#95×C47D412yes—
71#95×C47D412yes—
72C22×C4×C47—22no—
73C22×C4×C47—22no—
74C22×C4×C47C2×D412yes—
75C22×C4×C47C2×D411yescharacteristic
76C22×C4×C47C2×D411yescharacteristic
77C22×C4×C47C2×D412yes—
78C22×C4×C47C2411yescharacteristic
79C22×Dic47—22no—
80C22×Dic47—22no—
81C4⋊C4×C47—28no—
82C4⋊C4×C47—22no—
83C4⋊C4×C47—22no—
84C4⋊C4×C47—22no—
85C4⋊C4×C47—82no—
86C4⋊C4×C47—82no—
87C4⋊C4×C47C2×Q814yes—
88C42×C47—21no—
89C42×C47—21no—
90C42×C47—21no—
91C42×C47—21no—
92C42×C47—82no—
93C42×C47C2×Q812yes—
94C42×C47#4112yes—
95C4⋊Dic47—22no—
96C4⋊Dic47—22no—
97C4⋊Dic47—22no—
98C4⋊Dic47—22no—
99C4⋊Dic47—82no—
100Dic47⋊C4—82no—
101Dic47⋊C4—82no—
102C2×C47⋊C8—21no—
103C2×C47⋊C8—21no—
104C2×C47⋊C8—21no—
105C2×C47⋊C8—21no—
106C2×C47⋊C8—21no—
107C2×C47⋊C8—21no—
108C2×C47⋊C8—21no—
109C2×C47⋊C8—21no—
110C2×C47⋊C8—21no—
111C2×C47⋊C8—21no—
112C2×C47⋊C8#4112yes—
113C2×C47⋊C8#4112yes—
114C23×C47C22×D411yescharacteristic
115C2×C4×C47—22no—
116C2×C4×C47—22no—
117C2×C4×C47—24no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—22no—
121C2×C4×C47—22no—
122C2×C4×C47—22no—
123C2×C4×C47—22no—
124C2×C4×C47—22no—
125C2×C4×C47—42no—
126C2×C4×C47—42no—
127C2×C4×C47—42no—
128C2×C4×C47—42no—
129C2×C4×C47—42no—
130C2×C4×C47C22⋊Q814yes—
131C2×C4×C47C22×Q811yescharacteristic
132C2×C4×C47C2×#4111yescharacteristic
133C2×C4×C47C2×#4111yescharacteristic
134C2×C4×C47C2×#4111yescharacteristic
135C2×C4×C472−1+411yescharacteristic
136C2×C4×C472−1+411yescharacteristic
137C2×Dic47—42no—
138C2×Dic47—42no—
139C2×Dic47—42no—
140C2×Dic47—42no—
141C2×Dic47—42no—
142C2×Dic47—42no—
143C47⋊C8—22no—
144C47⋊C8—22no—
145C47⋊C8—41no—
146C47⋊C8—41no—
147#29186—471nomaximal, Sylow
148C22×C47C2×C22⋊Q811yescharacteristic
149C22×C47#53211yescharacteristic
150C22×C47#53611yescharacteristic
151C22×C47#57612yes—
152C22×C47#57812yes—
153C4×C47—24no—
154C4×C47—44no—
155C4×C47—41no—
156C4×C47—41no—
157C4×C47—42no—
158C4×C47—82no—
159C4×C47#55211yescharacteristic
160C4×C47#55211yescharacteristic
161C4×C47#55711yescharacteristic
162C4×C47#55711yescharacteristic
163Dic47—82no—
164Dic47—82no—
165#2647—471no—
166#2330D4711yescharacteristic
167#2087—472no—
168#2086—472no—
169#1992—471no—
170#1991—471no—
171#1921—472no—
172#1918—472no—
173#1845—471no—
174#1836—471no—
175#1768—471no—
176C2×C47#256511yescharacteristic
177C2×C47#308312yes—
178C2×C47#317611yescharacteristic
179C2×C47#317711yescharacteristic
180C2×C47#324312yes—
181C2×#125C2×D4711yescharacteristic
182C2×#107—472no—
183C2×#107—472no—
184C2×C4⋊C8—471no—
185C2×C4⋊C8—471no—
186C2×#97—471no—
187C2×C4×C8—471no—
188#400—942no—
189#398—942no—
190#389—22no—
191#389—472no—
192#389—472no—
193#389C2×D4712yes—
194#387—22no—
195#384—471no—
196#384C2×D4711yescharacteristic
197#382—471no—
198C4×C4⋊C4C2×D4712yes—
199#376C2×D4711yescharacteristic
200#340—472no—
201#340—472no—
202#340—472no—
203#340—472no—
204#340—472no—
205#340—472no—
206#336—471no—
207#336—471no—
208C47#2918611yescharacteristic, complemented, Sylow
209C22×C8—471no—
210C22×C8—471no—
211C22×C8—471no—
212C22×C8—471no—
213#125—22no—
214#125Dic9414yes—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—472no—
219C2×C4⋊C4—472no—
220C2×C4⋊C4—942no—
221C2×C4⋊C4—942no—
222C2×C4⋊C4—942no—
223C2×C4⋊C4C22×D4712yes—
224C2×C4⋊C4C22×D4712yes—
225C2×C42—22no—
226C2×C42C22×D4711yescharacteristic
227C2×C42C22×D4711yescharacteristic
228C2×C42C22×D4711yescharacteristic
229#107—944no—
230#107—944no—
231C4⋊C8—942no—
232C4⋊C8—942no—
233#97—942no—
234C4×C8—942no—
235#95—22no—
236#95—22no—
237#95—942no—
238#95—942no—
239#95—942no—
240#95C22⋊D4712yes—
241#95C22⋊D4712yes—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—942no—
245C22×C4—942no—
246C22×C4C2×C22⋊D4711yescharacteristic
247C22×C4C2×C22⋊D4712yes—
248C22×C4C2×C22⋊D4711yescharacteristic
249C22×C4C2×C22⋊D4712yes—
250C22×C4C23×D4711yescharacteristic
251C2×C8—472no—
252C2×C8—472no—
253C2×C8—941no—
254C2×C8—941no—
255C2×C8—941no—
256C2×C8—941no—
257C2×C8—941no—
258C2×C8—941no—
259C2×C8—941no—
260C2×C8—941no—
261C2×C8—941no—
262C2×C8—941no—
263C4⋊C4—28no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—82no—
268C4⋊C4—82no—
269C4⋊C4—942no—
270C4⋊C4—942no—
271C4⋊C4—942no—
272C4⋊C4—942no—
273C4⋊C4—3762no—
274C4⋊C4—3762no—
275C4⋊C4—3762no—
276C4⋊C4C2×Dic9414yes—
277C42—21no—
278C42—21no—
279C42—21no—
280C42—21no—
281C42—82no—
282C42C2×Dic9412yes—
283C42#1062535012yes—
284C23C22×C22⋊D4711yescharacteristic
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—24no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—1882no—
301C2×C4—1882no—
302C2×C4—1882no—
303C2×C4—1882no—
304C2×C4—1882no—
305C2×C4—1882no—
306C2×C4#1309400314yes—
307C2×C4C22×Dic9411yescharacteristic
308C2×C4#41×D4711yescharacteristic
309C2×C4#41×D4711yescharacteristic
310C2×C4C2×#1062535011yescharacteristic
311C2×C4#1309407211yescharacteristic
312C2×C4#1309407211yescharacteristic
313C8—942no—
314C8—942no—
315C8—1881no—
316C8—1881no—
317C22C2×#1309400311yescharacteristic
318C22#1568966911yescharacteristic
319C22#1568969711yescharacteristic
320C22#1568992612yes—
321C22#1568993812yes—
322C4—24no—
323C4—44no—
324C4—41no—
325C4—41no—
326C4—42no—
327C4—82no—
328C4—3762no—
329C4—3762no—
330C4#1568981411yescharacteristic
331C4#1568981411yescharacteristic
332C4#1568984911yescharacteristic
333C4#1568984911yescharacteristic
334C2#2024857511yescharacteristic
335C2#2025323912yes—
336C2#2025403211yescharacteristic
337C2#2025404111yescharacteristic
338C2#2025467112yes—
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2330C2
socle, prime radicalC23×C47C22×D4
hypercenter#2330D47
hypocenterC47#29186
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ #376 ◁ #2330

Complements

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

NH ≅ G/Ntype
208. C47#29186semidirect

Maximal subgroups

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

subgroupindex
#202493632
#202448842
#202448792
#202443582
#202443542
#202439802
#202439592
#202435472
#202435232
#202432452
C47×#23302
#2918647