Finite Group Databasebeta

← #26120308

Subgroups — #26120308

Order 12032.

374 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20254541C211yesmaximal, characteristic
2#20244377C211yesmaximal, characteristic
3#20244335C211yesmaximal, characteristic
4#20244332C211yesmaximal, characteristic
5#20242076C211yesmaximal, characteristic
6#20241290C211yesmaximal, characteristic
7C47×#1565C211yesmaximal, characteristic
8#15689680C2211yescharacteristic
9C2×#13094024C2211yescharacteristic
10#15689528—21no—
11#15689474—21no—
12#15689459—22no—
13#15689419—21no—
14#15689419—21no—
15#15689147C2211yescharacteristic
16C4×C4⋊Dic47C2211yescharacteristic
17#15688891—21no—
18#15688891—21no—
19#15688886—22no—
20#15688884—21no—
21#15688884—21no—
22#15688871—21no—
23#15688870—21no—
24C47×#431C2211yescharacteristic
25C2×C4⋊C8×C47C2211yescharacteristic
26C4×M16×C47C2211yescharacteristic
27C47×#335—21no—
28C47×#334—21no—
29C22×Dic94—21no—
30C2×#10625329—21no—
31#13094024—21no—
32#13094024—21no—
33#13094024—21no—
34#13094024—21no—
35#13094024D411yescharacteristic
36#13094024D411yescharacteristic
37#13094016—21no—
38#13094003—21no—
39#13094003—21no—
40C4×Dic94—21no—
41C4×Dic94—21no—
42#13093983—21no—
43C2×C4⋊Dic47—21no—
44C2×C4⋊Dic47—21no—
45C2×C4⋊Dic47D412yes—
46C2×C4×Dic47—21no—
47#13093958—22no—
48#13093958—22no—
49C4⋊(C47⋊C8)—21no—
50C4⋊(C47⋊C8)—21no—
51#13093949—22no—
52#13093949—22no—
53C47⋊#95—21no—
54C2×M16×C47D411yescharacteristic
55C2×M16×C47D411yescharacteristic
56C22×C8×C47—21no—
57C2×C42×C47C2311yescharacteristic
58C4⋊C8×C47—21no—
59C4⋊C8×C47—21no—
60C4⋊C8×C47D411yescharacteristic
61C4⋊C8×C47D411yescharacteristic
62C22⋊C8×C47—21no—
63#97×C47—21no—
64C4×C8×C47—21no—
65C4×C8×C47—21no—
66C22×C4×C47C2×D411yescharacteristic
67C22×C4×C47C2×D411yescharacteristic
68C22×C4×C47#4111yescharacteristic
69C22×Dic47—22no—
70C22×Dic47—41no—
71C2×Dic94—21no—
72C2×Dic94—21no—
73C2×Dic94—41no—
74C2×Dic94—41no—
75C2×Dic94—82no—
76M16×C47—21no—
77M16×C47—21no—
78M16×C47—21no—
79M16×C47Q1612yes—
80C2×C8×C47—21no—
81C2×C8×C47—21no—
82C2×C8×C47—21no—
83C2×C8×C47—21no—
84C2×C8×C47—42no—
85C2×C8×C47—41no—
86C42×C47C2×D411yescharacteristic
87C42×C47C2×D411yescharacteristic
88C42×C47#4111yescharacteristic
89C42×C47#4111yescharacteristic
90C22⋊Dic47—41no—
91C4⋊Dic47—22no—
92C4⋊Dic47—22no—
93C4⋊Dic47—21no—
94C4⋊Dic47—21no—
95C4⋊Dic47—21no—
96C4⋊Dic47—22no—
97C4⋊Dic47—21no—
98C4⋊Dic47—41no—
99C4⋊Dic47—41no—
100C4⋊Dic47—41no—
101Dic47⋊C4—41no—
102Dic47⋊C4—41no—
103C4×Dic47—41no—
104C4×Dic47—41no—
105C4×Dic47—41no—
106#10625329—41no—
107#10625329—41no—
108C2×C47⋊C8—41no—
109C23×C47#12111yescharacteristic
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—41no—
113C2×C4×C47#12011yescharacteristic
114C2×C4×C47#12111yescharacteristic
115C2×C4×C47#12111yescharacteristic
116C2×C4×C47#12311yescharacteristic
117C2×C4×C47#12311yescharacteristic
118C2×C4×C47#12411yescharacteristic
119C2×C4×C47C2×Q1611yescharacteristic
120C2×C4×C47#13511yescharacteristic
121C2×C4×C47#13711yescharacteristic
122C2×C4×C47#13711yescharacteristic
123C2×Dic47—42no—
124C2×Dic47—41no—
125C2×Dic47—41no—
126C2×Dic47—42no—
127C2×Dic47—81no—
128C2×Dic47—81no—
129C2×Dic47—82no—
130Dic94—41no—
131Dic94—41no—
132Dic94—82no—
133Dic94—82no—
134Dic94—81no—
135C8×C47—22no—
136C8×C47—41no—
137C8×C47—41no—
138C8×C47—41no—
139C8×C47—81no—
140C47⋊C8—81no—
141#10506—471nomaximal, Sylow
142C22×C47—21no—
143C22×C47—21no—
144C22×C47#39411yescharacteristic
145C22×C47#46211yescharacteristic
146C22×C47#46411yescharacteristic
147C4×C47—21no—
148C4×C47—21no—
149C4×C47—21no—
150C4×C47#45411yescharacteristic
151C4×C47#45611yescharacteristic
152C4×C47#46211yescharacteristic
153C4×C47#46411yescharacteristic
154C4×C47#46711yescharacteristic
155C4×C47#47011yescharacteristic
156Dic47—82no—
157Dic47—82no—
158Dic47—81no—
159Dic47—81no—
160#3230—471no—
161#1997—471no—
162#1987—471no—
163#1986—471no—
164#1565D4711yescharacteristic
165#1550—471no—
166#1303—471no—
167C2×C47—21no—
168C2×C47—21no—
169C2×C47#203811yescharacteristic
170C2×C47#204811yescharacteristic
171C2×C47#205611yescharacteristic
172#533—471no—
173C2×C4⋊Q8—471no—
174#500—941no—
175#487—941no—
176#484—942no—
177#477—941no—
178#477—941no—
179#431C2×D4711yescharacteristic
180#423—471no—
181C2×C4⋊C8C2×D4711yescharacteristic
182C4×M16C2×D4711yescharacteristic
183C4×C4⋊C4—471no—
184#343—941no—
185#343—941no—
186#340—942no—
187#339—941no—
188#339—941no—
189#335—21no—
190#334—21no—
191#333—941no—
192#332—941no—
193C47#1050611yescharacteristic, complemented, Sylow
194C22×Q8—941no—
195C2×M16—941no—
196C2×M16D18811yescharacteristic
197C2×M16D18811yescharacteristic
198C22×C8—21no—
199C4⋊Q8—471no—
200C4⋊Q8—471no—
201C4⋊Q8—941no—
202C4⋊Q8—941no—
203C4⋊Q8—941no—
204C4⋊Q8—941no—
205#125—941no—
206C22⋊Q8—941no—
207C22⋊Q8—941no—
208C4×Q8—941no—
209C4×Q8—941no—
210#117—941no—
211C2×C4⋊C4—472no—
212C2×C4⋊C4—941no—
213C2×C4⋊C4—941no—
214C2×C42—941no—
215C2×C42C22×D4711yescharacteristic
216#107—942no—
217#107—942no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—941no—
221C4⋊C8—941no—
222C4⋊C8C22⋊D4711yescharacteristic
223C4⋊C8C22⋊D4711yescharacteristic
224#103—942no—
225#103—942no—
226C22⋊C8—21no—
227#97—21no—
228C4×C8—21no—
229C4×C8—21no—
230#95—941no—
231C2×Q8—941no—
232C2×Q8—941no—
233C2×Q8—3762no—
234C2×Q8—1881no—
235C2×Q8—1881no—
236C22×C4—942no—
237C22×C4—1881no—
238C22×C4C2×D18811yescharacteristic
239C22×C4D4×D4711yescharacteristic
240C22×C4#1062535411yescharacteristic
241M16—21no—
242M16—21no—
243M16—21no—
244M16—1881no—
245M16—1881no—
246M16Dic18812yes—
247C2×C8—21no—
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—42no—
252C2×C8—41no—
253C2×C8—1881no—
254C4⋊C4—942no—
255C4⋊C4—942no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4—942no—
260C4⋊C4—941no—
261C4⋊C4—1881no—
262C4⋊C4—1881no—
263C4⋊C4—1881no—
264C4⋊C4—1881no—
265C4⋊C4—1881no—
266C22⋊C4—1881no—
267C42—1881no—
268C42—1881no—
269C42—1881no—
270C42#1062535011yescharacteristic
271C42D4×D4711yescharacteristic
272C42#1062535411yescharacteristic
273C42C2×C22⋊D4711yescharacteristic
274C23#1309399911yescharacteristic
275Q8—3761no—
276Q8—3762no—
277Q8—3762no—
278Q8—1881no—
279Q8—1881no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—41no—
283C2×C4—3761no—
284C2×C4—3761no—
285C2×C4—3762no—
286C2×C4—1882no—
287C2×C4—1881no—
288C2×C4—1881no—
289C2×C4—1882no—
290C2×C4#1309399211yescharacteristic
291C2×C4#1309399811yescharacteristic
292C2×C4#1309399911yescharacteristic
293C2×C4#1309400911yescharacteristic
294C2×C4#1309400911yescharacteristic
295C2×C4#1309401311yescharacteristic
296C2×C4C2×Dic18811yescharacteristic
297C2×C4#1309404611yescharacteristic
298C2×C4#1309405711yescharacteristic
299C2×C4#1309405711yescharacteristic
300C8—22no—
301C8—41no—
302C8—41no—
303C8—41no—
304C8—81no—
305C8—3761no—
306C22—21no—
307C22—21no—
308C22#1568904011yescharacteristic
309C22#1568933411yescharacteristic
310C22#1568934611yescharacteristic
311C4—21no—
312C4—21no—
313C4—21no—
314C4—3762no—
315C4—3761no—
316C4—3762no—
317C4—3761no—
318C4#1568929411yescharacteristic
319C4#1568930411yescharacteristic
320C4#1568933411yescharacteristic
321C4#1568934611yescharacteristic
322C4#1568936411yescharacteristic
323C4#1568938111yescharacteristic
324C2—21no—
325C2—21no—
326C2#2024460711yescharacteristic
327C2#2024466311yescharacteristic
328C2#2024471111yescharacteristic
subgroupG/H
centerC22#15689040
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1565C2
socleC22×C47#394
prime radicalC23×C47#121
hypercenter#1565D47
hypocenterC47#10506
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
193. C47#10506semidirect

Maximal subgroups

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

subgroupindex
#202545412
#202443772
#202443352
#202443322
#202420762
#202412902
C47×#15652
#1050647