Finite Group Databasebeta

← #26116874

Subgroups — #26116874

Order 12032.

632 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×#15689454C212yesmaximal
2#20249502C211yesmaximal, characteristic
3C2×#15688861C212yesmaximal
4#20241655C211yesmaximal, characteristic
5C47×#1280C211yesmaximal, characteristic
6C2×#13094003C2212yes—
7C22×C4⋊Dic47C2211yescharacteristic
8#15689454—24no—
9#15689454—24no—
10C2×#13093956—22no—
11C2×#13093949—22no—
12#15689055—22no—
13#15689044—22no—
14#15688983—22no—
15C2×C47⋊#95—22no—
16C2×C47⋊#95C2211yescharacteristic
17#15688861—24no—
18C2×C22⋊C8×C47C2212yes—
19C2×#95×C47C2211yescharacteristic
20C22×Dic94D412yes—
21C23×Dic47—21no—
22C23×Dic47—21no—
23#13094003—22no—
24#13094003—22no—
25#13094003—22no—
26#13094003—22no—
27C2×C4⋊Dic47—22no—
28C2×C4⋊Dic47—22no—
29C2×C4⋊Dic47—21no—
30C2×C4⋊Dic47—22no—
31C2×C4⋊Dic47—22no—
32C2×C4⋊Dic47D412yes—
33C2×C4⋊Dic47D412yes—
34C2×Dic47⋊C4—22no—
35C2×C22⋊Dic47—22no—
36#13093956—28no—
37#13093949—28no—
38C47⋊#95—24no—
39C47⋊#95—22no—
40C47⋊#95—44no—
41C23×C4×C47D412yes—
42C23×C4×C47C2311yescharacteristic
43C22×C8×C47—22no—
44C22⋊C8×C47—22no—
45C22⋊C8×C47D414yes—
46#95×C47—22no—
47C24×C47C2×D411yescharacteristic
48C22×C4×C47—22no—
49C22×C4×C47—22no—
50C22×C4×C47—42no—
51C22×C4×C47—42no—
52C22×C4×C47—42no—
53C22×C4×C47SD1614yes—
54C22×C4×C47C2×D412yes—
55C22×C4×C47C2×D411yescharacteristic
56C22×C4×C47C2×D412yes—
57C22×C4×C47#4111yescharacteristic
58C22×Dic47—22no—
59C22×Dic47—22no—
60C22×Dic47—22no—
61C22×Dic47—22no—
62C22×Dic47—41no—
63C22×Dic47—42no—
64C22×Dic47—41no—
65C22×Dic47—41no—
66C22×Dic47—41no—
67C22×Dic47—42no—
68C22×Dic47—42no—
69C22×Dic47—42no—
70C2×Dic94—22no—
71C2×Dic94—22no—
72C2×Dic94—44no—
73C2×C8×C47—24no—
74C2×C8×C47—44no—
75C22⋊Dic47—42no—
76C22⋊Dic47—42no—
77C4⋊Dic47—24no—
78C4⋊Dic47—22no—
79C4⋊Dic47—22no—
80C4⋊Dic47—42no—
81C4⋊Dic47—82no—
82C4⋊Dic47—82no—
83Dic47⋊C4—42no—
84Dic47⋊C4—42no—
85C23×C47—21no—
86C23×C47—21no—
87C23×C47—22no—
88C23×C47#12011yescharacteristic
89C23×C47#12111yescharacteristic
90C23×C47#12711yescharacteristic
91C23×C47C2×SD1612yes—
92C23×C47#13712yes—
93C2×C4×C47—24no—
94C2×C4×C47—24no—
95C2×C4×C47—42no—
96C2×C4×C47—41no—
97C2×C4×C47—41no—
98C2×C4×C47—42no—
99C2×C4×C47—42no—
100C2×C4×C47—44no—
101C2×C4×C47—82no—
102C2×C4×C47#12012yes—
103C2×C4×C47#12112yes—
104C2×Dic47—44no—
105C2×Dic47—42no—
106C2×Dic47—42no—
107C2×Dic47—42no—
108C2×Dic47—42no—
109C2×Dic47—42no—
110C2×Dic47—42no—
111C2×Dic47—44no—
112C2×Dic47—44no—
113C2×Dic47—82no—
114C2×Dic47—81no—
115C2×Dic47—82no—
116C2×Dic47—81no—
117C2×Dic47—81no—
118C2×Dic47—81no—
119Dic94—44no—
120Dic94—82no—
121C8×C47—44no—
122#9973—471nomaximal, Sylow
123C22×C47—22no—
124C22×C47—22no—
125C22×C47—22no—
126C22×C47—22no—
127C22×C47—21no—
128C22×C47—21no—
129C22×C47—21no—
130C22×C47—21no—
131C22×C47#39211yescharacteristic
132C22×C47#44812yes—
133C22×C47#45511yescharacteristic
134C22×C47#45611yescharacteristic
135C22×C47#45812yes—
136C22×C47#46112yes—
137C22×C47#49211yescharacteristic
138C22×C47#49711yescharacteristic
139C4×C47—22no—
140C4×C47—22no—
141C4×C47—44no—
142Dic47—82no—
143Dic47—82no—
144Dic47—82no—
145Dic47—82no—
146C2×#483—472no—
147#2659—471no—
148C2×#328—472no—
149#1445—471no—
150#1280D4711yescharacteristic
151C2×C47—21no—
152C2×C47—22no—
153C2×C47—21no—
154C2×C47#160812yes—
155C2×C47#161112yes—
156C2×C47#200711yescharacteristic
157C2×C47#201311yescharacteristic
158C2×C47#202211yescharacteristic
159C2×C22⋊Q8—472no—
160C22×C4⋊C4—471no—
161#483—944no—
162#483—944no—
163C2×#106—942no—
164C2×#103—942no—
165C2×C22⋊C8C2×D4712yes—
166#398—942no—
167#395—942no—
168#380—942no—
169C2×#95—471no—
170C2×#95—942no—
171C2×#95C2×D4711yescharacteristic
172#328—944no—
173C47#997311yescharacteristic, complemented, Sylow
174C22×Q8—472no—
175C23×C4—941no—
176C23×C4—941no—
177C23×C4D18812yes—
178C23×C4C22×D4711yescharacteristic
179C22×C8—22no—
180C22⋊Q8—942no—
181C22⋊Q8—942no—
182C22⋊Q8—942no—
183C22⋊Q8—942no—
184C2×C4⋊C4—472no—
185C2×C4⋊C4—472no—
186C2×C4⋊C4—942no—
187C2×C4⋊C4—942no—
188C2×C4⋊C4—942no—
189C2×C4⋊C4—942no—
190C2×C4⋊C4—942no—
191C2×C4⋊C4—941no—
192C2×C22⋊C4—942no—
193#106—948no—
194#103—948no—
195C22⋊C8—22no—
196C22⋊C8D18814yes—
197#95—22no—
198#95—944no—
199#95—942no—
200#95—1884no—
201C24C2×D18811yescharacteristic
202C2×Q8—942no—
203C2×Q8—942no—
204C2×Q8—1884no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—942no—
211C22×C4—942no—
212C22×C4—942no—
213C22×C4—942no—
214C22×C4—1881no—
215C22×C4—1882no—
216C22×C4—1881no—
217C22×C4—1881no—
218C22×C4—1881no—
219C22×C4—1882no—
220C22×C4—1882no—
221C22×C4—1882no—
222C22×C4#1062532514yes—
223C22×C4C2×D18812yes—
224C22×C4D4×D4712yes—
225C22×C4D4×D4711yescharacteristic
226C22×C4#1062535411yescharacteristic
227C2×C8—24no—
228C2×C8—44no—
229C4⋊C4—944no—
230C4⋊C4—942no—
231C4⋊C4—942no—
232C4⋊C4—3762no—
233C4⋊C4—3762no—
234C4⋊C4—1882no—
235C4⋊C4—1882no—
236C4⋊C4—1882no—
237C22⋊C4—1882no—
238C22⋊C4—1882no—
239C23—21no—
240C23—21no—
241C23—22no—
242C23#1309399411yescharacteristic
243C23#1309399911yescharacteristic
244C23#1309402111yescharacteristic
245C23C2×#1062532512yes—
246C23#1309405712yes—
247Q8—3762no—
248Q8—1884no—
249C2×C4—24no—
250C2×C4—24no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—44no—
257C2×C4—82no—
258C2×C4—3761no—
259C2×C4—3762no—
260C2×C4—3761no—
261C2×C4—3761no—
262C2×C4—3761no—
263C2×C4—3762no—
264C2×C4—1882no—
265C2×C4—1884no—
266C2×C4—1882no—
267C2×C4—1882no—
268C2×C4—1882no—
269C2×C4—1882no—
270C2×C4—1882no—
271C2×C4—1884no—
272C2×C4—1884no—
273C2×C4#1309399412yes—
274C2×C4#1309399912yes—
275C8—44no—
276C22—21no—
277C22—21no—
278C22—22no—
279C22—22no—
280C22—21no—
281C22—21no—
282C22—22no—
283C22—22no—
284C22#1568903311yescharacteristic
285C22#1568926412yes—
286C22#1568930311yescharacteristic
287C22#1568930811yescharacteristic
288C22#1568931412yes—
289C22#1568932912yes—
290C22#1568949611yescharacteristic
291C22#1568951711yescharacteristic
292C4—22no—
293C4—22no—
294C4—44no—
295C4—3762no—
296C4—3762no—
297C4—3762no—
298C4—3762no—
299C2—21no—
300C2—21no—
301C2—22no—
302C2#2024238112yes—
303C2#2024239812yes—
304C2#2024443711yescharacteristic
305C2#2024447311yescharacteristic
306C2#2024452011yescharacteristic
subgroupG/H
centerC23#13093994
commutator, cosocleC23×C4×C47C23
FrattiniC23×C4C22×D47
FittingC47×#1280C2
socleC23×C47#120
prime radicalC24×C47C2×D4
hypercenter#1280D47
hypocenterC47#9973
LCSG ▷ C23×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
173. C47#9973semidirect

Maximal subgroups

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

subgroupindex
C2×#156894542
#202495022
C2×#156888612
#202416552
C47×#12802
#997347