Finite Group Databasebeta

← #26119356

Subgroups — #26119356

Order 12032.

476 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 91 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#20251663C211yesmaximal, characteristic, complemented
2#20244213C212yesmaximal
3#20241270C212yesmaximal, complemented
4#20241269C211yesmaximal, characteristic, complemented
5C47×#1961C211yesmaximal, characteristic
6C2×#13093945—22no—
7C2×#13093945—22no—
8C2×#13093935C2212yes—
9#15689057—22no—
10#15689056—22no—
11#15689055—22no—
12#15688989C2212yes—
13C2×#127×C47C2211yescharacteristic
14C2×#102×C47—22no—
15C2×#97×C47C2211yescharacteristic
16C47×#382C2211yescharacteristic
17C22×C47⋊C8—22no—
18C2×C4⋊Dic47—22no—
19C2×C4⋊Dic47D412yes—
20C2×C4⋊Dic47D412yes—
21C2×Dic47⋊C4—22no—
22C2×Dic47⋊C4—22no—
23#13093945—44no—
24#13093945—44no—
25#13093935—22no—
26#13093935—22no—
27C47⋊#95—22no—
28C47⋊#95—22no—
29C47⋊#95—22no—
30C22×D4×C47—22no—
31C22×D4×C47—21no—
32C22×C8×C47—21no—
33#127×C47—21no—
34#127×C47—22no—
35#127×C47Q812yes—
36C2×C4⋊C4×C47D412yes—
37C2×C42×C47C2311yescharacteristic
38#102×C47—44no—
39#97×C47—22no—
40#95×C47—22no—
41C24×C47—41no—
42C2×D4×C47—24no—
43C2×D4×C47—22no—
44C2×D4×C47—42no—
45C2×D4×C47—42no—
46C2×D4×C47—42no—
47C2×D4×C47—42no—
48C2×D4×C47—42no—
49C2×D4×C47—42no—
50C2×D4×C47—42no—
51C2×D4×C47—41no—
52C22×C4×C47—22no—
53C22×C4×C47C2×D412yes—
54C22×C4×C47C2×D411yescharacteristic
55C22×Dic47—22no—
56C22×Dic47—22no—
57C2×C8×C47—22no—
58C2×C8×C47—41no—
59C2×C8×C47—41no—
60C4⋊C4×C47—42no—
61C42×C47C2×Q811yescharacteristic
62C42×C47#4111yescharacteristic
63C42×C47#4112yes—
64C4⋊Dic47—42no—
65C4⋊Dic47—42no—
66C4⋊Dic47—82no—
67Dic47⋊C4—82no—
68Dic47⋊C4—82no—
69C2×C47⋊C8—24no—
70C2×C47⋊C8—42no—
71C2×C47⋊C8—42no—
72C23×C47—42no—
73C23×C47—82no—
74C23×C47—81no—
75C23×C47—82no—
76C23×C47—81no—
77C23×C47#12011yescharacteristic
78D4×C47—44no—
79D4×C47—44no—
80D4×C47—44no—
81D4×C47—82no—
82D4×C47—82no—
83D4×C47—82no—
84C2×C4×C47—22no—
85C2×C4×C47—21no—
86C2×C4×C47—22no—
87C2×C4×C47—21no—
88C2×C4×C47—42no—
89C2×C4×C47—42no—
90C2×C4×C47—42no—
91C2×C4×C47C22⋊Q812yes—
92C2×C4×C47C22⋊Q811yescharacteristic
93C2×C4×C47#12412yes—
94C2×C4×C47#12411yescharacteristic
95C2×Dic47—42no—
96C2×Dic47—42no—
97C2×Dic47—42no—
98C2×Dic47—42no—
99C2×Dic47—42no—
100C2×Dic47—42no—
101C8×C47—42no—
102C47⋊C8—44no—
103#10360—471nomaximal, Sylow
104C22×C47—84no—
105C22×C47—82no—
106C22×C47—162no—
107C22×C47—161no—
108C22×C47—161no—
109C22×C47#39311yescharacteristic
110C22×C47#45312yes—
111C22×C47#45311yescharacteristic
112C22×C47#45412yes—
113C22×C47#45411yescharacteristic
114C4×C47—22no—
115C4×C47—21no—
116C4×C47—22no—
117C4×C47—21no—
118C4×C47—82no—
119Dic47—82no—
120Dic47—82no—
121#2845—471no—
122#1961—472no—
123#1961D4711yescharacteristic
124#1295—472no—
125#1295—471no—
126C2×C47—162no—
127C2×C47#165612yes—
128C2×C47#165611yescharacteristic
129C2×C47#165811yescharacteristic
130C2×C47#202712yes—
131C2×C47#202711yescharacteristic
132C2×#127C2×D4711yescharacteristic
133C2×#102—22no—
134C2×#102—942no—
135C2×#102—942no—
136C2×#97—472no—
137C2×#97C2×D4711yescharacteristic
138#398—942no—
139#398—942no—
140#398—942no—
141#382—472no—
142#382C2×D4711yescharacteristic
143C47#1036011yescharacteristic, complemented, Sylow
144C22×D4—22no—
145C22×D4—21no—
146C22×C8—21no—
147C22×C8—942no—
148#127—21no—
149#127—22no—
150#127Dic9412yes—
151C2×C4⋊C4—472no—
152C2×C4⋊C4—472no—
153C2×C4⋊C4—942no—
154C2×C4⋊C4—942no—
155C2×C4⋊C4—942no—
156C2×C4⋊C4C22⋊D4712yes—
157C2×C42C22×D4711yescharacteristic
158#102—44no—
159#102—1884no—
160#102—1884no—
161#97—22no—
162#97—942no—
163#97—942no—
164#95—22no—
165#95—942no—
166#95—942no—
167#95—942no—
168C24—41no—
169C2×D4—24no—
170C2×D4—22no—
171C2×D4—42no—
172C2×D4—42no—
173C2×D4—42no—
174C2×D4—42no—
175C2×D4—42no—
176C2×D4—42no—
177C2×D4—42no—
178C2×D4—41no—
179C22×C4—22no—
180C22×C4—942no—
181C22×C4—942no—
182C22×C4D4×D4712yes—
183C22×C4C2×C22⋊D4711yescharacteristic
184C2×C8—22no—
185C2×C8—41no—
186C2×C8—41no—
187C2×C8—944no—
188C2×C8—1882no—
189C2×C8—1882no—
190C4⋊C4—42no—
191C4⋊C4—3762no—
192C4⋊C4—3762no—
193C4⋊C4—3762no—
194C4⋊C4—1882no—
195C4⋊C4—1882no—
196C42C2×Dic9411yescharacteristic
197C42#1062535011yescharacteristic
198C42#1062535212yes—
199C23—42no—
200C23—82no—
201C23—81no—
202C23—82no—
203C23—81no—
204C23#1309399211yescharacteristic
205D4—44no—
206D4—44no—
207D4—44no—
208D4—82no—
209D4—82no—
210D4—82no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—1882no—
219C2×C4—1882no—
220C2×C4—1882no—
221C2×C4—1882no—
222C2×C4—1882no—
223C2×C4—1882no—
224C2×C4#1309400112yes—
225C2×C4#1309400311yescharacteristic
226C2×C4#1309401012yes—
227C2×C4#1309401111yescharacteristic
228C8—42no—
229C8—1884no—
230C22—84no—
231C22—82no—
232C22—161no—
233C22—162no—
234C22—161no—
235C22#1568903511yescharacteristic
236C22#1568928912yes—
237C22#1568929011yescharacteristic
238C22#1568929412yes—
239C22#1568929511yescharacteristic
240C4—22no—
241C4—22no—
242C4—21no—
243C4—21no—
244C4—82no—
245C4—3762no—
246C4—3762no—
247C2—162no—
248C2#2024267912yes—
249C2#2024268011yescharacteristic
250C2#2024268911yescharacteristic
251C2#2024454212yes—
252C2#2024454411yescharacteristic
subgroupG/H
centerC23#13093992
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1961C2
socleC23×C47#120
prime radicalC2×#127×C47C22
hypercenter#1961D47
hypocenterC47#10360
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1961

Complements

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

NH ≅ G/Ntype
1. #20251663C2semidirect
3. #20241270C2semidirect
4. #20241269C2semidirect
143. C47#10360semidirect

Maximal subgroups

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

subgroupindex
#202516632
#202442132
#202412702
#202412692
C47×#19612
#1036047