Finite Group Databasebeta

← #26119350

Subgroups — #26119350

Order 12032.

400 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 93 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#20244360C212yesmaximal
2#20244207C211yesmaximal, characteristic
3#20241269C211yesmaximal, characteristic
4#20241269C212yesmaximal
5C47×#2844C211yesmaximal, characteristic
6C2×#13094024C2211yescharacteristic
7C2×#13093947—21no—
8C2×#13093947—21no—
9C2×#13093935C2212yes—
10C2×#13093935C2211yescharacteristic
11#15688885—22no—
12#15688885—22no—
13C47×#400—21no—
14C47×#400—22no—
15C47×#395—21no—
16C47×#395—22no—
17C47×#382C2212yes—
18C47×#382C2211yescharacteristic
19C22×Dic94—21no—
20C22×C47⋊C8—21no—
21C22×C47⋊C8—22no—
22#13094024—22no—
23#13094024—21no—
24#13094024Q812yescomplemented
25C2×C4⋊Dic47—22no—
26#13093947—42no—
27#13093947—42no—
28#13093935—22no—
29#13093935—22no—
30#13093935—22no—
31C22×Q8×C47—21no—
32C2×C4⋊C4×C47—21no—
33C2×C4⋊C4×C47—22no—
34C2×C4⋊C4×C47D411yescharacteristic
35C2×C4⋊C4×C47D411yescharacteristic
36C2×C4⋊C4×C47D412yes—
37C2×C4⋊C4×C47D412yes—
38C2×C42×C47C2311yescharacteristic
39#95×C47—21no—
40#95×C47—22no—
41#95×C47—21no—
42#95×C47—22no—
43#95×C47—22no—
44#95×C47—22no—
45C2×Q8×C47—81no—
46C2×Q8×C47—82no—
47C22×C4×C47—21no—
48C22×C4×C47—22no—
49C22×C4×C47—21no—
50C22×C4×C47—22no—
51C22×C4×C47C2×D412yes—
52C22×C4×C47C2×D411yescharacteristic
53C22×Dic47—41no—
54C2×Dic94—22no—
55C2×Dic94—41no—
56C2×Dic94—41no—
57C2×Dic94—41no—
58C2×Dic94—41no—
59C2×Dic94—41no—
60C4⋊C4×C47—42no—
61C4⋊C4×C47—42no—
62C4⋊C4×C47—41no—
63C4⋊C4×C47—41no—
64C4⋊C4×C47—81no—
65C4⋊C4×C47—82no—
66C42×C47C2×Q811yescharacteristic
67C42×C47#4112yes—
68C42×C47#4111yescharacteristic
69C4⋊Dic47—24no—
70C4⋊Dic47—42no—
71C2×C47⋊C8—22no—
72C2×C47⋊C8—24no—
73C2×C47⋊C8—41no—
74C2×C47⋊C8—42no—
75C2×C47⋊C8—42no—
76C2×C47⋊C8—41no—
77C23×C47#12011yescharacteristic
78Q8×C47—84no—
79C2×C4×C47—21no—
80C2×C4×C47—21no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—41no—
84C2×C4×C47—41no—
85C2×C4×C47—42no—
86C2×C4×C47—42no—
87C2×C4×C47—42no—
88C2×C4×C47—42no—
89C2×C4×C47—42no—
90C2×C4×C47—42no—
91C2×C4×C47—42no—
92C2×C4×C47—42no—
93C2×C4×C47C22⋊Q812yes—
94C2×C4×C47C22⋊Q811yescharacteristic
95C2×C4×C47#12412yes—
96C2×C4×C47#12411yescharacteristic
97C2×Dic47—42no—
98C2×Dic47—81no—
99C2×Dic47—81no—
100Dic94—42no—
101Dic94—42no—
102Dic94—81no—
103Dic94—81no—
104C47⋊C8—42no—
105C47⋊C8—44no—
106#10359—471nomaximal, Sylow
107C22×C47#39311yescharacteristic
108C22×C47#45311yescharacteristic
109C22×C47#45411yescharacteristic
110C22×C47#45512yes—
111C22×C47#45612yes—
112C4×C47—21no—
113C4×C47—21no—
114C4×C47—22no—
115C4×C47—22no—
116C4×C47—81no—
117C4×C47—82no—
118C4×C47—81no—
119C4×C47—82no—
120Dic47—82no—
121#2844D4711yescharacteristic
122#1993—472no—
123#1960—471no—
124#1295—471no—
125#1295—472no—
126C2×C47#165911yescharacteristic
127C2×C47#166011yescharacteristic
128C2×C47#166412yes—
129C2×C47#202711yescharacteristic
130C2×C47#202812yes—
131C2×C4⋊Q8—471no—
132C2×#103—941no—
133C2×#103—941no—
134C2×#97—471no—
135C2×#97—472no—
136#400—22no—
137#400—21no—
138#395—22no—
139#395—21no—
140#382C2×D4711yescharacteristic
141#382C2×D4712yes—
142#340—942no—
143#340—942no—
144C47#1035911yescharacteristic, complemented, Sylow
145C22×Q8—21no—
146C22×Q8—941no—
147C22×C8—942no—
148C22×C8—941no—
149C4⋊Q8—472no—
150C4⋊Q8—942no—
151C4⋊Q8—941no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—942no—
155C2×C4⋊C4C22⋊D4712yes—
156C2×C4⋊C4C22⋊D4712yes—
157C2×C4⋊C4C22⋊D4711yescharacteristic
158C2×C4⋊C4C22⋊D4711yescharacteristic
159C2×C42C22×D4711yescharacteristic
160#103—1882no—
161#103—1882no—
162#97—942no—
163#97—942no—
164#97—942no—
165#95—22no—
166#95—21no—
167#95—21no—
168#95—22no—
169#95—22no—
170#95—22no—
171C2×Q8—81no—
172C2×Q8—82no—
173C2×Q8—942no—
174C2×Q8—1881no—
175C2×Q8—1881no—
176C2×Q8—1881no—
177C2×Q8—1881no—
178C2×Q8—1881no—
179C22×C4—21no—
180C22×C4—22no—
181C22×C4—21no—
182C22×C4—22no—
183C22×C4—1881no—
184C22×C4C2×C22⋊D4712yes—
185C22×C4C2×C22⋊D4711yescharacteristic
186C2×C8—942no—
187C2×C8—944no—
188C2×C8—1881no—
189C2×C8—1882no—
190C2×C8—1882no—
191C2×C8—1881no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—81no—
197C4⋊C4—82no—
198C4⋊C4—944no—
199C4⋊C4—1882no—
200C42Q8×D4711yescharacteristic
201C42#1062535412yes—
202C42#1062535411yescharacteristic
203C23#1309399311yescharacteristic
204Q8—84no—
205Q8—3761no—
206Q8—3761no—
207Q8—1882no—
208Q8—1882no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—3761no—
224C2×C4—3761no—
225C2×C4—1882no—
226C2×C4#1309400012yes—
227C2×C4#1309400011yescharacteristic
228C2×C4#1309401312yes—
229C2×C4#1309401311yescharacteristic
230C8—1882no—
231C8—1884no—
232C22#1568903411yescharacteristic
233C22#1568929111yescharacteristic
234C22#1568929611yescharacteristic
235C22#1568930112yes—
236C22#1568930612yes—
237C4—21no—
238C4—21no—
239C4—22no—
240C4—22no—
241C4—81no—
242C4—82no—
243C4—81no—
244C4—82no—
245C4—3762no—
246C2#2024269411yescharacteristic
247C2#2024269911yescharacteristic
248C2#2024272212yes—
249C2#2024454111yescharacteristic
250C2#2024454612yes—
subgroupG/H
centerC23#13093993
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#2844C2
socle, prime radicalC23×C47#120
hypercenter#2844D47
hypocenterC47#10359
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2844

Complements

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

NH ≅ G/Ntype
24. #13094024Q8semidirect
144. C47#10359semidirect

Maximal subgroups

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

subgroupindex
#202443602
#202442072
#202412692
C47×#28442
#1035947