Finite Group Databasebeta

← #26119352

Subgroups — #26119352

Order 12032.

400 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 89 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#20251660C211yesmaximal, characteristic
2#20244361C212yesmaximal
3#20244207C211yesmaximal, characteristic
4#20241270C212yesmaximal
5C47×#1295C211yesmaximal, characteristic
6C2×#13094024C2211yescharacteristic
7C2×#13093947—21no—
8C2×#13093947—21no—
9C2×#13093935C2211yescharacteristic
10#15689065—22no—
11#15689062—21no—
12#15689044—22no—
13#15689043—21no—
14#15688989C2212yes—
15#15688886—22no—
16#15688886—22no—
17C2×#97×C47C2212yes—
18C47×#382C2211yescharacteristic
19C22×Dic94—21no—
20C22×Dic94—21no—
21C22×C47⋊C8—21no—
22#13094024—22no—
23#13094024—21no—
24#13094024Q812yescomplemented
25C2×C4⋊Dic47—22no—
26C2×C4⋊Dic47—21no—
27C2×C4⋊Dic47D412yes—
28C2×C4⋊Dic47D412yes—
29C2×Dic47⋊C4—22no—
30#13093947—42no—
31#13093947—42no—
32#13093935—22no—
33C47⋊#95—21no—
34C47⋊#95—22no—
35C47⋊#95—21no—
36C47⋊#95—22no—
37C47⋊#95—22no—
38C22×C8×C47—22no—
39C2×C4⋊C4×C47D411yescharacteristic
40C2×C4⋊C4×C47D411yescharacteristic
41C2×C42×C47C2311yescharacteristic
42#97×C47—22no—
43#97×C47—22no—
44#95×C47—22no—
45C22×C4×C47—21no—
46C22×C4×C47—21no—
47C22×C4×C47C2×D411yescharacteristic
48C22×C4×C47C2×D412yes—
49C22×Dic47—22no—
50C22×Dic47—22no—
51C22×Dic47—41no—
52C2×Dic94—22no—
53C2×Dic94—41no—
54C2×Dic94—41no—
55C2×Dic94—41no—
56C2×Dic94—41no—
57C2×Dic94—41no—
58C2×Dic94—81no—
59C2×Dic94—82no—
60C2×C8×C47—24no—
61C2×C8×C47—42no—
62C2×C8×C47—42no—
63C4⋊C4×C47—41no—
64C4⋊C4×C47—41no—
65C42×C47C2×Q811yescharacteristic
66C42×C47#4112yes—
67C42×C47#4111yescharacteristic
68C4⋊Dic47—24no—
69C4⋊Dic47—42no—
70C4⋊Dic47—42no—
71C4⋊Dic47—42no—
72C4⋊Dic47—81no—
73Dic47⋊C4—82no—
74C2×C47⋊C8—22no—
75C2×C47⋊C8—41no—
76C2×C47⋊C8—41no—
77C23×C47#12011yescharacteristic
78C2×C4×C47—21no—
79C2×C4×C47—21no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—41no—
83C2×C4×C47—41no—
84C2×C4×C47—42no—
85C2×C4×C47—42no—
86C2×C4×C47C22⋊Q812yes—
87C2×C4×C47C22⋊Q811yescharacteristic
88C2×C4×C47#12412yes—
89C2×C4×C47#12411yescharacteristic
90C2×Dic47—42no—
91C2×Dic47—42no—
92C2×Dic47—42no—
93C2×Dic47—42no—
94C2×Dic47—42no—
95C2×Dic47—42no—
96C2×Dic47—42no—
97C2×Dic47—81no—
98C2×Dic47—81no—
99Dic94—42no—
100Dic94—42no—
101Dic94—81no—
102Dic94—81no—
103Dic94—84no—
104C8×C47—44no—
105C47⋊C8—42no—
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—81no—
118Dic47—82no—
119Dic47—82no—
120Dic47—82no—
121#2844—471no—
122#1993—472no—
123#1960—471no—
124#1295—472no—
125#1295D4711yescharacteristic
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×#97C2×D4712yes—
136#400—942no—
137#400—941no—
138#395—942no—
139#395—941no—
140#382—472no—
141#382C2×D4711yescharacteristic
142#340—942no—
143#340—942no—
144C47#1035911yescharacteristic, complemented, Sylow
145C22×Q8—941no—
146C22×Q8—941no—
147C22×C8—22no—
148C22×C8—941no—
149C4⋊Q8—472no—
150C4⋊Q8—942no—
151C4⋊Q8—941no—
152C2×C4⋊C4—472no—
153C2×C4⋊C4—472no—
154C2×C4⋊C4—942no—
155C2×C4⋊C4—942no—
156C2×C4⋊C4—941no—
157C2×C4⋊C4D18811yescharacteristic
158C2×C4⋊C4D18811yescharacteristic
159C2×C42C22×D4711yescharacteristic
160#103—1882no—
161#103—1882no—
162#97—22no—
163#97—22no—
164#97—942no—
165#95—22no—
166#95—942no—
167#95—941no—
168#95—941no—
169#95—942no—
170#95—942no—
171C2×Q8—942no—
172C2×Q8—3761no—
173C2×Q8—3762no—
174C2×Q8—1881no—
175C2×Q8—1881no—
176C2×Q8—1881no—
177C2×Q8—1881no—
178C2×Q8—1881no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—942no—
182C22×C4—942no—
183C22×C4—1881no—
184C22×C4C2×D18811yescharacteristic
185C22×C4D4×D4712yes—
186C2×C8—24no—
187C2×C8—42no—
188C2×C8—42no—
189C2×C8—942no—
190C2×C8—1881no—
191C2×C8—1881no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—944no—
195C4⋊C4—3762no—
196C4⋊C4—3761no—
197C4⋊C4—1882no—
198C4⋊C4—1882no—
199C4⋊C4—1882no—
200C42#1062535012yes—
201C42#1062535211yescharacteristic
202C42Q8×D4711yescharacteristic
203C23#1309399411yescharacteristic
204Q8—3761no—
205Q8—3761no—
206Q8—3764no—
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—3761no—
218C2×C4—3761no—
219C2×C4—1882no—
220C2×C4—1882no—
221C2×C4—1882no—
222C2×C4—1882no—
223C2×C4—1882no—
224C2×C4—1882no—
225C2×C4—1882no—
226C2×C4#1309400212yes—
227C2×C4#1309400411yescharacteristic
228C2×C4#1309401012yes—
229C2×C4#1309401211yescharacteristic
230C8—44no—
231C8—1882no—
232C22#1568903611yescharacteristic
233C22#1568929311yescharacteristic
234C22#1568929811yescharacteristic
235C22#1568930212yes—
236C22#1568930712yes—
237C4—21no—
238C4—21no—
239C4—22no—
240C4—22no—
241C4—81no—
242C4—81no—
243C4—3762no—
244C4—3762no—
245C4—3762no—
246C2#2024269511yescharacteristic
247C2#2024270011yescharacteristic
248C2#2024272312yes—
249C2#2024454511yescharacteristic
250C2#2024454812yes—
subgroupG/H
centerC23#13093994
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1295C2
socle, prime radicalC23×C47#120
hypercenter#1295D47
hypocenterC47#10359
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

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
#202516602
#202443612
#202442072
#202412702
C47×#12952
#1035947