Finite Group Databasebeta

← #26119360

Subgroups — #26119360

Order 12032.

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

normal subgroups only

This group has 392 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#20251663C211yesmaximal, characteristic
2#20244361C212yesmaximal
3#20244207C211yesmaximal, characteristic
4#20241270C212yesmaximal
5C47×#1295C211yesmaximal, characteristic
6C2×#13094024C2211yescharacteristic
7C2×#13093947—22no—
8C2×#13093935C2211yescharacteristic
9#15689057—22no—
10#15689056—22no—
11#15689055—22no—
12#15688989C2212yes—
13#15688886—22no—
14#15688886—22no—
15C2×#97×C47C2212yes—
16C47×#382C2211yescharacteristic
17C22×Dic94—21no—
18C22×C47⋊C8—21no—
19#13094024—22no—
20#13094024—21no—
21#13094024Q812yes—
22C2×C4⋊Dic47—22no—
23C2×C4⋊Dic47—22no—
24C2×C4⋊Dic47D412yes—
25C2×C4⋊Dic47D412yes—
26C2×Dic47⋊C4—22no—
27C2×Dic47⋊C4—22no—
28#13093947—44no—
29#13093935—22no—
30C47⋊#95—22no—
31C47⋊#95—22no—
32C47⋊#95—22no—
33C22×C8×C47—22no—
34C2×C4⋊C4×C47D412yes—
35C2×C42×C47C2311yescharacteristic
36#97×C47—22no—
37#97×C47—22no—
38#95×C47—22no—
39C22×C4×C47—22no—
40C22×C4×C47C2×D411yescharacteristic
41C22×C4×C47C2×D412yes—
42C22×Dic47—22no—
43C22×Dic47—22no—
44C22×Dic47—41no—
45C2×Dic94—22no—
46C2×Dic94—42no—
47C2×Dic94—42no—
48C2×Dic94—41no—
49C2×C8×C47—24no—
50C2×C8×C47—42no—
51C2×C8×C47—42no—
52C4⋊C4×C47—42no—
53C42×C47C2×Q811yescharacteristic
54C42×C47#4112yes—
55C42×C47#4111yescharacteristic
56C4⋊Dic47—24no—
57C4⋊Dic47—42no—
58C4⋊Dic47—42no—
59C4⋊Dic47—42no—
60C4⋊Dic47—82no—
61Dic47⋊C4—82no—
62Dic47⋊C4—82no—
63C2×C47⋊C8—22no—
64C2×C47⋊C8—41no—
65C2×C47⋊C8—41no—
66C23×C47#12011yescharacteristic
67C2×C4×C47—21no—
68C2×C4×C47—21no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—42no—
72C2×C4×C47—42no—
73C2×C4×C47—42no—
74C2×C4×C47C22⋊Q812yes—
75C2×C4×C47C22⋊Q811yescharacteristic
76C2×C4×C47#12412yes—
77C2×C4×C47#12411yescharacteristic
78C2×Dic47—42no—
79C2×Dic47—42no—
80C2×Dic47—42no—
81C2×Dic47—42no—
82C2×Dic47—42no—
83C2×Dic47—42no—
84C2×Dic47—42no—
85C2×Dic47—81no—
86C2×Dic47—81no—
87Dic94—44no—
88Dic94—82no—
89C8×C47—44no—
90C47⋊C8—42no—
91#10361—471nomaximal, Sylow
92C22×C47#39311yescharacteristic
93C22×C47#45311yescharacteristic
94C22×C47#45411yescharacteristic
95C22×C47#45512yes—
96C22×C47#45612yes—
97C4×C47—21no—
98C4×C47—21no—
99C4×C47—22no—
100C4×C47—22no—
101C4×C47—82no—
102Dic47—82no—
103Dic47—82no—
104Dic47—82no—
105#2845—471no—
106#1993—472no—
107#1960—471no—
108#1295—472no—
109#1295D4711yescharacteristic
110C2×C47#166112yes—
111C2×C47#166211yescharacteristic
112C2×C47#166311yescharacteristic
113C2×C47#202711yescharacteristic
114C2×C47#202812yes—
115C2×C4⋊Q8—471no—
116C2×#103—942no—
117C2×#97—471no—
118C2×#97C2×D4712yes—
119#398—942no—
120#398—942no—
121#398—942no—
122#382—472no—
123#382C2×D4711yescharacteristic
124#340—942no—
125#340—942no—
126C47#1036111yescharacteristic, complemented, Sylow
127C22×Q8—941no—
128C22×C8—22no—
129C22×C8—941no—
130C4⋊Q8—472no—
131C4⋊Q8—942no—
132C4⋊Q8—941no—
133C2×C4⋊C4—472no—
134C2×C4⋊C4—472no—
135C2×C4⋊C4—942no—
136C2×C4⋊C4—942no—
137C2×C4⋊C4—942no—
138C2×C4⋊C4—942no—
139C2×C4⋊C4D18812yes—
140C2×C42C22×D4711yescharacteristic
141#103—1884no—
142#97—22no—
143#97—22no—
144#97—942no—
145#95—22no—
146#95—942no—
147#95—942no—
148#95—942no—
149C2×Q8—942no—
150C2×Q8—1882no—
151C2×Q8—1882no—
152C2×Q8—1881no—
153C22×C4—22no—
154C22×C4—942no—
155C22×C4—942no—
156C22×C4—1881no—
157C22×C4C2×D18811yescharacteristic
158C22×C4D4×D4712yes—
159C2×C8—24no—
160C2×C8—42no—
161C2×C8—42no—
162C2×C8—942no—
163C2×C8—1881no—
164C2×C8—1881no—
165C4⋊C4—42no—
166C4⋊C4—944no—
167C4⋊C4—3762no—
168C4⋊C4—3762no—
169C4⋊C4—3762no—
170C4⋊C4—1882no—
171C4⋊C4—1882no—
172C4⋊C4—1882no—
173C42#1062535012yes—
174C42#1062535211yescharacteristic
175C42Q8×D4711yescharacteristic
176C23#1309399411yescharacteristic
177Q8—3762no—
178Q8—1884no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—3761no—
187C2×C4—3761no—
188C2×C4—1882no—
189C2×C4—1882no—
190C2×C4—1882no—
191C2×C4—1882no—
192C2×C4—1882no—
193C2×C4—1882no—
194C2×C4—1882no—
195C2×C4#1309400212yes—
196C2×C4#1309400411yescharacteristic
197C2×C4#1309401012yes—
198C2×C4#1309401211yescharacteristic
199C8—44no—
200C8—1882no—
201C22#1568903611yescharacteristic
202C22#1568929311yescharacteristic
203C22#1568929811yescharacteristic
204C22#1568930212yes—
205C22#1568930712yes—
206C4—21no—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—82no—
211C4—3762no—
212C4—3762no—
213C4—3762no—
214C2#2024270612yes—
215C2#2024271211yescharacteristic
216C2#2024271711yescharacteristic
217C2#2024454511yescharacteristic
218C2#2024454812yes—
subgroupG/H
centerC23#13093994
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1295C2
socle, prime radicalC23×C47#120
hypercenter#1295D47
hypocenterC47#10361
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
126. C47#10361semidirect

Maximal subgroups

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

subgroupindex
#202516632
#202443612
#202442072
#202412702
C47×#12952
#1036147