Finite Group Databasebeta

← #26120411

Subgroups — #26120411

Order 12032.

382 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 99 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#20254733C211yesmaximal, characteristic
2#20244365C212yesmaximal
3#20242076C212yesmaximal
4#20241263C211yesmaximal, characteristic
5C47×#1831C211yesmaximal, characteristic
6#15689680C2212yes—
7#15689419—22no—
8#15689364—22no—
9#15689334—22no—
10#15689147C2212yes—
11#15688883—22no—
12#15688883—22no—
13#15688871—22no—
14#15688870—22no—
15C2×C4⋊C8×C47C2211yescharacteristic
16C2×C4⋊C8×C47C2211yescharacteristic
17C43×C47C2211yescharacteristic
18C47×#336—22no—
19C2×Dic188—22no—
20C2×#10625329—22no—
21#13094024D412yes—
22#13094024D412yes—
23#13094016—22no—
24#13094003—22no—
25#13094003—22no—
26C4×Dic94—22no—
27C4×Dic94—22no—
28#13093983—22no—
29#13093958—22no—
30C4⋊(C47⋊C8)—22no—
31C4⋊(C47⋊C8)—22no—
32#13093949—24no—
33C22×C8×C47—21no—
34C22×C8×C47D412yes—
35C2×C42×C47—21no—
36C2×C42×C47—21no—
37C2×C42×C47D411yescharacteristic
38C2×C42×C47D411yescharacteristic
39C2×C42×C47C2311yescharacteristic
40C4⋊C8×C47—22no—
41C4⋊C8×C47—22no—
42C22×C4×C47—21no—
43C22×C4×C47—21no—
44C22×C4×C47C2×D411yescharacteristic
45C22×C4×C47C2×D411yescharacteristic
46C22×C4×C47#4111yescharacteristic
47C2×Dic94—22no—
48C2×Dic94—22no—
49C2×C8×C47—22no—
50C2×C8×C47—42no—
51C2×C8×C47—42no—
52C2×C8×C47—41no—
53C42×C47—21no—
54C42×C47—22no—
55C42×C47—41no—
56C42×C47—41no—
57C42×C47—42no—
58C42×C47Q1612yescomplemented
59C42×C47C2×D412yes—
60C42×C47#4112yes—
61C22⋊Dic47—42no—
62C4⋊Dic47—22no—
63C4⋊Dic47—22no—
64C4⋊Dic47—22no—
65C4⋊Dic47—22no—
66Dic47⋊C4—42no—
67Dic47⋊C4—42no—
68C4×Dic47—42no—
69#10625329—42no—
70#10625329—42no—
71C2×C47⋊C8—42no—
72Dic188—82no—
73C23×C47#12111yescharacteristic
74C2×C4×C47—21no—
75C2×C4×C47—21no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47—41no—
79C2×C4×C47—41no—
80C2×C4×C47—41no—
81C2×C4×C47—41no—
82C2×C4×C47—41no—
83C2×C4×C47#12011yescharacteristic
84C2×C4×C47#12112yes—
85C2×C4×C47#12312yes—
86C2×C4×C47#12411yescharacteristic
87C2×C4×C47C2×Q1611yescharacteristic
88C2×C4×C47#13511yescharacteristic
89C2×C4×C47#13712yes—
90C2×Dic47—42no—
91C2×Dic47—42no—
92Dic94—42no—
93Dic94—42no—
94Dic94—82no—
95C8×C47—42no—
96C8×C47—81no—
97C47⋊C8—82no—
98#10523—471nomaximal, Sylow
99C22×C47—21no—
100C22×C47—21no—
101C22×C47#39411yescharacteristic
102C22×C47#46711yescharacteristic
103C22×C47#47011yescharacteristic
104C4×C47—22no—
105C4×C47—21no—
106C4×C47—42no—
107C4×C47—42no—
108C4×C47#45411yescharacteristic
109C4×C47#45511yescharacteristic
110C4×C47#46212yes—
111C4×C47#46412yes—
112Dic47—82no—
113Dic47—82no—
114#3249—471no—
115#1994—472no—
116#1831D4711yescharacteristic
117#1550—472no—
118#1292—471no—
119C2×C47—21no—
120C2×C47—21no—
121C2×C47#204011yescharacteristic
122C2×C47#205011yescharacteristic
123C2×C47#205611yescharacteristic
124#533—472no—
125#477—942no—
126#467—942no—
127#462—942no—
128#423—472no—
129C2×C4⋊C8C2×D4711yescharacteristic
130C2×C4⋊C8C2×D4711yescharacteristic
131C43C2×D4711yescharacteristic
132#339—942no—
133#339—942no—
134#336—22no—
135#333—942no—
136#332—942no—
137C47#1052311yescharacteristic, complemented, Sylow
138C2×Q16—942no—
139C2×M16—942no—
140C22×C8—21no—
141C22×C8C22⋊D4712yes—
142C4⋊Q8—472no—
143C4⋊Q8—472no—
144#125—942no—
145C22⋊Q8—942no—
146C22⋊Q8—942no—
147C4×Q8—942no—
148C4×Q8—942no—
149#117—942no—
150C2×C42—21no—
151C2×C42—21no—
152C2×C42D18811yescharacteristic
153C2×C42D18811yescharacteristic
154C2×C42C22×D4711yescharacteristic
155#107—942no—
156C4⋊C8—22no—
157C4⋊C8—22no—
158C4⋊C8—942no—
159C4⋊C8—942no—
160#103—944no—
161C2×Q8—942no—
162C2×Q8—942no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4C2×D18811yescharacteristic
166C22×C4#1062535011yescharacteristic
167C22×C4C2×C22⋊D4711yescharacteristic
168Q16—3762no—
169M16—1882no—
170M16—1882no—
171C2×C8—22no—
172C2×C8—42no—
173C2×C8—42no—
174C2×C8—41no—
175C2×C8—1882no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4—942no—
179C4⋊C4—942no—
180C4⋊C4—1882no—
181C4⋊C4—1882no—
182C22⋊C4—1882no—
183C42—21no—
184C42—22no—
185C42—41no—
186C42—41no—
187C42—42no—
188C42—1882no—
189C42Dic18812yescomplemented
190C42D4×D4712yes—
191C42#1062535412yes—
192C23#1309399811yescharacteristic
193Q8—3762no—
194Q8—1882no—
195Q8—1882no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—1882no—
206C2×C4—1882no—
207C2×C4#1309399211yescharacteristic
208C2×C4#1309399912yes—
209C2×C4#1309400912yes—
210C2×C4#1309401311yescharacteristic
211C2×C4C2×Dic18811yescharacteristic
212C2×C4#1309404611yescharacteristic
213C2×C4#1309405712yes—
214C8—42no—
215C8—81no—
216C8—3762no—
217C22—21no—
218C22—21no—
219C22#1568904011yescharacteristic
220C22#1568936411yescharacteristic
221C22#1568938111yescharacteristic
222C4—21no—
223C4—22no—
224C4—42no—
225C4—42no—
226C4—3762no—
227C4—3762no—
228C4#1568929511yescharacteristic
229C4#1568930011yescharacteristic
230C4#1568933412yes—
231C4#1568934612yes—
232C2—21no—
233C2—21no—
234C2#2024461711yescharacteristic
235C2#2024467511yescharacteristic
236C2#2024471111yescharacteristic
subgroupG/H
centerC22#15689040
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1831C2
socleC22×C47#394
prime radicalC23×C47#121
hypercenter#1831D47
hypocenterC47#10523
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1831

Complements

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

NH ≅ G/Ntype
58. C42×C47Q16semidirect
137. C47#10523semidirect
189. C42Dic188semidirect

Maximal subgroups

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

subgroupindex
#202547332
#202443652
#202420762
#202412632
C47×#18312
#1052347