Finite Group Databasebeta

← #26120406

Subgroups — #26120406

Order 12032.

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

normal subgroups only

This group has 402 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×#1842C211yesmaximal, 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×C47—22no—
16C2×C4⋊C8×C47C2211yescharacteristic
17C2×C4⋊C8×C47C2211yescharacteristic
18C43×C47C2211yescharacteristic
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—
42C4⋊C8×C47—44no—
43C22×C4×C47—21no—
44C22×C4×C47—21no—
45C22×C4×C47C2×D411yescharacteristic
46C22×C4×C47C2×D411yescharacteristic
47C22×C4×C47#4111yescharacteristic
48C2×Dic94—22no—
49C2×Dic94—22no—
50C2×C8×C47—22no—
51C2×C8×C47—42no—
52C2×C8×C47—42no—
53C2×C8×C47—41no—
54C42×C47—22no—
55C42×C47—22no—
56C42×C47—21no—
57C42×C47—22no—
58C42×C47—42no—
59C42×C47Q1612yescomplemented
60C42×C47C2×D412yes—
61C42×C47#4112yes—
62C22⋊Dic47—42no—
63C4⋊Dic47—22no—
64C4⋊Dic47—22no—
65C4⋊Dic47—22no—
66C4⋊Dic47—22no—
67Dic47⋊C4—42no—
68Dic47⋊C4—42no—
69C4×Dic47—42no—
70#10625329—42no—
71#10625329—42no—
72C2×C47⋊C8—42no—
73Dic188—82no—
74C23×C47#12111yescharacteristic
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47—21no—
79C2×C4×C47—21no—
80C2×C4×C47—22no—
81C2×C4×C47—41no—
82C2×C4×C47—41no—
83C2×C4×C47—41no—
84C2×C4×C47#12011yescharacteristic
85C2×C4×C47#12112yes—
86C2×C4×C47#12312yes—
87C2×C4×C47#12411yescharacteristic
88C2×C4×C47C2×Q1611yescharacteristic
89C2×C4×C47#13511yescharacteristic
90C2×C4×C47#13712yes—
91C2×Dic47—42no—
92C2×Dic47—42no—
93Dic94—42no—
94Dic94—42no—
95Dic94—82no—
96C8×C47—42no—
97C8×C47—81no—
98C47⋊C8—82no—
99#10522—471nomaximal, Sylow
100C22×C47—21no—
101C22×C47—21no—
102C22×C47#39411yescharacteristic
103C22×C47#46711yescharacteristic
104C22×C47#47011yescharacteristic
105C4×C47—24no—
106C4×C47—22no—
107C4×C47—21no—
108C4×C47—42no—
109C4×C47#45311yescharacteristic
110C4×C47#45611yescharacteristic
111C4×C47#46212yes—
112C4×C47#46412yes—
113Dic47—82no—
114Dic47—82no—
115#3249—471no—
116#1994—472no—
117#1842D4711yescharacteristic
118#1550—472no—
119#1292—471no—
120C2×C47—21no—
121C2×C47—21no—
122C2×C47#203911yescharacteristic
123C2×C47#205011yescharacteristic
124C2×C47#205611yescharacteristic
125#533—472no—
126#477—942no—
127#467—942no—
128#462—942no—
129#423—472no—
130C2×C4⋊C8—22no—
131C2×C4⋊C8C2×D4711yescharacteristic
132C2×C4⋊C8C2×D4711yescharacteristic
133C43C2×D4711yescharacteristic
134#339—942no—
135#339—942no—
136#333—942no—
137#332—942no—
138C47#1052211yescharacteristic, complemented, Sylow
139C2×Q16—942no—
140C2×M16—942no—
141C22×C8—21no—
142C22×C8C22⋊D4712yes—
143C4⋊Q8—472no—
144C4⋊Q8—472no—
145#125—942no—
146C22⋊Q8—942no—
147C22⋊Q8—942no—
148C4×Q8—942no—
149C4×Q8—942no—
150#117—942no—
151C2×C42—21no—
152C2×C42—21no—
153C2×C42D18811yescharacteristic
154C2×C42D18811yescharacteristic
155C2×C42C22×D4711yescharacteristic
156#107—942no—
157C4⋊C8—22no—
158C4⋊C8—22no—
159C4⋊C8—44no—
160C4⋊C8—942no—
161C4⋊C8—942no—
162#103—944no—
163C2×Q8—942no—
164C2×Q8—942no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4C2×D18811yescharacteristic
168C22×C4#1062535011yescharacteristic
169C22×C4C2×C22⋊D4711yescharacteristic
170Q16—3762no—
171M16—1882no—
172M16—1882no—
173C2×C8—22no—
174C2×C8—42no—
175C2×C8—42no—
176C2×C8—41no—
177C2×C8—1882no—
178C4⋊C4—942no—
179C4⋊C4—942no—
180C4⋊C4—942no—
181C4⋊C4—942no—
182C4⋊C4—1882no—
183C4⋊C4—1882no—
184C22⋊C4—1882no—
185C42—22no—
186C42—22no—
187C42—21no—
188C42—22no—
189C42—42no—
190C42—1882no—
191C42Dic18812yescomplemented
192C42D4×D4712yes—
193C42#1062535412yes—
194C23#1309399811yescharacteristic
195Q8—3762no—
196Q8—1882no—
197Q8—1882no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—1882no—
208C2×C4—1882no—
209C2×C4#1309399211yescharacteristic
210C2×C4#1309399912yes—
211C2×C4#1309400912yes—
212C2×C4#1309401311yescharacteristic
213C2×C4C2×Dic18811yescharacteristic
214C2×C4#1309404611yescharacteristic
215C2×C4#1309405712yes—
216C8—42no—
217C8—81no—
218C8—3762no—
219C22—21no—
220C22—21no—
221C22#1568904011yescharacteristic
222C22#1568936411yescharacteristic
223C22#1568938111yescharacteristic
224C4—24no—
225C4—21no—
226C4—22no—
227C4—42no—
228C4—3762no—
229C4—3762no—
230C4#1568929011yescharacteristic
231C4#1568930511yescharacteristic
232C4#1568933412yes—
233C4#1568934612yes—
234C2—21no—
235C2—21no—
236C2#2024461211yescharacteristic
237C2#2024467511yescharacteristic
238C2#2024471111yescharacteristic
subgroupG/H
centerC22#15689040
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1842C2
socleC22×C47#394
prime radicalC23×C47#121
hypercenter#1842D47
hypocenterC47#10522
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1842

Complements

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

NH ≅ G/Ntype
59. C42×C47Q16semidirect
138. C47#10522semidirect
191. 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×#18422
#1052247