Finite Group Databasebeta

← #26120412

Subgroups — #26120412

Order 12032.

382 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 95 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#20244364C212yesmaximal
3#20243504C211yesmaximal, characteristic
4#20242079C212yesmaximal
5C47×#1292C211yesmaximal, characteristic
6#15689680C2212yes—
7#15689419—22no—
8#15689364—22no—
9#15689334—22no—
10C2×C4⋊(C47⋊C8)C2211yescharacteristic
11C42×Dic47C2211yescharacteristic
12#15688884—22no—
13#15688884—22no—
14#15688877—22no—
15#15688871—22no—
16#15688868—22no—
17C47×#423C2212yes—
18C2×C4⋊C8×C47C2211yescharacteristic
19C2×Dic188—22no—
20C22×C47⋊C8—21no—
21#13094024D412yes—
22#13094024D412yes—
23#13094016—22no—
24#13094003—22no—
25#13094003—22no—
26C4×Dic94—22no—
27C4×Dic94—22no—
28#13093983—22no—
29C2×C4×Dic47—21no—
30C2×C4×Dic47—21no—
31C2×C4×Dic47D411yescharacteristic
32C2×C4×Dic47D411yescharacteristic
33#13093958—22no—
34C4⋊(C47⋊C8)—22no—
35#13093949—24no—
36C2×M16×C47—22no—
37C22×C8×C47D412yes—
38C2×C42×C47C2311yescharacteristic
39C4⋊C8×C47—22no—
40C4⋊C8×C47—22no—
41C4⋊C8×C47—22no—
42C22×C4×C47C2×D411yescharacteristic
43C22×C4×C47C2×D411yescharacteristic
44C22×C4×C47#4111yescharacteristic
45C22×Dic47—21no—
46C22×Dic47—21no—
47C2×Dic94—22no—
48C2×Dic94—22no—
49M16×C47—42no—
50M16×C47—42no—
51C2×C8×C47—22no—
52C2×C8×C47—42no—
53C2×C8×C47—42no—
54C42×C47C2×D412yes—
55C42×C47#4112yes—
56C22⋊Dic47—42no—
57C4⋊Dic47—22no—
58C4⋊Dic47—22no—
59C4⋊Dic47—22no—
60C4⋊Dic47—22no—
61Dic47⋊C4—42no—
62Dic47⋊C4—42no—
63C4×Dic47—21no—
64C4×Dic47—22no—
65C4×Dic47—42no—
66C4×Dic47—41no—
67C4×Dic47—41no—
68C4×Dic47—42no—
69C4×Dic47Q1612yescomplemented
70C2×C47⋊C8—42no—
71C2×C47⋊C8—41no—
72Dic188—82no—
73C23×C47#12111yescharacteristic
74C2×C4×C47—21no—
75C2×C4×C47—21no—
76C2×C4×C47—41no—
77C2×C4×C47#12011yescharacteristic
78C2×C4×C47#12112yes—
79C2×C4×C47#12312yes—
80C2×C4×C47#12411yescharacteristic
81C2×C4×C47C2×Q1611yescharacteristic
82C2×C4×C47#13511yescharacteristic
83C2×C4×C47#13712yes—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—41no—
87C2×Dic47—41no—
88C2×Dic47—41no—
89C2×Dic47—41no—
90C2×Dic47—42no—
91C2×Dic47—42no—
92Dic94—42no—
93Dic94—42no—
94Dic94—82no—
95C8×C47—42no—
96C8×C47—82no—
97C47⋊C8—81no—
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#45411yescharacteristic
107C4×C47#45511yescharacteristic
108C4×C47#46212yes—
109C4×C47#46412yes—
110Dic47—42no—
111Dic47—42no—
112Dic47—82no—
113Dic47—82no—
114#3249—471no—
115#1994—472no—
116#1831—471no—
117#1550—472no—
118#1292D4711yescharacteristic
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#423C2×D4712yes—
129C2×C4⋊C8—471no—
130C2×C4⋊C8C2×D4711yescharacteristic
131C43—471no—
132#339—942no—
133#339—942no—
134#336—942no—
135#333—942no—
136#332—942no—
137C47#1052311yescharacteristic, complemented, Sylow
138C2×Q16—942no—
139C2×M16—22no—
140C22×C8—941no—
141C22×C8D18812yes—
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—471no—
151C2×C42—471no—
152C2×C42—941no—
153C2×C42—941no—
154C2×C42C22×D4711yescharacteristic
155#107—942no—
156C4⋊C8—22no—
157C4⋊C8—22no—
158C4⋊C8—22no—
159C4⋊C8—942no—
160#103—944no—
161C2×Q8—942no—
162C2×Q8—942no—
163C22×C4—941no—
164C22×C4—941no—
165C22×C4C2×D18811yescharacteristic
166C22×C4D4×D4711yescharacteristic
167C22×C4#1062535411yescharacteristic
168Q16—3762no—
169M16—42no—
170M16—42no—
171C2×C8—22no—
172C2×C8—42no—
173C2×C8—42no—
174C2×C8—1882no—
175C2×C8—1881no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4—942no—
179C4⋊C4—942no—
180C4⋊C4—1882no—
181C4⋊C4—1882no—
182C22⋊C4—1882no—
183C42—472no—
184C42—941no—
185C42—942no—
186C42—1881no—
187C42—1881no—
188C42—1882no—
189C42—1882no—
190C42#1062535012yes—
191C42D4×D4712yes—
192C23#1309399911yescharacteristic
193Q8—3762no—
194Q8—1882no—
195Q8—1882no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—41no—
199C2×C4—942no—
200C2×C4—942no—
201C2×C4—1882no—
202C2×C4—1882no—
203C2×C4—1881no—
204C2×C4—1881no—
205C2×C4—1881no—
206C2×C4—1881no—
207C2×C4#1309399411yescharacteristic
208C2×C4#1309399712yes—
209C2×C4#1309400912yes—
210C2×C4#1309401211yescharacteristic
211C2×C4Q16×D4711yescharacteristic
212C2×C4#1309404311yescharacteristic
213C2×C4#1309405312yes—
214C8—42no—
215C8—82no—
216C8—3761no—
217C22—21no—
218C22—21no—
219C22#1568904111yescharacteristic
220C22#1568936511yescharacteristic
221C22#1568938211yescharacteristic
222C4—21no—
223C4—22no—
224C4—3762no—
225C4—3762no—
226C4—1882no—
227C4—1882no—
228C4#1568929811yescharacteristic
229C4#1568930311yescharacteristic
230C4#1568933212yes—
231C4#1568934412yes—
232C2—21no—
233C2—21no—
234C2#2024461811yescharacteristic
235C2#2024467611yescharacteristic
236C2#2024471211yescharacteristic
subgroupG/H
centerC22#15689041
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1292C2
socleC22×C47#394
prime radicalC23×C47#121
hypercenter#1292D47
hypocenterC47#10523
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
69. C4×Dic47Q16semidirect
137. C47#10523semidirect

Maximal subgroups

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

subgroupindex
#202547332
#202443642
#202435042
#202420792
C47×#12922
#1052347