Finite Group Databasebeta

← #26120372

Subgroups — #26120372

Order 12032.

364 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 79 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#20242086C212yesmaximal
3#20241899C212yesmaximal
4#20241258C211yesmaximal, characteristic
5C47×#1843C211yesmaximal, characteristic
6#15689680C2212yes—
7#15689419—22no—
8#15689364—22no—
9#15689334—22no—
10#15689180C2212yes—
11#15688870—22no—
12#15688868—22no—
13#15688859—24no—
14C2×C4⋊C8×C47—22no—
15C2×C4⋊C8×C47C2211yescharacteristic
16C2×C4⋊C8×C47C2211yescharacteristic
17C47×#376C2211yescharacteristic
18C2×Dic188—22no—
19#13094024D412yes—
20#13094024D412yes—
21#13094016—22no—
22#13094003—22no—
23#13094003—22no—
24C4×Dic94—22no—
25C4×Dic94—22no—
26#13093983—22no—
27#13093958—22no—
28C4⋊(C47⋊C8)—22no—
29#13093949—24no—
30C22⋊(C47⋊C8)—22no—
31#13093935—22no—
32C22×C8×C47—21no—
33C22×C8×C47D412yes—
34C2×C42×C47—21no—
35C2×C42×C47C2311yescharacteristic
36C4⋊C8×C47—22no—
37C4⋊C8×C47—22no—
38C4⋊C8×C47—44no—
39#95×C47—21no—
40#95×C47D412yes—
41C22×C4×C47—22no—
42C22×C4×C47C2×D411yescharacteristic
43C22×C4×C47C2×D411yescharacteristic
44C22×C4×C47#4111yescharacteristic
45C2×Dic94—22no—
46C2×Dic94—22no—
47C2×C8×C47—22no—
48C2×C8×C47—42no—
49C2×C8×C47—42no—
50C2×C8×C47—41no—
51C42×C47—22no—
52C42×C47—22no—
53C42×C47C2×D412yes—
54C42×C47#4112yes—
55C22⋊Dic47—42no—
56C4⋊Dic47—22no—
57C4⋊Dic47—22no—
58C4⋊Dic47—22no—
59C4⋊Dic47—22no—
60Dic47⋊C4—42no—
61Dic47⋊C4—42no—
62C4×Dic47—42no—
63C2×C47⋊C8—42no—
64Dic188—82no—
65C23×C47#12111yescharacteristic
66C2×C4×C47—22no—
67C2×C4×C47—21no—
68C2×C4×C47—21no—
69C2×C4×C47—24no—
70C2×C4×C47—41no—
71C2×C4×C47—42no—
72C2×C4×C47—42no—
73C2×C4×C47#12011yescharacteristic
74C2×C4×C47#12112yes—
75C2×C4×C47#12312yes—
76C2×C4×C47#12411yescharacteristic
77C2×Dic47—42no—
78C2×Dic47—42no—
79Dic94—42no—
80Dic94—42no—
81Dic94—82no—
82C8×C47—42no—
83C8×C47—81no—
84C47⋊C8—82no—
85#10516—471nomaximal, Sylow
86C22×C47—21no—
87C22×C47—21no—
88C22×C47#39411yescharacteristic
89C22×C47#47312yes—
90C4×C47—22no—
91C4×C47—21no—
92C4×C47—22no—
93C4×C47—44no—
94C4×C47#45311yescharacteristic
95C4×C47#45611yescharacteristic
96Dic47—82no—
97Dic47—82no—
98#3249—471no—
99#1843D4711yescharacteristic
100#1552—472no—
101#1506—472no—
102#1290—471no—
103C2×C47—22no—
104C2×C47#203911yescharacteristic
105C2×C47#204711yescharacteristic
106C2×C47#205311yescharacteristic
107#533—472no—
108#477—942no—
109#467—942no—
110#462—942no—
111#432—472no—
112C2×C4⋊C8—22no—
113C2×C4⋊C8C2×D4711yescharacteristic
114C2×C4⋊C8C2×D4711yescharacteristic
115#376C2×D4711yescharacteristic
116#332—942no—
117#332—942no—
118#328—944no—
119C47#1051611yescharacteristic, complemented, Sylow
120C2×Q16—942no—
121C22×C8—21no—
122C22×C8C22⋊D4712yes—
123C4⋊Q8—472no—
124C4⋊Q8—472no—
125#125—942no—
126C22⋊Q8—942no—
127C22⋊Q8—942no—
128C4×Q8—942no—
129C4×Q8—942no—
130#117—942no—
131C2×C42—21no—
132C2×C42C22×D4711yescharacteristic
133#107—942no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—44no—
137C4⋊C8—942no—
138#103—944no—
139C22⋊C8—942no—
140#97—942no—
141#95—21no—
142#95D18812yes—
143C2×Q8—942no—
144C2×Q8—942no—
145C22×C4—22no—
146C22×C4C2×D18811yescharacteristic
147C22×C4#1062535011yescharacteristic
148C22×C4C2×C22⋊D4711yescharacteristic
149Q16—3762no—
150C2×C8—22no—
151C2×C8—42no—
152C2×C8—42no—
153C2×C8—41no—
154C2×C8—1882no—
155C4⋊C4—942no—
156C4⋊C4—942no—
157C4⋊C4—942no—
158C4⋊C4—942no—
159C4⋊C4—1882no—
160C4⋊C4—1882no—
161C22⋊C4—1882no—
162C42—22no—
163C42—22no—
164C42—1882no—
165C42D4×D4712yes—
166C42#1062535412yes—
167C23#1309399811yescharacteristic
168Q8—3762no—
169Q8—1882no—
170Q8—1882no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—24no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—1882no—
179C2×C4—1882no—
180C2×C4#1309399211yescharacteristic
181C2×C4#1309399912yes—
182C2×C4#1309400912yes—
183C2×C4#1309401311yescharacteristic
184C8—42no—
185C8—81no—
186C8—3762no—
187C22—21no—
188C22—21no—
189C22#1568904011yescharacteristic
190C22#1568939812yes—
191C4—21no—
192C4—22no—
193C4—22no—
194C4—44no—
195C4—3762no—
196C4—3762no—
197C4#1568929011yescharacteristic
198C4#1568930511yescharacteristic
199C2—22no—
200C2#2024461211yescharacteristic
201C2#2024465611yescharacteristic
202C2#2024469411yescharacteristic
subgroupG/H
centerC22#15689040
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1843C2
socleC22×C47#394
prime radicalC23×C47#121
hypercenter#1843D47
hypocenterC47#10516
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1843

Complements

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

NH ≅ G/Ntype
119. C47#10516semidirect

Maximal subgroups

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

subgroupindex
#202547332
#202420862
#202418992
#202412582
C47×#18432
#1051647