Finite Group Databasebeta

← #26120789

Subgroups — #26120789

Order 12032.

350 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 97 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#20243522C212yesmaximal
3#20243521C211yesmaximal, characteristic
4#20241270C212yesmaximal
5C47×#1295C211yesmaximal, characteristic
6C2×#13093935C2211yescharacteristic
7#15689057—22no—
8#15689056—22no—
9#15689055—22no—
10#15688993C2211yescharacteristic
11#15688989C2212yes—
12#15688886—22no—
13#15688886—22no—
14#15688885—22no—
15C2×#97×C47C2212yes—
16C47×#382C2211yescharacteristic
17C22×C47⋊C8—21no—
18C2×C4⋊Dic47—21no—
19C2×C4⋊Dic47—22no—
20C2×C4⋊Dic47—22no—
21C2×C4⋊Dic47D412yes—
22C2×C4⋊Dic47D412yes—
23C2×Dic47⋊C4—22no—
24C2×Dic47⋊C4—22no—
25#13093935—21no—
26#13093935Q812yes—
27C47⋊#95—22no—
28C47⋊#95—22no—
29C47⋊#95—22no—
30C22×C8×C47—22no—
31C2×C4⋊C4×C47D412yes—
32C2×C42×C47C2311yescharacteristic
33#97×C47—22no—
34#97×C47Q814yes—
35#95×C47—22no—
36C22×C4×C47—22no—
37C22×C4×C47C2×D411yescharacteristic
38C22×C4×C47C2×D412yes—
39C22×Dic47—22no—
40C22×Dic47—22no—
41C22×Dic47—41no—
42C2×C8×C47—24no—
43C2×C8×C47—42no—
44C2×C8×C47—42no—
45C4⋊C4×C47—42no—
46C42×C47C2×Q812yes—
47C42×C47C2×Q811yescharacteristic
48C42×C47#4111yescharacteristic
49C4⋊Dic47—42no—
50C4⋊Dic47—42no—
51C4⋊Dic47—42no—
52C4⋊Dic47—44no—
53C4⋊Dic47—82no—
54Dic47⋊C4—82no—
55Dic47⋊C4—82no—
56C2×C47⋊C8—22no—
57C2×C47⋊C8—41no—
58C2×C47⋊C8—41no—
59C23×C47#12011yescharacteristic
60C2×C4×C47—21no—
61C2×C4×C47—22no—
62C2×C4×C47—21no—
63C2×C4×C47—22no—
64C2×C4×C47—42no—
65C2×C4×C47—42no—
66C2×C4×C47—42no—
67C2×C4×C47C22⋊Q812yes—
68C2×C4×C47C22⋊Q811yescharacteristic
69C2×C4×C47C4⋊Q812yes—
70C2×C4×C47C4⋊Q811yescharacteristic
71C2×Dic47—42no—
72C2×Dic47—42no—
73C2×Dic47—42no—
74C2×Dic47—42no—
75C2×Dic47—42no—
76C2×Dic47—42no—
77C2×Dic47—82no—
78C2×Dic47—81no—
79C8×C47—44no—
80C47⋊C8—42no—
81#10586—471nomaximal, Sylow
82C22×C47#39511yescharacteristic
83C22×C47#45412yes—
84C22×C47#45411yescharacteristic
85C22×C47#45512yes—
86C22×C47#45511yescharacteristic
87C4×C47—21no—
88C4×C47—22no—
89C4×C47—22no—
90C4×C47—21no—
91C4×C47—82no—
92Dic47—82no—
93Dic47—82no—
94Dic47—161no—
95#2845—471no—
96#1836—472no—
97#1836—471no—
98#1295—472no—
99#1295D4711yescharacteristic
100C2×C47#165811yescharacteristic
101C2×C47#166211yescharacteristic
102C2×C47#166212yes—
103C2×C47#206112yes—
104C2×C47#206111yescharacteristic
105C2×#97—471no—
106C2×#97C2×D4712yes—
107#398—942no—
108#398—942no—
109#398—942no—
110#384—471no—
111#382—472no—
112#382C2×D4711yescharacteristic
113#340—942no—
114#340—942no—
115#340—942no—
116C47#1058611yescharacteristic, complemented, Sylow
117C22×C8—22no—
118C22×C8—941no—
119C2×C4⋊C4—472no—
120C2×C4⋊C4—472no—
121C2×C4⋊C4—942no—
122C2×C4⋊C4—942no—
123C2×C4⋊C4—942no—
124C2×C4⋊C4—941no—
125C2×C4⋊C4—942no—
126C2×C4⋊C4D18812yes—
127C2×C42C22×D4711yescharacteristic
128#97—22no—
129#97—472no—
130#97—941no—
131#97Dic9414yes—
132#95—22no—
133#95—942no—
134#95—942no—
135#95—942no—
136C22×C4—22no—
137C22×C4—942no—
138C22×C4—942no—
139C22×C4—1881no—
140C22×C4C2×D18811yescharacteristic
141C22×C4D4×D4712yes—
142C2×C8—24no—
143C2×C8—42no—
144C2×C8—42no—
145C2×C8—942no—
146C2×C8—1881no—
147C2×C8—1881no—
148C4⋊C4—42no—
149C4⋊C4—3762no—
150C4⋊C4—3762no—
151C4⋊C4—3762no—
152C4⋊C4—1884no—
153C4⋊C4—1882no—
154C4⋊C4—1882no—
155C4⋊C4—1882no—
156C42C2×Dic9412yes—
157C42#1062535211yescharacteristic
158C42Q8×D4711yescharacteristic
159C23#1309399411yescharacteristic
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—21no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—3762no—
168C2×C4—3761no—
169C2×C4—1882no—
170C2×C4—1882no—
171C2×C4—1882no—
172C2×C4—1882no—
173C2×C4—1882no—
174C2×C4—1882no—
175C2×C4#1309400112yes—
176C2×C4#1309400411yescharacteristic
177C2×C4#1309402312yes—
178C2×C4#1309402411yescharacteristic
179C8—44no—
180C8—1882no—
181C22#1568904411yescharacteristic
182C22#1568929712yes—
183C22#1568929811yescharacteristic
184C22#1568930212yes—
185C22#1568930311yescharacteristic
186C4—22no—
187C4—22no—
188C4—21no—
189C4—21no—
190C4—82no—
191C4—3762no—
192C4—3762no—
193C4—7521no—
194C2#2024269111yescharacteristic
195C2#2024271211yescharacteristic
196C2#2024271312yes—
197C2#2024473712yes—
198C2#2024473911yescharacteristic
subgroupG/H
centerC23#13093994
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1295C2
socle, prime radicalC23×C47#120
hypercenter#1295D47
hypocenterC47#10586
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
116. C47#10586semidirect

Maximal subgroups

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

subgroupindex
#202516632
#202435222
#202435212
#202412702
C47×#12952
#1058647