Finite Group Databasebeta

← #26120786

Subgroups — #26120786

Order 12032.

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

normal subgroups only

This group has 382 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#20243556C212yesmaximal
3#20243521C211yesmaximal, characteristic
4#20241270C212yesmaximal
5C47×#1295C211yesmaximal, characteristic
6C2×#13093958—22no—
7C2×#13093956—22no—
8C2×#13093935C2211yescharacteristic
9#15689057—22no—
10#15689056—22no—
11#15689055—22no—
12#15688993C2211yescharacteristic
13#15688989C2212yes—
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#13093958—44no—
26#13093956—44no—
27#13093935—21no—
28#13093935Q812yes—
29C47⋊#95—22no—
30C47⋊#95—22no—
31C47⋊#95—22no—
32C22×C8×C47—22no—
33C2×C4⋊C4×C47D412yes—
34C2×C42×C47C2311yescharacteristic
35#97×C47—22no—
36#97×C47Q814yes—
37#95×C47—22no—
38C22×C4×C47—22no—
39C22×C4×C47C2×D411yescharacteristic
40C22×C4×C47C2×D412yes—
41C22×Dic47—22no—
42C22×Dic47—22no—
43C22×Dic47—41no—
44C2×C8×C47—24no—
45C2×C8×C47—24no—
46C2×C8×C47—24no—
47C4⋊C4×C47—42no—
48C42×C47C2×Q812yes—
49C42×C47C2×Q811yescharacteristic
50C42×C47#4111yescharacteristic
51C4⋊Dic47—42no—
52C4⋊Dic47—42no—
53C4⋊Dic47—42no—
54C4⋊Dic47—42no—
55C4⋊Dic47—42no—
56C4⋊Dic47—82no—
57Dic47⋊C4—82no—
58Dic47⋊C4—82no—
59C2×C47⋊C8—22no—
60C2×C47⋊C8—41no—
61C2×C47⋊C8—41no—
62C23×C47#12011yescharacteristic
63C2×C4×C47—22no—
64C2×C4×C47—21no—
65C2×C4×C47—21no—
66C2×C4×C47—22no—
67C2×C4×C47—42no—
68C2×C4×C47—42no—
69C2×C4×C47—42no—
70C2×C4×C47C22⋊Q812yes—
71C2×C4×C47C22⋊Q811yescharacteristic
72C2×C4×C47C4⋊Q812yes—
73C2×C4×C47C4⋊Q811yescharacteristic
74C2×Dic47—42no—
75C2×Dic47—42no—
76C2×Dic47—42no—
77C2×Dic47—42no—
78C2×Dic47—42no—
79C2×Dic47—42no—
80C2×Dic47—82no—
81C2×Dic47—81no—
82C8×C47—28no—
83C47⋊C8—42no—
84#10585—471nomaximal, Sylow
85C22×C47#39511yescharacteristic
86C22×C47#45312yes—
87C22×C47#45411yescharacteristic
88C22×C47#45511yescharacteristic
89C22×C47#45612yes—
90C4×C47—22no—
91C4×C47—22no—
92C4×C47—21no—
93C4×C47—21no—
94C4×C47—82no—
95Dic47—82no—
96Dic47—82no—
97Dic47—161no—
98#2845—471no—
99#1847—472no—
100#1836—471no—
101#1295—472no—
102#1295D4711yescharacteristic
103C2×C47#165611yescharacteristic
104C2×C47#166112yes—
105C2×C47#166311yescharacteristic
106C2×C47#206012yes—
107C2×C47#206111yescharacteristic
108C2×#107—942no—
109C2×#106—942no—
110C2×#97—471no—
111C2×#97C2×D4712yes—
112#398—942no—
113#398—942no—
114#398—942no—
115#384—471no—
116#382—472no—
117#382C2×D4711yescharacteristic
118#340—942no—
119C47#1058511yescharacteristic, complemented, Sylow
120C22×C8—22no—
121C22×C8—941no—
122C2×C4⋊C4—472no—
123C2×C4⋊C4—472no—
124C2×C4⋊C4—942no—
125C2×C4⋊C4—942no—
126C2×C4⋊C4—942no—
127C2×C4⋊C4—941no—
128C2×C4⋊C4—942no—
129C2×C4⋊C4D18812yes—
130C2×C42C22×D4711yescharacteristic
131#107—1884no—
132#106—1884no—
133#97—22no—
134#97—472no—
135#97—941no—
136#97Dic9414yes—
137#95—22no—
138#95—942no—
139#95—942no—
140#95—942no—
141C22×C4—22no—
142C22×C4—942no—
143C22×C4—942no—
144C22×C4—1881no—
145C22×C4C2×D18811yescharacteristic
146C22×C4D4×D4712yes—
147C2×C8—24no—
148C2×C8—24no—
149C2×C8—24no—
150C2×C8—942no—
151C2×C8—1881no—
152C2×C8—1881no—
153C4⋊C4—42no—
154C4⋊C4—3762no—
155C4⋊C4—3762no—
156C4⋊C4—3762no—
157C4⋊C4—1882no—
158C4⋊C4—1882no—
159C4⋊C4—1882no—
160C4⋊C4—1882no—
161C4⋊C4—1882no—
162C42C2×Dic9412yes—
163C42#1062535211yescharacteristic
164C42Q8×D4711yescharacteristic
165C23#1309399411yescharacteristic
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—3762no—
174C2×C4—3761no—
175C2×C4—1882no—
176C2×C4—1882no—
177C2×C4—1882no—
178C2×C4—1882no—
179C2×C4—1882no—
180C2×C4—1882no—
181C2×C4#1309400112yes—
182C2×C4#1309400411yescharacteristic
183C2×C4#1309402312yes—
184C2×C4#1309402411yescharacteristic
185C8—28no—
186C8—1882no—
187C22#1568904411yescharacteristic
188C22#1568929212yes—
189C22#1568929811yescharacteristic
190C22#1568930311yescharacteristic
191C22#1568930712yes—
192C4—21no—
193C4—21no—
194C4—22no—
195C4—22no—
196C4—82no—
197C4—3762no—
198C4—3762no—
199C4—7521no—
200C2#2024268311yescharacteristic
201C2#2024270812yes—
202C2#2024271711yescharacteristic
203C2#2024473212yes—
204C2#2024473911yescharacteristic
subgroupG/H
centerC23#13093994
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1295C2
socle, prime radicalC23×C47#120
hypercenter#1295D47
hypocenterC47#10585
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
119. C47#10585semidirect

Maximal subgroups

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

subgroupindex
#202516632
#202435562
#202435212
#202412702
C47×#12952
#1058547