Finite Group Databasebeta

← #26120369

Subgroups — #26120369

Order 12032.

364 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 81 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#20243541C211yesmaximal, characteristic
2#20242088C212yesmaximal
3#20241900C212yesmaximal
4#20241258C211yesmaximal, characteristic
5C47×#3249C211yesmaximal, characteristic
6#15689180C2212yes—
7C2×C4⋊(C47⋊C8)C2211yescharacteristic
8C2×Dic47⋊C8—22no—
9#15688969C2211yescharacteristic
10#15688869—22no—
11#15688869—22no—
12#15688860—24no—
13C47×#533C2212yes—
14C47×#477—22no—
15C47×#467—22no—
16C47×#462—22no—
17C2×C4⋊C8×C47C2211yescharacteristic
18C22×C47⋊C8—21no—
19C2×C4×Dic47—21no—
20C4⋊(C47⋊C8)—22no—
21C4⋊(C47⋊C8)—22no—
22Dic47⋊C8—44no—
23C22⋊(C47⋊C8)—22no—
24#13093935—22no—
25C47⋊#95—21no—
26C47⋊#95D412yes—
27C2×Q16×C47—22no—
28C22×C8×C47D412yes—
29C4⋊Q8×C47D412yes—
30C4⋊Q8×C47D412yes—
31#125×C47—22no—
32C22⋊Q8×C47—22no—
33C22⋊Q8×C47—22no—
34C4×Q8×C47—22no—
35C4×Q8×C47—22no—
36#117×C47—22no—
37C2×C42×C47C2311yescharacteristic
38#107×C47—22no—
39C4⋊C8×C47—22no—
40#103×C47—24no—
41C2×Q8×C47—22no—
42C2×Q8×C47—22no—
43C22×C4×C47C2×D411yescharacteristic
44C22×C4×C47C2×D411yescharacteristic
45C22×C4×C47#4111yescharacteristic
46C22×Dic47—22no—
47Q16×C47—82no—
48C2×C8×C47—22no—
49C2×C8×C47—42no—
50C4⋊C4×C47—22no—
51C4⋊C4×C47—22no—
52C4⋊C4×C47—22no—
53C4⋊C4×C47—22no—
54C4⋊C4×C47—42no—
55C4⋊C4×C47—42no—
56C22⋊C4×C47—42no—
57C42×C47—42no—
58C42×C47C2×D412yes—
59C42×C47#4112yes—
60C4×Dic47—22no—
61C4×Dic47—22no—
62C2×C47⋊C8—42no—
63C2×C47⋊C8—41no—
64C2×C47⋊C8—42no—
65C23×C47#12111yescharacteristic
66Q8×C47—42no—
67Q8×C47—42no—
68Q8×C47—82no—
69C2×C4×C47—22no—
70C2×C4×C47—21no—
71C2×C4×C47—21no—
72C2×C4×C47—41no—
73C2×C4×C47—42no—
74C2×C4×C47—42no—
75C2×C4×C47#12011yescharacteristic
76C2×C4×C47#12112yes—
77C2×C4×C47#12312yes—
78C2×C4×C47#12411yescharacteristic
79C2×Dic47—24no—
80C2×Dic47—42no—
81C2×Dic47—42no—
82C8×C47—42no—
83C47⋊C8—82no—
84C47⋊C8—81no—
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—82no—
94C4×C47—82no—
95C4×C47#45311yescharacteristic
96C4×C47#45611yescharacteristic
97Dic47—44no—
98#3249D4711yescharacteristic
99#1843—471no—
100#1552—472no—
101#1506—472no—
102#1290—471no—
103C2×C47—22no—
104C2×C47#203911yescharacteristic
105C2×C47#204711yescharacteristic
106C2×C47#205311yescharacteristic
107#533C2×D4712yes—
108#477—22no—
109#467—22no—
110#462—22no—
111#432—472no—
112C2×C4⋊C8—471no—
113C2×C4⋊C8—942no—
114C2×C4⋊C8C2×D4711yescharacteristic
115#376—471no—
116#332—942no—
117#332—942no—
118#328—944no—
119C47#1051611yescharacteristic, complemented, Sylow
120C2×Q16—22no—
121C22×C8—941no—
122C22×C8C22⋊D4712yes—
123C4⋊Q8C22⋊D4712yes—
124C4⋊Q8C22⋊D4712yes—
125#125—22no—
126C22⋊Q8—22no—
127C22⋊Q8—22no—
128C4×Q8—22no—
129C4×Q8—22no—
130#117—22no—
131C2×C42—941no—
132C2×C42C22×D4711yescharacteristic
133#107—22no—
134C4⋊C8—22no—
135C4⋊C8—942no—
136C4⋊C8—942no—
137C4⋊C8—1884no—
138#103—24no—
139C22⋊C8—942no—
140#97—942no—
141#95—472no—
142#95—941no—
143C2×Q8—22no—
144C2×Q8—22no—
145C22×C4—942no—
146C22×C4D4×D4711yescharacteristic
147C22×C4#1062535211yescharacteristic
148C22×C4C2×C22⋊D4711yescharacteristic
149Q16—82no—
150C2×C8—22no—
151C2×C8—42no—
152C2×C8—1882no—
153C2×C8—1881no—
154C2×C8—1882no—
155C4⋊C4—22no—
156C4⋊C4—22no—
157C4⋊C4—22no—
158C4⋊C4—22no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C22⋊C4—42no—
162C42—42no—
163C42—942no—
164C42—942no—
165C42#1062535212yes—
166C42C2×C22⋊D4712yes—
167C23#1309399511yescharacteristic
168Q8—42no—
169Q8—42no—
170Q8—82no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—944no—
178C2×C4—1882no—
179C2×C4—1882no—
180C2×C4#1309399311yescharacteristic
181C2×C4#1309399612yes—
182C2×C4#1309400512yes—
183C2×C4#1309401111yescharacteristic
184C8—42no—
185C8—3762no—
186C8—3761no—
187C22—21no—
188C22—21no—
189C22#1568903711yescharacteristic
190C22#1568939512yes—
191C4—21no—
192C4—22no—
193C4—22no—
194C4—82no—
195C4—82no—
196C4—1884no—
197C4#1568929111yescharacteristic
198C4#1568930611yescharacteristic
199C2—22no—
200C2#2024460911yescharacteristic
201C2#2024465311yescharacteristic
202C2#2024469111yescharacteristic
subgroupG/H
centerC22#15689037
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#3249C2
socleC22×C47#394
prime radicalC23×C47#121
hypercenter#3249D47
hypocenterC47#10516
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3249

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
#202435412
#202420882
#202419002
#202412582
C47×#32492
#1051647