Finite Group Databasebeta

← #26102908

Subgroups — #26102908

Order 12032.

240 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 47 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#20244185C211yesmaximal, characteristic
2#20241328C211yesmaximal, characteristic, complemented
3C47×#1322C211yesmaximal, characteristic, complemented
4C2×C4×D188C411yescharacteristic
5C2×(C2×D47)⋊C8—21no—
6C2×(C2×D47)⋊C8—21no—
7C2×#13093935C411yescharacteristic
8C22⋊(C47⋊C16)—21no—
9C2×C4⋊C8×C47C2211yescharacteristic
10C47×C22⋊C16—21no—
11C22×D188C811yescharacteristic
12C22×C4×D47—21no—
13C22×C47⋊C8—21no—
14C4×D188—41no—
15C4×D188—41no—
16C2×C4⋊Dic47C811yescharacteristic
17C2×(C2×D47)⋊C4—21no—
18C2×C47⋊C16—41no—
19(C2×D47)⋊C8—42no—
20(C2×D47)⋊C8—42no—
21#13093935—41no—
22C22×C8×C47D411yescharacteristic
23C22×C8×C47D411yescharacteristic
24C2×C42×C47C2×C411yescharacteristic
25C2×C16×C47—41no—
26C4⋊C8×C47—41no—
27C23×D47—21no—
28C22×C4×C47C22⋊C411yescharacteristic
29C22×C4×C47C2×C811yescharacteristic
30C22×C4×C47M1611yescharacteristic
31C22×Dic47—21no—
32C2×D188—41no—
33C2×D188—42no—
34C2×C4×D47—41no—
35C2×C4×D47—41no—
36C2×C4×D47—41no—
37C2×C4×D47—41no—
38C2×C4×D47—41no—
39C2×C4×D47—41no—
40C2×C8×C47—21no—
41C2×C8×C47—21no—
42C2×C8×C47—41no—
43C2×C8×C47—41no—
44C42×C47—21no—
45C42×C47—21no—
46(C2×D47)⋊C4—42no—
47C4⋊Dic47—41no—
48C2×C47⋊C8—22no—
49C2×C47⋊C8—41no—
50C2×C47⋊C8—41no—
51C16×C47—81no—
52C47⋊C16—81no—
53C23×C47C22⋊C811yescharacteristic
54C22×D47—22no—
55C22×D47—41no—
56C22×D47—41no—
57C22×D47—41no—
58C22×D47—41no—
59C22×D47—41no—
60C22×D47—41no—
61C2×C4×C47—21no—
62C2×C4×C47—21no—
63C2×C4×C47—21no—
64C2×C4×C47—21no—
65C2×C4×C47—21no—
66C2×C4×C47—21no—
67C2×C4×C47—41no—
68C2×C4×C47#9911yescharacteristic
69C2×C4×C47#10011yescharacteristic
70C2×Dic47—41no—
71C2×Dic47—41no—
72C2×Dic47—41no—
73D188—42no—
74D188—42no—
75C4×D47—81no—
76C4×D47—81no—
77C4×D47—81no—
78C4×D47—81no—
79C8×C47—41no—
80C8×C47—41no—
81C47⋊C8—42no—
82#7060—471nomaximal, Sylow
83C22×C47—21no—
84C22×C47—21no—
85C22×C47#32311yescharacteristic
86C22×C47#35011yescharacteristic
87C22×C47#35011yescharacteristic
88C2×D47—42no—
89C2×D47—42no—
90C2×D47—42no—
91C2×D47—81no—
92C2×D47—81no—
93C2×D47—81no—
94C2×D47—81no—
95C4×C47—21no—
96C4×C47—41no—
97C4×C47—41no—
98C4×C47#35311yescharacteristic
99C4×C47#35511yescharacteristic
100Dic47—81no—
101#1955—471no—
102#1322—471no—
103#1322D4711yescharacteristic, complemented
104C2×C47—21no—
105C2×C47—21no—
106C2×C47#131511yescharacteristic
107C2×C47#131811yescharacteristic
108C2×C47#132011yescharacteristic
109D47—82no—
110C2×C4×D4—471no—
111C2×C4⋊C8C2×D4711yescharacteristic
112C2×C22⋊C8—941no—
113C2×C22⋊C8—941no—
114C2×#97—471no—
115C22⋊C16—21no—
116C22⋊C16—941no—
117C47#706011yescharacteristic, complemented, Sylow
118C22×D4—471no—
119C23×C4—941no—
120C22×C8—941no—
121C22×C8D18811yescharacteristic
122C22×C8C22⋊D4711yescharacteristic
123C4×D4—1881no—
124C4×D4—1881no—
125C2×C4⋊C4—471no—
126C2×C22⋊C4—941no—
127C2×C42C4×D4711yescharacteristic
128C2×C16—41no—
129C2×C16—1881no—
130C4⋊C8—41no—
131C22⋊C8—1882no—
132C22⋊C8—1882no—
133#97—1881no—
134C24—941no—
135C2×D4—1881no—
136C2×D4—1882no—
137C22×C4—941no—
138C22×C4—1881no—
139C22×C4—1881no—
140C22×C4—1881no—
141C22×C4—1881no—
142C22×C4—1881no—
143C22×C4—1881no—
144C22×C4C8×D4711yescharacteristic
145C22×C4#1062532411yescharacteristic
146C22×C4(C2×D47)⋊C411yescharacteristic
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—41no—
150C2×C8—41no—
151C2×C8—942no—
152C2×C8—1881no—
153C2×C8—1881no—
154C4⋊C4—1881no—
155C22⋊C4—1882no—
156C42—21no—
157C42—21no—
158C16—81no—
159C16—3761no—
160C23—942no—
161C23—1881no—
162C23—1881no—
163C23—1881no—
164C23—1881no—
165C23—1881no—
166C23—1881no—
167C23(C2×D47)⋊C811yescharacteristic
168D4—1882no—
169D4—1882no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—41no—
177C2×C4—3761no—
178C2×C4—3761no—
179C2×C4—3761no—
180C2×C4—3761no—
181C2×C4—1881no—
182C2×C4—1881no—
183C2×C4—1881no—
184C2×C4#1309393811yescharacteristic
185C2×C4#1309394011yescharacteristic
186C8—41no—
187C8—41no—
188C8—1882no—
189C22—21no—
190C22—21no—
191C22—3761no—
192C22—3761no—
193C22—3761no—
194C22—3761no—
195C22—1882no—
196C22—1882no—
197C22—1882no—
198C22#1568884611yescharacteristic
199C22#1568890611yescharacteristic
200C22#1568890811yescharacteristic
201C4—21no—
202C4—41no—
203C4—41no—
204C4—3761no—
205C4#1568891511yescharacteristic
206C4#1568891911yescharacteristic
207C2—21no—
208C2—21no—
209C2—3762no—
210C2#2024131311yescharacteristic
211C2#2024131911yescharacteristic
212C2#2024132311yescharacteristic
subgroupG/H
centerC2×C4#13093938
commutatorC22×C4×C47C2×C8
FrattiniC2×C4⋊C8C2×D47
FittingC47×#1322C2
socleC22×C47#323
prime radicalC22×D188C8
cosocleC2×C4⋊C8×C47C22
hypercenter#1322D47
hypocenterC47#7060
LCSG ▷ C22×C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #1322

Complements

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

NH ≅ G/Ntype
2. #20241328C2semidirect
3. C47×#1322C2semidirect
103. #1322D47semidirect
117. C47#7060semidirect

Maximal subgroups

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

subgroupindex
#202441852
#202413282
C47×#13222
#706047