Finite Group Databasebeta

← #26128252

Subgroups — #26128252

Order 12032.

218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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#20245254C211yesmaximal, characteristic
2#20242303C211yesmaximal, characteristic
3#20242208C211yesmaximal, characteristic, complemented
4#20241454C211yesmaximal, characteristic, complemented
5#20241359C211yesmaximal, characteristic, complemented
6#20241356C211yesmaximal, characteristic
7C47×#1313C211yesmaximal, characteristic, complemented
8C2×#13093969C411yescharacteristic
9C8×Dic94—21no—
10C4×Dic188C2211yescharacteristic
11C4×D376C2211yescharacteristic
12#15689202—21no—
13#15688949C411yescharacteristic
14#15688928C411yescharacteristic
15#15688925C411yescharacteristic
16#15688874C2211yescharacteristic
17#15688874C2211yescharacteristic
18#15688855—21no—
19#15688852—21no—
20C47×#346C2211yescharacteristic
21C47×#346C2211yescharacteristic
22C47×#322C2211yescharacteristic
23C2×Dic188C2×C411yescharacteristic
24C2×D376C2×C411yescharacteristic
25C2×#10625324—41no—
26C4×Dic94—21no—
27C4×D188—21no—
28#13093969—22no—
29#13093958C2×C411yescharacteristic
30#13093958C2×C411yescharacteristic
31C4⋊(C47⋊C8)—21no—
32C4⋊(C47⋊C8)—21no—
33Dic47⋊C8—41no—
34#13093949—21no—
35#13093946—21no—
36(C2×D47)⋊C8—41no—
37C8×Dic47—41no—
38C2×C16×C47—21no—
39C2×C16×C47C2×C411yescharacteristic
40C2×C16×C47C2×C411yescharacteristic
41C4×C8×C47D411yescharacteristic
42C4×C8×C47D411yescharacteristic
43C4×C8×C47C2311yescharacteristic
44C2×D188—21no—
45C2×C4×D47—41no—
46C2×Dic94—21no—
47C2×C8×C47—21no—
48C2×C8×C47—21no—
49C2×C8×C47C22×C411yescharacteristic
50C2×C8×C47#4111yescharacteristic
51C42×C47C2×D411yescharacteristic
52(C2×D47)⋊C4—41no—
53C4⋊Dic47—21no—
54C4⋊Dic47—21no—
55Dic47⋊C4—41no—
56C4×Dic47—41no—
57C2×C47⋊C8—41no—
58C2×C47⋊C8—41no—
59Dic188—21no—
60Dic188M1612yescomplemented
61D376—21no—
62D376—21no—
63#10625324—82no—
64C16×C47—22no—
65C16×C47—21no—
66C16×C47—21no—
67C22×D47—41no—
68C2×C4×C47C4×D411yescharacteristic
69C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
70C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
71C2×Dic47—41no—
72C2×Dic47—41no—
73C2×Dic47—41no—
74D188—41no—
75D188—41no—
76C4×D47—81no—
77C4×D47—81no—
78Dic94—22no—
79Dic94—41no—
80C8×C47—21no—
81C8×C47—41no—
82C8×C47—41no—
83C8×C47C2×M1611yescharacteristic
84C8×C47#13111yescharacteristic
85C47⋊C8—81no—
86C47⋊C8—81no—
87#12080—471nomaximal, Sylow
88C22×C47#44211yescharacteristic
89C2×D47—81no—
90C2×D47—81no—
91C2×D47—81no—
92C4×C47—21no—
93C4×C47—21no—
94C4×C47#43511yescharacteristic
95C4×C47#44311yescharacteristic
96Dic47—42no—
97Dic47—81no—
98Dic47—81no—
99#2175—471no—
100#1594—471no—
101#1579—471no—
102#1368—471no—
103#1334—471no—
104#1333—471no—
105#1313D4711yescharacteristic, complemented
106C2×C47#158611yescharacteristic
107C2×C47#218011yescharacteristic
108C2×C47AGL(1,ℤ/16)11yescharacteristic
109D47—161no—
110C2×SD32—471no—
111C8×Q8—941no—
112C4×Q16—471no—
113C4×D8—471no—
114#436—941no—
115#366—471no—
116#358—471no—
117#357—471no—
118#346C2×D4711yescharacteristic
119#346C2×D4711yescharacteristic
120#334—471no—
121#334—471no—
122Q8⋊C8—941no—
123D4⋊C8—941no—
124#322C2×D4711yescharacteristic
125C47#1208011yescharacteristic, complemented, Sylow
126C2×Q16—471no—
127C2×D8—471no—
128C2×M16—1881no—
129C4×Q8—941no—
130C4×D4—941no—
131SD32—942no—
132C2×C16—21no—
133C2×C16C4×D4711yescharacteristic
134C2×C16C4×D4711yescharacteristic
135#107—471no—
136#107—471no—
137C4⋊C8—941no—
138C4⋊C8—941no—
139C4⋊C8—1881no—
140#103—941no—
141#102—941no—
142C22⋊C8—1881no—
143C4×C8—1881no—
144C4×C8D18811yescharacteristic
145C4×C8D18811yescharacteristic
146C4×C8C22×D4711yescharacteristic
147C2×Q8—941no—
148C2×D4—941no—
149C22×C4—1881no—
150Q16—472no—
151Q16—941no—
152D8—941no—
153D8—941no—
154M16—3762no—
155C2×C8—21no—
156C2×C8—21no—
157C2×C8—1881no—
158C2×C8—1881no—
159C2×C8C2×C4×D4711yescharacteristic
160C2×C8#1062535011yescharacteristic
161C4⋊C4—941no—
162C4⋊C4—941no—
163C4⋊C4—1881no—
164C22⋊C4—1881no—
165C42—1881no—
166C42C2×D18811yescharacteristic
167C16—22no—
168C16—21no—
169C16—21no—
170C23—1881no—
171Q8—942no—
172Q8—1881no—
173D4—1881no—
174D4—1881no—
175C2×C4—3761no—
176C2×C4—3761no—
177C2×C4—1881no—
178C2×C4—1881no—
179C2×C4—1881no—
180C2×C4C4×D18811yescharacteristic
181C2×C4#1309405211yescharacteristic
182C2×C4#1309405211yescharacteristic
183C8—21no—
184C8—41no—
185C8—41no—
186C8—3761no—
187C8—3761no—
188C8M16×D4711yescharacteristic
189C8#1309403211yescharacteristic
190C22—3761no—
191C22—3761no—
192C22—3761no—
193C22#1568923611yescharacteristic
194C4—21no—
195C4—21no—
196C4—3761no—
197C4—3761no—
198C4—1882no—
199C4#1568919611yescharacteristic
200C4#1568924111yescharacteristic
201C2—7521no—
202C2#2024225411yescharacteristic
203C2#2024528111yescharacteristic
204C2#2024528811yescharacteristic
subgroupG/H
centerC22#15689236
commutatorC2×C8×C47C22×C4
FrattiniC4×C8C22×D47
FittingC47×#1313C2
socleC22×C47#442
prime radicalC2×D376C2×C4
cosocleC4×C8×C47C23
hypercenter#1313D47
hypocenterC47#12080
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #322 ◁ #1313

Complements

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

NH ≅ G/Ntype
3. #20242208C2semidirect
4. #20241454C2semidirect
5. #20241359C2semidirect
7. C47×#1313C2semidirect
60. Dic188M16semidirect
105. #1313D47semidirect
125. C47#12080semidirect

Maximal subgroups

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

subgroupindex
#202452542
#202423032
#202422082
#202414542
#202413592
#202413562
C47×#13132
#1208047