Finite Group Databasebeta

← #26128186

Subgroups — #26128186

Order 12032.

224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C4×#13093969C211yesmaximal, characteristic
2#20242272C211yesmaximal, characteristic
3#20242194C211yesmaximal, characteristic, complemented
4#20241351C211yesmaximal, characteristic, complemented
5#20241348C211yesmaximal, characteristic
6#20241307C211yesmaximal, characteristic, complemented
7C47×#1372C211yesmaximal, characteristic, complemented
8C2×#13093969C411yescharacteristic
9#15689247—21no—
10C4×Dic188C2211yescharacteristic
11C4×D376C2211yescharacteristic
12#15689200—21no—
13#15688951C411yescharacteristic
14#15688928C411yescharacteristic
15#15688925C411yescharacteristic
16C4×C47⋊C16C2211yescharacteristic
17#15688853—21no—
18#15688850—21no—
19C8×C47⋊C8C2211yescharacteristic
20C4×C16×C47C2211yescharacteristic
21C47×#335C2211yescharacteristic
22C47×#335C2211yescharacteristic
23C2×Dic188C2×C411yescharacteristic
24C2×D376C2×C411yescharacteristic
25C2×#10625324—41no—
26C4×Dic94—21no—
27C4×D188—21no—
28#13093969—22no—
29C2×C47⋊C16—21no—
30#13093958C2×C411yescharacteristic
31#13093958C2×C411yescharacteristic
32Dic47⋊C8—41no—
33#13093949—21no—
34#13093946—21no—
35(C2×D47)⋊C8—41no—
36C4×C47⋊C8D411yescharacteristic
37C4×C47⋊C8D411yescharacteristic
38C8×Dic47—41no—
39C2×C16×C47C2×C411yescharacteristic
40C2×C16×C47C2×C411yescharacteristic
41C4⋊C8×C47—21no—
42C4⋊C8×C47—21no—
43C4×C8×C47C2311yescharacteristic
44C2×D188—21no—
45C2×C4×D47—41no—
46C2×Dic94—21no—
47C2×C8×C47—41no—
48C2×C8×C47—41no—
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—21no—
58C2×C47⋊C8D811yescharacteristic
59C2×C47⋊C8D811yescharacteristic
60Dic188—21no—
61Dic188M1612yescomplemented
62D376—21no—
63D376—21no—
64#10625324—82no—
65C16×C47—21no—
66C16×C47—21no—
67C47⋊C16—41no—
68C22×D47—41no—
69C2×C4×C47C4×D411yescharacteristic
70C2×C4×C47C2×D811yescharacteristic
71C2×C4×C47#13511yescharacteristic
72C2×Dic47—41no—
73C2×Dic47—41no—
74C2×Dic47—41no—
75D188—41no—
76D188—41no—
77C4×D47—81no—
78C4×D47—81no—
79Dic94—22no—
80Dic94—41no—
81C8×C47—21no—
82C8×C47—81no—
83C8×C47—81no—
84C8×C47C2×M1611yescharacteristic
85C8×C47#13111yescharacteristic
86C47⋊C8—21no—
87C47⋊C8—41no—
88C47⋊C8SD3212yescomplemented
89#12071—471nomaximal, Sylow
90C22×C47C4×D811yescharacteristic
91C2×D47—81no—
92C2×D47—81no—
93C2×D47—81no—
94C4×C47—21no—
95C4×C47#43511yescharacteristic
96C4×C47#44411yescharacteristic
97C4×C47C2×SD3211yescharacteristic
98C4×C47#50811yescharacteristic
99Dic47—42no—
100Dic47—81no—
101Dic47—81no—
102C4×SD32—471no—
103#1589—471no—
104C8×Q16—471no—
105#1372D4711yescharacteristic, complemented
106#1332—471no—
107#1331—471no—
108#1312—471no—
109C2×C47#158111yescharacteristic
110C2×C47C4×SD3211yescharacteristic
111C2×C47#217911yescharacteristic
112D47—161no—
113C2×SD32—471no—
114C8×Q8—941no—
115C4×Q16—471no—
116C4×D8—471no—
117#436—941no—
118#367—471no—
119#358—471no—
120#357—471no—
121C4×C16—471no—
122C4×C16C2×D4711yescharacteristic
123#335C2×D4711yescharacteristic
124#335C2×D4711yescharacteristic
125Q8⋊C8—941no—
126D4⋊C8—941no—
127C82—471no—
128C47#1207111yescharacteristic, complemented, Sylow
129C2×Q16—471no—
130C2×D8—471no—
131C2×M16—1881no—
132C4×Q8—941no—
133C4×D4—941no—
134SD32—942no—
135C2×C16—941no—
136C2×C16C4×D4711yescharacteristic
137C2×C16C4×D4711yescharacteristic
138#107—471no—
139#107—471no—
140C4⋊C8—21no—
141C4⋊C8—21no—
142C4⋊C8—1881no—
143#103—941no—
144#102—941no—
145C22⋊C8—1881no—
146C4×C8—471no—
147C4×C8—471no—
148C4×C8—1881no—
149C4×C8C22×D4711yescharacteristic
150C2×Q8—941no—
151C2×D4—941no—
152C22×C4—1881no—
153Q16—472no—
154Q16—941no—
155D8—941no—
156D8—941no—
157M16—3762no—
158C2×C8—41no—
159C2×C8—41no—
160C2×C8—471no—
161C2×C8—471no—
162C2×C8—941no—
163C2×C8C2×C4×D4711yescharacteristic
164C2×C8#1062535411yescharacteristic
165C4⋊C4—941no—
166C4⋊C4—941no—
167C4⋊C4—1881no—
168C22⋊C4—1881no—
169C42—1881no—
170C42D4×D4711yescharacteristic
171C16—21no—
172C16—21no—
173C16—1881no—
174C23—1881no—
175Q8—942no—
176Q8—1881no—
177D4—1881no—
178D4—1881no—
179C2×C4—3761no—
180C2×C4—3761no—
181C2×C4—1881no—
182C2×C4—1881no—
183C2×C4—1881no—
184C2×C4#1309398611yescharacteristic
185C2×C4D8×D4711yescharacteristic
186C2×C4#1309404711yescharacteristic
187C8—21no—
188C8—81no—
189C8—81no—
190C8—472no—
191C8—941no—
192C8—1881no—
193C8M16×D4711yescharacteristic
194C8#1309403011yescharacteristic
195C22—3761no—
196C22—3761no—
197C22—3761no—
198C22#1568920511yescharacteristic
199C4—21no—
200C4—3761no—
201C4—3761no—
202C4—1882no—
203C4#1568919311yescharacteristic
204C4#1568924411yescharacteristic
205C4SD32×D4711yescharacteristic
206C4#1568955411yescharacteristic
207C2—7521no—
208C2#2024221611yescharacteristic
209C2#2024523911yescharacteristic
210C2#2024527311yescharacteristic
subgroupG/H
centerC2×C4D8×D47
commutatorC2×C8×C47C22×C4
FrattiniC4×C8C22×D47
FittingC47×#1372C2
socleC22×C47C4×D8
prime radicalC2×D376C2×C4
cosocleC4×C8×C47C23
hypercenter#1372D47
hypocenterC47#12071
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #1372

Complements

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

NH ≅ G/Ntype
3. #20242194C2semidirect
4. #20241351C2semidirect
6. #20241307C2semidirect
7. C47×#1372C2semidirect
61. Dic188M16semidirect
88. C47⋊C8SD32semidirect
105. #1372D47semidirect
128. C47#12071semidirect

Maximal subgroups

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

subgroupindex
C4×#130939692
#202422722
#202421942
#202413512
#202413482
#202413072
C47×#13722
#1207147