Finite Group Databasebeta

← #26130416

Subgroups — #26130416

Order 12032.

240 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 67 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#20245541C211yesmaximal, characteristic, complemented
2#20245429C211yesmaximal, characteristic
3#20242980C211yesmaximal, characteristic
4C8×Dic188C211yesmaximal, characteristic, complemented
5#20241445C211yesmaximal, characteristic, complemented
6#20241435C211yesmaximal, characteristic
7C47×#1367C211yesmaximal, characteristic, complemented
8C2×#13093969—21no—
9#15689528C2211yescharacteristic
10#15689500C2211yescharacteristic
11#15689496—21no—
12#15689470—21no—
13C8×Dic94—21no—
14C4×Dic188C2211yescharacteristic
15#15688949—21no—
16#15688928—21no—
17#15688925—21no—
18#15688876C2211yescharacteristic
19#15688855—21no—
20C47×C4⋊C16C2211yescharacteristic
21C47×C4⋊C16C2211yescharacteristic
22C82×C47C2211yescharacteristic
23C2×Dic188D411yescharacteristic
24C2×#10625325—42no—
25C2×D376—21no—
26C2×D376—21no—
27#13094024—21no—
28#13094021—21no—
29C4×Dic94—21no—
30#13093969—42no—
31#13093958—21no—
32#13093958—21no—
33#13093958D411yescharacteristic
34C4⋊(C47⋊C8)—21no—
35Dic47⋊C8—41no—
36#13093949—21no—
37#13093946—41no—
38#13093946—41no—
39C8×Dic47—41no—
40C2×C16×C47—21no—
41C2×C16×C47—21no—
42C4×C8×C47D411yescharacteristic
43C4×C8×C47D411yescharacteristic
44C4×C8×C47C2311yescharacteristic
45C2×D188—41no—
46C2×D188—41no—
47C2×D188—41no—
48C2×Dic94—21no—
49C2×Dic94—41no—
50C2×C8×C47—21no—
51C2×C8×C47D811yescharacteristic
52C2×C8×C47D811yescharacteristic
53C2×C8×C47C2×D411yescharacteristic
54C2×C8×C47#4111yescharacteristic
55C42×C47C2×D411yescharacteristic
56C4⋊Dic47—21no—
57C4⋊Dic47—41no—
58C4⋊Dic47—41no—
59Dic47⋊C4—41no—
60C4×Dic47—41no—
61C2×C47⋊C8—41no—
62Dic188—21no—
63Dic188SD1612yescomplemented
64D376—41no—
65D376—41no—
66D376—81no—
67#10625325—84no—
68C16×C47—41no—
69C16×C47—41no—
70C22×D47—81no—
71C2×C4×C47#12111yescharacteristic
72C2×C4×C47C2×D811yescharacteristic
73C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
74C2×Dic47—41no—
75C2×Dic47—41no—
76C2×Dic47—81no—
77D188—82no—
78D188—81no—
79D188—81no—
80D188—81no—
81D188—81no—
82Dic94—22no—
83Dic94—41no—
84Dic94—82no—
85C8×C47—22no—
86C8×C47—21no—
87C8×C47—21no—
88C8×C47—21no—
89C8×C47C2×SD1611yescharacteristic
90C8×C47#13511yescharacteristic
91C47⋊C8—81no—
92#12419—471nomaximal, Sylow
93C22×C47#45911yescharacteristic
94C2×D47—161no—
95C2×D47—161no—
96C2×D47—161no—
97C4×C47—21no—
98C4×C47#46511yescharacteristic
99C4×C47#47111yescharacteristic
100C4×C47#50811yescharacteristic
101C4×C47#51011yescharacteristic
102Dic47—42no—
103Dic47—81no—
104Dic47—161no—
105#2227—471no—
106#2207—471no—
107#1706—471no—
108C8×Q16—471no—
109#1367D4711yescharacteristic, complemented
110#1365—471no—
111#1361—471no—
112C2×C47#166511yescharacteristic
113C2×C47#221111yescharacteristic
114C2×C47#221311yescharacteristic
115D47—321no—
116C2×SD32—941no—
117#500—471no—
118#493—471no—
119#492—941no—
120#486—941no—
121C8×Q8—941no—
122C4×Q16—471no—
123#366—941no—
124C4⋊C16C2×D4711yescharacteristic
125C4⋊C16C2×D4711yescharacteristic
126#358—941no—
127#357—941no—
128#335—471no—
129Q8⋊C8—941no—
130C82C2×D4711yescharacteristic
131C47#1241911yescharacteristic, complemented, Sylow
132C2×Q16—471no—
133C2×SD16—1882no—
134C2×D8—941no—
135C2×D8—941no—
136C4⋊Q8—941no—
137#127—941no—
138C4×Q8—941no—
139SD32—1882no—
140C2×C16—21no—
141C2×C16—21no—
142#107—471no—
143#107—941no—
144#107—941no—
145C4⋊C8—941no—
146C4⋊C8—1881no—
147#103—941no—
148#102—1881no—
149#102—1881no—
150C4×C8—1881no—
151C4×C8D18811yescharacteristic
152C4×C8D18811yescharacteristic
153C4×C8C22×D4711yescharacteristic
154C2×Q8—941no—
155C2×Q8—1881no—
156C2×D4—1881no—
157C2×D4—1881no—
158C2×D4—1881no—
159Q16—472no—
160Q16—941no—
161SD16—3764no—
162D8—3761no—
163D8—1881no—
164D8—1881no—
165C2×C8—21no—
166C2×C8—1881no—
167C2×C8D37611yescharacteristic
168C2×C8D37611yescharacteristic
169C2×C8D4×D4711yescharacteristic
170C2×C8#1062535411yescharacteristic
171C4⋊C4—941no—
172C4⋊C4—1881no—
173C4⋊C4—1881no—
174C4⋊C4—1881no—
175C42—1881no—
176C42C2×D18811yescharacteristic
177C16—41no—
178C16—41no—
179C23—3761no—
180Q8—942no—
181Q8—3762no—
182Q8—1881no—
183D4—3762no—
184D4—3761no—
185D4—3761no—
186D4—3761no—
187D4—3761no—
188C2×C4—3761no—
189C2×C4—1881no—
190C2×C4—1881no—
191C2×C4#1309399911yescharacteristic
192C2×C4C2×D37611yescharacteristic
193C2×C4#1309405211yescharacteristic
194C8—22no—
195C8—21no—
196C8—21no—
197C8—21no—
198C8—3761no—
199C8SD16×D4711yescharacteristic
200C8#1309404511yescharacteristic
201C22—7521no—
202C22—7521no—
203C22—7521no—
204C22#1568931911yescharacteristic
205C4—21no—
206C4—3761no—
207C4—1882no—
208C4—7521no—
209C4#1568935311yescharacteristic
210C4#1568938711yescharacteristic
211C4#1568955511yescharacteristic
212C4#1568956611yescharacteristic
213C2—15041no—
214C2#2024273011yescharacteristic
215C2#2024545111yescharacteristic
216C2#2024546511yescharacteristic
subgroupG/H
centerC22#15689319
commutator, cosocleC4×C8×C47C23
FrattiniC4×C8C22×D47
FittingC47×#1367C2
socleC22×C47#459
prime radical#15689500C22
hypercenter#1367D47
hypocenterC47#12419
LCSG ▷ C4×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C82 ◁ #1367

Complements

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

NH ≅ G/Ntype
1. #20245541C2semidirect
4. C8×Dic188C2semidirect
5. #20241445C2semidirect
7. C47×#1367C2semidirect
63. Dic188SD16semidirect
109. #1367D47semidirect
131. C47#12419semidirect

Maximal subgroups

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

subgroupindex
#202455412
#202454292
#202429802
C8×Dic1882
#202414452
#202414352
C47×#13672
#1241947