Finite Group Databasebeta

← #26130480

Subgroups — #26130480

Order 12032.

240 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 63 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#20245435C211yesmaximal, characteristic, complemented
2#20245429C211yesmaximal, characteristic
3#20242995C211yesmaximal, characteristic
4#20242194C211yesmaximal, characteristic, complemented
5#20241457C211yesmaximal, characteristic, complemented
6#20241433C211yesmaximal, characteristic
7C47×#1362C211yesmaximal, characteristic, complemented
8C2×#13093970—21no—
9C2×#13093969—21no—
10#15689500C2211yescharacteristic
11#15689471—21no—
12#15689471—21no—
13#15689247—21no—
14C4×Dic188C2211yescharacteristic
15C4⋊(C47⋊C16)C2211yescharacteristic
16#15688927—21no—
17#15688925—21no—
18#15688853—21no—
19C8×C47⋊C8C2211yescharacteristic
20C47×#494C2211yescharacteristic
21C47×C4⋊C16C2211yescharacteristic
22C47×#335C2211yescharacteristic
23C2×Dic188D411yescharacteristic
24C2×D376—21no—
25C2×D376—21no—
26#13094021—21no—
27C4×Dic94—21no—
28#13093970—42no—
29#13093969—42no—
30C2×C47⋊C16—21no—
31#13093958D411yescharacteristic
32Dic47⋊C8—41no—
33#13093949—21no—
34#13093944—42no—
35#13093944—41no—
36#13093944—41no—
37C4×C47⋊C8D411yescharacteristic
38C4×C47⋊C8D411yescharacteristic
39C8×Dic47—41no—
40C2×Q16×C47—21no—
41C2×Q16×C47—21no—
42C4⋊Q8×C47—21no—
43C2×C16×C47—21no—
44C4⋊C8×C47—21no—
45C4×C8×C47C2311yescharacteristic
46C2×Q8×C47—41no—
47C2×D188—41no—
48C2×D188—41no—
49C2×D188—41no—
50C2×Dic94—21no—
51Q16×C47—41no—
52Q16×C47—41no—
53Q16×C47—81no—
54C2×C8×C47—41no—
55C2×C8×C47C2×D411yescharacteristic
56C2×C8×C47#4111yescharacteristic
57C4⋊C4×C47—41no—
58C4⋊C4×C47—41no—
59C42×C47C2×D411yescharacteristic
60C4⋊Dic47—21no—
61Dic47⋊C4—41no—
62C4×Dic47—41no—
63C2×C47⋊C8—21no—
64C2×C47⋊C8D811yescharacteristic
65C2×C47⋊C8D811yescharacteristic
66Dic188—21no—
67Dic188D812yes—
68D376—41no—
69D376—41no—
70D376—81no—
71C16×C47—41no—
72C47⋊C16—41no—
73C22×D47—81no—
74Q8×C47—81no—
75Q8×C47—81no—
76C2×C4×C47—81no—
77C2×C4×C47#12111yescharacteristic
78C2×C4×C47C2×D811yescharacteristic
79C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
80C2×Dic47—41no—
81C2×Dic47—41no—
82D188—82no—
83D188—81no—
84D188—81no—
85D188—81no—
86D188—81no—
87Dic94—22no—
88Dic94—41no—
89C8×C47—21no—
90C8×C47—81no—
91C8×C47C2×D811yescharacteristic
92C8×C47#13511yescharacteristic
93C47⋊C8—21no—
94C47⋊C8—21no—
95C47⋊C8—41no—
96#12429—471nomaximal, Sylow
97C22×C47#45911yescharacteristic
98C2×D47—161no—
99C2×D47—161no—
100C2×D47—161no—
101C4×C47—21no—
102C4×C47—161no—
103C4×C47#46611yescharacteristic
104C4×C47#47211yescharacteristic
105C4×C47#50811yescharacteristic
106C4×C47#51011yescharacteristic
107Dic47—42no—
108Dic47—81no—
109#2209—471no—
110#2207—471no—
111#1709—471no—
112C8×Q16—471no—
113#1370—471no—
114#1362D4711yescharacteristic, complemented
115#1361—471no—
116C2×C47#166711yescharacteristic
117C2×C47#221111yescharacteristic
118C2×C47#221211yescharacteristic
119D47—321no—
120C2×Q32—941no—
121C2×SD32—941no—
122#494C2×D4711yescharacteristic
123#493—471no—
124#486—941no—
125#486—941no—
126C8×Q8—941no—
127C4×Q16—471no—
128C4⋊C16—471no—
129C4⋊C16C2×D4711yescharacteristic
130#358—941no—
131#357—941no—
132#335C2×D4711yescharacteristic
133Q8⋊C8—941no—
134C82—471no—
135C47#1242911yescharacteristic, complemented, Sylow
136C2×Q16—21no—
137C2×Q16—21no—
138C2×Q16—471no—
139C2×D8—941no—
140C2×D8—941no—
141C4⋊Q8—21no—
142#127—941no—
143C4×Q8—941no—
144Q32—1882no—
145SD32—1882no—
146C2×C16—21no—
147C2×C16—941no—
148#107—471no—
149C4⋊C8—21no—
150C4⋊C8—1881no—
151#103—941no—
152#102—1881no—
153#102—1881no—
154#102—1882no—
155C4×C8—471no—
156C4×C8—471no—
157C4×C8—1881no—
158C4×C8C22×D4711yescharacteristic
159C2×Q8—41no—
160C2×Q8—941no—
161C2×D4—1881no—
162C2×D4—1881no—
163C2×D4—1881no—
164Q16—41no—
165Q16—41no—
166Q16—81no—
167Q16—472no—
168Q16—941no—
169D8—3761no—
170D8—1881no—
171D8—1881no—
172C2×C8—41no—
173C2×C8—471no—
174C2×C8—471no—
175C2×C8—941no—
176C2×C8#1062535011yescharacteristic
177C2×C8D4×D4711yescharacteristic
178C4⋊C4—41no—
179C4⋊C4—41no—
180C4⋊C4—941no—
181C4⋊C4—1881no—
182C42—1881no—
183C42D4×D4711yescharacteristic
184C16—41no—
185C16—1881no—
186C23—3761no—
187Q8—81no—
188Q8—81no—
189Q8—942no—
190Q8—1881no—
191D4—3762no—
192D4—3761no—
193D4—3761no—
194D4—3761no—
195D4—3761no—
196C2×C4—81no—
197C2×C4—1881no—
198C2×C4—1881no—
199C2×C4#1309399711yescharacteristic
200C2×C4D8×D4711yescharacteristic
201C2×C4#1309405111yescharacteristic
202C8—21no—
203C8—81no—
204C8—941no—
205C8—941no—
206C8—1881no—
207C8D8×D4711yescharacteristic
208C8#1309404511yescharacteristic
209C22—7521no—
210C22—7521no—
211C22—7521no—
212C22#1568931711yescharacteristic
213C4—21no—
214C4—161no—
215C4—3761no—
216C4—1882no—
217C4#1568935811yescharacteristic
218C4#1568939211yescharacteristic
219C4#1568955411yescharacteristic
220C4#1568956511yescharacteristic
221C2—15041no—
222C2#2024274211yescharacteristic
223C2#2024545311yescharacteristic
224C2#2024546011yescharacteristic
subgroupG/H
centerC22#15689317
commutator, cosocleC4×C8×C47C23
FrattiniC4×C8C22×D47
FittingC47×#1362C2
socleC22×C47#459
prime radical#15689500C22
hypercenter#1362D47
hypocenterC47#12429
LCSG ▷ C4×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
1. #20245435C2semidirect
4. #20242194C2semidirect
5. #20241457C2semidirect
7. C47×#1362C2semidirect
114. #1362D47semidirect
135. C47#12429semidirect

Maximal subgroups

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

subgroupindex
#202454352
#202454292
#202429952
#202421942
#202414572
#202414332
C47×#13622
#1242947