Finite Group Databasebeta

← #26130488

Subgroups — #26130488

Order 12032.

236 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 65 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#20245640C211yesmaximal, characteristic, complemented
2#20245207C211yesmaximal, characteristic
3#20242754C211yesmaximal, characteristic
4#20242750C211yesmaximal, characteristic
5#20241459C211yesmaximal, characteristic, complemented
6#20241438C211yesmaximal, characteristic, complemented
7C47×#1362C211yesmaximal, characteristic, complemented
8C2×#13093970—21no—
9C2×#13093970—21no—
10C2×C16×D47—21no—
11#15689503C2211yescharacteristic
12#15689404—21no—
13#15689400—21no—
14C8×D188C2211yescharacteristic
15(C2×D47)⋊C16—21no—
16C4×C47⋊C16C2211yescharacteristic
17#15688876C2211yescharacteristic
18#15688869—21no—
19#15688868—21no—
20C47×#494C2211yescharacteristic
21C47×C4⋊C16C2211yescharacteristic
22C47×#335C2211yescharacteristic
23C2×Dic188—21no—
24C2×Dic188—21no—
25C2×C8×D47—21no—
26#13094024—21no—
27C4×D188D411yescharacteristic
28#13093970—42no—
29#13093970—42no—
30C2×C47⋊C16D411yescharacteristic
31C2×C47⋊C16D411yescharacteristic
32C16×D47—42no—
33#13093958—41no—
34#13093957—41no—
35C4⋊(C47⋊C8)—21no—
36C4⋊(C47⋊C8)D411yescharacteristic
37#13093946—41no—
38#13093944—41no—
39(C2×D47)⋊C8—21no—
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×D188D811yescharacteristic
48C2×C4×D47—21no—
49C2×Dic94—41no—
50Q16×C47—41no—
51Q16×C47—41no—
52Q16×C47—81no—
53C2×C8×C47—41no—
54C2×C8×C47C2×D411yescharacteristic
55C2×C8×C47#4111yescharacteristic
56C4⋊C4×C47—41no—
57C4⋊C4×C47—41no—
58C42×C47C2×D411yescharacteristic
59(C2×D47)⋊C4—21no—
60C4⋊Dic47—41no—
61C4⋊Dic47—41no—
62C4⋊Dic47D811yescharacteristic
63C2×C47⋊C8—21no—
64C2×C47⋊C8—41no—
65Dic188—41no—
66Dic188—41no—
67Dic188—81no—
68C8×D47—41no—
69C8×D47—41no—
70C16×C47—41no—
71C47⋊C16—21no—
72C47⋊C16D812yes—
73C22×D47—21no—
74Q8×C47—81no—
75Q8×C47—81no—
76C2×C4×C47—81no—
77C2×C4×C47#12111yescharacteristic
78C2×C4×C47C2×D811yescharacteristic
79C2×C4×C47#13511yescharacteristic
80C2×Dic47—21no—
81C2×Dic47—81no—
82D188—21no—
83D188Q3212yescomplemented
84C4×D47—41no—
85C4×D47—41no—
86Dic94—81no—
87Dic94—81no—
88C8×C47—21no—
89C8×C47—81no—
90C8×C47C2×D811yescharacteristic
91C8×C47AGL(1,ℤ/8)11yescharacteristic
92C47⋊C8—41no—
93C47⋊C8—81no—
94#12431—471nomaximal, Sylow
95C22×C47#46611yescharacteristic
96C2×D47—22no—
97C2×D47—41no—
98C2×D47—41no—
99C4×C47—21no—
100C4×C47—161no—
101C4×C47#45911yescharacteristic
102C4×C47#47211yescharacteristic
103C4×C47C2×Q3211yescharacteristic
104C4×C47#50811yescharacteristic
105Dic47—41no—
106Dic47—161no—
107#2247—471no—
108D4×C16—471no—
109#1669—471no—
110#1669—471no—
111#1371—471no—
112#1362—471no—
113#1362D4711yescharacteristic, complemented
114C2×C47#166711yescharacteristic
115C2×C47#221611yescharacteristic
116C2×C47#222211yescharacteristic
117D47—42no—
118C2×Q32—941no—
119C2×Q32—941no—
120C22×C16—941no—
121#494—471no—
122#494C2×D4711yescharacteristic
123#474—941no—
124#474—941no—
125C8×D4—471no—
126C4⋊C16C2×D4711yescharacteristic
127C22⋊C16—941no—
128C4×C16—471no—
129#335—471no—
130#335C2×D4711yescharacteristic
131#332—941no—
132#332—941no—
133C47#1243111yescharacteristic, complemented, Sylow
134C2×Q16—21no—
135C2×Q16—21no—
136C2×Q16—941no—
137C2×Q16—941no—
138C22×C8—941no—
139C4⋊Q8—21no—
140C4⋊Q8—941no—
141C4×D4—471no—
142Q32—1882no—
143Q32—1882no—
144C2×C16—21no—
145C2×C16—471no—
146C2×C16—471no—
147C2×C16—1882no—
148#107—1881no—
149#107—1881no—
150C4⋊C8—21no—
151C4⋊C8—471no—
152C4⋊C8—941no—
153#102—1881no—
154#102—1881no—
155C22⋊C8—941no—
156C4×C8C22×D4711yescharacteristic
157C2×Q8—41no—
158C2×Q8—1881no—
159C2×D4—471no—
160C22×C4—941no—
161Q16—41no—
162Q16—41no—
163Q16—81no—
164Q16—3761no—
165Q16—1881no—
166Q16—1881no—
167C2×C8—41no—
168C2×C8—941no—
169C2×C8—1881no—
170C2×C8—1881no—
171C2×C8—1881no—
172C2×C8#1062535011yescharacteristic
173C2×C8D4×D4711yescharacteristic
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—471no—
177C4⋊C4—1881no—
178C4⋊C4—1881no—
179C22⋊C4—941no—
180C42D4×D4711yescharacteristic
181C16—41no—
182C16—472no—
183C16—941no—
184C23—941no—
185Q8—81no—
186Q8—81no—
187Q8—3761no—
188Q8—3761no—
189D4—472no—
190D4—941no—
191C2×C4—81no—
192C2×C4—941no—
193C2×C4—3761no—
194C2×C4—1881no—
195C2×C4—1881no—
196C2×C4#1309399711yescharacteristic
197C2×C4D8×D4711yescharacteristic
198C2×C4#1309404511yescharacteristic
199C8—21no—
200C8—81no—
201C8—3761no—
202C8—1881no—
203C8D8×D4711yescharacteristic
204C8#1309405111yescharacteristic
205C22—942no—
206C22—1881no—
207C22—1881no—
208C22#1568935811yescharacteristic
209C4—21no—
210C4—161no—
211C4—1881no—
212C4—7521no—
213C4#1568931711yescharacteristic
214C4#1568939211yescharacteristic
215C4Q32×D4711yescharacteristic
216C4#1568955411yescharacteristic
217C2—1882no—
218C2#2024274211yescharacteristic
219C2#2024547811yescharacteristic
220C2#2024551211yescharacteristic
subgroupG/H
centerC22#15689358
commutator, cosocleC4×C8×C47C23
FrattiniC4×C8C22×D47
FittingC47×#1362C2
socleC22×C47#466
prime radicalC2×D188D8
hypercenter#1362D47
hypocenterC47#12431
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. #20245640C2semidirect
5. #20241459C2semidirect
6. #20241438C2semidirect
7. C47×#1362C2semidirect
83. D188Q32semidirect
113. #1362D47semidirect
133. C47#12431semidirect

Maximal subgroups

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

subgroupindex
#202456402
#202452072
#202427542
#202427502
#202414592
#202414382
C47×#13622
#1243147