Finite Group Databasebeta

← #26130525

Subgroups — #26130525

Order 12032.

224 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 59 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#20245466C211yesmaximal, characteristic, complemented
2#20245461C211yesmaximal, characteristic
3#20245226C211yesmaximal, characteristic, complemented
4#20241464C211yesmaximal, characteristic, complemented
5#20241427C211yesmaximal, characteristic, complemented
6#20241425C211yesmaximal, characteristic, complemented
7C47×#2248C211yesmaximal, characteristic, complemented
8#15689564—21no—
9#15689559—21no—
10#15689539—21no—
11#15689241C2211yescharacteristic
12#15688944C2211yescharacteristic
13#15688944C2211yescharacteristic
14#15688944C2211yescharacteristic
15#15688939—21no—
16#15688936—21no—
17#15688906—21no—
18C2×SD32×C47—21no—
19C2×SD32×C47—21no—
20C47×#494C2211yescharacteristic
21C47×#493C2211yescharacteristic
22C4×C16×C47C2211yescharacteristic
23#13094046D411yescharacteristic
24#13094030—21no—
25#13093970—41no—
26#13093968—41no—
27#13093967—41no—
28#13093965—41no—
29#13093964—21no—
30#13093964—21no—
31#13093964—21no—
32#13093963—41no—
33C16×D47—41no—
34#13093960D411yescharacteristic
35#13093952—21no—
36C2×Q16×C47—21no—
37C2×Q16×C47—21no—
38C2×D8×C47—21no—
39C2×D8×C47—21no—
40C4⋊Q8×C47—21no—
41#127×C47—21no—
42SD32×C47—42no—
43SD32×C47—41no—
44SD32×C47—41no—
45C2×C16×C47D411yescharacteristic
46C2×C16×C47D411yescharacteristic
47C4×C8×C47C2311yescharacteristic
48C2×Q8×C47—41no—
49C2×D4×C47—41no—
50C2×D4×C47—81no—
51#10625350—21no—
52Q16×C47—41no—
53Q16×C47—41no—
54Q16×C47—41no—
55Q16×C47—41no—
56D8×C47—41no—
57D8×C47—41no—
58D8×C47—41no—
59D8×C47—41no—
60C2×C8×C47C2×D411yescharacteristic
61C2×C8×C47C2×D411yescharacteristic
62C4⋊C4×C47—81no—
63C42×C47#4111yescharacteristic
64#10625329—21no—
65Dic188D811yescharacteristic
66D376D811yescharacteristic
67#10625325—21no—
68#10625324—41no—
69C8×D47—41no—
70C16×C47—21no—
71C16×C47D811yescharacteristic
72C16×C47D811yescharacteristic
73C47⋊C16—41no—
74C47⋊C16—41no—
75C47⋊C16—41no—
76C23×C47—81no—
77Q8×C47—81no—
78Q8×C47—81no—
79D4×C47—81no—
80D4×C47—81no—
81D4×C47—162no—
82C2×C4×C47—21no—
83C2×C4×C47—81no—
84C2×C4×C47#12111yescharacteristic
85C22⋊D47—41no—
86D188—21no—
87C4×D47—41no—
88Dic94—21no—
89C8×C47C2×D811yescharacteristic
90C8×C47C2×D811yescharacteristic
91C8×C47#13511yescharacteristic
92C8×C47AGL(1,ℤ/8)11yescharacteristic
93C47⋊C8—41no—
94#12438—471nomaximal, Sylow
95C22×C47—162no—
96C22×C47—161no—
97C22×C47#47211yescharacteristic
98C2×D47—41no—
99C4×C47—22no—
100C4×C47—161no—
101C4×C47#45911yescharacteristic
102C4×C47#46611yescharacteristic
103Dic47—41no—
104#2248D4711yescharacteristic, complemented
105#2214—471no—
106#2213—471no—
107#2170—471no—
108#1373—471no—
109#1358—471no—
110#1357—471no—
111C2×C47—21no—
112C2×C47—321no—
113C2×C47#166711yescharacteristic
114D47—81no—
115#510—941no—
116#509—941no—
117C2×SD32—21no—
118C2×SD32—21no—
119#504—941no—
120#494C2×D4711yescharacteristic
121#493C2×D4711yescharacteristic
122#443—471no—
123#364—471no—
124#364—471no—
125#364—471no—
126#362—941no—
127#361—941no—
128#350—941no—
129C4×C16C2×D4711yescharacteristic
130C47#1243811yescharacteristic, complemented, Sylow
131#135—471no—
132C2×Q16—21no—
133C2×Q16—21no—
134C2×D8—21no—
135C2×D8—21no—
136#131—941no—
137C4⋊Q8—21no—
138#127—21no—
139Q32—1881no—
140SD32—42no—
141SD32—41no—
142SD32—41no—
143SD32—1881no—
144SD32—1881no—
145D16—1881no—
146M32—941no—
147M32—941no—
148M32—941no—
149M32—1881no—
150C2×C16—1881no—
151C2×C16C22⋊D4711yescharacteristic
152C2×C16C22⋊D4711yescharacteristic
153#108—471no—
154#104—941no—
155C4×C8C22×D4711yescharacteristic
156#41—941no—
157C2×Q8—41no—
158C2×D4—41no—
159C2×D4—81no—
160Q16—41no—
161Q16—41no—
162Q16—41no—
163Q16—41no—
164Q16—471no—
165SD16—941no—
166D8—41no—
167D8—41no—
168D8—41no—
169D8—41no—
170D8—471no—
171M16—941no—
172M16—1881no—
173C2×C8—1881no—
174C2×C8D4×D4711yescharacteristic
175C2×C8C2×C22⋊D4711yescharacteristic
176C4⋊C4—81no—
177C42#1062535211yescharacteristic
178C16—21no—
179C16—1881no—
180C16—1881no—
181C16—1881no—
182C16#1062533411yescharacteristic
183C16#1062533411yescharacteristic
184C23—81no—
185Q8—81no—
186Q8—81no—
187Q8—941no—
188D4—81no—
189D4—81no—
190D4—162no—
191D4—941no—
192D4—1881no—
193C2×C4—21no—
194C2×C4—81no—
195C2×C4—1881no—
196C2×C4#1309399511yescharacteristic
197C8—1881no—
198C8D8×D4711yescharacteristic
199C8C2×#1062533411yescharacteristic
200C8#1309404311yescharacteristic
201C8#1309405011yescharacteristic
202C22—162no—
203C22—161no—
204C22—1881no—
205C22#1568939011yescharacteristic
206C4—22no—
207C4—161no—
208C4—1881no—
209C4#1568931511yescharacteristic
210C4#1568935611yescharacteristic
211C2—21no—
212C2—321no—
213C2—3761no—
214C2#2024274011yescharacteristic
subgroupG/H
centerC2#20242740
commutator, cosocleC4×C8×C47C23
FrattiniC4×C8C22×D47
FittingC47×#2248C2
socleC2×C47#1667
prime radical#20245461C2
hypercenter#2248D47
hypocenterC47#12438
LCSG ▷ C4×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2248

Complements

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

NH ≅ G/Ntype
1. #20245466C2semidirect
3. #20245226C2semidirect
4. #20241464C2semidirect
5. #20241427C2semidirect
6. #20241425C2semidirect
7. C47×#2248C2semidirect
104. #2248D47semidirect
130. C47#12438semidirect

Maximal subgroups

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

subgroupindex
#202454662
#202454612
#202452262
#202414642
#202414272
#202414252
C47×#22482
#1243847