Finite Group Databasebeta

← #26137094

Subgroups — #26137094

Order 12032.

200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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#20245700C211yesmaximal, characteristic
2#20245650C211yesmaximal, characteristic, complemented
3#20245269C211yesmaximal, characteristic, complemented
4#20241585C211yesmaximal, characteristic, complemented
5#20241581C211yesmaximal, characteristic, complemented
6#20241579C211yesmaximal, characteristic, complemented
7C47×#2264C211yesmaximal, characteristic, complemented
8C2×#13093967—21no—
9C2×D752C2211yescharacteristic
10#15689508—21no—
11#15689240—21no—
12#15688960—21no—
13#15688958—21no—
14#15688957C2211yescharacteristic
15#15688953C2211yescharacteristic
16#15688930—21no—
17C16×Dic47C2211yescharacteristic
18C47×#508C2211yescharacteristic
19C2×Q32×C47C2211yescharacteristic
20C47×Q64—21no—
21C47×SD64—21no—
22C47×M64C2211yescharacteristic
23C2×#10625336—41no—
24C2×D376—21no—
25#13094031—41no—
26#13094013—41no—
27#13093967—42no—
28D752—21no—
29D752—21no—
30C2×C47⋊C16D411yescharacteristic
31#13093960—21no—
32#13093951—41no—
33C8×Dic47D411yescharacteristic
34C47⋊C32—21no—
35#135×C47—21no—
36C2×Q16×C47—21no—
37Q32×C47—21no—
38Q32×C47—21no—
39Q32×C47D411yescharacteristic
40SD32×C47—21no—
41D16×C47D411yescharacteristic
42C2×C16×C47C2311yescharacteristic
43C32×C47—21no—
44#41×C47—41no—
45C2×Q8×C47—41no—
46C2×D188—41no—
47Q16×C47—21no—
48Q16×C47—41no—
49Q16×C47—41no—
50SD16×C47—41no—
51D8×C47—21no—
52C2×C8×C47C2×D411yescharacteristic
53#10625336—81no—
54#10625336—81no—
55(C2×D47)⋊C4—82no—
56C4×Dic47D811yescharacteristic
57#10625329—41no—
58#10625329—81no—
59C2×C47⋊C8—81no—
60C2×C47⋊C8D811yescharacteristic
61D376—41no—
62D376—41no—
63C16×C47C2×D411yescharacteristic
64C16×C47#4111yescharacteristic
65C47⋊C16—21no—
66C22×D47—81no—
67Q8×C47—41no—
68Q8×C47—81no—
69Q8×C47—81no—
70D4×C47—41no—
71D4×C47—81no—
72C2×C4×C47—81no—
73C2×C4×C47—81no—
74C2×C4×C47C2×D811yescharacteristic
75C2×Dic47—21no—
76D188—81no—
77D188—81no—
78C8×C47#12111yescharacteristic
79C8×C47AGL(1,ℤ/8)11yescharacteristic
80C47⋊C8—81no—
81C47⋊C8D1611yescharacteristic
82C47⋊C8D1611yescharacteristic
83#13691—471nomaximal, Sylow
84C22×C47—81no—
85C22×C47#50911yescharacteristic
86C2×D47—162no—
87C2×D47—161no—
88C4×C47—81no—
89C4×C47—161no—
90C4×C47#45911yescharacteristic
91C4×C47C2×D1611yescharacteristic
92Dic47—41no—
93#2264D4711yescharacteristic, complemented
94#2263—471no—
95#2249—471no—
96#2178—471no—
97#1422—471no—
98#1420—471no—
99#1419—471no—
100C2×C47—21no—
101C2×C47—161no—
102C2×C47#220611yescharacteristic
103D47—321no—
104#508C2×D4711yescharacteristic
105C2×Q32C2×D4711yescharacteristic
106C2×SD32—941no—
107C2×D16—471no—
108#495—941no—
109#443—941no—
110Q64—21no—
111SD64—21no—
112SD64—941no—
113D32—941no—
114M64—471no—
115M64C2×D4711yescharacteristic
116#368—471no—
117#359—941no—
118C4×C16—471no—
119C47#1369111yescharacteristic, complemented, Sylow
120#135—21no—
121C2×Q16—21no—
122C2×SD16—1881no—
123C2×D8—941no—
124#131—1881no—
125#124—1881no—
126Q32—21no—
127Q32—21no—
128Q32C22⋊D4711yescharacteristic
129SD32—21no—
130SD32—1882no—
131D16—941no—
132D16—941no—
133D16C22⋊D4711yescharacteristic
134C2×C16—471no—
135C2×C16C22×D4711yescharacteristic
136#108—941no—
137#104—1881no—
138C4×C8—471no—
139C32—21no—
140C32—941no—
141#41—41no—
142C2×Q8—41no—
143C2×D4—1881no—
144Q16—21no—
145Q16—41no—
146Q16—41no—
147SD16—41no—
148SD16—3761no—
149SD16—3761no—
150D8—21no—
151D8—1881no—
152D8—1881no—
153M16—3761no—
154M16—1881no—
155C2×C8—471no—
156C2×C8—3761no—
157C2×C8D4×D4711yescharacteristic
158C22⋊C4—3762no—
159C42—471no—
160C16—941no—
161C16#1062535211yescharacteristic
162C16C2×C22⋊D4711yescharacteristic
163C23—3761no—
164Q8—41no—
165Q8—81no—
166Q8—81no—
167D4—41no—
168D4—81no—
169D4—3761no—
170D4—3761no—
171C2×C4—81no—
172C2×C4—81no—
173C2×C4—941no—
174C2×C4D8×D4711yescharacteristic
175C8—471no—
176C8—471no—
177C8—3761no—
178C8#1309399611yescharacteristic
179C8#1309404811yescharacteristic
180C22—81no—
181C22—7522no—
182C22—7521no—
183C22#1568955711yescharacteristic
184C4—81no—
185C4—161no—
186C4—1881no—
187C4#1568931611yescharacteristic
188C4D16×D4711yescharacteristic
189C2—21no—
190C2—161no—
191C2—15041no—
192C2#2024542111yescharacteristic
subgroupG/H
centerC2#20245421
commutator, cosocleC2×C16×C47C23
FrattiniC2×C16C22×D47
FittingC47×#2264C2
socleC2×C47#2206
prime radical#20245700C2
hypercenter#2264D47
hypocenterC47#13691
LCSG ▷ C2×C16×C47 ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #2264

Complements

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

NH ≅ G/Ntype
2. #20245650C2semidirect
3. #20245269C2semidirect
4. #20241585C2semidirect
5. #20241581C2semidirect
6. #20241579C2semidirect
7. C47×#2264C2semidirect
93. #2264D47semidirect
119. C47#13691semidirect

Maximal subgroups

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

subgroupindex
#202457002
#202456502
#202452692
#202415852
#202415812
#202415792
C47×#22642
#1369147