Finite Group Databasebeta

← #46809589

Subgroups — #46809589

Order 34432.

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

normal subgroups only

This group has 242 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#31771156C211yesmaximal, characteristic
2#31770661C211yesmaximal, characteristic, complemented
3#31770657C211yesmaximal, characteristic, complemented
4#31770351C211yesmaximal, characteristic, complemented
5#31770348C211yesmaximal, characteristic, complemented
6#31770348C211yesmaximal, characteristic, complemented
7#332×C269C211yesmaximal, characteristic, complemented
8C2×#16864403—21no—
9#22575450C2211yescharacteristic
10#22575442—21no—
11#22575428—21no—
12#22575428C412yes—
13#22575415—21no—
14#22575415C412yes—
15C42×D269C2211yescharacteristic
16C4⋊#14524130C2211yescharacteristic
17C4⋊#14524130C2211yescharacteristic
18#22575365—21no—
19#22575365—21no—
20#22575363—21no—
21C8×Dic269—21no—
22C4⋊Q8×C269C2211yescharacteristic
23C4⋊C8×C269C2211yescharacteristic
24C4⋊C8×C269C2211yescharacteristic
25#16864403—42no—
26#16864403—42no—
27C2×D1076—22no—
28C2×D1076—21no—
29C2×D1076—21no—
30C2×D1076C2×C412yes—
31C2×C4×D269—22no—
32C2×C4×D269C2×C411yescharacteristic
33C2×C4×D269D411yescharacteristic
34C2×C4×D269D411yescharacteristic
35C2×#14524130—21no—
36C2×#14524130—21no—
37#16864379—22no—
38#16864379—22no—
39C4×Dic269C2×C411yescharacteristic
40C4×Dic269D411yescharacteristic
41C4×Dic269D411yescharacteristic
42C2×Q8×C269—21no—
43C2×C8×C269—21no—
44C2×C8×C269—21no—
45C4⋊C4×C269—21no—
46C4⋊C4×C269C2×C412yes—
47C42×C269C2311yescharacteristic
48C22×D269—22no—
49C22×D269C22⋊C411yescharacteristic
50D1076—42no—
51D1076—44no—
52D1076—41no—
53D1076—41no—
54D1076—41no—
55D1076—41no—
56C2×Dic269C22⋊C411yescharacteristic
57C2×Dic269C22⋊C411yescharacteristic
58C2×Dic269C22⋊C411yescharacteristic
59C4×D269—21no—
60C4×D269—21no—
61C4×D269—21no—
62C4×D269—21no—
63C4×D269—41no—
64C4×D269—44no—
65#14524130—41no—
66#14524130—41no—
67Q8×C269—41no—
68Q8×C269—41no—
69C2×C4×C269—22no—
70C2×C4×C269C22×C411yescharacteristic
71C2×C4×C269C2×D411yescharacteristic
72C2×C4×C269C2×D411yescharacteristic
73C8×C269—41no—
74C8×C269—41no—
75C22×C269C2×C22⋊C411yescharacteristic
76C2×D269—21no—
77C2×D269—21no—
78C2×D269—21no—
79C2×D269—42no—
80C2×D269—42no—
81C2×D269—42no—
82C4×C269—21no—
83C4×C269—42no—
84C4×C269#13511yescharacteristic
85C4×C269#13511yescharacteristic
86C4×C269AGL(1,ℤ/8)11yescharacteristic
87C4×C269AGL(1,ℤ/8)11yescharacteristic
88Dic269—21no—
89Dic269—21no—
90Dic269—21no—
91C2×C269#41311yescharacteristic
92C2×C269#41611yescharacteristic
93C2×C269#41811yescharacteristic
94D269—41no—
95D269—82no—
96C269#155311yescharacteristic, complemented, Sylow
97#1553—2691nomaximal, Sylow
98#532—2691no—
99#432—2691no—
100#431—2691no—
101#332—2691no—
102#332D26911yescharacteristic, complemented
103#331—2691no—
104#331—2691no—
105C2×#41—5381no—
106C4⋊Q8C2×D26911yescharacteristic
107#127—2691no—
108#124—5381no—
109#121—2692no—
110#121—5381no—
111C4×D4—2692no—
112C4×D4—5381no—
113C2×C42—2691no—
114C4⋊C8—2691no—
115C4⋊C8—2691no—
116C4⋊C8C2×D26911yescharacteristic
117C4⋊C8C2×D26911yescharacteristic
118C22⋊C8—5381no—
119C22⋊C8—5381no—
120#97—5381no—
121C4×C8—5381no—
122#41—10762no—
123#41—10762no—
124C2×Q8—21no—
125C2×D4—2692no—
126C2×D4—5382no—
127C2×D4—5381no—
128C2×D4—5381no—
129C22×C4—2691no—
130C22×C4—2691no—
131C22×C4—2691no—
132C22×C4—5382no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—5381no—
136C2×C8—5381no—
137C4⋊C4—21no—
138C4⋊C4C4×D26912yes—
139C22⋊C4—5382no—
140C22⋊C4—5382no—
141C42—2691no—
142C42—2691no—
143C42—2691no—
144C42C22×D26911yescharacteristic
145C23—2691no—
146C23—5382no—
147Q8—41no—
148Q8—41no—
149D4—10762no—
150D4—10764no—
151D4—10761no—
152D4—10761no—
153D4—10761no—
154D4—10761no—
155C2×C4—22no—
156C2×C4—2691no—
157C2×C4—2691no—
158C2×C4—2691no—
159C2×C4—5381no—
160C2×C4—5381no—
161C2×C4—5381no—
162C2×C4—5381no—
163C2×C4—10761no—
164C2×C4—10764no—
165C2×C4C2×C4×D26911yescharacteristic
166C2×C4D4×D26911yescharacteristic
167C2×C4D4×D26911yescharacteristic
168C8—41no—
169C8—41no—
170C8—10761no—
171C8—10761no—
172C22—5381no—
173C22—5381no—
174C22—5381no—
175C22—10762no—
176C22—10762no—
177C22—10762no—
178C22C22⋊C4×D26911yescharacteristic
179C4—21no—
180C4—42no—
181C4—5381no—
182C4—5381no—
183C4—5381no—
184C4#2257547411yescharacteristic
185C4#2257547611yescharacteristic
186C4#2257547711yescharacteristic
187C4#2257548011yescharacteristic
188C2—10761no—
189C2—21522no—
190C2#3177058811yescharacteristic
191C2#3177060011yescharacteristic
192C2#3177060811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D269
commutatorC2×C4×C269C22×C4
FrattiniC42C22×D269
Fitting#332×C269C2
socleC22×C269C2×C22⋊C4
prime radical#31771156C2
cosocleC42×C269C23
hypercenter#332D269
hypocenterC269#1553
LCSG ▷ C2×C4×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #31770661C2semidirect
3. #31770657C2semidirect
4. #31770351C2semidirect
5. #31770348C2semidirect
6. #31770348C2semidirect
7. #332×C269C2semidirect
96. C269#1553semidirect
102. #332D269semidirect

Maximal subgroups

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

subgroupindex
#317711562
#317706612
#317706572
#317703512
#317703482
#332×C2692
#1553269