Finite Group Databasebeta

← #46809515

Subgroups — #46809515

Order 34432.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#31771140C211yesmaximal, characteristic
2#31770660C211yesmaximal, characteristic, complemented
3#31770660C211yesmaximal, characteristic, complemented
4#31770347C211yesmaximal, characteristic, complemented
5#31770344C211yesmaximal, characteristic, complemented
6#31770344C211yesmaximal, characteristic, complemented
7#330×C269C211yesmaximal, characteristic, complemented
8#22575448—21no—
9#22575441C2211yescharacteristic
10#22575438—21no—
11#22575433C411yescharacteristic
12#22575428C411yescharacteristic
13#22575418C411yescharacteristic
14#22575415—21no—
15#22575415C411yescharacteristic
16#22575411—21no—
17C42×D269C2211yescharacteristic
18#22575382—21no—
19#22575382—21no—
20#22575365—21no—
21#22575365—21no—
22#22575364C2211yescharacteristic
23#22575364C2211yescharacteristic
24#125×C269C2211yescharacteristic
25#97×C269C2211yescharacteristic
26#97×C269C2211yescharacteristic
27C2×Dic538C2×C411yescharacteristic
28C2×D1076—21no—
29C2×D1076C2×C411yescharacteristic
30C2×C4×D269—21no—
31C2×C4×D269C2×C411yescharacteristic
32C2×C4×D269D411yescharacteristic
33C2×C4×D269D411yescharacteristic
34C2×#14524130—21no—
35C2×#14524130—21no—
36C4⋊Dic269—21no—
37#16864381—21no—
38#16864379—21no—
39#16864379—21no—
40#16864379—21no—
41#16864379—21no—
42#16864379—21no—
43C4×Dic269—21no—
44C4×Dic269C2×C411yescharacteristic
45C4×Dic269D411yescharacteristic
46C4×Dic269D411yescharacteristic
47C2×C8×C269—21no—
48C2×C8×C269—21no—
49C4⋊C4×C269—21no—
50C4⋊C4×C269—21no—
51C4⋊C4×C269C2×C411yescharacteristic
52C4⋊C4×C269C2×C411yescharacteristic
53C42×C269C2311yescharacteristic
54C22×D269—21no—
55C22×D269C22⋊C411yescharacteristic
56Dic538—41no—
57D1076—41no—
58D1076—42no—
59C2×Dic269—21no—
60C2×Dic269C22⋊C411yescharacteristic
61C2×Dic269C22⋊C411yescharacteristic
62C2×Dic269C22⋊C411yescharacteristic
63C4×D269—41no—
64C4×D269—41no—
65C4×D269—41no—
66C4×D269—42no—
67#14524130—41no—
68#14524130—41no—
69C2×C4×C269—21no—
70C2×C4×C269—21no—
71C2×C4×C269C22×C411yescharacteristic
72C2×C4×C269C2×D411yescharacteristic
73C2×C4×C269C2×D411yescharacteristic
74C8×C269—41no—
75C8×C269—41no—
76C22×C269C2×C22⋊C411yescharacteristic
77C2×D269—21no—
78C2×D269—21no—
79C2×D269—21no—
80C2×D269—41no—
81C2×D269—41no—
82C2×D269—41no—
83C4×C269—21no—
84C4×C269—21no—
85C4×C269—21no—
86C4×C269—41no—
87C4×C269—41no—
88Dic269—21no—
89Dic269—21no—
90Dic269—21no—
91Dic269—41no—
92C2×C269#41311yescharacteristic
93C2×C269#42111yescharacteristic
94C2×C269#42111yescharacteristic
95D269—41no—
96D269—81no—
97C269#153511yescharacteristic, complemented, Sylow
98#1535—2691nomaximal, Sylow
99#529—2691no—
100#432—2691no—
101#432—2691no—
102#330—2691no—
103#330D26911yescharacteristic, complemented
104#329—2691no—
105#329—2691no—
106#126—5381no—
107#125C2×D26911yescharacteristic
108#124—2691no—
109#123—5381no—
110C22⋊Q8—2691no—
111#121—2691no—
112C4×Q8—2691no—
113C4×D4—2691no—
114C4×D4—5381no—
115#117—5381no—
116C2×C42—2691no—
117C4⋊C8—5381no—
118C4⋊C8—5381no—
119C22⋊C8—5381no—
120C22⋊C8—5381no—
121#97—2691no—
122#97—2691no—
123#97C2×D26911yescharacteristic
124#97C2×D26911yescharacteristic
125C2×Q8—2691no—
126C2×D4—2691no—
127C2×D4—5381no—
128C22×C4—2691no—
129C22×C4—2691no—
130C22×C4—2691no—
131C22×C4—5381no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—5381no—
135C2×C8—5381no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—5381no—
139C4⋊C4—5381no—
140C4⋊C4C4×D26911yescharacteristic
141C4⋊C4C4×D26911yescharacteristic
142C22⋊C4—5381no—
143C22⋊C4—5381no—
144C22⋊C4—5381no—
145C22⋊C4—5381no—
146C22⋊C4—5381no—
147C42—2691no—
148C42—2691no—
149C42—2691no—
150C42—5381no—
151C42C22×D26911yescharacteristic
152C23—2691no—
153C23—5381no—
154Q8—10761no—
155D4—10761no—
156D4—10762no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—2691no—
160C2×C4—2691no—
161C2×C4—2691no—
162C2×C4—5381no—
163C2×C4—10761no—
164C2×C4—10761no—
165C2×C4—10761no—
166C2×C4—10762no—
167C2×C4C2×C4×D26911yescharacteristic
168C2×C4D4×D26911yescharacteristic
169C2×C4D4×D26911yescharacteristic
170C8—41no—
171C8—41no—
172C8—10761no—
173C8—10761no—
174C22—5381no—
175C22—5381no—
176C22—5381no—
177C22—10761no—
178C22—10761no—
179C22—10761no—
180C22C22⋊C4×D26911yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—41no—
186C4—5381no—
187C4—5381no—
188C4—5381no—
189C4—10761no—
190C2—10761no—
191C2—21521no—
192C2#3177058811yescharacteristic
193C2#3177062011yescharacteristic
194C2#3177062011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D269
commutatorC2×C4×C269C22×C4
FrattiniC42C22×D269
Fitting#330×C269C2
socleC22×C269C2×C22⋊C4
prime radical#22575428C4
cosocleC42×C269C23
hypercenter#330D269
hypocenterC269#1535
LCSG ▷ C2×C4×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #31770660C2semidirect
3. #31770660C2semidirect
4. #31770347C2semidirect
5. #31770344C2semidirect
6. #31770344C2semidirect
7. #330×C269C2semidirect
97. C269#1535semidirect
103. #330D269semidirect

Maximal subgroups

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

subgroupindex
#317711402
#317706602
#317703472
#317703442
#330×C2692
#1535269