Finite Group Databasebeta

← #46810037

Subgroups — #46810037

Order 34432.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#31771258C211yesmaximal, characteristic
2#31770957C211yesmaximal, characteristic, complemented
3#31770896C211yesmaximal, characteristic, complemented
4#31770896C211yesmaximal, characteristic, complemented
5#31770332C211yesmaximal, characteristic, complemented
6#31770332C211yesmaximal, characteristic, complemented
7#332×C269C211yesmaximal, characteristic, complemented
8C2×#16864403—21no—
9#22575453C2211yescharacteristic
10#22575438—22no—
11#22575429—21no—
12#22575428—21no—
13C4×D1076C2211yescharacteristic
14C4×D1076C2211yescharacteristic
15C4⋊C4×D269—21no—
16#22575385—21no—
17#22575385—21no—
18#22575376—22no—
19#22575375—21no—
20#22575375—21no—
21C4×#14524130C2211yescharacteristic
22C4⋊Q8×C269C2211yescharacteristic
23C4⋊C8×C269C2211yescharacteristic
24C4⋊C8×C269C2211yescharacteristic
25#16864403—42no—
26#16864403—42no—
27C2×Dic538—21no—
28C2×D1076—22no—
29C2×D1076D411yescharacteristic
30C2×D1076D411yescharacteristic
31C2×C4×D269—22no—
32C2×C4×D269—21no—
33C2×C4×D269—21no—
34C2×#14524130—21no—
35C4⋊Dic269—21no—
36C4⋊Dic269—21no—
37C4⋊Dic269D411yescharacteristic
38C4⋊Dic269D411yescharacteristic
39#16864381—22no—
40#16864379—22no—
41#16864379—21no—
42#16864379—21no—
43C2×Q8×C269—21no—
44C2×C8×C269—21no—
45C2×C8×C269—21no—
46C4⋊C4×C269—21no—
47C4⋊C4×C269D412yes—
48C42×C269C2311yescharacteristic
49C22×D269—21no—
50C22×D269—21no—
51Dic538—42no—
52D1076—21no—
53D1076—21no—
54D1076—21no—
55D1076—44no—
56D1076SD1612yes—
57C2×Dic269—21no—
58C2×Dic269—21no—
59C2×Dic269—41no—
60C4×D269—44no—
61C4×D269—41no—
62C4×D269—41no—
63C4×D269—41no—
64C4×D269—41no—
65#14524130—41no—
66Q8×C269—41no—
67Q8×C269—41no—
68C2×C4×C269—22no—
69C2×C4×C269C2×D411yescharacteristic
70C2×C4×C269C2×D411yescharacteristic
71C2×C4×C269C2×D411yescharacteristic
72C8×C269—41no—
73C8×C269—41no—
74C22×C269#12011yescharacteristic
75C2×D269—22no—
76C2×D269—41no—
77C2×D269—41no—
78C2×D269—41no—
79C2×D269—41no—
80C2×D269—41no—
81C4×C269—21no—
82C4×C269—42no—
83C4×C269C2×SD1611yescharacteristic
84C4×C269#13511yescharacteristic
85C4×C269AGL(1,ℤ/8)11yescharacteristic
86C4×C269#13711yescharacteristic
87Dic269—41no—
88Dic269—41no—
89Dic269—81no—
90C2×C269#45011yescharacteristic
91C2×C269#45211yescharacteristic
92C2×C269#45411yescharacteristic
93D269—42no—
94D269—81no—
95C269#163511yescharacteristic, complemented, Sylow
96#1635—2691nomaximal, Sylow
97#547—2691no—
98#487—2691no—
99#476—2691no—
100#476—2691no—
101#332D26911yescharacteristic, complemented
102D4⋊C8—2691no—
103D4⋊C8—2691no—
104C2×#41—5381no—
105C4⋊Q8—2691no—
106C4⋊Q8C2×D26911yescharacteristic
107#123—5382no—
108C22⋊Q8—5381no—
109#121—5381no—
110C4×D4—2691no—
111C4×D4—2691no—
112C2×C4⋊C4—5381no—
113#106—5381no—
114#106—5381no—
115C4⋊C8C2×D26911yescharacteristic
116C4⋊C8C2×D26911yescharacteristic
117#103—5382no—
118#102—5381no—
119#102—5381no—
120C4×C8—2691no—
121#41—10762no—
122#41—10762no—
123C2×Q8—21no—
124C2×Q8—5381no—
125C2×D4—2691no—
126C2×D4—2691no—
127C2×D4—5382no—
128C22×C4—5382no—
129C22×C4—5381no—
130C22×C4—5381no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—5381no—
134C4⋊C4—21no—
135C4⋊C4—2691no—
136C4⋊C4—2691no—
137C4⋊C4—5382no—
138C4⋊C4—5381no—
139C4⋊C4—5381no—
140C4⋊C4D107612yes—
141C22⋊C4—5382no—
142C22⋊C4—5381no—
143C22⋊C4—5381no—
144C42C22×D26911yescharacteristic
145C23—5381no—
146C23—5381no—
147Q8—41no—
148Q8—41no—
149Q8—10762no—
150D4—2692no—
151D4—5381no—
152D4—5381no—
153D4—5381no—
154D4—10764no—
155C2×C4—22no—
156C2×C4—5381no—
157C2×C4—5381no—
158C2×C4—10764no—
159C2×C4—10761no—
160C2×C4—10761no—
161C2×C4—10761no—
162C2×C4—10761no—
163C2×C4—10761no—
164C2×C4D4×D26911yescharacteristic
165C2×C4D4×D26911yescharacteristic
166C2×C4C2×D107611yescharacteristic
167C8—41no—
168C8—41no—
169C8—10761no—
170C22—5382no—
171C22—10761no—
172C22—10761no—
173C22—10761no—
174C22—10761no—
175C22—10761no—
176C22#2257542311yescharacteristic
177C4—21no—
178C4—42no—
179C4—10761no—
180C4—10761no—
181C4—21521no—
182C4SD16×D26911yescharacteristic
183C4#2257547411yescharacteristic
184C4#2257547711yescharacteristic
185C4#2257548511yescharacteristic
186C2—10762no—
187C2—21521no—
188C2#3177075711yescharacteristic
189C2#3177077011yescharacteristic
190C2#3177078011yescharacteristic
subgroupG/H
centerC22#22575423
commutator, cosocleC42×C269C23
FrattiniC42C22×D269
Fitting#332×C269C2
socleC22×C269#120
prime radical#31771258C2
hypercenter#332D269
hypocenterC269#1635
LCSG ▷ C42×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #31770957C2semidirect
3. #31770896C2semidirect
4. #31770896C2semidirect
5. #31770332C2semidirect
6. #31770332C2semidirect
7. #332×C269C2semidirect
95. C269#1635semidirect
101. #332D269semidirect

Maximal subgroups

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

subgroupindex
#317712582
#317709572
#317708962
#317703322
#332×C2692
#1635269