Finite Group Databasebeta

← #46809993

Subgroups — #46809993

Order 34432.

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

normal subgroups only

This group has 216 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#31771325C211yesmaximal, characteristic, complemented
2#31770951C211yesmaximal, characteristic, complemented
3#31770802C211yesmaximal, characteristic, complemented
4#31770352C211yesmaximal, characteristic, complemented
5#31770335C211yesmaximal, characteristic, complemented
6D4⋊#14524130C211yesmaximal, characteristic, complemented
7#459×C269C211yesmaximal, characteristic
8C2×#16864390—21no—
9#22575453C2211yescharacteristic
10#22575446—22no—
11#22575440—21no—
12#22575432—21no—
13C4×Dic538C2211yescharacteristic
14#22575418—21no—
15#22575412—21no—
16C4⋊#14524130C2211yescharacteristic
17#22575374—22no—
18#22575374—21no—
19C4×#14524130C2211yescharacteristic
20C2×D8×C269—21no—
21#127×C269C2211yescharacteristic
22C4×D4×C269C2211yescharacteristic
23C4⋊C8×C269C2211yescharacteristic
24#102×C269—21no—
25C2×Dic538—21no—
26C2×Dic538D411yescharacteristic
27#16864390—42no—
28C2×#14524130—21no—
29C2×#14524130—21no—
30C4⋊Dic269—21no—
31C4⋊Dic269D411yescharacteristic
32C4⋊Dic269D412yes—
33#16864381—22no—
34#16864381—21no—
35C22⋊Dic269—22no—
36C22⋊Dic269—22no—
37C4×Dic269—22no—
38C4×Dic269—21no—
39C2×D4×C269—21no—
40C2×D4×C269—21no—
41C2×D4×C269—21no—
42C2×D4×C269D411yescharacteristic
43C22×C4×C269—21no—
44D8×C269—42no—
45C2×C8×C269—21no—
46C4⋊C4×C269D411yescharacteristic
47C22⋊C4×C269—21no—
48C42×C269C2311yescharacteristic
49Dic538—21no—
50Dic538—21no—
51Dic538—41no—
52Dic538—41no—
53C2×Dic269—21no—
54C2×Dic269—21no—
55C2×Dic269—22no—
56#14524130—41no—
57#14524130—41no—
58C23×C269—21no—
59C23×C269—41no—
60D4×C269—21no—
61D4×C269—21no—
62D4×C269—42no—
63D4×C269—41no—
64D4×C269—41no—
65D4×C269—41no—
66D4×C269—41no—
67C2×C4×C269—21no—
68C2×C4×C269—41no—
69C2×C4×C269—41no—
70C2×C4×C269C2×D411yescharacteristic
71C2×C4×C269C2×D411yescharacteristic
72C2×C4×C269C2×D411yescharacteristic
73C8×C269—41no—
74C22×C269—41no—
75C22×C269—41no—
76C22×C269—41no—
77C22×C269—81no—
78C22×C269—81no—
79C22×C269—81no—
80C22×C269#12011yescharacteristic
81C4×C269—21no—
82C4×C269—41no—
83C4×C269#13511yescharacteristic
84C4×C269#13511yescharacteristic
85C4×C269AGL(1,ℤ/8)11yescharacteristic
86C4×C269AGL(1,ℤ/8)11yescharacteristic
87Dic269—41no—
88Dic269—42no—
89Dic269—41no—
90C2×C269—81no—
91C2×C269—161no—
92C2×C269#44911yescharacteristic
93C2×C269#44911yescharacteristic
94C2×C269#45411yescharacteristic
95C269#162811yescharacteristic, complemented, Sylow
96#1628—2691nomaximal, Sylow
97#556—2691no—
98#486—2691no—
99#460—2691no—
100#459D26911yescharacteristic
101#332—2691no—
102Q8⋊C8—2691no—
103D4⋊C8—2691no—
104C2×SD16—5381no—
105C2×D8—21no—
106C4⋊Q8—2691no—
107#127C2×D26911yescharacteristic
108#126—5382no—
109#124—5381no—
110C22⋊Q8—5381no—
111C4×Q8—2691no—
112C4×Q8—5381no—
113C4×D4C2×D26911yescharacteristic
114#117—5381no—
115C4⋊C8—2691no—
116C4⋊C8C2×D26911yescharacteristic
117#102—21no—
118#102—5381no—
119#102—5382no—
120C4×C8—2691no—
121C2×Q8—2691no—
122C2×Q8—5381no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4C22⋊D26911yescharacteristic
127C22×C4—21no—
128SD16—10762no—
129D8—42no—
130C2×C8—21no—
131C2×C8—5381no—
132C2×C8—5381no—
133C4⋊C4—2691no—
134C4⋊C4—2692no—
135C4⋊C4—5382no—
136C4⋊C4—5381no—
137C4⋊C4—5381no—
138C4⋊C4C22⋊D26911yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—5382no—
141C22⋊C4—5382no—
142C42—5382no—
143C42—5381no—
144C42C22×D26911yescharacteristic
145C23—21no—
146C23—41no—
147Q8—5381no—
148Q8—5381no—
149Q8—10761no—
150Q8—10761no—
151D4—21no—
152D4—21no—
153D4—42no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—5381no—
162C2×C4—5382no—
163C2×C4—5381no—
164C2×C4D4×D26911yescharacteristic
165C2×C4D4×D26911yescharacteristic
166C2×C4C2×C22⋊D26911yescharacteristic
167C8—41no—
168C8—10761no—
169C8—10761no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—81no—
174C22—81no—
175C22—81no—
176C22#2257542111yescharacteristic
177C4—21no—
178C4—41no—
179C4—10761no—
180C4—10762no—
181C4—10761no—
182C4#2257547211yescharacteristic
183C4#2257547311yescharacteristic
184C4#2257547711yescharacteristic
185C4#2257547911yescharacteristic
186C2—81no—
187C2—161no—
188C2#3177074711yescharacteristic
189C2#3177074811yescharacteristic
190C2#3177077611yescharacteristic
subgroupG/H
centerC22#22575421
commutator, cosocleC42×C269C23
FrattiniC42C22×D269
Fitting, prime radical#459×C269C2
socleC22×C269#120
hypercenter#459D269
hypocenterC269#1628
LCSG ▷ C42×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #31771325C2semidirect
2. #31770951C2semidirect
3. #31770802C2semidirect
4. #31770352C2semidirect
5. #31770335C2semidirect
6. D4⋊#14524130C2semidirect
95. C269#1628semidirect

Maximal subgroups

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

subgroupindex
#317713252
#317709512
#317708022
#317703522
#317703352
D4⋊#145241302
#459×C2692
#1628269