Finite Group Databasebeta

← #46812848

Subgroups — #46812848

Order 34432.

210 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 47 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#31771418C211yesmaximal, characteristic, complemented
2#31771041C211yesmaximal, characteristic, complemented
3#31770872C211yesmaximal, characteristic, complemented
4#31770421C211yesmaximal, characteristic, complemented
5#31770413C211yesmaximal, characteristic, complemented
6#31770388C211yesmaximal, characteristic, complemented
7C2×SD32×C269C211yesmaximal, characteristic, complemented
8#22575501—21no—
9#22575485—22no—
10#22575484—21no—
11#22575479—21no—
12#22575476—21no—
13#22575475C2211yescharacteristic
14Q16×D269—21no—
15#22575459C2211yescharacteristic
16#22575397—21no—
17#22575394—21no—
18#22575393C2211yescharacteristic
19#22575389C2211yescharacteristic
20#22575370—21no—
21C2×Q16×C269C2211yescharacteristic
22C2×D8×C269C2211yescharacteristic
23SD32×C269—22no—
24C2×C16×C269C2211yescharacteristic
25#16864403—22no—
26#16864403—41no—
27#16864402—21no—
28#16864402—42no—
29#16864402D411yescharacteristic
30Q8×D269—22no—
31Q8×D269—41no—
32Dic1076D411yescharacteristic
33#16864392—22no—
34#16864391—21no—
35#16864390—41no—
36#16864389—22no—
37D2152D411yescharacteristic
38#16864387—41no—
39#16864386—21no—
40#16864386D411yescharacteristic
41#16864385—21no—
42C8×D269—21no—
43#16864377—21no—
44C2×Q8×C269—21no—
45C2×D4×C269—21no—
46Q16×C269—21no—
47Q16×C269D412yes—
48D8×C269—21no—
49D8×C269—21no—
50C2×C8×C269C2311yescharacteristic
51C16×C269—21no—
52Dic538—21no—
53Dic538—42no—
54Dic538D811yescharacteristic
55D1076—21no—
56D1076—42no—
57D1076D811yescharacteristic
58C22⋊D269—21no—
59C22⋊D269—41no—
60C4×D269—21no—
61C4×D269—42no—
62C4×D269—42no—
63C4×D269—41no—
64#14524130—21no—
65#14524130—41no—
66C23×C269—41no—
67Q8×C269—22no—
68Q8×C269—41no—
69D4×C269—41no—
70D4×C269—41no—
71C2×C4×C269—41no—
72C2×C4×C269C2×D411yescharacteristic
73C8×C269C2×D411yescharacteristic
74C8×C269C2×D411yescharacteristic
75C22×C269—81no—
76C22×C269—161no—
77C22×C269AGL(1,ℤ/8)11yescharacteristic
78C2×D269—21no—
79C2×D269—41no—
80C4×C269—42no—
81C4×C269#12011yescharacteristic
82C4×C269C2×D811yescharacteristic
83Dic269—21no—
84Dic269—41no—
85C2×C269—21no—
86C2×C269—161no—
87C2×C269#44711yescharacteristic
88D269—41no—
89D269—81no—
90C269#219311yescharacteristic, complemented, Sylow
91#2193—2691nomaximal, Sylow
92#578—2691no—
93#509—2691no—
94C2×SD32D26911yescharacteristic, complemented
95#472—2691no—
96#362—2691no—
97#359—2691no—
98#350—2691no—
992−1+4—5381no—
100#137—5381no—
101#137—5382no—
102AGL(1,ℤ/8)—5381no—
103#135—2691no—
104#135—5381no—
105C2×Q16—5381no—
106C2×Q16C2×D26911yescharacteristic
107C2×D8C2×D26911yescharacteristic
108#131—2691no—
109SD32—22no—
110SD32—5381no—
111D16—5381no—
112M32—2691no—
113C2×C16C2×D26911yescharacteristic
114#108—2691no—
115#100—5381no—
116#41—2691no—
117#41—5382no—
118#41—5381no—
119#41—10762no—
120#41—10761no—
121C2×Q8—21no—
122C2×Q8—5382no—
123C2×Q8—10761no—
124C2×D4—21no—
125Q16—21no—
126Q16—2691no—
127Q16—5382no—
128Q16C22⋊D26912yes—
129SD16—5382no—
130SD16—5381no—
131SD16—10761no—
132D8—21no—
133D8—21no—
134D8—2691no—
135D8—10761no—
136M16—2691no—
137M16—5381no—
138M16—5381no—
139C2×C8—5381no—
140C2×C8C22×D26911yescharacteristic
141C16—21no—
142C16—5381no—
143C23—41no—
144Q8—22no—
145Q8—41no—
146Q8—2691no—
147Q8—5381no—
148Q8—10762no—
149D4—41no—
150D4—41no—
151D4—2691no—
152D4—5381no—
153D4—5381no—
154D4—10762no—
155D4—10761no—
156C2×C4—41no—
157C2×C4—5381no—
158C2×C4—10762no—
159C2×C4—10762no—
160C2×C4—10761no—
161C2×C4D4×D26911yescharacteristic
162C8—5381no—
163C8—10761no—
164C8D4×D26911yescharacteristic
165C8C2×C22⋊D26911yescharacteristic
166C22—81no—
167C22—161no—
168C22—5381no—
169C22—10761no—
170C22#2257547711yescharacteristic
171C4—42no—
172C4—5381no—
173C4—10761no—
174C4#2257542111yescharacteristic
175C4D8×D26911yescharacteristic
176C2—21no—
177C2—161no—
178C2—10761no—
179C2—21521no—
180C2#3177073711yescharacteristic
subgroupG/H
centerC2#31770737
commutator, cosocleC2×C8×C269C23
FrattiniC2×C8C22×D269
FittingC2×SD32×C269C2
socleC2×C269#447
hypercenterC2×SD32D269
hypocenterC269#2193
LCSG ▷ C2×C8×C269 ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #31771418C2semidirect
2. #31771041C2semidirect
3. #31770872C2semidirect
4. #31770421C2semidirect
5. #31770413C2semidirect
6. #31770388C2semidirect
7. C2×SD32×C269C2semidirect
90. C269#2193semidirect
94. C2×SD32D269semidirect

Maximal subgroups

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

subgroupindex
#317714182
#317710412
#317708722
#317704212
#317704132
#317703882
C2×SD32×C2692
#2193269