Finite Group Databasebeta

← #46809967

Subgroups — #46809967

Order 34432.

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

normal subgroups only

This group has 240 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#31771320C211yesmaximal, characteristic, complemented
2#31770977C211yesmaximal, characteristic, complemented
3#31770797C211yesmaximal, characteristic, complemented
4#31770353C211yesmaximal, characteristic, complemented
5D4⋊#14524130C211yesmaximal, characteristic, complemented
6#31770332C211yesmaximal, characteristic, complemented
7#459×C269C211yesmaximal, characteristic, complemented
8C2×#16864390—22no—
9C2×#16864387—21no—
10#22575453C2211yescharacteristic
11#22575439—22no—
12#22575427—21no—
13#22575424—21no—
14C4×D1076C2211yescharacteristic
15#22575412—21no—
16#22575411—21no—
17C4⋊#14524130C2211yescharacteristic
18#22575374—21no—
19C4×#14524130C2211yescharacteristic
20C2×D8×C269—21no—
21#127×C269C2211yescharacteristic
22C4×D4×C269C2211yescharacteristic
23C4⋊C8×C269C2211yescharacteristic
24#102×C269—21no—
25C2×Dic538D412yes—
26C2×D1076D411yescharacteristic
27C2×C22⋊D269—22no—
28C2×C4×D269—21no—
29#16864390—44no—
30#16864387—42no—
31C2×#14524130—21no—
32C2×#14524130—21no—
33C4⋊Dic269—21no—
34C4⋊Dic269—21no—
35C4⋊Dic269D411yescharacteristic
36C22⋊Dic269—22no—
37#16864379—22no—
38#16864379—21no—
39C4×Dic269—22no—
40C2×D4×C269—21no—
41C2×D4×C269—21no—
42C2×D4×C269—21no—
43C2×D4×C269D411yescharacteristic
44C22×C4×C269—21no—
45D8×C269—42no—
46C2×C8×C269—21no—
47C4⋊C4×C269D411yescharacteristic
48C22⋊C4×C269—21no—
49C42×C269C2311yescharacteristic
50C22×D269—21no—
51Dic538—42no—
52D1076—21no—
53D1076—21no—
54C22⋊D269—82no—
55C2×Dic269—21no—
56C2×Dic269—22no—
57C4×D269—41no—
58C4×D269—41no—
59#14524130—22no—
60#14524130—41no—
61C23×C269—21no—
62C23×C269—41no—
63D4×C269—21no—
64D4×C269—21no—
65D4×C269—42no—
66D4×C269—41no—
67D4×C269—41no—
68D4×C269—41no—
69D4×C269—41no—
70C2×C4×C269—21no—
71C2×C4×C269—41no—
72C2×C4×C269—41no—
73C2×C4×C269C2×D411yescharacteristic
74C2×C4×C269C2×D411yescharacteristic
75C2×C4×C269C2×D411yescharacteristic
76C8×C269—41no—
77C22×C269—41no—
78C22×C269—41no—
79C22×C269—41no—
80C22×C269—81no—
81C22×C269—81no—
82C22×C269—81no—
83C22×C269#12011yescharacteristic
84C2×D269—41no—
85C2×D269—41no—
86C2×D269—41no—
87C4×C269—21no—
88C4×C269—41no—
89C4×C269#13511yescharacteristic
90C4×C269#13511yescharacteristic
91C4×C269AGL(1,ℤ/8)11yescharacteristic
92C4×C269AGL(1,ℤ/8)11yescharacteristic
93Dic269—41no—
94Dic269—42no—
95C2×C269—81no—
96C2×C269—161no—
97C2×C269#44911yescharacteristic
98C2×C269#44911yescharacteristic
99C2×C269#45311yescharacteristic
100D269—81no—
101C269#162411yescharacteristic, complemented, Sylow
102#1624—2691nomaximal, Sylow
103#555—2691no—
104#492—2691no—
105#459—2691no—
106#459D26911yescharacteristic, complemented
107#333—2691no—
108D4⋊C8—2691no—
109D4⋊C8—2691no—
110C2×SD16—5382no—
111C2×D8—21no—
112C2×D8—5381no—
113C4⋊Q8—2691no—
114#127C2×D26911yescharacteristic
115#124—5382no—
116#121—5381no—
117#121—5381no—
118C4×D4—2691no—
119C4×D4C2×D26911yescharacteristic
120#117—5381no—
121#117—5381no—
122C4⋊C8—2691no—
123C4⋊C8C2×D26911yescharacteristic
124#102—21no—
125#102—5381no—
126C4×C8—2691no—
127C2×Q8—2692no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—2691no—
132C2×D4—5382no—
133C2×D4C22⋊D26911yescharacteristic
134C22×C4—21no—
135C22×C4—5381no—
136SD16—10764no—
137D8—42no—
138D8—10762no—
139C2×C8—21no—
140C2×C8—5381no—
141C2×C8—5381no—
142C4⋊C4—2691no—
143C4⋊C4—5381no—
144C4⋊C4—5381no—
145C4⋊C4C22⋊D26911yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—5382no—
148C22⋊C4—5382no—
149C22⋊C4—5381no—
150C42—5382no—
151C42C22×D26911yescharacteristic
152C23—21no—
153C23—41no—
154C23—5381no—
155Q8—10762no—
156D4—21no—
157D4—21no—
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—5381no—
164D4—5381no—
165D4—21522no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—5381no—
170C2×C4—5382no—
171C2×C4—10761no—
172C2×C4—10761no—
173C2×C4D4×D26911yescharacteristic
174C2×C4D4×D26911yescharacteristic
175C2×C4C2×C22⋊D26911yescharacteristic
176C8—41no—
177C8—5382no—
178C8—10761no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—81no—
183C22—81no—
184C22—81no—
185C22—10761no—
186C22—10761no—
187C22—10761no—
188C22#2257542111yescharacteristic
189C4—21no—
190C4—41no—
191C4—10761no—
192C4—10762no—
193C4#2257547211yescharacteristic
194C4#2257547311yescharacteristic
195C4#2257547711yescharacteristic
196C4#2257547911yescharacteristic
197C2—81no—
198C2—161no—
199C2—21521no—
200C2#3177074711yescharacteristic
201C2#3177074811yescharacteristic
202C2#3177077111yescharacteristic
subgroupG/H
centerC22#22575421
commutator, cosocleC42×C269C23
FrattiniC42C22×D269
Fitting#459×C269C2
socleC22×C269#120
hypercenter#459D269
hypocenterC269#1624
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. #31771320C2semidirect
2. #31770977C2semidirect
3. #31770797C2semidirect
4. #31770353C2semidirect
5. D4⋊#14524130C2semidirect
6. #31770332C2semidirect
7. #459×C269C2semidirect
101. C269#1624semidirect
106. #459D269semidirect

Maximal subgroups

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

subgroupindex
#317713202
#317709772
#317707972
#317703532
D4⋊#145241302
#317703322
#459×C2692
#1624269