Finite Group Databasebeta

← #46810086

Subgroups — #46810086

Order 34432.

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

normal subgroups only

This group has 250 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#31771275C211yesmaximal, characteristic
2#31770951C211yesmaximal, characteristic, complemented
3#31770891C211yesmaximal, characteristic, complemented
4#31770811C211yesmaximal, characteristic, complemented
5#31770335C211yesmaximal, characteristic, complemented
6#31770332C211yesmaximal, characteristic, complemented
7#331×C269C211yesmaximal, characteristic, complemented
8C2×#16864401—21no—
9C2×#16864391—21no—
10#22575453C2211yescharacteristic
11#22575449—21no—
12#22575425—22no—
13#22575424—21no—
14C4×Dic538C2211yescharacteristic
15C4×D1076C2211yescharacteristic
16D4×Dic269—21no—
17#22575385—21no—
18#22575378—21no—
19#22575378—21no—
20#22575374—22no—
21C4×#14524130C2211yescharacteristic
22#127×C269C2211yescharacteristic
23C4⋊C8×C269C2211yescharacteristic
24C4⋊C8×C269C2211yescharacteristic
25#16864401—42no—
26#16864401—42no—
27C2×Dic538—21no—
28C2×Dic538D411yescharacteristic
29C2×D1076D411yescharacteristic
30C2×C22⋊D269—22no—
31C2×C22⋊D269—22no—
32C22×Dic269—22no—
33C2×C4×D269—21no—
34#16864391—42no—
35C2×#14524130—21no—
36C4⋊Dic269—21no—
37C4⋊Dic269—21no—
38C4⋊Dic269D411yescharacteristic
39C4⋊Dic269D411yescharacteristic
40#16864381—21no—
41C22⋊Dic269—22no—
42#16864379—21no—
43C4×Dic269—21no—
44C2×D4×C269—21no—
45C2×D4×C269—21no—
46C2×D4×C269D412yes—
47C2×C8×C269—21no—
48C2×C8×C269—21no—
49C42×C269C2311yescharacteristic
50C22×D269—21no—
51Dic538—21no—
52Dic538—41no—
53Dic538—41no—
54Dic538SD1612yescomplemented
55D1076—21no—
56D1076—21no—
57C22⋊D269—44no—
58C22⋊D269—82no—
59C2×Dic269—21no—
60C2×Dic269—21no—
61C2×Dic269—21no—
62C2×Dic269—44no—
63C2×Dic269—41no—
64C4×D269—41no—
65C4×D269—41no—
66#14524130—41no—
67C23×C269—22no—
68D4×C269—42no—
69D4×C269—41no—
70D4×C269—41no—
71D4×C269—41no—
72D4×C269—41no—
73C2×C4×C269C2×D411yescharacteristic
74C2×C4×C269C2×D411yescharacteristic
75C2×C4×C269C2×D411yescharacteristic
76C8×C269—41no—
77C8×C269—41no—
78C22×C269—42no—
79C22×C269—42no—
80C22×C269—42no—
81C22×C269#12011yescharacteristic
82C2×D269—41no—
83C2×D269—41no—
84C2×D269—41no—
85C4×C269—21no—
86C4×C269C2×SD1611yescharacteristic
87C4×C269#13511yescharacteristic
88C4×C269AGL(1,ℤ/8)11yescharacteristic
89C4×C269AGL(1,ℤ/8)11yescharacteristic
90Dic269—22no—
91Dic269—41no—
92Dic269—41no—
93Dic269—81no—
94C2×C269—82no—
95C2×C269#44911yescharacteristic
96C2×C269#45011yescharacteristic
97C2×C269#45511yescharacteristic
98D269—81no—
99C269#164211yescharacteristic, complemented, Sylow
100#1642—2691nomaximal, Sylow
101#550—2691no—
102#486—2691no—
103#475—2691no—
104#461—2691no—
105#331D26911yescharacteristic, complemented
106Q8⋊C8—2691no—
107D4⋊C8—2691no—
108C2×#41—5381no—
109C2×SD16—5381no—
110C4⋊Q8—2691no—
111#127—5381no—
112#127C2×D26911yescharacteristic
113#121—5381no—
114#121—5382no—
115C4×Q8—2691no—
116C4×D4—2691no—
117C4×D4—5381no—
118#106—5381no—
119C4⋊C8C2×D26911yescharacteristic
120C4⋊C8C2×D26911yescharacteristic
121#103—5381no—
122#103—5381no—
123#102—5382no—
124C4×C8—2691no—
125#41—10762no—
126#41—10762no—
127C2×Q8—2691no—
128C2×Q8—5381no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—2691no—
132C2×D4—5382no—
133C2×D4—5382no—
134C2×D4D107612yes—
135C22×C4—5382no—
136C22×C4—5381no—
137SD16—10762no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—5381no—
141C4⋊C4—2691no—
142C4⋊C4—2691no—
143C4⋊C4—5381no—
144C4⋊C4—5381no—
145C4⋊C4—5381no—
146C22⋊C4—5382no—
147C22⋊C4—5381no—
148C42—5381no—
149C42C22×D26911yescharacteristic
150C23—22no—
151C23—5381no—
152Q8—2692no—
153Q8—5381no—
154Q8—10761no—
155Q8—10761no—
156D4—42no—
157D4—41no—
158D4—41no—
159D4—41no—
160D4—41no—
161D4—5381no—
162D4—5381no—
163D4—10764no—
164D4—21522no—
165C2×C4—5381no—
166C2×C4—5381no—
167C2×C4—5381no—
168C2×C4—10764no—
169C2×C4—10761no—
170C2×C4—10761no—
171C2×C4—10761no—
172C2×C4D4×D26911yescharacteristic
173C2×C4D4×D26911yescharacteristic
174C2×C4C2×D107611yescharacteristic
175C8—41no—
176C8—41no—
177C8—10761no—
178C22—42no—
179C22—42no—
180C22—42no—
181C22—10761no—
182C22—10761no—
183C22—10761no—
184C22#2257542311yescharacteristic
185C4—21no—
186C4—5382no—
187C4—10761no—
188C4—10761no—
189C4—21521no—
190C4SD16×D26911yescharacteristic
191C4#2257547411yescharacteristic
192C4#2257547711yescharacteristic
193C4#2257547711yescharacteristic
194C2—82no—
195C2—21521no—
196C2#3177075111yescharacteristic
197C2#3177075711yescharacteristic
198C2#3177078511yescharacteristic
subgroupG/H
centerC22#22575423
commutator, cosocleC42×C269C23
FrattiniC42C22×D269
Fitting#331×C269C2
socleC22×C269#120
prime radical#31771275C2
hypercenter#331D269
hypocenterC269#1642
LCSG ▷ C42×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #31770951C2semidirect
3. #31770891C2semidirect
4. #31770811C2semidirect
5. #31770335C2semidirect
6. #31770332C2semidirect
7. #331×C269C2semidirect
54. Dic538SD16semidirect
99. C269#1642semidirect
105. #331D269semidirect

Maximal subgroups

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

subgroupindex
#317712752
#317709512
#317708912
#317708112
#317703352
#317703322
#331×C2692
#1642269