Finite Group Databasebeta

← #46809447

Subgroups — #46809447

Order 34432.

220 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 69 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#31771157C211yesmaximal, characteristic
2#31770655C211yesmaximal, characteristic
3#31770469C211yesmaximal, characteristic
4#31770343C211yesmaximal, characteristic
5#31770342C211yesmaximal, characteristic
6#31770341C211yesmaximal, characteristic
7#328×C269C211yesmaximal, characteristic
8#22575452C411yescharacteristic, complemented
9#22575451C411yescharacteristic, complemented
10#22575443—21no—
11#22575432C2211yescharacteristic
12#22575430—21no—
13Q8×Dic269C411yescharacteristic, complemented
14#22575418—21no—
15#22575418C411yescharacteristic, complemented
16#22575409—21no—
17C2×#16864381—21no—
18C2×C4×Dic269C2211yescharacteristic
19#22575382—21no—
20C22⋊#14524130C2211yescharacteristic
21C8×Dic269—21no—
22#22575360—21no—
23#22575360C2211yescharacteristic
24C22⋊Q8×C269C2211yescharacteristic
25C22⋊C8×C269C2211yescharacteristic
26#95×C269C2211yescharacteristic
27C2×Dic538—21no—
28C2×Dic538C2×C411yescharacteristic
29C22×Dic269—21no—
30C22×Dic269D411yescharacteristic
31C22×Dic269D411yescharacteristic
32C2×#14524130—21no—
33C4⋊Dic269—21no—
34C4⋊Dic269C2×C411yescharacteristic
35#16864381—21no—
36#16864381—21no—
37#16864381—21no—
38#16864381—21no—
39#16864381—21no—
40#16864381—42no—
41C22⋊Dic269—21no—
42C4×Dic269—21no—
43C4×Dic269—21no—
44C4×Dic269C2×C411yescharacteristic
45C4×Dic269C2×C411yescharacteristic
46C4×Dic269D411yescharacteristic
47C4×Dic269D411yescharacteristic
48C2×Q8×C269C2×C411yescharacteristic
49C22×C4×C269—21no—
50C22×C4×C269C2311yescharacteristic
51C2×C8×C269—21no—
52C4⋊C4×C269—21no—
53C4⋊C4×C269C2×C411yescharacteristic
54C22⋊C4×C269—21no—
55Dic538—42no—
56Dic538—41no—
57C2×Dic269—21no—
58C2×Dic269—21no—
59C2×Dic269—41no—
60C2×Dic269—41no—
61C2×Dic269—41no—
62C2×Dic269—41no—
63C2×Dic269C22⋊C411yescharacteristic
64C2×Dic269C22⋊C411yescharacteristic
65C2×Dic269C22⋊C411yescharacteristic
66C2×Dic269C22⋊C411yescharacteristic
67C2×Dic269SD1612yes—
68C2×Dic269Q1612yes—
69#14524130—41no—
70C23×C269C2×D411yescharacteristic
71Q8×C269—41no—
72C2×C4×C269—21no—
73C2×C4×C269—21no—
74C2×C4×C269—41no—
75C2×C4×C269—41no—
76C2×C4×C269—41no—
77C2×C4×C269—41no—
78C2×C4×C269C22×C411yescharacteristic
79C2×C4×C269C2×D411yescharacteristic
80C8×C269—41no—
81C22×C269—21no—
82C22×C269—21no—
83C22×C269C2×C22⋊C411yescharacteristic
84C22×C269C2×SD1611yescharacteristic
85C22×C269C2×Q1611yescharacteristic
86C4×C269—21no—
87C4×C269—21no—
88C4×C269—41no—
89C4×C269—41no—
90C4×C269—81no—
91Dic269—21no—
92Dic269—21no—
93Dic269—41no—
94Dic269—41no—
95Dic269—81no—
96Dic269#10312yes—
97Dic269#10312yes—
98C2×C269—21no—
99C2×C269—21no—
100C2×C269#41011yescharacteristic
101C2×C269C2×#10311yescharacteristic
102C2×C269#42111yescharacteristic
103C269#151811yescharacteristic, complemented, Sylow
104#1518—2691nomaximal, Sylow
105#533—2691no—
106#431—2691no—
107#382—2691no—
108#328—2691no—
109#328—2691no—
110#328—2691no—
111#328D26911yescharacteristic
112C4⋊Q8—2691no—
113C4⋊Q8—2691no—
114#125—5381no—
115C22⋊Q8—2691no—
116C22⋊Q8—5381no—
117C22⋊Q8C2×D26911yescharacteristic
118C4×Q8—2691no—
119C4×Q8—2691no—
120C4×Q8—5381no—
121#117—5381no—
122C2×C4⋊C4—5381no—
123C2×C42—2691no—
124C4⋊C8—5381no—
125C22⋊C8—2691no—
126C22⋊C8C2×D26911yescharacteristic
127C4×C8—5381no—
128#95—2691no—
129#95—5381no—
130#95C2×D26911yescharacteristic
131C2×Q8—2691no—
132C2×Q8—5381no—
133C2×Q8C4×D26911yescharacteristic
134C22×C4—21no—
135C22×C4—2691no—
136C22×C4—2691no—
137C22×C4—5381no—
138C22×C4C22×D26911yescharacteristic
139C2×C8—21no—
140C2×C8—5381no—
141C4⋊C4—21no—
142C4⋊C4—2691no—
143C4⋊C4—5381no—
144C4⋊C4—5381no—
145C4⋊C4—5381no—
146C4⋊C4—5381no—
147C4⋊C4—5381no—
148C4⋊C4—5381no—
149C4⋊C4—10762no—
150C4⋊C4C4×D26911yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—5381no—
153C42—2691no—
154C42—2691no—
155C42—2691no—
156C42—2691no—
157C42—5381no—
158C42—5381no—
159C23D4×D26911yescharacteristic
160Q8—41no—
161Q8—10761no—
162Q8—10762no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—2691no—
170C2×C4—2691no—
171C2×C4—2692no—
172C2×C4—2692no—
173C2×C4—2691no—
174C2×C4—2691no—
175C2×C4—5381no—
176C2×C4—5381no—
177C2×C4—10761no—
178C2×C4—10761no—
179C2×C4—10761no—
180C2×C4—10761no—
181C2×C4C2×C4×D26911yescharacteristic
182C2×C4D4×D26911yescharacteristic
183C8—41no—
184C8—10761no—
185C22—21no—
186C22—21no—
187C22C22⋊C4×D26911yescharacteristic
188C22SD16×D26911yescharacteristic
189C22Q16×D26911yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—2692no—
196C4—2692no—
197C4—5381no—
198C4—5381no—
199C4—10761no—
200C4—10761no—
201C4—21521no—
202C2—21no—
203C2—21no—
204C2#3177057711yescharacteristic
205C2#103×D26911yescharacteristic
206C2#3177062011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D269
commutatorC2×C4×C269C22×C4
FrattiniC22×C4C22×D269
Fitting#328×C269C2
socleC22×C269C2×C22⋊C4
prime radicalC23×C269C2×D4
cosocleC22×C4×C269C23
hypercenter#328D269
hypocenterC269#1518
LCSG ▷ C2×C4×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. #22575452C4semidirect
9. #22575451C4semidirect
13. Q8×Dic269C4semidirect
15. #22575418C4semidirect
103. C269#1518semidirect

Maximal subgroups

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

subgroupindex
#317711572
#317706552
#317704692
#317703432
#317703422
#317703412
#328×C2692
#1518269