Finite Group Databasebeta

← #46821269

Subgroups — #46821269

Order 34432.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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#31771158C211yesmaximal, characteristic, complemented
2C2×#22575440C211yesmaximal, characteristic
3#31770963C214yesmaximal, complemented
4#31770958C214yesmaximal, complemented
5#31770615C211yesmaximal, characteristic, complemented
6#31770613C211yesmaximal, characteristic, complemented
7#31770610C211yesmaximal, characteristic
8M16×Dic269C211yesmaximal, characteristic, complemented
9#418×C269C211yesmaximal, characteristic
10C22×Dic538C2211yescharacteristic
11C2×#16864386C2211yescharacteristic
12#22575452C2212yescomplemented
13#22575444C2212yescomplemented
14#22575440—22no—
15#22575440C2212yes—
16#22575440C2212yes—
17#22575430—22no—
18C4×Dic538—22no—
19#22575412C2211yescharacteristic
20C2×C22⋊Dic269—22no—
21C2×C4×Dic269C2211yescharacteristic
22#22575378C2214yescomplemented
23#22575376C2214yescomplemented
24#22575374C2214yes—
25#22575363C2212yescomplemented
26C8×Dic269C2212yescomplemented
27C22×D4×C269C2211yescharacteristic
28C2×M16×C269C2211yescharacteristic
29#117×C269C2211yescharacteristic
30#102×C269C2214yes—
31C2×Dic538—22no—
32C2×Dic538—21no—
33C2×Dic538—22no—
34C2×Dic538—22no—
35C2×Dic538C2312yes—
36C22×Dic269—21no—
37C22×Dic269D412yes—
38#16864386—22no—
39C2×#14524130C2312yes—
40C4⋊Dic269—22no—
41C4⋊Dic269C2312yes—
42#16864381—22no—
43#16864381—22no—
44C22⋊Dic269—24no—
45C22⋊Dic269—24no—
46C22⋊Dic269—21no—
47C4×Dic269—21no—
48C4×Dic269D412yes—
49C4×Dic269C2311yescharacteristic
50C4×Dic269C2311yescharacteristic
51C24×C269—21no—
52C2×D4×C269—21no—
53C2×D4×C269—22no—
54C2×D4×C269—22no—
55C2×D4×C269C2312yes—
56C22×C4×C269C2311yescharacteristic
57M16×C269—22no—
58C2×C8×C269C2312yes—
59C4⋊C4×C269C2312yes—
60C22⋊C4×C269—21no—
61C42×C269—21no—
62Dic538—22no—
63Dic538—22no—
64Dic538—44no—
65Dic538—42no—
66C2×Dic269—22no—
67C2×Dic269—22no—
68C2×Dic269—42no—
69C2×Dic269—42no—
70C2×Dic269C2×D412yes—
71C2×Dic269C2×D412yes—
72#14524130—22no—
73C23×C269—22no—
74C23×C269—44no—
75C23×C269—42no—
76C23×C269C2×D411yescharacteristic
77D4×C269—22no—
78D4×C269—22no—
79D4×C269—42no—
80C2×C4×C269—22no—
81C2×C4×C269C2×D411yescharacteristic
82C2×C4×C269#4112yes—
83C2×C4×C269#4112yes—
84C2×C4×C269C2411yescharacteristic
85C8×C269—22no—
86C22×C269—22no—
87C22×C269—42no—
88C22×C269—44no—
89C22×C269—84no—
90C22×C269#12412yes—
91C22×C269C22×D411yescharacteristic
92C4×C269—42no—
93C4×C269#12412yes—
94C4×C269C2×#4111yescharacteristic
95C4×C269C2×#4111yescharacteristic
96Dic269—22no—
97Dic269—22no—
98Dic269—42no—
99Dic269—42no—
100C2×C269—22no—
101C2×C269—82no—
102C2×C269C2×#12411yescharacteristic
103C2×C269#57512yes—
104C269#314011yescharacteristic, complemented, Sylow
105#3140—2691nomaximal, Sylow
106#533—2691no—
107C2×#124—2691no—
108#489—2694no—
109#488—2694no—
110#419—2691no—
111#419—2691no—
112#418—2691no—
113#418D26911yescharacteristic
114C4×M16—2691no—
115C22×Q8—2691no—
116C22×D4C2×D26911yescharacteristic
117C2×M16—2691no—
118C2×M16C2×D26911yescharacteristic
119C4⋊Q8—2692no—
120#125—2692no—
121#124—2692no—
122#124—2692no—
123#124—5382no—
124C22⋊Q8—5382no—
125C4×Q8—5382no—
126#117—2691no—
127#117C2×D26911yescharacteristic
128C2×C22⋊C4—5382no—
129C2×C42—2691no—
130#103—2694no—
131#103—2694no—
132#102—2694no—
133#102C2×D26914yes—
134#97—2692no—
135C4×C8—2692no—
136C24—21no—
137C2×Q8—2692no—
138C2×Q8—5382no—
139C2×Q8—5381no—
140C2×Q8—5382no—
141C2×Q8—5382no—
142C2×D4—21no—
143C2×D4—22no—
144C2×D4—22no—
145C2×D4C22×D26912yes—
146C22×C4—2692no—
147C22×C4—5381no—
148C22×C4C22×D26911yescharacteristic
149M16—22no—
150M16—5382no—
151C2×C8—2692no—
152C2×C8C22×D26912yes—
153C4⋊C4—2692no—
154C4⋊C4—5382no—
155C4⋊C4—5382no—
156C4⋊C4—5382no—
157C4⋊C4C22×D26912yes—
158C22⋊C4—21no—
159C22⋊C4—5384no—
160C22⋊C4—5384no—
161C22⋊C4—5381no—
162C42—21no—
163C42—2692no—
164C42—2691no—
165C42—2691no—
166C42—5381no—
167C23—22no—
168C23—44no—
169C23—42no—
170C23D4×D26911yescharacteristic
171Q8—5382no—
172Q8—5382no—
173Q8—10764no—
174Q8—10762no—
175D4—22no—
176D4—22no—
177D4—42no—
178C2×C4—22no—
179C2×C4—2692no—
180C2×C4—2692no—
181C2×C4—5382no—
182C2×C4—5382no—
183C2×C4—10762no—
184C2×C4—10762no—
185C2×C4D4×D26911yescharacteristic
186C2×C4#1686440112yes—
187C2×C4#1686440212yes—
188C2×C4C23×D26911yescharacteristic
189C8—22no—
190C8—5382no—
191C22—22no—
192C22—44no—
193C22—42no—
194C22—84no—
195C22#2257543912yes—
196C22C2×D4×D26911yescharacteristic
197C4—42no—
198C4—5382no—
199C4—5382no—
200C4—10762no—
201C4—10762no—
202C4#2257543912yes—
203C4C2×#1686440111yescharacteristic
204C4C2×#1686440211yescharacteristic
205C2—22no—
206C2—82no—
207C2C2×#2257543911yescharacteristic
208C2#3177140112yes—
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#418×C269C2
socleC22×C269C22×D4
prime radicalC22×D4×C269C22
hypercenter#418D269
hypocenterC269#3140
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #31771158C2semidirect
3. #31770963C2semidirect
4. #31770958C2semidirect
5. #31770615C2semidirect
6. #31770613C2semidirect
8. M16×Dic269C2semidirect
12. #22575452C22semidirect
13. #22575444C22semidirect
22. #22575378C22semidirect
23. #22575376C22semidirect
25. #22575363C22semidirect
26. C8×Dic269C22semidirect
104. C269#3140semidirect

Maximal subgroups

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

subgroupindex
#317711582
C2×#225754402
#317709632
#317709582
#317706152
#317706132
#317706102
M16×Dic2692
#418×C2692
#3140269