Finite Group Databasebeta

← #46813638

Subgroups — #46813638

Order 34432.

484 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 177 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
1C2×#22575432C211yesmaximal, characteristic
2#31770509C212yesmaximal, complemented
3#31770499C212yesmaximal
4#31770493C212yesmaximal
5#31770488C212yesmaximal, complemented
6#31770487C212yesmaximal, complemented
7#31770456C212yesmaximal, complemented
8C4×C22⋊Dic269C211yesmaximal, characteristic
9#381×C269C211yesmaximal, characteristic
10C22×Dic538C2211yescharacteristic
11#22575432C418yescomplemented
12C2×C4⋊Dic269C2211yescharacteristic
13C2×#16864381C2212yes—
14C2×#16864381C2212yes—
15C2×#16864381C2212yes—
16C2×C22⋊Dic269C2212yes—
17C2×C22⋊Dic269C2212yes—
18C2×C4×Dic269C2212yes—
19C2×C4×Dic269C2211yescharacteristic
20C2×C4×Dic269C2211yescharacteristic
21C2×C4×Dic269C2212yes—
22#22575360C2212yes—
23#22575360C2212yes—
24#22575360C2212yes—
25#22575360C2212yes—
26#22575360C2212yes—
27C23×C4×C269C2211yescharacteristic
28C2×C22⋊C4×C269C2211yescharacteristic
29C2×C22⋊C4×C269C2211yescharacteristic
30#95×C269C2212yes—
31#95×C269C2212yes—
32C2×Dic538—41no—
33C2×Dic538—41no—
34C2×Dic538C2×C414yes—
35C22×Dic269C2312yes—
36C22×Dic269C2312yes—
37C22×Dic269C2312yes—
38C22×Dic269C2312yes—
39C4⋊Dic269C2×C414yes—
40#16864381—24no—
41#16864381—42no—
42#16864381C2×C418yes—
43C22⋊Dic269—24no—
44C22⋊Dic269C2×C418yes—
45C4×Dic269—24no—
46C4×Dic269—41no—
47C4×Dic269—41no—
48C4×Dic269—42no—
49C24×C269C2311yescharacteristic
50C22×C4×C269—41no—
51C22×C4×C269—41no—
52C22×C4×C269C2×C414yes—
53C22×C4×C269C2312yes—
54C22×C4×C269C2312yes—
55C22×C4×C269C2311yescharacteristic
56C22×C4×C269C2311yescharacteristic
57C22⋊C4×C269—41no—
58C22⋊C4×C269—41no—
59Dic538—44no—
60C2×Dic269—22no—
61C2×Dic269—22no—
62C2×Dic269—22no—
63C2×Dic269—22no—
64C2×Dic269—22no—
65C2×Dic269—22no—
66C2×Dic269—22no—
67C2×Dic269—22no—
68C2×Dic269—22no—
69C2×Dic269C22×C414yes—
70C2×Dic269C22×C414yes—
71C2×Dic269#4114yes—
72C23×C269—22no—
73C23×C269—21no—
74C23×C269—21no—
75C23×C269—22no—
76C23×C269C22×C412yes—
77C23×C269C2411yescharacteristic
78C2×C4×C269—21no—
79C2×C4×C269—21no—
80C2×C4×C269—21no—
81C2×C4×C269—21no—
82C2×C4×C269—22no—
83C2×C4×C269—22no—
84C2×C4×C269—22no—
85C2×C4×C269—22no—
86C2×C4×C269—22no—
87C2×C4×C269—22no—
88C2×C4×C269—44no—
89C2×C4×C269C22×C412yes—
90C2×C4×C269C22×C412yes—
91C22×C269—22no—
92C22×C269—22no—
93C22×C269—22no—
94C22×C269—42no—
95C22×C269—42no—
96C22×C269C23×C411yescharacteristic
97C22×C269C2×#4112yes—
98C22×C269H(5,𝔽2)11yescharacteristic
99C22×C269H(5,𝔽2)11yescharacteristic
100C22×C2692−1+412yes—
101C4×C269—22no—
102C4×C269—22no—
103C4×C269—42no—
104C4×C269—42no—
105Dic269—24no—
106Dic269—24no—
107Dic269—24no—
108Dic269—42no—
109C2×C269—42no—
110C2×C269C4×#4111yescharacteristic
111C2×C269#51811yescharacteristic
112C2×C269#51911yescharacteristic
113C2×C269#53912yes—
114C2×C269#54212yes—
115C269#233211yescharacteristic, complemented, Sylow
116#2332—2691nomaximal, Sylow
117C2×C22⋊Q8—2691no—
118#391—2692no—
119#388—2692no—
120#388—2692no—
121#387—2692no—
122#387—2692no—
123#381D26911yescharacteristic
124C4×C4⋊C4—2692no—
125C4×C22⋊C4—2691no—
126C22×Q8—2691no—
127C23×C4C2×D26911yescharacteristic
128C22⋊Q8—2698no—
129C2×C4⋊C4—2692no—
130C2×C4⋊C4—2691no—
131C2×C4⋊C4—2692no—
132C2×C4⋊C4—2692no—
133C2×C22⋊C4—2692no—
134C2×C22⋊C4—2692no—
135C2×C22⋊C4C2×D26911yescharacteristic
136C2×C22⋊C4C2×D26911yescharacteristic
137C2×C42—2692no—
138C2×C42—2691no—
139C2×C42—2691no—
140C2×C42—2692no—
141#95—2692no—
142#95—2692no—
143#95—2692no—
144#95—2692no—
145#95—2692no—
146#95C2×D26912yes—
147#95C2×D26912yes—
148C24C22×D26911yescharacteristic
149C2×Q8—2694no—
150C2×Q8—10761no—
151C2×Q8—10761no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—2692no—
155C22×C4—2692no—
156C22×C4—2692no—
157C22×C4—2692no—
158C22×C4C4×D26914yes—
159C22×C4C22×D26912yes—
160C22×C4C22×D26912yes—
161C22×C4C22×D26911yescharacteristic
162C22×C4C22×D26911yescharacteristic
163C4⋊C4—2698no—
164C4⋊C4—2694no—
165C4⋊C4—5384no—
166C4⋊C4—10762no—
167C22⋊C4—41no—
168C22⋊C4—41no—
169C22⋊C4—2698no—
170C22⋊C4—5384no—
171C42—5384no—
172C42—10761no—
173C42—10761no—
174C42—10762no—
175C23—22no—
176C23—21no—
177C23—21no—
178C23—22no—
179C23C2×C4×D26912yes—
180C23C23×D26911yescharacteristic
181Q8—10764no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—44no—
193C2×C4—2694no—
194C2×C4—2694no—
195C2×C4—2694no—
196C2×C4—5382no—
197C2×C4—5382no—
198C2×C4—5382no—
199C2×C4—5382no—
200C2×C4—5382no—
201C2×C4—5382no—
202C2×C4—5382no—
203C2×C4—5382no—
204C2×C4—5382no—
205C2×C4C2×C4×D26912yes—
206C2×C4C2×C4×D26912yes—
207C22—22no—
208C22—22no—
209C22—22no—
210C22—42no—
211C22—42no—
212C22C22×C4×D26911yescharacteristic
213C22#41×D26912yes—
214C22#2257549811yescharacteristic
215C22#2257549811yescharacteristic
216C22#2257550012yes—
217C4—22no—
218C4—22no—
219C4—42no—
220C4—42no—
221C4—5384no—
222C4—5384no—
223C4—5384no—
224C4—10762no—
225C2—42no—
226C2#3177107311yescharacteristic
227C2#3177107811yescharacteristic
228C2#3177108211yescharacteristic
229C2#3177119812yes—
230C2#3177122312yes—
subgroupG/H
center, FrattiniC23C23×D269
commutatorC22×C269C23×C4
Fitting#381×C269C2
socle, cosocleC23×C269C24
prime radicalC24×C269C23
hypercenter#381D269
hypocenterC269#2332
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. #31770509C2semidirect
5. #31770488C2semidirect
6. #31770487C2semidirect
7. #31770456C2semidirect
11. #22575432C4semidirect
115. C269#2332semidirect

Maximal subgroups

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

subgroupindex
C2×#225754322
#317705092
#317704992
#317704932
#317704882
#317704872
#317704562
C4×C22⋊Dic2692
#381×C2692
#2332269