Finite Group Databasebeta

← #46814048

Subgroups — #46814048

Order 34432.

464 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 173 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#31770500C212yesmaximal, complemented
4#31770499C212yesmaximal
5#31770493C212yesmaximal
6#31770488C212yesmaximal, complemented
7#31770486C212yesmaximal, complemented
8#31770468C211yesmaximal, characteristic
9#380×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×Dic269C2212yes—
20#22575360C2211yescharacteristic
21#22575360C2212yes—
22#22575360C2211yescharacteristic
23#22575360C2212yes—
24#22575360C2212yes—
25#22575360C2212yes—
26#22575360C2212yes—
27C23×C4×C269C2211yescharacteristic
28C2×C4⋊C4×C269C2212yes—
29C2×C22⋊C4×C269C2211yescharacteristic
30C2×C22⋊C4×C269C2211yescharacteristic
31#95×C269C2212yes—
32C2×Dic538—42no—
33C2×Dic538C2×C414yes—
34C22×Dic269C2312yes—
35C22×Dic269C2312yes—
36C22×Dic269C2312yes—
37C22×Dic269C2312yes—
38C4⋊Dic269C2×C414yes—
39#16864381—42no—
40#16864381—42no—
41#16864381C2×C418yes—
42C22⋊Dic269—42no—
43C22⋊Dic269C2×C418yes—
44C4×Dic269—42no—
45C4×Dic269—42no—
46C24×C269C2311yescharacteristic
47C22×C4×C269—42no—
48C22×C4×C269C2×C414yes—
49C22×C4×C269C2312yes—
50C22×C4×C269C2312yes—
51C22×C4×C269C2311yescharacteristic
52C22×C4×C269C2311yescharacteristic
53C4⋊C4×C269—42no—
54C22⋊C4×C269—41no—
55C22⋊C4×C269—41no—
56Dic538—44no—
57C2×Dic269—22no—
58C2×Dic269—22no—
59C2×Dic269—22no—
60C2×Dic269—22no—
61C2×Dic269—22no—
62C2×Dic269—22no—
63C2×Dic269—22no—
64C2×Dic269—22no—
65C2×Dic269—22no—
66C2×Dic269—22no—
67C2×Dic269C22×C414yes—
68C2×Dic269C22×C414yes—
69C23×C269—21no—
70C23×C269—22no—
71C23×C269—22no—
72C23×C269—21no—
73C23×C269C22×C412yes—
74C23×C269C2411yescharacteristic
75C2×C4×C269—22no—
76C2×C4×C269—22no—
77C2×C4×C269—22no—
78C2×C4×C269—22no—
79C2×C4×C269—22no—
80C2×C4×C269—22no—
81C2×C4×C269—22no—
82C2×C4×C269—22no—
83C2×C4×C269—44no—
84C2×C4×C269C22×C412yes—
85C2×C4×C269C22×C412yes—
86C22×C269—22no—
87C22×C269—22no—
88C22×C269—22no—
89C22×C269—42no—
90C22×C269—42no—
91C22×C269C23×C411yescharacteristic
92C22×C269H(5,𝔽2)12yes—
93C22×C269H(5,𝔽2)11yescharacteristic
94C22×C2692−1+412yes—
95C22×C2692−1+411yescharacteristic
96C4×C269—22no—
97C4×C269—22no—
98C4×C269—42no—
99C4×C269—42no—
100Dic269—24no—
101Dic269—24no—
102Dic269—42no—
103Dic269—42no—
104C2×C269—42no—
105C2×C269#51811yescharacteristic
106C2×C269#51911yescharacteristic
107C2×C269#52011yescharacteristic
108C2×C269#56212yes—
109C2×C269#56312yes—
110C269#237811yescharacteristic, complemented, Sylow
111#2378—2691nomaximal, Sylow
112C2×C22⋊Q8—2691no—
113#391—2692no—
114#389—2692no—
115#388—2692no—
116#388—2692no—
117#387—2692no—
118#387—2692no—
119#381—2691no—
120#380D26911yescharacteristic
121C22×Q8—2691no—
122C23×C4C2×D26911yescharacteristic
123C22⋊Q8—2698no—
124C2×C4⋊C4—2692no—
125C2×C4⋊C4—2691no—
126C2×C4⋊C4—2692no—
127C2×C4⋊C4—2692no—
128C2×C4⋊C4C2×D26912yes—
129C2×C22⋊C4—2692no—
130C2×C22⋊C4—2692no—
131C2×C22⋊C4C2×D26911yescharacteristic
132C2×C22⋊C4C2×D26911yescharacteristic
133C2×C42—2692no—
134C2×C42—2692no—
135#95—2691no—
136#95—2692no—
137#95—2691no—
138#95—2692no—
139#95—2692no—
140#95—2692no—
141#95—2692no—
142#95C2×D26912yes—
143C24C22×D26911yescharacteristic
144C2×Q8—2694no—
145C2×Q8—10762no—
146C22×C4—42no—
147C22×C4—2692no—
148C22×C4—2692no—
149C22×C4—2692no—
150C22×C4—2692no—
151C22×C4C4×D26914yes—
152C22×C4C22×D26912yes—
153C22×C4C22×D26912yes—
154C22×C4C22×D26911yescharacteristic
155C22×C4C22×D26911yescharacteristic
156C4⋊C4—42no—
157C4⋊C4—2698no—
158C4⋊C4—2694no—
159C4⋊C4—10762no—
160C4⋊C4—10762no—
161C22⋊C4—41no—
162C22⋊C4—41no—
163C22⋊C4—2698no—
164C22⋊C4—10762no—
165C42—10762no—
166C42—10762no—
167C23—21no—
168C23—22no—
169C23—22no—
170C23—21no—
171C23C2×C4×D26912yes—
172C23C23×D26911yescharacteristic
173Q8—10764no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—44no—
183C2×C4—2694no—
184C2×C4—2694no—
185C2×C4—5382no—
186C2×C4—5382no—
187C2×C4—5382no—
188C2×C4—5382no—
189C2×C4—5382no—
190C2×C4—5382no—
191C2×C4—5382no—
192C2×C4—5382no—
193C2×C4—5382no—
194C2×C4—5382no—
195C2×C4C2×C4×D26912yes—
196C2×C4C2×C4×D26912yes—
197C22—22no—
198C22—22no—
199C22—22no—
200C22—42no—
201C22—42no—
202C22C22×C4×D26911yescharacteristic
203C22#2257549812yes—
204C22#2257549811yescharacteristic
205C22#2257550012yes—
206C22#2257550111yescharacteristic
207C4—22no—
208C4—22no—
209C4—42no—
210C4—42no—
211C4—5384no—
212C4—5384no—
213C4—10762no—
214C4—10762no—
215C2—42no—
216C2#3177107811yescharacteristic
217C2#3177108211yescharacteristic
218C2#3177108611yescharacteristic
219C2#3177135012yes—
220C2#3177135612yes—
subgroupG/H
center, FrattiniC23C23×D269
commutatorC22×C269C23×C4
Fitting#380×C269C2
socle, cosocleC23×C269C24
prime radicalC24×C269C23
hypercenter#380D269
hypocenterC269#2378
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. #31770509C2semidirect
3. #31770500C2semidirect
6. #31770488C2semidirect
7. #31770486C2semidirect
11. #22575432C4semidirect
110. C269#2378semidirect

Maximal subgroups

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

subgroupindex
C2×#225754322
#317705092
#317705002
#317704992
#317704932
#317704882
#317704862
#317704682
#380×C2692
#2378269