Finite Group Databasebeta

← #46822261

Subgroups — #46822261

Order 34432.

348 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 113 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#31771160C211yesmaximal, characteristic, complemented
2#31771142C211yesmaximal, characteristic
3#31770911C212yesmaximal, complemented
4#31770892C211yesmaximal, characteristic, complemented
5#31770862C212yesmaximal, complemented
6#31770852C212yesmaximal
7#31770830C212yesmaximal, complemented
8#31770815C211yesmaximal, characteristic, complemented
9#31770811C211yesmaximal, characteristic, complemented
10#31770627C211yesmaximal, characteristic, complemented
11#477×C269C211yesmaximal, characteristic, complemented
12C2×#16864392C2212yes—
13C2×#16864391C2212yes—
14C2×#16864385C2212yes—
15#22575453C2211yescharacteristic
16#22575448—21no—
17#22575444—21no—
18#22575444C2211yescharacteristic
19#22575442C2211yescharacteristic
20#22575438—21no—
21#22575433C2212yes—
22#22575429—21no—
23#22575429C2211yescharacteristic
24#22575428C2211yescharacteristic
25Q8×Dic269—21no—
26#22575418C2212yes—
27C4×D1076—21no—
28C4×D1076C2211yescharacteristic
29#22575411—21no—
30#22575410—21no—
31C42×D269C2211yescharacteristic
32#22575384C2212yes—
33C4⋊#14524130C2211yescharacteristic
34#22575382C2212yes—
35#22575378C2212yes—
36#22575376C2212yes—
37#22575373C2212yes—
38C4⋊Q8×C269C2211yescharacteristic
39C4×Q8×C269C2211yescharacteristic
40#107×C269C2212yes—
41C4⋊C8×C269C2211yescharacteristic
42#103×C269C2212yes—
43C2×Dic538C2312yes—
44C2×D1076—21no—
45C2×D1076C2311yescharacteristic
46C2×C4×D269—21no—
47C2×C4×D269D411yescharacteristic
48C2×C4×D269D411yescharacteristic
49C2×C4×D269C2311yescharacteristic
50#16864392—42no—
51#16864391—42no—
52#16864385—42no—
53C2×#14524130C2312yes—
54C4⋊Dic269—21no—
55C4⋊Dic269—22no—
56C4⋊Dic269—21no—
57C4⋊Dic269—21no—
58C4⋊Dic269C2311yescharacteristic
59#16864381—21no—
60#16864381—21no—
61#16864381—22no—
62#16864379—22no—
63#16864379—21no—
64#16864379—21no—
65#16864379—21no—
66#16864379—21no—
67#16864379—21no—
68C4×Dic269—22no—
69C4×Dic269D411yescharacteristic
70C4×Dic269D411yescharacteristic
71C4×Dic269C2311yescharacteristic
72C2×Q8×C269—21no—
73C2×Q8×C269C2311yescharacteristic
74C2×C8×C269C2312yes—
75C4⋊C4×C269—21no—
76C4⋊C4×C269—21no—
77C4⋊C4×C269C2312yes—
78C4⋊C4×C269C2311yescharacteristic
79C42×C269—21no—
80C42×C269C2311yescharacteristic
81C22×D269—21no—
82C22×D269C2×D411yescharacteristic
83Dic538—22no—
84Dic538—22no—
85D1076—21no—
86D1076—21no—
87D1076—42no—
88C2×Dic269—22no—
89C2×Dic269—21no—
90C2×Dic269C2×D411yescharacteristic
91C2×Dic269C2×D411yescharacteristic
92C2×Dic269C2×D411yescharacteristic
93C4×D269—22no—
94C4×D269—21no—
95C4×D269—21no—
96C4×D269—41no—
97C4×D269—42no—
98#14524130—22no—
99Q8×C269—21no—
100Q8×C269—21no—
101Q8×C269—42no—
102C2×C4×C269—21no—
103C2×C4×C269—21no—
104C2×C4×C269—22no—
105C2×C4×C269C2×D411yescharacteristic
106C2×C4×C269C2×D411yescharacteristic
107C2×C4×C269C2411yescharacteristic
108C8×C269—22no—
109C22×C269C22×D411yescharacteristic
110C2×D269—21no—
111C2×D269—21no—
112C2×D269—21no—
113C2×D269—41no—
114C2×D269—41no—
115C2×D269—41no—
116C4×C269—21no—
117C4×C269—41no—
118C4×C269—42no—
119C4×C269—41no—
120C4×C269#13712yes—
121C4×C269H(5,𝔽2)11yescharacteristic
122C4×C2692−1+411yescharacteristic
123Dic269—21no—
124Dic269—21no—
125Dic269—21no—
126Dic269—42no—
127Dic269—41no—
128C2×C269#53711yescharacteristic
129C2×C269C2×#13711yescharacteristic
130C2×C269#57511yescharacteristic
131D269—41no—
132D269—81no—
133C269#325211yescharacteristic, complemented, Sylow
134#3252—2691nomaximal, Sylow
135#533—2691no—
136#529—2691no—
137#479—2692no—
138#477D26911yescharacteristic, complemented
139#476—2691no—
140#470—2692no—
141#468—2692no—
142#464—2692no—
143#462—2691no—
144#461—2691no—
145#423—2691no—
146C2×Q16—2692no—
147C2×SD16—2692no—
148C2×M16—2692no—
149C4⋊Q8—2691no—
150C4⋊Q8C2×D26911yescharacteristic
151#126—5381no—
152#125—2691no—
153#125—5381no—
154#124—2691no—
155#123—5381no—
156C22⋊Q8—2691no—
157C22⋊Q8—2692no—
158C22⋊Q8—5381no—
159#121—2691no—
160C4×Q8—2692no—
161C4×Q8—5381no—
162C4×Q8C2×D26911yescharacteristic
163C4×D4—2691no—
164C4×D4—5381no—
165#117—5381no—
166#117—5381no—
167C2×C42—2691no—
168#107C2×D26912yes—
169#106—2692no—
170C4⋊C8—2692no—
171C4⋊C8—2691no—
172C4⋊C8C2×D26911yescharacteristic
173#103—2692no—
174#103—2692no—
175#103C2×D26912yes—
176#102—2692no—
177C2×Q8—21no—
178C2×Q8—2692no—
179C2×Q8C22×D26911yescharacteristic
180C2×D4—2691no—
181C2×D4—5381no—
182C22×C4—2691no—
183C22×C4—2691no—
184C22×C4—2691no—
185C22×C4—5381no—
186Q16—10762no—
187SD16—10762no—
188M16—10762no—
189C2×C8—2692no—
190C2×C8C22×D26912yes—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—2691no—
194C4⋊C4—5381no—
195C4⋊C4—5381no—
196C4⋊C4—5381no—
197C4⋊C4—5382no—
198C4⋊C4—5382no—
199C4⋊C4—5381no—
200C4⋊C4—5381no—
201C4⋊C4C22×D26912yes—
202C4⋊C4C22×D26911yescharacteristic
203C22⋊C4—5381no—
204C22⋊C4—5381no—
205C22⋊C4—5381no—
206C22⋊C4—5382no—
207C22⋊C4—5381no—
208C22⋊C4—5381no—
209C42—21no—
210C42—2691no—
211C42—2691no—
212C42—2691no—
213C42—5382no—
214C42C22×D26911yescharacteristic
215C23—2691no—
216C23—5381no—
217Q8—21no—
218Q8—21no—
219Q8—42no—
220Q8—5382no—
221Q8—5382no—
222D4—5381no—
223D4—5381no—
224D4—10762no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—2691no—
229C2×C4—2691no—
230C2×C4—2691no—
231C2×C4—5382no—
232C2×C4—5381no—
233C2×C4—5381no—
234C2×C4—5382no—
235C2×C4—5381no—
236C2×C4—10761no—
237C2×C4—10762no—
238C2×C4D4×D26911yescharacteristic
239C2×C4D4×D26911yescharacteristic
240C2×C4C23×D26911yescharacteristic
241C8—22no—
242C8—5382no—
243C22—5381no—
244C22—5381no—
245C22—5381no—
246C22—10761no—
247C22—10761no—
248C22—10761no—
249C22C2×D4×D26911yescharacteristic
250C4—21no—
251C4—41no—
252C4—42no—
253C4—41no—
254C4—5381no—
255C4—5381no—
256C4—5381no—
257C4—10761no—
258C4—10762no—
259C4#2257548512yes—
260C4#2257549911yescharacteristic
261C4#2257550111yescharacteristic
262C2—10761no—
263C2—21521no—
264C2#3177118511yescharacteristic
265C2C2×#2257548511yescharacteristic
266C2#3177140111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#477×C269C2
socleC22×C269C22×D4
prime radical#22575428C22
hypercenter#477D269
hypocenterC269#3252
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #31771160C2semidirect
3. #31770911C2semidirect
4. #31770892C2semidirect
5. #31770862C2semidirect
7. #31770830C2semidirect
8. #31770815C2semidirect
9. #31770811C2semidirect
10. #31770627C2semidirect
11. #477×C269C2semidirect
133. C269#3252semidirect
138. #477D269semidirect

Maximal subgroups

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

subgroupindex
#317711602
#317711422
#317709112
#317708922
#317708622
#317708522
#317708302
#317708152
#317708112
#317706272
#477×C2692
#3252269