Finite Group Databasebeta

← #46822209

Subgroups — #46822209

Order 34432.

398 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 115 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#31771153C211yesmaximal, characteristic, complemented
2#31771142C211yesmaximal, characteristic, complemented
3#31770907C212yesmaximal, complemented
4#31770900C211yesmaximal, characteristic, complemented
5#31770896C211yesmaximal, characteristic, complemented
6#31770840C212yesmaximal, complemented
7#31770831C212yesmaximal, complemented
8#31770822C212yesmaximal, complemented
9#31770797C211yesmaximal, characteristic, complemented
10C4⋊C8×D269C211yesmaximal, characteristic, complemented
11#460×C269C211yesmaximal, characteristic, complemented
12C2×#16864401—21no—
13C2×#16864387C2212yes—
14C2×C8×D269C2212yes—
15#22575453C2211yescharacteristic
16#22575448—21no—
17#22575444C2211yescharacteristic
18#22575442C2211yescharacteristic
19#22575440—21no—
20#22575438—21no—
21#22575429C2211yescharacteristic
22#22575428C2211yescharacteristic
23#22575424—21no—
24#22575424C2212yes—
25C4×D1076—21no—
26C4×D1076C2211yescharacteristic
27D4×Dic269—21no—
28D4×Dic269C2212yes—
29#22575410—21no—
30C42×D269C2211yescharacteristic
31#22575386C2212yes—
32#22575385C2212yes—
33C4⋊#14524130C2211yescharacteristic
34#22575382C2212yes—
35#22575377C2212yes—
36#22575375C2212yes—
37#22575374C2212yes—
38C2×SD16×C269C2212yes—
39#127×C269C2211yescharacteristic
40C4×Q8×C269C2211yescharacteristic
41C4⋊C8×C269C2211yescharacteristic
42#102×C269C2212yes—
43#16864401—44no—
44C2×Dic538—21no—
45C2×D1076—21no—
46C2×D1076C2311yescharacteristic
47C2×C22⋊D269—22no—
48C22×Dic269—22no—
49C2×C4×D269—21no—
50C2×C4×D269D411yescharacteristic
51C2×C4×D269D411yescharacteristic
52C2×C4×D269C2311yescharacteristic
53#16864387—42no—
54C2×#14524130C2312yes—
55C8×D269—42no—
56C4⋊Dic269—21no—
57C4⋊Dic269—21no—
58C4⋊Dic269C2311yescharacteristic
59C4⋊Dic269C2312yes—
60#16864381—21no—
61#16864381—21no—
62C22⋊Dic269—22no—
63C22⋊Dic269—22no—
64#16864379—21no—
65#16864379—21no—
66#16864379—21no—
67#16864379—21no—
68#16864379—21no—
69C4×Dic269D411yescharacteristic
70C4×Dic269D411yescharacteristic
71C4×Dic269C2311yescharacteristic
72C2×Q8×C269C2311yescharacteristic
73C2×D4×C269—21no—
74C2×D4×C269—21no—
75C2×D4×C269C2312yes—
76SD16×C269—42no—
77C2×C8×C269C2312yes—
78C4⋊C4×C269—21no—
79C4⋊C4×C269C2311yescharacteristic
80C42×C269—21no—
81C42×C269C2311yescharacteristic
82C22×D269—21no—
83C22×D269C2×D411yescharacteristic
84Dic538—42no—
85D1076—21no—
86D1076—21no—
87D1076—42no—
88C22⋊D269—44no—
89C2×Dic269—21no—
90C2×Dic269—22no—
91C2×Dic269—44no—
92C2×Dic269C2×D411yescharacteristic
93C2×Dic269C2×D411yescharacteristic
94C2×Dic269C2×D411yescharacteristic
95C4×D269—22no—
96C4×D269—22no—
97C4×D269—21no—
98C4×D269—21no—
99C4×D269—42no—
100#14524130—22no—
101C23×C269—22no—
102Q8×C269—21no—
103Q8×C269—21no—
104D4×C269—22no—
105D4×C269—22no—
106D4×C269—42no—
107D4×C269—42no—
108C2×C4×C269—21no—
109C2×C4×C269—21no—
110C2×C4×C269C2×D411yescharacteristic
111C2×C4×C269C2×D411yescharacteristic
112C2×C4×C269C2411yescharacteristic
113C8×C269—22no—
114C22×C269—42no—
115C22×C269—42no—
116C22×C269—42no—
117C22×C269C22×D411yescharacteristic
118C2×D269—21no—
119C2×D269—21no—
120C2×D269—41no—
121C2×D269—41no—
122C2×D269—41no—
123C2×D269AGL(1,ℤ/8)12yes—
124C4×C269—21no—
125C4×C269—41no—
126C4×C269—41no—
127C4×C269#13512yes—
128C4×C269H(5,𝔽2)11yescharacteristic
129C4×C2692−1+411yescharacteristic
130Dic269—21no—
131Dic269—21no—
132Dic269—21no—
133Dic269—41no—
134Dic269—42no—
135C2×C269—82no—
136C2×C269#53711yescharacteristic
137C2×C269C2×#13511yescharacteristic
138C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
139D269—22no—
140D269—81no—
141C269#324711yescharacteristic, complemented, Sylow
142#3247—2691nomaximal, Sylow
143#532—2691no—
144#529—2691no—
145#478—2692no—
146#477—2691no—
147#476—2691no—
148#466—2692no—
149#465—2692no—
150#463—2692no—
151#460D26911yescharacteristic, complemented
152#459—2691no—
153C2×C4⋊C8—2691no—
154C2×#41—5381no—
155C2×SD16C2×D26912yes—
156C2×D8—2692no—
157C22×C8—2692no—
158C4⋊Q8—2691no—
159#127C2×D26911yescharacteristic
160#126—5381no—
161#125—2691no—
162#124—2691no—
163#124—5381no—
164#123—5381no—
165C22⋊Q8—2691no—
166#121—2692no—
167#121—2691no—
168#121—5381no—
169C4×Q8C2×D26911yescharacteristic
170C4×D4—2692no—
171C4×D4—2691no—
172C4×D4—5381no—
173C4×D4—5381no—
174#117—5381no—
175C2×C42—2691no—
176#107—2692no—
177#106—2692no—
178C4⋊C8—2692no—
179C4⋊C8—2691no—
180C4⋊C8C2×D26911yescharacteristic
181#103—2692no—
182#102—2692no—
183#102—2692no—
184#102C2×D26912yes—
185#41—10764no—
186C2×Q8—5381no—
187C2×Q8C22×D26911yescharacteristic
188C2×D4—21no—
189C2×D4—21no—
190C2×D4—2691no—
191C2×D4—5381no—
192C2×D4—5382no—
193C2×D4C22×D26912yes—
194C22×C4—2691no—
195C22×C4—2691no—
196C22×C4—2691no—
197C22×C4—5382no—
198C22×C4—5381no—
199SD16—42no—
200D8—10762no—
201C2×C8—2692no—
202C2×C8—10762no—
203C2×C8C22×D26912yes—
204C4⋊C4—21no—
205C4⋊C4—2691no—
206C4⋊C4—2692no—
207C4⋊C4—5381no—
208C4⋊C4—5381no—
209C4⋊C4—5381no—
210C4⋊C4—5381no—
211C4⋊C4C22×D26911yescharacteristic
212C22⋊C4—5381no—
213C22⋊C4—5381no—
214C22⋊C4—5381no—
215C22⋊C4—5381no—
216C22⋊C4—5382no—
217C22⋊C4—5382no—
218C22⋊C4—5381no—
219C42—21no—
220C42—2691no—
221C42—2691no—
222C42—2691no—
223C42C22×D26911yescharacteristic
224C23—22no—
225C23—2691no—
226C23—5381no—
227Q8—21no—
228Q8—21no—
229Q8—10762no—
230D4—22no—
231D4—22no—
232D4—42no—
233D4—42no—
234D4—5381no—
235D4—5381no—
236D4—10762no—
237D4—10764no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—2691no—
241C2×C4—2691no—
242C2×C4—2691no—
243C2×C4—5382no—
244C2×C4—5382no—
245C2×C4—5381no—
246C2×C4—5381no—
247C2×C4—5381no—
248C2×C4—5382no—
249C2×C4—10764no—
250C2×C4—10762no—
251C2×C4D4×D26911yescharacteristic
252C2×C4D4×D26911yescharacteristic
253C2×C4C23×D26911yescharacteristic
254C8—22no—
255C8—5382no—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—2692no—
260C22—5381no—
261C22—5381no—
262C22—10761no—
263C22—10761no—
264C22—10761no—
265C22C2×D4×D26911yescharacteristic
266C4—21no—
267C4—41no—
268C4—41no—
269C4—5381no—
270C4—5381no—
271C4—5381no—
272C4—10761no—
273C4—10762no—
274C4#2257547412yes—
275C4#2257549811yescharacteristic
276C4#2257550011yescharacteristic
277C2—82no—
278C2—5382no—
279C2—21521no—
280C2#3177118411yescharacteristic
281C2C2×#2257547411yescharacteristic
282C2AGL(1,ℤ/8)×D26911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#460×C269C2
socleC22×C269C22×D4
hypercenter#460D269
hypocenterC269#3247
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #31771153C2semidirect
2. #31771142C2semidirect
3. #31770907C2semidirect
4. #31770900C2semidirect
5. #31770896C2semidirect
6. #31770840C2semidirect
7. #31770831C2semidirect
8. #31770822C2semidirect
9. #31770797C2semidirect
10. C4⋊C8×D269C2semidirect
11. #460×C269C2semidirect
141. C269#3247semidirect
151. #460D269semidirect

Maximal subgroups

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

subgroupindex
#317711532
#317711422
#317709072
#317709002
#317708962
#317708402
#317708312
#317708222
#317707972
C4⋊C8×D2692
#460×C2692
#3247269