Finite Group Databasebeta

← #46820683

Subgroups — #46820683

Order 34432.

440 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 131 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
2C4×D4×D269C211yesmaximal, characteristic
3#31770904C212yesmaximal, complemented
4#31770903C212yesmaximal, complemented
5#31770892C211yesmaximal, characteristic, complemented
6#31770886C211yesmaximal, characteristic, complemented
7#31770885C211yesmaximal, characteristic, complemented
8#31770644C212yesmaximal, complemented
9#31770627C211yesmaximal, characteristic, complemented
10#31770608C212yesmaximal
11#476×C269C211yesmaximal, characteristic, complemented
12C2×D4×D269C2211yescharacteristic
13C22×C4×D269—21no—
14C2×#16864385C2212yes—
15#22575453C2211yescharacteristic, complemented
16#22575444C2212yescomplemented
17#22575433—21no—
18#22575429—21no—
19Q8×Dic269—21no—
20#22575418—21no—
21C4×D1076C2211yescharacteristic
22D4×Dic269C2211yescharacteristic
23#22575415C2211yescharacteristic
24C4×C22⋊D269—21no—
25#22575413—21no—
26#22575411C2212yes—
27C4⋊C4×D269C2211yescharacteristic
28C22⋊C4×D269—21no—
29C42×D269C2211yescharacteristic
30#22575387C2212yescomplemented
31#22575386C2212yescomplemented
32#22575384C2212yescomplemented
33C4⋊#14524130C2211yescharacteristic, complemented
34#22575382C2212yescomplemented
35#22575375C2212yes—
36#22575374C2212yes—
37#22575373C2212yes—
38C4⋊Q8×C269C2211yescharacteristic, complemented
39C4×D4×C269C2211yescharacteristic
40#106×C269C2212yescomplemented
41C4⋊C8×C269C2211yescharacteristic, complemented
42#102×C269C2212yes—
43C23×D269—21no—
44C2×Dic538—21no—
45C2×D1076C2311yescharacteristic
46C2×C22⋊D269—21no—
47D4×D269—22no—
48D4×D269Q814yescomplemented
49C22×Dic269—21no—
50C2×C4×D269—21no—
51C2×C4×D269—21no—
52C2×C4×D269—21no—
53C2×C4×D269—44no—
54C2×C4×D269D411yescharacteristic
55C2×C4×D269D411yescharacteristic
56C2×C4×D269C2311yescharacteristic
57#16864385—24no—
58C2×#14524130C2312yes—
59C4⋊Dic269—22no—
60C4⋊Dic269—21no—
61C4⋊Dic269C2312yes—
62C4⋊Dic269C2311yescharacteristic
63#16864381—21no—
64#16864381—22no—
65C22⋊Dic269—21no—
66#16864379—22no—
67#16864379—21no—
68#16864379—21no—
69C4×Dic269—22no—
70C4×Dic269D411yescharacteristic
71C4×Dic269D411yescharacteristic
72C4×Dic269C2311yescharacteristic
73C2×Q8×C269—21no—
74C2×D4×C269C2311yescharacteristic
75C22×C4×C269—21no—
76C2×C8×C269C2312yes—
77C4⋊C4×C269—21no—
78C4⋊C4×C269C2312yes—
79C4⋊C4×C269C2311yescharacteristic
80C22⋊C4×C269—21no—
81C42×C269C2311yescharacteristic
82C22×D269—21no—
83C22×D269—24no—
84C22×D269—42no—
85C22×D269—42no—
86C22×D269C2×D411yescharacteristic
87Dic538—42no—
88D1076—21no—
89D1076C2×Q812yes—
90C22⋊D269—24no—
91C2×Dic269—22no—
92C2×Dic269—21no—
93C2×Dic269—42no—
94C2×Dic269C2×D411yescharacteristic
95C2×Dic269C2×D411yescharacteristic
96C2×Dic269C2×D411yescharacteristic
97C4×D269—22no—
98C4×D269—41no—
99C4×D269—42no—
100C4×D269—42no—
101C4×D269—42no—
102C4×D269C2×Q812yes—
103C4×D269#4112yes—
104#14524130—22no—
105C23×C269—21no—
106Q8×C269—42no—
107D4×C269—21no—
108D4×C269C2×Q812yes—
109C2×C4×C269—21no—
110C2×C4×C269—22no—
111C2×C4×C269—42no—
112C2×C4×C269C2×D411yescharacteristic
113C2×C4×C269C2×D411yescharacteristic
114C2×C4×C269C2411yescharacteristic
115C8×C269—22no—
116C22×C269—22no—
117C22×C269—41no—
118C22×C269—41no—
119C22×C269C22×D411yescharacteristic
120C2×D269—21no—
121C2×D269—21no—
122C2×D269—22no—
123C2×D269—48no—
124C2×D269—41no—
125C2×D269—41no—
126C2×D269C22⋊Q812yes—
127C4×C269—21no—
128C4×C269—41no—
129C4×C269—42no—
130C4×C269AGL(1,ℤ/8)12yes—
131C4×C269C22×Q811yescharacteristic
132C4×C269C2×#4111yescharacteristic
133Dic269—21no—
134Dic269—21no—
135Dic269—41no—
136Dic269—42no—
137Dic269C22⋊Q812yes—
138C2×C269—42no—
139C2×C269C2×C22⋊Q811yescharacteristic
140C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
141C2×C269#57511yescharacteristic
142D269—22no—
143D269—42no—
144C269#307711yescharacteristic, complemented, Sylow
145#3077—2691nomaximal, Sylow
146#533—2691no—
147C2×C4×D4—2691no—
148#478—2692no—
149#478—2692no—
150#476—2691no—
151#476D26911yescharacteristic, complemented
152#474—2691no—
153#474—2691no—
154#428—2692no—
155#423—2691no—
156#418—2692no—
157C22×D4—2691no—
158C23×C4—5381no—
159C2×M16—2692no—
160C4⋊Q8—2691no—
161C4⋊Q8C2×D26911yescharacteristic, complemented
162#125—2692no—
163C22⋊Q8—5381no—
164C22⋊Q8—5381no—
165C4×Q8—5381no—
166C4×Q8—5381no—
167C4×D4—2691no—
168C4×D4—2691no—
169C4×D4—2691no—
170C4×D4—5381no—
171C4×D4—5381no—
172C4×D4C2×D26911yescharacteristic
173#117—2692no—
174C2×C4⋊C4—2691no—
175C2×C22⋊C4—5381no—
176C2×C42—2691no—
177#107—2692no—
178#107—2692no—
179#106—2692no—
180#106C2×D26912yescomplemented
181C4⋊C8—2692no—
182C4⋊C8—2691no—
183C4⋊C8C2×D26911yescharacteristic, complemented
184#102—2692no—
185#102—2692no—
186#102—2692no—
187#102C2×D26912yes—
188C24—5381no—
189C2×Q8—21no—
190C2×Q8—5381no—
191C2×D4—2694no—
192C2×D4—2691no—
193C2×D4—5382no—
194C2×D4—5381no—
195C2×D4C22×D26911yescharacteristic
196C22×C4—21no—
197C22×C4—2691no—
198C22×C4—2691no—
199C22×C4—2691no—
200C22×C4—5381no—
201C22×C4—5381no—
202C22×C4—5381no—
203C22×C4—5381no—
204C22×C4—10764no—
205M16—5384no—
206C2×C8—2692no—
207C2×C8C22×D26912yes—
208C4⋊C4—21no—
209C4⋊C4—2692no—
210C4⋊C4—2691no—
211C4⋊C4—5381no—
212C4⋊C4—5382no—
213C4⋊C4—5382no—
214C4⋊C4—5381no—
215C4⋊C4C22×D26912yes—
216C4⋊C4C22×D26911yescharacteristic
217C22⋊C4—21no—
218C22⋊C4—5381no—
219C22⋊C4—5382no—
220C22⋊C4—5381no—
221C22⋊C4—5381no—
222C42—2691no—
223C42—2691no—
224C42—2691no—
225C42—5382no—
226C42C22×D26911yescharacteristic
227C23—21no—
228C23—2691no—
229C23—5384no—
230C23—5381no—
231C23—10762no—
232C23—10762no—
233Q8—42no—
234Q8—10762no—
235D4—21no—
236D4—2692no—
237D4—5384no—
238D4—5381no—
239D4Q8×D26912yes—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—2691no—
244C2×C4—2692no—
245C2×C4—2692no—
246C2×C4—2691no—
247C2×C4—2691no—
248C2×C4—5382no—
249C2×C4—5382no—
250C2×C4—5381no—
251C2×C4—10761no—
252C2×C4—10762no—
253C2×C4—10762no—
254C2×C4—10762no—
255C2×C4—10762no—
256C2×C4D4×D26911yescharacteristic
257C2×C4D4×D26911yescharacteristic
258C2×C4C23×D26911yescharacteristic
259C8—22no—
260C8—5382no—
261C22—22no—
262C22—41no—
263C22—41no—
264C22—2692no—
265C22—5381no—
266C22—5381no—
267C22—5382no—
268C22—10768no—
269C22—10761no—
270C22—10761no—
271C22C2×D4×D26911yescharacteristic
272C4—21no—
273C4—41no—
274C4—42no—
275C4—2692no—
276C4—5381no—
277C4—5381no—
278C4—10761no—
279C4—10762no—
280C4#2257548012yes—
281C4C2×Q8×D26911yescharacteristic
282C4#41×D26911yescharacteristic
283C2—42no—
284C2—5382no—
285C2—10762no—
286C2C22⋊Q8×D26911yescharacteristic
287C2C2×#2257548011yescharacteristic
288C2#3177140111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#476×C269C2
socleC22×C269C22×D4
prime radicalC2×D4×D269C22
hypercenter#476D269
hypocenterC269#3077
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #31771160C2semidirect
3. #31770904C2semidirect
4. #31770903C2semidirect
5. #31770892C2semidirect
6. #31770886C2semidirect
7. #31770885C2semidirect
8. #31770644C2semidirect
9. #31770627C2semidirect
11. #476×C269C2semidirect
15. #22575453C22semidirect
16. #22575444C22semidirect
30. #22575387C22semidirect
31. #22575386C22semidirect
32. #22575384C22semidirect
33. C4⋊#14524130C22semidirect
34. #22575382C22semidirect
38. C4⋊Q8×C269C22semidirect
40. #106×C269C22semidirect
41. C4⋊C8×C269C22semidirect
48. D4×D269Q8semidirect
144. C269#3077semidirect
151. #476D269semidirect
161. C4⋊Q8C2×D269semidirect
180. #106C2×D269semidirect
183. C4⋊C8C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317711602
C4×D4×D2692
#317709042
#317709032
#317708922
#317708862
#317708852
#317706442
#317706272
#317706082
#476×C2692
#3077269