Finite Group Databasebeta

← #46822700

Subgroups — #46822700

Order 34432.

494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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#31771260C211yesmaximal, characteristic, complemented
2D4×D1076C211yesmaximal, characteristic, complemented
3#31770952C211yesmaximal, characteristic, complemented
4#31770920C212yesmaximal, complemented
5#31770885C211yesmaximal, characteristic, complemented
6#31770840C212yesmaximal, complemented
7#31770800C211yesmaximal, characteristic, complemented
8#31770737C212yesmaximal, complemented
9C8×D1076C211yesmaximal, characteristic, complemented
10#102×D269C212yesmaximal, complemented
11C4×D8×C269C211yesmaximal, characteristic, complemented
12C2×#16864402—21no—
13C22×D1076—21no—
14C2×D4×D269C2212yes—
15C2×#16864387C2212yescomplemented
16C2×C8×D269C2212yescomplemented
17#22575453C2211yescharacteristic, complemented
18#22575450C2211yescharacteristic
19#22575435—22no—
20#22575432—21no—
21#22575428C2212yes—
22#22575427—21no—
23#22575424C2212yescomplemented
24#22575423—22no—
25C4×D1076C2211yescharacteristic
26C4⋊C4×D269C2212yescomplemented
27#22575386C2212yescomplemented
28C4⋊#14524130C2211yescharacteristic, complemented
29#22575375C2212yescomplemented
30#22575375C2212yescomplemented
31#22575374C2212yes—
32#22575373C2212yescomplemented
33#22575365C2212yescomplemented
34C2×D8×C269C2211yescharacteristic
35C4×D4×C269C2211yescharacteristic
36C4×D4×C269C2211yescharacteristic, complemented
37#107×C269C2211yescharacteristic, complemented
38#102×C269C2211yescharacteristic
39#102×C269C2211yescharacteristic, complemented
40C4×C8×C269C2211yescharacteristic, complemented
41C23×D269—22no—
42#16864402—44no—
43C2×Dic538—21no—
44C2×D1076—22no—
45C2×D1076—21no—
46C2×D1076—21no—
47C2×D1076—44no—
48C2×D1076D411yescharacteristic
49C2×D1076C2312yes—
50C2×C22⋊D269—22no—
51C2×C22⋊D269—22no—
52D4×D269—24no—
53D4×D269—42no—
54C2×C4×D269—22no—
55C2×C4×D269C2312yes—
56#16864387—42no—
57C2×#14524130C2312yes—
58C8×D269—42no—
59C4⋊Dic269—21no—
60C4⋊Dic269D411yescharacteristic
61C4⋊Dic269C2312yes—
62#16864381—22no—
63C22⋊Dic269—22no—
64#16864379—22no—
65#16864379D412yes—
66C2×D4×C269C2311yescharacteristic
67C2×D4×C269C2311yescharacteristic
68C22×C4×C269—21no—
69C22×C4×C269—21no—
70D8×C269—22no—
71C2×C8×C269C2311yescharacteristic
72C2×C8×C269C2311yescharacteristic
73C4⋊C4×C269C2311yescharacteristic
74C4⋊C4×C269C2311yescharacteristic
75C22⋊C4×C269—21no—
76C22⋊C4×C269—21no—
77C42×C269C2311yescharacteristic
78C22×D269—22no—
79C22×D269—44no—
80C22×D269—44no—
81C22×D269—82no—
82C22×D269C2×D412yes—
83Dic538—42no—
84D1076—22no—
85D1076—22no—
86D1076—44no—
87D1076—42no—
88D1076—81no—
89D1076D814yescomplemented
90C22⋊D269—44no—
91C22⋊D269—44no—
92C2×Dic269—22no—
93C2×Dic269C2×D412yes—
94C4×D269—22no—
95C4×D269—22no—
96C4×D269—44no—
97#14524130—22no—
98C23×C269—21no—
99C23×C269—21no—
100D4×C269—21no—
101D4×C269—21no—
102D4×C269—21no—
103D4×C269#4112yescomplemented
104C2×C4×C269—21no—
105C2×C4×C269—21no—
106C2×C4×C269—42no—
107C2×C4×C269—42no—
108C2×C4×C269C2×D411yescharacteristic
109C2×C4×C269C2×D411yescharacteristic
110C2×C4×C269C2411yescharacteristic
111C8×C269—21no—
112C8×C269—21no—
113C22×C269—22no—
114C22×C269—41no—
115C22×C269—41no—
116C22×C269—41no—
117C22×C269—41no—
118C22×C269—41no—
119C22×C269C22×D411yescharacteristic
120C2×D269—22no—
121C2×D269—22no—
122C2×D269—42no—
123C2×D269—42no—
124C2×D269—42no—
125C2×D269—88no—
126C2×D269C2×D814yes—
127C4×C269—21no—
128C4×C269—41no—
129C4×C269—41no—
130C4×C269C2×D812yes—
131C4×C269C2×#4111yescharacteristic
132C4×C269H(5,𝔽2)11yescharacteristic
133Dic269—22no—
134Dic269—42no—
135C2×C269—42no—
136C2×C269—81no—
137C2×C269#54611yescharacteristic
138C2×C269C22×D811yescharacteristic
139C2×C269#57711yescharacteristic
140D269—24no—
141D269—82no—
142C269#329411yescharacteristic, complemented, Sylow
143#3294—2691nomaximal, Sylow
144#547—2691no—
145D42—2691no—
146#486—2691no—
147#480—2692no—
148#474—2691no—
149#466—2692no—
150#459—2691no—
151#447—2692no—
152C4×D8D26911yescharacteristic, complemented
153C8×D4—2691no—
154C2×#102—2692no—
155C2×#41—5381no—
156C22×D4—2692no—
157C22×D4—5381no—
158C2×D8—2692no—
159C2×D8C2×D26911yescharacteristic
160C22×C8—2692no—
161C4⋊Q8—2691no—
162#127—2691no—
163#123—5382no—
164C22⋊Q8—5381no—
165#121—2692no—
166#121—2692no—
167#121—5381no—
168#120—5382no—
169C4×D4—2691no—
170C4×D4C2×D26911yescharacteristic
171C4×D4C2×D26911yescharacteristic, complemented
172C2×C4⋊C4—2692no—
173#107—2692no—
174#107C2×D26911yescharacteristic, complemented
175C4⋊C8—2691no—
176#102—2692no—
177#102—2692no—
178#102—2692no—
179#102—2692no—
180#102C2×D26911yescharacteristic
181#102C2×D26911yescharacteristic, complemented
182C22⋊C8—2692no—
183C4×C8C2×D26911yescharacteristic, complemented
184C24—5382no—
185#41—10764no—
186C2×Q8—5381no—
187C2×D4—2691no—
188C2×D4—2692no—
189C2×D4—5382no—
190C2×D4—5382no—
191C2×D4—5384no—
192C2×D4—5382no—
193C2×D4—5381no—
194C2×D4—5381no—
195C2×D4—10764no—
196C2×D4—10762no—
197C2×D4C22×D26911yescharacteristic
198C2×D4C22×D26911yescharacteristic
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—2692no—
202C22×C4—5382no—
203D8—22no—
204D8—10762no—
205C2×C8—2692no—
206C2×C8—10762no—
207C2×C8C22×D26911yescharacteristic
208C2×C8C22×D26911yescharacteristic
209C4⋊C4—2691no—
210C4⋊C4—2692no—
211C4⋊C4—5382no—
212C4⋊C4—5381no—
213C4⋊C4C22×D26911yescharacteristic
214C4⋊C4C22×D26911yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—21no—
217C22⋊C4—2692no—
218C22⋊C4—5382no—
219C22⋊C4—5382no—
220C42C22×D26911yescharacteristic
221C23—21no—
222C23—21no—
223C23—2692no—
224C23—5382no—
225C23—10764no—
226C23—10764no—
227C23—21522no—
228Q8—10762no—
229D4—21no—
230D4—21no—
231D4—21no—
232D4—2694no—
233D4—5382no—
234D4—5382no—
235D4—10764no—
236D4—10764no—
237D4—10764no—
238D4—10762no—
239D4—21521no—
240D4#1686440212yescomplemented
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—2692no—
246C2×C4—5382no—
247C2×C4—5382no—
248C2×C4—5382no—
249C2×C4—10764no—
250C2×C4D4×D26911yescharacteristic
251C2×C4D4×D26911yescharacteristic
252C2×C4C23×D26911yescharacteristic
253C8—21no—
254C8—21no—
255C8—5382no—
256C22—22no—
257C22—41no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—2694no—
263C22—5382no—
264C22—5382no—
265C22—10762no—
266C22—10762no—
267C22—10762no—
268C22—21528no—
269C22C2×D4×D26911yescharacteristic
270C4—21no—
271C4—41no—
272C4—41no—
273C4—5382no—
274C4—10762no—
275C4D8×D26912yes—
276C4C2×#1686440211yescharacteristic
277C4#2257549911yescharacteristic
278C2—42no—
279C2—81no—
280C2—5384no—
281C2—21522no—
282C2#3177125111yescharacteristic
283C2C2×D8×D26911yescharacteristic
284C2#3177141211yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
FittingC4×D8×C269C2
socleC22×C269C22×D4
hypercenterC4×D8D269
hypocenterC269#3294
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #31771260C2semidirect
2. D4×D1076C2semidirect
3. #31770952C2semidirect
4. #31770920C2semidirect
5. #31770885C2semidirect
6. #31770840C2semidirect
7. #31770800C2semidirect
8. #31770737C2semidirect
9. C8×D1076C2semidirect
10. #102×D269C2semidirect
11. C4×D8×C269C2semidirect
15. C2×#16864387C22semidirect
16. C2×C8×D269C22semidirect
17. #22575453C22semidirect
23. #22575424C22semidirect
26. C4⋊C4×D269C22semidirect
27. #22575386C22semidirect
28. C4⋊#14524130C22semidirect
29. #22575375C22semidirect
30. #22575375C22semidirect
32. #22575373C22semidirect
33. #22575365C22semidirect
36. C4×D4×C269C22semidirect
37. #107×C269C22semidirect
39. #102×C269C22semidirect
40. C4×C8×C269C22semidirect
89. D1076D8semidirect
103. D4×C269#41semidirect
142. C269#3294semidirect
152. C4×D8D269semidirect
171. C4×D4C2×D269semidirect
174. #107C2×D269semidirect
181. #102C2×D269semidirect
183. C4×C8C2×D269semidirect
240. D4#16864402semidirect

Maximal subgroups

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

subgroupindex
#317712602
D4×D10762
#317709522
#317709202
#317708852
#317708402
#317708002
#317707372
C8×D10762
#102×D2692
C4×D8×C2692
#3294269