Finite Group Databasebeta

← #46820531

Subgroups — #46820531

Order 34432.

524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 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×D8×D269C211yesmaximal, characteristic, complemented
2C2×#22575461C211yesmaximal, characteristic, complemented
3#31771171C212yesmaximal, complemented
4#31770859C211yesmaximal, characteristic, complemented
5#31770858C211yesmaximal, characteristic, complemented
6#31770855C211yesmaximal, characteristic, complemented
7#31770840C212yesmaximal, complemented
8#31770839C212yesmaximal, complemented
9#31770640C211yesmaximal, characteristic, complemented
10#31770608C212yesmaximal, complemented
11#469×C269C211yesmaximal, characteristic, complemented
12C2×#16864402C2211yescharacteristic
13C2×D4×D269C2212yes—
14C2×D2152C2211yescharacteristic
15C2×#16864387C2212yes—
16D8×D269—24no—
17#22575461—24no—
18C2×#16864385C2211yescharacteristic
19C2×#16864385C2211yescharacteristic, complemented
20C22×#14524130C2211yescharacteristic, complemented
21C2×C8×D269C2211yescharacteristic
22C2×C8×D269C2211yescharacteristic, complemented
23#22575449—22no—
24#22575439—22no—
25#22575428C2212yescomplemented
26#22575427C2212yescomplemented
27#22575424C2212yescomplemented
28#22575423—22no—
29#22575421—22no—
30#22575411C2212yes—
31#22575386C2212yescomplemented
32#22575385C2211yescharacteristic, complemented
33#22575375C2212yescomplemented
34#22575374C2212yescomplemented
35#22575373C2212yescomplemented
36C2×D8×C269C2211yescharacteristic
37C2×M16×C269C2211yescharacteristic, complemented
38#121×C269C2212yescomplemented
39#106×C269C2211yescharacteristic, complemented
40#102×C269C2212yescomplemented
41C23×D269—22no—
42#16864402—22no—
43#16864402—22no—
44C2×Dic538D411yescharacteristic
45C2×D1076—22no—
46C2×D1076D411yescharacteristic
47C2×D1076C2312yes—
48C2×C22⋊D269—22no—
49C2×C22⋊D269—22no—
50C2×C22⋊D269—22no—
51C2×C22⋊D269D411yescharacteristic
52C2×C22⋊D269D411yescharacteristic
53D4×D269—24no—
54D4×D269—24no—
55C2×C4×D269C2311yescharacteristic
56C2×C4×D269C2311yescharacteristic
57D2152—22no—
58#16864387—24no—
59#16864385—22no—
60#16864385—22no—
61C2×#14524130—22no—
62C2×#14524130C2311yescharacteristic
63C2×#14524130C2311yescharacteristic
64C8×D269—22no—
65C8×D269D414yescomplemented
66C4⋊Dic269C2312yes—
67C22⋊Dic269—22no—
68#16864379—22no—
69#16864379—22no—
70#16864379—22no—
71C4×Dic269—22no—
72C2×D4×C269—22no—
73C2×D4×C269C2312yes—
74C22×C4×C269C2311yescharacteristic
75D8×C269—22no—
76M16×C269—22no—
77C2×C8×C269C2311yescharacteristic
78C2×C8×C269C2311yescharacteristic
79C4⋊C4×C269C2312yes—
80C22⋊C4×C269—22no—
81C22×D269—22no—
82C22×D269—44no—
83C22×D269—82no—
84C22×D269—82no—
85C22×D269C2×D411yescharacteristic
86C22×D269C2×D411yescharacteristic
87Dic538—22no—
88D1076—22no—
89D1076—22no—
90D1076—22no—
91D1076—82no—
92C22⋊D269—22no—
93C22⋊D269—22no—
94C22⋊D269—44no—
95C22⋊D269—82no—
96C22⋊D269—82no—
97C2×Dic269—22no—
98C2×Dic269C2×D411yescharacteristic
99C2×Dic269C2×D411yescharacteristic
100C4×D269—21no—
101C4×D269—21no—
102C4×D269C2×D412yes—
103C4×D269#4112yes—
104#14524130—21no—
105#14524130C2×D412yes—
106C23×C269—22no—
107C23×C269C2×D411yescharacteristic
108D4×C269—22no—
109D4×C269—22no—
110D4×C269—82no—
111C2×C4×C269—21no—
112C2×C4×C269—21no—
113C2×C4×C269—22no—
114C2×C4×C269C2×D411yescharacteristic
115C2×C4×C269C2411yescharacteristic
116C8×C269—21no—
117C8×C269C2×D412yes—
118C22×C269—21no—
119C22×C269—22no—
120C22×C269—42no—
121C22×C269—42no—
122C22×C269—42no—
123C22×C269C22×D411yescharacteristic
124C2×D269—22no—
125C2×D269—21no—
126C2×D269—22no—
127C2×D269—42no—
128C2×D269—42no—
129C2×D269—42no—
130C2×D269—88no—
131C2×D269#12112yes—
132C4×C269—21no—
133C4×C269—42no—
134C4×C269C22×D411yescharacteristic
135C4×C269C2×#4111yescharacteristic
136Dic269—21no—
137Dic269—42no—
138Dic269#12112yes—
139C2×C269—41no—
140C2×C269—82no—
141C2×C269C2×#12111yescharacteristic
142C2×C269#57612yes—
143D269—22no—
144D269—41no—
145D269—82no—
146C269#305811yescharacteristic, complemented, Sylow
147#3058—2691nomaximal, Sylow
148C22×D8—2691no—
149C2×#131—2691no—
150#535—2692no—
151#469—2691no—
152#469—2691no—
153#469—2691no—
154#469D26911yescharacteristic, complemented
155#466—2692no—
156#466—2692no—
157#427—2691no—
158#418—2692no—
159C2×#41—2691no—
160C22×D4—2692no—
161C2×D8—2692no—
162C2×D8—2691no—
163C2×D8—5384no—
164C2×D8C2×D26911yescharacteristic
165#131—5384no—
166C2×M16—2691no—
167C2×M16—2691no—
168C2×M16C2×D26911yescharacteristic, complemented
169C22×C8—2691no—
170C22×C8—2691no—
171C22×C8—2691no—
172#127—5382no—
173#124—5382no—
174#121—2692no—
175#121—2692no—
176#121—2692no—
177#121C2×D26912yescomplemented
178#120—5382no—
179#120—5382no—
180#117—2692no—
181#107—2692no—
182#106—2691no—
183#106C2×D26911yescharacteristic, complemented
184#102—2692no—
185#102—2692no—
186#102—2692no—
187#102C2×D26912yescomplemented
188C24—5382no—
189#41—5382no—
190#41—5382no—
191C2×Q8—2691no—
192C2×D4—22no—
193C2×D4—2691no—
194C2×D4—2691no—
195C2×D4—2691no—
196C2×D4—2692no—
197C2×D4—5382no—
198C2×D4—5384no—
199C2×D4—5384no—
200C2×D4—5382no—
201C2×D4—5382no—
202C2×D4—5382no—
203C2×D4C22×D26912yes—
204C22×C4—2691no—
205C22×C4—2691no—
206C22×C4C22×D26911yescharacteristic
207D8—22no—
208D8—5384no—
209D8—5382no—
210M16—22no—
211M16—5382no—
212M16—5382no—
213C2×C8—2691no—
214C2×C8—2694no—
215C2×C8—2691no—
216C2×C8—5382no—
217C2×C8—5382no—
218C2×C8C22×D26911yescharacteristic
219C2×C8C22×D26911yescharacteristic
220C4⋊C4—2692no—
221C4⋊C4C22×D26912yes—
222C22⋊C4—22no—
223C22⋊C4—5382no—
224C22⋊C4—5382no—
225C22⋊C4—5382no—
226C22⋊C4—5382no—
227C42—5382no—
228C23—22no—
229C23—2691no—
230C23—2691no—
231C23—5382no—
232C23—10764no—
233C23—21522no—
234C23—21522no—
235C23D4×D26911yescharacteristic
236Q8—5382no—
237D4—22no—
238D4—22no—
239D4—82no—
240D4—5382no—
241D4—5382no—
242D4—5382no—
243D4—5382no—
244D4—5382no—
245D4—10764no—
246D4—21522no—
247D4—21522no—
248D4—21522no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—2691no—
253C2×C4—2692no—
254C2×C4—2692no—
255C2×C4—2691no—
256C2×C4—5381no—
257C2×C4—5381no—
258C2×C4—5382no—
259C2×C4D4×D26911yescharacteristic
260C2×C4C23×D26911yescharacteristic
261C8—21no—
262C8—2692no—
263C8—5381no—
264C8D4×D26912yes—
265C22—22no—
266C22—21no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—2692no—
271C22—5382no—
272C22—5382no—
273C22—5381no—
274C22—10762no—
275C22—10762no—
276C22—10762no—
277C22—21528no—
278C22C2×D4×D26911yescharacteristic
279C4—21no—
280C4—42no—
281C4—2692no—
282C4—5381no—
283C4—10762no—
284C4C2×D4×D26911yescharacteristic
285C4#41×D26911yescharacteristic
286C2—41no—
287C2—82no—
288C2—5382no—
289C2—10761no—
290C2—21522no—
291C2#121×D26911yescharacteristic
292C2#3177140912yes—
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#469×C269C2
socleC22×C269C22×D4
hypercenter#469D269
hypocenterC269#3058
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×D8×D269C2semidirect
2. C2×#22575461C2semidirect
3. #31771171C2semidirect
4. #31770859C2semidirect
5. #31770858C2semidirect
6. #31770855C2semidirect
7. #31770840C2semidirect
8. #31770839C2semidirect
9. #31770640C2semidirect
10. #31770608C2semidirect
11. #469×C269C2semidirect
19. C2×#16864385C22semidirect
20. C22×#14524130C22semidirect
22. C2×C8×D269C22semidirect
25. #22575428C22semidirect
26. #22575427C22semidirect
27. #22575424C22semidirect
31. #22575386C22semidirect
32. #22575385C22semidirect
33. #22575375C22semidirect
34. #22575374C22semidirect
35. #22575373C22semidirect
37. C2×M16×C269C22semidirect
38. #121×C269C22semidirect
39. #106×C269C22semidirect
40. #102×C269C22semidirect
65. C8×D269D4semidirect
146. C269#3058semidirect
154. #469D269semidirect
168. C2×M16C2×D269semidirect
177. #121C2×D269semidirect
183. #106C2×D269semidirect
187. #102C2×D269semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D2692
C2×#225754612
#317711712
#317708592
#317708582
#317708552
#317708402
#317708392
#317706402
#317706082
#469×C2692
#3058269