Finite Group Databasebeta

← #46820528

Subgroups — #46820528

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×#22575459C211yesmaximal, characteristic, complemented
3#31771171C212yesmaximal, complemented
4#31770857C212yesmaximal, complemented
5#31770856C212yesmaximal, complemented
6#31770842C211yesmaximal, characteristic, complemented
7#31770841C211yesmaximal, characteristic, complemented
8#31770838C211yesmaximal, characteristic, complemented
9#31770642C211yesmaximal, characteristic, complemented
10#31770608C212yesmaximal, complemented
11#466×C269C211yesmaximal, characteristic, complemented
12C2×#16864402C2211yescharacteristic
13C2×D4×D269C2212yes—
14C2×D2152C2211yescharacteristic
15C2×#16864387C2212yes—
16D8×D269—24no—
17#22575459—24no—
18C2×#16864386C2211yescharacteristic, complemented
19C2×#16864385C2211yescharacteristic
20C2×#16864385C2211yescharacteristic, 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#22575387C2211yescharacteristic, complemented
32#22575384C2212yescomplemented
33#22575375C2212yescomplemented
34#22575374C2212yescomplemented
35#22575373C2212yescomplemented
36C2×D8×C269C2211yescharacteristic
37C22×C8×C269C2211yescharacteristic, complemented
38#121×C269C2212yescomplemented
39#107×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#16864386—22no—
60#16864385—22no—
61#16864385—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—
76C2×C8×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—21no—
120C22×C269—21no—
121C22×C269—42no—
122C22×C269—42no—
123C22×C269—42no—
124C22×C269C22×D411yescharacteristic
125C2×D269—21no—
126C2×D269—21no—
127C2×D269—21no—
128C2×D269—21no—
129C2×D269—21no—
130C2×D269—42no—
131C2×D269—42no—
132C2×D269—42no—
133C2×D269—88no—
134C2×D269#12112yes—
135C4×C269—21no—
136C4×C269—42no—
137C4×C269C22×D411yescharacteristic
138C4×C269C2×#4111yescharacteristic
139Dic269—21no—
140Dic269—42no—
141Dic269#12112yes—
142C2×C269—41no—
143C2×C269—82no—
144C2×C269C2×#12111yescharacteristic
145C2×C269#57611yescharacteristic
146C2×C269#57611yescharacteristic
147D269—22no—
148D269—41no—
149D269—82no—
150C269#305811yescharacteristic, complemented, Sylow
151#3058—2691nomaximal, Sylow
152C22×D8—2691no—
153C2×#131—2691no—
154#535—2692no—
155#469—2692no—
156#469—2692no—
157#466—2691no—
158#466—2691no—
159#466—2691no—
160#466D26911yescharacteristic, complemented
161#427—2691no—
162#418—2692no—
163C2×#41—2691no—
164C22×D4—2692no—
165C2×D8—2692no—
166C2×D8—2691no—
167C2×D8—5384no—
168C2×D8C2×D26911yescharacteristic
169#131—5384no—
170C2×M16—2691no—
171C2×M16—2691no—
172C2×M16—2691no—
173C22×C8—2691no—
174C22×C8—2691no—
175C22×C8C2×D26911yescharacteristic, complemented
176#127—5382no—
177#124—5382no—
178#121—2692no—
179#121—2692no—
180#121—2692no—
181#121C2×D26912yescomplemented
182#120—5382no—
183#120—5382no—
184#117—2692no—
185#107—2691no—
186#107C2×D26911yescharacteristic, complemented
187#106—2692no—
188#102—2692no—
189#102—2692no—
190#102—2692no—
191#102C2×D26912yescomplemented
192C24—5382no—
193#41—5382no—
194#41—5382no—
195C2×Q8—2691no—
196C2×D4—22no—
197C2×D4—2691no—
198C2×D4—2691no—
199C2×D4—2691no—
200C2×D4—2692no—
201C2×D4—5382no—
202C2×D4—5384no—
203C2×D4—5384no—
204C2×D4—5382no—
205C2×D4—5382no—
206C2×D4—5382no—
207C2×D4C22×D26912yes—
208C22×C4—2691no—
209C22×C4—2691no—
210C22×C4C22×D26911yescharacteristic
211D8—22no—
212D8—5384no—
213D8—5382no—
214M16—5382no—
215M16—5382no—
216M16—5382no—
217C2×C8—22no—
218C2×C8—2691no—
219C2×C8—2694no—
220C2×C8—2691no—
221C2×C8—5382no—
222C2×C8C22×D26911yescharacteristic
223C2×C8C22×D26911yescharacteristic
224C4⋊C4—2692no—
225C4⋊C4C22×D26912yes—
226C22⋊C4—22no—
227C22⋊C4—5382no—
228C22⋊C4—5382no—
229C22⋊C4—5382no—
230C22⋊C4—5382no—
231C42—5382no—
232C23—22no—
233C23—2691no—
234C23—2691no—
235C23—5382no—
236C23—10764no—
237C23—21522no—
238C23—21522no—
239C23D4×D26911yescharacteristic
240Q8—5382no—
241D4—22no—
242D4—22no—
243D4—82no—
244D4—5382no—
245D4—5382no—
246D4—5382no—
247D4—5382no—
248D4—5382no—
249D4—10764no—
250D4—21522no—
251D4—21522no—
252D4—21522no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—2691no—
257C2×C4—2692no—
258C2×C4—2692no—
259C2×C4—2691no—
260C2×C4—5381no—
261C2×C4—5381no—
262C2×C4—5382no—
263C2×C4D4×D26911yescharacteristic
264C2×C4C23×D26911yescharacteristic
265C8—21no—
266C8—2692no—
267C8—5381no—
268C8D4×D26912yes—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—42no—
273C22—42no—
274C22—42no—
275C22—2692no—
276C22—5381no—
277C22—5381no—
278C22—5381no—
279C22—5381no—
280C22—5381no—
281C22—10762no—
282C22—10762no—
283C22—10762no—
284C22—21528no—
285C22C2×D4×D26911yescharacteristic
286C4—21no—
287C4—42no—
288C4—2692no—
289C4—5381no—
290C4—10762no—
291C4C2×D4×D26911yescharacteristic
292C4#41×D26911yescharacteristic
293C2—41no—
294C2—82no—
295C2—5382no—
296C2—10761no—
297C2—21522no—
298C2#121×D26911yescharacteristic
299C2#3177140611yescharacteristic
300C2#3177140711yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#466×C269C2
socleC22×C269C22×D4
hypercenter#466D269
hypocenterC269#3058
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×D8×D269C2semidirect
2. C2×#22575459C2semidirect
3. #31771171C2semidirect
4. #31770857C2semidirect
5. #31770856C2semidirect
6. #31770842C2semidirect
7. #31770841C2semidirect
8. #31770838C2semidirect
9. #31770642C2semidirect
10. #31770608C2semidirect
11. #466×C269C2semidirect
18. C2×#16864386C22semidirect
20. C2×#16864385C22semidirect
22. C2×C8×D269C22semidirect
25. #22575428C22semidirect
26. #22575427C22semidirect
27. #22575424C22semidirect
31. #22575387C22semidirect
32. #22575384C22semidirect
33. #22575375C22semidirect
34. #22575374C22semidirect
35. #22575373C22semidirect
37. C22×C8×C269C22semidirect
38. #121×C269C22semidirect
39. #107×C269C22semidirect
40. #102×C269C22semidirect
65. C8×D269D4semidirect
150. C269#3058semidirect
160. #466D269semidirect
175. C22×C8C2×D269semidirect
181. #121C2×D269semidirect
186. #107C2×D269semidirect
191. #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×#225754592
#317711712
#317708572
#317708562
#317708422
#317708412
#317708382
#317706422
#317706082
#466×C2692
#3058269