Finite Group Databasebeta

← #46821270

Subgroups — #46821270

Order 34432.

400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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
2#124×D269C211yesmaximal, characteristic
3#31770967C211yesmaximal, characteristic, complemented
4#31770965C211yesmaximal, characteristic, complemented
5#31770964C211yesmaximal, characteristic, complemented
6#31770961C212yesmaximal, complemented
7#31770958C212yesmaximal, complemented
8#31770612C212yesmaximal, complemented
9#31770608C212yesmaximal
10#31770557C211yesmaximal, characteristic, complemented
11#489×C269C211yesmaximal, characteristic, complemented
12C2×Q8×D269C2211yescharacteristic
13C2×D4×D269C2211yescharacteristic
14C2×#16864385C2212yes—
15#22575453C2211yescharacteristic, complemented
16#22575444C2212yescomplemented
17#22575442C2211yescharacteristic
18#22575441C2211yescharacteristic
19#22575440C2211yescharacteristic
20#22575439—21no—
21#22575439—21no—
22#22575433—21no—
23#22575429—21no—
24Q8×Dic269—21no—
25#22575418—21no—
26#22575411C2212yes—
27C22⋊C4×D269—21no—
28C22⋊C4×D269—21no—
29C42×D269C2211yescharacteristic
30#22575378C2212yescomplemented
31#22575377C2212yescomplemented
32#22575376C2212yescomplemented
33#22575375C2212yes—
34#22575374C2212yes—
35#22575373C2212yes—
36#22575364C2211yescharacteristic, complemented
37C8×Dic269C2212yescomplemented
38C4⋊Q8×C269C2211yescharacteristic, complemented
39#124×C269C2211yescharacteristic
40#103×C269C2212yescomplemented
41#102×C269C2212yes—
42#97×C269C2211yescharacteristic, complemented
43C23×D269—21no—
44C2×Dic538—21no—
45C2×Dic538—21no—
46C2×Dic538C2311yescharacteristic
47Q8×D269—24no—
48C2×D1076C2311yescharacteristic
49C2×C22⋊D269—21no—
50D4×D269—24no—
51C2×C4×D269—21no—
52C2×C4×D269D411yescharacteristic
53C2×C4×D269D411yescharacteristic
54C2×C4×D269C2311yescharacteristic
55#16864385—24no—
56C2×#14524130C2312yes—
57C4⋊Dic269—22no—
58C4⋊Dic269—21no—
59C4⋊Dic269C2312yes—
60#16864381—22no—
61C22⋊Dic269—21no—
62C22⋊Dic269—21no—
63#16864379—22no—
64#16864379—21no—
65#16864379—21no—
66#16864379—21no—
67#16864379—21no—
68C4×Dic269—22no—
69C4×Dic269D411yescharacteristic
70C4×Dic269D411yescharacteristic
71C4×Dic269C2311yescharacteristic
72C2×Q8×C269—21no—
73C2×Q8×C269C2311yescharacteristic
74C2×D4×C269C2311yescharacteristic
75C2×C8×C269C2312yes—
76C4⋊C4×C269—21no—
77C4⋊C4×C269C2312yes—
78C22⋊C4×C269—21no—
79C22⋊C4×C269—21no—
80C42×C269C2311yescharacteristic
81C22×D269—21no—
82C22×D269—42no—
83C22×D269—42no—
84C22×D269—42no—
85C22×D269C2×D411yescharacteristic
86Dic538—22no—
87Dic538—42no—
88Dic538—42no—
89D1076—22no—
90C22⋊D269—42no—
91C2×Dic269—22no—
92C2×Dic269—21no—
93C2×Dic269C2×D411yescharacteristic
94C2×Dic269C2×D411yescharacteristic
95C2×Dic269C2×D411yescharacteristic
96C4×D269—41no—
97C4×D269—41no—
98C4×D269—42no—
99C4×D269#4114yes—
100#14524130—22no—
101C23×C269—21no—
102Q8×C269—22no—
103Q8×C269—42no—
104D4×C269—22no—
105C2×C4×C269—21no—
106C2×C4×C269—22no—
107C2×C4×C269C2×D411yescharacteristic
108C2×C4×C269C2×D411yescharacteristic
109C2×C4×C269C2411yescharacteristic
110C8×C269—22no—
111C22×C269—41no—
112C22×C269—41no—
113C22×C269—41no—
114C22×C269C22×D411yescharacteristic
115C2×D269—21no—
116C2×D269—21no—
117C2×D269—41no—
118C2×D269—41no—
119C2×D269—41no—
120C2×D269—84no—
121C2×D269#12412yes—
122C4×C269—21no—
123C4×C269—21no—
124C4×C269—41no—
125C4×C269—42no—
126C4×C269C2×#4112yes—
127Dic269—21no—
128Dic269—21no—
129Dic269—41no—
130Dic269—42no—
131Dic269#12412yes—
132C2×C269—81no—
133C2×C269C2×#12411yescharacteristic
134C2×C269#57511yescharacteristic
135C2×C269#57511yescharacteristic
136D269—22no—
137D269—81no—
138C269#314011yescharacteristic, complemented, Sylow
139#3140—2691nomaximal, Sylow
140#533—2691no—
141C2×#124—2691no—
142#489—2691no—
143#489—2691no—
144#489—2691no—
145#489D26911yescharacteristic, complemented
146#488—2692no—
147#488—2692no—
148#419—2692no—
149#418—2692no—
150C4×M16—2691no—
151C22×Q8—2691no—
152C22×D4—2691no—
153C2×M16—2692no—
154C4⋊Q8—2691no—
155C4⋊Q8C2×D26911yescharacteristic, complemented
156#125—2692no—
157#124—2691no—
158#124—2691no—
159#124—2691no—
160#124—5381no—
161#124—5381no—
162#124C2×D26911yescharacteristic
163C22⋊Q8—5381no—
164C22⋊Q8—5381no—
165C4×Q8—5381no—
166C4×Q8—5381no—
167#117—2692no—
168C2×C22⋊C4—5381no—
169C2×C22⋊C4—5381no—
170C2×C42—2691no—
171#103—2692no—
172#103—2692no—
173#103—2692no—
174#103C2×D26912yescomplemented
175#102—2692no—
176#102—2692no—
177#102—2692no—
178#102C2×D26912yes—
179#97—2691no—
180#97C2×D26911yescharacteristic, complemented
181C4×C8—2692no—
182C24—5381no—
183C2×Q8—21no—
184C2×Q8—2691no—
185C2×Q8—5381no—
186C2×Q8—5384no—
187C2×Q8—5381no—
188C2×Q8C22×D26911yescharacteristic
189C2×D4—2691no—
190C2×D4—5384no—
191C2×D4—5381no—
192C2×D4C22×D26911yescharacteristic
193C22×C4—2691no—
194C22×C4—2691no—
195C22×C4—2691no—
196C22×C4—5381no—
197M16—5384no—
198C2×C8—2692no—
199C2×C8C22×D26912yes—
200C4⋊C4—21no—
201C4⋊C4—2692no—
202C4⋊C4—5382no—
203C4⋊C4—5382no—
204C4⋊C4—5381no—
205C4⋊C4C22×D26912yes—
206C22⋊C4—21no—
207C22⋊C4—21no—
208C22⋊C4—5381no—
209C22⋊C4—5381no—
210C22⋊C4—5382no—
211C22⋊C4—5381no—
212C22⋊C4—5381no—
213C22⋊C4—5381no—
214C22⋊C4—5381no—
215C42—2691no—
216C42—2691no—
217C42—2691no—
218C42—5382no—
219C42C22×D26911yescharacteristic
220C23—21no—
221C23—2691no—
222C23—5381no—
223C23—10762no—
224C23—10762no—
225C23—10762no—
226Q8—22no—
227Q8—42no—
228Q8—5382no—
229Q8—10762no—
230Q8—10762no—
231D4—22no—
232D4—5382no—
233D4—10762no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—2691no—
237C2×C4—2694no—
238C2×C4—2691no—
239C2×C4—2691no—
240C2×C4—5382no—
241C2×C4—5381no—
242C2×C4—10761no—
243C2×C4—10761no—
244C2×C4—10762no—
245C2×C4D4×D26911yescharacteristic
246C2×C4D4×D26911yescharacteristic
247C2×C4C23×D26911yescharacteristic
248C8—22no—
249C8—5382no—
250C22—41no—
251C22—41no—
252C22—41no—
253C22—2692no—
254C22—5381no—
255C22—5381no—
256C22—10761no—
257C22—10761no—
258C22—10761no—
259C22—21524no—
260C22C2×D4×D26911yescharacteristic
261C4—21no—
262C4—21no—
263C4—42no—
264C4—41no—
265C4—2692no—
266C4—5381no—
267C4—5381no—
268C4—10762no—
269C4—10761no—
270C4#41×D26912yes—
271C2—81no—
272C2—5382no—
273C2—21521no—
274C2#124×D26911yescharacteristic
275C2#3177140111yescharacteristic
276C2#3177140411yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#489×C269C2
socleC22×C269C22×D4
prime radicalC2×D4×D269C22
hypercenter#489D269
hypocenterC269#3140
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #31771160C2semidirect
3. #31770967C2semidirect
4. #31770965C2semidirect
5. #31770964C2semidirect
6. #31770961C2semidirect
7. #31770958C2semidirect
8. #31770612C2semidirect
10. #31770557C2semidirect
11. #489×C269C2semidirect
15. #22575453C22semidirect
16. #22575444C22semidirect
30. #22575378C22semidirect
31. #22575377C22semidirect
32. #22575376C22semidirect
36. #22575364C22semidirect
37. C8×Dic269C22semidirect
38. C4⋊Q8×C269C22semidirect
40. #103×C269C22semidirect
42. #97×C269C22semidirect
138. C269#3140semidirect
145. #489D269semidirect
155. C4⋊Q8C2×D269semidirect
174. #103C2×D269semidirect
180. #97C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317711602
#124×D2692
#317709672
#317709652
#317709642
#317709612
#317709582
#317706122
#317706082
#317705572
#489×C2692
#3140269