Finite Group Databasebeta

← #46820169

Subgroups — #46820169

Order 34432.

732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22575500C211yesmaximal, characteristic, complemented
2C2×#22575479C211yesmaximal, characteristic, complemented
3C22×#16864390C211yesmaximal, characteristic, complemented
4#31770748C214yesmaximal, complemented
5#31770743C214yesmaximal, complemented
6#31770613C211yesmaximal, characteristic, complemented
7#31770599C211yesmaximal, characteristic, complemented
8#31770572C211yesmaximal, characteristic, complemented
9#535×C269C211yesmaximal, characteristic, complemented
10#22575500—24no—
11#22575500—24no—
12C2×#16864402C2211yescharacteristic
13C2×#16864402C2212yescomplemented
14C2×#16864401—22no—
15C2×#16864401—21no—
16C22×Dic538C2211yescharacteristic
17C22×Dic538C2212yescomplemented
18C2×Q8×D269—21no—
19#22575479—24no—
20C2×#16864390—24no—
21C2×#16864390C2212yes—
22C2×#16864390C2214yes—
23C2×#16864387C2212yes—
24C2×#16864386C2211yescharacteristic
25C22×#14524130C2211yescharacteristic
26#22575376C2212yescomplemented
27#22575376C2214yescomplemented
28#22575373C2212yescomplemented
29C22⋊#14524130C2214yescomplemented
30C2×#41×C269C2211yescharacteristic
31C22×D4×C269C2211yescharacteristic
32#127×C269—21no—
33#124×C269—21no—
34#121×C269C2214yes—
35#120×C269—22no—
36#117×C269C2211yescharacteristic
37#16864402—24no—
38#16864402—24no—
39#16864402—22no—
40#16864402D414yescomplemented
41#16864401—216no—
42#16864401—28no—
43C2×Dic538—24no—
44C2×Dic538—24no—
45C2×Dic538—21no—
46C2×Dic538—22no—
47C2×Dic538—22no—
48C2×Dic538D414yescomplemented
49C2×Dic538C2312yes—
50C2×Dic538C2311yescharacteristic
51Q8×D269—28no—
52C2×D1076C2311yescharacteristic
53C2×C22⋊D269—21no—
54C2×C22⋊D269—22no—
55C22×Dic269—21no—
56C22×Dic269—22no—
57C2×C4×D269—21no—
58C2×C4×D269—22no—
59#16864390—28no—
60#16864390—24no—
61#16864387—24no—
62#16864386—22no—
63C2×#14524130—22no—
64C2×#14524130C2312yes—
65C2×#14524130C2312yes—
66C24×C269—21no—
67#41×C269—22no—
68#41×C269—22no—
69C2×Q8×C269D411yescharacteristic
70C2×D4×C269—24no—
71C2×D4×C269—22no—
72C2×D4×C269—22no—
73C2×D4×C269—21no—
74C2×D4×C269D412yes—
75C2×D4×C269D411yescharacteristic
76C2×D4×C269C2312yes—
77C22×C4×C269C2312yes—
78C22×C4×C269C2311yescharacteristic
79C4⋊C4×C269C2312yes—
80C22⋊C4×C269—21no—
81C22⋊C4×C269—24no—
82C42×C269—21no—
83C22×D269—21no—
84Dic538—28no—
85Dic538—24no—
86Dic538—21no—
87Dic538—22no—
88Dic538C2×D412yes—
89Dic538C2×D414yes—
90D1076—21no—
91D1076C2×D412yes—
92C22⋊D269—28no—
93C22⋊D269—24no—
94C2×Dic269—28no—
95C2×Dic269—24no—
96C2×Dic269—21no—
97C2×Dic269—22no—
98C4×D269—28no—
99C4×D269—24no—
100#14524130—22no—
101#14524130—22no—
102C23×C269—22no—
103C23×C269—42no—
104C23×C269—82no—
105C23×C269C2×D412yes—
106C23×C269C2×D411yescharacteristic
107Q8×C269—22no—
108D4×C269—24no—
109D4×C269—22no—
110D4×C269—22no—
111D4×C269—22no—
112D4×C269—42no—
113D4×C269—84no—
114C2×C4×C269—22no—
115C2×C4×C269—22no—
116C2×C4×C269—22no—
117C2×C4×C269C2×D412yes—
118C2×C4×C269C2×D412yes—
119C2×C4×C269C2×D412yes—
120C2×C4×C269C2×D411yescharacteristic
121C2×C4×C269C2411yescharacteristic
122C22×C269—22no—
123C22×C269—22no—
124C22×C269—24no—
125C22×C269—42no—
126C22×C269—44no—
127C22×C269—84no—
128C22×C269#12012yes—
129C22×C269C22×D411yescharacteristic
130C2×D269—22no—
131C2×D269—42no—
132C4×C269—22no—
133C4×C269—42no—
134C4×C269#12012yes—
135C4×C269C22×D411yescharacteristic
136C4×C269C22×D411yescharacteristic
137Dic269—24no—
138Dic269—22no—
139C2×C269—22no—
140C2×C269—42no—
141C2×C269—82no—
142C2×C269C2×#12011yescharacteristic
143C2×C269#57712yes—
144D269—42no—
145C269#301011yescharacteristic, complemented, Sylow
146#3010—2691nomaximal, Sylow
147C2×2−1+4—2691no—
148C2×AGL(1,ℤ/8)—2691no—
149C22×SD16—2691no—
150#535D26911yescharacteristic, complemented
151#449—2694no—
152#448—2694no—
153#419—2691no—
154#416—2691no—
155#408—2691no—
1562−1+4—5384no—
1572−1+4—5384no—
158C2×#41—2691no—
159C2×#41—2692no—
160C2×#41—5382no—
161C2×#41—5381no—
162C2×#41C2×D26911yescharacteristic
163C22×Q8—2691no—
164C22×Q8—2692no—
165C22×Q8—5381no—
166C22×D4C2×D26911yescharacteristic
167AGL(1,ℤ/8)—5384no—
168C2×SD16—2694no—
169C2×SD16—2692no—
170C2×SD16—5384no—
171C2×D8—2692no—
172C2×M16—2691no—
173C22×C8—2691no—
174#127—21no—
175#124—21no—
176#121C2×D26914yes—
177#120—22no—
178#117C2×D26911yescharacteristic
179#103—2692no—
180#103—2694no—
181#102—2692no—
182C22⋊C8—2694no—
183C24—21no—
184#41—22no—
185#41—22no—
186#41—2694no—
187#41—5384no—
188#41—5384no—
189#41—53816no—
190#41—5388no—
191#41—5382no—
192C2×Q8—2694no—
193C2×Q8—2692no—
194C2×Q8—2691no—
195C2×Q8—5384no—
196C2×Q8—5384no—
197C2×Q8—5388no—
198C2×Q8—5382no—
199C2×Q8—5382no—
200C2×Q8—5381no—
201C2×Q8C22⋊D26911yescharacteristic
202C2×D4—24no—
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—21no—
206C2×D4—2691no—
207C2×D4—5382no—
208C2×D4—5381no—
209C2×D4C22⋊D26912yes—
210C2×D4C22⋊D26911yescharacteristic
211C2×D4C22×D26912yes—
212C22×C4—5382no—
213C22×C4—5381no—
214C22×C4—5382no—
215C22×C4—5381no—
216C22×C4C22×D26912yes—
217C22×C4C22×D26911yescharacteristic
218SD16—5388no—
219SD16—5384no—
220D8—5384no—
221M16—5382no—
222C2×C8—2692no—
223C2×C8—2692no—
224C2×C8—5382no—
225C4⋊C4C22×D26912yes—
226C22⋊C4—21no—
227C22⋊C4—24no—
228C42—21no—
229C23—22no—
230C23—42no—
231C23—82no—
232C23—5381no—
233C23C2×C22⋊D26912yes—
234C23C2×C22⋊D26911yescharacteristic
235Q8—22no—
236Q8—2694no—
237Q8—2692no—
238Q8—5388no—
239Q8—5384no—
240Q8—5382no—
241Q8—5381no—
242D4—24no—
243D4—22no—
244D4—22no—
245D4—22no—
246D4—42no—
247D4—84no—
248D4—2692no—
249D4—5388no—
250D4—5384no—
251D4—5381no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—5388no—
256C2×C4—5388no—
257C2×C4—5384no—
258C2×C4—5382no—
259C2×C4—5381no—
260C2×C4—5384no—
261C2×C4D4×D26912yes—
262C2×C4D4×D26912yes—
263C2×C4C2×C22⋊D26912yes—
264C2×C4C2×C22⋊D26911yescharacteristic
265C2×C4C23×D26911yescharacteristic
266C8—5382no—
267C8—5382no—
268C22—22no—
269C22—24no—
270C22—22no—
271C22—44no—
272C22—42no—
273C22—84no—
274C22—5382no—
275C22—10762no—
276C22#2257542112yes—
277C22C22×C22⋊D26911yescharacteristic
278C4—22no—
279C4—42no—
280C4—5384no—
281C4—5382no—
282C4#2257542112yes—
283C4C2×D4×D26911yescharacteristic
284C4C2×D4×D26911yescharacteristic
285C2—22no—
286C2—42no—
287C2—82no—
288C2—10762no—
289C2C2×#2257542111yescharacteristic
290C2#3177141612yes—
subgroupG/H
centerC22C22×C22⋊D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#535×C269C2
socleC22×C269C22×D4
hypercenter#535D269
hypocenterC269#3010
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#22575500C2semidirect
2. C2×#22575479C2semidirect
3. C22×#16864390C2semidirect
4. #31770748C2semidirect
5. #31770743C2semidirect
6. #31770613C2semidirect
7. #31770599C2semidirect
8. #31770572C2semidirect
9. #535×C269C2semidirect
13. C2×#16864402C22semidirect
17. C22×Dic538C22semidirect
26. #22575376C22semidirect
27. #22575376C22semidirect
28. #22575373C22semidirect
29. C22⋊#14524130C22semidirect
40. #16864402D4semidirect
48. C2×Dic538D4semidirect
145. C269#3010semidirect
150. #535D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225755002
C2×#225754792
C22×#168643902
#317707482
#317707432
#317706132
#317705992
#317705722
#535×C2692
#3010269