Finite Group Databasebeta

← #46823565

Subgroups — #46823565

Order 34432.

336 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771331C211yesmaximal, characteristic, complemented
2#31771324C211yesmaximal, characteristic
3#31770959C211yesmaximal, characteristic
4#31770958C211yesmaximal, characteristic
5#31770954C211yesmaximal, characteristic, complemented
6#31770913C211yesmaximal, characteristic, complemented
7#31770910C211yesmaximal, characteristic, complemented
8#31770883C211yesmaximal, characteristic
9#31770825C211yesmaximal, characteristic
10#31770813C211yesmaximal, characteristic, complemented
11#31770729C211yesmaximal, characteristic, complemented
12Q16×Dic269C211yesmaximal, characteristic, complemented
13C4×#16864392C211yesmaximal, characteristic, complemented
14SD16×Dic269C211yesmaximal, characteristic
15#464×C269C211yesmaximal, characteristic
16C2×#16864392C2211yescharacteristic
17#22575452—21no—
18#22575452C2211yescharacteristic
19#22575451C2211yescharacteristic
20#22575446—21no—
21#22575446—21no—
22#22575445—21no—
23#22575445C2211yescharacteristic
24#22575444—21no—
25#22575444C2211yescharacteristic
26#22575440C2211yescharacteristic
27#22575430—21no—
28Q8×Dic269C2211yescharacteristic
29Q8×Dic269C2211yescharacteristic
30Q8×Dic269C2211yescharacteristic
31C4×Dic538—21no—
32C4×Dic538C2211yescharacteristic
33C4×Dic538C2211yescharacteristic
34D4×Dic269C2211yescharacteristic
35#22575409—21no—
36#22575387C2211yescharacteristic
37#22575386C2211yescharacteristic
38#22575385C2211yescharacteristic
39#22575382C2211yescharacteristic
40#22575382C2211yescharacteristic
41#22575378C2211yescharacteristic
42#22575378C2211yescharacteristic
43#22575377C2211yescharacteristic
44#22575377C2211yescharacteristic
45#22575377C2211yescharacteristic
46#22575376C2211yescharacteristic
47#22575374C2211yescharacteristic
48#22575374C2211yescharacteristic
49C4×#14524130C2211yescharacteristic
50C8×Dic269C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52C2×Q16×C269C2211yescharacteristic
53C2×SD16×C269C2211yescharacteristic
54#124×C269C2211yescharacteristic
55C4×Q8×C269C2211yescharacteristic
56C4⋊C8×C269C2211yescharacteristic
57#103×C269C2211yescharacteristic
58#102×C269C2211yescharacteristic
59C2×Dic538—21no—
60C2×Dic538D411yescharacteristic
61C2×Dic538C2311yescharacteristic
62C22×Dic269—21no—
63#16864392—22no—
64C2×#14524130C2311yescharacteristic
65C2×#14524130C2311yescharacteristic
66C4⋊Dic269—21no—
67C4⋊Dic269—21no—
68C4⋊Dic269—21no—
69C4⋊Dic269—21no—
70C4⋊Dic269D411yescharacteristic
71C4⋊Dic269C2311yescharacteristic
72C4⋊Dic269C2311yescharacteristic
73C4⋊Dic269C2311yescharacteristic
74#16864381—21no—
75#16864381—21no—
76#16864381—21no—
77#16864381—21no—
78#16864381—21no—
79#16864381—21no—
80#16864381—21no—
81#16864381D411yescharacteristic
82#16864381D411yescharacteristic
83C22⋊Dic269—21no—
84C22⋊Dic269—21no—
85C22⋊Dic269—21no—
86C4×Dic269—21no—
87C4×Dic269—21no—
88C4×Dic269—21no—
89C4×Dic269—21no—
90C4×Dic269C2311yescharacteristic
91C4×Dic269C2311yescharacteristic
92C2×Q8×C269C2311yescharacteristic
93C2×Q8×C269C2311yescharacteristic
94C2×D4×C269C2311yescharacteristic
95Q16×C269—22no—
96SD16×C269—22no—
97C2×C8×C269C2311yescharacteristic
98C2×C8×C269C2311yescharacteristic
99C4⋊C4×C269—21no—
100C4⋊C4×C269C2311yescharacteristic
101C22⋊C4×C269—21no—
102C22⋊C4×C269—21no—
103C42×C269—21no—
104C42×C269C2311yescharacteristic
105Dic538—22no—
106Dic538—21no—
107Dic538—21no—
108Dic538—42no—
109C2×Dic269—21no—
110C2×Dic269—21no—
111C2×Dic269—21no—
112C2×Dic269—21no—
113C2×Dic269—42no—
114C2×Dic269C2×D411yescharacteristic
115C2×Dic269C2×D411yescharacteristic
116C2×Dic269C2×D411yescharacteristic
117C2×Dic269C2×D411yescharacteristic
118#14524130—21no—
119#14524130—21no—
120C23×C269—21no—
121Q8×C269—21no—
122Q8×C269—21no—
123Q8×C269—21no—
124Q8×C269#4112yes—
125D4×C269—21no—
126D4×C269—21no—
127C2×C4×C269—21no—
128C2×C4×C269—21no—
129C2×C4×C269—21no—
130C2×C4×C269C2×D411yescharacteristic
131C2×C4×C269C2×D411yescharacteristic
132C2×C4×C269C2411yescharacteristic
133C8×C269—21no—
134C8×C269—21no—
135C22×C269—41no—
136C22×C269—41no—
137C22×C269—41no—
138C22×C269C22×D411yescharacteristic
139C4×C269—22no—
140C4×C269—21no—
141C4×C269—21no—
142C4×C269—41no—
143C4×C269—41no—
144C4×C269C2×#4111yescharacteristic
145C4×C2692−1+411yescharacteristic
146Dic269—21no—
147Dic269—21no—
148Dic269—21no—
149Dic269—41no—
150Dic269—41no—
151Dic269—41no—
152Dic269—41no—
153Dic269#13512yes—
154C2×C269—81no—
155C2×C269#54811yescharacteristic
156C2×C269C2×#13511yescharacteristic
157C2×C269#57811yescharacteristic
158C269#336411yescharacteristic, complemented, Sylow
159#3364—2691nomaximal, Sylow
160#557—2691no—
161#556—2691no—
162#488—2691no—
163#488—2691no—
164#487—2691no—
165#479—2691no—
166#479—2691no—
167#474—2691no—
168#464—2691no—
169#464D26911yescharacteristic
170#462—2691no—
171C8×Q8—2691no—
172C4×Q16—2691no—
173C4×Q16—2691no—
174C4×SD16—2691no—
175C2×Q16—2691no—
176C2×Q16C2×D26911yescharacteristic
177C2×SD16C2×D26911yescharacteristic
178C4⋊Q8—2691no—
179C4⋊Q8—2691no—
180C4⋊Q8—5381no—
181#126—5381no—
182#126—5381no—
183#125—2691no—
184#125—2691no—
185#125—5381no—
186#125—5381no—
187#124—2691no—
188#124C2×D26911yescharacteristic
189C22⋊Q8—5381no—
190C4×Q8—2691no—
191C4×Q8—2691no—
192C4×Q8—2691no—
193C4×Q8—2691no—
194C4×Q8—2691no—
195C4×Q8—5381no—
196C4×Q8C2×D26911yescharacteristic
197C4×D4—2691no—
198#117—5381no—
199#107—2691no—
200#107—2691no—
201#106—2691no—
202C4⋊C8—2691no—
203C4⋊C8—2691no—
204C4⋊C8C2×D26911yescharacteristic
205#103—2691no—
206#103—2691no—
207#103—2691no—
208#103—2691no—
209#103—2691no—
210#103—2691no—
211#103C2×D26911yescharacteristic
212#102—2691no—
213#102—2691no—
214#102C2×D26911yescharacteristic
215C4×C8—2691no—
216C4×C8—2691no—
217C4×C8—2691no—
218C2×Q8—2691no—
219C2×Q8—2691no—
220C2×Q8—5381no—
221C2×Q8C22×D26911yescharacteristic
222C2×Q8C22×D26911yescharacteristic
223C2×D4C22×D26911yescharacteristic
224C22×C4—5381no—
225Q16—22no—
226Q16—5382no—
227SD16—22no—
228C2×C8—2691no—
229C2×C8—2691no—
230C2×C8C22×D26911yescharacteristic
231C2×C8C22×D26911yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—2691no—
234C4⋊C4—2691no—
235C4⋊C4—2691no—
236C4⋊C4—2691no—
237C4⋊C4—2691no—
238C4⋊C4—2691no—
239C4⋊C4—5381no—
240C4⋊C4—5381no—
241C4⋊C4—5381no—
242C4⋊C4—5381no—
243C4⋊C4—5381no—
244C4⋊C4—5381no—
245C4⋊C4—5381no—
246C4⋊C4—5381no—
247C4⋊C4—5381no—
248C4⋊C4—5381no—
249C4⋊C4—5381no—
250C4⋊C4C22×D26911yescharacteristic
251C22⋊C4—21no—
252C22⋊C4—21no—
253C22⋊C4—5381no—
254C22⋊C4—5381no—
255C22⋊C4—5381no—
256C42—21no—
257C42—2691no—
258C42—2691no—
259C42—5381no—
260C42—5381no—
261C42—5381no—
262C42—5381no—
263C42C22×D26911yescharacteristic
264C23—21no—
265Q8—21no—
266Q8—21no—
267Q8—21no—
268Q8—5382no—
269Q8—5381no—
270Q8—5381no—
271Q8—10762no—
272Q8#1686440112yes—
273D4—21no—
274D4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—2691no—
279C2×C4—2691no—
280C2×C4—2691no—
281C2×C4—2691no—
282C2×C4—5381no—
283C2×C4—5381no—
284C2×C4—5381no—
285C2×C4—5381no—
286C2×C4—10762no—
287C2×C4D4×D26911yescharacteristic
288C2×C4D4×D26911yescharacteristic
289C2×C4C23×D26911yescharacteristic
290C8—21no—
291C8—21no—
292C8—5381no—
293C8—5381no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22C2×D4×D26911yescharacteristic
298C4—21no—
299C4—22no—
300C4—21no—
301C4—41no—
302C4—41no—
303C4—2692no—
304C4—5381no—
305C4—5381no—
306C4—5381no—
307C4—10761no—
308C4—10761no—
309C4—10761no—
310C4—10761no—
311C4C2×#1686440111yescharacteristic
312C4#2257550011yescharacteristic
313C2—81no—
314C2#3177126111yescharacteristic
315C2#135×D26911yescharacteristic
316C2#3177142111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#464×C269C2
socleC22×C269C22×D4
prime radicalC2×D4×C269C23
hypercenter#464D269
hypocenterC269#3364
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #31771331C2semidirect
5. #31770954C2semidirect
6. #31770913C2semidirect
7. #31770910C2semidirect
10. #31770813C2semidirect
11. #31770729C2semidirect
12. Q16×Dic269C2semidirect
13. C4×#16864392C2semidirect
158. C269#3364semidirect

Maximal subgroups

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

subgroupindex
#317713312
#317713242
#317709592
#317709582
#317709542
#317709132
#317709102
#317708832
#317708252
#317708132
#317707292
Q16×Dic2692
C4×#168643922
SD16×Dic2692
#464×C2692
#3364269