Finite Group Databasebeta

← #46821163

Subgroups — #46821163

Order 34432.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771222C211yesmaximal, characteristic, complemented
2#31771088C211yesmaximal, characteristic, complemented
3#31770936C211yesmaximal, characteristic, complemented
4#31770921C211yesmaximal, characteristic, complemented
5#31770893C211yesmaximal, characteristic, complemented
6#31770888C211yesmaximal, characteristic, complemented
7#31770825C211yesmaximal, characteristic, complemented
8#31770818C211yesmaximal, characteristic, complemented
9#31770767C211yesmaximal, characteristic, complemented
10#31770717C211yesmaximal, characteristic, complemented
11#31770709C211yesmaximal, characteristic, complemented
12#31770696C211yesmaximal, characteristic, complemented
13SD16×Dic269C211yesmaximal, characteristic, complemented
14#31770663C211yesmaximal, characteristic, complemented
15#449×C269C211yesmaximal, characteristic
16C2×#16864392C2211yescharacteristic
17C2×#16864390C2211yescharacteristic
18#22575452C2211yescharacteristic
19#22575446—21no—
20#22575440—21no—
21#22575440C2211yescharacteristic
22#22575434—21no—
23#22575432C2211yescharacteristic
24#22575430—21no—
25Q8×Dic269C2211yescharacteristic
26Q8×Dic269C2211yescharacteristic
27#22575418C2211yescharacteristic
28D4×Dic269—21no—
29D4×Dic269—21no—
30D4×Dic269C2211yescharacteristic
31D4×Dic269C2211yescharacteristic
32D4×Dic269C2211yescharacteristic
33#22575412—21no—
34#22575412C2211yescharacteristic
35C2×C4⋊Dic269—21no—
36C2×C4⋊Dic269C2211yescharacteristic
37#22575385C2211yescharacteristic
38#22575385C2211yescharacteristic
39#22575384C2211yescharacteristic
40#22575384C2211yescharacteristic
41#22575382C2211yescharacteristic
42#22575382C2211yescharacteristic
43#22575378C2211yescharacteristic
44#22575378C2211yescharacteristic
45#22575377C2211yescharacteristic
46#22575374C2211yescharacteristic
47#22575374C2211yescharacteristic
48#22575374C2211yescharacteristic
49C22⋊#14524130C2211yescharacteristic
50#22575363C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52C2×#41×C269C2211yescharacteristic
53C2×SD16×C269C2211yescharacteristic
54C2×D8×C269C2211yescharacteristic
55#121×C269C2211yescharacteristic
56#103×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58C22⋊C8×C269C2211yescharacteristic
59C2×Dic538—21no—
60C2×Dic538C2311yescharacteristic
61C22×Dic269—21no—
62C22×Dic269—21no—
63C22×Dic269—21no—
64C22×Dic269—21no—
65#16864392—22no—
66#16864390—22no—
67C2×#14524130C2311yescharacteristic
68C2×#14524130C2311yescharacteristic
69C4⋊Dic269—21no—
70C4⋊Dic269—21no—
71C4⋊Dic269—21no—
72C4⋊Dic269D411yescharacteristic
73C4⋊Dic269D411yescharacteristic
74C4⋊Dic269C2311yescharacteristic
75C4⋊Dic269C2311yescharacteristic
76C4⋊Dic269C2311yescharacteristic
77#16864381—21no—
78#16864381—21no—
79#16864381—21no—
80C22⋊Dic269—21no—
81C22⋊Dic269—21no—
82C22⋊Dic269—21no—
83C22⋊Dic269—21no—
84C22⋊Dic269—21no—
85C22⋊Dic269—21no—
86C22⋊Dic269D411yescharacteristic
87C22⋊Dic269D411yescharacteristic
88C4×Dic269—21no—
89C4×Dic269—21no—
90C4×Dic269—21no—
91C4×Dic269C2311yescharacteristic
92C4×Dic269C2311yescharacteristic
93#41×C269—22no—
94#41×C269—22no—
95C2×Q8×C269C2311yescharacteristic
96C2×D4×C269—21no—
97C2×D4×C269—21no—
98C2×D4×C269C2311yescharacteristic
99C2×D4×C269C2311yescharacteristic
100C22×C4×C269—21no—
101C22×C4×C269C2311yescharacteristic
102SD16×C269—22no—
103D8×C269—22no—
104C2×C8×C269C2311yescharacteristic
105C2×C8×C269C2311yescharacteristic
106C4⋊C4×C269C2311yescharacteristic
107C22⋊C4×C269—21no—
108Dic538—21no—
109Dic538—21no—
110Dic538—81no—
111C2×Dic269—21no—
112C2×Dic269—21no—
113C2×Dic269—21no—
114C2×Dic269—21no—
115C2×Dic269—81no—
116C2×Dic269—81no—
117C2×Dic269—81no—
118C2×Dic269—81no—
119C2×Dic269C2×D411yescharacteristic
120C2×Dic269C2×D411yescharacteristic
121C2×Dic269C2×D411yescharacteristic
122C2×Dic269C2×D411yescharacteristic
123#14524130—21no—
124#14524130—21no—
125C23×C269—21no—
126C23×C269—21no—
127C23×C269C2×D411yescharacteristic
128Q8×C269—21no—
129Q8×C269#4112yes—
130D4×C269—24no—
131D4×C269—21no—
132D4×C269—21no—
133D4×C269—21no—
134D4×C269—81no—
135D4×C269#4112yes—
136C2×C4×C269—24no—
137C2×C4×C269—21no—
138C2×C4×C269—21no—
139C2×C4×C269—21no—
140C2×C4×C269—21no—
141C2×C4×C269C2×D411yescharacteristic
142C2×C4×C269C2411yescharacteristic
143C8×C269—21no—
144C8×C269—21no—
145C22×C269—21no—
146C22×C269—22no—
147C22×C269—21no—
148C22×C269—21no—
149C22×C269—41no—
150C22×C269—41no—
151C22×C269—41no—
152C22×C269—41no—
153C22×C269—41no—
154C22×C269C22×D411yescharacteristic
155C4×C269—21no—
156C4×C269—22no—
157C4×C269—41no—
158C4×C269C2×#4111yescharacteristic
159C4×C269C2×#4111yescharacteristic
160Dic269—21no—
161Dic269—21no—
162Dic269—21no—
163Dic269—21no—
164Dic269—41no—
165Dic269—41no—
166Dic269—41no—
167Dic269—41no—
168C2×C269—41no—
169C2×C269—42no—
170C2×C269—81no—
171C2×C269#52511yescharacteristic
172C2×C269#57711yescharacteristic
173C2×C269#57711yescharacteristic
174C269#312511yescharacteristic, complemented, Sylow
175#3125—2691nomaximal, Sylow
176#542—2691no—
177#520—2691no—
178#483—2691no—
179#481—2691no—
180#476—2691no—
181#475—2691no—
182#464—2691no—
183#463—2691no—
184#452—2691no—
185#449D26911yescharacteristic
186#442—2691no—
187#441—2691no—
188C4×SD16—2691no—
189C4×SD16—2691no—
190#433—2691no—
191C2×#41C2×D26911yescharacteristic
192C2×Q16—2691no—
193C2×SD16—2691no—
194C2×SD16C2×D26911yescharacteristic
195C2×D8C2×D26911yescharacteristic
196C4⋊Q8—2691no—
197#126—5381no—
198#124—2691no—
199#124—5381no—
200#123—5381no—
201C22⋊Q8—2691no—
202C22⋊Q8—5381no—
203#121C2×D26911yescharacteristic
204C4×Q8—2691no—
205C4×Q8—2691no—
206C4×Q8—2691no—
207C4×D4—2691no—
208C4×D4—2691no—
209C4×D4—2691no—
210C4×D4—5381no—
211C4×D4—5381no—
212#117—2691no—
213#117—5381no—
214C2×C4⋊C4—2691no—
215C2×C4⋊C4—5381no—
216#106—2691no—
217#106—2691no—
218#106—2691no—
219#106—2691no—
220C4⋊C8—2691no—
221C4⋊C8—2691no—
222#103—2691no—
223#103—2691no—
224#103—2691no—
225#103C2×D26911yescharacteristic
226#102—2691no—
227#102—2691no—
228#102—2691no—
229#102C2×D26911yescharacteristic
230C22⋊C8—2691no—
231C22⋊C8C2×D26911yescharacteristic
232#97—2691no—
233C4×C8—2691no—
234#41—22no—
235#41—22no—
236C2×Q8—2691no—
237C2×Q8—5381no—
238C2×Q8C22×D26911yescharacteristic
239C2×D4—21no—
240C2×D4—21no—
241C2×D4C22×D26911yescharacteristic
242C2×D4C22×D26911yescharacteristic
243C22×C4—21no—
244C22×C4—5381no—
245C22×C4—5381no—
246C22×C4—5381no—
247C22×C4—5381no—
248C22×C4C22×D26911yescharacteristic
249Q16—5382no—
250SD16—22no—
251SD16—5382no—
252D8—22no—
253C2×C8—2691no—
254C2×C8—2691no—
255C2×C8C22×D26911yescharacteristic
256C2×C8C22×D26911yescharacteristic
257C4⋊C4—2691no—
258C4⋊C4—2691no—
259C4⋊C4—2691no—
260C4⋊C4—2691no—
261C4⋊C4—2691no—
262C4⋊C4—5381no—
263C4⋊C4—5381no—
264C4⋊C4—5381no—
265C4⋊C4—5381no—
266C4⋊C4—5381no—
267C4⋊C4—5381no—
268C4⋊C4C22×D26911yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—2691no—
271C22⋊C4—2691no—
272C22⋊C4—5381no—
273C22⋊C4—5381no—
274C22⋊C4—5381no—
275C22⋊C4—5381no—
276C22⋊C4—5381no—
277C22⋊C4—5381no—
278C42—2691no—
279C42—2691no—
280C42—5381no—
281C42—5381no—
282C42—5381no—
283C23—21no—
284C23—21no—
285C23D4×D26911yescharacteristic
286Q8—21no—
287Q8—5381no—
288Q8—5381no—
289Q8—21521no—
290Q8#1686440112yes—
291D4—24no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—81no—
296D4#1686440112yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—2691no—
303C2×C4—2691no—
304C2×C4—2691no—
305C2×C4—2691no—
306C2×C4—5381no—
307C2×C4—5381no—
308C2×C4—5381no—
309C2×C4—5381no—
310C2×C4—21521no—
311C2×C4—21521no—
312C2×C4—21521no—
313C2×C4—21521no—
314C2×C4D4×D26911yescharacteristic
315C2×C4C23×D26911yescharacteristic
316C8—21no—
317C8—21no—
318C8—5381no—
319C8—5381no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—22no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22C2×D4×D26911yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—5381no—
334C4—5381no—
335C4—5381no—
336C4—5381no—
337C4—10761no—
338C4—10761no—
339C4—10761no—
340C4—10761no—
341C4C2×#1686440111yescharacteristic
342C4C2×#1686440111yescharacteristic
343C2—41no—
344C2—42no—
345C2—81no—
346C2#3177111111yescharacteristic
347C2#3177141211yescharacteristic
348C2#3177141511yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting, prime radical#449×C269C2
socleC22×C269C22×D4
hypercenter#449D269
hypocenterC269#3125
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #31771222C2semidirect
2. #31771088C2semidirect
3. #31770936C2semidirect
4. #31770921C2semidirect
5. #31770893C2semidirect
6. #31770888C2semidirect
7. #31770825C2semidirect
8. #31770818C2semidirect
9. #31770767C2semidirect
10. #31770717C2semidirect
11. #31770709C2semidirect
12. #31770696C2semidirect
13. SD16×Dic269C2semidirect
14. #31770663C2semidirect
174. C269#3125semidirect

Maximal subgroups

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

subgroupindex
#317712222
#317710882
#317709362
#317709212
#317708932
#317708882
#317708252
#317708182
#317707672
#317707172
#317707092
#317706962
SD16×Dic2692
#317706632
#449×C2692
#3125269