Finite Group Databasebeta

← #46821070

Subgroups — #46821070

Order 34432.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771228C211yesmaximal, characteristic, complemented
2#31771080C211yesmaximal, characteristic, complemented
3#31770943C211yesmaximal, characteristic, complemented
4#31770930C211yesmaximal, characteristic, complemented
5#31770893C211yesmaximal, characteristic, complemented
6#31770883C211yesmaximal, characteristic, complemented
7#31770822C211yesmaximal, characteristic, complemented
8#31770822C211yesmaximal, characteristic, complemented
9#31770739C211yesmaximal, characteristic
10#31770714C211yesmaximal, characteristic, complemented
11#31770706C211yesmaximal, characteristic, complemented
12SD16×Dic269C211yesmaximal, characteristic, complemented
13#31770685C211yesmaximal, characteristic, complemented
14#31770663C211yesmaximal, characteristic, complemented
15#450×C269C211yesmaximal, characteristic, complemented
16C2×#16864387C2211yescharacteristic
17C2×#16864387C2211yescharacteristic
18#22575452C2211yescharacteristic, complemented
19#22575448—21no—
20#22575442C2211yescharacteristic, complemented
21#22575439—21no—
22#22575435—21no—
23#22575433—21no—
24#22575427C2211yescharacteristic
25Q8×Dic269C2211yescharacteristic, complemented
26D4×Dic269—21no—
27D4×Dic269—21no—
28D4×Dic269C2211yescharacteristic
29D4×Dic269C2211yescharacteristic
30D4×Dic269C2211yescharacteristic
31D4×Dic269C2211yescharacteristic
32#22575415C2211yescharacteristic, complemented
33#22575412C2211yescharacteristic
34#22575412C2211yescharacteristic
35C2×C22⋊Dic269—21no—
36C2×C22⋊Dic269—21no—
37#22575387C2211yescharacteristic, complemented
38#22575386C2211yescharacteristic, complemented
39#22575385C2211yescharacteristic, complemented
40#22575384C2211yescharacteristic, complemented
41#22575382C2211yescharacteristic, complemented
42#22575382C2211yescharacteristic, complemented
43#22575377C2211yescharacteristic, complemented
44#22575377C2211yescharacteristic, complemented
45#22575375C2211yescharacteristic, complemented
46#22575375C2211yescharacteristic, complemented
47#22575374C2211yescharacteristic
48#22575374C2211yescharacteristic
49C22⋊#14524130C2211yescharacteristic
50#22575363C2211yescharacteristic, complemented
51C8×Dic269C2211yescharacteristic, complemented
52C22×D4×C269C2211yescharacteristic
53C2×SD16×C269C2211yescharacteristic
54C2×SD16×C269C2211yescharacteristic
55C22⋊Q8×C269C2211yescharacteristic
56#102×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58C22⋊C8×C269C2211yescharacteristic
59C2×Dic538—21no—
60C2×D1076C2311yescharacteristic
61C2×C22⋊D269—21no—
62C22×Dic269—21no—
63C22×Dic269—21no—
64C22×Dic269—21no—
65C22×Dic269—21no—
66C2×C4×D269—21no—
67#16864387—22no—
68#16864387—22no—
69C2×#14524130C2311yescharacteristic
70C2×#14524130C2311yescharacteristic
71C4⋊Dic269—21no—
72C4⋊Dic269D411yescharacteristic
73C4⋊Dic269D411yescharacteristic
74C4⋊Dic269C2311yescharacteristic
75C4⋊Dic269C2311yescharacteristic
76C4⋊Dic269C2311yescharacteristic
77#16864381—21no—
78C22⋊Dic269—21no—
79C22⋊Dic269—21no—
80C22⋊Dic269—21no—
81C22⋊Dic269—21no—
82C22⋊Dic269—21no—
83C22⋊Dic269D411yescharacteristic
84C22⋊Dic269D411yescharacteristic
85#16864379—21no—
86#16864379—21no—
87#16864379—21no—
88#16864379—21no—
89C4×Dic269—21no—
90C4×Dic269—21no—
91C4×Dic269C2311yescharacteristic
92C4×Dic269C2311yescharacteristic
93C24×C269—21no—
94C2×Q8×C269C2311yescharacteristic
95C2×D4×C269—22no—
96C2×D4×C269—22no—
97C2×D4×C269—21no—
98C2×D4×C269C2311yescharacteristic
99C2×D4×C269C2311yescharacteristic
100C22×C4×C269C2311yescharacteristic
101SD16×C269—22no—
102SD16×C269—22no—
103C2×C8×C269C2311yescharacteristic
104C2×C8×C269C2311yescharacteristic
105C4⋊C4×C269—21no—
106C4⋊C4×C269C2311yescharacteristic
107C22⋊C4×C269—21no—
108C22×D269—21no—
109Dic538—81no—
110D1076—21no—
111D1076—21no—
112C22⋊D269—81no—
113C2×Dic269—21no—
114C2×Dic269—21no—
115C2×Dic269—21no—
116C2×Dic269—81no—
117C2×Dic269—81no—
118C2×Dic269—81no—
119C2×Dic269—81no—
120C2×Dic269C2×D411yescharacteristic
121C2×Dic269C2×D411yescharacteristic
122C2×Dic269C2×D411yescharacteristic
123C2×Dic269C2×D411yescharacteristic
124C4×D269—81no—
125#14524130—21no—
126#14524130—21no—
127C23×C269—24no—
128C23×C269—21no—
129C23×C269—21no—
130C23×C269—81no—
131C23×C269—81no—
132C23×C269C2×D411yescharacteristic
133Q8×C269—21no—
134Q8×C269—21no—
135D4×C269—24no—
136D4×C269—21no—
137D4×C269—21no—
138D4×C269#4112yes—
139D4×C269#4112yes—
140C2×C4×C269—21no—
141C2×C4×C269—21no—
142C2×C4×C269—21no—
143C2×C4×C269—21no—
144C2×C4×C269C2×D411yescharacteristic
145C2×C4×C269C2411yescharacteristic
146C8×C269—21no—
147C8×C269—21no—
148C22×C269—21no—
149C22×C269—22no—
150C22×C269—22no—
151C22×C269—21no—
152C22×C269—21no—
153C22×C269—41no—
154C22×C269—41no—
155C22×C269—41no—
156C22×C269—41no—
157C22×C269—84no—
158C22×C269C22×D411yescharacteristic
159C2×D269—41no—
160C2×D269—41no—
161C2×D269—41no—
162C4×C269—21no—
163C4×C269—41no—
164C4×C269—41no—
165C4×C269C2×#4111yescharacteristic
166C4×C269C2×#4111yescharacteristic
167Dic269—21no—
168Dic269—21no—
169Dic269—21no—
170Dic269—21no—
171Dic269—41no—
172Dic269—41no—
173Dic269—41no—
174C2×C269—41no—
175C2×C269—42no—
176C2×C269—42no—
177C2×C269#52511yescharacteristic
178C2×C269#57611yescharacteristic
179C2×C269#57711yescharacteristic
180D269—81no—
181C269#311811yescharacteristic, complemented, Sylow
182#3118—2691nomaximal, Sylow
183#542—2691no—
184#518—2691no—
185#485—2691no—
186#482—2691no—
187#476—2691no—
188#474—2691no—
189#463—2691no—
190#463—2691no—
191#450D26911yescharacteristic, complemented
192#447—2691no—
193#442—2691no—
194#440—2691no—
195C4×SD16—2691no—
196C4×D8—2691no—
197#433—2691no—
198C22×D4C2×D26911yescharacteristic
199C2×SD16C2×D26911yescharacteristic
200C2×SD16C2×D26911yescharacteristic
201C2×D8—2691no—
202C2×D8—2691no—
203C4⋊Q8—2691no—
204#126—5381no—
205#124—2691no—
206#124—5381no—
207#123—5381no—
208C22⋊Q8—5381no—
209C22⋊Q8C2×D26911yescharacteristic
210#121—2691no—
211C4×Q8—2691no—
212C4×D4—2691no—
213C4×D4—2691no—
214C4×D4—2691no—
215C4×D4—2691no—
216C4×D4—2691no—
217C4×D4—5381no—
218C4×D4—5381no—
219#117—2691no—
220#117—2691no—
221C2×C22⋊C4—5381no—
222C2×C22⋊C4—5381no—
223#107—2691no—
224#107—2691no—
225#106—2691no—
226#106—2691no—
227C4⋊C8—2691no—
228C4⋊C8—2691no—
229#103—2691no—
230#103—2691no—
231#102—2691no—
232#102—2691no—
233#102—2691no—
234#102—2691no—
235#102C2×D26911yescharacteristic
236#102C2×D26911yescharacteristic
237C22⋊C8—2691no—
238C22⋊C8C2×D26911yescharacteristic
239#97—2691no—
240C4×C8—2691no—
241C24—21no—
242C2×Q8—5381no—
243C2×Q8C22×D26911yescharacteristic
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—2691no—
248C2×D4—5381no—
249C2×D4C22×D26911yescharacteristic
250C2×D4C22×D26911yescharacteristic
251C22×C4—5381no—
252C22×C4—5381no—
253C22×C4—5381no—
254C22×C4—5381no—
255C22×C4—5381no—
256C22×C4C22×D26911yescharacteristic
257SD16—22no—
258SD16—22no—
259D8—5382no—
260D8—5382no—
261C2×C8—2691no—
262C2×C8—2691no—
263C2×C8C22×D26911yescharacteristic
264C2×C8C22×D26911yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—2691no—
267C4⋊C4—2691no—
268C4⋊C4—2691no—
269C4⋊C4—2691no—
270C4⋊C4—2691no—
271C4⋊C4—5381no—
272C4⋊C4—5381no—
273C4⋊C4C22×D26911yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—2691no—
276C22⋊C4—2691no—
277C22⋊C4—5381no—
278C22⋊C4—5381no—
279C22⋊C4—5381no—
280C22⋊C4—5381no—
281C22⋊C4—5381no—
282C22⋊C4—5381no—
283C22⋊C4—5381no—
284C22⋊C4—5381no—
285C22⋊C4—5381no—
286C42—2691no—
287C42—2691no—
288C42—5381no—
289C42—5381no—
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—5381no—
296C23D4×D26911yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—21521no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—5381no—
304D4—5381no—
305D4—21521no—
306D4#1686440112yes—
307D4#1686440112yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—2691no—
313C2×C4—2691no—
314C2×C4—2691no—
315C2×C4—2691no—
316C2×C4—5381no—
317C2×C4—5381no—
318C2×C4—5381no—
319C2×C4—21521no—
320C2×C4—21521no—
321C2×C4—21521no—
322C2×C4—21521no—
323C2×C4—21521no—
324C2×C4D4×D26911yescharacteristic
325C2×C4C23×D26911yescharacteristic
326C8—21no—
327C8—21no—
328C8—5381no—
329C8—5381no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—84no—
340C22—10761no—
341C22—10761no—
342C22—10761no—
343C22C2×D4×D26911yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—5381no—
348C4—5381no—
349C4—5381no—
350C4—5381no—
351C4—10761no—
352C4—10761no—
353C4—10761no—
354C4C2×#1686440111yescharacteristic
355C4C2×#1686440111yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—21521no—
360C2#3177111111yescharacteristic
361C2#3177140911yescharacteristic
362C2#3177141111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#450×C269C2
socleC22×C269C22×D4
prime radical#31770739C2
hypercenter#450D269
hypocenterC269#3118
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #31771228C2semidirect
2. #31771080C2semidirect
3. #31770943C2semidirect
4. #31770930C2semidirect
5. #31770893C2semidirect
6. #31770883C2semidirect
7. #31770822C2semidirect
8. #31770822C2semidirect
10. #31770714C2semidirect
11. #31770706C2semidirect
12. SD16×Dic269C2semidirect
13. #31770685C2semidirect
14. #31770663C2semidirect
15. #450×C269C2semidirect
18. #22575452C22semidirect
20. #22575442C22semidirect
25. Q8×Dic269C22semidirect
32. #22575415C22semidirect
37. #22575387C22semidirect
38. #22575386C22semidirect
39. #22575385C22semidirect
40. #22575384C22semidirect
41. #22575382C22semidirect
42. #22575382C22semidirect
43. #22575377C22semidirect
44. #22575377C22semidirect
45. #22575375C22semidirect
46. #22575375C22semidirect
50. #22575363C22semidirect
51. C8×Dic269C22semidirect
181. C269#3118semidirect
191. #450D269semidirect

Maximal subgroups

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

subgroupindex
#317712282
#317710802
#317709432
#317709302
#317708932
#317708832
#317708222
#317707392
#317707142
#317707062
SD16×Dic2692
#317706852
#317706632
#450×C2692
#3118269