Finite Group Databasebeta

← #46822742

Subgroups — #46822742

Order 34432.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771305C211yesmaximal, characteristic, complemented
2#31771248C211yesmaximal, characteristic, complemented
3#31770959C211yesmaximal, characteristic, complemented
4#31770939C211yesmaximal, characteristic, complemented
5#31770928C211yesmaximal, characteristic, complemented
6#31770906C211yesmaximal, characteristic, complemented
7#31770838C211yesmaximal, characteristic, complemented
8#31770831C211yesmaximal, characteristic, complemented
9#31770749C211yesmaximal, characteristic, complemented
10#31770737C211yesmaximal, characteristic, complemented
11C4×#16864387C211yesmaximal, characteristic, complemented
12#31770670C211yesmaximal, characteristic, complemented
13#31770600C211yesmaximal, characteristic, complemented
14#102×D269C211yesmaximal, characteristic, complemented
15#463×C269C211yesmaximal, characteristic, complemented
16C2×#16864403C2211yescharacteristic
17C2×D4×D269C2211yescharacteristic
18C2×#16864387C2211yescharacteristic
19C2×C8×D269C2211yescharacteristic
20C2×C8×D269C2211yescharacteristic, complemented
21#22575446—21no—
22#22575445C2211yescharacteristic, complemented
23#22575436—21no—
24#22575435—21no—
25#22575429C2211yescharacteristic
26#22575426—21no—
27#22575426—21no—
28#22575424C2211yescharacteristic
29#22575424C2211yescharacteristic
30#22575424C2211yescharacteristic, complemented
31#22575423—21no—
32C4×D1076C2211yescharacteristic
33C4×D1076C2211yescharacteristic
34C4×C22⋊D269—21no—
35#22575411C2211yescharacteristic, complemented
36C4⋊C4×D269C2211yescharacteristic
37C22⋊C4×D269—21no—
38#22575387C2211yescharacteristic, complemented
39#22575386C2211yescharacteristic, complemented
40#22575385C2211yescharacteristic, complemented
41#22575377C2211yescharacteristic, complemented
42#22575377C2211yescharacteristic, complemented
43#22575375C2211yescharacteristic
44#22575375C2211yescharacteristic
45#22575374C2211yescharacteristic
46#22575374C2211yescharacteristic
47#22575374C2211yescharacteristic, complemented
48#22575373C2211yescharacteristic
49#22575365C2211yescharacteristic
50#22575365C2211yescharacteristic, complemented
51C4×#14524130C2211yescharacteristic, complemented
52C2×SD16×C269C2211yescharacteristic, complemented
53C2×D8×C269C2211yescharacteristic
54#124×C269C2211yescharacteristic
55C4×D4×C269C2211yescharacteristic, complemented
56C4⋊C8×C269C2211yescharacteristic, complemented
57#103×C269C2211yescharacteristic, complemented
58#102×C269C2211yescharacteristic
59C23×D269—21no—
60#16864403—22no—
61#16864403—41no—
62C2×D1076—21no—
63C2×D1076D411yescharacteristic
64C2×D1076C2311yescharacteristic
65C2×C22⋊D269—21no—
66C2×C22⋊D269—21no—
67C2×C22⋊D269—21no—
68C2×C22⋊D269—21no—
69D4×D269—22no—
70D4×D269—41no—
71C2×C4×D269—21no—
72C2×C4×D269—21no—
73C2×C4×D269—21no—
74C2×C4×D269C2311yescharacteristic
75C2×C4×D269C2311yescharacteristic
76#16864387—22no—
77C2×#14524130C2311yescharacteristic
78C2×#14524130C2311yescharacteristic
79C8×D269—41no—
80C8×D269—41no—
81C4⋊Dic269D411yescharacteristic
82C4⋊Dic269C2311yescharacteristic
83C4⋊Dic269C2311yescharacteristic
84C4⋊Dic269C2311yescharacteristic
85#16864381—21no—
86#16864381—21no—
87#16864381—21no—
88#16864381—21no—
89C22⋊Dic269—21no—
90C22⋊Dic269—21no—
91C22⋊Dic269—21no—
92#16864379—21no—
93#16864379—21no—
94#16864379—21no—
95#16864379D411yescharacteristic
96#16864379D411yescharacteristic
97C4×Dic269—21no—
98C2×Q8×C269C2311yescharacteristic
99C2×D4×C269C2311yescharacteristic
100C2×D4×C269C2311yescharacteristic
101C22×C4×C269—21no—
102SD16×C269—41no—
103D8×C269—41no—
104C2×C8×C269C2311yescharacteristic
105C2×C8×C269C2311yescharacteristic
106C4⋊C4×C269C2311yescharacteristic
107C22⋊C4×C269—21no—
108C22⋊C4×C269—21no—
109C22⋊C4×C269—21no—
110C42×C269C2311yescharacteristic
111C22×D269—21no—
112C22×D269—42no—
113C22×D269—42no—
114C22×D269—81no—
115C22×D269C2×D411yescharacteristic
116C22×D269C2×D411yescharacteristic
117D1076—22no—
118D1076—21no—
119D1076—42no—
120D1076#4112yes—
121C22⋊D269—42no—
122C22⋊D269—42no—
123C22⋊D269—81no—
124C22⋊D269—81no—
125C2×Dic269—21no—
126C2×Dic269—21no—
127C2×Dic269—21no—
128C2×Dic269C2×D411yescharacteristic
129C2×Dic269C2×D411yescharacteristic
130C4×D269—21no—
131C4×D269—21no—
132C4×D269—21no—
133C4×D269—21no—
134C4×D269—42no—
135C4×D269—81no—
136C4×D269—81no—
137#14524130—21no—
138#14524130—21no—
139C23×C269—21no—
140C23×C269—21no—
141Q8×C269—21no—
142Q8×C269—21no—
143D4×C269—21no—
144D4×C269—21no—
145D4×C269—21no—
146D4×C269—21no—
147C2×C4×C269—21no—
148C2×C4×C269—21no—
149C2×C4×C269—81no—
150C2×C4×C269C2×D411yescharacteristic
151C2×C4×C269C2×D411yescharacteristic
152C2×C4×C269C2411yescharacteristic
153C8×C269—21no—
154C8×C269—21no—
155C22×C269—41no—
156C22×C269—41no—
157C22×C269—41no—
158C22×C269—41no—
159C22×C269—41no—
160C22×C269—41no—
161C22×C269C22×D411yescharacteristic
162C2×D269—21no—
163C2×D269—21no—
164C2×D269—21no—
165C2×D269—22no—
166C2×D269—21no—
167C2×D269—21no—
168C2×D269—41no—
169C2×D269—41no—
170C2×D269—84no—
171C2×D269#13512yes—
172C4×C269—21no—
173C4×C269—21no—
174C4×C269—41no—
175C4×C269—41no—
176C4×C269C2×#4111yescharacteristic
177C4×C269H(5,𝔽2)11yescharacteristic
178Dic269—21no—
179Dic269—21no—
180Dic269—41no—
181Dic269—41no—
182Dic269—41no—
183C2×C269—81no—
184C2×C269—81no—
185C2×C269#54611yescharacteristic
186C2×C269C2×#13511yescharacteristic
187C2×C269#57611yescharacteristic
188D269—22no—
189D269—41no—
190D269—42no—
191C269#329711yescharacteristic, complemented, Sylow
192#3297—2691nomaximal, Sylow
193#553—2691no—
194#546—2691no—
195#488—2691no—
196#484—2691no—
197#482—2691no—
198#478—2691no—
199#466—2691no—
200#465—2691no—
201#463D26911yescharacteristic, complemented
202#449—2691no—
203#447—2691no—
204C4×D8—2691no—
205C8×D4—2691no—
206#416—2691no—
207C2×#102—2691no—
208C2×#41—2691no—
209C22×D4—2691no—
210C2×SD16C2×D26911yescharacteristic, complemented
211C2×D8—2691no—
212C2×D8C2×D26911yescharacteristic
213C22×C8—2691no—
214C22×C8—2691no—
215#126—5381no—
216#125—2691no—
217#124C2×D26911yescharacteristic
218#123—5381no—
219#123—5381no—
220C22⋊Q8—2691no—
221#121—2691no—
222#121—2691no—
223#121—2691no—
224#121—5381no—
225#121—5381no—
226#120—5381no—
227C4×D4—2691no—
228C4×D4—2691no—
229C4×D4—5381no—
230C4×D4C2×D26911yescharacteristic, complemented
231#117—2691no—
232C2×C4⋊C4—2691no—
233C2×C22⋊C4—5381no—
234#107—2691no—
235#107—2691no—
236#106—2691no—
237C4⋊C8C2×D26911yescharacteristic, complemented
238#103—2691no—
239#103—2691no—
240#103C2×D26911yescharacteristic, complemented
241#102—2691no—
242#102—2691no—
243#102—2691no—
244#102—2691no—
245#102—2691no—
246#102—2691no—
247#102C2×D26911yescharacteristic
248C22⋊C8—2691no—
249C22⋊C8—2691no—
250C4×C8—2691no—
251C24—5381no—
252#41—5382no—
253#41—10761no—
254C2×Q8C22×D26911yescharacteristic
255C2×D4—2691no—
256C2×D4—2691no—
257C2×D4—5381no—
258C2×D4—5381no—
259C2×D4—5382no—
260C2×D4—5381no—
261C2×D4—5381no—
262C2×D4—5381no—
263C2×D4—10761no—
264C2×D4C22×D26911yescharacteristic
265C2×D4C22×D26911yescharacteristic
266C22×C4—21no—
267C22×C4—2691no—
268C22×C4—2691no—
269C22×C4—5381no—
270C22×C4—5381no—
271C22×C4—5381no—
272SD16—41no—
273D8—41no—
274D8—5382no—
275C2×C8—2691no—
276C2×C8—2691no—
277C2×C8—10761no—
278C2×C8—10761no—
279C2×C8C22×D26911yescharacteristic
280C2×C8C22×D26911yescharacteristic
281C4⋊C4—2691no—
282C4⋊C4—2691no—
283C4⋊C4—2691no—
284C4⋊C4—2691no—
285C4⋊C4—5381no—
286C4⋊C4—5381no—
287C4⋊C4—5381no—
288C4⋊C4—5381no—
289C4⋊C4C22×D26911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—2691no—
294C22⋊C4—2691no—
295C22⋊C4—5381no—
296C22⋊C4—5381no—
297C22⋊C4—5381no—
298C22⋊C4—5381no—
299C22⋊C4—5381no—
300C22⋊C4—5381no—
301C42—5381no—
302C42C22×D26911yescharacteristic
303C23—21no—
304C23—21no—
305C23—2691no—
306C23—2691no—
307C23—5381no—
308C23—10762no—
309C23—10762no—
310C23—21521no—
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—2692no—
318D4—5382no—
319D4—5381no—
320D4—10762no—
321D4—10762no—
322D4—10762no—
323D4—21521no—
324D4—21521no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—2691no—
329C2×C4—2691no—
330C2×C4—5381no—
331C2×C4—5381no—
332C2×C4—5381no—
333C2×C4—5381no—
334C2×C4—5381no—
335C2×C4—5381no—
336C2×C4—5381no—
337C2×C4—10762no—
338C2×C4—21521no—
339C2×C4—21521no—
340C2×C4D4×D26911yescharacteristic
341C2×C4D4×D26911yescharacteristic
342C2×C4C23×D26911yescharacteristic
343C8—21no—
344C8—21no—
345C8—5381no—
346C8—5381no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—2692no—
354C22—5381no—
355C22—5381no—
356C22—5381no—
357C22—5381no—
358C22—5382no—
359C22—5381no—
360C22—10761no—
361C22—10761no—
362C22—21524no—
363C22C2×D4×D26911yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—5381no—
369C4—5381no—
370C4—10761no—
371C4—10761no—
372C4—10761no—
373C4#41×D26911yescharacteristic
374C4#2257549811yescharacteristic
375C2—81no—
376C2—81no—
377C2—5382no—
378C2—10761no—
379C2—10762no—
380C2#3177125211yescharacteristic
381C2#135×D26911yescharacteristic
382C2#3177140911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#463×C269C2
socleC22×C269C22×D4
hypercenter#463D269
hypocenterC269#3297
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #31771305C2semidirect
2. #31771248C2semidirect
3. #31770959C2semidirect
4. #31770939C2semidirect
5. #31770928C2semidirect
6. #31770906C2semidirect
7. #31770838C2semidirect
8. #31770831C2semidirect
9. #31770749C2semidirect
10. #31770737C2semidirect
11. C4×#16864387C2semidirect
12. #31770670C2semidirect
13. #31770600C2semidirect
14. #102×D269C2semidirect
15. #463×C269C2semidirect
20. C2×C8×D269C22semidirect
22. #22575445C22semidirect
30. #22575424C22semidirect
35. #22575411C22semidirect
38. #22575387C22semidirect
39. #22575386C22semidirect
40. #22575385C22semidirect
41. #22575377C22semidirect
42. #22575377C22semidirect
47. #22575374C22semidirect
50. #22575365C22semidirect
51. C4×#14524130C22semidirect
52. C2×SD16×C269C22semidirect
55. C4×D4×C269C22semidirect
56. C4⋊C8×C269C22semidirect
57. #103×C269C22semidirect
191. C269#3297semidirect
201. #463D269semidirect
210. C2×SD16C2×D269semidirect
230. C4×D4C2×D269semidirect
237. C4⋊C8C2×D269semidirect
240. #103C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317713052
#317712482
#317709592
#317709392
#317709282
#317709062
#317708382
#317708312
#317707492
#317707372
C4×#168643872
#317706702
#317706002
#102×D2692
#463×C2692
#3297269