Finite Group Databasebeta

← #46821236

Subgroups — #46821236

Order 34432.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771232C211yesmaximal, characteristic, complemented
2#31771173C211yesmaximal, characteristic
3#31770970C211yesmaximal, characteristic, complemented
4#31770968C211yesmaximal, characteristic, complemented
5#31770966C211yesmaximal, characteristic, complemented
6#31770961C211yesmaximal, characteristic, complemented
7#31770959C211yesmaximal, characteristic, complemented
8#31770953C211yesmaximal, characteristic, complemented
9#31770950C211yesmaximal, characteristic, complemented
10#31770608C211yesmaximal, characteristic, complemented
11#31770605C211yesmaximal, characteristic, complemented
12#31770600C211yesmaximal, characteristic, complemented
13#102×D269C211yesmaximal, characteristic, complemented
14#31770562C211yesmaximal, characteristic, complemented
15#489×C269C211yesmaximal, characteristic, complemented
16C2×#16864403C2211yescharacteristic
17C2×D4×D269C2211yescharacteristic
18C2×#16864385C2211yescharacteristic
19C2×C8×D269C2211yescharacteristic
20#22575452C2211yescharacteristic, complemented
21#22575451—21no—
22#22575450C2211yescharacteristic
23#22575449C2211yescharacteristic
24#22575445C2211yescharacteristic, complemented
25#22575444C2211yescharacteristic, complemented
26#22575443—21no—
27#22575442C2211yescharacteristic
28#22575431—21no—
29#22575429—21no—
30#22575426—21no—
31#22575426—21no—
32#22575423—21no—
33#22575423—21no—
34#22575411C2211yescharacteristic
35#22575410C2211yescharacteristic
36C4⋊C4×D269C2211yescharacteristic
37#22575377C2211yescharacteristic, complemented
38#22575377C2211yescharacteristic, complemented
39#22575375C2211yescharacteristic
40#22575375C2211yescharacteristic
41#22575375C2211yescharacteristic, complemented
42#22575375C2211yescharacteristic, complemented
43#22575374C2211yescharacteristic
44#22575374C2211yescharacteristic
45#22575373C2211yescharacteristic
46#22575373C2211yescharacteristic
47#22575373C2211yescharacteristic, complemented
48#22575373C2211yescharacteristic, complemented
49#22575363C2211yescharacteristic, complemented
50C4×#14524130C2211yescharacteristic, complemented
51C8×Dic269C2211yescharacteristic, complemented
52C4⋊Q8×C269C2211yescharacteristic, complemented
53#124×C269C2211yescharacteristic
54#103×C269C2211yescharacteristic, complemented
55#103×C269C2211yescharacteristic, complemented
56#102×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58#97×C269C2211yescharacteristic, complemented
59C23×D269—21no—
60#16864403—22no—
61#16864403—22no—
62C2×Dic538—21no—
63C2×D1076—21no—
64C2×D1076—21no—
65C2×D1076—21no—
66C2×D1076C2311yescharacteristic
67C2×D1076C2311yescharacteristic
68C2×C22⋊D269—21no—
69C2×C22⋊D269—21no—
70C2×C22⋊D269—21no—
71D4×D269—22no—
72D4×D269—22no—
73C2×C4×D269—21no—
74C2×C4×D269—21no—
75C2×C4×D269C2311yescharacteristic
76#16864385—22no—
77C2×#14524130C2311yescharacteristic
78C2×#14524130C2311yescharacteristic
79C8×D269—22no—
80C4⋊Dic269—21no—
81C4⋊Dic269C2311yescharacteristic
82C4⋊Dic269C2311yescharacteristic
83#16864381—21no—
84#16864381—21no—
85#16864381—21no—
86#16864381—21no—
87#16864381—21no—
88#16864381D411yescharacteristic
89#16864381D411yescharacteristic
90#16864379—21no—
91#16864379—21no—
92#16864379—21no—
93#16864379D411yescharacteristic
94#16864379D411yescharacteristic
95C4×Dic269—21no—
96C4×Dic269C2311yescharacteristic
97C2×Q8×C269—21no—
98C2×Q8×C269C2311yescharacteristic
99C2×D4×C269C2311yescharacteristic
100C2×C8×C269C2311yescharacteristic
101C2×C8×C269C2311yescharacteristic
102C4⋊C4×C269—21no—
103C4⋊C4×C269C2311yescharacteristic
104C4⋊C4×C269C2311yescharacteristic
105C22⋊C4×C269—21no—
106C22⋊C4×C269—21no—
107C42×C269C2311yescharacteristic
108C22×D269—21no—
109C22×D269—21no—
110C22×D269—42no—
111C22×D269—81no—
112C22×D269—81no—
113C22×D269C2×D411yescharacteristic
114Dic538—81no—
115D1076—21no—
116D1076—21no—
117D1076—21no—
118D1076—21no—
119D1076—42no—
120D1076—81no—
121D1076—81no—
122C22⋊D269—42no—
123C22⋊D269—81no—
124C22⋊D269—81no—
125C2×Dic269—21no—
126C2×Dic269—21no—
127C2×Dic269C2×D411yescharacteristic
128C2×Dic269C2×D411yescharacteristic
129C2×Dic269C2×D411yescharacteristic
130C4×D269—42no—
131C4×D269—81no—
132C4×D269#4112yes—
133C4×D269#4112yes—
134#14524130—21no—
135#14524130—21no—
136C23×C269—21no—
137Q8×C269—21no—
138Q8×C269—21no—
139Q8×C269—81no—
140D4×C269—21no—
141D4×C269—21no—
142C2×C4×C269—21no—
143C2×C4×C269—21no—
144C2×C4×C269—21no—
145C2×C4×C269C2×D411yescharacteristic
146C2×C4×C269C2×D411yescharacteristic
147C2×C4×C269C2411yescharacteristic
148C8×C269—21no—
149C8×C269—21no—
150C22×C269—41no—
151C22×C269—41no—
152C22×C269—41no—
153C22×C269C22×D411yescharacteristic
154C2×D269—21no—
155C2×D269—21no—
156C2×D269—41no—
157C2×D269—41no—
158C2×D269—41no—
159C2×D269—41no—
160C2×D269—41no—
161C2×D269—41no—
162C2×D269—84no—
163C2×D269#12412yes—
164C4×C269—21no—
165C4×C269—21no—
166C4×C269—41no—
167C4×C269—41no—
168C4×C269—41no—
169C4×C269C2×#4111yescharacteristic
170C4×C269C2×#4111yescharacteristic
171Dic269—21no—
172Dic269—21no—
173Dic269—41no—
174Dic269—41no—
175Dic269#12412yes—
176C2×C269—81no—
177C2×C269C2×#12411yescharacteristic
178C2×C269#57611yescharacteristic
179C2×C269#57711yescharacteristic
180D269—22no—
181D269—81no—
182D269—81no—
183C269#313611yescharacteristic, complemented, Sylow
184#3136—2691nomaximal, Sylow
185#544—2691no—
186#535—2691no—
187#490—2691no—
188#490—2691no—
189#489—2691no—
190#489D26911yescharacteristic, complemented
191#488—2691no—
192#488—2691no—
193#486—2691no—
194#486—2691no—
195#418—2691no—
196#417—2691no—
197#416—2691no—
198C2×#102—2691no—
199#405—2691no—
200C2×#41—2691no—
201C22×D4—2691no—
202C2×M16—2691no—
203C22×C8—2691no—
204C4⋊Q8—2691no—
205C4⋊Q8—5381no—
206C4⋊Q8C2×D26911yescharacteristic, complemented
207#127—2691no—
208#127—2691no—
209#125—2691no—
210#125—2691no—
211#125—5381no—
212#124—2691no—
213#124C2×D26911yescharacteristic
214C22⋊Q8—5381no—
215C22⋊Q8—5381no—
216#121—5381no—
217#121—5381no—
218#120—5381no—
219#120—5381no—
220#117—2691no—
221#117—2691no—
222C2×C4⋊C4—2691no—
223#103—2691no—
224#103—2691no—
225#103C2×D26911yescharacteristic, complemented
226#103C2×D26911yescharacteristic, complemented
227#102—2691no—
228#102—2691no—
229#102—2691no—
230#102—2691no—
231#102—2691no—
232#102—2691no—
233#102—2691no—
234#102—2691no—
235#102—2691no—
236#102—2691no—
237#102C2×D26911yescharacteristic
238#102C2×D26911yescharacteristic
239#97—2691no—
240#97C2×D26911yescharacteristic, complemented
241C4×C8—2691no—
242C4×C8—2691no—
243C24—5381no—
244#41—5382no—
245#41—5382no—
246C2×Q8—21no—
247C2×Q8—5381no—
248C2×Q8C22×D26911yescharacteristic
249C2×D4—2691no—
250C2×D4—2691no—
251C2×D4—5381no—
252C2×D4—5382no—
253C2×D4—5382no—
254C2×D4—5381no—
255C2×D4—5381no—
256C2×D4—5381no—
257C2×D4—5381no—
258C2×D4—5381no—
259C2×D4C22×D26911yescharacteristic
260C22×C4—2691no—
261C22×C4—5381no—
262C22×C4—5381no—
263M16—5382no—
264C2×C8—2691no—
265C2×C8—2691no—
266C2×C8—5382no—
267C2×C8C22×D26911yescharacteristic
268C2×C8C22×D26911yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—2691no—
271C4⋊C4—2691no—
272C4⋊C4—2691no—
273C4⋊C4—2691no—
274C4⋊C4—5381no—
275C4⋊C4—5381no—
276C4⋊C4—5381no—
277C4⋊C4—5381no—
278C4⋊C4—5381no—
279C4⋊C4—5381no—
280C4⋊C4C22×D26911yescharacteristic
281C4⋊C4C22×D26911yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—2691no—
285C22⋊C4—2691no—
286C22⋊C4—5381no—
287C22⋊C4—5381no—
288C22⋊C4—5381no—
289C42—2691no—
290C42—5381no—
291C42C22×D26911yescharacteristic
292C23—21no—
293C23—2691no—
294C23—5381no—
295C23—5381no—
296C23—10762no—
297C23—21521no—
298C23—21521no—
299Q8—21no—
300Q8—21no—
301Q8—81no—
302Q8—21521no—
303D4—21no—
304D4—21no—
305D4—5381no—
306D4—5381no—
307D4—5381no—
308D4—5381no—
309D4—10762no—
310D4—10762no—
311D4—21521no—
312D4—21521no—
313D4—21521no—
314D4—21521no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—2691no—
319C2×C4—2692no—
320C2×C4—2692no—
321C2×C4—2691no—
322C2×C4—2691no—
323C2×C4—5381no—
324C2×C4—5381no—
325C2×C4—10762no—
326C2×C4—21521no—
327C2×C4D4×D26911yescharacteristic
328C2×C4D4×D26911yescharacteristic
329C2×C4C23×D26911yescharacteristic
330C8—21no—
331C8—21no—
332C8—5381no—
333C8—5381no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—2692no—
338C22—5381no—
339C22—5381no—
340C22—10761no—
341C22—10761no—
342C22—10761no—
343C22—10761no—
344C22—10761no—
345C22—10761no—
346C22—21524no—
347C22C2×D4×D26911yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—2692no—
354C4—5381no—
355C4—5381no—
356C4—10761no—
357C4—10761no—
358C4#41×D26911yescharacteristic
359C4#41×D26911yescharacteristic
360C2—81no—
361C2—5382no—
362C2—21521no—
363C2—21521no—
364C2#124×D26911yescharacteristic
365C2#3177140911yescharacteristic
366C2#3177141411yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#489×C269C2
socleC22×C269C22×D4
prime radical#31771173C2
hypercenter#489D269
hypocenterC269#3136
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #31771232C2semidirect
3. #31770970C2semidirect
4. #31770968C2semidirect
5. #31770966C2semidirect
6. #31770961C2semidirect
7. #31770959C2semidirect
8. #31770953C2semidirect
9. #31770950C2semidirect
10. #31770608C2semidirect
11. #31770605C2semidirect
12. #31770600C2semidirect
13. #102×D269C2semidirect
14. #31770562C2semidirect
15. #489×C269C2semidirect
20. #22575452C22semidirect
24. #22575445C22semidirect
25. #22575444C22semidirect
37. #22575377C22semidirect
38. #22575377C22semidirect
41. #22575375C22semidirect
42. #22575375C22semidirect
47. #22575373C22semidirect
48. #22575373C22semidirect
49. #22575363C22semidirect
50. C4×#14524130C22semidirect
51. C8×Dic269C22semidirect
52. C4⋊Q8×C269C22semidirect
54. #103×C269C22semidirect
55. #103×C269C22semidirect
58. #97×C269C22semidirect
183. C269#3136semidirect
190. #489D269semidirect
206. C4⋊Q8C2×D269semidirect
225. #103C2×D269semidirect
226. #103C2×D269semidirect
240. #97C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317712322
#317711732
#317709702
#317709682
#317709662
#317709612
#317709592
#317709532
#317709502
#317706082
#317706052
#317706002
#102×D2692
#317705622
#489×C2692
#3136269