Finite Group Databasebeta

← #46820813

Subgroups — #46820813

Order 34432.

414 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771115C211yesmaximal, characteristic
2#117×D269C211yesmaximal, characteristic, complemented
3#31770949C211yesmaximal, characteristic, complemented
4#31770948C211yesmaximal, characteristic, complemented
5#31770947C211yesmaximal, characteristic, complemented
6#31770946C211yesmaximal, characteristic, complemented
7#31770928C211yesmaximal, characteristic, complemented
8#31770927C211yesmaximal, characteristic, complemented
9#31770926C211yesmaximal, characteristic, complemented
10#31770646C211yesmaximal, characteristic, complemented
11#31770644C211yesmaximal, characteristic, complemented
12#31770603C211yesmaximal, characteristic, complemented
13#31770603C211yesmaximal, characteristic, complemented
14#31770567C211yesmaximal, characteristic, complemented
15#482×C269C211yesmaximal, characteristic, complemented
16C2×#16864401C2211yescharacteristic
17C22×C4×D269C2211yescharacteristic
18C2×#16864385C2211yescharacteristic
19C2×#16864385C2211yescharacteristic
20#22575435—21no—
21#22575433C2211yescharacteristic
22#22575432C2211yescharacteristic
23#22575424C2211yescharacteristic
24#22575421—21no—
25D4×Dic269—21no—
26#22575413—21no—
27#22575412C2211yescharacteristic
28#22575411C2211yescharacteristic
29#22575411C2211yescharacteristic
30#22575411C2211yescharacteristic
31#22575410—21no—
32#22575409—21no—
33C4⋊C4×D269C2211yescharacteristic
34C4⋊C4×D269C2211yescharacteristic
35C22⋊C4×D269—21no—
36C42×D269—21no—
37#22575387C2211yescharacteristic, complemented
38#22575386C2211yescharacteristic, complemented
39#22575386C2211yescharacteristic, complemented
40#22575385C2211yescharacteristic, complemented
41#22575384C2211yescharacteristic, complemented
42#22575384C2211yescharacteristic, complemented
43#22575378C2211yescharacteristic, complemented
44#22575378C2211yescharacteristic, complemented
45#22575376C2211yescharacteristic, complemented
46#22575376C2211yescharacteristic, complemented
47#22575374C2211yescharacteristic, complemented
48#22575374C2211yescharacteristic, complemented
49C22⋊#14524130C2211yescharacteristic
50#22575365C2211yescharacteristic
51#22575365C2211yescharacteristic
52#121×C269C2211yescharacteristic
53#117×C269C2211yescharacteristic
54#107×C269C2211yescharacteristic, complemented
55#106×C269C2211yescharacteristic, complemented
56#102×C269C2211yescharacteristic, complemented
57#102×C269C2211yescharacteristic, complemented
58C22⋊C8×C269C2211yescharacteristic
59C23×D269D411yescharacteristic
60#16864401—22no—
61#16864401—22no—
62C2×Dic538C2311yescharacteristic
63C2×C22⋊D269—21no—
64C2×C22⋊D269—21no—
65C22×Dic269—21no—
66C22×Dic269D411yescharacteristic
67C2×C4×D269—22no—
68C2×C4×D269—22no—
69C2×C4×D269—21no—
70C2×C4×D269—21no—
71C2×C4×D269D411yescharacteristic
72C2×C4×D269D411yescharacteristic
73C2×C4×D269C2311yescharacteristic
74C2×C4×D269C2311yescharacteristic
75#16864385—22no—
76#16864385—22no—
77C2×#14524130C2311yescharacteristic
78C2×#14524130C2311yescharacteristic
79C4⋊Dic269—21no—
80C4⋊Dic269C2311yescharacteristic
81C4⋊Dic269C2311yescharacteristic
82C4⋊Dic269C2311yescharacteristic
83#16864381—21no—
84#16864381—21no—
85#16864381—21no—
86C22⋊Dic269—21no—
87C22⋊Dic269—21no—
88C22⋊Dic269—21no—
89#16864379—21no—
90#16864379—21no—
91#16864379—21no—
92#16864379—21no—
93C4×Dic269—21no—
94C4×Dic269—21no—
95C4×Dic269—21no—
96C4×Dic269—21no—
97C2×D4×C269—21no—
98C2×D4×C269C2311yescharacteristic
99C22×C4×C269C2311yescharacteristic
100C2×C8×C269C2311yescharacteristic
101C2×C8×C269C2311yescharacteristic
102C4⋊C4×C269C2311yescharacteristic
103C4⋊C4×C269C2311yescharacteristic
104C4⋊C4×C269C2311yescharacteristic
105C22⋊C4×C269—21no—
106C22⋊C4×C269—21no—
107C42×C269—21no—
108C22×D269—22no—
109C22×D269—41no—
110C22×D269—41no—
111C22×D269C2×D411yescharacteristic
112C22×D269C2×D411yescharacteristic
113Dic538—21no—
114Dic538—21no—
115C22⋊D269—42no—
116C22⋊D269—42no—
117C2×Dic269—22no—
118C2×Dic269—21no—
119C2×Dic269—21no—
120C2×Dic269—21no—
121C2×Dic269—21no—
122C2×Dic269—42no—
123C2×Dic269C2×D411yescharacteristic
124C2×Dic269C2×D411yescharacteristic
125C4×D269—22no—
126C4×D269—21no—
127C4×D269—21no—
128C4×D269—22no—
129C4×D269—42no—
130C4×D269—42no—
131C4×D269#4112yes—
132C4×D269#4112yes—
133#14524130—21no—
134#14524130—21no—
135C23×C269—21no—
136C23×C269C2×D411yescharacteristic
137D4×C269—21no—
138D4×C269—21no—
139D4×C269—42no—
140C2×C4×C269—21no—
141C2×C4×C269—21no—
142C2×C4×C269—21no—
143C2×C4×C269—21no—
144C2×C4×C269—21no—
145C2×C4×C269C2×D411yescharacteristic
146C2×C4×C269C2411yescharacteristic
147C8×C269—21no—
148C8×C269—21no—
149C22×C269—21no—
150C22×C269—21no—
151C22×C269—21no—
152C22×C269—41no—
153C22×C269—41no—
154C22×C269—41no—
155C22×C269C22×D411yescharacteristic
156C2×D269—21no—
157C2×D269—21no—
158C2×D269—21no—
159C2×D269—21no—
160C2×D269—21no—
161C2×D269—44no—
162C2×D269#12312yes—
163C4×C269—21no—
164C4×C269—41no—
165C4×C269—41no—
166C4×C269—41no—
167C4×C269C2×#4111yescharacteristic
168C4×C269C2×#4111yescharacteristic
169Dic269—21no—
170Dic269—41no—
171Dic269—41no—
172Dic269—41no—
173Dic269—41no—
174Dic269#12312yes—
175C2×C269—41no—
176C2×C269—81no—
177C2×C269C2×#12311yescharacteristic
178C2×C269#57511yescharacteristic
179C2×C269#57511yescharacteristic
180D269—22no—
181D269—41no—
182C269#309311yescharacteristic, complemented, Sylow
183#3093—2691nomaximal, Sylow
184#525—2691no—
185C2×#117—2691no—
186#485—2691no—
187#485—2691no—
188#485—2691no—
189#485—2691no—
190#482—2691no—
191#482—2691no—
192#482—2691no—
193#482D26911yescharacteristic, complemented
194#428—2691no—
195#428—2691no—
196#417—2691no—
197#417—2691no—
198#407—2691no—
199C2×#41—2691no—
200C23×C4—2691no—
201C2×M16—2691no—
202C2×M16—2691no—
203#123—5381no—
204C22⋊Q8—2691no—
205C22⋊Q8—2691no—
206#121—2691no—
207#121C2×D26911yescharacteristic
208#120—5381no—
209C4×D4—5381no—
210C4×D4—5381no—
211#117—2691no—
212#117—2691no—
213#117—2691no—
214#117—2691no—
215#117—5381no—
216#117—5381no—
217#117C2×D26911yescharacteristic
218C2×C4⋊C4—2691no—
219C2×C4⋊C4—2691no—
220C2×C22⋊C4—5381no—
221C2×C42—5381no—
222#107—2691no—
223#107—2691no—
224#107—2691no—
225#107C2×D26911yescharacteristic, complemented
226#106—2691no—
227#106—2691no—
228#106—2691no—
229#106C2×D26911yescharacteristic, complemented
230#103—2691no—
231#103—2691no—
232#103—2691no—
233#103—2691no—
234#102—2691no—
235#102—2691no—
236#102C2×D26911yescharacteristic, complemented
237#102C2×D26911yescharacteristic, complemented
238C22⋊C8—2691no—
239C22⋊C8—2691no—
240C22⋊C8—2691no—
241C22⋊C8C2×D26911yescharacteristic
242C24—2691no—
243#41—5382no—
244#41—5382no—
245C2×Q8—2691no—
246C2×D4—21no—
247C2×D4—5381no—
248C2×D4—5381no—
249C2×D4C22×D26911yescharacteristic
250C22×C4—2691no—
251C22×C4—2691no—
252C22×C4—2691no—
253C22×C4—2691no—
254C22×C4—2691no—
255C22×C4—5382no—
256C22×C4—5382no—
257C22×C4—5381no—
258C22×C4—5381no—
259C22×C4—5381no—
260C22×C4C22×D26911yescharacteristic
261M16—5382no—
262M16—5382no—
263C2×C8—2691no—
264C2×C8—2691no—
265C2×C8C22×D26911yescharacteristic
266C2×C8C22×D26911yescharacteristic
267C4⋊C4—2691no—
268C4⋊C4—2691no—
269C4⋊C4—2691no—
270C4⋊C4—5381no—
271C4⋊C4—5381no—
272C4⋊C4—5381no—
273C4⋊C4—5381no—
274C4⋊C4C22×D26911yescharacteristic
275C4⋊C4C22×D26911yescharacteristic
276C4⋊C4C22×D26911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—5381no—
280C22⋊C4—5381no—
281C22⋊C4—5381no—
282C22⋊C4—5381no—
283C22⋊C4—5381no—
284C22⋊C4—5381no—
285C22⋊C4—5381no—
286C42—21no—
287C42—5381no—
288C42—5381no—
289C42—5381no—
290C42—5381no—
291C23—21no—
292C23—2691no—
293C23—2691no—
294C23—5382no—
295C23—10761no—
296C23—10761no—
297C23D4×D26911yescharacteristic
298Q8—5381no—
299Q8—5381no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—10762no—
304D4—10762no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—2691no—
311C2×C4—2692no—
312C2×C4—2692no—
313C2×C4—2691no—
314C2×C4—5382no—
315C2×C4—5382no—
316C2×C4—5382no—
317C2×C4—5381no—
318C2×C4—5381no—
319C2×C4—5381no—
320C2×C4—5381no—
321C2×C4—5381no—
322C2×C4—5381no—
323C2×C4—10762no—
324C2×C4—10762no—
325C2×C4—10762no—
326C2×C4D4×D26911yescharacteristic
327C2×C4C23×D26911yescharacteristic
328C8—21no—
329C8—21no—
330C8—5381no—
331C8—5381no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—2692no—
339C22—5381no—
340C22—5381no—
341C22—5381no—
342C22—5381no—
343C22—5381no—
344C22—10764no—
345C22C2×D4×D26911yescharacteristic
346C4—21no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—2692no—
351C4—5381no—
352C4—10761no—
353C4—10761no—
354C4—10761no—
355C4—10761no—
356C4#41×D26911yescharacteristic
357C4#41×D26911yescharacteristic
358C2—41no—
359C2—81no—
360C2—5382no—
361C2—10761no—
362C2#123×D26911yescharacteristic
363C2#3177140111yescharacteristic
364C2#3177140211yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#482×C269C2
socleC22×C269C22×D4
prime radical#31771115C2
hypercenter#482D269
hypocenterC269#3093
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #117×D269C2semidirect
3. #31770949C2semidirect
4. #31770948C2semidirect
5. #31770947C2semidirect
6. #31770946C2semidirect
7. #31770928C2semidirect
8. #31770927C2semidirect
9. #31770926C2semidirect
10. #31770646C2semidirect
11. #31770644C2semidirect
12. #31770603C2semidirect
13. #31770603C2semidirect
14. #31770567C2semidirect
15. #482×C269C2semidirect
37. #22575387C22semidirect
38. #22575386C22semidirect
39. #22575386C22semidirect
40. #22575385C22semidirect
41. #22575384C22semidirect
42. #22575384C22semidirect
43. #22575378C22semidirect
44. #22575378C22semidirect
45. #22575376C22semidirect
46. #22575376C22semidirect
47. #22575374C22semidirect
48. #22575374C22semidirect
54. #107×C269C22semidirect
55. #106×C269C22semidirect
56. #102×C269C22semidirect
57. #102×C269C22semidirect
182. C269#3093semidirect
193. #482D269semidirect
225. #107C2×D269semidirect
229. #106C2×D269semidirect
236. #102C2×D269semidirect
237. #102C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317711152
#117×D2692
#317709492
#317709482
#317709472
#317709462
#317709282
#317709272
#317709262
#317706462
#317706442
#317706032
#317705672
#482×C2692
#3093269