Finite Group Databasebeta

← #46821071

Subgroups — #46821071

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#31771226C211yesmaximal, characteristic, complemented
2#31771079C211yesmaximal, characteristic, complemented
3#31770947C211yesmaximal, characteristic, complemented
4#31770930C211yesmaximal, characteristic, complemented
5#31770896C211yesmaximal, characteristic, complemented
6#31770886C211yesmaximal, characteristic, complemented
7#31770821C211yesmaximal, characteristic, complemented
8#31770821C211yesmaximal, characteristic, complemented
9#31770758C211yesmaximal, characteristic, complemented
10#31770741C211yesmaximal, characteristic
11#31770718C211yesmaximal, characteristic, complemented
12#31770707C211yesmaximal, characteristic, complemented
13C4×#16864391C211yesmaximal, characteristic, complemented
14C4×D2152C211yesmaximal, characteristic, complemented
15#433×C269C211yesmaximal, characteristic, complemented
16C22×D1076C2211yescharacteristic
17C2×#16864391C2211yescharacteristic
18C2×#16864391C2211yescharacteristic
19C2×D2152C2211yescharacteristic
20C2×D2152C2211yescharacteristic
21#22575453C2211yescharacteristic, complemented
22#22575448—21no—
23#22575441C2211yescharacteristic, complemented
24#22575439—21no—
25#22575435—21no—
26#22575432C2211yescharacteristic
27#22575431—21no—
28#22575427C2211yescharacteristic
29C4×Dic538C2211yescharacteristic, complemented
30C4×D1076C2211yescharacteristic
31C4×D1076C2211yescharacteristic
32C4×D1076C2211yescharacteristic
33C4×D1076C2211yescharacteristic
34C4×D1076C2211yescharacteristic, complemented
35#22575415—21no—
36#22575415—21no—
37#22575412C2211yescharacteristic
38C22⋊C4×D269—21no—
39C22⋊C4×D269—21no—
40#22575387C2211yescharacteristic, complemented
41#22575387C2211yescharacteristic, complemented
42#22575385C2211yescharacteristic, complemented
43#22575385C2211yescharacteristic, complemented
44#22575378C2211yescharacteristic, complemented
45#22575378C2211yescharacteristic, complemented
46#22575375C2211yescharacteristic
47#22575375C2211yescharacteristic
48#22575375C2211yescharacteristic
49#22575375C2211yescharacteristic
50#22575375C2211yescharacteristic, complemented
51#22575375C2211yescharacteristic, complemented
52#117×C269C2211yescharacteristic
53C4⋊C8×C269C2211yescharacteristic, complemented
54C4⋊C8×C269C2211yescharacteristic, complemented
55C22⋊C8×C269C2211yescharacteristic
56C22⋊C8×C269C2211yescharacteristic
57#97×C269C2211yescharacteristic, complemented
58C4×C8×C269C2211yescharacteristic, complemented
59C23×D269—21no—
60C2×Dic538—21no—
61C2×Dic538C2311yescharacteristic
62C2×D1076—22no—
63C2×D1076—22no—
64C2×D1076—21no—
65C2×D1076C2311yescharacteristic
66C2×D1076C2311yescharacteristic
67C2×D1076C2311yescharacteristic
68C2×C22⋊D269—21no—
69C2×C4×D269—21no—
70C2×C4×D269—21no—
71C2×C4×D269—21no—
72C2×C4×D269—21no—
73C2×C4×D269—21no—
74#16864391—22no—
75#16864391—22no—
76D2152—22no—
77D2152—22no—
78C4⋊Dic269—21no—
79C4⋊Dic269C2311yescharacteristic
80C4⋊Dic269C2311yescharacteristic
81C4⋊Dic269C2311yescharacteristic
82C4⋊Dic269C2311yescharacteristic
83#16864381—21no—
84#16864381—21no—
85C22⋊Dic269—21no—
86C22⋊Dic269—21no—
87#16864379—21no—
88#16864379—21no—
89#16864379—21no—
90#16864379—21no—
91#16864379—21no—
92#16864379—21no—
93#16864379—21no—
94#16864379—21no—
95C4×Dic269—21no—
96C4×Dic269—21no—
97C22×C4×C269C2311yescharacteristic
98C2×C8×C269C2311yescharacteristic
99C2×C8×C269C2311yescharacteristic
100C2×C8×C269C2311yescharacteristic
101C2×C8×C269C2311yescharacteristic
102C4⋊C4×C269D411yescharacteristic
103C4⋊C4×C269D411yescharacteristic
104C22⋊C4×C269D411yescharacteristic
105C22⋊C4×C269D411yescharacteristic
106C42×C269C2311yescharacteristic
107C42×C269C2311yescharacteristic
108C22×D269—21no—
109C22×D269—21no—
110C22×D269—24no—
111C22×D269—21no—
112C22×D269—81no—
113C22×D269—81no—
114Dic538—21no—
115Dic538—21no—
116Dic538—81no—
117D1076—24no—
118D1076—21no—
119D1076—21no—
120D1076—21no—
121D1076—21no—
122D1076#4112yes—
123D1076#4112yes—
124C22⋊D269—81no—
125C2×Dic269—21no—
126C2×Dic269—21no—
127C2×Dic269—21no—
128C2×Dic269—21no—
129C2×Dic269—21no—
130C4×D269—81no—
131C4×D269—81no—
132C4×D269—81no—
133C4×D269—81no—
134C4×D269—81no—
135C23×C269C2×D411yescharacteristic
136C2×C4×C269—21no—
137C2×C4×C269—21no—
138C2×C4×C269C2×D411yescharacteristic
139C2×C4×C269C2×D411yescharacteristic
140C2×C4×C269C2×D411yescharacteristic
141C2×C4×C269C2×D411yescharacteristic
142C2×C4×C269C2×D411yescharacteristic
143C2×C4×C269C2411yescharacteristic
144C8×C269—21no—
145C8×C269—21no—
146C8×C269—21no—
147C8×C269—21no—
148C22×C269—21no—
149C22×C269—21no—
150C22×C269—21no—
151C22×C269C22×D411yescharacteristic
152C2×D269—22no—
153C2×D269—22no—
154C2×D269—41no—
155C2×D269—41no—
156C2×D269—41no—
157C2×D269—41no—
158C2×D269—41no—
159C2×D269—41no—
160C2×D269—41no—
161C2×D269—84no—
162C4×C269—21no—
163C4×C269—21no—
164C4×C269—21no—
165C4×C269—21no—
166C4×C269—21no—
167C4×C269C2×#4111yescharacteristic
168C4×C269C2×#4111yescharacteristic
169Dic269—41no—
170Dic269—41no—
171Dic269—41no—
172Dic269—41no—
173Dic269—41no—
174C2×C269—41no—
175C2×C269#52511yescharacteristic
176C2×C269#57611yescharacteristic
177C2×C269#57711yescharacteristic
178D269—42no—
179D269—42no—
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#450—2691no—
192#447—2691no—
193#442—2691no—
194#440—2691no—
195C4×SD16—2691no—
196C4×D8—2691no—
197#433D26911yescharacteristic, complemented
198C22×D4—2691no—
199C2×SD16—2691no—
200C2×SD16—2691no—
201C2×D8—2691no—
202C2×D8—2691no—
203C4⋊Q8—2691no—
204#126—5381no—
205#124—2691no—
206#124—5381no—
207#123—5381no—
208C22⋊Q8—2691no—
209C22⋊Q8—5381no—
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#117C2×D26911yescharacteristic
221C2×C22⋊C4—5381no—
222C2×C22⋊C4—5381no—
223#107—2691no—
224#107—2691no—
225#106—2691no—
226#106—2691no—
227C4⋊C8C2×D26911yescharacteristic, complemented
228C4⋊C8C2×D26911yescharacteristic, complemented
229#103—2691no—
230#103—2691no—
231#102—2691no—
232#102—2691no—
233#102—2691no—
234#102—2691no—
235#102—2691no—
236#102—2691no—
237C22⋊C8C2×D26911yescharacteristic
238C22⋊C8C2×D26911yescharacteristic
239#97C2×D26911yescharacteristic, complemented
240C4×C8C2×D26911yescharacteristic, complemented
241C24—5381no—
242C2×Q8—2691no—
243C2×Q8—5381no—
244C2×D4—2691no—
245C2×D4—2691no—
246C2×D4—2691no—
247C2×D4—5382no—
248C2×D4—5382no—
249C2×D4—5381no—
250C2×D4—5381no—
251C22×C4—5381no—
252C22×C4—5381no—
253C22×C4—5381no—
254C22×C4—5381no—
255C22×C4—5381no—
256C22×C4C22×D26911yescharacteristic
257SD16—5382no—
258SD16—5382no—
259D8—5382no—
260D8—5382no—
261C2×C8C22×D26911yescharacteristic
262C2×C8C22×D26911yescharacteristic
263C2×C8C22×D26911yescharacteristic
264C2×C8C22×D26911yescharacteristic
265C4⋊C4—2691no—
266C4⋊C4—2691no—
267C4⋊C4—2691no—
268C4⋊C4—2691no—
269C4⋊C4—5381no—
270C4⋊C4—5381no—
271C4⋊C4—5381no—
272C4⋊C4D107611yescharacteristic
273C4⋊C4D107611yescharacteristic
274C22⋊C4—5381no—
275C22⋊C4—5381no—
276C22⋊C4—5381no—
277C22⋊C4—5381no—
278C22⋊C4—5381no—
279C22⋊C4—5381no—
280C22⋊C4—5381no—
281C22⋊C4—5381no—
282C22⋊C4—5381no—
283C22⋊C4—5381no—
284C22⋊C4D107611yescharacteristic
285C22⋊C4D107611yescharacteristic
286C42—5381no—
287C42—5381no—
288C42C22×D26911yescharacteristic
289C42C22×D26911yescharacteristic
290C23—5384no—
291C23—5381no—
292C23—5381no—
293C23—5381no—
294C23—21521no—
295C23—21521no—
296C23C2×D107611yescharacteristic
297Q8—5381no—
298Q8—5381no—
299Q8—21521no—
300D4—2692no—
301D4—2692no—
302D4—5384no—
303D4—5381no—
304D4—5381no—
305D4—5381no—
306D4—5381no—
307D4—21521no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—5381no—
311C2×C4—5381no—
312C2×C4—5381no—
313C2×C4—5381no—
314C2×C4—5381no—
315C2×C4—21521no—
316C2×C4—21521no—
317C2×C4—21521no—
318C2×C4—21521no—
319C2×C4—21521no—
320C2×C4C2×D107611yescharacteristic
321C2×C4C2×D107611yescharacteristic
322C2×C4C2×D107611yescharacteristic
323C2×C4C2×D107611yescharacteristic
324C2×C4C2×D107611yescharacteristic
325C2×C4C23×D26911yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—5382no—
334C22—5382no—
335C22—10761no—
336C22—10761no—
337C22—10761no—
338C22—10761no—
339C22—10761no—
340C22—10761no—
341C22—10761no—
342C22—21524no—
343C22C22×D107611yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—10761no—
350C4—10761no—
351C4—10761no—
352C4—10761no—
353C4—10761no—
354C4#41×D26911yescharacteristic
355C4#41×D26911yescharacteristic
356C2—41no—
357C2—10762no—
358C2—10762no—
359C2—21521no—
360C2#3177111711yescharacteristic
361C2#3177141011yescharacteristic
362C2#3177141711yescharacteristic
subgroupG/H
centerC22C22×D1076
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#433×C269C2
socleC22×C269C22×D4
prime radical#31770741C2
hypercenter#433D269
hypocenterC269#3118
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #31771226C2semidirect
2. #31771079C2semidirect
3. #31770947C2semidirect
4. #31770930C2semidirect
5. #31770896C2semidirect
6. #31770886C2semidirect
7. #31770821C2semidirect
8. #31770821C2semidirect
9. #31770758C2semidirect
11. #31770718C2semidirect
12. #31770707C2semidirect
13. C4×#16864391C2semidirect
14. C4×D2152C2semidirect
15. #433×C269C2semidirect
21. #22575453C22semidirect
23. #22575441C22semidirect
29. C4×Dic538C22semidirect
34. C4×D1076C22semidirect
40. #22575387C22semidirect
41. #22575387C22semidirect
42. #22575385C22semidirect
43. #22575385C22semidirect
44. #22575378C22semidirect
45. #22575378C22semidirect
50. #22575375C22semidirect
51. #22575375C22semidirect
53. C4⋊C8×C269C22semidirect
54. C4⋊C8×C269C22semidirect
57. #97×C269C22semidirect
58. C4×C8×C269C22semidirect
181. C269#3118semidirect
197. #433D269semidirect
227. C4⋊C8C2×D269semidirect
228. C4⋊C8C2×D269semidirect
239. #97C2×D269semidirect
240. C4×C8C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317712262
#317710792
#317709472
#317709302
#317708962
#317708862
#317708212
#317707582
#317707412
#317707182
#317707072
C4×#168643912
C4×D21522
#433×C2692
#3118269