Finite Group Databasebeta

← #44560551

Subgroups — #44560551

Order 32128.

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#30632308C211yesmaximal, characteristic, complemented
2#30632161C211yesmaximal, characteristic, complemented
3#30632029C211yesmaximal, characteristic, complemented
4#30632012C211yesmaximal, characteristic, complemented
5#30631978C211yesmaximal, characteristic, complemented
6#30631968C211yesmaximal, characteristic, complemented
7#30631903C211yesmaximal, characteristic, complemented
8#30631903C211yesmaximal, characteristic, complemented
9#30631840C211yesmaximal, characteristic, complemented
10#30631823C211yesmaximal, characteristic
11#30631800C211yesmaximal, characteristic, complemented
12#30631789C211yesmaximal, characteristic, complemented
13C4×#16860799C211yesmaximal, characteristic, complemented
14C4×D2008C211yesmaximal, characteristic, complemented
15#433×C251C211yesmaximal, characteristic, complemented
16C22×D1004C2211yescharacteristic
17C2×#16860799C2211yescharacteristic
18C2×#16860799C2211yescharacteristic
19C2×D2008C2211yescharacteristic
20C2×D2008C2211yescharacteristic
21#22548715C2211yescharacteristic, complemented
22#22548710—21no—
23#22548703C2211yescharacteristic, complemented
24#22548701—21no—
25#22548697—21no—
26#22548694C2211yescharacteristic
27#22548693—21no—
28#22548689C2211yescharacteristic
29C4×Dic502C2211yescharacteristic, complemented
30C4×D1004C2211yescharacteristic
31C4×D1004C2211yescharacteristic
32C4×D1004C2211yescharacteristic
33C4×D1004C2211yescharacteristic
34C4×D1004C2211yescharacteristic, complemented
35#22548677—21no—
36#22548677—21no—
37#22548674C2211yescharacteristic
38C22⋊C4×D251—21no—
39C22⋊C4×D251—21no—
40#22548649C2211yescharacteristic, complemented
41#22548649C2211yescharacteristic, complemented
42#22548647C2211yescharacteristic, complemented
43#22548647C2211yescharacteristic, complemented
44#22548640C2211yescharacteristic, complemented
45#22548640C2211yescharacteristic, complemented
46#22548637C2211yescharacteristic
47#22548637C2211yescharacteristic
48#22548637C2211yescharacteristic
49#22548637C2211yescharacteristic
50#22548637C2211yescharacteristic, complemented
51#22548637C2211yescharacteristic, complemented
52#117×C251C2211yescharacteristic
53C4⋊C8×C251C2211yescharacteristic, complemented
54C4⋊C8×C251C2211yescharacteristic, complemented
55C22⋊C8×C251C2211yescharacteristic
56C22⋊C8×C251C2211yescharacteristic
57#97×C251C2211yescharacteristic, complemented
58C4×C8×C251C2211yescharacteristic, complemented
59C23×D251—21no—
60C2×Dic502—21no—
61C2×Dic502C2311yescharacteristic
62C2×D1004—22no—
63C2×D1004—22no—
64C2×D1004—21no—
65C2×D1004C2311yescharacteristic
66C2×D1004C2311yescharacteristic
67C2×D1004C2311yescharacteristic
68C2×C22⋊D251—21no—
69C2×C4×D251—21no—
70C2×C4×D251—21no—
71C2×C4×D251—21no—
72C2×C4×D251—21no—
73C2×C4×D251—21no—
74#16860799—22no—
75#16860799—22no—
76D2008—22no—
77D2008—22no—
78C4⋊Dic251—21no—
79C4⋊Dic251C2311yescharacteristic
80C4⋊Dic251C2311yescharacteristic
81C4⋊Dic251C2311yescharacteristic
82C4⋊Dic251C2311yescharacteristic
83Dic251⋊C4—21no—
84Dic251⋊C4—21no—
85C22⋊Dic251—21no—
86C22⋊Dic251—21no—
87(C2×D251)⋊C4—21no—
88(C2×D251)⋊C4—21no—
89(C2×D251)⋊C4—21no—
90(C2×D251)⋊C4—21no—
91(C2×D251)⋊C4—21no—
92(C2×D251)⋊C4—21no—
93(C2×D251)⋊C4—21no—
94(C2×D251)⋊C4—21no—
95C4×Dic251—21no—
96C4×Dic251—21no—
97C22×C4×C251C2311yescharacteristic
98C2×C8×C251C2311yescharacteristic
99C2×C8×C251C2311yescharacteristic
100C2×C8×C251C2311yescharacteristic
101C2×C8×C251C2311yescharacteristic
102C4⋊C4×C251D411yescharacteristic
103C4⋊C4×C251D411yescharacteristic
104C22⋊C4×C251D411yescharacteristic
105C22⋊C4×C251D411yescharacteristic
106C42×C251C2311yescharacteristic
107C42×C251C2311yescharacteristic
108C22×D251—21no—
109C22×D251—21no—
110C22×D251—24no—
111C22×D251—21no—
112C22×D251—81no—
113C22×D251—81no—
114Dic502—21no—
115Dic502—21no—
116Dic502—81no—
117D1004—24no—
118D1004—21no—
119D1004—21no—
120D1004—21no—
121D1004—21no—
122D1004#4112yes—
123D1004#4112yes—
124C22⋊D251—81no—
125C2×Dic251—21no—
126C2×Dic251—21no—
127C2×Dic251—21no—
128C2×Dic251—21no—
129C2×Dic251—21no—
130C4×D251—81no—
131C4×D251—81no—
132C4×D251—81no—
133C4×D251—81no—
134C4×D251—81no—
135C23×C251C2×D411yescharacteristic
136C2×C4×C251—21no—
137C2×C4×C251—21no—
138C2×C4×C251C2×D411yescharacteristic
139C2×C4×C251C2×D411yescharacteristic
140C2×C4×C251C2×D411yescharacteristic
141C2×C4×C251C2×D411yescharacteristic
142C2×C4×C251C2×D411yescharacteristic
143C2×C4×C251C2411yescharacteristic
144C8×C251—21no—
145C8×C251—21no—
146C8×C251—21no—
147C8×C251—21no—
148C22×C251—21no—
149C22×C251—21no—
150C22×C251—21no—
151C22×C251C22×D411yescharacteristic
152C2×D251—22no—
153C2×D251—22no—
154C2×D251—41no—
155C2×D251—41no—
156C2×D251—41no—
157C2×D251—41no—
158C2×D251—41no—
159C2×D251—41no—
160C2×D251—41no—
161C2×D251—84no—
162C4×C251—21no—
163C4×C251—21no—
164C4×C251—21no—
165C4×C251—21no—
166C4×C251—21no—
167C4×C251C2×#4111yescharacteristic
168C4×C251C2×#4111yescharacteristic
169Dic251—41no—
170Dic251—41no—
171Dic251—41no—
172Dic251—41no—
173Dic251—41no—
174C2×C251—41no—
175C2×C251#52511yescharacteristic
176C2×C251#57611yescharacteristic
177C2×C251#57711yescharacteristic
178D251—42no—
179D251—42no—
180D251—81no—
181C251#311811yescharacteristic, complemented, Sylow
182#3118—2511nomaximal, Sylow
183#542—2511no—
184#518—2511no—
185#485—2511no—
186#482—2511no—
187#476—2511no—
188#474—2511no—
189#463—2511no—
190#463—2511no—
191#450—2511no—
192#447—2511no—
193#442—2511no—
194#440—2511no—
195C4×SD16—2511no—
196C4×D8—2511no—
197#433D25111yescharacteristic, complemented
198C22×D4—2511no—
199C2×SD16—2511no—
200C2×SD16—2511no—
201C2×D8—2511no—
202C2×D8—2511no—
203C4⋊Q8—2511no—
204#126—5021no—
205#124—5021no—
206#124—2511no—
207#123—5021no—
208C22⋊Q8—5021no—
209C22⋊Q8—2511no—
210#121—2511no—
211C4×Q8—2511no—
212C4×D4—5021no—
213C4×D4—5021no—
214C4×D4—2511no—
215C4×D4—2511no—
216C4×D4—2511no—
217C4×D4—2511no—
218C4×D4—2511no—
219#117—2511no—
220#117C2×D25111yescharacteristic
221C2×C22⋊C4—5021no—
222C2×C22⋊C4—5021no—
223#107—2511no—
224#107—2511no—
225#106—2511no—
226#106—2511no—
227C4⋊C8C2×D25111yescharacteristic, complemented
228C4⋊C8C2×D25111yescharacteristic, complemented
229#103—2511no—
230#103—2511no—
231#102—2511no—
232#102—2511no—
233#102—2511no—
234#102—2511no—
235#102—2511no—
236#102—2511no—
237C22⋊C8C2×D25111yescharacteristic
238C22⋊C8C2×D25111yescharacteristic
239#97C2×D25111yescharacteristic, complemented
240C4×C8C2×D25111yescharacteristic, complemented
241C24—5021no—
242C2×Q8—5021no—
243C2×Q8—2511no—
244C2×D4—5022no—
245C2×D4—5022no—
246C2×D4—5021no—
247C2×D4—5021no—
248C2×D4—2511no—
249C2×D4—2511no—
250C2×D4—2511no—
251C22×C4—5021no—
252C22×C4—5021no—
253C22×C4—5021no—
254C22×C4—5021no—
255C22×C4—5021no—
256C22×C4C22×D25111yescharacteristic
257SD16—5022no—
258SD16—5022no—
259D8—5022no—
260D8—5022no—
261C2×C8C22×D25111yescharacteristic
262C2×C8C22×D25111yescharacteristic
263C2×C8C22×D25111yescharacteristic
264C2×C8C22×D25111yescharacteristic
265C4⋊C4—5021no—
266C4⋊C4—5021no—
267C4⋊C4—5021no—
268C4⋊C4—2511no—
269C4⋊C4—2511no—
270C4⋊C4—2511no—
271C4⋊C4—2511no—
272C4⋊C4D100411yescharacteristic
273C4⋊C4D100411yescharacteristic
274C22⋊C4—5021no—
275C22⋊C4—5021no—
276C22⋊C4—5021no—
277C22⋊C4—5021no—
278C22⋊C4—5021no—
279C22⋊C4—5021no—
280C22⋊C4—5021no—
281C22⋊C4—5021no—
282C22⋊C4—5021no—
283C22⋊C4—5021no—
284C22⋊C4D100411yescharacteristic
285C22⋊C4D100411yescharacteristic
286C42—5021no—
287C42—5021no—
288C42C22×D25111yescharacteristic
289C42C22×D25111yescharacteristic
290C23—20081no—
291C23—20081no—
292C23—5024no—
293C23—5021no—
294C23—5021no—
295C23—5021no—
296C23C2×D100411yescharacteristic
297Q8—20081no—
298Q8—5021no—
299Q8—5021no—
300D4—20081no—
301D4—5024no—
302D4—5021no—
303D4—5021no—
304D4—5021no—
305D4—5021no—
306D4—2512no—
307D4—2512no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—20081no—
311C2×C4—20081no—
312C2×C4—20081no—
313C2×C4—20081no—
314C2×C4—20081no—
315C2×C4—5021no—
316C2×C4—5021no—
317C2×C4—5021no—
318C2×C4—5021no—
319C2×C4—5021no—
320C2×C4C2×D100411yescharacteristic
321C2×C4C2×D100411yescharacteristic
322C2×C4C2×D100411yescharacteristic
323C2×C4C2×D100411yescharacteristic
324C2×C4C2×D100411yescharacteristic
325C2×C4C23×D25111yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—20084no—
334C22—10041no—
335C22—10041no—
336C22—10041no—
337C22—10041no—
338C22—10041no—
339C22—10041no—
340C22—10041no—
341C22—5022no—
342C22—5022no—
343C22C22×D100411yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—10041no—
350C4—10041no—
351C4—10041no—
352C4—10041no—
353C4—10041no—
354C4#41×D25111yescharacteristic
355C4#41×D25111yescharacteristic
356C2—41no—
357C2—20081no—
358C2—10042no—
359C2—10042no—
360C2#3063219911yescharacteristic
361C2#3063249211yescharacteristic
362C2#3063249911yescharacteristic
subgroupG/H
centerC22C22×D1004
commutator, cosocleC2×C4×C251C24
FrattiniC2×C4C23×D251
Fitting#433×C251C2
socleC22×C251C22×D4
prime radical#30631823C2
hypercenter#433D251
hypocenterC251#3118
LCSG ▷ C2×C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #30632308C2semidirect
2. #30632161C2semidirect
3. #30632029C2semidirect
4. #30632012C2semidirect
5. #30631978C2semidirect
6. #30631968C2semidirect
7. #30631903C2semidirect
8. #30631903C2semidirect
9. #30631840C2semidirect
11. #30631800C2semidirect
12. #30631789C2semidirect
13. C4×#16860799C2semidirect
14. C4×D2008C2semidirect
15. #433×C251C2semidirect
21. #22548715C22semidirect
23. #22548703C22semidirect
29. C4×Dic502C22semidirect
34. C4×D1004C22semidirect
40. #22548649C22semidirect
41. #22548649C22semidirect
42. #22548647C22semidirect
43. #22548647C22semidirect
44. #22548640C22semidirect
45. #22548640C22semidirect
50. #22548637C22semidirect
51. #22548637C22semidirect
53. C4⋊C8×C251C22semidirect
54. C4⋊C8×C251C22semidirect
57. #97×C251C22semidirect
58. C4×C8×C251C22semidirect
181. C251#3118semidirect
197. #433D251semidirect
227. C4⋊C8C2×D251semidirect
228. C4⋊C8C2×D251semidirect
239. #97C2×D251semidirect
240. C4×C8C2×D251semidirect

Maximal subgroups

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

subgroupindex
#306323082
#306321612
#306320292
#306320122
#306319782
#306319682
#306319032
#306318402
#306318232
#306318002
#306317892
C4×#168607992
C4×D20082
#433×C2512
#3118251