Finite Group Databasebeta

← #44560363

Subgroups — #44560363

Order 32128.

492 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#30632234C211yesmaximal, characteristic, complemented
2C4×D4×D251C211yesmaximal, characteristic, complemented
3#30632002C211yesmaximal, characteristic, complemented
4#30631999C211yesmaximal, characteristic, complemented
5#30631966C211yesmaximal, characteristic, complemented
6#30631965C211yesmaximal, characteristic, complemented
7#30631881C211yesmaximal, characteristic, complemented
8#30631880C211yesmaximal, characteristic, complemented
9#30631822C211yesmaximal, characteristic, complemented
10#30631819C211yesmaximal, characteristic, complemented
11C4×D2008C211yesmaximal, characteristic, complemented
12C4×#16860795C211yesmaximal, characteristic, complemented
13C4×#16860795C211yesmaximal, characteristic, complemented
14#30631738C211yesmaximal, characteristic, complemented
15C4×D8×C251C211yesmaximal, characteristic, complemented
16C2×#16860810—21no—
17C2×D4×D251C2211yescharacteristic
18C22×C4×D251—21no—
19C2×D2008C2211yescharacteristic
20C2×#16860795C2211yescharacteristic
21C2×#16860795C2211yescharacteristic
22#22548714C2211yescharacteristic, complemented
23#22548711C2211yescharacteristic, complemented
24#22548701—21no—
25#22548690C2211yescharacteristic
26#22548688—21no—
27#22548686C2211yescharacteristic
28C4×D1004C2211yescharacteristic
29C4×D1004C2211yescharacteristic, complemented
30D4×Dic251C2211yescharacteristic
31#22548677C2211yescharacteristic
32C4×C22⋊D251—21no—
33C4×C22⋊D251—21no—
34(C22⋊D251)⋊C4—21no—
35C4⋊C4×D251C2211yescharacteristic
36C22⋊C4×D251—21no—
37C42×D251C2211yescharacteristic
38#22548649C2211yescharacteristic, complemented
39#22548648C2211yescharacteristic, complemented
40#22548648C2211yescharacteristic, complemented
41Dic251⋊C8C2211yescharacteristic, complemented
42Dic251⋊C8C2211yescharacteristic, complemented
43#22548637C2211yescharacteristic
44#22548637C2211yescharacteristic, complemented
45#22548636C2211yescharacteristic
46#22548636C2211yescharacteristic, complemented
47#22548635C2211yescharacteristic
48#22548635C2211yescharacteristic, complemented
49(C2×D251)⋊C8C2211yescharacteristic
50(C2×D251)⋊C8C2211yescharacteristic
51C4×C251⋊C8C2211yescharacteristic, complemented
52C2×D8×C251C2211yescharacteristic
53C4×D4×C251C2211yescharacteristic
54C4×D4×C251C2211yescharacteristic, complemented
55#107×C251C2211yescharacteristic, complemented
56#102×C251C2211yescharacteristic
57#102×C251C2211yescharacteristic, complemented
58C4×C8×C251C2211yescharacteristic, complemented
59C23×D251—21no—
60#16860810—44no—
61C2×Dic502—21no—
62C2×D1004—21no—
63C2×D1004C2311yescharacteristic
64C2×D1004C2311yescharacteristic
65C2×C22⋊D251—21no—
66C2×C22⋊D251—21no—
67C2×C22⋊D251—21no—
68C2×C22⋊D251—21no—
69D4×D251—22no—
70D4×D251—22no—
71C22×Dic251—21no—
72C2×C4×D251—21no—
73C2×C4×D251—21no—
74C2×C4×D251—21no—
75C2×C4×D251—21no—
76C2×C4×D251—44no—
77C2×C4×D251D411yescharacteristic
78C2×C4×D251D411yescharacteristic
79C2×C4×D251C2311yescharacteristic
80D2008—22no—
81#16860795—22no—
82#16860795—22no—
83C2×C251⋊C8C2311yescharacteristic
84C2×C251⋊C8C2311yescharacteristic
85C4⋊Dic251C2311yescharacteristic
86C4⋊Dic251C2311yescharacteristic
87Dic251⋊C4—21no—
88Dic251⋊C4—21no—
89C22⋊Dic251—21no—
90C22⋊Dic251—21no—
91(C2×D251)⋊C4—21no—
92(C2×D251)⋊C4—21no—
93(C2×D251)⋊C4—21no—
94(C2×D251)⋊C4—21no—
95C4×Dic251D411yescharacteristic
96C4×Dic251D411yescharacteristic
97C4×Dic251C2311yescharacteristic
98C2×D4×C251C2311yescharacteristic
99C2×D4×C251C2311yescharacteristic
100C22×C4×C251—21no—
101C22×C4×C251—21no—
102D8×C251—22no—
103C2×C8×C251C2311yescharacteristic
104C2×C8×C251C2311yescharacteristic
105C4⋊C4×C251C2311yescharacteristic
106C4⋊C4×C251C2311yescharacteristic
107C22⋊C4×C251—21no—
108C22⋊C4×C251—21no—
109C42×C251C2311yescharacteristic
110C22×D251—24no—
111C22×D251—21no—
112C22×D251—21no—
113C22×D251—42no—
114C22×D251—42no—
115C22×D251C2×D411yescharacteristic
116Dic502—42no—
117D1004—21no—
118D1004—21no—
119D1004—21no—
120D1004—42no—
121D1004#4112yescomplemented
122C22⋊D251—24no—
123C22⋊D251—42no—
124C22⋊D251—42no—
125C22⋊D251—42no—
126C2×Dic251—21no—
127C2×Dic251—21no—
128C2×Dic251—42no—
129C2×Dic251C2×D411yescharacteristic
130C2×Dic251C2×D411yescharacteristic
131C2×Dic251C2×D411yescharacteristic
132C4×D251—21no—
133C4×D251—21no—
134C4×D251—41no—
135C4×D251—42no—
136C4×D251—42no—
137C4×D251—42no—
138C4×D251—42no—
139C4×D251D814yescomplemented
140C251⋊C8—21no—
141C251⋊C8—21no—
142C23×C251—21no—
143C23×C251—21no—
144D4×C251—21no—
145D4×C251—21no—
146D4×C251—21no—
147D4×C251#4112yescomplemented
148C2×C4×C251—21no—
149C2×C4×C251—21no—
150C2×C4×C251—42no—
151C2×C4×C251—42no—
152C2×C4×C251C2×D411yescharacteristic
153C2×C4×C251C2×D411yescharacteristic
154C2×C4×C251C2411yescharacteristic
155C8×C251—21no—
156C8×C251—21no—
157C22×C251—22no—
158C22×C251—41no—
159C22×C251—41no—
160C22×C251—41no—
161C22×C251—41no—
162C22×C251—41no—
163C22×C251C22×D411yescharacteristic
164C2×D251—21no—
165C2×D251—21no—
166C2×D251—22no—
167C2×D251—48no—
168C2×D251—41no—
169C2×D251—41no—
170C2×D251—41no—
171C2×D251—41no—
172C2×D251—41no—
173C2×D251C2×D812yes—
174C4×C251—21no—
175C4×C251—41no—
176C4×C251—41no—
177C4×C251C2×D812yes—
178C4×C251C2×#4111yescharacteristic
179C4×C251C2×#4111yescharacteristic
180Dic251—21no—
181Dic251—21no—
182Dic251—41no—
183Dic251—41no—
184Dic251C2×D812yes—
185C2×C251—42no—
186C2×C251—81no—
187C2×C251#52511yescharacteristic
188C2×C251C22×D811yescharacteristic
189C2×C251#57511yescharacteristic
190D251—22no—
191D251—42no—
192D251—81no—
193C251#310011yescharacteristic, complemented, Sylow
194#3100—2511nomaximal, Sylow
195#532—2511no—
196C2×C4×D4—2511no—
197#480—2511no—
198#480—2511no—
199#474—2511no—
200#474—2511no—
201#459—2511no—
202#459—2511no—
203#447—2511no—
204#447—2511no—
205C4×D8—2511no—
206C4×D8—2511no—
207C4×D8—2511no—
208C4×D8D25111yescharacteristic, complemented
209#431—2511no—
210C2×#41—5021no—
211C22×D4—2511no—
212C23×C4—5021no—
213C2×D8—2511no—
214C2×D8—2511no—
215C2×D8—2511no—
216C2×D8C2×D25111yescharacteristic
217C4⋊Q8—2511no—
218#127—2511no—
219#124—5021no—
220#121—5021no—
221#121—2511no—
222#121—2511no—
223C4×D4—5021no—
224C4×D4—5021no—
225C4×D4—5021no—
226C4×D4—2511no—
227C4×D4—2511no—
228C4×D4—2511no—
229C4×D4—2511no—
230C4×D4C2×D25111yescharacteristic
231C4×D4C2×D25111yescharacteristic, complemented
232C2×C4⋊C4—2511no—
233C2×C22⋊C4—5021no—
234C2×C42—2511no—
235#107—2511no—
236#107—2511no—
237#107—2511no—
238#107C2×D25111yescharacteristic, complemented
239C4⋊C8—2511no—
240C4⋊C8—2511no—
241#102—2511no—
242#102—2511no—
243#102—2511no—
244#102—2511no—
245#102—2511no—
246#102—2511no—
247#102C2×D25111yescharacteristic
248#102C2×D25111yescharacteristic, complemented
249C22⋊C8—2511no—
250C22⋊C8—2511no—
251C4×C8—2511no—
252C4×C8C2×D25111yescharacteristic, complemented
253C24—5021no—
254#41—10044no—
255C2×Q8—5021no—
256C2×D4—5021no—
257C2×D4—5022no—
258C2×D4—5021no—
259C2×D4—5022no—
260C2×D4—5021no—
261C2×D4—5021no—
262C2×D4—5021no—
263C2×D4—2511no—
264C2×D4—2511no—
265C2×D4C22×D25111yescharacteristic
266C2×D4C22×D25111yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—10044no—
270C22×C4—5021no—
271C22×C4—5021no—
272C22×C4—5021no—
273C22×C4—5021no—
274C22×C4—5021no—
275C22×C4—2511no—
276C22×C4—2511no—
277C22×C4—2511no—
278D8—22no—
279D8—5022no—
280D8—5022no—
281D8—5022no—
282C2×C8—2511no—
283C2×C8—2511no—
284C2×C8C22×D25111yescharacteristic
285C2×C8C22×D25111yescharacteristic
286C4⋊C4—5021no—
287C4⋊C4—5021no—
288C4⋊C4—2511no—
289C4⋊C4—2511no—
290C4⋊C4C22×D25111yescharacteristic
291C4⋊C4C22×D25111yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—5021no—
295C22⋊C4—5021no—
296C22⋊C4—5021no—
297C22⋊C4—5021no—
298C22⋊C4—5021no—
299C22⋊C4—5021no—
300C42—2511no—
301C42—2511no—
302C42—2511no—
303C42C22×D25111yescharacteristic
304C23—21no—
305C23—21no—
306C23—10042no—
307C23—10042no—
308C23—5024no—
309C23—5021no—
310C23—5021no—
311C23—2511no—
312Q8—10042no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—10042no—
317D4—10042no—
318D4—10042no—
319D4—10042no—
320D4—5024no—
321D4—5021no—
322D4—5021no—
323D4—5021no—
324D4—2512no—
325D4#1686081012yescomplemented
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—10041no—
331C2×C4—10042no—
332C2×C4—10042no—
333C2×C4—10042no—
334C2×C4—10042no—
335C2×C4—10042no—
336C2×C4—5021no—
337C2×C4—5021no—
338C2×C4—5021no—
339C2×C4—5021no—
340C2×C4—2511no—
341C2×C4—2511no—
342C2×C4—2511no—
343C2×C4—2514no—
344C2×C4D4×D25111yescharacteristic
345C2×C4D4×D25111yescharacteristic
346C2×C4C23×D25111yescharacteristic
347C8—21no—
348C8—21no—
349C8—5021no—
350C8—5021no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—10048no—
358C22—10041no—
359C22—10041no—
360C22—10041no—
361C22—10041no—
362C22—10041no—
363C22—5022no—
364C22—5021no—
365C22—5021no—
366C22—2512no—
367C22C2×D4×D25111yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—10041no—
372C4—10041no—
373C4—5021no—
374C4—5021no—
375C4—2512no—
376C4D8×D25112yes—
377C4#41×D25111yescharacteristic
378C4C2×#1686081011yescharacteristic
379C2—42no—
380C2—81no—
381C2—20081no—
382C2—10042no—
383C2—5022no—
384C2#3063219611yescharacteristic
385C2C2×D8×D25111yescharacteristic
386C2#3063248411yescharacteristic
subgroupG/H
centerC2×C4D4×D251
commutator, cosocleC2×C4×C251C24
FrattiniC2×C4C23×D251
FittingC4×D8×C251C2
socleC22×C251C22×D4
hypercenterC4×D8D251
hypocenterC251#3100
LCSG ▷ C2×C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #30632234C2semidirect
2. C4×D4×D251C2semidirect
3. #30632002C2semidirect
4. #30631999C2semidirect
5. #30631966C2semidirect
6. #30631965C2semidirect
7. #30631881C2semidirect
8. #30631880C2semidirect
9. #30631822C2semidirect
10. #30631819C2semidirect
11. C4×D2008C2semidirect
12. C4×#16860795C2semidirect
13. C4×#16860795C2semidirect
14. #30631738C2semidirect
15. C4×D8×C251C2semidirect
22. #22548714C22semidirect
23. #22548711C22semidirect
29. C4×D1004C22semidirect
38. #22548649C22semidirect
39. #22548648C22semidirect
40. #22548648C22semidirect
41. Dic251⋊C8C22semidirect
42. Dic251⋊C8C22semidirect
44. #22548637C22semidirect
46. #22548636C22semidirect
48. #22548635C22semidirect
51. C4×C251⋊C8C22semidirect
54. C4×D4×C251C22semidirect
55. #107×C251C22semidirect
57. #102×C251C22semidirect
58. C4×C8×C251C22semidirect
121. D1004#41semidirect
139. C4×D251D8semidirect
147. D4×C251#41semidirect
193. C251#3100semidirect
208. C4×D8D251semidirect
231. C4×D4C2×D251semidirect
238. #107C2×D251semidirect
248. #102C2×D251semidirect
252. C4×C8C2×D251semidirect
325. D4#16860810semidirect

Maximal subgroups

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

subgroupindex
#306322342
C4×D4×D2512
#306320022
#306319992
#306319662
#306319652
#306318812
#306318802
#306318222
#306318192
C4×D20082
C4×#168607952
#306317382
C4×D8×C2512
#3100251