Finite Group Databasebeta

← #44559243

Subgroups — #44559243

Order 32128.

484 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
1C2×#22548736C211yesmaximal, characteristic
2#30632169C211yesmaximal, characteristic, complemented
3#30632166C211yesmaximal, characteristic, complemented
4#30631797C211yesmaximal, characteristic, complemented
5#30631796C211yesmaximal, characteristic, complemented
6#30631792C211yesmaximal, characteristic, complemented
7#30631791C211yesmaximal, characteristic, complemented
8C4×#16860799C211yesmaximal, characteristic, complemented
9SD16×Dic251C211yesmaximal, characteristic, complemented
10#30631774C211yesmaximal, characteristic, complemented
11#106×D251C211yesmaximal, characteristic, complemented
12#30631687C211yesmaximal, characteristic, complemented
13#30631685C211yesmaximal, characteristic, complemented
14#30631641C211yesmaximal, characteristic, complemented
15C4×SD16×C251C211yesmaximal, characteristic, complemented
16C2×#16860811C2211yescharacteristic
17C2×#16860809C2211yescharacteristic
18#22548736C418yescomplemented
19C2×#16860800C2211yescharacteristic
20C2×#16860799C2211yescharacteristic
21C2×#16860795C2211yescharacteristic
22C2×#16860793C2211yescharacteristic
23C2×C8×D251C2211yescharacteristic
24Q8×Dic251C2211yescharacteristic
25C4×Dic502C2211yescharacteristic
26#22548680C2211yescharacteristic
27C4×D1004—21no—
28C4×D1004C2211yescharacteristic
29D4×Dic251C2211yescharacteristic
30#22548677—21no—
31#22548677C2211yescharacteristic
32C4×C22⋊D251—21no—
33(C22⋊D251)⋊C4—21no—
34#22548672—21no—
35#22548672C2211yescharacteristic
36#22548671—21no—
37C2×Dic251⋊C4—21no—
38C4⋊C4×D251—21no—
39C4⋊C4×D251C2211yescharacteristic
40C4⋊C4×D251C2211yescharacteristic
41#22548647C2211yescharacteristic
42#22548646C2211yescharacteristic
43#22548646C2211yescharacteristic
44#22548640C2211yescharacteristic
45#22548639C2211yescharacteristic
46#22548638C2211yescharacteristic
47#22548637C2211yescharacteristic
48#22548636C2211yescharacteristic
49#22548635C2211yescharacteristic
50#22548626C2211yescharacteristic
51#22548625C2211yescharacteristic
52C8×Dic251C2211yescharacteristic
53C2×SD16×C251C2211yescharacteristic
54C4×Q8×C251C2211yescharacteristic
55C4×D4×C251C2211yescharacteristic
56#106×C251C2211yescharacteristic
57#103×C251C2211yescharacteristic
58#102×C251C2211yescharacteristic
59C4×C8×C251C2211yescharacteristic
60#16860811—22no—
61#16860811C2×C414yescomplemented
62#16860809—22no—
63#16860809C2×C414yescomplemented
64C2×Dic502C2311yescharacteristic
65C2×D1004—21no—
66C2×D1004C2311yescharacteristic
67C2×C22⋊D251—21no—
68C22×Dic251—21no—
69C22×Dic251—21no—
70C2×C4×D251—21no—
71C2×C4×D251—21no—
72C2×C4×D251—21no—
73C2×C4×D251—21no—
74C2×C4×D251—21no—
75C2×C4×D251C2311yescharacteristic
76#16860800C2×C414yescomplemented
77#16860799C2×C414yescomplemented
78#16860795C2×C414yescomplemented
79#16860793—22no—
80C2×C251⋊C8C2311yescharacteristic
81C2×C251⋊C8C2311yescharacteristic
82C8×D251C2×C414yescomplemented
83C4⋊Dic251—21no—
84C4⋊Dic251C2311yescharacteristic
85C4⋊Dic251C2311yescharacteristic
86Dic251⋊C4—21no—
87Dic251⋊C4—21no—
88Dic251⋊C4—21no—
89Dic251⋊C4—21no—
90Dic251⋊C4D411yescharacteristic
91Dic251⋊C4D411yescharacteristic
92C22⋊Dic251—21no—
93(C2×D251)⋊C4—21no—
94(C2×D251)⋊C4—21no—
95(C2×D251)⋊C4D411yescharacteristic
96(C2×D251)⋊C4D411yescharacteristic
97C4×Dic251—21no—
98C4×Dic251—21no—
99C4×Dic251—21no—
100C4×Dic251C2311yescharacteristic
101C2×Q8×C251C2311yescharacteristic
102C2×D4×C251C2311yescharacteristic
103C22×C4×C251—21no—
104SD16×C251C2×C414yescomplemented
105C2×C8×C251C2311yescharacteristic
106C2×C8×C251C2311yescharacteristic
107C4⋊C4×C251—21no—
108C4⋊C4×C251C2311yescharacteristic
109C4⋊C4×C251C2311yescharacteristic
110C22⋊C4×C251—21no—
111C42×C251—21no—
112C42×C251C2311yescharacteristic
113C22×D251—21no—
114C22×D251C2×D411yescharacteristic
115Dic502—21no—
116Dic502C22×C412yes—
117D1004—24no—
118D1004—21no—
119D1004C22×C412yes—
120C22⋊D251—24no—
121C2×Dic251—21no—
122C2×Dic251—24no—
123C2×Dic251—21no—
124C2×Dic251—21no—
125C2×Dic251—81no—
126C2×Dic251C2×D411yescharacteristic
127C2×Dic251C2×D411yescharacteristic
128C2×Dic251C2×D411yescharacteristic
129C4×D251—24no—
130C4×D251—81no—
131C4×D251—81no—
132C4×D251—81no—
133C4×D251—81no—
134C4×D251C22×C412yes—
135C4×D251#4112yes—
136C251⋊C8—21no—
137C251⋊C8C22×C412yes—
138C23×C251—21no—
139Q8×C251—21no—
140Q8×C251C22×C412yes—
141D4×C251—21no—
142D4×C251C22×C412yes—
143C2×C4×C251—21no—
144C2×C4×C251—21no—
145C2×C4×C251—21no—
146C2×C4×C251—81no—
147C2×C4×C251C2×D411yescharacteristic
148C2×C4×C251C2×D411yescharacteristic
149C2×C4×C251C2411yescharacteristic
150C8×C251—21no—
151C8×C251C22×C412yes—
152C22×C251—22no—
153C22×C251—41no—
154C22×C251—41no—
155C22×C251C22×D411yescharacteristic
156C2×D251—21no—
157C2×D251—21no—
158C2×D251—22no—
159C2×D251—41no—
160C2×D251—41no—
161C2×D251C4×D412yes—
162C4×C251—22no—
163C4×C251—21no—
164C4×C251—21no—
165C4×C251—41no—
166C4×C251—41no—
167C4×C251C23×C411yescharacteristic
168C4×C251C2×#4111yescharacteristic
169Dic251—22no—
170Dic251—21no—
171Dic251—21no—
172Dic251—41no—
173Dic251—41no—
174Dic251C4×D412yes—
175C2×C251—42no—
176C2×C251C2×C4×D411yescharacteristic
177C2×C251#57711yescharacteristic
178C2×C251#57711yescharacteristic
179D251—22no—
180D251—42no—
181C251#295211yescharacteristic, complemented, Sylow
182#2952—2511nomaximal, Sylow
183C2×#135—2511no—
184#520—2511no—
185#520—2511no—
186#442—2511no—
187#442—2511no—
188#441—2511no—
189#441—2511no—
190C4×SD16—2511no—
191C4×SD16—2511no—
192C4×SD16—2511no—
193C4×SD16D25111yescharacteristic, complemented
194C2×#106—2511no—
195#417—2511no—
196#417—2511no—
197#405—2511no—
198C2×#41—2511no—
199C2×#41—2511no—
200#135—2518no—
201C2×Q16—2511no—
202C2×SD16—2511no—
203C2×SD16C2×D25111yescharacteristic
204C2×D8—2511no—
205C2×M16—2511no—
206C22×C8—2511no—
207C4×Q8—2511no—
208C4×Q8—2511no—
209C4×Q8—2511no—
210C4×Q8C2×D25111yescharacteristic
211C4×D4—5021no—
212C4×D4—5021no—
213C4×D4—5021no—
214C4×D4—5021no—
215C4×D4—2511no—
216C4×D4—2511no—
217C4×D4—2511no—
218C4×D4C2×D25111yescharacteristic
219#117—5021no—
220#117—5021no—
221#117—2511no—
222C2×C4⋊C4—5021no—
223C2×C4⋊C4—5021no—
224C2×C4⋊C4—2511no—
225C2×C4⋊C4—2511no—
226#106—2511no—
227#106—2511no—
228#106—2511no—
229#106C2×D25111yescharacteristic
230#103—2511no—
231#103—2511no—
232#103—2511no—
233#103C2×D25111yescharacteristic
234#102—2511no—
235#102—2511no—
236#102—2511no—
237#102C2×D25111yescharacteristic
238#97—2511no—
239#97—2511no—
240C4×C8—2511no—
241C4×C8C2×D25111yescharacteristic
242#41—5022no—
243#41—5022no—
244#41—2514no—
245#41—2514no—
246C2×Q8—2511no—
247C2×Q8C22×D25111yescharacteristic
248C2×D4—5021no—
249C2×D4—5021no—
250C2×D4—2511no—
251C2×D4C22×D25111yescharacteristic
252C22×C4—21no—
253C22×C4—5021no—
254C22×C4—5021no—
255C22×C4—5021no—
256C22×C4—5021no—
257C22×C4—5021no—
258C22×C4—5021no—
259C22×C4—5021no—
260C22×C4—2511no—
261Q16—2514no—
262SD16—2514no—
263SD16C4×D25114yescomplemented
264D8—2514no—
265M16—5022no—
266C2×C8—2511no—
267C2×C8—2511no—
268C2×C8—2514no—
269C2×C8C22×D25111yescharacteristic
270C2×C8C22×D25111yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—5021no—
273C4⋊C4—5021no—
274C4⋊C4—5021no—
275C4⋊C4—5021no—
276C4⋊C4—5021no—
277C4⋊C4—2511no—
278C4⋊C4—2511no—
279C4⋊C4—2511no—
280C4⋊C4—2511no—
281C4⋊C4C22×D25111yescharacteristic
282C4⋊C4C22×D25111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—5021no—
285C22⋊C4—5021no—
286C22⋊C4—5021no—
287C22⋊C4—2511no—
288C22⋊C4—2511no—
289C42—21no—
290C42—5021no—
291C42—5021no—
292C42—5021no—
293C42—2511no—
294C42C22×D25111yescharacteristic
295C23—21no—
296C23—5021no—
297C23—2511no—
298Q8—21no—
299Q8—5021no—
300Q8—2512no—
301Q8C2×C4×D25112yes—
302D4—21no—
303D4—5024no—
304D4—5024no—
305D4—5021no—
306D4—2512no—
307D4C2×C4×D25112yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—20081no—
313C2×C4—20081no—
314C2×C4—20081no—
315C2×C4—20081no—
316C2×C4—20081no—
317C2×C4—5024no—
318C2×C4—5021no—
319C2×C4—5021no—
320C2×C4—5021no—
321C2×C4—5024no—
322C2×C4—2511no—
323C2×C4—2511no—
324C2×C4—2511no—
325C2×C4—2512no—
326C2×C4—2512no—
327C2×C4D4×D25111yescharacteristic
328C2×C4D4×D25111yescharacteristic
329C2×C4C23×D25111yescharacteristic
330C8—21no—
331C8—5021no—
332C8—2512no—
333C8C2×C4×D25112yes—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—10041no—
338C22—10041no—
339C22—5022no—
340C22—5021no—
341C22—5021no—
342C22—2512no—
343C22C2×D4×D25111yescharacteristic
344C4—21no—
345C4—21no—
346C4—22no—
347C4—41no—
348C4—41no—
349C4—10041no—
350C4—10041no—
351C4—5021no—
352C4—5021no—
353C4—5022no—
354C4—2512no—
355C4C22×C4×D25111yescharacteristic
356C4#41×D25111yescharacteristic
357C2—42no—
358C2—10042no—
359C2—5022no—
360C2C4×D4×D25111yescharacteristic
361C2#3063249311yescharacteristic
362C2#3063249411yescharacteristic
subgroupG/H
centerC22C2×D4×D251
commutatorC4×C251C23×C4
FrattiniC2×C4C23×D251
FittingC4×SD16×C251C2
socleC22×C251C22×D4
prime radicalC2×#22548736C2
cosocleC2×C4×C251C24
hypercenterC4×SD16D251
hypocenterC251#2952
LCSG ▷ C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #30632169C2semidirect
3. #30632166C2semidirect
4. #30631797C2semidirect
5. #30631796C2semidirect
6. #30631792C2semidirect
7. #30631791C2semidirect
8. C4×#16860799C2semidirect
9. SD16×Dic251C2semidirect
10. #30631774C2semidirect
11. #106×D251C2semidirect
12. #30631687C2semidirect
13. #30631685C2semidirect
14. #30631641C2semidirect
15. C4×SD16×C251C2semidirect
18. #22548736C4semidirect
61. #16860811C2×C4semidirect
63. #16860809C2×C4semidirect
76. #16860800C2×C4semidirect
77. #16860799C2×C4semidirect
78. #16860795C2×C4semidirect
82. C8×D251C2×C4semidirect
104. SD16×C251C2×C4semidirect
181. C251#2952semidirect
193. C4×SD16D251semidirect
263. SD16C4×D251semidirect

Maximal subgroups

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

subgroupindex
C2×#225487362
#306321692
#306321662
#306317972
#306317962
#306317922
#306317912
C4×#168607992
SD16×Dic2512
#306317742
#106×D2512
#306316872
#306316852
#306316412
C4×SD16×C2512
#2952251