Finite Group Databasebeta

← #44562269

Subgroups — #44562269

Order 32128.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#30632383C211yesmaximal, characteristic, complemented
2#30632346C211yesmaximal, characteristic, complemented
3#30632042C211yesmaximal, characteristic, complemented
4#30632029C211yesmaximal, characteristic, complemented
5#30632006C211yesmaximal, characteristic, complemented
6#30631995C211yesmaximal, characteristic, complemented
7#30631923C211yesmaximal, characteristic, complemented
8#30631916C211yesmaximal, characteristic, complemented
9#30631903C211yesmaximal, characteristic, complemented
10#30631834C211yesmaximal, characteristic, complemented
11#30631828C211yesmaximal, characteristic, complemented
12C4×#16860799C211yesmaximal, characteristic, complemented
13#30631684C211yesmaximal, characteristic, complemented
14C2×#22548640C211yesmaximal, characteristic, complemented
15C8×D4×C251C211yesmaximal, characteristic, complemented
16C2×#16860810C2211yescharacteristic
17C22×Dic502C2211yescharacteristic
18C2×#16860799C2211yescharacteristic
19C2×#16860799C2211yescharacteristic
20C2×D2008C2211yescharacteristic
21#22548710—21no—
22#22548707C2211yescharacteristic
23#22548703C2211yescharacteristic
24#22548701—21no—
25#22548697—21no—
26#22548694C2211yescharacteristic
27#22548693—21no—
28#22548689C2211yescharacteristic
29#22548689C2211yescharacteristic
30#22548689C2211yescharacteristic
31#22548687—21no—
32#22548687—21no—
33C4×Dic502C2211yescharacteristic
34C4×D1004C2211yescharacteristic
35(C22⋊D251)⋊C4—21no—
36(C22⋊D251)⋊C4—21no—
37#22548674C2211yescharacteristic
38C2×C4⋊Dic251C2211yescharacteristic
39#22548649C2211yescharacteristic
40#22548647C2211yescharacteristic
41#22548647C2211yescharacteristic
42#22548640C2211yescharacteristic
43#22548640C2211yescharacteristic
44#22548640C2211yescharacteristic
45#22548640C2211yescharacteristic
46#22548640C2211yescharacteristic
47#22548640C2211yescharacteristic
48#22548637C2211yescharacteristic
49#22548637C2211yescharacteristic
50#22548637C2211yescharacteristic
51#22548637C2211yescharacteristic
52C22×C8×C251C2211yescharacteristic
53C22×C8×C251C2211yescharacteristic
54C4×D4×C251C2211yescharacteristic
55C4⋊C8×C251C2211yescharacteristic
56C22⋊C8×C251C2211yescharacteristic
57C22⋊C8×C251C2211yescharacteristic
58C4×C8×C251C2211yescharacteristic
59#16860810—22no—
60#16860810—41no—
61C2×Dic502—22no—
62C2×Dic502—21no—
63C2×Dic502—41no—
64C2×Dic502C2311yescharacteristic
65C2×Dic502C2311yescharacteristic
66C2×D1004C2311yescharacteristic
67C2×D1004C2311yescharacteristic
68C2×C22⋊D251—21no—
69C2×C22⋊D251—21no—
70C2×C22⋊D251—21no—
71C2×C22⋊D251—21no—
72C22×Dic251—21no—
73C22×Dic251—21no—
74C2×C4×D251—21no—
75C2×C4×D251—21no—
76#16860799—22no—
77#16860799—41no—
78D2008—41no—
79C4⋊Dic251—21no—
80C4⋊Dic251C2311yescharacteristic
81C4⋊Dic251C2311yescharacteristic
82C4⋊Dic251C2311yescharacteristic
83C4⋊Dic251C2311yescharacteristic
84Dic251⋊C4—21no—
85Dic251⋊C4—21no—
86Dic251⋊C4—21no—
87Dic251⋊C4—21no—
88C22⋊Dic251—21no—
89C22⋊Dic251—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—
95(C2×D251)⋊C4—21no—
96C4×Dic251—21no—
97C4×Dic251—21no—
98C2×D4×C251D411yescharacteristic
99C22×C4×C251C2311yescharacteristic
100C22×C4×C251C2311yescharacteristic
101C2×C8×C251—41no—
102C2×C8×C251—41no—
103C2×C8×C251C2311yescharacteristic
104C2×C8×C251C2311yescharacteristic
105C2×C8×C251C2311yescharacteristic
106C2×C8×C251C2311yescharacteristic
107C4⋊C4×C251D411yescharacteristic
108C22⋊C4×C251D411yescharacteristic
109C22⋊C4×C251D411yescharacteristic
110C42×C251C2311yescharacteristic
111C22×D251—21no—
112C22×D251—21no—
113Dic502—21no—
114Dic502—21no—
115Dic502—21no—
116Dic502—42no—
117Dic502#4112yes—
118D1004—21no—
119D1004—21no—
120D1004—21no—
121D1004—21no—
122C22⋊D251—42no—
123C22⋊D251—42no—
124C22⋊D251—42no—
125C22⋊D251—81no—
126C2×Dic251—21no—
127C2×Dic251—21no—
128C2×Dic251—21no—
129C2×Dic251—21no—
130C2×Dic251—21no—
131C2×Dic251—21no—
132C2×Dic251—42no—
133C2×Dic251—81no—
134C4×D251—42no—
135C4×D251—81no—
136C23×C251C2×D411yescharacteristic
137C23×C251C2×D411yescharacteristic
138D4×C251—22no—
139C2×C4×C251—21no—
140C2×C4×C251—21no—
141C2×C4×C251—21no—
142C2×C4×C251—21no—
143C2×C4×C251C2×D411yescharacteristic
144C2×C4×C251C2×D411yescharacteristic
145C2×C4×C251C2×D411yescharacteristic
146C2×C4×C251C2×D411yescharacteristic
147C2×C4×C251C2411yescharacteristic
148C8×C251—21no—
149C8×C251—21no—
150C8×C251—21no—
151C8×C251—21no—
152C22×C251—21no—
153C22×C251—21no—
154C22×C251—21no—
155C22×C251—21no—
156C22×C251—21no—
157C22×C251#13512yes—
158C22×C251C22×D411yescharacteristic
159C2×D251—41no—
160C2×D251—41no—
161C2×D251—41no—
162C2×D251—41no—
163C2×D251—41no—
164C2×D251—41no—
165C4×C251—21no—
166C4×C251—21no—
167C4×C251—21no—
168C4×C251—21no—
169C4×C251C2×#4111yescharacteristic
170C4×C251H(5,𝔽2)11yescharacteristic
171Dic251—22no—
172Dic251—41no—
173Dic251—41no—
174Dic251—41no—
175Dic251—41no—
176Dic251—41no—
177C2×C251—22no—
178C2×C251—41no—
179C2×C251#54611yescharacteristic
180C2×C251C2×#13511yescharacteristic
181C2×C251#57711yescharacteristic
182D251—81no—
183D251—81no—
184C251#330111yescharacteristic, complemented, Sylow
185#3301—2511nomaximal, Sylow
186#553—2511no—
187#548—2511no—
188#488—2511no—
189#485—2511no—
190#481—2511no—
191#479—2511no—
192#466—2511no—
193#465—2511no—
194#463—2511no—
195#449—2511no—
196#448—2511no—
197C4×SD16—2511no—
198C8×D4D25111yescharacteristic, complemented
199#416—2511no—
200C2×#103—2511no—
201C2×#41—2511no—
202C22×Q8—2511no—
203C2×SD16—2511no—
204C2×SD16—2511no—
205C2×D8—2511no—
206C22×C8C2×D25111yescharacteristic
207C22×C8C2×D25111yescharacteristic
208#126—5021no—
209#125—2511no—
210#124—5021no—
211#124—2511no—
212#123—5021no—
213C22⋊Q8—5021no—
214C22⋊Q8—2511no—
215#121—5021no—
216#121—5021no—
217#121—2511no—
218#121—2511no—
219#121—2511no—
220C4×Q8—2511no—
221C4×D4—5021no—
222C4×D4—5021no—
223C4×D4—2511no—
224C4×D4C2×D25111yescharacteristic
225#117—2511no—
226C2×C4⋊C4—2511no—
227#107—2511no—
228#106—2511no—
229#106—2511no—
230C4⋊C8C2×D25111yescharacteristic
231#103—2511no—
232#103—2511no—
233#103—2511no—
234#103—2511no—
235#103—2511no—
236#103—2511no—
237#102—2511no—
238#102—2511no—
239#102—2511no—
240#102—2511no—
241C22⋊C8C2×D25111yescharacteristic
242C22⋊C8C2×D25111yescharacteristic
243C4×C8C2×D25111yescharacteristic
244#41—10041no—
245#41—5022no—
246C2×Q8—10041no—
247C2×Q8—5022no—
248C2×Q8—5021no—
249C2×Q8—2511no—
250C2×Q8—2511no—
251C2×D4—5021no—
252C2×D4—5021no—
253C2×D4—5021no—
254C2×D4—5021no—
255C2×D4—2511no—
256C2×D4—2511no—
257C2×D4D100411yescharacteristic
258C22×C4—5021no—
259C22×C4—5021no—
260C22×C4—5021no—
261C22×C4—5021no—
262C22×C4C22×D25111yescharacteristic
263C22×C4C22×D25111yescharacteristic
264SD16—10041no—
265SD16—5022no—
266D8—10041no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8C22×D25111yescharacteristic
270C2×C8C22×D25111yescharacteristic
271C2×C8C22×D25111yescharacteristic
272C2×C8C22×D25111yescharacteristic
273C4⋊C4—5021no—
274C4⋊C4—5021no—
275C4⋊C4—5021no—
276C4⋊C4—5021no—
277C4⋊C4—5021no—
278C4⋊C4—2511no—
279C4⋊C4—2511no—
280C4⋊C4—2511no—
281C4⋊C4—2511no—
282C4⋊C4D100411yescharacteristic
283C22⋊C4—5021no—
284C22⋊C4—5021no—
285C22⋊C4—5021no—
286C22⋊C4—5021no—
287C22⋊C4—5021no—
288C22⋊C4—5021no—
289C22⋊C4—5021no—
290C22⋊C4—5021no—
291C22⋊C4D100411yescharacteristic
292C22⋊C4D100411yescharacteristic
293C42—5021no—
294C42—5021no—
295C42C22×D25111yescharacteristic
296C23—5021no—
297C23—5021no—
298C23C2×D100411yescharacteristic
299C23C2×D100411yescharacteristic
300Q8—10042no—
301Q8—5021no—
302Q8—5021no—
303Q8—5021no—
304Q8—2512no—
305D4—22no—
306D4—20081no—
307D4—10042no—
308D4—10042no—
309D4—10042no—
310D4—5021no—
311D4—5021no—
312D4—5021no—
313D4—5021no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—20081no—
319C2×C4—20081no—
320C2×C4—10042no—
321C2×C4—10042no—
322C2×C4—5021no—
323C2×C4—5021no—
324C2×C4—5021no—
325C2×C4—5021no—
326C2×C4—5021no—
327C2×C4—5021no—
328C2×C4C2×D100411yescharacteristic
329C2×C4C2×D100411yescharacteristic
330C2×C4C2×D100411yescharacteristic
331C2×C4C2×D100411yescharacteristic
332C2×C4C23×D25111yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—10041no—
343C22—10041no—
344C22—10041no—
345C22—10041no—
346C22—10041no—
347C22—10041no—
348C22#2254873712yes—
349C22C22×D100411yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—10041no—
355C4—10041no—
356C4—10041no—
357C4—10041no—
358C4—10041no—
359C4—5022no—
360C4#41×D25111yescharacteristic
361C4#2254876011yescharacteristic
362C2—22no—
363C2—41no—
364C2—20081no—
365C2—20081no—
366C2#3063233211yescharacteristic
367C2C2×#2254873711yescharacteristic
368C2#3063249911yescharacteristic
subgroupG/H
centerC22C22×D1004
commutator, cosocleC2×C4×C251C24
FrattiniC2×C4C23×D251
FittingC8×D4×C251C2
socleC22×C251C22×D4
hypercenterC8×D4D251
hypocenterC251#3301
LCSG ▷ C2×C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #30632383C2semidirect
2. #30632346C2semidirect
3. #30632042C2semidirect
4. #30632029C2semidirect
5. #30632006C2semidirect
6. #30631995C2semidirect
7. #30631923C2semidirect
8. #30631916C2semidirect
9. #30631903C2semidirect
10. #30631834C2semidirect
11. #30631828C2semidirect
12. C4×#16860799C2semidirect
13. #30631684C2semidirect
14. C2×#22548640C2semidirect
15. C8×D4×C251C2semidirect
184. C251#3301semidirect
198. C8×D4D251semidirect

Maximal subgroups

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

subgroupindex
#306323832
#306323462
#306320422
#306320292
#306320062
#306319952
#306319232
#306319162
#306319032
#306318342
#306318282
C4×#168607992
#306316842
C2×#225486402
C8×D4×C2512
#3301251