Finite Group Databasebeta

← #44560338

Subgroups — #44560338

Order 32128.

398 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#30632266C211yesmaximal, characteristic
2#30632168C211yesmaximal, characteristic, complemented
3#30632030C211yesmaximal, characteristic, complemented
4#30632029C211yesmaximal, characteristic, complemented
5#30632024C211yesmaximal, characteristic, complemented
6#30632022C211yesmaximal, characteristic, complemented
7#30632010C211yesmaximal, characteristic, complemented
8#30632008C211yesmaximal, characteristic, complemented
9#30631999C211yesmaximal, characteristic, complemented
10#30631728C211yesmaximal, characteristic, complemented
11#107×D251C211yesmaximal, characteristic, complemented
12#30631685C211yesmaximal, characteristic, complemented
13#30631680C211yesmaximal, characteristic, complemented
14#30631652C211yesmaximal, characteristic, complemented
15#480×C251C211yesmaximal, characteristic, complemented
16C2×#16860810C2211yescharacteristic
17C2×#16860809C2211yescharacteristic
18C2×#16860793C2211yescharacteristic
19C2×C8×D251C2211yescharacteristic
20#22548695C2211yescharacteristic
21#22548694C2211yescharacteristic
22#22548692—21no—
23#22548688—21no—
24#22548687—21no—
25#22548686—21no—
26#22548686C2211yescharacteristic
27#22548680—21no—
28#22548677—21no—
29C4×C22⋊D251—21no—
30C4×C22⋊D251—21no—
31#22548674C2211yescharacteristic
32#22548673C2211yescharacteristic
33#22548673C2211yescharacteristic
34C4⋊C4×D251C2211yescharacteristic
35C4⋊C4×D251C2211yescharacteristic
36C4⋊C4×D251C2211yescharacteristic
37#22548649C2211yescharacteristic
38#22548648C2211yescharacteristic
39#22548648C2211yescharacteristic
40#22548648C2211yescharacteristic
41#22548647C2211yescharacteristic
42#22548646C2211yescharacteristic
43#22548640C2211yescharacteristic
44#22548640C2211yescharacteristic
45#22548638C2211yescharacteristic
46#22548638C2211yescharacteristic
47#22548636C2211yescharacteristic
48#22548636C2211yescharacteristic
49C22⋊(C251⋊C8)C2211yescharacteristic
50(C2×D251)⋊C8C2211yescharacteristic
51(C2×D251)⋊C8C2211yescharacteristic
52#121×C251C2211yescharacteristic
53C2×C4⋊C4×C251C2211yescharacteristic
54#107×C251C2211yescharacteristic
55#107×C251C2211yescharacteristic
56#102×C251C2211yescharacteristic
57#102×C251C2211yescharacteristic
58C22⋊C8×C251C2211yescharacteristic
59#16860810—22no—
60#16860810—22no—
61#16860809—22no—
62#16860809—22no—
63C2×Dic502D411yescharacteristic
64C2×Dic502C2311yescharacteristic
65C2×D1004D411yescharacteristic
66C2×C22⋊D251—21no—
67C2×C22⋊D251—21no—
68C2×C22⋊D251D411yescharacteristic
69C2×C22⋊D251D411yescharacteristic
70C22×Dic251—21no—
71C2×C4×D251—21no—
72C2×C4×D251—21no—
73C2×C4×D251—21no—
74C2×C4×D251C2311yescharacteristic
75C2×C4×D251C2311yescharacteristic
76#16860793—22no—
77C2×C251⋊C8C2311yescharacteristic
78C2×C251⋊C8C2311yescharacteristic
79C8×D251—22no—
80C4⋊Dic251—21no—
81C4⋊Dic251C2311yescharacteristic
82C4⋊Dic251C2311yescharacteristic
83C4⋊Dic251C2311yescharacteristic
84Dic251⋊C4—21no—
85Dic251⋊C4—21no—
86Dic251⋊C4—21no—
87Dic251⋊C4—21no—
88C22⋊Dic251—21no—
89C22⋊Dic251—21no—
90C22⋊Dic251—21no—
91(C2×D251)⋊C4—21no—
92(C2×D251)⋊C4—21no—
93(C2×D251)⋊C4—21no—
94C4×Dic251—21no—
95C4×Dic251—21no—
96C4×Dic251—21no—
97C2×D4×C251—21no—
98C2×D4×C251C2311yescharacteristic
99C22×C4×C251—21no—
100C22×C4×C251C2311yescharacteristic
101C2×C8×C251C2311yescharacteristic
102C2×C8×C251C2311yescharacteristic
103C4⋊C4×C251—21no—
104C4⋊C4×C251C2311yescharacteristic
105C4⋊C4×C251C2311yescharacteristic
106C4⋊C4×C251C2311yescharacteristic
107C22⋊C4×C251—21no—
108C22×D251C2×D411yescharacteristic
109C22×D251C2×D411yescharacteristic
110Dic502—22no—
111Dic502—21no—
112Dic502—21no—
113D1004—22no—
114C22⋊D251—22no—
115C22⋊D251—22no—
116C22⋊D251—42no—
117C22⋊D251—81no—
118C2×Dic251—21no—
119C2×Dic251—21no—
120C2×Dic251—21no—
121C2×Dic251—21no—
122C2×Dic251—42no—
123C2×Dic251C2×D411yescharacteristic
124C2×Dic251C2×D411yescharacteristic
125C4×D251—21no—
126C4×D251—21no—
127C4×D251—81no—
128C4×D251—81no—
129C4×D251—81no—
130C4×D251#4112yes—
131C4×D251#4112yes—
132C251⋊C8—21no—
133C251⋊C8—21no—
134C23×C251—21no—
135C23×C251C2×D411yescharacteristic
136D4×C251—21no—
137D4×C251—21no—
138D4×C251—81no—
139C2×C4×C251—21no—
140C2×C4×C251—21no—
141C2×C4×C251—21no—
142C2×C4×C251—21no—
143C2×C4×C251—21no—
144C2×C4×C251—81no—
145C2×C4×C251C2×D411yescharacteristic
146C2×C4×C251C2411yescharacteristic
147C8×C251—21no—
148C8×C251—21no—
149C22×C251—21no—
150C22×C251—21no—
151C22×C251—21no—
152C22×C251—41no—
153C22×C251—41no—
154C22×C251—41no—
155C22×C251C22×D411yescharacteristic
156C2×D251—21no—
157C2×D251—21no—
158C2×D251—21no—
159C2×D251—21no—
160C2×D251—21no—
161C2×D251#12312yes—
162C4×C251—21no—
163C4×C251—41no—
164C4×C251—41no—
165C4×C251—41no—
166C4×C251C2×#4111yescharacteristic
167C4×C251C2×#4111yescharacteristic
168Dic251—21no—
169Dic251—41no—
170Dic251—41no—
171Dic251—41no—
172Dic251—41no—
173Dic251#12312yes—
174C2×C251—41no—
175C2×C251—81no—
176C2×C251C2×#12311yescharacteristic
177C2×C251#57611yescharacteristic
178C2×C251#57811yescharacteristic
179D251—22no—
180D251—41no—
181C251#309811yescharacteristic, complemented, Sylow
182#3098—2511nomaximal, Sylow
183#537—2511no—
184#520—2511no—
185#485—2511no—
186#485—2511no—
187#484—2511no—
188#484—2511no—
189#482—2511no—
190#482—2511no—
191#480—2511no—
192#480D25111yescharacteristic, complemented
193#428—2511no—
194C2×#107—2511no—
195#417—2511no—
196#416—2511no—
197#408—2511no—
198C2×#41—2511no—
199C2×#41—2511no—
200C2×M16—2511no—
201C22×C8—2511no—
202C22⋊Q8—5021no—
203C22⋊Q8—2511no—
204C22⋊Q8—2511no—
205#121—5021no—
206#121—5021no—
207#121—5021no—
208#121—2511no—
209#121C2×D25111yescharacteristic
210C4×Q8—5021no—
211C4×D4—5021no—
212C4×D4—5021no—
213C4×D4—5021no—
214#117—2511no—
215#117—2511no—
216#117—2511no—
217C2×C4⋊C4—2511no—
218C2×C4⋊C4—2511no—
219C2×C4⋊C4—2511no—
220C2×C4⋊C4C2×D25111yescharacteristic
221#107—2511no—
222#107—2511no—
223#107—2511no—
224#107—2511no—
225#107C2×D25111yescharacteristic
226#107C2×D25111yescharacteristic
227#106—2511no—
228#106—2511no—
229#103—2511no—
230#103—2511no—
231#103—2511no—
232#103—2511no—
233#102—2511no—
234#102—2511no—
235#102C2×D25111yescharacteristic
236#102C2×D25111yescharacteristic
237C22⋊C8—2511no—
238C22⋊C8—2511no—
239C22⋊C8—2511no—
240C22⋊C8C2×D25111yescharacteristic
241#41—5022no—
242#41—5022no—
243#41—5022no—
244#41—5022no—
245C2×Q8—2511no—
246C2×Q8—2511no—
247C2×D4—21no—
248C2×D4—5021no—
249C2×D4—5021no—
250C2×D4—2511no—
251C2×D4—2511no—
252C2×D4—2511no—
253C2×D4C22×D25111yescharacteristic
254C22×C4—21no—
255C22×C4—5021no—
256C22×C4—5021no—
257C22×C4—5021no—
258C22×C4—5021no—
259C22×C4—2511no—
260C22×C4—2511no—
261C22×C4C22×D25111yescharacteristic
262M16—5022no—
263C2×C8—5022no—
264C2×C8—2511no—
265C2×C8—2511no—
266C2×C8C22×D25111yescharacteristic
267C2×C8C22×D25111yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—5021no—
270C4⋊C4—5021no—
271C4⋊C4—5021no—
272C4⋊C4—5021no—
273C4⋊C4—5021no—
274C4⋊C4—2511no—
275C4⋊C4—2511no—
276C4⋊C4—2511no—
277C4⋊C4C22×D25111yescharacteristic
278C4⋊C4C22×D25111yescharacteristic
279C4⋊C4C22×D25111yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—5021no—
282C22⋊C4—5021no—
283C22⋊C4—5021no—
284C22⋊C4—5021no—
285C22⋊C4—5021no—
286C22⋊C4—5021no—
287C42—5021no—
288C42—5021no—
289C42—5021no—
290C23—21no—
291C23—2511no—
292C23—2511no—
293C23D4×D25111yescharacteristic
294Q8—5022no—
295Q8—5021no—
296Q8—5021no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—20081no—
301D4—10042no—
302D4—5022no—
303D4—5022no—
304D4—5022no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—20081no—
312C2×C4—20081no—
313C2×C4—20081no—
314C2×C4—10042no—
315C2×C4—5021no—
316C2×C4—5021no—
317C2×C4—5021no—
318C2×C4—5021no—
319C2×C4—5021no—
320C2×C4—5021no—
321C2×C4—2511no—
322C2×C4—2511no—
323C2×C4—2512no—
324C2×C4—2512no—
325C2×C4D4×D25111yescharacteristic
326C2×C4C23×D25111yescharacteristic
327C8—21no—
328C8—21no—
329C8—5021no—
330C8—5021no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—5021no—
338C22—5021no—
339C22—5021no—
340C22—5021no—
341C22—5021no—
342C22—2512no—
343C22C2×D4×D25111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—10041no—
349C4—10041no—
350C4—10041no—
351C4—10041no—
352C4—5021no—
353C4—2512no—
354C4#41×D25111yescharacteristic
355C4#41×D25111yescharacteristic
356C2—41no—
357C2—81no—
358C2—10041no—
359C2—5022no—
360C2#123×D25111yescharacteristic
361C2#3063248811yescharacteristic
362C2#3063250311yescharacteristic
subgroupG/H
centerC22C2×D4×D251
commutator, cosocleC2×C4×C251C24
FrattiniC2×C4C23×D251
Fitting#480×C251C2
socleC22×C251C22×D4
prime radical#30632266C2
hypercenter#480D251
hypocenterC251#3098
LCSG ▷ C2×C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #30632168C2semidirect
3. #30632030C2semidirect
4. #30632029C2semidirect
5. #30632024C2semidirect
6. #30632022C2semidirect
7. #30632010C2semidirect
8. #30632008C2semidirect
9. #30631999C2semidirect
10. #30631728C2semidirect
11. #107×D251C2semidirect
12. #30631685C2semidirect
13. #30631680C2semidirect
14. #30631652C2semidirect
15. #480×C251C2semidirect
181. C251#3098semidirect
192. #480D251semidirect

Maximal subgroups

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

subgroupindex
#306322662
#306321682
#306320302
#306320292
#306320242
#306320222
#306320102
#306320082
#306319992
#306317282
#107×D2512
#306316852
#306316802
#306316522
#480×C2512
#3098251