Finite Group Databasebeta

← #44558566

Subgroups — #44558566

Order 32128.

358 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#30631628C211yesmaximal, characteristic, complemented
2#30631626C211yesmaximal, characteristic, complemented
3#30631623C211yesmaximal, characteristic
4#30631620C211yesmaximal, characteristic, complemented
5#30631619C211yesmaximal, characteristic, complemented
6#30631618C211yesmaximal, characteristic, complemented
7#30631617C211yesmaximal, characteristic, complemented
8#30631615C211yesmaximal, characteristic
9#30631615C211yesmaximal, characteristic
10#30631612C211yesmaximal, characteristic
11#30631610C211yesmaximal, characteristic
12#30631583C211yesmaximal, characteristic, complemented
13#30631580C211yesmaximal, characteristic
14#30631573C211yesmaximal, characteristic, complemented
15#396×C251C211yesmaximal, characteristic
16C2×C4⋊Dic251C2211yescharacteristic
17C2×C4⋊Dic251C2211yescharacteristic
18C2×C4⋊Dic251C2211yescharacteristic
19C2×C4⋊Dic251C2211yescharacteristic
20C2×Dic251⋊C4C2211yescharacteristic
21C2×Dic251⋊C4C2211yescharacteristic
22C2×Dic251⋊C4C2211yescharacteristic
23C2×Dic251⋊C4C2211yescharacteristic
24C2×Dic251⋊C4C2211yescharacteristic
25C2×Dic251⋊C4C2211yescharacteristic
26C2×C22⋊Dic251C2211yescharacteristic
27C2×C22⋊Dic251C2211yescharacteristic
28C2×C22⋊Dic251C2211yescharacteristic
29C2×C22⋊Dic251C2211yescharacteristic
30C2×C4×Dic251C2211yescharacteristic
31C251⋊#95C2211yescharacteristic
32C251⋊#95C2211yescharacteristic
33C251⋊#95C2211yescharacteristic
34C251⋊#95C2211yescharacteristic
35C251⋊#95C2211yescharacteristic
36C251⋊#95C2211yescharacteristic
37C251⋊#95C2211yescharacteristic
38C251⋊#95C2211yescharacteristic
39C251⋊#95C2211yescharacteristic
40C251⋊#95C2211yescharacteristic
41C251⋊#95C2211yescharacteristic
42C251⋊#95C2211yescharacteristic
43C251⋊#95C2211yescharacteristic
44C2×C4⋊C4×C251C2211yescharacteristic
45C2×C4⋊C4×C251C2211yescharacteristic
46C2×C4⋊C4×C251C2211yescharacteristic
47C2×C22⋊C4×C251C2211yescharacteristic
48C2×C22⋊C4×C251C2211yescharacteristic
49C2×C22⋊C4×C251C2211yescharacteristic
50#95×C251C2211yescharacteristic
51C22×Dic251C2311yescharacteristic
52C22×Dic251C2311yescharacteristic
53C22×Dic251C2311yescharacteristic
54C22×Dic251C2311yescharacteristic
55C22×Dic251C2311yescharacteristic
56C22×Dic251C2311yescharacteristic
57C22×Dic251C2311yescharacteristic
58C22×Dic251C2311yescharacteristic
59C4⋊Dic251—22no—
60C4⋊Dic251—41no—
61C4⋊Dic251—41no—
62C4⋊Dic251—41no—
63Dic251⋊C4—41no—
64Dic251⋊C4—41no—
65Dic251⋊C4—41no—
66Dic251⋊C4—41no—
67Dic251⋊C4—41no—
68Dic251⋊C4—41no—
69C22⋊Dic251—41no—
70C22⋊Dic251—41no—
71C22⋊Dic251—41no—
72C22⋊Dic251—41no—
73C4×Dic251—41no—
74C24×C251C2311yescharacteristic
75C22×C4×C251C2311yescharacteristic
76C22×C4×C251C2311yescharacteristic
77C22×C4×C251C2311yescharacteristic
78C22×C4×C251C2311yescharacteristic
79C22×C4×C251C2311yescharacteristic
80C22×C4×C251C2311yescharacteristic
81C4⋊C4×C251—22no—
82C4⋊C4×C251—41no—
83C4⋊C4×C251—41no—
84C22⋊C4×C251—22no—
85C22⋊C4×C251—41no—
86C22⋊C4×C251—41no—
87C2×Dic251—21no—
88C2×Dic251—21no—
89C2×Dic251—21no—
90C2×Dic251—21no—
91C2×Dic251—21no—
92C2×Dic251—21no—
93C2×Dic251—21no—
94C2×Dic251—21no—
95C2×Dic251—21no—
96C2×Dic251—21no—
97C2×Dic251—21no—
98C2×Dic251—21no—
99C2×Dic251—21no—
100C2×Dic251—21no—
101C2×Dic251—21no—
102C2×Dic251—21no—
103C2×Dic251—21no—
104C2×Dic251—21no—
105C2×Dic251—21no—
106C2×Dic251—21no—
107C2×Dic251—21no—
108C2×Dic251—21no—
109C2×Dic251—21no—
110C2×Dic251—21no—
111C23×C251—21no—
112C23×C251—21no—
113C23×C251—21no—
114C23×C251—21no—
115C23×C251—21no—
116C23×C251—21no—
117C23×C251—21no—
118C23×C251C2411yescharacteristic
119C2×C4×C251—21no—
120C2×C4×C251—21no—
121C2×C4×C251—21no—
122C2×C4×C251—21no—
123C2×C4×C251—21no—
124C2×C4×C251—21no—
125C2×C4×C251—21no—
126C2×C4×C251—21no—
127C2×C4×C251—21no—
128C2×C4×C251—21no—
129C2×C4×C251—21no—
130C2×C4×C251—21no—
131C2×C4×C251—21no—
132C2×C4×C251—21no—
133C2×C4×C251—21no—
134C2×C4×C251—21no—
135C2×C4×C251—21no—
136C2×C4×C251#4112yes—
137C22×C251—41no—
138C22×C251—41no—
139C22×C251—41no—
140C22×C251—41no—
141C22×C251—41no—
142C22×C251—41no—
143C22×C251—41no—
144C22×C251C2×#4111yescharacteristic
145C22×C251H(5,𝔽2)11yescharacteristic
146C22×C251H(5,𝔽2)11yescharacteristic
147C22×C251H(5,𝔽2)11yescharacteristic
148C22×C2512−1+411yescharacteristic
149C22×C2512−1+411yescharacteristic
150C22×C2512−1+411yescharacteristic
151C4×C251—22no—
152C4×C251—41no—
153C4×C251—41no—
154C4×C251—41no—
155C4×C251—41no—
156C4×C251—41no—
157Dic251—41no—
158Dic251—41no—
159Dic251—41no—
160Dic251—41no—
161Dic251—41no—
162Dic251—41no—
163Dic251—41no—
164Dic251—41no—
165C2×C251—81no—
166C2×C251#53911yescharacteristic
167C2×C251#54011yescharacteristic
168C2×C251#54111yescharacteristic
169C2×C251#56211yescharacteristic
170C2×C251#56211yescharacteristic
171C2×C251#56311yescharacteristic
172C2×C251#56311yescharacteristic
173C251#283611yescharacteristic, complemented, Sylow
174#2836—2511nomaximal, Sylow
175#400—2511no—
176#400—2511no—
177#399—2511no—
178#398—2511no—
179#398—2511no—
180#398—2511no—
181#398—2511no—
182#397—2511no—
183#397—2511no—
184#397—2511no—
185#396—2511no—
186#396D25111yescharacteristic
187#389—2511no—
188#388—2511no—
189#387—2511no—
190C2×C4⋊C4—2511no—
191C2×C4⋊C4—2511no—
192C2×C4⋊C4—2511no—
193C2×C4⋊C4—2511no—
194C2×C4⋊C4—2511no—
195C2×C4⋊C4—2511no—
196C2×C4⋊C4—2511no—
197C2×C4⋊C4—2511no—
198C2×C4⋊C4—2511no—
199C2×C4⋊C4—2511no—
200C2×C4⋊C4C2×D25111yescharacteristic
201C2×C4⋊C4C2×D25111yescharacteristic
202C2×C4⋊C4C2×D25111yescharacteristic
203C2×C22⋊C4—2511no—
204C2×C22⋊C4—2511no—
205C2×C22⋊C4—2511no—
206C2×C22⋊C4—2511no—
207C2×C22⋊C4C2×D25111yescharacteristic
208C2×C22⋊C4C2×D25111yescharacteristic
209C2×C22⋊C4C2×D25111yescharacteristic
210C2×C42—2511no—
211#95—2511no—
212#95—2511no—
213#95—2511no—
214#95—2511no—
215#95—2511no—
216#95—2511no—
217#95—2511no—
218#95—2511no—
219#95—2511no—
220#95—2511no—
221#95—2511no—
222#95—2511no—
223#95—2511no—
224#95C2×D25111yescharacteristic
225C24C22×D25111yescharacteristic
226C22×C4—2511no—
227C22×C4—2511no—
228C22×C4—2511no—
229C22×C4—2511no—
230C22×C4—2511no—
231C22×C4—2511no—
232C22×C4—2511no—
233C22×C4—2511no—
234C22×C4C22×D25111yescharacteristic
235C22×C4C22×D25111yescharacteristic
236C22×C4C22×D25111yescharacteristic
237C22×C4C22×D25111yescharacteristic
238C22×C4C22×D25111yescharacteristic
239C22×C4C22×D25111yescharacteristic
240C4⋊C4—22no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—10041no—
244C4⋊C4—10041no—
245C4⋊C4—10041no—
246C4⋊C4—10041no—
247C4⋊C4—10041no—
248C4⋊C4—10041no—
249C4⋊C4—10041no—
250C4⋊C4—10041no—
251C4⋊C4—10041no—
252C4⋊C4—5022no—
253C22⋊C4—22no—
254C22⋊C4—41no—
255C22⋊C4—41no—
256C22⋊C4—10041no—
257C22⋊C4—10041no—
258C22⋊C4—10041no—
259C22⋊C4—10041no—
260C42—10041no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23C23×D25111yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—5021no—
287C2×C4—5021no—
288C2×C4—5021no—
289C2×C4—5021no—
290C2×C4—5021no—
291C2×C4—5021no—
292C2×C4—5021no—
293C2×C4—5021no—
294C2×C4—5021no—
295C2×C4—5021no—
296C2×C4—5021no—
297C2×C4—5021no—
298C2×C4—5021no—
299C2×C4—5021no—
300C2×C4—5021no—
301C2×C4—5021no—
302C2×C4—5021no—
303C2×C4—5021no—
304C2×C4—5021no—
305C2×C4—5021no—
306C2×C4—5021no—
307C2×C4—5021no—
308C2×C4—5021no—
309C2×C4—5021no—
310C2×C4#1686080912yes—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22C2×#1686080911yescharacteristic
319C22#2254876011yescharacteristic
320C22#2254876011yescharacteristic
321C22#2254876111yescharacteristic
322C22#2254876211yescharacteristic
323C22#2254876211yescharacteristic
324C22#2254876311yescharacteristic
325C4—22no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—10041no—
332C4—10041no—
333C4—10041no—
334C4—10041no—
335C4—10041no—
336C4—10041no—
337C4—10041no—
338C4—10041no—
339C2—81no—
340C2#3063228211yescharacteristic
341C2#3063229011yescharacteristic
342C2#3063229711yescharacteristic
343C2#3063243211yescharacteristic
344C2#3063243311yescharacteristic
345C2#3063243811yescharacteristic
346C2#3063243911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D251
commutator, socle, cosocleC23×C251C24
Fitting#396×C251C2
prime radicalC24×C251C23
hypercenter#396D251
hypocenterC251#2836
LCSG ▷ C23×C251 ▷ C251
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. #30631628C2semidirect
2. #30631626C2semidirect
4. #30631620C2semidirect
5. #30631619C2semidirect
6. #30631618C2semidirect
7. #30631617C2semidirect
12. #30631583C2semidirect
14. #30631573C2semidirect
173. C251#2836semidirect

Maximal subgroups

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

subgroupindex
#306316282
#306316262
#306316232
#306316202
#306316192
#306316182
#306316172
#306316152
#306316122
#306316102
#306315832
#306315802
#306315732
#396×C2512
#2836251