Finite Group Databasebeta

← #44558582

Subgroups — #44558582

Order 32128.

400 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#30631628C211yesmaximal, characteristic, complemented
2#30631623C211yesmaximal, characteristic, complemented
3#30631623C211yesmaximal, characteristic, complemented
4#30631620C211yesmaximal, characteristic, complemented
5#30631618C211yesmaximal, characteristic, complemented
6#30631615C211yesmaximal, characteristic, complemented
7#30631615C211yesmaximal, characteristic, complemented
8#30631610C211yesmaximal, characteristic, complemented
9#30631610C211yesmaximal, characteristic, complemented
10#30631601C211yesmaximal, characteristic
11#30631601C211yesmaximal, characteristic
12#30631584C211yesmaximal, characteristic, complemented
13#30631581C211yesmaximal, characteristic, complemented
14#30631575C211yesmaximal, characteristic, complemented
15#394×C251C211yesmaximal, characteristic
16C2×C4⋊Dic251C2211yescharacteristic
17C2×C4⋊Dic251C2211yescharacteristic
18C2×Dic251⋊C4C2211yescharacteristic
19C2×Dic251⋊C4C2211yescharacteristic
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×C22⋊Dic251C2211yescharacteristic
31C2×C22⋊Dic251C2211yescharacteristic
32C2×C22⋊Dic251C2211yescharacteristic
33C2×C22⋊Dic251C2211yescharacteristic
34C2×C4×Dic251C2211yescharacteristic
35C251⋊#95C2211yescharacteristic
36C251⋊#95C2211yescharacteristic
37C251⋊#95C2211yescharacteristic
38C251⋊#95C2211yescharacteristic
39C251⋊#95C2211yescharacteristic
40C251⋊#95C2211yescharacteristic
41C251⋊#95C2211yescharacteristic
42C251⋊#95C2211yescharacteristic
43C251⋊#95C2211yescharacteristic
44C22×D4×C251C2211yescharacteristic
45C2×C4⋊C4×C251C2211yescharacteristic
46C2×C22⋊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—41no—
60C4⋊Dic251—41no—
61Dic251⋊C4—22no—
62Dic251⋊C4—41no—
63Dic251⋊C4—41no—
64Dic251⋊C4—41no—
65Dic251⋊C4—41no—
66Dic251⋊C4—41no—
67Dic251⋊C4—41no—
68Dic251⋊C4—41no—
69C22⋊Dic251—22no—
70C22⋊Dic251—22no—
71C22⋊Dic251—41no—
72C22⋊Dic251—41no—
73C22⋊Dic251—41no—
74C22⋊Dic251—41no—
75C22⋊Dic251—41no—
76C22⋊Dic251—41no—
77C4×Dic251—41no—
78C24×C251C2311yescharacteristic
79C24×C251C2311yescharacteristic
80C2×D4×C251—41no—
81C2×D4×C251—41no—
82C2×D4×C251—41no—
83C22×C4×C251C2311yescharacteristic
84C22×C4×C251C2311yescharacteristic
85C22×C4×C251C2311yescharacteristic
86C22×C4×C251C2311yescharacteristic
87C22×C4×C251C2311yescharacteristic
88C4⋊C4×C251—41no—
89C22⋊C4×C251—41no—
90C22⋊C4×C251—41no—
91C22⋊C4×C251—41no—
92C22⋊C4×C251—41no—
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—
111C2×Dic251—21no—
112C2×Dic251—21no—
113C2×Dic251—21no—
114C2×Dic251—21no—
115C2×Dic251—21no—
116C2×Dic251#4112yes—
117C23×C251—21no—
118C23×C251—21no—
119C23×C251—21no—
120C23×C251—21no—
121C23×C251—21no—
122C23×C251—21no—
123C23×C251—21no—
124C23×C251—21no—
125C23×C251—21no—
126C23×C251—21no—
127C23×C251—21no—
128C23×C251—21no—
129C23×C251—21no—
130C23×C251—21no—
131C23×C251C2411yescharacteristic
132D4×C251—44no—
133C2×C4×C251—21no—
134C2×C4×C251—21no—
135C2×C4×C251—21no—
136C2×C4×C251—21no—
137C2×C4×C251—21no—
138C2×C4×C251—21no—
139C2×C4×C251—21no—
140C2×C4×C251—21no—
141C2×C4×C251—21no—
142C2×C4×C251—21no—
143C2×C4×C251—21no—
144C2×C4×C251—21no—
145C2×C4×C251—21no—
146C2×C4×C251—21no—
147C2×C4×C251—21no—
148C22×C251—41no—
149C22×C251—41no—
150C22×C251—41no—
151C22×C251—41no—
152C22×C251—41no—
153C22×C251—41no—
154C22×C251—41no—
155C22×C251—41no—
156C22×C251—41no—
157C22×C251—41no—
158C22×C251—41no—
159C22×C251—41no—
160C22×C251—41no—
161C22×C251—41no—
162C22×C251C2×#4111yescharacteristic
163C22×C251H(5,𝔽2)11yescharacteristic
164C22×C251H(5,𝔽2)11yescharacteristic
165C22×C251H(5,𝔽2)11yescharacteristic
166C22×C251H(5,𝔽2)11yescharacteristic
167C22×C2512−1+411yescharacteristic
168C22×C2512−1+411yescharacteristic
169C4×C251—41no—
170C4×C251—41no—
171C4×C251—41no—
172C4×C251—41no—
173C4×C251—41no—
174Dic251—22no—
175Dic251—41no—
176Dic251—41no—
177Dic251—41no—
178Dic251—41no—
179Dic251—41no—
180Dic251—41no—
181Dic251—41no—
182C2×C251—81no—
183C2×C251—81no—
184C2×C251#53911yescharacteristic
185C2×C251#54011yescharacteristic
186C2×C251#54211yescharacteristic
187C2×C251#56011yescharacteristic
188C2×C251#56211yescharacteristic
189C2×C251#56211yescharacteristic
190C2×C251#56311yescharacteristic
191C251#283711yescharacteristic, complemented, Sylow
192#2837—2511nomaximal, Sylow
193#400—2511no—
194#399—2511no—
195#399—2511no—
196#398—2511no—
197#398—2511no—
198#397—2511no—
199#397—2511no—
200#396—2511no—
201#396—2511no—
202#394—2511no—
203#394—2511no—
204#394D25111yescharacteristic
205#389—2511no—
206#388—2511no—
207#388—2511no—
208C22×D4C2×D25111yescharacteristic
209C2×C4⋊C4—2511no—
210C2×C4⋊C4—2511no—
211C2×C4⋊C4—2511no—
212C2×C4⋊C4—2511no—
213C2×C4⋊C4—2511no—
214C2×C4⋊C4—2511no—
215C2×C4⋊C4—2511no—
216C2×C4⋊C4—2511no—
217C2×C4⋊C4—2511no—
218C2×C4⋊C4—2511no—
219C2×C4⋊C4C2×D25111yescharacteristic
220C2×C22⋊C4—2511no—
221C2×C22⋊C4—2511no—
222C2×C22⋊C4—2511no—
223C2×C22⋊C4—2511no—
224C2×C22⋊C4—2511no—
225C2×C22⋊C4—2511no—
226C2×C22⋊C4—2511no—
227C2×C22⋊C4—2511no—
228C2×C22⋊C4C2×D25111yescharacteristic
229C2×C22⋊C4C2×D25111yescharacteristic
230C2×C22⋊C4C2×D25111yescharacteristic
231C2×C22⋊C4C2×D25111yescharacteristic
232C2×C42—2511no—
233#95—2511no—
234#95—2511no—
235#95—2511no—
236#95—2511no—
237#95—2511no—
238#95—2511no—
239#95—2511no—
240#95—2511no—
241#95—2511no—
242#95C2×D25111yescharacteristic
243C24C22×D25111yescharacteristic
244C24C22×D25111yescharacteristic
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—41no—
248C22×C4—2511no—
249C22×C4—2511no—
250C22×C4—2511no—
251C22×C4—2511no—
252C22×C4—2511no—
253C22×C4—2511no—
254C22×C4—2511no—
255C22×C4—2511no—
256C22×C4C22×D25111yescharacteristic
257C22×C4C22×D25111yescharacteristic
258C22×C4C22×D25111yescharacteristic
259C22×C4C22×D25111yescharacteristic
260C22×C4C22×D25111yescharacteristic
261C4⋊C4—41no—
262C4⋊C4—10041no—
263C4⋊C4—10041no—
264C4⋊C4—10041no—
265C4⋊C4—10041no—
266C4⋊C4—10041no—
267C4⋊C4—10041no—
268C4⋊C4—10041no—
269C4⋊C4—10041no—
270C4⋊C4—10041no—
271C4⋊C4—5022no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—10041no—
277C22⋊C4—10041no—
278C22⋊C4—10041no—
279C22⋊C4—10041no—
280C22⋊C4—10041no—
281C22⋊C4—10041no—
282C22⋊C4—5022no—
283C22⋊C4—5022no—
284C42—10041no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23C23×D25111yescharacteristic
300D4—44no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—5021no—
317C2×C4—5021no—
318C2×C4—5021no—
319C2×C4—5021no—
320C2×C4—5021no—
321C2×C4—5021no—
322C2×C4—5021no—
323C2×C4—5021no—
324C2×C4—5021no—
325C2×C4—5021no—
326C2×C4—5021no—
327C2×C4—5021no—
328C2×C4—5021no—
329C2×C4—5021no—
330C2×C4—5021no—
331C2×C4—5021no—
332C2×C4—5021no—
333C2×C4—5021no—
334C2×C4—5021no—
335C2×C4—5021no—
336C2×C4—5021no—
337C2×C4—5021no—
338C2×C4—5021no—
339C2×C4—2512no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22#41×D25111yescharacteristic
355C22#2254876011yescharacteristic
356C22#2254876011yescharacteristic
357C22#2254876011yescharacteristic
358C22#2254876011yescharacteristic
359C22#2254876211yescharacteristic
360C22#2254876211yescharacteristic
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—10041no—
367C4—10041no—
368C4—10041no—
369C4—10041no—
370C4—10041no—
371C4—10041no—
372C4—10041no—
373C4—5022no—
374C2—81no—
375C2—81no—
376C2#3063228011yescharacteristic
377C2#3063228711yescharacteristic
378C2#3063230111yescharacteristic
379C2#3063242611yescharacteristic
380C2#3063243211yescharacteristic
381C2#3063243211yescharacteristic
382C2#3063244011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D251
commutator, socle, cosocleC23×C251C24
Fitting#394×C251C2
prime radicalC22×D4×C251C22
hypercenter#394D251
hypocenterC251#2837
LCSG ▷ C23×C251 ▷ C251
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #30631628C2semidirect
2. #30631623C2semidirect
3. #30631623C2semidirect
4. #30631620C2semidirect
5. #30631618C2semidirect
6. #30631615C2semidirect
7. #30631615C2semidirect
8. #30631610C2semidirect
9. #30631610C2semidirect
12. #30631584C2semidirect
13. #30631581C2semidirect
14. #30631575C2semidirect
191. C251#2837semidirect

Maximal subgroups

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

subgroupindex
#306316282
#306316232
#306316202
#306316182
#306316152
#306316102
#306316012
#306315842
#306315812
#306315752
#394×C2512
#2837251