Finite Group Databasebeta

← #44558334

Subgroups — #44558334

Order 32128.

408 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#30631627C211yesmaximal, characteristic, complemented
2#30631626C211yesmaximal, characteristic, complemented
3#30631624C211yesmaximal, characteristic
4#30631622C211yesmaximal, characteristic
5#30631620C211yesmaximal, characteristic, complemented
6#30631620C211yesmaximal, characteristic, complemented
7#30631585C211yesmaximal, characteristic, complemented
8#30631584C211yesmaximal, characteristic, complemented
9#30631583C211yesmaximal, characteristic, complemented
10#30631578C211yesmaximal, characteristic
11#30631577C211yesmaximal, characteristic
12#30631561C211yesmaximal, characteristic
13#30631558C211yesmaximal, characteristic
14#30631558C211yesmaximal, characteristic
15#389×C251C211yesmaximal, characteristic, complemented
16C22×C4×D251C2211yescharacteristic
17C2×C4⋊Dic251C2211yescharacteristic
18C2×C4⋊Dic251C2211yescharacteristic
19C2×C4⋊Dic251C2211yescharacteristic
20C2×C4⋊Dic251C2211yescharacteristic
21C2×Dic251⋊C4C2211yescharacteristic
22C2×Dic251⋊C4C2211yescharacteristic
23C2×Dic251⋊C4C2211yescharacteristic
24C2×Dic251⋊C4C2211yescharacteristic
25C2×Dic251⋊C4C2211yescharacteristic
26C2×Dic251⋊C4C2211yescharacteristic
27C2×(C2×D251)⋊C4C2211yescharacteristic
28C2×(C2×D251)⋊C4C2211yescharacteristic
29C2×(C2×D251)⋊C4C2211yescharacteristic
30C2×(C2×D251)⋊C4C2211yescharacteristic
31C2×(C2×D251)⋊C4C2211yescharacteristic
32C2×(C2×D251)⋊C4C2211yescharacteristic
33C2×C4×Dic251C2211yescharacteristic
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×C4⋊C4×C251C2211yescharacteristic
48C2×C42×C251C2211yescharacteristic
49#95×C251C2211yescharacteristic
50#95×C251C2211yescharacteristic
51C23×D251C2311yescharacteristic
52C22×Dic251C2311yescharacteristic
53C22×Dic251C2311yescharacteristic
54C22×Dic251C2311yescharacteristic
55C22×Dic251C2311yescharacteristic
56C22×Dic251C2311yescharacteristic
57C22×Dic251C2311yescharacteristic
58C22×Dic251C2311yescharacteristic
59C2×C4×D251—41no—
60C2×C4×D251—41no—
61C2×C4×D251—41no—
62C4⋊Dic251—22no—
63C4⋊Dic251—22no—
64C4⋊Dic251—41no—
65C4⋊Dic251—41no—
66Dic251⋊C4—22no—
67Dic251⋊C4—41no—
68Dic251⋊C4—41no—
69Dic251⋊C4—41no—
70Dic251⋊C4—41no—
71Dic251⋊C4—41no—
72(C2×D251)⋊C4—22no—
73(C2×D251)⋊C4—22no—
74(C2×D251)⋊C4—41no—
75(C2×D251)⋊C4—41no—
76(C2×D251)⋊C4—41no—
77(C2×D251)⋊C4Q814yes—
78C4×Dic251—41no—
79C22×C4×C251C2311yescharacteristic
80C22×C4×C251C2311yescharacteristic
81C22×C4×C251C2311yescharacteristic
82C22×C4×C251C2311yescharacteristic
83C22×C4×C251C2311yescharacteristic
84C22×C4×C251C2311yescharacteristic
85C22×C4×C251C2311yescharacteristic
86C4⋊C4×C251—22no—
87C4⋊C4×C251—41no—
88C4⋊C4×C251—41no—
89C4⋊C4×C251—41no—
90C42×C251—41no—
91C22×D251—21no—
92C22×D251—21no—
93C22×D251—21no—
94C22×D251—21no—
95C22×D251—21no—
96C22×D251—21no—
97C22×D251C2×Q812yes—
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—21no—
117C2×Dic251—21no—
118C2×Dic251C2×Q812yes—
119C4×D251—44no—
120C23×C251C2411yescharacteristic
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—21no—
137C2×C4×C251—21no—
138C2×C4×C251—21no—
139C2×C4×C251C2×Q812yes—
140C2×C4×C251#4112yes—
141C2×C4×C251#4112yes—
142C22×C251C22×Q811yescharacteristic
143C22×C251C2×#4111yescharacteristic
144C22×C251C2×#4111yescharacteristic
145C22×C251H(5,𝔽2)11yescharacteristic
146C22×C251H(5,𝔽2)11yescharacteristic
147C22×C251H(5,𝔽2)11yescharacteristic
148C22×C2512−1+411yescharacteristic
149C2×D251—22no—
150C2×D251—22no—
151C2×D251—22no—
152C2×D251—41no—
153C2×D251—41no—
154C2×D251—41no—
155C2×D251—41no—
156C4×C251—22no—
157C4×C251—22no—
158C4×C251—22no—
159C4×C251—41no—
160C4×C251—41no—
161C4×C251—41no—
162C4×C251—41no—
163Dic251—22no—
164Dic251—41no—
165Dic251—41no—
166Dic251—41no—
167Dic251—41no—
168Dic251—41no—
169Dic251—41no—
170C2×C251#53911yescharacteristic
171C2×C251#53911yescharacteristic
172C2×C251#54411yescharacteristic
173C2×C251#55411yescharacteristic
174C2×C251#55411yescharacteristic
175C2×C251#55911yescharacteristic
176C2×C251#56011yescharacteristic
177D251—42no—
178C251#280711yescharacteristic, complemented, Sylow
179#2807—2511nomaximal, Sylow
180#400—2511no—
181#400—2511no—
182#399—2511no—
183#399—2511no—
184#398—2511no—
185#398—2511no—
186#389—2511no—
187#389—2511no—
188#389—2511no—
189#389D25111yescharacteristic, complemented
190#388—2511no—
191#388—2511no—
192#385—2511no—
193#385—2511no—
194#385—2511no—
195C23×C4—2511no—
196C2×C4⋊C4—2511no—
197C2×C4⋊C4—2511no—
198C2×C4⋊C4—2511no—
199C2×C4⋊C4—2511no—
200C2×C4⋊C4—2511no—
201C2×C4⋊C4—2511no—
202C2×C4⋊C4—2511no—
203C2×C4⋊C4—2511no—
204C2×C4⋊C4—2511no—
205C2×C4⋊C4—2511no—
206C2×C4⋊C4C2×D25111yescharacteristic
207C2×C4⋊C4C2×D25111yescharacteristic
208C2×C4⋊C4C2×D25111yescharacteristic
209C2×C4⋊C4C2×D25111yescharacteristic
210C2×C22⋊C4—2511no—
211C2×C22⋊C4—2511no—
212C2×C22⋊C4—2511no—
213C2×C22⋊C4—2511no—
214C2×C22⋊C4—2511no—
215C2×C22⋊C4—2511no—
216C2×C42—2511no—
217C2×C42C2×D25111yescharacteristic
218#95—2511no—
219#95—2511no—
220#95—2511no—
221#95—2511no—
222#95—2511no—
223#95—2511no—
224#95—2511no—
225#95—2511no—
226#95—2511no—
227#95—2511no—
228#95C2×D25111yescharacteristic
229#95C2×D25111yescharacteristic
230C24—2511no—
231C22×C4—10041no—
232C22×C4—10041no—
233C22×C4—10041no—
234C22×C4—2511no—
235C22×C4—2511no—
236C22×C4—2511no—
237C22×C4—2511no—
238C22×C4—2511no—
239C22×C4—2511no—
240C22×C4—2511no—
241C22×C4C22×D25111yescharacteristic
242C22×C4C22×D25111yescharacteristic
243C22×C4C22×D25111yescharacteristic
244C22×C4C22×D25111yescharacteristic
245C22×C4C22×D25111yescharacteristic
246C22×C4C22×D25111yescharacteristic
247C22×C4C22×D25111yescharacteristic
248C4⋊C4—22no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—10041no—
253C4⋊C4—10041no—
254C4⋊C4—10041no—
255C4⋊C4—10041no—
256C4⋊C4—10041no—
257C4⋊C4—10041no—
258C4⋊C4—10041no—
259C4⋊C4—5022no—
260C4⋊C4—5022no—
261C4⋊C4—5022no—
262C22⋊C4—10041no—
263C22⋊C4—10041no—
264C22⋊C4—10041no—
265C22⋊C4—5022no—
266C22⋊C4—5022no—
267C22⋊C4—2514no—
268C42—41no—
269C42—10041no—
270C23—5021no—
271C23—5021no—
272C23—5021no—
273C23—5021no—
274C23—5021no—
275C23—5021no—
276C23—2512no—
277C23C23×D25111yescharacteristic
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—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—10044no—
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—5021no—
311C2×C4—5021no—
312C2×C4—5021no—
313C2×C4—5021no—
314C2×C4—5021no—
315C2×C4—5021no—
316C2×C4—5021no—
317C2×C4—2512no—
318C2×C4Q8×D25112yes—
319C2×C4#1686081012yes—
320C2×C4#1686081112yes—
321C22—10041no—
322C22—10041no—
323C22—10041no—
324C22—10041no—
325C22—5022no—
326C22—5022no—
327C22—5022no—
328C22C2×Q8×D25111yescharacteristic
329C22C2×#1686081011yescharacteristic
330C22C2×#1686081111yescharacteristic
331C22#2254876011yescharacteristic
332C22#2254876011yescharacteristic
333C22#2254876111yescharacteristic
334C22#2254876211yescharacteristic
335C4—22no—
336C4—22no—
337C4—22no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—10041no—
343C4—10041no—
344C4—10041no—
345C4—10041no—
346C4—10041no—
347C4—10041no—
348C4—5022no—
349C2—10042no—
350C2#3063227911yescharacteristic
351C2#3063228611yescharacteristic
352C2#3063231711yescharacteristic
353C2#3063239211yescharacteristic
354C2#3063239811yescharacteristic
355C2#3063242211yescharacteristic
356C2#3063242511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D251
commutator, socle, cosocleC23×C251C24
Fitting#389×C251C2
prime radicalC23×D251C23
hypercenter#389D251
hypocenterC251#2807
LCSG ▷ C23×C251 ▷ C251
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. #30631627C2semidirect
2. #30631626C2semidirect
5. #30631620C2semidirect
6. #30631620C2semidirect
7. #30631585C2semidirect
8. #30631584C2semidirect
9. #30631583C2semidirect
15. #389×C251C2semidirect
178. C251#2807semidirect
189. #389D251semidirect

Maximal subgroups

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

subgroupindex
#306316272
#306316262
#306316242
#306316222
#306316202
#306315852
#306315842
#306315832
#306315782
#306315772
#306315612
#306315582
#389×C2512
#2807251