Finite Group Databasebeta

← #44560629

Subgroups — #44560629

Order 32128.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#30632308C211yesmaximal, characteristic, complemented
2#30632167C211yesmaximal, characteristic, complemented
3#30632023C211yesmaximal, characteristic, complemented
4#30632001C211yesmaximal, characteristic, complemented
5#30631983C211yesmaximal, characteristic, complemented
6#30631968C211yesmaximal, characteristic, complemented
7#30631910C211yesmaximal, characteristic, complemented
8#30631903C211yesmaximal, characteristic, complemented
9#30631851C211yesmaximal, characteristic, complemented
10#30631834C211yesmaximal, characteristic
11#30631789C211yesmaximal, characteristic, complemented
12#30631789C211yesmaximal, characteristic, complemented
13C4×Dic1004C211yesmaximal, characteristic, complemented
14C4×D2008C211yesmaximal, characteristic, complemented
15#433×C251C211yesmaximal, characteristic, complemented
16C2×#16860810C2211yescharacteristic
17C2×Dic1004C2211yescharacteristic
18C2×#16860799C2211yescharacteristic
19C2×#16860799C2211yescharacteristic
20C2×D2008C2211yescharacteristic
21#22548715C2211yescharacteristic
22#22548710—21no—
23#22548703C2211yescharacteristic
24#22548701—21no—
25#22548697—21no—
26#22548694C2211yescharacteristic
27#22548693—21no—
28#22548689C2211yescharacteristic
29C4×Dic502C2211yescharacteristic
30C4×Dic502C2211yescharacteristic
31C4×Dic502C2211yescharacteristic
32C4×D1004C2211yescharacteristic
33C4×D1004C2211yescharacteristic
34C4×D1004C2211yescharacteristic
35(C22⋊D251)⋊C4—21no—
36(C22⋊D251)⋊C4—21no—
37#22548673—21no—
38C2×C4⋊Dic251C2211yescharacteristic
39C4⋊C4×D251—21no—
40#22548649C2211yescharacteristic
41#22548649C2211yescharacteristic
42#22548649C2211yescharacteristic
43#22548649C2211yescharacteristic
44#22548640C2211yescharacteristic
45#22548640C2211yescharacteristic
46#22548640C2211yescharacteristic
47#22548640C2211yescharacteristic
48#22548637C2211yescharacteristic
49#22548637C2211yescharacteristic
50#22548637C2211yescharacteristic
51#22548637C2211yescharacteristic
52#117×C251C2211yescharacteristic
53C4⋊C8×C251C2211yescharacteristic
54C4⋊C8×C251C2211yescharacteristic
55C22⋊C8×C251C2211yescharacteristic
56C22⋊C8×C251C2211yescharacteristic
57#97×C251C2211yescharacteristic
58C4×C8×C251C2211yescharacteristic
59#16860810—22no—
60#16860810—22no—
61C2×Dic502—21no—
62C2×Dic502C2311yescharacteristic
63C2×Dic502C2311yescharacteristic
64C2×D1004C2311yescharacteristic
65C2×D1004C2311yescharacteristic
66C2×C22⋊D251—21no—
67C2×C22⋊D251—21no—
68C22×Dic251—21no—
69C2×C4×D251—21no—
70C2×C4×D251—21no—
71C2×C4×D251—21no—
72C2×C4×D251—21no—
73Dic1004—22no—
74#16860799—22no—
75#16860799—22no—
76D2008—22no—
77C4⋊Dic251—21no—
78C4⋊Dic251—21no—
79C4⋊Dic251C2311yescharacteristic
80C4⋊Dic251C2311yescharacteristic
81C4⋊Dic251C2311yescharacteristic
82C4⋊Dic251C2311yescharacteristic
83Dic251⋊C4—21no—
84Dic251⋊C4—21no—
85Dic251⋊C4—21no—
86Dic251⋊C4—21no—
87C22⋊Dic251—21no—
88(C2×D251)⋊C4—21no—
89(C2×D251)⋊C4—21no—
90(C2×D251)⋊C4—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—
97C22×C4×C251C2311yescharacteristic
98C2×C8×C251C2311yescharacteristic
99C2×C8×C251C2311yescharacteristic
100C2×C8×C251C2311yescharacteristic
101C2×C8×C251C2311yescharacteristic
102C4⋊C4×C251D411yescharacteristic
103C4⋊C4×C251D411yescharacteristic
104C22⋊C4×C251D411yescharacteristic
105C22⋊C4×C251D411yescharacteristic
106C42×C251C2311yescharacteristic
107C42×C251C2311yescharacteristic
108C22×D251—21no—
109C22×D251—21no—
110Dic502—21no—
111Dic502—21no—
112Dic502—21no—
113Dic502—81no—
114Dic502#4112yes—
115D1004—21no—
116D1004—21no—
117D1004—21no—
118D1004#4112yes—
119C22⋊D251—24no—
120C22⋊D251—81no—
121C2×Dic251—21no—
122C2×Dic251—21no—
123C2×Dic251—21no—
124C2×Dic251—21no—
125C2×Dic251—21no—
126C2×Dic251—21no—
127C2×Dic251—81no—
128C4×D251—24no—
129C4×D251—81no—
130C4×D251—81no—
131C4×D251—81no—
132C23×C251C2×D411yescharacteristic
133C2×C4×C251—21no—
134C2×C4×C251—21no—
135C2×C4×C251C2×D411yescharacteristic
136C2×C4×C251C2×D411yescharacteristic
137C2×C4×C251C2×D411yescharacteristic
138C2×C4×C251C2×D411yescharacteristic
139C2×C4×C251C2×D411yescharacteristic
140C2×C4×C251C2411yescharacteristic
141C8×C251—21no—
142C8×C251—21no—
143C8×C251—21no—
144C8×C251—21no—
145C22×C251—21no—
146C22×C251—21no—
147C22×C251—21no—
148C22×C251C22×D411yescharacteristic
149C2×D251—22no—
150C2×D251—41no—
151C2×D251—41no—
152C2×D251—41no—
153C2×D251—41no—
154C2×D251—41no—
155C4×C251—21no—
156C4×C251—21no—
157C4×C251—21no—
158C4×C251—21no—
159C4×C251—21no—
160C4×C251C2×#4111yescharacteristic
161C4×C251C2×#4111yescharacteristic
162Dic251—22no—
163Dic251—41no—
164Dic251—41no—
165Dic251—41no—
166Dic251—41no—
167Dic251—41no—
168C2×C251—41no—
169C2×C251#52511yescharacteristic
170C2×C251#57611yescharacteristic
171C2×C251#57811yescharacteristic
172D251—42no—
173D251—81no—
174C251#312411yescharacteristic, complemented, Sylow
175#3124—2511nomaximal, Sylow
176#542—2511no—
177#520—2511no—
178#484—2511no—
179#480—2511no—
180#477—2511no—
181#474—2511no—
182#464—2511no—
183#463—2511no—
184#452—2511no—
185#449—2511no—
186#440—2511no—
187#440—2511no—
188C4×Q16—2511no—
189C4×D8—2511no—
190#433D25111yescharacteristic, complemented
191C2×#41—2511no—
192C2×Q16—2511no—
193C2×SD16—2511no—
194C2×SD16—2511no—
195C2×D8—2511no—
196C4⋊Q8—2511no—
197#126—5021no—
198#124—5021no—
199#124—2511no—
200#123—5021no—
201C22⋊Q8—5021no—
202C22⋊Q8—2511no—
203#121—2511no—
204C4×Q8—2511no—
205C4×Q8—2511no—
206C4×Q8—2511no—
207C4×D4—5021no—
208C4×D4—5021no—
209C4×D4—2511no—
210C4×D4—2511no—
211C4×D4—2511no—
212#117—5021no—
213#117C2×D25111yescharacteristic
214C2×C4⋊C4—5021no—
215C2×C4⋊C4—2511no—
216#107—2511no—
217#107—2511no—
218#107—2511no—
219#107—2511no—
220C4⋊C8C2×D25111yescharacteristic
221C4⋊C8C2×D25111yescharacteristic
222#103—2511no—
223#103—2511no—
224#103—2511no—
225#103—2511no—
226#102—2511no—
227#102—2511no—
228#102—2511no—
229#102—2511no—
230C22⋊C8C2×D25111yescharacteristic
231C22⋊C8C2×D25111yescharacteristic
232#97C2×D25111yescharacteristic
233C4×C8C2×D25111yescharacteristic
234#41—5022no—
235#41—5022no—
236C2×Q8—5021no—
237C2×Q8—2511no—
238C2×Q8—2511no—
239C2×D4—5021no—
240C2×D4—5021no—
241C2×D4—2511no—
242C2×D4—2511no—
243C22×C4—5021no—
244C22×C4—5021no—
245C22×C4—5021no—
246C22×C4—5021no—
247C22×C4—5021no—
248C22×C4C22×D25111yescharacteristic
249Q16—5022no—
250SD16—5022no—
251SD16—5022no—
252D8—5022no—
253C2×C8C22×D25111yescharacteristic
254C2×C8C22×D25111yescharacteristic
255C2×C8C22×D25111yescharacteristic
256C2×C8C22×D25111yescharacteristic
257C4⋊C4—5021no—
258C4⋊C4—5021no—
259C4⋊C4—5021no—
260C4⋊C4—5021no—
261C4⋊C4—5021no—
262C4⋊C4—5021no—
263C4⋊C4—2511no—
264C4⋊C4—2511no—
265C4⋊C4—2511no—
266C4⋊C4—2511no—
267C4⋊C4D100411yescharacteristic
268C4⋊C4D100411yescharacteristic
269C22⋊C4—5021no—
270C22⋊C4—5021no—
271C22⋊C4—5021no—
272C22⋊C4—5021no—
273C22⋊C4—5021no—
274C22⋊C4—5021no—
275C22⋊C4—5021no—
276C22⋊C4D100411yescharacteristic
277C22⋊C4D100411yescharacteristic
278C42—5021no—
279C42—5021no—
280C42—5021no—
281C42C22×D25111yescharacteristic
282C42C22×D25111yescharacteristic
283C23—5021no—
284C23—5021no—
285C23C2×D100411yescharacteristic
286Q8—20081no—
287Q8—5021no—
288Q8—5021no—
289Q8—5021no—
290Q8—2512no—
291D4—20081no—
292D4—5024no—
293D4—5021no—
294D4—5021no—
295D4—5021no—
296D4—2512no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—20081no—
300C2×C4—20081no—
301C2×C4—20081no—
302C2×C4—20081no—
303C2×C4—5024no—
304C2×C4—5021no—
305C2×C4—5021no—
306C2×C4—5021no—
307C2×C4—5021no—
308C2×C4—5021no—
309C2×C4—5021no—
310C2×C4C2×D100411yescharacteristic
311C2×C4C2×D100411yescharacteristic
312C2×C4C2×D100411yescharacteristic
313C2×C4C2×D100411yescharacteristic
314C2×C4C2×D100411yescharacteristic
315C2×C4C23×D25111yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—10041no—
324C22—10041no—
325C22—10041no—
326C22—10041no—
327C22—10041no—
328C22—5022no—
329C22C22×D100411yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—10041no—
336C4—10041no—
337C4—10041no—
338C4—10041no—
339C4—10041no—
340C4—5022no—
341C4#41×D25111yescharacteristic
342C4#41×D25111yescharacteristic
343C2—41no—
344C2—20081no—
345C2—10042no—
346C2#3063219911yescharacteristic
347C2#3063249211yescharacteristic
348C2#3063250411yescharacteristic
subgroupG/H
centerC22C22×D1004
commutator, cosocleC2×C4×C251C24
FrattiniC2×C4C23×D251
Fitting#433×C251C2
socleC22×C251C22×D4
prime radical#30631834C2
hypercenter#433D251
hypocenterC251#3124
LCSG ▷ C2×C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #30632308C2semidirect
2. #30632167C2semidirect
3. #30632023C2semidirect
4. #30632001C2semidirect
5. #30631983C2semidirect
6. #30631968C2semidirect
7. #30631910C2semidirect
8. #30631903C2semidirect
9. #30631851C2semidirect
11. #30631789C2semidirect
12. #30631789C2semidirect
13. C4×Dic1004C2semidirect
14. C4×D2008C2semidirect
15. #433×C251C2semidirect
174. C251#3124semidirect
190. #433D251semidirect

Maximal subgroups

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

subgroupindex
#306323082
#306321672
#306320232
#306320012
#306319832
#306319682
#306319102
#306319032
#306318512
#306318342
#306317892
C4×Dic10042
C4×D20082
#433×C2512
#3124251