Finite Group Databasebeta

← #49130904

Subgroups — #49130904

Order 36224.

524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×D283C211yesmaximal, characteristic, complemented
2C2×#22583616C211yesmaximal, characteristic, complemented
3#31827031C212yesmaximal, complemented
4#31826717C212yesmaximal, complemented
5#31826716C212yesmaximal, complemented
6#31826702C211yesmaximal, characteristic, complemented
7#31826701C211yesmaximal, characteristic, complemented
8#31826698C211yesmaximal, characteristic, complemented
9#31826502C211yesmaximal, characteristic, complemented
10#31826468C212yesmaximal, complemented
11#466×C283C211yesmaximal, characteristic, complemented
12C2×#17985392C2211yescharacteristic
13C2×D4×D283C2212yes—
14C2×D2264C2211yescharacteristic
15C2×#17985377C2212yes—
16D8×D283—24no—
17#22583616—24no—
18C2×#17985376C2211yescharacteristic, complemented
19C2×#17985375C2211yescharacteristic
20C2×#17985375C2211yescharacteristic, complemented
21C2×C8×D283C2211yescharacteristic
22C2×C8×D283C2211yescharacteristic, complemented
23#22583606—22no—
24#22583596—22no—
25#22583585C2212yescomplemented
26#22583584C2212yescomplemented
27#22583581C2212yescomplemented
28#22583580—22no—
29#22583578—22no—
30#22583568C2212yes—
31#22583544C2211yescharacteristic, complemented
32#22583541C2212yescomplemented
33#22583532C2212yescomplemented
34#22583531C2212yescomplemented
35#22583530C2212yescomplemented
36C2×D8×C283C2211yescharacteristic
37C22×C8×C283C2211yescharacteristic, complemented
38#121×C283C2212yescomplemented
39#107×C283C2211yescharacteristic, complemented
40#102×C283C2212yescomplemented
41C23×D283—22no—
42#17985392—22no—
43#17985392—22no—
44C2×Dic566D411yescharacteristic
45C2×D1132—22no—
46C2×D1132D411yescharacteristic
47C2×D1132C2312yes—
48C2×C22⋊D283—22no—
49C2×C22⋊D283—22no—
50C2×C22⋊D283—22no—
51C2×C22⋊D283D411yescharacteristic
52C2×C22⋊D283D411yescharacteristic
53D4×D283—24no—
54D4×D283—24no—
55C2×C4×D283C2311yescharacteristic
56C2×C4×D283C2311yescharacteristic
57D2264—22no—
58#17985377—24no—
59#17985376—22no—
60#17985375—22no—
61#17985375—22no—
62C2×C283⋊C8C2311yescharacteristic
63C2×C283⋊C8C2311yescharacteristic
64C8×D283—22no—
65C8×D283D414yescomplemented
66C4⋊Dic283C2312yes—
67C22⋊Dic283—22no—
68(C2×D283)⋊C4—22no—
69(C2×D283)⋊C4—22no—
70(C2×D283)⋊C4—22no—
71C4×Dic283—22no—
72C2×D4×C283—22no—
73C2×D4×C283C2312yes—
74C22×C4×C283C2311yescharacteristic
75D8×C283—22no—
76C2×C8×C283—22no—
77C2×C8×C283C2311yescharacteristic
78C2×C8×C283C2311yescharacteristic
79C4⋊C4×C283C2312yes—
80C22⋊C4×C283—22no—
81C22×D283—22no—
82C22×D283—44no—
83C22×D283—82no—
84C22×D283—82no—
85C22×D283C2×D411yescharacteristic
86C22×D283C2×D411yescharacteristic
87Dic566—22no—
88D1132—22no—
89D1132—22no—
90D1132—22no—
91D1132—82no—
92C22⋊D283—22no—
93C22⋊D283—22no—
94C22⋊D283—44no—
95C22⋊D283—82no—
96C22⋊D283—82no—
97C2×Dic283—22no—
98C2×Dic283C2×D411yescharacteristic
99C2×Dic283C2×D411yescharacteristic
100C4×D283—21no—
101C4×D283—21no—
102C4×D283C2×D412yes—
103C4×D283#4112yes—
104C283⋊C8—21no—
105C283⋊C8C2×D412yes—
106C23×C283—22no—
107C23×C283C2×D411yescharacteristic
108D4×C283—22no—
109D4×C283—22no—
110D4×C283—82no—
111C2×C4×C283—21no—
112C2×C4×C283—21no—
113C2×C4×C283—22no—
114C2×C4×C283C2×D411yescharacteristic
115C2×C4×C283C2411yescharacteristic
116C8×C283—21no—
117C8×C283C2×D412yes—
118C22×C283—21no—
119C22×C283—21no—
120C22×C283—21no—
121C22×C283—42no—
122C22×C283—42no—
123C22×C283—42no—
124C22×C283C22×D411yescharacteristic
125C2×D283—21no—
126C2×D283—21no—
127C2×D283—21no—
128C2×D283—21no—
129C2×D283—21no—
130C2×D283—42no—
131C2×D283—42no—
132C2×D283—42no—
133C2×D283—88no—
134C2×D283#12112yes—
135C4×C283—21no—
136C4×C283—42no—
137C4×C283C22×D411yescharacteristic
138C4×C283C2×#4111yescharacteristic
139Dic283—21no—
140Dic283—42no—
141Dic283#12112yes—
142C2×C283—41no—
143C2×C283—82no—
144C2×C283C2×#12111yescharacteristic
145C2×C283#57611yescharacteristic
146C2×C283#57611yescharacteristic
147D283—22no—
148D283—41no—
149D283—82no—
150C283#305811yescharacteristic, complemented, Sylow
151#3058—2831nomaximal, Sylow
152C22×D8—2831no—
153C2×#131—2831no—
154#535—2832no—
155#469—2832no—
156#469—2832no—
157#466—2831no—
158#466—2831no—
159#466—2831no—
160#466D28311yescharacteristic, complemented
161#427—2831no—
162#418—2832no—
163C2×#41—2831no—
164C22×D4—2832no—
165C2×D8—2832no—
166C2×D8—2831no—
167C2×D8—5664no—
168C2×D8C2×D28311yescharacteristic
169#131—5664no—
170C2×M16—2831no—
171C2×M16—2831no—
172C2×M16—2831no—
173C22×C8—2831no—
174C22×C8—2831no—
175C22×C8C2×D28311yescharacteristic, complemented
176#127—5662no—
177#124—5662no—
178#121—2832no—
179#121—2832no—
180#121—2832no—
181#121C2×D28312yescomplemented
182#120—5662no—
183#120—5662no—
184#117—2832no—
185#107—2831no—
186#107C2×D28311yescharacteristic, complemented
187#106—2832no—
188#102—2832no—
189#102—2832no—
190#102—2832no—
191#102C2×D28312yescomplemented
192C24—5662no—
193#41—5662no—
194#41—5662no—
195C2×Q8—2831no—
196C2×D4—22no—
197C2×D4—2831no—
198C2×D4—2831no—
199C2×D4—2831no—
200C2×D4—2832no—
201C2×D4—5662no—
202C2×D4—5664no—
203C2×D4—5664no—
204C2×D4—5662no—
205C2×D4—5662no—
206C2×D4—5662no—
207C2×D4C22×D28312yes—
208C22×C4—2831no—
209C22×C4—2831no—
210C22×C4C22×D28311yescharacteristic
211D8—22no—
212D8—5664no—
213D8—5662no—
214M16—5662no—
215M16—5662no—
216M16—5662no—
217C2×C8—22no—
218C2×C8—2831no—
219C2×C8—2834no—
220C2×C8—2831no—
221C2×C8—5662no—
222C2×C8C22×D28311yescharacteristic
223C2×C8C22×D28311yescharacteristic
224C4⋊C4—2832no—
225C4⋊C4C22×D28312yes—
226C22⋊C4—22no—
227C22⋊C4—5662no—
228C22⋊C4—5662no—
229C22⋊C4—5662no—
230C22⋊C4—5662no—
231C42—5662no—
232C23—22no—
233C23—2831no—
234C23—2831no—
235C23—5662no—
236C23—11324no—
237C23—22642no—
238C23—22642no—
239C23D4×D28311yescharacteristic
240Q8—5662no—
241D4—22no—
242D4—22no—
243D4—82no—
244D4—5662no—
245D4—5662no—
246D4—5662no—
247D4—5662no—
248D4—5662no—
249D4—11324no—
250D4—22642no—
251D4—22642no—
252D4—22642no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—2831no—
257C2×C4—2832no—
258C2×C4—2832no—
259C2×C4—2831no—
260C2×C4—5661no—
261C2×C4—5661no—
262C2×C4—5662no—
263C2×C4D4×D28311yescharacteristic
264C2×C4C23×D28311yescharacteristic
265C8—21no—
266C8—2832no—
267C8—5661no—
268C8D4×D28312yes—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—42no—
273C22—42no—
274C22—42no—
275C22—2832no—
276C22—5661no—
277C22—5661no—
278C22—5661no—
279C22—5661no—
280C22—5661no—
281C22—11322no—
282C22—11322no—
283C22—11322no—
284C22—22648no—
285C22C2×D4×D28311yescharacteristic
286C4—21no—
287C4—42no—
288C4—2832no—
289C4—5661no—
290C4—11322no—
291C4C2×D4×D28311yescharacteristic
292C4#41×D28311yescharacteristic
293C2—41no—
294C2—82no—
295C2—5662no—
296C2—11321no—
297C2—22642no—
298C2#121×D28311yescharacteristic
299C2#3182726611yescharacteristic
300C2#3182726711yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#466×C283C2
socleC22×C283C22×D4
hypercenter#466D283
hypocenterC283#3058
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×D8×D283C2semidirect
2. C2×#22583616C2semidirect
3. #31827031C2semidirect
4. #31826717C2semidirect
5. #31826716C2semidirect
6. #31826702C2semidirect
7. #31826701C2semidirect
8. #31826698C2semidirect
9. #31826502C2semidirect
10. #31826468C2semidirect
11. #466×C283C2semidirect
18. C2×#17985376C22semidirect
20. C2×#17985375C22semidirect
22. C2×C8×D283C22semidirect
25. #22583585C22semidirect
26. #22583584C22semidirect
27. #22583581C22semidirect
31. #22583544C22semidirect
32. #22583541C22semidirect
33. #22583532C22semidirect
34. #22583531C22semidirect
35. #22583530C22semidirect
37. C22×C8×C283C22semidirect
38. #121×C283C22semidirect
39. #107×C283C22semidirect
40. #102×C283C22semidirect
65. C8×D283D4semidirect
150. C283#3058semidirect
160. #466D283semidirect
175. C22×C8C2×D283semidirect
181. #121C2×D283semidirect
186. #107C2×D283semidirect
191. #102C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D2832
C2×#225836162
#318270312
#318267172
#318267162
#318267022
#318267012
#318266982
#318265022
#318264682
#466×C2832
#3058283