Finite Group Databasebeta

← #49130907

Subgroups — #49130907

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×#22583618C211yesmaximal, characteristic, complemented
3#31827031C212yesmaximal, complemented
4#31826719C211yesmaximal, characteristic, complemented
5#31826718C211yesmaximal, characteristic, complemented
6#31826715C211yesmaximal, characteristic, complemented
7#31826700C212yesmaximal, complemented
8#31826699C212yesmaximal, complemented
9#31826500C211yesmaximal, characteristic, complemented
10#31826468C212yesmaximal, complemented
11#469×C283C211yesmaximal, characteristic, complemented
12C2×#17985392C2211yescharacteristic
13C2×D4×D283C2212yes—
14C2×D2264C2211yescharacteristic
15C2×#17985377C2212yes—
16D8×D283—24no—
17#22583618—24no—
18C2×#17985375C2211yescharacteristic
19C2×#17985375C2211yescharacteristic, complemented
20C22×C283⋊C8C2211yescharacteristic, 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#22583543C2212yescomplemented
32#22583542C2211yescharacteristic, complemented
33#22583532C2212yescomplemented
34#22583531C2212yescomplemented
35#22583530C2212yescomplemented
36C2×D8×C283C2211yescharacteristic
37C2×M16×C283C2211yescharacteristic, complemented
38#121×C283C2212yescomplemented
39#106×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#17985375—22no—
60#17985375—22no—
61C2×C283⋊C8—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—
76M16×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—22no—
120C22×C283—42no—
121C22×C283—42no—
122C22×C283—42no—
123C22×C283C22×D411yescharacteristic
124C2×D283—22no—
125C2×D283—21no—
126C2×D283—22no—
127C2×D283—42no—
128C2×D283—42no—
129C2×D283—42no—
130C2×D283—88no—
131C2×D283#12112yes—
132C4×C283—21no—
133C4×C283—42no—
134C4×C283C22×D411yescharacteristic
135C4×C283C2×#4111yescharacteristic
136Dic283—21no—
137Dic283—42no—
138Dic283#12112yes—
139C2×C283—41no—
140C2×C283—82no—
141C2×C283C2×#12111yescharacteristic
142C2×C283#57612yes—
143D283—22no—
144D283—41no—
145D283—82no—
146C283#305811yescharacteristic, complemented, Sylow
147#3058—2831nomaximal, Sylow
148C22×D8—2831no—
149C2×#131—2831no—
150#535—2832no—
151#469—2831no—
152#469—2831no—
153#469—2831no—
154#469D28311yescharacteristic, complemented
155#466—2832no—
156#466—2832no—
157#427—2831no—
158#418—2832no—
159C2×#41—2831no—
160C22×D4—2832no—
161C2×D8—2832no—
162C2×D8—2831no—
163C2×D8—5664no—
164C2×D8C2×D28311yescharacteristic
165#131—5664no—
166C2×M16—2831no—
167C2×M16—2831no—
168C2×M16C2×D28311yescharacteristic, complemented
169C22×C8—2831no—
170C22×C8—2831no—
171C22×C8—2831no—
172#127—5662no—
173#124—5662no—
174#121—2832no—
175#121—2832no—
176#121—2832no—
177#121C2×D28312yescomplemented
178#120—5662no—
179#120—5662no—
180#117—2832no—
181#107—2832no—
182#106—2831no—
183#106C2×D28311yescharacteristic, complemented
184#102—2832no—
185#102—2832no—
186#102—2832no—
187#102C2×D28312yescomplemented
188C24—5662no—
189#41—5662no—
190#41—5662no—
191C2×Q8—2831no—
192C2×D4—22no—
193C2×D4—2831no—
194C2×D4—2831no—
195C2×D4—2831no—
196C2×D4—2832no—
197C2×D4—5662no—
198C2×D4—5664no—
199C2×D4—5664no—
200C2×D4—5662no—
201C2×D4—5662no—
202C2×D4—5662no—
203C2×D4C22×D28312yes—
204C22×C4—2831no—
205C22×C4—2831no—
206C22×C4C22×D28311yescharacteristic
207D8—22no—
208D8—5664no—
209D8—5662no—
210M16—22no—
211M16—5662no—
212M16—5662no—
213C2×C8—2831no—
214C2×C8—2834no—
215C2×C8—2831no—
216C2×C8—5662no—
217C2×C8—5662no—
218C2×C8C22×D28311yescharacteristic
219C2×C8C22×D28311yescharacteristic
220C4⋊C4—2832no—
221C4⋊C4C22×D28312yes—
222C22⋊C4—22no—
223C22⋊C4—5662no—
224C22⋊C4—5662no—
225C22⋊C4—5662no—
226C22⋊C4—5662no—
227C42—5662no—
228C23—22no—
229C23—2831no—
230C23—2831no—
231C23—5662no—
232C23—11324no—
233C23—22642no—
234C23—22642no—
235C23D4×D28311yescharacteristic
236Q8—5662no—
237D4—22no—
238D4—22no—
239D4—82no—
240D4—5662no—
241D4—5662no—
242D4—5662no—
243D4—5662no—
244D4—5662no—
245D4—11324no—
246D4—22642no—
247D4—22642no—
248D4—22642no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—2831no—
253C2×C4—2832no—
254C2×C4—2832no—
255C2×C4—2831no—
256C2×C4—5661no—
257C2×C4—5661no—
258C2×C4—5662no—
259C2×C4D4×D28311yescharacteristic
260C2×C4C23×D28311yescharacteristic
261C8—21no—
262C8—2832no—
263C8—5661no—
264C8D4×D28312yes—
265C22—21no—
266C22—22no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—2832no—
271C22—5662no—
272C22—5661no—
273C22—5662no—
274C22—11322no—
275C22—11322no—
276C22—11322no—
277C22—22648no—
278C22C2×D4×D28311yescharacteristic
279C4—21no—
280C4—42no—
281C4—2832no—
282C4—5661no—
283C4—11322no—
284C4C2×D4×D28311yescharacteristic
285C4#41×D28311yescharacteristic
286C2—41no—
287C2—82no—
288C2—5662no—
289C2—11321no—
290C2—22642no—
291C2#121×D28311yescharacteristic
292C2#3182726912yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#469×C283C2
socleC22×C283C22×D4
hypercenter#469D283
hypocenterC283#3058
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×D8×D283C2semidirect
2. C2×#22583618C2semidirect
3. #31827031C2semidirect
4. #31826719C2semidirect
5. #31826718C2semidirect
6. #31826715C2semidirect
7. #31826700C2semidirect
8. #31826699C2semidirect
9. #31826500C2semidirect
10. #31826468C2semidirect
11. #469×C283C2semidirect
19. C2×#17985375C22semidirect
20. C22×C283⋊C8C22semidirect
22. C2×C8×D283C22semidirect
25. #22583585C22semidirect
26. #22583584C22semidirect
27. #22583581C22semidirect
31. #22583543C22semidirect
32. #22583542C22semidirect
33. #22583532C22semidirect
34. #22583531C22semidirect
35. #22583530C22semidirect
37. C2×M16×C283C22semidirect
38. #121×C283C22semidirect
39. #106×C283C22semidirect
40. #102×C283C22semidirect
65. C8×D283D4semidirect
146. C283#3058semidirect
154. #469D283semidirect
168. C2×M16C2×D283semidirect
177. #121C2×D283semidirect
183. #106C2×D283semidirect
187. #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×#225836182
#318270312
#318267192
#318267182
#318267152
#318267002
#318266992
#318265002
#318264682
#469×C2832
#3058283