Finite Group Databasebeta

← #49130925

Subgroups — #49130925

Order 36224.

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

normal subgroups only

This group has 484 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×#22583633C211yesmaximal, characteristic, complemented
2C2×#22583618C211yesmaximal, characteristic, complemented
3#31827045C212yesmaximal, complemented
4#31826720C211yesmaximal, characteristic, complemented
5#31826719C211yesmaximal, characteristic, complemented
6#31826718C211yesmaximal, characteristic, complemented
7#31826697C212yesmaximal, complemented
8#31826696C212yesmaximal, complemented
9#106×D283C211yesmaximal, characteristic, complemented
10#31826465C212yesmaximal, complemented
11#470×C283C211yesmaximal, characteristic, complemented
12C2×#17985393C2212yes—
13C2×#17985392C2211yescharacteristic
14#22583633—24no—
15C2×#17985379C2212yes—
16C2×D2264C2211yescharacteristic
17#22583618—24no—
18C2×#17985375C2211yescharacteristic
19C2×#17985375C2211yescharacteristic
20C22×C283⋊C8C2211yescharacteristic
21C2×C8×D283C2211yescharacteristic
22C2×C8×D283C2211yescharacteristic
23#22583588—22no—
24#22583586C2212yes—
25#22583585—22no—
26#22583585C2212yes—
27#22583584C2212yes—
28#22583583—22no—
29#22583583—22no—
30C4⋊C4×D283C2212yes—
31#22583542C2211yescharacteristic
32#22583541C2212yes—
33#22583534C2212yes—
34#22583532C2212yes—
35#22583530C2212yes—
36C2×Q16×C283C2211yescharacteristic
37C2×M16×C283C2211yescharacteristic
38C22⋊Q8×C283C2212yes—
39#106×C283C2211yescharacteristic
40#103×C283C2212yes—
41#17985393—24no—
42#17985393—24no—
43#17985392—22no—
44#17985392—22no—
45C2×Dic566D411yescharacteristic
46C2×D1132—22no—
47C2×D1132—22no—
48C2×D1132D411yescharacteristic
49C2×D1132C2312yes—
50C2×C22⋊D283—22no—
51C2×C22⋊D283D411yescharacteristic
52C2×C22⋊D283D411yescharacteristic
53C2×C4×D283—22no—
54C2×C4×D283—22no—
55C2×C4×D283C2311yescharacteristic
56C2×C4×D283C2311yescharacteristic
57#17985379—24no—
58D2264—22no—
59#17985375—22no—
60#17985375—22no—
61C2×C283⋊C8—22no—
62C2×C283⋊C8C2311yescharacteristic
63C2×C283⋊C8C2311yescharacteristic
64C8×D283—22no—
65C8×D283D414yescomplemented
66C4⋊Dic283C2312yes—
67Dic283⋊C4—22no—
68Dic283⋊C4—22no—
69(C2×D283)⋊C4—22no—
70(C2×D283)⋊C4—22no—
71(C2×D283)⋊C4—22no—
72C2×Q8×C283C2312yes—
73C22×C4×C283C2311yescharacteristic
74Q16×C283—22no—
75M16×C283—22no—
76C2×C8×C283C2311yescharacteristic
77C2×C8×C283C2311yescharacteristic
78C4⋊C4×C283—22no—
79C4⋊C4×C283C2312yes—
80C22⋊C4×C283—22no—
81C22×D283—22no—
82C22×D283C2×D411yescharacteristic
83C22×D283C2×D411yescharacteristic
84Dic566—22no—
85D1132—22no—
86D1132—22no—
87D1132—22no—
88D1132—44no—
89D1132—82no—
90C22⋊D283—22no—
91C22⋊D283—22no—
92C22⋊D283—82no—
93C2×Dic283—22no—
94C2×Dic283C2×D411yescharacteristic
95C2×Dic283C2×D411yescharacteristic
96C4×D283—21no—
97C4×D283—21no—
98C4×D283—44no—
99C4×D283—82no—
100C4×D283C2×D412yes—
101C4×D283#4112yes—
102C283⋊C8—21no—
103C283⋊C8C2×D412yes—
104C23×C283C2×D411yescharacteristic
105Q8×C283—22no—
106Q8×C283—22no—
107C2×C4×C283—21no—
108C2×C4×C283—21no—
109C2×C4×C283—22no—
110C2×C4×C283—22no—
111C2×C4×C283C2×D411yescharacteristic
112C2×C4×C283C2411yescharacteristic
113C8×C283—21no—
114C8×C283C2×D412yes—
115C22×C283—21no—
116C22×C283—22no—
117C22×C283C22×D411yescharacteristic
118C2×D283—22no—
119C2×D283—21no—
120C2×D283—22no—
121C2×D283—42no—
122C2×D283—42no—
123C2×D283—42no—
124C2×D283#12112yes—
125C4×C283—21no—
126C4×C283—42no—
127C4×C283—42no—
128C4×C283C22×D411yescharacteristic
129C4×C283C2×#4111yescharacteristic
130Dic283—21no—
131Dic283—42no—
132Dic283#12112yes—
133C2×C283—41no—
134C2×C283C2×#12111yescharacteristic
135C2×C283#57712yes—
136D283—22no—
137D283—41no—
138D283—82no—
139C283#306011yescharacteristic, complemented, Sylow
140#3060—2831nomaximal, Sylow
141C2×#135—2831no—
142C2×#131—2831no—
143#537—2832no—
144#470—2831no—
145#470D28311yescharacteristic, complemented
146#469—2831no—
147#469—2831no—
148#465—2832no—
149#465—2832no—
150C2×#106—2831no—
151#417—2832no—
152C2×#41—2831no—
153C2×#41—2832no—
154#135—5664no—
155C2×Q16C2×D28311yescharacteristic
156C2×SD16—2832no—
157C2×D8—2831no—
158#131—5664no—
159C2×M16—2831no—
160C2×M16—2831no—
161C2×M16C2×D28311yescharacteristic
162C22×C8—2831no—
163C22×C8—2831no—
164C22×C8—2831no—
165C22⋊Q8—2832no—
166C22⋊Q8—5662no—
167C22⋊Q8C2×D28312yes—
168#121—2832no—
169#121—2832no—
170#121—5662no—
171#121—5662no—
172#121—5662no—
173C2×C4⋊C4—2832no—
174#106—2831no—
175#106—2832no—
176#106C2×D28311yescharacteristic
177#103—2832no—
178#103C2×D28312yes—
179#102—2832no—
180#102—2832no—
181#41—5662no—
182#41—5662no—
183#41—5664no—
184#41—5664no—
185C2×Q8—2831no—
186C2×Q8C22×D28312yes—
187C2×D4—2831no—
188C2×D4—2831no—
189C2×D4—2831no—
190C2×D4—2832no—
191C2×D4—5662no—
192C2×D4—5662no—
193C2×D4—5662no—
194C22×C4—2831no—
195C22×C4—2831no—
196C22×C4—5662no—
197C22×C4—5662no—
198C22×C4C22×D28311yescharacteristic
199Q16—22no—
200SD16—5664no—
201D8—5662no—
202M16—22no—
203M16—5662no—
204M16—5662no—
205C2×C8—2831no—
206C2×C8—2834no—
207C2×C8—2831no—
208C2×C8—5662no—
209C2×C8—5662no—
210C2×C8C22×D28311yescharacteristic
211C2×C8C22×D28311yescharacteristic
212C4⋊C4—22no—
213C4⋊C4—2832no—
214C4⋊C4—5662no—
215C4⋊C4—5662no—
216C4⋊C4C22×D28312yes—
217C22⋊C4—22no—
218C22⋊C4—5662no—
219C22⋊C4—5662no—
220C22⋊C4—5662no—
221C23—2831no—
222C23—2831no—
223C23—5662no—
224C23D4×D28311yescharacteristic
225Q8—22no—
226Q8—22no—
227Q8—5662no—
228D4—5662no—
229D4—5662no—
230D4—5662no—
231D4—5662no—
232D4—5662no—
233D4—11324no—
234D4—22642no—
235D4—22642no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—2831no—
241C2×C4—2832no—
242C2×C4—2832no—
243C2×C4—2831no—
244C2×C4—5661no—
245C2×C4—5661no—
246C2×C4—5662no—
247C2×C4—11324no—
248C2×C4—22642no—
249C2×C4D4×D28311yescharacteristic
250C2×C4C23×D28311yescharacteristic
251C8—21no—
252C8—2832no—
253C8—5661no—
254C8D4×D28312yes—
255C22—21no—
256C22—22no—
257C22—2832no—
258C22—5662no—
259C22—5661no—
260C22—5662no—
261C22—11322no—
262C22—11322no—
263C22—11322no—
264C22C2×D4×D28311yescharacteristic
265C4—21no—
266C4—42no—
267C4—42no—
268C4—2832no—
269C4—5661no—
270C4—11322no—
271C4C2×D4×D28311yescharacteristic
272C4#41×D28311yescharacteristic
273C2—41no—
274C2—5662no—
275C2—11321no—
276C2—22642no—
277C2#121×D28311yescharacteristic
278C2#3182727412yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#470×C283C2
socleC22×C283C22×D4
hypercenter#470D283
hypocenterC283#3060
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. C2×#22583633C2semidirect
2. C2×#22583618C2semidirect
3. #31827045C2semidirect
4. #31826720C2semidirect
5. #31826719C2semidirect
6. #31826718C2semidirect
7. #31826697C2semidirect
8. #31826696C2semidirect
9. #106×D283C2semidirect
10. #31826465C2semidirect
11. #470×C283C2semidirect
65. C8×D283D4semidirect
139. C283#3060semidirect
145. #470D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836332
C2×#225836182
#318270452
#318267202
#318267192
#318267182
#318266972
#318266962
#106×D2832
#318264652
#470×C2832
#3060283