Finite Group Databasebeta

← #49130784

Subgroups — #49130784

Order 36224.

490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C22×#17985379C211yesmaximal, characteristic, complemented
2#31827029C211yesmaximal, characteristic
3#31826943C211yesmaximal, characteristic, complemented
4#31826689C214yesmaximal, complemented
5#31826663C214yesmaximal, complemented
6#31826493C211yesmaximal, characteristic, complemented
7#31826471C211yesmaximal, characteristic, complemented
8#31826461C211yesmaximal, characteristic, complemented
9C2×#137×C283C211yesmaximal, characteristic, complemented
10C22×D1132C2211yescharacteristic
11C2×#17985379—24no—
12C2×#17985379C2214yes—
13C22×C283⋊C8C2211yescharacteristic
14#22583606C2212yes—
15#22583599C2212yes—
16#22583584—22no—
17#22583578—22no—
18Q8×Dic283—22no—
19Q8×Dic283C2214yescomplemented
20#22583569—22no—
21#22583569C2211yescharacteristic
22#22583569C2211yescharacteristic
23Dic283⋊C8C2214yescomplemented
24#22583534C2212yescomplemented
25#22583532C2214yes—
26#22583531C2212yescomplemented
27C2×#41×C283C2211yescharacteristic
28C22×Q8×C283C2211yescharacteristic
29#137×C283—24no—
30C2×Q16×C283C2212yescomplemented
31C2×SD16×C283C2212yescomplemented
32C2×M16×C283C2211yescharacteristic
33C23×D283—21no—
34C2×D1132—22no—
35C2×D1132—21no—
36C2×D1132—22no—
37C2×D1132C2312yes—
38C2×C22⋊D283—24no—
39#17985379—28no—
40C2×C283⋊C8—22no—
41C2×C283⋊C8C2312yes—
42C4⋊Dic283—24no—
43C4⋊Dic283D412yes—
44C4⋊Dic283C2312yes—
45C22⋊Dic283—21no—
46C22⋊Dic283D412yes—
47(C2×D283)⋊C4—24no—
48C4×Dic283—24no—
49C4×Dic283—21no—
50C4×Dic283C2312yes—
51#41×C283—22no—
52#41×C283—22no—
53C2×Q8×C283—21no—
54C2×Q8×C283—22no—
55C2×Q8×C283D414yescomplemented
56C2×Q8×C283C2311yescharacteristic
57C2×Q8×C283C2312yes—
58C2×D4×C283—21no—
59C2×D4×C283C2311yescharacteristic
60C22×C4×C283—21no—
61C22×C4×C283—21no—
62C22×C4×C283C2311yescharacteristic
63Q16×C283—24no—
64SD16×C283—24no—
65M16×C283—22no—
66C2×C8×C283C2312yes—
67C22×D283—22no—
68C22×D283—42no—
69C22×D283—82no—
70D1132—22no—
71D1132—22no—
72D1132—42no—
73C22⋊D283—84no—
74C2×Dic283—22no—
75C2×Dic283C2×D414yes—
76C283⋊C8—22no—
77C23×C283—21no—
78C23×C283C2×D411yescharacteristic
79Q8×C283—24no—
80Q8×C283—22no—
81Q8×C283—21no—
82Q8×C283—21no—
83Q8×C283C2×D414yes—
84D4×C283—21no—
85D4×C283—21no—
86D4×C283—42no—
87C2×C4×C283—24no—
88C2×C4×C283—22no—
89C2×C4×C283—21no—
90C2×C4×C283—42no—
91C2×C4×C283C2×D411yescharacteristic
92C2×C4×C283C2×D412yes—
93C2×C4×C283#4112yes—
94C2×C4×C283C2411yescharacteristic
95C8×C283—22no—
96C22×C283—22no—
97C22×C283—41no—
98C22×C283—42no—
99C22×C283#12112yes—
100C22×C283C22×D411yescharacteristic
101C2×D283—42no—
102C2×D283—44no—
103C2×D283—84no—
104C4×C283—24no—
105C4×C283—41no—
106C4×C283#12112yes—
107C4×C283C22×D411yescharacteristic
108C4×C283C2×#4111yescharacteristic
109Dic283—24no—
110Dic283—42no—
111C2×C283—22no—
112C2×C283—81no—
113C2×C283C2×#12111yescharacteristic
114C2×C283#57712yes—
115D283—82no—
116C283#304311yescharacteristic, complemented, Sylow
117#3043—2831nomaximal, Sylow
118C2×#137D28311yescharacteristic, complemented
119C22×SD16—2831no—
120#535—2831no—
121#519—2831no—
122#464—2834no—
123#460—2834no—
124#424—2831no—
125#418—2831no—
126#416—2831no—
127C2×#41C2×D28311yescharacteristic
128C22×Q8C2×D28311yescharacteristic
129C22×D4—2831no—
130#137—24no—
131C2×Q16C2×D28312yescomplemented
132C2×SD16—2834no—
133C2×SD16—5664no—
134C2×SD16C2×D28312yescomplemented
135C2×M16C2×D28311yescharacteristic
136C22×C8—2831no—
137#127—2832no—
138#124—2832no—
139#121—5662no—
140#120—5662no—
141C4×Q8—2834no—
142C4×Q8—5662no—
143#117—2831no—
144#117—2831no—
145#117—5662no—
146C4⋊C8—2834no—
147#103—2832no—
148#102—2832no—
149#102—2834no—
150C24—5661no—
151#41—22no—
152#41—22no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8C22⋊D28314yescomplemented
156C2×Q8C22×D28311yescharacteristic
157C2×Q8C22×D28312yes—
158C2×D4—21no—
159C2×D4—2832no—
160C2×D4—5664no—
161C2×D4—5661no—
162C2×D4—5662no—
163C2×D4—5662no—
164C2×D4C22×D28311yescharacteristic
165C22×C4—21no—
166C22×C4—21no—
167C22×C4C22×D28311yescharacteristic
168Q16—24no—
169SD16—24no—
170SD16—5668no—
171M16—22no—
172C2×C8—2832no—
173C2×C8—5662no—
174C2×C8C22×D28312yes—
175C4⋊C4—2832no—
176C4⋊C4—2832no—
177C4⋊C4—5664no—
178C22⋊C4—2832no—
179C22⋊C4—5664no—
180C22⋊C4—5661no—
181C42—2832no—
182C42—5664no—
183C42—5661no—
184C23—21no—
185C23—5662no—
186C23—11322no—
187C23—22642no—
188C23D4×D28311yescharacteristic
189Q8—24no—
190Q8—22no—
191Q8—21no—
192Q8—21no—
193Q8C2×C22⋊D28314yes—
194D4—21no—
195D4—21no—
196D4—42no—
197D4—5662no—
198D4—5662no—
199D4—11322no—
200D4—22644no—
201C2×C4—24no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—42no—
205C2×C4—2834no—
206C2×C4—5662no—
207C2×C4D4×D28311yescharacteristic
208C2×C4C2×C22⋊D28312yes—
209C2×C4#1798539112yes—
210C2×C4C23×D28311yescharacteristic
211C8—22no—
212C8—5662no—
213C22—22no—
214C22—41no—
215C22—42no—
216C22—11322no—
217C22—11324no—
218C22—22644no—
219C22#2258358212yes—
220C22C2×D4×D28311yescharacteristic
221C4—24no—
222C4—41no—
223C4—5664no—
224C4—11322no—
225C4#2258358212yes—
226C4C22×C22⋊D28311yescharacteristic
227C4C2×#1798539111yescharacteristic
228C2—22no—
229C2—81no—
230C2—22642no—
231C2C2×#2258358211yescharacteristic
232C2#3182727412yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#137×C283C2
socleC22×C283C22×D4
prime radical#31827029C2
hypercenterC2×#137D283
hypocenterC283#3043
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C22×#17985379C2semidirect
3. #31826943C2semidirect
4. #31826689C2semidirect
5. #31826663C2semidirect
6. #31826493C2semidirect
7. #31826471C2semidirect
8. #31826461C2semidirect
9. C2×#137×C283C2semidirect
19. Q8×Dic283C22semidirect
23. Dic283⋊C8C22semidirect
24. #22583534C22semidirect
26. #22583531C22semidirect
30. C2×Q16×C283C22semidirect
31. C2×SD16×C283C22semidirect
55. C2×Q8×C283D4semidirect
116. C283#3043semidirect
118. C2×#137D283semidirect
131. C2×Q16C2×D283semidirect
134. C2×SD16C2×D283semidirect
155. C2×Q8C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
C22×#179853792
#318270292
#318269432
#318266892
#318266632
#318264932
#318264712
#318264612
C2×#137×C2832
#3043283