Finite Group Databasebeta

← #49131585

Subgroups — #49131585

Order 36224.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#31827020C211yesmaximal, characteristic, complemented
2#31827016C211yesmaximal, characteristic
3#31826821C214yesmaximal, complemented
4#31826815C211yesmaximal, characteristic, complemented
5#31826813C211yesmaximal, characteristic, complemented
6#31826812C211yesmaximal, characteristic, complemented
7#31826460C214yesmaximal, complemented
8C4×C8×D283C211yesmaximal, characteristic, complemented
9#487×C283C211yesmaximal, characteristic, complemented
10C2×#17985393C2212yes—
11C2×C8×D283C2212yes—
12#22583610C2211yescharacteristic
13#22583607C2211yescharacteristic
14#22583601C2212yes—
15#22583599C2212yes—
16#22583590—21no—
17#22583586—21no—
18#22583585—21no—
19#22583585—21no—
20Q8×Dic283—21no—
21#22583575—21no—
22#22583572—21no—
23#22583572—21no—
24#22583568C2212yes—
25C42×D283C2211yescharacteristic
26#22583534C2214yes—
27#22583532C2214yes—
28#22583530C2214yes—
29C4×C283⋊C8C2211yescharacteristic
30C8×Dic283C2212yes—
31C4⋊Q8×C283C2211yescharacteristic
32C4⋊Q8×C283C2211yescharacteristic
33#103×C283C2214yes—
34C4×C8×C283C2211yescharacteristic
35#17985393—28no—
36C2×Dic566—21no—
37C2×D1132—22no—
38C2×D1132—21no—
39C2×D1132—21no—
40C2×D1132C2312yes—
41C2×C4×D283—22no—
42C2×C4×D283D411yescharacteristic
43C2×C4×D283D411yescharacteristic
44C2×C4×D283C2311yescharacteristic
45C2×C283⋊C8C2312yes—
46C8×D283—24no—
47C4⋊Dic283—22no—
48C4⋊Dic283—21no—
49C4⋊Dic283C2312yes—
50Dic283⋊C4—22no—
51(C2×D283)⋊C4—22no—
52(C2×D283)⋊C4—22no—
53(C2×D283)⋊C4—22no—
54C4×Dic283—22no—
55C4×Dic283D411yescharacteristic
56C4×Dic283D411yescharacteristic
57C4×Dic283C2311yescharacteristic
58C2×Q8×C283—21no—
59C2×Q8×C283C2312yes—
60C2×C8×C283C2312yes—
61C4⋊C4×C283—21no—
62C4⋊C4×C283—21no—
63C4⋊C4×C283—21no—
64C4⋊C4×C283C2312yes—
65C42×C283C2311yescharacteristic
66C22×D283—22no—
67C22×D283C2×D411yescharacteristic
68Dic566—42no—
69D1132—24no—
70D1132—44no—
71D1132—42no—
72D1132—42no—
73C2×Dic283—22no—
74C2×Dic283C2×D411yescharacteristic
75C2×Dic283C2×D411yescharacteristic
76C2×Dic283C2×D411yescharacteristic
77C4×D283—22no—
78C4×D283—22no—
79C4×D283—44no—
80C4×D283#4114yes—
81C283⋊C8—22no—
82Q8×C283—24no—
83Q8×C283—42no—
84C2×C4×C283—22no—
85C2×C4×C283—22no—
86C2×C4×C283C2×D411yescharacteristic
87C2×C4×C283C2×D411yescharacteristic
88C2×C4×C283C2411yescharacteristic
89C8×C283—22no—
90C22×C283C22×D411yescharacteristic
91C2×D283—21no—
92C2×D283—21no—
93C2×D283—42no—
94C2×D283—42no—
95C2×D283—42no—
96C2×D283#12412yes—
97C4×C283—42no—
98C4×C283—42no—
99C4×C283#13512yes—
100C4×C283#13512yes—
101C4×C283C2×#4112yes—
102Dic283—21no—
103Dic283—21no—
104Dic283—42no—
105Dic283#12412yes—
106C2×C283C2×#12411yescharacteristic
107C2×C283C2×#13511yescharacteristic
108C2×C283C2×#13511yescharacteristic
109D283—22no—
110D283—82no—
111C283#313111yescharacteristic, complemented, Sylow
112#3131—2831nomaximal, Sylow
113#533—2831no—
114#532—2831no—
115#488—2834no—
116#487—2831no—
117#487D28311yescharacteristic, complemented
118#486—2831no—
119#486—2831no—
120#416—2834no—
121C2×C4×C8—2831no—
122C2×#41—2832no—
123C22×C8—2832no—
124C4⋊Q8—2831no—
125C4⋊Q8C2×D28311yescharacteristic
126C4⋊Q8C2×D28311yescharacteristic
127#127—2831no—
128#125—2832no—
129#124—2832no—
130C22⋊Q8—5661no—
131C22⋊Q8—5661no—
132#121—5661no—
133#121—5661no—
134C4×Q8—5661no—
135C4×Q8—5661no—
136C4×D4—5661no—
137C4×D4—5661no—
138#117—2832no—
139C2×C42—2831no—
140#103—2834no—
141#103C2×D28314yes—
142#102—2834no—
143#102—2834no—
144C4×C8—2832no—
145C4×C8—2831no—
146C4×C8C2×D28311yescharacteristic
147#41—5668no—
148C2×Q8—21no—
149C2×Q8—5661no—
150C2×Q8C22×D28312yes—
151C2×D4—2832no—
152C2×D4—5662no—
153C2×D4—5661no—
154C2×D4—5661no—
155C22×C4—2831no—
156C22×C4—2831no—
157C22×C4—2831no—
158C22×C4—5662no—
159C2×C8—2832no—
160C2×C8—5664no—
161C2×C8C22×D28312yes—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—2832no—
166C4⋊C4—5662no—
167C4⋊C4—5662no—
168C4⋊C4—5661no—
169C4⋊C4C22×D28312yes—
170C22⋊C4—5662no—
171C22⋊C4—5662no—
172C22⋊C4—5662no—
173C42—2831no—
174C42—2831no—
175C42—2831no—
176C42—5662no—
177C42C22×D28311yescharacteristic
178C23—2831no—
179C23—5662no—
180Q8—24no—
181Q8—42no—
182Q8—11322no—
183D4—5664no—
184D4—11324no—
185D4—11322no—
186D4—11322no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—2831no—
190C2×C4—2834no—
191C2×C4—2831no—
192C2×C4—2831no—
193C2×C4—5662no—
194C2×C4—5662no—
195C2×C4—5662no—
196C2×C4—11324no—
197C2×C4D4×D28311yescharacteristic
198C2×C4D4×D28311yescharacteristic
199C2×C4C23×D28311yescharacteristic
200C8—22no—
201C8—5662no—
202C22—2832no—
203C22—5661no—
204C22—5661no—
205C22—11322no—
206C22—11322no—
207C22—11322no—
208C22C2×D4×D28311yescharacteristic
209C4—42no—
210C4—42no—
211C4—2832no—
212C4—5661no—
213C4—5661no—
214C4—11322no—
215C4#2258363112yes—
216C4#2258363312yes—
217C4#41×D28312yes—
218C2—5662no—
219C2—22642no—
220C2#124×D28311yescharacteristic
221C2C2×#2258363111yescharacteristic
222C2C2×#2258363311yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#487×C283C2
socleC22×C283C22×D4
prime radical#31827016C2
hypercenter#487D283
hypocenterC283#3131
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #31827020C2semidirect
3. #31826821C2semidirect
4. #31826815C2semidirect
5. #31826813C2semidirect
6. #31826812C2semidirect
7. #31826460C2semidirect
8. C4×C8×D283C2semidirect
9. #487×C283C2semidirect
111. C283#3131semidirect
117. #487D283semidirect

Maximal subgroups

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

subgroupindex
#318270202
#318270162
#318268212
#318268152
#318268132
#318268122
#318264602
C4×C8×D2832
#487×C2832
#3131283