Finite Group Databasebeta

← #49131504

Subgroups — #49131504

Order 36224.

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

normal subgroups only

This group has 418 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#31827070C211yesmaximal, characteristic, complemented
2#31826789C212yesmaximal, complemented
3#31826765C212yesmaximal, complemented
4#31826660C212yesmaximal, complemented
5#31826599C212yesmaximal, complemented
6#31826575C212yesmaximal, complemented
7C4×#17985377C212yesmaximal, complemented
8#31826526C211yesmaximal, characteristic, complemented
9#518×C283C211yesmaximal, characteristic, complemented
10C2×#17985377C2212yes—
11C2×#17985377C2212yes—
12#22583607C2211yescharacteristic, complemented
13#22583602C2211yescharacteristic, complemented
14#22583595—22no—
15#22583584C2212yes—
16#22583583—22no—
17C4×D1132C2212yescomplemented
18#22583543C2212yescomplemented
19#22583541C2212yescomplemented
20C4⋊(C283⋊C8)C2212yescomplemented
21#22583531C2212yes—
22#22583531C2212yes—
23#22583530C2212yescomplemented
24#22583530C2212yescomplemented
25C22⋊(C283⋊C8)C2212yes—
26#22583521C2211yescharacteristic, complemented
27C4×C283⋊C8C2211yescharacteristic, complemented
28C22×D4×C283C2211yescharacteristic
29C4×D4×C283—22no—
30C4×D4×C283C2212yes—
31C4×D4×C283C2212yes—
32#117×C283C2211yescharacteristic
33#117×C283C2211yescharacteristic
34C2×C22⋊C4×C283—22no—
35C2×D1132—22no—
36C2×D1132C2312yes—
37C2×C22⋊D283—22no—
38C2×C4×D283—22no—
39#17985377—24no—
40#17985377—24no—
41C2×C283⋊C8C2312yes—
42C2×C283⋊C8C2312yes—
43C4⋊Dic283C2312yes—
44Dic283⋊C4—22no—
45(C2×D283)⋊C4—22no—
46(C2×D283)⋊C4—22no—
47C24×C283—21no—
48C2×D4×C283—24no—
49C2×D4×C283—21no—
50C2×D4×C283C2312yes—
51C22×C4×C283—22no—
52C22×C4×C283—22no—
53C22×C4×C283C2311yescharacteristic
54C4⋊C4×C283D412yes—
55C4⋊C4×C283C2312yes—
56C22⋊C4×C283—21no—
57C22⋊C4×C283—22no—
58C22⋊C4×C283—22no—
59C22⋊C4×C283D412yes—
60C42×C283—21no—
61C42×C283C2311yescharacteristic
62C42×C283C2311yescharacteristic
63C22×D283—22no—
64D1132—22no—
65D1132—22no—
66D1132—82no—
67C22⋊D283—82no—
68C2×Dic283—22no—
69C4×D283—82no—
70C283⋊C8—22no—
71C283⋊C8—22no—
72C23×C283—24no—
73C23×C283—22no—
74C23×C283—82no—
75C23×C283C2×D411yescharacteristic
76D4×C283—24no—
77D4×C283—22no—
78D4×C283#4114yes—
79C2×C4×C283—22no—
80C2×C4×C283—22no—
81C2×C4×C283—82no—
82C2×C4×C283—82no—
83C2×C4×C283C2×D411yescharacteristic
84C2×C4×C283C2×D412yes—
85C2×C4×C283C2×D412yes—
86C2×C4×C283C2411yescharacteristic
87C22×C283—21no—
88C22×C283—24no—
89C22×C283—22no—
90C22×C283—42no—
91C22×C283—42no—
92C22×C283—84no—
93C22×C283C22×D411yescharacteristic
94C2×D283—42no—
95C2×D283—42no—
96C2×D283—42no—
97C4×C283—21no—
98C4×C283—22no—
99C4×C283—22no—
100C4×C283—42no—
101C4×C283C2×#4112yes—
102Dic283—42no—
103C2×C283—41no—
104C2×C283—44no—
105C2×C283#52511yescharacteristic
106C2×C283#57612yes—
107D283—82no—
108C283#312211yescharacteristic, complemented, Sylow
109#3122—2831nomaximal, Sylow
110#540—2831no—
111#518D28311yescharacteristic, complemented
112#482—2832no—
113#478—2832no—
114#459—2832no—
115#447—2832no—
116#442—2832no—
117C4×D8—2832no—
118#433—2831no—
119C22×D4C2×D28311yescharacteristic
120C2×D8—2832no—
121C2×D8—2832no—
122#127—2831no—
123#125—2831no—
124#123—5662no—
125#121—2832no—
126#121—5662no—
127C4×D4—22no—
128C4×D4—2832no—
129C4×D4C2×D28312yes—
130C4×D4C2×D28312yes—
131#117C2×D28311yescharacteristic
132#117C2×D28311yescharacteristic
133C2×C22⋊C4—22no—
134#107—2832no—
135#106—2832no—
136C4⋊C8—2832no—
137#102—2832no—
138#102—2832no—
139#102—2832no—
140#102—2832no—
141C22⋊C8—2832no—
142#97—2831no—
143C4×C8—2831no—
144C24—21no—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—2832no—
148C2×D4—5662no—
149C2×D4—5662no—
150C2×D4C22×D28312yes—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—5662no—
154C22×C4C22×D28311yescharacteristic
155D8—5664no—
156D8—5664no—
157C2×C8—2832no—
158C2×C8—2832no—
159C4⋊C4—2832no—
160C4⋊C4—5662no—
161C4⋊C4C22⋊D28312yes—
162C4⋊C4C22×D28312yes—
163C22⋊C4—21no—
164C22⋊C4—22no—
165C22⋊C4—22no—
166C22⋊C4—5662no—
167C22⋊C4—5662no—
168C22⋊C4C22⋊D28312yes—
169C42—21no—
170C42C22×D28311yescharacteristic
171C42C22×D28311yescharacteristic
172C23—24no—
173C23—22no—
174C23—82no—
175C23—5662no—
176C23C2×C22⋊D28311yescharacteristic
177D4—24no—
178D4—22no—
179D4—5662no—
180D4—5662no—
181D4—22642no—
182D4—22642no—
183D4#1798539214yes—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—82no—
188C2×C4—5662no—
189C2×C4—22642no—
190C2×C4C2×C22⋊D28311yescharacteristic
191C2×C4C2×C22⋊D28312yes—
192C2×C4C2×C22⋊D28312yes—
193C2×C4C23×D28311yescharacteristic
194C8—5662no—
195C8—5662no—
196C22—21no—
197C22—24no—
198C22—22no—
199C22—42no—
200C22—42no—
201C22—84no—
202C22—11322no—
203C22—11322no—
204C22—11322no—
205C22C22×C22⋊D28311yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—11322no—
211C4C2×#1798539212yes—
212C2—41no—
213C2—44no—
214C2—22642no—
215C2#3182697611yescharacteristic
216C2#3182726812yes—
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#518×C283C2
socleC22×C283C22×D4
hypercenter#518D283
hypocenterC283#3122
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #31827070C2semidirect
2. #31826789C2semidirect
3. #31826765C2semidirect
4. #31826660C2semidirect
5. #31826599C2semidirect
6. #31826575C2semidirect
7. C4×#17985377C2semidirect
8. #31826526C2semidirect
9. #518×C283C2semidirect
12. #22583607C22semidirect
13. #22583602C22semidirect
17. C4×D1132C22semidirect
18. #22583543C22semidirect
19. #22583541C22semidirect
20. C4⋊(C283⋊C8)C22semidirect
23. #22583530C22semidirect
24. #22583530C22semidirect
26. #22583521C22semidirect
27. C4×C283⋊C8C22semidirect
108. C283#3122semidirect
111. #518D283semidirect

Maximal subgroups

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

subgroupindex
#318270702
#318267892
#318267652
#318266602
#318265992
#318265752
C4×#179853772
#318265262
#518×C2832
#3122283