Finite Group Databasebeta

← #49131499

Subgroups — #49131499

Order 36224.

418 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 121 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#31826939C211yesmaximal, characteristic, complemented
2#31826786C212yesmaximal, complemented
3#31826762C212yesmaximal, complemented
4#31826657C212yesmaximal, complemented
5#31826598C212yesmaximal, complemented
6#31826575C212yesmaximal, complemented
7C4×#17985377C212yesmaximal, complemented
8#31826526C211yesmaximal, characteristic, complemented
9#540×C283C211yesmaximal, characteristic, complemented
10C22×D1132C2211yescharacteristic
11C2×#17985377C2212yes—
12C2×#17985377C2212yes—
13C4×D1132C2212yes—
14C4×D1132C2212yes—
15#22583572—22no—
16#22583569C2211yescharacteristic
17C22⋊C4×D283—22no—
18#22583543C2212yescomplemented
19#22583541C2212yescomplemented
20C4⋊(C283⋊C8)C2212yescomplemented
21#22583531C2212yescomplemented
22#22583531C2212yescomplemented
23#22583530C2212yes—
24#22583530C2212yes—
25C22⋊(C283⋊C8)C2212yes—
26#22583521C2211yescharacteristic, complemented
27C4×C283⋊C8C2211yescharacteristic, complemented
28#127×C283C2211yescharacteristic, complemented
29#125×C283C2211yescharacteristic, complemented
30#123×C283—22no—
31#121×C283—22no—
32#121×C283C2212yes—
33C4×D4×C283C2212yescomplemented
34#117×C283C2211yescharacteristic
35C23×D283—21no—
36C2×D1132—24no—
37C2×D1132—21no—
38C2×D1132C2312yes—
39C2×C4×D283—22no—
40C2×C4×D283—22no—
41#17985377—24no—
42#17985377—24no—
43C2×C283⋊C8C2312yes—
44C2×C283⋊C8C2312yes—
45C4⋊Dic283C2312yes—
46C22⋊Dic283—21no—
47(C2×D283)⋊C4—22no—
48(C2×D283)⋊C4—22no—
49C4×Dic283—21no—
50C2×D4×C283—22no—
51C2×D4×C283—22no—
52C2×D4×C283C2312yes—
53C22×C4×C283—22no—
54C22×C4×C283C2311yescharacteristic
55C4⋊C4×C283—22no—
56C4⋊C4×C283D412yes—
57C4⋊C4×C283C2312yes—
58C22⋊C4×C283—22no—
59C22⋊C4×C283—22no—
60C22⋊C4×C283D412yes—
61C42×C283C2311yescharacteristic
62C42×C283C2311yescharacteristic
63C22×D283—22no—
64C22×D283—24no—
65C22×D283—82no—
66D1132—24no—
67D1132—22no—
68D1132#4114yes—
69C2×Dic283—22no—
70C4×D283—82no—
71C4×D283—82no—
72C283⋊C8—22no—
73C283⋊C8—22no—
74C23×C283—22no—
75C23×C283C2×D411yescharacteristic
76D4×C283—22no—
77D4×C283—22no—
78D4×C283—82no—
79D4×C283—82no—
80C2×C4×C283—22no—
81C2×C4×C283—22no—
82C2×C4×C283—82no—
83C2×C4×C283C2×D412yes—
84C2×C4×C283C2×D412yes—
85C2×C4×C283C2×D411yescharacteristic
86C2×C4×C283C2411yescharacteristic
87C22×C283—21no—
88C22×C283—22no—
89C22×C283—42no—
90C22×C283—42no—
91C22×C283—42no—
92C22×C283C22×D411yescharacteristic
93C2×D283—24no—
94C2×D283—42no—
95C2×D283—42no—
96C2×D283—84no—
97C4×C283—21no—
98C4×C283—22no—
99C4×C283—22no—
100C4×C283—42no—
101C4×C283C2×#4112yes—
102Dic283—42no—
103C2×C283—41no—
104C2×C283—82no—
105C2×C283#52511yescharacteristic
106C2×C283#57612yes—
107D283—44no—
108C283#312211yescharacteristic, complemented, Sylow
109#3122—2831nomaximal, Sylow
110#540D28311yescharacteristic, complemented
111#518—2831no—
112#482—2832no—
113#478—2832no—
114#459—2832no—
115#447—2832no—
116#442—2832no—
117C4×D8—2832no—
118#433—2831no—
119C22×D4—2831no—
120C2×D8—2832no—
121C2×D8—2832no—
122#127C2×D28311yescharacteristic, complemented
123#125C2×D28311yescharacteristic, complemented
124#123—22no—
125#121—22no—
126#121C2×D28312yes—
127C4×D4—2832no—
128C4×D4—2832no—
129C4×D4—5662no—
130C4×D4C2×D28312yescomplemented
131#117—2831no—
132#117C2×D28311yescharacteristic
133C2×C22⋊C4—5662no—
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—5661no—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4—2832no—
148C2×D4—5664no—
149C2×D4—5661no—
150C2×D4C22×D28312yes—
151C22×C4—22no—
152C22×C4—5662no—
153C22×C4—5662no—
154C22×C4C22×D28311yescharacteristic
155D8—5664no—
156D8—5664no—
157C2×C8—2832no—
158C2×C8—2832no—
159C4⋊C4—22no—
160C4⋊C4—2832no—
161C4⋊C4C22⋊D28312yes—
162C4⋊C4C22×D28312yes—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C22⋊C4—5661no—
166C22⋊C4—5662no—
167C22⋊C4—5662no—
168C22⋊C4C22⋊D28312yes—
169C42—5661no—
170C42C22×D28311yescharacteristic
171C42C22×D28311yescharacteristic
172C23—22no—
173C23—5664no—
174C23—5662no—
175C23—22642no—
176C23C2×C22⋊D28311yescharacteristic
177D4—22no—
178D4—22no—
179D4—82no—
180D4—82no—
181D4—2834no—
182D4—5664no—
183D4—5662no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—5662no—
188C2×C4—22642no—
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—22no—
198C22—42no—
199C22—42no—
200C22—42no—
201C22—5664no—
202C22—11322no—
203C22—11322no—
204C22—22644no—
205C22C22×C22⋊D28311yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—11322no—
211C4#41×D28312yes—
212C2—41no—
213C2—82no—
214C2—11324no—
215C2#3182697211yescharacteristic
216C2#3182726812yes—
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#540×C283C2
socleC22×C283C22×D4
hypercenter#540D283
hypocenterC283#3122
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #31826939C2semidirect
2. #31826786C2semidirect
3. #31826762C2semidirect
4. #31826657C2semidirect
5. #31826598C2semidirect
6. #31826575C2semidirect
7. C4×#17985377C2semidirect
8. #31826526C2semidirect
9. #540×C283C2semidirect
18. #22583543C22semidirect
19. #22583541C22semidirect
20. C4⋊(C283⋊C8)C22semidirect
21. #22583531C22semidirect
22. #22583531C22semidirect
26. #22583521C22semidirect
27. C4×C283⋊C8C22semidirect
28. #127×C283C22semidirect
29. #125×C283C22semidirect
33. C4×D4×C283C22semidirect
108. C283#3122semidirect
110. #540D283semidirect
122. #127C2×D283semidirect
123. #125C2×D283semidirect
130. C4×D4C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318269392
#318267862
#318267622
#318266572
#318265982
#318265752
C4×#179853772
#318265262
#540×C2832
#3122283