Finite Group Databasebeta

← #49134673

Subgroups — #49134673

Order 36224.

1160 conjugacy classes of subgroups; only the 471 normal subgroups are shown.

normal subgroups only

This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 471 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#31827064C216yesmaximal, complemented
2#31827055C216yesmaximal, complemented
3#31827027C213yesmaximal, complemented
4#31827001C216yesmaximal, complemented
5#31826978C216yesmaximal, complemented
6C2×(C22⋊D283)⋊C4C213yesmaximal, complemented
7#543×C283C211yesmaximal, characteristic, complemented
8C2×#17985393C2212yescomplemented
9C22×C22⋊D283C2213yes—
10C23×Dic283C2211yescharacteristic
11C22×C4×D283C2213yescomplemented
12#22583605C22112yescomplemented
13#22583601C2216yescomplemented
14#22583599C2216yescomplemented
15#22583595C22112yescomplemented
16#22583594C22112yescomplemented
17#22583586C2216yescomplemented
18#22583585C2216yescomplemented
19#22583584C2216yes—
20#22583584C2216yes—
21#22583580C22112yescomplemented
22Q8×Dic283C2212yescomplemented
23#22583572C2216yescomplemented
24(C22⋊D283)⋊C4C22112yescomplemented
25(C22⋊D283)⋊C4C22112yescomplemented
26#22583568C2216yescomplemented
27C2×Dic283⋊C4C2213yescomplemented
28C2×(C2×D283)⋊C4C2213yescomplemented
29C2×C4×Dic283C2213yescomplemented
30C22⋊Q8×C283C2216yescomplemented
31C22⋊Q8×C283C2216yescomplemented
32C2×C22⋊C4×C283C2213yes—
33C23×D283C2313yes—
34#17985393—44no—
35C2×D1132C2316yes—
36C2×D1132C2316yes—
37C2×C22⋊D283—212no—
38C2×C22⋊D283C23112yes—
39C22×Dic283—42no—
40C22×Dic283C2313yes—
41C22×Dic283C2313yes—
42C22×Dic283C2313yes—
43C2×C4×D283—46no—
44C2×C4×D283C2316yes—
45C2×C4×D283C2316yes—
46C4⋊Dic283C2316yes—
47C4⋊Dic283C2316yes—
48Dic283⋊C4C23112yes—
49(C2×D283)⋊C4C23112yes—
50(C2×D283)⋊C4C23112yes—
51(C2×D283)⋊C4C23112yes—
52C4×Dic283C2316yes—
53C4×Dic283C2316yes—
54C24×C283C2311yescharacteristic
55C2×Q8×C283C2312yes—
56C2×Q8×C283C2312yes—
57C22×C4×C283C2313yes—
58C22×C4×C283C2313yes—
59C4⋊C4×C283C2316yes—
60C4⋊C4×C283C2316yes—
61C22⋊C4×C283C23112yes—
62C22×D283—26no—
63C22×D283—43no—
64C22×D283—43no—
65C22×D283C2416yes—
66D1132—46no—
67D1132—46no—
68C22⋊D283—224no—
69C2×Dic283—26no—
70C2×Dic283—26no—
71C2×Dic283—43no—
72C2×Dic283C2413yes—
73C2×Dic283C2416yes—
74C2×Dic283C2411yescharacteristic
75C4×D283—212no—
76C4×D283—46no—
77C23×C283—41no—
78C23×C283—41no—
79C23×C283#4114yescomplemented
80C23×C283C2413yes—
81Q8×C283—42no—
82Q8×C283—42no—
83C2×C4×C283—43no—
84C2×C4×C283—43no—
85C2×C4×C283C2416yes—
86C2×C4×C283C2416yes—
87C22×C283—23no—
88C22×C283—23no—
89C22×C283—44no—
90C22×C283C2×#4116yes—
91C22×C283C2511yescharacteristic
92C2×D283—26no—
93C2×D283—26no—
94C2×D283—26no—
95C2×D283—412no—
96C4×C283—26no—
97C4×C283—26no—
98Dic283—26no—
99Dic283—23no—
100Dic283H(5,𝔽2)12yes—
101C2×C283—26no—
102C2×C283C22×#4111yescharacteristic
103C2×C283C2×H(5,𝔽2)11yescharacteristic
104C2×C283#58511yescharacteristic
105D283—46no—
106C283#345911yescharacteristic, complemented, Sylow
107#3459—2831nomaximal, Sylow
108#543D28311yescharacteristic, complemented
109#539—2836no—
110#538—2836no—
111#534—2833no—
112#529—2836no—
113#525—2836no—
114C2×C4×D4—2833no—
115C2×#41—2832no—
116C22×D4—2833no—
117C23×C4—2831no—
118C23×C4—2833no—
119#126—28312no—
120#125—2836no—
121#124—2836no—
122#123—28312no—
123#123—28312no—
124C22⋊Q8—2836no—
125C22⋊Q8C2×D28316yescomplemented
126C22⋊Q8C2×D28316yescomplemented
127#121—2836no—
128#121—2836no—
129#121—2836no—
130#120—28312no—
131C4×Q8—2832no—
132C4×D4—2836no—
133C4×D4—28312no—
134C4×D4—28312no—
135#117—2836no—
136C2×C4⋊C4—2833no—
137C2×C22⋊C4—2833no—
138C2×C22⋊C4C2×D28313yes—
139C2×C42—2833no—
140C24—2833no—
141C24C22×D28311yescharacteristic
142#41—11324no—
143C2×Q8C22×D28312yes—
144C2×Q8C22×D28312yes—
145C2×D4—28312no—
146C2×D4—2836no—
147C2×D4—2836no—
148C2×D4—56612no—
149C22×C4—2833no—
150C22×C4—2833no—
151C22×C4—2833no—
152C22×C4—2836no—
153C22×C4—2836no—
154C22×C4—11326no—
155C22×C4—11322no—
156C22×C4C22×D28313yes—
157C22×C4C22×D28313yes—
158C4⋊C4—28312no—
159C4⋊C4—2836no—
160C4⋊C4—2836no—
161C4⋊C4C22×D28316yes—
162C4⋊C4C22×D28316yes—
163C22⋊C4—28312no—
164C22⋊C4—28312no—
165C22⋊C4—28312no—
166C22⋊C4C22×D283112yes—
167C42—2836no—
168C42—2836no—
169C23—41no—
170C23—41no—
171C23—2836no—
172C23—5666no—
173C23—11323no—
174C23—11323no—
175C23#1798539314yescomplemented
176C23C23×D28313yes—
177Q8—42no—
178Q8—42no—
179D4—56624no—
180D4—11326no—
181D4—11326no—
182C2×C4—43no—
183C2×C4—43no—
184C2×C4—2831no—
185C2×C4—2836no—
186C2×C4—2833no—
187C2×C4—56612no—
188C2×C4—5666no—
189C2×C4—5666no—
190C2×C4—11326no—
191C2×C4—11323no—
192C2×C4C23×D28316yes—
193C2×C4C23×D28316yes—
194C22—23no—
195C22—23no—
196C22—44no—
197C22—5666no—
198C22—5666no—
199C22—5666no—
200C22—113212no—
201C22C2×#1798539316yes—
202C22C24×D28311yescharacteristic
203C4—26no—
204C4—26no—
205C4—2832no—
206C4—5666no—
207C4—5663no—
208C2—26no—
209C2—11326no—
210C2C22×#1798539311yescharacteristic
211C2H(5,𝔽2)×D28311yescharacteristic
212C2#3182730011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D283
commutator, socle, cosocleC22×C283C25
Fitting#543×C283C2
hypercenter#543D283
hypocenterC283#3459
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ #543

Complements

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

NH ≅ G/Ntype
1. #31827064C2semidirect
2. #31827055C2semidirect
3. #31827027C2semidirect
4. #31827001C2semidirect
5. #31826978C2semidirect
6. C2×(C22⋊D283)⋊C4C2semidirect
7. #543×C283C2semidirect
8. C2×#17985393C22semidirect
11. C22×C4×D283C22semidirect
12. #22583605C22semidirect
13. #22583601C22semidirect
14. #22583599C22semidirect
15. #22583595C22semidirect
16. #22583594C22semidirect
17. #22583586C22semidirect
18. #22583585C22semidirect
21. #22583580C22semidirect
22. Q8×Dic283C22semidirect
23. #22583572C22semidirect
24. (C22⋊D283)⋊C4C22semidirect
25. (C22⋊D283)⋊C4C22semidirect
26. #22583568C22semidirect
27. C2×Dic283⋊C4C22semidirect
28. C2×(C2×D283)⋊C4C22semidirect
29. C2×C4×Dic283C22semidirect
30. C22⋊Q8×C283C22semidirect
31. C22⋊Q8×C283C22semidirect
79. C23×C283#41semidirect
106. C283#3459semidirect
108. #543D283semidirect
125. C22⋊Q8C2×D283semidirect
126. C22⋊Q8C2×D283semidirect
175. C23#17985393semidirect

Maximal subgroups

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

subgroupindex
#318270642
#318270552
#318270272
#318270012
#318269782
C2×(C22⋊D283)⋊C42
#543×C2832
#3459283