Finite Group Databasebeta

← #16832904

Subgroups — #16832904

Order 3712.

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#14271762C216yesmaximal, complemented
2#14271753C216yesmaximal, complemented
3#14271725C213yesmaximal, complemented
4#14271699C216yesmaximal, complemented
5#14271676C216yesmaximal, complemented
6C2×#11745243C213yesmaximal, complemented
7C29×#543C211yesmaximal, characteristic, complemented
8C22×C22⋊D29C2213yes—
9C23×Dic29C2211yescharacteristic
10C2×#90809C2212yescomplemented
11C22×C4×D29C2213yescomplemented
12C29×C22⋊Q8C2216yescomplemented
13C29×C22⋊Q8C2216yescomplemented
14C2×C22⋊C4×C29C2213yes—
15#11745309C2216yescomplemented
16#11745308C2216yescomplemented
17Q8×Dic29C2212yescomplemented
18#11745292C2216yes—
19#11745292C2216yes—
20C2×#90781C2213yescomplemented
21C2×#90779C2213yescomplemented
22C2×C4×Dic29C2213yescomplemented
23#11745260C22112yescomplemented
24#11745257C2216yescomplemented
25#11745256C22112yescomplemented
26#11745255C2216yescomplemented
27#11745254C2216yescomplemented
28#11745252C2216yescomplemented
29#11745248C22112yescomplemented
30#11745244C22112yescomplemented
31#11745243C22112yescomplemented
32#11745243C22112yescomplemented
33C24×C29C2311yescharacteristic
34C23×D29C2313yes—
35C2×Q8×C29C2312yes—
36C2×Q8×C29C2312yes—
37C22×C4×C29C2313yes—
38C22×C4×C29C2313yes—
39C2×C22⋊D29—212no—
40C2×C22⋊D29C23112yes—
41C22×Dic29—42no—
42C22×Dic29C2313yes—
43C22×Dic29C2313yes—
44C22×Dic29C2313yes—
45#90809—44no—
46C2×D116C2316yes—
47C2×D116C2316yes—
48C2×C4×D29—46no—
49C2×C4×D29C2316yes—
50C2×C4×D29C2316yes—
51C4⋊C4×C29C2316yes—
52C4⋊C4×C29C2316yes—
53C22⋊C4×C29C23112yes—
54#90781C23112yes—
55#90781C23112yes—
56#90781C23112yes—
57C4⋊Dic29C2316yes—
58C4⋊Dic29C2316yes—
59#90779C23112yes—
60C4×Dic29C2316yes—
61C4×Dic29C2316yes—
62C23×C29—41no—
63C23×C29—41no—
64C23×C29#4114yescomplemented
65C23×C29C2413yes—
66C22×D29—26no—
67C22×D29—43no—
68C22×D29—43no—
69C22×D29C2416yes—
70Q8×C29—42no—
71Q8×C29—42no—
72C2×C4×C29—43no—
73C2×C4×C29—43no—
74C2×C4×C29C2416yes—
75C2×C4×C29C2416yes—
76C22⋊D29—224no—
77C2×Dic29—26no—
78C2×Dic29—26no—
79C2×Dic29—43no—
80C2×Dic29C2413yes—
81C2×Dic29C2416yes—
82C2×Dic29C2411yescharacteristic
83D116—46no—
84D116—46no—
85C4×D29—212no—
86C4×D29—46no—
87#3459—291nomaximal, Sylow
88C22×C29—23no—
89C22×C29—23no—
90C22×C29—44no—
91C22×C29C2×#4116yes—
92C22×C29C2511yescharacteristic
93C2×D29—26no—
94C2×D29—26no—
95C2×D29—26no—
96C2×D29—412no—
97C4×C29—26no—
98C4×C29—26no—
99Dic29—26no—
100Dic29—23no—
101Dic29H(5,𝔽2)12yes—
102#543D2911yescharacteristic, complemented
103#539—296no—
104#538—296no—
105#534—293no—
106#529—296no—
107#525—296no—
108C2×C4×D4—293no—
109C2×C29—26no—
110C2×C29C22×#4111yescharacteristic
111C2×C29C2×H(5,𝔽2)11yescharacteristic
112C2×C29#58511yescharacteristic
113D29—46no—
114C2×#41—292no—
115C22×D4—293no—
116C23×C4—291no—
117C23×C4—293no—
118#126—2912no—
119#125—296no—
120#124—296no—
121#123—2912no—
122#123—2912no—
123C22⋊Q8—296no—
124C22⋊Q8C2×D2916yescomplemented
125C22⋊Q8C2×D2916yescomplemented
126#121—296no—
127#121—296no—
128#121—296no—
129#120—2912no—
130C4×Q8—292no—
131C4×D4—296no—
132C4×D4—2912no—
133C4×D4—2912no—
134#117—296no—
135C2×C4⋊C4—293no—
136C2×C22⋊C4—293no—
137C2×C22⋊C4C2×D2913yes—
138C2×C42—293no—
139C29#345911yescharacteristic, complemented, Sylow
140C24—293no—
141C24C22×D2911yescharacteristic
142#41—1164no—
143C2×Q8C22×D2912yes—
144C2×Q8C22×D2912yes—
145C2×D4—2912no—
146C2×D4—296no—
147C2×D4—296no—
148C2×D4—5812no—
149C22×C4—293no—
150C22×C4—293no—
151C22×C4—293no—
152C22×C4—296no—
153C22×C4—296no—
154C22×C4—1166no—
155C22×C4—1162no—
156C22×C4C22×D2913yes—
157C22×C4C22×D2913yes—
158C4⋊C4—2912no—
159C4⋊C4—296no—
160C4⋊C4—296no—
161C4⋊C4C22×D2916yes—
162C4⋊C4C22×D2916yes—
163C22⋊C4—2912no—
164C22⋊C4—2912no—
165C22⋊C4—2912no—
166C22⋊C4C22×D29112yes—
167C42—296no—
168C42—296no—
169C23—41no—
170C23—41no—
171C23—296no—
172C23—586no—
173C23—1163no—
174C23—1163no—
175C23#9080914yescomplemented
176C23C23×D2913yes—
177Q8—42no—
178Q8—42no—
179D4—5824no—
180D4—1166no—
181D4—1166no—
182C2×C4—43no—
183C2×C4—43no—
184C2×C4—291no—
185C2×C4—296no—
186C2×C4—293no—
187C2×C4—5812no—
188C2×C4—586no—
189C2×C4—586no—
190C2×C4—1166no—
191C2×C4—1163no—
192C2×C4C23×D2916yes—
193C2×C4C23×D2916yes—
194C22—23no—
195C22—23no—
196C22—44no—
197C22—586no—
198C22—586no—
199C22—586no—
200C22—11612no—
201C22C2×#9080916yes—
202C22C24×D2911yescharacteristic
203C4—26no—
204C4—26no—
205C4—292no—
206C4—586no—
207C4—583no—
208C2—26no—
209C2—1166no—
210C2C22×#9080911yescharacteristic
211C2H(5,𝔽2)×D2911yescharacteristic
212C2#1427199811yescharacteristic
subgroupG/H
center, FrattiniC22C24×D29
commutator, socle, cosocleC22×C29C25
FittingC29×#543C2
hypercenter#543D29
hypocenterC29#3459
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ #543

Complements

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

NH ≅ G/Ntype
1. #14271762C2semidirect
2. #14271753C2semidirect
3. #14271725C2semidirect
4. #14271699C2semidirect
5. #14271676C2semidirect
6. C2×#11745243C2semidirect
7. C29×#543C2semidirect
10. C2×#90809C22semidirect
11. C22×C4×D29C22semidirect
12. C29×C22⋊Q8C22semidirect
13. C29×C22⋊Q8C22semidirect
15. #11745309C22semidirect
16. #11745308C22semidirect
17. Q8×Dic29C22semidirect
20. C2×#90781C22semidirect
21. C2×#90779C22semidirect
22. C2×C4×Dic29C22semidirect
23. #11745260C22semidirect
24. #11745257C22semidirect
25. #11745256C22semidirect
26. #11745255C22semidirect
27. #11745254C22semidirect
28. #11745252C22semidirect
29. #11745248C22semidirect
30. #11745244C22semidirect
31. #11745243C22semidirect
32. #11745243C22semidirect
64. C23×C29#41semidirect
102. #543D29semidirect
124. C22⋊Q8C2×D29semidirect
125. C22⋊Q8C2×D29semidirect
139. C29#3459semidirect
175. C23#90809semidirect

Maximal subgroups

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

subgroupindex
#142717622
#142717532
#142717252
#142716992
#142716762
C2×#117452432
C29×#5432
#345929