Finite Group Databasebeta

← C2×#14271904 #16833610

Subgroups — C2×#14271904 #16833610

Order 3712.

1344 conjugacy classes of subgroups; only the 469 normal subgroups are shown.

normal subgroups only

This group has 1344 conjugacy classes of subgroups — too many to draw. Only its 469 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#14271904C2116yesmaximal, direct product factor
2C2×#11745236C211yesmaximal, characteristic, complemented
3C2×#11745238C211yesmaximal, characteristic, complemented
4C2×#11745256C213yesmaximal, complemented
5C2×#11745257C213yesmaximal, complemented
6C2×#11745246C213yesmaximal, complemented
7C2×#11745244C213yesmaximal, complemented
8C2×C29×#126C211yesmaximal, characteristic, complemented
9C24×D29C2211yescharacteristic
10C22×C22⋊D29C2213yes—
11C22×D116C2213yes—
12C22×D116C2213yes—
13C22×D116C2213yescomplemented
14C22×C4×D29C2213yescomplemented
15C29×#126C2218yescomplemented
16C2×C4⋊C4×C29C2213yescomplemented
17C2×C22⋊C4×C29C2213yes—
18C2×C42×C29C2211yescharacteristic, complemented
19C2×#90781C2213yes—
20C2×#90781C2213yes—
21C2×#90781C2213yescomplemented
22C2×#90779C2213yescomplemented
23#11745257C22124yescomplemented
24#11745256C22124yescomplemented
25#11745246C22124yescomplemented
26#11745244C22124yescomplemented
27#11745238C2218yescomplemented
28#11745236C2218yescomplemented
29C24×C29C2311yescharacteristic
30C23×D29—46no—
31C23×D29C2311yescharacteristic
32C23×D29C2311yescharacteristic
33C23×D29C2313yes—
34C23×D29C2314yes—
35C22×C4×C29C2313yes—
36C22×C4×C29C2313yes—
37C2×C22⋊D29—46no—
38C2×C22⋊D29C23112yes—
39C22×Dic29C2313yes—
40C2×D116—46no—
41C2×D116—46no—
42C2×D116—46no—
43C2×D116C23112yes—
44C2×D116C23112yes—
45C2×D116C23112yescomplemented
46C2×C4×D29—46no—
47C2×C4×D29C23112yescomplemented
48C4⋊C4×C29C23112yescomplemented
49C22⋊C4×C29C23112yes—
50C42×C29C2314yescomplemented
51#90781C23112yes—
52#90781C23112yes—
53#90781C23112yescomplemented
54#90779C23112yescomplemented
55C23×C29—26no—
56C23×C29C2412yes—
57C23×C29C2411yescharacteristic
58C22×D29—26no—
59C22×D29—26no—
60C22×D29—26no—
61C22×D29—26no—
62C22×D29—26no—
63C22×D29—412no—
64C22×D29—416no—
65C22×D29C2412yes—
66C22×D29C2412yes—
67C22×D29C2416yes—
68C2×C4×C29—26no—
69C2×C4×C29—26no—
70C2×C4×C29C2416yes—
71C2×C4×C29C2416yes—
72C22⋊D29—412no—
73C2×Dic29—26no—
74C2×Dic29C2416yes—
75D116—412no—
76D116—412no—
77D116—412no—
78C4×D29—412no—
79C2×#560—291nomaximal, Sylow
80C22×C29—26no—
81C22×C29—44no—
82C22×C29H(5,𝔽2)16yes—
83C22×C29C2511yescharacteristic
84C2×D29—26no—
85C2×D29—26no—
86C2×D29—26no—
87C2×D29—26no—
88C2×D29—26no—
89C2×D29—416no—
90C2×D29—412no—
91C2×D29—44no—
92C2×D29—44no—
93C4×C29—26no—
94C4×C29—26no—
95Dic29—26no—
96#560—2916no—
97C2×#127—291no—
98C2×#126—291no—
99C2×#126D2911yescharacteristic, complemented
100C2×#123—293no—
101C2×#121—293no—
102C2×#121—293no—
103C2×#120—293no—
104C2×C29—42no—
105C2×C29#56014yescomplemented
106C2×C29C2×H(5,𝔽2)13yes—
107D29—46no—
108D29—42no—
109D29—42no—
110C25—291no—
111C22×D4—293no—
112C22×D4—293no—
113C22×D4—293no—
114C22×D4—293no—
115C23×C4—293no—
116#127—298no—
117#126—298no—
118#126C2×D2918yescomplemented
119#123—2924no—
120#121—2924no—
121#121—2924no—
122#120—2924no—
123C2×C4⋊C4—293no—
124C2×C4⋊C4C2×D2913yescomplemented
125C2×C22⋊C4—293no—
126C2×C22⋊C4—293no—
127C2×C22⋊C4—293no—
128C2×C22⋊C4C2×D2913yes—
129C2×C42C2×D2911yescharacteristic, complemented
130C29C2×#56011yescharacteristic, complemented, Sylow
131C24—291no—
132C24—291no—
133C24—293no—
134C24—294no—
135C24—1166no—
136C24C22×D2911yescharacteristic
137C2×D4—2912no—
138C2×D4—2912no—
139C2×D4—2912no—
140C2×D4—2912no—
141C2×D4—1166no—
142C2×D4—1166no—
143C2×D4—1166no—
144C2×D4—1166no—
145C22×C4—293no—
146C22×C4—2912no—
147C22×C4—1166no—
148C22×C4C22×D2913yes—
149C22×C4C22×D2913yes—
150C4⋊C4—2912no—
151C4⋊C4C22×D29112yescomplemented
152C22⋊C4—2912no—
153C22⋊C4—2912no—
154C22⋊C4—2912no—
155C22⋊C4C22×D29112yes—
156C42C22×D2914yescomplemented
157C23—26no—
158C23—292no—
159C23—292no—
160C23—296no—
161C23—586no—
162C23—586no—
163C23—586no—
164C23—586no—
165C23—586no—
166C23—11612no—
167C23—11616no—
168C23C23×D2912yes—
169C23C23×D2911yescharacteristic
170D4—11612no—
171D4—11612no—
172D4—11612no—
173D4—11612no—
174C2×C4—26no—
175C2×C4—26no—
176C2×C4—296no—
177C2×C4—586no—
178C2×C4—11612no—
179C2×C4C23×D2916yes—
180C2×C4C23×D2916yes—
181C22—26no—
182C22—44no—
183C22—586no—
184C22—586no—
185C22—586no—
186C22—586no—
187C22—586no—
188C22—11616no—
189C22—1164no—
190C22—1164no—
191C22—11612no—
192C22#1174536416yes—
193C22C24×D2911yescharacteristic
194C4—26no—
195C4—26no—
196C4—586no—
197C2—42no—
198C2—1162no—
199C2—1162no—
200C2—1166no—
201C2#1427190414yesdirect product factor
202C2C2×#1174536413yes—
subgroupG/H
centerC23C23×D29
commutator, cosocleC22×C29C25
FrattiniC22C24×D29
FittingC2×C29×#126C2
socleC23×C29C24
hypercenterC2×#126D29
hypocenterC29C2×#560
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #14271904C2direct (N × H)
2. C2×#11745236C2semidirect
3. C2×#11745238C2semidirect
4. C2×#11745256C2semidirect
5. C2×#11745257C2semidirect
6. C2×#11745246C2semidirect
7. C2×#11745244C2semidirect
8. C2×C29×#126C2semidirect
13. C22×D116C22semidirect
14. C22×C4×D29C22semidirect
15. C29×#126C22semidirect
16. C2×C4⋊C4×C29C22semidirect
18. C2×C42×C29C22semidirect
21. C2×#90781C22semidirect
22. C2×#90779C22semidirect
23. #11745257C22semidirect
24. #11745256C22semidirect
25. #11745246C22semidirect
26. #11745244C22semidirect
27. #11745238C22semidirect
28. #11745236C22semidirect
45. C2×D116C23semidirect
47. C2×C4×D29C23semidirect
48. C4⋊C4×C29C23semidirect
50. C42×C29C23semidirect
53. #90781C23semidirect
54. #90779C23semidirect
99. C2×#126D29semidirect
105. C2×C29#560semidirect
118. #126C2×D29semidirect
124. C2×C4⋊C4C2×D29semidirect
129. C2×C42C2×D29semidirect
130. C29C2×#560semidirect
151. C4⋊C4C22×D29semidirect
156. C42C22×D29semidirect
201. C2#14271904direct (N × H)

Maximal subgroups

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

subgroupindex
#142719042
C2×#117452362
C2×#117452382
C2×#117452562
C2×#117452572
C2×#117452462
C2×#117452442
C2×C29×#1262
C2×#56029