Finite Group Databasebeta

← C2×#14271769 #16832853

Subgroups — C2×#14271769 #16832853

Order 3712.

1260 conjugacy classes of subgroups; only the 485 normal subgroups are shown.

normal subgroups only

This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 485 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#14271769C2116yesmaximal, direct product factor
2C2×#11745236C211yesmaximal, characteristic, complemented
3C2×#11745256C214yesmaximal, complemented
4C2×#11745257C214yesmaximal, complemented
5C2×#11745257C212yesmaximal, complemented
6C2×#11745255C212yesmaximal, complemented
7C2×#11745234C211yesmaximal, characteristic, complemented
8C2×C29×#125C211yesmaximal, characteristic, complemented
9C22×D116C2212yes—
10C22×D116C2214yes—
11C22×D116C2214yes—
12C22×C4×D29C2211yescharacteristic
13C22×C4×D29C2214yes—
14C29×#125C2218yescomplemented
15C2×C4⋊C4×C29C2212yes—
16C2×C4⋊C4×C29C2214yes—
17C2×C42×C29C2211yescharacteristic
18C2×#90781C2212yes—
19C2×#90781C2214yes—
20C2×#90781C2214yes—
21C2×#90779C2212yes—
22C2×C4×Dic29C2211yescharacteristic
23#11745257C22132yescomplemented
24#11745257C22116yescomplemented
25#11745256C22132yescomplemented
26#11745255C22116yescomplemented
27#11745236C2218yescomplemented
28#11745234C2218yescomplemented
29C23×D29C2311yescharacteristic
30C23×D29C2314yes—
31C22×C4×C29C2312yes—
32C22×C4×C29C2314yes—
33C22×C4×C29C2311yescharacteristic
34C22×Dic29C2312yes—
35C22×Dic29C2311yescharacteristic
36C2×D116—28no—
37C2×D116—48no—
38C2×D116—48no—
39C2×D116C2318yes—
40C2×D116C23116yes—
41C2×D116C23116yes—
42C2×C4×D29—24no—
43C2×C4×D29—48no—
44C2×C4×D29C2314yes—
45C2×C4×D29C23116yes—
46C4⋊C4×C29C2318yes—
47C4⋊C4×C29C23116yes—
48C42×C29C2314yes—
49#90781C2318yes—
50#90781C23116yes—
51#90781C23116yes—
52#90779C2318yes—
53C4×Dic29C2314yes—
54C23×C29C2411yescharacteristic
55C22×D29—22no—
56C22×D29—28no—
57C22×D29—28no—
58C22×D29—24no—
59C22×D29—28no—
60C22×D29C2412yes—
61C22×D29C2418yes—
62C2×C4×C29—28no—
63C2×C4×C29—24no—
64C2×C4×C29#4114yes—
65C2×C4×C29C2414yes—
66C2×C4×C29C2418yes—
67C2×C4×C29C2412yes—
68C2×Dic29—22no—
69C2×Dic29—24no—
70C2×Dic29C2414yes—
71C2×Dic29C2412yes—
72D116—216no—
73D116—416no—
74D116—416no—
75C4×D29—28no—
76C4×D29—416no—
77C2×#540—291nomaximal, Sylow
78C22×C29C2×#4112yes—
79C22×C29H(5,𝔽2)14yes—
80C22×C29C2511yescharacteristic
81C2×D29—22no—
82C2×D29—28no—
83C2×D29—28no—
84C2×D29—24no—
85C2×D29—28no—
86C2×D29—44no—
87C2×D29—416no—
88C4×C29—28no—
89C4×C29—24no—
90C4×C29C2×#4114yes—
91Dic29—22no—
92Dic29—24no—
93#540—2916no—
94C2×#127—291no—
95C2×#125D2911yescharacteristic, complemented
96C2×#123—294no—
97C2×#121—294no—
98C2×#121—292no—
99C2×C4×D4—292no—
100C2×#117—291no—
101C2×C29#54014yescomplemented
102C2×C29C22×#4111yescharacteristic
103C2×C29C2×H(5,𝔽2)12yes—
104D29—42no—
105D29—48no—
106C22×D4—292no—
107C22×D4—294no—
108C22×D4—294no—
109C23×C4—291no—
110C23×C4—294no—
111#127—298no—
112#125C2×D2918yescomplemented
113#123—2932no—
114#121—2932no—
115#121—2916no—
116C4×D4—2916no—
117#117—298no—
118C2×C4⋊C4—292no—
119C2×C4⋊C4C2×D2912yes—
120C2×C4⋊C4C2×D2914yes—
121C2×C22⋊C4—292no—
122C2×C22⋊C4—294no—
123C2×C22⋊C4—294no—
124C2×C42—291no—
125C2×C42C2×D2911yescharacteristic
126C29C2×#54011yescharacteristic, complemented, Sylow
127C24—291no—
128C24—294no—
129C2×D4—298no—
130C2×D4—2916no—
131C2×D4—2916no—
132C2×D4—588no—
133C2×D4—1168no—
134C2×D4—1168no—
135C22×C4—292no—
136C22×C4—291no—
137C22×C4—294no—
138C22×C4—2916no—
139C22×C4—584no—
140C22×C4—1168no—
141C22×C4C22×D2912yes—
142C22×C4C22×D2914yes—
143C22×C4C22×D2911yescharacteristic
144C4⋊C4—298no—
145C4⋊C4C22×D2918yes—
146C4⋊C4C22×D29116yes—
147C22⋊C4—298no—
148C22⋊C4—2916no—
149C22⋊C4—2916no—
150C42—294no—
151C42C22×D2914yes—
152C23—292no—
153C23—298no—
154C23—582no—
155C23—588no—
156C23—588no—
157C23—584no—
158C23—588no—
159C23C23×D2911yescharacteristic
160D4—5816no—
161D4—11616no—
162D4—11616no—
163C2×C4—28no—
164C2×C4—24no—
165C2×C4—294no—
166C2×C4—292no—
167C2×C4—582no—
168C2×C4—584no—
169C2×C4—588no—
170C2×C4—11616no—
171C2×C4#9080914yes—
172C2×C4C23×D2914yes—
173C2×C4C23×D2918yes—
174C2×C4C23×D2912yes—
175C22—582no—
176C22—588no—
177C22—588no—
178C22—584no—
179C22—588no—
180C22—1164no—
181C22—11616no—
182C22C2×#9080912yes—
183C22#1174536414yes—
184C22C24×D2911yescharacteristic
185C4—28no—
186C4—24no—
187C4—582no—
188C4—584no—
189C4C2×#9080914yes—
190C2—1162no—
191C2—1168no—
192C2#1427176914yesdirect product factor
193C2C22×#9080911yescharacteristic
194C2C2×#1174536412yes—
subgroupG/H
centerC23C23×D29
commutator, cosocleC22×C29C25
FrattiniC22C24×D29
FittingC2×C29×#125C2
socleC23×C29C24
hypercenterC2×#125D29
hypocenterC29C2×#540
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. #14271769C2direct (N × H)
2. C2×#11745236C2semidirect
3. C2×#11745256C2semidirect
4. C2×#11745257C2semidirect
5. C2×#11745257C2semidirect
6. C2×#11745255C2semidirect
7. C2×#11745234C2semidirect
8. C2×C29×#125C2semidirect
14. C29×#125C22semidirect
23. #11745257C22semidirect
24. #11745257C22semidirect
25. #11745256C22semidirect
26. #11745255C22semidirect
27. #11745236C22semidirect
28. #11745234C22semidirect
95. C2×#125D29semidirect
101. C2×C29#540semidirect
112. #125C2×D29semidirect
126. C29C2×#540semidirect
192. C2#14271769direct (N × H)

Maximal subgroups

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

subgroupindex
#142717692
C2×#117452362
C2×#117452562
C2×#117452572
C2×#117452552
C2×#117452342
C2×C29×#1252
C2×#54029