Finite Group Databasebeta

← C2×#11718551 #13124580

Subgroups — C2×#11718551 #13124580

Order 1664.

480 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C2×#88147C211yesmaximal, characteristic
2C2×#88142C211yesmaximal, characteristic, complemented
3C2×C13×#107C211yesmaximal, characteristic, complemented
4C2×#88061C211yesmaximal, characteristic
5C2×#88054C211yesmaximal, characteristic, complemented
6C2×#88049C211yesmaximal, characteristic
7C2×#88047C211yesmaximal, characteristic, complemented
8#11718551C218yesmaximal, direct product factor
9C22×D52C2211yescharacteristic
10C22×C4×D13—21no—
11C22×Dic26—21no—
12C22×C8×C13C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×#6103—21no—
16C2×C4⋊Dic13C2211yescharacteristic
17C2×#6101—21no—
18C2×C4×Dic13C2211yescharacteristic
19C22×#1055C2211yescharacteristic
20#88147—22no—
21#88147C2214yes—
22#88142—22no—
23#88142C2214yescomplemented
24C13×#107C2214yescomplemented
25#88061C2214yes—
26#88054C2214yescomplemented
27#88049C2214yes—
28#88047C2214yescomplemented
29C23×D13—21no—
30C22×C4×C13—21no—
31C22×C4×C13—21no—
32C22×C4×C13C2311yescharacteristic
33C22×Dic13—21no—
34C22×Dic13D411yescharacteristic
35C22×Dic13D411yescharacteristic
36C2×D52—21no—
37C2×D52—22no—
38C2×D52Q814yescomplemented
39C2×D52C2312yes—
40C2×C4×D13—24no—
41C2×C4×D13—44no—
42C2×Dic26—24no—
43C2×Dic26—44no—
44C2×C8×C13—22no—
45C2×C8×C13C2312yes—
46C13×C4⋊C4—21no—
47C13×C4⋊C4—21no—
48C13×C4⋊C4C2312yes—
49C13×C4⋊C4C2312yes—
50#6103—24no—
51C4⋊Dic13—21no—
52C4⋊Dic13C2312yes—
53#6101—24no—
54C4×Dic13D412yes—
55C4×Dic13C2312yes—
56C2×#1055—22no—
57C2×#1055C2312yes—
58C2×#474—131nomaximal, Sylow
59C23×C13C2×D411yescharacteristic
60C22×D13—24no—
61C22×D13—22no—
62C22×D13—42no—
63C22×D13—42no—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—42no—
67C2×C4×C13—42no—
68C2×C4×C13C2×D411yescharacteristic
69C2×C4×C13C2×Q812yes—
70C2×C4×C13#4112yes—
71C2×C4×C13C2411yescharacteristic
72C2×Dic13—22no—
73C2×Dic13—22no—
74C2×Dic13—42no—
75C2×Dic13D814yes—
76C2×Dic13C2×D412yes—
77C2×Dic13C2×D412yes—
78D52—24no—
79D52—22no—
80D52C2×Q814yescomplemented
81C4×D13—48no—
82Dic26—48no—
83C8×C13—22no—
84#1055—22no—
85C2×C4⋊Q8—131no—
86C2×C4×D4—131no—
87#474—138no—
88C2×#107—131no—
89C2×#107D1311yescharacteristic, complemented
90C2×C4⋊C8—131no—
91C2×#102—131no—
92C2×#102—131no—
93C22×C13C22⋊Q812yes—
94C22×C13C2×D812yes—
95C22×C13#13712yes—
96C22×C13C22×D411yescharacteristic
97C2×D13—24no—
98C2×D13—42no—
99C2×D13—42no—
100C2×D13—48no—
101C4×C13—42no—
102C4×C13—42no—
103C4×C13C22⋊Q812yes—
104C4×C13C22×Q811yescharacteristic
105C4×C13C2×#4111yescharacteristic
106Dic13—22no—
107Dic13—42no—
108Dic13C2×D814yes—
109C22×Q8—261no—
110C22×D4—131no—
111C23×C4—261no—
112C22×C8—131no—
113C22×C8C2×D1311yescharacteristic
114C4⋊Q8—134no—
115C4⋊Q8—262no—
116C4×D4—134no—
117C4×D4—262no—
118C2×C4⋊C4—131no—
119C2×C4⋊C4—261no—
120C2×C4⋊C4C2×D1311yescharacteristic
121C2×C4⋊C4C2×D1311yescharacteristic
122C2×C22⋊C4—261no—
123C2×C42—131no—
124#107—134no—
125#107C2×D1314yescomplemented
126C4⋊C8—134no—
127#102—134no—
128#102—134no—
129C2×C13#47414yescomplemented
130C2×C13C2×C22⋊Q811yescharacteristic
131C2×C13C22×D811yescharacteristic
132C2×C13C2×#13711yescharacteristic
133D13—44no—
134C24—261no—
135C2×Q8—264no—
136C2×Q8—524no—
137C2×D4—134no—
138C2×D4—132no—
139C2×D4—262no—
140C2×D4—261no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—131no—
144C22×C4—131no—
145C22×C4—264no—
146C22×C4—261no—
147C22×C4—524no—
148C22×C4C22×D1311yescharacteristic
149C2×C8—22no—
150C2×C8—132no—
151C2×C8—262no—
152C2×C8C22×D1312yes—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—132no—
156C4⋊C4—264no—
157C4⋊C4—261no—
158C4⋊C4C22×D1312yes—
159C4⋊C4C22×D1312yes—
160C22⋊C4—264no—
161C42—132no—
162C42—132no—
163C13C2×#47411yescharacteristic, complemented, Sylow
164C23—264no—
165C23—262no—
166C23—522no—
167C23—522no—
168C23D4×D1311yescharacteristic
169Q8—528no—
170D4—134no—
171D4—264no—
172D4—262no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—134no—
178C2×C4—132no—
179C2×C4—132no—
180C2×C4—262no—
181C2×C4—262no—
182C2×C4—528no—
183C2×C4—522no—
184C2×C4#612712yes—
185C2×C4D4×D1311yescharacteristic
186C2×C4Q8×D1312yes—
187C2×C4C23×D1311yescharacteristic
188C8—22no—
189C8—262no—
190C22—264no—
191C22—522no—
192C22—522no—
193C22—528no—
194C22#8815012yes—
195C22D8×D1312yes—
196C22#8817212yes—
197C22C2×D4×D1311yescharacteristic
198C4—42no—
199C4—42no—
200C4—134no—
201C4—262no—
202C4—522no—
203C4#8815012yes—
204C4C2×#612711yescharacteristic
205C4C2×Q8×D1311yescharacteristic
206C2—524no—
207C2#1171855114yesdirect product factor
208C2C2×#8815011yescharacteristic
209C2C2×D8×D1311yescharacteristic
210C2C2×#8817211yescharacteristic
subgroupG/H
centerC23D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×#107C2
socleC23×C13C2×D4
prime radicalC22×D52C22
hypercenterC2×#107D13
hypocenterC13C2×#474
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. C2×#88142C2semidirect
3. C2×C13×#107C2semidirect
5. C2×#88054C2semidirect
7. C2×#88047C2semidirect
8. #11718551C2direct (N × H)
23. #88142C22semidirect
24. C13×#107C22semidirect
26. #88054C22semidirect
28. #88047C22semidirect
38. C2×D52Q8semidirect
80. D52C2×Q8semidirect
89. C2×#107D13semidirect
125. #107C2×D13semidirect
129. C2×C13#474semidirect
163. C13C2×#474semidirect
207. C2#11718551direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#881472
C2×#881422
C2×C13×#1072
C2×#880612
C2×#880542
C2×#880492
C2×#880472
#117185512
C2×#47413