Finite Group Databasebeta

← C2×#11718907 #13124178

Subgroups — C2×#11718907 #13124178

Order 1664.

708 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 165 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×C13×2−1+4C211yesmaximal, characteristic
2C2×#88205C212yesmaximal, complemented
3C2×#88198C211yesmaximal, characteristic, complemented
4#11718907C218yesmaximal, direct product factor
5C2×#88077C212yesmaximal, complemented
6C2×#88076C211yesmaximal, characteristic, complemented
7C13×2−1+4—24no—
8C13×2−1+4—22no—
9C13×2−1+4C2214yes—
10C2×C13×#41—22no—
11C2×C13×#41—22no—
12C2×C13×#41C2212yes—
13C22×Q8×C13—22no—
14C22×Q8×C13C2211yescharacteristic
15C22×Dic26C2211yescharacteristic
16#88205—24no—
17#88205C2218yescomplemented
18#88198—22no—
19#88198C2214yescomplemented
20C2×#6107—22no—
21C2×#6105—22no—
22C2×#6101—22no—
23C2×C4×Dic13C2211yescharacteristic
24C2×#6099C2212yes—
25#88077C2218yescomplemented
26#88076C2214yescomplemented
27C13×#41—28no—
28C13×#41—28no—
29C13×#41—28no—
30C13×#41—28no—
31C13×#41—22no—
32C13×#41—22no—
33C13×#41D414yes—
34C13×#41C2314yes—
35C2×Q8×C13—22no—
36C2×Q8×C13—28no—
37C2×Q8×C13—28no—
38C2×Q8×C13—22no—
39C2×Q8×C13—22no—
40C2×Q8×C13D412yes—
41C2×Q8×C13D412yes—
42C2×Q8×C13C2312yes—
43C2×D4×C13—22no—
44C2×D4×C13—22no—
45C2×D4×C13D412yes—
46C22×C4×C13—24no—
47C22×C4×C13—22no—
48C22×C4×C13D412yes—
49C22×C4×C13C2311yescharacteristic
50C22×Dic13—21no—
51C22×Dic13—21no—
52C2×Dic26—22no—
53C2×Dic26—22no—
54C2×Dic26—21no—
55C2×Dic26C2312yes—
56#6107—28no—
57#6105—28no—
58#6101—28no—
59C4×Dic13—21no—
60C4×Dic13C2312yes—
61#6099—22no—
62#6099C2314yes—
63C2×#1055—22no—
64C2×#456—131nomaximal, Sylow
65C23×C13—22no—
66C23×C13C2×D411yescharacteristic
67Q8×C13—28no—
68Q8×C13—22no—
69Q8×C13—24no—
70Q8×C13—24no—
71Q8×C13C2×D414yes—
72D4×C13—28no—
73D4×C13—24no—
74D4×C13—24no—
75D4×C13—22no—
76D4×C13C2×D414yes—
77C2×C4×C13—216no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—24no—
82C2×C4×C13—24no—
83C2×C4×C13C2×D414yes—
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13C2×D412yes—
86C2×C4×C13C2×D412yes—
87C2×C4×C13C2411yescharacteristic
88C2×Dic13—24no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—41no—
92C2×Dic13—41no—
93Dic26—24no—
94Dic26—42no—
95#1055—24no—
96C2×2−1+4D1311yescharacteristic
97C2×#137—132no—
98C2×C4⋊Q8—131no—
99#456—138no—
100C2×#104—132no—
101C2×#101—131no—
102C22×C13—22no—
103C22×C13—24no—
104C22×C13—44no—
105C22×C13#12011yescharacteristic
106C22×C13#12011yescharacteristic
107C22×C13C22×D411yescharacteristic
108C4×C13—24no—
109C4×C13—24no—
110C4×C13#12012yes—
111C4×C13C22×D412yes—
112Dic13—24no—
113Dic13—42no—
1142−1+4—24no—
1152−1+4—22no—
1162−1+4C2×D1314yes—
117C2×#41—22no—
118C2×#41—22no—
119C2×#41C2×D1312yes—
120C22×Q8—22no—
121C22×Q8—131no—
122C22×Q8C2×D1311yescharacteristic
123#137—138no—
124#137—264no—
125C2×Q16—262no—
126C2×SD16—262no—
127C2×M16—132no—
128C4⋊Q8—134no—
129C4⋊Q8—262no—
130C2×C4⋊C4—262no—
131C2×C42—131no—
132#104—138no—
133#101—134no—
134C2×C13—21no—
135C2×C13—21no—
136C2×C13—44no—
137C2×C13#45612yescomplemented
138C2×C13C2×#12011yescharacteristic
139#41—28no—
140#41—28no—
141#41—28no—
142#41—28no—
143#41—22no—
144#41—22no—
145#41C22⋊D1314yes—
146#41C22×D1314yes—
147C2×Q8—22no—
148C2×Q8—28no—
149C2×Q8—28no—
150C2×Q8—22no—
151C2×Q8—22no—
152C2×Q8—132no—
153C2×Q8—261no—
154C2×Q8—262no—
155C2×Q8—262no—
156C2×Q8C22⋊D1312yes—
157C2×Q8C22⋊D1312yes—
158C2×Q8C22×D1312yes—
159C2×D4—22no—
160C2×D4—22no—
161C2×D4C22⋊D1312yes—
162C22×C4—24no—
163C22×C4—22no—
164C22×C4—261no—
165C22×C4—261no—
166C22×C4C22⋊D1312yes—
167C22×C4C22×D1311yescharacteristic
168Q16—268no—
169SD16—268no—
170M16—134no—
171M16—262no—
172C2×C8—262no—
173C4⋊C4—268no—
174C42—132no—
175C42—261no—
176C13C2×#45611yescharacteristic, complemented, Sylow
177C23—22no—
178C23C2×C22⋊D1311yescharacteristic
179Q8—28no—
180Q8—22no—
181Q8—24no—
182Q8—24no—
183Q8—264no—
184Q8—522no—
185Q8C2×C22⋊D1314yes—
186D4—28no—
187D4—24no—
188D4—24no—
189D4—22no—
190D4C2×C22⋊D1314yes—
191C2×C4—216no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—264no—
198C2×C4—262no—
199C2×C4—262no—
200C2×C4—521no—
201C2×C4—521no—
202C2×C4C2×C22⋊D1314yes—
203C2×C4C2×C22⋊D1311yescharacteristic
204C2×C4C2×C22⋊D1312yes—
205C2×C4C2×C22⋊D1312yes—
206C2×C4C23×D1311yescharacteristic
207C8—264no—
208C22—22no—
209C22—24no—
210C22—44no—
211C22#8820711yescharacteristic
212C22#8820711yescharacteristic
213C22C22×C22⋊D1311yescharacteristic
214C4—24no—
215C4—24no—
216C4—264no—
217C4—522no—
218C4#8820712yes—
219C4C22×C22⋊D1312yes—
220C2—21no—
221C2—21no—
222C2—44no—
223C2#1171890712yesdirect product factor
224C2C2×#8820711yescharacteristic
subgroupG/H
centerC22#88207
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
Fitting, prime radicalC2×C13×2−1+4C2
socleC22×C13#120
hypercenterC2×2−1+4D13
hypocenterC13C2×#456
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
2. C2×#88205C2semidirect
3. C2×#88198C2semidirect
4. #11718907C2direct (N × H)
5. C2×#88077C2semidirect
6. C2×#88076C2semidirect
17. #88205C22semidirect
19. #88198C22semidirect
25. #88077C22semidirect
26. #88076C22semidirect
137. C2×C13#456semidirect
176. C13C2×#456semidirect
223. C2#11718907direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×2−1+42
C2×#882052
C2×#881982
#117189072
C2×#880772
C2×#880762
C2×#45613