Finite Group Databasebeta

← #13120601

Subgroups — #13120601

Order 1664.

528 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 143 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×#88142C211yesmaximal, characteristic, complemented
2C2×#88132C212yesmaximal
3C2×#88131C211yesmaximal, characteristic
4C13×#397C211yesmaximal, characteristic
5#11718641C211yesmaximal, characteristic, complemented
6#11718614C211yesmaximal, characteristic
7#11718613C212yesmaximal
8#11718322C211yesmaximal, characteristic, complemented
9#11718318C212yesmaximal, complemented
10#11718311C211yesmaximal, characteristic, complemented
11#11718307C212yesmaximal, complemented
12C23×Dic13C2211yescharacteristic
13C22×Dic26C2212yes—
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C22⋊C4C2211yescharacteristic
16C2×C13×C22⋊C4C2212yes—
17C2×C22⋊Dic13C2211yescharacteristic
18C2×C22⋊Dic13C2212yes—
19C2×C4⋊Dic13C2212yes—
20C2×C4⋊Dic13C2211yescharacteristic
21C2×#6101C2211yescharacteristic
22C2×#6101C2211yescharacteristic
23C2×#6101C2212yes—
24C2×#6101C2212yes—
25C2×#6101C2212yes—
26C2×C4×Dic13C2211yescharacteristic
27C2×C4×Dic13C2211yescharacteristic
28#88142—24no—
29#88132—28no—
30#88131—24no—
31C13×#95C2212yes—
32C13×#95C2211yescharacteristic
33#88071C2212yes—
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37#88071C2211yescharacteristic
38C24×C13C2311yescharacteristic
39C22×C4×C13C2311yescharacteristic
40C22×C4×C13C2312yes—
41C22×C4×C13C2312yes—
42C22×C4×C13C2311yescharacteristic
43C22×Dic13—22no—
44C22×Dic13—22no—
45C22×Dic13D414yes—
46C22×Dic13C2311yescharacteristic
47C22×Dic13C2312yes—
48C22×Dic13C2312yes—
49C22×Dic13C2311yescharacteristic
50C22×Dic13C2311yescharacteristic
51C22×Dic13C2311yescharacteristic
52C2×Dic26—24no—
53C2×Dic26—24no—
54C2×Dic26—24no—
55C13×C4⋊C4—22no—
56C13×C22⋊C4—24no—
57C13×C22⋊C4—22no—
58C22⋊Dic13—24no—
59C22⋊Dic13—22no—
60C4⋊Dic13—22no—
61C4⋊Dic13—24no—
62#6101—22no—
63#6101—22no—
64#6101—24no—
65#6101—24no—
66#6101—24no—
67C4×Dic13—22no—
68C4×Dic13D414yes—
69#2621—131nomaximal, Sylow
70C23×C13—21no—
71C23×C13—21no—
72C23×C13—22no—
73C23×C13—22no—
74C23×C13C2×D412yes—
75C23×C13C2411yescharacteristic
76C2×C4×C13—22no—
77C2×C4×C13—21no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13C2×D412yes—
86C2×Dic13—21no—
87C2×Dic13—21no—
88C2×Dic13—22no—
89C2×Dic13—28no—
90C2×Dic13—21no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13C2×D412yes—
99C2×Dic13C2×D412yes—
100C2×Dic13C2×D412yes—
101C2×Dic13C2×D412yes—
102C2×Dic13#4112yes—
103Dic26—48no—
104C2×C4⋊Q8—131no—
105C2×C22⋊Q8—132no—
106C2×#117—131no—
107#398—131no—
108#398—132no—
109#398—131no—
110#397—132no—
111#397—131no—
112#397D1311yescharacteristic
113#391—132no—
114#382—131no—
115C22×C13—22no—
116C22×C13—24no—
117C22×C13—41no—
118C22×C13—41no—
119C22×C13—42no—
120C22×C13C22×D411yescharacteristic
121C22×C13C22×D411yescharacteristic
122C22×C13C2×#4111yescharacteristic
123C22×C132−1+412yes—
124C22×C132−1+412yes—
125C4×C13—22no—
126C4×C13—42no—
127C4×C13—42no—
128C4×C13—41no—
129Dic13—22no—
130Dic13—22no—
131Dic13—42no—
132Dic13—41no—
133Dic13—42no—
134Dic13#12114yes—
135C22×Q8—132no—
136C23×C4—131no—
137C4⋊Q8—264no—
138C22⋊Q8—268no—
139#117—264no—
140C2×C4⋊C4—131no—
141C2×C4⋊C4—131no—
142C2×C4⋊C4—132no—
143C2×C4⋊C4—132no—
144C2×C4⋊C4—132no—
145C2×C4⋊C4—132no—
146C2×C4⋊C4—131no—
147C2×C4⋊C4C2×D1311yescharacteristic
148C2×C22⋊C4—131no—
149C2×C22⋊C4—132no—
150C2×C22⋊C4C2×D1311yescharacteristic
151C2×C22⋊C4C2×D1312yes—
152C2×C42—131no—
153C2×C42—131no—
154#95—132no—
155#95—131no—
156#95—132no—
157#95—132no—
158#95—132no—
159#95C2×D1311yescharacteristic
160#95C2×D1312yes—
161C2×C13—42no—
162C2×C13C2×#12111yescharacteristic
163C2×C13#53611yescharacteristic
164C2×C13#53612yes—
165C2×C13#53611yescharacteristic
166C2×C13#54112yes—
167C24C22×D1311yescharacteristic
168C2×Q8—264no—
169C2×Q8—264no—
170C2×Q8—264no—
171C22×C4—131no—
172C22×C4—134no—
173C22×C4—131no—
174C22×C4—131no—
175C22×C4—131no—
176C22×C4—132no—
177C22×C4—132no—
178C22×C4—262no—
179C22×C4—262no—
180C22×C4C22×D1311yescharacteristic
181C22×C4C22×D1312yes—
182C22×C4C22×D1312yes—
183C22×C4C22×D1311yescharacteristic
184C4⋊C4—22no—
185C4⋊C4—262no—
186C4⋊C4—264no—
187C4⋊C4—264no—
188C4⋊C4—264no—
189C4⋊C4—264no—
190C4⋊C4—262no—
191C4⋊C4—262no—
192C22⋊C4—24no—
193C22⋊C4—22no—
194C22⋊C4—262no—
195C22⋊C4—264no—
196C42—134no—
197C42—262no—
198C13#262111yescharacteristic, complemented, Sylow
199C23—21no—
200C23—21no—
201C23—22no—
202C23—22no—
203C23D4×D1312yes—
204C23C23×D1311yescharacteristic
205Q8—528no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—132no—
216C2×C4—132no—
217C2×C4—132no—
218C2×C4—132no—
219C2×C4—132no—
220C2×C4—268no—
221C2×C4—261no—
222C2×C4—261no—
223C2×C4—262no—
224C2×C4—261no—
225C2×C4—262no—
226C2×C4—262no—
227C2×C4—262no—
228C2×C4—262no—
229C2×C4—262no—
230C2×C4—262no—
231C2×C4—262no—
232C2×C4D4×D1312yes—
233C22—22no—
234C22—24no—
235C22—41no—
236C22—41no—
237C22—42no—
238C22C2×D4×D1311yescharacteristic
239C22C2×D4×D1311yescharacteristic
240C22#41×D1311yescharacteristic
241C22#8825712yes—
242C22#8825712yes—
243C4—22no—
244C4—42no—
245C4—42no—
246C4—41no—
247C4—134no—
248C4—262no—
249C4—262no—
250C4—522no—
251C4—521no—
252C4—522no—
253C2—42no—
254C2D13×#12111yescharacteristic
255C2#1171935311yescharacteristic
256C2#1171935312yes—
257C2#1171938011yescharacteristic
258C2#1171940612yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#397C2
prime radicalC24×C13C23
hypercenter#397D13
hypocenterC13#2621
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#88142C2semidirect
5. #11718641C2semidirect
8. #11718322C2semidirect
9. #11718318C2semidirect
10. #11718311C2semidirect
11. #11718307C2semidirect
198. C13#2621semidirect

Maximal subgroups

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

subgroupindex
C2×#881422
C2×#881322
C2×#881312
C13×#3972
#117186412
#117186142
#117186132
#117183222
#117183182
#117183112
#117183072
#262113