Finite Group Databasebeta

← #13120604

Subgroups — #13120604

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×#88150C212yesmaximal
2C2×#88146C211yesmaximal, characteristic
3C2×#88142C211yesmaximal, characteristic, complemented
4C13×#398C211yesmaximal, characteristic, complemented
5#11718654C211yesmaximal, characteristic
6#11718645C212yesmaximal, complemented
7#11718644C211yesmaximal, characteristic, complemented
8#11718336C212yesmaximal
9#11718335C211yesmaximal, characteristic
10#11718311C211yesmaximal, characteristic, complemented
11#11718307C212yesmaximal, complemented
12C22×C4×D13C2211yescharacteristic
13C22×Dic26C2212yes—
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C13×C4⋊C4C2212yes—
17C2×#6103C2211yescharacteristic
18C2×#6103C2211yescharacteristic
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×C4⋊Dic13C2211yescharacteristic
22C2×C4⋊Dic13C2211yescharacteristic
23C2×#6101C2212yes—
24C2×#6101C2212yes—
25C2×#6101C2212yes—
26C2×C4×Dic13C2211yescharacteristic
27C2×C4×Dic13C2211yescharacteristic
28#88150—28no—
29#88146—24no—
30#88142—24no—
31C13×#95C2212yes—
32C13×#95C2211yescharacteristic
33#88071C2212yes—
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37#88071C2211yescharacteristic
38C23×D13C2311yescharacteristic
39C22×C4×C13C2311yescharacteristic
40C22×C4×C13C2312yes—
41C22×C4×C13C2312yes—
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2311yescharacteristic
44C22×Dic13C2311yescharacteristic
45C22×Dic13C2312yes—
46C22×Dic13C2312yes—
47C22×Dic13C2311yescharacteristic
48C22×Dic13C2311yescharacteristic
49C2×C4×D13—22no—
50C2×C4×D13—22no—
51C2×C4×D13D414yes—
52C2×Dic26—24no—
53C2×Dic26—24no—
54C2×Dic26—24no—
55C13×C4⋊C4—22no—
56C13×C4⋊C4—22no—
57C13×C4⋊C4—24no—
58#6103—24no—
59#6103—24no—
60#6103—22no—
61#6103—22no—
62C4⋊Dic13—22no—
63C4⋊Dic13—22no—
64#6101—24no—
65#6101—24no—
66#6101—24no—
67C4×Dic13—22no—
68C4×Dic13D414yes—
69#2621—131nomaximal, Sylow
70C23×C13C2411yescharacteristic
71C22×D13—21no—
72C22×D13—21no—
73C22×D13—22no—
74C22×D13—22no—
75C22×D13C2×D412yes—
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—22no—
79C2×C4×C13—21no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13C2×D412yes—
88C2×C4×C13C2×D412yes—
89C2×Dic13—22no—
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×Dic13#4112yes—
102C4×D13—28no—
103Dic26—48no—
104C2×C4⋊Q8—131no—
105C2×C22⋊Q8—132no—
106C2×#117—131no—
107#398—131no—
108#398—132no—
109#398D1311yescharacteristic, complemented
110#397—131no—
111#397—131no—
112#397—132no—
113#391—132no—
114#382—131no—
115C22×C13C22×D411yescharacteristic
116C22×C13C22×D411yescharacteristic
117C22×C13C2×#4111yescharacteristic
118C22×C132−1+412yes—
119C22×C132−1+412yes—
120C2×D13—22no—
121C2×D13—24no—
122C2×D13—41no—
123C2×D13—41no—
124C2×D13—42no—
125C4×C13—22no—
126C4×C13—22no—
127C4×C13—42no—
128C4×C13—42no—
129C4×C13—41no—
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—132no—
142C2×C4⋊C4—132no—
143C2×C4⋊C4—132no—
144C2×C4⋊C4—131no—
145C2×C4⋊C4C2×D1311yescharacteristic
146C2×C4⋊C4C2×D1312yes—
147C2×C4⋊C4C2×D1311yescharacteristic
148C2×C22⋊C4—131no—
149C2×C22⋊C4—131no—
150C2×C22⋊C4—132no—
151C2×C22⋊C4—132no—
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×C13C2×#12111yescharacteristic
162C2×C13#53611yescharacteristic
163C2×C13#53612yes—
164C2×C13#53611yescharacteristic
165C2×C13#54112yes—
166D13—42no—
167C24—131no—
168C2×Q8—264no—
169C2×Q8—264no—
170C2×Q8—264no—
171C22×C4—131no—
172C22×C4—131no—
173C22×C4—134no—
174C22×C4—131no—
175C22×C4—132no—
176C22×C4—132no—
177C22×C4—262no—
178C22×C4—262no—
179C22×C4C22×D1311yescharacteristic
180C22×C4C22×D1312yes—
181C22×C4C22×D1312yes—
182C22×C4C22×D1311yescharacteristic
183C22×C4C22×D1311yescharacteristic
184C4⋊C4—22no—
185C4⋊C4—24no—
186C4⋊C4—22no—
187C4⋊C4—262no—
188C4⋊C4—264no—
189C4⋊C4—264no—
190C4⋊C4—264no—
191C4⋊C4—262no—
192C22⋊C4—262no—
193C22⋊C4—264no—
194C22⋊C4—264no—
195C22⋊C4—262no—
196C42—134no—
197C42—262no—
198C13#262111yescharacteristic, complemented, Sylow
199C23—132no—
200C23—261no—
201C23—262no—
202C23—261no—
203C23—262no—
204C23C23×D1311yescharacteristic
205Q8—528no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—132no—
218C2×C4—132no—
219C2×C4—132no—
220C2×C4—132no—
221C2×C4—268no—
222C2×C4—262no—
223C2×C4—261no—
224C2×C4—262no—
225C2×C4—262no—
226C2×C4—262no—
227C2×C4—262no—
228C2×C4—262no—
229C2×C4—262no—
230C2×C4—262no—
231C2×C4D4×D1312yes—
232C2×C4D4×D1312yes—
233C22—262no—
234C22—264no—
235C22—521no—
236C22—521no—
237C22—522no—
238C22C2×D4×D1311yescharacteristic
239C22C2×D4×D1311yescharacteristic
240C22#8825412yes—
241C22#41×D1311yescharacteristic
242C22#8825712yes—
243C4—22no—
244C4—22no—
245C4—42no—
246C4—42no—
247C4—41no—
248C4—134no—
249C4—262no—
250C4—521no—
251C4—522no—
252C4—522no—
253C2—522no—
254C2D13×#12111yescharacteristic
255C2#1171933312yes—
256C2#1171935311yescharacteristic
257C2#1171940112yes—
258C2#1171942911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#398C2
prime radicalC23×D13C23
hypercenter#398D13
hypocenterC13#2621
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. C2×#88142C2semidirect
4. C13×#398C2semidirect
6. #11718645C2semidirect
7. #11718644C2semidirect
10. #11718311C2semidirect
11. #11718307C2semidirect
109. #398D13semidirect
198. C13#2621semidirect

Maximal subgroups

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

subgroupindex
C2×#881502
C2×#881462
C2×#881422
C13×#3982
#117186542
#117186452
#117186442
#117183362
#117183352
#117183112
#117183072
#262113