Finite Group Databasebeta

← #13127152

Subgroups — #13127152

Order 1664.

388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C13×#547C211yesmaximal, characteristic
2#11719248C211yesmaximal, characteristic, complemented
3#11718900C212yesmaximal, complemented
4#11718893C212yesmaximal, complemented
5#11718751C211yesmaximal, characteristic, complemented
6#11718742C211yesmaximal, characteristic, complemented
7#11718713C212yesmaximal, complemented
8#11718704C212yesmaximal, complemented
9C4×#6105C211yesmaximal, characteristic, complemented
10#11718673C211yesmaximal, characteristic, complemented
11#11718669C211yesmaximal, characteristic, complemented
12C2×C13×#41C2212yes—
13C13×C4⋊Q8C2211yescharacteristic
14C13×#123—22no—
15C13×C22⋊Q8C2212yes—
16C13×#121—21no—
17C4×D4×C13C2211yescharacteristic
18C4×D4×C13C2211yescharacteristic
19C2×C13×C4⋊C4—21no—
20C2×#6107C2212yes—
21D4×Dic13—21no—
22C2×#6105C2211yescharacteristic
23C2×C4⋊Dic13C2212yes—
24#88178C2212yes—
25C2×#6099C2212yes—
26#88144—21no—
27#88132—22no—
28#88123C2211yescharacteristic
29C4×Dic26C2211yescharacteristic
30#88075C2212yes—
31#88075C2212yes—
32#88075C2212yes—
33#88072C2212yes—
34#88072C2211yescharacteristic
35C22⋊#1055C2212yes—
36#88050C2211yescharacteristic
37#88048C2212yes—
38#88048C2211yescharacteristic
39C4⋊#1055C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C13×#41—24no—
42C13×#41—42no—
43C2×Q8×C13C2312yes—
44C2×D4×C13—22no—
45C2×D4×C13D411yescharacteristic
46C2×D4×C13C2311yescharacteristic
47C22×C4×C13—21no—
48C22×C4×C13—22no—
49C22×C4×C13C2312yes—
50C22×Dic13—22no—
51C2×Dic26—21no—
52C2×Dic26C2311yescharacteristic
53C13×C4⋊C4—21no—
54C13×C4⋊C4—22no—
55C13×C4⋊C4—21no—
56C13×C4⋊C4D411yescharacteristic
57C13×C4⋊C4C2311yescharacteristic
58C13×C22⋊C4—22no—
59C13×C22⋊C4—21no—
60C13×C22⋊C4D412yes—
61C42×C13C2311yescharacteristic
62C22⋊Dic13—22no—
63#6107—42no—
64#6105—22no—
65C4⋊Dic13—21no—
66C4⋊Dic13—22no—
67C4⋊Dic13C2311yescharacteristic
68C4⋊Dic13C2312yes—
69#6101—21no—
70#6101—22no—
71C4×Dic13—21no—
72#6099—42no—
73C2×#1055C2311yescharacteristic
74C2×#1055C2312yes—
75C2×#1055C2311yescharacteristic
76#3331—131nomaximal, Sylow
77C23×C13—21no—
78C23×C13C2×D412yes—
79Q8×C13—22no—
80Q8×C13—22no—
81D4×C13—22no—
82D4×C13—21no—
83D4×C13—44no—
84D4×C13#4112yes—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—21no—
88C2×C4×C13—22no—
89C2×C4×C13—44no—
90C2×C4×C13—42no—
91C2×C4×C13C2×D412yes—
92C2×C4×C13C2×D411yescharacteristic
93C2×C4×C13C2×D411yescharacteristic
94C2×C4×C13C2411yescharacteristic
95C2×Dic13—21no—
96C2×Dic13—21no—
97C2×Dic13—22no—
98C2×Dic13—82no—
99Dic26—21no—
100Dic26—21no—
101Dic26—81no—
102#1055—21no—
103#1055—21no—
104#1055—22no—
105#554—131no—
106#547D1311yescharacteristic
107#487—131no—
108#483—132no—
109#476—131no—
110#470—132no—
111#462—131no—
112#452—132no—
113C4×SD16—131no—
114#436—131no—
115#417—132no—
116C22×C13—22no—
117C22×C13—22no—
118C22×C13—22no—
119C22×C13—22no—
120C22×C13—41no—
121C22×C13—41no—
122C22×C13C22×D411yescharacteristic
123C4×C13—22no—
124C4×C13—21no—
125C4×C13—42no—
126C4×C13—41no—
127C4×C13#13712yes—
128C4×C13C2×#4111yescharacteristic
129C4×C13H(5,𝔽2)11yescharacteristic
130Dic13—41no—
131Dic13—42no—
132Dic13—41no—
133C2×#41C2×D1312yes—
134C2×Q16—132no—
135C2×SD16—131no—
136C2×M16—132no—
137C4⋊Q8—131no—
138C4⋊Q8C2×D1311yescharacteristic
139#125—261no—
140#123—22no—
141C22⋊Q8—132no—
142C22⋊Q8—262no—
143C22⋊Q8C2×D1312yes—
144#121—21no—
145C4×Q8—131no—
146C4×D4—261no—
147C4×D4C2×D1311yescharacteristic
148C4×D4C2×D1311yescharacteristic
149C2×C4⋊C4—21no—
150C2×C4⋊C4—132no—
151#106—131no—
152#106—132no—
153C4⋊C8—131no—
154#103—132no—
155#103—132no—
156#103—132no—
157#103—131no—
158#102—131no—
159#102—132no—
160C22⋊C8—132no—
161C4×C8—131no—
162C2×C13—42no—
163C2×C13—42no—
164C2×C13#54611yescharacteristic
165C2×C13C2×#13711yescharacteristic
166C2×C13#57711yescharacteristic
167#41—24no—
168#41—42no—
169C2×Q8—131no—
170C2×Q8—261no—
171C2×Q8C22×D1312yes—
172C2×D4—22no—
173C2×D4C22⋊D1311yescharacteristic
174C2×D4C22×D1311yescharacteristic
175C22×C4—21no—
176C22×C4—22no—
177C22×C4—262no—
178C22×C4C22×D1312yes—
179Q16—522no—
180SD16—262no—
181M16—522no—
182C2×C8—131no—
183C2×C8—131no—
184C2×C8—132no—
185C4⋊C4—21no—
186C4⋊C4—22no—
187C4⋊C4—21no—
188C4⋊C4—131no—
189C4⋊C4—132no—
190C4⋊C4—262no—
191C4⋊C4—261no—
192C4⋊C4—261no—
193C4⋊C4—262no—
194C4⋊C4C22⋊D1311yescharacteristic
195C4⋊C4C22×D1311yescharacteristic
196C22⋊C4—22no—
197C22⋊C4—21no—
198C22⋊C4—262no—
199C22⋊C4C22⋊D1312yes—
200C42—261no—
201C42C22×D1311yescharacteristic
202C13#333111yescharacteristic, complemented, Sylow
203C23—21no—
204C23C2×C22⋊D1312yes—
205Q8—22no—
206Q8—22no—
207Q8—261no—
208Q8—261no—
209Q8—1041no—
210D4—22no—
211D4—21no—
212D4—44no—
213D4#612912yes—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—44no—
219C2×C4—42no—
220C2×C4—261no—
221C2×C4—261no—
222C2×C4—262no—
223C2×C4—1042no—
224C2×C4C2×C22⋊D1311yescharacteristic
225C2×C4C2×C22⋊D1312yes—
226C2×C4C2×C22⋊D1311yescharacteristic
227C2×C4C23×D1311yescharacteristic
228C8—261no—
229C8—261no—
230C8—262no—
231C22—22no—
232C22—22no—
233C22—22no—
234C22—22no—
235C22—41no—
236C22—41no—
237C22C22×C22⋊D1311yescharacteristic
238C4—22no—
239C4—21no—
240C4—42no—
241C4—41no—
242C4—521no—
243C4—521no—
244C4—522no—
245C4#8820512yes—
246C4C2×#612911yescharacteristic
247C4#8825111yescharacteristic
248C2—42no—
249C2—42no—
250C2#1171951111yescharacteristic
251C2C2×#8820511yescharacteristic
252C2#1171954211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
Fitting, prime radicalC13×#547C2
socleC22×C13C22×D4
hypercenter#547D13
hypocenterC13#3331
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
2. #11719248C2semidirect
3. #11718900C2semidirect
4. #11718893C2semidirect
5. #11718751C2semidirect
6. #11718742C2semidirect
7. #11718713C2semidirect
8. #11718704C2semidirect
9. C4×#6105C2semidirect
10. #11718673C2semidirect
11. #11718669C2semidirect
202. C13#3331semidirect

Maximal subgroups

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

subgroupindex
C13×#5472
#117192482
#117189002
#117188932
#117187512
#117187422
#117187132
#117187042
C4×#61052
#117186732
#117186692
#333113