Finite Group Databasebeta

← #13126552

Subgroups — #13126552

Order 1664.

484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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×#135C211yesmaximal, characteristic, complemented
2#11719529C212yesmaximal, complemented
3C2×#88166C211yesmaximal, characteristic, complemented
4#11718900C212yesmaximal, complemented
5#11718849C211yesmaximal, characteristic, complemented
6#11718842C211yesmaximal, characteristic, complemented
7#11718834C212yesmaximal, complemented
8#11718823C212yesmaximal, complemented
9D8×Dic13C211yesmaximal, characteristic, complemented
10#11718777C211yesmaximal, characteristic, complemented
11C8×C22⋊D13C211yesmaximal, characteristic, complemented
12C2×C13×#41C2212yes—
13C2×#6129C2212yes—
14C13×#135—24no—
15C2×C13×Q16C2211yescharacteristic
16C2×C13×SD16C2212yes—
17C2×C13×D8C2211yescharacteristic
18C22×C8×C13C2211yescharacteristic
19#88200C2212yes—
20#88198C2212yes—
21C2×#6107C2212yes—
22#88193—22no—
23#88189—22no—
24D4×Dic13C2212yes—
25C2×#6105C2212yes—
26#88183—22no—
27C4×C22⋊D13C2211yescharacteristic
28#88178C2212yes—
29C2×#6101—22no—
30#88166—24no—
31C2×Dic52C2211yescharacteristic
32C2×C8×D13C2211yescharacteristic
33#88075C2212yes—
34#88072C2212yes—
35C22⋊#1055C2211yescharacteristic
36#88060C2211yescharacteristic
37#88058C2211yescharacteristic
38#88056C2212yes—
39#88054C2211yescharacteristic
40C8×Dic13C2211yescharacteristic
41C13×#41—24no—
42C13×#41—42no—
43C2×Q8×C13C2312yes—
44C2×D4×C13—22no—
45C2×D4×C13C2312yes—
46C22×C4×C13—22no—
47C22×C4×C13C2311yescharacteristic
48C2×C22⋊D13—22no—
49C2×C22⋊D13D411yescharacteristic
50C22×Dic13—22no—
51C22×Dic13—22no—
52#6129—24no—
53#6129—42no—
54C2×C4×D13C2311yescharacteristic
55C2×Dic26C2312yes—
56C13×Q16—22no—
57C13×SD16—24no—
58C13×D8D414yescomplemented
59C2×C8×C13—22no—
60C2×C8×C13C2311yescharacteristic
61C2×C8×C13C2311yescharacteristic
62C22⋊Dic13—22no—
63C22⋊Dic13—22no—
64C22⋊Dic13D411yescharacteristic
65#6107—42no—
66#6105—24no—
67#6103—22no—
68#6103D411yescharacteristic
69C4⋊Dic13C2312yes—
70#6101—22no—
71#6101—22no—
72#6101—22no—
73#6101—22no—
74#6101D411yescharacteristic
75C4×Dic13C2311yescharacteristic
76C2×#1055C2311yescharacteristic
77C2×#1055C2311yescharacteristic
78Dic52—22no—
79C8×D13—22no—
80#3283—131nomaximal, Sylow
81C23×C13—22no—
82C23×C13C2×D411yescharacteristic
83C22×D13C2×D411yescharacteristic
84Q8×C13—22no—
85Q8×C13—22no—
86D4×C13—22no—
87D4×C13—44no—
88D4×C13C2×D414yes—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—22no—
92C2×C4×C13—44no—
93C2×C4×C13C2×D411yescharacteristic
94C2×C4×C13C2411yescharacteristic
95C22⋊D13—22no—
96C22⋊D13—44no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—44no—
100C2×Dic13—44no—
101C2×Dic13C2×D411yescharacteristic
102C2×Dic13C2×D411yescharacteristic
103C2×Dic13C2×D411yescharacteristic
104C4×D13—21no—
105C4×D13—21no—
106Dic26—22no—
107Dic26—22no—
108C8×C13—21no—
109C8×C13C2×D412yes—
110#1055—21no—
111#1055—21no—
112C2×#135—131no—
113C2×#135D1311yescharacteristic, complemented
114#547—132no—
115#494—131no—
116#467—131no—
117#467—131no—
118#461—132no—
119#452—132no—
120#452—132no—
121C4×D8—131no—
122C8×D4—131no—
123C22×C13—24no—
124C22×C13—21no—
125C22×C13—21no—
126C22×C13—21no—
127C22×C13—42no—
128C22×C13—42no—
129C22×C13C22×D411yescharacteristic
130C2×D13—21no—
131C2×D13—21no—
132C2×D13—21no—
133C4×C13—21no—
134C4×C13—42no—
135C4×C13C22×D411yescharacteristic
136C4×C13H(5,𝔽2)11yescharacteristic
137Dic13—21no—
138Dic13—21no—
139Dic13—42no—
140Dic13—42no—
141Dic13#13512yescomplemented
142C2×#41—132no—
143C2×#41C2×D1312yes—
144#135—24no—
145#135—264no—
146C2×Q16—132no—
147C2×Q16—131no—
148C2×Q16C2×D1311yescharacteristic
149C2×SD16—132no—
150C2×SD16C2×D1312yes—
151C2×D8C2×D1311yescharacteristic
152C22×C8—131no—
153C22×C8C2×D1311yescharacteristic
154C4⋊Q8—132no—
155#123—262no—
156#123—262no—
157C22⋊Q8—132no—
158C22⋊Q8—132no—
159#121—262no—
160C4×D4—131no—
161C4×D4—132no—
162C2×C4⋊C4—262no—
163#107—131no—
164C4⋊C8—131no—
165#103—132no—
166#103—132no—
167#102—132no—
168C22⋊C8—131no—
169C22⋊C8—131no—
170C4×C8—131no—
171C2×C13—41no—
172C2×C13—44no—
173C2×C13D4211yescharacteristic
174C2×C13C2×#13511yescharacteristic
175C2×C13#57811yescharacteristic
176D13—41no—
177#41—24no—
178#41—42no—
179#41—264no—
180#41—522no—
181C2×Q8—132no—
182C2×Q8C22×D1312yes—
183C2×D4—22no—
184C2×D4—131no—
185C2×D4—262no—
186C2×D4C22×D1312yes—
187C22×C4—22no—
188C22×C4—131no—
189C22×C4—262no—
190C22×C4—262no—
191C22×C4C22×D1311yescharacteristic
192Q16—22no—
193Q16—262no—
194Q16—522no—
195SD16—24no—
196SD16—264no—
197D8C22⋊D1314yescomplemented
198C2×C8—22no—
199C2×C8—131no—
200C2×C8—131no—
201C2×C8—262no—
202C2×C8C22×D1311yescharacteristic
203C2×C8C22×D1311yescharacteristic
204C4⋊C4—131no—
205C4⋊C4—132no—
206C4⋊C4—262no—
207C4⋊C4—262no—
208C4⋊C4—262no—
209C4⋊C4—262no—
210C22⋊C4—131no—
211C22⋊C4—131no—
212C22⋊C4—262no—
213C22⋊C4—262no—
214C22⋊C4—262no—
215C42—131no—
216C13#328311yescharacteristic, complemented, Sylow
217C23—22no—
218C23—131no—
219C23D4×D1311yescharacteristic
220Q8—22no—
221Q8—22no—
222Q8—262no—
223Q8—262no—
224D4—22no—
225D4—44no—
226D4—262no—
227D4—524no—
228D4C2×C22⋊D1314yes—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—44no—
233C2×C4—131no—
234C2×C4—131no—
235C2×C4—131no—
236C2×C4—261no—
237C2×C4—261no—
238C2×C4—262no—
239C2×C4—262no—
240C2×C4—524no—
241C2×C4—524no—
242C2×C4D4×D1311yescharacteristic
243C2×C4C23×D1311yescharacteristic
244C8—21no—
245C8—261no—
246C8—261no—
247C8C2×C22⋊D1312yes—
248C22—21no—
249C22—21no—
250C22—21no—
251C22—24no—
252C22—42no—
253C22—42no—
254C22—261no—
255C22—261no—
256C22—261no—
257C22C2×D4×D1311yescharacteristic
258C4—21no—
259C4—42no—
260C4—132no—
261C4—261no—
262C4—261no—
263C4—522no—
264C4—522no—
265C4#8825111yescharacteristic
266C4C22×C22⋊D1311yescharacteristic
267C2—41no—
268C2—44no—
269C2—521no—
270C2D13×#13511yescharacteristic
271C2#1171947611yescharacteristic
272C2D4×C22⋊D1311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×#135C2
socleC22×C13C22×D4
hypercenterC2×#135D13
hypocenterC13#3283
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×C13×#135C2semidirect
2. #11719529C2semidirect
3. C2×#88166C2semidirect
4. #11718900C2semidirect
5. #11718849C2semidirect
6. #11718842C2semidirect
7. #11718834C2semidirect
8. #11718823C2semidirect
9. D8×Dic13C2semidirect
10. #11718777C2semidirect
11. C8×C22⋊D13C2semidirect
58. C13×D8D4semidirect
113. C2×#135D13semidirect
141. Dic13#135semidirect
197. D8C22⋊D13semidirect
216. C13#3283semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1352
#117195292
C2×#881662
#117189002
#117188492
#117188422
#117188342
#117188232
D8×Dic132
#117187772
C8×C22⋊D132
#328313