Finite Group Databasebeta

← #13127820

Subgroups — #13127820

Order 1664.

360 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 123 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×#556C211yesmaximal, characteristic, complemented
2#11719289C211yesmaximal, characteristic, complemented
3#11718753C211yesmaximal, characteristic, complemented
4#11718744C211yesmaximal, characteristic, complemented
5#11718720C212yesmaximal
6#11718715C212yesmaximal, complemented
7C4×#6107C212yesmaximal, complemented
8#11718689C212yesmaximal, complemented
9Q8×#1055C211yesmaximal, characteristic, complemented
10#11718680C211yesmaximal, characteristic, complemented
11C4×#6104C211yesmaximal, characteristic
12C13×C4⋊Q8C2211yescharacteristic
13C13×#126—22no—
14C13×#124C2212yes—
15C13×C22⋊Q8—21no—
16C4×Q8×C13C2212yes—
17C4×Q8×C13C2211yescharacteristic
18C4×D4×C13C2211yescharacteristic
19C13×#117—21no—
20#88200—21no—
21C2×#6107C2212yes—
22C2×#6107C2212yes—
23C2×#6106C2212yes—
24C2×#6105C2212yes—
25C2×#6104C2211yescharacteristic
26#88152—22no—
27#88146—21no—
28#88129C2212yes—
29C4×D52C2211yescharacteristic
30#88123C2211yescharacteristic
31C4×Dic26C2212yes—
32#88075C2212yes—
33#88072C2211yescharacteristic
34#88050C2212yes—
35#88049C2211yescharacteristic
36#88047C2211yescharacteristic
37C4⋊#1055C2211yescharacteristic
38C4⋊#1055C2212yes—
39C4×#1055C2211yescharacteristic
40C4×#1055C2212yes—
41C2×Q8×C13D411yescharacteristic
42C2×Q8×C13C2312yes—
43C2×D4×C13C2311yescharacteristic
44C22×C4×C13—21no—
45C2×D52C2311yescharacteristic
46C2×C4×D13—21no—
47C2×Dic26C2312yes—
48C13×C4⋊C4—21no—
49C13×C4⋊C4—22no—
50C13×C4⋊C4—21no—
51C13×C4⋊C4D411yescharacteristic
52C13×C4⋊C4D412yes—
53C13×C4⋊C4C2311yescharacteristic
54C13×C22⋊C4—22no—
55C13×C22⋊C4—21no—
56C13×C22⋊C4—22no—
57C42×C13—22no—
58C42×C13C2312yes—
59C42×C13C2311yescharacteristic
60#6107—24no—
61#6107—42no—
62#6106—42no—
63#6105—42no—
64#6104—22no—
65#6103—21no—
66#6103—22no—
67#6103—22no—
68C4⋊Dic13—21no—
69C4⋊Dic13—21no—
70C4⋊Dic13C2311yescharacteristic
71#6101—22no—
72C4×Dic13—22no—
73C2×#1055C2311yescharacteristic
74C2×#1055C2312yes—
75C2×#1055C2311yescharacteristic
76#3393—131nomaximal, Sylow
77C23×C13—21no—
78C22×D13—21no—
79Q8×C13—22no—
80Q8×C13—22no—
81Q8×C13—22no—
82D4×C13—21no—
83D4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—22no—
86C2×C4×C13—42no—
87C2×C4×C13C2×D412yes—
88C2×C4×C13C2×D412yes—
89C2×C4×C13C2×D411yescharacteristic
90C2×C4×C13C2×D411yescharacteristic
91C2×C4×C13C2411yescharacteristic
92C2×Dic13—21no—
93C2×Dic13—22no—
94D52—21no—
95D52—21no—
96C4×D13—42no—
97Dic26—22no—
98Dic26—22no—
99#1055—22no—
100#1055—21no—
101#1055#4112yes—
102#556—131no—
103#556D1311yescharacteristic, complemented
104#495—132no—
105#494—131no—
106#464—132no—
107#464—132no—
108#461—131no—
109#461—131no—
110C8×Q8—131no—
111C4×Q16—132no—
112C4×D8—131no—
113C22×C13—41no—
114C22×C13—41no—
115C22×C13—41no—
116C22×C13C22×D411yescharacteristic
117C2×D13—41no—
118C2×D13—41no—
119C2×D13—41no—
120C4×C13—22no—
121C4×C13—22no—
122C4×C13—21no—
123C4×C13—42no—
124C4×C13—41no—
125C4×C13#13512yes—
126C4×C13C2×#4111yescharacteristic
127C4×C13H(5,𝔽2)11yescharacteristic
128Dic13—42no—
129Dic13—41no—
130C2×Q16—132no—
131C2×Q16—132no—
132C2×SD16—132no—
133C2×SD16—132no—
134C2×D8—131no—
135C4⋊Q8—131no—
136C4⋊Q8C2×D1311yescharacteristic
137#126—22no—
138#126—262no—
139#124—132no—
140#124C2×D1312yes—
141C22⋊Q8—21no—
142C22⋊Q8—261no—
143C4×Q8—132no—
144C4×Q8C2×D1312yes—
145C4×Q8C2×D1311yescharacteristic
146C4×D4—131no—
147C4×D4C2×D1311yescharacteristic
148#117—21no—
149#117—261no—
150#107—131no—
151C4⋊C8—131no—
152C4⋊C8—132no—
153#103—132no—
154#103—132no—
155#102—131no—
156#102—131no—
157C4×C8—131no—
158C4×C8—132no—
159C2×C13—81no—
160C2×C13#55011yescharacteristic
161C2×C13C2×#13511yescharacteristic
162C2×C13#57811yescharacteristic
163D13—81no—
164C2×Q8—132no—
165C2×Q8C22⋊D1311yescharacteristic
166C2×Q8C22×D1312yes—
167C2×D4—131no—
168C2×D4C22×D1311yescharacteristic
169C22×C4—21no—
170C22×C4—261no—
171Q16—264no—
172Q16—522no—
173SD16—522no—
174SD16—522no—
175D8—262no—
176C2×C8—131no—
177C2×C8—131no—
178C2×C8—132no—
179C4⋊C4—21no—
180C4⋊C4—22no—
181C4⋊C4—21no—
182C4⋊C4—131no—
183C4⋊C4—261no—
184C4⋊C4—262no—
185C4⋊C4—261no—
186C4⋊C4C22⋊D1311yescharacteristic
187C4⋊C4C22⋊D1312yes—
188C4⋊C4C22×D1311yescharacteristic
189C22⋊C4—22no—
190C22⋊C4—21no—
191C22⋊C4—22no—
192C22⋊C4—262no—
193C22⋊C4—261no—
194C22⋊C4—262no—
195C42—22no—
196C42—262no—
197C42C22×D1311yescharacteristic
198C42C22×D1312yes—
199C13#339311yescharacteristic, complemented, Sylow
200C23—21no—
201C23—261no—
202Q8—22no—
203Q8—22no—
204Q8—22no—
205Q8—262no—
206Q8—262no—
207D4—21no—
208D4—21no—
209D4—261no—
210D4—261no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—42no—
214C2×C4—261no—
215C2×C4—262no—
216C2×C4—522no—
217C2×C4C2×C22⋊D1312yes—
218C2×C4C2×C22⋊D1311yescharacteristic
219C2×C4C2×C22⋊D1312yes—
220C2×C4C2×C22⋊D1311yescharacteristic
221C2×C4C23×D1311yescharacteristic
222C8—132no—
223C8—262no—
224C8—261no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22—521no—
229C22—521no—
230C22—521no—
231C22C22×C22⋊D1311yescharacteristic
232C4—22no—
233C4—22no—
234C4—21no—
235C4—41no—
236C4—42no—
237C4—521no—
238C4—522no—
239C4#8820412yes—
240C4#41×D1311yescharacteristic
241C4#8825611yescharacteristic
242C2—81no—
243C2—1041no—
244C2C2×#8820411yescharacteristic
245C2#1171953911yescharacteristic
246C2#1171954311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#556C2
socleC22×C13C22×D4
prime radicalC2×#6104C22
hypercenter#556D13
hypocenterC13#3393
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
1. C13×#556C2semidirect
2. #11719289C2semidirect
3. #11718753C2semidirect
4. #11718744C2semidirect
6. #11718715C2semidirect
7. C4×#6107C2semidirect
8. #11718689C2semidirect
9. Q8×#1055C2semidirect
10. #11718680C2semidirect
103. #556D13semidirect
199. C13#3393semidirect

Maximal subgroups

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

subgroupindex
C13×#5562
#117192892
#117187532
#117187442
#117187202
#117187152
C4×#61072
#117186892
Q8×#10552
#117186802
C4×#61042
#339313