Finite Group Databasebeta

← #13130725

Subgroups — #13130725

Order 1664.

264 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 74 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
1D13×#131C211yesmaximal, characteristic
2#11719164C212yesmaximal
3D13⋊#108C211yesmaximal, characteristic, complemented
4C2×#88102C211yesmaximal, characteristic, complemented
5#11718271C212yesmaximal, complemented
6#41×D13C2211yescharacteristic
7C2×C4⋊#261C2212yes—
8D13⋊M16C2212yes—
9C13×#131C411yescharacteristic, complemented
10#88202C411yescharacteristic, complemented
11#88161—21no—
12#88161C411yescharacteristic, complemented
13M16×D13—21no—
14M16×D13C2211yescharacteristic
15#88155—21no—
16#88155C411yescharacteristic, complemented
17C2×C8×D13—21no—
18C2×C8×D13C2211yescharacteristic
19#88117—22no—
20#88115—22no—
21#88104—21no—
22#88103—21no—
23#88102—21no—
24#88102—21no—
25C22×#261—22no—
26C13×#41C2×C411yescharacteristic
27#6131Q811yescharacteristic
28Q8×D13D411yescharacteristic
29#6129—21no—
30#6129Q811yescharacteristic
31D4×D13—21no—
32D4×D13D411yescharacteristic
33#6127—21no—
34#6127C2×C411yescharacteristic
35C2×C4×D13—21no—
36C2×C4×D13C2311yescharacteristic
37#6122—22no—
38C4⋊#261—22no—
39C4⋊#261—22no—
40#6118—22no—
41D13⋊C8—22no—
42C13×M16—21no—
43C13×M16C2×C411yescharacteristic
44C2×C8×C13—21no—
45C2×C8×C13C2×C411yescharacteristic
46#6099—21no—
47#6099C2×C411yescharacteristic
48C2×#1055—21no—
49C2×#1055C2×C411yescharacteristic
50#6094—21no—
51#6094—21no—
52#6094—21no—
53C8×D13—21no—
54C8×D13—21no—
55C8×D13—21no—
56C8×D13D411yescharacteristic
57C8×D13D411yescharacteristic
58C8×D13D411yescharacteristic
59C8×D13D411yescharacteristic
60#1816—131nomaximal, Sylow
61C22×D13—21no—
62C22×D13#4111yescharacteristic
63C2×#261—42no—
64C2×#261—82no—
65Q8×C13C4⋊C411yescharacteristic
66D4×C13—21no—
67D4×C13C4⋊C411yescharacteristic
68C2×C4×C13—21no—
69C2×C4×C13C22×C411yescharacteristic
70C22⋊D13—21no—
71C22⋊D13—21no—
72C22⋊D13—21no—
73C2×Dic13—21no—
74C2×Dic13#4111yescharacteristic
75D52—21no—
76D52C4⋊C411yescharacteristic
77C4×D13—21no—
78C4×D13—21no—
79C4×D13—21no—
80C4×D13C2×D411yescharacteristic
81C4×D13C2×D411yescharacteristic
82C4×D13C2×D411yescharacteristic
83C4×D13C2×Q811yescharacteristic
84Dic26—21no—
85Dic26C4⋊C411yescharacteristic
86#1057—42no—
87C8×C13—21no—
88C8×C13C22⋊C411yescharacteristic
89C8×C13C22⋊C411yescharacteristic
90#1055—21no—
91#1055C22⋊C411yescharacteristic
92#1055C22⋊C411yescharacteristic
93C2×#131—131no—
94C2×#108—131no—
95C2×#107—131no—
96#417—132no—
97#343—132no—
98C22×C13—21no—
99C22×C13#11711yescharacteristic
100C2×D13—21no—
101C2×D13—21no—
102C2×D13—21no—
103C2×D13—41no—
104C2×D13—41no—
105C2×D13#12111yescharacteristic
106C2×D13C22⋊Q811yescharacteristic
107#261—82no—
108C4×C13—21no—
109C4×C13C2×C22⋊C411yescharacteristic
110C4×C13C2×C4⋊C411yescharacteristic
111Dic13—21no—
112Dic13#12111yescharacteristic
113Dic13C22⋊Q811yescharacteristic
114C2×#41—131no—
115#131—131no—
116#131—131no—
117#131—131no—
118#131—261no—
119#131—261no—
120#131#26111yescharacteristic, complemented
121C2×M16—131no—
122C2×M16—132no—
123C2×M16—261no—
124C22×C8—131no—
125C22×C8—261no—
126C2×C4⋊C4—132no—
127#108—261no—
128#108—261no—
129#107—261no—
130#107—261no—
131#103—262no—
132#102—262no—
133C2×C13—21no—
134C2×C13—41no—
135C2×C13#38011yescharacteristic
136D13—21no—
137D13—41no—
138D13#47211yescharacteristic
139D13#47311yescharacteristic
140#41—131no—
141#41—131no—
142#41—131no—
143#41—261no—
144#41—261no—
145#41C2×#26111yescharacteristic
146C2×Q8—131no—
147C2×D4—131no—
148C2×D4—261no—
149C22×C4—131no—
150C22×C4—261no—
151C22×C4—262no—
152M16—21no—
153M16—131no—
154M16—261no—
155M16—261no—
156M16—261no—
157M16—261no—
158M16—262no—
159M16—262no—
160M16C2×#26111yescharacteristic
161C2×C8—21no—
162C2×C8—131no—
163C2×C8—131no—
164C2×C8—131no—
165C2×C8—131no—
166C2×C8—131no—
167C2×C8—261no—
168C2×C8—261no—
169C2×C8—261no—
170C2×C8—261no—
171C2×C8—262no—
172C2×C8C2×#26111yescharacteristic
173C4⋊C4—262no—
174C4⋊C4—262no—
175C13#181611yescharacteristic, complemented, Sylow
176C23—131no—
177C23—261no—
178Q8—131no—
179Q8—261no—
180Q8C4⋊#26111yescharacteristic
181D4—21no—
182D4—131no—
183D4—261no—
184D4—261no—
185D4—261no—
186D4—261no—
187D4C4⋊#26111yescharacteristic
188C2×C4—21no—
189C2×C4—131no—
190C2×C4—131no—
191C2×C4—131no—
192C2×C4—131no—
193C2×C4—131no—
194C2×C4—261no—
195C2×C4—261no—
196C2×C4—261no—
197C2×C4—261no—
198C2×C4—522no—
199C2×C4—1042no—
200C2×C4C22×#26111yescharacteristic
201C8—21no—
202C8—131no—
203C8—131no—
204C8—261no—
205C8—522no—
206C8C22⋊#26111yescharacteristic
207C8C22⋊#26111yescharacteristic
208C22—21no—
209C22—131no—
210C22—131no—
211C22—261no—
212C22—261no—
213C22—261no—
214C22—521no—
215C22—521no—
216C22#8823711yescharacteristic
217C4—21no—
218C4—131no—
219C4—131no—
220C4—261no—
221C4—1042no—
222C4C2×C4⋊#26111yescharacteristic
223C4C2×C22⋊#26111yescharacteristic
224C2—21no—
225C2—41no—
226C2—131no—
227C2—131no—
228C2—261no—
229C2—521no—
230C2#1171913611yescharacteristic
subgroupG/H
centerC2#11719136
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#131C4
socleC2×C13#380
prime radical#41×D13C22
cosocleC2×C4×D13C23
hypercenter#131#261
hypocenterC13#1816
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131

Complements

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

NH ≅ G/Ntype
3. D13⋊#108C2semidirect
4. C2×#88102C2semidirect
5. #11718271C2semidirect
9. C13×#131C4semidirect
10. #88202C4semidirect
12. #88161C4semidirect
16. #88155C4semidirect
120. #131#261semidirect
175. C13#1816semidirect

Maximal subgroups

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

subgroupindex
D13×#1312
#117191642
D13⋊#1082
C2×#881022
#117182712
#181613