Finite Group Databasebeta

← #13113300

Subgroups — #13113300

Order 1664.

216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 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
1#11719285C211yesmaximal, characteristic
2#11718498C211yesmaximal, characteristic, complemented
3#11718346C211yesmaximal, characteristic, complemented
4C13×Q8⋊C8C211yesmaximal, characteristic, complemented
5Q8⋊#1055C211yesmaximal, characteristic, complemented
6#11718075C211yesmaximal, characteristic, complemented
7#11718051C211yesmaximal, characteristic, complemented
8C4×Q8×C13C2211yescharacteristic
9#88201C411yescharacteristic
10#88200C411yescharacteristic
11C2×#6094—21no—
12#88152—21no—
13#88149C411yescharacteristic
14#88148—21no—
15#88144C411yescharacteristic
16C4×D52—21no—
17C4×D52C2211yescharacteristic
18#88126—21no—
19C42×D13C2211yescharacteristic
20C13×C4⋊C8C2211yescharacteristic
21C4×C8×C13C2211yescharacteristic
22#88060—21no—
23#88054—21no—
24#88054—21no—
25C4⋊#1055C2211yescharacteristic
26C4×#1055C2211yescharacteristic
27C2×Q8×C13C2×C411yescharacteristic
28C2×D52—21no—
29C2×D52C2×C411yescharacteristic
30C2×C4×D13—21no—
31C2×C4×D13C2×C411yescharacteristic
32C2×C4×D13D411yescharacteristic
33C2×C4×D13D411yescharacteristic
34C2×C8×C13—21no—
35C2×C8×C13—21no—
36C13×C4⋊C4—21no—
37C13×C4⋊C4C2×C411yescharacteristic
38C42×C13—21no—
39C42×C13C2311yescharacteristic
40#6103—21no—
41#6103—21no—
42#6103—21no—
43#6103—21no—
44#6103—21no—
45C4⋊Dic13—21no—
46C4⋊Dic13C2×C411yescharacteristic
47#6101—21no—
48#6101—21no—
49C4×Dic13C2×C411yescharacteristic
50C4×Dic13D411yescharacteristic
51C4×Dic13D411yescharacteristic
52C2×#1055—21no—
53C2×#1055—21no—
54#6094—42no—
55#1495—131nomaximal, Sylow
56C22×D13—21no—
57C22×D13C22⋊C411yescharacteristic
58Q8×C13—21no—
59Q8×C13—21no—
60C2×C4×C13—21no—
61C2×C4×C13—21no—
62C2×C4×C13C22×C411yescharacteristic
63C2×C4×C13C2×D411yescharacteristic
64C2×C4×C13C2×D411yescharacteristic
65C2×Dic13—21no—
66C2×Dic13C22⋊C411yescharacteristic
67C2×Dic13C22⋊C411yescharacteristic
68C2×Dic13C22⋊C411yescharacteristic
69D52—21no—
70D52—21no—
71D52—42no—
72C4×D13—21no—
73C4×D13—21no—
74C4×D13—21no—
75C4×D13—21no—
76C4×D13—41no—
77C4×D13—41no—
78C4×D13—41no—
79C8×C13—41no—
80C8×C13—41no—
81#1055—41no—
82#1055—41no—
83#529—131no—
84#431—131no—
85#423—131no—
86Q8⋊C8—131no—
87Q8⋊C8D1311yescharacteristic, complemented
88D4⋊C8—131no—
89D4⋊C8—131no—
90C22×C13C2×C22⋊C411yescharacteristic
91C2×D13—21no—
92C2×D13—21no—
93C2×D13—21no—
94C2×D13—41no—
95C2×D13—41no—
96C2×D13—41no—
97C4×C13—21no—
98C4×C13—41no—
99C4×C13—41no—
100C4×C13#13111yescharacteristic
101C4×C13#13111yescharacteristic
102C4×C13AGL(1,ℤ/8)11yescharacteristic
103C4×C13#13711yescharacteristic
104Dic13—21no—
105Dic13—21no—
106Dic13—21no—
107Dic13—41no—
108C2×M16—261no—
109#126—261no—
110#125—131no—
111#124—131no—
112#123—261no—
113C22⋊Q8—131no—
114#121—131no—
115C4×Q8C2×D1311yescharacteristic
116C4×D4—131no—
117C4×D4—261no—
118#117—261no—
119C2×C42—131no—
120C4⋊C8—131no—
121C4⋊C8—261no—
122C4⋊C8—261no—
123C4⋊C8C2×D1311yescharacteristic
124C22⋊C8—261no—
125C4×C8—131no—
126C4×C8C2×D1311yescharacteristic
127C2×C13#40811yescharacteristic
128C2×C13#41711yescharacteristic
129C2×C13#42111yescharacteristic
130D13—41no—
131D13—81no—
132C2×Q8C4×D1311yescharacteristic
133C2×D4—131no—
134C2×D4—261no—
135C22×C4—131no—
136C22×C4—131no—
137C22×C4—131no—
138C22×C4—261no—
139M16—522no—
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—261no—
143C2×C8—261no—
144C4⋊C4—21no—
145C4⋊C4—131no—
146C4⋊C4—261no—
147C4⋊C4—261no—
148C4⋊C4—261no—
149C4⋊C4C4×D1311yescharacteristic
150C22⋊C4—261no—
151C22⋊C4—261no—
152C22⋊C4—261no—
153C22⋊C4—261no—
154C22⋊C4—261no—
155C42—21no—
156C42—131no—
157C42—131no—
158C42—131no—
159C42C22×D1311yescharacteristic
160C13#149511yescharacteristic, complemented, Sylow
161C23—131no—
162C23—261no—
163Q8—21no—
164Q8—21no—
165D4—261no—
166D4—261no—
167D4—522no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—131no—
171C2×C4—131no—
172C2×C4—131no—
173C2×C4—261no—
174C2×C4—261no—
175C2×C4—261no—
176C2×C4—261no—
177C2×C4—261no—
178C2×C4—521no—
179C2×C4—521no—
180C2×C4—521no—
181C2×C4C2×C4×D1311yescharacteristic
182C2×C4D4×D1311yescharacteristic
183C2×C4D4×D1311yescharacteristic
184C8—41no—
185C8—41no—
186C8—521no—
187C8—521no—
188C22—261no—
189C22—261no—
190C22—261no—
191C22—521no—
192C22—521no—
193C22—521no—
194C22C22⋊C4×D1311yescharacteristic
195C4—21no—
196C4—41no—
197C4—41no—
198C4—261no—
199C4—261no—
200C4—261no—
201C4—521no—
202C4#8815511yescharacteristic
203C4#8816111yescharacteristic
204C4#8816811yescharacteristic
205C4#8817211yescharacteristic
206C2—521no—
207C2—1041no—
208C2#1171838811yescharacteristic
209C2#1171846411yescharacteristic
210C2#1171848211yescharacteristic
subgroupG/H
centerC2×C4D4×D13
commutatorC2×C4×C13C22×C4
FrattiniC42C22×D13
FittingC13×Q8⋊C8C2
socleC22×C13C2×C22⋊C4
prime radical#88149C4
cosocleC42×C13C23
hypercenterQ8⋊C8D13
hypocenterC13#1495
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #11718498C2semidirect
3. #11718346C2semidirect
4. C13×Q8⋊C8C2semidirect
5. Q8⋊#1055C2semidirect
6. #11718075C2semidirect
7. #11718051C2semidirect
87. Q8⋊C8D13semidirect
160. C13#1495semidirect

Maximal subgroups

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

subgroupindex
#117192852
#117184982
#117183462
C13×Q8⋊C82
Q8⋊#10552
#117180752
#117180512
#149513