Finite Group Databasebeta

← #13130174

Subgroups — #13130174

Order 1664.

266 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C4×#6131C211yesmaximal, characteristic
2#11719052C211yesmaximal, characteristic, complemented
3C4×#6118C211yesmaximal, characteristic, complemented
4Q8⋊#1057C212yesmaximal, complemented
5#11718243C212yesmaximal, complemented
6C2×#6131C411yescharacteristic
7C2×#6118—21no—
8C2×#6118—21no—
9C4×Q8×C13C411yescharacteristic
10Q8×Dic13C2211yescharacteristic
11#88147—21no—
12#88147C2211yescharacteristic
13#88146—21no—
14#88146C411yescharacteristic
15C4×D52—21no—
16C4×D52C411yescharacteristic
17C42×D13—21no—
18C42×D13C2211yescharacteristic
19#88110—21no—
20C4⋊#1057—21no—
21C4⋊#1057C2212yes—
22C4×#1057C2212yes—
23C2×Q8×C13C2×C411yescharacteristic
24#6131—22no—
25#6131—22no—
26C2×D52—21no—
27C2×D52C2×C411yescharacteristic
28C2×C4×D13—21no—
29C2×C4×D13—21no—
30C2×C4×D13—21no—
31C2×C4×D13C2×C411yescharacteristic
32C2×C4×D13D411yescharacteristic
33C2×C4×D13D411yescharacteristic
34C2×#1057—22no—
35C2×#1057—22no—
36#6118—24no—
37#6118—42no—
38C13×C4⋊C4—21no—
39C13×C4⋊C4C2×C411yescharacteristic
40C42×C13—21no—
41C42×C13C2×C411yescharacteristic
42#6103—21no—
43#6103—21no—
44#6103—21no—
45C4⋊Dic13—21no—
46C4⋊Dic13C2×C411yescharacteristic
47C4×Dic13—21no—
48C4×Dic13—21no—
49C4×Dic13D411yescharacteristic
50C4×Dic13D411yescharacteristic
51C4×Dic13C2311yescharacteristic
52#1489—131nomaximal, Sylow
53C22×D13—21no—
54C22×D13C22⋊C411yescharacteristic
55Q8×C13—21no—
56Q8×C13M1612yescomplemented
57C2×C4×C13—21no—
58C2×C4×C13—21no—
59C2×C4×C13C22⋊C411yescharacteristic
60C2×C4×C13C22⋊C411yescharacteristic
61C2×C4×C13C22×C411yescharacteristic
62C2×Dic13—21no—
63C2×Dic13C22⋊C411yescharacteristic
64C2×Dic13C2×D411yescharacteristic
65C2×Dic13C2×D411yescharacteristic
66D52—24no—
67D52—21no—
68D52M1612yescomplemented
69C4×D13—24no—
70C4×D13—22no—
71C4×D13—21no—
72C4×D13—21no—
73C4×D13—21no—
74C4×D13—21no—
75C4×D13—42no—
76C4×D13—41no—
77C4×D13—41no—
78#1057—24no—
79#1057—42no—
80C4×#41—131no—
81#423—131no—
82C4×M16—131no—
83Q8⋊C8—132no—
84D4⋊C8—132no—
85C22×C13C2×C22⋊C411yescharacteristic
86C2×D13—21no—
87C2×D13—22no—
88C2×D13—21no—
89C2×D13—21no—
90C2×D13—41no—
91C2×D13—41no—
92C4×C13—22no—
93C4×C13—21no—
94C4×C13—41no—
95C4×C13#10412yes—
96C4×C13C2×M1611yescharacteristic
97C4×C13C2×M1611yescharacteristic
98Dic13—21no—
99Dic13—21no—
100Dic13—41no—
101Dic13AGL(1,ℤ/8)11yescharacteristic
102Dic13#13711yescharacteristic
103C2×#41—131no—
104C2×M16—261no—
105C2×M16—261no—
106C4×Q8—131no—
107C4×Q8#26111yescharacteristic
108C4×D4—131no—
109C4×D4—131no—
110C4×D4—261no—
111C4×D4—261no—
112#117—131no—
113#117—261no—
114C2×C42—131no—
115C2×C42—261no—
116C4⋊C8—132no—
117C4⋊C8—261no—
118#97—261no—
119C4×C8—132no—
120C2×C13#40711yescharacteristic
121C2×C13#41711yescharacteristic
122C2×C13C2×#10411yescharacteristic
123D13—41no—
124D13—42no—
125#41—262no—
126#41—262no—
127C2×Q8C2×#26111yescharacteristic
128C2×D4—131no—
129C2×D4—261no—
130C22×C4—131no—
131C22×C4—131no—
132C22×C4—131no—
133C22×C4—261no—
134C22×C4—261no—
135C22×C4—261no—
136M16—264no—
137M16—522no—
138C2×C8—262no—
139C2×C8—262no—
140C4⋊C4—21no—
141C4⋊C4—131no—
142C4⋊C4—261no—
143C4⋊C4C2×#26111yescharacteristic
144C22⋊C4—261no—
145C22⋊C4—261no—
146C22⋊C4—261no—
147C42—21no—
148C42—131no—
149C42—131no—
150C42—131no—
151C42—261no—
152C42—261no—
153C42C2×#26111yescharacteristic
154C13#148911yescharacteristic, complemented, Sylow
155C23—131no—
156C23—261no—
157Q8—21no—
158Q8#611812yescomplemented
159D4—132no—
160D4—264no—
161D4—261no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—131no—
165C2×C4—131no—
166C2×C4—131no—
167C2×C4—261no—
168C2×C4—261no—
169C2×C4—264no—
170C2×C4—262no—
171C2×C4—261no—
172C2×C4—261no—
173C2×C4—261no—
174C2×C4—521no—
175C2×C4—521no—
176C2×C4—522no—
177C2×C4C22⋊#26111yescharacteristic
178C2×C4C22⋊#26111yescharacteristic
179C2×C4C22×#26111yescharacteristic
180C8—264no—
181C8—522no—
182C22—262no—
183C22—261no—
184C22—261no—
185C22—261no—
186C22—521no—
187C22—521no—
188C22C2×C22⋊#26111yescharacteristic
189C4—22no—
190C4—21no—
191C4—41no—
192C4—131no—
193C4—131no—
194C4—261no—
195C4—261no—
196C4—521no—
197C4#8811812yes—
198C4C2×#611811yescharacteristic
199C4D13⋊M1611yescharacteristic
200C2—521no—
201C2—522no—
202C2#1171912711yescharacteristic
203C2C2×#8811811yescharacteristic
204C2#1171916411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC4×Q8×C13C4
socleC22×C13C2×C22⋊C4
prime radicalC2×#6131C4
cosocleC4×Dic13C23
hypercenterC4×Q8#261
hypocenterC13#1489
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. #11719052C2semidirect
3. C4×#6118C2semidirect
4. Q8⋊#1057C2semidirect
5. #11718243C2semidirect
56. Q8×C13M16semidirect
68. D52M16semidirect
154. C13#1489semidirect
158. Q8#6118semidirect

Maximal subgroups

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

subgroupindex
C4×#61312
#117190522
C4×#61182
Q8⋊#10572
#117182432
#148913