Finite Group Databasebeta

← #13115807

Subgroups — #13115807

Order 1664.

276 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 99 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×#88142C211yesmaximal, characteristic
2C2×#88055C211yesmaximal, characteristic
3#11718638C211yesmaximal, characteristic
4C13×#340C211yesmaximal, characteristic
5#11718143C211yesmaximal, characteristic
6#11718121C211yesmaximal, characteristic
7#11718121C211yesmaximal, characteristic
8C22×Dic26—21no—
9C22×C8×C13C2211yescharacteristic
10C2×C13×C4⋊C4C2211yescharacteristic
11C2×C13×C4⋊C4C2211yescharacteristic
12C2×C4⋊Dic13C2211yescharacteristic
13C2×C4⋊Dic13C2211yescharacteristic
14C2×#6101—21no—
15C2×C4×Dic13C2211yescharacteristic
16C22×#1055C2211yescharacteristic
17#88142—22no—
18#88142C414yescomplemented
19#88071—21no—
20#88071—21no—
21#88055—22no—
22C22×C4×C13—21no—
23C22×C4×C13—21no—
24C22×C4×C13C2311yescharacteristic
25C22×Dic13—21no—
26C22×Dic13—21no—
27C22×Dic13D411yescharacteristic
28C22×Dic13D411yescharacteristic
29C2×Dic26—24no—
30C2×Dic26—42no—
31C2×Dic26—42no—
32C2×C8×C13—21no—
33C2×C8×C13—21no—
34C2×C8×C13Q812yescomplemented
35C13×C4⋊C4—21no—
36C13×C4⋊C4—21no—
37C13×C4⋊C4—21no—
38C13×C4⋊C4C2×C412yes—
39C4⋊Dic13—21no—
40C4⋊Dic13—21no—
41C4⋊Dic13—21no—
42C4⋊Dic13C2×C412yes—
43#6101—24no—
44C4×Dic13C2×C412yes—
45C4×Dic13D412yes—
46C2×#1055—21no—
47C2×#1055—21no—
48C2×#1055Q812yescomplemented
49#1993—131nomaximal, Sylow
50C23×C13C2×D411yescharacteristic
51C2×C4×C13—22no—
52C2×C4×C13—41no—
53C2×C4×C13—41no—
54C2×C4×C13—41no—
55C2×C4×C13—41no—
56C2×C4×C13—41no—
57C2×C4×C13C22×C411yescharacteristic
58C2×C4×C13C2×D411yescharacteristic
59C2×C4×C13C2×Q811yescharacteristic
60C2×C4×C13C2×Q811yescharacteristic
61C2×C4×C13#4111yescharacteristic
62C2×C4×C13#4111yescharacteristic
63C2×Dic13—21no—
64C2×Dic13—21no—
65C2×Dic13—21no—
66C2×Dic13—21no—
67C2×Dic13—22no—
68C2×Dic13—41no—
69C2×Dic13—41no—
70C2×Dic13—41no—
71C2×Dic13—41no—
72C2×Dic13—41no—
73C2×Dic13C22⋊C412yes—
74C2×Dic13C22⋊C412yes—
75Dic26—48no—
76C8×C13—22no—
77#1055—22no—
78C2×C4⋊Q8—131no—
79C2×#97—131no—
80#382—131no—
81#340—131no—
82#340—131no—
83#340—131no—
84#340D1311yescharacteristic
85C22×C13C2×C22⋊C411yescharacteristic
86C22×C13#12411yescharacteristic
87C22×C13C4⋊Q811yescharacteristic
88C22×C13AGL(1,ℤ/8)11yescharacteristic
89C22×C13AGL(1,ℤ/8)11yescharacteristic
90C22×C13#13711yescharacteristic
91C22×C13#13711yescharacteristic
92C4×C13—42no—
93C4×C13—81no—
94C4×C13C4×Q811yescharacteristic
95C4×C13C4×Q811yescharacteristic
96C4×C13C22⋊Q811yescharacteristic
97C4×C13C22⋊Q811yescharacteristic
98Dic13—22no—
99Dic13—22no—
100Dic13—42no—
101Dic13—81no—
102C22×Q8—261no—
103C22×C8—131no—
104C22×C8C2×D1311yescharacteristic
105C4⋊Q8—134no—
106C4⋊Q8—262no—
107C2×C4⋊C4—131no—
108C2×C4⋊C4—131no—
109C2×C4⋊C4—261no—
110C2×C4⋊C4C2×D1311yescharacteristic
111C2×C4⋊C4C2×D1311yescharacteristic
112C2×C42—131no—
113#97—262no—
114#95—261no—
115#95—261no—
116C2×C13#39111yescharacteristic
117C2×C13#41811yescharacteristic
118C2×C13#41911yescharacteristic
119C2×C13#48911yescharacteristic
120C2×C13#48911yescharacteristic
121C2×C13#50111yescharacteristic
122C2×C13#50111yescharacteristic
123C2×Q8—264no—
124C2×Q8—522no—
125C2×Q8—522no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—131no—
129C22×C4—131no—
130C22×C4—261no—
131C22×C4—261no—
132C22×C4C22×D1311yescharacteristic
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—132no—
136C2×C8—261no—
137C2×C8—261no—
138C2×C8Dic2612yescomplemented
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—132no—
143C4⋊C4—264no—
144C4⋊C4—261no—
145C4⋊C4—261no—
146C4⋊C4—261no—
147C4⋊C4C4×D1312yes—
148C42—132no—
149C42—132no—
150C13#199311yescharacteristic, complemented, Sylow
151C23D4×D1311yescharacteristic
152Q8—528no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—132no—
160C2×C4—132no—
161C2×C4—261no—
162C2×C4—261no—
163C2×C4—261no—
164C2×C4—261no—
165C2×C4—262no—
166C2×C4—521no—
167C2×C4—521no—
168C2×C4—521no—
169C2×C4—521no—
170C2×C4—521no—
171C2×C4C2×Dic2611yescharacteristic
172C2×C4C2×C4×D1311yescharacteristic
173C2×C4#612711yescharacteristic
174C2×C4D4×D1311yescharacteristic
175C2×C4#612911yescharacteristic
176C2×C4Q8×D1311yescharacteristic
177C8—22no—
178C8—262no—
179C22C22⋊C4×D1311yescharacteristic
180C22#8813911yescharacteristic
181C22#8814211yescharacteristic
182C22#8816511yescharacteristic
183C22#8816811yescharacteristic
184C22#8816911yescharacteristic
185C22#8817211yescharacteristic
186C4—42no—
187C4—81no—
188C4—262no—
189C4—262no—
190C4—522no—
191C4—1041no—
192C4C4×Dic2611yescharacteristic
193C4#8813211yescharacteristic
194C4#8814111yescharacteristic
195C4#8815011yescharacteristic
196C2#1171830711yescharacteristic
197C2#1171842611yescharacteristic
198C2#1171843111yescharacteristic
199C2#1171845611yescharacteristic
200C2#1171846311yescharacteristic
201C2#1171851711yescharacteristic
202C2#1171853711yescharacteristic
subgroupG/H
centerC23D4×D13
commutatorC2×C4×C13C22×C4
FrattiniC22×C4C22×D13
FittingC13×#340C2
socle, prime radicalC23×C13C2×D4
cosocleC22×C4×C13C23
hypercenter#340D13
hypocenterC13#1993
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
18. #88142C4semidirect
34. C2×C8×C13Q8semidirect
48. C2×#1055Q8semidirect
138. C2×C8Dic26semidirect
150. C13#1993semidirect

Maximal subgroups

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

subgroupindex
C2×#881422
C2×#880552
#117186382
C13×#3402
#117181432
#117181212
#199313