Finite Group Databasebeta

← #13114774

Subgroups — #13114774

Order 1664.

612 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C22×#6127C211yesmaximal, characteristic
2C13×#380C211yesmaximal, characteristic, complemented
3C2×C22⋊#1055C211yesmaximal, characteristic, complemented
4C2×#88050C212yesmaximal, complemented
5C2×#88049C212yesmaximal, complemented
6C23×C4×C13C2211yescharacteristic
7C22×C22⋊D13—21no—
8C2×#6127—22no—
9C2×#6127—24no—
10C2×#6127—24no—
11C2×#6127C414yescomplemented
12C22×D52C2211yescharacteristic
13C22×C4×D13—21no—
14C22×Dic26C2211yescharacteristic
15C2×C13×C4⋊C4C2212yes—
16C2×C13×C22⋊C4—21no—
17C22×#1055C2212yes—
18C13×#95—21no—
19C22⋊#1055—22no—
20#88050—24no—
21#88049—24no—
22C24×C13D411yescharacteristic
23C23×D13—21no—
24C22×C4×C13—22no—
25C22×C4×C13—22no—
26C22×C4×C13—22no—
27C22×C4×C13C2×C412yes—
28C22×C4×C13D412yes—
29C22×C4×C13D411yescharacteristic
30C22×C4×C13C2311yescharacteristic
31C2×C22⋊D13—28no—
32C2×C22⋊D13—24no—
33C22×Dic13—21no—
34#6127—216no—
35#6127—28no—
36#6127—28no—
37C2×D52—22no—
38C2×D52—21no—
39C2×D52C2×C412yes—
40C2×D52D414yes—
41C2×C4×D13—28no—
42C2×C4×D13—24no—
43C2×Dic26—22no—
44C2×Dic26—21no—
45C2×Dic26C2×C412yes—
46C2×Dic26D414yes—
47C13×C4⋊C4—22no—
48C13×C4⋊C4—22no—
49C13×C22⋊C4—42no—
50C2×#1055—22no—
51C2×#1055—22no—
52C2×#1055—22no—
53#1788—131nomaximal, Sylow
54C23×C13—22no—
55C23×C13—22no—
56C23×C13—21no—
57C23×C13—21no—
58C23×C13C22⋊C412yes—
59C23×C13C2×D411yescharacteristic
60C22×D13—22no—
61C22×D13—24no—
62C22×D13—42no—
63C22×D13—41no—
64C22×D13—41no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—22no—
68C2×C4×C13—24no—
69C2×C4×C13—42no—
70C2×C4×C13—42no—
71C2×C4×C13—42no—
72C2×C4×C13C22⋊C412yes—
73C2×C4×C13C22×C411yescharacteristic
74C2×C4×C13C2×D412yes—
75C2×C4×C13C2×D412yes—
76C2×C4×C13C2×D411yescharacteristic
77C22⋊D13—216no—
78C2×Dic13—22no—
79C2×Dic13—24no—
80D52—22no—
81D52—24no—
82D52C22⋊C414yescomplemented
83C4×D13—216no—
84Dic26—22no—
85Dic26—24no—
86Dic26C22⋊C414yescomplemented
87#1055—42no—
88C22×#41—131no—
89C2×#103—132no—
90C2×#102—132no—
91C2×C22⋊C8—131no—
92#380D1311yescharacteristic, complemented
93C22×C13—22no—
94C22×C13—22no—
95C22×C13—22no—
96C22×C13—42no—
97C22×C13—42no—
98C22×C13C2×C22⋊C411yescharacteristic
99C22×C13#12012yes—
100C22×C13#13512yes—
101C22×C13AGL(1,ℤ/8)11yescharacteristic
102C22×C13#13711yescharacteristic
103C2×D13—24no—
104C2×D13—42no—
105C2×D13—42no—
106C2×D13—44no—
107C2×D13—44no—
108C4×C13—22no—
109C4×C13—82no—
110C4×C13C2×C22⋊C411yescharacteristic
111C4×C13C2×C22⋊C411yescharacteristic
112C4×C13#12012yes—
113Dic13—24no—
114C2×#41—134no—
115C2×#41—264no—
116C2×#41—264no—
117C2×#41—262no—
118C22×Q8—131no—
119C22×D4—131no—
120C22×D4—261no—
121C23×C4—261no—
122C23×C4C2×D1311yescharacteristic
123C22×C8—132no—
124C2×C4⋊C4C2×D1312yes—
125C2×C22⋊C4—21no—
126#103—264no—
127#102—264no—
128C22⋊C8—262no—
129#95—21no—
130C2×C13—42no—
131C2×C13#37911yescharacteristic
132C2×C13#41611yescharacteristic
133C2×C13#41711yescharacteristic
134C2×C13#44912yes—
135C2×C13#45212yes—
136D13—44no—
137C24—261no—
138C24C22⋊D1311yescharacteristic
139#41—268no—
140#41—268no—
141#41—2616no—
142C2×Q8—132no—
143C2×Q8—134no—
144C2×Q8—261no—
145C2×Q8—262no—
146C2×D4—132no—
147C2×D4—134no—
148C2×D4—268no—
149C2×D4—264no—
150C2×D4—261no—
151C2×D4—262no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—268no—
156C22×C4—261no—
157C22×C4—264no—
158C22×C4C4×D1312yes—
159C22×C4D5212yes—
160C22×C4C22⋊D1311yescharacteristic
161C22×C4C22×D1311yescharacteristic
162C2×C8—262no—
163C2×C8—262no—
164C2×C8—262no—
165C4⋊C4—22no—
166C4⋊C4—22no—
167C22⋊C4—42no—
168C13#178811yescharacteristic, complemented, Sylow
169C23—21no—
170C23—22no—
171C23—21no—
172C23—22no—
173C23—262no—
174C23—264no—
175C23—521no—
176C23—521no—
177C23—522no—
178C23#610312yes—
179C23C2×C22⋊D1311yescharacteristic
180Q8—134no—
181Q8—262no—
182Q8—264no—
183D4—134no—
184D4—2616no—
185D4—262no—
186D4—264no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—2616no—
195C2×C4—262no—
196C2×C4—264no—
197C2×C4#610312yes—
198C2×C4C2×C4×D1311yescharacteristic
199C2×C4C2×D5211yescharacteristic
200C2×C4D4×D1312yes—
201C2×C4D4×D1312yes—
202C8—522no—
203C22—22no—
204C22—22no—
205C22—22no—
206C22—42no—
207C22—42no—
208C22—264no—
209C22—522no—
210C22—524no—
211C22—524no—
212C22—522no—
213C22C2×#610311yescharacteristic
214C22#8818611yescharacteristic
215C22#8819112yes—
216C22#8819611yescharacteristic
217C22#8820412yes—
218C4—22no—
219C4—82no—
220C4—264no—
221C4C22⋊C4×D1311yescharacteristic
222C4C22⋊C4×D1311yescharacteristic
223C4#8813612yes—
224C2—42no—
225C2—524no—
226C2#1171861611yescharacteristic
227C2#1171862711yescharacteristic
228C2#1171866311yescharacteristic
229C2#1171869812yes—
230C2#1171870812yes—
subgroupG/H
centerC23C2×C22⋊D13
commutatorC2×C4×C13C22×C4
FrattiniC22×C4C22×D13
FittingC13×#380C2
socleC23×C13C2×D4
prime radicalC22×#6127C2
cosocleC22×C4×C13C23
hypercenter#380D13
hypocenterC13#1788
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C13×#380C2semidirect
3. C2×C22⋊#1055C2semidirect
4. C2×#88050C2semidirect
5. C2×#88049C2semidirect
11. C2×#6127C4semidirect
82. D52C22⋊C4semidirect
86. Dic26C22⋊C4semidirect
92. #380D13semidirect
168. C13#1788semidirect

Maximal subgroups

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

subgroupindex
C22×#61272
C13×#3802
C2×C22⋊#10552
C2×#880502
C2×#880492
#178813