Finite Group Databasebeta

← #13130980

Subgroups — #13130980

Order 1664.

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

normal subgroups only

This group has 312 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
1C2×#88139C211yesmaximal, characteristic
2C2×#88121C212yesmaximal
3C2×#88113C212yesmaximal, complemented
4#11719129C211yesmaximal, characteristic, complemented
5C4×#6122C211yesmaximal, characteristic, complemented
6C22×C22⋊D13C2211yescharacteristic
7C22×Dic26C2211yescharacteristic
8C2×#6122C2212yes—
9C2×#6122C2212yes—
10C2×C13×C22⋊C4C411yescharacteristic
11C2×C22⋊Dic13C411yescharacteristic
12C2×#6103C411yescharacteristic
13C2×#6103C411yescharacteristic
14C2×C4×Dic13C2211yescharacteristic
15#88139—21no—
16#88139—21no—
17#88139—21no—
18#88139—21no—
19#88121—24no—
20#88113—24no—
21#88112—21no—
22#88110—21no—
23C4⋊#1057—21no—
24C4×#1057—21no—
25C24×C13C2×C411yescharacteristic
26C23×D13C2×C411yescharacteristic
27C22×C4×C13C2×C411yescharacteristic
28C22×C4×C13C2×C411yescharacteristic
29C2×C22⋊D13—22no—
30C2×C22⋊D13—21no—
31C2×C22⋊D13—21no—
32C2×C22⋊D13—22no—
33C22×Dic13C2×C411yescharacteristic
34C22×Dic13C2×C411yescharacteristic
35C22×Dic13C2311yescharacteristic
36C2×Dic26—22no—
37C2×Dic26—21no—
38C2×Dic26—21no—
39C2×Dic26—22no—
40#6122—22no—
41#6122—22no—
42#6122—22no—
43#6122D414yes—
44C2×#1057—22no—
45C2×#1057—22no—
46C13×C22⋊C4—21no—
47C13×C22⋊C4—21no—
48C22⋊Dic13—21no—
49C22⋊Dic13—21no—
50#6103—21no—
51#6103—21no—
52#6103—21no—
53#6103—21no—
54C4×Dic13D411yescharacteristic
55C4×Dic13D411yescharacteristic
56C4×Dic13D411yescharacteristic
57C4×Dic13D411yescharacteristic
58#1967—131nomaximal, Sylow
59C23×C13—21no—
60C23×C13—22no—
61C23×C13—41no—
62C23×C13—41no—
63C23×C13C22×C411yescharacteristic
64C22×D13—21no—
65C22×D13—22no—
66C22×D13—41no—
67C22×D13—41no—
68C2×C4×C13—21no—
69C2×C4×C13—22no—
70C2×C4×C13—41no—
71C2×C4×C13C22⋊C411yescharacteristic
72C2×C4×C13C22⋊C411yescharacteristic
73C22⋊D13—42no—
74C22⋊D13—41no—
75C22⋊D13—41no—
76C2×Dic13—21no—
77C2×Dic13—22no—
78C2×Dic13—41no—
79C2×Dic13C22⋊C411yescharacteristic
80C2×Dic13C22⋊C411yescharacteristic
81C2×Dic13C2×D411yescharacteristic
82C2×Dic13C2×D412yes—
83C2×Dic13C2×D411yescharacteristic
84C2×Dic13#4112yes—
85Dic26—42no—
86Dic26—41no—
87Dic26—41no—
88#1057—24no—
89#1057—42no—
90C2×#124—131no—
91#423—131no—
92C2×#101—132no—
93C2×#100—132no—
94C4×M16—131no—
95C22×C13—21no—
96C22×C13—21no—
97C22×C13—41no—
98C22×C13—41no—
99C22×C13—41no—
100C22×C13—82no—
101C22×C13C2×C22⋊C411yescharacteristic
102C22×C13C4×D412yes—
103C2×D13—41no—
104C2×D13—41no—
105C2×D13—41no—
106C2×D13—82no—
107C4×C13—21no—
108C4×C13—21no—
109C4×C13—41no—
110Dic13—21no—
111Dic13—21no—
112Dic13—41no—
113Dic13#12112yes—
114Dic13#12411yescharacteristic
115Dic13#12711yescharacteristic
116C22×Q8—131no—
117C22×D4—131no—
118C2×M16—132no—
119C2×M16—132no—
120#124—261no—
121#124—261no—
122#124—261no—
123#124—261no—
124C2×C22⋊C4—131no—
125C2×C22⋊C4—131no—
126C2×C22⋊C4—131no—
127C2×C22⋊C4#26111yescharacteristic
128C2×C42—131no—
129C4⋊C8—261no—
130C4⋊C8—261no—
131#101—264no—
132#100—264no—
133#97—261no—
134C4×C8—261no—
135C2×C13—22no—
136C2×C13—81no—
137C2×C13#39011yescharacteristic
138C2×C13#41311yescharacteristic
139C2×C13#41311yescharacteristic
140D13—81no—
141C24—131no—
142C24C2×#26111yescharacteristic
143C2×Q8—262no—
144C2×Q8—261no—
145C2×Q8—261no—
146C2×Q8—262no—
147C2×D4—262no—
148C2×D4—261no—
149C2×D4—261no—
150C2×D4—262no—
151C22×C4—131no—
152C22×C4—131no—
153C22×C4—131no—
154C22×C4C2×#26111yescharacteristic
155C22×C4C2×#26111yescharacteristic
156M16—134no—
157M16—262no—
158M16—262no—
159M16—262no—
160C2×C8—262no—
161C2×C8—262no—
162C22⋊C4—21no—
163C22⋊C4—21no—
164C22⋊C4—261no—
165C22⋊C4—261no—
166C22⋊C4—261no—
167C22⋊C4—261no—
168C22⋊C4—261no—
169C22⋊C4—261no—
170C42—131no—
171C42—131no—
172C42—131no—
173C42—131no—
174C13#196711yescharacteristic, complemented, Sylow
175C23—21no—
176C23—22no—
177C23—41no—
178C23—41no—
179C23—261no—
180C23—262no—
181C23—521no—
182C23—521no—
183C23C22×#26111yescharacteristic
184Q8—522no—
185Q8—521no—
186Q8—521no—
187D4—522no—
188D4—521no—
189D4—521no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—132no—
194C2×C4—132no—
195C2×C4—131no—
196C2×C4—131no—
197C2×C4—131no—
198C2×C4—131no—
199C2×C4—262no—
200C2×C4—261no—
201C2×C4—521no—
202C2×C4C22⋊#26111yescharacteristic
203C2×C4C22⋊#26111yescharacteristic
204C8—264no—
205C8—522no—
206C22—21no—
207C22—21no—
208C22—41no—
209C22—41no—
210C22—41no—
211C22—82no—
212C22—521no—
213C22—521no—
214C22—521no—
215C22—1042no—
216C22D4×#26112yes—
217C22C2×C22⋊#26111yescharacteristic
218C4—21no—
219C4—21no—
220C4—41no—
221C4—132no—
222C4—131no—
223C4—131no—
224C4—261no—
225C4—261no—
226C4—521no—
227C2—22no—
228C2—81no—
229C2—1041no—
230C2#1171913211yescharacteristic
231C2#1171914811yescharacteristic
232C2#1171915111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC2×C13×C22⋊C4C4
socleC22×C13C2×C22⋊C4
prime radicalC22×C22⋊D13C22
cosocleC22×Dic13C23
hypercenterC2×C22⋊C4#261
hypocenterC13#1967
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#88113C2semidirect
4. #11719129C2semidirect
5. C4×#6122C2semidirect
174. C13#1967semidirect

Maximal subgroups

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

subgroupindex
C2×#881392
C2×#881212
C2×#881132
#117191292
C4×#61222
#196713