Finite Group Databasebeta

← #16777402

Subgroups — #16777402

Order 3328.

292 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 64 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
1D13⋊(C22⋊C16)C211yesmaximal, characteristic
2#13130712C211yesmaximal, characteristic
3#13114873C211yesmaximal, characteristic
4C22×C8×D13C2211yescharacteristic
5#11719136—21no—
6C2×#88101—21no—
7C2×D13⋊C16C412yescomplemented
8#11718787—21no—
9C2×#88062—21no—
10C22⋊#6092—21no—
11#11718265C412yes—
12#11718259—21no—
13C13×#341C411yescharacteristic, complemented
14#11718144C411yescharacteristic, complemented
15C22×C4×D13D411yescharacteristic
16C2×C22⋊#261—41no—
17C2×C4⋊#261—22no—
18C2×C13×M16—21no—
19C22×C8×C13C2×C411yescharacteristic
20C2×#6099—21no—
21C22×#1055D411yescharacteristic
22C2×C8×D13—42no—
23C2×C8×D13C2×C411yescharacteristic
24C2×C8×D13C2×C411yescharacteristic
25C2×C8×D13D411yescharacteristic
26C2×C8×D13Q811yescharacteristic
27(C2×#261)⋊C4—41no—
28C2×#6092—22no—
29#88101—42no—
30D13⋊C16—42no—
31#88062—42no—
32#88060—41no—
33#88060—41no—
34#7232—131nomaximal, Sylow
35C23×D13SD1611yescharacteristic
36C22×#261—42no—
37C22×C4×C13C22⋊C411yescharacteristic
38C22×Dic13Q1611yescharacteristic
39C2×C4×D13—41no—
40C2×C4×D13—41no—
41C2×C4×D13C22⋊C411yescharacteristic
42C2×C4×D13C4⋊C411yescharacteristic
43C2×C4×D13D811yescharacteristic
44C2×C4×D13SD1611yescharacteristic
45C22⋊#261—82no—
46C4⋊#261—42no—
47C4⋊#261—42no—
48C13×M16—41no—
49C13×M16—41no—
50C2×C8×C13—41no—
51C2×C8×C13—41no—
52C2×C8×C13C4211yescharacteristic
53C2×C8×C13C4⋊C411yescharacteristic
54#6099—41no—
55#6099—41no—
56C2×#1055—22no—
57C2×#1055—41no—
58C2×#1055C22⋊C411yescharacteristic
59C2×#1055C4⋊C411yescharacteristic
60C8×D13—22no—
61C8×D13—22no—
62C8×D13—41no—
63C8×D13—41no—
64#6092—42no—
65C2×C22⋊C16—131no—
66#1810—131no—
67#1807—131no—
68C23×C13#10311yescharacteristic
69C22×D13—22no—
70C22×D13—22no—
71C22×D13—41no—
72C22×D13#10211yescharacteristic
73C22×D13#10611yescharacteristic
74C2×#261—82no—
75C2×#261—82no—
76C2×#261—82no—
77C2×C4×C13—21no—
78C2×C4×C13—21no—
79C2×C4×C13#9511yescharacteristic
80C2×C4×C13#10211yescharacteristic
81C2×Dic13—41no—
82C2×Dic13#10311yescharacteristic
83C2×Dic13#10711yescharacteristic
84C4×D13—21no—
85C4×D13—21no—
86C4×D13—21no—
87C4×D13—21no—
88C4×D13—41no—
89C4×D13—41no—
90C8×C13—21no—
91C8×C13—21no—
92C8×C13—81no—
93#1055—21no—
94#1055—81no—
95#1055#9912yes—
96C23×C8—131no—
97C22×C16—132no—
98C2×#108—261no—
99C2×#106—261no—
100#407—261no—
101#380—261no—
102C22⋊C16—261no—
103C22⋊C16—261no—
104#341—131no—
105#341#26111yescharacteristic, complemented
106#340—132no—
107C22×C13—21no—
108C22×C13—21no—
109C22×C13—21no—
110C22×C13#34011yescharacteristic
111C2×D13—21no—
112C2×D13—21no—
113C2×D13—21no—
114C2×D13—21no—
115C2×D13—44no—
116C2×D13#35912yes—
117C2×D13#36512yes—
118#261—162no—
119C4×C13—21no—
120C4×C13H(3,ℤ/4)11yescharacteristic
121C4×C13#34211yescharacteristic
122Dic13—21no—
123Dic13—21no—
124C23×C4—131no—
125C2×M16—21no—
126C2×M16—261no—
127C22×C8—131no—
128C22×C8—131no—
129C22×C8—131no—
130C22×C8—131no—
131C22×C8—131no—
132C22×C8—522no—
133C22×C8C2×#26111yescharacteristic
134C2×C4⋊C4—262no—
135C2×C22⋊C4—521no—
136C2×C16—262no—
137C2×C16—522no—
138#108—522no—
139#106—522no—
140C22⋊C8—521no—
141C22⋊C8—521no—
142#95—521no—
143C2×C13—41no—
144C2×C13#128911yescharacteristic
145C2×C13#138211yescharacteristic
146C2×C13#138311yescharacteristic
147D13—22no—
148D13—22no—
149C24—131no—
150C22×C4—131no—
151C22×C4—131no—
152C22×C4—131no—
153C22×C4—131no—
154C22×C4—131no—
155C22×C4—521no—
156C22×C4—521no—
157C22×C4—522no—
158C22×C4C22⋊#26111yescharacteristic
159M16—41no—
160M16—41no—
161M16—521no—
162M16—521no—
163C2×C8—41no—
164C2×C8—41no—
165C2×C8—131no—
166C2×C8—131no—
167C2×C8—262no—
168C2×C8—262no—
169C2×C8—262no—
170C2×C8—521no—
171C2×C8—521no—
172C2×C8—521no—
173C2×C8C4×#26111yescharacteristic
174C2×C8C4⋊#26111yescharacteristic
175C4⋊C4—522no—
176C4⋊C4—522no—
177C22⋊C4—1042no—
178C16—522no—
179C13#723211yescharacteristic, complemented, Sylow
180C23—131no—
181C23—131no—
182C23—262no—
183C23—262no—
184C23—521no—
185C23#8811711yescharacteristic
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—131no—
189C2×C4—131no—
190C2×C4—261no—
191C2×C4—261no—
192C2×C4—261no—
193C2×C4—261no—
194C2×C4—521no—
195C2×C4—521no—
196C2×C4—521no—
197C2×C4—1042no—
198C2×C4—1042no—
199C2×C4—1042no—
200C2×C4(C2×#261)⋊C411yescharacteristic
201C2×C4#8811511yescharacteristic
202C8—21no—
203C8—21no—
204C8—81no—
205C8—132no—
206C8—261no—
207C8—1041no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—132no—
212C22—132no—
213C22—261no—
214C22—261no—
215C22—261no—
216C22—261no—
217C22—524no—
218C22#1171824611yescharacteristic
219C4—21no—
220C4—261no—
221C4—261no—
222C4—2082no—
223C4#1171823511yescharacteristic
224C4#1171823811yescharacteristic
225C2—41no—
226C2—262no—
227C2—262no—
228C2#1312969811yescharacteristic
229C2#1312989911yescharacteristic
230C2#1312990211yescharacteristic
subgroupG/H
centerC22#11718246
commutatorC2×C8×C13C42
FrattiniC22×C8C2×#261
FittingC13×#341C4
socleC22×C13#340
prime radicalC23×D13SD16
cosocleC22×C8×D13C22
hypercenter#341#261
hypocenterC13#7232
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #341

Complements

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

NH ≅ G/Ntype
7. C2×D13⋊C16C4semidirect
13. C13×#341C4semidirect
14. #11718144C4semidirect
105. #341#261semidirect
179. C13#7232semidirect

Maximal subgroups

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

subgroupindex
D13⋊(C22⋊C16)2
#131307122
#131148732
#723213