Finite Group Databasebeta

← #16777530

Subgroups — #16777530

Order 3328.

262 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 94 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⋊(C4⋊C16)C211yesmaximal, characteristic
2#13130772C211yesmaximal, characteristic
3D13×#335C211yesmaximal, characteristic
4C2×#88102—21no—
5C2×#88102C412yes—
6C2×D13⋊C16—21no—
7#11719059—21no—
8D13×C4⋊C8—21no—
9C4×C8×D13C2211yescharacteristic
10#11718260C412yescomplemented
11C4⋊#6092—21no—
12C13×#335C411yescharacteristic, complemented
13#11718071—21no—
14#11718050C411yescharacteristic, complemented
15C2×C4⋊#261—22no—
16C2×C4⋊#261—41no—
17C2×C4⋊#261—41no—
18C2×C8×D13—41no—
19C2×C8×D13C2×C411yescharacteristic
20C2×C8×D13D411yescharacteristic
21C42×D13D411yescharacteristic
22C2×#6092—22no—
23#88102—42no—
24#88102—41no—
25#88102—41no—
26D13⋊C16—41no—
27D13⋊C16—41no—
28C13×C4⋊C8—21no—
29C4×C8×C13C2×C411yescharacteristic
30#88054—41no—
31C8×Dic13C2×C411yescharacteristic
32C8×Dic13Q811yescharacteristic
33C4⋊#1055—21no—
34C4×#1055D411yescharacteristic
35#7274—131nomaximal, Sylow
36C22×#261—42no—
37C2×C4×D13C22⋊C411yescharacteristic
38C2×C4×D13D811yescharacteristic
39C2×C4×D13SD1611yescharacteristic
40C4⋊#261—42no—
41C4⋊#261—42no—
42C4⋊#261—82no—
43C4⋊#261—81no—
44C4⋊#261—81no—
45C2×C8×C13—41no—
46C2×C8×C13C4211yescharacteristic
47C2×C8×C13C4⋊C411yescharacteristic
48C42×C13C22⋊C411yescharacteristic
49C4×Dic13C4⋊C411yescharacteristic
50C4×Dic13SD1611yescharacteristic
51C4×Dic13Q1611yescharacteristic
52C2×#1055—41no—
53C2×#1055C22⋊C411yescharacteristic
54C2×#1055C4⋊C411yescharacteristic
55C8×D13—21no—
56C8×D13—21no—
57C8×D13—81no—
58C8×D13—81no—
59C8×D13D811yescharacteristic
60C8×D13SD1611yescharacteristic
61C8×D13SD1611yescharacteristic
62C8×D13Q1611yescharacteristic
63#6092—42no—
64C2×C4⋊C16—131no—
65#1845—131no—
66C2×#335—131no—
67C22×D13#10211yescharacteristic
68C2×#261—82no—
69C2×#261—82no—
70C2×#261—82no—
71C2×C4×C13#9511yescharacteristic
72C2×C4×C13#10211yescharacteristic
73C2×C4×C13#10311yescharacteristic
74C2×Dic13#10311yescharacteristic
75C2×Dic13#10611yescharacteristic
76C2×Dic13#10711yescharacteristic
77C4×D13—21no—
78C4×D13—21no—
79C4×D13#10011yescharacteristic
80C4×D13#10111yescharacteristic
81C4×D13#10211yescharacteristic
82C4×D13#10311yescharacteristic
83C4×D13D1611yescharacteristic
84C4×D13SD3211yescharacteristic
85C4×D13SD3211yescharacteristic
86C4×D13Q3211yescharacteristic
87C8×C13—21no—
88C8×C13—81no—
89C8×C13#10611yescharacteristic
90C8×C13#10711yescharacteristic
91#1055—21no—
92#1055—81no—
93#1055#10211yescharacteristic
94#1055#10311yescharacteristic
95C22×C16—261no—
96C2×#107—132no—
97C2×#107—261no—
98C2×C4⋊C8—261no—
99C2×C4×C8—131no—
100#384—261no—
101C4⋊C16—132no—
102C4⋊C16—261no—
103#335—131no—
104#335—261no—
105#335#26111yescharacteristic, complemented
106C22×C13#34011yescharacteristic
107C2×D13#33111yescharacteristic
108C2×D13#33211yescharacteristic
109C2×D13#35711yescharacteristic
110C2×D13#35811yescharacteristic
111C2×D13#36111yescharacteristic
112C2×D13#36211yescharacteristic
113#261—162no—
114C4×C13—21no—
115C4×C13#34011yescharacteristic
116C4×C13#34311yescharacteristic
117C4×C13#35711yescharacteristic
118C4×C13#35811yescharacteristic
119Dic13—21no—
120Dic13#33211yescharacteristic
121Dic13#33311yescharacteristic
122Dic13#36611yescharacteristic
123Dic13#36711yescharacteristic
124C22×C8—131no—
125C22×C8—131no—
126C22×C8—521no—
127C2×C4⋊C4—262no—
128C2×C4⋊C4—521no—
129C2×C4⋊C4—521no—
130C2×C42—131no—
131C2×C16—262no—
132C2×C16—521no—
133C2×C16—521no—
134#107—521no—
135#107—521no—
136#107—522no—
137C4⋊C8—21no—
138C4⋊C8—261no—
139C4⋊C8—521no—
140C4×C8—131no—
141C4×C8—131no—
142C4×C8—131no—
143C4×C8C2×#26111yescharacteristic
144C2×C13#129611yescharacteristic
145C2×C13#138011yescharacteristic
146C2×C13#138711yescharacteristic
147D13#136111yescharacteristic
148D13#136211yescharacteristic
149D13#136411yescharacteristic
150D13#136511yescharacteristic
151C22×C4—131no—
152C22×C4—131no—
153C22×C4—131no—
154C22×C4—522no—
155C2×C8—41no—
156C2×C8—131no—
157C2×C8—131no—
158C2×C8—131no—
159C2×C8—131no—
160C2×C8—131no—
161C2×C8—131no—
162C2×C8—261no—
163C2×C8—261no—
164C2×C8—521no—
165C2×C8—1041no—
166C2×C8—1041no—
167C2×C8C4×#26111yescharacteristic
168C2×C8C4⋊#26111yescharacteristic
169C4⋊C4—522no—
170C4⋊C4—522no—
171C4⋊C4—1041no—
172C4⋊C4—1041no—
173C4⋊C4—1042no—
174C42—131no—
175C42—131no—
176C42—131no—
177C42C22⋊#26111yescharacteristic
178C16—522no—
179C13#727411yescharacteristic, complemented, Sylow
180C23—131no—
181C2×C4—131no—
182C2×C4—131no—
183C2×C4—131no—
184C2×C4—131no—
185C2×C4—131no—
186C2×C4—131no—
187C2×C4—131no—
188C2×C4—131no—
189C2×C4—131no—
190C2×C4—131no—
191C2×C4—131no—
192C2×C4—261no—
193C2×C4—261no—
194C2×C4—1042no—
195C2×C4—1042no—
196C2×C4—1042no—
197C2×C4(C2×#261)⋊C411yescharacteristic
198C2×C4#8811511yescharacteristic
199C2×C4#8811711yescharacteristic
200C8—21no—
201C8—81no—
202C8—131no—
203C8—131no—
204C8—261no—
205C8—1041no—
206C8#8810111yescharacteristic
207C8#8810211yescharacteristic
208C22—131no—
209C22—131no—
210C22—131no—
211C22—131no—
212C22—131no—
213C22—131no—
214C22#1171824611yescharacteristic
215C4—21no—
216C4—131no—
217C4—131no—
218C4—131no—
219C4—131no—
220C4—261no—
221C4—2082no—
222C4#1171826511yescharacteristic
223C4#1171827111yescharacteristic
224C4#1171827611yescharacteristic
225C4#1171828011yescharacteristic
226C2—131no—
227C2—131no—
228C2—131no—
229C2—131no—
230C2#1312971511yescharacteristic
231C2#1312989311yescharacteristic
232C2#1312991211yescharacteristic
subgroupG/H
centerC22#11718246
commutatorC2×C8×C13C42
FrattiniC4×C8C2×#261
FittingC13×#335C4
socleC22×C13#340
prime radicalC22×D13#102
cosocleC4×C8×D13C22
hypercenter#335#261
hypocenterC13#7274
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #335

Complements

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

NH ≅ G/Ntype
10. #11718260C4semidirect
12. C13×#335C4semidirect
14. #11718050C4semidirect
105. #335#261semidirect
179. C13#7274semidirect

Maximal subgroups

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

subgroupindex
D13⋊(C4⋊C16)2
#131307722
D13×#3352
#727413