Finite Group Databasebeta

← #16791700

Subgroups — #16791700

Order 3328.

1422 conjugacy classes of subgroups; only the 336 normal subgroups are shown.

normal subgroups only

This group has 1422 conjugacy classes of subgroups — too many to draw. Only its 336 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×C4×C4⋊#261C212yesmaximal
2#13130022C218yesmaximal
3C4×(C2×#261)⋊C4C214yesmaximal
4D13×#376C211yesmaximal, characteristic
5C22×C4⋊#261C2214yes—
6C22×C4×#261C2214yes—
7C2×C42×D13C2212yes—
8C2×C42×D13C2211yescharacteristic
9C2×(C2×#261)⋊C4C2214yes—
10C2×(C2×#261)⋊C4C22116yes—
11C4×C4⋊#261—28no—
12C13×#376C411yescharacteristic, complemented
13#11718593C411yescharacteristic, complemented
14#11718593C412yescomplemented
15D13×#95C2214yes—
16#11718309C414yescomplemented
17C23×#261C2318yes—
18C22×C4×D13C2314yes—
19C22×C4×D13C2312yes—
20C22×C4×D13C2311yescharacteristic
21C2×C4⋊#261—216no—
22C2×C4⋊#261—28no—
23C2×C4×#261—28no—
24C2×C4×#261—216no—
25C2×C42×C13C2×C412yes—
26C2×C42×C13C2×C411yescharacteristic
27C2×C4×Dic13C2×C414yes—
28C2×C4×Dic13C2×C412yes—
29C2×C4×Dic13C2×C412yes—
30C2×C4×Dic13C2×C411yescharacteristic
31C42×D13—28no—
32C42×D13D414yes—
33C42×D13Q814yes—
34(C2×#261)⋊C4—232no—
35(C2×#261)⋊C4—28no—
36C13×#95C2×C414yes—
37#88071C2×C414yes—
38#88071C2×C418yes—
39#13854—131nomaximal, Sylow
40C23×D13C2411yescharacteristic
41C22×#261—28no—
42C22×#261—216no—
43C22×#261—216no—
44C22×#261—28no—
45C22×#261#41116yes—
46C22×C4×C13C22×C414yes—
47C22×C4×C13C22×C412yes—
48C22×C4×C13C22×C411yescharacteristic
49C22×Dic13C22×C414yes—
50C22×Dic13C22×C412yes—
51C22×Dic13C22×C411yescharacteristic
52C2×C4×D13—28no—
53C2×C4×D13—216no—
54C2×C4×D13—28no—
55C2×C4×D13C2×D414yes—
56C2×C4×D13C2×D412yes—
57C2×C4×D13C2×Q814yes—
58C2×C4×D13C2×Q812yes—
59C2×C4×D13#4118yes—
60C4⋊#261—232no—
61C4×#261—416no—
62C42×C13—24no—
63C42×C13C4⋊C414yes—
64C4×Dic13—24no—
65C4×Dic13—28no—
66C4×Dic13C4⋊C414yes—
67C4×Dic13C4⋊C418yes—
68C2×C4×C4⋊C4—132no—
69C2×#376—131no—
70#1442—138no—
71C4×#95—134no—
72C23×C13C23×C411yescharacteristic
73C22×D13C22×D411yescharacteristic
74C22×D13C22×Q811yescharacteristic
75C22×D13C2×#4118yes—
76C22×D13C2×#4114yes—
77C2×#261—216no—
78C2×#261—232no—
79C2×#261—48no—
80C2×#261—48no—
81C2×#261—416no—
82C2×C4×C13—24no—
83C2×C4×C13—24no—
84C2×C4×C13—28no—
85C2×C4×C13C2×C4⋊C414yes—
86C2×C4×C13C2×C4⋊C412yes—
87C2×C4×C13#11714yes—
88C2×Dic13—24no—
89C2×Dic13—24no—
90C2×Dic13—28no—
91C2×Dic13C2×C4⋊C414yes—
92C2×Dic13C2×C4⋊C412yes—
93C2×Dic13#11714yes—
94C4×D13—28no—
95C4×D13—28no—
96C4×D13—416no—
97C4×D13#12418yes—
98C4×D13#12518yes—
99C22×C4⋊C4—134no—
100C22×C42—131no—
101C22×C42—132no—
102C22×C42—134no—
103C4×C4⋊C4—268no—
104#376—132no—
105#376—131no—
106#376—134no—
107#376#26111yescharacteristic, complemented
108C2×#95—134no—
109C2×#95—1316no—
110C2×#95—134no—
111C22×C13C22×C4⋊C411yescharacteristic
112C22×C13C2×#11712yes—
113C22×C13C4×#4114yes—
114C2×D13#52514yes—
115C2×D13C2×#12412yes—
116C2×D13C2×#12512yes—
117C2×D13#529116yes—
118C2×D13#53314yes—
119#261—416no—
120C4×C13—24no—
121C4×C13—44no—
122C4×C13#38214yes—
123Dic13—24no—
124Dic13—44no—
125Dic13#38214yes—
126C23×C4—131no—
127C23×C4—132no—
128C23×C4—138no—
129C23×C4—134no—
130C2×C4⋊C4—268no—
131C2×C4⋊C4—2616no—
132C2×C42—132no—
133C2×C42—131no—
134C2×C42—134no—
135C2×C42—134no—
136C2×C42—134no—
137C2×C42—132no—
138C2×C42—268no—
139C2×C42—268no—
140C2×C42—2616no—
141C2×C42C2×#26112yes—
142C2×C42C2×#26111yescharacteristic
143#95—138no—
144#95—134no—
145#95—2632no—
146#95—268no—
147#95C2×#26114yes—
148C2×C13C2×#38211yescharacteristic
149C2×C13#229612yes—
150C2×C13#229814yes—
151D13#239814yes—
152D13#240214yes—
153C24—131no—
154C22×C4—131no—
155C22×C4—132no—
156C22×C4—132no—
157C22×C4—138no—
158C22×C4—132no—
159C22×C4—134no—
160C22×C4—134no—
161C22×C4—1316no—
162C22×C4—134no—
163C22×C4—268no—
164C22×C4—2616no—
165C22×C4—268no—
166C22×C4—268no—
167C22×C4—2616no—
168C22×C4—2616no—
169C22×C4—268no—
170C22×C4C22×#26114yes—
171C22×C4C22×#26112yes—
172C22×C4C22×#26111yescharacteristic
173C4⋊C4—2632no—
174C42—24no—
175C42—138no—
176C42—134no—
177C42—268no—
178C42—264no—
179C42—5216no—
180C42C4⋊#26114yes—
181C13#1385411yescharacteristic, complemented, Sylow
182C23—131no—
183C23—131no—
184C23—134no—
185C23—138no—
186C23C23×#26111yescharacteristic
187C2×C4—24no—
188C2×C4—24no—
189C2×C4—28no—
190C2×C4—132no—
191C2×C4—134no—
192C2×C4—138no—
193C2×C4—138no—
194C2×C4—134no—
195C2×C4—268no—
196C2×C4—268no—
197C2×C4—264no—
198C2×C4—2616no—
199C2×C4—2632no—
200C2×C4—264no—
201C2×C4—268no—
202C2×C4—5216no—
203C2×C4—528no—
204C2×C4—528no—
205C2×C4—5216no—
206C2×C4C2×C4⋊#26114yes—
207C2×C4C2×C4⋊#26112yes—
208C2×C4#8823714yes—
209C22—132no—
210C22—132no—
211C22—134no—
212C22—134no—
213C22—1316no—
214C22C22×C4⋊#26111yescharacteristic
215C22C2×#8823712yes—
216C22#41×#26114yes—
217C4—24no—
218C4—44no—
219C4—134no—
220C4—264no—
221C4—5216no—
222C4—524no—
223C4#1171906014yes—
224C2—134no—
225C2—134no—
226C2C2×#1171906011yescharacteristic
227C2#1313129612yes—
228C2#1313129814yes—
subgroupG/H
centerC22×C4C22×#261
commutator, socleC23×C13C23×C4
FrattiniC23C23×#261
FittingC13×#376C4
prime radical, cosocleC23×D13C24
hypercenter#376#261
hypocenterC13#13854
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #376

Complements

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

NH ≅ G/Ntype
12. C13×#376C4semidirect
13. #11718593C4semidirect
14. #11718593C4semidirect
16. #11718309C4semidirect
107. #376#261semidirect
181. C13#13854semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊#2612
#131300222
C4×(C2×#261)⋊C42
D13×#3762
#1385413