Finite Group Databasebeta

← #16778271

Subgroups — #16778271

Order 3328.

684 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 166 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
1C4×C4⋊#1057C212yesmaximal, complemented
2#13129652C214yesmaximal, complemented
3#127×Dic13C211yesmaximal, characteristic
4C2×C13×#127C411yescharacteristic
5C2×D4×Dic13—22no—
6C2×D4×Dic13C412yes—
7C2×C4⋊#1057—22no—
8C2×C4×#1057—22no—
9#11718882—22no—
10#11718882C2212yes—
11#11718596C411yescharacteristic
12C42×Dic13C2211yescharacteristic
13#11718290C2214yes—
14C22×D4×C13—22no—
15C22×D4×C13C2×C412yes—
16C23×Dic13—22no—
17C22×#1057—24no—
18C13×#127—22no—
19C13×#127C814yescomplemented
20C2×C42×C13C2×C411yescharacteristic
21C2×C22⋊Dic13—22no—
22C2×C22⋊Dic13—24no—
23D4×Dic13—44no—
24D4×Dic13—44no—
25D4×Dic13—44no—
26C2×C4⋊Dic13—22no—
27C2×C4⋊Dic13C2×C412yes—
28C2×C4×Dic13C2×C411yescharacteristic
29C2×C4×Dic13D412yes—
30C2×C4×Dic13D412yes—
31C2×C4×Dic13C2311yescharacteristic
32C4⋊#1057—28no—
33C4×#1057—44no—
34#7569—131nomaximal, Sylow
35C24×C13—22no—
36C2×D4×C13—28no—
37C2×D4×C13—22no—
38C2×D4×C13—42no—
39C2×D4×C13—42no—
40C2×D4×C13—44no—
41C2×D4×C13—44no—
42C2×D4×C13C2×C814yes—
43C22×C4×C13C22⋊C412yes—
44C22×C4×C13C22×C411yescharacteristic
45C22×Dic13—22no—
46C22×Dic13—44no—
47C22×Dic13—48no—
48C22×Dic13C22⋊C411yescharacteristic
49C22×Dic13C22⋊C411yescharacteristic
50C22×Dic13C2×D412yes—
51C2×#1057—28no—
52C2×#1057—44no—
53C2×#1057—44no—
54C42×C13C2×C812yes—
55C42×C13M1612yes—
56C22⋊Dic13—44no—
57C22⋊Dic13—44no—
58C22⋊Dic13—44no—
59C4⋊Dic13—44no—
60C4⋊Dic13—42no—
61C4×Dic13—24no—
62C4×Dic13—22no—
63C4×Dic13—41no—
64C4×Dic13D814yes—
65C4×Dic13SD1614yes—
66C4×#127—131no—
67C4×C4⋊C8—132no—
68#1270—134no—
69C23×C13—24no—
70C23×C13—42no—
71C23×C13—42no—
72C23×C13—44no—
73C23×C13—44no—
74C23×C13C2×C22⋊C411yescharacteristic
75D4×C13—44no—
76D4×C13—44no—
77D4×C13—416no—
78C2×C4×C13—21no—
79C2×C4×C13—21no—
80C2×C4×C13C22⋊C814yes—
81C2×C4×C13#10214yes—
82C2×C4×C13#10414yes—
83C2×C4×C13C22×C811yescharacteristic
84C2×C4×C13C2×M1611yescharacteristic
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13—21no—
88C2×Dic13—22no—
89C2×Dic13—42no—
90C2×Dic13—44no—
91C2×Dic13—88no—
92C2×Dic13#10012yes—
93C2×Dic13#10214yes—
94C2×Dic13C2×D812yes—
95C2×Dic13C2×SD1612yes—
96#1057—48no—
97C2×#127#26111yescharacteristic
98C2×C4×D4—132no—
99C2×C4×D4—262no—
100C2×C4⋊C8—262no—
101C2×C4×C8—262no—
102#390—132no—
103#390—262no—
104#384—131no—
105C43—131no—
106#336—134no—
107C22×C13—44no—
108C22×C13—48no—
109C22×C13—82no—
110C22×C13—84no—
111C22×C13—82no—
112C22×C13C2×C22⋊C811yescharacteristic
113C22×C13#41011yescharacteristic
114C22×C13C2×#10011yescharacteristic
115C22×C13C2×#10212yes—
116C22×C13C2×#10412yes—
117C4×C13—21no—
118C4×C13—21no—
119C4×C13D4⋊C818yes—
120Dic13—22no—
121Dic13—22no—
122Dic13—41no—
123Dic13—82no—
124Dic13#33114yes—
125C22×D4—22no—
126C22×D4C2×#26112yes—
127C23×C4—262no—
128C22×C8—264no—
129#127—22no—
130#127#105714yescomplemented
131C4×D4—524no—
132C4×D4—524no—
133C4×D4—524no—
134C2×C4⋊C4—132no—
135C2×C4⋊C4—262no—
136C2×C22⋊C4—262no—
137C2×C22⋊C4—264no—
138C2×C42—132no—
139C2×C42—132no—
140C2×C42—131no—
141C2×C42—131no—
142C2×C42C2×#26111yescharacteristic
143C4⋊C8—268no—
144C4×C8—524no—
145C2×C13—84no—
146C2×C13#146011yescharacteristic
147C2×C13C2×D4⋊C812yes—
148C2×C13#150212yes—
149C2×C13#152511yescharacteristic
150C2×C13C2×#33111yescharacteristic
151C24—22no—
152C2×D4—28no—
153C2×D4—22no—
154C2×D4—42no—
155C2×D4—42no—
156C2×D4—44no—
157C2×D4—44no—
158C2×D4C2×#105714yes—
159C22×C4—131no—
160C22×C4—132no—
161C22×C4—131no—
162C22×C4—262no—
163C22×C4—528no—
164C22×C4—524no—
165C22×C4C22⋊#26112yes—
166C22×C4C22×#26111yescharacteristic
167C2×C8—268no—
168C2×C8—524no—
169C2×C8—524no—
170C4⋊C4—522no—
171C4⋊C4—524no—
172C22⋊C4—524no—
173C22⋊C4—524no—
174C22⋊C4—524no—
175C42—134no—
176C42—134no—
177C42—262no—
178C42—264no—
179C42—521no—
180C42C2×#105712yes—
181C42#612212yes—
182C13#756911yescharacteristic, complemented, Sylow
183C23—24no—
184C23—44no—
185C23—44no—
186C23—42no—
187C23—42no—
188C23C2×C22⋊#26111yescharacteristic
189D4—44no—
190D4—44no—
191D4—416no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—134no—
195C2×C4—132no—
196C2×C4—132no—
197C2×C4—132no—
198C2×C4—262no—
199C2×C4—262no—
200C2×C4—262no—
201C2×C4—261no—
202C2×C4—524no—
203C2×C4—522no—
204C2×C4—1048no—
205C2×C4#8811514yes—
206C2×C4#8811614yes—
207C2×C4C22⋊#105714yes—
208C2×C4C22×#105711yescharacteristic
209C2×C4C2×#612211yescharacteristic
210C8—528no—
211C22—44no—
212C22—48no—
213C22—82no—
214C22—82no—
215C22—84no—
216C22C2×#8811512yes—
217C22C2×#8811612yes—
218C22#1171914211yescharacteristic
219C22D13⋊#10011yescharacteristic
220C22C2×C22⋊#105711yescharacteristic
221C4—21no—
222C4—21no—
223C4—134no—
224C4—262no—
225C4—262no—
226C4—521no—
227C4—1042no—
228C4D4⋊#105718yes—
229C2—84no—
230C2#1313007611yescharacteristic
231C2C2×D4⋊#105712yes—
232C2#1313021612yes—
233C2#1313029111yescharacteristic
234C2D13⋊#33111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
Fitting, prime radicalC2×C13×#127C4
socleC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×#127#261
hypocenterC13#7569
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C4×C4⋊#1057C2semidirect
2. #13129652C2semidirect
19. C13×#127C8semidirect
130. #127#1057semidirect
182. C13#7569semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊#10572
#131296522
#127×Dic132
#756913