Finite Group Databasebeta

← #16778351

Subgroups — #16778351

Order 3328.

846 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 846 conjugacy classes of subgroups — too many to draw. Only its 132 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
1#13130726C212yesmaximal, complemented
2#13129652C214yesmaximal, complemented
3C2×#11718882C211yesmaximal, characteristic
4C23×D4×C13C411yescharacteristic
5C22×C22⋊Dic13—22no—
6C22×C4⋊Dic13C411yescharacteristic
7C22×C4×Dic13C2211yescharacteristic
8C2×C22⋊#1057—22no—
9#11718882—22no—
10#11718882C412yes—
11#11718882C2212yes—
12#11718290—22no—
13#11718290C2214yescomplemented
14C25×C13—21no—
15C22×D4×C13—21no—
16C22×D4×C13—22no—
17C22×D4×C13—42no—
18C22×D4×C13—42no—
19C22×D4×C13C814yescomplemented
20C22×D4×C13C2×C412yes—
21C23×C4×C13C2×C411yescharacteristic
22C23×Dic13—21no—
23C23×Dic13D412yes—
24C22×#1057—24no—
25C2×C22⋊Dic13—24no—
26C2×C22⋊Dic13—24no—
27C2×C22⋊Dic13—48no—
28C2×C4⋊Dic13—21no—
29C2×C4⋊Dic13—42no—
30C2×C4⋊Dic13C2×C412yes—
31C2×C4×Dic13—42no—
32C2×C4×Dic13C2×C411yescharacteristic
33C2×C4×Dic13D412yes—
34C2×C4×Dic13C2311yescharacteristic
35C22⋊#1057—44no—
36#7592—131nomaximal, Sylow
37C24×C13—24no—
38C24×C13—22no—
39C24×C13—44no—
40C24×C13—44no—
41C24×C13—42no—
42C24×C13—42no—
43C24×C13C22⋊C411yescharacteristic
44C2×D4×C13—24no—
45C2×D4×C13—22no—
46C2×D4×C13—48no—
47C2×D4×C13—42no—
48C2×D4×C13—42no—
49C2×D4×C13—48no—
50C2×D4×C13—42no—
51C2×D4×C13—42no—
52C2×D4×C13C2×C814yes—
53C22×C4×C13—22no—
54C22×C4×C13—22no—
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C2×C812yes—
57C22×C4×C13M1612yes—
58C22×C4×C13C22×C411yescharacteristic
59C22×Dic13—24no—
60C22×Dic13—24no—
61C22×Dic13—22no—
62C22×Dic13—42no—
63C22×Dic13—44no—
64C22×Dic13—42no—
65C22×Dic13C22⋊C412yes—
66C22×Dic13C2×D412yes—
67C2×#1057—44no—
68C2×#1057—44no—
69C2×#1057—44no—
70C22⋊Dic13—48no—
71C22⋊Dic13—48no—
72C4⋊Dic13—42no—
73C4⋊Dic13—42no—
74C4×Dic13—41no—
75C4×Dic13—42no—
76C4×Dic13—41no—
77C2×#390—131no—
78#1817—132no—
79#1270—134no—
80C23×C13—22no—
81C23×C13—22no—
82C23×C13—24no—
83C23×C13—416no—
84C23×C13—48no—
85C23×C13—42no—
86C23×C13—42no—
87C23×C13—44no—
88C23×C13—44no—
89C23×C13—84no—
90C23×C13—88no—
91C23×C13—84no—
92C23×C13C22⋊C812yes—
93C23×C13#9912yes—
94C23×C13#10012yes—
95C23×C13C2×C22⋊C411yescharacteristic
96D4×C13—48no—
97D4×C13—44no—
98D4×C13—44no—
99C2×C4×C13—24no—
100C2×C4×C13—24no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13C22⋊C812yes—
106C2×C4×C13C22×C811yescharacteristic
107C2×C4×C13C2×M1611yescharacteristic
108C2×Dic13—22no—
109C2×Dic13—22no—
110C2×Dic13—22no—
111C2×Dic13—22no—
112C2×Dic13—22no—
113C2×Dic13—48no—
114C2×Dic13—42no—
115C2×Dic13—44no—
116C2×Dic13—84no—
117C2×Dic13AGL(1,ℤ/8)14yes—
118#1057—84no—
119C23×D4#26111yescharacteristic
120C22×C4⋊C4—131no—
121C22×C22⋊C4—262no—
122C22×C42—131no—
123C2×C22⋊C8—262no—
124#390—132no—
125#390—132no—
126#390—262no—
127#336—134no—
128#336—262no—
129C22×C13—22no—
130C22×C13—24no—
131C22×C13—24no—
132C22×C13—22no—
133C22×C13—44no—
134C22×C13—48no—
135C22×C13—816no—
136C22×C13—82no—
137C22×C13—84no—
138C22×C13—82no—
139C22×C13#32314yes—
140C22×C13C2×C22⋊C811yescharacteristic
141C22×C13C2×#9911yescharacteristic
142C22×C13C2×#10011yescharacteristic
143C22×C13#41812yes—
144C22×C13#42112yes—
145C4×C13—22no—
146C4×C13—21no—
147C4×C13—21no—
148Dic13—24no—
149Dic13—42no—
150Dic13—82no—
151C25—21no—
152C22×D4—22no—
153C22×D4—21no—
154C22×D4—42no—
155C22×D4—42no—
156C22×D4#105714yescomplemented
157C22×D4C2×#26112yes—
158C23×C4—132no—
159C23×C4—261no—
160C23×C4C2×#26111yescharacteristic
161C22×C8—264no—
162C2×C4⋊C4—132no—
163C2×C4⋊C4—261no—
164C2×C4⋊C4—522no—
165C2×C22⋊C4—264no—
166C2×C22⋊C4—264no—
167C2×C22⋊C4—528no—
168C2×C42—132no—
169C2×C42—131no—
170C2×C42—131no—
171C2×C42—522no—
172C22⋊C8—524no—
173C2×C13—24no—
174C2×C13—84no—
175C2×C13C2×#32311yescharacteristic
176C2×C13#147812yes—
177C2×C13#151012yes—
178C2×C13#153311yescharacteristic
179C2×C13#155511yescharacteristic
180C24—24no—
181C24—22no—
182C24—44no—
183C24—44no—
184C24—42no—
185C24—42no—
186C24C22⋊#26111yescharacteristic
187C2×D4—24no—
188C2×D4—22no—
189C2×D4—48no—
190C2×D4—42no—
191C2×D4—42no—
192C2×D4—42no—
193C2×D4—48no—
194C2×D4—42no—
195C2×D4C2×#105714yes—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—132no—
199C22×C4—132no—
200C22×C4—264no—
201C22×C4—264no—
202C22×C4—262no—
203C22×C4—522no—
204C22×C4—524no—
205C22×C4—522no—
206C22×C4C2×#105712yes—
207C22×C4#612212yes—
208C22×C4C22⋊#26111yescharacteristic
209C22×C4C22×#26111yescharacteristic
210C2×C8—524no—
211C2×C8—524no—
212C2×C8—524no—
213C4⋊C4—522no—
214C4⋊C4—522no—
215C22⋊C4—528no—
216C22⋊C4—528no—
217C42—522no—
218C42—521no—
219C42—521no—
220C13#759211yescharacteristic, complemented, Sylow
221C23—22no—
222C23—22no—
223C23—24no—
224C23—416no—
225C23—42no—
226C23—48no—
227C23—44no—
228C23—44no—
229C23—42no—
230C23—88no—
231C23—84no—
232C23—84no—
233C23#8811912yes—
234C23C22⋊#105712yes—
235C23#8812112yes—
236C23C2×C22⋊#26111yescharacteristic
237D4—44no—
238D4—48no—
239D4—44no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—24no—
243C2×C4—24no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—134no—
247C2×C4—262no—
248C2×C4—262no—
249C2×C4—262no—
250C2×C4—262no—
251C2×C4—262no—
252C2×C4—528no—
253C2×C4—522no—
254C2×C4—524no—
255C2×C4—1044no—
256C2×C4C22⋊#105712yes—
257C2×C4C22×#105711yescharacteristic
258C2×C4C2×#612211yescharacteristic
259C8—1044no—
260C22—24no—
261C22—22no—
262C22—22no—
263C22—24no—
264C22—44no—
265C22—48no—
266C22—816no—
267C22—84no—
268C22—82no—
269C22—82no—
270C22#1171830514yes—
271C22#1171913812yes—
272C22#1171914012yes—
273C22C2×#8811911yescharacteristic
274C22C2×C22⋊#105711yescharacteristic
275C22C2×#8812111yescharacteristic
276C4—22no—
277C4—21no—
278C4—21no—
279C4—264no—
280C4—522no—
281C4—1042no—
282C2—24no—
283C2—84no—
284C2C2×#1171830511yescharacteristic
285C2#1313013512yes—
286C2#1313024112yes—
287C2#1313031511yescharacteristic
288C2#1313036311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
Fitting, prime radicalC23×D4×C13C4
socleC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC23×D4#261
hypocenterC13#7592
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. #13130726C2semidirect
2. #13129652C2semidirect
13. #11718290C22semidirect
19. C22×D4×C13C8semidirect
156. C22×D4#1057semidirect
220. C13#7592semidirect

Maximal subgroups

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

subgroupindex
#131307262
#131296522
C2×#117188822
#759213