Finite Group Databasebeta

← #16778402

Subgroups — #16778402

Order 3328.

612 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 122 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#13130727C211yesmaximal, characteristic
2#13130499C211yesmaximal, characteristic
3#13129654C214yesmaximal, complemented
4C2×#11718646C211yesmaximal, characteristic
5C22×#6122—21no—
6C22×C13×C4⋊C4C411yescharacteristic
7C22×C4⋊Dic13—21no—
8C22×C4⋊Dic13C411yescharacteristic
9C22×C4×Dic13C2211yescharacteristic
10C2×C22⋊#1057—21no—
11C2×#88071—21no—
12#11718646—21no—
13#11718646—21no—
14#11718646C412yes—
15#11718646C2212yes—
16#11718290—21no—
17#11718290—21no—
18#11718290C2212yes—
19#11718290C2212yes—
20C23×C4×C13—21no—
21C23×C4×C13C2×C411yescharacteristic
22C23×Dic13—21no—
23C23×Dic13D411yescharacteristic
24C23×Dic13D411yescharacteristic
25C2×#6122—24no—
26C2×#6122—42no—
27C2×#6122—42no—
28C22×#1057—22no—
29C22×#1057—22no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—24no—
32C2×C13×C4⋊C4C2×C412yes—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—22no—
35C2×C4⋊Dic13—22no—
36C2×C4⋊Dic13—44no—
37C2×C4⋊Dic13—42no—
38C2×C4⋊Dic13C2×C412yes—
39C2×C4×Dic13—42no—
40C2×C4×Dic13C2×C411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13C2311yescharacteristic
44C22⋊#1057—42no—
45#88071—22no—
46#88071—22no—
47#7607—131nomaximal, Sylow
48C24×C13C22⋊C411yescharacteristic
49C22×C4×C13—22no—
50C22×C4×C13—22no—
51C22×C4×C13—22no—
52C22×C4×C13—24no—
53C22×C4×C13—22no—
54C22×C4×C13—42no—
55C22×C4×C13—42no—
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22×C411yescharacteristic
58C22×Dic13—22no—
59C22×Dic13—22no—
60C22×Dic13—22no—
61C22×Dic13—22no—
62C22×Dic13—22no—
63C22×Dic13—41no—
64C22×Dic13—42no—
65C22×Dic13—42no—
66C22×Dic13—42no—
67C22×Dic13C22⋊C411yescharacteristic
68C22×Dic13C22⋊C411yescharacteristic
69C22×Dic13SD1612yes—
70C22×Dic13Q1612yes—
71C22×Dic13C2×D411yescharacteristic
72C22×Dic13C2×D411yescharacteristic
73#6122—48no—
74C2×#1057—24no—
75C2×#1057—42no—
76C2×#1057—42no—
77C2×#1057—42no—
78C2×#1057—42no—
79C2×#1057—42no—
80C13×C4⋊C4—24no—
81C13×C4⋊C4—22no—
82C13×C4⋊C4M1614yescomplemented
83C4⋊Dic13—44no—
84C4⋊Dic13—42no—
85C4⋊Dic13—44no—
86C4⋊Dic13—42no—
87C4×Dic13—41no—
88C4×Dic13—41no—
89C4×Dic13—41no—
90C4×Dic13—41no—
91C2×#389—131no—
92#1817—131no—
93#1728—131no—
94#1271—134no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13#9912yes—
100C23×C13#10312yes—
101C23×C13#10412yes—
102C23×C13C2×C22⋊C411yescharacteristic
103C2×C4×C13—28no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—24no—
109C2×C4×C13—48no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13#10112yes—
113C2×C4×C13C2×M1612yes—
114C2×Dic13—24no—
115C2×Dic13—24no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—44no—
126C2×Dic13—42no—
127C2×Dic13—42no—
128C2×Dic13—42no—
129C2×Dic13—84no—
130C2×Dic13#10312yes—
131C2×Dic13C2×SD1611yescharacteristic
132C2×Dic13C2×Q1611yescharacteristic
133C2×Dic13AGL(1,ℤ/8)12yes—
134#1057—44no—
135#1057—82no—
136C22×M16—261no—
137C22×C4⋊C4—131no—
138C22×C4⋊C4—261no—
139C22×C4⋊C4#26111yescharacteristic
140C22×C42—131no—
141C2×C22⋊C8—261no—
142#389—132no—
143#389—132no—
144#389—261no—
145#389—261no—
146C2×#95—261no—
147#336—132no—
148#336—132no—
149#336—261no—
150#336—261no—
151C22×C13—22no—
152C22×C13—22no—
153C22×C13—22no—
154C22×C13—22no—
155C22×C13—22no—
156C22×C13—22no—
157C22×C13#32814yes—
158C22×C13#40711yescharacteristic
159C22×C13C2×#9911yescharacteristic
160C22×C13C2×#10111yescharacteristic
161C22×C13C2×#10311yescharacteristic
162C22×C13#41811yescharacteristic
163C22×C13C2×#10411yescharacteristic
164C22×C13#42111yescharacteristic
165C4×C13—22no—
166C4×C13—22no—
167C4×C13—44no—
168Dic13—21no—
169Dic13—22no—
170Dic13—21no—
171Dic13—22no—
172Dic13—41no—
173Dic13—82no—
174C23×C4—21no—
175C23×C4—131no—
176C23×C4—131no—
177C23×C4—261no—
178C23×C4C2×#26111yescharacteristic
179C2×M16—264no—
180C2×M16—522no—
181C2×M16—522no—
182C22×C8—262no—
183C22×C8—262no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—24no—
186C2×C4⋊C4—132no—
187C2×C4⋊C4—262no—
188C2×C4⋊C4—262no—
189C2×C4⋊C4—261no—
190C2×C4⋊C4—522no—
191C2×C4⋊C4—524no—
192C2×C4⋊C4C2×#26112yes—
193C2×C42—131no—
194C2×C42—131no—
195C2×C42—131no—
196C2×C42—131no—
197C2×C42—522no—
198C22⋊C8—522no—
199#95—262no—
200#95—262no—
201C2×C13—24no—
202C2×C13#146311yescharacteristic
203C2×C13#148711yescharacteristic
204C2×C13#149011yescharacteristic
205C2×C13C2×#32811yescharacteristic
206C2×C13#151011yescharacteristic
207C2×C13#152811yescharacteristic
208C2×C13#154911yescharacteristic
209C24C22⋊#26111yescharacteristic
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—24no—
214C22×C4—22no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—132no—
218C22×C4—132no—
219C22×C4—131no—
220C22×C4—131no—
221C22×C4—131no—
222C22×C4—131no—
223C22×C4—262no—
224C22×C4—262no—
225C22×C4—262no—
226C22×C4—262no—
227C22×C4—262no—
228C22×C4—521no—
229C22×C4—522no—
230C22×C4—522no—
231C22×C4—522no—
232C22×C4C22⋊#26111yescharacteristic
233C22×C4C22×#26111yescharacteristic
234M16—528no—
235C2×C8—264no—
236C2×C8—522no—
237C2×C8—522no—
238C2×C8—522no—
239C2×C8—522no—
240C2×C8—522no—
241C4⋊C4—24no—
242C4⋊C4—22no—
243C4⋊C4—522no—
244C4⋊C4—522no—
245C4⋊C4—524no—
246C4⋊C4—524no—
247C4⋊C4#612214yescomplemented
248C42—521no—
249C42—521no—
250C42—521no—
251C42—521no—
252C13#760711yescharacteristic, complemented, Sylow
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23#8810712yes—
258C23#8811612yes—
259C23#8811712yes—
260C23C2×C22⋊#26111yescharacteristic
261C2×C4—28no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—24no—
267C2×C4—48no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—132no—
271C2×C4—131no—
272C2×C4—132no—
273C2×C4—131no—
274C2×C4—264no—
275C2×C4—264no—
276C2×C4—261no—
277C2×C4—261no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—261no—
281C2×C4—261no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—524no—
286C2×C4—522no—
287C2×C4—522no—
288C2×C4—522no—
289C2×C4—1044no—
290C2×C4#8811312yes—
291C2×C4C2×#612212yes—
292C8—524no—
293C8—1042no—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22#1171824114yes—
301C22C2×#8810711yescharacteristic
302C22C2×#8811311yescharacteristic
303C22#1171913811yescharacteristic
304C22C2×#8811611yescharacteristic
305C22C2×#8811711yescharacteristic
306C22#1171915511yescharacteristic
307C22#1171916911yescharacteristic
308C4—22no—
309C4—22no—
310C4—44no—
311C4—262no—
312C4—261no—
313C4—262no—
314C4—261no—
315C4—521no—
316C4—1042no—
317C2—24no—
318C2#1313008411yescharacteristic
319C2#1313016411yescharacteristic
320C2#1313017511yescharacteristic
321C2C2×#1171824111yescharacteristic
322C2#1313024311yescharacteristic
323C2#1313029811yescharacteristic
324C2#1313035111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC22×C4⋊C4#261
hypocenterC13#7607
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13129654C2semidirect
82. C13×C4⋊C4M16semidirect
247. C4⋊C4#6122semidirect
252. C13#7607semidirect

Maximal subgroups

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

subgroupindex
#131307272
#131304992
#131296542
C2×#117186462
#760713