Finite Group Databasebeta

← #16778412

Subgroups — #16778412

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—42no—
37C2×C4⋊Dic13—42no—
38C2×C4⋊Dic13—42no—
39C2×C4⋊Dic13C2×C412yes—
40C2×C4×Dic13—42no—
41C2×C4×Dic13C2×C411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×C4×Dic13C2311yescharacteristic
45C22⋊#1057—42no—
46#88071—22no—
47#88071—22no—
48#7610—131nomaximal, Sylow
49C24×C13C22⋊C411yescharacteristic
50C22×C4×C13—22no—
51C22×C4×C13—22no—
52C22×C4×C13—22no—
53C22×C4×C13—24no—
54C22×C4×C13—22no—
55C22×C4×C13—42no—
56C22×C4×C13—42no—
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22×C411yescharacteristic
59C22×Dic13—22no—
60C22×Dic13—22no—
61C22×Dic13—22no—
62C22×Dic13—22no—
63C22×Dic13—22no—
64C22×Dic13—41no—
65C22×Dic13—42no—
66C22×Dic13—42no—
67C22×Dic13—42no—
68C22×Dic13C22⋊C411yescharacteristic
69C22×Dic13C22⋊C411yescharacteristic
70C22×Dic13D812yes—
71C22×Dic13SD1612yes—
72C22×Dic13C2×D411yescharacteristic
73C22×Dic13C2×D411yescharacteristic
74#6122—48no—
75C2×#1057—24no—
76C2×#1057—42no—
77C2×#1057—42no—
78C2×#1057—42no—
79C2×#1057—42no—
80C2×#1057—42no—
81C13×C4⋊C4—24no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4M1614yescomplemented
84C4⋊Dic13—42no—
85C4⋊Dic13—44no—
86C4⋊Dic13—42no—
87C4⋊Dic13—42no—
88C4⋊Dic13—42no—
89C4×Dic13—41no—
90C4×Dic13—41no—
91C4×Dic13—41no—
92C4×Dic13—41no—
93C2×#389—131no—
94#1817—131no—
95#1728—131no—
96#1271—134no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13#9912yes—
102C23×C13#10212yes—
103C23×C13#10412yes—
104C23×C13C2×C22⋊C411yescharacteristic
105C2×C4×C13—28no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—24no—
111C2×C4×C13—48no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13#10112yes—
115C2×C4×C13C2×M1612yes—
116C2×Dic13—24no—
117C2×Dic13—24no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—44no—
128C2×Dic13—42no—
129C2×Dic13—42no—
130C2×Dic13—42no—
131C2×Dic13—84no—
132C2×Dic13#10212yes—
133C2×Dic13C2×D811yescharacteristic
134C2×Dic13C2×SD1611yescharacteristic
135C2×Dic13#13712yes—
136#1057—44no—
137#1057—82no—
138C22×M16—261no—
139C22×C4⋊C4—131no—
140C22×C4⋊C4—261no—
141C22×C4⋊C4#26111yescharacteristic
142C22×C42—131no—
143C2×C22⋊C8—261no—
144#389—132no—
145#389—132no—
146#389—261no—
147#389—261no—
148C2×#95—261no—
149#336—132no—
150#336—132no—
151#336—261no—
152#336—261no—
153C22×C13—22no—
154C22×C13—22no—
155C22×C13—22no—
156C22×C13—22no—
157C22×C13—22no—
158C22×C13—22no—
159C22×C13#32714yes—
160C22×C13#40711yescharacteristic
161C22×C13C2×#9911yescharacteristic
162C22×C13C2×#10111yescharacteristic
163C22×C13C2×#10211yescharacteristic
164C22×C13#41911yescharacteristic
165C22×C13C2×#10411yescharacteristic
166C22×C13#42111yescharacteristic
167C4×C13—22no—
168C4×C13—22no—
169C4×C13—44no—
170Dic13—21no—
171Dic13—22no—
172Dic13—21no—
173Dic13—22no—
174Dic13—41no—
175Dic13—82no—
176C23×C4—21no—
177C23×C4—131no—
178C23×C4—131no—
179C23×C4—261no—
180C23×C4C2×#26111yescharacteristic
181C2×M16—264no—
182C2×M16—522no—
183C2×M16—522no—
184C22×C8—262no—
185C22×C8—262no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—24no—
188C2×C4⋊C4—132no—
189C2×C4⋊C4—262no—
190C2×C4⋊C4—262no—
191C2×C4⋊C4—261no—
192C2×C4⋊C4—522no—
193C2×C4⋊C4—522no—
194C2×C4⋊C4—522no—
195C2×C4⋊C4C2×#26112yes—
196C2×C42—131no—
197C2×C42—131no—
198C2×C42—131no—
199C2×C42—131no—
200C2×C42—522no—
201C22⋊C8—522no—
202#95—262no—
203#95—262no—
204C2×C13—24no—
205C2×C13#146311yescharacteristic
206C2×C13#148611yescharacteristic
207C2×C13#149111yescharacteristic
208C2×C13C2×#32711yescharacteristic
209C2×C13#151111yescharacteristic
210C2×C13#152811yescharacteristic
211C2×C13#154611yescharacteristic
212C24C22⋊#26111yescharacteristic
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—24no—
217C22×C4—22no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—132no—
221C22×C4—132no—
222C22×C4—131no—
223C22×C4—131no—
224C22×C4—131no—
225C22×C4—131no—
226C22×C4—262no—
227C22×C4—262no—
228C22×C4—262no—
229C22×C4—262no—
230C22×C4—262no—
231C22×C4—521no—
232C22×C4—522no—
233C22×C4—522no—
234C22×C4—522no—
235C22×C4C22⋊#26111yescharacteristic
236C22×C4C22×#26111yescharacteristic
237M16—528no—
238C2×C8—264no—
239C2×C8—522no—
240C2×C8—522no—
241C2×C8—522no—
242C2×C8—522no—
243C2×C8—522no—
244C4⋊C4—24no—
245C4⋊C4—22no—
246C4⋊C4—522no—
247C4⋊C4—522no—
248C4⋊C4—522no—
249C4⋊C4—524no—
250C4⋊C4—522no—
251C4⋊C4#612214yescomplemented
252C42—521no—
253C42—521no—
254C42—521no—
255C42—521no—
256C13#761011yescharacteristic, complemented, Sylow
257C23—21no—
258C23—21no—
259C23—21no—
260C23—21no—
261C23#8810712yes—
262C23#8811512yes—
263C23#8811812yes—
264C23C2×C22⋊#26111yescharacteristic
265C2×C4—28no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—24no—
271C2×C4—48no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—131no—
275C2×C4—132no—
276C2×C4—131no—
277C2×C4—132no—
278C2×C4—264no—
279C2×C4—264no—
280C2×C4—261no—
281C2×C4—261no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—524no—
290C2×C4—522no—
291C2×C4—522no—
292C2×C4—522no—
293C2×C4—1044no—
294C2×C4#8811312yes—
295C2×C4C2×#612212yes—
296C8—524no—
297C8—1042no—
298C22—22no—
299C22—22no—
300C22—22no—
301C22—22no—
302C22—22no—
303C22—22no—
304C22#1171824014yes—
305C22C2×#8810711yescharacteristic
306C22C2×#8811311yescharacteristic
307C22C2×#8811511yescharacteristic
308C22#1171914011yescharacteristic
309C22#1171915311yescharacteristic
310C22C2×#8811811yescharacteristic
311C22#1171916911yescharacteristic
312C4—22no—
313C4—22no—
314C4—44no—
315C4—262no—
316C4—261no—
317C4—262no—
318C4—261no—
319C4—521no—
320C4—1042no—
321C2—24no—
322C2#1313008411yescharacteristic
323C2#1313016111yescharacteristic
324C2#1313017811yescharacteristic
325C2C2×#1171824011yescharacteristic
326C2#1313024411yescharacteristic
327C2#1313030011yescharacteristic
328C2#1313034511yescharacteristic
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#7610
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
83. C13×C4⋊C4M16semidirect
251. C4⋊C4#6122semidirect
256. C13#7610semidirect

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
#761013