Finite Group Databasebeta

← #15832669

Subgroups — #15832669

Order 3328.

682 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123803C212yesmaximal, complemented
2#13113733C212yesmaximal, complemented
3#13113727C214yesmaximal, complemented
4#13113721C212yesmaximal, complemented
5#13113584C211yesmaximal, characteristic, complemented
6#13113218C212yesmaximal, complemented
7C2×C8×#1055C211yesmaximal, characteristic, complemented
8C4×C13×#135C211yesmaximal, characteristic
9C2×C13×#135C411yescharacteristic
10C4×C13×#41C2212yes—
11C4×C13×Q16C411yescharacteristic
12C4×C13×Q16C2211yescharacteristic
13C4×C13×SD16C412yes—
14C4×C13×SD16C2212yes—
15C4×C13×D8C411yescharacteristic
16C4×C13×D8C2211yescharacteristic
17C13×#427C411yescharacteristic
18C13×#416C412yes—
19C2×C4×C8×C13C2211yescharacteristic
20#11718685C2214yes—
21#11718673C2214yes—
22#11718672—24no—
23#11718586—22no—
24#11718586C2212yes—
25C4×#6099—22no—
26C2×C4×#1055C2211yescharacteristic
27C2×C4×#1055C2211yescharacteristic
28Q8⋊#1055C2214yes—
29D4⋊#1055C2214yes—
30#11718050C2212yes—
31#11718049C2212yes—
32C8×#1055C2212yes—
33C8×#1055C2212yes—
34C2×C13×#41C2×C412yes—
35C13×#135—24no—
36C2×C13×Q16C2×C411yescharacteristic
37C2×C13×SD16C2×C412yes—
38C2×C13×D8C2×C411yescharacteristic
39C22×C8×C13C2×C411yescharacteristic
40C22×C8×C13C2×C411yescharacteristic
41C4×Q8×C13C2×C412yes—
42C4×Q8×C13C2312yes—
43C4×D4×C13—22no—
44C4×D4×C13—22no—
45C4×D4×C13C2×C412yes—
46C4×D4×C13C2312yes—
47C13×#117—22no—
48C13×#117C2×C412yes—
49C2×C42×C13—22no—
50C2×C42×C13C2311yescharacteristic
51C2×#6099—24no—
52C22×#1055—21no—
53C22×#1055D412yes—
54C13×#107C2×C411yescharacteristic
55C13×#107C2×C411yescharacteristic
56C13×#106C2×C412yes—
57C13×#103C2×C412yes—
58C13×#103C2×C412yes—
59C13×#102C2×C412yes—
60C13×#102C2×C412yes—
61C4×C8×C13C2×C411yescharacteristic
62C4×C8×C13C2×C411yescharacteristic
63C4×C8×C13C2311yescharacteristic
64C4×C8×C13C2311yescharacteristic
65C22⋊#1055—22no—
66C22⋊#1055—24no—
67C4⋊#1055—24no—
68C4⋊#1055C2314yes—
69#88043—24no—
70C4×#1055—22no—
71C4×#1055—21no—
72C4×#1055D411yescharacteristic
73C4×#1055D411yescharacteristic
74C4×#1055C2312yes—
75C4×#1055C2312yes—
76#17886—131nomaximal, Sylow
77C13×#41—24no—
78C13×#41—24no—
79C2×Q8×C13C22×C412yes—
80C2×D4×C13—22no—
81C2×D4×C13C22×C412yes—
82C22×C4×C13—22no—
83C22×C4×C13—22no—
84C22×C4×C13—22no—
85C22×C4×C13C22×C411yescharacteristic
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13#4111yescharacteristic
88C13×Q16—22no—
89C13×SD16—24no—
90C13×D8—22no—
91C2×C8×C13—22no—
92C2×C8×C13M1614yescomplemented
93C2×C8×C13C22×C411yescharacteristic
94C2×C8×C13C22×C411yescharacteristic
95C2×C8×C13C22×C411yescharacteristic
96C2×C8×C13C22×C411yescharacteristic
97C13×C4⋊C4—22no—
98C13×C4⋊C4—22no—
99C13×C4⋊C4C22×C412yes—
100C13×C4⋊C4C22×C412yes—
101C13×C22⋊C4—22no—
102C13×C22⋊C4—22no—
103C13×C22⋊C4—22no—
104C42×C13—22no—
105C42×C13—22no—
106C42×C13—22no—
107C42×C13C22×C411yescharacteristic
108C42×C13C2×D411yescharacteristic
109C42×C13#4111yescharacteristic
110C42×C13C2411yescharacteristic
111#6099—48no—
112C2×#1055—24no—
113C2×#1055—22no—
114C2×#1055—24no—
115C2×#1055—24no—
116C2×#1055C2×D412yes—
117C2×#1055C2×D412yes—
118#2965—132no—
119C4×#135D1311yescharacteristic
120#1591—132no—
121#1590—134no—
122#1589—132no—
123#1564—131no—
124#1476—132no—
125C2×C82—131no—
126C23×C13—22no—
127C23×C13C4×D411yescharacteristic
128Q8×C13—22no—
129Q8×C13—22no—
130D4×C13—22no—
131D4×C13—22no—
132D4×C13—44no—
133C2×C4×C13—22no—
134C2×C4×C13—22no—
135C2×C4×C13—22no—
136C2×C4×C13—22no—
137C2×C4×C13—22no—
138C2×C4×C13—44no—
139C2×C4×C13—44no—
140C2×C4×C13—44no—
141C2×C4×C13C4×D411yescharacteristic
142C2×C4×C13C4×D411yescharacteristic
143C2×C4×C13C4×D411yescharacteristic
144C2×C4×C13C2×M1612yes—
145C2×C4×C13#13112yes—
146C2×C4×C13C23×C411yescharacteristic
147C2×C4×C13C22×D411yescharacteristic
148C2×C4×C13C2×#4111yescharacteristic
149C8×C13—21no—
150C8×C13—21no—
151C8×C13C2×M1612yes—
152C8×C13C2×M1612yes—
153#1055—24no—
154#1055—22no—
155#1055—44no—
156#1055#13514yescomplemented
157C2×#135Dic1311yescharacteristic
158C4×#41C2×D1312yes—
159#446—134no—
160C4×Q16Dic1311yescharacteristic
161C4×Q16C2×D1311yescharacteristic
162C4×SD16Dic1312yes—
163C4×SD16C2×D1312yes—
164C4×D8Dic1311yescharacteristic
165C4×D8C2×D1311yescharacteristic
166#436—134no—
167#435—264no—
168#431—132no—
169#431—262no—
170#427Dic1311yescharacteristic
171#416Dic1312yes—
172C4×M16—262no—
173C2×C4×C8—131no—
174C2×C4×C8—131no—
175C2×C4×C8C2×D1311yescharacteristic
176#335—132no—
177#334—132no—
178Q8⋊C8—134no—
179D4⋊C8—134no—
180C82—132no—
181C82—132no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—42no—
185C22×C13—42no—
186C22×C13—42no—
187C22×C13#43612yes—
188C22×C13C2×C4×D411yescharacteristic
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—42no—
192C4×C13—42no—
193C4×C13—42no—
194C4×C13#43612yes—
195C4×C13#44312yes—
196C4×C13C22×M1611yescharacteristic
197C4×C13C2×#13111yescharacteristic
198C4×C13C2×#13512yes—
199C2×#41C2×Dic1312yes—
200#135—24no—
201C2×Q16C2×Dic1311yescharacteristic
202C2×SD16C2×Dic1312yes—
203C2×D8C2×Dic1311yescharacteristic
204C2×M16—264no—
205C22×C8—132no—
206C22×C8—261no—
207C22×C8C2×Dic1311yescharacteristic
208C22×C8C2×Dic1311yescharacteristic
209C4×Q8C2×Dic1312yes—
210C4×Q8C22×D1312yes—
211C4×D4—22no—
212C4×D4—22no—
213C4×D4C2×Dic1312yes—
214C4×D4C22×D1312yes—
215#117—22no—
216#117C2×Dic1312yes—
217C2×C42—22no—
218C2×C42C22×D1311yescharacteristic
219#107C2×Dic1311yescharacteristic
220#107C2×Dic1311yescharacteristic
221#106C2×Dic1312yes—
222C4⋊C8—134no—
223C4⋊C8—264no—
224#103C2×Dic1312yes—
225#103C2×Dic1312yes—
226#102C2×Dic1312yes—
227#102C2×Dic1312yes—
228C22⋊C8—264no—
229C22⋊C8—262no—
230#97—264no—
231C4×C8—131no—
232C4×C8—131no—
233C4×C8—132no—
234C4×C8—132no—
235C4×C8—262no—
236C4×C8—261no—
237C4×C8C2×Dic1311yescharacteristic
238C4×C8C2×Dic1311yescharacteristic
239C4×C8C22×D1311yescharacteristic
240C4×C8C22×D1311yescharacteristic
241C2×C13—22no—
242C2×C13—82no—
243C2×C13C2×#43611yescharacteristic
244C2×C13C4×#13511yescharacteristic
245C2×C13C2×#44311yescharacteristic
246#41—24no—
247#41—24no—
248C2×Q8C22×Dic1312yes—
249C2×D4—22no—
250C2×D4C22×Dic1312yes—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4D4×D1311yescharacteristic
255C22×C4#612911yescharacteristic
256C22×C4C22×Dic1311yescharacteristic
257Q16—22no—
258SD16—24no—
259D8—22no—
260M16—528no—
261C2×C8—22no—
262C2×C8—132no—
263C2×C8—132no—
264C2×C8—264no—
265C2×C8—264no—
266C2×C8—262no—
267C2×C8—264no—
268C2×C8#609914yescomplemented
269C2×C8C22×Dic1311yescharacteristic
270C2×C8C22×Dic1311yescharacteristic
271C2×C8C22×Dic1311yescharacteristic
272C2×C8C22×Dic1311yescharacteristic
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4C22×Dic1312yes—
276C4⋊C4C22×Dic1312yes—
277C22⋊C4—22no—
278C22⋊C4—22no—
279C22⋊C4—22no—
280C42—22no—
281C42—22no—
282C42—22no—
283C42D4×D1311yescharacteristic
284C42#612911yescharacteristic
285C42C22×Dic1311yescharacteristic
286C42C23×D1311yescharacteristic
287C13#1788611yescharacteristic, complemented, Sylow
288C23—22no—
289C23D4×Dic1311yescharacteristic
290Q8—22no—
291Q8—22no—
292D4—22no—
293D4—22no—
294D4—44no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—44no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4C2×#609912yes—
304C2×C4D4×Dic1311yescharacteristic
305C2×C4D4×Dic1311yescharacteristic
306C2×C4D4×Dic1311yescharacteristic
307C2×C4#8820212yes—
308C2×C4C2×D4×D1311yescharacteristic
309C2×C4C2×#612911yescharacteristic
310C2×C4C23×Dic1311yescharacteristic
311C8—21no—
312C8—21no—
313C8—134no—
314C8—264no—
315C8—262no—
316C8—524no—
317C8C2×#609912yes—
318C8C2×#609912yes—
319C22—21no—
320C22—21no—
321C22—42no—
322C22—42no—
323C22—42no—
324C22#1171867312yes—
325C22C2×D4×Dic1311yescharacteristic
326C4—21no—
327C4—21no—
328C4—42no—
329C4—42no—
330C4—42no—
331C4#1171867312yes—
332C4#1171885712yes—
333C4D13×#13512yes—
334C4C22×#609911yescharacteristic
335C4C2×#8820211yescharacteristic
336C2—22no—
337C2—82no—
338C2C2×#1171867311yescharacteristic
339C2#135×Dic1311yescharacteristic
340C2C2×#1171885711yescharacteristic
subgroupG/H
centerC42D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC4×C13×#135C2
socleC22×C13C2×C4×D4
prime radicalC2×C13×#135C4
cosocleC42×C13C24
hypercenterC4×#135D13
hypocenterC13#17886
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C42 ◁ C2×C42 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
1. #13123803C2semidirect
2. #13113733C2semidirect
3. #13113727C2semidirect
4. #13113721C2semidirect
5. #13113584C2semidirect
6. #13113218C2semidirect
7. C2×C8×#1055C2semidirect
92. C2×C8×C13M16semidirect
156. #1055#135semidirect
268. C2×C8#6099semidirect
287. C13#17886semidirect

Maximal subgroups

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

subgroupindex
#131238032
#131137332
#131137272
#131137212
#131135842
#131132182
C2×C8×#10552
C4×C13×#1352
#1788613