Finite Group Databasebeta

← #15756799

Subgroups — #15756799

Order 3328.

466 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123944C211yesmaximal, characteristic
2#13114987C211yesmaximal, characteristic, complemented
3C4×#88065C211yesmaximal, characteristic
4#13113221C211yesmaximal, characteristic
5#13112687C211yesmaximal, characteristic, complemented
6#13112668C211yesmaximal, characteristic, complemented
7C13×#1565C211yesmaximal, characteristic, complemented
8C4×#6127C2211yescharacteristic
9C13×#431C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C4×C13×M16C2211yescharacteristic
12C2×#88065C411yescharacteristic
13C2×#88065C411yescharacteristic
14C2×#88054—22no—
15C42×Dic13C2211yescharacteristic
16#11718586C2211yescharacteristic
17C2×C4⋊#1055C2211yescharacteristic
18#11718494—21no—
19D13×C4⋊C8—21no—
20#11718386—22no—
21C8×D52—21no—
22C8×Dic26—21no—
23C13×#335—21no—
24C13×#334—21no—
25#11718147C411yescharacteristic
26#11718147C411yescharacteristic
27#11718076—21no—
28#11718075—21no—
29C2×#6127C2×C411yescharacteristic
30C2×C13×M16C2×C411yescharacteristic
31C2×C13×M16C2×C411yescharacteristic
32C22×C8×C13—21no—
33C2×C42×C13C2311yescharacteristic
34C4×C22⋊D13—21no—
35C4×C22⋊D13—21no—
36#88180C2×C411yescharacteristic
37C2×C4×Dic13—21no—
38C2×C4×Dic13—21no—
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13C2×C411yescharacteristic
41C22×#1055D412yes—
42C2×C8×D13—22no—
43C4×D52D411yescharacteristic
44C4×D52Q811yescharacteristic
45#88126—21no—
46C42×D13—21no—
47C4×Dic26D411yescharacteristic
48C4×Dic26Q811yescharacteristic
49C13×C4⋊C8—21no—
50C13×C4⋊C8—21no—
51C13×C4⋊C8D411yescharacteristic
52C13×C4⋊C8D411yescharacteristic
53C13×C22⋊C8—21no—
54C13×#97—21no—
55C4×C8×C13—21no—
56C4×C8×C13—21no—
57C22⋊#1055—21no—
58#88065—22no—
59#88065C814yescomplemented
60#88060—22no—
61#88054—22no—
62#88054—44no—
63C8×Dic13—22no—
64C4⋊#1055—21no—
65C4⋊#1055—21no—
66C4⋊#1055—21no—
67C4×#1055—21no—
68#8839—131nomaximal, Sylow
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13#4111yescharacteristic
72C2×C22⋊D13—21no—
73C22×Dic13—21no—
74C22×Dic13—21no—
75#6127—21no—
76#6127—21no—
77#6127C2×C812yes—
78#6127M1612yes—
79C2×D52C4⋊C411yescharacteristic
80C2×C4×D13—21no—
81C2×C4×D13—21no—
82C2×C4×D13—21no—
83C2×Dic26C4⋊C411yescharacteristic
84C13×M16—21no—
85C13×M16—21no—
86C13×M16—21no—
87C13×M16C2×C812yescomplemented
88C2×C8×C13—21no—
89C2×C8×C13—21no—
90C2×C8×C13—21no—
91C2×C8×C13—21no—
92C2×C8×C13—42no—
93C2×C8×C13—41no—
94C42×C13C2×D411yescharacteristic
95C42×C13C2×D411yescharacteristic
96C42×C13C2×Q811yescharacteristic
97C42×C13#4111yescharacteristic
98C22⋊Dic13—21no—
99#6103—21no—
100#6103—21no—
101C4⋊Dic13C4⋊C411yescharacteristic
102C4⋊Dic13C4⋊C411yescharacteristic
103#6101—21no—
104#6101—21no—
105C4×Dic13—22no—
106C4×Dic13—22no—
107C4×Dic13—21no—
108C4×Dic13—21no—
109C4×Dic13—21no—
110C4×Dic13—21no—
111C4×Dic13—21no—
112C4×Dic13—21no—
113C4×Dic13—42no—
114C4×Dic13C2×C812yescomplemented
115C2×#1055—22no—
116C2×#1055—42no—
117C2×#1055—41no—
118C8×D13—82no—
119#2988—131no—
120#1842—131no—
121C4×#104—131no—
122#1565D1311yescharacteristic, complemented
123#1477—131no—
124#1283—131no—
125#1276—131no—
126C23×C13C4×D411yescharacteristic
127C22×D13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—41no—
131C2×C4×C13C2×C4⋊C411yescharacteristic
132C2×C4×C13C4×D411yescharacteristic
133C2×C4×C13#12011yescharacteristic
134C2×C4×C13C22⋊Q811yescharacteristic
135C2×C4×C13C22⋊Q811yescharacteristic
136C2×C4×C13#12311yescharacteristic
137C2×C4×C13C22×C811yescharacteristic
138C2×C4×C13C2×M1611yescharacteristic
139C2×C4×C13#13111yescharacteristic
140C2×C4×C13#13111yescharacteristic
141C22⋊D13—22no—
142C22⋊D13—22no—
143C2×Dic13—22no—
144C2×Dic13—22no—
145C2×Dic13—21no—
146C2×Dic13—22no—
147C2×Dic13—22no—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152D52—21no—
153D52C4⋊C812yescomplemented
154C4×D13—22no—
155C4×D13—22no—
156C4×D13—41no—
157C4×D13—41no—
158C4×D13—81no—
159Dic26—21no—
160Dic26C4⋊C812yescomplemented
161C8×C13—22no—
162C8×C13—41no—
163C8×C13—41no—
164C8×C13—41no—
165C8×C13—81no—
166#1055—42no—
167#1055—81no—
168C4×#41—131no—
169C8×Q8—261no—
170C8×D4—261no—
171C8×D4—262no—
172#431—131no—
173#431—261no—
174#431C2×D1311yescharacteristic
175C2×C4⋊C8—131no—
176C2×C4⋊C8—261no—
177C2×C4⋊C8—262no—
178C2×C4⋊C8C2×D1311yescharacteristic
179C2×#104—131no—
180C2×#104—131no—
181C4×M16C2×D1311yescharacteristic
182C43—131no—
183#339—131no—
184#339—131no—
185#335—21no—
186#334—21no—
187Q8⋊C8—261no—
188D4⋊C8—261no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13#38511yescharacteristic
192C22×C13C8×D411yescharacteristic
193C22×C13#43511yescharacteristic
194C2×D13—22no—
195C2×D13—41no—
196C2×D13—41no—
197C4×C13—21no—
198C4×C13—21no—
199C4×C13—21no—
200C4×C13C2×C4⋊C811yescharacteristic
201C4×C13#42411yescharacteristic
202C4×C13C8×D411yescharacteristic
203C4×C13#43511yescharacteristic
204C4×C13#45311yescharacteristic
205C4×C13#45611yescharacteristic
206Dic13—24no—
207Dic13—22no—
208Dic13—42no—
209Dic13—41no—
210Dic13—41no—
211C2×#41—131no—
212C2×M16C4×D1311yescharacteristic
213C2×M16C4×D1311yescharacteristic
214C22×C8—21no—
215C22×C8—132no—
216C22×C8—262no—
217C4×Q8—131no—
218C4×Q8—131no—
219C4×D4—131no—
220C4×D4—131no—
221C4×D4—261no—
222C4×D4—261no—
223#117—131no—
224#117—261no—
225C2×C42—131no—
226C2×C42—131no—
227C2×C42—261no—
228C2×C42—261no—
229C2×C42—261no—
230C2×C42C22×D1311yescharacteristic
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8—262no—
234C4⋊C8—261no—
235C4⋊C8—261no—
236C4⋊C8—261no—
237C4⋊C8—524no—
238C4⋊C8C22⋊D1311yescharacteristic
239C4⋊C8C22⋊D1311yescharacteristic
240#104—134no—
241#104—262no—
242C22⋊C8—21no—
243C22⋊C8—262no—
244C22⋊C8—261no—
245#97—21no—
246C4×C8—21no—
247C4×C8—21no—
248C4×C8—262no—
249C4×C8—261no—
250C2×C13—21no—
251C2×C13—21no—
252C2×C13#185011yescharacteristic
253C2×C13#185911yescharacteristic
254C2×C13#186111yescharacteristic
255D13—42no—
256#41—132no—
257#41—132no—
258#41—261no—
259#41—261no—
260C2×Q8—131no—
261C2×D4—131no—
262C2×D4—261no—
263C22×C4—261no—
264C22×C4—261no—
265C22×C4—261no—
266C22×C4—261no—
267C22×C4—261no—
268C22×C4C2×C4×D1311yescharacteristic
269C22×C4D4×D1311yescharacteristic
270C22×C4#613111yescharacteristic
271M16—21no—
272M16—21no—
273M16—21no—
274M16C8×D1312yescomplemented
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—42no—
280C2×C8—41no—
281C2×C8—262no—
282C2×C8—522no—
283C2×C8—521no—
284C2×C8—1042no—
285C4⋊C4—131no—
286C4⋊C4—131no—
287C4⋊C4—261no—
288C4⋊C4—261no—
289C22⋊C4—261no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C42—132no—
293C42—262no—
294C42—262no—
295C42—261no—
296C42—261no—
297C42—261no—
298C42—261no—
299C42—261no—
300C42—261no—
301C42—522no—
302C42#612711yescharacteristic
303C42D4×D1311yescharacteristic
304C42Q8×D1311yescharacteristic
305C42C2×C22⋊D1311yescharacteristic
306C13#883911yescharacteristic, complemented, Sylow
307C23—261no—
308C23#8814711yescharacteristic
309Q8—132no—
310Q8—261no—
311D4—132no—
312D4—262no—
313D4—262no—
314D4—261no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—262no—
319C2×C4—262no—
320C2×C4—262no—
321C2×C4—261no—
322C2×C4—262no—
323C2×C4—262no—
324C2×C4—262no—
325C2×C4—261no—
326C2×C4—261no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—1041no—
332C2×C4C4⋊C4×D1311yescharacteristic
333C2×C4#8814811yescharacteristic
334C2×C4#8815011yescharacteristic
335C2×C4C2×C8×D1311yescharacteristic
336C2×C4#8815511yescharacteristic
337C2×C4M16×D1311yescharacteristic
338C2×C4#8816111yescharacteristic
339C2×C4C4×C22⋊D1311yescharacteristic
340C2×C4#8819111yescharacteristic
341C2×C4#8820011yescharacteristic
342C8—22no—
343C8—41no—
344C8—41no—
345C8—41no—
346C8—81no—
347C8—522no—
348C8—1041no—
349C22—21no—
350C22—21no—
351C22—262no—
352C22—521no—
353C22—521no—
354C22#1171849511yescharacteristic
355C22#1171849711yescharacteristic
356C22#1171865011yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—264no—
361C4—262no—
362C4—522no—
363C4—521no—
364C4—521no—
365C4D13×C4⋊C811yescharacteristic
366C4#1171850011yescharacteristic
367C4C8×C22⋊D1311yescharacteristic
368C4#1171878811yescharacteristic
369C4#1171885911yescharacteristic
370C4#1171886611yescharacteristic
371C2—21no—
372C2—21no—
373C2—522no—
374C2#1311501211yescharacteristic
375C2#1311505911yescharacteristic
376C2#1311507311yescharacteristic
subgroupG/H
centerC2×C4#88191
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1565C2
socleC22×C13#385
prime radicalC2×#6127C2×C4
cosocleC2×C42×C13C23
hypercenter#1565D13
hypocenterC13#8839
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
2. #13114987C2semidirect
5. #13112687C2semidirect
6. #13112668C2semidirect
7. C13×#1565C2semidirect
59. #88065C8semidirect
87. C13×M16C2×C8semidirect
114. C4×Dic13C2×C8semidirect
122. #1565D13semidirect
153. D52C4⋊C8semidirect
160. Dic26C4⋊C8semidirect
274. M16C8×D13semidirect
306. C13#8839semidirect

Maximal subgroups

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

subgroupindex
#131239442
#131149872
C4×#880652
#131132212
#131126872
#131126682
C13×#15652
#883913