Finite Group Databasebeta

← #15751028

Subgroups — #15751028

Order 3328.

504 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117374C211yesmaximal, characteristic
2#13114903C211yesmaximal, characteristic
3#13114815C211yesmaximal, characteristic
4#13112662C211yesmaximal, characteristic, complemented
5#13112660C211yesmaximal, characteristic, complemented
6#13112658C211yesmaximal, characteristic, complemented
7C13×#1272C211yesmaximal, characteristic, complemented
8C2×#88200C411yescharacteristic
9C2×Q8×Dic13C411yescharacteristic
10C2×C42×D13C2211yescharacteristic
11C13×#391C2211yescharacteristic
12C2×#88060—21no—
13C2×#88060—21no—
14C2×#88054—21no—
15#11718648C411yescharacteristic
16C4⋊C4×Dic13C411yescharacteristic
17#11718589C2211yescharacteristic
18#11718329—21no—
19#11718327—21no—
20#11718316—21no—
21#11718310—21no—
22C13×#336C2211yescharacteristic
23C13×#336C2211yescharacteristic
24#11718142—21no—
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×Q8×C13C2×C411yescharacteristic
28C22×C4×D13C2×C411yescharacteristic
29C22×C4×D13D411yescharacteristic
30C22×C4×D13D411yescharacteristic
31C22×C8×C13—21no—
32C22×C8×C13—21no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C42×C13C2311yescharacteristic
35#88200—22no—
36#88200C814yescomplemented
37Q8×Dic13—42no—
38C2×#6103—21no—
39C2×#6103—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13C2×C411yescharacteristic
42C2×C4⋊Dic13C2×C411yescharacteristic
43C2×#6101—21no—
44C2×#6101—21no—
45C2×C4×Dic13—21no—
46C2×C4×Dic13—21no—
47C2×C4×Dic13C2×C411yescharacteristic
48C2×C4×Dic13D411yescharacteristic
49C2×C4×Dic13D411yescharacteristic
50C22×#1055—21no—
51C22×#1055—21no—
52C42×D13—42no—
53C13×#95—21no—
54C13×#95—21no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#88060—42no—
59#88060—42no—
60#88054—42no—
61#7600—131nomaximal, Sylow
62C23×D13C22⋊C411yescharacteristic
63C2×Q8×C13—21no—
64C2×Q8×C13—41no—
65C2×Q8×C13—41no—
66C2×Q8×C13C2×C812yes—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13C22⋊C411yescharacteristic
75C22×Dic13C22⋊C411yescharacteristic
76C22×Dic13C22⋊C411yescharacteristic
77C2×C4×D13—21no—
78C2×C4×D13—21no—
79C2×C4×D13—21no—
80C2×C4×D13—21no—
81C2×C4×D13—22no—
82C2×C4×D13—41no—
83C2×C4×D13—41no—
84C2×C4×D13—41no—
85C2×C4×D13—41no—
86C2×C4×D13—41no—
87C2×C4×D13C2×C812yes—
88C2×C4×D13M1612yes—
89C2×C8×C13—41no—
90C2×C8×C13—41no—
91C2×C8×C13—41no—
92C2×C8×C13—41no—
93C2×C8×C13—41no—
94C2×C8×C13—41no—
95C13×C4⋊C4—41no—
96C42×C13—41no—
97#6103—24no—
98#6103—42no—
99C4⋊Dic13—21no—
100C4⋊Dic13—42no—
101C4⋊Dic13—41no—
102C4⋊Dic13C2×C812yes—
103#6101—24no—
104#6101—41no—
105#6101—41no—
106C4×Dic13—22no—
107C4×Dic13—22no—
108C4×Dic13—41no—
109C4×Dic13—42no—
110C4×Dic13—42no—
111C2×#1055—41no—
112C2×#1055—41no—
113C2×#1055—41no—
114C2×#1055—41no—
115C2×#1055—41no—
116C2×#1055—41no—
117C4×C22⋊Q8—131no—
118#1817—131no—
119#1797—131no—
120#1272—131no—
121#1272D1311yescharacteristic, complemented
122#1271—131no—
123#1271—131no—
124C23×C13C2×C22⋊C411yescharacteristic
125C22×D13—21no—
126C22×D13—21no—
127C22×D13—21no—
128C22×D13—21no—
129C22×D13—21no—
130C22×D13—21no—
131C22×D13C22⋊C812yes—
132Q8×C13—42no—
133Q8×C13—42no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—22no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13C22×C811yescharacteristic
147C2×C4×C13C2×M1611yescharacteristic
148C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C13#13711yescharacteristic
150C2×C4×C13#13711yescharacteristic
151C2×C4×C13#13711yescharacteristic
152C2×Dic13—21no—
153C2×Dic13—21no—
154C2×Dic13—21no—
155C2×Dic13—21no—
156C2×Dic13—22no—
157C2×Dic13—21no—
158C2×Dic13—21no—
159C2×Dic13—21no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—41no—
163C2×Dic13—41no—
164C2×Dic13—41no—
165C2×Dic13C22⋊C812yes—
166C2×Dic13#9912yes—
167C4×D13—42no—
168C4×D13—42no—
169C4×D13—42no—
170C4×D13—42no—
171C4×D13—42no—
172C4×D13—42no—
173C8×C13—81no—
174C8×C13—81no—
175#1055—81no—
176#1055—81no—
177C2×C22⋊Q8—131no—
178C2×C4×Q8—131no—
179C22×C42—131no—
180C2×C4⋊C8—261no—
181C2×C22⋊C8—261no—
182C2×C22⋊C8—261no—
183#391C2×D1311yescharacteristic
184#389—131no—
185#387—261no—
186#385—261no—
187#380—131no—
188C4×C4⋊C4—131no—
189C4×C4⋊C4—261no—
190C4×C22⋊C4—261no—
191#336—131no—
192#336—131no—
193#336—261no—
194#336C2×D1311yescharacteristic
195#336C2×D1311yescharacteristic
196C22×C13C2×C22⋊C811yescharacteristic
197C22×C13C2×#9911yescharacteristic
198C22×C13#41311yescharacteristic
199C22×C13#41711yescharacteristic
200C22×C13#41911yescharacteristic
201C22×C13#42111yescharacteristic
202C22×C13#42111yescharacteristic
203C2×D13—22no—
204C2×D13—22no—
205C2×D13—22no—
206C2×D13—41no—
207C2×D13—41no—
208C2×D13—41no—
209C2×D13—41no—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—21no—
213C4×C13—21no—
214C4×C13—21no—
215C4×C13—21no—
216C4×C13—42no—
217C4×C13—81no—
218Dic13—22no—
219Dic13—22no—
220Dic13—42no—
221Dic13—41no—
222Dic13—81no—
223C22×Q8C4×D1311yescharacteristic
224C23×C4—131no—
225C23×C4—131no—
226C23×C4—131no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—261no—
230C22×C8—261no—
231C22⋊Q8—134no—
232C22⋊Q8—262no—
233C4×Q8—522no—
234C2×C4⋊C4—131no—
235C2×C4⋊C4—131no—
236C2×C4⋊C4—261no—
237C2×C4⋊C4—261no—
238C2×C4⋊C4—261no—
239C2×C4⋊C4C4×D1311yescharacteristic
240C2×C22⋊C4—261no—
241C2×C22⋊C4—261no—
242C2×C42—131no—
243C2×C42—131no—
244C2×C42—131no—
245C2×C42—261no—
246C2×C42—261no—
247C2×C42—522no—
248C2×C42C22×D1311yescharacteristic
249C4⋊C8—522no—
250C22⋊C8—522no—
251C22⋊C8—522no—
252#95—21no—
253#95—21no—
254#95—261no—
255#95—261no—
256#95—261no—
257C2×C13#145911yescharacteristic
258C2×C13#147711yescharacteristic
259C2×C13#147911yescharacteristic
260C2×C13#151111yescharacteristic
261C2×C13#151311yescharacteristic
262C2×C13#153511yescharacteristic
263C2×C13#155911yescharacteristic
264D13—42no—
265C24—131no—
266C2×Q8—21no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8C8×D1312yes—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—131no—
273C22×C4—131no—
274C22×C4—132no—
275C22×C4—132no—
276C22×C4—131no—
277C22×C4—262no—
278C22×C4—261no—
279C22×C4—261no—
280C22×C4—261no—
281C22×C4—261no—
282C22×C4—261no—
283C22×C4—261no—
284C22×C4—521no—
285C22×C4—521no—
286C22×C4—521no—
287C22×C4—521no—
288C22×C4—521no—
289C22×C4C2×C4×D1311yescharacteristic
290C22×C4D4×D1311yescharacteristic
291C22×C4D4×D1311yescharacteristic
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—521no—
299C2×C8—521no—
300C2×C8—521no—
301C2×C8—521no—
302C2×C8—521no—
303C2×C8—521no—
304C4⋊C4—41no—
305C4⋊C4—132no—
306C4⋊C4—264no—
307C4⋊C4—261no—
308C4⋊C4—521no—
309C4⋊C4—522no—
310C4⋊C4—521no—
311C4⋊C4—521no—
312C22⋊C4—264no—
313C22⋊C4—522no—
314C42—41no—
315C42—262no—
316C42—262no—
317C42—521no—
318C42—522no—
319C42—522no—
320C13#760011yescharacteristic, complemented, Sylow
321C23—132no—
322C23—261no—
323C23—261no—
324C23—261no—
325C23—261no—
326C23—261no—
327C23—261no—
328C23C22⋊C4×D1311yescharacteristic
329Q8—42no—
330Q8—42no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—132no—
344C2×C4—132no—
345C2×C4—261no—
346C2×C4—261no—
347C2×C4—261no—
348C2×C4—261no—
349C2×C4—261no—
350C2×C4—261no—
351C2×C4—261no—
352C2×C4—262no—
353C2×C4—522no—
354C2×C4—522no—
355C2×C4—522no—
356C2×C4—522no—
357C2×C4—522no—
358C2×C4—522no—
359C2×C4—521no—
360C2×C4—521no—
361C2×C4—521no—
362C2×C4—521no—
363C2×C4—521no—
364C2×C4C2×C8×D1311yescharacteristic
365C2×C4M16×D1311yescharacteristic
366C2×C4#8816811yescharacteristic
367C2×C4#8816911yescharacteristic
368C2×C4#8817211yescharacteristic
369C2×C4#8817211yescharacteristic
370C8—81no—
371C8—81no—
372C8—1041no—
373C8—1041no—
374C22—262no—
375C22—262no—
376C22—262no—
377C22—521no—
378C22—521no—
379C22—521no—
380C22—521no—
381C22D13×C22⋊C811yescharacteristic
382C22D13×#9911yescharacteristic
383C22#1171840611yescharacteristic
384C22#1171846311yescharacteristic
385C22#1171846411yescharacteristic
386C22#1171848211yescharacteristic
387C22#1171848211yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—42no—
395C4—81no—
396C4—262no—
397C4—262no—
398C4—521no—
399C4—522no—
400C4—1041no—
401C2—522no—
402C2#1311315111yescharacteristic
403C2#1311322211yescharacteristic
404C2#1311322911yescharacteristic
405C2#1311336711yescharacteristic
406C2#1311337811yescharacteristic
407C2#1311346411yescharacteristic
408C2#1311356311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1272C2
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1272D13
hypocenterC13#7600
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
4. #13112662C2semidirect
5. #13112660C2semidirect
6. #13112658C2semidirect
7. C13×#1272C2semidirect
36. #88200C8semidirect
121. #1272D13semidirect
320. C13#7600semidirect

Maximal subgroups

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

subgroupindex
#131173742
#131149032
#131148152
#131126622
#131126602
#131126582
C13×#12722
#760013