Finite Group Databasebeta

← #15757829

Subgroups — #15757829

Order 3328.

414 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124006C211yesmaximal, characteristic
2#13115818C211yesmaximal, characteristic, complemented
3#13113322C211yesmaximal, characteristic
4#13113309C211yesmaximal, characteristic, complemented
5#13112730C211yesmaximal, characteristic, complemented
6#13112726C211yesmaximal, characteristic, complemented
7C13×#3172C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C13×#529C2211yescharacteristic
10C13×#501C411yescharacteristic, complemented
11C13×#497C411yescharacteristic, complemented
12C13×#491C411yescharacteristic, complemented
13C13×#489C411yescharacteristic, complemented
14C13×#470—21no—
15C13×#468—21no—
16C4×C13×Q16—21no—
17C4×C13×SD16—21no—
18C4×C13×M16C2211yescharacteristic
19#11718685—21no—
20#11718673—21no—
21#11718672—21no—
22#11718672—21no—
23#11718661—21no—
24#11718660—21no—
25#11718593C2211yescharacteristic
26#11718587C2211yescharacteristic
27#11718586C2211yescharacteristic
28#11718585C2211yescharacteristic
29#11718130—21no—
30#11718129—21no—
31Q8⋊#1055—21no—
32Q8⋊#1055—21no—
33#11718124—21no—
34#11718124—21no—
35C2×C13×Q16—21no—
36C2×C13×SD16—21no—
37C2×C13×M16—21no—
38C13×C4⋊Q8C2×C411yescharacteristic
39C13×C4⋊Q8C2×C411yescharacteristic
40C13×#126—21no—
41C13×#125—21no—
42C13×#125C2×C411yescharacteristic
43C13×#124C2×C411yescharacteristic
44C13×#123—21no—
45C13×C22⋊Q8—21no—
46C13×C22⋊Q8—21no—
47C13×C22⋊Q8D411yescharacteristic
48C13×#121D411yescharacteristic
49C4×Q8×C13—21no—
50C4×Q8×C13—21no—
51C4×Q8×C13D411yescharacteristic
52C4×D4×C13—21no—
53C4×D4×C13D411yescharacteristic
54C13×#117—21no—
55C13×#117—21no—
56C2×C42×C13C2311yescharacteristic
57C2×C4×Dic13—21no—
58C2×#6099—21no—
59C2×#6099D411yescharacteristic
60C2×#6099D411yescharacteristic
61C22×#1055—21no—
62C13×#107—21no—
63C13×#106—21no—
64C13×#103—21no—
65C13×#103—21no—
66C13×#103—21no—
67C13×#102—21no—
68C13×#97C2×C411yescharacteristic
69C13×#97C2×C411yescharacteristic
70C4×C8×C13—21no—
71#88071—21no—
72#88071—21no—
73C22⋊#1055—21no—
74C22⋊#1055—21no—
75C22⋊#1055—21no—
76C22⋊#1055—21no—
77C4⋊#1055—21no—
78C4⋊#1055—21no—
79C4⋊#1055—21no—
80C4⋊#1055—21no—
81C4⋊#1055—21no—
82C4⋊#1055D411yescharacteristic
83C4⋊#1055D411yescharacteristic
84#88043—21no—
85#88043—21no—
86C4×#1055—21no—
87C4×#1055—21no—
88#8998—131nomaximal, Sylow
89C2×Q8×C13—21no—
90C2×Q8×C13—21no—
91C2×Q8×C13C22⋊C411yescharacteristic
92C2×D4×C13—21no—
93C2×D4×C13C22⋊C411yescharacteristic
94C22×C4×C13—21no—
95C22×C4×C13C2×D411yescharacteristic
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13#4111yescharacteristic
98C22×Dic13—41no—
99C13×Q16—42no—
100C13×SD16—42no—
101C13×M16—42no—
102C2×C8×C13—21no—
103C2×C8×C13—21no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—21no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—21no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—41no—
113C13×C4⋊C4—41no—
114C13×C4⋊C4C22⋊C411yescharacteristic
115C13×C4⋊C4C22⋊C411yescharacteristic
116C13×C22⋊C4—21no—
117C13×C22⋊C4—21no—
118C13×C22⋊C4—21no—
119C13×C22⋊C4—21no—
120C13×C22⋊C4—21no—
121C13×C22⋊C4—41no—
122C42×C13—21no—
123C42×C13—41no—
124C42×C13C22×C411yescharacteristic
125C42×C13C2×D411yescharacteristic
126C42×C13C2×D411yescharacteristic
127C42×C13#4111yescharacteristic
128C4×Dic13—22no—
129C4×Dic13—41no—
130#6099—41no—
131#6099—41no—
132#6099—81no—
133C2×#1055—21no—
134C2×#1055—21no—
135C2×#1055—21no—
136C2×#1055—21no—
137C2×#1055—41no—
138C2×#1055—81no—
139#3172D1311yescharacteristic
140#2995—131no—
141#1995—131no—
142#1500—131no—
143#1497—131no—
144#1300—131no—
145#1299—131no—
146C23×C13—21no—
147C23×C13#12111yescharacteristic
148Q8×C13—41no—
149Q8×C13—41no—
150Q8×C13—41no—
151Q8×C13—42no—
152D4×C13—41no—
153D4×C13—81no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13C2×C22⋊C411yescharacteristic
166C2×C4×C13C4×D411yescharacteristic
167C2×C4×C13C4×D411yescharacteristic
168C2×C4×C13#12011yescharacteristic
169C2×C4×C13#12111yescharacteristic
170C2×C4×C13#12311yescharacteristic
171C2×Dic13—42no—
172C2×Dic13—81no—
173C2×Dic13—81no—
174C8×C13—22no—
175C8×C13—41no—
176#1055—41no—
177#1055—41no—
178#1055—41no—
179#1055—41no—
180#1055—81no—
181#533C2×D1311yescharacteristic
182#529C2×D1311yescharacteristic
183#501Dic1311yescharacteristic, complemented
184#497Dic1311yescharacteristic, complemented
185#491Dic1311yescharacteristic, complemented
186#489Dic1311yescharacteristic, complemented
187#470—21no—
188#468—21no—
189#446—261no—
190C4×Q16—21no—
191C4×SD16—21no—
192#436—261no—
193#435—261no—
194#435—261no—
195#433—261no—
196#432—131no—
197#431—131no—
198#424—261no—
199#423—131no—
200C4×M16C2×D1311yescharacteristic
201#376—131no—
202#339—261no—
203#339—261no—
204#328—261no—
205#327—261no—
206Q8⋊C8—261no—
207Q8⋊C8—261no—
208C22×C13—21no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—41no—
212C22×C13—41no—
213C22×C13—41no—
214C22×C13#38611yescharacteristic
215C4×C13—21no—
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—21no—
220C4×C13—41no—
221C4×C13—41no—
222C4×C13—41no—
223C4×C13—81no—
224C4×C13—81no—
225C4×C13#45511yescharacteristic
226C4×C13#45611yescharacteristic
227Dic13—82no—
228C2×Q16—21no—
229C2×SD16—21no—
230C2×M16—21no—
231C2×M16—131no—
232C2×M16—131no—
233C2×M16—261no—
234C22×C8—261no—
235C4⋊Q8C2×Dic1311yescharacteristic
236C4⋊Q8C2×Dic1311yescharacteristic
237#126—21no—
238#125—21no—
239#125C2×Dic1311yescharacteristic
240#124C2×Dic1311yescharacteristic
241#123—21no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244C22⋊Q8C22⋊D1311yescharacteristic
245#121C22⋊D1311yescharacteristic
246C4×Q8—21no—
247C4×Q8—21no—
248C4×Q8C22⋊D1311yescharacteristic
249C4×D4—21no—
250C4×D4C22⋊D1311yescharacteristic
251#117—21no—
252#117—21no—
253C2×C42—261no—
254C2×C42C22×D1311yescharacteristic
255#107—21no—
256#106—21no—
257C4⋊C8—131no—
258C4⋊C8—131no—
259C4⋊C8—261no—
260C4⋊C8—261no—
261C4⋊C8—261no—
262C4⋊C8—261no—
263C4⋊C8—261no—
264#103—21no—
265#103—21no—
266#103—21no—
267#102—21no—
268C22⋊C8—261no—
269C22⋊C8—261no—
270C22⋊C8—261no—
271C22⋊C8—261no—
272#97—261no—
273#97—261no—
274#97C2×Dic1311yescharacteristic
275#97C2×Dic1311yescharacteristic
276C4×C8—21no—
277C4×C8—261no—
278C4×C8—261no—
279#95—261no—
280#95—261no—
281C2×C13—41no—
282C2×C13—81no—
283C2×C13#188111yescharacteristic
284C2×C13#188211yescharacteristic
285C2×C13#188411yescharacteristic
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8C22⋊Dic1311yescharacteristic
289C2×D4—21no—
290C2×D4C22⋊Dic1311yescharacteristic
291C22×C4—21no—
292C22×C4—521no—
293C22×C4D4×D1311yescharacteristic
294C22×C4#612911yescharacteristic
295C22×C4C2×C22⋊D1311yescharacteristic
296Q16—42no—
297SD16—42no—
298M16—42no—
299M16—521no—
300M16—521no—
301M16—1041no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—261no—
305C2×C8—261no—
306C2×C8—261no—
307C2×C8—261no—
308C2×C8—521no—
309C2×C8—1041no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4C22⋊Dic1311yescharacteristic
321C4⋊C4C22⋊Dic1311yescharacteristic
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—41no—
328C42—21no—
329C42—41no—
330C42—262no—
331C42—521no—
332C42D4×D1311yescharacteristic
333C42#612911yescharacteristic
334C42C22×Dic1311yescharacteristic
335C42C2×C22⋊D1311yescharacteristic
336C13#899811yescharacteristic, complemented, Sylow
337C23—21no—
338C23#8819311yescharacteristic
339Q8—41no—
340Q8—41no—
341Q8—41no—
342Q8—42no—
343D4—41no—
344D4—81no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—522no—
357C2×C4—1041no—
358C2×C4—1041no—
359C2×C4D4×Dic1311yescharacteristic
360C2×C4D4×Dic1311yescharacteristic
361C2×C4#8818911yescharacteristic
362C2×C4#8819111yescharacteristic
363C2×C4#8819311yescharacteristic
364C2×C4C2×C22⋊Dic1311yescharacteristic
365C8—22no—
366C8—41no—
367C8—521no—
368C8—521no—
369C8—521no—
370C8—521no—
371C8—1041no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22#1171888111yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—81no—
388C4—81no—
389C4—1042no—
390C4#1171886311yescharacteristic
391C4#1171886611yescharacteristic
392C2—41no—
393C2—81no—
394C2#1311520011yescharacteristic
395C2#1311520711yescharacteristic
396C2#1311522011yescharacteristic
subgroupG/H
centerC2×C4#88191
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#3172C2
socleC22×C13#386
prime radicalC13×#121D4
cosocleC2×C42×C13C23
hypercenter#3172D13
hypocenterC13#8998
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3172

Complements

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

NH ≅ G/Ntype
2. #13115818C2semidirect
4. #13113309C2semidirect
5. #13112730C2semidirect
6. #13112726C2semidirect
10. C13×#501C4semidirect
11. C13×#497C4semidirect
12. C13×#491C4semidirect
13. C13×#489C4semidirect
183. #501Dic13semidirect
184. #497Dic13semidirect
185. #491Dic13semidirect
186. #489Dic13semidirect
336. C13#8998semidirect

Maximal subgroups

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

subgroupindex
#131240062
#131158182
#131133222
#131133092
#131127302
#131127262
C13×#31722
#899813