Finite Group Databasebeta

← #15757822

Subgroups — #15757822

Order 3328.

452 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124006C211yesmaximal, characteristic, complemented
2#13115669C211yesmaximal, characteristic, complemented
3#13113322C211yesmaximal, characteristic, complemented
4#13113305C211yesmaximal, characteristic, complemented
5#13112730C211yesmaximal, characteristic, complemented
6#13112726C211yesmaximal, characteristic, complemented
7C13×#3171C211yesmaximal, characteristic
8C13×#532C2211yescharacteristic
9C13×#529C2211yescharacteristic
10C13×#501C411yescharacteristic, complemented
11C13×#496C411yescharacteristic, complemented
12C13×#490C411yescharacteristic, complemented
13C13×#489C411yescharacteristic, complemented
14C13×#469—21no—
15C13×#468—21no—
16C4×C13×SD16—21no—
17C4×C13×D8—21no—
18C4×C13×M16C2211yescharacteristic
19C2×#88077—21no—
20C2×#88077—21no—
21#11718685—21no—
22#11718673—21no—
23#11718672—21no—
24#11718672—21no—
25#11718661—21no—
26#11718660—21no—
27#11718593C2211yescharacteristic
28#11718587C2211yescharacteristic
29#11718586C2211yescharacteristic
30#11718585C2211yescharacteristic
31#11718130—21no—
32#11718129—21no—
33D4⋊#1055—21no—
34D4⋊#1055—21no—
35C2×C13×#41—21no—
36C2×C13×SD16—21no—
37C2×C13×D8—21no—
38C2×C13×M16—21no—
39C13×C4⋊Q8C2×C411yescharacteristic
40C13×#127C2×C411yescharacteristic
41C13×#126—21no—
42C13×#125C2×C411yescharacteristic
43C13×#124—21no—
44C13×#124C2×C411yescharacteristic
45C13×#123—21no—
46C13×C22⋊Q8D411yescharacteristic
47C13×#121—21no—
48C13×#121—21no—
49C13×#121D411yescharacteristic
50C4×Q8×C13D411yescharacteristic
51C4×D4×C13—21no—
52C4×D4×C13—21no—
53C4×D4×C13—21no—
54C4×D4×C13D411yescharacteristic
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×#102—21no—
66C13×#102—21no—
67C13×#102—21no—
68C13×#97C2×C411yescharacteristic
69C13×#97C2×C411yescharacteristic
70C4×C8×C13—21no—
71#88077—42no—
72#88077—42no—
73#88071—21no—
74#88071—21no—
75C22⋊#1055—21no—
76C22⋊#1055—21no—
77C22⋊#1055—21no—
78C22⋊#1055—21no—
79C4⋊#1055—21no—
80C4⋊#1055—21no—
81C4⋊#1055—21no—
82C4⋊#1055—21no—
83C4⋊#1055—21no—
84C4⋊#1055D411yescharacteristic
85C4⋊#1055D411yescharacteristic
86#88043—21no—
87#88043—21no—
88C4×#1055—21no—
89C4×#1055—21no—
90#8997—131nomaximal, Sylow
91C13×#41—41no—
92C13×#41—41no—
93C13×#41—41no—
94C13×#41—41no—
95C2×Q8×C13—21no—
96C2×Q8×C13C22⋊C411yescharacteristic
97C2×D4×C13—21no—
98C2×D4×C13—21no—
99C2×D4×C13—21no—
100C2×D4×C13—21no—
101C2×D4×C13—41no—
102C2×D4×C13C22⋊C411yescharacteristic
103C22×C4×C13—21no—
104C22×C4×C13—41no—
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13#4111yescharacteristic
108C22×Dic13—41no—
109C13×SD16—42no—
110C13×D8—42no—
111C13×M16—42no—
112C2×C8×C13—21no—
113C2×C8×C13—21no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—21no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—21no—
119C13×C4⋊C4—21no—
120C13×C4⋊C4C22⋊C411yescharacteristic
121C13×C4⋊C4C22⋊C411yescharacteristic
122C13×C22⋊C4—21no—
123C13×C22⋊C4—21no—
124C13×C22⋊C4—21no—
125C13×C22⋊C4—21no—
126C13×C22⋊C4—21no—
127C13×C22⋊C4—41no—
128C13×C22⋊C4—41no—
129C42×C13—21no—
130C42×C13C22×C411yescharacteristic
131C42×C13C2×D411yescharacteristic
132C42×C13C2×D411yescharacteristic
133C42×C13#4111yescharacteristic
134C4×Dic13—22no—
135C4×Dic13—41no—
136#6099—41no—
137#6099—41no—
138#6099—81no—
139C2×#1055—21no—
140C2×#1055—21no—
141C2×#1055—21no—
142C2×#1055—21no—
143C2×#1055—41no—
144C2×#1055—81no—
145#3171D1311yescharacteristic
146#2995—131no—
147#1963—131no—
148#1500—131no—
149#1496—131no—
150#1300—131no—
151#1299—131no—
152C23×C13—21no—
153C23×C13—41no—
154C23×C13#12111yescharacteristic
155Q8×C13—41no—
156Q8×C13—41no—
157Q8×C13—41no—
158D4×C13—41no—
159D4×C13—41no—
160D4×C13—41no—
161D4×C13—42no—
162D4×C13—41no—
163D4×C13—41no—
164D4×C13—81no—
165D4×C13—81no—
166D4×C13—81no—
167C2×C4×C13—21no—
168C2×C4×C13—21no—
169C2×C4×C13—21no—
170C2×C4×C13—21no—
171C2×C4×C13—21no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—81no—
178C2×C4×C13—81no—
179C2×C4×C13C2×C22⋊C411yescharacteristic
180C2×C4×C13C4×D411yescharacteristic
181C2×C4×C13C4×D411yescharacteristic
182C2×C4×C13#12011yescharacteristic
183C2×C4×C13#12111yescharacteristic
184C2×C4×C13#12311yescharacteristic
185C2×Dic13—42no—
186C2×Dic13—81no—
187C2×Dic13—81no—
188C8×C13—22no—
189C8×C13—41no—
190#1055—41no—
191#1055—41no—
192#1055—41no—
193#1055—41no—
194#1055—81no—
195#532C2×D1311yescharacteristic
196#529C2×D1311yescharacteristic
197#501Dic1311yescharacteristic, complemented
198#496Dic1311yescharacteristic, complemented
199#490Dic1311yescharacteristic, complemented
200#489Dic1311yescharacteristic, complemented
201#469—21no—
202#468—21no—
203#446—261no—
204C4×SD16—21no—
205C4×D8—21no—
206#436—261no—
207#435—261no—
208#435—261no—
209#433—261no—
210#432—131no—
211#431—131no—
212#424—261no—
213#423—131no—
214C2×#104—261no—
215C2×#104—261no—
216C4×M16C2×D1311yescharacteristic
217#376—131no—
218#328—261no—
219#327—261no—
220D4⋊C8—261no—
221D4⋊C8—261no—
222C22×C13—21no—
223C22×C13—21no—
224C22×C13—21no—
225C22×C13—41no—
226C22×C13—41no—
227C22×C13—41no—
228C22×C13—81no—
229C22×C13—81no—
230C22×C13—81no—
231C22×C13#38611yescharacteristic
232C4×C13—21no—
233C4×C13—21no—
234C4×C13—21no—
235C4×C13—21no—
236C4×C13—21no—
237C4×C13—41no—
238C4×C13—41no—
239C4×C13—41no—
240C4×C13—81no—
241C4×C13#45311yescharacteristic
242C4×C13#45411yescharacteristic
243Dic13—82no—
244C2×#41—21no—
245C2×SD16—21no—
246C2×D8—21no—
247C2×M16—21no—
248C2×M16—131no—
249C2×M16—131no—
250C2×M16—261no—
251C22×C8—261no—
252C4⋊Q8C2×Dic1311yescharacteristic
253#127C2×Dic1311yescharacteristic
254#126—21no—
255#125C2×Dic1311yescharacteristic
256#124—21no—
257#124C2×Dic1311yescharacteristic
258#123—21no—
259C22⋊Q8C22⋊D1311yescharacteristic
260#121—21no—
261#121—21no—
262#121C22⋊D1311yescharacteristic
263C4×Q8C22⋊D1311yescharacteristic
264C4×D4—21no—
265C4×D4—21no—
266C4×D4—21no—
267C4×D4C22⋊D1311yescharacteristic
268#117—21no—
269C2×C42—261no—
270C2×C42C22×D1311yescharacteristic
271#107—21no—
272#106—21no—
273C4⋊C8—131no—
274C4⋊C8—131no—
275C4⋊C8—261no—
276C4⋊C8—261no—
277C4⋊C8—261no—
278C4⋊C8—261no—
279C4⋊C8—261no—
280#104—522no—
281#104—522no—
282#103—21no—
283#102—21no—
284#102—21no—
285#102—21no—
286C22⋊C8—261no—
287C22⋊C8—261no—
288C22⋊C8—261no—
289C22⋊C8—261no—
290#97—261no—
291#97—261no—
292#97C2×Dic1311yescharacteristic
293#97C2×Dic1311yescharacteristic
294C4×C8—21no—
295C4×C8—261no—
296C4×C8—261no—
297#95—261no—
298#95—261no—
299C2×C13—41no—
300C2×C13—81no—
301C2×C13—161no—
302C2×C13#188111yescharacteristic
303C2×C13#188311yescharacteristic
304C2×C13#188411yescharacteristic
305#41—41no—
306#41—41no—
307#41—41no—
308#41—41no—
309C2×Q8—21no—
310C2×Q8C22⋊Dic1311yescharacteristic
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—41no—
316C2×D4C22⋊Dic1311yescharacteristic
317C22×C4—21no—
318C22×C4—41no—
319C22×C4—521no—
320C22×C4D4×D1311yescharacteristic
321C22×C4#612911yescharacteristic
322C22×C4C2×C22⋊D1311yescharacteristic
323SD16—42no—
324D8—42no—
325M16—42no—
326M16—521no—
327M16—521no—
328M16—1041no—
329C2×C8—21no—
330C2×C8—21no—
331C2×C8—261no—
332C2×C8—261no—
333C2×C8—261no—
334C2×C8—261no—
335C2×C8—521no—
336C2×C8—1041no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4C22⋊Dic1311yescharacteristic
344C4⋊C4C22⋊Dic1311yescharacteristic
345C22⋊C4—21no—
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C42—21no—
353C42—262no—
354C42—521no—
355C42D4×D1311yescharacteristic
356C42#612911yescharacteristic
357C42C22×Dic1311yescharacteristic
358C42C2×C22⋊D1311yescharacteristic
359C13#899711yescharacteristic, complemented, Sylow
360C23—21no—
361C23—41no—
362C23#8819311yescharacteristic
363Q8—41no—
364Q8—41no—
365Q8—41no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—42no—
370D4—41no—
371D4—41no—
372D4—81no—
373D4—81no—
374D4—81no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—522no—
388C2×C4—1041no—
389C2×C4—1041no—
390C2×C4D4×Dic1311yescharacteristic
391C2×C4D4×Dic1311yescharacteristic
392C2×C4#8818911yescharacteristic
393C2×C4#8819111yescharacteristic
394C2×C4#8819311yescharacteristic
395C2×C4C2×C22⋊Dic1311yescharacteristic
396C8—22no—
397C8—41no—
398C8—521no—
399C8—521no—
400C8—521no—
401C8—521no—
402C8—1041no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22#1171888111yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—81no—
422C4—1042no—
423C4#1171885911yescharacteristic
424C4#1171886211yescharacteristic
425C2—41no—
426C2—81no—
427C2—161no—
428C2#1311520011yescharacteristic
429C2#1311521411yescharacteristic
430C2#1311522011yescharacteristic
subgroupG/H
centerC2×C4#88191
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
Fitting, prime radicalC13×#3171C2
socleC22×C13#386
cosocleC2×C42×C13C23
hypercenter#3171D13
hypocenterC13#8997
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3171

Complements

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

NH ≅ G/Ntype
1. #13124006C2semidirect
2. #13115669C2semidirect
3. #13113322C2semidirect
4. #13113305C2semidirect
5. #13112730C2semidirect
6. #13112726C2semidirect
10. C13×#501C4semidirect
11. C13×#496C4semidirect
12. C13×#490C4semidirect
13. C13×#489C4semidirect
197. #501Dic13semidirect
198. #496Dic13semidirect
199. #490Dic13semidirect
200. #489Dic13semidirect
359. C13#8997semidirect

Maximal subgroups

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

subgroupindex
#131240062
#131156692
#131133222
#131133052
#131127302
#131127262
C13×#31712
#899713