Finite Group Databasebeta

← #15846344

Subgroups — #15846344

Order 3328.

630 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125808C212yesmaximal, complemented
2#13125415C211yesmaximal, characteristic, complemented
3#13114354C211yesmaximal, characteristic, complemented
4#13114349C211yesmaximal, characteristic, complemented
5#13114320C211yesmaximal, characteristic, complemented
6#13114315C211yesmaximal, characteristic, complemented
7#13114280C212yesmaximal, complemented
8#13114273C212yesmaximal, complemented
9#13113584C211yesmaximal, characteristic, complemented
10#13113542C212yesmaximal, complemented
11C13×#2966C211yesmaximal, characteristic, complemented
12C13×#529C2211yescharacteristic
13#11719182C2212yes—
14C13×#446C2211yescharacteristic
15C8×Q8×C13C2211yescharacteristic
16C13×#436C2211yescharacteristic
17C13×#435—21no—
18C8×D4×C13—21no—
19C8×D4×C13C2211yescharacteristic
20C13×#433—21no—
21C13×#432C2211yescharacteristic
22C13×#405—21no—
23C2×C4×C8×C13C2211yescharacteristic
24#11718776—21no—
25#11718776—21no—
26#11718729—22no—
27#11718720—22no—
28#11718708—22no—
29#11718698—22no—
30#11718692C2212yes—
31#11718688C2212yes—
32#11718680C2212yes—
33#11718676C2212yes—
34#11718586C2212yes—
35#11718356C2211yescharacteristic
36#11718355C2212yes—
37C4×D104—21no—
38C4×D104—21no—
39#11718343C2211yescharacteristic
40#11718078C2212yes—
41#11718078C2212yes—
42#11718077C2212yes—
43#11718077C2212yes—
44#11718050C2212yes—
45#11718049C2211yescharacteristic
46#11718049C2211yescharacteristic
47C2×#6127—22no—
48C2×C13×M16—21no—
49C22×C8×C13—21no—
50C22×C8×C13D411yescharacteristic
51C22×C8×C13D411yescharacteristic
52C13×#126—21no—
53C13×#125D411yescharacteristic
54C13×#124D411yescharacteristic
55C13×#123—21no—
56C13×C22⋊Q8D411yescharacteristic
57C13×#121D411yescharacteristic
58C4×Q8×C13C2311yescharacteristic
59C4×D4×C13—21no—
60C4×D4×C13C2311yescharacteristic
61C13×#117—21no—
62C2×C42×C13C2311yescharacteristic
63C2×#6107—22no—
64C2×#6106—22no—
65C2×#6105—22no—
66C2×#6104—22no—
67#88184—22no—
68#88184—22no—
69C2×D104—21no—
70C2×D104—21no—
71#88129—22no—
72#88128C2312yes—
73C4×D52—22no—
74C4×D52—22no—
75#88123C2312yes—
76C13×C4⋊C8—21no—
77C13×C4⋊C8—21no—
78C13×C4⋊C8C2311yescharacteristic
79C13×C4⋊C8C2311yescharacteristic
80C13×C22⋊C8—21no—
81C13×C22⋊C8—21no—
82C13×C22⋊C8—21no—
83C13×#97—21no—
84C13×#97—21no—
85C4×C8×C13—21no—
86C4×C8×C13D411yescharacteristic
87C4×C8×C13D411yescharacteristic
88C4×C8×C13C2311yescharacteristic
89C4×C8×C13C2311yescharacteristic
90C22⋊#1055—22no—
91#88061—22no—
92#88061—22no—
93#88058—21no—
94#88058—21no—
95#88050—22no—
96#88050—22no—
97#88049—22no—
98#88049—22no—
99C4⋊#1055C2312yes—
100C4⋊#1055C2312yes—
101C4×#1055—22no—
102#19225—131nomaximal, Sylow
103C2×Q8×C13C2×D411yescharacteristic
104C2×D4×C13—21no—
105C2×D4×C13C2×D411yescharacteristic
106C22×C4×C13—21no—
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13#4111yescharacteristic
110C2×C22⋊D13—42no—
111#6127—82no—
112#6127—82no—
113C2×D52—22no—
114C2×D52—22no—
115C2×D52—22no—
116C2×C4×D13—42no—
117C2×Dic26—22no—
118C13×M16—42no—
119C2×C8×C13—22no—
120C2×C8×C13—21no—
121C2×C8×C13—21no—
122C2×C8×C13—41no—
123C2×C8×C13—42no—
124C2×C8×C13C2×D411yescharacteristic
125C2×C8×C13C2×D411yescharacteristic
126C2×C8×C13C2×D411yescharacteristic
127C2×C8×C13C2×D411yescharacteristic
128C13×C4⋊C4—21no—
129C13×C4⋊C4—21no—
130C13×C4⋊C4—21no—
131C13×C4⋊C4—21no—
132C13×C4⋊C4C2×D411yescharacteristic
133C13×C4⋊C4C2×D411yescharacteristic
134C13×C22⋊C4—21no—
135C13×C22⋊C4—21no—
136C13×C22⋊C4—21no—
137C13×C22⋊C4—21no—
138C13×C22⋊C4—21no—
139C42×C13—21no—
140C42×C13C2×D411yescharacteristic
141C42×C13C2×D411yescharacteristic
142C42×C13#4111yescharacteristic
143C42×C13C2411yescharacteristic
144#6107—82no—
145#6106—82no—
146#6105—82no—
147#6104—82no—
148#6103—42no—
149#6103—42no—
150C4⋊Dic13—22no—
151C4⋊Dic13—22no—
152C2×#1055—22no—
153C2×#1055—22no—
154D104—42no—
155D104—42no—
156#3212—132no—
157#3169—131no—
158#2966D1311yescharacteristic, complemented
159#1694—131no—
160#1693—131no—
161#1688—131no—
162#1687—131no—
163#1682—132no—
164#1681—132no—
165#1564—131no—
166#1553—132no—
167C23×C13—21no—
168C23×C13#12111yescharacteristic
169C22×D13—42no—
170Q8×C13—22no—
171D4×C13—22no—
172D4×C13—42no—
173C2×C4×C13—21no—
174C2×C4×C13—21no—
175C2×C4×C13—22no—
176C2×C4×C13—21no—
177C2×C4×C13—21no—
178C2×C4×C13—21no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13#12111yescharacteristic
183C2×C4×C13#12111yescharacteristic
184C2×C4×C13#12111yescharacteristic
185C2×C4×C13C22×D411yescharacteristic
186C2×C4×C13C22×D411yescharacteristic
187C2×C4×C13C2×#4111yescharacteristic
188C22⋊D13—84no—
189C2×Dic13—42no—
190D52—42no—
191D52—42no—
192D52—42no—
193D52—42no—
194D52—82no—
195C4×D13—84no—
196Dic26—42no—
197Dic26—42no—
198C8×C13—21no—
199C8×C13—21no—
200C8×C13—21no—
201C8×C13—41no—
202C8×C13—41no—
203C8×C13#13512yes—
204#1055—42no—
205#1055—42no—
206#532—132no—
207#529C2×D1311yescharacteristic
208#500—131no—
209#495—262no—
210#493—131no—
211#488—262no—
212#486—132no—
213#466—261no—
214#466—261no—
215#462—132no—
216#461—132no—
217#460—132no—
218#459—132no—
219#452—262no—
220#449—262no—
221#446C2×D1311yescharacteristic
222C8×Q8C2×D1311yescharacteristic
223C4×D8—261no—
224C4×D8—261no—
225#436C2×D1311yescharacteristic
226#435—21no—
227C8×D4—21no—
228C8×D4C2×D1311yescharacteristic
229#433—21no—
230#432C2×D1311yescharacteristic
231#431—132no—
232#405—21no—
233C2×C4×C8C2×D1311yescharacteristic
234#335—132no—
235#334—131no—
236#334—131no—
237#332—132no—
238#332—132no—
239#331—132no—
240#331—132no—
241C22×C13—21no—
242C22×C13—21no—
243C22×C13—21no—
244C22×C13—41no—
245C22×C13—41no—
246C22×C13—41no—
247C22×C13C2×#12111yescharacteristic
248C2×D13—82no—
249C2×D13—82no—
250C2×D13—82no—
251C4×C13—21no—
252C4×C13—21no—
253C4×C13—21no—
254C4×C13—21no—
255C4×C13—41no—
256C4×C13—41no—
257C4×C13—41no—
258C4×C13C2×#13511yescharacteristic
259C4×C13#57511yescharacteristic
260C4×C13#57612yes—
261Dic13—82no—
262C2×#41—262no—
263C2×Q16—262no—
264C2×SD16—262no—
265C2×SD16—262no—
266C2×D8—262no—
267C2×D8—261no—
268C2×D8—261no—
269C2×M16—21no—
270C22×C8—21no—
271C22×C8C22⋊D1311yescharacteristic
272C22×C8C22⋊D1311yescharacteristic
273C4⋊Q8—132no—
274#127—132no—
275#126—21no—
276#125D5211yescharacteristic
277#124—262no—
278#124D5211yescharacteristic
279#123—21no—
280C22⋊Q8D5211yescharacteristic
281#121—262no—
282#121—262no—
283#121D5211yescharacteristic
284C4×Q8C22×D1311yescharacteristic
285C4×D4—21no—
286C4×D4—262no—
287C4×D4—262no—
288C4×D4C22×D1311yescharacteristic
289#117—21no—
290C2×C42C22×D1311yescharacteristic
291#107—261no—
292#107—261no—
293C4⋊C8—21no—
294C4⋊C8—21no—
295C4⋊C8—132no—
296C4⋊C8—132no—
297C4⋊C8C22×D1311yescharacteristic
298C4⋊C8C22×D1311yescharacteristic
299#103—262no—
300#103—262no—
301#102—262no—
302#102—262no—
303#102—262no—
304#102—262no—
305C22⋊C8—21no—
306C22⋊C8—21no—
307C22⋊C8—21no—
308C22⋊C8—262no—
309#97—21no—
310#97—21no—
311C4×C8—21no—
312C4×C8—262no—
313C4×C8C22⋊D1311yescharacteristic
314C4×C8C22⋊D1311yescharacteristic
315C4×C8C22×D1311yescharacteristic
316C4×C8C22×D1311yescharacteristic
317C2×C13—41no—
318C2×C13—81no—
319C2×C13#303511yescharacteristic
320C2×C13#305811yescharacteristic
321C2×C13#306711yescharacteristic
322D13—162no—
323#41—1042no—
324#41—1042no—
325C2×Q8—262no—
326C2×Q8C2×D5211yescharacteristic
327C2×D4—21no—
328C2×D4—262no—
329C2×D4—262no—
330C2×D4—262no—
331C2×D4—522no—
332C2×D4C2×D5211yescharacteristic
333C22×C4—21no—
334C22×C4—522no—
335C22×C4C2×D5211yescharacteristic
336C22×C4#612711yescharacteristic
337C22×C4C2×C22⋊D1311yescharacteristic
338Q16—1042no—
339SD16—1042no—
340SD16—1042no—
341D8—522no—
342D8—522no—
343D8—1042no—
344M16—42no—
345C2×C8—22no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—41no—
349C2×C8—42no—
350C2×C8—262no—
351C2×C8—262no—
352C2×C8C2×C22⋊D1311yescharacteristic
353C2×C8C2×C22⋊D1311yescharacteristic
354C2×C8C2×C22⋊D1311yescharacteristic
355C2×C8C2×C22⋊D1311yescharacteristic
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—262no—
361C4⋊C4—262no—
362C4⋊C4C2×D5211yescharacteristic
363C4⋊C4C2×D5211yescharacteristic
364C22⋊C4—21no—
365C22⋊C4—21no—
366C22⋊C4—21no—
367C22⋊C4—21no—
368C22⋊C4—21no—
369C22⋊C4—522no—
370C22⋊C4—522no—
371C42—21no—
372C42C2×D5211yescharacteristic
373C42#612711yescharacteristic
374C42C2×C22⋊D1311yescharacteristic
375C42C23×D1311yescharacteristic
376C13#1922511yescharacteristic, complemented, Sylow
377C23—21no—
378C23—522no—
379C23#8818411yescharacteristic
380Q8—22no—
381Q8—522no—
382Q8—522no—
383D4—22no—
384D4—42no—
385D4—522no—
386D4—522no—
387D4—522no—
388D4—522no—
389D4—1042no—
390D4—1044no—
391C2×C4—22no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—522no—
401C2×C4—1044no—
402C2×C4#8818411yescharacteristic
403C2×C4#8818411yescharacteristic
404C2×C4#8818411yescharacteristic
405C2×C4C22×D5211yescharacteristic
406C2×C4C2×#612711yescharacteristic
407C2×C4C22×C22⋊D1311yescharacteristic
408C8—21no—
409C8—21no—
410C8—21no—
411C8—41no—
412C8—41no—
413C8—522no—
414C8—522no—
415C8#8820412yes—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—1042no—
423C22—1042no—
424C22—1042no—
425C22C2×#8818411yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—21no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—1042no—
434C4#1171945712yes—
435C4C2×#8820411yescharacteristic
436C4#1171952711yescharacteristic
437C2—41no—
438C2—81no—
439C2—2082no—
440C2#1312429111yescharacteristic
441C2#1312448411yescharacteristic
442C2#1312455611yescharacteristic
subgroupG/H
centerC22C2×#88184
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC13×#2966C2
socleC22×C13C2×#121
hypercenter#2966D13
hypocenterC13#19225
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2966

Complements

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

NH ≅ G/Ntype
1. #13125808C2semidirect
2. #13125415C2semidirect
3. #13114354C2semidirect
4. #13114349C2semidirect
5. #13114320C2semidirect
6. #13114315C2semidirect
7. #13114280C2semidirect
8. #13114273C2semidirect
9. #13113584C2semidirect
10. #13113542C2semidirect
11. C13×#2966C2semidirect
158. #2966D13semidirect
376. C13#19225semidirect

Maximal subgroups

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

subgroupindex
#131258082
#131254152
#131143542
#131143492
#131143202
#131143152
#131142802
#131142732
#131135842
#131135422
C13×#29662
#1922513