Finite Group Databasebeta

← #15846708

Subgroups — #15846708

Order 3328.

798 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#13125415C211yesmaximal, characteristic, complemented
2#13124300C212yesmaximal, complemented
3#13114273C214yesmaximal, complemented
4#13114225C212yesmaximal, complemented
5#13114191C212yesmaximal, complemented
6#13113595C211yesmaximal, characteristic, complemented
7#13113511C212yesmaximal, complemented
8C2×C8×D4×C13C211yesmaximal, characteristic, complemented
9C23×C8×C13—21no—
10C2×C4×D4×C13C2211yescharacteristic
11C2×#88186—22no—
12#11719182C2212yes—
13C8×D4×C13—21no—
14C8×D4×C13—21no—
15C8×D4×C13C2212yes—
16C8×D4×C13C2212yes—
17C2×C13×C4⋊C8C2211yescharacteristic
18C2×C13×C22⋊C8—21no—
19C2×C4×C8×C13C2211yescharacteristic
20#11718776—21no—
21#11718776—21no—
22#11718680C2214yes—
23#11718677—24no—
24#11718676C2214yes—
25#11718627—22no—
26#11718585C2212yes—
27#11718356C2211yescharacteristic, complemented
28#11718355C2212yescomplemented
29C4×D104—21no—
30C4×D104—21no—
31#11718343C2211yescharacteristic, complemented
32#11718078C2214yescomplemented
33#11718077C2214yescomplemented
34#11718050C2212yescomplemented
35#11718050C2212yescomplemented
36C22×D4×C13D411yescharacteristic
37C23×C4×C13—21no—
38C2×#6127—22no—
39C22×C8×C13—21no—
40C22×C8×C13—22no—
41C22×C8×C13—22no—
42C22×C8×C13—44no—
43C22×C8×C13D411yescharacteristic
44C22×C8×C13D411yescharacteristic
45C4×D4×C13—21no—
46C4×D4×C13—21no—
47C4×D4×C13D412yes—
48C4×D4×C13C2312yes—
49C2×C13×C4⋊C4D411yescharacteristic
50C2×C13×C22⋊C4—21no—
51C2×C42×C13C2311yescharacteristic
52C2×#6105—24no—
53#88186—48no—
54C2×#6104—24no—
55#88184—22no—
56#88184—22no—
57C2×#6099—22no—
58C2×D104—21no—
59C2×D104—21no—
60#88129—22no—
61#88128C2312yes—
62C4×D52—22no—
63C4×D52—22no—
64#88123C2312yes—
65C13×C4⋊C8—21no—
66C13×C4⋊C8C2312yes—
67C13×C22⋊C8—22no—
68C13×C22⋊C8—22no—
69C4×C8×C13D411yescharacteristic
70C4×C8×C13D411yescharacteristic
71C4×C8×C13C2311yescharacteristic
72C4×C8×C13C2311yescharacteristic
73#88061—22no—
74#88061—22no—
75#88058—21no—
76#88058—21no—
77#88050—24no—
78#88049—24no—
79C4⋊#1055—22no—
80C4⋊#1055C2314yes—
81#19255—131nomaximal, Sylow
82C24×C13—21no—
83C2×D4×C13—21no—
84C2×D4×C13—22no—
85C2×D4×C13D814yescomplemented
86C2×D4×C13C2×D412yes—
87C22×C4×C13—21no—
88C22×C4×C13—22no—
89C22×C4×C13—22no—
90C22×C4×C13—42no—
91C22×C4×C13—42no—
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13#4111yescharacteristic
95C2×C22⋊D13—42no—
96#6127—44no—
97#6127—44no—
98C2×D52—22no—
99C2×D52—22no—
100C2×D52—22no—
101C2×C4×D13—42no—
102C2×Dic26—22no—
103C2×C8×C13—22no—
104C2×C8×C13—22no—
105C2×C8×C13—41no—
106C2×C8×C13—44no—
107C2×C8×C13—42no—
108C2×C8×C13—44no—
109C2×C8×C13C2×D411yescharacteristic
110C2×C8×C13C2×D411yescharacteristic
111C2×C8×C13C2×D411yescharacteristic
112C2×C8×C13C2×D411yescharacteristic
113C13×C4⋊C4—21no—
114C13×C4⋊C4C2×D412yes—
115C13×C22⋊C4—22no—
116C13×C22⋊C4—22no—
117C42×C13C2×D411yescharacteristic
118C42×C13C2×D411yescharacteristic
119C42×C13#4111yescharacteristic
120C42×C13C2411yescharacteristic
121#6105—48no—
122#6104—48no—
123#6103—42no—
124#6103—42no—
125C4⋊Dic13—22no—
126C4⋊Dic13—22no—
127#6099—44no—
128C2×#1055—24no—
129D104—42no—
130D104—42no—
131#3169—131no—
132#3036—132no—
133C2×C8×D4D1311yescharacteristic, complemented
134#1681—134no—
135#1673—132no—
136#1667—132no—
137#1567—131no—
138#1547—132no—
139C23×C13—22no—
140C23×C13—24no—
141C23×C13—42no—
142C23×C13—42no—
143C23×C13#12111yescharacteristic
144C22×D13—42no—
145D4×C13—22no—
146D4×C13—24no—
147D4×C13C2×D814yes—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—22no—
151C2×C4×C13—41no—
152C2×C4×C13—44no—
153C2×C4×C13—42no—
154C2×C4×C13—42no—
155C2×C4×C13—42no—
156C2×C4×C13#12111yescharacteristic
157C2×C4×C13#12111yescharacteristic
158C2×C4×C13#12111yescharacteristic
159C2×C4×C13C2×D812yes—
160C2×C4×C13#13512yes—
161C2×C4×C13C22×D411yescharacteristic
162C2×C4×C13C22×D411yescharacteristic
163C2×C4×C13C2×#4111yescharacteristic
164C22⋊D13—84no—
165C2×Dic13—42no—
166D52—42no—
167D52—42no—
168D52—42no—
169D52—42no—
170D52—82no—
171C4×D13—84no—
172Dic26—42no—
173Dic26—42no—
174C8×C13—21no—
175C8×C13—21no—
176C8×C13—21no—
177C8×C13—42no—
178C8×C13AGL(1,ℤ/8)12yescomplemented
179#1055—44no—
180C2×AGL(1,ℤ/8)—262no—
181C23×C8—21no—
182#532—132no—
183C2×C4×D4C2×D1311yescharacteristic
184#500—131no—
185#493—131no—
186#486—132no—
187#466—261no—
188#466—261no—
189#463—264no—
190#461—134no—
191#459—134no—
192C4×D8—261no—
193C4×D8—261no—
194C8×D4—21no—
195C8×D4—21no—
196C8×D4C2×D1312yes—
197C8×D4C2×D1312yes—
198#423—132no—
199C2×C4⋊C8C2×D1311yescharacteristic
200#417—262no—
201C2×C22⋊C8—21no—
202C2×C4×C8C2×D1311yescharacteristic
203#335—132no—
204#335—132no—
205#332—134no—
206#331—134no—
207C22×C13—21no—
208C22×C13—21no—
209C22×C13—24no—
210C22×C13—48no—
211C22×C13—42no—
212C22×C13—42no—
213C22×C13#46612yes—
214C22×C13C2×#12111yescharacteristic
215C2×D13—82no—
216C2×D13—82no—
217C2×D13—82no—
218C4×C13—21no—
219C4×C13—21no—
220C4×C13—21no—
221C4×C13—42no—
222C4×C13#46612yes—
223C4×C13C22×D811yescharacteristic
224C4×C13C2×#13511yescharacteristic
225C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
226C4×C13#57511yescharacteristic
227Dic13—82no—
228C2×#41—262no—
229C22×D4D5211yescharacteristic
230C23×C4—21no—
231AGL(1,ℤ/8)—528no—
232C2×SD16—264no—
233C2×D8—264no—
234C2×D8—261no—
235C2×D8—261no—
236C2×M16—262no—
237C22×C8—21no—
238C22×C8—22no—
239C22×C8—22no—
240C22×C8—44no—
241C22×C8C22⋊D1311yescharacteristic
242C22×C8C22⋊D1311yescharacteristic
243C4⋊Q8—132no—
244#127—132no—
245#124—262no—
246#121—262no—
247#121—262no—
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—262no—
251C4×D4—262no—
252C4×D4D5212yes—
253C4×D4C22×D1312yes—
254C2×C4⋊C4D5211yescharacteristic
255C2×C22⋊C4—21no—
256C2×C42C22×D1311yescharacteristic
257#107—261no—
258#107—261no—
259C4⋊C8—21no—
260C4⋊C8—134no—
261C4⋊C8—262no—
262C4⋊C8C22×D1312yes—
263#103—264no—
264#102—262no—
265#102—262no—
266#102—264no—
267C22⋊C8—22no—
268C22⋊C8—22no—
269C4×C8C22⋊D1311yescharacteristic
270C4×C8C22⋊D1311yescharacteristic
271C4×C8C22×D1311yescharacteristic
272C4×C8C22×D1311yescharacteristic
273C2×C13—22no—
274C2×C13—44no—
275C2×C13#303611yescharacteristic
276C2×C13C2×#46611yescharacteristic
277C2×C13#306711yescharacteristic
278D13—162no—
279C24—21no—
280#41—524no—
281#41—524no—
282C2×Q8—262no—
283C2×D4—22no—
284C2×D4—21no—
285C2×D4—262no—
286C2×D4—262no—
287C2×D4—262no—
288C2×D4—522no—
289C2×D4D10414yescomplemented
290C2×D4C2×D5212yes—
291C22×C4—21no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—522no—
297C22×C4C2×D5211yescharacteristic
298C22×C4#612711yescharacteristic
299C22×C4C2×C22⋊D1311yescharacteristic
300SD16—528no—
301D8—522no—
302D8—528no—
303D8—522no—
304M16—524no—
305C2×C8—22no—
306C2×C8—22no—
307C2×C8—41no—
308C2×C8—44no—
309C2×C8—42no—
310C2×C8—44no—
311C2×C8—264no—
312C2×C8C2×C22⋊D1311yescharacteristic
313C2×C8C2×C22⋊D1311yescharacteristic
314C2×C8C2×C22⋊D1311yescharacteristic
315C2×C8C2×C22⋊D1311yescharacteristic
316C4⋊C4—21no—
317C4⋊C4—262no—
318C4⋊C4—262no—
319C4⋊C4C2×D5212yes—
320C22⋊C4—22no—
321C22⋊C4—22no—
322C22⋊C4—522no—
323C22⋊C4—522no—
324C42C2×D5211yescharacteristic
325C42#612711yescharacteristic
326C42C2×C22⋊D1311yescharacteristic
327C42C23×D1311yescharacteristic
328C13#1925511yescharacteristic, complemented, Sylow
329C23—22no—
330C23—24no—
331C23—42no—
332C23—42no—
333C23—522no—
334C23#8818411yescharacteristic
335Q8—522no—
336Q8—522no—
337D4—22no—
338D4—24no—
339D4—522no—
340D4—522no—
341D4—522no—
342D4—522no—
343D4—1042no—
344D4—1044no—
345D4C2×D10414yes—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—41no—
350C2×C4—44no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—522no—
355C2×C4—1044no—
356C2×C4C2×D10412yes—
357C2×C4#8815812yes—
358C2×C4#8818411yescharacteristic
359C2×C4#8818411yescharacteristic
360C2×C4#8818411yescharacteristic
361C2×C4C22×D5211yescharacteristic
362C2×C4C2×#612711yescharacteristic
363C2×C4C22×C22⋊D1311yescharacteristic
364C8—21no—
365C8—21no—
366C8—21no—
367C8—42no—
368C8—524no—
369C8#8818612yescomplemented
370C22—21no—
371C22—21no—
372C22—24no—
373C22—48no—
374C22—42no—
375C22—42no—
376C22—1042no—
377C22—1042no—
378C22—1042no—
379C22#1171877612yes—
380C22C2×#8818411yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—42no—
385C4—1042no—
386C4#1171877612yes—
387C4C22×D10411yescharacteristic
388C4C2×#8815811yescharacteristic
389C4C2×#8818611yescharacteristic
390C4#1171952711yescharacteristic
391C2—22no—
392C2—44no—
393C2—2082no—
394C2#1312430011yescharacteristic
395C2C2×#1171877611yescharacteristic
396C2#1312455611yescharacteristic
subgroupG/H
centerC22C2×#88184
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C8×D4×C13C2
socleC22×C13C2×#121
hypercenterC2×C8×D4D13
hypocenterC13#19255
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. #13125415C2semidirect
2. #13124300C2semidirect
3. #13114273C2semidirect
4. #13114225C2semidirect
5. #13114191C2semidirect
6. #13113595C2semidirect
7. #13113511C2semidirect
8. C2×C8×D4×C13C2semidirect
27. #11718356C22semidirect
28. #11718355C22semidirect
31. #11718343C22semidirect
32. #11718078C22semidirect
33. #11718077C22semidirect
34. #11718050C22semidirect
35. #11718050C22semidirect
85. C2×D4×C13D8semidirect
133. C2×C8×D4D13semidirect
178. C8×C13AGL(1,ℤ/8)semidirect
289. C2×D4D104semidirect
328. C13#19255semidirect
369. C8#88186semidirect

Maximal subgroups

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

subgroupindex
#131254152
#131243002
#131142732
#131142252
#131141912
#131135952
#131135112
C2×C8×D4×C132
#1925513