Finite Group Databasebeta

← #13124513

Subgroups — #13124513

Order 1664.

504 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88165C211yesmaximal, characteristic, complemented
2C2×#88161C211yesmaximal, characteristic, complemented
3#11719313C211yesmaximal, characteristic, complemented
4#11719312C211yesmaximal, characteristic, complemented
5C13×#469C211yesmaximal, characteristic, complemented
6#11718818C211yesmaximal, characteristic, complemented
7#11718795C211yesmaximal, characteristic, complemented
8#11718702C211yesmaximal, characteristic, complemented
9#11718699C211yesmaximal, characteristic, complemented
10#11718525C211yesmaximal, characteristic, complemented
11#11718522C211yesmaximal, characteristic, complemented
12#11718443C211yesmaximal, characteristic, complemented
13#11718441C211yesmaximal, characteristic, complemented
14#11718433C211yesmaximal, characteristic, complemented
15D13×#102C211yesmaximal, characteristic, complemented
16C2×#6129C2211yescharacteristic
17C2×D4×D13C2211yescharacteristic
18C2×#6127C2211yescharacteristic
19C2×C13×D8C2211yescharacteristic
20C2×C13×M16C2211yescharacteristic, complemented
21C13×#121C2211yescharacteristic
22C13×#121C2211yescharacteristic, complemented
23#88194—21no—
24#88193—21no—
25#88192—21no—
26#88192C2211yescharacteristic
27#88192C2211yescharacteristic, complemented
28#88191—21no—
29C2×#6105C2211yescharacteristic
30C2×#6104C2211yescharacteristic
31#88184C2211yescharacteristic
32#88178C2211yescharacteristic, complemented
33C22×#1055C2211yescharacteristic, complemented
34#88165—24no—
35#88161—24no—
36C2×#6095C2211yescharacteristic
37C2×#6094C2211yescharacteristic
38C2×#6094C2211yescharacteristic, complemented
39C2×C8×D13C2211yescharacteristic
40C2×C8×D13C2211yescharacteristic, complemented
41#88151C2211yescharacteristic, complemented
42#88149C2211yescharacteristic
43#88146C2211yescharacteristic
44C4⋊C4×D13C2211yescharacteristic
45#88139—21no—
46#88138—21no—
47#88136—21no—
48#88132—21no—
49C13×#106C2211yescharacteristic, complemented
50C13×#102C2211yescharacteristic
51C13×#102C2211yescharacteristic, complemented
52#88072C2211yescharacteristic
53#88072C2211yescharacteristic, complemented
54#88061C2211yescharacteristic
55#88058C2211yescharacteristic, complemented
56#88056C2211yescharacteristic, complemented
57#88050C2211yescharacteristic, complemented
58#88049C2211yescharacteristic
59#88048C2211yescharacteristic, complemented
60#88047C2211yescharacteristic, complemented
61C23×D13—21no—
62C2×D4×C13—21no—
63C2×D4×C13—21no—
64C2×D4×C13C2311yescharacteristic
65C2×D4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C2×C22⋊D13—21no—
68C2×C22⋊D13—21no—
69C2×C22⋊D13—21no—
70C2×C22⋊D13—21no—
71C2×C22⋊D13—21no—
72C2×C22⋊D13D411yescharacteristic
73C2×C22⋊D13D411yescharacteristic
74C22×Dic13—21no—
75#6129—22no—
76#6129—22no—
77D4×D13—22no—
78D4×D13—22no—
79#6127—22no—
80#6127—22no—
81C2×D52—21no—
82C2×D52D411yescharacteristic
83C2×D52C2311yescharacteristic
84C2×C4×D13—21no—
85C2×C4×D13C2311yescharacteristic
86C2×C4×D13C2311yescharacteristic
87C2×Dic26D411yescharacteristic
88C2×Dic26C2311yescharacteristic
89C13×D8—22no—
90C13×M16—22no—
91C2×C8×C13C2311yescharacteristic
92C2×C8×C13C2311yescharacteristic
93C13×C4⋊C4C2311yescharacteristic
94C13×C4⋊C4C2311yescharacteristic
95C13×C22⋊C4—21no—
96C13×C22⋊C4—21no—
97C22⋊Dic13—21no—
98C22⋊Dic13—21no—
99C22⋊Dic13—21no—
100#6105—22no—
101#6104—22no—
102#6103—21no—
103#6103—21no—
104#6103—21no—
105#6103—21no—
106C4⋊Dic13—21no—
107C4⋊Dic13C2311yescharacteristic
108C4⋊Dic13C2311yescharacteristic
109#6101—21no—
110#6101—21no—
111C4×Dic13—21no—
112C2×#1055—22no—
113C2×#1055C2311yescharacteristic
114C2×#1055C2311yescharacteristic
115#6095—22no—
116#6094—22no—
117#6094D414yescomplemented
118C8×D13—22no—
119C8×D13—22no—
120#3062—131nomaximal, Sylow
121C23×C13—21no—
122C23×C13—21no—
123C23×C13C2×D411yescharacteristic
124C22×D13—21no—
125C22×D13—42no—
126C22×D13—81no—
127C22×D13—81no—
128C22×D13C2×D411yescharacteristic
129C22×D13C2×D411yescharacteristic
130D4×C13—21no—
131D4×C13—21no—
132D4×C13—21no—
133D4×C13—21no—
134D4×C13—81no—
135D4×C13—81no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13C2×D411yescharacteristic
141C2×C4×C13C2411yescharacteristic
142C22⋊D13—22no—
143C22⋊D13—22no—
144C22⋊D13—42no—
145C22⋊D13—42no—
146C22⋊D13—81no—
147C22⋊D13—81no—
148C22⋊D13—81no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—42no—
153C2×Dic13C2×D411yescharacteristic
154C2×Dic13C2×D411yescharacteristic
155D52—22no—
156D52—21no—
157D52—21no—
158D52—81no—
159C4×D13—21no—
160C4×D13—21no—
161C4×D13—81no—
162C4×D13C2×D412yes—
163C4×D13#4112yes—
164Dic26—22no—
165Dic26—21no—
166Dic26—21no—
167C8×C13—21no—
168C8×C13C2×D412yes—
169#1055—21no—
170#1055C2×D412yes—
171C2×AGL(1,ℤ/8)—131no—
172C2×#131—131no—
173#537—131no—
174#535—131no—
175#469—131no—
176#469D1311yescharacteristic, complemented
177#468—131no—
178#468—131no—
179#466—131no—
180#466—131no—
181#465—131no—
182#465—131no—
183#428—131no—
184#416—131no—
185C2×#102—131no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13—41no—
192C22×C13—41no—
193C22×C13—41no—
194C22×C13—41no—
195C22×C13C22×D411yescharacteristic
196C2×D13—21no—
197C2×D13—21no—
198C2×D13—21no—
199C2×D13—21no—
200C2×D13—21no—
201C2×D13—41no—
202C2×D13—41no—
203C2×D13—41no—
204C2×D13—84no—
205C2×D13#12112yes—
206C4×C13—21no—
207C4×C13—41no—
208C4×C13—41no—
209C4×C13C22×D411yescharacteristic
210C4×C13C2×#4111yescharacteristic
211Dic13—21no—
212Dic13—41no—
213Dic13—41no—
214Dic13—41no—
215Dic13#12112yes—
216C2×#41—131no—
217C2×#41—131no—
218C22×D4—131no—
219AGL(1,ℤ/8)—264no—
220C2×SD16—131no—
221C2×SD16—131no—
222C2×D8—131no—
223C2×D8C2×D1311yescharacteristic
224#131—264no—
225C2×M16—131no—
226C2×M16—131no—
227C2×M16C2×D1311yescharacteristic, complemented
228C22×C8—131no—
229C22×C8—131no—
230C22×C8—131no—
231#127—261no—
232#124—261no—
233C22⋊Q8—131no—
234C22⋊Q8—131no—
235C22⋊Q8—261no—
236#121—131no—
237#121—131no—
238#121—131no—
239#121—131no—
240#121—261no—
241#121—261no—
242#121—261no—
243#121C2×D1311yescharacteristic
244#121C2×D1311yescharacteristic, complemented
245#120—261no—
246#120—261no—
247#117—131no—
248C2×C4⋊C4—131no—
249#107—131no—
250#107—131no—
251#106—131no—
252#106C2×D1311yescharacteristic, complemented
253#103—131no—
254#103—131no—
255#102—131no—
256#102—131no—
257#102—131no—
258#102—131no—
259#102C2×D1311yescharacteristic
260#102C2×D1311yescharacteristic, complemented
261C2×C13—41no—
262C2×C13—81no—
263C2×C13—81no—
264C2×C13C2×#12111yescharacteristic
265C2×C13#57611yescharacteristic
266C2×C13#57711yescharacteristic
267D13—22no—
268D13—41no—
269D13—81no—
270C24—261no—
271#41—262no—
272#41—262no—
273#41—262no—
274#41—262no—
275C2×Q8—131no—
276C2×Q8—131no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—131no—
280C2×D4—131no—
281C2×D4—131no—
282C2×D4—131no—
283C2×D4—261no—
284C2×D4—262no—
285C2×D4—262no—
286C2×D4—261no—
287C2×D4—261no—
288C2×D4—261no—
289C2×D4—261no—
290C2×D4—261no—
291C2×D4C22×D1311yescharacteristic
292C2×D4C22×D1311yescharacteristic
293C22×C4—131no—
294C22×C4—131no—
295C22×C4—261no—
296C22×C4—261no—
297C22×C4C22×D1311yescharacteristic
298SD16—262no—
299SD16—262no—
300D8—22no—
301D8—262no—
302M16—22no—
303M16—134no—
304M16—262no—
305C2×C8—131no—
306C2×C8—131no—
307C2×C8—262no—
308C2×C8—262no—
309C2×C8—262no—
310C2×C8C22×D1311yescharacteristic
311C2×C8C22×D1311yescharacteristic
312C4⋊C4—131no—
313C4⋊C4—131no—
314C4⋊C4—261no—
315C4⋊C4—261no—
316C4⋊C4—261no—
317C4⋊C4C22×D1311yescharacteristic
318C4⋊C4C22×D1311yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—261no—
322C22⋊C4—261no—
323C22⋊C4—261no—
324C22⋊C4—261no—
325C22⋊C4—261no—
326C22⋊C4—261no—
327C22⋊C4—261no—
328C42—261no—
329C13#306211yescharacteristic, complemented, Sylow
330C23—21no—
331C23—21no—
332C23—131no—
333C23—131no—
334C23—261no—
335C23—522no—
336C23—1041no—
337C23—1041no—
338C23D4×D1311yescharacteristic
339Q8—262no—
340Q8—261no—
341Q8—261no—
342D4—21no—
343D4—21no—
344D4—21no—
345D4—21no—
346D4—81no—
347D4—81no—
348D4—262no—
349D4—262no—
350D4—262no—
351D4—261no—
352D4—261no—
353D4—522no—
354D4—522no—
355D4—1041no—
356D4—1041no—
357D4—1041no—
358D4—1041no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—131no—
364C2×C4—132no—
365C2×C4—132no—
366C2×C4—131no—
367C2×C4—261no—
368C2×C4—261no—
369C2×C4—261no—
370C2×C4—261no—
371C2×C4—261no—
372C2×C4—522no—
373C2×C4—1041no—
374C2×C4D4×D1311yescharacteristic
375C2×C4C23×D1311yescharacteristic
376C8—21no—
377C8—132no—
378C8—261no—
379C8D4×D1312yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—132no—
390C22—261no—
391C22—261no—
392C22—261no—
393C22—261no—
394C22—261no—
395C22—521no—
396C22—521no—
397C22—521no—
398C22—1044no—
399C22C2×D4×D1311yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—132no—
404C4—261no—
405C4—521no—
406C4—521no—
407C4—521no—
408C4C2×D4×D1311yescharacteristic
409C4#41×D1311yescharacteristic
410C2—41no—
411C2—81no—
412C2—81no—
413C2—262no—
414C2—521no—
415C2—1041no—
416C2D13×#12111yescharacteristic
417C2#1171947911yescharacteristic
418C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#469C2
socleC22×C13C22×D4
hypercenter#469D13
hypocenterC13#3062
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×#88165C2semidirect
2. C2×#88161C2semidirect
3. #11719313C2semidirect
4. #11719312C2semidirect
5. C13×#469C2semidirect
6. #11718818C2semidirect
7. #11718795C2semidirect
8. #11718702C2semidirect
9. #11718699C2semidirect
10. #11718525C2semidirect
11. #11718522C2semidirect
12. #11718443C2semidirect
13. #11718441C2semidirect
14. #11718433C2semidirect
15. D13×#102C2semidirect
20. C2×C13×M16C22semidirect
22. C13×#121C22semidirect
27. #88192C22semidirect
32. #88178C22semidirect
33. C22×#1055C22semidirect
38. C2×#6094C22semidirect
40. C2×C8×D13C22semidirect
41. #88151C22semidirect
49. C13×#106C22semidirect
51. C13×#102C22semidirect
53. #88072C22semidirect
55. #88058C22semidirect
56. #88056C22semidirect
57. #88050C22semidirect
59. #88048C22semidirect
60. #88047C22semidirect
117. #6094D4semidirect
176. #469D13semidirect
227. C2×M16C2×D13semidirect
244. #121C2×D13semidirect
252. #106C2×D13semidirect
260. #102C2×D13semidirect
329. C13#3062semidirect

Maximal subgroups

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

subgroupindex
C2×#881652
C2×#881612
#117193132
#117193122
C13×#4692
#117188182
#117187952
#117187022
#117186992
#117185252
#117185222
#117184432
#117184412
#117184332
D13×#1022
#306213