Finite Group Databasebeta

← #13124142

Subgroups — #13124142

Order 1664.

764 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 764 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88256C211yesmaximal, characteristic, complemented
2C2×#88204C211yesmaximal, characteristic, complemented
3C2×#88162C211yesmaximal, characteristic, complemented
4#11719215C211yesmaximal, characteristic, complemented
5C13×#417C211yesmaximal, characteristic, complemented
6#11718790C211yesmaximal, characteristic, complemented
7C2×#88049C211yesmaximal, characteristic, complemented
8#11718472C212yesmaximal, complemented
9#11718471C212yesmaximal, complemented
10#11718437C212yesmaximal, complemented
11#11718434C212yesmaximal, complemented
12C2×C13×#41C2211yescharacteristic
13#88256—24no—
14#88256—24no—
15C2×#6131C2212yes—
16C2×D4×D13—22no—
17C2×D4×D13C2212yes—
18C2×#6127—21no—
19C2×#6127C2211yescharacteristic
20C2×#6127C2211yescharacteristic, complemented
21C22×D52—21no—
22C22×D52C2211yescharacteristic
23C2×C13×M16C2211yescharacteristic, complemented
24C2×C13×C4⋊C4C2211yescharacteristic, complemented
25#88204—24no—
26C2×#6107C2211yescharacteristic, complemented
27C2×#6106C2211yescharacteristic, complemented
28C2×#6105C2211yescharacteristic, complemented
29C2×#6104C2211yescharacteristic, complemented
30#88184—22no—
31C22×#1055C2211yescharacteristic, complemented
32#88162—24no—
33C2×D104C2212yescomplemented
34C2×#6095C2212yescomplemented
35#88151—21no—
36#88151C2212yescomplemented
37#88149—21no—
38#88149C2212yescomplemented
39C13×#103C2212yescomplemented
40C13×#102C2212yescomplemented
41#88060C2212yescomplemented
42#88060C2212yescomplemented
43#88049C2212yescomplemented
44#88049C2212yescomplemented
45C23×D13—21no—
46C23×D13—22no—
47C13×#41—22no—
48C13×#41D414yescomplemented
49C2×Q8×C13C2311yescharacteristic
50C2×D4×C13—21no—
51C2×D4×C13C2311yescharacteristic
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13C2311yescharacteristic
55C2×C22⋊D13—21no—
56C2×C22⋊D13—22no—
57C2×C22⋊D13D412yes—
58#6131—24no—
59#6131—24no—
60D4×D13—216no—
61D4×D13—24no—
62D4×D13—24no—
63#6127—28no—
64#6127—22no—
65#6127—22no—
66#6127—22no—
67#6127—22no—
68C2×D52—28no—
69C2×D52—22no—
70C2×D52—21no—
71C2×D52—22no—
72C2×D52—22no—
73C2×D52D411yescharacteristic
74C2×D52D414yescomplemented
75C2×D52C2311yescharacteristic
76C2×D52C2312yes—
77C2×C4×D13—22no—
78C2×C4×D13—21no—
79C2×C4×D13C2312yes—
80C2×Dic26D411yescharacteristic
81C2×Dic26C2311yescharacteristic
82C13×M16—22no—
83C2×C8×C13C2312yes—
84C13×C4⋊C4—21no—
85C13×C4⋊C4C2312yes—
86#6107—22no—
87#6106—22no—
88#6105—22no—
89#6104—22no—
90#6103—22no—
91#6103—22no—
92C4⋊Dic13—22no—
93C2×#1055—22no—
94C2×#1055C2311yescharacteristic
95C2×#1055C2311yescharacteristic
96D104—24no—
97#6095—24no—
98#3012—131nomaximal, Sylow
99C23×C13—21no—
100C23×C13C2×D411yescharacteristic
101C22×D13—22no—
102C22×D13—28no—
103C22×D13—24no—
104C22×D13—21no—
105C22×D13—82no—
106C22×D13—82no—
107C22×D13—81no—
108C22×D13—81no—
109C22×D13C2×D412yes—
110Q8×C13—21no—
111Q8×C13C2×D412yes—
112D4×C13—24no—
113D4×C13—21no—
114D4×C13C2×D412yes—
115C2×C4×C13—21no—
116C2×C4×C13—24no—
117C2×C4×C13—22no—
118C2×C4×C13—81no—
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2×D412yes—
121C2×C4×C13C2×D412yes—
122C2×C4×C13C2411yescharacteristic
123C22⋊D13—28no—
124C22⋊D13—24no—
125C22⋊D13—42no—
126C2×Dic13—21no—
127C2×Dic13C2×D412yes—
128D52—28no—
129D52—22no—
130D52—24no—
131D52—22no—
132D52—21no—
133D52—21no—
134D52—82no—
135D52C2×D414yes—
136C4×D13—28no—
137C4×D13—22no—
138C4×D13—22no—
139C4×D13—42no—
140Dic26—22no—
141Dic26—21no—
142Dic26—21no—
143C8×C13—22no—
144#1055—21no—
145#1055—21no—
146C2×H(5,𝔽2)—131no—
147C2×AGL(1,ℤ/8)—131no—
148C2×#135—131no—
149#537—131no—
150#452—132no—
151#450—132no—
152#449—132no—
153#447—132no—
154#417D1311yescharacteristic, complemented
155C2×#102—131no—
156#408—131no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—22no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13#12012yes—
163C22×C13C22×D411yescharacteristic
164C2×D13—22no—
165C2×D13—24no—
166C2×D13—22no—
167C2×D13—22no—
168C2×D13—42no—
169C2×D13—42no—
170C2×D13—41no—
171C2×D13—41no—
172C2×D13—41no—
173C2×D13—84no—
174C2×D13—88no—
175C4×C13—22no—
176C4×C13—42no—
177C4×C13#12012yes—
178C4×C13C22×D411yescharacteristic
179C4×C13C22×D411yescharacteristic
180Dic13—22no—
181Dic13—41no—
182H(5,𝔽2)—264no—
183H(5,𝔽2)—264no—
184C2×#41—131no—
185C2×#41—132no—
186C2×#41—131no—
187C2×#41—261no—
188C2×#41C2×D1311yescharacteristic
189C22×D4—132no—
190C22×D4—131no—
191C22×D4—261no—
192C22×D4—262no—
193AGL(1,ℤ/8)—264no—
194#135—264no—
195C2×Q16—131no—
196C2×SD16—131no—
197C2×SD16—131no—
198C2×SD16—132no—
199C2×D8—131no—
200C2×D8—132no—
201C2×M16C2×D1311yescharacteristic, complemented
202C22×C8—131no—
203C22⋊Q8—132no—
204C22⋊Q8—261no—
205#121—132no—
206#121—261no—
207#121—262no—
208C2×C4⋊C4C2×D1311yescharacteristic, complemented
209#103C2×D1312yescomplemented
210#102—132no—
211#102—132no—
212#102C2×D1312yescomplemented
213C22⋊C8—132no—
214C22⋊C8—132no—
215C2×C13—22no—
216C2×C13—42no—
217C2×C13C2×#12011yescharacteristic
218C2×C13#57611yescharacteristic
219C2×C13#57711yescharacteristic
220D13—42no—
221D13—44no—
222D13—81no—
223C24—262no—
224C24—261no—
225#41—22no—
226#41—268no—
227#41—264no—
228#41—264no—
229#41—262no—
230#41—262no—
231#41—262no—
232#41—262no—
233#41D5214yescomplemented
234C2×Q8—131no—
235C2×Q8—131no—
236C2×Q8C22×D1311yescharacteristic
237C2×D4—21no—
238C2×D4—132no—
239C2×D4—134no—
240C2×D4—131no—
241C2×D4—132no—
242C2×D4—131no—
243C2×D4—262no—
244C2×D4—268no—
245C2×D4—262no—
246C2×D4—262no—
247C2×D4—264no—
248C2×D4—2616no—
249C2×D4—264no—
250C2×D4—261no—
251C2×D4—262no—
252C2×D4—261no—
253C2×D4C22×D1311yescharacteristic
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—132no—
257C22×C4—262no—
258C22×C4—261no—
259C22×C4C22×D1311yescharacteristic
260Q16—262no—
261SD16—264no—
262SD16—262no—
263SD16—262no—
264D8—264no—
265D8—262no—
266M16—22no—
267C2×C8—131no—
268C2×C8—131no—
269C2×C8—262no—
270C2×C8C22×D1312yes—
271C4⋊C4—21no—
272C4⋊C4—262no—
273C4⋊C4C22×D1312yes—
274C22⋊C4—262no—
275C22⋊C4—262no—
276C13#301211yescharacteristic, complemented, Sylow
277C23—21no—
278C23—132no—
279C23—268no—
280C23—262no—
281C23—264no—
282C23—261no—
283C23—1041no—
284C23—1041no—
285C23—1042no—
286C23—1042no—
287C23D4×D1311yescharacteristic
288Q8—21no—
289Q8—262no—
290Q8—261no—
291Q8—261no—
292Q8C2×D5212yes—
293D4—24no—
294D4—21no—
295D4—134no—
296D4—268no—
297D4—268no—
298D4—264no—
299D4—264no—
300D4—262no—
301D4—262no—
302D4—261no—
303D4—261no—
304D4—522no—
305D4—1042no—
306D4C2×D5212yes—
307C2×C4—21no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—81no—
311C2×C4—132no—
312C2×C4—268no—
313C2×C4—262no—
314C2×C4—262no—
315C2×C4—261no—
316C2×C4—522no—
317C2×C4C2×D5212yes—
318C2×C4D4×D1311yescharacteristic
319C2×C4D4×D1312yes—
320C2×C4C23×D1311yescharacteristic
321C8—22no—
322C8—261no—
323C8—261no—
324C22—21no—
325C22—21no—
326C22—22no—
327C22—41no—
328C22—41no—
329C22—264no—
330C22—262no—
331C22—262no—
332C22—262no—
333C22—522no—
334C22—522no—
335C22—521no—
336C22—521no—
337C22—521no—
338C22—1044no—
339C22—1048no—
340C22#8813612yes—
341C22C2×D4×D1311yescharacteristic
342C4—22no—
343C4—42no—
344C4—262no—
345C4—521no—
346C4#8813612yes—
347C4C22×D5211yescharacteristic
348C4C2×D4×D1311yescharacteristic
349C2—22no—
350C2—42no—
351C2—522no—
352C2—524no—
353C2—1041no—
354C2C2×#8813611yescharacteristic
355C2#1171947911yescharacteristic
356C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#417C2
socleC22×C13C22×D4
hypercenter#417D13
hypocenterC13#3012
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. C2×#88256C2semidirect
2. C2×#88204C2semidirect
3. C2×#88162C2semidirect
4. #11719215C2semidirect
5. C13×#417C2semidirect
6. #11718790C2semidirect
7. C2×#88049C2semidirect
8. #11718472C2semidirect
9. #11718471C2semidirect
10. #11718437C2semidirect
11. #11718434C2semidirect
20. C2×#6127C22semidirect
23. C2×C13×M16C22semidirect
24. C2×C13×C4⋊C4C22semidirect
26. C2×#6107C22semidirect
27. C2×#6106C22semidirect
28. C2×#6105C22semidirect
29. C2×#6104C22semidirect
31. C22×#1055C22semidirect
33. C2×D104C22semidirect
34. C2×#6095C22semidirect
36. #88151C22semidirect
38. #88149C22semidirect
39. C13×#103C22semidirect
40. C13×#102C22semidirect
41. #88060C22semidirect
42. #88060C22semidirect
43. #88049C22semidirect
44. #88049C22semidirect
48. C13×#41D4semidirect
74. C2×D52D4semidirect
154. #417D13semidirect
201. C2×M16C2×D13semidirect
208. C2×C4⋊C4C2×D13semidirect
209. #103C2×D13semidirect
212. #102C2×D13semidirect
233. #41D52semidirect
276. C13#3012semidirect

Maximal subgroups

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

subgroupindex
C2×#882562
C2×#882042
C2×#881622
#117192152
C13×#4172
#117187902
C2×#880492
#117184722
#117184712
#117184372
#117184342
#301213