Finite Group Databasebeta

← #16018344

Subgroups — #16018344

Order 3328.

918 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 918 conjugacy classes of subgroups — too many to draw. Only its 179 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×#11718572C214yesmaximal, complemented
2#13125263C211yesmaximal, characteristic, complemented
3D13×#493C211yesmaximal, characteristic, complemented
4#13117099C214yesmaximal, complemented
5#13117092C211yesmaximal, characteristic, complemented
6#13117091C211yesmaximal, characteristic, complemented
7#13117085C211yesmaximal, characteristic, complemented
8C4×#88038C211yesmaximal, characteristic, complemented
9C13×#2246C211yesmaximal, characteristic, complemented
10C2×#88166—21no—
11C2×#88166C2212yes—
12C2×D8×D13—21no—
13C2×D8×D13C2212yes—
14#11719421—21no—
15D13×#127—21no—
16C2×C13×D16C2214yescomplemented
17C13×#493C2211yescharacteristic
18C13×#493C2211yescharacteristic, complemented
19#11718816—21no—
20#11718816C2212yescomplemented
21#11718812—21no—
22#11718812C2212yes—
23C2×#88067C2214yescomplemented
24C2×#88066C2214yescomplemented
25#11718737—21no—
26#11718734—21no—
27#11718572—216no—
28C2×#88040C2214yescomplemented
29C2×#88038C2212yes—
30#11718360C2211yescharacteristic, complemented
31#11718356C2211yescharacteristic
32C4×C8×D13C2211yescharacteristic
33C4×C13×C16C2211yescharacteristic, complemented
34#11718094C2212yescomplemented
35C4×#6090C2211yescharacteristic, complemented
36C2×#6129—22no—
37C2×D4×D13—22no—
38C2×D4×D13—42no—
39C2×C13×D8—21no—
40C2×C13×D8—21no—
41C2×C13×D8C2312yes—
42C2×C13×D8C2312yes—
43C13×#127—21no—
44C13×#127—21no—
45#88194—22no—
46#88194—42no—
47#88192—42no—
48#88190—22no—
49D4×Dic13—42no—
50C2×#6105—22no—
51C2×#6105—22no—
52C2×#6104—22no—
53C2×#6104—22no—
54#88166—28no—
55#88166—44no—
56D8×D13—28no—
57D8×D13—44no—
58C2×Dic52—21no—
59C2×Dic52C2312yes—
60C2×D104—21no—
61C2×D104C2312yes—
62C2×C8×D13D411yescharacteristic
63C2×C8×D13C2311yescharacteristic
64#88128—21no—
65C42×D13D411yescharacteristic
66#88123—21no—
67C13×D16—28no—
68C2×C13×C16C2312yes—
69C4×C8×C13C2311yescharacteristic
70#88067—28no—
71#88066—28no—
72C8×Dic13D411yescharacteristic
73C8×Dic13C2311yescharacteristic
74C2×#6090C2312yes—
75C4×#1055D411yescharacteristic
76#88040—28no—
77#88038D418yescomplemented
78#33717—131nomaximal, Sylow
79C23×D13—42no—
80C2×D4×C13—22no—
81C2×D4×C13—22no—
82C2×D4×C13—42no—
83C2×D4×C13—42no—
84C2×C22⋊D13—42no—
85C2×C22⋊D13—44no—
86C2×C22⋊D13—42no—
87C22×Dic13—42no—
88#6129—44no—
89#6129—44no—
90D4×D13—44no—
91D4×D13—44no—
92D4×D13—88no—
93C2×D52—22no—
94C2×D52—42no—
95C2×C4×D13D812yes—
96C2×C4×D13C2×D411yescharacteristic
97C2×Dic26—22no—
98C13×D8—24no—
99C13×D8—24no—
100C13×D8—42no—
101C13×D8—42no—
102C2×C8×C13C2×D411yescharacteristic
103C2×C8×C13C2411yescharacteristic
104C42×C13C2×D411yescharacteristic
105C22⋊Dic13—44no—
106#6105—44no—
107#6105—44no—
108#6104—44no—
109#6104—44no—
110C4⋊Dic13—42no—
111C4×Dic13D812yes—
112C4×Dic13C2×D411yescharacteristic
113C2×#1055C2×D411yescharacteristic
114C2×#1055C2×D411yescharacteristic
115Dic52—24no—
116Dic52—42no—
117D104—24no—
118D104—42no—
119C8×D13D814yes—
120C8×D13C2×D414yes—
121C13×C16C2×D414yescomplemented
122#6090C2×D414yescomplemented
123C2×#509—134no—
124#3147—131no—
125C2×#493—131no—
126#2250—134no—
127#2248—131no—
128#2248—131no—
129#2246—131no—
130#2246D1311yescharacteristic, complemented
131C4×M32—131no—
132C23×C13—42no—
133C23×C13—42no—
134C22×D13—42no—
135C22×D13—88no—
136C22×D13—84no—
137C22×D13C2×D811yescharacteristic
138D4×C13—42no—
139D4×C13—42no—
140D4×C13—42no—
141D4×C13—42no—
142D4×C13—84no—
143D4×C13—84no—
144C2×C4×C13C2×D812yes—
145C2×C4×C13C22×D411yescharacteristic
146C22⋊D13—88no—
147C22⋊D13—84no—
148C22⋊D13—84no—
149C2×Dic13—42no—
150C2×Dic13—84no—
151C2×Dic13C2×D812yes—
152C2×Dic13C2×D811yescharacteristic
153D52—42no—
154D52—42no—
155D52—84no—
156C4×D13—24no—
157C4×D13#12712yes—
158C4×D13C2×D812yes—
159Dic26—42no—
160Dic26—42no—
161C8×C13C2×D812yes—
162C8×C13C22×D412yes—
163#1055#12712yes—
164#1055C2×D812yes—
165C2×#135—132no—
166C2×#135—261no—
167C22×D8—132no—
168C22×D8—261no—
169#532—261no—
170C2×#127—261no—
171#509—2616no—
172C2×SD32—134no—
173C2×SD32—134no—
174C2×D16—134no—
175C2×D16C2×D1314yescomplemented
176C2×M32—132no—
177#495—132no—
178#495—261no—
179#494—131no—
180#493—132no—
181#493—131no—
182#493—261no—
183#493—261no—
184#493C2×D1311yescharacteristic
185#493C2×D1311yescharacteristic, complemented
186#492—261no—
187C2×C4×C8—131no—
188#346—132no—
189C4×C16—131no—
190C4×C16C2×D1311yescharacteristic, complemented
191C22×C13—82no—
192C22×C13—82no—
193C22×C13—84no—
194C22×C13—84no—
195C22×C13C22×D811yescharacteristic
196C2×D13—22no—
197C2×D13—82no—
198C2×D13—84no—
199C2×D13—168no—
200C2×D13#49312yes—
201C4×C13#50914yescomplemented
202C4×C13C2×#12711yescharacteristic
203C4×C13C22×D811yescharacteristic
204Dic13—22no—
205Dic13—82no—
206Dic13#49312yes—
207C2×#41—262no—
208C22×D4—262no—
209C22×D4—522no—
210#135—268no—
211#135—524no—
212C2×Q16—132no—
213C2×Q16—261no—
214C2×SD16—262no—
215C2×SD16—262no—
216C2×D8—21no—
217C2×D8—21no—
218C2×D8—132no—
219C2×D8—268no—
220C2×D8—262no—
221C2×D8—262no—
222C2×D8—261no—
223C2×D8—524no—
224C2×D8C22×D1312yes—
225C2×D8C22×D1312yes—
226C22×C8—131no—
227C22×C8—131no—
228C4⋊Q8—261no—
229#127—21no—
230#127—21no—
231#127—262no—
232#127—261no—
233#127—522no—
234#124—262no—
235#121—522no—
236C4×D4—522no—
237C2×C42—131no—
238SD32—268no—
239SD32—268no—
240D16—28no—
241D16—268no—
242M32—138no—
243C2×C16—132no—
244C2×C16C22×D1312yes—
245C4×C8—131no—
246C4×C8—131no—
247C4×C8—131no—
248C4×C8C22×D1311yescharacteristic
249C2×C13—162no—
250C2×C13—162no—
251C2×C13C2×#49311yescharacteristic
252C2×C13C2×#50912yes—
253D13—22no—
254D13—162no—
255C24—522no—
256#41—524no—
257#41—524no—
258C2×Q8—262no—
259C2×D4—22no—
260C2×D4—22no—
261C2×D4—42no—
262C2×D4—42no—
263C2×D4—262no—
264C2×D4—524no—
265C2×D4—524no—
266C2×D4—524no—
267C2×D4—522no—
268C2×D4—522no—
269C2×D4—522no—
270C2×D4—1048no—
271C22×C4—131no—
272C22×C4—132no—
273C22×C4—522no—
274Q16—264no—
275Q16—522no—
276SD16—524no—
277SD16—524no—
278D8—24no—
279D8—24no—
280D8—42no—
281D8—42no—
282D8—264no—
283D8—524no—
284D8—524no—
285D8—522no—
286C2×C8—131no—
287C2×C8—131no—
288C2×C8—134no—
289C2×C8—134no—
290C2×C8D4×D1311yescharacteristic
291C2×C8C23×D1311yescharacteristic
292C4⋊C4—522no—
293C22⋊C4—524no—
294C42—132no—
295C42—131no—
296C42D4×D1311yescharacteristic
297C16—134no—
298C16D4×D1314yescomplemented
299C13#3371711yescharacteristic, complemented, Sylow
300C23—42no—
301C23—42no—
302C23—131no—
303C23—522no—
304C23—1044no—
305C23—1048no—
306Q8—522no—
307Q8—522no—
308D4—42no—
309D4—42no—
310D4—42no—
311D4—42no—
312D4—84no—
313D4—84no—
314D4—522no—
315D4—522no—
316D4—1044no—
317D4—1048no—
318D4—1044no—
319D4—1044no—
320C2×C4—131no—
321C2×C4—132no—
322C2×C4—132no—
323C2×C4—132no—
324C2×C4—264no—
325C2×C4—522no—
326C2×C4—1044no—
327C2×C4D8×D1312yes—
328C2×C4C2×D4×D1311yescharacteristic
329C8—132no—
330C8—132no—
331C8D8×D1312yes—
332C8C2×D4×D1312yes—
333C22—84no—
334C22—84no—
335C22—82no—
336C22—82no—
337C22—132no—
338C22—262no—
339C22—1044no—
340C22—1042no—
341C22—2088no—
342C22C2×D8×D1311yescharacteristic
343C4—132no—
344C4—262no—
345C4—1042no—
346C4#1171857214yescomplemented
347C4D13×#12711yescharacteristic
348C4C2×D8×D1311yescharacteristic
349C2—162no—
350C2—162no—
351C2—262no—
352C2—2082no—
353C2D13×#49311yescharacteristic
354C2C2×#1171857212yes—
subgroupG/H
centerC22C2×D8×D13
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#2246C2
socleC22×C13C22×D8
hypercenter#2246D13
hypocenterC13#33717
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2246

Complements

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

NH ≅ G/Ntype
1. C2×#11718572C2semidirect
2. #13125263C2semidirect
3. D13×#493C2semidirect
4. #13117099C2semidirect
5. #13117092C2semidirect
6. #13117091C2semidirect
7. #13117085C2semidirect
8. C4×#88038C2semidirect
9. C13×#2246C2semidirect
16. C2×C13×D16C22semidirect
18. C13×#493C22semidirect
20. #11718816C22semidirect
23. C2×#88067C22semidirect
24. C2×#88066C22semidirect
28. C2×#88040C22semidirect
30. #11718360C22semidirect
33. C4×C13×C16C22semidirect
34. #11718094C22semidirect
35. C4×#6090C22semidirect
77. #88038D4semidirect
121. C13×C16C2×D4semidirect
122. #6090C2×D4semidirect
130. #2246D13semidirect
175. C2×D16C2×D13semidirect
185. #493C2×D13semidirect
190. C4×C16C2×D13semidirect
201. C4×C13#509semidirect
298. C16D4×D13semidirect
299. C13#33717semidirect
346. C4#11718572semidirect

Maximal subgroups

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

subgroupindex
C2×#117185722
#131252632
D13×#4932
#131170992
#131170922
#131170912
#131170852
C4×#880382
C13×#22462
#3371713