Finite Group Databasebeta

← C2×#13128488 #16771087

Subgroups — C2×#13128488 #16771087

Order 3328.

11254 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88254C211yesmaximal, characteristic, complemented
2C23×Q8×D13C211yesmaximal, characteristic, complemented
3#13128488C2132yesmaximal, direct product factor
4C2×Q8×D52C218yesmaximal, complemented
5C2×#11719281C218yesmaximal, complemented
6C2×#11719231C216yesmaximal, complemented
7C2×#11719229C216yesmaximal, complemented
8C2×C13×#519C211yesmaximal, characteristic, complemented
9C23×Q8×C13C2211yescharacteristic
10C2×#88254—216no—
11C2×#88254C22116yescomplemented
12C22×#6131C2214yescomplemented
13C22×Q8×D13—216no—
14C22×Q8×D13C2218yes—
15C22×Q8×D13C22116yescomplemented
16C22×Q8×D13C2214yescomplemented
17C22×#6127C2216yes—
18C23×C4×D13C2213yes—
19C23×Dic26C2213yes—
20C13×#519C22116yescomplemented
21C2×C4×Q8×C13C2218yescomplemented
22C2×C13×#117C2216yes—
23#11719281C221128yescomplemented
24Q8×D52C221128yescomplemented
25#11719231C22196yescomplemented
26#11719229C22196yescomplemented
27C2×#88151C22112yes—
28C2×#88151C22124yescomplemented
29C2×#88149C22112yes—
30C2×#88140C22112yes—
31C2×#88136C2214yes—
32C2×#88129C22112yescomplemented
33C2×C4×D52C22124yes—
34C2×#88123C22112yescomplemented
35C24×D13C2311yescharacteristic
36C22×Q8×C13D4116yescomplemented
37C22×Q8×C13C2314yes—
38C22×Q8×C13C2318yes—
39C23×C4×C13C2313yes—
40C22×C22⋊D13C2314yes—
41C23×Dic13C2313yes—
42#88254—2128no—
43C2×#6131—232no—
44C2×#6131C23132yescomplemented
45C2×Q8×D13—264no—
46C2×Q8×D13—232no—
47C2×Q8×D13—2128no—
48C2×Q8×D13C23164yes—
49C2×Q8×D13C23132yescomplemented
50C2×#6127—248no—
51C2×#6127C23148yes—
52C22×D52C2318yes—
53C22×D52C2316yes—
54C22×C4×D13—224no—
55C22×C4×D13C23112yes—
56C22×C4×D13C23112yes—
57C22×C4×D13C23124yes—
58C22×Dic26—224no—
59C22×Dic26C2316yes—
60C22×Dic26C23112yes—
61C22×Dic26C23124yes—
62C4×Q8×C13C23164yescomplemented
63C13×#117C23148yes—
64C2×C13×C4⋊C4C23112yes—
65C2×C13×C22⋊C4C2314yes—
66C2×C42×C13C23112yes—
67C2×#6103C2318yes—
68C2×#6103C23124yes—
69C2×C4⋊Dic13C23124yes—
70#88151C23196yes—
71#88151C231192yescomplemented
72#88149C23196yes—
73#88140C23196yes—
74#88136C23132yes—
75#88129C23196yescomplemented
76C4×D52C231192yes—
77#88123C23196yescomplemented
78C2×#3486—131nomaximal, Sylow
79C24×C13C2411yescharacteristic
80C23×D13—24no—
81C23×D13—28no—
82C23×D13C2414yes—
83C23×D13C2414yes—
84C23×D13C2412yes—
85C2×Q8×C13C2×D4132yes—
86C2×Q8×C13C2×D4164yescomplemented
87C2×Q8×C13C24116yes—
88C22×C4×C13C2×D4124yes—
89C22×C4×C13C2418yes—
90C22×C4×C13C2416yes—
91C22×C4×C13C24112yes—
92C2×C22⋊D13—216no—
93C2×C22⋊D13C24116yes—
94C22×Dic13—212no—
95C22×Dic13C24112yes—
96C22×Dic13C2414yes—
97C22×Dic13C2416yes—
98#6131—2128no—
99Q8×D13—2256no—
100Q8×D13—2128no—
101#6127—2192no—
102C2×D52—232no—
103C2×D52—224no—
104C2×D52C24132yes—
105C2×D52C24124yes—
106C2×C4×D13—248no—
107C2×C4×D13—296no—
108C2×C4×D13—248no—
109C2×C4×D13C24148yes—
110C2×C4×D13C24148yes—
111C2×Dic26—248no—
112C2×Dic26—296no—
113C2×Dic26—224no—
114C2×Dic26C24124yes—
115C2×Dic26C24148yes—
116C13×C4⋊C4C24148yes—
117C13×C22⋊C4C24116yes—
118C42×C13C24148yes—
119#6103C24132yes—
120#6103C24196yes—
121C4⋊Dic13C24196yes—
122C22×2−1+4—131no—
123C24×Q8—131no—
124#3486—1332no—
125C2×D4×Q8—138no—
126C2×#548—138no—
127C2×#536—136no—
128C2×#525—136no—
129C2×#519D1311yescharacteristic, complemented
130C23×C13—24no—
131C23×C13C22×D414yes—
132C23×C13C2512yes—
133C23×C13C2511yescharacteristic
134C22×D13—232no—
135C22×D13—28no—
136C22×D13—24no—
137C22×D13—24no—
138C22×D13—216no—
139C22×D13—28no—
140C22×D13—216no—
141C22×D132−1+418yescomplemented
142C22×D13C2518yes—
143C22×D13C2514yes—
144Q8×C13C22×D4164yes—
145C2×C4×C13—216no—
146C2×C4×C13C22×D4124yes—
147C2×C4×C13C22×D4148yes—
148C2×C4×C13C25116yes—
149C2×C4×C13C25112yes—
150C22⋊D13—232no—
151C2×Dic13—224no—
152C2×Dic13—212no—
153C2×Dic13—28no—
154C2×Dic13C2518yes—
155C2×Dic13C25112yes—
156D52—264no—
157D52—248no—
158C4×D13—296no—
159C4×D13—296no—
160Dic26—296no—
161Dic26—248no—
162C2×2−1+4—1316no—
163C2×2−1+4—2616no—
164C22×#41—134no—
165C22×#41—136no—
166C23×Q8—138no—
167C23×Q8—1316no—
168C23×Q8—134no—
169C23×Q8—133no—
170C23×Q8—2616no—
171C23×Q8C2×D1311yescharacteristic
172C24×C4—133no—
173D4×Q8—13128no—
174#548—13128no—
175#536—1396no—
176C2×C4⋊Q8—1312no—
177C2×#124—1312no—
178#525—1396no—
179C2×#123—1312no—
180C2×C22⋊Q8—1312no—
181C2×C22⋊Q8—1324no—
182C2×#121—1312no—
183C2×#120—134no—
184#519C2×D13116yescomplemented
185C2×C4×Q8C2×D1318yescomplemented
186C2×C4×D4—1324no—
187C2×#117C2×D1316yes—
188C22×C13—24no—
189C22×C13—28no—
190C22×C13C23×D414yes—
191C22×C13C23×D412yes—
192C22×C13C2×2−1+414yes—
193C22×C13C2611yescharacteristic
194C2×D13—232no—
195C2×D13—24no—
196C2×D13—24no—
197C2×D13—216no—
198C2×D13—28no—
199C2×D13—216no—
200C2×D13—416no—
201C2×D13C2×2−1+418yescomplemented
202C4×C13—216no—
203C4×C13C23×D4124yes—
204Dic13—212no—
205Dic13—28no—
206C25—131no—
2072−1+4—26128no—
208C2×#41—1332no—
209C2×#41—1348no—
210C2×#41—2632no—
211C2×#41—2648no—
212C22×Q8—1364no—
213C22×Q8—1332no—
214C22×Q8—1312no—
215C22×Q8—136no—
216C22×Q8—1324no—
217C22×Q8—2664no—
218C22×Q8—2632no—
219C22×Q8—26128no—
220C22×Q8—2624no—
221C22×Q8D52116yescomplemented
222C22×Q8C22×D1314yes—
223C22×Q8C22×D1318yes—
224C22×D4—134no—
225C22×D4—138no—
226C22×D4—136no—
227C23×C4—133no—
228C23×C4—1312no—
229C23×C4—1312no—
230C23×C4—1324no—
231C23×C4—2624no—
232C23×C4C22×D1313yes—
233C4⋊Q8—1396no—
234#124—1396no—
235#123—1396no—
236C22⋊Q8—1396no—
237C22⋊Q8—13192no—
238#121—1396no—
239#120—1332no—
240C4×Q8C22×D13164yescomplemented
241C4×D4—13192no—
242#117C22×D13148yes—
243C2×C4⋊C4—1324no—
244C2×C4⋊C4C22×D13112yes—
245C2×C22⋊C4—138no—
246C2×C22⋊C4—1324no—
247C2×C22⋊C4C22×D1314yes—
248C2×C42C22×D13112yes—
249C2×C13—24no—
250C2×C13#348614yescomplemented
251C2×C13C24×D411yescharacteristic
252C2×C13C22×2−1+412yes—
253D13—28no—
254D13—48no—
255C24—132no—
256C24—134no—
257C24—134no—
258C24—268no—
259C24—264no—
260C24C23×D1311yescharacteristic
261#41—26128no—
262#41—26192no—
263C2×Q8—1348no—
264C2×Q8—1324no—
265C2×Q8—26256no—
266C2×Q8—26128no—
267C2×Q8—2648no—
268C2×Q8—2696no—
269C2×Q8—2624no—
270C2×Q8C2×D52132yes—
271C2×Q8C2×D52164yescomplemented
272C2×Q8C23×D13116yes—
273C2×D4—1316no—
274C2×D4—1332no—
275C2×D4—1324no—
276C2×D4—2632no—
277C2×D4—2616no—
278C2×D4—2624no—
279C22×C4—1312no—
280C22×C4—136no—
281C22×C4—134no—
282C22×C4—1348no—
283C22×C4—1348no—
284C22×C4—2612no—
285C22×C4—2648no—
286C22×C4—2696no—
287C22×C4—2648no—
288C22×C4C2×D52124yes—
289C22×C4C23×D1318yes—
290C22×C4C23×D13112yes—
291C22×C4C23×D1316yes—
292C4⋊C4—1396no—
293C4⋊C4C23×D13148yes—
294C22⋊C4—1332no—
295C22⋊C4—1396no—
296C22⋊C4C23×D13116yes—
297C42C23×D13148yes—
298C13C2×#348611yescharacteristic, complemented, Sylow
299C23—24no—
300C23—138no—
301C23—134no—
302C23—138no—
303C23—2616no—
304C23—2632no—
305C23—268no—
306C23—264no—
307C23—264no—
308C23—268no—
309C23—2616no—
310C23C22×D5214yes—
311C23C24×D1312yes—
312C23C24×D1311yescharacteristic
313Q8—2696no—
314Q8—2648no—
315Q8C22×D52164yes—
316D4—2664no—
317D4—2632no—
318D4—2648no—
319C2×C4—216no—
320C2×C4—1312no—
321C2×C4—138no—
322C2×C4—268no—
323C2×C4—2624no—
324C2×C4—2612no—
325C2×C4—2696no—
326C2×C4—2696no—
327C2×C4C22×D52124yes—
328C2×C4C22×D52148yes—
329C2×C4C24×D13116yes—
330C2×C4C24×D13112yes—
331C22—28no—
332C22—24no—
333C22—138no—
334C22—2632no—
335C22—2616no—
336C22—264no—
337C22—264no—
338C22—268no—
339C22—2616no—
340C22—5216no—
341C22C23×D5214yes—
342C22C23×D5212yes—
343C22D13×2−1+414yes—
344C22C25×D1311yescharacteristic
345C4—216no—
346C4—268no—
347C4—2612no—
348C4C23×D52124yes—
349C2—24no—
350C2—268no—
351C2—528no—
352C2#1312848814yesdirect product factor
353C2C24×D5211yescharacteristic
354C2C2×D13×2−1+412yes—
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#519C2
socleC23×C13C25
hypercenterC2×#519D13
hypocenterC13C2×#3486
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
1. C22×#88254C2semidirect
2. C23×Q8×D13C2semidirect
3. #13128488C2direct (N × H)
4. C2×Q8×D52C2semidirect
5. C2×#11719281C2semidirect
6. C2×#11719231C2semidirect
7. C2×#11719229C2semidirect
8. C2×C13×#519C2semidirect
11. C2×#88254C22semidirect
12. C22×#6131C22semidirect
15. C22×Q8×D13C22semidirect
16. C22×Q8×D13C22semidirect
20. C13×#519C22semidirect
21. C2×C4×Q8×C13C22semidirect
23. #11719281C22semidirect
24. Q8×D52C22semidirect
25. #11719231C22semidirect
26. #11719229C22semidirect
28. C2×#88151C22semidirect
32. C2×#88129C22semidirect
34. C2×#88123C22semidirect
36. C22×Q8×C13D4semidirect
44. C2×#6131C23semidirect
49. C2×Q8×D13C23semidirect
62. C4×Q8×C13C23semidirect
71. #88151C23semidirect
75. #88129C23semidirect
77. #88123C23semidirect
86. C2×Q8×C13C2×D4semidirect
129. C2×#519D13semidirect
141. C22×D132−1+4semidirect
184. #519C2×D13semidirect
185. C2×C4×Q8C2×D13semidirect
201. C2×D13C2×2−1+4semidirect
221. C22×Q8D52semidirect
240. C4×Q8C22×D13semidirect
250. C2×C13#3486semidirect
271. C2×Q8C2×D52semidirect
298. C13C2×#3486semidirect
352. C2#13128488direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#882542
C23×Q8×D132
#131284882
C2×Q8×D522
C2×#117192812
C2×#117192312
C2×#117192292
C2×C13×#5192
C2×#348613