Finite Group Databasebeta

← C2×#13131276 #16807457

Subgroups — C2×#13131276 #16807457

Order 3328.

3654 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×#261C212yesmaximal
2#13131276C2116yesmaximal, direct product factor
3C2×C4⋊C4×#261C216yesmaximal
4C2×C4×C4⋊#261C213yesmaximal
5C2×#11719057C213yesmaximal
6C2×C4×Q8×D13C211yesmaximal, characteristic
7C22×Q8×D13C2211yescharacteristic
8C2×Q8×#261C4132yescomplemented
9C2×Q8×#261C22116yes—
10C22×C4⋊#261C2216yes—
11C22×C4×#261C2216yes—
12C22×C4×#261C2216yes—
13C2×C4×Q8×C13C411yescharacteristic, complemented
14C2×Q8×Dic13C411yescharacteristic, complemented
15C4×Q8×D13C418yescomplemented
16C4×Q8×D13C2218yes—
17C2×C4⋊C4×D13C2213yes—
18C2×#88141C413yescomplemented
19C2×C42×D13C2213yes—
20C2×C4×Dic26C413yescomplemented
21C2×(C2×#261)⋊C4C2213yes—
22C2×(C2×#261)⋊C4C2216yes—
23C2×(C2×#261)⋊C4C2211yescharacteristic
24C4⋊C4×#261C22148yes—
25C4×C4⋊#261C22124yes—
26#11719057C22124yes—
27C23×#261C2316yes—
28C23×#261C2312yes—
29C22×Q8×C13C2×C411yescharacteristic
30C2×Q8×D13C2×C4116yes—
31C2×Q8×D13C2×C414yes—
32C2×Q8×D13C2314yes—
33C22×C4×D13C2311yescharacteristic
34C22×C4×D13C2313yes—
35C22×C4×D13C2313yes—
36C22×Dic26C2×C413yes—
37Q8×#261C2×C41128yescomplemented
38C2×C4⋊#261C2×C4148yes—
39C2×C4⋊#261C23124yes—
40C2×C4×#261—412no—
41C2×C4×#261C2×C4148yes—
42C2×C4×#261C23124yes—
43C2×C4×#261C23124yes—
44C4×Q8×C13C2×C418yescomplemented
45C2×C13×C4⋊C4C2×C413yes—
46C2×C42×C13C2×C413yes—
47Q8×Dic13C2×C418yescomplemented
48C2×C4⋊Dic13C2×C413yes—
49C2×#6101C2×C416yes—
50C2×C4×Dic13C2×C413yes—
51C2×C4×Dic13C2×C413yes—
52C2×C4×Dic13C2×C413yes—
53C4⋊C4×D13C2×C4112yes—
54C4⋊C4×D13C23112yes—
55#88141C2×C4124yescomplemented
56C42×D13C2×C4112yes—
57C42×D13C23112yes—
58C4×Dic26C2×C4124yescomplemented
59(C2×#261)⋊C4C2314yes—
60(C2×#261)⋊C4C23112yes—
61(C2×#261)⋊C4C23124yes—
62C2×#2276—131nomaximal, Sylow
63C23×D13C2411yescharacteristic
64C22×#261—212no—
65C22×#261—24no—
66C22×#261—24no—
67C22×#261—212no—
68C22×#261C22×C418yes—
69C22×#261C22×C4124yes—
70C22×#261C2414yes—
71C22×#261C24112yes—
72C2×Q8×C13C4218yescomplemented
73C2×Q8×C13C22×C414yes—
74C22×C4×C13C22×C411yescharacteristic
75C22×C4×C13C22×C413yes—
76C22×C4×C13C22×C413yes—
77C22×Dic13C22×C411yescharacteristic
78C22×Dic13C22×C413yes—
79C22×Dic13C22×C413yes—
80Q8×D13C42132yescomplemented
81Q8×D13C22×C4132yes—
82C2×C4×D13—26no—
83C2×C4×D13—24no—
84C2×C4×D13—26no—
85C2×C4×D13C22×C412yes—
86C2×C4×D13C22×C416yes—
87C2×C4×D13C22×C416yes—
88C2×C4×D13C22×C4124yes—
89C2×C4×D13C2412yes—
90C2×C4×D13C2416yes—
91C2×C4×D13C2416yes—
92C2×Dic26C42124yescomplemented
93C2×Dic26C22×C4112yes—
94C4⋊#261C22×C4196yes—
95C4×#261—424no—
96C4×#261C22×C4196yes—
97C13×C4⋊C4C22×C4112yes—
98C42×C13C22×C4112yes—
99C4⋊Dic13C22×C4112yes—
100#6101C22×C4124yes—
101C4×Dic13C22×C4112yes—
102C4×Dic13C22×C4112yes—
103C4×Dic13C22×C4112yes—
104C22×C4×Q8—132no—
105C22×C4×Q8—131no—
106#2276—1316no—
107C2×C4×C4⋊C4—133no—
108C2×C4×C4⋊C4—136no—
109C2×#376—133no—
110C23×C13C23×C411yescharacteristic
111C22×D13C23×C414yes—
112C22×D13C23×C411yescharacteristic
113C22×D13H(5,𝔽2)12yes—
114C22×D132−1+412yes—
115C22×D132−1+414yes—
116C22×D13C2511yescharacteristic
117C2×#261—216no—
118C2×#261—248no—
119C2×#261—212no—
120C2×#261—24no—
121C2×#261—24no—
122C2×#261—212no—
123C2×#261C23×C418yes—
124C2×#261C23×C4124yes—
125Q8×C13C2×C42116yescomplemented
126C2×C4×C13—22no—
127C2×C4×C13—26no—
128C2×C4×C13C2×C42112yes—
129C2×C4×C13C23×C412yes—
130C2×C4×C13C23×C416yes—
131C2×C4×C13C23×C416yes—
132C2×Dic13—22no—
133C2×Dic13—26no—
134C2×Dic13C2×C42112yes—
135C2×Dic13C23×C412yes—
136C2×Dic13C23×C416yes—
137C2×Dic13C23×C416yes—
138C4×D13—24no—
139C4×D13—212no—
140C4×D13—26no—
141C4×D13—24no—
142C4×D13—26no—
143C4×D13C2×C42124yes—
144C4×D13C23×C4124yes—
145Dic26C2×C42148yescomplemented
146C23×Q8—131no—
147C2×C4×Q8—1332no—
148C2×C4×Q8—1316no—
149C2×C4×Q8—131no—
150C2×C4×Q8—138no—
151C2×C4×Q8—138no—
152C2×C4×Q8—133no—
153C2×C4×Q8—133no—
154C2×C4×Q8#26111yescharacteristic, complemented
155C22×C4⋊C4—136no—
156C22×C4⋊C4—133no—
157C22×C42—136no—
158C22×C42—133no—
159C22×C42—136no—
160C4×C4⋊C4—1324no—
161C4×C4⋊C4—1348no—
162#376—1324no—
163C2×#95—131no—
164C2×#95—133no—
165C2×#95—136no—
166C22×C13C22×C4212yes—
167C22×C13#51912yes—
168C22×C13#52012yes—
169C22×C13C24×C411yescharacteristic
170C2×D13C22×C4212yes—
171C2×D13#51918yes—
172C2×D13#51912yes—
173C2×D13#52018yes—
174C2×D13#52012yes—
175C2×D13C24×C412yes—
176C2×D13C2×H(5,𝔽2)11yescharacteristic
177C2×D13C2×2−1+411yescharacteristic
178C2×D13C2×2−1+412yes—
179#261—28no—
180#261—224no—
181C4×C13—22no—
182C4×C13—26no—
183C4×C13C22×C42112yes—
184Dic13—22no—
185Dic13—26no—
186Dic13C22×C42112yes—
187C22×Q8—1316no—
188C22×Q8—134no—
189C22×Q8—134no—
190C22×Q8—133no—
191C22×Q8C2×#26111yescharacteristic
192C23×C4—133no—
193C23×C4—136no—
194C23×C4—132no—
195C23×C4—133no—
196C23×C4—131no—
197C4×Q8—13128no—
198C4×Q8—138no—
199C4×Q8—1324no—
200C4×Q8—1324no—
201C4×Q8C2×#26118yescomplemented
202C2×C4⋊C4—1324no—
203C2×C4⋊C4—1348no—
204C2×C4⋊C4—136no—
205C2×C4⋊C4—133no—
206C2×C4⋊C4—1312no—
207C2×C4⋊C4—1312no—
208C2×C4⋊C4C2×#26113yes—
209C2×C42—1324no—
210C2×C42—1348no—
211C2×C42—133no—
212C2×C42—133no—
213C2×C42—133no—
214C2×C42—1312no—
215C2×C42—1312no—
216C2×C42—1324no—
217C2×C42—5212no—
218C2×C42C2×#26113yes—
219#95—134no—
220#95—1324no—
221#95—1312no—
222C2×C13#227614yescomplemented
223C2×C13C23×C4211yescharacteristic
224C2×C13C2×#51911yescharacteristic
225C2×C13C2×#52011yescharacteristic
226D13#227614yescomplemented
227D13C2×#51912yes—
228D13C2×#52012yes—
229C24—131no—
230C2×Q8—1332no—
231C2×Q8—1332no—
232C2×Q8—1324no—
233C2×Q8—1312no—
234C2×Q8C4×#26118yescomplemented
235C2×Q8C22×#26114yes—
236C22×C4—133no—
237C22×C4—1324no—
238C22×C4—136no—
239C22×C4—136no—
240C22×C4—134no—
241C22×C4—1312no—
242C22×C4—138no—
243C22×C4—1324no—
244C22×C4—131no—
245C22×C4—133no—
246C22×C4—132no—
247C22×C4—136no—
248C22×C4—132no—
249C22×C4—136no—
250C22×C4—266no—
251C22×C4—264no—
252C22×C4—266no—
253C22×C4—2612no—
254C22×C4—2612no—
255C22×C4—264no—
256C22×C4—264no—
257C22×C4C22×#26111yescharacteristic
258C22×C4C22×#26113yes—
259C22×C4C22×#26113yes—
260C4⋊C4—1396no—
261C4⋊C4—1324no—
262C4⋊C4—1312no—
263C4⋊C4C22×#261112yes—
264C42—1396no—
265C42—1312no—
266C42—1312no—
267C42—1312no—
268C42—5224no—
269C42C22×#261112yes—
270C13C2×#227611yescharacteristic, complemented, Sylow
271C23—134no—
272C23—134no—
273C23—132no—
274C23—132no—
275C23—131no—
276C23—131no—
277C23C23×#26111yescharacteristic
278Q8—1348no—
279Q8C2×C4×#261116yescomplemented
280C2×C4—22no—
281C2×C4—26no—
282C2×C4—1312no—
283C2×C4—136no—
284C2×C4—1324no—
285C2×C4—1324no—
286C2×C4—138no—
287C2×C4—1324no—
288C2×C4—132no—
289C2×C4—136no—
290C2×C4—266no—
291C2×C4—264no—
292C2×C4—264no—
293C2×C4—2612no—
294C2×C4—266no—
295C2×C4—2612no—
296C2×C4—2616no—
297C2×C4—2648no—
298C2×C4—264no—
299C2×C4—2612no—
300C2×C4—264no—
301C2×C4—262no—
302C2×C4—266no—
303C2×C4C2×C4×#261112yes—
304C2×C4C23×#26112yes—
305C2×C4C23×#26116yes—
306C2×C4C23×#26116yes—
307C22—138no—
308C22—138no—
309C22—132no—
310C22—132no—
311C22—132no—
312C22—132no—
313C22—132no—
314C22—131no—
315C22—131no—
316C22C22×C4×#26112yes—
317C22#1171962712yes—
318C22#1171963112yes—
319C22C24×#26111yescharacteristic
320C4—22no—
321C4—26no—
322C4—1312no—
323C4—2624no—
324C4—268no—
325C4—262no—
326C4—266no—
327C4C22×C4×#261112yes—
328C2—132no—
329C2—132no—
330C2—134no—
331C2#1313127614yesdirect product factor
332C2C23×C4×#26111yescharacteristic
333C2C2×#1171962711yescharacteristic
334C2C2×#1171963111yescharacteristic
subgroupG/H
centerC23C23×#261
commutatorC2×C13C23×C42
FrattiniC22C24×#261
FittingC2×C4×Q8×C13C4
socleC23×C13C23×C4
prime radicalC23×D13C24
cosocleC22×D13C25
hypercenterC2×C4×Q8#261
hypocenterC13C2×#2276
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #13131276C2direct (N × H)
8. C2×Q8×#261C4semidirect
13. C2×C4×Q8×C13C4semidirect
14. C2×Q8×Dic13C4semidirect
15. C4×Q8×D13C4semidirect
18. C2×#88141C4semidirect
20. C2×C4×Dic26C4semidirect
37. Q8×#261C2×C4semidirect
44. C4×Q8×C13C2×C4semidirect
47. Q8×Dic13C2×C4semidirect
55. #88141C2×C4semidirect
58. C4×Dic26C2×C4semidirect
72. C2×Q8×C13C42semidirect
80. Q8×D13C42semidirect
92. C2×Dic26C42semidirect
125. Q8×C13C2×C42semidirect
145. Dic26C2×C42semidirect
154. C2×C4×Q8#261semidirect
201. C4×Q8C2×#261semidirect
222. C2×C13#2276semidirect
226. D13#2276semidirect
234. C2×Q8C4×#261semidirect
270. C13C2×#2276semidirect
279. Q8C2×C4×#261semidirect
331. C2#13131276direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×#2612
#131312762
C2×C4⋊C4×#2612
C2×C4×C4⋊#2612
C2×#117190572
C2×C4×Q8×D132
C2×#227613