Finite Group Databasebeta

← C2×#13127503 #16742511

Subgroups — C2×#13127503 #16742511

Order 3328.

2174 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×Dic26C211yesmaximal, characteristic, complemented
2#13127503C2116yesmaximal, direct product factor
3C2×#11718731C213yesmaximal, complemented
4C2×#11718669C213yesmaximal, complemented
5C2×#11718736C213yesmaximal, complemented
6C2×Q8×#1055C211yesmaximal, characteristic, complemented
7C2×C4×#6105C213yesmaximal, complemented
8C2×C13×#550C211yesmaximal, characteristic
9C22×C13×#41—21no—
10C13×#550—24no—
11C13×#550C2218yes—
12C2×C13×#127C2213yes—
13C2×C13×#121—23no—
14C2×C4×Q8×C13C2211yescharacteristic
15C2×C4×D4×C13C2213yes—
16C2×Q8×Dic13—21no—
17C22×#6105C2213yes—
18Q8×Dic26—24no—
19Q8×Dic26C2218yescomplemented
20C2×#88142—23no—
21C2×#88123C2213yes—
22C2×C4×Dic26C2213yes—
23C2×#88072C2213yes—
24C2×#88072C2216yes—
25#11718736C22124yescomplemented
26#11718731C22124yescomplemented
27Q8×#1055C2218yescomplemented
28C4×#6105C22124yescomplemented
29#11718669C22124yescomplemented
30C2×#88050C2211yescharacteristic
31C2×#88048C2213yes—
32C2×C4⋊#1055C2213yes—
33C2×C4×#1055C2213yes—
34C2×C13×#41—28no—
35C2×C13×#41—48no—
36C22×Q8×C13D411yescharacteristic
37C22×D4×C13—23no—
38C22×D4×C13—23no—
39C22×D4×C13C2313yes—
40C23×C4×C13—23no—
41C22×Dic26—23no—
42C22×Dic26C2311yescharacteristic
43C13×#127—26no—
44C13×#127C23112yes—
45C13×#121—224no—
46C4×Q8×C13D414yes—
47C4×Q8×C13C2314yes—
48C4×D4×C13—26no—
49C4×D4×C13C23112yes—
50C2×C13×C4⋊C4D413yes—
51C2×C13×C4⋊C4C2311yescharacteristic
52C2×C13×C22⋊C4—23no—
53C2×C42×C13C2313yes—
54Q8×Dic13—28no—
55C2×#6105—212no—
56C2×#6105C23112yes—
57C2×C4⋊Dic13—23no—
58C2×C4⋊Dic13C2313yes—
59C2×#6101—23no—
60C2×C4×Dic13—23no—
61C22×#1055C2313yes—
62C22×#1055C2311yescharacteristic
63#88142—224no—
64#88123—26no—
65#88123C23112yes—
66C4×Dic26—26no—
67C4×Dic26C23112yes—
68#88072C23124yes—
69#88072C23112yes—
70#88050C2314yes—
71#88048C23112yes—
72C4⋊#1055C23112yes—
73C4×#1055C23112yes—
74C2×#3362—131nomaximal, Sylow
75C24×C13—23no—
76C13×#41—432no—
77C2×Q8×C13SD1618yescomplemented
78C2×Q8×C13C2×D414yes—
79C2×D4×C13—23no—
80C2×D4×C13—212no—
81C2×D4×C13—212no—
82C2×D4×C13—26no—
83C2×D4×C13—26no—
84C2×D4×C13—412no—
85C2×D4×C13—86no—
86C2×D4×C13C2416yes—
87C22×C4×C13—21no—
88C22×C4×C13—212no—
89C22×C4×C13—412no—
90C22×C4×C13C2×D413yes—
91C22×C4×C13C2×D413yes—
92C22×C4×C13C2411yescharacteristic
93C22×Dic13—21no—
94C22×Dic13—23no—
95C2×Dic26—21no—
96C2×Dic26—22no—
97C2×Dic26—212no—
98C2×Dic26—86no—
99C2×Dic26#4114yescomplemented
100C2×Dic26C2412yes—
101C13×C4⋊C4—21no—
102C13×C4⋊C4C2×D4112yes—
103C13×C4⋊C4C2412yes—
104C13×C22⋊C4—212no—
105C42×C13C2×D416yes—
106C42×C13C2416yes—
107#6105—224no—
108C4⋊Dic13—23no—
109C4⋊Dic13—212no—
110C4⋊Dic13C2416yes—
111#6101—212no—
112C4×Dic13—212no—
113C2×#1055—26no—
114C2×#1055—22no—
115C2×#1055C2412yes—
116C2×#1055C2416yes—
117C2×Q82—131no—
118C2×#550D1311yescharacteristic
119#3362—1316no—
120C2×#486—133no—
121C2×#476—133no—
122C2×#460—133no—
123C2×C8×Q8—131no—
124C2×C4×SD16—133no—
125C23×C13—26no—
126C23×C13—46no—
127C23×C13—46no—
128C23×C13—46no—
129C23×C13C22×D411yescharacteristic
130Q8×C13C2×SD16116yescomplemented
131D4×C13—26no—
132D4×C13—26no—
133D4×C13—46no—
134D4×C13—424no—
135D4×C13—812no—
136C2×C4×C13—26no—
137C2×C4×C13—22no—
138C2×C4×C13—42no—
139C2×C4×C13—424no—
140C2×C4×C13C2×SD16112yes—
141C2×C4×C13C22×D416yes—
142C2×C4×C13C22×D411yescharacteristic
143C2×C4×C13C22×D416yes—
144C2×C4×C13C2×#4112yes—
145C2×C4×C132−1+412yes—
146C2×C4×C13C2511yescharacteristic
147C2×Dic13—24no—
148C2×Dic13—22no—
149C2×Dic13—26no—
150C2×Dic13—46no—
151Dic26—24no—
152Dic26—22no—
153Dic26—812no—
154Dic26C2×#4114yescomplemented
155#1055—26no—
156#1055—22no—
157C22×#41—21no—
158C22×SD16—133no—
159Q82—138no—
160Q82—264no—
161#550—24no—
162#550C2×D1318yes—
163C2×C4⋊Q8—133no—
164C2×C4⋊Q8—263no—
165C2×#127C2×D1313yes—
166C2×#121—23no—
167C2×C4×Q8—133no—
168C2×C4×Q8—261no—
169C2×C4×Q8C2×D1311yescharacteristic
170C2×C4×D4C2×D1313yes—
171#486—1324no—
172#476—1324no—
173#460—1324no—
174C8×Q8—138no—
175C4×SD16—1324no—
176C2×#106—133no—
177C2×C4⋊C8—133no—
178C2×#103—131no—
179C2×#102—133no—
180C2×#102—136no—
181C2×C4×C8—133no—
182C22×C13—46no—
183C22×C13—46no—
184C22×C13—46no—
185C22×C13—812no—
186C22×C13#54812yes—
187C22×C13C22×SD1612yes—
188C22×C13#57612yes—
189C22×C13C23×D411yescharacteristic
190C4×C13—26no—
191C4×C13—42no—
192C4×C13#54812yes—
193C4×C13C22×SD16112yes—
194C4×C13C22×#4111yescharacteristic
195C4×C13C2×2−1+411yescharacteristic
196Dic13—24no—
197Dic13—46no—
198C2×#41—28no—
199C2×#41—48no—
200C22×Q8—131no—
201C22×Q8—263no—
202C22×Q8C22⋊D1311yescharacteristic
203C22×D4—23no—
204C22×D4—23no—
205C22×D4C22×D1313yes—
206C23×C4—23no—
207C2×SD16—1312no—
208C2×SD16—2612no—
209C22×C8—133no—
210C22×C8—131no—
211C4⋊Q8—1312no—
212C4⋊Q8—2624no—
213C4⋊Q8—266no—
214#127—26no—
215#127C22×D13112yes—
216#121—224no—
217C4×Q8—1312no—
218C4×Q8—268no—
219C4×Q8—266no—
220C4×Q8C22⋊D1314yes—
221C4×Q8C22×D1314yes—
222C4×D4—26no—
223C4×D4C22×D13112yes—
224C2×C4⋊C4—133no—
225C2×C4⋊C4—263no—
226C2×C4⋊C4—263no—
227C2×C4⋊C4C22⋊D1313yes—
228C2×C4⋊C4C22×D1311yescharacteristic
229C2×C22⋊C4—23no—
230C2×C42—263no—
231C2×C42C22×D1313yes—
232#106—1312no—
233C4⋊C8—1312no—
234#103—134no—
235#102—1312no—
236#102—1324no—
237C4×C8—1312no—
238C2×C13—86no—
239C2×C13#336214yescomplemented
240C2×C13C2×#54811yescharacteristic
241C2×C13C23×SD1611yescharacteristic
242C2×C13C2×#57611yescharacteristic
243C24—23no—
244#41—432no—
245C2×Q8—134no—
246C2×Q8—132no—
247C2×Q8—262no—
248C2×Q8—261no—
249C2×Q8—2612no—
250C2×Q8—1046no—
251C2×Q8#610518yescomplemented
252C2×Q8C2×C22⋊D1314yes—
253C2×D4—26no—
254C2×D4—26no—
255C2×D4—23no—
256C2×D4—212no—
257C2×D4—212no—
258C2×D4—412no—
259C2×D4—86no—
260C2×D4C23×D1316yes—
261C22×C4—21no—
262C22×C4—212no—
263C22×C4—412no—
264C22×C4—261no—
265C22×C4—263no—
266C22×C4C2×C22⋊D1313yes—
267C22×C4C2×C22⋊D1313yes—
268C22×C4C23×D1311yescharacteristic
269SD16—2624no—
270C2×C8—132no—
271C2×C8—136no—
272C2×C8—266no—
273C2×C8—262no—
274C4⋊C4—21no—
275C4⋊C4—136no—
276C4⋊C4—263no—
277C4⋊C4—2612no—
278C4⋊C4—2612no—
279C4⋊C4C2×C22⋊D13112yes—
280C4⋊C4C23×D1312yes—
281C22⋊C4—212no—
282C42—2612no—
283C42C2×C22⋊D1316yes—
284C42C23×D1316yes—
285C13C2×#336211yescharacteristic, complemented, Sylow
286C23—26no—
287C23—46no—
288C23—46no—
289C23—46no—
290C23C22×C22⋊D1311yescharacteristic
291Q8—134no—
292Q8—264no—
293Q8—262no—
294Q8—10412no—
295Q8C2×#6105116yescomplemented
296D4—26no—
297D4—26no—
298D4—424no—
299D4—46no—
300D4—812no—
301C2×C4—26no—
302C2×C4—22no—
303C2×C4—42no—
304C2×C4—424no—
305C2×C4—264no—
306C2×C4—262no—
307C2×C4—266no—
308C2×C4—526no—
309C2×C4C2×#6105112yes—
310C2×C4#41×D1312yes—
311C2×C4#8825712yes—
312C2×C4C22×C22⋊D1316yes—
313C2×C4C22×C22⋊D1316yes—
314C2×C4C22×C22⋊D1311yescharacteristic
315C2×C4C24×D1311yescharacteristic
316C8—266no—
317C8—262no—
318C22—46no—
319C22—46no—
320C22—46no—
321C22—812no—
322C22C22×#610512yes—
323C22#1171953612yes—
324C22#1171954012yes—
325C22C23×C22⋊D1311yescharacteristic
326C4—26no—
327C4—42no—
328C4—264no—
329C4—526no—
330C4C22×#6105112yes—
331C4#1171953612yes—
332C4C2×#41×D1311yescharacteristic
333C4C2×#8825711yescharacteristic
334C2—86no—
335C2#1312750314yesdirect product factor
336C2C2×#1171953611yescharacteristic
337C2C23×#610511yescharacteristic
338C2C2×#1171954011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
Fitting, prime radicalC2×C13×#550C2
socleC23×C13C22×D4
hypercenterC2×#550D13
hypocenterC13C2×#3362
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic26C2semidirect
2. #13127503C2direct (N × H)
3. C2×#11718731C2semidirect
4. C2×#11718669C2semidirect
5. C2×#11718736C2semidirect
6. C2×Q8×#1055C2semidirect
7. C2×C4×#6105C2semidirect
19. Q8×Dic26C22semidirect
25. #11718736C22semidirect
26. #11718731C22semidirect
27. Q8×#1055C22semidirect
28. C4×#6105C22semidirect
29. #11718669C22semidirect
77. C2×Q8×C13SD16semidirect
99. C2×Dic26#41semidirect
130. Q8×C13C2×SD16semidirect
154. Dic26C2×#41semidirect
239. C2×C13#3362semidirect
251. C2×Q8#6105semidirect
285. C13C2×#3362semidirect
295. Q8C2×#6105semidirect
335. C2#13127503direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×Dic262
#131275032
C2×#117187312
C2×#117186692
C2×#117187362
C2×Q8×#10552
C2×C4×#61052
C2×C13×#5502
C2×#336213