Finite Group Databasebeta

← C2×#13127507 #16742515

Subgroups — C2×#13127507 #16742515

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×#11719282C211yesmaximal, characteristic
2#13127507C2116yesmaximal, direct product factor
3C2×#11718749C213yesmaximal, complemented
4C2×#11718745C213yesmaximal, complemented
5C2×#11718688C213yesmaximal, complemented
6C2×Q8×#1055C211yesmaximal, characteristic, complemented
7C2×C4×#6106C213yesmaximal, complemented
8C2×Q82×C13C211yesmaximal, characteristic, complemented
9C22×#6131—21no—
10Q82×C13—24no—
11Q82×C13C2218yescomplemented
12C2×C13×C4⋊Q8—23no—
13C2×C13×C4⋊Q8C2213yes—
14C2×C4×Q8×C13—21no—
15C2×C4×Q8×C13C2213yes—
16C2×C4×Q8×C13C2211yescharacteristic
17C22×#6106C2213yes—
18#11719282—24no—
19#11719282C2218yes—
20C2×#88149—23no—
21C2×#88128C2213yes—
22C2×C4×D52C2213yes—
23C2×#88075C2211yescharacteristic
24#11718749C22124yescomplemented
25#11718745C22124yescomplemented
26#11718688C22124yescomplemented
27C4×#6106C22124yescomplemented
28Q8×#1055C2218yescomplemented
29C2×#88049C2213yes—
30C2×#88049C2216yes—
31C2×#88048C2213yes—
32C2×C4⋊#1055C2213yes—
33C2×C4×#1055C2213yes—
34C22×Q8×C13—23no—
35C22×Q8×C13D411yescharacteristic
36C22×Q8×C13C2311yescharacteristic
37C2×#6131—28no—
38C2×#6131—48no—
39C22×D52—23no—
40C22×D52—23no—
41C22×D52C2313yes—
42C22×C4×D13—23no—
43C13×C4⋊Q8—224no—
44C13×C4⋊Q8—26no—
45C13×C4⋊Q8C23112yes—
46C4×Q8×C13—28no—
47C4×Q8×C13—26no—
48C4×Q8×C13D414yes—
49C4×Q8×C13C23112yes—
50C4×Q8×C13C2314yes—
51C2×C13×C4⋊C4—23no—
52C2×C13×C4⋊C4—23no—
53C2×C13×C4⋊C4D413yes—
54C2×C13×C4⋊C4C2313yes—
55C2×C42×C13—23no—
56C2×C42×C13C2313yes—
57C2×#6106—212no—
58C2×#6106C23112yes—
59C2×#6103—23no—
60C2×C4⋊Dic13C2311yescharacteristic
61C22×#1055C2313yes—
62C22×#1055C2311yescharacteristic
63#88149—224no—
64#88128—26no—
65#88128C23112yes—
66C4×D52—26no—
67C4×D52C23112yes—
68#88075C2314yes—
69#88049C23112yes—
70#88049C23124yes—
71#88048C23112yes—
72C4⋊#1055C23112yes—
73C4×#1055C23112yes—
74C2×#3362—131nomaximal, Sylow
75C23×D13—23no—
76C2×Q8×C13—21no—
77C2×Q8×C13—212no—
78C2×Q8×C13—22no—
79C2×Q8×C13—86no—
80C2×Q8×C13SD1618yescomplemented
81C2×Q8×C13C2×D414yes—
82C2×Q8×C13#4114yescomplemented
83C2×Q8×C13C2412yes—
84C22×C4×C13—21no—
85C22×C4×C13—23no—
86C22×C4×C13C2×D413yes—
87C22×C4×C13C2×D413yes—
88C22×C4×C13C2411yescharacteristic
89C22×Dic13—21no—
90#6131—432no—
91C2×D52—26no—
92C2×D52—26no—
93C2×D52—23no—
94C2×D52—212no—
95C2×D52—212no—
96C2×D52—412no—
97C2×D52—86no—
98C2×D52C2416yes—
99C2×C4×D13—212no—
100C2×C4×D13—412no—
101C13×C4⋊C4—212no—
102C13×C4⋊C4—212no—
103C13×C4⋊C4—23no—
104C13×C4⋊C4C2×D4112yes—
105C13×C4⋊C4C2416yes—
106C42×C13—212no—
107C42×C13C2×D416yes—
108C42×C13C2416yes—
109#6106—224no—
110#6103—212no—
111C4⋊Dic13—21no—
112C4⋊Dic13C2412yes—
113C2×#1055—26no—
114C2×#1055—22no—
115C2×#1055C2412yes—
116C2×#1055C2416yes—
117C2×Q82D1311yescharacteristic, complemented
118C2×#550—131no—
119#3362—1316no—
120C2×#486—133no—
121C2×#476—133no—
122C2×#460—133no—
123C2×C8×Q8—131no—
124C2×C4×SD16—133no—
125C23×C13C22×D411yescharacteristic
126C22×D13—26no—
127C22×D13—46no—
128C22×D13—46no—
129C22×D13—46no—
130Q8×C13—24no—
131Q8×C13—22no—
132Q8×C13—812no—
133Q8×C13C2×SD16116yescomplemented
134Q8×C13C2×#4114yescomplemented
135C2×C4×C13—24no—
136C2×C4×C13—26no—
137C2×C4×C13—22no—
138C2×C4×C13—26no—
139C2×C4×C13—46no—
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—22no—
148C2×Dic13—42no—
149D52—26no—
150D52—26no—
151D52—46no—
152D52—424no—
153D52—812no—
154C4×D13—424no—
155#1055—26no—
156#1055—22no—
157C22×#41—261no—
158C22×SD16—133no—
159Q82—24no—
160Q82C2×D1318yescomplemented
161#550—138no—
162#550—264no—
163C2×C4⋊Q8—23no—
164C2×C4⋊Q8C2×D1313yes—
165C2×#127—133no—
166C2×#121—263no—
167C2×C4×Q8—21no—
168C2×C4×Q8C2×D1313yes—
169C2×C4×Q8C2×D1311yescharacteristic
170C2×C4×D4—133no—
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#54812yes—
183C22×C13C22×SD1612yes—
184C22×C13#57612yes—
185C22×C13C23×D411yescharacteristic
186C2×D13—46no—
187C2×D13—46no—
188C2×D13—46no—
189C2×D13—812no—
190C4×C13—24no—
191C4×C13—26no—
192C4×C13—46no—
193C4×C13#54812yes—
194C4×C13C22×SD16112yes—
195C4×C13C22×#4111yescharacteristic
196C4×C13C2×2−1+411yescharacteristic
197Dic13—42no—
198C2×#41—268no—
199C2×#41—528no—
200C22×Q8—23no—
201C22×Q8C22⋊D1311yescharacteristic
202C22×Q8C22×D1311yescharacteristic
203C22×D4—133no—
204C22×D4—263no—
205C22×D4—263no—
206C23×C4—263no—
207C2×SD16—1312no—
208C2×SD16—2612no—
209C22×C8—133no—
210C22×C8—131no—
211C4⋊Q8—224no—
212C4⋊Q8—26no—
213C4⋊Q8C22×D13112yes—
214#127—1312no—
215#127—266no—
216#121—2624no—
217C4×Q8—28no—
218C4×Q8—26no—
219C4×Q8C22⋊D1314yes—
220C4×Q8C22×D13112yes—
221C4×Q8C22×D1314yes—
222C4×D4—1312no—
223C4×D4—266no—
224C2×C4⋊C4—23no—
225C2×C4⋊C4—23no—
226C2×C4⋊C4—131no—
227C2×C4⋊C4C22⋊D1313yes—
228C2×C4⋊C4C22×D1313yes—
229C2×C22⋊C4—263no—
230C2×C42—23no—
231C2×C42C22×D1313yes—
232#106—1312no—
233C4⋊C8—1312no—
234#103—134no—
235#102—1312no—
236#102—1324no—
237C4×C8—1312no—
238C2×C13#336214yescomplemented
239C2×C13C2×#54811yescharacteristic
240C2×C13C23×SD1611yescharacteristic
241C2×C13C2×#57611yescharacteristic
242D13—86no—
243C24—263no—
244#41—5232no—
245C2×Q8—22no—
246C2×Q8—21no—
247C2×Q8—212no—
248C2×Q8—86no—
249C2×Q8#610618yescomplemented
250C2×Q8#613114yescomplemented
251C2×Q8C2×C22⋊D1314yes—
252C2×Q8C23×D1312yes—
253C2×D4—136no—
254C2×D4—266no—
255C2×D4—266no—
256C2×D4—263no—
257C2×D4—2612no—
258C2×D4—2612no—
259C2×D4—5212no—
260C2×D4—1046no—
261C22×C4—21no—
262C22×C4—23no—
263C22×C4—261no—
264C22×C4—2612no—
265C22×C4—5212no—
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—212no—
275C4⋊C4—212no—
276C4⋊C4—23no—
277C4⋊C4—132no—
278C4⋊C4—261no—
279C4⋊C4C2×C22⋊D13112yes—
280C4⋊C4C23×D1316yes—
281C22⋊C4—2612no—
282C42—212no—
283C42C2×C22⋊D1316yes—
284C42C23×D1316yes—
285C13C2×#336211yescharacteristic, complemented, Sylow
286C23—266no—
287C23—526no—
288C23—526no—
289C23—526no—
290C23C22×C22⋊D1311yescharacteristic
291Q8—24no—
292Q8—22no—
293Q8—812no—
294Q8C2×#6106116yescomplemented
295Q8C2×#613114yescomplemented
296D4—266no—
297D4—266no—
298D4—5224no—
299D4—526no—
300D4—10412no—
301C2×C4—24no—
302C2×C4—26no—
303C2×C4—22no—
304C2×C4—26no—
305C2×C4—46no—
306C2×C4—262no—
307C2×C4—522no—
308C2×C4—5224no—
309C2×C4C2×#6106112yes—
310C2×C4C2×#613112yes—
311C2×C4#8825412yes—
312C2×C4C22×C22⋊D1316yes—
313C2×C4C22×C22⋊D1316yes—
314C2×C4C22×C22⋊D1311yescharacteristic
315C2×C4C24×D1311yescharacteristic
316C8—266no—
317C8—262no—
318C22—526no—
319C22—526no—
320C22—526no—
321C22—10412no—
322C22C22×#610612yes—
323C22#1171952212yes—
324C22#1171954012yes—
325C22C23×C22⋊D1311yescharacteristic
326C4—24no—
327C4—26no—
328C4—46no—
329C4—522no—
330C4C22×#6106112yes—
331C4#1171952212yes—
332C4C22×#613111yescharacteristic
333C4C2×#8825411yescharacteristic
334C2—1046no—
335C2#1312750714yesdirect product factor
336C2C2×#1171952211yescharacteristic
337C2C23×#610611yescharacteristic
338C2C2×#1171954011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×Q82×C13C2
socleC23×C13C22×D4
prime radicalC2×#11719282C2
hypercenterC2×Q82D13
hypocenterC13C2×#3362
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×Q82

Complements

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

NH ≅ G/Ntype
2. #13127507C2direct (N × H)
3. C2×#11718749C2semidirect
4. C2×#11718745C2semidirect
5. C2×#11718688C2semidirect
6. C2×Q8×#1055C2semidirect
7. C2×C4×#6106C2semidirect
8. C2×Q82×C13C2semidirect
11. Q82×C13C22semidirect
24. #11718749C22semidirect
25. #11718745C22semidirect
26. #11718688C22semidirect
27. C4×#6106C22semidirect
28. Q8×#1055C22semidirect
80. C2×Q8×C13SD16semidirect
82. C2×Q8×C13#41semidirect
117. C2×Q82D13semidirect
133. Q8×C13C2×SD16semidirect
134. Q8×C13C2×#41semidirect
160. Q82C2×D13semidirect
238. C2×C13#3362semidirect
249. C2×Q8#6106semidirect
250. C2×Q8#6131semidirect
285. C13C2×#3362semidirect
294. Q8C2×#6106semidirect
295. Q8C2×#6131semidirect
335. C2#13127507direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192822
#131275072
C2×#117187492
C2×#117187452
C2×#117186882
C2×Q8×#10552
C2×C4×#61062
C2×Q82×C132
C2×#336213