Finite Group Databasebeta

← C2×#13127508 #16742516

Subgroups — C2×#13127508 #16742516

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
2C2×#11719282C211yesmaximal, characteristic
3#13127508C2116yesmaximal, direct product factor
4C2×#11718355C213yesmaximal, complemented
5C2×#11718503C213yesmaximal, complemented
6C2×#11718509C213yesmaximal, complemented
7C2×C4×#6095C213yesmaximal, complemented
8C2×C8×Q8×C13C211yesmaximal, characteristic, complemented
9C22×#6131—21no—
10C2×C4×Q8×C13C2211yescharacteristic
11C2×Q8×Dic13—21no—
12C22×#6095C2213yes—
13#11719282—24no—
14#11719282C2218yes—
15Q8×Dic26—24no—
16Q8×Dic26C2218yescomplemented
17C2×#88149—23no—
18C2×#88142—23no—
19C2×#88128C2213yes—
20C2×C4×D52C2213yes—
21C2×#88123C2213yes—
22C2×C4×Dic26C2213yes—
23C8×Q8×C13C2218yescomplemented
24C2×C13×C4⋊C8C2213yes—
25C2×C4×C8×C13C2213yes—
26C2×#88061C2213yes—
27C2×#88061C2216yes—
28C2×#88057C2213yes—
29C2×#88056C2211yescharacteristic
30#11718509C22124yescomplemented
31#11718503C22124yescomplemented
32#11718355C22124yescomplemented
33C4×#6095C22124yescomplemented
34C22×Q8×C13D411yescharacteristic
35C2×#6131—28no—
36C2×#6131—48no—
37C22×D52—23no—
38C22×D52—23no—
39C22×D52C2313yes—
40C22×C4×D13—23no—
41C22×Dic26—23no—
42C22×Dic26C2311yescharacteristic
43C22×C8×C13C2313yes—
44C22×C8×C13C2311yescharacteristic
45C4×Q8×C13D414yes—
46C4×Q8×C13C2314yes—
47C2×C13×C4⋊C4D413yes—
48C2×C42×C13C2313yes—
49Q8×Dic13—28no—
50C2×#6103—23no—
51C2×C4⋊Dic13—23no—
52C2×C4⋊Dic13C2313yes—
53C2×C4⋊Dic13C2311yescharacteristic
54C2×#6101—23no—
55C2×C4×Dic13—23no—
56C2×#6095—212no—
57C2×#6095C23112yes—
58#88149—224no—
59#88142—224no—
60#88128—26no—
61#88128C23112yes—
62C4×D52—26no—
63C4×D52C23112yes—
64#88123—26no—
65#88123C23112yes—
66C4×Dic26—26no—
67C4×Dic26C23112yes—
68C13×C4⋊C8C23112yes—
69C4×C8×C13C23112yes—
70#88061C23124yes—
71#88061C23112yes—
72#88057C23112yes—
73#88056C2314yes—
74C2×#3362—131nomaximal, Sylow
75C23×D13—23no—
76C2×Q8×C13SD1618yescomplemented
77C2×Q8×C13C2×D414yes—
78C22×C4×C13C2×D413yes—
79C22×C4×C13C2×D413yes—
80C22×C4×C13C2411yescharacteristic
81C22×Dic13—21no—
82C22×Dic13—23no—
83C22×Dic13—21no—
84#6131—432no—
85C2×D52—26no—
86C2×D52—26no—
87C2×D52—23no—
88C2×D52—212no—
89C2×D52—212no—
90C2×D52—412no—
91C2×D52—86no—
92C2×D52C2416yes—
93C2×C4×D13—212no—
94C2×C4×D13—412no—
95C2×Dic26—21no—
96C2×Dic26—22no—
97C2×Dic26—212no—
98C2×Dic26—86no—
99C2×Dic26#4114yescomplemented
100C2×Dic26C2412yes—
101C2×C8×C13—26no—
102C2×C8×C13—22no—
103C2×C8×C13C2412yes—
104C2×C8×C13C2416yes—
105C13×C4⋊C4C2×D4112yes—
106C42×C13C2×D416yes—
107C42×C13C2416yes—
108#6103—212no—
109C4⋊Dic13—23no—
110C4⋊Dic13—212no—
111C4⋊Dic13—21no—
112C4⋊Dic13C2416yes—
113C4⋊Dic13C2412yes—
114#6101—212no—
115C4×Dic13—212no—
116#6095—224no—
117C2×Q82—131no—
118C2×#550—131no—
119#3362—1316no—
120C2×#486—133no—
121C2×#476—133no—
122C2×#460—133no—
123C2×C8×Q8D1311yescharacteristic, complemented
124C2×C4×SD16—133no—
125C23×C13C22×D411yescharacteristic
126C22×D13—26no—
127C22×D13—46no—
128C22×D13—46no—
129C22×D13—46no—
130Q8×C13C2×SD16116yescomplemented
131C2×C4×C13—26no—
132C2×C4×C13C2×SD16112yes—
133C2×C4×C13C22×D416yes—
134C2×C4×C13C22×D411yescharacteristic
135C2×C4×C13C22×D416yes—
136C2×C4×C13C2×#4112yes—
137C2×C4×C132−1+412yes—
138C2×C4×C13C2511yescharacteristic
139C2×Dic13—24no—
140C2×Dic13—22no—
141C2×Dic13—26no—
142C2×Dic13—22no—
143C2×Dic13—42no—
144C2×Dic13—46no—
145D52—26no—
146D52—26no—
147D52—46no—
148D52—424no—
149D52—812no—
150C4×D13—424no—
151Dic26—24no—
152Dic26—22no—
153Dic26—812no—
154Dic26C2×#4114yescomplemented
155C8×C13—26no—
156C8×C13—22no—
157C22×#41—261no—
158C22×SD16—133no—
159Q82—138no—
160Q82—264no—
161#550—138no—
162#550—264no—
163C2×C4⋊Q8—133no—
164C2×C4⋊Q8—263no—
165C2×#127—133no—
166C2×#121—263no—
167C2×C4×Q8—133no—
168C2×C4×Q8—261no—
169C2×C4×Q8C2×D1311yescharacteristic
170C2×C4×D4—133no—
171#486—1324no—
172#476—1324no—
173#460—1324no—
174C8×Q8C2×D1318yescomplemented
175C4×SD16—1324no—
176C2×#106—133no—
177C2×C4⋊C8C2×D1313yes—
178C2×#103—131no—
179C2×#102—133no—
180C2×#102—136no—
181C2×C4×C8C2×D1313yes—
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—26no—
191C4×C13#54812yes—
192C4×C13C22×SD16112yes—
193C4×C13C22×#4111yescharacteristic
194C4×C13C2×2−1+411yescharacteristic
195Dic13—24no—
196Dic13—42no—
197Dic13—46no—
198C2×#41—268no—
199C2×#41—528no—
200C22×Q8—131no—
201C22×Q8—263no—
202C22×Q8D5211yescharacteristic
203C22×D4—133no—
204C22×D4—263no—
205C22×D4—263no—
206C23×C4—263no—
207C2×SD16—1312no—
208C2×SD16—2612no—
209C22×C8C22×D1313yes—
210C22×C8C22×D1311yescharacteristic
211C4⋊Q8—1312no—
212C4⋊Q8—2624no—
213C4⋊Q8—266no—
214#127—1312no—
215#127—266no—
216#121—2624no—
217C4×Q8—1312no—
218C4×Q8—268no—
219C4×Q8—266no—
220C4×Q8D5214yes—
221C4×Q8C22×D1314yes—
222C4×D4—1312no—
223C4×D4—266no—
224C2×C4⋊C4—131no—
225C2×C4⋊C4—133no—
226C2×C4⋊C4—263no—
227C2×C4⋊C4—263no—
228C2×C4⋊C4D5213yes—
229C2×C22⋊C4—263no—
230C2×C42—263no—
231C2×C42C22×D1313yes—
232#106—1312no—
233C4⋊C8C22×D13112yes—
234#103—134no—
235#102—1312no—
236#102—1324no—
237C4×C8C22×D13112yes—
238C2×C13#336214yescomplemented
239C2×C13C2×#54811yescharacteristic
240C2×C13C23×SD1611yescharacteristic
241C2×C13C2×#57611yescharacteristic
242D13—86no—
243C24—263no—
244#41—5232no—
245C2×Q8—134no—
246C2×Q8—132no—
247C2×Q8—261no—
248C2×Q8—2612no—
249C2×Q8—262no—
250C2×Q8—1046no—
251C2×Q8#609518yescomplemented
252C2×Q8C2×D5214yes—
253C2×D4—136no—
254C2×D4—263no—
255C2×D4—2612no—
256C2×D4—2612no—
257C2×D4—266no—
258C2×D4—266no—
259C2×D4—5212no—
260C2×D4—1046no—
261C22×C4—261no—
262C22×C4—263no—
263C22×C4—261no—
264C22×C4—2612no—
265C22×C4—5212no—
266C22×C4C2×D5213yes—
267C22×C4C2×D5213yes—
268C22×C4C23×D1311yescharacteristic
269SD16—2624no—
270C2×C8—22no—
271C2×C8—26no—
272C2×C8C23×D1312yes—
273C2×C8C23×D1316yes—
274C4⋊C4—136no—
275C4⋊C4—132no—
276C4⋊C4—261no—
277C4⋊C4—263no—
278C4⋊C4—2612no—
279C4⋊C4—2612no—
280C4⋊C4C2×D52112yes—
281C22⋊C4—2612no—
282C42—2612no—
283C42C2×D5216yes—
284C42C23×D1316yes—
285C13C2×#336211yescharacteristic, complemented, Sylow
286C23—266no—
287C23—526no—
288C23—526no—
289C23—526no—
290C23C22×D5211yescharacteristic
291Q8—134no—
292Q8—264no—
293Q8—262no—
294Q8—10412no—
295Q8C2×#6095116yescomplemented
296D4—266no—
297D4—266no—
298D4—5224no—
299D4—526no—
300D4—10412no—
301C2×C4—26no—
302C2×C4—264no—
303C2×C4—262no—
304C2×C4—266no—
305C2×C4—262no—
306C2×C4—522no—
307C2×C4—526no—
308C2×C4—5224no—
309C2×C4C2×#6095112yes—
310C2×C4C22×D5216yes—
311C2×C4C22×D5216yes—
312C2×C4C22×D5211yescharacteristic
313C2×C4#8825412yes—
314C2×C4#41×D1312yes—
315C2×C4C24×D1311yescharacteristic
316C8—22no—
317C8—26no—
318C22—526no—
319C22—526no—
320C22—526no—
321C22—10412no—
322C22#1171928112yes—
323C22C22×#609512yes—
324C22#1171945712yes—
325C22C23×D5211yescharacteristic
326C4—26no—
327C4—264no—
328C4—522no—
329C4—526no—
330C4#1171928112yes—
331C4C22×#6095112yes—
332C4C2×#8825411yescharacteristic
333C4C2×#41×D1311yescharacteristic
334C2—1046no—
335C2#1312750814yesdirect product factor
336C2C2×#1171928111yescharacteristic
337C2C23×#609511yescharacteristic
338C2C2×#1171945711yescharacteristic
subgroupG/H
centerC23C22×D52
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C8×Q8×C13C2
socleC23×C13C22×D4
prime radicalC2×#11719282C2
hypercenterC2×C8×Q8D13
hypocenterC13C2×#3362
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic26C2semidirect
3. #13127508C2direct (N × H)
4. C2×#11718355C2semidirect
5. C2×#11718503C2semidirect
6. C2×#11718509C2semidirect
7. C2×C4×#6095C2semidirect
8. C2×C8×Q8×C13C2semidirect
16. Q8×Dic26C22semidirect
23. C8×Q8×C13C22semidirect
30. #11718509C22semidirect
31. #11718503C22semidirect
32. #11718355C22semidirect
33. C4×#6095C22semidirect
76. C2×Q8×C13SD16semidirect
99. C2×Dic26#41semidirect
123. C2×C8×Q8D13semidirect
130. Q8×C13C2×SD16semidirect
154. Dic26C2×#41semidirect
174. C8×Q8C2×D13semidirect
238. C2×C13#3362semidirect
251. C2×Q8#6095semidirect
285. C13C2×#3362semidirect
295. Q8C2×#6095semidirect
335. C2#13127508direct (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
C2×#117192822
#131275082
C2×#117183552
C2×#117185032
C2×#117185092
C2×C4×#60952
C2×C8×Q8×C132
C2×#336213