Finite Group Databasebeta

← C4×#11718663 #15860673

Subgroups — C4×#11718663 #15860673

Order 3328.

1670 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#6127C211yesmaximal, characteristic
2C2×#11718663C212yesmaximal
3C22×C4×#1055C211yesmaximal, characteristic, complemented
4C4×#88050C214yesmaximal, complemented
5C4×#88049C214yesmaximal, complemented
6#13114552C212yesmaximal, complemented
7C4×C13×#117C211yesmaximal, characteristic, complemented
8C22×#6127C2211yescharacteristic
9C2×C13×#117C2212yes—
10C22×C42×C13C2211yescharacteristic
11C2×C4×C22⋊D13—22no—
12C2×#88180C2211yescharacteristic
13C23×#1055C2212yes—
14C4×#6127—24no—
15C4×#6127C418yescomplemented
16C2×C4×D52C2212yes—
17C2×#88126—21no—
18C2×C42×D13—21no—
19C2×C4×Dic26C2212yes—
20C4×C13×C4⋊C4C2214yes—
21C4×C13×C22⋊C4—22no—
22C13×#376—21no—
23C43×C13—21no—
24#11718663C4116yesdirect product factor
25C2×#88050C2214yes—
26C2×#88049C2214yes—
27C2×C4×#1055—24no—
28C2×C4×#1055C2214yes—
29#11718121C2218yes—
30C23×C4×C13D412yes—
31C23×C4×C13C2311yescharacteristic
32C22×C22⋊D13—21no—
33C2×#6127—22no—
34C2×#6127—24no—
35C2×#6127C2×C418yes—
36C2×#6127C2×C414yes—
37C22×D52C2311yescharacteristic
38C22×C4×D13—21no—
39C22×C4×D13—22no—
40C22×Dic26C2311yescharacteristic
41C13×#117—24no—
42C13×#117C2×C418yescomplemented
43C2×C13×C4⋊C4C2314yes—
44C2×C13×C22⋊C4—22no—
45C2×C42×C13—22no—
46C2×C42×C13—24no—
47C2×C42×C13C2×C414yes—
48C2×C42×C13D414yes—
49C2×C42×C13D411yescharacteristic
50C2×C42×C13D411yescharacteristic
51C2×C42×C13C2312yes—
52C2×C22⋊Dic13—21no—
53C4×C22⋊D13—216no—
54C2×#6103—22no—
55#88180—22no—
56#88180C2×C414yes—
57C2×C4⋊Dic13C2312yes—
58C2×#6101—22no—
59C2×C4×Dic13—22no—
60C2×C4×Dic13—21no—
61C22×#1055—24no—
62C22×#1055—24no—
63C22×#1055C2×C418yescomplemented
64C22×#1055C2314yes—
65C4×D52—24no—
66C4×D52C2×C418yes—
67#88126—28no—
68C42×D13—28no—
69C4×Dic26—24no—
70C4×Dic26C2×C418yes—
71C13×#95—24no—
72#88050C2×C4116yescomplemented
73#88049C2×C4116yescomplemented
74C4×#1055—28no—
75C4×#416—131nomaximal, Sylow
76C24×C13C2×D411yescharacteristic
77C23×D13—21no—
78C22×C4×C13—28no—
79C22×C4×C13—24no—
80C22×C4×C13C22⋊C418yes—
81C22×C4×C13C22×C412yes—
82C22×C4×C13C22×C414yes—
83C22×C4×C13C2×D412yes—
84C22×C4×C13C2×D412yes—
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13C2×D412yes—
87C22×C4×C13#4114yes—
88C22×C4×C13C2411yescharacteristic
89C2×C22⋊D13—24no—
90C2×C22⋊D13—28no—
91C22×Dic13—21no—
92C22×Dic13—22no—
93#6127—28no—
94#6127—216no—
95#6127C42116yescomplemented
96C2×D52—21no—
97C2×D52—22no—
98C2×D52C22×C412yes—
99C2×D52C22×C414yes—
100C2×C4×D13—24no—
101C2×C4×D13—28no—
102C2×C4×D13—28no—
103C2×C4×D13—48no—
104C2×Dic26—21no—
105C2×Dic26—22no—
106C2×Dic26C22×C412yes—
107C2×Dic26C22×C414yes—
108C13×C4⋊C4—24no—
109C13×C4⋊C4C22×C418yes—
110C13×C22⋊C4—28no—
111C42×C13—28no—
112C42×C13—48no—
113C42×C13C22⋊C414yes—
114C42×C13C22⋊C414yes—
115C42×C13C22×C414yes—
116C42×C13C2×D414yes—
117C22⋊Dic13—24no—
118#6103—28no—
119C4⋊Dic13—22no—
120C4⋊Dic13C22×C414yes—
121#6101—28no—
122C4×Dic13—28no—
123C4×Dic13—24no—
124C2×#1055—216no—
125C2×#1055—24no—
126C2×#1055—24no—
127C2×#1055C22×C418yes—
128C2×C4×#41—131no—
129C2×#416—132no—
130C22×C4×C8—131no—
131C4×#117D1311yescharacteristic, complemented
132C4×#103—134no—
133C4×#102—134no—
134#1735—132no—
135C23×C13—24no—
136C23×C13C2×C22⋊C412yes—
137C23×C13C4×D414yes—
138C23×C13C22×D411yescharacteristic
139C22×D13—22no—
140C22×D13—24no—
141C22×D13—44no—
142C2×C4×C13—24no—
143C2×C4×C13—216no—
144C2×C4×C13—28no—
145C2×C4×C13—48no—
146C2×C4×C13C2×C4214yes—
147C2×C4×C13C2×C22⋊C414yes—
148C2×C4×C13C2×C22⋊C412yes—
149C2×C4×C13C2×C22⋊C414yes—
150C2×C4×C13#11714yes—
151C2×C4×C13C4×D418yes—
152C2×C4×C13C4×D414yes—
153C2×C4×C13#13518yes—
154C2×C4×C13C23×C411yescharacteristic
155C2×C4×C13C23×C412yes—
156C2×C4×C13C22×D411yescharacteristic
157C2×C4×C13C2×#4112yes—
158C22⋊D13—216no—
159C2×Dic13—22no—
160C2×Dic13—24no—
161C2×Dic13—24no—
162C2×Dic13—44no—
163D52—22no—
164D52—24no—
165D52C2×C4214yes—
166C4×D13—216no—
167C4×D13—416no—
168Dic26—22no—
169Dic26—24no—
170Dic26C2×C4214yes—
171#1055—28no—
172C22×#41—131no—
173C23×C8—132no—
174C4×#41—138no—
175C4×#41—264no—
176C2×C4×Q8—132no—
177C2×C4×D4—132no—
178C2×C4×D4—262no—
179C2×#117—131no—
180C2×#117—261no—
181C2×#117C2×D1312yes—
182C22×C42—261no—
183C22×C42C2×D1311yescharacteristic
184#416—1316no—
185C2×#103—134no—
186C2×#102—134no—
187C2×C4×C8—134no—
188C2×C4×C8—264no—
189C4×C4⋊C4C2×D1314yes—
190C4×C22⋊C4—22no—
191#376—21no—
192C43—21no—
193#340—138no—
194C22×C13—24no—
195C22×C13—28no—
196C22×C13C4×C22⋊C414yes—
197C22×C13C22×C22⋊C411yescharacteristic
198C22×C13C2×C4×D412yes—
199C22×C13C2×#13514yes—
200C2×D13—24no—
201C2×D13—44no—
202C2×D13—48no—
203C4×C13—24no—
204C4×C13—48no—
205C4×C13C4×C22⋊C414yes—
206C4×C13#41618yescomplemented
207C4×C13C22×C4211yescharacteristic
208C4×C13C2×#11711yescharacteristic
209C4×C13C2×C4×D412yes—
210Dic13—24no—
211Dic13—44no—
212C2×#41—134no—
213C2×#41—138no—
214C2×#41—262no—
215C2×#41—264no—
216C22×Q8—131no—
217C22×D4—131no—
218C22×D4—261no—
219C23×C4—261no—
220C23×C4—262no—
221C23×C4C22⋊D1312yes—
222C23×C4C22×D1311yescharacteristic
223C22×C8—138no—
224C22×C8—134no—
225C22×C8—264no—
226C22×C8—264no—
227C4×Q8—138no—
228C4×Q8—264no—
229C4×D4—138no—
230C4×D4—2616no—
231C4×D4—264no—
232#117—24no—
233#117—134no—
234#117—262no—
235#117—268no—
236#117C4×D1318yescomplemented
237C2×C4⋊C4—132no—
238C2×C4⋊C4—262no—
239C2×C4⋊C4C22×D1314yes—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—261no—
242C2×C22⋊C4—262no—
243C2×C42—22no—
244C2×C42—24no—
245C2×C42—261no—
246C2×C42—262no—
247C2×C42—268no—
248C2×C42C4×D1314yes—
249C2×C42D5214yes—
250C2×C42C22⋊D1311yescharacteristic
251C2×C42C22⋊D1311yescharacteristic
252C2×C42C22×D1312yes—
253#103—1316no—
254#102—1316no—
255C4×C8—268no—
256#95—24no—
257C2×C13—24no—
258C2×C13C2×C4×C22⋊C411yescharacteristic
259C2×C13C2×#41612yes—
260C2×C13C4×#13514yes—
261D13—44no—
262C24—261no—
263C24C2×C22⋊D1311yescharacteristic
264#41—1316no—
265#41—268no—
266#41—2616no—
267C2×Q8—134no—
268C2×Q8—132no—
269C2×Q8—261no—
270C2×Q8—262no—
271C2×D4—134no—
272C2×D4—132no—
273C2×D4—264no—
274C2×D4—268no—
275C2×D4—261no—
276C2×D4—262no—
277C22×C4—28no—
278C22×C4—24no—
279C22×C4—261no—
280C22×C4—264no—
281C22×C4—268no—
282C22×C4—262no—
283C22×C4—268no—
284C22×C4—528no—
285C22×C4#610318yes—
286C22×C4C2×C4×D1312yes—
287C22×C4C2×C4×D1314yes—
288C22×C4C2×D5212yes—
289C22×C4#612714yes—
290C22×C4C2×C22⋊D1312yes—
291C22×C4C2×C22⋊D1311yescharacteristic
292C22×C4C2×C22⋊D1312yes—
293C22×C4C23×D1311yescharacteristic
294C2×C8—138no—
295C2×C8—2616no—
296C2×C8—264no—
297C2×C8—264no—
298C4⋊C4—24no—
299C4⋊C4—134no—
300C4⋊C4—268no—
301C4⋊C4—262no—
302C4⋊C4C2×C4×D1318yes—
303C22⋊C4—28no—
304C22⋊C4—264no—
305C22⋊C4—268no—
306C42—28no—
307C42—48no—
308C42—264no—
309C42—268no—
310C42#610314yes—
311C42#610314yes—
312C42C2×C4×D1314yes—
313C42C2×D5214yes—
314C13C4×#41611yescharacteristic, complemented, Sylow
315C23—24no—
316C23—262no—
317C23—264no—
318C23—524no—
319C23C2×#610312yes—
320C23C4×C22⋊D1314yes—
321C23C22×C22⋊D1311yescharacteristic
322Q8—134no—
323Q8—262no—
324Q8—264no—
325D4—134no—
326D4—2616no—
327D4—262no—
328D4—264no—
329C2×C4—24no—
330C2×C4—216no—
331C2×C4—28no—
332C2×C4—48no—
333C2×C4—262no—
334C2×C4—264no—
335C2×C4—2616no—
336C2×C4—264no—
337C2×C4—524no—
338C2×C4—5216no—
339C2×C4C42×D1314yes—
340C2×C4#8812614yes—
341C2×C4C4×D5218yes—
342C2×C4C2×#610314yes—
343C2×C4C2×#610314yes—
344C2×C4C2×#610312yes—
345C2×C4C4×C22⋊D1314yes—
346C2×C4#8820418yes—
347C2×C4C22×C4×D1311yescharacteristic
348C2×C4C22×C4×D1312yes—
349C2×C4C22×D5211yescharacteristic
350C2×C4C2×#612712yes—
351C8—268no—
352C22—24no—
353C22—28no—
354C22—264no—
355C22—524no—
356C22—528no—
357C22C4×#610314yes—
358C22C22×#610311yescharacteristic
359C22C2×C4×C22⋊D1312yes—
360C22C2×#8820414yes—
361C4—24no—
362C4—48no—
363C4—264no—
364C4—524no—
365C4C4×#610314yes—
366C4#1171866318yesdirect product factor
367C4C2×C42×D1311yescharacteristic
368C4C2×#8812611yescharacteristic
369C4C2×C4×D5212yes—
370C2—24no—
371C2—524no—
372C2C2×C4×#610311yescharacteristic
373C2C2×#1171866312yes—
374C2C4×#8820414yes—
subgroupG/H
centerC2×C42C22⋊D13
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC4×C13×#117C2
socleC23×C13C22×D4
prime radicalC22×#6127C22
cosocleC22×C4×C13C24
hypercenterC4×#117D13
hypocenterC13C4×#416
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C42 ◁ C22×C42 ◁ C4×#117

Complements

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

NH ≅ G/Ntype
3. C22×C4×#1055C2semidirect
4. C4×#88050C2semidirect
5. C4×#88049C2semidirect
6. #13114552C2semidirect
7. C4×C13×#117C2semidirect
15. C4×#6127C4semidirect
24. #11718663C4direct (N × H)
42. C13×#117C2×C4semidirect
63. C22×#1055C2×C4semidirect
72. #88050C2×C4semidirect
73. #88049C2×C4semidirect
95. #6127C42semidirect
131. C4×#117D13semidirect
206. C4×C13#416semidirect
236. #117C4×D13semidirect
314. C13C4×#416semidirect
366. C4#11718663direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#61272
C2×#117186632
C22×C4×#10552
C4×#880502
C4×#880492
#131145522
C4×C13×#1172
C4×#41613