Finite Group Databasebeta

← C2×#13115974 #15890198

Subgroups — C2×#13115974 #15890198

Order 3328.

1518 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88050C212yesmaximal
2C2×#11718590C211yesmaximal, characteristic
3#13115974C218yesmaximal, direct product factor
4C2×#11718121C212yesmaximal
5C2×#11718116C211yesmaximal, characteristic
6C22×C13×C4⋊Q8C211yesmaximal, characteristic
7C23×Q8×C13—21no—
8C23×Dic26C2211yescharacteristic
9C2×C13×C4⋊Q8—28no—
10C2×C13×C4⋊Q8—22no—
11C2×C13×C4⋊Q8C2214yes—
12C22×C13×C4⋊C4—21no—
13C22×C13×C4⋊C4C2212yes—
14C22×C42×C13C2211yescharacteristic
15C22×C4⋊Dic13C2211yescharacteristic
16C23×#1055C2212yes—
17C2×#88071—21no—
18C2×#88071—21no—
19C2×#88050—28no—
20C2×#88050C2218yes—
21#11718590—22no—
22#11718590C2214yes—
23#11718121C2218yes—
24#11718116C2214yes—
25C22×Q8×C13—28no—
26C22×Q8×C13—24no—
27C22×Q8×C13—44no—
28C22×Q8×C13—44no—
29C23×C4×C13—22no—
30C23×C4×C13D411yescharacteristic
31C23×C4×C13D411yescharacteristic
32C23×C4×C13C2311yescharacteristic
33C23×Dic13—21no—
34C23×Dic13—21no—
35C22×Dic26—24no—
36C22×Dic26—24no—
37C22×Dic26—21no—
38C22×Dic26—22no—
39C22×Dic26Q814yescomplemented
40C22×Dic26C2312yes—
41C13×C4⋊Q8—216no—
42C13×C4⋊Q8—216no—
43C2×C13×C4⋊C4—28no—
44C2×C13×C4⋊C4—24no—
45C2×C13×C4⋊C4—22no—
46C2×C13×C4⋊C4—24no—
47C2×C13×C4⋊C4D418yes—
48C2×C13×C4⋊C4C2314yes—
49C2×C42×C13—24no—
50C2×C42×C13D412yes—
51C2×C42×C13C2312yes—
52C2×C4⋊Dic13—24no—
53C2×C4⋊Dic13—21no—
54C2×C4⋊Dic13C2312yes—
55C22×#1055—24no—
56C22×#1055—24no—
57C22×#1055—24no—
58C22×#1055C2314yes—
59#88071—24no—
60#88071—24no—
61#88050—216no—
62C2×#2024—131nomaximal, Sylow
63C24×C13C2×D411yescharacteristic
64C2×Q8×C13—216no—
65C2×Q8×C13—48no—
66C2×Q8×C13—432no—
67C2×Q8×C13—48no—
68C22×C4×C13—22no—
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—22no—
72C22×C4×C13—28no—
73C22×C4×C13—24no—
74C22×C4×C13—44no—
75C22×C4×C13—44no—
76C22×C4×C13SD1614yes—
77C22×C4×C13Q1614yes—
78C22×C4×C13C2×D412yes—
79C22×C4×C13C2×D412yes—
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13C2×D414yes—
82C22×C4×C13C2×Q812yes—
83C22×C4×C13#4114yes—
84C22×C4×C13#4112yes—
85C22×C4×C13C2411yescharacteristic
86C22×Dic13—24no—
87C22×Dic13—22no—
88C22×Dic13—22no—
89C22×Dic13—42no—
90C22×Dic13—42no—
91C22×Dic13—42no—
92C22×Dic13—42no—
93C22×Dic13—42no—
94C2×Dic26—216no—
95C2×Dic26—24no—
96C2×Dic26—24no—
97C2×Dic26—24no—
98C2×Dic26—22no—
99C2×Dic26—42no—
100C2×Dic26—48no—
101C2×Dic26—42no—
102C2×Dic26C2×Q814yescomplemented
103C13×C4⋊C4—216no—
104C13×C4⋊C4—28no—
105C13×C4⋊C4—24no—
106C13×C4⋊C4C2×D418yes—
107C42×C13—24no—
108C42×C13—24no—
109C4⋊Dic13—24no—
110C4⋊Dic13—42no—
111C2×#1055—24no—
112C2×#1055—24no—
113C2×#1055—24no—
114C2×#1055—48no—
115C22×C4⋊Q8D1311yescharacteristic
116C22×#103—132no—
117C2×#391—131no—
118#2024—138no—
119C2×#340—132no—
120C2×#336—131no—
121C23×C13#12012yes—
122C23×C13C22⋊Q812yes—
123C23×C13#12412yes—
124C23×C13C2×SD1612yes—
125C23×C13C2×Q1612yes—
126C23×C13AGL(1,ℤ/8)12yes—
127C23×C13#13712yes—
128C23×C13C22×D411yescharacteristic
129Q8×C13—432no—
130C2×C4×C13—22no—
131C2×C4×C13—22no—
132C2×C4×C13—22no—
133C2×C4×C13—22no—
134C2×C4×C13—28no—
135C2×C4×C13—28no—
136C2×C4×C13—28no—
137C2×C4×C13—44no—
138C2×C4×C13—44no—
139C2×C4×C13—416no—
140C2×C4×C13#12012yes—
141C2×C4×C13C22⋊Q818yes—
142C2×C4×C13C22⋊Q812yes—
143C2×C4×C13#12418yes—
144C2×C4×C13#12412yes—
145C2×C4×C13C2×SD1614yes—
146C2×C4×C13C2×Q1614yes—
147C2×C4×C13C22×D412yes—
148C2×C4×C13C22×Q811yescharacteristic
149C2×C4×C13C2×#4112yes—
150C2×C4×C13C2×#4111yescharacteristic
151C2×Dic13—24no—
152C2×Dic13—42no—
153C2×Dic13—42no—
154C2×Dic13—48no—
155C2×Dic13—42no—
156C2×Dic13—42no—
157C2×Dic13—42no—
158C2×Dic13—84no—
159Dic26—28no—
160Dic26—44no—
161Dic26—48no—
162#1055—44no—
163C23×Q8—21no—
164C23×Q8—131no—
165C23×C8—132no—
166C2×C4⋊Q8—28no—
167C2×C4⋊Q8—22no—
168C2×C4⋊Q8C2×D1314yes—
169C22×C4⋊C4—21no—
170C22×C4⋊C4—131no—
171C22×C4⋊C4C2×D1312yes—
172C22×C42C2×D1311yescharacteristic
173C2×#103—138no—
174C2×#103—268no—
175#391—134no—
176#391—262no—
177C2×#95—261no—
178C2×#95—261no—
179#340—138no—
180#336—134no—
181C22×C13#39314yes—
182C22×C13#45014yes—
183C22×C13#45114yes—
184C22×C13#47514yes—
185C22×C13#47714yes—
186C22×C13#48714yes—
187C22×C13#48914yes—
188C22×C13C2×#12011yescharacteristic
189C22×C13C2×C22⋊Q811yescharacteristic
190C22×C13C2×#12411yescharacteristic
191C22×C13C22×SD1611yescharacteristic
192C22×C13C22×Q1611yescharacteristic
193C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
194C22×C13C2×#13711yescharacteristic
195C4×C13—24no—
196C4×C13—24no—
197C4×C13—48no—
198C4×C13#39314yes—
199C4×C13C2×C22⋊Q812yes—
200C4×C13C2×#12412yes—
201Dic13—44no—
202Dic13—82no—
203C22×Q8—28no—
204C22×Q8—24no—
205C22×Q8—44no—
206C22×Q8—44no—
207C22×Q8—134no—
208C22×Q8—132no—
209C22×Q8—262no—
210C22×Q8—261no—
211C22×Q8—264no—
212C22×Q8—264no—
213C23×C4—22no—
214C23×C4—261no—
215C23×C4—261no—
216C23×C4C22⋊D1311yescharacteristic
217C23×C4C22⋊D1311yescharacteristic
218C23×C4C22×D1311yescharacteristic
219C22×C8—134no—
220C22×C8—264no—
221C22×C8—264no—
222C22×C8—264no—
223C4⋊Q8—216no—
224C4⋊Q8—216no—
225C2×C4⋊C4—28no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—24no—
229C2×C4⋊C4—132no—
230C2×C4⋊C4—264no—
231C2×C4⋊C4—261no—
232C2×C4⋊C4C22⋊D1318yes—
233C2×C4⋊C4C22×D1314yes—
234C2×C42—24no—
235C2×C42C22⋊D1312yes—
236C2×C42C22×D1312yes—
237#103—2616no—
238#95—264no—
239#95—264no—
240C2×C13#202418yescomplemented
241C2×C13C2×#39311yescharacteristic
242C2×C13C2×#45011yescharacteristic
243C2×C13C2×#45111yescharacteristic
244C2×C13C2×#47511yescharacteristic
245C2×C13C2×#47711yescharacteristic
246C2×C13C2×#48711yescharacteristic
247C2×C13C2×#48911yescharacteristic
248C24C2×C22⋊D1311yescharacteristic
249C2×Q8—216no—
250C2×Q8—48no—
251C2×Q8—432no—
252C2×Q8—48no—
253C2×Q8—134no—
254C2×Q8—264no—
255C2×Q8—262no—
256C2×Q8—2616no—
257C2×Q8—264no—
258C2×Q8—264no—
259C2×Q8—522no—
260C2×Q8—528no—
261C2×Q8—522no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—28no—
267C22×C4—24no—
268C22×C4—44no—
269C22×C4—44no—
270C22×C4—264no—
271C22×C4—262no—
272C22×C4—262no—
273C22×C4—522no—
274C22×C4—522no—
275C22×C4—522no—
276C22×C4—522no—
277C22×C4—522no—
278C22×C4#610514yes—
279C22×C4#610714yes—
280C22×C4Q8×D1312yes—
281C22×C4#613114yes—
282C22×C4#613112yes—
283C22×C4C2×C22⋊D1312yes—
284C22×C4C2×C22⋊D1312yes—
285C22×C4C2×C22⋊D1311yescharacteristic
286C22×C4C2×C22⋊D1314yes—
287C22×C4C23×D1311yescharacteristic
288C2×C8—264no—
289C2×C8—264no—
290C2×C8—264no—
291C2×C8—528no—
292C4⋊C4—216no—
293C4⋊C4—28no—
294C4⋊C4—24no—
295C4⋊C4—264no—
296C4⋊C4—522no—
297C4⋊C4C2×C22⋊D1318yes—
298C42—24no—
299C42—24no—
300C13C2×#202411yescharacteristic, complemented, Sylow
301C23#8818612yes—
302C23C2×#610512yes—
303C23#8819612yes—
304C23C2×#610712yes—
305C23#8820012yes—
306C23#8820112yes—
307C23#8820712yes—
308C23C22×C22⋊D1311yescharacteristic
309Q8—432no—
310Q8—268no—
311Q8—524no—
312Q8—528no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—28no—
318C2×C4—28no—
319C2×C4—28no—
320C2×C4—44no—
321C2×C4—44no—
322C2×C4—416no—
323C2×C4—264no—
324C2×C4—522no—
325C2×C4—522no—
326C2×C4—528no—
327C2×C4—522no—
328C2×C4—522no—
329C2×C4—522no—
330C2×C4—1044no—
331C2×C4C2×#610514yes—
332C2×C4C2×#610714yes—
333C2×C4#8820018yes—
334C2×C4#8820012yes—
335C2×C4#8820118yes—
336C2×C4#8820112yes—
337C2×C4#8820712yes—
338C2×C4C2×Q8×D1311yescharacteristic
339C2×C4C2×#613112yes—
340C2×C4C2×#613111yescharacteristic
341C2×C4C22×C22⋊D1312yes—
342C8—524no—
343C22#1171875014yes—
344C22#1171875214yes—
345C22#1171875414yes—
346C22#1171875514yes—
347C22#1171887914yes—
348C22#1171888914yes—
349C22#1171889214yes—
350C22C2×#8818611yescharacteristic
351C22C22×#610511yescharacteristic
352C22C2×#8819611yescharacteristic
353C22C22×#610711yescharacteristic
354C22C2×#8820011yescharacteristic
355C22C2×#8820111yescharacteristic
356C22C2×#8820711yescharacteristic
357C4—24no—
358C4—24no—
359C4—48no—
360C4—524no—
361C4—1042no—
362C4#1171889214yes—
363C4C2×#8820012yes—
364C4C2×#8820112yes—
365C2#1311597418yesdirect product factor
366C2C2×#1171889211yescharacteristic
367C2C2×#1171887911yescharacteristic
368C2C2×#1171888911yescharacteristic
369C2C2×#1171875511yescharacteristic
370C2C2×#1171875211yescharacteristic
371C2C2×#1171875411yescharacteristic
372C2C2×#1171875011yescharacteristic
subgroupG/H
centerC24C2×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC22×C13×C4⋊Q8C2
socle, prime radicalC24×C13C2×D4
hypercenterC22×C4⋊Q8D13
hypocenterC13C2×#2024
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13115974C2direct (N × H)
39. C22×Dic26Q8semidirect
102. C2×Dic26C2×Q8semidirect
240. C2×C13#2024semidirect
300. C13C2×#2024semidirect
365. C2#13115974direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#880502
C2×#117185902
#131159742
C2×#117181212
C2×#117181162
C22×C13×C4⋊Q82
C2×#202413