Finite Group Databasebeta

← C2×#13119123 #16032738

Subgroups — C2×#13119123 #16032738

Order 3328.

2918 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
1C22×#88180C211yesmaximal, characteristic
2#13119123C2116yesmaximal, direct product factor
3C2×#11718647C212yesmaximal, complemented
4C2×#11718644C212yesmaximal, complemented
5C2×#11718639C214yesmaximal, complemented
6C2×#11718871C212yesmaximal
7C2×#11718872C211yesmaximal, characteristic
8C2×#11718872C212yesmaximal
9C23×C13×C4⋊C4C211yesmaximal, characteristic
10C24×C4×C13C2211yescharacteristic
11C24×C4×C13C2211yescharacteristic
12C24×C4×C13C2211yescharacteristic
13C22×C13×C4⋊C4—28no—
14C22×C13×C4⋊C4C2212yes—
15C22×C13×C4⋊C4C2212yes—
16C22×C13×C4⋊C4C2218yes—
17C22×C22⋊Dic13C2212yes—
18C22×C22⋊Dic13C2212yes—
19C2×#88180—28no—
20C2×#88180C2218yes—
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C22×#6101C2214yes—
24C22×C4×Dic13C2212yes—
25#11718872C2218yes—
26#11718872C22116yes—
27#11718871C22116yes—
28C2×#88071C2212yes—
29C2×#88071C2214yes—
30C2×#88071C2214yes—
31C2×#88071C2212yes—
32C2×#88071C2214yes—
33#11718647C22116yescomplemented
34#11718644C22116yescomplemented
35#11718639C22132yescomplemented
36C25×C13C2311yescharacteristic
37C23×C4×C13—24no—
38C23×C4×C13—28no—
39C23×C4×C13—28no—
40C23×C4×C13—24no—
41C23×C4×C13—28no—
42C23×C4×C13D418yes—
43C23×C4×C13C2312yes—
44C23×C4×C13C2314yes—
45C23×C4×C13C2314yes—
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2311yescharacteristic
48C23×C4×C13C2314yes—
49C23×C4×C13C2312yes—
50C23×Dic13C2312yes—
51C23×Dic13C2312yes—
52C23×Dic13C2314yes—
53C2×C13×C4⋊C4—28no—
54C2×C13×C4⋊C4—28no—
55C2×C13×C4⋊C4—232no—
56C2×C13×C4⋊C4C2318yes—
57C2×C13×C4⋊C4C2318yes—
58C2×C22⋊Dic13—28no—
59C2×C22⋊Dic13—28no—
60C2×C22⋊Dic13C2318yes—
61C2×C22⋊Dic13C2318yes—
62#88180—232no—
63C2×C4⋊Dic13—24no—
64C2×C4⋊Dic13—24no—
65C2×C4⋊Dic13C2314yes—
66C2×C4⋊Dic13C2314yes—
67C2×#6101—216no—
68C2×#6101C23116yes—
69C2×C4×Dic13—28no—
70C2×C4×Dic13C2318yes—
71#88071C23116yes—
72#88071C2318yes—
73#88071C23116yes—
74#88071C23116yes—
75#88071C2318yes—
76C2×#2484—131nomaximal, Sylow
77C24×C13—24no—
78C24×C13—24no—
79C24×C13C2×D414yes—
80C24×C13#4118yes—
81C24×C13C2412yes—
82C24×C13C2411yescharacteristic
83C22×C4×C13—232no—
84C22×C4×C13—232no—
85C22×C4×C13—28no—
86C22×C4×C13—24no—
87C22×C4×C13—24no—
88C22×C4×C13—216no—
89C22×C4×C13—24no—
90C22×C4×C13—24no—
91C22×C4×C13—216no—
92C22×C4×C13—28no—
93C22×C4×C13—24no—
94C22×C4×C13—216no—
95C22×C4×C13—28no—
96C22×C4×C13—416no—
97C22×C4×C13C2×D414yes—
98C22×C4×C13C2×D414yes—
99C22×C4×C13C2×D4116yes—
100C22×C4×C13#4118yes—
101C22×C4×C13C2414yes—
102C22×C4×C13C2412yes—
103C22×C4×C13C2412yes—
104C22×C4×C13C2414yes—
105C22×Dic13—24no—
106C22×Dic13—24no—
107C22×Dic13—28no—
108C22×Dic13—28no—
109C22×Dic13—28no—
110C22×Dic13—28no—
111C22×Dic13—28no—
112C22×Dic13C2418yes—
113C22×Dic13C2414yes—
114C22×Dic13C2414yes—
115C13×C4⋊C4—216no—
116C13×C4⋊C4—216no—
117C22⋊Dic13—216no—
118C22⋊Dic13—216no—
119C4⋊Dic13—28no—
120C4⋊Dic13—28no—
121#6101—232no—
122C4×Dic13—216no—
123C22×#117—131no—
124C23×C4⋊C4D1311yescharacteristic
125#2484—1316no—
126C2×#400—132no—
127C2×#398—132no—
128C2×#387—134no—
129C2×#385—132no—
130C2×#381—132no—
131C2×#381—131no—
132C23×C13—28no—
133C23×C13—28no—
134C23×C13—232no—
135C23×C13—24no—
136C23×C13—24no—
137C23×C13#123116yes—
138C23×C13C22×D414yes—
139C23×C13C22×D412yes—
140C23×C13C2×#4118yes—
141C23×C13C2×#4114yes—
142C23×C13C2×#4114yes—
143C23×C132−1+414yes—
144C23×C13C2511yescharacteristic
145C2×C4×C13—232no—
146C2×C4×C13—232no—
147C2×C4×C13—28no—
148C2×C4×C13—28no—
149C2×C4×C13—216no—
150C2×C4×C13—24no—
151C2×C4×C13—24no—
152C2×C4×C13—24no—
153C2×C4×C13—24no—
154C2×C4×C13—24no—
155C2×C4×C13—28no—
156C2×C4×C13—416no—
157C2×C4×C13—48no—
158C2×C4×C13C22×D414yes—
159C2×C4×C13C22×D414yes—
160C2×C4×C13C2×#4118yes—
161C2×Dic13—24no—
162C2×Dic13—24no—
163C2×Dic13—28no—
164C2×Dic13—28no—
165C2×Dic13—28no—
166C2×Dic13—28no—
167C2×Dic13—28no—
168C2×Dic13—48no—
169C2×Dic13—48no—
170C2×Dic13—416no—
171C24×C4C2×D1311yescharacteristic
172C24×C4C2×D1311yescharacteristic
173C24×C4C2×D1311yescharacteristic
174C2×#117—138no—
175C2×#117—268no—
176C22×C4⋊C4—28no—
177C22×C4⋊C4—134no—
178C22×C4⋊C4—131no—
179C22×C4⋊C4—131no—
180C22×C4⋊C4C2×D1312yes—
181C22×C4⋊C4C2×D1318yes—
182C22×C4⋊C4C2×D1312yes—
183C22×C22⋊C4—132no—
184C22×C22⋊C4—132no—
185C22×C42—132no—
186#400—1316no—
187#398—1316no—
188#387—1332no—
189#385—1316no—
190#381—138no—
191#381—1316no—
192C2×#95—132no—
193C2×#95—134no—
194C2×#95—134no—
195C2×#95—134no—
196C2×#95—132no—
197C22×C13—24no—
198C22×C13—24no—
199C22×C13—216no—
200C22×C13—232no—
201C22×C13C2×#12318yes—
202C22×C13C2×#12314yes—
203C22×C13#52514yes—
204C22×C13#53614yes—
205C22×C13#552116yes—
206C22×C13C23×D411yescharacteristic
207C22×C13C22×#4112yes—
208C22×C13C22×#4112yes—
209C22×C13C2×2−1+412yes—
210C4×C13—24no—
211C4×C13—24no—
212C4×C13—28no—
213C4×C13—44no—
214Dic13—44no—
215Dic13—44no—
216Dic13—48no—
217C25C22×D1311yescharacteristic
218C23×C4—28no—
219C23×C4—24no—
220C23×C4—28no—
221C23×C4—28no—
222C23×C4—24no—
223C23×C4—132no—
224C23×C4—134no—
225C23×C4—132no—
226C23×C4C22⋊D1318yes—
227C23×C4C22×D1314yes—
228C23×C4C22×D1314yes—
229C23×C4C22×D1312yes—
230C23×C4C22×D1312yes—
231C23×C4C22×D1314yes—
232C23×C4C22×D1311yescharacteristic
233C23×C4C22×D1311yescharacteristic
234#117—2632no—
235C2×C4⋊C4—28no—
236C2×C4⋊C4—28no—
237C2×C4⋊C4—232no—
238C2×C4⋊C4—134no—
239C2×C4⋊C4—134no—
240C2×C4⋊C4—1316no—
241C2×C4⋊C4—2616no—
242C2×C4⋊C4—264no—
243C2×C4⋊C4—264no—
244C2×C4⋊C4C22×D1318yes—
245C2×C4⋊C4C22×D1318yes—
246C2×C22⋊C4—138no—
247C2×C22⋊C4—138no—
248C2×C22⋊C4—268no—
249C2×C22⋊C4—268no—
250C2×C42—138no—
251C2×C42—268no—
252#95—138no—
253#95—1316no—
254#95—1316no—
255#95—138no—
256#95—1316no—
257C2×C13—28no—
258C2×C13#248418yescomplemented
259C2×C13C22×#12311yescharacteristic
260C2×C13C2×#52511yescharacteristic
261C2×C13C2×#53611yescharacteristic
262C2×C13C2×#55214yes—
263C24—24no—
264C24—24no—
265C24#612918yes—
266C24C2×C22⋊D1314yes—
267C24C23×D1312yes—
268C24C23×D1311yescharacteristic
269C22×C4—232no—
270C22×C4—232no—
271C22×C4—24no—
272C22×C4—216no—
273C22×C4—24no—
274C22×C4—24no—
275C22×C4—28no—
276C22×C4—24no—
277C22×C4—216no—
278C22×C4—216no—
279C22×C4—28no—
280C22×C4—28no—
281C22×C4—24no—
282C22×C4—416no—
283C22×C4—138no—
284C22×C4—134no—
285C22×C4—134no—
286C22×C4—268no—
287C22×C4—268no—
288C22×C4—268no—
289C22×C4—268no—
290C22×C4—268no—
291C22×C4—264no—
292C22×C4—264no—
293C22×C4#612718yes—
294C22×C4C2×C22⋊D1314yes—
295C22×C4C2×C22⋊D1314yes—
296C22×C4C2×C22⋊D13116yes—
297C22×C4C23×D1314yes—
298C22×C4C23×D1314yes—
299C22×C4C23×D1312yes—
300C22×C4C23×D1312yes—
301C4⋊C4—216no—
302C4⋊C4—216no—
303C4⋊C4—2632no—
304C4⋊C4—268no—
305C4⋊C4—268no—
306C22⋊C4—2616no—
307C22⋊C4—2616no—
308C42—2616no—
309C13C2×#248411yescharacteristic, complemented, Sylow
310C23—232no—
311C23—28no—
312C23—28no—
313C23—24no—
314C23—24no—
315C23#88189116yes—
316C23C2×#612714yes—
317C23C2×#612918yes—
318C23C2×#612914yes—
319C23#8825414yes—
320C23C22×C22⋊D1314yes—
321C23C22×C22⋊D1312yes—
322C23C24×D1311yescharacteristic
323C2×C4—232no—
324C2×C4—216no—
325C2×C4—232no—
326C2×C4—28no—
327C2×C4—28no—
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—28no—
333C2×C4—24no—
334C2×C4—416no—
335C2×C4—48no—
336C2×C4—268no—
337C2×C4—268no—
338C2×C4—268no—
339C2×C4—268no—
340C2×C4—268no—
341C2×C4—264no—
342C2×C4—264no—
343C2×C4—5216no—
344C2×C4—528no—
345C2×C4—528no—
346C2×C4C2×#612718yes—
347C2×C4C22×C22⋊D1314yes—
348C2×C4C22×C22⋊D1314yes—
349C22—24no—
350C22—232no—
351C22—216no—
352C22—24no—
353C22#11719218116yes—
354C22#1171949614yes—
355C22C2×#8818918yes—
356C22C2×#8818914yes—
357C22#1171952114yes—
358C22C22×#612712yes—
359C22C22×#612912yes—
360C22C2×#8825412yes—
361C22C23×C22⋊D1311yescharacteristic
362C4—24no—
363C4—24no—
364C4—28no—
365C4—44no—
366C4—524no—
367C4—528no—
368C4—524no—
369C2—28no—
370C2#1311912318yesdirect product factor
371C2C22×#8818911yescharacteristic
372C2C2×#1171949611yescharacteristic
373C2C2×#1171952111yescharacteristic
374C2C2×#1171921814yes—
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC23×C13×C4⋊C4C2
socleC24×C13C24
prime radicalC25×C13C23
hypercenterC23×C4⋊C4D13
hypocenterC13C2×#2484
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13119123C2direct (N × H)
3. C2×#11718647C2semidirect
4. C2×#11718644C2semidirect
5. C2×#11718639C2semidirect
33. #11718647C22semidirect
34. #11718644C22semidirect
35. #11718639C22semidirect
258. C2×C13#2484semidirect
309. C13C2×#2484semidirect
370. C2#13119123direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881802
#131191232
C2×#117186472
C2×#117186442
C2×#117186392
C2×#117188712
C2×#117188722
C23×C13×C4⋊C42
C2×#248413