Finite Group Databasebeta

← C2×#13130084 #16792845

Subgroups — C2×#13130084 #16792845

Order 3328.

1718 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719169C212yesmaximal
2#13130084C218yesmaximal, direct product factor
3C2×#11718285C214yesmaximal, complemented
4C23×C4⋊Dic13C211yesmaximal, characteristic
5C24×C4×C13C411yescharacteristic
6C24×Dic13C411yescharacteristic
7C24×Dic13C2211yescharacteristic
8C22×#6122—22no—
9C22×C4⋊Dic13—22no—
10C22×C4⋊Dic13—22no—
11C22×C4⋊Dic13—24no—
12C22×C4⋊Dic13C414yes—
13C22×C4⋊Dic13C412yes—
14C22×C4⋊Dic13C2212yes—
15C22×C4⋊Dic13C2214yes—
16#11719169—24no—
17#11719169C2218yes—
18C2×C22⋊#1057—22no—
19C2×C22⋊#1057C2214yes—
20#11718285C22116yescomplemented
21C25×C13C2×C411yescharacteristic
22C23×C4×C13—22no—
23C23×C4×C13—21no—
24C23×C4×C13—21no—
25C23×C4×C13—28no—
26C23×C4×C13C2×C414yes—
27C23×C4×C13C2×C412yes—
28C23×Dic13—22no—
29C23×Dic13—21no—
30C23×Dic13—21no—
31C23×Dic13—44no—
32C23×Dic13—44no—
33C23×Dic13C2×C414yes—
34C23×Dic13C2×C412yes—
35C23×Dic13C2×C412yes—
36C23×Dic13C2×C411yescharacteristic
37C23×Dic13D412yes—
38C23×Dic13D412yes—
39C23×Dic13D414yes—
40C23×Dic13C2311yescharacteristic
41C23×Dic13C2312yes—
42C2×#6122—28no—
43C2×#6122—48no—
44C22×#1057—24no—
45C2×C4⋊Dic13—28no—
46C2×C4⋊Dic13—24no—
47C2×C4⋊Dic13—24no—
48C2×C4⋊Dic13—28no—
49C2×C4⋊Dic13—24no—
50C2×C4⋊Dic13—28no—
51C2×C4⋊Dic13—24no—
52C2×C4⋊Dic13—28no—
53C2×C4⋊Dic13C2×C414yes—
54C2×C4⋊Dic13C2×C418yes—
55C2×C4⋊Dic13C2314yes—
56C22⋊#1057—28no—
57C22⋊#1057—24no—
58C22⋊#1057C2318yes—
59C2×#1463—131nomaximal, Sylow
60C24×C13—24no—
61C24×C13—24no—
62C24×C13—24no—
63C24×C13C22⋊C412yes—
64C24×C13C22⋊C411yescharacteristic
65C24×C13C22⋊C411yescharacteristic
66C24×C13C22×C412yes—
67C24×C13C22×C411yescharacteristic
68C22×C4×C13—216no—
69C22×C4×C13—28no—
70C22×C4×C13—28no—
71C22×C4×C13—24no—
72C22×C4×C13—24no—
73C22×C4×C13—22no—
74C22×C4×C13—22no—
75C22×C4×C13—24no—
76C22×C4×C13—216no—
77C22×C4×C13M1618yescomplemented
78C22×C4×C13C22×C414yes—
79C22×Dic13—28no—
80C22×Dic13—22no—
81C22×Dic13—24no—
82C22×Dic13—24no—
83C22×Dic13—22no—
84C22×Dic13—44no—
85C22×Dic13—42no—
86C22×Dic13—44no—
87C22×Dic13—48no—
88C22×Dic13—42no—
89C22×Dic13—44no—
90C22×Dic13—48no—
91C22×Dic13—44no—
92C22×Dic13—44no—
93C22×Dic13—48no—
94C22×Dic13—44no—
95C22×Dic13C22⋊C414yes—
96C22×Dic13C22⋊C412yes—
97C22×Dic13C22⋊C412yes—
98C22×Dic13C22⋊C414yes—
99C22×Dic13C22×C414yes—
100C22×Dic13C22×C411yescharacteristic
101C22×Dic13C22×C412yes—
102C22×Dic13C2×D412yes—
103C22×Dic13C2×D414yes—
104C22×Dic13C2×D412yes—
105C22×Dic13C2×D414yes—
106C22×Dic13C2411yescharacteristic
107#6122—416no—
108C2×#1057—28no—
109C2×#1057—48no—
110C4⋊Dic13—28no—
111C4⋊Dic13—216no—
112C4⋊Dic13—28no—
113C23×C4⋊C4—131no—
114C2×#407—132no—
115#1463—138no—
116C2×#324—134no—
117C23×C13—232no—
118C23×C13—24no—
119C23×C13—24no—
120C23×C13—22no—
121C23×C13—22no—
122C23×C13—24no—
123C23×C13—22no—
124C23×C13—24no—
125C23×C13—22no—
126C23×C13—24no—
127C23×C13—22no—
128C23×C13—24no—
129C23×C13—22no—
130C23×C13#9914yes—
131C23×C13#10114yes—
132C23×C13C2×C22⋊C411yescharacteristic
133C23×C13C2×C22⋊C412yes—
134C23×C13C2×C22⋊C412yes—
135C23×C13C2×C22⋊C411yescharacteristic
136C23×C13C2×M1614yes—
137C23×C13C23×C411yescharacteristic
138C2×C4×C13—216no—
139C2×C4×C13—216no—
140C2×C4×C13—24no—
141C2×C4×C13—24no—
142C2×C4×C13—28no—
143C2×C4×C13—28no—
144C2×C4×C13C2×M1618yescomplemented
145C2×Dic13—24no—
146C2×Dic13—28no—
147C2×Dic13—28no—
148C2×Dic13—24no—
149C2×Dic13—24no—
150C2×Dic13—44no—
151C2×Dic13—42no—
152C2×Dic13—41no—
153C2×Dic13—42no—
154C2×Dic13—42no—
155C2×Dic13—44no—
156C2×Dic13—41no—
157C2×Dic13—44no—
158C2×Dic13—48no—
159C2×Dic13—48no—
160C2×Dic13—44no—
161C2×Dic13—44no—
162C2×Dic13C2×C22⋊C412yes—
163C2×Dic13C2×C22⋊C414yes—
164C2×Dic13C22×D412yes—
165#1057—48no—
166C24×C4—131no—
167C24×C4—131no—
168C24×C4#26111yescharacteristic
169C22×M16—262no—
170C22×C4⋊C4—134no—
171C22×C4⋊C4—132no—
172C22×C4⋊C4—132no—
173C22×C4⋊C4—134no—
174C22×C4⋊C4—262no—
175C22×C4⋊C4—262no—
176C22×C4⋊C4—264no—
177#407—138no—
178#407—264no—
179C2×C22⋊C8—134no—
180C2×C22⋊C8—262no—
181#324—1316no—
182C22×C13—216no—
183C22×C13—216no—
184C22×C13—22no—
185C22×C13—22no—
186C22×C13—21no—
187C22×C13—22no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—22no—
191C22×C13—21no—
192C22×C13—28no—
193C22×C13—28no—
194C22×C13—28no—
195C22×C13#40712yes—
196C22×C13#40712yes—
197C22×C13C2×#9914yes—
198C22×C13C2×#9912yes—
199C22×C13C2×#10114yes—
200C22×C13C2×#10112yes—
201C22×C13C22×C22⋊C411yescharacteristic
202C22×C13C22×M1612yes—
203C4×C13—28no—
204Dic13—22no—
205Dic13—22no—
206Dic13—24no—
207Dic13—44no—
208C25C2×#26111yescharacteristic
209C23×C4—22no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—28no—
213C23×C4—132no—
214C23×C4—132no—
215C23×C4—134no—
216C23×C4—131no—
217C23×C4—132no—
218C23×C4—132no—
219C23×C4—131no—
220C23×C4—134no—
221C23×C4—132no—
222C23×C4—262no—
223C23×C4—261no—
224C23×C4—261no—
225C23×C4—524no—
226C23×C4—524no—
227C23×C4C2×#26114yes—
228C23×C4C2×#26112yes—
229C2×M16—268no—
230C2×M16—528no—
231C22×C8—264no—
232C2×C4⋊C4—134no—
233C2×C4⋊C4—134no—
234C2×C4⋊C4—138no—
235C2×C4⋊C4—268no—
236C2×C4⋊C4—268no—
237C2×C4⋊C4—264no—
238C2×C4⋊C4—268no—
239C2×C4⋊C4—268no—
240C2×C4⋊C4—264no—
241C2×C4⋊C4—264no—
242C2×C4⋊C4—264no—
243C22⋊C8—138no—
244C22⋊C8—264no—
245C22⋊C8—268no—
246C2×C13—22no—
247C2×C13—22no—
248C2×C13—24no—
249C2×C13—24no—
250C2×C13#146314yescomplemented
251C2×C13C2×#40711yescharacteristic
252C2×C13C22×#9911yescharacteristic
253C2×C13C22×#10111yescharacteristic
254C24—24no—
255C24—24no—
256C24—24no—
257C24C22⋊#26112yes—
258C24C22⋊#26111yescharacteristic
259C24C22⋊#26111yescharacteristic
260C24C22×#26112yes—
261C24C22×#26111yescharacteristic
262C22×C4—216no—
263C22×C4—28no—
264C22×C4—28no—
265C22×C4—24no—
266C22×C4—24no—
267C22×C4—24no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—216no—
271C22×C4—134no—
272C22×C4—134no—
273C22×C4—132no—
274C22×C4—132no—
275C22×C4—132no—
276C22×C4—134no—
277C22×C4—132no—
278C22×C4—134no—
279C22×C4—131no—
280C22×C4—131no—
281C22×C4—132no—
282C22×C4—134no—
283C22×C4—268no—
284C22×C4—262no—
285C22×C4—264no—
286C22×C4—264no—
287C22×C4—262no—
288C22×C4—522no—
289C22×C4—524no—
290C22×C4—524no—
291C22×C4—528no—
292C22×C4—524no—
293C22×C4—522no—
294C22×C4—528no—
295C22×C4—524no—
296C22×C4—524no—
297C22×C4—528no—
298C22×C4—524no—
299C22×C4#612218yescomplemented
300C22×C4C22×#26114yes—
301M16—5216no—
302C2×C8—268no—
303C2×C8—528no—
304C4⋊C4—268no—
305C4⋊C4—2616no—
306C4⋊C4—268no—
307C13C2×#146311yescharacteristic, complemented, Sylow
308C23—232no—
309C23—24no—
310C23—22no—
311C23—22no—
312C23—24no—
313C23—22no—
314C23—24no—
315C23—22no—
316C23—24no—
317C23—24no—
318C23—22no—
319C23—24no—
320C23—22no—
321C23#8810714yes—
322C23#8811314yes—
323C23C2×#612214yes—
324C23C2×C22⋊#26111yescharacteristic
325C23C2×C22⋊#26112yes—
326C23C2×C22⋊#26112yes—
327C23C2×C22⋊#26111yescharacteristic
328C23C23×#26111yescharacteristic
329C2×C4—216no—
330C2×C4—216no—
331C2×C4—28no—
332C2×C4—28no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—132no—
336C2×C4—134no—
337C2×C4—132no—
338C2×C4—264no—
339C2×C4—268no—
340C2×C4—268no—
341C2×C4—264no—
342C2×C4—264no—
343C2×C4—521no—
344C2×C4—522no—
345C2×C4—524no—
346C2×C4—524no—
347C2×C4—522no—
348C2×C4—521no—
349C2×C4—522no—
350C2×C4—524no—
351C2×C4—528no—
352C2×C4—528no—
353C2×C4—524no—
354C2×C4—524no—
355C2×C4C2×#612218yescomplemented
356C8—528no—
357C22—216no—
358C22—216no—
359C22—28no—
360C22—28no—
361C22—28no—
362C22—22no—
363C22—22no—
364C22—21no—
365C22—22no—
366C22—21no—
367C22—21no—
368C22—22no—
369C22—21no—
370C22C2×#8810714yes—
371C22C2×#8810712yes—
372C22C2×#8811314yes—
373C22C2×#8811312yes—
374C22#1171916912yes—
375C22#1171916912yes—
376C22C22×#612212yes—
377C22C22×C22⋊#26111yescharacteristic
378C4—28no—
379C4—262no—
380C4—262no—
381C4—264no—
382C4—524no—
383C2—22no—
384C2—24no—
385C2—22no—
386C2—24no—
387C2#1313008414yesdirect product factor
388C2C2×#1171916911yescharacteristic
389C2C22×#8810711yescharacteristic
390C2C22×#8811311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC23×C13C23×C4
FrattiniC23C23×#261
FittingC24×C4×C13C4
socleC23×C13C2×C22⋊C4
prime radicalC25×C13C2×C4
cosocleC22×Dic13C24
hypercenterC24×C4#261
hypocenterC13C2×#1463
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C25 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
2. #13130084C2direct (N × H)
3. C2×#11718285C2semidirect
20. #11718285C22semidirect
77. C22×C4×C13M16semidirect
144. C2×C4×C13C2×M16semidirect
250. C2×C13#1463semidirect
299. C22×C4#6122semidirect
307. C13C2×#1463semidirect
355. C2×C4C2×#6122semidirect
387. C2#13130084direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117191692
#131300842
C2×#117182852
C23×C4⋊Dic132
C2×#146313