Finite Group Databasebeta

← C2×#13130967 #16799129

Subgroups — C2×#13130967 #16799129

Order 3328.

1598 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88117C214yesmaximal
2C2×#11719047C211yesmaximal, characteristic
3C2×#11719060C211yesmaximal, characteristic
4#13130967C218yesmaximal, direct product factor
5C2×D13×C4⋊Q8C211yesmaximal, characteristic
6C22×Q8×D13C2212yes—
7C22×C4⋊#261C2212yes—
8C22×D13⋊C8C2212yes—
9C2×C13×C4⋊Q8C411yescharacteristic, complemented
10C2×#88198C412yescomplemented
11D13×C4⋊Q8—22no—
12D13×C4⋊Q8—22no—
13D13×C4⋊Q8C414yescomplemented
14D13×C4⋊Q8C2214yes—
15C2×C4⋊C4×D13—22no—
16C2×#88142—22no—
17C2×C42×D13C2211yescharacteristic
18C2×#88123C411yescharacteristic, complemented
19C2×#88117—216no—
20C2×#88117C22116yes—
21C2×(C2×#261)⋊C4—22no—
22C2×#88110—22no—
23#11719060—22no—
24#11719060C2214yes—
25#11719047—22no—
26#11719047C2214yes—
27C23×#261—22no—
28C22×Q8×C13C2×C412yes—
29C2×Q8×D13—22no—
30C2×Q8×D13—22no—
31C2×Q8×D13—28no—
32C2×Q8×D13—28no—
33C2×Q8×D13C2×C414yes—
34C2×Q8×D13C2314yes—
35C22×C4×D13—22no—
36C22×C4×D13D412yes—
37C22×C4×D13C2311yescharacteristic
38C22×Dic26—22no—
39C22×Dic26C2×C412yes—
40C22×#1057—22no—
41C2×C4⋊#261—28no—
42C2×C4⋊#261—22no—
43C2×C4⋊#261C2314yes—
44C2×D13⋊C8—22no—
45C2×D13⋊C8—24no—
46C2×D13⋊C8D418yes—
47C2×D13⋊C8C2314yes—
48C13×C4⋊Q8—22no—
49C13×C4⋊Q8C2×C414yescomplemented
50C2×C13×C4⋊C4—22no—
51C2×C42×C13C2×C411yescharacteristic
52#88198—24no—
53#88198C2×C418yescomplemented
54C2×C4⋊Dic13—22no—
55C2×#6101—24no—
56C2×C4×Dic13C2×C411yescharacteristic
57C2×C4×Dic13D412yes—
58C4⋊C4×D13—28no—
59C4⋊C4×D13—28no—
60#88142—28no—
61#88142—28no—
62C42×D13C2×C412yes—
63C42×D13D412yes—
64C42×D13D412yes—
65C42×D13C2312yes—
66#88123—22no—
67#88123C2×C414yescomplemented
68#88117—232no—
69(C2×#261)⋊C4—28no—
70#88110—28no—
71C2×#1960—131nomaximal, Sylow
72C23×D13C2×D411yescharacteristic
73C22×#261—24no—
74C22×#261—44no—
75C22×#261—48no—
76C2×Q8×C13—22no—
77C2×Q8×C13—28no—
78C2×Q8×C13C22×C414yes—
79C22×C4×C13—22no—
80C22×C4×C13C22⋊C412yes—
81C22×C4×C13C22×C411yescharacteristic
82C22×Dic13—22no—
83C22×Dic13C22⋊C412yes—
84C22×Dic13C2×D411yescharacteristic
85Q8×D13—216no—
86Q8×D13—28no—
87Q8×D13—28no—
88Q8×D13—48no—
89Q8×D13—44no—
90Q8×D13—44no—
91C2×C4×D13—28no—
92C2×C4×D13—24no—
93C2×C4×D13—24no—
94C2×C4×D13—44no—
95C2×C4×D13—44no—
96C2×C4×D13C22⋊C414yes—
97C2×C4×D13C22×C411yescharacteristic
98C2×C4×D13C2×D414yes—
99C2×C4×D13C2×D414yes—
100C2×C4×D13C2×D411yescharacteristic
101C2×C4×D13C2×D411yescharacteristic
102C2×C4×D13#4114yes—
103C2×C4×D13C2411yescharacteristic
104C2×Dic26—28no—
105C2×Dic26—22no—
106C2×Dic26—24no—
107C2×Dic26—24no—
108C2×Dic26—48no—
109C2×Dic26C22×C414yes—
110C2×#1057—28no—
111C2×#1057—24no—
112C4⋊#261—28no—
113C4⋊#261—44no—
114D13⋊C8—28no—
115D13⋊C8—24no—
116D13⋊C8C2×D418yes—
117C13×C4⋊C4—28no—
118C42×C13C22⋊C412yes—
119C42×C13C22×C412yes—
120C4⋊Dic13—28no—
121#6101—216no—
122C4×Dic13C22⋊C414yes—
123C4×Dic13C22⋊C412yes—
124C4×Dic13C22×C412yes—
125C4×Dic13C2×D414yes—
126C22×C4⋊Q8—131no—
127C22×#103—134no—
128C22×#97—131no—
129C2×#382—131no—
130#1960—138no—
131C23×C13C2×C22⋊C411yescharacteristic
132C22×D13C2×C22⋊C411yescharacteristic
133C22×D13#12412yes—
134C22×D13#12712yes—
135C22×D13#13718yes—
136C22×D13C22×D411yescharacteristic
137C2×#261—44no—
138C2×#261—48no—
139C2×#261—88no—
140Q8×C13—28no—
141Q8×C13—44no—
142C2×C4×C13—24no—
143C2×C4×C13—24no—
144C2×C4×C13—44no—
145C2×C4×C13C2×C22⋊C414yes—
146C2×C4×C13C2×C22⋊C411yescharacteristic
147C2×C4×C13C4×D414yes—
148C2×C4×C13C23×C411yescharacteristic
149C2×Dic13—24no—
150C2×Dic13—24no—
151C2×Dic13—44no—
152C2×Dic13C2×C22⋊C414yes—
153C2×Dic13C2×C22⋊C411yescharacteristic
154C2×Dic13#12114yes—
155C2×Dic13C22×D411yescharacteristic
156C4×D13—28no—
157C4×D13—28no—
158C4×D13—44no—
159C4×D13—44no—
160C4×D13—48no—
161C4×D13C4×D414yes—
162C4×D13#12114yes—
163C4×D13#12412yes—
164C4×D13#12712yes—
165C4×D13C22×D412yes—
166C4×D13C2×#4112yes—
167Dic26—28no—
168Dic26—44no—
169Dic26—48no—
170Dic26—48no—
171#1057—28no—
172C23×Q8—132no—
173C23×C8—132no—
174C2×C4⋊Q8—132no—
175C2×C4⋊Q8—134no—
176C2×C4⋊Q8—134no—
177C2×C4⋊Q8—131no—
178C2×C4⋊Q8—262no—
179C2×C4⋊Q8—262no—
180C2×C4⋊Q8—262no—
181C2×C4⋊Q8#26111yescharacteristic, complemented
182C22×C4⋊C4—132no—
183C22×C4⋊C4—262no—
184C22×C42—131no—
185C2×#103—1316no—
186C2×#103—2616no—
187C2×#97—134no—
188C2×#97—262no—
189C2×#97—262no—
190#382—134no—
191#382—262no—
192C2×#95—262no—
193C22×C13#39012yes—
194C22×C13#41914yes—
195C22×C13C22×C22⋊C411yescharacteristic
196C2×D13#39012yes—
197C2×D13#41914yes—
198C2×D13#49118yes—
199C2×D13#49718yes—
200C2×D13C2×#12411yescharacteristic
201C2×D13C2×#12711yescharacteristic
202C2×D13C2×#13714yes—
203#261—84no—
204C4×C13—24no—
205C4×C13—44no—
206C4×C13#39012yes—
207C4×C13C2×C4×D412yes—
208Dic13—24no—
209Dic13—44no—
210Dic13#39012yes—
211Dic13C2×#12112yes—
212C22×Q8—134no—
213C22×Q8—134no—
214C22×Q8—132no—
215C22×Q8—262no—
216C22×Q8—262no—
217C22×Q8—262no—
218C22×Q8—268no—
219C22×Q8—268no—
220C22×Q8C2×#26112yes—
221C23×C4—131no—
222C23×C4—132no—
223C23×C4—262no—
224C23×C4—262no—
225C22×C8—134no—
226C22×C8—138no—
227C22×C8—262no—
228C22×C8—262no—
229C22×C8—264no—
230C4⋊Q8—22no—
231C4⋊Q8—138no—
232C4⋊Q8—134no—
233C4⋊Q8—268no—
234C4⋊Q8—268no—
235C4⋊Q8—264no—
236C4⋊Q8—262no—
237C4⋊Q8C2×#26114yescomplemented
238C2×C4⋊C4—22no—
239C2×C4⋊C4—134no—
240C2×C4⋊C4—268no—
241C2×C4⋊C4—268no—
242C2×C4⋊C4—264no—
243C2×C4⋊C4—262no—
244C2×C4⋊C4—268no—
245C2×C4⋊C4—262no—
246C2×C42—132no—
247C2×C42—131no—
248C2×C42—132no—
249C2×C42—132no—
250C2×C42—132no—
251C2×C42—132no—
252C2×C42C2×#26111yescharacteristic
253#103—2632no—
254#97—268no—
255#95—268no—
256C2×C13#196014yescomplemented
257C2×C13C2×#39011yescharacteristic
258C2×C13C2×#41912yes—
259D13#196014yescomplemented
260D13C2×#49112yes—
261D13C2×#49712yes—
262C24—131no—
263C2×Q8—22no—
264C2×Q8—28no—
265C2×Q8—134no—
266C2×Q8—264no—
267C2×Q8—264no—
268C2×Q8—268no—
269C2×Q8—268no—
270C2×Q8—2616no—
271C2×Q8—262no—
272C2×Q8—268no—
273C2×Q8—528no—
274C2×Q8—524no—
275C2×Q8—528no—
276C2×Q8—524no—
277C2×Q8C22×#26114yes—
278C22×C4—22no—
279C22×C4—131no—
280C22×C4—134no—
281C22×C4—134no—
282C22×C4—131no—
283C22×C4—131no—
284C22×C4—131no—
285C22×C4—131no—
286C22×C4—132no—
287C22×C4—134no—
288C22×C4—134no—
289C22×C4—268no—
290C22×C4—264no—
291C22×C4—264no—
292C22×C4—262no—
293C22×C4—264no—
294C22×C4—524no—
295C22×C4—524no—
296C22×C4—524no—
297C22×C4—528no—
298C22×C4C22⋊#26112yes—
299C22×C4C22×#26111yescharacteristic
300C2×C8—138no—
301C2×C8—264no—
302C2×C8—264no—
303C2×C8—268no—
304C2×C8—268no—
305C4⋊C4—28no—
306C4⋊C4—2616no—
307C4⋊C4—268no—
308C4⋊C4—268no—
309C4⋊C4—524no—
310C42—134no—
311C42—134no—
312C42—132no—
313C42—132no—
314C42C22⋊#26112yes—
315C42C22×#26112yes—
316C13C2×#196011yescharacteristic, complemented, Sylow
317C23—131no—
318C23—131no—
319C23—132no—
320C23—132no—
321C23—138no—
322C23C2×C22⋊#26111yescharacteristic
323Q8—28no—
324Q8—44no—
325Q8—268no—
326Q8—528no—
327Q8—528no—
328Q8—524no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—44no—
332C2×C4—131no—
333C2×C4—131no—
334C2×C4—134no—
335C2×C4—132no—
336C2×C4—132no—
337C2×C4—134no—
338C2×C4—132no—
339C2×C4—134no—
340C2×C4—132no—
341C2×C4—134no—
342C2×C4—268no—
343C2×C4—268no—
344C2×C4—264no—
345C2×C4—264no—
346C2×C4—524no—
347C2×C4—524no—
348C2×C4—528no—
349C2×C4—524no—
350C2×C4—524no—
351C2×C4—528no—
352C2×C4—1048no—
353C2×C4D4×#26114yes—
354C2×C4C2×C22⋊#26114yes—
355C2×C4C2×C22⋊#26111yescharacteristic
356C2×C4C23×#26111yescharacteristic
357C8—268no—
358C22—131no—
359C22—131no—
360C22—132no—
361C22—134no—
362C22—134no—
363C22—138no—
364C22—138no—
365C22#1171915112yes—
366C22#1171915314yes—
367C22C22×C22⋊#26111yescharacteristic
368C4—24no—
369C4—44no—
370C4—132no—
371C4—132no—
372C4—264no—
373C4—524no—
374C4—1044no—
375C4#1171915112yes—
376C4C2×D4×#26112yes—
377C2—132no—
378C2—132no—
379C2—134no—
380C2#1313096714yesdirect product factor
381C2C2×#1171915111yescharacteristic
382C2C2×#1171915312yes—
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C13×C4⋊Q8C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C2×D4
cosocleC2×C4×D13C24
hypercenterC2×C4⋊Q8#261
hypocenterC13C2×#1960
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. #13130967C2direct (N × H)
9. C2×C13×C4⋊Q8C4semidirect
10. C2×#88198C4semidirect
13. D13×C4⋊Q8C4semidirect
18. C2×#88123C4semidirect
49. C13×C4⋊Q8C2×C4semidirect
53. #88198C2×C4semidirect
67. #88123C2×C4semidirect
181. C2×C4⋊Q8#261semidirect
237. C4⋊Q8C2×#261semidirect
256. C2×C13#1960semidirect
259. D13#1960semidirect
316. C13C2×#1960semidirect
380. C2#13130967direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881172
C2×#117190472
C2×#117190602
#131309672
C2×D13×C4⋊Q82
C2×#196013