Finite Group Databasebeta

← C2×#13114183 #15845238

Subgroups — C2×#13114183 #15845238

Order 3328.

786 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718737C211yesmaximal, characteristic
2C2×#11718512C211yesmaximal, characteristic, complemented
3C2×#11718736C211yesmaximal, characteristic
4C2×#11718491C211yesmaximal, characteristic, complemented
5#13114183C218yesmaximal, direct product factor
6C2×#11718072C211yesmaximal, characteristic, complemented
7C2×#11718074C211yesmaximal, characteristic, complemented
8C2×C13×#331C211yesmaximal, characteristic
9C2×C13×#127C2211yescharacteristic
10C22×#6105—21no—
11C22×#6105—21no—
12C22×#6105—21no—
13C2×#88123C2211yescharacteristic
14C2×C4×Dic26C2211yescharacteristic
15C2×C13×C4⋊C8C2211yescharacteristic
16C2×C13×C4⋊C8C2211yescharacteristic
17C2×#88072—21no—
18C2×#88057—21no—
19C2×#88056—21no—
20C2×#88054—21no—
21C2×C8×Dic13—21no—
22#11718737—22no—
23#11718737C2214yes—
24#11718736—22no—
25#11718736C2214yes—
26C2×C4⋊#1055C2211yescharacteristic
27C2×C4×#1055C2211yescharacteristic
28#11718512—22no—
29#11718512C2214yescomplemented
30#11718491—22no—
31#11718491C2214yescomplemented
32C13×#331C2214yes—
33#11718074C2214yescomplemented
34#11718072C2214yescomplemented
35C22×D4×C13—21no—
36C22×D4×C13—21no—
37C22×D4×C13—21no—
38C22×Dic26—21no—
39C22×Dic26D411yescharacteristic
40C22×C8×C13—21no—
41C22×C8×C13—21no—
42C13×#127—21no—
43C13×#127—21no—
44C13×#127—21no—
45C13×#127C2312yes—
46C2×C42×C13C2311yescharacteristic
47C2×#6105—24no—
48C2×#6105—24no—
49C2×#6105—24no—
50C2×#6105—44no—
51C2×#6105—44no—
52C2×#6105—44no—
53C2×C4⋊Dic13—21no—
54C2×C4⋊Dic13—21no—
55C2×C4⋊Dic13D411yescharacteristic
56C2×#6101—21no—
57C2×C4×Dic13—21no—
58C22×#1055—21no—
59C22×#1055D411yescharacteristic
60C22×#1055D411yescharacteristic
61#88123—21no—
62#88123—21no—
63#88123—21no—
64#88123C2312yes—
65C4×Dic26—21no—
66C4×Dic26—21no—
67C4×Dic26D412yes—
68C4×Dic26C2312yes—
69C13×C4⋊C8—21no—
70C13×C4⋊C8—21no—
71C13×C4⋊C8C2312yes—
72C13×C4⋊C8C2312yes—
73#88072—24no—
74#88057—24no—
75#88056—24no—
76#88054—24no—
77C8×Dic13—24no—
78C4⋊#1055—21no—
79C4⋊#1055C2312yes—
80C4×#1055D412yes—
81C4×#1055C2312yes—
82C2×#1666—131nomaximal, Sylow
83C24×C13—41no—
84C2×D4×C13—22no—
85C2×D4×C13—22no—
86C2×D4×C13—22no—
87C2×D4×C13—41no—
88C2×D4×C13—41no—
89C2×D4×C13—41no—
90C2×D4×C13—42no—
91C2×D4×C13—42no—
92C2×D4×C13—42no—
93C2×D4×C13—42no—
94C2×D4×C13—82no—
95C22×C4×C13C2×D411yescharacteristic
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13#4111yescharacteristic
98C22×Dic13—21no—
99C22×Dic13—21no—
100C22×Dic13—41no—
101C2×Dic26—21no—
102C2×Dic26—22no—
103C2×Dic26—22no—
104C2×Dic26—42no—
105C2×Dic26—42no—
106C2×Dic26—41no—
107C2×Dic26SD1614yescomplemented
108C2×Dic26C2×D412yes—
109C2×C8×C13—22no—
110C2×C8×C13—22no—
111C2×C8×C13—42no—
112C2×C8×C13—42no—
113C42×C13C2×D411yescharacteristic
114C42×C13C2×D411yescharacteristic
115C42×C13#4111yescharacteristic
116C42×C13C2411yescharacteristic
117#6105—48no—
118#6105—48no—
119#6105—48no—
120C4⋊Dic13—21no—
121C4⋊Dic13—22no—
122C4⋊Dic13—22no—
123C4⋊Dic13—41no—
124C4⋊Dic13—41no—
125C4⋊Dic13C2×D412yes—
126#6101—22no—
127#6101—22no—
128C4×Dic13—22no—
129C4×Dic13—22no—
130C2×#1055—22no—
131C2×#1055—22no—
132C2×#1055—42no—
133C2×#1055SD1614yescomplemented
134C2×#1055C2×D412yes—
135C2×#1055C2×D412yes—
136C2×#492—131no—
137C2×#475—131no—
138C2×#460—131no—
139C2×C8×Q8—131no—
140#1666—138no—
141C2×#334—131no—
142C2×#332—131no—
143C2×#331D1311yescharacteristic
144C23×C13—42no—
145C23×C13—82no—
146C23×C13—82no—
147C23×C13—82no—
148C23×C13#12111yescharacteristic
149D4×C13—42no—
150D4×C13—42no—
151D4×C13—42no—
152D4×C13—42no—
153D4×C13—82no—
154D4×C13—82no—
155D4×C13—82no—
156D4×C13—82no—
157C2×C4×C13—22no—
158C2×C4×C13#12111yescharacteristic
159C2×C4×C13#12111yescharacteristic
160C2×C4×C13#12111yescharacteristic
161C2×C4×C13C2×SD1612yes—
162C2×C4×C13C2×SD1612yes—
163C2×C4×C13#13512yes—
164C2×C4×C13AGL(1,ℤ/8)12yes—
165C2×C4×C13C22×D411yescharacteristic
166C2×C4×C13C22×D411yescharacteristic
167C2×C4×C13C2×#4111yescharacteristic
168C2×Dic13—22no—
169C2×Dic13—24no—
170C2×Dic13—22no—
171C2×Dic13—42no—
172C2×Dic13—42no—
173C2×Dic13—82no—
174Dic26—22no—
175Dic26—24no—
176Dic26—42no—
177Dic26—42no—
178Dic26—82no—
179Dic26C2×SD1614yescomplemented
180C8×C13—42no—
181C8×C13—42no—
182#1055—22no—
183#1055—42no—
184#1055C2×SD1614yescomplemented
185C22×SD16—261no—
186C22×SD16—261no—
187C22×SD16—261no—
188C2×C4⋊Q8—131no—
189C2×#127C2×D1311yescharacteristic
190C2×C4×Q8—131no—
191#492—134no—
192#492—262no—
193#475—134no—
194#475—262no—
195#460—134no—
196#460—262no—
197C8×Q8—134no—
198C8×Q8—262no—
199C2×#106—261no—
200C2×C4⋊C8—131no—
201C2×C4⋊C8—261no—
202C2×C4⋊C8C2×D1311yescharacteristic
203C2×C4⋊C8C2×D1311yescharacteristic
204C2×#103—261no—
205C2×#102—261no—
206C2×C4×C8—131no—
207C2×C4×C8—261no—
208#334—134no—
209#332—134no—
210#331C2×D1314yes—
211C22×C13—82no—
212C22×C13—82no—
213C22×C13—82no—
214C22×C13—164no—
215C22×C13#46012yes—
216C22×C13#46512yes—
217C22×C13#47112yes—
218C22×C13C2×#12111yescharacteristic
219C4×C13—21no—
220C4×C13—21no—
221C4×C13#46012yes—
222C4×C13#46512yes—
223C4×C13C22×SD1611yescharacteristic
224C4×C13C22×SD1611yescharacteristic
225C4×C13C2×#13511yescharacteristic
226C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
227Dic13—24no—
228Dic13—42no—
229Dic13—82no—
230C22×Q8—131no—
231C22×Q8—261no—
232C22×D4—21no—
233C22×D4—21no—
234C22×D4—21no—
235C2×SD16—264no—
236C2×SD16—264no—
237C2×SD16—264no—
238C2×SD16—524no—
239C2×SD16—524no—
240C2×SD16—524no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—131no—
244C22×C8—131no—
245C22×C8—261no—
246C4⋊Q8—132no—
247C4⋊Q8—261no—
248C4⋊Q8—261no—
249C4⋊Q8—261no—
250#127—21no—
251#127—21no—
252#127—21no—
253#127C22×D1312yes—
254C4×Q8—132no—
255C4×Q8—132no—
256C4×Q8—261no—
257C4×Q8—261no—
258C2×C4⋊C4—131no—
259C2×C4⋊C4—261no—
260C2×C4⋊C4—261no—
261C2×C4⋊C4—261no—
262C2×C42—261no—
263C2×C42C22×D1311yescharacteristic
264#106—264no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—132no—
268C4⋊C8—264no—
269C4⋊C8—261no—
270C4⋊C8C22×D1312yes—
271C4⋊C8C22×D1312yes—
272#103—264no—
273#102—264no—
274C4×C8—132no—
275C4×C8—132no—
276C4×C8—264no—
277C2×C13—162no—
278C2×C13#166614yescomplemented
279C2×C13C2×#46011yescharacteristic
280C2×C13C2×#46511yescharacteristic
281C2×C13C2×#47111yescharacteristic
282C24—41no—
283C2×Q8—134no—
284C2×Q8—132no—
285C2×Q8—261no—
286C2×Q8—262no—
287C2×Q8—262no—
288C2×Q8—521no—
289C2×Q8—522no—
290C2×Q8—522no—
291C2×D4—22no—
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—42no—
298C2×D4—42no—
299C2×D4—42no—
300C2×D4—42no—
301C2×D4—82no—
302C22×C4—261no—
303C22×C4—261no—
304C22×C4—521no—
305C22×C4#612711yescharacteristic
306C22×C4D4×D1311yescharacteristic
307C22×C4D4×D1311yescharacteristic
308SD16—528no—
309SD16—528no—
310SD16—528no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—42no—
314C2×C8—42no—
315C2×C8—134no—
316C2×C8—132no—
317C2×C8—132no—
318C2×C8—262no—
319C2×C8—262no—
320C2×C8—522no—
321C4⋊C4—132no—
322C4⋊C4—261no—
323C4⋊C4—262no—
324C4⋊C4—262no—
325C4⋊C4—262no—
326C4⋊C4—262no—
327C4⋊C4—521no—
328C4⋊C4—521no—
329C42—262no—
330C42—262no—
331C42#612711yescharacteristic
332C42D4×D1311yescharacteristic
333C42D4×D1311yescharacteristic
334C42C23×D1311yescharacteristic
335C13C2×#166611yescharacteristic, complemented, Sylow
336C23—42no—
337C23—82no—
338C23—82no—
339C23—82no—
340C23#8813811yescharacteristic
341Q8—134no—
342Q8—262no—
343Q8—264no—
344Q8—522no—
345Q8—522no—
346Q8—1042no—
347D4—42no—
348D4—42no—
349D4—42no—
350D4—42no—
351D4—82no—
352D4—82no—
353D4—82no—
354D4—82no—
355C2×C4—22no—
356C2×C4—262no—
357C2×C4—264no—
358C2×C4—262no—
359C2×C4—522no—
360C2×C4—522no—
361C2×C4—1042no—
362C2×C4#8813811yescharacteristic
363C2×C4#8813811yescharacteristic
364C2×C4#8813811yescharacteristic
365C2×C4#8816512yes—
366C2×C4#8816612yes—
367C2×C4SD16×D1312yes—
368C2×C4SD16×D1312yes—
369C2×C4C2×#612711yescharacteristic
370C2×C4C2×D4×D1311yescharacteristic
371C2×C4C2×D4×D1311yescharacteristic
372C8—42no—
373C8—42no—
374C8—134no—
375C8—262no—
376C8—522no—
377C22—82no—
378C22—82no—
379C22—82no—
380C22—164no—
381C22#1171840912yes—
382C22#1171842312yes—
383C22#1171843912yes—
384C22C2×#8813811yescharacteristic
385C4—21no—
386C4—21no—
387C4—264no—
388C4—522no—
389C4—1042no—
390C4#1171842312yes—
391C4#1171843912yes—
392C4C2×#8816511yescharacteristic
393C4C2×#8816611yescharacteristic
394C4C2×SD16×D1311yescharacteristic
395C4C2×SD16×D1311yescharacteristic
396C2—162no—
397C2#1311418314yesdirect product factor
398C2C2×#1171842311yescharacteristic
399C2C2×#1171843911yescharacteristic
400C2C2×#1171840911yescharacteristic
subgroupG/H
centerC23#88138
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C13×#331C2
socleC23×C13#121
prime radicalC2×C13×#127C22
hypercenterC2×#331D13
hypocenterC13C2×#1666
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
2. C2×#11718512C2semidirect
4. C2×#11718491C2semidirect
5. #13114183C2direct (N × H)
6. C2×#11718072C2semidirect
7. C2×#11718074C2semidirect
29. #11718512C22semidirect
31. #11718491C22semidirect
33. #11718074C22semidirect
34. #11718072C22semidirect
107. C2×Dic26SD16semidirect
133. C2×#1055SD16semidirect
179. Dic26C2×SD16semidirect
184. #1055C2×SD16semidirect
278. C2×C13#1666semidirect
335. C13C2×#1666semidirect
397. C2#13114183direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117187372
C2×#117185122
C2×#117187362
C2×#117184912
#131141832
C2×#117180722
C2×#117180742
C2×C13×#3312
C2×#166613