Finite Group Databasebeta

← C2×#13114323 #15845424

Subgroups — C2×#13114323 #15845424

Order 3328.

758 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718753C211yesmaximal, characteristic, complemented
2C2×#11718668C211yesmaximal, characteristic
3C2×#11718673C211yesmaximal, characteristic
4#13114323C218yesmaximal, direct product factor
5C2×#11718072C211yesmaximal, characteristic, complemented
6C2×#11718139C211yesmaximal, characteristic, complemented
7C2×#11718078C211yesmaximal, characteristic, complemented
8C2×C13×#474C211yesmaximal, characteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C13C2211yescharacteristic
11C22×#6107—21no—
12C22×#6107—21no—
13C22×#6099—21no—
14C2×#88123C2211yescharacteristic
15C13×#474—22no—
16C13×#474C2214yes—
17C2×C13×#107—21no—
18C2×C13×C4⋊C8C2211yescharacteristic
19C2×C13×#102—21no—
20C2×#88072—21no—
21C2×C22⋊#1055—21no—
22#11718753—22no—
23#11718753C2214yescomplemented
24#11718673—22no—
25#11718673C2214yes—
26#11718668—22no—
27#11718668C2214yes—
28C2×#88047—21no—
29C2×C4⋊#1055C2211yescharacteristic
30C2×C4⋊#1055C2211yescharacteristic
31C2×C4×#1055C2211yescharacteristic
32#11718139C2214yescomplemented
33#11718078C2214yescomplemented
34#11718072C2214yescomplemented
35C22×Q8×C13—21no—
36C22×D4×C13D411yescharacteristic
37C23×C4×C13—21no—
38C22×Dic26—21no—
39C22×C8×C13—21no—
40C13×C4⋊Q8—21no—
41C13×C4⋊Q8—21no—
42C13×C4⋊Q8—21no—
43C13×C4⋊Q8C2312yes—
44C4×D4×C13—21no—
45C4×D4×C13—21no—
46C4×D4×C13D412yes—
47C4×D4×C13C2312yes—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4D411yescharacteristic
51C2×C13×C22⋊C4—21no—
52C2×C42×C13C2311yescharacteristic
53C2×#6107—24no—
54C2×#6107—24no—
55C2×#6107—44no—
56C2×#6107—44no—
57C2×C4⋊Dic13—21no—
58C2×C4⋊Dic13—21no—
59C2×#6099—24no—
60C2×#6099—44no—
61C22×#1055—21no—
62C22×#1055—21no—
63C22×#1055D411yescharacteristic
64C22×#1055D411yescharacteristic
65#88123—21no—
66#88123—21no—
67#88123—21no—
68#88123C2312yes—
69C13×#107—24no—
70C13×C4⋊C8—21no—
71C13×C4⋊C8C2312yes—
72C13×#102—24no—
73#88072—24no—
74C22⋊#1055—24no—
75#88047—24no—
76C4⋊#1055—21no—
77C4⋊#1055—21no—
78C4⋊#1055C2312yes—
79C4⋊#1055C2312yes—
80C4×#1055D412yes—
81C4×#1055C2312yes—
82C2×#1689—131nomaximal, Sylow
83C24×C13—21no—
84C2×Q8×C13—22no—
85C2×Q8×C13—41no—
86C2×Q8×C13—42no—
87C2×Q8×C13—42no—
88C2×D4×C13—21no—
89C2×D4×C13—22no—
90C2×D4×C13—22no—
91C2×D4×C13C2×D412yes—
92C22×C4×C13—21no—
93C22×C4×C13—22no—
94C22×C4×C13—22no—
95C22×C4×C13—42no—
96C22×C4×C13—42no—
97C22×C4×C13—41no—
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13#4111yescharacteristic
101C22×Dic13—41no—
102C2×Dic26—22no—
103C2×Dic26—42no—
104C2×Dic26—42no—
105C2×Dic26—41no—
106C2×C8×C13—22no—
107C2×C8×C13—42no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—22no—
110C13×C4⋊C4—22no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4—41no—
113C13×C4⋊C4C2×D412yes—
114C13×C22⋊C4—22no—
115C13×C22⋊C4—22no—
116C42×C13C2×D411yescharacteristic
117C42×C13C2×D411yescharacteristic
118C42×C13#4111yescharacteristic
119C42×C13C2411yescharacteristic
120#6107—48no—
121#6107—48no—
122C4⋊Dic13—22no—
123C4⋊Dic13—22no—
124C4⋊Dic13—41no—
125C4⋊Dic13—41no—
126#6099—48no—
127C2×#1055—22no—
128C2×#1055—22no—
129C2×#1055—22no—
130C2×#1055—42no—
131C2×#1055—42no—
132C2×#1055D814yes—
133C2×#1055C2×D412yes—
134C2×#1055C2×D412yes—
135C2×#494—131no—
136C2×#474—131no—
137C2×#474D1311yescharacteristic
138C2×#436—131no—
139#1689—138no—
140C2×#334—131no—
141C2×#332—131no—
142C2×#332—131no—
143C23×C13—22no—
144C23×C13—42no—
145C23×C13—42no—
146C23×C13—42no—
147C23×C13#12111yescharacteristic
148Q8×C13—42no—
149Q8×C13—42no—
150Q8×C13—82no—
151D4×C13—22no—
152D4×C13—22no—
153D4×C13—42no—
154C2×C4×C13—22no—
155C2×C4×C13—22no—
156C2×C4×C13—42no—
157C2×C4×C13—42no—
158C2×C4×C13—42no—
159C2×C4×C13—44no—
160C2×C4×C13—42no—
161C2×C4×C13—82no—
162C2×C4×C13#12111yescharacteristic
163C2×C4×C13#12111yescharacteristic
164C2×C4×C13#12111yescharacteristic
165C2×C4×C13C2×D812yes—
166C2×C4×C13AGL(1,ℤ/8)12yes—
167C2×C4×C13#13712yes—
168C2×C4×C13#13712yes—
169C2×C4×C13C22×D411yescharacteristic
170C2×C4×C13C22×D411yescharacteristic
171C2×C4×C13C2×#4111yescharacteristic
172C2×Dic13—42no—
173C2×Dic13—82no—
174Dic26—42no—
175Dic26—42no—
176Dic26—82no—
177C8×C13—42no—
178#1055—22no—
179#1055—42no—
180#1055—42no—
181#1055C2×D814yes—
182C22×Q16—261no—
183C22×Q16—261no—
184C22×M16—261no—
185C2×C4⋊Q8—131no—
186C2×C4⋊Q8C2×D1311yescharacteristic
187C2×C4×D4C2×D1311yescharacteristic
188#494—134no—
189#494—262no—
190#474—22no—
191#474—134no—
192#474—262no—
193#474C2×D1314yes—
194#436—134no—
195#436—262no—
196C2×#107—21no—
197C2×#107—261no—
198C2×C4⋊C8—131no—
199C2×C4⋊C8—131no—
200C2×C4⋊C8C2×D1311yescharacteristic
201C2×#102—21no—
202C2×#102—261no—
203C2×C22⋊C8—261no—
204C2×C4×C8—131no—
205#334—134no—
206#332—134no—
207#332—134no—
208C22×C13—42no—
209C22×C13—42no—
210C22×C13—42no—
211C22×C13—84no—
212C22×C13#45912yes—
213C22×C13#47012yes—
214C22×C13#47312yes—
215C22×C13C2×#12111yescharacteristic
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—42no—
219C4×C13—82no—
220C4×C13#45912yes—
221C4×C13#47012yes—
222C4×C13C22×D811yescharacteristic
223C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
224C4×C13C2×#13711yescharacteristic
225C4×C13C2×#13711yescharacteristic
226Dic13—82no—
227C22×Q8—21no—
228C22×Q8—261no—
229C22×D4C22⋊D1311yescharacteristic
230C23×C4—21no—
231C2×Q16—264no—
232C2×Q16—264no—
233C2×Q16—524no—
234C2×Q16—524no—
235C2×M16—264no—
236C2×M16—524no—
237C22×C8—21no—
238C22×C8—131no—
239C22×C8—131no—
240C22×C8—261no—
241C22×C8—261no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—132no—
246C4⋊Q8—261no—
247C4⋊Q8—261no—
248C4⋊Q8—261no—
249C4⋊Q8C22×D1312yes—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4C22⋊D1312yes—
253C4×D4C22×D1312yes—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—261no—
257C2×C4⋊C4—261no—
258C2×C4⋊C4C22⋊D1311yescharacteristic
259C2×C22⋊C4—21no—
260C2×C42C22×D1311yescharacteristic
261#107—24no—
262#107—264no—
263C4⋊C8—21no—
264C4⋊C8—132no—
265C4⋊C8—132no—
266C4⋊C8—261no—
267C4⋊C8—261no—
268C4⋊C8C22×D1312yes—
269#102—24no—
270#102—264no—
271C22⋊C8—264no—
272C4×C8—132no—
273C4×C8—132no—
274C2×C13—82no—
275C2×C13#168914yescomplemented
276C2×C13C2×#45911yescharacteristic
277C2×C13C2×#47011yescharacteristic
278C2×C13C2×#47311yescharacteristic
279C24—21no—
280C2×Q8—22no—
281C2×Q8—41no—
282C2×Q8—42no—
283C2×Q8—42no—
284C2×Q8—262no—
285C2×Q8—521no—
286C2×Q8—522no—
287C2×Q8—522no—
288C2×D4—21no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4C2×C22⋊D1312yes—
292C22×C4—21no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—41no—
298C22×C4—521no—
299C22×C4D4×D1311yescharacteristic
300C22×C4#612911yescharacteristic
301C22×C4C2×C22⋊D1311yescharacteristic
302Q16—528no—
303Q16—528no—
304M16—528no—
305C2×C8—22no—
306C2×C8—42no—
307C2×C8—134no—
308C2×C8—132no—
309C2×C8—132no—
310C2×C8—262no—
311C2×C8—262no—
312C2×C8—262no—
313C2×C8—522no—
314C2×C8—522no—
315C4⋊C4—21no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—262no—
321C4⋊C4—262no—
322C4⋊C4—521no—
323C4⋊C4—521no—
324C4⋊C4C2×C22⋊D1312yes—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C42D4×D1311yescharacteristic
328C42#612911yescharacteristic
329C42C2×C22⋊D1311yescharacteristic
330C42C23×D1311yescharacteristic
331C13C2×#168911yescharacteristic, complemented, Sylow
332C23—22no—
333C23—42no—
334C23—42no—
335C23—42no—
336C23#8819311yescharacteristic
337Q8—42no—
338Q8—42no—
339Q8—82no—
340Q8—522no—
341Q8—522no—
342Q8—1042no—
343D4—22no—
344D4—22no—
345D4—42no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—44no—
352C2×C4—42no—
353C2×C4—82no—
354C2×C4—522no—
355C2×C4—1042no—
356C2×C4D8×D1312yes—
357C2×C4#8816512yes—
358C2×C4#8819311yescharacteristic
359C2×C4#8819311yescharacteristic
360C2×C4#8819311yescharacteristic
361C2×C4#8819612yes—
362C2×C4#8820512yes—
363C2×C4C2×D4×D1311yescharacteristic
364C2×C4C2×#612911yescharacteristic
365C2×C4C22×C22⋊D1311yescharacteristic
366C8—42no—
367C8—134no—
368C8—262no—
369C8—522no—
370C8—522no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—84no—
375C22#1171871312yes—
376C22#1171881112yes—
377C22#1171886512yes—
378C22C2×#8819311yescharacteristic
379C4—21no—
380C4—21no—
381C4—42no—
382C4—82no—
383C4—1042no—
384C4#1171871312yes—
385C4#1171881112yes—
386C4C2×D8×D1311yescharacteristic
387C4C2×#8816511yescharacteristic
388C4C2×#8819611yescharacteristic
389C4C2×#8820511yescharacteristic
390C2—82no—
391C2#1311432314yesdirect product factor
392C2C2×#1171881111yescharacteristic
393C2C2×#1171871311yescharacteristic
394C2C2×#1171886511yescharacteristic
subgroupG/H
centerC23#88193
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C13×#474C2
socleC23×C13#121
prime radicalC22×D4×C13D4
hypercenterC2×#474D13
hypocenterC13C2×#1689
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#11718753C2semidirect
4. #13114323C2direct (N × H)
5. C2×#11718072C2semidirect
6. C2×#11718139C2semidirect
7. C2×#11718078C2semidirect
23. #11718753C22semidirect
32. #11718139C22semidirect
33. #11718078C22semidirect
34. #11718072C22semidirect
275. C2×C13#1689semidirect
331. C13C2×#1689semidirect
391. C2#13114323direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117187532
C2×#117186682
C2×#117186732
#131143232
C2×#117180722
C2×#117181392
C2×#117180782
C2×C13×#4742
C2×#168913