Finite Group Databasebeta

← C2×#13130436 #16795262

Subgroups — C2×#13130436 #16795262

Order 3328.

838 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719076C211yesmaximal, characteristic, complemented
2C2×#11719073C211yesmaximal, characteristic, complemented
3#13130436C218yesmaximal, direct product factor
4C2×#11718256C211yesmaximal, characteristic, complemented
5C2×#11718243C211yesmaximal, characteristic, complemented
6C2×#11718243C211yesmaximal, characteristic, complemented
7C2×#1057⋊C8C211yesmaximal, characteristic, complemented
8C2×#11718533C211yesmaximal, characteristic
9C22×#6118—21no—
10C22×D13⋊C8—21no—
11C22×D104C411yescharacteristic
12C2×#88147C2211yescharacteristic
13C2×#88147C2211yescharacteristic
14C2×#88111—21no—
15C2×#88111—21no—
16C2×C4⋊#1057C2211yescharacteristic
17C2×C4⋊#1057C2211yescharacteristic
18C2×C4×#1057C2211yescharacteristic
19C2×C4×#1057C2211yescharacteristic
20#11719076—22no—
21#11719076C2214yescomplemented
22#11719073—22no—
23#11719073C2214yescomplemented
24C2×C13×#107C411yescharacteristic
25C2×C8×Dic13C2211yescharacteristic
26C2×#88049C411yescharacteristic
27C2×#88049C411yescharacteristic
28#11718533C414yes—
29#11718533C2214yes—
30#11718256C2214yescomplemented
31#1057⋊C8C2214yescomplemented
32#11718243C2214yescomplemented
33#11718243C2214yescomplemented
34C22×D52C2×C411yescharacteristic
35C22×D52C2×C411yescharacteristic
36C22×C4×D13—21no—
37C22×C4×D13—21no—
38C22×#1057—21no—
39C22×#1057—21no—
40C22×#1057—21no—
41C22×#1057D411yescharacteristic
42C22×#1057D411yescharacteristic
43C2×#6118—24no—
44C2×#6118—44no—
45C2×D13⋊C8—24no—
46C2×D13⋊C8—44no—
47C22×C8×C13C2×C411yescharacteristic
48C2×C13×C4⋊C4C2×C411yescharacteristic
49C2×C13×C4⋊C4C2×C411yescharacteristic
50C2×#6103—21no—
51C2×#6103—21no—
52C2×C4×Dic13C2311yescharacteristic
53C22×#1055C2×C411yescharacteristic
54C2×D104—24no—
55C2×D104C2×C414yes—
56#88147—21no—
57#88147—21no—
58#88147—21no—
59#88147—21no—
60#88147C2×C412yes—
61#88147C2×C412yes—
62#88147C2312yes—
63#88147C2312yes—
64#88111—24no—
65#88111—24no—
66C4⋊#1057—21no—
67C4⋊#1057—21no—
68C4⋊#1057C2312yes—
69C4⋊#1057C2312yes—
70C4×#1057—21no—
71C4×#1057D412yes—
72C4×#1057C2312yes—
73C4×#1057C2312yes—
74C13×#107C2×C414yes—
75C8×Dic13C2×C412yes—
76C8×Dic13C2312yes—
77#88049C2×C414yes—
78#88049C2×C414yes—
79C2×#1581—131nomaximal, Sylow
80C23×D13—21no—
81C23×D13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13C22×C411yescharacteristic
85C22×Dic13C2×D411yescharacteristic
86C22×Dic13#4111yescharacteristic
87C2×D52—21no—
88C2×D52—22no—
89C2×D52—22no—
90C2×D52—22no—
91C2×D52—21no—
92C2×D52M1614yescomplemented
93C2×D52C22×C412yes—
94C2×D52C22×C412yes—
95C2×C4×D13—22no—
96C2×C4×D13—22no—
97C2×C4×D13—22no—
98C2×C4×D13—22no—
99C2×C4×D13—42no—
100C2×C4×D13—42no—
101C2×C4×D13—42no—
102C2×C4×D13—42no—
103C2×#1057—22no—
104C2×#1057—22no—
105C2×#1057—22no—
106C2×#1057—22no—
107C2×#1057—42no—
108C2×#1057—42no—
109C2×#1057—42no—
110C2×#1057D814yescomplemented
111C2×#1057C2×D412yes—
112C2×#1057C2×D412yes—
113#6118—48no—
114D13⋊C8—48no—
115C2×C8×C13—22no—
116C2×C8×C13C22×C412yes—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—21no—
119C13×C4⋊C4C22×C412yes—
120C13×C4⋊C4C22×C412yes—
121#6103—22no—
122#6103—22no—
123#6103—22no—
124#6103—22no—
125C4×Dic13C22×C411yescharacteristic
126C4×Dic13C2×D411yescharacteristic
127C4×Dic13#4111yescharacteristic
128C4×Dic13C2411yescharacteristic
129C2×#1055—22no—
130C2×#1055C22×C412yes—
131D104—28no—
132C2×C4×D8—131no—
133C2×#436—131no—
134C2×C8×D4—131no—
135#1581—138no—
136C2×#335—131no—
137C2×D4⋊C8—131no—
138C2×D4⋊C8—131no—
139C2×#322—131no—
140C23×C13C4×D411yescharacteristic
141C22×D13—22no—
142C22×D13—24no—
143C22×D13—22no—
144C22×D13—42no—
145C22×D13—42no—
146C22×D13—42no—
147C22×D13—42no—
148C22×D13—42no—
149C2×C4×C13—22no—
150C2×C4×C13—22no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13C4×D411yescharacteristic
154C2×C4×C13C2×M1612yes—
155C2×C4×C13#13112yes—
156C2×C4×C13C23×C411yescharacteristic
157C2×Dic13—22no—
158C2×Dic13C4×D411yescharacteristic
159C2×Dic13C4×D411yescharacteristic
160C2×Dic13C2×D812yes—
161C2×Dic13#13512yes—
162C2×Dic13C22×D411yescharacteristic
163C2×Dic13C2×#4111yescharacteristic
164D52—22no—
165D52—22no—
166D52—22no—
167D52—24no—
168D52—42no—
169D52C2×M1614yescomplemented
170C4×D13—42no—
171C4×D13—42no—
172C4×D13—42no—
173C4×D13—42no—
174C4×D13—44no—
175C4×D13—44no—
176#1057—22no—
177#1057—42no—
178#1057—42no—
179#1057—42no—
180#1057C2×D814yescomplemented
181C8×C13—22no—
182#1055—22no—
183C22×D8—131no—
184C22×M16—261no—
185C23×C8—261no—
186C2×C4×D4—131no—
187C2×C4×D4—131no—
188C4×D8—134no—
189C4×D8—134no—
190#436—134no—
191#436—262no—
192C8×D4—134no—
193C8×D4—262no—
194C2×#107#26111yescharacteristic
195C2×C4⋊C8—131no—
196C2×C4⋊C8—131no—
197C2×#102—131no—
198C2×#102—131no—
199C2×C22⋊C8—261no—
200C2×C22⋊C8—261no—
201C2×C4×C8—131no—
202C2×C4×C8—131no—
203C2×C4×C8—131no—
204#335—134no—
205D4⋊C8—134no—
206D4⋊C8—134no—
207#322—134no—
208C22×C13#43512yes—
209C22×C13C4×D812yes—
210C22×C13#44412yes—
211C22×C13C2×C4×D411yescharacteristic
212C2×D13—24no—
213C2×D13—48no—
214C2×D13—42no—
215C2×D13—42no—
216C2×D13—42no—
217C2×D13—42no—
218C2×D13—42no—
219C2×D13—84no—
220C4×C13—42no—
221C4×C13—42no—
222C4×C13#43512yes—
223C4×C13C22×M1611yescharacteristic
224C4×C13C2×#13111yescharacteristic
225Dic13—21no—
226Dic13—21no—
227Dic13C4×D812yes—
228Dic13C22×D811yescharacteristic
229Dic13C2×#13511yescharacteristic
230C22×D4—131no—
231C22×D4—131no—
232C23×C4—261no—
233C23×C4—261no—
234C2×D8—134no—
235C2×D8—264no—
236C2×M16—264no—
237C2×M16—524no—
238C22×C8—131no—
239C22×C8—131no—
240C22×C8—131no—
241C22×C8—264no—
242C22×C8—261no—
243C22×C8—261no—
244C22×C8—261no—
245C22×C8—524no—
246C22×C8C2×#26111yescharacteristic
247C4×D4—132no—
248C4×D4—132no—
249C4×D4—132no—
250C4×D4—132no—
251C4×D4—261no—
252C4×D4—261no—
253C4×D4—261no—
254C4×D4—261no—
255C2×C4⋊C4C2×#26111yescharacteristic
256C2×C4⋊C4C2×#26111yescharacteristic
257C2×C22⋊C4—261no—
258C2×C22⋊C4—261no—
259C2×C42—131no—
260#107C2×#26114yes—
261C4⋊C8—132no—
262C4⋊C8—132no—
263C4⋊C8—261no—
264C4⋊C8—261no—
265#102—134no—
266#102—134no—
267C22⋊C8—264no—
268C22⋊C8—264no—
269C4×C8—132no—
270C4×C8—132no—
271C4×C8—132no—
272C4×C8—132no—
273C4×C8—132no—
274C4×C8—261no—
275C2×C13#158114yescomplemented
276C2×C13C2×#43511yescharacteristic
277C2×C13C2×C4×D811yescharacteristic
278C2×C13C2×#44411yescharacteristic
279D13—44no—
280D13—82no—
281C24—261no—
282C24—261no—
283C2×D4—134no—
284C2×D4—132no—
285C2×D4—132no—
286C2×D4—262no—
287C2×D4—261no—
288C2×D4—261no—
289C2×D4—262no—
290C2×D4—262no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—131no—
294C22×C4—131no—
295C22×C4—262no—
296C22×C4—262no—
297C22×C4—262no—
298C22×C4—262no—
299C22×C4—522no—
300C22×C4—522no—
301C22×C4—522no—
302C22×C4—522no—
303C22×C4C22×#26111yescharacteristic
304D8—268no—
305M16—528no—
306C2×C8—22no—
307C2×C8—132no—
308C2×C8—134no—
309C2×C8—132no—
310C2×C8—132no—
311C2×C8—262no—
312C2×C8—262no—
313C2×C8—262no—
314C2×C8—262no—
315C2×C8—262no—
316C2×C8—528no—
317C2×C8—522no—
318C2×C8—522no—
319C2×C8—522no—
320C2×C8C22×#26112yes—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4C22×#26112yes—
324C4⋊C4C22×#26112yes—
325C22⋊C4—262no—
326C22⋊C4—262no—
327C22⋊C4—262no—
328C22⋊C4—262no—
329C42—131no—
330C42—131no—
331C42—131no—
332C42—131no—
333C13C2×#158111yescharacteristic, complemented, Sylow
334C23—264no—
335C23—262no—
336C23—262no—
337C23—522no—
338C23—522no—
339C23—522no—
340C23—522no—
341C23—522no—
342C23D4×#26111yescharacteristic
343D4—134no—
344D4—264no—
345D4—262no—
346D4—262no—
347D4—262no—
348D4—522no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—132no—
354C2×C4—132no—
355C2×C4—131no—
356C2×C4—131no—
357C2×C4—131no—
358C2×C4—131no—
359C2×C4—262no—
360C2×C4—522no—
361C2×C4—522no—
362C2×C4—522no—
363C2×C4—522no—
364C2×C4—524no—
365C2×C4—524no—
366C2×C4D13⋊M1612yes—
367C2×C4D4×#26111yescharacteristic
368C2×C4#8824012yes—
369C2×C4C23×#26111yescharacteristic
370C8—22no—
371C8—134no—
372C8—262no—
373C8—262no—
374C8—522no—
375C8—522no—
376C8—522no—
377C22—264no—
378C22—522no—
379C22—522no—
380C22—528no—
381C22—522no—
382C22—522no—
383C22—522no—
384C22—1044no—
385C22#1171907512yes—
386C22D8×#26112yes—
387C22#1171911212yes—
388C22C2×D4×#26111yescharacteristic
389C4—42no—
390C4—42no—
391C4—131no—
392C4—131no—
393C4—132no—
394C4—261no—
395C4—261no—
396C4#1171907512yes—
397C4C2×D13⋊M1611yescharacteristic
398C4C2×#8824011yescharacteristic
399C2—524no—
400C2—1042no—
401C2#1313043614yesdirect product factor
402C2C2×#1171907511yescharacteristic
403C2C2×D8×#26111yescharacteristic
404C2C2×#1171911211yescharacteristic
subgroupG/H
centerC23D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C13×#107C4
socleC23×C13C4×D4
prime radicalC22×D104C4
cosocleC4×Dic13C24
hypercenterC2×#107#261
hypocenterC13C2×#1581
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C2×#11719076C2semidirect
2. C2×#11719073C2semidirect
3. #13130436C2direct (N × H)
4. C2×#11718256C2semidirect
5. C2×#11718243C2semidirect
6. C2×#11718243C2semidirect
7. C2×#1057⋊C8C2semidirect
21. #11719076C22semidirect
23. #11719073C22semidirect
30. #11718256C22semidirect
31. #1057⋊C8C22semidirect
32. #11718243C22semidirect
33. #11718243C22semidirect
92. C2×D52M16semidirect
110. C2×#1057D8semidirect
169. D52C2×M16semidirect
180. #1057C2×D8semidirect
275. C2×C13#1581semidirect
333. C13C2×#1581semidirect
401. C2#13130436direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117190762
C2×#117190732
#131304362
C2×#117182562
C2×#117182432
C2×#1057⋊C82
C2×#117185332
C2×#158113