Finite Group Databasebeta

← C2×#13116902 #16017288

Subgroups — C2×#13116902 #16017288

Order 3328.

706 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718840C211yesmaximal, characteristic, complemented
2C2×#11718808C211yesmaximal, characteristic
3C2×#11718361C211yesmaximal, characteristic, complemented
4#13116902C218yesmaximal, direct product factor
5C2×#11718055C211yesmaximal, characteristic, complemented
6C2×#11718157C211yesmaximal, characteristic, complemented
7C2×#11718155C211yesmaximal, characteristic, complemented
8C2×C13×#495C211yesmaximal, characteristic, complemented
9C22×C13×Q16C2211yescharacteristic
10C22×C13×SD16—21no—
11C22×C13×D8C2211yescharacteristic
12C2×C13×#124—21no—
13C2×#88158C2211yescharacteristic
14C2×#88155—21no—
15C13×#495—22no—
16C13×#495C2214yescomplemented
17C2×C4×C8×C13C2211yescharacteristic
18C2×#88069—21no—
19#11718840—22no—
20#11718840C2214yescomplemented
21C2×#88068—21no—
22C2×#88067—21no—
23#11718808—22no—
24#11718808C2214yes—
25C2×#88066—21no—
26C2×#88059C2211yescharacteristic
27C2×#88052C2211yescharacteristic
28C2×#88052C2211yescharacteristic
29C2×#88045—21no—
30#11718361—22no—
31#11718361C2214yescomplemented
32#11718157C2214yescomplemented
33#11718155C2214yescomplemented
34#11718055C2214yescomplemented
35C22×Q8×C13—21no—
36C22×D4×C13—21no—
37C2×#6127—21no—
38C2×C13×Q16—21no—
39C2×C13×Q16—21no—
40C2×C13×Q16—21no—
41C2×C13×Q16—21no—
42C2×C13×Q16—21no—
43C2×C13×Q16C2312yes—
44C2×C13×SD16—24no—
45C2×C13×SD16—41no—
46C2×C13×SD16—41no—
47C2×C13×SD16—42no—
48C2×C13×D8—21no—
49C2×C13×D8—21no—
50C2×C13×D8—21no—
51C2×C13×D8—21no—
52C2×C13×D8—21no—
53C2×C13×D8C2312yes—
54C22×C8×C13D411yescharacteristic
55C22×C8×C13C2311yescharacteristic
56C13×#124—24no—
57C13×#124—42no—
58C2×C13×C22⋊C4—42no—
59C2×C42×C13D411yescharacteristic
60C2×#6099—21no—
61C2×Dic52D411yescharacteristic
62#88158—21no—
63#88158—21no—
64#88158D412yes—
65#88158C2312yes—
66C2×D104D411yescharacteristic
67C2×#6095—21no—
68#88155—24no—
69#88155—42no—
70C2×#6094—41no—
71C2×C8×D13—41no—
72C4×C8×C13D412yes—
73C4×C8×C13C2312yes—
74#88069—24no—
75#88068—24no—
76#88067—24no—
77#88066—24no—
78#88059—21no—
79#88059C2312yes—
80#88052—21no—
81#88052—21no—
82#88052C2312yes—
83#88052C2312yes—
84C2×#6090—21no—
85C2×#6090—21no—
86#88045—24no—
87C2×#2212—131nomaximal, Sylow
88C24×C13—41no—
89C2×Q8×C13—22no—
90C2×Q8×C13—41no—
91C2×Q8×C13—41no—
92C2×Q8×C13—41no—
93C2×Q8×C13—41no—
94C2×Q8×C13—41no—
95C2×D4×C13—22no—
96C2×D4×C13—41no—
97C2×D4×C13—41no—
98C2×D4×C13—41no—
99C2×D4×C13—41no—
100C2×D4×C13—41no—
101C22×C4×C13—21no—
102C22×C4×C13—41no—
103C22×C4×C13C2×D411yescharacteristic
104C2×C22⋊D13—41no—
105#6127—22no—
106#6127—22no—
107#6127—41no—
108#6127—41no—
109C2×D52—21no—
110C2×C4×D13—41no—
111C2×Dic26—21no—
112C13×Q16—22no—
113C13×Q16—22no—
114C13×Q16—41no—
115C13×Q16—41no—
116C13×SD16—44no—
117C13×SD16—44no—
118C13×D8—22no—
119C13×D8—22no—
120C13×D8—41no—
121C13×D8—41no—
122C2×C8×C13D811yescharacteristic
123C2×C8×C13D811yescharacteristic
124C2×C8×C13D812yes—
125C2×C8×C13C2×D411yescharacteristic
126C2×C8×C13C2×D411yescharacteristic
127C2×C8×C13C2×D411yescharacteristic
128C2×C8×C13C2×D412yes—
129C2×C8×C13#4111yescharacteristic
130C2×C8×C13#4111yescharacteristic
131C2×C8×C13C2411yescharacteristic
132C13×C22⋊C4—48no—
133C42×C13—21no—
134C42×C13C2×D412yes—
135#6099—22no—
136#6099—41no—
137C2×#1055—41no—
138Dic52—21no—
139Dic52C2×D412yes—
140D104—21no—
141D104C2×D412yes—
142#6095—22no—
143#6095—22no—
144#6094—44no—
145C8×D13—44no—
146#6090—22no—
147#6090—22no—
148C2×#510—131no—
149C2×#509—131no—
150C2×#495D1311yescharacteristic, complemented
151C2×#443—131no—
152#2212—138no—
153C2×#364—131no—
154C2×#362—131no—
155C2×#361—131no—
156C23×C13—42no—
157C23×C13—84no—
158C23×C13—81no—
159C23×C13—81no—
160C23×C13AGL(1,ℤ/8)11yescharacteristic
161C22×D13—41no—
162Q8×C13—42no—
163Q8×C13—42no—
164Q8×C13—81no—
165Q8×C13—81no—
166D4×C13—42no—
167D4×C13—42no—
168D4×C13—81no—
169D4×C13—81no—
170C2×C4×C13—22no—
171C2×C4×C13—42no—
172C2×C4×C13—42no—
173C2×C4×C13—81no—
174C2×C4×C13—81no—
175C2×C4×C13#12111yescharacteristic
176C2×C4×C13#12111yescharacteristic
177C2×C4×C13C2×D811yescharacteristic
178C2×C4×C13C2×D811yescharacteristic
179C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C13C22×D411yescharacteristic
181C22⋊D13—42no—
182C22⋊D13—42no—
183C2×Dic13—41no—
184D52—22no—
185D52—41no—
186C4×D13—42no—
187C4×D13—42no—
188Dic26—22no—
189Dic26—41no—
190C8×C13#12111yescharacteristic
191C8×C13#12111yescharacteristic
192C8×C13C2×D812yes—
193C8×C13C2×D812yes—
194C8×C13C22×D411yescharacteristic
195C8×C13C2×#4111yescharacteristic
196#1055—42no—
197C2×#135—131no—
198C22×Q16C2×D1311yescharacteristic
199C22×SD16—21no—
200C22×D8C2×D1311yescharacteristic
201C2×#131—261no—
202C2×#124—21no—
203#510—134no—
204#510—262no—
205#509—134no—
206#509—262no—
207C2×Q32—261no—
208C2×SD32—261no—
209C2×SD32—261no—
210C2×D16—261no—
211C2×M32—131no—
212C2×M32—131no—
213#495—22no—
214#495C2×D1314yescomplemented
215#443—134no—
216#443—262no—
217C2×#108—131no—
218C2×#104—261no—
219C2×C4×C8C2×D1311yescharacteristic
220#364—134no—
221#362—134no—
222#361—134no—
223C22×C13—22no—
224C22×C13—84no—
225C22×C13—82no—
226C22×C13—162no—
227C22×C13—162no—
228C22×C13#45911yescharacteristic
229C22×C13#45911yescharacteristic
230C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
231C2×D13—42no—
232C2×D13—82no—
233C4×C13—42no—
234C4×C13—82no—
235C4×C13#45911yescharacteristic
236C4×C13#45911yescharacteristic
237C4×C13C2×#12111yescharacteristic
238C4×C13C22×D811yescharacteristic
239Dic13—42no—
240C2×#41—261no—
241C22×Q8—21no—
242C22×D4—21no—
243#135—132no—
244#135—132no—
245#135—261no—
246#135—261no—
247C2×Q16—21no—
248C2×Q16—21no—
249C2×Q16—21no—
250C2×Q16—21no—
251C2×Q16—21no—
252C2×Q16—131no—
253C2×Q16C22×D1312yes—
254C2×SD16—24no—
255C2×SD16—41no—
256C2×SD16—41no—
257C2×SD16—42no—
258C2×SD16—261no—
259C2×D8—21no—
260C2×D8—21no—
261C2×D8—21no—
262C2×D8—21no—
263C2×D8—21no—
264C2×D8—131no—
265C2×D8C22×D1312yes—
266#131—264no—
267#131—522no—
268C2×M16—261no—
269C2×M16—521no—
270C22×C8—521no—
271C22×C8C22⋊D1311yescharacteristic
272C22×C8C22×D1311yescharacteristic
273#124—24no—
274#124—42no—
275C2×C22⋊C4—42no—
276C2×C42C22⋊D1311yescharacteristic
277Q32—264no—
278SD32—264no—
279SD32—264no—
280D16—264no—
281M32—132no—
282M32—132no—
283M32—261no—
284M32—261no—
285C2×C16—261no—
286C2×C16—261no—
287#108—132no—
288#108—261no—
289#104—264no—
290C4×C8C22⋊D1312yes—
291C4×C8C22×D1312yes—
292C2×C13—21no—
293C2×C13—21no—
294C2×C13—162no—
295C2×C13#221212yescomplemented
296C2×C13C2×#45911yescharacteristic
297D13—82no—
298C24—41no—
299#41—262no—
300#41—262no—
301#41—521no—
302#41—521no—
303C2×Q8—22no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—261no—
310C2×D4—22no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—261no—
317C2×D4—521no—
318C22×C4—21no—
319C22×C4—41no—
320C22×C4—521no—
321C22×C4C2×C22⋊D1311yescharacteristic
322Q16—22no—
323Q16—22no—
324Q16—41no—
325Q16—41no—
326Q16—132no—
327Q16—261no—
328SD16—44no—
329SD16—44no—
330SD16—262no—
331SD16—262no—
332D8—22no—
333D8—22no—
334D8—41no—
335D8—41no—
336D8—132no—
337D8—261no—
338M16—262no—
339M16—521no—
340M16—524no—
341C2×C8—521no—
342C2×C8—524no—
343C2×C8#610411yescharacteristic
344C2×C8#610411yescharacteristic
345C2×C8#610412yes—
346C2×C8D4×D1311yescharacteristic
347C2×C8D4×D1311yescharacteristic
348C2×C8#612911yescharacteristic
349C2×C8#612911yescharacteristic
350C2×C8C2×C22⋊D1312yes—
351C2×C8C2×C22⋊D1311yescharacteristic
352C2×C8C23×D1311yescharacteristic
353C22⋊C4—48no—
354C42—21no—
355C42C2×C22⋊D1312yes—
356C16—262no—
357C16—262no—
358C13C2×#221211yescharacteristic, complemented, Sylow
359C23—42no—
360C23—84no—
361C23—81no—
362C23—81no—
363C23—521no—
364C23#8818611yescharacteristic
365Q8—42no—
366Q8—42no—
367Q8—81no—
368Q8—81no—
369Q8—262no—
370Q8—521no—
371D4—42no—
372D4—42no—
373D4—81no—
374D4—81no—
375D4—262no—
376D4—522no—
377D4—522no—
378D4—521no—
379C2×C4—22no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—521no—
385C2×C4—522no—
386C2×C4—522no—
387C2×C4C2×#610411yescharacteristic
388C2×C4C2×#610411yescharacteristic
389C2×C4#8818611yescharacteristic
390C2×C4#8819211yescharacteristic
391C2×C4#8819211yescharacteristic
392C2×C4C22×C22⋊D1311yescharacteristic
393C8—522no—
394C8C2×#610412yes—
395C8C2×#610412yes—
396C8#8819211yescharacteristic
397C8#8819211yescharacteristic
398C8C2×D4×D1311yescharacteristic
399C8C2×#612911yescharacteristic
400C22—22no—
401C22—84no—
402C22—82no—
403C22—162no—
404C22—162no—
405C22—522no—
406C22—1042no—
407C22#1171873311yescharacteristic
408C22#1171873311yescharacteristic
409C22C2×#8818611yescharacteristic
410C4—42no—
411C4—82no—
412C4—522no—
413C4#1171873311yescharacteristic
414C4#1171873311yescharacteristic
415C4C22×#610411yescharacteristic
416C4C2×#8819211yescharacteristic
417C2—21no—
418C2—21no—
419C2—162no—
420C2—1042no—
421C2#1311690212yesdirect product factor
422C2C2×#1171873311yescharacteristic
subgroupG/H
centerC22#11718733
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC2×C13×#495C2
socleC22×C13#459
prime radicalC2×#11718808C2
hypercenterC2×#495D13
hypocenterC13C2×#2212
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#495

Complements

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

NH ≅ G/Ntype
1. C2×#11718840C2semidirect
3. C2×#11718361C2semidirect
4. #13116902C2direct (N × H)
5. C2×#11718055C2semidirect
6. C2×#11718157C2semidirect
7. C2×#11718155C2semidirect
8. C2×C13×#495C2semidirect
16. C13×#495C22semidirect
20. #11718840C22semidirect
31. #11718361C22semidirect
32. #11718157C22semidirect
33. #11718155C22semidirect
34. #11718055C22semidirect
150. C2×#495D13semidirect
214. #495C2×D13semidirect
295. C2×C13#2212semidirect
358. C13C2×#2212semidirect
421. C2#13116902direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117188402
C2×#117188082
C2×#117183612
#131169022
C2×#117180552
C2×#117181572
C2×#117181552
C2×C13×#4952
C2×#221213