Finite Group Databasebeta

← C2×#13116905 #16017291

Subgroups — C2×#13116905 #16017291

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×#11718856C211yesmaximal, characteristic, complemented
2C2×#11718854C211yesmaximal, characteristic
3C2×#11718357C211yesmaximal, characteristic, complemented
4#13116905C218yesmaximal, direct product factor
5C2×#11718055C211yesmaximal, characteristic, complemented
6C2×#11718088C211yesmaximal, characteristic, complemented
7C2×#11718087C211yesmaximal, characteristic, complemented
8C2×C13×#443C211yesmaximal, characteristic, complemented
9C2×C13×#135C2211yescharacteristic
10C2×C13×#131—21no—
11C22×Dic52C2211yescharacteristic
12C22×D104C2211yescharacteristic
13C22×#6095—21no—
14C2×#88129—21no—
15C13×#443—22no—
16C13×#443C2214yescomplemented
17C2×C13×#108C2211yescharacteristic
18C2×C13×#104—21no—
19C2×C4×C8×C13C2211yescharacteristic
20#11718856—22no—
21#11718856C2214yescomplemented
22#11718854—22no—
23#11718854C2214yes—
24C2×#88069—21no—
25C2×#88068—21no—
26C2×#88067—21no—
27C2×#88066—21no—
28C2×#88052C2211yescharacteristic
29C2×#88052C2211yescharacteristic
30#11718357—22no—
31#11718357C2214yescomplemented
32#11718088C2214yescomplemented
33#11718087C2214yescomplemented
34#11718055C2214yescomplemented
35C2×C13×#41—21no—
36C22×D52—21no—
37C22×Dic26—21no—
38C13×#135—21no—
39C13×#135—21no—
40C13×#135D412yes—
41C13×#135C2312yes—
42C2×C13×Q16D411yescharacteristic
43C2×C13×SD16—21no—
44C2×C13×D8D411yescharacteristic
45C13×#131—24no—
46C13×#131—42no—
47C2×C13×M16—21no—
48C2×C13×M16—41no—
49C22×C8×C13—41no—
50C22×C8×C13D411yescharacteristic
51C22×C8×C13C2311yescharacteristic
52C2×C42×C13D411yescharacteristic
53C2×#6103—42no—
54C2×Dic52—21no—
55C2×Dic52—21no—
56C2×Dic52—21no—
57C2×Dic52—21no—
58C2×Dic52—21no—
59C2×Dic52C2312yes—
60C2×D104—21no—
61C2×D104—21no—
62C2×D104—21no—
63C2×D104—21no—
64C2×D104—21no—
65C2×D104C2312yes—
66C2×#6095—24no—
67C2×#6095—41no—
68C2×#6095—41no—
69C2×#6095—42no—
70#88129—24no—
71#88129—42no—
72C13×#108—21no—
73C13×#108C2312yes—
74C13×#104—24no—
75C4×C8×C13D412yes—
76C4×C8×C13C2312yes—
77#88069—24no—
78#88068—24no—
79#88067—24no—
80#88066—24no—
81#88052—21no—
82#88052—21no—
83#88052C2312yes—
84#88052C2312yes—
85C2×#6090—21no—
86C2×#6090—21no—
87C2×#2212—131nomaximal, Sylow
88C23×D13—41no—
89C13×#41—22no—
90C13×#41—22no—
91C13×#41—41no—
92C13×#41—41no—
93C2×Q8×C13—21no—
94C2×D4×C13—21no—
95C2×D4×C13—41no—
96C22×C4×C13—21no—
97C22×C4×C13—41no—
98C22×C4×C13C2×D411yescharacteristic
99C22×Dic13—41no—
100C2×D52—22no—
101C2×D52—41no—
102C2×D52—41no—
103C2×D52—41no—
104C2×D52—41no—
105C2×D52—41no—
106C2×Dic26—22no—
107C2×Dic26—41no—
108C2×Dic26—41no—
109C2×Dic26—41no—
110C2×Dic26—41no—
111C2×Dic26—41no—
112C13×Q16—21no—
113C13×Q16C2×D412yes—
114C13×SD16—22no—
115C13×SD16—22no—
116C13×D8—21no—
117C13×D8C2×D412yes—
118C13×M16—22no—
119C13×M16—41no—
120C13×M16—44no—
121C2×C8×C13—41no—
122C2×C8×C13—44no—
123C2×C8×C13D811yescharacteristic
124C2×C8×C13D811yescharacteristic
125C2×C8×C13D812yes—
126C2×C8×C13C2×D411yescharacteristic
127C2×C8×C13C2×D411yescharacteristic
128C2×C8×C13C2×D411yescharacteristic
129C2×C8×C13C2×D412yes—
130C2×C8×C13#4111yescharacteristic
131C2×C8×C13#4111yescharacteristic
132C2×C8×C13C2411yescharacteristic
133C42×C13—21no—
134C42×C13C2×D412yes—
135#6103—48no—
136Dic52—22no—
137Dic52—22no—
138Dic52—41no—
139Dic52—41no—
140D104—22no—
141D104—22no—
142D104—41no—
143D104—41no—
144#6095—44no—
145#6095—44no—
146#6090—22no—
147#6090—22no—
148C2×#510—131no—
149C2×#509—131no—
150C2×#495—131no—
151C2×#443D1311yescharacteristic, complemented
152#2212—138no—
153C2×#364—131no—
154C2×#362—131no—
155C2×#361—131no—
156C23×C13—41no—
157C23×C13AGL(1,ℤ/8)11yescharacteristic
158C22×D13—42no—
159C22×D13—84no—
160C22×D13—81no—
161C22×D13—81no—
162Q8×C13—22no—
163Q8×C13—41no—
164D4×C13—22no—
165D4×C13—42no—
166D4×C13—42no—
167D4×C13—41no—
168C2×C4×C13—22no—
169C2×C4×C13—42no—
170C2×C4×C13—41no—
171C2×C4×C13—42no—
172C2×C4×C13—42no—
173C2×C4×C13#12111yescharacteristic
174C2×C4×C13#12111yescharacteristic
175C2×C4×C13C2×D811yescharacteristic
176C2×C4×C13C2×D811yescharacteristic
177C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C13C22×D411yescharacteristic
179C2×Dic13—42no—
180C2×Dic13—81no—
181C2×Dic13—81no—
182D52—42no—
183D52—42no—
184D52—81no—
185D52—81no—
186Dic26—42no—
187Dic26—42no—
188Dic26—81no—
189Dic26—81no—
190C8×C13—42no—
191C8×C13#12111yescharacteristic
192C8×C13#12111yescharacteristic
193C8×C13C2×D812yes—
194C8×C13C2×D812yes—
195C8×C13C22×D411yescharacteristic
196C8×C13C2×#4111yescharacteristic
197C2×#135C2×D1311yescharacteristic
198C22×Q16—131no—
199C22×SD16—261no—
200C22×D8—131no—
201C2×#131—21no—
202C2×#124—261no—
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—134no—
214#495—262no—
215#443—22no—
216#443C2×D1314yescomplemented
217C2×#108C2×D1311yescharacteristic
218C2×#104—21no—
219C2×C4×C8C2×D1311yescharacteristic
220#364—134no—
221#362—134no—
222#361—134no—
223C22×C13—22no—
224C22×C13—42no—
225C22×C13—82no—
226C22×C13#45911yescharacteristic
227C22×C13#45911yescharacteristic
228C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
229C2×D13—84no—
230C2×D13—82no—
231C2×D13—162no—
232C2×D13—162no—
233C4×C13—42no—
234C4×C13—42no—
235C4×C13#45911yescharacteristic
236C4×C13#45911yescharacteristic
237C4×C13C2×#12111yescharacteristic
238C4×C13C22×D811yescharacteristic
239Dic13—82no—
240C2×#41—21no—
241C22×Q8—261no—
242C22×D4—261no—
243#135—21no—
244#135—21no—
245#135D5212yes—
246#135C22×D1312yes—
247C2×Q16—132no—
248C2×Q16—261no—
249C2×Q16—261no—
250C2×Q16—261no—
251C2×Q16—261no—
252C2×Q16—261no—
253C2×Q16D5211yescharacteristic
254C2×SD16—21no—
255C2×SD16—264no—
256C2×SD16—521no—
257C2×SD16—521no—
258C2×SD16—522no—
259C2×D8—132no—
260C2×D8—261no—
261C2×D8—261no—
262C2×D8—261no—
263C2×D8—261no—
264C2×D8—261no—
265C2×D8D5211yescharacteristic
266#131—24no—
267#131—42no—
268C2×M16—21no—
269C2×M16—41no—
270C22×C8—41no—
271C22×C8C22⋊D1311yescharacteristic
272C22×C8C22×D1311yescharacteristic
273#124—264no—
274#124—522no—
275C2×C22⋊C4—522no—
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—21no—
288#108C22×D1312yes—
289#104—24no—
290C4×C8C22⋊D1312yes—
291C4×C8C22×D1312yes—
292C2×C13—21no—
293C2×C13—21no—
294C2×C13—82no—
295C2×C13#221212yescomplemented
296C2×C13C2×#45911yescharacteristic
297D13—162no—
298C24—521no—
299#41—22no—
300#41—22no—
301#41—41no—
302#41—41no—
303C2×Q8—21no—
304C2×Q8—262no—
305C2×Q8—521no—
306C2×Q8—521no—
307C2×Q8—521no—
308C2×Q8—521no—
309C2×Q8—521no—
310C2×D4—21no—
311C2×D4—41no—
312C2×D4—262no—
313C2×D4—521no—
314C2×D4—521no—
315C2×D4—521no—
316C2×D4—521no—
317C2×D4—521no—
318C22×C4—21no—
319C22×C4—41no—
320C22×C4—521no—
321C22×C4C2×C22⋊D1311yescharacteristic
322Q16—21no—
323Q16—262no—
324Q16—262no—
325Q16—521no—
326Q16—521no—
327Q16C2×D5212yes—
328SD16—22no—
329SD16—22no—
330SD16—524no—
331SD16—524no—
332D8—21no—
333D8—262no—
334D8—262no—
335D8—521no—
336D8—521no—
337D8C2×D5212yes—
338M16—22no—
339M16—41no—
340M16—44no—
341C2×C8—41no—
342C2×C8—44no—
343C2×C8#610411yescharacteristic
344C2×C8#610411yescharacteristic
345C2×C8#610412yes—
346C2×C8C2×D5211yescharacteristic
347C2×C8C2×D5211yescharacteristic
348C2×C8#612711yescharacteristic
349C2×C8#612711yescharacteristic
350C2×C8C2×C22⋊D1311yescharacteristic
351C2×C8C2×C22⋊D1312yes—
352C2×C8C23×D1311yescharacteristic
353C22⋊C4—528no—
354C42—21no—
355C42C2×C22⋊D1312yes—
356C16—262no—
357C16—262no—
358C13C2×#221211yescharacteristic, complemented, Sylow
359C23—41no—
360C23—522no—
361C23—1044no—
362C23—1041no—
363C23—1041no—
364C23#8820311yescharacteristic
365Q8—22no—
366Q8—41no—
367Q8—522no—
368Q8—522no—
369Q8—1041no—
370Q8—1041no—
371D4—22no—
372D4—42no—
373D4—42no—
374D4—41no—
375D4—522no—
376D4—522no—
377D4—1041no—
378D4—1041no—
379C2×C4—22no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—522no—
385C2×C4—1041no—
386C2×C4—1041no—
387C2×C4#8818411yescharacteristic
388C2×C4#8818411yescharacteristic
389C2×C4C2×#610411yescharacteristic
390C2×C4C2×#610411yescharacteristic
391C2×C4#8820311yescharacteristic
392C2×C4C22×C22⋊D1311yescharacteristic
393C8—42no—
394C8#8818411yescharacteristic
395C8#8818411yescharacteristic
396C8C2×#610412yes—
397C8C2×#610412yes—
398C8C22×D5211yescharacteristic
399C8C2×#612711yescharacteristic
400C22—22no—
401C22—42no—
402C22—82no—
403C22—1044no—
404C22—1042no—
405C22—2082no—
406C22—2082no—
407C22#1171867611yescharacteristic
408C22#1171867611yescharacteristic
409C22C2×#8820311yescharacteristic
410C4—42no—
411C4—42no—
412C4—1042no—
413C4#1171867611yescharacteristic
414C4#1171867611yescharacteristic
415C4C2×#8818411yescharacteristic
416C4C22×#610411yescharacteristic
417C2—21no—
418C2—21no—
419C2—82no—
420C2—2082no—
421C2#1311690512yesdirect product factor
422C2C2×#1171867611yescharacteristic
subgroupG/H
centerC22#11718676
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC2×C13×#443C2
socleC22×C13#459
prime radicalC2×#11718854C2
hypercenterC2×#443D13
hypocenterC13C2×#2212
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#443

Complements

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

NH ≅ G/Ntype
1. C2×#11718856C2semidirect
3. C2×#11718357C2semidirect
4. #13116905C2direct (N × H)
5. C2×#11718055C2semidirect
6. C2×#11718088C2semidirect
7. C2×#11718087C2semidirect
8. C2×C13×#443C2semidirect
16. C13×#443C22semidirect
21. #11718856C22semidirect
31. #11718357C22semidirect
32. #11718088C22semidirect
33. #11718087C22semidirect
34. #11718055C22semidirect
151. C2×#443D13semidirect
216. #443C2×D13semidirect
295. C2×C13#2212semidirect
358. C13C2×#2212semidirect
421. C2#13116905direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117188562
C2×#117188542
C2×#117183572
#131169052
C2×#117180552
C2×#117180882
C2×#117180872
C2×C13×#4432
C2×#221213