Finite Group Databasebeta

← C2×#13116963 #16017485

Subgroups — C2×#13116963 #16017485

Order 3328.

658 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718562C211yesmaximal, characteristic, complemented
2C2×#11718853C211yesmaximal, characteristic, complemented
3C2×#11718821C211yesmaximal, characteristic
4#13116963C218yesmaximal, direct product factor
5C2×#11718098C211yesmaximal, characteristic, complemented
6C2×#11718157C211yesmaximal, characteristic, complemented
7C2×#11718155C211yesmaximal, characteristic, complemented
8C22×C13×SD32C211yesmaximal, characteristic, complemented
9C22×C13×Q16C2211yescharacteristic
10C22×C13×D8C2211yescharacteristic
11C2×#88196—21no—
12C2×#88186—21no—
13C2×#88155C2211yescharacteristic
14C2×C13×SD32—21no—
15C2×C13×SD32—21no—
16C2×C13×SD32—22no—
17C2×C13×SD32C2214yescomplemented
18C22×C13×C16C2211yescharacteristic
19C2×#88076—21no—
20C2×#88073—21no—
21#11718853—22no—
22#11718853C2214yescomplemented
23#11718821—22no—
24#11718821C2214yes—
25C2×#88059C2211yescharacteristic
26C2×#88059C2211yescharacteristic
27C2×#88052C2211yescharacteristic
28#11718562—22no—
29#11718562C2214yescomplemented
30C2×#88038—21no—
31C2×C16×D13—21no—
32#11718157C2214yescomplemented
33#11718155C2214yescomplemented
34#11718098C2214yescomplemented
35C22×Q8×C13—21no—
36C22×D4×C13—21no—
37C2×#6127D411yescharacteristic
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×D8—21no—
45C2×C13×D8—21no—
46C2×C13×D8—21no—
47C2×C13×D8—21no—
48C2×C13×D8—21no—
49C2×C13×D8C2312yes—
50C22×C8×C13C2311yescharacteristic
51C2×#6107—41no—
52#88196—24no—
53#88196—42no—
54C2×#6106—41no—
55C2×#6105—41no—
56#88186—24no—
57#88186—42no—
58C2×#6104—41no—
59C2×#6099—21no—
60C2×#6099—21no—
61C2×#6099D411yescharacteristic
62#88155—21no—
63#88155—21no—
64#88155D412yes—
65#88155C2312yes—
66C2×#6094—21no—
67C2×C8×D13—21no—
68C13×SD32—24no—
69C13×SD32—24no—
70C2×C13×C16D411yescharacteristic
71C2×C13×C16D411yescharacteristic
72C2×C13×C16D412yes—
73C2×C13×C16C2312yes—
74#88076—24no—
75#88073—24no—
76#88059—21no—
77#88059—21no—
78#88059C2312yes—
79#88059C2312yes—
80#88052—21no—
81#88052C2312yes—
82C2×#6090—21no—
83#88038—24no—
84C16×D13—24no—
85C2×#2223—131nomaximal, Sylow
86C24×C13—41no—
87C2×Q8×C13—22no—
88C2×Q8×C13—41no—
89C2×Q8×C13—41no—
90C2×Q8×C13—41no—
91C2×Q8×C13—41no—
92C2×Q8×C13—41no—
93C2×D4×C13—22no—
94C2×D4×C13—41no—
95C2×D4×C13—41no—
96C2×D4×C13—41no—
97C2×D4×C13—41no—
98C2×D4×C13—41no—
99C22×C4×C13—41no—
100C22×C4×C13C2×D411yescharacteristic
101C2×C22⋊D13—21no—
102#6127—21no—
103#6127—21no—
104#6127D812yes—
105#6127C2×D412yes—
106C2×D52D811yescharacteristic
107C2×C4×D13—21no—
108C2×Dic26D811yescharacteristic
109C13×Q16—22no—
110C13×Q16—22no—
111C13×Q16—41no—
112C13×Q16—41no—
113C13×D8—22no—
114C13×D8—22no—
115C13×D8—41no—
116C13×D8—41no—
117C2×C8×C13C2×D411yescharacteristic
118C2×C8×C13C2×D411yescharacteristic
119C2×C8×C13C2×D411yescharacteristic
120C2×C8×C13#4111yescharacteristic
121C2×C8×C13#4111yescharacteristic
122C2×C8×C13C2411yescharacteristic
123#6107—44no—
124#6106—44no—
125#6105—44no—
126#6104—44no—
127#6099—21no—
128#6099—22no—
129#6099—22no—
130#6099—41no—
131#6099—41no—
132#6099C2×D412yes—
133C2×#1055—21no—
134C2×#1055—41no—
135C2×#1055—41no—
136#6094—22no—
137#6094—22no—
138C8×D13—22no—
139C8×D13—22no—
140C13×C16C2×D412yes—
141C13×C16C2×D412yes—
142#6090—22no—
143C22×SD32D1311yescharacteristic, complemented
144C2×#504—131no—
145C2×#473—131no—
146C2×#472—131no—
147#2223—138no—
148C2×#368—131no—
149C2×#362—131no—
150C2×#361—131no—
151C23×C13—42no—
152C23×C13—81no—
153C23×C13—81no—
154C23×C13—162no—
155C23×C13#13511yescharacteristic
156C22×D13—21no—
157Q8×C13—42no—
158Q8×C13—42no—
159Q8×C13—81no—
160Q8×C13—81no—
161D4×C13—42no—
162D4×C13—42no—
163D4×C13—81no—
164D4×C13—81no—
165C2×C4×C13—42no—
166C2×C4×C13—81no—
167C2×C4×C13—81no—
168C2×C4×C13#12111yescharacteristic
169C2×C4×C13#12111yescharacteristic
170C2×C4×C13C2×D811yescharacteristic
171C2×C4×C13C2×D811yescharacteristic
172C2×C4×C13#13511yescharacteristic
173C2×C4×C13C22×D411yescharacteristic
174C22⋊D13—22no—
175C22⋊D13—22no—
176C2×Dic13—21no—
177D52—21no—
178D52C2×D812yes—
179C4×D13—22no—
180C4×D13—22no—
181Dic26—21no—
182Dic26C2×D812yes—
183C8×C13#12111yescharacteristic
184C8×C13#12111yescharacteristic
185C8×C13C22×D411yescharacteristic
186C8×C13C2×#4111yescharacteristic
187#1055—22no—
188#1055—42no—
189#1055—42no—
190C2×#137—261no—
191C2×AGL(1,ℤ/8)—261no—
192C22×Q16C2×D1311yescharacteristic
193C22×D8C2×D1311yescharacteristic
194C2×#131—131no—
195C2×SD32—21no—
196C2×SD32—21no—
197C2×SD32—22no—
198C2×SD32C2×D1314yescomplemented
199#504—134no—
200#504—262no—
201C2×M32—131no—
202C2×M32—261no—
203C22×C16—261no—
204C22×C16C2×D1311yescharacteristic
205#473—134no—
206#473—262no—
207#472—134no—
208#472—262no—
209C2×#108—131no—
210C2×#108—131no—
211C2×#101—261no—
212C2×#100—261no—
213#368—134no—
214#362—134no—
215#361—134no—
216C22×C13—22no—
217C22×C13—82no—
218C22×C13—162no—
219C22×C13—162no—
220C22×C13—162no—
221C22×C13#46611yescharacteristic
222C22×C13#46611yescharacteristic
223C22×C13C2×#13511yescharacteristic
224C2×D13—22no—
225C2×D13—42no—
226C4×C13—82no—
227C4×C13#46611yescharacteristic
228C4×C13#46611yescharacteristic
229C4×C13C2×#12111yescharacteristic
230C4×C13C22×D811yescharacteristic
231Dic13—22no—
232C2×#41—131no—
233C22×Q8—21no—
234C22×D4—21no—
235#137—264no—
236#137—522no—
237AGL(1,ℤ/8)—264no—
238AGL(1,ℤ/8)—522no—
239C2×Q16—21no—
240C2×Q16—21no—
241C2×Q16—21no—
242C2×Q16—21no—
243C2×Q16—21no—
244C2×Q16—521no—
245C2×Q16C22×D1312yes—
246C2×SD16—521no—
247C2×SD16—521no—
248C2×D8—21no—
249C2×D8—21no—
250C2×D8—21no—
251C2×D8—21no—
252C2×D8—21no—
253C2×D8—521no—
254C2×D8C22×D1312yes—
255#131—132no—
256#131—132no—
257#131—261no—
258#131—261no—
259C2×M16—131no—
260C2×M16—261no—
261C2×M16—261no—
262C2×M16—261no—
263C22×C8—261no—
264C22×C8C22×D1311yescharacteristic
265SD32—24no—
266SD32—24no—
267M32—132no—
268M32—261no—
269M32—264no—
270C2×C16—261no—
271C2×C16—264no—
272C2×C16C22⋊D1311yescharacteristic
273C2×C16C22⋊D1311yescharacteristic
274C2×C16C22⋊D1312yes—
275C2×C16C22×D1312yes—
276#108—132no—
277#108—132no—
278#108—261no—
279#108—261no—
280#101—264no—
281#100—264no—
282C2×C13—21no—
283C2×C13—21no—
284C2×C13—162no—
285C2×C13#222312yescomplemented
286C2×C13C2×#46611yescharacteristic
287D13—42no—
288C24—41no—
289#41—132no—
290#41—132no—
291#41—261no—
292#41—261no—
293C2×Q8—22no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—131no—
300C2×D4—22no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—131no—
307C2×D4—261no—
308C22×C4—41no—
309C22×C4—261no—
310C22×C4D4×D1311yescharacteristic
311Q16—22no—
312Q16—22no—
313Q16—41no—
314Q16—41no—
315Q16—524no—
316SD16—524no—
317SD16—524no—
318D8—22no—
319D8—22no—
320D8—41no—
321D8—41no—
322D8—524no—
323M16—132no—
324M16—261no—
325M16—262no—
326M16—262no—
327M16—262no—
328M16—262no—
329M16—521no—
330M16—521no—
331C2×C8—261no—
332C2×C8—262no—
333C2×C8—262no—
334C2×C8—521no—
335C2×C8—521no—
336C2×C8D4×D1311yescharacteristic
337C2×C8#612911yescharacteristic
338C2×C8#612911yescharacteristic
339C2×C8C2×C22⋊D1311yescharacteristic
340C2×C8C2×C22⋊D1311yescharacteristic
341C2×C8C23×D1311yescharacteristic
342C16—262no—
343C16C2×C22⋊D1312yes—
344C16C2×C22⋊D1312yes—
345C13C2×#222311yescharacteristic, complemented, Sylow
346C23—42no—
347C23—81no—
348C23—81no—
349C23—162no—
350C23—261no—
351C23#8816611yescharacteristic
352Q8—42no—
353Q8—42no—
354Q8—81no—
355Q8—81no—
356Q8—132no—
357Q8—261no—
358D4—42no—
359D4—42no—
360D4—81no—
361D4—81no—
362D4—132no—
363D4—262no—
364D4—262no—
365D4—261no—
366C2×C4—42no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—261no—
370C2×C4—262no—
371C2×C4—262no—
372C2×C4D8×D1311yescharacteristic
373C2×C4D8×D1311yescharacteristic
374C2×C4#8816611yescharacteristic
375C2×C4#8819211yescharacteristic
376C2×C4#8819211yescharacteristic
377C2×C4C2×D4×D1311yescharacteristic
378C8—262no—
379C8—522no—
380C8—522no—
381C8#8819211yescharacteristic
382C8#8819211yescharacteristic
383C8C2×#612911yescharacteristic
384C8C22×C22⋊D1311yescharacteristic
385C22—22no—
386C22—82no—
387C22—162no—
388C22—162no—
389C22—162no—
390C22—262no—
391C22—522no—
392C22#1171881811yescharacteristic
393C22#1171881811yescharacteristic
394C22C2×#8816611yescharacteristic
395C4—82no—
396C4—262no—
397C4#1171881811yescharacteristic
398C4#1171881811yescharacteristic
399C4C2×D8×D1311yescharacteristic
400C4C2×#8819211yescharacteristic
401C2—21no—
402C2—21no—
403C2—162no—
404C2—522no—
405C2#1311696312yesdirect product factor
406C2C2×#1171881811yescharacteristic
subgroupG/H
centerC22#11718818
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC22×C13×SD32C2
socleC22×C13#466
prime radicalC2×#11718821C2
hypercenterC22×SD32D13
hypocenterC13C2×#2223
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×SD32

Complements

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

NH ≅ G/Ntype
1. C2×#11718562C2semidirect
2. C2×#11718853C2semidirect
4. #13116963C2direct (N × H)
5. C2×#11718098C2semidirect
6. C2×#11718157C2semidirect
7. C2×#11718155C2semidirect
8. C22×C13×SD32C2semidirect
17. C2×C13×SD32C22semidirect
22. #11718853C22semidirect
29. #11718562C22semidirect
32. #11718157C22semidirect
33. #11718155C22semidirect
34. #11718098C22semidirect
143. C22×SD32D13semidirect
198. C2×SD32C2×D13semidirect
285. C2×C13#2223semidirect
345. C13C2×#2223semidirect
405. C2#13116963direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117185622
C2×#117188532
C2×#117188212
#131169632
C2×#117180982
C2×#117181572
C2×#117181552
C22×C13×SD322
C2×#222313