Finite Group Databasebeta

← C2×#13116966 #16017488

Subgroups — C2×#13116966 #16017488

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
1C22×#88040C211yesmaximal, characteristic, complemented
2C2×#11718804C211yesmaximal, characteristic, complemented
3C2×#11718803C211yesmaximal, characteristic
4#13116966C218yesmaximal, direct product factor
5C2×#11718098C211yesmaximal, characteristic, complemented
6C2×#11718109C211yesmaximal, characteristic, complemented
7C2×#11718108C211yesmaximal, characteristic, complemented
8C2×C13×#504C211yesmaximal, characteristic, complemented
9C2×C13×#131C2211yescharacteristic
10C2×#88205—21no—
11C2×#88203—21no—
12C22×Dic52C2211yescharacteristic
13C22×D104C2211yescharacteristic
14C13×#504—22no—
15C13×#504C2214yescomplemented
16C2×C13×M32—21no—
17C2×C13×M32C2211yescharacteristic
18C22×C13×C16—21no—
19C22×C13×C16C2211yescharacteristic
20#11718804—22no—
21#11718804C2214yescomplemented
22#11718803—22no—
23#11718803C2214yes—
24C2×#88064—21no—
25C2×#88063—21no—
26C2×#88059C2211yescharacteristic
27C2×#88059C2211yescharacteristic
28C2×#88040—21no—
29C2×#88040—21no—
30C2×#88040—22no—
31C2×#88040C2214yescomplemented
32#11718109C2214yescomplemented
33#11718108C2214yescomplemented
34#11718098C2214yescomplemented
35C2×C13×#41D411yescharacteristic
36C22×D52—21no—
37C22×Dic26—21no—
38C13×#131—21no—
39C13×#131—21no—
40C13×#131D412yes—
41C13×#131C2312yes—
42C2×C13×M16—21no—
43C2×C13×M16D411yescharacteristic
44C22×C8×C13—21no—
45C22×C8×C13C2311yescharacteristic
46#88205—24no—
47#88205—42no—
48#88203—24no—
49#88203—42no—
50C2×#6107—41no—
51C2×#6106—41no—
52C2×#6105—41no—
53C2×#6104—41no—
54C2×#6099—21no—
55C2×#6099—21no—
56C2×Dic52—21no—
57C2×Dic52—21no—
58C2×Dic52—21no—
59C2×Dic52—21no—
60C2×Dic52—21no—
61C2×Dic52C2312yes—
62C2×D104—21no—
63C2×D104—21no—
64C2×D104—21no—
65C2×D104—21no—
66C2×D104—21no—
67C2×D104C2312yes—
68C13×M32—21no—
69C13×M32—24no—
70C13×M32C2312yes—
71C2×C13×C16—21no—
72C2×C13×C16—24no—
73C2×C13×C16D411yescharacteristic
74C2×C13×C16D411yescharacteristic
75C2×C13×C16D412yes—
76C2×C13×C16C2312yes—
77#88064—24no—
78#88063—24no—
79#88059—21no—
80#88059—21no—
81#88059C2312yes—
82#88059C2312yes—
83#88040—24no—
84#88040—24no—
85C2×#2223—131nomaximal, Sylow
86C23×D13—41no—
87C13×#41—21no—
88C13×#41—21no—
89C13×#41D812yes—
90C13×#41C2×D412yes—
91C2×Q8×C13D811yescharacteristic
92C2×D4×C13—21no—
93C2×D4×C13D811yescharacteristic
94C22×C4×C13—21no—
95C22×C4×C13C2×D411yescharacteristic
96C22×Dic13—41no—
97C2×D52—22no—
98C2×D52—41no—
99C2×D52—41no—
100C2×D52—41no—
101C2×D52—41no—
102C2×D52—41no—
103C2×Dic26—22no—
104C2×Dic26—41no—
105C2×Dic26—41no—
106C2×Dic26—41no—
107C2×Dic26—41no—
108C2×Dic26—41no—
109C13×M16—21no—
110C13×M16—22no—
111C13×M16—22no—
112C13×M16C2×D412yes—
113C2×C8×C13—21no—
114C2×C8×C13—22no—
115C2×C8×C13—22no—
116C2×C8×C13C2×D411yescharacteristic
117C2×C8×C13C2×D411yescharacteristic
118C2×C8×C13C2×D411yescharacteristic
119C2×C8×C13#4111yescharacteristic
120C2×C8×C13#4111yescharacteristic
121C2×C8×C13C2411yescharacteristic
122#6107—44no—
123#6106—44no—
124#6105—44no—
125#6104—44no—
126#6099—22no—
127#6099—22no—
128#6099—41no—
129#6099—41no—
130C2×#1055—41no—
131C2×#1055—41no—
132Dic52—22no—
133Dic52—22no—
134Dic52—41no—
135Dic52—41no—
136D104—22no—
137D104—22no—
138D104—41no—
139D104—41no—
140C13×C16—22no—
141C13×C16C2×D412yes—
142C13×C16C2×D412yes—
143C22×SD32—131no—
144C2×#504D1311yescharacteristic, complemented
145C2×#473—131no—
146C2×#472—131no—
147#2223—138no—
148C2×#368—131no—
149C2×#362—131no—
150C2×#361—131no—
151C23×C13—21no—
152C23×C13#13511yescharacteristic
153C22×D13—42no—
154C22×D13—81no—
155C22×D13—81no—
156C22×D13—162no—
157Q8×C13—21no—
158Q8×C13C2×D812yes—
159D4×C13—22no—
160D4×C13—22no—
161D4×C13—21no—
162D4×C13C2×D812yes—
163C2×C4×C13—21no—
164C2×C4×C13—22no—
165C2×C4×C13—22no—
166C2×C4×C13#12111yescharacteristic
167C2×C4×C13#12111yescharacteristic
168C2×C4×C13C2×D811yescharacteristic
169C2×C4×C13C2×D811yescharacteristic
170C2×C4×C13#13511yescharacteristic
171C2×C4×C13C22×D411yescharacteristic
172C2×Dic13—42no—
173C2×Dic13—81no—
174C2×Dic13—81no—
175D52—42no—
176D52—42no—
177D52—81no—
178D52—81no—
179Dic26—42no—
180Dic26—42no—
181Dic26—81no—
182Dic26—81no—
183C8×C13—22no—
184C8×C13#12111yescharacteristic
185C8×C13#12111yescharacteristic
186C8×C13C22×D411yescharacteristic
187C8×C13C2×#4111yescharacteristic
188#1055—42no—
189#1055—42no—
190C2×#137—261no—
191C2×AGL(1,ℤ/8)—261no—
192C22×Q16—131no—
193C22×D8—131no—
194C2×#131C2×D1311yescharacteristic
195C2×SD32—134no—
196C2×SD32—261no—
197C2×SD32—261no—
198C2×SD32—262no—
199#504—22no—
200#504C2×D1314yescomplemented
201C2×M32—21no—
202C2×M32C2×D1311yescharacteristic
203C22×C16—21no—
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—22no—
218C22×C13—42no—
219C22×C13#46611yescharacteristic
220C22×C13#46611yescharacteristic
221C22×C13C2×#13511yescharacteristic
222C2×D13—82no—
223C2×D13—162no—
224C2×D13—162no—
225C2×D13—162no—
226C4×C13—22no—
227C4×C13#46611yescharacteristic
228C4×C13#46611yescharacteristic
229C4×C13C2×#12111yescharacteristic
230C4×C13C22×D811yescharacteristic
231Dic13—82no—
232C2×#41D5211yescharacteristic
233C22×Q8—261no—
234C22×D4—261no—
235#137—264no—
236#137—522no—
237AGL(1,ℤ/8)—264no—
238AGL(1,ℤ/8)—522no—
239C2×Q16—132no—
240C2×Q16—261no—
241C2×Q16—261no—
242C2×Q16—261no—
243C2×Q16—261no—
244C2×Q16—261no—
245C2×Q16—521no—
246C2×SD16—521no—
247C2×SD16—521no—
248C2×D8—132no—
249C2×D8—261no—
250C2×D8—261no—
251C2×D8—261no—
252C2×D8—261no—
253C2×D8—261no—
254C2×D8—521no—
255#131—21no—
256#131—21no—
257#131D5212yes—
258#131C22×D1312yes—
259C2×M16—21no—
260C2×M16—261no—
261C2×M16—261no—
262C2×M16D5211yescharacteristic
263C22×C8—21no—
264C22×C8C22×D1311yescharacteristic
265SD32—264no—
266SD32—264no—
267M32—21no—
268M32—24no—
269M32C22×D1312yes—
270C2×C16—21no—
271C2×C16—24no—
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—42no—
285C2×C13#222312yescomplemented
286C2×C13C2×#46611yescharacteristic
287D13—162no—
288C24—521no—
289#41—21no—
290#41—21no—
291#41D10412yes—
292#41C2×D5212yes—
293C2×Q8—262no—
294C2×Q8—521no—
295C2×Q8—521no—
296C2×Q8—521no—
297C2×Q8—521no—
298C2×Q8—521no—
299C2×Q8D10411yescharacteristic
300C2×D4—21no—
301C2×D4—262no—
302C2×D4—521no—
303C2×D4—521no—
304C2×D4—521no—
305C2×D4—521no—
306C2×D4—521no—
307C2×D4D10411yescharacteristic
308C22×C4—21no—
309C22×C4—521no—
310C22×C4C2×D5211yescharacteristic
311Q16—262no—
312Q16—262no—
313Q16—524no—
314Q16—521no—
315Q16—521no—
316SD16—524no—
317SD16—524no—
318D8—262no—
319D8—262no—
320D8—524no—
321D8—521no—
322D8—521no—
323M16—21no—
324M16—22no—
325M16—22no—
326M16—262no—
327M16—262no—
328M16—521no—
329M16—521no—
330M16C2×D5212yes—
331C2×C8—21no—
332C2×C8—22no—
333C2×C8—22no—
334C2×C8—521no—
335C2×C8—521no—
336C2×C8C2×D5211yescharacteristic
337C2×C8#612711yescharacteristic
338C2×C8#612711yescharacteristic
339C2×C8C2×C22⋊D1311yescharacteristic
340C2×C8C2×C22⋊D1311yescharacteristic
341C2×C8C23×D1311yescharacteristic
342C16—22no—
343C16C2×C22⋊D1312yes—
344C16C2×C22⋊D1312yes—
345C13C2×#222311yescharacteristic, complemented, Sylow
346C23—21no—
347C23—522no—
348C23—1041no—
349C23—1041no—
350C23—2082no—
351C23#8815811yescharacteristic
352Q8—21no—
353Q8—522no—
354Q8—522no—
355Q8—1041no—
356Q8—1041no—
357Q8C2×D10412yes—
358D4—22no—
359D4—22no—
360D4—21no—
361D4—522no—
362D4—522no—
363D4—1041no—
364D4—1041no—
365D4C2×D10412yes—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—522no—
370C2×C4—1041no—
371C2×C4—1041no—
372C2×C4C2×D10411yescharacteristic
373C2×C4C2×D10411yescharacteristic
374C2×C4#8815811yescharacteristic
375C2×C4#8818411yescharacteristic
376C2×C4#8818411yescharacteristic
377C2×C4C22×D5211yescharacteristic
378C8—22no—
379C8—522no—
380C8—522no—
381C8#8818411yescharacteristic
382C8#8818411yescharacteristic
383C8C2×#612711yescharacteristic
384C8C22×C22⋊D1311yescharacteristic
385C22—22no—
386C22—22no—
387C22—42no—
388C22—1042no—
389C22—2082no—
390C22—2082no—
391C22—2082no—
392C22#1171877611yescharacteristic
393C22#1171877611yescharacteristic
394C22C2×#8815811yescharacteristic
395C4—22no—
396C4—1042no—
397C4#1171877611yescharacteristic
398C4#1171877611yescharacteristic
399C4C22×D10411yescharacteristic
400C4C2×#8818411yescharacteristic
401C2—21no—
402C2—21no—
403C2—42no—
404C2—2082no—
405C2#1311696612yesdirect product factor
406C2C2×#1171877611yescharacteristic
subgroupG/H
centerC22#11718776
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC2×C13×#504C2
socleC22×C13#466
prime radicalC2×#11718803C2
hypercenterC2×#504D13
hypocenterC13C2×#2223
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#504

Complements

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

NH ≅ G/Ntype
1. C22×#88040C2semidirect
2. C2×#11718804C2semidirect
4. #13116966C2direct (N × H)
5. C2×#11718098C2semidirect
6. C2×#11718109C2semidirect
7. C2×#11718108C2semidirect
8. C2×C13×#504C2semidirect
15. C13×#504C22semidirect
21. #11718804C22semidirect
31. C2×#88040C22semidirect
32. #11718109C22semidirect
33. #11718108C22semidirect
34. #11718098C22semidirect
144. C2×#504D13semidirect
200. #504C2×D13semidirect
285. C2×C13#2223semidirect
345. C13C2×#2223semidirect
405. C2#13116966direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#880402
C2×#117188042
C2×#117188032
#131169662
C2×#117180982
C2×#117181092
C2×#117181082
C2×C13×#5042
C2×#222313