Finite Group Databasebeta

← C2×#13116964 #16017486

Subgroups — C2×#13116964 #16017486

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×#88067C211yesmaximal, characteristic, complemented
2C2×#11718801C211yesmaximal, characteristic, complemented
3C2×#11718804C211yesmaximal, characteristic, complemented
4#13116964C218yesmaximal, direct product factor
5C2×#11718085C211yesmaximal, characteristic, complemented
6C2×#11718088C211yesmaximal, characteristic, complemented
7C2×#11718155C211yesmaximal, characteristic, complemented
8C2×C13×#472C211yesmaximal, characteristic
9C2×C13×AGL(1,ℤ/8)—21no—
10C22×C13×D8C2211yescharacteristic
11C2×C13×#131C2211yescharacteristic
12C2×#88205—21no—
13C22×Dic52C2211yescharacteristic
14C13×#472—22no—
15C13×#472C2214yes—
16C2×C13×#108C2211yescharacteristic
17C2×C13×#100—21no—
18C2×#88067—21no—
19C2×#88067—21no—
20C2×#88067—22no—
21C2×#88067C2214yescomplemented
22#11718804—22no—
23#11718804C2214yescomplemented
24#11718801—22no—
25#11718801C2214yescomplemented
26C2×#88064—21no—
27C2×#88059C2211yescharacteristic
28C2×#88052—21no—
29C2×#88052C2211yescharacteristic
30C22×#6090—21no—
31C22×#6090C2211yescharacteristic
32#11718155C2214yescomplemented
33#11718088C2214yescomplemented
34#11718085C2214yescomplemented
35C2×C13×#41D411yescharacteristic
36C22×D4×C13—21no—
37C22×Dic26—21no—
38C13×AGL(1,ℤ/8)—24no—
39C13×AGL(1,ℤ/8)—42no—
40C2×C13×SD16—41no—
41C2×C13×D8—21no—
42C2×C13×D8—21no—
43C2×C13×D8—21no—
44C2×C13×D8—21no—
45C2×C13×D8—21no—
46C2×C13×D8—41no—
47C2×C13×D8C2312yes—
48C13×#131—21no—
49C13×#131—21no—
50C13×#131D412yes—
51C13×#131C2312yes—
52C2×C13×M16—21no—
53C2×C13×M16—21no—
54C2×C13×M16D411yescharacteristic
55C22×C8×C13—21no—
56C22×C8×C13C2311yescharacteristic
57#88205—24no—
58#88205—42no—
59C2×#6107—41no—
60C2×#6105—41no—
61C2×#6099—21no—
62C2×Dic52—21no—
63C2×Dic52—21no—
64C2×Dic52—21no—
65C2×Dic52—21no—
66C2×Dic52—21no—
67C2×Dic52C2312yes—
68C13×#108—21no—
69C13×#108C2312yes—
70C13×#100—24no—
71#88067—24no—
72#88067—24no—
73#88064—24no—
74#88059—21no—
75#88059C2312yes—
76#88052—21no—
77#88052—24no—
78#88052C2312yes—
79C2×#6090—21no—
80C2×#6090—24no—
81C2×#6090D411yescharacteristic
82C2×#6090D411yescharacteristic
83C2×#6090D412yes—
84C2×#6090C2312yes—
85C2×#2223—131nomaximal, Sylow
86C24×C13—41no—
87C13×#41—21no—
88C13×#41—21no—
89C13×#41D812yes—
90C13×#41C2×D412yes—
91C2×Q8×C13D811yescharacteristic
92C2×D4×C13—21no—
93C2×D4×C13—22no—
94C2×D4×C13—41no—
95C2×D4×C13—41no—
96C2×D4×C13—41no—
97C2×D4×C13—41no—
98C2×D4×C13—41no—
99C2×D4×C13D811yescharacteristic
100C22×C4×C13—21no—
101C22×C4×C13C2×D411yescharacteristic
102C22×Dic13—41no—
103C2×Dic26—22no—
104C2×Dic26—41no—
105C2×Dic26—41no—
106C2×Dic26—41no—
107C2×Dic26—41no—
108C2×Dic26—41no—
109C13×SD16—44no—
110C13×D8—22no—
111C13×D8—22no—
112C13×D8—44no—
113C13×D8—41no—
114C13×D8—41no—
115C13×M16—21no—
116C13×M16—22no—
117C13×M16—22no—
118C13×M16—22no—
119C13×M16—41no—
120C13×M16C2×D412yes—
121C2×C8×C13—21no—
122C2×C8×C13—22no—
123C2×C8×C13—22no—
124C2×C8×C13—41no—
125C2×C8×C13C2×D411yescharacteristic
126C2×C8×C13C2×D411yescharacteristic
127C2×C8×C13C2×D411yescharacteristic
128C2×C8×C13#4111yescharacteristic
129C2×C8×C13#4111yescharacteristic
130C2×C8×C13C2411yescharacteristic
131#6107—44no—
132#6105—44no—
133#6099—22no—
134#6099—41no—
135C2×#1055—41no—
136Dic52—22no—
137Dic52—22no—
138Dic52—41no—
139Dic52—41no—
140#6090—22no—
141#6090C2×D412yes—
142#6090C2×D412yes—
143C22×SD32—131no—
144C2×#504—131no—
145C2×#473—131no—
146C2×#472D1311yescharacteristic
147#2223—138no—
148C2×#368—131no—
149C2×#362—131no—
150C2×#361—131no—
151C23×C13—21no—
152C23×C13—42no—
153C23×C13—81no—
154C23×C13—81no—
155C23×C13—162no—
156C23×C13#13511yescharacteristic
157Q8×C13—21no—
158Q8×C13C2×D812yes—
159D4×C13—22no—
160D4×C13—22no—
161D4×C13—21no—
162D4×C13—42no—
163D4×C13—42no—
164D4×C13—81no—
165D4×C13—81no—
166D4×C13C2×D812yes—
167C2×C4×C13—21no—
168C2×C4×C13—22no—
169C2×C4×C13—22no—
170C2×C4×C13#12111yescharacteristic
171C2×C4×C13#12111yescharacteristic
172C2×C4×C13C2×D811yescharacteristic
173C2×C4×C13C2×D811yescharacteristic
174C2×C4×C13#13511yescharacteristic
175C2×C4×C13C22×D411yescharacteristic
176C2×Dic13—42no—
177C2×Dic13—81no—
178C2×Dic13—81no—
179Dic26—42no—
180Dic26—42no—
181Dic26—81no—
182Dic26—81no—
183C8×C13—22no—
184C8×C13—42no—
185C8×C13#12111yescharacteristic
186C8×C13#12111yescharacteristic
187C8×C13C22×D411yescharacteristic
188C8×C13C2×#4111yescharacteristic
189#1055—42no—
190C2×#137—261no—
191C2×AGL(1,ℤ/8)—21no—
192C22×Q16—131no—
193C22×D8C2×D1311yescharacteristic
194C2×#131C2×D1311yescharacteristic
195C2×SD32—134no—
196C2×SD32—261no—
197C2×SD32—261no—
198C2×SD32—262no—
199#504—134no—
200#504—262no—
201C2×M32—131no—
202C2×M32—261no—
203C22×C16—131no—
204C22×C16—261no—
205#473—134no—
206#473—262no—
207#472—22no—
208#472C2×D1314yes—
209C2×#108—131no—
210C2×#108C2×D1311yescharacteristic
211C2×#101—261no—
212C2×#100—21no—
213#368—134no—
214#362—134no—
215#361—134no—
216C22×C13—22no—
217C22×C13—22no—
218C22×C13—42no—
219C22×C13—82no—
220C22×C13—162no—
221C22×C13—162no—
222C22×C13—162no—
223C22×C13#46611yescharacteristic
224C22×C13#46611yescharacteristic
225C22×C13C2×#13511yescharacteristic
226C4×C13—22no—
227C4×C13#46611yescharacteristic
228C4×C13#46611yescharacteristic
229C4×C13C2×#12111yescharacteristic
230C4×C13C22×D811yescharacteristic
231Dic13—82no—
232C2×#41C22⋊D1311yescharacteristic
233C22×Q8—261no—
234C22×D4—21no—
235#137—264no—
236#137—522no—
237AGL(1,ℤ/8)—24no—
238AGL(1,ℤ/8)—42no—
239C2×Q16—132no—
240C2×Q16—261no—
241C2×Q16—261no—
242C2×Q16—261no—
243C2×Q16—261no—
244C2×Q16—261no—
245C2×Q16—521no—
246C2×SD16—41no—
247C2×SD16—521no—
248C2×D8—21no—
249C2×D8—21no—
250C2×D8—21no—
251C2×D8—21no—
252C2×D8—21no—
253C2×D8—41no—
254C2×D8C22×D1312yes—
255#131—21no—
256#131—21no—
257#131C22⋊D1312yes—
258#131C22×D1312yes—
259C2×M16—21no—
260C2×M16—21no—
261C2×M16—261no—
262C2×M16C22⋊D1311yescharacteristic
263C22×C8—21no—
264C22×C8C22×D1311yescharacteristic
265SD32—264no—
266SD32—264no—
267M32—132no—
268M32—264no—
269M32—261no—
270C2×C16—131no—
271C2×C16—131no—
272C2×C16—132no—
273C2×C16—132no—
274C2×C16—264no—
275C2×C16—261no—
276#108—21no—
277#108—132no—
278#108—261no—
279#108C22×D1312yes—
280#101—264no—
281#100—24no—
282C2×C13—21no—
283C2×C13—21no—
284C2×C13—42no—
285C2×C13—162no—
286C2×C13#222312yescomplemented
287C2×C13C2×#46611yescharacteristic
288C24—41no—
289#41—21no—
290#41—21no—
291#41#610412yes—
292#41C2×C22⋊D1312yes—
293C2×Q8—262no—
294C2×Q8—521no—
295C2×Q8—521no—
296C2×Q8—521no—
297C2×Q8—521no—
298C2×Q8—521no—
299C2×Q8#610411yescharacteristic
300C2×D4—21no—
301C2×D4—22no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4#610411yescharacteristic
308C22×C4—21no—
309C22×C4—521no—
310C22×C4C2×C22⋊D1311yescharacteristic
311Q16—262no—
312Q16—262no—
313Q16—524no—
314Q16—521no—
315Q16—521no—
316SD16—44no—
317SD16—524no—
318D8—22no—
319D8—22no—
320D8—44no—
321D8—41no—
322D8—41no—
323M16—21no—
324M16—22no—
325M16—22no—
326M16—22no—
327M16—41no—
328M16—262no—
329M16—521no—
330M16C2×C22⋊D1312yes—
331C2×C8—21no—
332C2×C8—22no—
333C2×C8—22no—
334C2×C8—41no—
335C2×C8—521no—
336C2×C8D4×D1311yescharacteristic
337C2×C8D4×D1311yescharacteristic
338C2×C8#612911yescharacteristic
339C2×C8#612911yescharacteristic
340C2×C8C2×C22⋊D1311yescharacteristic
341C2×C8C23×D1311yescharacteristic
342C16—132no—
343C16—132no—
344C16—262no—
345C13C2×#222311yescharacteristic, complemented, Sylow
346C23—21no—
347C23—42no—
348C23—81no—
349C23—81no—
350C23—162no—
351C23#8820411yescharacteristic
352Q8—21no—
353Q8—522no—
354Q8—522no—
355Q8—1041no—
356Q8—1041no—
357Q8C2×#610412yes—
358D4—22no—
359D4—22no—
360D4—21no—
361D4—42no—
362D4—42no—
363D4—81no—
364D4—81no—
365D4C2×#610412yes—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—522no—
370C2×C4—1041no—
371C2×C4—1041no—
372C2×C4C2×#610411yescharacteristic
373C2×C4C2×#610411yescharacteristic
374C2×C4#8819311yescharacteristic
375C2×C4#8819311yescharacteristic
376C2×C4#8820411yescharacteristic
377C2×C4C22×C22⋊D1311yescharacteristic
378C8—22no—
379C8—42no—
380C8—522no—
381C8#8819311yescharacteristic
382C8#8819311yescharacteristic
383C8C2×D4×D1311yescharacteristic
384C8C2×#612911yescharacteristic
385C22—22no—
386C22—22no—
387C22—42no—
388C22—82no—
389C22—162no—
390C22—162no—
391C22—162no—
392C22#1171869911yescharacteristic
393C22#1171869911yescharacteristic
394C22C2×#8820411yescharacteristic
395C4—22no—
396C4—1042no—
397C4#1171869911yescharacteristic
398C4#1171869911yescharacteristic
399C4C22×#610411yescharacteristic
400C4C2×#8819311yescharacteristic
401C2—21no—
402C2—21no—
403C2—42no—
404C2—162no—
405C2#1311696412yesdirect product factor
406C2C2×#1171869911yescharacteristic
subgroupG/H
centerC22#11718699
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
Fitting, prime radicalC2×C13×#472C2
socleC22×C13#466
hypercenterC2×#472D13
hypocenterC13C2×#2223
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#472

Complements

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

NH ≅ G/Ntype
1. C22×#88067C2semidirect
2. C2×#11718801C2semidirect
3. C2×#11718804C2semidirect
4. #13116964C2direct (N × H)
5. C2×#11718085C2semidirect
6. C2×#11718088C2semidirect
7. C2×#11718155C2semidirect
21. C2×#88067C22semidirect
23. #11718804C22semidirect
25. #11718801C22semidirect
32. #11718155C22semidirect
33. #11718088C22semidirect
34. #11718085C22semidirect
286. C2×C13#2223semidirect
345. C13C2×#2223semidirect
405. C2#13116964direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#880672
C2×#117188012
C2×#117188042
#131169642
C2×#117180852
C2×#117180882
C2×#117181552
C2×C13×#4722
C2×#222313