Finite Group Databasebeta

← C2×#13116954 #16017474

Subgroups — C2×#13116954 #16017474

Order 3328.

678 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88066C211yesmaximal, characteristic, complemented
2C2×#11718801C211yesmaximal, characteristic, complemented
3C2×#11718803C211yesmaximal, characteristic, complemented
4#13116954C218yesmaximal, direct product factor
5C2×#11718085C211yesmaximal, characteristic, complemented
6C2×#11718155C211yesmaximal, characteristic, complemented
7C2×#11718087C211yesmaximal, characteristic, complemented
8C2×C13×#472C211yesmaximal, characteristic, complemented
9C2×C13×AGL(1,ℤ/8)—21no—
10C22×C13×D8C2211yescharacteristic
11C2×C13×#131C2211yescharacteristic
12C2×#88203—21no—
13C22×D104C2211yescharacteristic
14C13×#472—22no—
15C13×#472C2214yescomplemented
16C2×C13×#108C2211yescharacteristic
17C2×C13×#100—21no—
18C2×#88066—21no—
19C2×#88066—21no—
20C2×#88066—22no—
21C2×#88066C2214yescomplemented
22#11718803—22no—
23#11718803C2214yescomplemented
24#11718801—22no—
25#11718801C2214yescomplemented
26C2×#88063—21no—
27C2×#88059C2211yescharacteristic
28C2×#88052—21no—
29C2×#88052C2211yescharacteristic
30C22×#6090—21no—
31C22×#6090C2211yescharacteristic
32#11718155C2214yescomplemented
33#11718087C2214yescomplemented
34#11718085C2214yescomplemented
35C2×C13×#41D411yescharacteristic
36C22×D4×C13—21no—
37C22×D52—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#88203—24no—
58#88203—42no—
59C2×#6106—41no—
60C2×#6104—41no—
61C2×#6099—21no—
62C2×D104—21no—
63C2×D104—21no—
64C2×D104—21no—
65C2×D104—21no—
66C2×D104—21no—
67C2×D104C2312yes—
68C13×#108—21no—
69C13×#108C2312yes—
70C13×#100—24no—
71#88066—24no—
72#88066—24no—
73#88063—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×#2221—131nomaximal, Sylow
86C24×C13—41no—
87C23×D13—41no—
88C13×#41—21no—
89C13×#41—21no—
90C13×#41D812yes—
91C13×#41C2×D412yes—
92C2×Q8×C13D811yescharacteristic
93C2×D4×C13—21no—
94C2×D4×C13—22no—
95C2×D4×C13—41no—
96C2×D4×C13—41no—
97C2×D4×C13—41no—
98C2×D4×C13—41no—
99C2×D4×C13—41no—
100C2×D4×C13D811yescharacteristic
101C22×C4×C13—21no—
102C22×C4×C13C2×D411yescharacteristic
103C2×D52—22no—
104C2×D52—41no—
105C2×D52—41no—
106C2×D52—41no—
107C2×D52—41no—
108C2×D52—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#6106—44no—
132#6104—44no—
133#6099—22no—
134#6099—41no—
135C2×#1055—41no—
136D104—22no—
137D104—22no—
138D104—41no—
139D104—41no—
140#6090—22no—
141#6090C2×D412yes—
142#6090C2×D412yes—
143C22×D16—131no—
144C2×#504—131no—
145C2×#472—131no—
146C2×#472D1311yescharacteristic, complemented
147#2221—138no—
148C2×#368—131no—
149C2×#361—131no—
150C2×#361—131no—
151C23×C13—21no—
152C23×C13—42no—
153C23×C13—81no—
154C23×C13—81no—
155C23×C13—162no—
156C23×C13#13511yescharacteristic
157C22×D13—42no—
158C22×D13—81no—
159C22×D13—81no—
160C22×D13—162no—
161Q8×C13—21no—
162Q8×C13C2×D812yes—
163D4×C13—22no—
164D4×C13—22no—
165D4×C13—21no—
166D4×C13—42no—
167D4×C13—42no—
168D4×C13—81no—
169D4×C13—81no—
170D4×C13C2×D812yes—
171C2×C4×C13—21no—
172C2×C4×C13—22no—
173C2×C4×C13—22no—
174C2×C4×C13#12111yescharacteristic
175C2×C4×C13#12111yescharacteristic
176C2×C4×C13C2×D811yescharacteristic
177C2×C4×C13C2×D811yescharacteristic
178C2×C4×C13#13511yescharacteristic
179C2×C4×C13C22×D411yescharacteristic
180D52—42no—
181D52—42no—
182D52—81no—
183D52—81no—
184C8×C13—22no—
185C8×C13—42no—
186C8×C13#12111yescharacteristic
187C8×C13#12111yescharacteristic
188C8×C13C22×D411yescharacteristic
189C8×C13C2×#4111yescharacteristic
190#1055—42no—
191C2×AGL(1,ℤ/8)—21no—
192C2×AGL(1,ℤ/8)—261no—
193C22×D8—131no—
194C22×D8C2×D1311yescharacteristic
195C2×#131C2×D1311yescharacteristic
196C2×D16—134no—
197C2×D16—261no—
198C2×D16—261no—
199C2×D16—262no—
200#504—134no—
201#504—262no—
202C2×M32—131no—
203C2×M32—261no—
204C22×C16—131no—
205C22×C16—261no—
206#472—22no—
207#472—134no—
208#472—262no—
209#472C2×D1314yescomplemented
210C2×#108—131no—
211C2×#108C2×D1311yescharacteristic
212C2×#100—21no—
213C2×#100—261no—
214#368—134no—
215#361—134no—
216#361—134no—
217C22×C13—22no—
218C22×C13—22no—
219C22×C13—42no—
220C22×C13—82no—
221C22×C13—162no—
222C22×C13—162no—
223C22×C13—162no—
224C22×C13#46611yescharacteristic
225C22×C13#46611yescharacteristic
226C22×C13C2×#13511yescharacteristic
227C2×D13—82no—
228C2×D13—162no—
229C2×D13—162no—
230C2×D13—162no—
231C4×C13—22no—
232C4×C13#46611yescharacteristic
233C4×C13#46611yescharacteristic
234C4×C13C2×#12111yescharacteristic
235C4×C13C22×D811yescharacteristic
236C2×#41C22⋊D1311yescharacteristic
237C22×D4—21no—
238C22×D4—261no—
239AGL(1,ℤ/8)—24no—
240AGL(1,ℤ/8)—42no—
241AGL(1,ℤ/8)—264no—
242AGL(1,ℤ/8)—522no—
243C2×SD16—41no—
244C2×SD16—521no—
245C2×D8—21no—
246C2×D8—21no—
247C2×D8—21no—
248C2×D8—21no—
249C2×D8—21no—
250C2×D8—41no—
251C2×D8—132no—
252C2×D8—261no—
253C2×D8—261no—
254C2×D8—261no—
255C2×D8—261no—
256C2×D8—261no—
257C2×D8—521no—
258C2×D8C22×D1312yes—
259#131—21no—
260#131—21no—
261#131C22⋊D1312yes—
262#131C22×D1312yes—
263C2×M16—21no—
264C2×M16—21no—
265C2×M16—261no—
266C2×M16C22⋊D1311yescharacteristic
267C22×C8—21no—
268C22×C8C22×D1311yescharacteristic
269D16—264no—
270D16—264no—
271M32—132no—
272M32—264no—
273M32—261no—
274C2×C16—131no—
275C2×C16—131no—
276C2×C16—132no—
277C2×C16—132no—
278C2×C16—264no—
279C2×C16—261no—
280#108—21no—
281#108—132no—
282#108—261no—
283#108C22×D1312yes—
284#100—24no—
285#100—264no—
286C2×C13—21no—
287C2×C13—21no—
288C2×C13—42no—
289C2×C13—162no—
290C2×C13#222112yescomplemented
291C2×C13C2×#46611yescharacteristic
292D13—162no—
293C24—41no—
294C24—521no—
295#41—21no—
296#41—21no—
297#41#610412yes—
298#41C2×C22⋊D1312yes—
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—262no—
308C2×D4—521no—
309C2×D4—521no—
310C2×D4—521no—
311C2×D4—521no—
312C2×D4—521no—
313C2×D4#610411yescharacteristic
314C22×C4—21no—
315C22×C4C2×C22⋊D1311yescharacteristic
316SD16—44no—
317SD16—524no—
318D8—22no—
319D8—22no—
320D8—44no—
321D8—41no—
322D8—41no—
323D8—262no—
324D8—262no—
325D8—524no—
326D8—521no—
327D8—521no—
328M16—21no—
329M16—22no—
330M16—22no—
331M16—22no—
332M16—41no—
333M16—262no—
334M16—521no—
335M16C2×C22⋊D1312yes—
336C2×C8—21no—
337C2×C8—22no—
338C2×C8—22no—
339C2×C8—41no—
340C2×C8—521no—
341C2×C8D4×D1311yescharacteristic
342C2×C8D4×D1311yescharacteristic
343C2×C8#612911yescharacteristic
344C2×C8#612911yescharacteristic
345C2×C8C2×C22⋊D1311yescharacteristic
346C2×C8C23×D1311yescharacteristic
347C16—132no—
348C16—132no—
349C16—262no—
350C13C2×#222111yescharacteristic, complemented, Sylow
351C23—21no—
352C23—42no—
353C23—81no—
354C23—81no—
355C23—162no—
356C23—522no—
357C23—1041no—
358C23—1041no—
359C23—2082no—
360C23#8820411yescharacteristic
361Q8—21no—
362Q8C2×#610412yes—
363D4—22no—
364D4—22no—
365D4—21no—
366D4—42no—
367D4—42no—
368D4—81no—
369D4—81no—
370D4—522no—
371D4—522no—
372D4—1041no—
373D4—1041no—
374D4C2×#610412yes—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4C2×#610411yescharacteristic
379C2×C4C2×#610411yescharacteristic
380C2×C4#8819311yescharacteristic
381C2×C4#8819311yescharacteristic
382C2×C4#8820411yescharacteristic
383C2×C4C22×C22⋊D1311yescharacteristic
384C8—22no—
385C8—42no—
386C8—522no—
387C8#8819311yescharacteristic
388C8#8819311yescharacteristic
389C8C2×D4×D1311yescharacteristic
390C8C2×#612911yescharacteristic
391C22—22no—
392C22—22no—
393C22—42no—
394C22—82no—
395C22—162no—
396C22—162no—
397C22—162no—
398C22—1042no—
399C22—2082no—
400C22—2082no—
401C22—2082no—
402C22#1171869911yescharacteristic
403C22#1171869911yescharacteristic
404C22C2×#8820411yescharacteristic
405C4—22no—
406C4#1171869911yescharacteristic
407C4#1171869911yescharacteristic
408C4C22×#610411yescharacteristic
409C4C2×#8819311yescharacteristic
410C2—21no—
411C2—21no—
412C2—42no—
413C2—162no—
414C2—2082no—
415C2#1311695412yesdirect product factor
416C2C2×#1171869911yescharacteristic
subgroupG/H
centerC22#11718699
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC2×C13×#472C2
socleC22×C13#466
hypercenterC2×#472D13
hypocenterC13C2×#2221
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×#88066C2semidirect
2. C2×#11718801C2semidirect
3. C2×#11718803C2semidirect
4. #13116954C2direct (N × H)
5. C2×#11718085C2semidirect
6. C2×#11718155C2semidirect
7. C2×#11718087C2semidirect
8. C2×C13×#472C2semidirect
15. C13×#472C22semidirect
21. C2×#88066C22semidirect
23. #11718803C22semidirect
25. #11718801C22semidirect
32. #11718155C22semidirect
33. #11718087C22semidirect
34. #11718085C22semidirect
146. C2×#472D13semidirect
209. #472C2×D13semidirect
290. C2×C13#2221semidirect
350. C13C2×#2221semidirect
415. C2#13116954direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#880662
C2×#117188012
C2×#117188032
#131169542
C2×#117180852
C2×#117181552
C2×#117180872
C2×C13×#4722
C2×#222113