Finite Group Databasebeta

← C2×#13117054 #16017808

Subgroups — C2×#13117054 #16017808

Order 3328.

552 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718850C211yesmaximal, characteristic
2C2×#11718554C211yesmaximal, characteristic
3#13117054C218yesmaximal, direct product factor
4C2×#11718086C211yesmaximal, characteristic, complemented
5C2×#11718105C211yesmaximal, characteristic, complemented
6C2×#11718157C211yesmaximal, characteristic, complemented
7C2×#11718106C211yesmaximal, characteristic
8C2×C13×#362C211yesmaximal, characteristic, complemented
9C22×C13×Q16C2211yescharacteristic
10C2×#88200—21no—
11C2×M16×D13—21no—
12C22×#6094C2211yescharacteristic
13C2×C13×M32C2211yescharacteristic
14C2×C13×#108C2211yescharacteristic
15C2×#88075—21no—
16#11718850—22no—
17#11718850C2214yes—
18C2×#88062—21no—
19C2×#88059C2211yescharacteristic
20C2×#88057C2211yescharacteristic
21C2×#88052C2211yescharacteristic
22#11718554—22no—
23#11718554C2214yes—
24C13×#362C2214yescomplemented
25#11718157C2214yescomplemented
26#11718106C2214yes—
27#11718105C2214yescomplemented
28#11718086C2214yescomplemented
29C22×Q8×C13—21no—
30C22×C4×D13D411yescharacteristic
31C2×C13×Q16—21no—
32C2×C13×Q16—21no—
33C2×C13×Q16—21no—
34C2×C13×Q16—21no—
35C2×C13×Q16—21no—
36C2×C13×Q16C2312yes—
37C2×C13×M16—21no—
38C22×C8×C13C2311yescharacteristic
39#88200—24no—
40#88200—42no—
41C2×#6103—41no—
42C2×C4⋊Dic13—21no—
43C2×#6101—41no—
44C2×#6099—21no—
45C22×#1055D411yescharacteristic
46M16×D13—24no—
47M16×D13—42no—
48C2×#6094—21no—
49C2×#6094—21no—
50C2×#6094—21no—
51C2×#6094—21no—
52C2×#6094—41no—
53C2×#6094D412yes—
54C2×#6094C2312yes—
55C2×C8×D13—41no—
56C13×M32—21no—
57C13×M32C2312yes—
58C2×C13×C16—21no—
59C13×#108—21no—
60C13×#108C2312yes—
61#88075—24no—
62#88062—24no—
63#88059—21no—
64#88059C2312yes—
65#88057—21no—
66#88057C2312yes—
67#88052—21no—
68#88052C2312yes—
69C2×#6090—21no—
70C2×#2239—131nomaximal, Sylow
71C23×D13SD1611yescharacteristic
72C2×Q8×C13—22no—
73C2×Q8×C13—41no—
74C2×Q8×C13—41no—
75C2×Q8×C13—41no—
76C2×Q8×C13—41no—
77C2×Q8×C13—41no—
78C22×C4×C13—41no—
79C22×C4×C13C2×D411yescharacteristic
80C22×Dic13—41no—
81C22×Dic13SD1611yescharacteristic
82C2×C4×D13—21no—
83C2×C4×D13—21no—
84C2×C4×D13—21no—
85C2×C4×D13—21no—
86C2×C4×D13SD1612yes—
87C2×C4×D13C2×D412yes—
88C13×Q16—22no—
89C13×Q16—22no—
90C13×Q16—41no—
91C13×Q16—41no—
92C13×M16—22no—
93C13×M16—41no—
94C2×C8×C13—41no—
95C2×C8×C13C2×D411yescharacteristic
96C2×C8×C13#4111yescharacteristic
97C2×C8×C13#4111yescharacteristic
98C2×C8×C13#4111yescharacteristic
99C2×C8×C13#4111yescharacteristic
100C2×C8×C13C2411yescharacteristic
101#6103—44no—
102C4⋊Dic13—22no—
103C4⋊Dic13—41no—
104#6101—44no—
105#6099—22no—
106#6099—41no—
107C2×#1055—21no—
108C2×#1055—21no—
109C2×#1055—41no—
110C2×#1055C2×D412yes—
111#6094—22no—
112#6094—22no—
113#6094—22no—
114#6094—22no—
115#6094—44no—
116C8×D13—44no—
117C13×C16—22no—
118#6090—22no—
119C2×#470—131no—
120C2×#430—131no—
121#2239—138no—
122C2×#365—131no—
123C2×#365—131no—
124C2×#362—131no—
125C2×#362D1311yescharacteristic, complemented
126C2×#349—131no—
127C23×C13C2×SD1611yescharacteristic
128C22×D13—21no—
129C22×D13—21no—
130C22×D13—42no—
131C22×D13C2×SD1612yes—
132Q8×C13—42no—
133Q8×C13—42no—
134Q8×C13—81no—
135Q8×C13—81no—
136C2×C4×C13—42no—
137C2×C4×C13—81no—
138C2×C4×C13—81no—
139C2×C4×C13#12311yescharacteristic
140C2×C4×C13#12311yescharacteristic
141C2×C4×C13C2×SD1611yescharacteristic
142C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C13C22×D411yescharacteristic
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—42no—
148C2×Dic13—82no—
149C2×Dic13C2×SD1612yes—
150C4×D13—22no—
151C4×D13—22no—
152C4×D13—22no—
153C4×D13—22no—
154C8×C13—42no—
155C8×C13#12311yescharacteristic
156C8×C13#12311yescharacteristic
157C8×C13C2×#4111yescharacteristic
158C8×C13C2×#4111yescharacteristic
159#1055—22no—
160#1055—42no—
161C22×Q16C2×D1311yescharacteristic
162C22×M16—131no—
163C22×M16—261no—
164C2×C22⋊Q8—261no—
165C2×M32—131no—
166C2×M32C2×D1311yescharacteristic
167#470—134no—
168#470—262no—
169#430—134no—
170#430—262no—
171C2×#108—131no—
172C2×#108—261no—
173C2×#108C2×D1311yescharacteristic
174C2×#106—131no—
175C2×#103—261no—
176#365—134no—
177#365—134no—
178#362—134no—
179#362C2×D1314yescomplemented
180#349—134no—
181C22×C13—22no—
182C22×C13#48111yescharacteristic
183C22×C13#48111yescharacteristic
184C22×C13C22×SD1611yescharacteristic
185C2×D13—22no—
186C2×D13—42no—
187C2×D13—42no—
188C2×D13—81no—
189C4×C13—82no—
190C4×C13#48111yescharacteristic
191C4×C13#48111yescharacteristic
192C4×C13C2×#12311yescharacteristic
193C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
194Dic13—22no—
195Dic13—82no—
196C22×Q8—21no—
197C23×C4—131no—
198C2×Q16—21no—
199C2×Q16—21no—
200C2×Q16—21no—
201C2×Q16—21no—
202C2×Q16—21no—
203C2×Q16C22×D1312yes—
204C2×M16—21no—
205C2×M16—132no—
206C2×M16—132no—
207C2×M16—261no—
208C2×M16—261no—
209C2×M16—261no—
210C2×M16—261no—
211C2×M16—264no—
212C2×M16—261no—
213C2×M16—521no—
214C2×M16—522no—
215C22×C8—131no—
216C22×C8—521no—
217C22×C8C22×D1311yescharacteristic
218C22⋊Q8—264no—
219C22⋊Q8—522no—
220C2×C4⋊C4—261no—
221C2×C4⋊C4—521no—
222C2×C22⋊C4—521no—
223M32—21no—
224M32—132no—
225M32—261no—
226M32C22×D1312yes—
227C2×C16—21no—
228C2×C16—261no—
229#108—21no—
230#108—132no—
231#108—264no—
232#108—261no—
233#108C22×D1312yes—
234#106—132no—
235#106—261no—
236#103—264no—
237C2×C13—21no—
238C2×C13—21no—
239C2×C13#223912yescomplemented
240C2×C13C2×#48111yescharacteristic
241D13—42no—
242C24—131no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—41no—
249C22×C4—41no—
250C22×C4—131no—
251C22×C4—132no—
252C22×C4—132no—
253C22×C4—261no—
254C22×C4—261no—
255C22×C4—261no—
256C22×C4—261no—
257C22×C4—521no—
258C22×C4D4×D1311yescharacteristic
259Q16—22no—
260Q16—22no—
261Q16—41no—
262Q16—41no—
263M16—22no—
264M16—41no—
265M16—262no—
266M16—262no—
267M16—262no—
268M16—262no—
269M16—262no—
270M16—524no—
271M16—521no—
272C2×C8—41no—
273C2×C8—132no—
274C2×C8—261no—
275C2×C8—261no—
276C2×C8—524no—
277C2×C8—521no—
278C2×C8#612711yescharacteristic
279C2×C8#612711yescharacteristic
280C2×C8D4×D1311yescharacteristic
281C2×C8#612911yescharacteristic
282C2×C8#612911yescharacteristic
283C2×C8C23×D1311yescharacteristic
284C4⋊C4—262no—
285C4⋊C4—524no—
286C4⋊C4—521no—
287C22⋊C4—524no—
288C16—22no—
289C16—262no—
290C13C2×#223911yescharacteristic, complemented, Sylow
291C23—132no—
292C23—261no—
293C23—261no—
294C23—522no—
295C23SD16×D1311yescharacteristic
296Q8—42no—
297Q8—42no—
298Q8—81no—
299Q8—81no—
300C2×C4—42no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—132no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—262no—
307C2×C4—262no—
308C2×C4—262no—
309C2×C4—262no—
310C2×C4—522no—
311C2×C4—1042no—
312C2×C4#8813711yescharacteristic
313C2×C4#8813711yescharacteristic
314C2×C4#8816511yescharacteristic
315C2×C4#8816511yescharacteristic
316C2×C4SD16×D1311yescharacteristic
317C2×C4C2×D4×D1311yescharacteristic
318C8—42no—
319C8—262no—
320C8—522no—
321C8#8813711yescharacteristic
322C8#8813711yescharacteristic
323C8C2×#612711yescharacteristic
324C8C2×#612911yescharacteristic
325C22—22no—
326C22—262no—
327C22—522no—
328C22—522no—
329C22—1041no—
330C22#1171843811yescharacteristic
331C22#1171843811yescharacteristic
332C22C2×SD16×D1311yescharacteristic
333C4—82no—
334C4—262no—
335C4—1042no—
336C4#1171843811yescharacteristic
337C4#1171843811yescharacteristic
338C4C2×#8813711yescharacteristic
339C4C2×#8816511yescharacteristic
340C2—21no—
341C2—21no—
342C2—522no—
343C2#1311705412yesdirect product factor
344C2C2×#1171843811yescharacteristic
subgroupG/H
centerC22#11718438
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC2×C13×#362C2
socleC22×C13#481
prime radicalC23×D13SD16
hypercenterC2×#362D13
hypocenterC13C2×#2239
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#362

Complements

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

NH ≅ G/Ntype
3. #13117054C2direct (N × H)
4. C2×#11718086C2semidirect
5. C2×#11718105C2semidirect
6. C2×#11718157C2semidirect
8. C2×C13×#362C2semidirect
24. C13×#362C22semidirect
25. #11718157C22semidirect
27. #11718105C22semidirect
28. #11718086C22semidirect
125. C2×#362D13semidirect
179. #362C2×D13semidirect
239. C2×C13#2239semidirect
290. C13C2×#2239semidirect
343. C2#13117054direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117188502
C2×#117185542
#131170542
C2×#117180862
C2×#117181052
C2×#117181572
C2×#117181062
C2×C13×#3622
C2×#223913