Finite Group Databasebeta

← C2×#13123315 #16726414

Subgroups — C2×#13123315 #16726414

Order 3328.

5114 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719524C212yesmaximal, complemented
2#13123315C2116yesmaximal, direct product factor
3C2×#11718898C216yesmaximal, complemented
4C22×#88073C216yesmaximal, complemented
5C22×C13×H(5,𝔽2)C211yesmaximal, characteristic
6C2×C13×H(5,𝔽2)—28no—
7C2×C13×H(5,𝔽2)—28no—
8C2×C13×H(5,𝔽2)C418yes—
9C2×C13×H(5,𝔽2)C2218yes—
10C22×C13×#41C412yes—
11C22×C13×#41C2213yes—
12C22×C13×#41C2211yescharacteristic
13C23×D4×C13C416yes—
14C23×D4×C13C2213yes—
15#11719524—28no—
16#11719524C22116yescomplemented
17C2×#88202—28no—
18C22×#6099C22112yescomplemented
19#11718898C22148yescomplemented
20C2×#88076C2214yescomplemented
21C2×#88073C22112yescomplemented
22C2×#88073C22148yescomplemented
23C25×C13C2×C416yes—
24C13×H(5,𝔽2)—264no—
25C13×H(5,𝔽2)—264no—
26C2×C13×#41—28no—
27C2×C13×#41—28no—
28C2×C13×#41—212no—
29C2×C13×#41—212no—
30C2×C13×#41C2×C4116yes—
31C2×C13×#41C2×C4112yes—
32C2×C13×#41C2×C414yes—
33C2×C13×#41D418yes—
34C2×C13×#41D418yes—
35C2×C13×#41C23112yes—
36C2×C13×#41C2314yes—
37C22×Q8×C13C2×C411yescharacteristic
38C22×Q8×C13C2311yescharacteristic
39C22×D4×C13—224no—
40C22×D4×C13—224no—
41C22×D4×C13—212no—
42C22×D4×C13—212no—
43C22×D4×C13C2×C416yes—
44C22×D4×C13C2×C416yes—
45C22×D4×C13C2×C4148yes—
46C22×D4×C13C2×C4112yes—
47C22×D4×C13C2×C413yes—
48C22×D4×C13C2313yes—
49C22×D4×C13C23112yes—
50C23×C4×C13C2×C416yes—
51C23×C4×C13C2313yes—
52#88202—264no—
53C2×#6099—212no—
54C2×#6099—224no—
55C2×#6099C2318yes—
56C2×#6099C23148yescomplemented
57C22×#1055—212no—
58#88076C23116yescomplemented
59#88073C23148yescomplemented
60C2×#2888—131nomaximal, Sylow
61C24×C13—212no—
62C24×C13—212no—
63C24×C13—812no—
64C24×C13C22×C416yes—
65C24×C13C22×C4124yes—
66C24×C13C22×C413yes—
67C13×#41—264no—
68C13×#41—248no—
69C13×#41—248no—
70C13×#41C22⋊C4132yes—
71C13×#41C2×D4132yes—
72C2×Q8×C13—22no—
73C2×Q8×C13—22no—
74C2×Q8×C13C22⋊C414yes—
75C2×Q8×C13C22⋊C414yes—
76C2×Q8×C13C22×C412yes—
77C2×Q8×C13C22×C414yes—
78C2×Q8×C13C2412yes—
79C2×D4×C13—212no—
80C2×D4×C13—212no—
81C2×D4×C13—2192no—
82C2×D4×C13—212no—
83C2×D4×C13—212no—
84C2×D4×C13—248no—
85C2×D4×C13—26no—
86C2×D4×C13—26no—
87C2×D4×C13—248no—
88C2×D4×C13C22⋊C4112yes—
89C2×D4×C13C22⋊C4112yes—
90C2×D4×C13C22×C4124yes—
91C2×D4×C13C22×C4124yes—
92C2×D4×C13C22×C416yes—
93C2×D4×C13C22×C4112yes—
94C2×D4×C13C2416yes—
95C22×C4×C13—212no—
96C22×C4×C13—212no—
97C22×C4×C13C22×C412yes—
98C22×C4×C13C22×C4124yes—
99C22×C4×C13C22×C413yes—
100C22×C4×C13C22×C416yes—
101C22×C4×C13C2×D4112yes—
102C22×C4×C13C2×D4112yes—
103C22×C4×C13C2411yescharacteristic
104C22×C4×C13C2416yes—
105#6099—28no—
106#6099—248no—
107#6099C24116yes—
108C2×#1055—28no—
109C2×#1055—248no—
110C22×H(5,𝔽2)D1311yescharacteristic
111C2×#568—132no—
112#2888—1316no—
113C2×#413—136no—
114C22×#100—136no—
115C23×C13—26no—
116C23×C13—26no—
117C23×C13—248no—
118C23×C13—46no—
119C23×C13—412no—
120C23×C13—824no—
121C23×C13—824no—
122C23×C13—824no—
123C23×C13C2×C22⋊C416yes—
124C23×C13C2×C22⋊C416yes—
125C23×C13C23×C411yescharacteristic
126C23×C13C23×C4112yes—
127C23×C13C23×C416yes—
128Q8×C13—24no—
129Q8×C13—24no—
130Q8×C13C2×C22⋊C4116yes—
131D4×C13—248no—
132D4×C13—248no—
133D4×C13—212no—
134D4×C13—212no—
135D4×C13C2×C22⋊C4148yes—
136C2×C4×C13—22no—
137C2×C4×C13—22no—
138C2×C4×C13—248no—
139C2×C4×C13C2×C22⋊C416yes—
140C2×C4×C13C2×C22⋊C416yes—
141C2×C4×C13C2×C22⋊C4124yes—
142C2×C4×C13C23×C414yes—
143C2×C4×C13C23×C416yes—
144C2×C4×C13C23×C411yescharacteristic
145C2×C4×C13C22×D412yes—
146C2×C4×C13C22×D4124yes—
147C2×C4×C13C22×D412yes—
148C2×C4×C13C2511yescharacteristic
149#1055—216no—
150C2×H(5,𝔽2)—28no—
151C2×H(5,𝔽2)—28no—
152C2×H(5,𝔽2)Dic1318yes—
153C2×H(5,𝔽2)C2×D1318yes—
154C22×#41Dic1312yes—
155C22×#41C2×D1313yes—
156C22×#41C2×D1311yescharacteristic
157C23×D4Dic1316yes—
158C23×D4C2×D1313yes—
159#568—1316no—
160#568—268no—
161C2×#131—268no—
162C22×M16—1312no—
163#413—1348no—
164C2×#101—134no—
165C2×#100—1312no—
166C2×#100—1348no—
167C22×C13—22no—
168C22×C13—212no—
169C22×C13—212no—
170C22×C13—46no—
171C22×C13—46no—
172C22×C13—412no—
173C22×C13—412no—
174C22×C13—412no—
175C22×C13—848no—
176C22×C13C22×C22⋊C411yescharacteristic
177C22×C13C22×C22⋊C4112yes—
178C22×C13C22×C22⋊C411yescharacteristic
179C22×C13C24×C411yescharacteristic
180C4×C13—24no—
181C4×C13C22×C22⋊C4112yes—
182C4×C13C22×C22⋊C412yes—
183C4×C13C23×D412yes—
184C25C2×Dic1316yes—
185H(5,𝔽2)—264no—
186H(5,𝔽2)—264no—
187C2×#41—28no—
188C2×#41—28no—
189C2×#41—212no—
190C2×#41—212no—
191C2×#41C2×Dic13116yes—
192C2×#41C2×Dic13112yes—
193C2×#41C2×Dic1314yes—
194C2×#41C22⋊D1318yes—
195C2×#41C22⋊D1318yes—
196C2×#41C22×D13112yes—
197C2×#41C22×D1314yes—
198C22×Q8C2×Dic1311yescharacteristic
199C22×Q8C22×D1311yescharacteristic
200C22×D4—224no—
201C22×D4—224no—
202C22×D4—212no—
203C22×D4—212no—
204C22×D4C2×Dic1316yes—
205C22×D4C2×Dic1316yes—
206C22×D4C2×Dic13148yes—
207C22×D4C2×Dic13112yes—
208C22×D4C2×Dic1313yes—
209C22×D4C22×D1313yes—
210C22×D4C22×D13112yes—
211C23×C4C2×Dic1316yes—
212C23×C4C22×D1313yes—
213#131—2664no—
214C2×M16—138no—
215C2×M16—1348no—
216C2×M16—2612no—
217C2×M16—2624no—
218C22×C8—2612no—
219#101—1316no—
220#100—1348no—
221C2×C13—21no—
222C2×C13—21no—
223C2×C13—212no—
224C2×C13—412no—
225C2×C13#288812yescomplemented
226C2×C13C23×C22⋊C411yescharacteristic
227C24—212no—
228C24—212no—
229C24—812no—
230C24C22×Dic1316yes—
231C24C22×Dic13124yes—
232C24C22×Dic1313yes—
233#41—264no—
234#41—248no—
235#41—248no—
236#41C22⋊Dic13132yes—
237#41C2×C22⋊D13132yes—
238C2×Q8—22no—
239C2×Q8—22no—
240C2×Q8C22⋊Dic1314yes—
241C2×Q8C22⋊Dic1314yes—
242C2×Q8C22×Dic1312yes—
243C2×Q8C22×Dic1314yes—
244C2×Q8C23×D1312yes—
245C2×D4—212no—
246C2×D4—212no—
247C2×D4—2192no—
248C2×D4—212no—
249C2×D4—212no—
250C2×D4—248no—
251C2×D4—26no—
252C2×D4—26no—
253C2×D4—248no—
254C2×D4C22⋊Dic13112yes—
255C2×D4C22⋊Dic13112yes—
256C2×D4C22×Dic13124yes—
257C2×D4C22×Dic13124yes—
258C2×D4C22×Dic1316yes—
259C2×D4C22×Dic13112yes—
260C2×D4C23×D1316yes—
261C22×C4—212no—
262C22×C4—212no—
263C22×C4C22×Dic1312yes—
264C22×C4C22×Dic13124yes—
265C22×C4C22×Dic1313yes—
266C22×C4C22×Dic1316yes—
267C22×C4C2×C22⋊D13112yes—
268C22×C4C2×C22⋊D13112yes—
269C22×C4C23×D1311yescharacteristic
270C22×C4C23×D1316yes—
271M16—1316no—
272M16—268no—
273M16—2648no—
274C2×C8—268no—
275C2×C8—2648no—
276C13C2×#288811yescharacteristic, complemented, Sylow
277C23—26no—
278C23—26no—
279C23—248no—
280C23—46no—
281C23—412no—
282C23—824no—
283C23—824no—
284C23—824no—
285C23C2×C22⋊Dic1316yes—
286C23C2×C22⋊Dic1316yes—
287C23C23×Dic1311yescharacteristic
288C23C23×Dic13112yes—
289C23C23×Dic1316yes—
290Q8—24no—
291Q8—24no—
292Q8C2×C22⋊Dic13116yes—
293D4—248no—
294D4—248no—
295D4—212no—
296D4—212no—
297D4C2×C22⋊Dic13148yes—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—248no—
301C2×C4C2×C22⋊Dic1316yes—
302C2×C4C2×C22⋊Dic13124yes—
303C2×C4C2×C22⋊Dic1316yes—
304C2×C4C23×Dic1314yes—
305C2×C4C23×Dic1316yes—
306C2×C4C23×Dic1311yescharacteristic
307C2×C4C22×C22⋊D13124yes—
308C2×C4C22×C22⋊D1312yes—
309C2×C4C22×C22⋊D1312yes—
310C2×C4C24×D1311yescharacteristic
311C8—2616no—
312C22—22no—
313C22—212no—
314C22—212no—
315C22—46no—
316C22—46no—
317C22—412no—
318C22—412no—
319C22—412no—
320C22—848no—
321C22C22×C22⋊Dic1311yescharacteristic
322C22C22×C22⋊Dic13112yes—
323C22C22×C22⋊Dic1311yescharacteristic
324C22C24×Dic1311yescharacteristic
325C4—24no—
326C4C22×C22⋊Dic13112yes—
327C4C22×C22⋊Dic1312yes—
328C4C23×C22⋊D1312yes—
329C2—21no—
330C2—21no—
331C2—212no—
332C2—412no—
333C2#1312331512yesdirect product factor
334C2C23×C22⋊Dic1311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic13
commutatorC22×C13C24×C4
FrattiniC2×C4C24×D13
Fitting, prime radicalC22×C13×H(5,𝔽2)C2
socleC22×C13C22×C22⋊C4
cosocleC2×C4×C13C25
hypercenterC22×H(5,𝔽2)D13
hypocenterC13C2×#2888
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×#41 ◁ C22×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C2×#11719524C2semidirect
2. #13123315C2direct (N × H)
3. C2×#11718898C2semidirect
4. C22×#88073C2semidirect
16. #11719524C22semidirect
18. C22×#6099C22semidirect
19. #11718898C22semidirect
20. C2×#88076C22semidirect
21. C2×#88073C22semidirect
22. C2×#88073C22semidirect
56. C2×#6099C23semidirect
58. #88076C23semidirect
59. #88073C23semidirect
225. C2×C13#2888semidirect
276. C13C2×#2888semidirect
333. C2#13123315direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117195242
#131233152
C2×#117188982
C22×#880732
C22×C13×H(5,𝔽2)2
C2×#288813