Finite Group Databasebeta

← C2×#13116546 #16015815

Subgroups — C2×#13116546 #16015815

Order 3328.

1214 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88158C211yesmaximal, characteristic
2C22×#88052C211yesmaximal, characteristic, complemented
3#13116546C218yesmaximal, direct product factor
4C2×#11718084C212yesmaximal, complemented
5C2×#11718083C212yesmaximal, complemented
6C22×C13×#107C211yesmaximal, characteristic, complemented
7C22×#6127—21no—
8C23×C8×C13C2211yescharacteristic
9C22×C13×C4⋊C4—21no—
10C22×Dic52C2211yescharacteristic
11C2×#88158—24no—
12C2×#88158—22no—
13C2×#88158C418yescomplemented
14C2×#88158C2214yes—
15C22×D104C2211yescharacteristic
16C22×#6095—21no—
17C2×C13×#107—22no—
18C2×C13×#107—21no—
19C2×C13×#107C2212yes—
20C2×C13×#107C2214yescomplemented
21C2×#88052—24no—
22C2×#88052C2214yescomplemented
23C22×#6090C2212yes—
24#11718084C2218yescomplemented
25#11718083C2218yescomplemented
26C23×C4×C13—41no—
27C23×C4×C13D411yescharacteristic
28C22×C22⋊D13—41no—
29C2×#6127—28no—
30C2×#6127—24no—
31C2×#6127—42no—
32C2×#6127—44no—
33C22×D52—21no—
34C22×C4×D13—41no—
35C22×Dic26—21no—
36C22×C8×C13C2×C414yes—
37C22×C8×C13D414yes—
38C22×C8×C13D411yescharacteristic
39C22×C8×C13D412yes—
40C22×C8×C13C2311yescharacteristic
41C22×C8×C13C2312yes—
42C2×C13×C4⋊C4—22no—
43C2×C13×C4⋊C4—24no—
44C2×C13×C4⋊C4—41no—
45C2×C13×C4⋊C4—42no—
46C2×Dic52—22no—
47C2×Dic52—21no—
48C2×Dic52C2×C414yescomplemented
49C2×Dic52C2312yes—
50#88158—216no—
51#88158—28no—
52#88158C2×C4116yescomplemented
53C2×D104—22no—
54C2×D104—21no—
55C2×D104C2×C414yescomplemented
56C2×D104C2312yes—
57C2×#6095—28no—
58C2×#6095—24no—
59C13×#107—22no—
60C13×#107—24no—
61C13×#107C2314yes—
62#88052—28no—
63C2×#6090—24no—
64C2×#6090C2314yes—
65C2×#2139—131nomaximal, Sylow
66C24×C13D811yescharacteristic
67C23×D13—41no—
68C22×C4×C13—44no—
69C22×C4×C13—42no—
70C22×C4×C13—84no—
71C22×C4×C13C22⋊C414yes—
72C22×C4×C13D811yescharacteristic
73C22×C4×C13D812yes—
74C22×C4×C13SD1614yes—
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D412yes—
77C2×C22⋊D13—48no—
78C2×C22⋊D13—44no—
79C22×Dic13—41no—
80#6127—216no—
81#6127—416no—
82#6127—48no—
83C2×D52—24no—
84C2×D52—22no—
85C2×D52—41no—
86C2×D52—42no—
87C2×C4×D13—48no—
88C2×C4×D13—44no—
89C2×Dic26—24no—
90C2×Dic26—22no—
91C2×Dic26—41no—
92C2×Dic26—42no—
93C2×C8×C13C22⋊C414yes—
94C2×C8×C13C22⋊C418yes—
95C2×C8×C13C22×C412yes—
96C2×C8×C13C22×C414yes—
97C2×C8×C13C2×D412yes—
98C2×C8×C13C2×D411yescharacteristic
99C2×C8×C13C2×D412yes—
100C2×C8×C13C2×D414yes—
101C2×C8×C13C2411yescharacteristic
102C13×C4⋊C4—24no—
103C13×C4⋊C4—42no—
104C13×C4⋊C4—44no—
105Dic52—24no—
106Dic52—22no—
107Dic52C22×C414yescomplemented
108D104—24no—
109D104—22no—
110D104C22×C414yescomplemented
111#6095—216no—
112#6090—24no—
113C22×#135—131no—
114C22×M32—131no—
115C22×#107D1311yescharacteristic, complemented
116#2139—138no—
117C2×#358—132no—
118C2×#357—132no—
119C23×C13—22no—
120C23×C13—22no—
121C23×C13#10214yes—
122C23×C13C2×D812yes—
123C23×C13C2×D811yescharacteristic
124C22×D13—42no—
125C22×D13—44no—
126C22×D13—82no—
127C22×D13—82no—
128C2×C4×C13—44no—
129C2×C4×C13—88no—
130C2×C4×C13—84no—
131C2×C4×C13#10214yes—
132C2×C4×C13#10218yes—
133C2×C4×C13C2×C22⋊C412yes—
134C2×C4×C13C2×C22⋊C414yes—
135C2×C4×C13C2×D811yescharacteristic
136C2×C4×C13C2×D812yes—
137C2×C4×C13C2×SD1612yes—
138C2×C4×C13C2×SD1614yes—
139C2×C4×C13C22×D411yescharacteristic
140C22⋊D13—416no—
141C2×Dic13—42no—
142C2×Dic13—44no—
143D52—24no—
144D52—42no—
145D52—44no—
146C4×D13—416no—
147Dic26—24no—
148Dic26—42no—
149Dic26—44no—
150C8×C13C2×C22⋊C414yes—
151C8×C13C2×C22⋊C412yes—
152C8×C13C23×C411yescharacteristic
153C8×C13C22×D411yescharacteristic
154C22×#41—261no—
155C2×#135—138no—
156C2×#135—134no—
157C2×#135—264no—
158C2×#135—262no—
159C22×Q16—131no—
160C22×SD16—261no—
161C22×D8—131no—
162C23×C8C2×D1311yescharacteristic
163C22×C4⋊C4—21no—
164C2×M32—134no—
165C2×M32—264no—
166C22×C16—132no—
167C2×#107—22no—
168C2×#107—21no—
169C2×#107C2×D1312yes—
170C2×#107C2×D1314yescomplemented
171#358—138no—
172#357—138no—
173C22×C13—22no—
174C22×C13—22no—
175C22×C13—28no—
176C22×C13C2×#10214yes—
177C22×C13C2×#10212yes—
178C22×C13#50912yes—
179C22×C13#51012yes—
180C22×C13C22×D811yescharacteristic
181C2×D13—44no—
182C2×D13—82no—
183C2×D13—82no—
184C2×D13—88no—
185C4×C13—84no—
186C4×C13C2×#10212yes—
187C4×C13C2×#10214yes—
188C4×C13C22×C22⋊C411yescharacteristic
189C4×C13C22×SD1611yescharacteristic
190Dic13—44no—
191C2×#41—268no—
192C2×#41—264no—
193C2×#41—522no—
194C2×#41—524no—
195C22×Q8—261no—
196C22×D4—261no—
197C22×D4—521no—
198C23×C4—41no—
199C23×C4—521no—
200C23×C4C22⋊D1311yescharacteristic
201#135—1316no—
202#135—2616no—
203#135—268no—
204C2×Q16—134no—
205C2×Q16—132no—
206C2×Q16—262no—
207C2×Q16—261no—
208C2×SD16—268no—
209C2×SD16—264no—
210C2×D8—134no—
211C2×D8—132no—
212C2×D8—262no—
213C2×D8—261no—
214C22×C8C4×D1314yes—
215C22×C8D5214yes—
216C22×C8C22⋊D1311yescharacteristic
217C22×C8C22⋊D1312yes—
218C22×C8C22×D1311yescharacteristic
219C22×C8C22×D1312yes—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—24no—
222C2×C4⋊C4—42no—
223C2×C4⋊C4—41no—
224M32—268no—
225C2×C16—134no—
226C2×C16—264no—
227#107—22no—
228#107—24no—
229#107C22×D1314yes—
230C2×C13—24no—
231C2×C13#213914yescomplemented
232C2×C13C22×#10211yescharacteristic
233C2×C13C2×#50911yescharacteristic
234C2×C13C2×#51011yescharacteristic
235D13—84no—
236C24—521no—
237C24#610411yescharacteristic
238#41—2616no—
239#41—528no—
240#41—5216no—
241C2×Q8—264no—
242C2×Q8—262no—
243C2×Q8—521no—
244C2×Q8—522no—
245C2×D4—264no—
246C2×D4—262no—
247C2×D4—524no—
248C2×D4—528no—
249C2×D4—521no—
250C2×D4—522no—
251C22×C4—44no—
252C22×C4—42no—
253C22×C4—84no—
254C22×C4—521no—
255C22×C4—524no—
256C22×C4—528no—
257C22×C4#610314yes—
258C22×C4#610412yes—
259C22×C4#610411yescharacteristic
260C22×C4#610614yes—
261C22×C4C2×C22⋊D1312yes—
262C22×C4C2×C22⋊D1311yescharacteristic
263Q16—134no—
264Q16—264no—
265Q16—262no—
266SD16—2616no—
267D8—134no—
268D8—264no—
269D8—262no—
270C2×C8#610314yes—
271C2×C8#610318yes—
272C2×C8C2×C4×D1312yes—
273C2×C8C2×C4×D1314yes—
274C2×C8C2×D5212yes—
275C2×C8C2×D5214yes—
276C2×C8C2×C22⋊D1311yescharacteristic
277C2×C8C2×C22⋊D1312yes—
278C2×C8C23×D1311yescharacteristic
279C4⋊C4—24no—
280C4⋊C4—44no—
281C4⋊C4—42no—
282C16—264no—
283C13C2×#213911yescharacteristic, complemented, Sylow
284C23—22no—
285C23—22no—
286C23—522no—
287C23—524no—
288C23—1042no—
289C23—1042no—
290C23#8804914yes—
291C23C2×#610412yes—
292C23C2×#610411yescharacteristic
293Q8—264no—
294Q8—522no—
295Q8—524no—
296D4—264no—
297D4—5216no—
298D4—522no—
299D4—524no—
300C2×C4—44no—
301C2×C4—88no—
302C2×C4—84no—
303C2×C4—522no—
304C2×C4—524no—
305C2×C4—5216no—
306C2×C4#8804914yes—
307C2×C4#8804918yes—
308C2×C4C2×#610312yes—
309C2×C4C2×#610314yes—
310C2×C4C2×#610412yes—
311C2×C4C2×#610411yescharacteristic
312C2×C4C2×#610612yes—
313C2×C4C2×#610614yes—
314C2×C4C22×C22⋊D1311yescharacteristic
315C8C2×#610312yes—
316C8C2×#610314yes—
317C8C22×C4×D1311yescharacteristic
318C8C22×D5211yescharacteristic
319C22—22no—
320C22—22no—
321C22—28no—
322C22—524no—
323C22—1042no—
324C22—1042no—
325C22—1048no—
326C22C2×#8804914yes—
327C22C2×#8804912yes—
328C22#1171880812yes—
329C22#1171884012yes—
330C22C22×#610411yescharacteristic
331C4—84no—
332C4—524no—
333C4C2×#8804914yes—
334C4C2×#8804912yes—
335C4C22×#610311yescharacteristic
336C4C22×#610611yescharacteristic
337C2—24no—
338C2—1044no—
339C2#1311654614yesdirect product factor
340C2C22×#8804911yescharacteristic
341C2C2×#1171880811yescharacteristic
342C2C2×#1171884011yescharacteristic
subgroupG/H
centerC23C2×#6104
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC22×C13×#107C2
socleC23×C13C2×D8
prime radicalC22×#88158C2
cosocleC2×C8×C13C24
hypercenterC22×#107D13
hypocenterC13C2×#2139
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
2. C22×#88052C2semidirect
3. #13116546C2direct (N × H)
4. C2×#11718084C2semidirect
5. C2×#11718083C2semidirect
6. C22×C13×#107C2semidirect
13. C2×#88158C4semidirect
20. C2×C13×#107C22semidirect
22. C2×#88052C22semidirect
24. #11718084C22semidirect
25. #11718083C22semidirect
48. C2×Dic52C2×C4semidirect
52. #88158C2×C4semidirect
55. C2×D104C2×C4semidirect
107. Dic52C22×C4semidirect
110. D104C22×C4semidirect
115. C22×#107D13semidirect
170. C2×#107C2×D13semidirect
231. C2×C13#2139semidirect
283. C13C2×#2139semidirect
339. C2#13116546direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881582
C22×#880522
#131165462
C2×#117180842
C2×#117180832
C22×C13×#1072
C2×#213913