Finite Group Databasebeta

← C2×#13116283 #15891817

Subgroups — C2×#13116283 #15891817

Order 3328.

950 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88057C211yesmaximal, characteristic, complemented
2C2×#11718794C212yesmaximal
3C2×#11718771C211yesmaximal, characteristic
4#13116283C218yesmaximal, direct product factor
5C2×#11718146C212yesmaximal, complemented
6C2×C13×#341C211yesmaximal, characteristic, complemented
7C22×#6127C2211yescharacteristic
8C22×C13×M16C2212yes—
9C23×C8×C13C2211yescharacteristic
10C22×C4⋊Dic13C2212yes—
11C22×#6099C2211yescharacteristic
12#11718794—24no—
13#11718794C2218yes—
14C2×#88061—22no—
15#11718771—22no—
16#11718771C2214yes—
17C2×#88060—22no—
18C2×#88057—22no—
19C2×#88057—22no—
20C2×#88057C2214yescomplemented
21C2×#88056—22no—
22C13×#341C2214yescomplemented
23#11718146C2218yescomplemented
24C23×C4×C13C2311yescharacteristic
25C22×C22⋊D13—21no—
26C23×Dic13—22no—
27C2×#6127—21no—
28C2×#6127—21no—
29C2×#6127—24no—
30C2×#6127—24no—
31C2×#6127D412yes—
32C2×#6127C2312yes—
33C22×D52D411yescharacteristic
34C22×C4×D13—21no—
35C22×Dic26D411yescharacteristic
36C2×C13×M16—22no—
37C2×C13×M16—24no—
38C2×C13×M16—24no—
39C2×C13×M16C2314yes—
40C22×C8×C13—24no—
41C22×C8×C13—22no—
42C22×C8×C13D412yes—
43C22×C8×C13D412yes—
44C22×C8×C13C2312yes—
45C2×C4⋊Dic13—22no—
46C2×C4⋊Dic13—22no—
47C2×C4⋊Dic13—22no—
48C2×C4⋊Dic13—22no—
49C2×C4⋊Dic13—22no—
50C2×C4⋊Dic13C2314yes—
51C2×#6099—21no—
52C2×#6099—24no—
53C2×#6099C2312yes—
54C22×#1055—21no—
55#88061—28no—
56#88060—28no—
57#88057—28no—
58#88056—28no—
59C2×#2079—131nomaximal, Sylow
60C24×C13#4111yescharacteristic
61C23×D13—21no—
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13#4114yes—
67C22×C4×C13#4114yes—
68C22×C4×C13#4111yescharacteristic
69C22×C4×C13C2411yescharacteristic
70C2×C22⋊D13—22no—
71C2×C22⋊D13—22no—
72C2×C22⋊D13—44no—
73C22×Dic13—21no—
74C22×Dic13—24no—
75C22×Dic13—42no—
76C22×Dic13—42no—
77C22×Dic13—84no—
78#6127—28no—
79#6127—24no—
80#6127—24no—
81#6127—42no—
82#6127—42no—
83#6127—44no—
84C2×D52—24no—
85C2×D52—21no—
86C2×D52C2×D412yes—
87C2×C4×D13—22no—
88C2×C4×D13—22no—
89C2×C4×D13—42no—
90C2×C4×D13—42no—
91C2×Dic26—24no—
92C2×Dic26—21no—
93C2×Dic26C2×D412yes—
94C13×M16—24no—
95C13×M16—24no—
96C13×M16—44no—
97C2×C8×C13—24no—
98C2×C8×C13—24no—
99C2×C8×C13—24no—
100C2×C8×C13—24no—
101C2×C8×C13—44no—
102C2×C8×C13C2×D414yes—
103C4⋊Dic13—24no—
104C4⋊Dic13—24no—
105C4⋊Dic13—42no—
106C4⋊Dic13—42no—
107#6099—24no—
108#6099—42no—
109C2×#1055—22no—
110C2×#1055—42no—
111C22×#106—131no—
112C2×#417—132no—
113C2×#408—131no—
114#2079—138no—
115C2×#343—132no—
116C2×#341D1311yescharacteristic, complemented
117C23×C13—24no—
118C23×C13#12111yescharacteristic
119C23×C13#12111yescharacteristic
120C23×C13#12614yes—
121C23×C13C2×#4111yescharacteristic
122C22×D13—22no—
123C22×D13—42no—
124C22×D13—44no—
125C2×C4×C13#12111yescharacteristic
126C2×C4×C13#12111yescharacteristic
127C2×C4×C13#12314yes—
128C2×C4×C13#12314yes—
129C2×C4×C13#12312yes—
130C2×C4×C13#12312yes—
131C2×C4×C13#12412yes—
132C2×C4×C13#12412yes—
133C2×C4×C13#12614yes—
134C2×C4×C13C22×D411yescharacteristic
135C2×C4×C13C22×D411yescharacteristic
136C2×C4×C13C2×#4112yes—
137C2×C4×C13C2×#4112yes—
138C22⋊D13—44no—
139C22⋊D13—44no—
140C2×Dic13—22no—
141C2×Dic13—42no—
142C2×Dic13—44no—
143C2×Dic13—84no—
144C2×Dic13—84no—
145C2×Dic13—84no—
146D52—24no—
147D52—42no—
148C4×D13—42no—
149C4×D13—42no—
150C4×D13—44no—
151Dic26—24no—
152Dic26—42no—
153C8×C13—24no—
154C8×C13—44no—
155#1055—42no—
156C22×#41—131no—
157C22×M16—131no—
158C22×M16C2×D1312yes—
159C23×C8C2×D1311yescharacteristic
160C22×C4⋊C4—132no—
161C2×#106—134no—
162C2×#106—262no—
163C2×#106—262no—
164#417—138no—
165#417—264no—
166C2×#103—262no—
167C2×#102—262no—
168#408—134no—
169#408—262no—
170C2×C22⋊C8—262no—
171#343—138no—
172#341C2×D1314yescomplemented
173C22×C13—28no—
174C22×C13—22no—
175C22×C13—22no—
176C22×C13#39712yes—
177C22×C13#39712yes—
178C22×C13#47114yes—
179C22×C13C2×#12111yescharacteristic
180C22×C13C2×#12612yes—
181C2×D13—42no—
182C2×D13—44no—
183C2×D13—84no—
184C4×C13#39712yes—
185C4×C13#39712yes—
186C4×C13C2×#12312yes—
187C4×C13C2×#12311yescharacteristic
188C4×C13C2×#12411yescharacteristic
189Dic13—42no—
190Dic13—84no—
191C2×#41—132no—
192C2×#41—132no—
193C2×#41—261no—
194C2×#41—261no—
195C2×#41—264no—
196C2×#41—264no—
197C22×Q8—131no—
198C22×D4—131no—
199C22×D4—261no—
200C23×C4—261no—
201C23×C4—262no—
202C23×C4C22×D1311yescharacteristic
203C2×M16—22no—
204C2×M16—24no—
205C2×M16—24no—
206C2×M16—132no—
207C2×M16—261no—
208C2×M16—264no—
209C2×M16C22×D1314yes—
210C22×C8—24no—
211C22×C8—22no—
212C22×C8—261no—
213C22×C8D5212yes—
214C22×C8D5212yes—
215C22×C8C22×D1312yes—
216C2×C4⋊C4—134no—
217C2×C4⋊C4—262no—
218C2×C4⋊C4—262no—
219C2×C4⋊C4—262no—
220C2×C4⋊C4—262no—
221C2×C4⋊C4—262no—
222#106—268no—
223#103—268no—
224#102—268no—
225C22⋊C8—268no—
226C2×C13—22no—
227C2×C13—22no—
228C2×C13#207914yescomplemented
229C2×C13C2×#39711yescharacteristic
230C2×C13C2×#47112yes—
231D13—82no—
232C24—261no—
233C24#613111yescharacteristic
234#41—268no—
235#41—264no—
236#41—264no—
237#41—522no—
238#41—522no—
239#41—524no—
240C2×Q8—132no—
241C2×Q8—261no—
242C2×Q8—264no—
243C2×D4—132no—
244C2×D4—262no—
245C2×D4—262no—
246C2×D4—264no—
247C2×D4—261no—
248C2×D4—524no—
249C22×C4—261no—
250C22×C4—262no—
251C22×C4—262no—
252C22×C4—264no—
253C22×C4—522no—
254C22×C4—522no—
255C22×C4—522no—
256C22×C4—522no—
257C22×C4—1044no—
258C22×C4C2×D5211yescharacteristic
259C22×C4C2×D5211yescharacteristic
260C22×C4#612714yes—
261C22×C4D4×D1311yescharacteristic
262C22×C4D4×D1311yescharacteristic
263C22×C4#612914yes—
264C22×C4#613111yescharacteristic
265C22×C4C23×D1311yescharacteristic
266M16—24no—
267M16—24no—
268M16—44no—
269M16—264no—
270M16—522no—
271C2×C8—24no—
272C2×C8—24no—
273C2×C8—24no—
274C2×C8—24no—
275C2×C8—44no—
276C2×C8—262no—
277C2×C8—522no—
278C2×C8C2×D5214yes—
279C4⋊C4—264no—
280C4⋊C4—264no—
281C4⋊C4—522no—
282C4⋊C4—522no—
283C13C2×#207911yescharacteristic, complemented, Sylow
284C23—24no—
285C23—262no—
286C23—524no—
287C23—522no—
288C23#8814911yescharacteristic
289C23#8814911yescharacteristic
290C23#8815214yes—
291C23C2×#613111yescharacteristic
292Q8—264no—
293Q8—522no—
294D4—264no—
295D4—524no—
296D4—524no—
297D4—522no—
298C2×C4—262no—
299C2×C4—522no—
300C2×C4—522no—
301C2×C4—522no—
302C2×C4—524no—
303C2×C4—524no—
304C2×C4—1044no—
305C2×C4—1044no—
306C2×C4—1044no—
307C2×C4#8812912yes—
308C2×C4#8812912yes—
309C2×C4#8813714yes—
310C2×C4#8813714yes—
311C2×C4#8814012yes—
312C2×C4#8814012yes—
313C2×C4#8814911yescharacteristic
314C2×C4#8814911yescharacteristic
315C2×C4#8815214yes—
316C2×C4C22×D5211yescharacteristic
317C2×C4C2×#612712yes—
318C2×C4C2×D4×D1311yescharacteristic
319C2×C4C2×#612912yes—
320C8—24no—
321C8—44no—
322C8—522no—
323C22—28no—
324C22—22no—
325C22—22no—
326C22—522no—
327C22—524no—
328C22—1044no—
329C22#1171833512yes—
330C22#1171833512yes—
331C22#1171855914yes—
332C22C2×#8814911yescharacteristic
333C22C2×#8815212yes—
334C4—522no—
335C4—1044no—
336C4#1171833512yes—
337C4#1171833512yes—
338C4C2×#8812911yescharacteristic
339C4C2×#8813712yes—
340C4C2×#8814011yescharacteristic
341C2—22no—
342C2—22no—
343C2—1042no—
344C2#1311628314yesdirect product factor
345C2C2×#1171833511yescharacteristic
346C2C2×#1171855912yes—
subgroupG/H
centerC23#88149
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#341C2
socleC23×C13#121
prime radicalC22×#6127C22
hypercenterC2×#341D13
hypocenterC13C2×#2079
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#341

Complements

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

NH ≅ G/Ntype
1. C22×#88057C2semidirect
4. #13116283C2direct (N × H)
5. C2×#11718146C2semidirect
6. C2×C13×#341C2semidirect
20. C2×#88057C22semidirect
22. C13×#341C22semidirect
23. #11718146C22semidirect
116. C2×#341D13semidirect
172. #341C2×D13semidirect
228. C2×C13#2079semidirect
283. C13C2×#2079semidirect
344. C2#13116283direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#880572
C2×#117187942
C2×#117187712
#131162832
C2×#117181462
C2×C13×#3412
C2×#207913