Finite Group Databasebeta

← C2×#13122897 #16069480

Subgroups — C2×#13122897 #16069480

Order 3328.

2370 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88123C211yesmaximal, characteristic, complemented
2C22×#88130C211yesmaximal, characteristic
3#13122897C2116yesmaximal, direct product factor
4C2×#11718320C212yesmaximal, complemented
5C2×#11718338C212yesmaximal
6C2×#11718322C212yesmaximal, complemented
7C2×#11718335C212yesmaximal
8C2×#11718317C212yesmaximal, complemented
9C2×#11718334C212yesmaximal
10C2×C13×#383C211yesmaximal, characteristic, complemented
11C23×Dic26C2212yes—
12C22×C42×C13C2211yescharacteristic
13C22×#6103C2211yescharacteristic
14C22×#6103C2211yescharacteristic
15C22×#6103C2211yescharacteristic
16C22×#6103C2214yes—
17C22×C4⋊Dic13C2212yes—
18C22×C4⋊Dic13C2212yes—
19C22×C4⋊Dic13C2214yes—
20C22×#6101C2211yescharacteristic
21C22×#6101C2211yescharacteristic
22C22×#6101C2211yescharacteristic
23C2×#88130—28no—
24C2×#88130C2218yes—
25C2×#88123—28no—
26C2×#88123C2218yescomplemented
27C13×#383C2218yescomplemented
28C2×C13×#95C2212yes—
29C2×C13×#95C2212yes—
30C2×C13×#95C2212yes—
31C2×#88071C2214yes—
32C2×#88071C2214yes—
33#11718338C22116yes—
34#11718335C22116yes—
35#11718334C22116yes—
36#11718322C22116yescomplemented
37#11718320C22116yescomplemented
38#11718317C22116yescomplemented
39C24×D13C2311yescharacteristic
40C23×C4×C13C2314yes—
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×Dic13C2311yescharacteristic
45C23×Dic13C2311yescharacteristic
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2314yes—
48C22×Dic26—28no—
49C22×Dic26—48no—
50C22×Dic26C2318yes—
51C2×C42×C13D418yes—
52C2×C42×C13C2314yes—
53C2×#6103—24no—
54C2×#6103—24no—
55C2×#6103—24no—
56C2×#6103—48no—
57C2×#6103C2314yes—
58C2×#6103C2314yes—
59C2×#6103C2314yes—
60C2×#6103C23116yes—
61C2×C4⋊Dic13—28no—
62C2×C4⋊Dic13—28no—
63C2×C4⋊Dic13—48no—
64C2×C4⋊Dic13C2318yes—
65C2×C4⋊Dic13C2318yes—
66C2×C4⋊Dic13C23116yes—
67C2×#6101—24no—
68C2×#6101—24no—
69C2×#6101—24no—
70C2×#6101C2314yes—
71C2×#6101C2314yes—
72C2×#6101C2314yes—
73#88130—232no—
74#88123—232no—
75C13×#95C2318yes—
76C13×#95C2318yes—
77C13×#95C2318yes—
78#88071C23116yes—
79#88071C23116yes—
80C2×#2821—131nomaximal, Sylow
81C24×C13C2411yescharacteristic
82C23×D13—22no—
83C23×D13—24no—
84C23×D13—24no—
85C23×D13—24no—
86C23×D13C2412yes—
87C22×C4×C13—24no—
88C22×C4×C13—24no—
89C22×C4×C13—24no—
90C22×C4×C13—28no—
91C22×C4×C13—28no—
92C22×C4×C13—28no—
93C22×C4×C13C2×D414yes—
94C22×C4×C13C2×D414yes—
95C22×C4×C13C2×D414yes—
96C22×C4×C13C2418yes—
97C22×C4×C13C2412yes—
98C22×C4×C13C2412yes—
99C22×C4×C13C2412yes—
100C22×Dic13—22no—
101C22×Dic13—22no—
102C22×Dic13—22no—
103C22×Dic13—28no—
104C22×Dic13—24no—
105C22×Dic13—28no—
106C22×Dic13—28no—
107C22×Dic13—24no—
108C22×Dic13—24no—
109C22×Dic13C2412yes—
110C22×Dic13C2412yes—
111C22×Dic13C2418yes—
112C22×Dic13C2412yes—
113C2×Dic26—216no—
114C2×Dic26—416no—
115C2×Dic26—432no—
116C42×C13C2×D4116yes—
117#6103—28no—
118#6103—28no—
119#6103—28no—
120#6103—416no—
121C4⋊Dic13—216no—
122C4⋊Dic13—216no—
123C4⋊Dic13—416no—
124#6101—28no—
125#6101—28no—
126#6101—28no—
127C22×C4⋊Q8—131no—
128C22×#126—131no—
129#2821—1316no—
130C2×#400—132no—
131C2×#399—132no—
132C2×#398—132no—
133C2×#397—132no—
134C2×#395—132no—
135C2×#393—132no—
136C2×#383D1311yescharacteristic, complemented
137C23×C13C22×D412yes—
138C23×C13H(5,𝔽2)14yes—
139C23×C132−1+414yes—
140C23×C132−1+414yes—
141C23×C13C2511yescharacteristic
142C22×D13—22no—
143C22×D13—24no—
144C22×D13—24no—
145C22×D13—24no—
146C22×D13—44no—
147C22×D13—44no—
148C22×D13—44no—
149C22×D13—416no—
150C2×C4×C13—28no—
151C2×C4×C13—28no—
152C2×C4×C13—28no—
153C2×C4×C13—24no—
154C2×C4×C13—24no—
155C2×C4×C13—24no—
156C2×C4×C13—28no—
157C2×C4×C13—28no—
158C2×C4×C13—28no—
159C2×C4×C13—416no—
160C2×C4×C13C22×D414yes—
161C2×C4×C13C22×D414yes—
162C2×C4×C13C22×D414yes—
163C2×Dic13—22no—
164C2×Dic13—22no—
165C2×Dic13—22no—
166C2×Dic13—28no—
167C2×Dic13—24no—
168C2×Dic13—28no—
169C2×Dic13—28no—
170C2×Dic13—24no—
171C2×Dic13—24no—
172C2×Dic13—416no—
173C2×Dic13—44no—
174C2×Dic13—44no—
175C2×Dic13—44no—
176Dic26—432no—
177C23×Q8—132no—
178C2×C4⋊Q8—138no—
179C2×C4⋊Q8—268no—
180C2×#126—138no—
181C2×#126—268no—
182C22×C4⋊C4—131no—
183C22×C4⋊C4—131no—
184C22×C4⋊C4—131no—
185C22×C4⋊C4—132no—
186C22×C4⋊C4—132no—
187C22×C4⋊C4—134no—
188C22×C22⋊C4—131no—
189C22×C22⋊C4—131no—
190C22×C22⋊C4—131no—
191C22×C22⋊C4—134no—
192C22×C42C2×D1311yescharacteristic
193#400—1316no—
194#399—1316no—
195#398—1316no—
196#397—1316no—
197#395—1316no—
198#393—1316no—
199#383C2×D1318yescomplemented
200C2×#95—134no—
201C2×#95—134no—
202C2×#95C2×D1312yes—
203C2×#95C2×D1312yes—
204C2×#95C2×D1312yes—
205C22×C13#53514yes—
206C22×C13#53614yes—
207C22×C13#53614yes—
208C22×C13#563116yes—
209C22×C13C23×D411yescharacteristic
210C22×C13C2×H(5,𝔽2)12yes—
211C22×C13C2×2−1+412yes—
212C22×C13C2×2−1+412yes—
213C2×D13—42no—
214C2×D13—42no—
215C2×D13—42no—
216C2×D13—48no—
217C2×D13—88no—
218C4×C13—24no—
219C4×C13—24no—
220C4×C13—24no—
221C4×C13—48no—
222Dic13—48no—
223Dic13—42no—
224Dic13—42no—
225Dic13—42no—
226C25—131no—
227C22×Q8—138no—
228C22×Q8—268no—
229C22×Q8—528no—
230C23×C4—131no—
231C23×C4—134no—
232C23×C4—131no—
233C23×C4—131no—
234C23×C4C22×D1314yes—
235C23×C4C22×D1311yescharacteristic
236C23×C4C22×D1311yescharacteristic
237C23×C4C22×D1311yescharacteristic
238C4⋊Q8—2632no—
239#126—2632no—
240C2×C4⋊C4—134no—
241C2×C4⋊C4—134no—
242C2×C4⋊C4—134no—
243C2×C4⋊C4—138no—
244C2×C4⋊C4—138no—
245C2×C4⋊C4—1316no—
246C2×C4⋊C4—264no—
247C2×C4⋊C4—264no—
248C2×C4⋊C4—264no—
249C2×C4⋊C4—268no—
250C2×C4⋊C4—268no—
251C2×C4⋊C4—528no—
252C2×C22⋊C4—134no—
253C2×C22⋊C4—134no—
254C2×C22⋊C4—134no—
255C2×C22⋊C4—1316no—
256C2×C22⋊C4—264no—
257C2×C22⋊C4—264no—
258C2×C22⋊C4—264no—
259C2×C22⋊C4—528no—
260C2×C42D5218yes—
261C2×C42C22×D1314yes—
262#95—1316no—
263#95—1316no—
264#95C22×D1318yes—
265#95C22×D1318yes—
266#95C22×D1318yes—
267C2×C13#282118yescomplemented
268C2×C13C2×#53511yescharacteristic
269C2×C13C2×#53611yescharacteristic
270C2×C13C2×#53611yescharacteristic
271C2×C13C2×#56314yes—
272D13—82no—
273C24—132no—
274C24—262no—
275C24—264no—
276C24—264no—
277C24—264no—
278C24C23×D1311yescharacteristic
279C2×Q8—2616no—
280C2×Q8—5216no—
281C2×Q8—5232no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—28no—
286C22×C4—28no—
287C22×C4—28no—
288C22×C4—132no—
289C22×C4—132no—
290C22×C4—138no—
291C22×C4—132no—
292C22×C4—262no—
293C22×C4—262no—
294C22×C4—262no—
295C22×C4—268no—
296C22×C4—268no—
297C22×C4—264no—
298C22×C4—268no—
299C22×C4—264no—
300C22×C4—264no—
301C22×C4C2×D5214yes—
302C22×C4C2×D5214yes—
303C22×C4C2×D5214yes—
304C22×C4C23×D1318yes—
305C22×C4C23×D1312yes—
306C22×C4C23×D1312yes—
307C22×C4C23×D1312yes—
308C4⋊C4—268no—
309C4⋊C4—268no—
310C4⋊C4—268no—
311C4⋊C4—2616no—
312C4⋊C4—2616no—
313C4⋊C4—5216no—
314C22⋊C4—268no—
315C22⋊C4—268no—
316C22⋊C4—268no—
317C22⋊C4—5216no—
318C42C2×D52116yes—
319C13C2×#282111yescharacteristic, complemented, Sylow
320C23—262no—
321C23—264no—
322C23—264no—
323C23—264no—
324C23—524no—
325C23—524no—
326C23—524no—
327C23—5216no—
328C23C22×D5212yes—
329C23#8825614yes—
330C23#8825714yes—
331C23#8825714yes—
332C23C24×D1311yescharacteristic
333Q8—5232no—
334C2×C4—28no—
335C2×C4—28no—
336C2×C4—28no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—28no—
341C2×C4—28no—
342C2×C4—28no—
343C2×C4—416no—
344C2×C4—262no—
345C2×C4—262no—
346C2×C4—262no—
347C2×C4—268no—
348C2×C4—268no—
349C2×C4—264no—
350C2×C4—268no—
351C2×C4—264no—
352C2×C4—264no—
353C2×C4—524no—
354C2×C4—5216no—
355C2×C4—524no—
356C2×C4—524no—
357C2×C4C22×D5214yes—
358C2×C4C22×D5214yes—
359C2×C4C22×D5214yes—
360C22—528no—
361C22—522no—
362C22—522no—
363C22—522no—
364C22—1048no—
365C22#1171923014yes—
366C22#1171923114yes—
367C22#1171923114yes—
368C22#11719417116yes—
369C22C23×D5211yescharacteristic
370C22C2×#8825612yes—
371C22C2×#8825712yes—
372C22C2×#8825712yes—
373C4—24no—
374C4—24no—
375C4—24no—
376C4—48no—
377C4—522no—
378C4—528no—
379C4—522no—
380C4—522no—
381C2—1042no—
382C2#1312289718yesdirect product factor
383C2C2×#1171923011yescharacteristic
384C2C2×#1171923111yescharacteristic
385C2C2×#1171923111yescharacteristic
386C2C2×#1171941714yes—
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#383C2
socleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#383D13
hypocenterC13C2×#2821
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#383

Complements

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

NH ≅ G/Ntype
1. C22×#88123C2semidirect
3. #13122897C2direct (N × H)
4. C2×#11718320C2semidirect
6. C2×#11718322C2semidirect
8. C2×#11718317C2semidirect
10. C2×C13×#383C2semidirect
26. C2×#88123C22semidirect
27. C13×#383C22semidirect
36. #11718322C22semidirect
37. #11718320C22semidirect
38. #11718317C22semidirect
136. C2×#383D13semidirect
199. #383C2×D13semidirect
267. C2×C13#2821semidirect
319. C13C2×#2821semidirect
382. C2#13122897direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881232
C22×#881302
#131228972
C2×#117183202
C2×#117183382
C2×#117183222
C2×#117183352
C2×#117183172
C2×#117183342
C2×C13×#3832
C2×#282113