Finite Group Databasebeta

← C2×#13120699 #16029842

Subgroups — C2×#13120699 #16029842

Order 3328.

2806 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88129C211yesmaximal, characteristic
2C22×C4×Dic26C211yesmaximal, characteristic, complemented
3#13120699C2116yesmaximal, direct product factor
4C2×#11718338C212yesmaximal, complemented
5C2×#11718317C212yesmaximal, complemented
6C2×#11718333C212yesmaximal
7C2×#11718334C212yesmaximal, complemented
8C2×#11718331C214yesmaximal, complemented
9C2×C13×#383C211yesmaximal, characteristic, complemented
10C23×D52C2211yescharacteristic
11C23×Dic26C2211yescharacteristic
12C23×Dic26C2211yescharacteristic
13C22×C42×C13C2211yescharacteristic
14C22×#6103C2212yes—
15C22×#6103C2214yes—
16C22×#6103C2212yes—
17C22×#6103C2214yes—
18C22×C4⋊Dic13C2211yescharacteristic
19C22×C4⋊Dic13C2214yes—
20C22×#6101C2212yes—
21C22×C4×Dic13C2212yes—
22C2×#88129—28no—
23C2×#88129C2218yes—
24C2×C4×Dic26—28no—
25C2×C4×Dic26C2218yescomplemented
26C13×#383C2218yescomplemented
27C2×C13×#95C2212yes—
28C2×C13×#95C2212yes—
29C2×C13×#95C2212yes—
30C2×#88071C2214yes—
31#11718338C22116yescomplemented
32#11718334C22116yescomplemented
33#11718333C22116yes—
34#11718331C22132yescomplemented
35#11718317C22116yescomplemented
36C24×D13C2312yes—
37C23×C4×C13C2314yes—
38C23×C4×C13C2311yescharacteristic
39C23×C4×C13C2311yescharacteristic
40C23×C4×C13C2311yescharacteristic
41C23×Dic13C2312yes—
42C23×Dic13C2312yes—
43C23×Dic13C2312yes—
44C22×D52—24no—
45C22×D52—44no—
46C22×D52C2314yes—
47C22×Dic26—24no—
48C22×Dic26—28no—
49C22×Dic26—24no—
50C22×Dic26—44no—
51C22×Dic26C2314yes—
52C22×Dic26C2314yes—
53C2×C42×C13D418yes—
54C2×C42×C13C2314yes—
55C2×#6103—28no—
56C2×#6103—28no—
57C2×#6103—216no—
58C2×#6103—48no—
59C2×#6103C2318yes—
60C2×#6103C2318yes—
61C2×#6103C23116yes—
62C2×#6103C23116yes—
63C2×C4⋊Dic13—24no—
64C2×C4⋊Dic13—48no—
65C2×C4⋊Dic13C2314yes—
66C2×C4⋊Dic13C23116yes—
67C2×#6101—28no—
68C2×#6101C2318yes—
69C2×C4×Dic13—28no—
70C2×C4×Dic13C2318yes—
71#88129—232no—
72C4×Dic26—232no—
73C13×#95C2318yes—
74C13×#95C2318yes—
75C13×#95C2318yes—
76#88071C23116yes—
77C2×#2632—131nomaximal, Sylow
78C24×C13C2411yescharacteristic
79C23×D13—24no—
80C23×D13—28no—
81C23×D13—28no—
82C23×D13—28no—
83C23×D13C2414yes—
84C22×C4×C13—24no—
85C22×C4×C13—24no—
86C22×C4×C13—24no—
87C22×C4×C13—28no—
88C22×C4×C13—28no—
89C22×C4×C13—28no—
90C22×C4×C13C2×D414yes—
91C22×C4×C13C2×D414yes—
92C22×C4×C13C2×D414yes—
93C22×C4×C13C2418yes—
94C22×C4×C13C2412yes—
95C22×C4×C13C2412yes—
96C22×C4×C13C2412yes—
97C22×Dic13—24no—
98C22×Dic13—24no—
99C22×Dic13—24no—
100C22×Dic13—24no—
101C22×Dic13—28no—
102C22×Dic13—28no—
103C22×Dic13#4118yes—
104C22×Dic13C2414yes—
105C22×Dic13C2414yes—
106C22×Dic13C2414yes—
107C2×D52—28no—
108C2×D52—48no—
109C2×D52—416no—
110C2×Dic26—232no—
111C2×Dic26—28no—
112C2×Dic26—216no—
113C2×Dic26—28no—
114C2×Dic26—48no—
115C2×Dic26—416no—
116C42×C13C2×D4116yes—
117#6103—216no—
118#6103—216no—
119#6103—232no—
120#6103—416no—
121C4⋊Dic13—28no—
122C4⋊Dic13—416no—
123#6101—216no—
124C4×Dic13—216no—
125C22×#124—131no—
126C22×C4×Q8—131no—
127#2632—1316no—
128C2×#399—132no—
129C2×#395—132no—
130C2×#394—132no—
131C2×#393—132no—
132C2×#388—134no—
133C2×#383D1311yescharacteristic, complemented
134C23×C13C22×D412yes—
135C23×C13C2×#4114yes—
136C23×C13H(5,𝔽2)14yes—
137C23×C132−1+414yes—
138C23×C13C2511yescharacteristic
139C22×D13—24no—
140C22×D13—28no—
141C22×D13—28no—
142C22×D13—28no—
143C22×D13—48no—
144C22×D13—48no—
145C22×D13—48no—
146C22×D13—432no—
147C2×C4×C13—28no—
148C2×C4×C13—28no—
149C2×C4×C13—28no—
150C2×C4×C13—24no—
151C2×C4×C13—24no—
152C2×C4×C13—24no—
153C2×C4×C13—28no—
154C2×C4×C13—28no—
155C2×C4×C13—28no—
156C2×C4×C13—416no—
157C2×C4×C13C22×D414yes—
158C2×C4×C13C22×D414yes—
159C2×C4×C13C22×D414yes—
160C2×Dic13—216no—
161C2×Dic13—24no—
162C2×Dic13—24no—
163C2×Dic13—24no—
164C2×Dic13—24no—
165C2×Dic13—28no—
166C2×Dic13—28no—
167C2×Dic13—48no—
168C2×Dic13—48no—
169C2×Dic13C2×#4118yes—
170D52—416no—
171Dic26—232no—
172Dic26—416no—
173C23×Q8—131no—
174C23×Q8—131no—
175C23×D4—131no—
176C2×#124—138no—
177C2×#124—268no—
178C2×C4×Q8—138no—
179C2×C4×Q8—268no—
180C22×C4⋊C4—132no—
181C22×C4⋊C4—131no—
182C22×C4⋊C4—134no—
183C22×C22⋊C4—134no—
184C22×C22⋊C4—132no—
185C22×C22⋊C4—132no—
186C22×C22⋊C4—134no—
187C22×C42—132no—
188C22×C42C2×D1311yescharacteristic
189#399—1316no—
190#395—1316no—
191#394—1316no—
192#393—1316no—
193#388—1332no—
194#383C2×D1318yescomplemented
195C2×#95—134no—
196C2×#95C2×D1312yes—
197C2×#95C2×D1312yes—
198C2×#95C2×D1312yes—
199C22×C13#52514yes—
200C22×C13#53514yes—
201C22×C13#53614yes—
202C22×C13#542116yes—
203C22×C13C23×D411yescharacteristic
204C22×C13C22×#4112yes—
205C22×C13C2×H(5,𝔽2)12yes—
206C22×C13C2×2−1+412yes—
207C2×D13—44no—
208C2×D13—44no—
209C2×D13—44no—
210C2×D13—416no—
211C2×D13—816no—
212C4×C13—24no—
213C4×C13—24no—
214C4×C13—24no—
215C4×C13—48no—
216Dic13—28no—
217Dic13—44no—
218Dic13—44no—
219C25—132no—
220C22×Q8—134no—
221C22×Q8—134no—
222C22×Q8—268no—
223C22×Q8—264no—
224C22×Q8—264no—
225C22×Q8—524no—
226C22×D4—134no—
227C22×D4—264no—
228C22×D4—524no—
229C23×C4—132no—
230C23×C4—132no—
231C23×C4—132no—
232C23×C4C22×D1314yes—
233C23×C4C22×D1311yescharacteristic
234C23×C4C22×D1311yescharacteristic
235C23×C4C22×D1311yescharacteristic
236#124—2632no—
237C4×Q8—2632no—
238C2×C4⋊C4—138no—
239C2×C4⋊C4—134no—
240C2×C4⋊C4—1316no—
241C2×C4⋊C4—268no—
242C2×C4⋊C4—264no—
243C2×C4⋊C4—528no—
244C2×C22⋊C4—138no—
245C2×C22⋊C4—138no—
246C2×C22⋊C4—1316no—
247C2×C22⋊C4—1316no—
248C2×C22⋊C4—2616no—
249C2×C22⋊C4—268no—
250C2×C22⋊C4—268no—
251C2×C22⋊C4—528no—
252C2×C42—138no—
253C2×C42—268no—
254C2×C42D5218yes—
255C2×C42C22×D1314yes—
256#95—1316no—
257#95C22×D1318yes—
258#95C22×D1318yes—
259#95C22×D1318yes—
260C2×C13#263218yescomplemented
261C2×C13C2×#52511yescharacteristic
262C2×C13C2×#53511yescharacteristic
263C2×C13C2×#53611yescharacteristic
264C2×C13C2×#54214yes—
265D13—84no—
266C24—134no—
267C24—264no—
268C24—268no—
269C24—268no—
270C24—268no—
271C24C23×D1311yescharacteristic
272C2×Q8—2616no—
273C2×Q8—2632no—
274C2×Q8—268no—
275C2×Q8—268no—
276C2×Q8—528no—
277C2×Q8—5216no—
278C2×D4—268no—
279C2×D4—528no—
280C2×D4—5216no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—28no—
285C22×C4—28no—
286C22×C4—28no—
287C22×C4—138no—
288C22×C4—134no—
289C22×C4—134no—
290C22×C4—134no—
291C22×C4—264no—
292C22×C4—264no—
293C22×C4—264no—
294C22×C4—264no—
295C22×C4—268no—
296C22×C4—268no—
297C22×C4C2×D5214yes—
298C22×C4C2×D5214yes—
299C22×C4C2×D5214yes—
300C22×C4C23×D1318yes—
301C22×C4C23×D1312yes—
302C22×C4C23×D1312yes—
303C22×C4C23×D1312yes—
304C4⋊C4—2616no—
305C4⋊C4—268no—
306C4⋊C4—5216no—
307C22⋊C4—2632no—
308C22⋊C4—2616no—
309C22⋊C4—2616no—
310C22⋊C4—5216no—
311C42—2616no—
312C42C2×D52116yes—
313C13C2×#263211yescharacteristic, complemented, Sylow
314C23—264no—
315C23—268no—
316C23—268no—
317C23—268no—
318C23—528no—
319C23—528no—
320C23—528no—
321C23—5232no—
322C23C22×D5212yes—
323C23#41×D1314yes—
324C23#8825614yes—
325C23#8825714yes—
326C23C24×D1311yescharacteristic
327Q8—2632no—
328Q8—5216no—
329D4—5216no—
330C2×C4—28no—
331C2×C4—28no—
332C2×C4—28no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—24no—
336C2×C4—28no—
337C2×C4—28no—
338C2×C4—28no—
339C2×C4—416no—
340C2×C4—138no—
341C2×C4—2616no—
342C2×C4—264no—
343C2×C4—264no—
344C2×C4—264no—
345C2×C4—264no—
346C2×C4—268no—
347C2×C4—268no—
348C2×C4—528no—
349C2×C4—528no—
350C2×C4C22×D5214yes—
351C2×C4C22×D5214yes—
352C2×C4C22×D5214yes—
353C22—5216no—
354C22—524no—
355C22—524no—
356C22—524no—
357C22—10416no—
358C22#1171922914yes—
359C22#1171923014yes—
360C22#1171923114yes—
361C22#11719415116yes—
362C22C23×D5211yescharacteristic
363C22C2×#41×D1312yes—
364C22C2×#8825612yes—
365C22C2×#8825712yes—
366C4—24no—
367C4—24no—
368C4—24no—
369C4—48no—
370C4—268no—
371C4—524no—
372C4—524no—
373C2—1044no—
374C2#1312069918yesdirect product factor
375C2C2×#1171922911yescharacteristic
376C2C2×#1171923011yescharacteristic
377C2C2×#1171923111yescharacteristic
378C2C2×#1171941514yes—
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#383C2
socleC24×C13C24
prime radicalC23×D52C22
hypercenterC2×#383D13
hypocenterC13C2×#2632
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#383

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic26C2semidirect
3. #13120699C2direct (N × H)
4. C2×#11718338C2semidirect
5. C2×#11718317C2semidirect
7. C2×#11718334C2semidirect
8. C2×#11718331C2semidirect
9. C2×C13×#383C2semidirect
25. C2×C4×Dic26C22semidirect
26. C13×#383C22semidirect
31. #11718338C22semidirect
32. #11718334C22semidirect
34. #11718331C22semidirect
35. #11718317C22semidirect
133. C2×#383D13semidirect
194. #383C2×D13semidirect
260. C2×C13#2632semidirect
313. C13C2×#2632semidirect
374. C2#13120699direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881292
C22×C4×Dic262
#131206992
C2×#117183382
C2×#117183172
C2×#117183332
C2×#117183342
C2×#117183312
C2×C13×#3832
C2×#263213