Finite Group Databasebeta

← C2×#13120707 #16029713

Subgroups — C2×#13120707 #16029713

Order 3328.

2894 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×#88124C211yesmaximal, characteristic, complemented
2C22×C4×D52C211yesmaximal, characteristic
3#13120707C2116yesmaximal, direct product factor
4C2×#11718338C212yesmaximal, complemented
5C2×#11718322C212yesmaximal, complemented
6C2×#11718335C212yesmaximal, complemented
7C2×#11718333C212yesmaximal
8C2×#11718329C214yesmaximal, complemented
9C2×C13×#383C211yesmaximal, characteristic, complemented
10C23×D52C2211yescharacteristic
11C23×C4×D13C2212yes—
12C22×C42×C13C2211yescharacteristic
13C22×#6103C2214yes—
14C22×#6103C2212yes—
15C22×#6103C2214yes—
16C22×C4⋊Dic13C2211yescharacteristic
17C22×C4⋊Dic13C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C22×C4⋊Dic13C2214yes—
20C22×#6101C2212yes—
21C22×#6101C2212yes—
22C2×C4×D52—28no—
23C2×C4×D52C2218yes—
24C2×#88124—28no—
25C2×#88124C2218yescomplemented
26C13×#383C2218yescomplemented
27C2×C13×#95C2212yes—
28C2×C13×#95C2212yes—
29C2×C13×#95C2212yes—
30C2×#88071C2214yes—
31#11718338C22116yescomplemented
32#11718335C22116yescomplemented
33#11718333C22116yes—
34#11718329C22132yescomplemented
35#11718322C22116yescomplemented
36C24×D13C2312yes—
37C23×C4×C13C2314yes—
38C23×C4×C13C2311yescharacteristic
39C23×C4×C13C2311yescharacteristic
40C23×C4×C13C2311yescharacteristic
41C23×Dic13C2312yes—
42C23×Dic13C2312yes—
43C23×Dic13C2312yes—
44C22×D52—28no—
45C22×D52—24no—
46C22×D52C2314yes—
47C22×C4×D13—28no—
48C22×C4×D13—48no—
49C22×C4×D13C2318yes—
50C2×C42×C13D418yes—
51C2×C42×C13C2314yes—
52C2×#6103—216no—
53C2×#6103—28no—
54C2×#6103—48no—
55C2×#6103C2318yes—
56C2×#6103C23116yes—
57C2×#6103C23116yes—
58C2×C4⋊Dic13—24no—
59C2×C4⋊Dic13—24no—
60C2×C4⋊Dic13—24no—
61C2×C4⋊Dic13—48no—
62C2×C4⋊Dic13C2314yes—
63C2×C4⋊Dic13C2314yes—
64C2×C4⋊Dic13C2314yes—
65C2×C4⋊Dic13C23116yes—
66C2×#6101—28no—
67C2×#6101—28no—
68C2×#6101C2318yes—
69C2×#6101C2318yes—
70C4×D52—232no—
71#88124—232no—
72C13×#95C2318yes—
73C13×#95C2318yes—
74C13×#95C2318yes—
75#88071C23116yes—
76C2×#2633—131nomaximal, Sylow
77C24×C13C2411yescharacteristic
78C23×D13—24no—
79C23×D13—24no—
80C23×D13—28no—
81C23×D13—28no—
82C23×D13#4118yes—
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—28no—
101C22×Dic13—24no—
102C22×Dic13—28no—
103C22×Dic13—24no—
104C22×Dic13C2414yes—
105C22×Dic13C2414yes—
106C22×Dic13C2414yes—
107C2×D52—232no—
108C2×D52—216no—
109C2×D52—28no—
110C2×C4×D13—216no—
111C2×C4×D13—416no—
112C2×C4×D13—432no—
113C42×C13C2×D4116yes—
114#6103—232no—
115#6103—216no—
116#6103—416no—
117C4⋊Dic13—28no—
118C4⋊Dic13—28no—
119C4⋊Dic13—28no—
120C4⋊Dic13—416no—
121#6101—216no—
122#6101—216no—
123C22×#125—131no—
124C22×C4×D4—131no—
125#2633—1316no—
126C2×#399—132no—
127C2×#398—132no—
128C2×#397—132no—
129C2×#394—132no—
130C2×#385—134no—
131C2×#383D1311yescharacteristic, complemented
132C23×C13C22×D412yes—
133C23×C13C2×#4114yes—
134C23×C13H(5,𝔽2)14yes—
135C23×C132−1+414yes—
136C23×C13C2511yescharacteristic
137C22×D13—216no—
138C22×D13—232no—
139C22×D13—24no—
140C22×D13—24no—
141C22×D13—28no—
142C22×D13—28no—
143C22×D13—48no—
144C22×D13—48no—
145C22×D13—416no—
146C22×D13C2×#4118yes—
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—24no—
161C2×Dic13—24no—
162C2×Dic13—24no—
163C2×Dic13—28no—
164C2×Dic13—24no—
165C2×Dic13—28no—
166C2×Dic13—24no—
167C2×Dic13—48no—
168C2×Dic13—48no—
169C2×Dic13—48no—
170D52—232no—
171C4×D13—432no—
172C23×D4—131no—
173C24×C4—132no—
174C2×#125—138no—
175C2×#125—268no—
176C2×C4×D4—138no—
177C2×C4×D4—268no—
178C22×C4⋊C4—132no—
179C22×C4⋊C4—132no—
180C22×C4⋊C4—131no—
181C22×C4⋊C4—131no—
182C22×C4⋊C4—131no—
183C22×C4⋊C4—134no—
184C22×C22⋊C4—134no—
185C22×C22⋊C4—132no—
186C22×C22⋊C4—134no—
187C22×C42C2×D1311yescharacteristic
188#399—1316no—
189#398—1316no—
190#397—1316no—
191#394—1316no—
192#385—1332no—
193#383C2×D1318yescomplemented
194C2×#95—134no—
195C2×#95C2×D1312yes—
196C2×#95C2×D1312yes—
197C2×#95C2×D1312yes—
198C22×C13#52514yes—
199C22×C13#53514yes—
200C22×C13#53614yes—
201C22×C13#539116yes—
202C22×C13C23×D411yescharacteristic
203C22×C13C22×#4112yes—
204C22×C13C2×H(5,𝔽2)12yes—
205C22×C13C2×2−1+412yes—
206C2×D13—28no—
207C2×D13—216no—
208C2×D13—432no—
209C2×D13—44no—
210C2×D13—44no—
211C2×D13—48no—
212C4×C13—24no—
213C4×C13—24no—
214C4×C13—24no—
215C4×C13—48no—
216Dic13—44no—
217Dic13—44no—
218Dic13—44no—
219C25—132no—
220C22×D4—134no—
221C22×D4—268no—
222C22×D4—264no—
223C23×C4—132no—
224C23×C4—132no—
225C23×C4—132no—
226C23×C4—138no—
227C23×C4—268no—
228C23×C4—528no—
229C23×C4C22×D1314yes—
230C23×C4C22×D1311yescharacteristic
231C23×C4C22×D1311yescharacteristic
232C23×C4C22×D1311yescharacteristic
233#125—2632no—
234C4×D4—2632no—
235C2×C4⋊C4—134no—
236C2×C4⋊C4—138no—
237C2×C4⋊C4—138no—
238C2×C4⋊C4—134no—
239C2×C4⋊C4—134no—
240C2×C4⋊C4—1316no—
241C2×C4⋊C4—264no—
242C2×C4⋊C4—268no—
243C2×C4⋊C4—268no—
244C2×C4⋊C4—264no—
245C2×C4⋊C4—264no—
246C2×C4⋊C4—528no—
247C2×C22⋊C4—138no—
248C2×C22⋊C4—1316no—
249C2×C22⋊C4—1316no—
250C2×C22⋊C4—2616no—
251C2×C22⋊C4—268no—
252C2×C22⋊C4—528no—
253C2×C42D5218yes—
254C2×C42C22×D1314yes—
255#95—1316no—
256#95C22×D1318yes—
257#95C22×D1318yes—
258#95C22×D1318yes—
259C2×C13#263318yescomplemented
260C2×C13C2×#52511yescharacteristic
261C2×C13C2×#53511yescharacteristic
262C2×C13C2×#53611yescharacteristic
263C2×C13C2×#53914yes—
264D13—48no—
265C24—138no—
266C24—134no—
267C24—264no—
268C24—264no—
269C24—268no—
270C24—268no—
271C24C23×D1311yescharacteristic
272C2×D4—2616no—
273C2×D4—2632no—
274C2×D4—268no—
275C22×C4—24no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—28no—
279C22×C4—28no—
280C22×C4—28no—
281C22×C4—134no—
282C22×C4—134no—
283C22×C4—134no—
284C22×C4—264no—
285C22×C4—264no—
286C22×C4—264no—
287C22×C4—268no—
288C22×C4—264no—
289C22×C4—264no—
290C22×C4—268no—
291C22×C4—2616no—
292C22×C4—5216no—
293C22×C4—5232no—
294C22×C4C2×D5214yes—
295C22×C4C2×D5214yes—
296C22×C4C2×D5214yes—
297C22×C4C23×D1318yes—
298C22×C4C23×D1312yes—
299C22×C4C23×D1312yes—
300C22×C4C23×D1312yes—
301C4⋊C4—268no—
302C4⋊C4—2616no—
303C4⋊C4—2616no—
304C4⋊C4—268no—
305C4⋊C4—268no—
306C4⋊C4—5216no—
307C22⋊C4—2632no—
308C22⋊C4—2616no—
309C22⋊C4—5216no—
310C42C2×D52116yes—
311C13C2×#263311yescharacteristic, complemented, Sylow
312C23—138no—
313C23—2616no—
314C23—264no—
315C23—264no—
316C23—268no—
317C23—268no—
318C23—2632no—
319C23—528no—
320C23—528no—
321C23—5216no—
322C23C22×D5212yes—
323C23#41×D1314yes—
324C23#8825614yes—
325C23#8825714yes—
326C23C24×D1311yescharacteristic
327D4—2632no—
328C2×C4—28no—
329C2×C4—28no—
330C2×C4—28no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—28no—
335C2×C4—28no—
336C2×C4—28no—
337C2×C4—416no—
338C2×C4—264no—
339C2×C4—264no—
340C2×C4—264no—
341C2×C4—268no—
342C2×C4—264no—
343C2×C4—264no—
344C2×C4—268no—
345C2×C4—5232no—
346C2×C4—528no—
347C2×C4—528no—
348C2×C4—528no—
349C2×C4C22×D5214yes—
350C2×C4C22×D5214yes—
351C2×C4C22×D5214yes—
352C22—268no—
353C22—2616no—
354C22—5232no—
355C22—524no—
356C22—524no—
357C22—528no—
358C22#1171922914yes—
359C22#1171923014yes—
360C22#1171923114yes—
361C22#11719412116yes—
362C22C23×D5211yescharacteristic
363C22C2×#41×D1312yes—
364C22C2×#8825612yes—
365C22C2×#8825712yes—
366C4—24no—
367C4—24no—
368C4—24no—
369C4—48no—
370C4—524no—
371C4—524no—
372C4—524no—
373C2—528no—
374C2#1312070718yesdirect product factor
375C2C2×#1171922911yescharacteristic
376C2C2×#1171923011yescharacteristic
377C2C2×#1171923111yescharacteristic
378C2C2×#1171941214yes—
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#383C2
socleC24×C13C24
prime radicalC23×D52C22
hypercenterC2×#383D13
hypocenterC13C2×#2633
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#383

Complements

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

NH ≅ G/Ntype
1. C22×#88124C2semidirect
3. #13120707C2direct (N × H)
4. C2×#11718338C2semidirect
5. C2×#11718322C2semidirect
6. C2×#11718335C2semidirect
8. C2×#11718329C2semidirect
9. C2×C13×#383C2semidirect
25. C2×#88124C22semidirect
26. C13×#383C22semidirect
31. #11718338C22semidirect
32. #11718335C22semidirect
34. #11718329C22semidirect
35. #11718322C22semidirect
131. C2×#383D13semidirect
193. #383C2×D13semidirect
259. C2×C13#2633semidirect
311. C13C2×#2633semidirect
374. C2#13120707direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881242
C22×C4×D522
#131207072
C2×#117183382
C2×#117183222
C2×#117183352
C2×#117183332
C2×#117183292
C2×C13×#3832
C2×#263313