Finite Group Databasebeta

← C2×#13125413 #16732653

Subgroups — C2×#13125413 #16732653

Order 3328.

2566 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719421C212yesmaximal, complemented
2#13125413C2116yesmaximal, direct product factor
3C2×#11718343C211yesmaximal, characteristic, complemented
4C2×#11718731C212yesmaximal, complemented
5C2×#11718818C214yesmaximal, complemented
6C2×D8×Dic13C214yesmaximal, complemented
7C2×C4×C8×D13C211yesmaximal, characteristic, complemented
8C2×C13×#493C211yesmaximal, characteristic, complemented
9C22×#6129—22no—
10C22×C13×D8C2214yes—
11C2×C13×#127C2212yes—
12C2×#88192—22no—
13C2×#88192C2214yes—
14C2×#88190—22no—
15C2×D4×Dic13—22no—
16C2×D4×Dic13C2214yes—
17C22×C8×D13C2212yes—
18#11719421—28no—
19#11719421C22116yescomplemented
20C2×C42×D13C2211yescharacteristic
21C2×#88123C2212yes—
22C13×#493C2218yescomplemented
23C2×C4×C8×C13C2211yescharacteristic
24C2×#88072C2218yes—
25#11718818C22132yescomplemented
26D8×Dic13C22132yescomplemented
27C2×#88058C2214yes—
28C2×C8×Dic13C2212yes—
29#11718731C22116yescomplemented
30C2×C4×#1055C2211yescharacteristic
31C4×C8×D13C2218yescomplemented
32#11718343C2218yescomplemented
33C22×D4×C13—22no—
34C22×D4×C13—22no—
35C22×D4×C13C2314yes—
36C22×C22⋊D13—24no—
37C23×Dic13—24no—
38C2×#6129—216no—
39C2×#6129—416no—
40C22×C4×D13D411yescharacteristic
41C22×C4×D13D411yescharacteristic
42C22×C4×D13C2311yescharacteristic
43C22×Dic26—22no—
44C2×C13×D8—216no—
45C2×C13×D8C23116yes—
46C22×C8×C13C2312yes—
47C13×#127—24no—
48C13×#127C2318yes—
49C2×C42×C13C2311yescharacteristic
50C2×C22⋊Dic13—24no—
51C2×C22⋊Dic13—24no—
52#88192—216no—
53#88192—28no—
54#88192C23116yes—
55#88190—216no—
56D4×Dic13—216no—
57D4×Dic13—28no—
58D4×Dic13C23116yes—
59C2×C4⋊Dic13—22no—
60C2×C4⋊Dic13C2314yes—
61C2×C4×Dic13D411yescharacteristic
62C2×C4×Dic13D411yescharacteristic
63C2×C4×Dic13C2311yescharacteristic
64C22×#1055C2312yes—
65C2×C8×D13—28no—
66C2×C8×D13C2318yes—
67C42×D13D414yes—
68C42×D13C2314yes—
69#88123—24no—
70#88123C2318yes—
71C4×C8×C13C2314yes—
72#88072C23132yes—
73#88058C23116yes—
74C8×Dic13C2318yes—
75C4×#1055C2314yes—
76C2×#3169—131nomaximal, Sylow
77C24×C13—24no—
78C23×D13C2×D411yescharacteristic
79C2×D4×C13—24no—
80C2×D4×C13—28no—
81C2×D4×C13—28no—
82C2×D4×C13—216no—
83C2×D4×C13—48no—
84C2×D4×C13—48no—
85C2×D4×C13C2418yes—
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13C2411yescharacteristic
89C2×C22⋊D13—216no—
90C2×C22⋊D13—416no—
91C22×Dic13—24no—
92C22×Dic13—216no—
93C22×Dic13—416no—
94C22×Dic13C2×D411yescharacteristic
95C22×Dic13C2×D411yescharacteristic
96C22×Dic13C2×D411yescharacteristic
97#6129—464no—
98C2×C4×D13—24no—
99C2×C4×D13—24no—
100C2×C4×D13D818yescomplemented
101C2×C4×D13C2×D412yes—
102C2×C4×D13C2×D414yes—
103C2×C4×D13C2×D414yes—
104C2×C4×D13C2412yes—
105C2×Dic26—28no—
106C2×Dic26—48no—
107C13×D8—232no—
108C2×C8×C13#4118yescomplemented
109C2×C8×C13C2414yes—
110C42×C13C2×D412yes—
111C42×C13C2412yes—
112C22⋊Dic13—216no—
113C22⋊Dic13—216no—
114C4⋊Dic13—24no—
115C4⋊Dic13—28no—
116C4⋊Dic13C2418yes—
117C4×Dic13C2×D412yes—
118C4×Dic13C2×D414yes—
119C4×Dic13C2×D414yes—
120C4×Dic13C2412yes—
121C2×#1055—24no—
122C2×#1055C2414yes—
123C8×D13—216no—
124C2×#532—132no—
125#3169—1316no—
126C2×#500—131no—
127C2×#493D1311yescharacteristic, complemented
128C2×#486—132no—
129C2×#466—134no—
130C2×C4×D8—134no—
131C22×C4×C8—131no—
132C23×C13—28no—
133C23×C13—48no—
134C23×C13—48no—
135C23×C13—48no—
136C23×C13C22×D411yescharacteristic
137C22×D13—22no—
138C22×D13—22no—
139C22×D13C2×D814yes—
140C22×D13C22×D412yes—
141D4×C13—216no—
142D4×C13—48no—
143D4×C13—416no—
144D4×C13—416no—
145C2×C4×C13C2×D814yes—
146C2×C4×C13#13514yes—
147C2×C4×C13C22×D411yescharacteristic
148C2×C4×C13C22×D412yes—
149C2×C4×C13C22×D412yes—
150C2×C4×C13C2×#4114yes—
151C2×C4×C13C2511yescharacteristic
152C22⋊D13—432no—
153C2×Dic13—22no—
154C2×Dic13—22no—
155C2×Dic13—28no—
156C2×Dic13—48no—
157C2×Dic13—432no—
158C2×Dic13C2×D814yes—
159C2×Dic13C22×D412yes—
160C2×Dic13C22×D412yes—
161C2×Dic13C22×D412yes—
162C4×D13—24no—
163C4×D13—28no—
164C4×D13—24no—
165C4×D13C2×D8116yescomplemented
166Dic26—416no—
167C8×C13C2×#4118yescomplemented
168#1055—24no—
169C22×#41—262no—
170C22×D8C2×D1314yes—
171C23×C8—132no—
172#532—1316no—
173#532—268no—
174C2×C4⋊Q8—132no—
175C2×#127C2×D1312yes—
176C2×#124—262no—
177C2×#121—134no—
178C2×#121—262no—
179C2×C4×D4—134no—
180C2×C4×D4—262no—
181C22×C42—131no—
182#500—138no—
183#493C2×D1318yescomplemented
184#486—1316no—
185#466—1332no—
186C4×D8—1332no—
187C2×#107—134no—
188C2×#102—138no—
189C2×C4×C8—132no—
190C2×C4×C8—131no—
191C2×C4×C8—138no—
192C2×C4×C8C2×D1311yescharacteristic
193C22×C13—48no—
194C22×C13—48no—
195C22×C13—48no—
196C22×C13—816no—
197C22×C13#53212yes—
198C22×C13C22×D812yes—
199C22×C13C2×#13512yes—
200C22×C13C23×D411yescharacteristic
201C2×D13—28no—
202C2×D13—22no—
203C2×D13—22no—
204C2×D13C22×D814yes—
205C4×C13#53212yes—
206C4×C13C22×D814yes—
207C4×C13C2×#13514yes—
208C4×C13C22×#4112yes—
209Dic13—22no—
210Dic13—22no—
211Dic13—48no—
212Dic13C22×D814yes—
213C2×#41—2616no—
214C2×#41—5216no—
215C22×Q8—262no—
216C22×D4—22no—
217C22×D4—22no—
218C22×D4—264no—
219C22×D4C22×D1314yes—
220C23×C4—131no—
221C23×C4—131no—
222C23×C4—131no—
223C23×C4—264no—
224C2×D8—216no—
225C2×D8C22×D13116yes—
226C22×C8—132no—
227C22×C8—138no—
228C22×C8—268no—
229C22×C8C22×D1312yes—
230C4⋊Q8—138no—
231C4⋊Q8—264no—
232#127—24no—
233#127C22×D1318yes—
234#124—2616no—
235#121—1316no—
236#121—268no—
237#121—2616no—
238C4×D4—1316no—
239C4×D4—268no—
240C4×D4—2616no—
241C2×C4⋊C4—134no—
242C2×C4⋊C4—262no—
243C2×C22⋊C4—264no—
244C2×C22⋊C4—264no—
245C2×C42—131no—
246C2×C42—131no—
247C2×C42—131no—
248C2×C42—134no—
249C2×C42—134no—
250C2×C42C22×D1311yescharacteristic
251#107—1316no—
252#102—1332no—
253C4×C8—138no—
254C4×C8—134no—
255C4×C8C22×D1314yes—
256C2×C13—88no—
257C2×C13#316914yescomplemented
258C2×C13C2×#53211yescharacteristic
259C2×C13C23×D811yescharacteristic
260C2×C13C22×#13511yescharacteristic
261D13—24no—
262C24—24no—
263C24—131no—
264#41—5264no—
265C2×Q8—268no—
266C2×Q8—528no—
267C2×D4—24no—
268C2×D4—28no—
269C2×D4—28no—
270C2×D4—216no—
271C2×D4—48no—
272C2×D4—48no—
273C2×D4—2616no—
274C2×D4—5216no—
275C2×D4C23×D1318yes—
276C22×C4—131no—
277C22×C4—138no—
278C22×C4—134no—
279C22×C4—131no—
280C22×C4—131no—
281C22×C4—134no—
282C22×C4—132no—
283C22×C4—132no—
284C22×C4—2616no—
285C22×C4—264no—
286C22×C4—264no—
287C22×C4—264no—
288C22×C4—5216no—
289C22×C4D4×D1311yescharacteristic
290C22×C4D4×D1311yescharacteristic
291C22×C4C23×D1311yescharacteristic
292D8—232no—
293C2×C8—134no—
294C2×C8—264no—
295C2×C8—2616no—
296C2×C8#612918yescomplemented
297C2×C8C23×D1314yes—
298C4⋊C4—138no—
299C4⋊C4—264no—
300C4⋊C4—268no—
301C22⋊C4—2616no—
302C22⋊C4—2616no—
303C42—134no—
304C42—132no—
305C42—134no—
306C42—132no—
307C42D4×D1312yes—
308C42C23×D1312yes—
309C13C2×#316911yescharacteristic, complemented, Sylow
310C23—28no—
311C23—48no—
312C23—48no—
313C23—48no—
314C23—134no—
315C23—132no—
316C23—262no—
317C23—262no—
318C23C2×D4×D1311yescharacteristic
319Q8—5216no—
320D4—216no—
321D4—416no—
322D4—416no—
323D4—48no—
324D4—5232no—
325C2×C4—134no—
326C2×C4—132no—
327C2×C4—1316no—
328C2×C4—132no—
329C2×C4—132no—
330C2×C4—262no—
331C2×C4—262no—
332C2×C4—268no—
333C2×C4—264no—
334C2×C4—264no—
335C2×C4—268no—
336C2×C4—5232no—
337C2×C4—528no—
338C2×C4D8×D1314yes—
339C2×C4#8816614yes—
340C2×C4C2×D4×D1312yes—
341C2×C4C2×D4×D1312yes—
342C2×C4C2×D4×D1311yescharacteristic
343C2×C4C2×#612914yes—
344C2×C4C24×D1311yescharacteristic
345C8—264no—
346C8C2×#612918yescomplemented
347C22—48no—
348C22—48no—
349C22—48no—
350C22—816no—
351C22—134no—
352C22—268no—
353C22—262no—
354C22—262no—
355C22#1171942112yes—
356C22C2×D8×D1312yes—
357C22C2×#8816612yes—
358C22C22×D4×D1311yescharacteristic
359C4—134no—
360C4—262no—
361C4—262no—
362C4—528no—
363C4#1171942112yes—
364C4C2×D8×D1314yes—
365C4C2×#8816614yes—
366C4C22×#612912yes—
367C2—88no—
368C2—264no—
369C2#1312541314yesdirect product factor
370C2C2×#1171942111yescharacteristic
371C2C22×D8×D1311yescharacteristic
372C2C22×#8816611yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#493C2
socleC23×C13C22×D4
hypercenterC2×#493D13
hypocenterC13C2×#3169
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#493

Complements

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

NH ≅ G/Ntype
1. C2×#11719421C2semidirect
2. #13125413C2direct (N × H)
3. C2×#11718343C2semidirect
4. C2×#11718731C2semidirect
5. C2×#11718818C2semidirect
6. C2×D8×Dic13C2semidirect
7. C2×C4×C8×D13C2semidirect
8. C2×C13×#493C2semidirect
19. #11719421C22semidirect
22. C13×#493C22semidirect
25. #11718818C22semidirect
26. D8×Dic13C22semidirect
29. #11718731C22semidirect
31. C4×C8×D13C22semidirect
32. #11718343C22semidirect
100. C2×C4×D13D8semidirect
108. C2×C8×C13#41semidirect
127. C2×#493D13semidirect
165. C4×D13C2×D8semidirect
167. C8×C13C2×#41semidirect
183. #493C2×D13semidirect
257. C2×C13#3169semidirect
296. C2×C8#6129semidirect
309. C13C2×#3169semidirect
346. C8C2×#6129semidirect
369. C2#13125413direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117194212
#131254132
C2×#117183432
C2×#117187312
C2×#117188182
C2×D8×Dic132
C2×C4×C8×D132
C2×C13×#4932
C2×#316913