Finite Group Databasebeta

← C2×#13120075 #16034875

Subgroups — C2×#13120075 #16034875

Order 3328.

1966 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13120075C2116yesmaximal, direct product factor
2C2×#11718321C214yesmaximal
3C2×#11718589C212yesmaximal
4C2×#11718634C212yesmaximal
5C2×#11718596C211yesmaximal, characteristic
6C2×#11718597C212yesmaximal
7C2×#11718638C212yesmaximal
8C2×C4×C4⋊Dic13C211yesmaximal, characteristic
9C2×C4×C13×C4⋊C4C211yesmaximal, characteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×C42×C13C2212yes—
13C22×C42×C13C2211yescharacteristic
14C22×C4⋊Dic13C2212yes—
15C22×C4⋊Dic13C2211yescharacteristic
16C22×C4⋊Dic13C2212yes—
17C22×C4⋊Dic13C2211yescharacteristic
18C22×C4⋊Dic13C2212yes—
19C22×#6101C2214yes—
20C22×C4×Dic13C2212yes—
21C4×C13×C4⋊C4C2218yes—
22C2×C13×#95C2212yes—
23C2×#88071C2214yes—
24C2×#88071C2214yes—
25C2×#88071C2214yes—
26C2×#88071C2212yes—
27#11718638C22116yes—
28#11718634C22116yes—
29#11718597C22116yes—
30#11718596C2218yes—
31C4×C4⋊Dic13C2218yes—
32#11718589C22116yes—
33#11718321C22132yes—
34C23×C4×C13C2312yes—
35C23×C4×C13C2312yes—
36C23×C4×C13C2311yescharacteristic
37C23×C4×C13C2311yescharacteristic
38C23×C4×C13C2311yescharacteristic
39C23×Dic13C2312yes—
40C23×Dic13C2312yes—
41C23×Dic13C2314yes—
42C2×C13×C4⋊C4—24no—
43C2×C13×C4⋊C4—24no—
44C2×C13×C4⋊C4C2314yes—
45C2×C13×C4⋊C4C2314yes—
46C2×C42×C13—28no—
47C2×C42×C13Q818yes—
48C2×C42×C13C2318yes—
49C2×C42×C13C2314yes—
50C2×C4⋊Dic13—28no—
51C2×C4⋊Dic13—24no—
52C2×C4⋊Dic13—24no—
53C2×C4⋊Dic13—28no—
54C2×C4⋊Dic13—44no—
55C2×C4⋊Dic13C2314yes—
56C2×C4⋊Dic13C2318yes—
57C2×C4⋊Dic13C2314yes—
58C2×C4⋊Dic13C2318yes—
59C2×C4⋊Dic13C2318yes—
60C2×#6101—48no—
61C2×#6101C23116yes—
62C2×C4×Dic13—28no—
63C2×C4×Dic13C2318yes—
64C13×#95C2318yes—
65#88071C2318yes—
66#88071C23116yes—
67#88071C23116yes—
68#88071C23116yes—
69C2×#2571—131nomaximal, Sylow
70C24×C13C2411yescharacteristic
71C22×C4×C13—22no—
72C22×C4×C13—22no—
73C22×C4×C13—24no—
74C22×C4×C13—24no—
75C22×C4×C13—24no—
76C22×C4×C13—24no—
77C22×C4×C13—24no—
78C22×C4×C13—24no—
79C22×C4×C13C2×Q814yes—
80C22×C4×C13C2×Q814yes—
81C22×C4×C13C2×Q814yes—
82C22×C4×C13#4114yes—
83C22×C4×C13#4114yes—
84C22×C4×C13#4114yes—
85C22×C4×C13#4114yes—
86C22×C4×C13C2414yes—
87C22×C4×C13C2414yes—
88C22×C4×C13C2412yes—
89C22×C4×C13C2412yes—
90C22×C4×C13C2412yes—
91C22×Dic13—24no—
92C22×Dic13—24no—
93C22×Dic13—24no—
94C22×Dic13—24no—
95C22×Dic13—28no—
96C22×Dic13—28no—
97C22×Dic13—24no—
98C22×Dic13—28no—
99C22×Dic13—24no—
100C22×Dic13C2414yes—
101C22×Dic13C2414yes—
102C22×Dic13C2418yes—
103C13×C4⋊C4—28no—
104C13×C4⋊C4—28no—
105C42×C13—216no—
106C42×C13C2×Q8116yes—
107C4⋊Dic13—216no—
108C4⋊Dic13—28no—
109C4⋊Dic13—216no—
110C4⋊Dic13—28no—
111C4⋊Dic13—48no—
112#6101—416no—
113C4×Dic13—216no—
114#2571—1316no—
115C2×#400—134no—
116C2×#389—132no—
117C2×#389—132no—
118C2×#384—131no—
119C2×#382—132no—
120C2×#382—132no—
121C2×C4×C4⋊C4—131no—
122C2×C4×C4⋊C4D1311yescharacteristic
123C23×C13C22×Q812yes—
124C23×C13C2×#4112yes—
125C23×C13C2×#4112yes—
126C23×C13C2×#4112yes—
127C23×C13C2×#4112yes—
128C23×C13H(5,𝔽2)12yes—
129C23×C132−1+412yes—
130C23×C13C2511yescharacteristic
131C2×C4×C13—28no—
132C2×C4×C13—22no—
133C2×C4×C13—22no—
134C2×C4×C13—24no—
135C2×C4×C13—24no—
136C2×C4×C13—24no—
137C2×C4×C13—24no—
138C2×C4×C13—24no—
139C2×C4×C13—24no—
140C2×C4×C13—48no—
141C2×C4×C13—48no—
142C2×C4×C13#125116yes—
143C2×C4×C13#125116yes—
144C2×C4×C13C22×Q814yes—
145C2×C4×C13C22×Q814yes—
146C2×C4×C13C22×Q814yes—
147C2×C4×C13C2×#4114yes—
148C2×C4×C13C2×#4114yes—
149C2×C4×C13C2×#4114yes—
150C2×C4×C13C2×#4114yes—
151C2×Dic13—24no—
152C2×Dic13—24no—
153C2×Dic13—24no—
154C2×Dic13—24no—
155C2×Dic13—28no—
156C2×Dic13—28no—
157C2×Dic13—24no—
158C2×Dic13—28no—
159C2×Dic13—24no—
160C2×Dic13—48no—
161C2×Dic13—48no—
162C2×Dic13—416no—
163C22×C4⋊C4—131no—
164C22×C4⋊C4—131no—
165C22×C4⋊C4—132no—
166C22×C4⋊C4—132no—
167C22×C4⋊C4—134no—
168C22×C4⋊C4—132no—
169C22×C4⋊C4C2×D1311yescharacteristic
170C22×C4⋊C4C2×D1311yescharacteristic
171C22×C42—132no—
172C22×C42C2×D1312yes—
173C22×C42C2×D1311yescharacteristic
174#400—1332no—
175#389—1316no—
176#389—1316no—
177#384—138no—
178#382—1316no—
179#382—1316no—
180C4×C4⋊C4—138no—
181C4×C4⋊C4C2×D1318yes—
182C2×#95—132no—
183C2×#95—134no—
184C2×#95—134no—
185C2×#95—134no—
186C2×#95C2×D1312yes—
187C22×C13C2×#12514yes—
188C22×C13C2×#12514yes—
189C22×C13#54414yes—
190C22×C13#55514yes—
191C22×C13#55614yes—
192C22×C13#55614yes—
193C22×C13#55914yes—
194C22×C13C23×Q811yescharacteristic
195C22×C13C22×#4111yescharacteristic
196C22×C13C22×#4111yescharacteristic
197C22×C13C22×#4111yescharacteristic
198C22×C13C22×#4111yescharacteristic
199C22×C13C2×H(5,𝔽2)11yescharacteristic
200C22×C13C2×2−1+411yescharacteristic
201C4×C13—24no—
202C4×C13—44no—
203C4×C13—44no—
204C4×C13C2×#12518yes—
205C4×C13C2×#12518yes—
206Dic13—44no—
207Dic13—44no—
208Dic13—48no—
209C23×C4—134no—
210C23×C4—132no—
211C23×C4—132no—
212C23×C4C22×D1312yes—
213C23×C4C22×D1312yes—
214C23×C4C22×D1311yescharacteristic
215C23×C4C22×D1311yescharacteristic
216C23×C4C22×D1311yescharacteristic
217C2×C4⋊C4—24no—
218C2×C4⋊C4—24no—
219C2×C4⋊C4—134no—
220C2×C4⋊C4—134no—
221C2×C4⋊C4—138no—
222C2×C4⋊C4—138no—
223C2×C4⋊C4—1316no—
224C2×C4⋊C4—138no—
225C2×C4⋊C4—268no—
226C2×C4⋊C4—264no—
227C2×C4⋊C4—264no—
228C2×C4⋊C4—268no—
229C2×C4⋊C4—528no—
230C2×C4⋊C4—524no—
231C2×C4⋊C4C22×D1314yes—
232C2×C4⋊C4C22×D1314yes—
233C2×C42—28no—
234C2×C42—138no—
235C2×C42—268no—
236C2×C42Dic2618yes—
237C2×C42C22×D1318yes—
238C2×C42C22×D1314yes—
239#95—138no—
240#95—1316no—
241#95—1316no—
242#95—1316no—
243#95C22×D1318yes—
244C2×C13#257118yescomplemented
245C2×C13C22×#12511yescharacteristic
246C2×C13C22×#12511yescharacteristic
247C2×C13C2×#54411yescharacteristic
248C2×C13C2×#55511yescharacteristic
249C2×C13C2×#55611yescharacteristic
250C2×C13C2×#55611yescharacteristic
251C2×C13C2×#55911yescharacteristic
252C24C23×D1311yescharacteristic
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—24no—
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—24no—
259C22×C4—24no—
260C22×C4—24no—
261C22×C4—134no—
262C22×C4—134no—
263C22×C4—138no—
264C22×C4—264no—
265C22×C4—264no—
266C22×C4—268no—
267C22×C4—264no—
268C22×C4—264no—
269C22×C4—268no—
270C22×C4—264no—
271C22×C4—268no—
272C22×C4—264no—
273C22×C4C2×Dic2614yes—
274C22×C4C2×Dic2614yes—
275C22×C4C2×Dic2614yes—
276C22×C4#612714yes—
277C22×C4#612714yes—
278C22×C4#612914yes—
279C22×C4#613114yes—
280C22×C4C23×D1314yes—
281C22×C4C23×D1314yes—
282C22×C4C23×D1312yes—
283C22×C4C23×D1312yes—
284C22×C4C23×D1312yes—
285C4⋊C4—28no—
286C4⋊C4—28no—
287C4⋊C4—2616no—
288C4⋊C4—268no—
289C4⋊C4—268no—
290C4⋊C4—2616no—
291C4⋊C4—5216no—
292C4⋊C4—528no—
293C42—216no—
294C42—2616no—
295C42C2×Dic26116yes—
296C13C2×#257111yescharacteristic, complemented, Sylow
297C23C22×Dic2612yes—
298C23C2×#612712yes—
299C23C2×#612712yes—
300C23C2×#612912yes—
301C23C2×#613112yes—
302C23#8825612yes—
303C23#8825712yes—
304C23C24×D1311yescharacteristic
305C2×C4—28no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—24no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—48no—
315C2×C4—48no—
316C2×C4—264no—
317C2×C4—264no—
318C2×C4—268no—
319C2×C4—264no—
320C2×C4—264no—
321C2×C4—268no—
322C2×C4—264no—
323C2×C4—268no—
324C2×C4—264no—
325C2×C4—528no—
326C2×C4—528no—
327C2×C4—5216no—
328C2×C4#88124116yes—
329C2×C4#88144116yes—
330C2×C4C22×Dic2614yes—
331C2×C4C22×Dic2614yes—
332C2×C4C22×Dic2614yes—
333C2×C4C2×#612714yes—
334C2×C4C2×#612714yes—
335C2×C4C2×#612914yes—
336C2×C4C2×#613114yes—
337C22C2×#8812414yes—
338C22C2×#8814414yes—
339C22#1171922414yes—
340C22#1171924714yes—
341C22#1171926814yes—
342C22#1171928914yes—
343C22#1171929014yes—
344C22C23×Dic2611yescharacteristic
345C22C22×#612711yescharacteristic
346C22C22×#612711yescharacteristic
347C22C22×#612911yescharacteristic
348C22C22×#613111yescharacteristic
349C22C2×#8825611yescharacteristic
350C22C2×#8825711yescharacteristic
351C4—24no—
352C4—44no—
353C4—44no—
354C4—524no—
355C4—524no—
356C4—528no—
357C4C2×#8812418yes—
358C4C2×#8814418yes—
359C2#1312007518yesdirect product factor
360C2C22×#8814411yescharacteristic
361C2C22×#8812411yescharacteristic
362C2C2×#1171922411yescharacteristic
363C2C2×#1171926811yescharacteristic
364C2C2×#1171924711yescharacteristic
365C2C2×#1171928911yescharacteristic
366C2C2×#1171929011yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C4×C13×C4⋊C4C2
socle, prime radicalC24×C13C24
hypercenterC2×C4×C4⋊C4D13
hypocenterC13C2×#2571
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #13120075C2direct (N × H)
244. C2×C13#2571semidirect
296. C13C2×#2571semidirect
359. C2#13120075direct (N × H)

Maximal subgroups

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

subgroupindex
#131200752
C2×#117183212
C2×#117185892
C2×#117186342
C2×#117185962
C2×#117185972
C2×#117186382
C2×C4×C4⋊Dic132
C2×C4×C13×C4⋊C42
C2×#257113