Finite Group Databasebeta

← C2×#13122902 #16069459

Subgroups — C2×#13122902 #16069459

Order 3328.

2046 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88143C212yesmaximal
2#13122902C2116yesmaximal, direct product factor
3C2×#11718321C212yesmaximal
4C2×#11718319C212yesmaximal
5C2×#11718318C212yesmaximal
6C2×#11718645C212yesmaximal
7C2×#11718645C212yesmaximal
8C2×#11718644C211yesmaximal, characteristic
9C2×#11718638C211yesmaximal, characteristic
10C2×C13×#398C211yesmaximal, characteristic
11C22×C13×C4⋊C4C2212yes—
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C4⋊Dic13C2212yes—
15C22×C4⋊Dic13C2211yescharacteristic
16C22×C4⋊Dic13C2211yescharacteristic
17C22×#6101C2212yes—
18C22×#6101C2212yes—
19C22×#6101C2212yes—
20C22×#6101C2212yes—
21C22×#6101C2212yes—
22C22×C4×Dic13C2211yescharacteristic
23C2×#88143—216no—
24C2×#88143C22116yes—
25C13×#398C2218yes—
26C2×C13×#95C2212yes—
27C2×C13×#95C2211yescharacteristic
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2211yescharacteristic
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35#11718645C22116yes—
36#11718645C22116yes—
37#11718644C2218yes—
38#11718638C2218yes—
39#11718321C22116yes—
40#11718319C22116yes—
41#11718318C22116yes—
42C23×C4×C13C2312yes—
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C23×Dic13C2312yes—
48C23×Dic13C2312yes—
49C23×Dic13C2312yes—
50C23×Dic13C2312yes—
51C2×C13×C4⋊C4—28no—
52C2×C13×C4⋊C4—42no—
53C2×C13×C4⋊C4—42no—
54C2×C13×C4⋊C4C2318yes—
55C2×C13×C4⋊C4C2314yes—
56C2×C13×C4⋊C4C2314yes—
57C2×C4⋊Dic13—28no—
58C2×C4⋊Dic13—42no—
59C2×C4⋊Dic13—42no—
60C2×C4⋊Dic13C2318yes—
61C2×C4⋊Dic13C2314yes—
62C2×C4⋊Dic13C2314yes—
63C2×#6101—28no—
64C2×#6101—28no—
65C2×#6101—28no—
66C2×#6101—28no—
67C2×#6101—44no—
68C2×#6101C2318yes—
69C2×#6101C2318yes—
70C2×#6101C2318yes—
71C2×#6101C2318yes—
72C2×#6101C2318yes—
73C2×C4×Dic13D418yes—
74C2×C4×Dic13C2314yes—
75#88143—264no—
76C13×#95C2318yes—
77C13×#95C2314yes—
78#88071C2318yes—
79#88071C2318yes—
80#88071C2318yes—
81#88071C2318yes—
82#88071C2318yes—
83#88071C2314yes—
84#88071C2318yes—
85C2×#2822—131nomaximal, Sylow
86C24×C13C2411yescharacteristic
87C22×C4×C13—22no—
88C22×C4×C13—22no—
89C22×C4×C13—24no—
90C22×C4×C13—24no—
91C22×C4×C13—24no—
92C22×C4×C13—22no—
93C22×C4×C13—22no—
94C22×C4×C13—24no—
95C22×C4×C13—24no—
96C22×C4×C13—24no—
97C22×C4×C13—24no—
98C22×C4×C13—24no—
99C22×C4×C13C2×D414yes—
100C22×C4×C13C2412yes—
101C22×C4×C13C2412yes—
102C22×C4×C13C2414yes—
103C22×C4×C13C2414yes—
104C22×C4×C13C2412yes—
105C22×Dic13—24no—
106C22×Dic13—24no—
107C22×Dic13—24no—
108C22×Dic13—24no—
109C22×Dic13—24no—
110C22×Dic13—24no—
111C22×Dic13—24no—
112C22×Dic13—24no—
113C22×Dic13—24no—
114C22×Dic13—28no—
115C22×Dic13C2×D418yes—
116C22×Dic13C2414yes—
117C22×Dic13C2414yes—
118C22×Dic13C2414yes—
119C22×Dic13C2414yes—
120C13×C4⋊C4—216no—
121C13×C4⋊C4—44no—
122C13×C4⋊C4—44no—
123C4⋊Dic13—216no—
124C4⋊Dic13—44no—
125C4⋊Dic13—44no—
126#6101—216no—
127#6101—216no—
128#6101—216no—
129#6101—216no—
130#6101—48no—
131C4×Dic13C2×D4116yes—
132C22×#125—132no—
133#2822—1316no—
134C2×#400—132no—
135C2×#400—132no—
136C2×#398—132no—
137C2×#398—131no—
138C2×#398—132no—
139C2×#398—132no—
140C2×#398D1311yescharacteristic
141C2×#382—131no—
142C23×C13C22×D412yes—
143C23×C13H(5,𝔽2)12yes—
144C23×C132−1+414yes—
145C23×C132−1+414yes—
146C23×C132−1+412yes—
147C23×C13C2511yescharacteristic
148C2×C4×C13—28no—
149C2×C4×C13—22no—
150C2×C4×C13—22no—
151C2×C4×C13—24no—
152C2×C4×C13—24no—
153C2×C4×C13—24no—
154C2×C4×C13—22no—
155C2×C4×C13—22no—
156C2×C4×C13—24no—
157C2×C4×C13—24no—
158C2×C4×C13—24no—
159C2×C4×C13—24no—
160C2×C4×C13—24no—
161C2×C4×C13—48no—
162C2×C4×C13—48no—
163C2×C4×C13—44no—
164C2×C4×C13—44no—
165C2×C4×C13C22×D414yes—
166C2×Dic13—216no—
167C2×Dic13—24no—
168C2×Dic13—24no—
169C2×Dic13—24no—
170C2×Dic13—24no—
171C2×Dic13—24no—
172C2×Dic13—24no—
173C2×Dic13—24no—
174C2×Dic13—24no—
175C2×Dic13—24no—
176C2×Dic13—28no—
177C2×Dic13—48no—
178C2×Dic13—48no—
179C2×Dic13—48no—
180C2×Dic13C22×D418yes—
181C2×#125—1316no—
182C2×#125—2616no—
183C22×C4⋊C4—132no—
184C22×C4⋊C4—132no—
185C22×C4⋊C4—132no—
186C22×C4⋊C4—132no—
187C22×C4⋊C4—132no—
188C22×C4⋊C4—132no—
189C22×C4⋊C4—131no—
190C22×C4⋊C4—131no—
191C22×C4⋊C4C2×D1312yes—
192C22×C4⋊C4C2×D1311yescharacteristic
193C22×C4⋊C4C2×D1311yescharacteristic
194C22×C42—131no—
195#400—1316no—
196#400—1316no—
197#398—138no—
198#398—1316no—
199#398—1316no—
200#398—1316no—
201#398C2×D1318yes—
202#382—138no—
203C2×#95—132no—
204C2×#95—132no—
205C2×#95—132no—
206C2×#95—131no—
207C2×#95—132no—
208C2×#95—132no—
209C2×#95—132no—
210C2×#95C2×D1312yes—
211C2×#95C2×D1311yescharacteristic
212C22×C13#53618yes—
213C22×C13#53714yes—
214C22×C13#56314yes—
215C22×C13#56314yes—
216C22×C13#56418yes—
217C22×C13C23×D411yescharacteristic
218C22×C13C2×H(5,𝔽2)11yescharacteristic
219C22×C13C2×2−1+412yes—
220C22×C13C2×2−1+412yes—
221C22×C13C2×2−1+411yescharacteristic
222C4×C13—24no—
223C4×C13—44no—
224C4×C13—44no—
225C4×C13—42no—
226C4×C13—42no—
227Dic13—28no—
228Dic13—44no—
229Dic13—44no—
230Dic13—44no—
231C23×C4—132no—
232C23×C4—132no—
233C23×C4—132no—
234C23×C4—132no—
235C23×C4C22×D1312yes—
236C23×C4C22×D1312yes—
237C23×C4C22×D1311yescharacteristic
238C23×C4C22×D1311yescharacteristic
239C23×C4C22×D1311yescharacteristic
240#125—2664no—
241C2×C4⋊C4—28no—
242C2×C4⋊C4—42no—
243C2×C4⋊C4—42no—
244C2×C4⋊C4—138no—
245C2×C4⋊C4—138no—
246C2×C4⋊C4—138no—
247C2×C4⋊C4—138no—
248C2×C4⋊C4—138no—
249C2×C4⋊C4—138no—
250C2×C4⋊C4—134no—
251C2×C4⋊C4—134no—
252C2×C4⋊C4—268no—
253C2×C4⋊C4—268no—
254C2×C4⋊C4—268no—
255C2×C4⋊C4—268no—
256C2×C4⋊C4—268no—
257C2×C4⋊C4—524no—
258C2×C4⋊C4—522no—
259C2×C4⋊C4—522no—
260C2×C4⋊C4C22×D1318yes—
261C2×C4⋊C4C22×D1314yes—
262C2×C4⋊C4C22×D1314yes—
263C2×C42—138no—
264C2×C42—134no—
265#95—138no—
266#95—138no—
267#95—138no—
268#95—138no—
269#95—138no—
270#95—138no—
271#95—134no—
272#95C22×D1318yes—
273#95C22×D1314yes—
274C2×C13#282218yescomplemented
275C2×C13C2×#53612yes—
276C2×C13C2×#53711yescharacteristic
277C2×C13C2×#56311yescharacteristic
278C2×C13C2×#56311yescharacteristic
279C2×C13C2×#56412yes—
280C24C23×D1311yescharacteristic
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—22no—
286C22×C4—24no—
287C22×C4—22no—
288C22×C4—24no—
289C22×C4—24no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—24no—
293C22×C4—138no—
294C22×C4—134no—
295C22×C4—134no—
296C22×C4—134no—
297C22×C4—134no—
298C22×C4—264no—
299C22×C4—264no—
300C22×C4—264no—
301C22×C4—264no—
302C22×C4—264no—
303C22×C4—264no—
304C22×C4—268no—
305C22×C4—264no—
306C22×C4—264no—
307C22×C4—264no—
308C22×C4D4×D1314yes—
309C22×C4C23×D1312yes—
310C22×C4C23×D1312yes—
311C22×C4C23×D1314yes—
312C22×C4C23×D1314yes—
313C22×C4C23×D1312yes—
314C4⋊C4—216no—
315C4⋊C4—44no—
316C4⋊C4—44no—
317C4⋊C4—2616no—
318C4⋊C4—2616no—
319C4⋊C4—2616no—
320C4⋊C4—2616no—
321C4⋊C4—2616no—
322C4⋊C4—528no—
323C4⋊C4—524no—
324C4⋊C4—524no—
325C42—1316no—
326C13C2×#282211yescharacteristic, complemented, Sylow
327C23C2×D4×D1312yes—
328C23#8825112yes—
329C23#8825414yes—
330C23#8825712yes—
331C23#8825714yes—
332C23C24×D1311yescharacteristic
333C2×C4—28no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—24no—
337C2×C4—24no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—48no—
347C2×C4—48no—
348C2×C4—44no—
349C2×C4—44no—
350C2×C4—138no—
351C2×C4—2616no—
352C2×C4—264no—
353C2×C4—264no—
354C2×C4—264no—
355C2×C4—264no—
356C2×C4—264no—
357C2×C4—264no—
358C2×C4—268no—
359C2×C4—264no—
360C2×C4—264no—
361C2×C4—264no—
362C2×C4—528no—
363C2×C4—528no—
364C2×C4—528no—
365C2×C4C2×D4×D1314yes—
366C22#1171930214yes—
367C22#1171933318yes—
368C22#1171935614yes—
369C22C13⋊#56418yes—
370C22#1171944014yes—
371C22C22×D4×D1311yescharacteristic
372C22C2×#8825111yescharacteristic
373C22C2×#8825412yes—
374C22C2×#8825712yes—
375C22C2×#8825711yescharacteristic
376C4—24no—
377C4—42no—
378C4—42no—
379C4—44no—
380C4—44no—
381C4—268no—
382C4—524no—
383C4—524no—
384C4—524no—
385C2#1312290218yesdirect product factor
386C2C2×#1171933312yes—
387C2C2×#1171930211yescharacteristic
388C2C2×#1171944011yescharacteristic
389C2C2×#1171935611yescharacteristic
390C2C2×C13⋊#56412yes—
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#398C2
socle, prime radicalC24×C13C24
hypercenterC2×#398D13
hypocenterC13C2×#2822
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
2. #13122902C2direct (N × H)
274. C2×C13#2822semidirect
326. C13C2×#2822semidirect
385. C2#13122902direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881432
#131229022
C2×#117183212
C2×#117183192
C2×#117183182
C2×#117186452
C2×#117186442
C2×#117186382
C2×C13×#3982
C2×#282213