Finite Group Databasebeta

← C2×#13071362 #14912610

Subgroups — C2×#13071362 #14912610

Order 2816.

2526 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66922C211yesmaximal, characteristic
2#13071362C2116yesmaximal, direct product factor
3C2×#10622259C214yesmaximal
4C2×#10622586C212yesmaximal
5C2×#10622266C214yesmaximal
6C2×C4⋊C4×Dic11C212yesmaximal
7C2×#10622545C211yesmaximal, characteristic
8C2×C11×#382C211yesmaximal, characteristic
9C23×Dic22C2212yes—
10C22×C11×C4⋊C4C2212yes—
11C22×C42×C11C2211yescharacteristic
12C22×C4⋊Dic11C2212yes—
13C22×C4⋊Dic11C2212yes—
14C22×Dic11⋊C4C2214yes—
15C22×C4×Dic11C2211yescharacteristic
16C22×C4×Dic11C2214yes—
17C22×C4×Dic11C2211yescharacteristic
18C2×#66922C4116yescomplemented
19C2×#66922C2218yes—
20C11×#382C2218yes—
21C2×C11×#95C2212yes—
22C2×C11×#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2214yes—
26C2×C11⋊#95C2214yes—
27C4⋊C4×Dic11C22116yes—
28#10622586C22116yes—
29#10622545C2218yes—
30#10622266C22132yes—
31#10622259C22132yes—
32C23×C4×C11C2314yes—
33C23×C4×C11C2311yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×Dic11C2312yes—
37C23×Dic11C2314yes—
38C23×Dic11C2312yes—
39C22×Dic22—48no—
40C22×Dic22C2×C4116yes—
41C22×Dic22C2318yes—
42C2×C11×C4⋊C4—28no—
43C2×C11×C4⋊C4C2318yes—
44C2×C42×C11C2×C418yes—
45C2×C42×C11C2314yes—
46C2×C4⋊Dic11C2×C4116yes—
47C2×C4⋊Dic11C2×C4116yes—
48C2×C4⋊Dic11C2318yes—
49C2×C4⋊Dic11C2318yes—
50C2×Dic11⋊C4—48no—
51C2×Dic11⋊C4C23116yes—
52C2×C4×Dic11—24no—
53C2×C4×Dic11—48no—
54C2×C4×Dic11Q818yescomplemented
55C2×C4×Dic11C2314yes—
56C2×C4×Dic11C23116yes—
57C2×C4×Dic11C2314yes—
58#66922C2×C4164yescomplemented
59C11×#95C2318yes—
60C11×#95C2318yes—
61C11⋊#95C2318yes—
62C11⋊#95C23116yes—
63C11⋊#95C23116yes—
64C11⋊#95C2318yes—
65C2×#2331—111nomaximal, Sylow
66C24×C11C2411yescharacteristic
67C22×C4×C11—24no—
68C22×C4×C11—24no—
69C22×C4×C11—28no—
70C22×C4×C11—28no—
71C22×C4×C11—28no—
72C22×C4×C11C22×C414yes—
73C22×C4×C11C22×C414yes—
74C22×C4×C11C22×C414yes—
75C22×C4×C11C2×Q814yes—
76C22×C4×C11#4114yes—
77C22×C4×C11C2418yes—
78C22×C4×C11C2412yes—
79C22×C4×C11C2412yes—
80C22×C4×C11C2412yes—
81C22×Dic11—24no—
82C22×Dic11—24no—
83C22×Dic11—28no—
84C22×Dic11—28no—
85C22×Dic11—24no—
86C22×Dic11—24no—
87C22×Dic11—24no—
88C22×Dic11C22×C4116yes—
89C22×Dic11C2×Q818yes—
90C22×Dic11C2414yes—
91C22×Dic11C2418yes—
92C22×Dic11C2414yes—
93C2×Dic22—432no—
94C2×Dic22—416no—
95C2×Dic22C22×C4132yes—
96C11×C4⋊C4—216no—
97C42×C11C22×C4116yes—
98C4⋊Dic11C22×C4132yes—
99C4⋊Dic11C22×C4132yes—
100Dic11⋊C4—416no—
101C4×Dic11—28no—
102C4×Dic11—416no—
103C4×Dic11C2×Q8116yescomplemented
104C22×C4⋊Q8—111no—
105#2331—1116no—
106C2×#391—114no—
107C2×#389—112no—
108C2×#387—114no—
109C2×#382D1111yescharacteristic
110C2×C4×C4⋊C4—112no—
111C2×#376—111no—
112C23×C11C23×C412yes—
113C23×C11C22×Q812yes—
114C23×C11C2×#4112yes—
115C23×C11H(5,𝔽2)14yes—
116C23×C112−1+414yes—
117C23×C11C2511yescharacteristic
118C2×C4×C11—28no—
119C2×C4×C11—28no—
120C2×C4×C11—24no—
121C2×C4×C11—24no—
122C2×C4×C11—28no—
123C2×C4×C11—28no—
124C2×C4×C11—28no—
125C2×C4×C11—416no—
126C2×C4×C11C4×Q8116yes—
127C2×C4×C11C23×C414yes—
128C2×C4×C11C23×C414yes—
129C2×C4×C11C23×C414yes—
130C2×C4×C11C22×Q814yes—
131C2×C4×C11C2×#4114yes—
132C2×Dic11—232no—
133C2×Dic11—216no—
134C2×Dic11—24no—
135C2×Dic11—28no—
136C2×Dic11—28no—
137C2×Dic11—24no—
138C2×Dic11—24no—
139C2×Dic11—24no—
140C2×Dic11—24no—
141C2×Dic11—48no—
142C2×Dic11C23×C4116yes—
143C2×Dic11C22×Q818yes—
144Dic22—432no—
145C23×Q8—112no—
146C2×C4⋊Q8—118no—
147C2×C4⋊Q8—1116no—
148C22×C4⋊C4—112no—
149C22×C4⋊C4—112no—
150C22×C4⋊C4—114no—
151C22×C4⋊C4C2×D1112yes—
152C22×C42—111no—
153C22×C42—111no—
154C22×C42—114no—
155C22×C42C2×D1111yescharacteristic
156#391—1132no—
157#389—1116no—
158#387—1132no—
159#382C2×D1118yes—
160C4×C4⋊C4—1116no—
161#376—118no—
162C2×#95—112no—
163C2×#95—112no—
164C2×#95—114no—
165C2×#95—114no—
166C2×#95C2×D1112yes—
167C2×#95C2×D1112yes—
168C22×C11C2×C4×Q814yes—
169C22×C11#51814yes—
170C22×C11#51914yes—
171C22×C11#54218yes—
172C22×C11#54418yes—
173C22×C11C24×C411yescharacteristic
174C22×C11C23×Q811yescharacteristic
175C22×C11C22×#4111yescharacteristic
176C22×C11C2×H(5,𝔽2)12yes—
177C22×C11C2×2−1+412yes—
178C4×C11—24no—
179C4×C11—24no—
180C4×C11—48no—
181C4×C11C2×C4×Q818yes—
182Dic11—216no—
183Dic11—28no—
184Dic11—44no—
185C22×Q8—1116no—
186C22×Q8—118no—
187C22×Q8—448no—
188C23×C4—114no—
189C23×C4—112no—
190C23×C4—112no—
191C23×C4C22×D1114yes—
192C23×C4C22×D1111yescharacteristic
193C23×C4C22×D1111yescharacteristic
194C23×C4C22×D1111yescharacteristic
195C4⋊Q8—1164no—
196C2×C4⋊C4—28no—
197C2×C4⋊C4—1116no—
198C2×C4⋊C4—1116no—
199C2×C4⋊C4—118no—
200C2×C4⋊C4—118no—
201C2×C4⋊C4—1116no—
202C2×C4⋊C4—448no—
203C2×C4⋊C4C22×D1118yes—
204C2×C42—118no—
205C2×C42—114no—
206C2×C42—114no—
207C2×C42—1116no—
208C2×C42—224no—
209C2×C42—448no—
210C2×C42C4×D1118yes—
211C2×C42C22×D1114yes—
212#95—118no—
213#95—118no—
214#95—1116no—
215#95—1116no—
216#95C22×D1118yes—
217#95C22×D1118yes—
218C2×C11#233118yescomplemented
219C2×C11C22×C4×Q811yescharacteristic
220C2×C11C2×#51811yescharacteristic
221C2×C11C2×#51911yescharacteristic
222C2×C11C2×#54212yes—
223C2×C11C2×#54412yes—
224C24C23×D1111yescharacteristic
225C2×Q8—1132no—
226C2×Q8—4432no—
227C2×Q8—4416no—
228C22×C4—24no—
229C22×C4—24no—
230C22×C4—28no—
231C22×C4—28no—
232C22×C4—28no—
233C22×C4—1116no—
234C22×C4—118no—
235C22×C4—114no—
236C22×C4—118no—
237C22×C4—114no—
238C22×C4—224no—
239C22×C4—228no—
240C22×C4—228no—
241C22×C4—224no—
242C22×C4—224no—
243C22×C4—224no—
244C22×C4—224no—
245C22×C4C2×C4×D1114yes—
246C22×C4C2×C4×D1114yes—
247C22×C4C2×C4×D1114yes—
248C22×C4#434114yes—
249C22×C4Q8×D1114yes—
250C22×C4C23×D1118yes—
251C22×C4C23×D1112yes—
252C22×C4C23×D1112yes—
253C22×C4C23×D1112yes—
254C4⋊C4—216no—
255C4⋊C4—1132no—
256C4⋊C4—1132no—
257C4⋊C4—4416no—
258C42—1116no—
259C42—228no—
260C42—4416no—
261C42C2×C4×D11116yes—
262C11C2×#233111yescharacteristic, complemented, Sylow
263C23C22×C4×D1112yes—
264C23C2×#434112yes—
265C23C2×Q8×D1112yes—
266C23#6704214yes—
267C23#6704314yes—
268C23C24×D1111yescharacteristic
269Q8—4432no—
270C2×C4—28no—
271C2×C4—28no—
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—28no—
275C2×C4—28no—
276C2×C4—28no—
277C2×C4—416no—
278C2×C4—1116no—
279C2×C4—118no—
280C2×C4—2232no—
281C2×C4—224no—
282C2×C4—228no—
283C2×C4—228no—
284C2×C4—224no—
285C2×C4—2216no—
286C2×C4—224no—
287C2×C4—224no—
288C2×C4—224no—
289C2×C4—448no—
290C2×C4#66940116yes—
291C2×C4C22×C4×D1114yes—
292C2×C4C22×C4×D1114yes—
293C2×C4C22×C4×D1114yes—
294C2×C4C2×#434114yes—
295C2×C4C2×Q8×D1114yes—
296C22C2×#6694014yes—
297C22#1062304714yes—
298C22#1062305214yes—
299C22#1062321318yes—
300C22#1062322018yes—
301C22C23×C4×D1111yescharacteristic
302C22C22×#434111yescharacteristic
303C22C22×Q8×D1111yescharacteristic
304C22C2×#6704212yes—
305C22C2×#6704312yes—
306C4—24no—
307C4—24no—
308C4—48no—
309C4—228no—
310C4—2216no—
311C4—444no—
312C4C2×#6694018yes—
313C2#1307136218yesdirect product factor
314C2C22×#6694011yescharacteristic
315C2C2×#1062305211yescharacteristic
316C2C2×#1062304711yescharacteristic
317C2C2×#1062321312yes—
318C2C2×#1062322012yes—
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#382C2
socle, prime radicalC24×C11C24
cosocleC23×C11C25
hypercenterC2×#382D11
hypocenterC11C2×#2331
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
2. #13071362C2direct (N × H)
18. C2×#66922C4semidirect
54. C2×C4×Dic11Q8semidirect
58. #66922C2×C4semidirect
103. C4×Dic11C2×Q8semidirect
218. C2×C11#2331semidirect
262. C11C2×#2331semidirect
313. C2#13071362direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669222
#130713622
C2×#106222592
C2×#106225862
C2×#106222662
C2×C4⋊C4×Dic112
C2×#106225452
C2×C11×#3822
C2×#233111