Finite Group Databasebeta

← C2×#13074552 #14920873

Subgroups — C2×#13074552 #14920873

Order 2816.

2806 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66922C211yesmaximal, characteristic, complemented
2C22×#66928C211yesmaximal, characteristic
3#13074552C2116yesmaximal, direct product factor
4C2×#10622287C214yesmaximal, complemented
5C2×#10622286C214yesmaximal, complemented
6C2×#10622542C212yesmaximal, complemented
7C2×#10622552C212yesmaximal
8C2×C11×#376C211yesmaximal, characteristic, complemented
9C23×D44C2211yescharacteristic
10C23×Dic22C2211yescharacteristic
11C23×Dic22C2212yes—
12C22×C42×C11C2212yes—
13C22×C42×C11C2211yescharacteristic
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2218yes—
17C22×C4⋊Dic11C2212yes—
18C22×C4⋊Dic11C2212yes—
19C2×#66928—28no—
20C2×#66928C2218yes—
21C2×#66922—28no—
22C2×#66922C2218yescomplemented
23C11×#376C2218yescomplemented
24C2×C11×#95C2212yes—
25C2×C11×#95C2212yes—
26C2×C11⋊#95C2218yes—
27#10622552C22116yes—
28#10622542C22116yescomplemented
29#10622287C22132yescomplemented
30#10622286C22132yescomplemented
31C24×D11C2312yes—
32C23×C4×C11C2314yes—
33C23×C4×C11C2311yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×Dic11C2314yes—
37C23×Dic11C2312yes—
38C22×D44—24no—
39C22×D44—28no—
40C22×D44C2314yes—
41C22×Dic22—28no—
42C22×Dic22—24no—
43C22×Dic22—28no—
44C22×Dic22—48no—
45C22×Dic22C2314yes—
46C22×Dic22C2318yes—
47C2×C42×C11—28no—
48C2×C42×C11D418yes—
49C2×C42×C11C2318yes—
50C2×C42×C11C2314yes—
51C2×(C2×D11)⋊C4—28no—
52C2×(C2×D11)⋊C4—28no—
53C2×(C2×D11)⋊C4—416no—
54C2×(C2×D11)⋊C4C2318yes—
55C2×(C2×D11)⋊C4C2318yes—
56C2×(C2×D11)⋊C4C23132yes—
57C2×C4⋊Dic11—28no—
58C2×C4⋊Dic11—28no—
59C2×C4⋊Dic11C2318yes—
60C2×C4⋊Dic11C2318yes—
61#66928—232no—
62#66922—232no—
63C11×#95C2318yes—
64C11×#95C2318yes—
65C11⋊#95C23132yes—
66C2×#2640—111nomaximal, Sylow
67C24×C11C2411yescharacteristic
68C23×D11—24no—
69C23×D11—28no—
70C23×D11—28no—
71C23×D11—28no—
72C23×D11C2414yes—
73C22×C4×C11—24no—
74C22×C4×C11—24no—
75C22×C4×C11—28no—
76C22×C4×C11—28no—
77C22×C4×C11—28no—
78C22×C4×C11C2×D414yes—
79C22×C4×C11C2×D414yes—
80C22×C4×C11C2×D414yes—
81C22×C4×C11#4118yes—
82C22×C4×C11C2418yes—
83C22×C4×C11C2412yes—
84C22×C4×C11C2412yes—
85C22×C4×C11C2412yes—
86C22×Dic11—28no—
87C22×Dic11—24no—
88C22×Dic11—28no—
89C22×Dic11—216no—
90C22×Dic11C2414yes—
91C22×Dic11C2418yes—
92C2×D44—28no—
93C2×D44—216no—
94C2×D44—416no—
95C2×Dic22—216no—
96C2×Dic22—28no—
97C2×Dic22—216no—
98C2×Dic22—416no—
99C2×Dic22—432no—
100C2×Dic22—416no—
101C42×C11—216no—
102C42×C11C2×D4116yes—
103(C2×D11)⋊C4—216no—
104(C2×D11)⋊C4—216no—
105(C2×D11)⋊C4—432no—
106C4⋊Dic11—216no—
107C4⋊Dic11—216no—
108C22×C4⋊Q8—111no—
109C22×#124—111no—
110#2640—1116no—
111C2×#397—114no—
112C2×#393—114no—
113C2×#391—112no—
114C2×#390—112no—
115C2×#376D1111yescharacteristic, complemented
116C23×C11C22×D412yes—
117C23×C11C2×#4114yes—
118C23×C11H(5,𝔽2)14yes—
119C23×C112−1+414yes—
120C23×C11C2511yescharacteristic
121C22×D11—24no—
122C22×D11—28no—
123C22×D11—28no—
124C22×D11—28no—
125C22×D11—48no—
126C22×D11—48no—
127C22×D11—48no—
128C22×D11—432no—
129C2×C4×C11—28no—
130C2×C4×C11—28no—
131C2×C4×C11—24no—
132C2×C4×C11—24no—
133C2×C4×C11—28no—
134C2×C4×C11—28no—
135C2×C4×C11—28no—
136C2×C4×C11—416no—
137C2×C4×C11#124116yes—
138C2×C4×C11C22×D414yes—
139C2×C4×C11C22×D414yes—
140C2×C4×C11C22×D414yes—
141C2×C4×C11C2×#4118yes—
142C2×Dic11—28no—
143C2×Dic11—24no—
144C2×Dic11—28no—
145C2×Dic11—216no—
146C2×Dic11—48no—
147C2×Dic11—416no—
148D44—416no—
149Dic22—432no—
150Dic22—416no—
151C23×Q8—111no—
152C23×Q8—112no—
153C23×D4—111no—
154C2×C4⋊Q8—118no—
155C2×C4⋊Q8—228no—
156C2×#124—118no—
157C2×#124—228no—
158C22×C4⋊C4—112no—
159C22×C4⋊C4—112no—
160C22×C22⋊C4—112no—
161C22×C22⋊C4—112no—
162C22×C22⋊C4—118no—
163C22×C42C2×D1112yes—
164C22×C42C2×D1111yescharacteristic
165#397—1132no—
166#393—1132no—
167#391—1116no—
168#390—1116no—
169#376C2×D1118yescomplemented
170C2×#95—118no—
171C2×#95C2×D1112yes—
172C2×#95C2×D1112yes—
173C22×C11C2×#12414yes—
174C22×C11#53514yes—
175C22×C11#53614yes—
176C22×C11#542116yes—
177C22×C11C23×D411yescharacteristic
178C22×C11C22×#4112yes—
179C22×C11C2×H(5,𝔽2)12yes—
180C22×C11C2×2−1+412yes—
181C2×D11—44no—
182C2×D11—44no—
183C2×D11—44no—
184C2×D11—416no—
185C2×D11—816no—
186C4×C11—24no—
187C4×C11—24no—
188C4×C11—48no—
189C4×C11C2×#12418yes—
190Dic11—44no—
191Dic11—48no—
192C25—112no—
193C22×Q8—114no—
194C22×Q8—118no—
195C22×Q8—224no—
196C22×Q8—228no—
197C22×Q8—228no—
198C22×Q8—448no—
199C22×D4—114no—
200C22×D4—224no—
201C22×D4—228no—
202C23×C4—114no—
203C23×C4—112no—
204C23×C4C22×D1114yes—
205C23×C4C22×D1111yescharacteristic
206C23×C4C22×D1111yescharacteristic
207C23×C4C22×D1111yescharacteristic
208C4⋊Q8—2232no—
209#124—2232no—
210C2×C4⋊C4—118no—
211C2×C4⋊C4—118no—
212C2×C4⋊C4—228no—
213C2×C4⋊C4—228no—
214C2×C22⋊C4—118no—
215C2×C22⋊C4—118no—
216C2×C22⋊C4—1132no—
217C2×C22⋊C4—228no—
218C2×C22⋊C4—228no—
219C2×C22⋊C4—4416no—
220C2×C42—28no—
221C2×C42D4418yes—
222C2×C42C22×D1118yes—
223C2×C42C22×D1114yes—
224#95—1132no—
225#95C22×D1118yes—
226#95C22×D1118yes—
227C2×C11#264018yescomplemented
228C2×C11C22×#12411yescharacteristic
229C2×C11C2×#53511yescharacteristic
230C2×C11C2×#53611yescharacteristic
231C2×C11C2×#54214yes—
232D11—84no—
233C24—114no—
234C24—224no—
235C24—228no—
236C24—228no—
237C24—228no—
238C24C23×D1111yescharacteristic
239C2×Q8—228no—
240C2×Q8—2216no—
241C2×Q8—2216no—
242C2×Q8—4416no—
243C2×Q8—4432no—
244C2×Q8—4416no—
245C2×D4—228no—
246C2×D4—2216no—
247C2×D4—4416no—
248C22×C4—24no—
249C22×C4—24no—
250C22×C4—28no—
251C22×C4—28no—
252C22×C4—28no—
253C22×C4—114no—
254C22×C4—118no—
255C22×C4—224no—
256C22×C4—228no—
257C22×C4—228no—
258C22×C4—2216no—
259C22×C4C2×D4414yes—
260C22×C4C2×D4414yes—
261C22×C4C2×D4414yes—
262C22×C4#433918yes—
263C22×C4C23×D1118yes—
264C22×C4C23×D1112yes—
265C22×C4C23×D1112yes—
266C22×C4C23×D1112yes—
267C4⋊C4—2216no—
268C4⋊C4—2216no—
269C22⋊C4—2216no—
270C22⋊C4—2216no—
271C22⋊C4—4432no—
272C42—216no—
273C42C2×D44116yes—
274C11C2×#264011yescharacteristic, complemented, Sylow
275C23—224no—
276C23—228no—
277C23—228no—
278C23—228no—
279C23—448no—
280C23—448no—
281C23—448no—
282C23—4432no—
283C23C22×D4412yes—
284C23C2×#433914yes—
285C23#6704214yes—
286C23#6704314yes—
287C23C24×D1111yescharacteristic
288Q8—4432no—
289Q8—4416no—
290D4—4416no—
291C2×C4—28no—
292C2×C4—28no—
293C2×C4—24no—
294C2×C4—24no—
295C2×C4—28no—
296C2×C4—28no—
297C2×C4—28no—
298C2×C4—416no—
299C2×C4—224no—
300C2×C4—228no—
301C2×C4—228no—
302C2×C4—2216no—
303C2×C4—448no—
304C2×C4—4416no—
305C2×C4#66928116yes—
306C2×C4C22×D4414yes—
307C2×C4C22×D4414yes—
308C2×C4C22×D4414yes—
309C2×C4C2×#433918yes—
310C22—444no—
311C22—444no—
312C22—444no—
313C22—4416no—
314C22—8816no—
315C22C2×#6692814yes—
316C22#1062305614yes—
317C22#1062305714yes—
318C22#10623065116yes—
319C22C23×D4411yescharacteristic
320C22C22×#433912yes—
321C22C2×#6704212yes—
322C22C2×#6704312yes—
323C4—24no—
324C4—24no—
325C4—48no—
326C4—444no—
327C4—448no—
328C4C2×#6692818yes—
329C2—884no—
330C2#1307455218yesdirect product factor
331C2C22×#6692811yescharacteristic
332C2C2×#1062305611yescharacteristic
333C2C2×#1062305711yescharacteristic
334C2C2×#1062306514yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#376C2
socleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#376D11
hypocenterC11C2×#2640
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#376

Complements

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

NH ≅ G/Ntype
1. C22×#66922C2semidirect
3. #13074552C2direct (N × H)
4. C2×#10622287C2semidirect
5. C2×#10622286C2semidirect
6. C2×#10622542C2semidirect
8. C2×C11×#376C2semidirect
22. C2×#66922C22semidirect
23. C11×#376C22semidirect
28. #10622542C22semidirect
29. #10622287C22semidirect
30. #10622286C22semidirect
115. C2×#376D11semidirect
169. #376C2×D11semidirect
227. C2×C11#2640semidirect
274. C11C2×#2640semidirect
330. C2#13074552direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669222
C22×#669282
#130745522
C2×#106222872
C2×#106222862
C2×#106225422
C2×#106225522
C2×C11×#3762
C2×#264011