Finite Group Databasebeta

← C2×#13074557 #14920875

Subgroups — C2×#13074557 #14920875

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×#66928C211yesmaximal, characteristic
2#13074557C2116yesmaximal, direct product factor
3C2×#10622606C214yesmaximal, complemented
4C2×#10622844C214yesmaximal, complemented
5C2×#10622587C212yesmaximal, complemented
6C2×#10622601C212yesmaximal
7C2×#10622545C211yesmaximal, characteristic, complemented
8C22×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2212yes—
10C23×D44C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C2×C11×C4⋊Q8—28no—
13C2×C11×C4⋊Q8C2218yescomplemented
14C22×C11×C4⋊C4C2212yes—
15C22×C11×C4⋊C4C2212yes—
16C22×C42×C11C2211yescharacteristic
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2218yes—
20C22×C4×Dic11C2212yes—
21C2×#66928—28no—
22C2×#66928C2218yes—
23#10622844C22132yescomplemented
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2218yes—
27#10622606C22132yescomplemented
28#10622601C22116yes—
29#10622587C22116yescomplemented
30#10622545C2218yescomplemented
31C24×D11C2312yes—
32C22×Q8×C11—28no—
33C22×Q8×C11—48no—
34C22×Q8×C11C2318yes—
35C23×C4×C11C2314yes—
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×Dic11C2314yes—
40C23×Dic11C2312yes—
41C22×D44—24no—
42C22×D44—28no—
43C22×D44C2314yes—
44C22×Dic22—24no—
45C22×Dic22—28no—
46C22×Dic22C2314yes—
47C11×C4⋊Q8—232no—
48C2×C11×C4⋊C4—28no—
49C2×C11×C4⋊C4—28no—
50C2×C11×C4⋊C4C2318yes—
51C2×C11×C4⋊C4C2318yes—
52C2×C42×C11D418yes—
53C2×C42×C11C2314yes—
54C2×(C2×D11)⋊C4—28no—
55C2×(C2×D11)⋊C4—28no—
56C2×(C2×D11)⋊C4—416no—
57C2×(C2×D11)⋊C4C2318yes—
58C2×(C2×D11)⋊C4C2318yes—
59C2×(C2×D11)⋊C4C23132yes—
60C2×C4×Dic11—28no—
61C2×C4×Dic11C2318yes—
62#66928—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—
73C2×Q8×C11—216no—
74C2×Q8×C11—416no—
75C2×Q8×C11—432no—
76C22×C4×C11—24no—
77C22×C4×C11—24no—
78C22×C4×C11—28no—
79C22×C4×C11—216no—
80C22×C4×C11C2×D414yes—
81C22×C4×C11C2×D414yes—
82C22×C4×C11C2×D414yes—
83C22×C4×C11#4118yes—
84C22×C4×C11C2418yes—
85C22×C4×C11C2412yes—
86C22×C4×C11C2412yes—
87C22×C4×C11C2412yes—
88C22×Dic11—24no—
89C22×Dic11—28no—
90C22×Dic11—28no—
91C22×Dic11—28no—
92C22×Dic11—28no—
93C22×Dic11C2418yes—
94C22×Dic11C2414yes—
95C2×D44—28no—
96C2×D44—216no—
97C2×D44—416no—
98C2×Dic22—28no—
99C2×Dic22—216no—
100C2×Dic22—416no—
101C11×C4⋊C4—216no—
102C11×C4⋊C4—216no—
103C42×C11C2×D4116yes—
104(C2×D11)⋊C4—216no—
105(C2×D11)⋊C4—216no—
106(C2×D11)⋊C4—432no—
107C4×Dic11—216no—
108C22×C4⋊Q8D1111yescharacteristic, complemented
109C22×#124—111no—
110#2640—1116no—
111C2×#397—114no—
112C2×#393—114no—
113C2×#391—112no—
114C2×#390—112no—
115C2×#376—111no—
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—
129Q8×C11—432no—
130C2×C4×C11—28no—
131C2×C4×C11—28no—
132C2×C4×C11—24no—
133C2×C4×C11—24no—
134C2×C4×C11—28no—
135C2×C4×C11—216no—
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—24no—
143C2×Dic11—28no—
144C2×Dic11—28no—
145C2×Dic11—28no—
146C2×Dic11—28no—
147C2×Dic11—48no—
148C2×Dic11—416no—
149D44—416no—
150Dic22—416no—
151C23×Q8—111no—
152C23×Q8C2×D1112yes—
153C23×D4—111no—
154C2×C4⋊Q8—28no—
155C2×C4⋊Q8C2×D1118yescomplemented
156C2×#124—118no—
157C2×#124—228no—
158C22×C4⋊C4C2×D1112yes—
159C22×C4⋊C4C2×D1112yes—
160C22×C22⋊C4—112no—
161C22×C22⋊C4—112no—
162C22×C22⋊C4—118no—
163C22×C42—112no—
164C22×C42C2×D1111yescharacteristic
165#397—1132no—
166#393—1132no—
167#391—1116no—
168#390—1116no—
169#376—118no—
170C2×#95—112no—
171C2×#95—118no—
172C2×#95—112no—
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—28no—
194C22×Q8—48no—
195C22×Q8—114no—
196C22×Q8—228no—
197C22×Q8—224no—
198C22×Q8C22×D1118yes—
199C22×D4—114no—
200C22×D4—228no—
201C22×D4—224no—
202C23×C4—112no—
203C23×C4—114no—
204C23×C4C22×D1114yes—
205C23×C4C22×D1111yescharacteristic
206C23×C4C22×D1111yescharacteristic
207C23×C4C22×D1111yescharacteristic
208C4⋊Q8—232no—
209#124—2232no—
210C2×C4⋊C4—28no—
211C2×C4⋊C4—28no—
212C2×C4⋊C4C22×D1118yes—
213C2×C4⋊C4C22×D1118yes—
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—118no—
221C2×C42—228no—
222C2×C42C22⋊D1118yes—
223C2×C42C22×D1114yes—
224#95—118no—
225#95—118no—
226#95—1132no—
227C2×C11#264018yescomplemented
228C2×C11C22×#12411yescharacteristic
229C2×C11C2×#53511yescharacteristic
230C2×C11C2×#53611yescharacteristic
231C2×C11C2×#54214yes—
232D11—84no—
233C24—114no—
234C24—228no—
235C24—228no—
236C24—228no—
237C24—224no—
238C24C23×D1111yescharacteristic
239C2×Q8—216no—
240C2×Q8—416no—
241C2×Q8—432no—
242C2×Q8—2216no—
243C2×Q8—228no—
244C2×Q8—4416no—
245C2×D4—2216no—
246C2×D4—228no—
247C2×D4—4416no—
248C22×C4—24no—
249C22×C4—24no—
250C22×C4—216no—
251C22×C4—28no—
252C22×C4—118no—
253C22×C4—114no—
254C22×C4—228no—
255C22×C4—228no—
256C22×C4—228no—
257C22×C4—228no—
258C22×C4—224no—
259C22×C4#434318yes—
260C22×C4C2×C22⋊D1114yes—
261C22×C4C2×C22⋊D1114yes—
262C22×C4C2×C22⋊D1114yes—
263C22×C4C23×D1118yes—
264C22×C4C23×D1112yes—
265C22×C4C23×D1112yes—
266C22×C4C23×D1112yes—
267C4⋊C4—216no—
268C4⋊C4—216no—
269C22⋊C4—2216no—
270C22⋊C4—2216no—
271C22⋊C4—4432no—
272C42—2216no—
273C42C2×C22⋊D11116yes—
274C11C2×#264011yescharacteristic, complemented, Sylow
275C23—228no—
276C23—228no—
277C23—228no—
278C23—224no—
279C23—4432no—
280C23—448no—
281C23—448no—
282C23—448no—
283C23#6703714yes—
284C23C2×#434314yes—
285C23#6704014yes—
286C23C22×C22⋊D1112yes—
287C23C24×D1111yescharacteristic
288Q8—432no—
289Q8—4416no—
290D4—4416no—
291C2×C4—28no—
292C2×C4—28no—
293C2×C4—24no—
294C2×C4—24no—
295C2×C4—216no—
296C2×C4—28no—
297C2×C4—416no—
298C2×C4—228no—
299C2×C4—228no—
300C2×C4—228no—
301C2×C4—228no—
302C2×C4—224no—
303C2×C4—4416no—
304C2×C4—448no—
305C2×C4#67000116yes—
306C2×C4C2×#434318yes—
307C2×C4C22×C22⋊D1114yes—
308C2×C4C22×C22⋊D1114yes—
309C2×C4C22×C22⋊D1114yes—
310C22—444no—
311C22—444no—
312C22—444no—
313C22—4416no—
314C22—8816no—
315C22#10623264116yes—
316C22#1062333614yes—
317C22C2×#6700014yes—
318C22#1062334714yes—
319C22C2×#6703712yes—
320C22C22×#434312yes—
321C22C2×#6704012yes—
322C22C23×C22⋊D1111yescharacteristic
323C4—24no—
324C4—24no—
325C4—48no—
326C4—444no—
327C4—448no—
328C4C2×#6700018yes—
329C2—884no—
330C2#1307455718yesdirect product factor
331C2C22×#6700011yescharacteristic
332C2C2×#1062333611yescharacteristic
333C2C2×#1062334711yescharacteristic
334C2C2×#1062326414yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×C4⋊Q8C2
socleC24×C11C24
prime radicalC23×D44C22
hypercenterC22×C4⋊Q8D11
hypocenterC11C2×#2640
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13074557C2direct (N × H)
3. C2×#10622606C2semidirect
4. C2×#10622844C2semidirect
5. C2×#10622587C2semidirect
7. C2×#10622545C2semidirect
8. C22×C11×C4⋊Q8C2semidirect
13. C2×C11×C4⋊Q8C22semidirect
23. #10622844C22semidirect
27. #10622606C22semidirect
29. #10622587C22semidirect
30. #10622545C22semidirect
108. C22×C4⋊Q8D11semidirect
155. C2×C4⋊Q8C2×D11semidirect
227. C2×C11#2640semidirect
274. C11C2×#2640semidirect
330. C2#13074557direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669282
#130745572
C2×#106226062
C2×#106228442
C2×#106225872
C2×#106226012
C2×#106225452
C22×C11×C4⋊Q82
C2×#264011