Finite Group Databasebeta

← C2×#13074485 #14920563

Subgroups — C2×#13074485 #14920563

Order 2816.

2894 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D44C211yesmaximal, characteristic
2#13074485C2116yesmaximal, direct product factor
3C2×#10622605C212yesmaximal, complemented
4C2×#10622596C212yesmaximal, complemented
5C2×#10622606C212yesmaximal, complemented
6C2×#10622604C212yesmaximal
7C2×#10622602C214yesmaximal, complemented
8C2×#10622550C211yesmaximal, characteristic, complemented
9C22×C11×#125C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C23×C4×D11C2212yes—
12C2×C11×#125—28no—
13C2×C11×#125C2218yescomplemented
14C22×C11×C4⋊C4C2212yes—
15C22×C11×C4⋊C4C2212yes—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2214yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2214yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2214yes—
24C2×C4×D44—28no—
25C2×C4×D44C2218yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2214yes—
30#10622606C22116yescomplemented
31#10622605C22116yescomplemented
32#10622604C22116yes—
33#10622602C22132yescomplemented
34#10622596C22116yescomplemented
35#10622550C2218yescomplemented
36C24×D11C2312yes—
37C23×C4×C11C2312yes—
38C23×C4×C11C2312yes—
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×Dic11C2312yes—
43C23×Dic11C2314yes—
44C22×D44—28no—
45C22×D44—24no—
46C22×D44C2314yes—
47C22×C4×D11—28no—
48C22×C4×D11—48no—
49C22×C4×D11C2318yes—
50C11×#125—232no—
51C2×C11×C4⋊C4—28no—
52C2×C11×C4⋊C4—24no—
53C2×C11×C4⋊C4—24no—
54C2×C11×C4⋊C4—28no—
55C2×C11×C4⋊C4C2318yes—
56C2×C11×C4⋊C4C2318yes—
57C2×C11×C4⋊C4C2314yes—
58C2×C11×C4⋊C4C2314yes—
59C2×C42×C11D418yes—
60C2×C42×C11C2314yes—
61C2×(C2×D11)⋊C4—216no—
62C2×(C2×D11)⋊C4—28no—
63C2×(C2×D11)⋊C4—48no—
64C2×(C2×D11)⋊C4C2318yes—
65C2×(C2×D11)⋊C4C23116yes—
66C2×(C2×D11)⋊C4C23116yes—
67C2×C4⋊Dic11—24no—
68C2×C4⋊Dic11C2314yes—
69C2×Dic11⋊C4—48no—
70C2×Dic11⋊C4C23116yes—
71C4×D44—232no—
72C11⋊#95C2318yes—
73C11⋊#95C2318yes—
74C11⋊#95C2318yes—
75C11⋊#95C23116yes—
76C2×#2633—111nomaximal, Sylow
77C24×C11C2411yescharacteristic
78C23×D11—24no—
79C23×D11—24no—
80C23×D11—28no—
81C23×D11—28no—
82C23×D11#4118yes—
83C23×D11C2414yes—
84C22×C4×C11—24no—
85C22×C4×C11—24no—
86C22×C4×C11—24no—
87C22×C4×C11—24no—
88C22×C4×C11—24no—
89C22×C4×C11—28no—
90C22×C4×C11—24no—
91C22×C4×C11—24no—
92C22×C4×C11C2×D414yes—
93C22×C4×C11C2×D414yes—
94C22×C4×C11C2×D414yes—
95C22×C4×C11C2414yes—
96C22×C4×C11C2414yes—
97C22×C4×C11C2412yes—
98C22×C4×C11C2412yes—
99C22×C4×C11C2412yes—
100C22×Dic11—24no—
101C22×Dic11—28no—
102C22×Dic11—28no—
103C22×Dic11—28no—
104C22×Dic11—28no—
105C22×Dic11C2418yes—
106C22×Dic11C2414yes—
107C2×D44—232no—
108C2×D44—216no—
109C2×D44—28no—
110C2×C4×D11—216no—
111C2×C4×D11—416no—
112C2×C4×D11—432no—
113C11×C4⋊C4—216no—
114C11×C4⋊C4—28no—
115C11×C4⋊C4—28no—
116C11×C4⋊C4—216no—
117C42×C11C2×D4116yes—
118(C2×D11)⋊C4—232no—
119(C2×D11)⋊C4—216no—
120(C2×D11)⋊C4—416no—
121C4⋊Dic11—28no—
122Dic11⋊C4—416no—
123C22×#125D1111yescharacteristic, complemented
124C22×C4×D4—111no—
125#2633—1116no—
126C2×#399—112no—
127C2×#398—112no—
128C2×#397—112no—
129C2×#394—112no—
130C2×#385—114no—
131C2×#383—111no—
132C23×C11C22×D412yes—
133C23×C11C2×#4114yes—
134C23×C11H(5,𝔽2)14yes—
135C23×C112−1+414yes—
136C23×C11C2511yescharacteristic
137C22×D11—216no—
138C22×D11—232no—
139C22×D11—24no—
140C22×D11—24no—
141C22×D11—28no—
142C22×D11—28no—
143C22×D11—48no—
144C22×D11—48no—
145C22×D11—416no—
146C22×D11C2×#4118yes—
147C2×C4×C11—28no—
148C2×C4×C11—28no—
149C2×C4×C11—28no—
150C2×C4×C11—24no—
151C2×C4×C11—24no—
152C2×C4×C11—24no—
153C2×C4×C11—24no—
154C2×C4×C11—24no—
155C2×C4×C11—28no—
156C2×C4×C11—24no—
157C2×C4×C11—24no—
158C2×C4×C11—48no—
159C2×C4×C11—48no—
160C2×C4×C11C22×D414yes—
161C2×C4×C11C22×D414yes—
162C2×C4×C11C22×D414yes—
163C2×Dic11—24no—
164C2×Dic11—28no—
165C2×Dic11—28no—
166C2×Dic11—28no—
167C2×Dic11—28no—
168C2×Dic11—48no—
169C2×Dic11—416no—
170D44—232no—
171C4×D11—432no—
172C23×D4—111no—
173C24×C4—112no—
174C2×#125—28no—
175C2×#125C2×D1118yescomplemented
176C2×C4×D4—118no—
177C2×C4×D4—228no—
178C22×C4⋊C4—111no—
179C22×C4⋊C4—114no—
180C22×C4⋊C4C2×D1112yes—
181C22×C4⋊C4C2×D1111yescharacteristic
182C22×C4⋊C4C2×D1111yescharacteristic
183C22×C4⋊C4C2×D1112yes—
184C22×C22⋊C4—114no—
185C22×C22⋊C4—112no—
186C22×C22⋊C4—114no—
187C22×C42C2×D1111yescharacteristic
188#399—1116no—
189#398—1116no—
190#397—1116no—
191#394—1116no—
192#385—1132no—
193#383—118no—
194C2×#95—112no—
195C2×#95—114no—
196C2×#95—112no—
197C2×#95—112no—
198C22×C11#52514yes—
199C22×C11#53514yes—
200C22×C11#53614yes—
201C22×C11#539116yes—
202C22×C11C23×D411yescharacteristic
203C22×C11C22×#4112yes—
204C22×C11C2×H(5,𝔽2)12yes—
205C22×C11C2×2−1+412yes—
206C2×D11—28no—
207C2×D11—216no—
208C2×D11—432no—
209C2×D11—44no—
210C2×D11—44no—
211C2×D11—48no—
212C4×C11—24no—
213C4×C11—24no—
214C4×C11—24no—
215C4×C11—44no—
216C4×C11—44no—
217Dic11—44no—
218Dic11—48no—
219C25—112no—
220C22×D4—114no—
221C22×D4—228no—
222C22×D4—224no—
223C23×C4—114no—
224C23×C4—112no—
225C23×C4—118no—
226C23×C4—228no—
227C23×C4—448no—
228C23×C4C22×D1112yes—
229C23×C4C22×D1112yes—
230C23×C4C22×D1111yescharacteristic
231C23×C4C22×D1111yescharacteristic
232C23×C4C22×D1111yescharacteristic
233#125—232no—
234C4×D4—2232no—
235C2×C4⋊C4—24no—
236C2×C4⋊C4—24no—
237C2×C4⋊C4—28no—
238C2×C4⋊C4—28no—
239C2×C4⋊C4—114no—
240C2×C4⋊C4—1116no—
241C2×C4⋊C4—224no—
242C2×C4⋊C4—448no—
243C2×C4⋊C4C22×D1118yes—
244C2×C4⋊C4C22×D1118yes—
245C2×C4⋊C4C22×D1114yes—
246C2×C4⋊C4C22×D1114yes—
247C2×C22⋊C4—118no—
248C2×C22⋊C4—1116no—
249C2×C22⋊C4—1116no—
250C2×C22⋊C4—2216no—
251C2×C22⋊C4—228no—
252C2×C22⋊C4—448no—
253C2×C42C22⋊D1118yes—
254C2×C42C22×D1114yes—
255#95—118no—
256#95—118no—
257#95—118no—
258#95—1116no—
259C2×C11#263318yescomplemented
260C2×C11C2×#52511yescharacteristic
261C2×C11C2×#53511yescharacteristic
262C2×C11C2×#53611yescharacteristic
263C2×C11C2×#53914yes—
264D11—48no—
265C24—118no—
266C24—114no—
267C24—228no—
268C24—224no—
269C24—228no—
270C24—224no—
271C24C23×D1111yescharacteristic
272C2×D4—2216no—
273C2×D4—2232no—
274C2×D4—228no—
275C22×C4—24no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—28no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—118no—
284C22×C4—114no—
285C22×C4—228no—
286C22×C4—228no—
287C22×C4—228no—
288C22×C4—228no—
289C22×C4—224no—
290C22×C4—2216no—
291C22×C4—4416no—
292C22×C4—4432no—
293C22×C4C2×C22⋊D1114yes—
294C22×C4C2×C22⋊D1114yes—
295C22×C4C2×C22⋊D1114yes—
296C22×C4C23×D1114yes—
297C22×C4C23×D1114yes—
298C22×C4C23×D1112yes—
299C22×C4C23×D1112yes—
300C22×C4C23×D1112yes—
301C4⋊C4—28no—
302C4⋊C4—28no—
303C4⋊C4—216no—
304C4⋊C4—216no—
305C4⋊C4—228no—
306C4⋊C4—4416no—
307C22⋊C4—2232no—
308C22⋊C4—2216no—
309C22⋊C4—4416no—
310C42C2×C22⋊D11116yes—
311C11C2×#263311yescharacteristic, complemented, Sylow
312C23—118no—
313C23—2216no—
314C23—228no—
315C23—224no—
316C23—228no—
317C23—224no—
318C23—2232no—
319C23—448no—
320C23—448no—
321C23—4416no—
322C23#6704014yes—
323C23#41×D1114yes—
324C23#6704214yes—
325C23C22×C22⋊D1112yes—
326C23C24×D1111yescharacteristic
327D4—2232no—
328C2×C4—28no—
329C2×C4—28no—
330C2×C4—28no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—28no—
335C2×C4—24no—
336C2×C4—24no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—48no—
340C2×C4—48no—
341C2×C4—228no—
342C2×C4—228no—
343C2×C4—228no—
344C2×C4—228no—
345C2×C4—224no—
346C2×C4—4432no—
347C2×C4—448no—
348C2×C4—4416no—
349C2×C4C22×C22⋊D1114yes—
350C2×C4C22×C22⋊D1114yes—
351C2×C4C22×C22⋊D1114yes—
352C22—2216no—
353C22—228no—
354C22—4432no—
355C22—444no—
356C22—444no—
357C22—448no—
358C22#10623223116yes—
359C22#1062334714yes—
360C22#1062335914yes—
361C22#1062336114yes—
362C22C2×#6704012yes—
363C22C2×#41×D1112yes—
364C22C2×#6704212yes—
365C22C23×C22⋊D1111yescharacteristic
366C4—24no—
367C4—24no—
368C4—24no—
369C4—44no—
370C4—44no—
371C4—444no—
372C4—448no—
373C2—448no—
374C2#1307448518yesdirect product factor
375C2C2×#1062335911yescharacteristic
376C2C2×#1062336111yescharacteristic
377C2C2×#1062334711yescharacteristic
378C2C2×#1062322314yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#125C2
socleC24×C11C24
prime radicalC23×D44C22
hypercenterC22×#125D11
hypocenterC11C2×#2633
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
2. #13074485C2direct (N × H)
3. C2×#10622605C2semidirect
4. C2×#10622596C2semidirect
5. C2×#10622606C2semidirect
7. C2×#10622602C2semidirect
8. C2×#10622550C2semidirect
9. C22×C11×#125C2semidirect
13. C2×C11×#125C22semidirect
30. #10622606C22semidirect
31. #10622605C22semidirect
33. #10622602C22semidirect
34. #10622596C22semidirect
35. #10622550C22semidirect
123. C22×#125D11semidirect
175. C2×#125C2×D11semidirect
259. C2×C11#2633semidirect
311. C11C2×#2633semidirect
374. C2#13074485direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D442
#130744852
C2×#106226052
C2×#106225962
C2×#106226062
C2×#106226042
C2×#106226022
C2×#106225502
C22×C11×#1252
C2×#263311