Finite Group Databasebeta

← C2×#13069863 #14781456

Subgroups — C2×#13069863 #14781456

Order 2816.

1542 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66922C211yesmaximal, characteristic
2C22×#66880C212yesmaximal
3C22×#66880C212yesmaximal
4C2×#10622541C211yesmaximal, characteristic
5#13069863C218yesmaximal, direct product factor
6C2×C11×#336C211yesmaximal, characteristic
7C23×Dic22C2212yes—
8C23×C8×C11C2212yes—
9C22×C42×C11C2211yescharacteristic
10C22×C4⋊Dic11—21no—
11C22×C4⋊Dic11—21no—
12C22×C4⋊Dic11C2211yescharacteristic
13C22×C4⋊Dic11C2211yescharacteristic
14C22×Dic11⋊C4—21no—
15C2×#66922—28no—
16C2×#66922—22no—
17C2×#66922C2214yes—
18C2×C11⋊#95—21no—
19C2×#66880—28no—
20C2×#66880—28no—
21C2×#66880C2218yes—
22C2×#66880C2218yes—
23#10622541—22no—
24#10622541C2214yes—
25C11×#336C2214yes—
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C23×C4×C11C2311yescharacteristic
29C23×Dic11—21no—
30C23×Dic11—22no—
31C23×Dic11—21no—
32C22×Dic22—24no—
33C22×Dic22—24no—
34C22×Dic22—24no—
35C22×Dic22—24no—
36C22×Dic22—22no—
37C22×Dic22—24no—
38C22×Dic22D418yes—
39C22×Dic22C2314yes—
40C22×C8×C11—24no—
41C22×C8×C11—24no—
42C22×C8×C11—24no—
43C22×C8×C11C2314yes—
44C2×C42×C11—24no—
45C2×C42×C11D412yes—
46C2×C42×C11C2312yes—
47C2×C4⋊Dic11—28no—
48C2×C4⋊Dic11—28no—
49C2×C4⋊Dic11—24no—
50C2×C4⋊Dic11—24no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—22no—
53C2×C4⋊Dic11—24no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11D414yes—
56C2×C4⋊Dic11C2312yes—
57C2×C4⋊Dic11C2312yes—
58C2×Dic11⋊C4—24no—
59C2×Dic11⋊C4—44no—
60#66922—216no—
61#66922—216no—
62C11⋊#95—24no—
63#66880—216no—
64#66880—216no—
65C2×#2043—111nomaximal, Sylow
66C24×C11C2×D411yescharacteristic
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11SD1614yes—
72C22×C4×C11Q1614yes—
73C22×C4×C11C2×D412yes—
74C22×C4×C11C2×D412yes—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D414yes—
77C22×C4×C11C2×D412yes—
78C22×C4×C11#4114yes—
79C22×C4×C11#4112yes—
80C22×C4×C11C2411yescharacteristic
81C22×Dic11—28no—
82C22×Dic11—24no—
83C22×Dic11—22no—
84C22×Dic11—24no—
85C22×Dic11—22no—
86C22×Dic11—42no—
87C22×Dic11—44no—
88C22×Dic11—44no—
89C22×Dic11—42no—
90C22×Dic11—42no—
91C22×Dic11—42no—
92C22×Dic11—42no—
93C2×Dic22—28no—
94C2×Dic22—216no—
95C2×Dic22—216no—
96C2×Dic22—24no—
97C2×Dic22—24no—
98C2×Dic22—24no—
99C2×Dic22—24no—
100C2×Dic22—24no—
101C2×Dic22—48no—
102C2×Dic22—44no—
103C2×Dic22—48no—
104C2×Dic22—44no—
105C2×Dic22C2×D418yes—
106C2×C8×C11—24no—
107C2×C8×C11—24no—
108C2×C8×C11—24no—
109C2×C8×C11—48no—
110C42×C11—24no—
111C42×C11—24no—
112C4⋊Dic11—216no—
113C4⋊Dic11—216no—
114C4⋊Dic11—24no—
115C4⋊Dic11—24no—
116C4⋊Dic11—22no—
117C4⋊Dic11—42no—
118C4⋊Dic11C2×D414yes—
119Dic11⋊C4—48no—
120C22×C4⋊Q8—111no—
121C22×#103—112no—
122C22×#103—112no—
123C2×#389—111no—
124#2043—118no—
125C2×#336D1111yescharacteristic
126C23×C11#12012yes—
127C23×C11#12112yes—
128C23×C11#12412yes—
129C23×C11C2×SD1612yes—
130C23×C11C2×Q1612yes—
131C23×C11#13712yes—
132C23×C11#13712yes—
133C23×C11C22×D411yescharacteristic
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—28no—
139C2×C4×C11—28no—
140C2×C4×C11#12012yes—
141C2×C4×C11#12118yes—
142C2×C4×C11#12112yes—
143C2×C4×C11#12318yes—
144C2×C4×C11#12412yes—
145C2×C4×C11C2×SD1614yes—
146C2×C4×C11C2×Q1614yes—
147C2×C4×C11C22×D411yescharacteristic
148C2×C4×C11C22×D412yes—
149C2×C4×C11C2×#4112yes—
150C2×C4×C11C2×#4111yescharacteristic
151C2×Dic11—28no—
152C2×Dic11—24no—
153C2×Dic11—44no—
154C2×Dic11—44no—
155C2×Dic11—42no—
156C2×Dic11—42no—
157C2×Dic11—416no—
158C2×Dic11—48no—
159C2×Dic11—42no—
160C2×Dic11—42no—
161C2×Dic11—42no—
162C2×Dic11—84no—
163Dic22—28no—
164Dic22—28no—
165Dic22—44no—
166Dic22—44no—
167Dic22—416no—
168C8×C11—44no—
169C23×Q8—112no—
170C23×C8C2×D1112yes—
171C2×C4⋊Q8—114no—
172C2×C4⋊Q8—228no—
173C2×C4⋊Q8—222no—
174C22×C4⋊C4—111no—
175C22×C4⋊C4—111no—
176C22×C4⋊C4—221no—
177C22×C4⋊C4—221no—
178C22×C4⋊C4—221no—
179C22×C42C2×D1111yescharacteristic
180C2×#103—118no—
181C2×#103—118no—
182C2×#103—228no—
183C2×#103—228no—
184#389—114no—
185#389—222no—
186C2×#95—221no—
187#336C2×D1114yes—
188C22×C11#39414yes—
189C22×C11#44814yes—
190C22×C11#45114yes—
191C22×C11#46114yes—
192C22×C11#46214yes—
193C22×C11#48714yes—
194C22×C11#49114yes—
195C22×C11C2×#12011yescharacteristic
196C22×C11C2×#12111yescharacteristic
197C22×C11C2×#12411yescharacteristic
198C22×C11C22×SD1611yescharacteristic
199C22×C11C22×Q1611yescharacteristic
200C22×C11C2×#13711yescharacteristic
201C22×C11C2×#13711yescharacteristic
202C4×C11—24no—
203C4×C11—24no—
204C4×C11#39414yes—
205C4×C11C2×#12112yes—
206C4×C11C2×#12312yes—
207Dic11—48no—
208Dic11—44no—
209Dic11—82no—
210C22×Q8—118no—
211C22×Q8—114no—
212C22×Q8—222no—
213C22×Q8—224no—
214C22×Q8—224no—
215C22×Q8—224no—
216C22×Q8—224no—
217C22×Q8—224no—
218C23×C4—221no—
219C23×C4—222no—
220C23×C4—221no—
221C23×C4D4411yescharacteristic
222C23×C4D4411yescharacteristic
223C23×C4C22×D1111yescharacteristic
224C22×C8—24no—
225C22×C8—24no—
226C22×C8—24no—
227C22×C8C22×D1114yes—
228C4⋊Q8—2216no—
229C4⋊Q8—2216no—
230C2×C4⋊C4—114no—
231C2×C4⋊C4—112no—
232C2×C4⋊C4—112no—
233C2×C4⋊C4—228no—
234C2×C4⋊C4—228no—
235C2×C4⋊C4—221no—
236C2×C4⋊C4—224no—
237C2×C4⋊C4—224no—
238C2×C4⋊C4—222no—
239C2×C4⋊C4—224no—
240C2×C4⋊C4—221no—
241C2×C4⋊C4—224no—
242C2×C4⋊C4—444no—
243C2×C42—24no—
244C2×C42D4412yes—
245C2×C42C22×D1112yes—
246#103—2216no—
247#103—2216no—
248#95—224no—
249C2×C11#204318yescomplemented
250C2×C11C2×#39411yescharacteristic
251C2×C11C2×#44811yescharacteristic
252C2×C11C2×#45111yescharacteristic
253C2×C11C2×#46111yescharacteristic
254C2×C11C2×#46211yescharacteristic
255C2×C11C2×#48711yescharacteristic
256C2×C11C2×#49111yescharacteristic
257C24C2×D4411yescharacteristic
258C2×Q8—118no—
259C2×Q8—228no—
260C2×Q8—224no—
261C2×Q8—2216no—
262C2×Q8—2216no—
263C2×Q8—224no—
264C2×Q8—224no—
265C2×Q8—224no—
266C2×Q8—224no—
267C2×Q8—444no—
268C2×Q8—448no—
269C2×Q8—448no—
270C2×Q8—444no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—228no—
276C22×C4—224no—
277C22×C4—222no—
278C22×C4—224no—
279C22×C4—222no—
280C22×C4—444no—
281C22×C4—444no—
282C22×C4—442no—
283C22×C4—442no—
284C22×C4—442no—
285C22×C4—442no—
286C22×C4—442no—
287C22×C4#431414yes—
288C22×C4Dic4414yes—
289C22×C4C2×D4412yes—
290C22×C4C2×D4412yes—
291C22×C4C2×D4411yescharacteristic
292C22×C4#433914yes—
293C22×C4D4×D1114yes—
294C22×C4D4×D1112yes—
295C22×C4#434312yes—
296C22×C4C23×D1111yescharacteristic
297C2×C8—24no—
298C2×C8—24no—
299C2×C8—24no—
300C2×C8—48no—
301C4⋊C4—114no—
302C4⋊C4—2216no—
303C4⋊C4—2216no—
304C4⋊C4—224no—
305C4⋊C4—222no—
306C4⋊C4—224no—
307C4⋊C4—442no—
308C4⋊C4—448no—
309C42—24no—
310C42—24no—
311C11C2×#204311yescharacteristic, complemented, Sylow
312C23#6692812yes—
313C23#6693512yes—
314C23#6694812yes—
315C23C2×#431412yes—
316C23C2×Dic4412yes—
317C23#6696212yes—
318C23#6696212yes—
319C23C22×D4411yescharacteristic
320Q8—228no—
321Q8—228no—
322Q8—444no—
323Q8—444no—
324Q8—4416no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—28no—
330C2×C4—28no—
331C2×C4—228no—
332C2×C4—224no—
333C2×C4—444no—
334C2×C4—442no—
335C2×C4—442no—
336C2×C4—444no—
337C2×C4—4416no—
338C2×C4—448no—
339C2×C4—442no—
340C2×C4—442no—
341C2×C4—442no—
342C2×C4—884no—
343C2×C4#6692812yes—
344C2×C4#6693512yes—
345C2×C4#6693718yes—
346C2×C4#6694718yes—
347C2×C4#6694812yes—
348C2×C4C2×#431414yes—
349C2×C4C2×Dic4414yes—
350C2×C4C2×#433912yes—
351C2×C4C2×D4×D1111yescharacteristic
352C2×C4C2×D4×D1112yes—
353C2×C4C2×#434311yescharacteristic
354C8—44no—
355C22#1062228514yes—
356C22#1062229414yes—
357C22#1062231614yes—
358C22#1062235114yes—
359C22#1062235214yes—
360C22#1062245414yes—
361C22#1062246214yes—
362C22C2×#6692811yescharacteristic
363C22C2×#6693511yescharacteristic
364C22C2×#6694811yescharacteristic
365C22C22×#431411yescharacteristic
366C22C22×Dic4411yescharacteristic
367C22C2×#6696211yescharacteristic
368C22C2×#6696211yescharacteristic
369C4—24no—
370C4—24no—
371C4—444no—
372C4—448no—
373C4—882no—
374C4#1062228514yes—
375C4C2×#6693712yes—
376C4C2×#6694712yes—
377C2#1306986318yesdirect product factor
378C2C2×#1062228511yescharacteristic
379C2C2×#1062235111yescharacteristic
380C2C2×#1062235211yescharacteristic
381C2C2×#1062245411yescharacteristic
382C2C2×#1062246211yescharacteristic
383C2C2×#1062229411yescharacteristic
384C2C2×#1062231611yescharacteristic
subgroupG/H
centerC24C2×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#336C2
socle, prime radicalC24×C11C2×D4
hypercenterC2×#336D11
hypocenterC11C2×#2043
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
5. #13069863C2direct (N × H)
249. C2×C11#2043semidirect
311. C11C2×#2043semidirect
377. C2#13069863direct (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×#668802
C2×#106225412
#130698632
C2×C11×#3362
C2×#204311