Finite Group Databasebeta

← C2×#13069777 #14781139

Subgroups — C2×#13069777 #14781139

Order 2816.

1238 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623031C211yesmaximal, characteristic
2C2×#10622838C212yesmaximal
3#13069777C218yesmaximal, direct product factor
4C2×#10622168C211yesmaximal, characteristic
5C2×#10622161C212yesmaximal
6C2×C11×#391C211yesmaximal, characteristic
7C23×Q8×C11C2211yescharacteristic
8C22×C11×C4⋊C4C2211yescharacteristic
9C22×C42×C11C2211yescharacteristic
10C2×#66979C2212yes—
11C2×#66977—22no—
12C22×#4318C2212yes—
13#10623031—22no—
14#10623031—24no—
15#10623031C2214yes—
16C2×#66943—22no—
17C2×#66941—22no—
18C11×#391—22no—
19C11×#391C2214yes—
20C2×C11×#95—22no—
21#10622838—24no—
22#10622838C2218yes—
23C2×#66899—22no—
24C2×#66899—22no—
25#10622168C2214yes—
26#10622161C2218yes—
27C22×Q8×C11—21no—
28C22×Q8×C11—22no—
29C22×Q8×C11—22no—
30C22×Q8×C11—22no—
31C22×Q8×C11—24no—
32C22×Q8×C11Q814yescomplemented
33C22×Q8×C11C2312yes—
34C23×C4×C11—21no—
35C23×C4×C11—21no—
36C23×C4×C11D412yes—
37C23×C4×C11C2311yescharacteristic
38C22×Dic22—22no—
39C2×C11×C4⋊C4—22no—
40C2×C11×C4⋊C4—22no—
41C2×C11×C4⋊C4D412yes—
42C2×C11×C4⋊C4C2312yes—
43C2×C42×C11—24no—
44C2×C42×C11—21no—
45C2×C42×C11C2312yes—
46C2×C22⋊Dic11—22no—
47#66979—22no—
48#66979—22no—
49#66979D414yes—
50#66979C2314yes—
51C2×C4⋊Dic11—22no—
52C2×C4⋊Dic11D412yes—
53C2×C4⋊Dic11D412yes—
54#66977—28no—
55#66977—28no—
56C2×Dic11⋊C4—24no—
57C2×C4×Dic11—22no—
58C2×#4318—22no—
59C2×#4318—24no—
60C2×#4318—24no—
61C2×#4318C2314yes—
62C22×C11⋊C8—22no—
63#66943—28no—
64#66943—28no—
65#66941—28no—
66#66941—28no—
67C11×#95—28no—
68#66899—28no—
69#66899—28no—
70C2×#2028—111nomaximal, Sylow
71C24×C11C2×D411yescharacteristic
72C2×Q8×C11—24no—
73C2×Q8×C11—22no—
74C2×Q8×C11—28no—
75C2×Q8×C11—28no—
76C2×Q8×C11—24no—
77C2×Q8×C11—24no—
78C2×Q8×C11—42no—
79C2×Q8×C11—42no—
80C2×Q8×C11—44no—
81C2×Q8×C11—44no—
82C2×Q8×C11C2×Q814yescomplemented
83C22×C4×C11—24no—
84C22×C4×C11—22no—
85C22×C4×C11—24no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—42no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11—44no—
95C22×C4×C11C2×D414yes—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×Q812yes—
100C22×C4×C11#4114yes—
101C22×C4×C11#4112yes—
102C22×C4×C11C2411yescharacteristic
103C22×Dic11—22no—
104C22×Dic11—22no—
105C2×Dic22—28no—
106C2×Dic22—84no—
107C11×C4⋊C4—24no—
108C11×C4⋊C4—24no—
109C42×C11—24no—
110C42×C11—42no—
111C22⋊Dic11—24no—
112C22⋊Dic11—24no—
113C4⋊Dic11—28no—
114C4⋊Dic11—22no—
115C4⋊Dic11—22no—
116C4⋊Dic11C2×D414yes—
117C4⋊Dic11C2×D414yes—
118Dic11⋊C4—216no—
119C4×Dic11—24no—
120C4×Dic11—24no—
121#4318—24no—
122#4318—24no—
123#4318—44no—
124C2×C11⋊C8—24no—
125C2×C11⋊C8—44no—
126C2×#544—111no—
127C2×#419—112no—
128C2×#391D1111yescharacteristic
129#2028—118no—
130C2×#343—111no—
131C2×#339—112no—
132C23×C11—22no—
133C23×C11—22no—
134C23×C11#12011yescharacteristic
135C23×C11#12011yescharacteristic
136C23×C11C22⋊Q812yes—
137C23×C11#12412yes—
138C23×C11C22×D411yescharacteristic
139Q8×C11—28no—
140Q8×C11—44no—
141Q8×C11—48no—
142C2×C4×C11—24no—
143C2×C4×C11—24no—
144C2×C4×C11—24no—
145C2×C4×C11—42no—
146C2×C4×C11—48no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—44no—
151C2×C4×C11—44no—
152C2×C4×C11—44no—
153C2×C4×C11—44no—
154C2×C4×C11—82no—
155C2×C4×C11#12012yes—
156C2×C4×C11C22⋊Q814yes—
157C2×C4×C11C22⋊Q814yes—
158C2×C4×C11C22⋊Q812yes—
159C2×C4×C11#12414yes—
160C2×C4×C11#12414yes—
161C2×C4×C11#12412yes—
162C2×C4×C11C22×D412yes—
163C2×C4×C11C22×Q811yescharacteristic
164C2×C4×C11C2×#4111yescharacteristic
165C2×C4×C11C2×#4112yes—
166C2×Dic11—24no—
167C2×Dic11—24no—
168C2×Dic11—44no—
169C2×Dic11—44no—
170Dic22—88no—
171C11⋊C8—44no—
172C23×Q8C2×D1111yescharacteristic
173C22×M16—112no—
174#544—114no—
175#544—224no—
176#544—222no—
177C2×C4⋊Q8—222no—
178C2×#125—222no—
179C2×C22⋊Q8—222no—
180C2×#117—112no—
181C22×C4⋊C4C2×D1111yescharacteristic
182C22×C42C2×D1111yescharacteristic
183#419—118no—
184#419—224no—
185C2×#103—222no—
186C2×#103—222no—
187#391—22no—
188#391C2×D1114yes—
189C2×#95—22no—
190#343—114no—
191#339—118no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—24no—
197C22×C11—24no—
198C22×C11#39312yes—
199C22×C11#39312yes—
200C22×C11#45512yes—
201C22×C11#45612yes—
202C22×C11C2×#12011yescharacteristic
203C22×C11C2×C22⋊Q811yescharacteristic
204C22×C11C2×#12411yescharacteristic
205C4×C11—44no—
206C4×C11—44no—
207C4×C11—44no—
208C4×C11#39314yes—
209C4×C11C2×C22⋊Q812yes—
210C4×C11C2×#12412yes—
211Dic11—44no—
212Dic11—44no—
213C22×Q8—22no—
214C22×Q8—21no—
215C22×Q8—22no—
216C22×Q8—22no—
217C22×Q8—24no—
218C22×Q8—222no—
219C22×Q8Dic2214yescomplemented
220C22×Q8C22×D1112yes—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4C22⋊D1112yes—
224C23×C4C22×D1111yescharacteristic
225C2×M16—114no—
226C2×M16—222no—
227C2×M16—224no—
228C2×M16—224no—
229C22×C8—222no—
230C4⋊Q8—228no—
231C4⋊Q8—228no—
232#125—228no—
233#125—228no—
234C22⋊Q8—228no—
235C22⋊Q8—228no—
236#117—114no—
237#117—114no—
238#117—222no—
239#117—222no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—112no—
243C2×C4⋊C4—112no—
244C2×C4⋊C4—222no—
245C2×C4⋊C4—224no—
246C2×C4⋊C4C22⋊D1112yes—
247C2×C4⋊C4C22×D1112yes—
248C2×C22⋊C4—222no—
249C2×C42—24no—
250C2×C42—21no—
251C2×C42—222no—
252C2×C42C22×D1112yes—
253#103—228no—
254#103—228no—
255#95—28no—
256C2×C11—21no—
257C2×C11—21no—
258C2×C11—22no—
259C2×C11#202814yescomplemented
260C2×C11C2×#39311yescharacteristic
261C2×C11C2×#45511yescharacteristic
262C2×C11C2×#45611yescharacteristic
263C24C2×C22⋊D1111yescharacteristic
264C2×Q8—24no—
265C2×Q8—22no—
266C2×Q8—28no—
267C2×Q8—28no—
268C2×Q8—24no—
269C2×Q8—24no—
270C2×Q8—44no—
271C2×Q8—44no—
272C2×Q8—42no—
273C2×Q8—42no—
274C2×Q8—228no—
275C2×Q8—884no—
276C2×Q8C2×Dic2214yescomplemented
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—44no—
289C22×C4—222no—
290C22×C4—222no—
291C22×C4C2×Dic2212yes—
292C22×C4#433912yes—
293C22×C4D4×D1112yes—
294C22×C4D4×D1112yes—
295C22×C4#434114yes—
296C22×C4C2×C22⋊D1114yes—
297C22×C4C2×C22⋊D1111yescharacteristic
298C22×C4C23×D1111yescharacteristic
299M16—224no—
300M16—224no—
301M16—444no—
302C2×C8—224no—
303C2×C8—444no—
304C4⋊C4—24no—
305C4⋊C4—24no—
306C4⋊C4—114no—
307C4⋊C4—114no—
308C4⋊C4—228no—
309C4⋊C4—2216no—
310C4⋊C4—222no—
311C4⋊C4—222no—
312C22⋊C4—224no—
313C22⋊C4—224no—
314C42—24no—
315C42—42no—
316C42—224no—
317C42—224no—
318C11C2×#202811yescharacteristic, complemented, Sylow
319C23—22no—
320C23—22no—
321C23#6697712yes—
322C23#6698912yes—
323C23#6699011yescharacteristic
324C23#6699011yescharacteristic
325C23C22×C22⋊D1111yescharacteristic
326Q8—28no—
327Q8—44no—
328Q8—48no—
329Q8—888no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—42no—
334C2×C4—48no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—44no—
341C2×C4—44no—
342C2×C4—82no—
343C2×C4—224no—
344C2×C4—224no—
345C2×C4—444no—
346C2×C4—444no—
347C2×C4#6693114yes—
348C2×C4#6693114yes—
349C2×C4#6693814yes—
350C2×C4#6693814yes—
351C2×C4#6697712yes—
352C2×C4#6698912yes—
353C2×C4#6699012yes—
354C2×C4C22×Dic2211yescharacteristic
355C2×C4C2×#433911yescharacteristic
356C2×C4C2×D4×D1112yes—
357C2×C4C2×#434112yes—
358C8—444no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—24no—
364C22—24no—
365C22#1062256012yes—
366C22#1062256012yes—
367C22#1062267412yes—
368C22#1062270812yes—
369C22C2×#6697711yescharacteristic
370C22C2×#6698911yescharacteristic
371C22C2×#6699011yescharacteristic
372C4—44no—
373C4—44no—
374C4—44no—
375C4—444no—
376C4—444no—
377C4#1062256014yes—
378C4C2×#6693112yes—
379C4C2×#6693812yes—
380C2—21no—
381C2—21no—
382C2—22no—
383C2#1306977714yesdirect product factor
384C2C2×#1062256011yescharacteristic
385C2C2×#1062267411yescharacteristic
386C2C2×#1062270811yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#391C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenterC2×#391D11
hypocenterC11C2×#2028
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
3. #13069777C2direct (N × H)
32. C22×Q8×C11Q8semidirect
82. C2×Q8×C11C2×Q8semidirect
219. C22×Q8Dic22semidirect
259. C2×C11#2028semidirect
276. C2×Q8C2×Dic22semidirect
318. C11C2×#2028semidirect
383. C2#13069777direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230312
C2×#106228382
#130697772
C2×#106221682
C2×#106221612
C2×C11×#3912
C2×#202811