Finite Group Databasebeta

← C2×#13069774 #14781136

Subgroups — C2×#13069774 #14781136

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×#10622617C212yesmaximal
2C2×#10622587C211yesmaximal, characteristic
3#13069774C218yesmaximal, direct product factor
4C2×#10622168C211yesmaximal, characteristic
5C2×#10622170C212yesmaximal
6C2×C11×#544C211yesmaximal, characteristic
7C23×Dic22C2211yescharacteristic
8C11×#544—24no—
9C11×#544—22no—
10C11×#544C2214yes—
11C2×C11×C4⋊Q8—22no—
12C2×C11×#125—22no—
13C2×C11×C22⋊Q8—22no—
14C2×C11×#117C2212yes—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C4×Dic11C2211yescharacteristic
17C22×#4318C2212yes—
18C2×C11⋊#95—22no—
19#10622617—24no—
20#10622617C2218yes—
21#10622587—22no—
22#10622587C2214yes—
23C2×#66874—22no—
24C2×#66874—22no—
25#10622170C2218yes—
26#10622168C2214yes—
27C22×Q8×C11—22no—
28C23×C4×C11D412yes—
29C23×C4×C11C2311yescharacteristic
30C23×Dic11—21no—
31C23×Dic11—21no—
32C22×Dic22—22no—
33C22×Dic22—22no—
34C22×Dic22—24no—
35C22×Dic22—21no—
36C22×Dic22—22no—
37C22×Dic22Q814yescomplemented
38C22×Dic22C2312yes—
39C11×C4⋊Q8—28no—
40C11×C4⋊Q8—28no—
41C11×#125—28no—
42C11×#125—28no—
43C11×C22⋊Q8—28no—
44C11×C22⋊Q8—28no—
45C11×#117—22no—
46C11×#117—22no—
47C11×#117D414yes—
48C11×#117C2314yes—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—24no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4D412yes—
54C2×C11×C4⋊C4D412yes—
55C2×C11×C4⋊C4D412yes—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C22⋊C4—22no—
58C2×C42×C11—22no—
59C2×C4×Dic11—24no—
60C2×C4×Dic11—21no—
61C2×C4×Dic11C2312yes—
62C2×#4318—22no—
63C2×#4318—24no—
64C2×#4318—24no—
65C2×#4318C2314yes—
66C22×C11⋊C8—22no—
67C11⋊#95—28no—
68#66874—28no—
69#66874—28no—
70C2×#2028—111nomaximal, Sylow
71C24×C11C2×D411yescharacteristic
72C2×Q8×C11—28no—
73C2×Q8×C11—84no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—44no—
79C22×C4×C11C2×D414yes—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D412yes—
82C22×C4×C11C2×D412yes—
83C22×C4×C11C2×Q812yes—
84C22×C4×C11#4114yes—
85C22×C4×C11#4112yes—
86C22×C4×C11C2411yescharacteristic
87C22×Dic11—24no—
88C22×Dic11—24no—
89C22×Dic11—22no—
90C22×Dic11—22no—
91C22×Dic11—42no—
92C22×Dic11—41no—
93C22×Dic11—41no—
94C22×Dic11—42no—
95C22×Dic11—42no—
96C2×Dic22—28no—
97C2×Dic22—28no—
98C2×Dic22—24no—
99C2×Dic22—24no—
100C2×Dic22—24no—
101C2×Dic22—22no—
102C2×Dic22—42no—
103C2×Dic22—44no—
104C2×Dic22—44no—
105C2×Dic22—42no—
106C2×Dic22C2×Q814yescomplemented
107C11×C4⋊C4—28no—
108C11×C4⋊C4—216no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4C2×D414yes—
114C11×C4⋊C4C2×D414yes—
115C11×C22⋊C4—24no—
116C11×C22⋊C4—24no—
117C42×C11—24no—
118C42×C11—24no—
119C4×Dic11—24no—
120C4×Dic11—42no—
121#4318—24no—
122#4318—24no—
123#4318—44no—
124C2×C11⋊C8—24no—
125C2×C11⋊C8—44no—
126C2×#544D1111yescharacteristic
127C2×#419—112no—
128C2×#391—111no—
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—88no—
140C2×C4×C11—24no—
141C2×C4×C11—24no—
142C2×C4×C11—24no—
143C2×C4×C11—44no—
144C2×C4×C11—44no—
145C2×C4×C11—44no—
146C2×C4×C11—44no—
147C2×C4×C11—82no—
148C2×C4×C11#12012yes—
149C2×C4×C11C22⋊Q814yes—
150C2×C4×C11C22⋊Q814yes—
151C2×C4×C11C22⋊Q812yes—
152C2×C4×C11#12414yes—
153C2×C4×C11#12414yes—
154C2×C4×C11#12412yes—
155C2×C4×C11C22×D412yes—
156C2×C4×C11C22×Q811yescharacteristic
157C2×C4×C11C2×#4112yes—
158C2×C4×C11C2×#4111yescharacteristic
159C2×Dic11—24no—
160C2×Dic11—24no—
161C2×Dic11—42no—
162C2×Dic11—48no—
163C2×Dic11—42no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—44no—
167C2×Dic11—44no—
168Dic22—28no—
169Dic22—44no—
170Dic22—48no—
171C11⋊C8—44no—
172C23×Q8—111no—
173C22×M16—112no—
174#544—24no—
175#544—22no—
176#544C2×D1114yes—
177C2×C4⋊Q8—22no—
178C2×#125—22no—
179C2×C22⋊Q8—22no—
180C2×#117C2×D1112yes—
181C22×C4⋊C4C2×D1111yescharacteristic
182C22×C42—111no—
183#419—118no—
184#419—224no—
185C2×#103—222no—
186C2×#103—222no—
187#391—114no—
188#391—222no—
189C2×#95—222no—
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—114no—
215C22×Q8—112no—
216C22×Q8—222no—
217C22×Q8—221no—
218C22×Q8—224no—
219C22×Q8—222no—
220C22×Q8—222no—
221C23×C4—221no—
222C23×C4—221no—
223C23×C4C22⋊D1112yes—
224C23×C4C22×D1111yescharacteristic
225C2×M16—114no—
226C2×M16—222no—
227C2×M16—224no—
228C2×M16—224no—
229C22×C8—222no—
230C4⋊Q8—28no—
231C4⋊Q8—28no—
232#125—28no—
233#125—28no—
234C22⋊Q8—28no—
235C22⋊Q8—28no—
236#117—22no—
237#117—22no—
238#117C22⋊D1114yes—
239#117C22×D1114yes—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—24no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4C22⋊D1112yes—
245C2×C4⋊C4C22⋊D1112yes—
246C2×C4⋊C4C22⋊D1112yes—
247C2×C4⋊C4C22×D1112yes—
248C2×C22⋊C4—22no—
249C2×C42—22no—
250C2×C42—112no—
251C2×C42—224no—
252C2×C42—221no—
253#103—228no—
254#103—228no—
255#95—228no—
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—28no—
265C2×Q8—84no—
266C2×Q8—114no—
267C2×Q8—224no—
268C2×Q8—222no—
269C2×Q8—228no—
270C2×Q8—228no—
271C2×Q8—224no—
272C2×Q8—224no—
273C2×Q8—442no—
274C2×Q8—444no—
275C2×Q8—444no—
276C2×Q8—442no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—44no—
282C22×C4—224no—
283C22×C4—224no—
284C22×C4—222no—
285C22×C4—222no—
286C22×C4—442no—
287C22×C4—442no—
288C22×C4—442no—
289C22×C4—441no—
290C22×C4—441no—
291C22×C4Q8×D1112yes—
292C22×C4#434314yes—
293C22×C4#434312yes—
294C22×C4C2×C22⋊D1114yes—
295C22×C4C2×C22⋊D1111yescharacteristic
296C22×C4C2×C22⋊D1112yes—
297C22×C4C2×C22⋊D1112yes—
298C22×C4C23×D1111yescharacteristic
299M16—224no—
300M16—224no—
301M16—444no—
302C2×C8—224no—
303C2×C8—444no—
304C4⋊C4—28no—
305C4⋊C4—216no—
306C4⋊C4—24no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—24no—
310C4⋊C4C2×C22⋊D1114yes—
311C4⋊C4C2×C22⋊D1114yes—
312C22⋊C4—24no—
313C22⋊C4—24no—
314C42—24no—
315C42—24no—
316C42—224no—
317C42—442no—
318C11C2×#202811yescharacteristic, complemented, Sylow
319C23—22no—
320C23—22no—
321C23#6699912yes—
322C23#6700012yes—
323C23#6700611yescharacteristic
324C23#6700611yescharacteristic
325C23C22×C22⋊D1111yescharacteristic
326Q8—88no—
327Q8—228no—
328Q8—444no—
329Q8—448no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—44no—
334C2×C4—44no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—82no—
338C2×C4—224no—
339C2×C4—224no—
340C2×C4—442no—
341C2×C4—448no—
342C2×C4—442no—
343C2×C4—442no—
344C2×C4—444no—
345C2×C4—444no—
346C2×C4—442no—
347C2×C4#6699914yes—
348C2×C4#6699914yes—
349C2×C4#6699912yes—
350C2×C4#6700014yes—
351C2×C4#6700014yes—
352C2×C4#6700012yes—
353C2×C4#6700612yes—
354C2×C4C2×Q8×D1111yescharacteristic
355C2×C4C2×#434312yes—
356C2×C4C2×#434311yescharacteristic
357C2×C4C22×C22⋊D1112yes—
358C8—444no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—24no—
364C22—24no—
365C22#1062284412yes—
366C22#1062284412yes—
367C22#1062285512yes—
368C22#1062285912yes—
369C22C2×#6699911yescharacteristic
370C22C2×#6700011yescharacteristic
371C22C2×#6700611yescharacteristic
372C4—44no—
373C4—44no—
374C4—44no—
375C4—444no—
376C4—444no—
377C4#1062284414yes—
378C4C2×#6699912yes—
379C4C2×#6700012yes—
380C2—21no—
381C2—21no—
382C2—22no—
383C2#1306977414yesdirect product factor
384C2C2×#1062284411yescharacteristic
385C2C2×#1062285511yescharacteristic
386C2C2×#1062285911yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#544C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenterC2×#544D11
hypocenterC11C2×#2028
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
3. #13069774C2direct (N × H)
37. C22×Dic22Q8semidirect
106. C2×Dic22C2×Q8semidirect
259. C2×C11#2028semidirect
318. C11C2×#2028semidirect
383. C2#13069774direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226172
C2×#106225872
#130697742
C2×#106221682
C2×#106221702
C2×C11×#5442
C2×#202811