Finite Group Databasebeta

← C2×#13067624 #14726002

Subgroups — C2×#13067624 #14726002

Order 2816.

1028 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622656C212yesmaximal
2C2×#10622596C211yesmaximal, characteristic
3#13067624C218yesmaximal, direct product factor
4C2×#10622176C212yesmaximal
5C2×#10622166C211yesmaximal, characteristic
6C2×C11×#544C211yesmaximal, characteristic
7C11×#544—24no—
8C11×#544—22no—
9C11×#544C2214yes—
10C2×C11×C4⋊Q8—22no—
11C2×C11×#125—22no—
12C2×C11×C22⋊Q8—21no—
13C2×C11×C22⋊Q8C2212yes—
14C2×C11×#117—21no—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×Dic11⋊C4—21no—
18C2×#66899—22no—
19C2×C11⋊#95—21no—
20C2×C11⋊#95C2211yescharacteristic
21C2×C22⋊(C11⋊C8)C2212yes—
22#10622656—24no—
23#10622656C2218yes—
24#10622596—22no—
25#10622596C2214yes—
26C2×#66872—22no—
27#10622176C2218yes—
28#10622166C2214yes—
29C22×Q8×C11—21no—
30C22×Q8×C11D412yes—
31C23×C4×C11D411yescharacteristic
32C23×C4×C11D411yescharacteristic
33C23×C4×C11C2311yescharacteristic
34C23×Dic11—21no—
35C23×Dic11—21no—
36C11×C4⋊Q8—28no—
37C11×C4⋊Q8—28no—
38C11×#125—28no—
39C11×#125—28no—
40C11×C22⋊Q8—24no—
41C11×C22⋊Q8—24no—
42C11×C22⋊Q8—22no—
43C11×C22⋊Q8—22no—
44C11×C22⋊Q8D414yes—
45C11×C22⋊Q8C2314yes—
46C11×#117—24no—
47C11×#117—24no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4D412yes—
56C2×C11×C4⋊C4D412yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C22⋊C4—22no—
59C2×C42×C11—22no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11C2312yes—
64C2×Dic11⋊C4—24no—
65C2×Dic11⋊C4—44no—
66C22×C11⋊C8—22no—
67#66899—28no—
68C11⋊#95—24no—
69C11⋊#95—21no—
70C11⋊#95C2312yes—
71C22⋊(C11⋊C8)—22no—
72C22⋊(C11⋊C8)C2314yes—
73#66872—28no—
74C2×#1611—111nomaximal, Sylow
75C24×C11C2×D411yescharacteristic
76C2×Q8×C11—24no—
77C2×Q8×C11—22no—
78C2×Q8×C11—44no—
79C2×Q8×C11—82no—
80C2×Q8×C11C2×D414yes—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—42no—
89C22×C4×C11—42no—
90C22×C4×C11SD1614yes—
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×D412yes—
93C22×C4×C11C2×D412yes—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2411yescharacteristic
97C22×Dic11—24no—
98C22×Dic11—22no—
99C22×Dic11—22no—
100C22×Dic11—42no—
101C22×Dic11—41no—
102C22×Dic11—41no—
103C22×Dic11—42no—
104C22×Dic11—42no—
105C22×Dic11—42no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4—24no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—28no—
110C11×C4⋊C4—24no—
111C11×C4⋊C4—24no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—24no—
114C11×C4⋊C4—24no—
115C11×C4⋊C4C2×D414yes—
116C11×C22⋊C4—24no—
117C11×C22⋊C4—24no—
118C42×C11—28no—
119C4⋊Dic11—24no—
120C4⋊Dic11—42no—
121Dic11⋊C4—48no—
122C2×C11⋊C8—24no—
123C2×C11⋊C8—44no—
124C2×#544D1111yescharacteristic
125C2×#483—112no—
126C2×#398—111no—
127#1611—118no—
128C2×#328—112no—
129C2×#324—111no—
130C23×C11—22no—
131C23×C11—22no—
132C23×C11#12011yescharacteristic
133C23×C11#12011yescharacteristic
134C23×C11C2×SD1612yes—
135C23×C11#13712yes—
136C23×C11C22×D411yescharacteristic
137Q8×C11—44no—
138Q8×C11—82no—
139Q8×C11—84no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—24no—
143C2×C4×C11—24no—
144C2×C4×C11—24no—
145C2×C4×C11—24no—
146C2×C4×C11—24no—
147C2×C4×C11—22no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—41no—
151C2×C4×C11—44no—
152C2×C4×C11—42no—
153C2×C4×C11—44no—
154C2×C4×C11—42no—
155C2×C4×C11—81no—
156C2×C4×C11#12012yes—
157C2×C4×C11C2×SD1614yes—
158C2×C4×C11C22×D412yes—
159C2×Dic11—24no—
160C2×Dic11—48no—
161C2×Dic11—42no—
162C2×Dic11—42no—
163C2×Dic11—42no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—82no—
167C2×Dic11—82no—
168C11⋊C8—44no—
169#544—24no—
170#544—22no—
171#544C2×D1114yes—
172C2×C4⋊Q8—22no—
173C2×#125—22no—
174C2×C22⋊Q8—21no—
175C2×C22⋊Q8C2×D1112yes—
176C2×#117—21no—
177C22×C4⋊C4—111no—
178C22×C4⋊C4—221no—
179C22×C4⋊C4C2×D1111yescharacteristic
180#483—118no—
181#483—224no—
182C2×#106—222no—
183C2×#103—222no—
184C2×C22⋊C8—112no—
185#398—114no—
186#398—222no—
187C2×#95—111no—
188C2×#95—221no—
189#328—118no—
190#324—114no—
191C22×C11—24no—
192C22×C11—24no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11#44812yes—
198C22×C11#44812yes—
199C22×C11#45612yes—
200C22×C11#45812yes—
201C22×C11C2×#12011yescharacteristic
202C22×C11C22×SD1611yescharacteristic
203C22×C11C2×#13711yescharacteristic
204C4×C11—24no—
205C4×C11—22no—
206C4×C11—22no—
207C4×C11—44no—
208C4×C11—42no—
209C4×C11—44no—
210Dic11—44no—
211Dic11—82no—
212C22×Q8—21no—
213C22×Q8C22⋊D1112yes—
214C23×C4—221no—
215C23×C4—221no—
216C23×C4C22⋊D1111yescharacteristic
217C23×C4C22⋊D1111yescharacteristic
218C23×C4C22×D1111yescharacteristic
219C22×C8—222no—
220C4⋊Q8—28no—
221C4⋊Q8—28no—
222#125—28no—
223#125—28no—
224C22⋊Q8—24no—
225C22⋊Q8—24no—
226C22⋊Q8—22no—
227C22⋊Q8—22no—
228C22⋊Q8C22⋊D1114yes—
229C22⋊Q8C22×D1114yes—
230#117—24no—
231#117—24no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—112no—
240C2×C4⋊C4—222no—
241C2×C4⋊C4—222no—
242C2×C4⋊C4—221no—
243C2×C4⋊C4—224no—
244C2×C4⋊C4—444no—
245C2×C4⋊C4C22⋊D1112yes—
246C2×C4⋊C4C22⋊D1112yes—
247C2×C4⋊C4C22×D1112yes—
248C2×C22⋊C4—22no—
249C2×C42—22no—
250#106—228no—
251#103—228no—
252C22⋊C8—114no—
253C22⋊C8—222no—
254#95—112no—
255#95—221no—
256#95—224no—
257C2×C11—21no—
258C2×C11—21no—
259C2×C11—22no—
260C2×C11#161114yescomplemented
261C2×C11C2×#44811yescharacteristic
262C2×C11C2×#45611yescharacteristic
263C2×C11C2×#45811yescharacteristic
264C24C2×C22⋊D1111yescharacteristic
265C2×Q8—24no—
266C2×Q8—22no—
267C2×Q8—44no—
268C2×Q8—82no—
269C2×Q8C2×C22⋊D1114yes—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—224no—
280C22×C4—222no—
281C22×C4—222no—
282C22×C4—442no—
283C22×C4—442no—
284C22×C4—442no—
285C22×C4—442no—
286C22×C4—441no—
287C22×C4—441no—
288C22×C4#432514yes—
289C22×C4C2×C22⋊D1112yes—
290C22×C4C2×C22⋊D1112yes—
291C22×C4C2×C22⋊D1112yes—
292C22×C4C2×C22⋊D1111yescharacteristic
293C22×C4C2×C22⋊D1112yes—
294C22×C4C23×D1111yescharacteristic
295C2×C8—224no—
296C2×C8—444no—
297C4⋊C4—24no—
298C4⋊C4—24no—
299C4⋊C4—24no—
300C4⋊C4—28no—
301C4⋊C4—24no—
302C4⋊C4—24no—
303C4⋊C4—22no—
304C4⋊C4—24no—
305C4⋊C4—24no—
306C4⋊C4—224no—
307C4⋊C4—448no—
308C4⋊C4—442no—
309C4⋊C4C2×C22⋊D1114yes—
310C22⋊C4—24no—
311C22⋊C4—24no—
312C42—28no—
313C11C2×#161111yescharacteristic, complemented, Sylow
314C23—22no—
315C23—22no—
316C23C2×#432512yes—
317C23#6699512yes—
318C23#6700611yescharacteristic
319C23#6700611yescharacteristic
320C23C22×C22⋊D1111yescharacteristic
321Q8—44no—
322Q8—82no—
323Q8—84no—
324C2×C4—22no—
325C2×C4—24no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—22no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—22no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—44no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—81no—
340C2×C4—224no—
341C2×C4—448no—
342C2×C4—442no—
343C2×C4—442no—
344C2×C4—442no—
345C2×C4—442no—
346C2×C4—442no—
347C2×C4—882no—
348C2×C4—882no—
349C2×C4C2×#432514yes—
350C2×C4#6700612yes—
351C2×C4C22×C22⋊D1112yes—
352C8—444no—
353C22—24no—
354C22—24no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22#1062284012yes—
360C22#1062284012yes—
361C22#1062285612yes—
362C22#1062285912yes—
363C22C22×#432511yescharacteristic
364C22C2×#6699511yescharacteristic
365C22C2×#6700611yescharacteristic
366C4—24no—
367C4—22no—
368C4—22no—
369C4—44no—
370C4—42no—
371C4—44no—
372C4—444no—
373C4—882no—
374C2—21no—
375C2—21no—
376C2—22no—
377C2#1306762414yesdirect product factor
378C2C2×#1062284011yescharacteristic
379C2C2×#1062285911yescharacteristic
380C2C2×#1062285611yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#544C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenterC2×#544D11
hypocenterC11C2×#1611
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
3. #13067624C2direct (N × H)
260. C2×C11#1611semidirect
313. C11C2×#1611semidirect
377. C2#13067624direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226562
C2×#106225962
#130676242
C2×#106221762
C2×#106221662
C2×C11×#5442
C2×#161111