Finite Group Databasebeta

← C2×#13067551 #14725939

Subgroups — C2×#13067551 #14725939

Order 2816.

1652 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622649C212yesmaximal, complemented
2C2×#10622604C211yesmaximal, characteristic, complemented
3#13067551C218yesmaximal, direct product factor
4C2×#10622175C212yesmaximal, complemented
5C2×#10622166C211yesmaximal, characteristic, complemented
6C2×C11×#537C211yesmaximal, characteristic, complemented
7C22×C11×#41—21no—
8C23×D44C2211yescharacteristic
9C11×#537—24no—
10C11×#537—22no—
11C11×#537C2214yescomplemented
12C2×C11×C22⋊Q8—22no—
13C2×C11×#121—22no—
14C2×C11×#121—21no—
15C2×C11×#121C2212yes—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×#4323—22no—
18C22×(C2×D11)⋊C4—21no—
19C22×(C2×D11)⋊C4—21no—
20C2×C11⋊#95C2211yescharacteristic
21C2×C22⋊(C11⋊C8)C2212yes—
22#10622649—24no—
23#10622649C2218yescomplemented
24#10622604—22no—
25#10622604C2214yescomplemented
26C2×#66873—22no—
27#10622175C2218yescomplemented
28#10622166C2214yescomplemented
29C24×D11—21no—
30C2×C11×#41—24no—
31C2×C11×#41—24no—
32C2×C11×#41—44no—
33C2×C11×#41—44no—
34C22×Q8×C11—21no—
35C22×D4×C11—21no—
36C22×D4×C11—22no—
37C22×D4×C11—21no—
38C22×D4×C11D412yes—
39C23×C4×C11—22no—
40C23×C4×C11D411yescharacteristic
41C23×C4×C11D411yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×Dic11—21no—
44C22×D44—22no—
45C22×D44—22no—
46C22×D44—21no—
47C22×D44—44no—
48C22×D44C2312yes—
49C11×C22⋊Q8—28no—
50C11×C22⋊Q8—28no—
51C11×#121—24no—
52C11×#121—28no—
53C11×#121—28no—
54C11×#121—24no—
55C11×#121—22no—
56C11×#121—22no—
57C11×#121D414yes—
58C11×#121C2314yes—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4D412yes—
63C2×C11×C4⋊C4D412yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×#4323—28no—
68C2×#4323—48no—
69C2×(C2×D11)⋊C4—24no—
70C2×(C2×D11)⋊C4—24no—
71C2×(C2×D11)⋊C4—44no—
72C2×(C2×D11)⋊C4—44no—
73C22×C11⋊C8—22no—
74C11⋊#95—21no—
75C11⋊#95C2312yes—
76C22⋊(C11⋊C8)—22no—
77C22⋊(C11⋊C8)C2314yes—
78#66873—28no—
79C2×#1598—111nomaximal, Sylow
80C24×C11—22no—
81C24×C11C2×D411yescharacteristic
82C23×D11—24no—
83C23×D11—22no—
84C23×D11—42no—
85C23×D11—42no—
86C23×D11—42no—
87C23×D11—41no—
88C23×D11—41no—
89C23×D11—42no—
90C23×D11—42no—
91C11×#41—48no—
92C11×#41—416no—
93C11×#41—48no—
94C2×Q8×C11—24no—
95C2×Q8×C11—44no—
96C2×D4×C11—24no—
97C2×D4×C11—24no—
98C2×D4×C11—24no—
99C2×D4×C11—24no—
100C2×D4×C11—22no—
101C2×D4×C11—44no—
102C2×D4×C11—44no—
103C2×D4×C11—44no—
104C2×D4×C11—44no—
105C2×D4×C11—82no—
106C2×D4×C11C2×D414yes—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—28no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—42no—
115C22×C4×C11—48no—
116C22×C4×C11—42no—
117C22×C4×C11D814yescomplemented
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2411yescharacteristic
124C22×Dic11—22no—
125C22×Dic11—42no—
126C22×Dic11—42no—
127C22×Dic11—42no—
128C2×D44—28no—
129C2×D44—24no—
130C2×D44—44no—
131C2×D44—44no—
132C2×D44—44no—
133C2×D44—48no—
134C2×D44—42no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4C2×D414yes—
140C11×C22⋊C4—28no—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—24no—
143#4323—416no—
144(C2×D11)⋊C4—48no—
145(C2×D11)⋊C4—48no—
146C2×C11⋊C8—24no—
147C2×C11⋊C8—44no—
148C2×#537D1111yescharacteristic, complemented
149C2×#447—112no—
150C2×#394—111no—
151#1598—118no—
152C2×#327—112no—
153C2×#324—111no—
154C23×C11—22no—
155C23×C11—22no—
156C23×C11—24no—
157C23×C11—44no—
158C23×C11—44no—
159C23×C11—44no—
160C23×C11#12011yescharacteristic
161C23×C11#12011yescharacteristic
162C23×C11C2×D812yes—
163C23×C11AGL(1,ℤ/8)12yes—
164C23×C11C22×D411yescharacteristic
165C22×D11—24no—
166C22×D11—42no—
167C22×D11—44no—
168C22×D11—48no—
169C22×D11—48no—
170C22×D11—42no—
171C22×D11—42no—
172C22×D11—42no—
173C22×D11—42no—
174C22×D11—42no—
175C22×D11—44no—
176C22×D11—84no—
177C22×D11—84no—
178C22×D11—82no—
179C22×D11—82no—
180C22×D11—82no—
181C22×D11—82no—
182Q8×C11—48no—
183D4×C11—44no—
184D4×C11—48no—
185D4×C11—44no—
186D4×C11—44no—
187D4×C11—48no—
188D4×C11—82no—
189D4×C11—84no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—24no—
193C2×C4×C11—24no—
194C2×C4×C11—24no—
195C2×C4×C11—22no—
196C2×C4×C11—24no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—41no—
200C2×C4×C11—416no—
201C2×C4×C11—44no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—81no—
205C2×C4×C11#12012yes—
206C2×C4×C11C2×D814yescomplemented
207C2×C4×C11C22×D412yes—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—84no—
212D44—28no—
213D44—48no—
214D44—44no—
215C11⋊C8—44no—
216C22×#41—21no—
217C23×D4—111no—
218C22×D8—222no—
219#537—24no—
220#537—22no—
221#537C2×D1114yescomplemented
222C2×C22⋊Q8—22no—
223C2×#121—22no—
224C2×#121—21no—
225C2×#121C2×D1112yes—
226C22×C4⋊C4C2×D1111yescharacteristic
227C22×C22⋊C4—221no—
228C22×C22⋊C4—221no—
229#447—118no—
230#447—224no—
231C2×#102—222no—
232C2×C22⋊C8—112no—
233#394—114no—
234#394—222no—
235C2×#95—111no—
236#327—118no—
237#324—114no—
238C22×C11—24no—
239C22×C11—24no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—44no—
245C22×C11—44no—
246C22×C11—44no—
247C22×C11—88no—
248C22×C11#44712yes—
249C22×C11#44712yes—
250C22×C11#45412yes—
251C22×C11B(4,𝔽2)12yes—
252C22×C11C2×#12011yescharacteristic
253C22×C11C22×D811yescharacteristic
254C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
255C2×D11—44no—
256C2×D11—44no—
257C2×D11—44no—
258C2×D11—82no—
259C2×D11—82no—
260C2×D11—88no—
261C2×D11—88no—
262C2×D11—82no—
263C2×D11—82no—
264C4×C11—24no—
265C4×C11—22no—
266C4×C11—22no—
267C4×C11—44no—
268C4×C11—42no—
269Dic11—82no—
270C25—221no—
271C2×#41—24no—
272C2×#41—24no—
273C2×#41—44no—
274C2×#41—44no—
275C22×Q8—21no—
276C22×D4—21no—
277C22×D4—22no—
278C22×D4—21no—
279C22×D4—112no—
280C22×D4—222no—
281C22×D4—222no—
282C22×D4—221no—
283C22×D4—444no—
284C22×D4C22⋊D1112yes—
285C23×C4—22no—
286C23×C4—221no—
287C23×C4C22⋊D1111yescharacteristic
288C23×C4C22⋊D1111yescharacteristic
289C23×C4C22×D1111yescharacteristic
290C2×D8—228no—
291C2×D8—448no—
292C22×C8—222no—
293C22⋊Q8—28no—
294C22⋊Q8—28no—
295#121—24no—
296#121—28no—
297#121—28no—
298#121—24no—
299#121—22no—
300#121—22no—
301#121C22⋊D1114yes—
302#121C22×D1114yes—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4C22⋊D1112yes—
307C2×C4⋊C4C22⋊D1112yes—
308C2×C4⋊C4C22×D1112yes—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—224no—
312C2×C22⋊C4—224no—
313C2×C22⋊C4—444no—
314C2×C22⋊C4—444no—
315#102—228no—
316C22⋊C8—114no—
317C22⋊C8—222no—
318#95—112no—
319#95—221no—
320C2×C11—21no—
321C2×C11—21no—
322C2×C11—22no—
323C2×C11—84no—
324C2×C11#159814yescomplemented
325C2×C11C2×#44711yescharacteristic
326C2×C11C2×#45411yescharacteristic
327C2×C11C2×B(4,𝔽2)11yescharacteristic
328D11—84no—
329C24—22no—
330C24—224no—
331C24—222no—
332C24—442no—
333C24—442no—
334C24—442no—
335C24—442no—
336C24—442no—
337C24—441no—
338C24—441no—
339C24C2×C22⋊D1111yescharacteristic
340#41—48no—
341#41—416no—
342#41—48no—
343C2×Q8—24no—
344C2×Q8—44no—
345C2×D4—24no—
346C2×D4—24no—
347C2×D4—24no—
348C2×D4—24no—
349C2×D4—22no—
350C2×D4—44no—
351C2×D4—44no—
352C2×D4—44no—
353C2×D4—44no—
354C2×D4—82no—
355C2×D4—228no—
356C2×D4—224no—
357C2×D4—444no—
358C2×D4—444no—
359C2×D4—448no—
360C2×D4—444no—
361C2×D4—442no—
362C2×D4C2×C22⋊D1114yes—
363C22×C4—22no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—28no—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—42no—
371C22×C4—48no—
372C22×C4—42no—
373C22×C4—222no—
374C22×C4—442no—
375C22×C4—442no—
376C22×C4—442no—
377C22×C4#432314yescomplemented
378C22×C4C2×C22⋊D1112yes—
379C22×C4C2×C22⋊D1112yes—
380C22×C4C2×C22⋊D1112yes—
381C22×C4C2×C22⋊D1111yescharacteristic
382C22×C4C2×C22⋊D1112yes—
383C22×C4C23×D1111yescharacteristic
384D8—4416no—
385C2×C8—224no—
386C2×C8—444no—
387C4⋊C4—24no—
388C4⋊C4—24no—
389C4⋊C4—22no—
390C4⋊C4—24no—
391C4⋊C4C2×C22⋊D1114yes—
392C22⋊C4—28no—
393C22⋊C4—24no—
394C22⋊C4—24no—
395C22⋊C4—448no—
396C22⋊C4—448no—
397C11C2×#159811yescharacteristic, complemented, Sylow
398C23—22no—
399C23—22no—
400C23—24no—
401C23—44no—
402C23—44no—
403C23—44no—
404C23—224no—
405C23—442no—
406C23—444no—
407C23—448no—
408C23—448no—
409C23—442no—
410C23—442no—
411C23—442no—
412C23—442no—
413C23—444no—
414C23—442no—
415C23—884no—
416C23—884no—
417C23—882no—
418C23—882no—
419C23—882no—
420C23—882no—
421C23C2×#432312yes—
422C23#6698512yes—
423C23#6700611yescharacteristic
424C23#6700611yescharacteristic
425C23C22×C22⋊D1111yescharacteristic
426Q8—48no—
427D4—44no—
428D4—48no—
429D4—44no—
430D4—44no—
431D4—48no—
432D4—82no—
433D4—84no—
434D4—228no—
435D4—444no—
436D4—448no—
437C2×C4—22no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—24no—
444C2×C4—42no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—416no—
448C2×C4—44no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—81no—
452C2×C4—442no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4—884no—
456C2×C4C2×#432314yescomplemented
457C2×C4#6700612yes—
458C2×C4C22×C22⋊D1112yes—
459C8—444no—
460C22—24no—
461C22—24no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—44no—
467C22—44no—
468C22—44no—
469C22—88no—
470C22—444no—
471C22—444no—
472C22—444no—
473C22—882no—
474C22—882no—
475C22—888no—
476C22—888no—
477C22—882no—
478C22—882no—
479C22#1062283012yes—
480C22#1062283012yes—
481C22#1062285712yes—
482C22#1062285812yes—
483C22C22×#432311yescharacteristic
484C22C2×#6698511yescharacteristic
485C22C2×#6700611yescharacteristic
486C4—24no—
487C4—22no—
488C4—22no—
489C4—44no—
490C4—42no—
491C4—882no—
492C2—21no—
493C2—21no—
494C2—22no—
495C2—84no—
496C2—884no—
497C2#1306755114yesdirect product factor
498C2C2×#1062283011yescharacteristic
499C2C2×#1062285811yescharacteristic
500C2C2×#1062285711yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#537C2
socleC23×C11#120
hypercenterC2×#537D11
hypocenterC11C2×#1598
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#10622649C2semidirect
2. C2×#10622604C2semidirect
3. #13067551C2direct (N × H)
4. C2×#10622175C2semidirect
5. C2×#10622166C2semidirect
6. C2×C11×#537C2semidirect
11. C11×#537C22semidirect
23. #10622649C22semidirect
25. #10622604C22semidirect
27. #10622175C22semidirect
28. #10622166C22semidirect
117. C22×C4×C11D8semidirect
148. C2×#537D11semidirect
206. C2×C4×C11C2×D8semidirect
221. #537C2×D11semidirect
324. C2×C11#1598semidirect
377. C22×C4#4323semidirect
397. C11C2×#1598semidirect
456. C2×C4C2×#4323semidirect
497. C2#13067551direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226492
C2×#106226042
#130675512
C2×#106221752
C2×#106221662
C2×C11×#5372
C2×#159811