Finite Group Databasebeta

← C2×#13067743 #14729636

Subgroups — C2×#13067743 #14729636

Order 2816.

1322 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622689C211yesmaximal, characteristic, complemented
2C2×#10622634C211yesmaximal, characteristic, complemented
3C2×#10622621C211yesmaximal, characteristic, complemented
4#13067743C218yesmaximal, direct product factor
5C2×#10622182C211yesmaximal, characteristic, complemented
6C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
8C2×C11×#550C211yesmaximal, characteristic
9C22×C11×#41—21no—
10C11×#550—22no—
11C11×#550—22no—
12C11×#550—22no—
13C11×#550C2214yes—
14C2×C11×#127—21no—
15C2×C11×#127C2211yescharacteristic
16C2×C11×#121—22no—
17C2×C11×#121—21no—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C22×#4324—22no—
22C2×#66922C2211yescharacteristic
23C2×#66899—21no—
24C2×#66896—21no—
25#10622689—22no—
26#10622689C2214yescomplemented
27#10622634—22no—
28#10622634C2214yescomplemented
29#10622621—22no—
30#10622621C2214yescomplemented
31C2×#66872—21no—
32C2×#66871—21no—
33C2×C4⋊(C11⋊C8)C2211yescharacteristic
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622182C2214yescomplemented
37Q8⋊(C11⋊C8)C2214yescomplemented
38D4⋊(C11⋊C8)C2214yescomplemented
39C2×C11×#41—24no—
40C2×C11×#41—24no—
41C2×C11×#41—44no—
42C2×C11×#41—44no—
43C22×Q8×C11D411yescharacteristic
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—21no—
47C22×D4×C11—21no—
48C22×D4×C11D411yescharacteristic
49C22×D4×C11D412yes—
50C23×C4×C11—22no—
51C23×C4×C11—21no—
52C22×Dic22—21no—
53C11×#127—24no—
54C11×#127—24no—
55C11×#127—21no—
56C11×#127—21no—
57C11×#127D412yes—
58C11×#127C2312yes—
59C11×#121—24no—
60C11×#121—28no—
61C11×#121—28no—
62C11×#121—24no—
63C4×Q8×C11—21no—
64C4×Q8×C11—21no—
65C4×Q8×C11D412yes—
66C4×Q8×C11C2312yes—
67C4×D4×C11—24no—
68C4×D4×C11—24no—
69C4×D4×C11—21no—
70C4×D4×C11—21no—
71C4×D4×C11D412yes—
72C4×D4×C11C2312yes—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—21no—
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80C2×#4324—28no—
81C2×#4324—48no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C22×C11⋊C8—21no—
85C22×C11⋊C8—21no—
86C22×C11⋊C8—21no—
87#66922—21no—
88#66922—21no—
89#66922—21no—
90#66922C2312yes—
91#66899—24no—
92#66896—24no—
93#66872—24no—
94#66871—24no—
95C4⋊(C11⋊C8)—21no—
96C4⋊(C11⋊C8)—21no—
97C4⋊(C11⋊C8)C2312yes—
98C4⋊(C11⋊C8)C2312yes—
99C4×C11⋊C8—21no—
100C4×C11⋊C8C2312yes—
101C2×#1631—111nomaximal, Sylow
102C24×C11—21no—
103C24×C11—22no—
104C11×#41—48no—
105C11×#41—416no—
106C11×#41—48no—
107C2×Q8×C11—21no—
108C2×Q8×C11—22no—
109C2×Q8×C11SD1614yescomplemented
110C2×Q8×C11C2×D412yes—
111C2×D4×C11—28no—
112C2×D4×C11—28no—
113C2×D4×C11—21no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—48no—
122C2×D4×C11—44no—
123C2×D4×C11—42no—
124C2×D4×C11—42no—
125C2×D4×C11—42no—
126C2×D4×C11—42no—
127C2×D4×C11—84no—
128C2×D4×C11C2×D412yes—
129C2×D4×C11C2×D414yes—
130C22×C4×C11—21no—
131C22×C4×C11—28no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—48no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×Dic11—41no—
143C2×Dic22—22no—
144C2×Dic22—44no—
145C2×Dic22—41no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4C2×D412yes—
151C11×C4⋊C4C2×D412yes—
152C11×C22⋊C4—28no—
153C11×C22⋊C4—22no—
154C11×C22⋊C4—22no—
155C42×C11—22no—
156C42×C11—22no—
157C42×C11C2×D411yescharacteristic
158C42×C11C2×D411yescharacteristic
159C42×C11C2×D411yescharacteristic
160C42×C11C2411yescharacteristic
161#4324—416no—
162C4⋊Dic11—22no—
163C4⋊Dic11—22no—
164C4⋊Dic11—41no—
165C4⋊Dic11—41no—
166C2×C11⋊C8—24no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—42no—
171C2×C11⋊C8—42no—
172C2×#550D1111yescharacteristic
173C2×#492—111no—
174C2×#477—111no—
175C2×#476—111no—
176#1631—118no—
177C2×#331—111no—
178C2×Q8⋊C8—111no—
179C2×D4⋊C8—111no—
180C23×C11—22no—
181C23×C11—24no—
182C23×C11—44no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—44no—
186C23×C11—44no—
187C23×C11—42no—
188C23×C11#12011yescharacteristic
189Q8×C11—22no—
190Q8×C11—24no—
191Q8×C11C2×SD1614yescomplemented
192D4×C11—22no—
193D4×C11—22no—
194D4×C11—44no—
195D4×C11—416no—
196D4×C11—42no—
197D4×C11—42no—
198D4×C11—42no—
199D4×C11—42no—
200D4×C11—44no—
201D4×C11—42no—
202D4×C11—44no—
203D4×C11—82no—
204D4×C11—88no—
205C2×C4×C11—22no—
206C2×C4×C11—24no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—416no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—44no—
216C2×C4×C11#12011yescharacteristic
217C2×C4×C11#12011yescharacteristic
218C2×C4×C11#12011yescharacteristic
219C2×C4×C11C2×SD1612yes—
220C2×C4×C11#13512yes—
221C2×C4×C11AGL(1,ℤ/8)12yes—
222C2×C4×C11#13712yes—
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×Dic11—42no—
227C2×Dic11—82no—
228Dic22—44no—
229Dic22—82no—
230C11⋊C8—24no—
231C11⋊C8—42no—
232C11⋊C8—42no—
233C22×#41—21no—
234C22×SD16—222no—
235#550—22no—
236#550—22no—
237#550—22no—
238#550C2×D1114yes—
239C2×C4⋊Q8—111no—
240C2×#127—21no—
241C2×#127C2×D1111yescharacteristic
242C2×#121—22no—
243C2×#121—21no—
244C2×C4×Q8C2×D1111yescharacteristic
245C2×C4×D4—21no—
246C2×C4×D4C2×D1111yescharacteristic
247#492—114no—
248#492—222no—
249#477—114no—
250#477—222no—
251#476—114no—
252#476—222no—
253C2×#107—221no—
254C2×#106—221no—
255C2×C4⋊C8—111no—
256C2×C4⋊C8—111no—
257C2×#103—221no—
258C2×#102—221no—
259C2×C4×C8—111no—
260#331—114no—
261Q8⋊C8—114no—
262D4⋊C8—114no—
263C22×C11—44no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—44no—
267C22×C11—44no—
268C22×C11—42no—
269C22×C11—84no—
270C22×C11—88no—
271C22×C11#45012yes—
272C22×C11#45212yes—
273C22×C11#45312yes—
274C22×C11C2×#12011yescharacteristic
275C4×C11—24no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—42no—
279C4×C11—42no—
280C4×C11#45012yes—
281C4×C11#45212yes—
282C4×C11C22×SD1611yescharacteristic
283C4×C11C2×#13511yescharacteristic
284C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
285C4×C11C2×#13711yescharacteristic
286Dic11—82no—
287C2×#41—24no—
288C2×#41—24no—
289C2×#41—44no—
290C2×#41—44no—
291C22×Q8—221no—
292C22×Q8C22⋊D1111yescharacteristic
293C22×D4—22no—
294C22×D4—22no—
295C22×D4—21no—
296C22×D4—21no—
297C22×D4C22⋊D1111yescharacteristic
298C22×D4C22⋊D1112yes—
299C23×C4—22no—
300C23×C4—21no—
301C2×SD16—228no—
302C2×SD16—448no—
303C22×C8—221no—
304C22×C8—221no—
305C22×C8—221no—
306C4⋊Q8—112no—
307C4⋊Q8—221no—
308C4⋊Q8—221no—
309C4⋊Q8—221no—
310#127—24no—
311#127—24no—
312#127—21no—
313#127—21no—
314#127C22⋊D1112yes—
315#127C22×D1112yes—
316#121—24no—
317#121—28no—
318#121—28no—
319#121—24no—
320C4×Q8—21no—
321C4×Q8—21no—
322C4×Q8C22⋊D1112yes—
323C4×Q8C22×D1112yes—
324C4×D4—24no—
325C4×D4—24no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4C22⋊D1112yes—
329C4×D4C22×D1112yes—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4C22⋊D1111yescharacteristic
334C2×C4⋊C4C22⋊D1111yescharacteristic
335C2×C22⋊C4—22no—
336C2×C22⋊C4—21no—
337C2×C42—21no—
338C2×C42C22×D1111yescharacteristic
339#107—224no—
340#106—224no—
341C4⋊C8—112no—
342C4⋊C8—112no—
343C4⋊C8—221no—
344C4⋊C8—221no—
345#103—224no—
346#102—224no—
347C4×C8—112no—
348C4×C8—221no—
349C2×C11—82no—
350C2×C11—84no—
351C2×C11#163114yescomplemented
352C2×C11C2×#45011yescharacteristic
353C2×C11C2×#45211yescharacteristic
354C2×C11C2×#45311yescharacteristic
355C24—21no—
356C24—22no—
357#41—48no—
358#41—416no—
359#41—48no—
360C2×Q8—22no—
361C2×Q8—21no—
362C2×Q8—222no—
363C2×Q8—444no—
364C2×Q8—441no—
365C2×Q8#432414yescomplemented
366C2×Q8C2×C22⋊D1112yes—
367C2×D4—28no—
368C2×D4—28no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—21no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—48no—
378C2×D4—44no—
379C2×D4—42no—
380C2×D4—42no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—84no—
384C2×D4C2×C22⋊D1112yes—
385C2×D4C2×C22⋊D1114yes—
386C22×C4—21no—
387C22×C4—28no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—48no—
393C22×C4—42no—
394C22×C4—42no—
395C22×C4—441no—
396C22×C4C2×C22⋊D1111yescharacteristic
397C22×C4C2×C22⋊D1111yescharacteristic
398C22×C4C2×C22⋊D1111yescharacteristic
399SD16—4416no—
400C2×C8—224no—
401C2×C8—222no—
402C2×C8—222no—
403C2×C8—222no—
404C2×C8—442no—
405C2×C8—442no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—222no—
411C4⋊C4—222no—
412C4⋊C4—441no—
413C4⋊C4—441no—
414C4⋊C4C2×C22⋊D1112yes—
415C4⋊C4C2×C22⋊D1112yes—
416C22⋊C4—28no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C42—22no—
420C42—22no—
421C42C2×C22⋊D1111yescharacteristic
422C42C2×C22⋊D1111yescharacteristic
423C42C2×C22⋊D1111yescharacteristic
424C42C23×D1111yescharacteristic
425C11C2×#163111yescharacteristic, complemented, Sylow
426C23—22no—
427C23—24no—
428C23—44no—
429C23—42no—
430C23—42no—
431C23—44no—
432C23—44no—
433C23—42no—
434C23#6700611yescharacteristic
435Q8—22no—
436Q8—24no—
437Q8—444no—
438Q8—882no—
439Q8C2×#432414yescomplemented
440D4—22no—
441D4—22no—
442D4—44no—
443D4—416no—
444D4—42no—
445D4—42no—
446D4—44no—
447D4—42no—
448D4—42no—
449D4—42no—
450D4—44no—
451D4—82no—
452D4—88no—
453C2×C4—24no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—416no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—44no—
464C2×C4—442no—
465C2×C4—882no—
466C2×C4#6698512yes—
467C2×C4C2×#432412yes—
468C2×C4#6700312yes—
469C2×C4#6700412yes—
470C2×C4#6700611yescharacteristic
471C2×C4#6700611yescharacteristic
472C2×C4#6700611yescharacteristic
473C2×C4C22×C22⋊D1111yescharacteristic
474C2×C4C22×C22⋊D1111yescharacteristic
475C2×C4C22×C22⋊D1111yescharacteristic
476C8—224no—
477C8—442no—
478C8—442no—
479C22—44no—
480C22—42no—
481C22—42no—
482C22—44no—
483C22—44no—
484C22—42no—
485C22—84no—
486C22—88no—
487C22#1062283112yes—
488C22#1062285212yes—
489C22#1062285412yes—
490C22C2×#6700611yescharacteristic
491C4—24no—
492C4—21no—
493C4—21no—
494C4—42no—
495C4—42no—
496C4—882no—
497C4#1062283112yes—
498C4#1062285212yes—
499C4C2×#6698511yescharacteristic
500C4C22×#432411yescharacteristic
501C4C2×#6700311yescharacteristic
502C4C2×#6700411yescharacteristic
503C2—82no—
504C2—84no—
505C2#1306774314yesdirect product factor
506C2C2×#1062283111yescharacteristic
507C2C2×#1062285211yescharacteristic
508C2C2×#1062285411yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC2×C11×#550C2
socleC23×C11#120
hypercenterC2×#550D11
hypocenterC11C2×#1631
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#10622689C2semidirect
2. C2×#10622634C2semidirect
3. C2×#10622621C2semidirect
4. #13067743C2direct (N × H)
5. C2×#10622182C2semidirect
6. C2×Q8⋊(C11⋊C8)C2semidirect
7. C2×D4⋊(C11⋊C8)C2semidirect
26. #10622689C22semidirect
28. #10622634C22semidirect
30. #10622621C22semidirect
36. #10622182C22semidirect
37. Q8⋊(C11⋊C8)C22semidirect
38. D4⋊(C11⋊C8)C22semidirect
109. C2×Q8×C11SD16semidirect
191. Q8×C11C2×SD16semidirect
351. C2×C11#1631semidirect
365. C2×Q8#4324semidirect
425. C11C2×#1631semidirect
439. Q8C2×#4324semidirect
505. C2#13067743direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226892
C2×#106226342
C2×#106226212
#130677432
C2×#106221822
C2×Q8⋊(C11⋊C8)2
C2×D4⋊(C11⋊C8)2
C2×C11×#5502
C2×#163111