Finite Group Databasebeta

← C2×#13067816 #14729687

Subgroups — C2×#13067816 #14729687

Order 2816.

1290 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622683C211yesmaximal, characteristic, complemented
2C2×#10622633C211yesmaximal, characteristic, complemented
3C2×#10622632C211yesmaximal, characteristic, complemented
4#13067816C218yesmaximal, 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—21no—
22C2×#66922C2211yescharacteristic
23C2×#66899—21no—
24C2×#66896—22no—
25#10622683—22no—
26#10622683C2214yescomplemented
27#10622633—22no—
28#10622633C2214yescomplemented
29#10622632—22no—
30#10622632C2214yescomplemented
31C2×#66874—21no—
32C2×#66872—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—24no—
81C2×#4324—44no—
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—28no—
93#66874—24no—
94#66872—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×#1642—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—41no—
145C2×Dic22—42no—
146C2×Dic22—42no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4C2×D412yes—
152C11×C4⋊C4C2×D412yes—
153C11×C22⋊C4—28no—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—22no—
156C42×C11—22no—
157C42×C11—22no—
158C42×C11C2×D411yescharacteristic
159C42×C11C2×D411yescharacteristic
160C42×C11C2×D411yescharacteristic
161C42×C11C2411yescharacteristic
162#4324—48no—
163C4⋊Dic11—22no—
164C4⋊Dic11—22no—
165C4⋊Dic11—41no—
166C4⋊Dic11—41no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—42no—
171C2×C11⋊C8—42no—
172C2×C11⋊C8—42no—
173C2×#550D1111yescharacteristic
174C2×#486—111no—
175C2×#475—111no—
176C2×#461—111no—
177#1642—118no—
178C2×#331—111no—
179C2×Q8⋊C8—111no—
180C2×D4⋊C8—111no—
181C23×C11—22no—
182C23×C11—24no—
183C23×C11—42no—
184C23×C11—44no—
185C23×C11—44no—
186C23×C11—42no—
187C23×C11—44no—
188C23×C11—42no—
189C23×C11#12011yescharacteristic
190Q8×C11—22no—
191Q8×C11—24no—
192Q8×C11C2×SD1614yescomplemented
193D4×C11—22no—
194D4×C11—22no—
195D4×C11—44no—
196D4×C11—416no—
197D4×C11—42no—
198D4×C11—42no—
199D4×C11—42no—
200D4×C11—42no—
201D4×C11—42no—
202D4×C11—44no—
203D4×C11—44no—
204D4×C11—82no—
205D4×C11—88no—
206C2×C4×C11—22no—
207C2×C4×C11—24no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—416no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—44no—
217C2×C4×C11#12011yescharacteristic
218C2×C4×C11#12011yescharacteristic
219C2×C4×C11#12011yescharacteristic
220C2×C4×C11C2×SD1612yes—
221C2×C4×C11#13512yes—
222C2×C4×C11AGL(1,ℤ/8)12yes—
223C2×C4×C11AGL(1,ℤ/8)12yes—
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×Dic11—42no—
228C2×Dic11—82no—
229Dic22—42no—
230Dic22—42no—
231Dic22—82no—
232C11⋊C8—42no—
233C11⋊C8—42no—
234C11⋊C8—42no—
235C22×#41—21no—
236C22×SD16—221no—
237#550—22no—
238#550—22no—
239#550—22no—
240#550C2×D1114yes—
241C2×C4⋊Q8—111no—
242C2×#127—21no—
243C2×#127C2×D1111yescharacteristic
244C2×#121—22no—
245C2×#121—21no—
246C2×C4×Q8C2×D1111yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4C2×D1111yescharacteristic
249#486—114no—
250#486—222no—
251#475—114no—
252#475—222no—
253#461—114no—
254#461—222no—
255C2×#106—221no—
256C2×C4⋊C8—111no—
257C2×C4⋊C8—111no—
258C2×#103—221no—
259C2×#103—221no—
260C2×#102—222no—
261C2×C4×C8—111no—
262#331—114no—
263Q8⋊C8—114no—
264D4⋊C8—114no—
265C22×C11—44no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—44no—
269C22×C11—44no—
270C22×C11—42no—
271C22×C11—84no—
272C22×C11—88no—
273C22×C11#44912yes—
274C22×C11#45012yes—
275C22×C11#45512yes—
276C22×C11C2×#12011yescharacteristic
277C4×C11—24no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11#44912yes—
283C4×C11#45012yes—
284C4×C11C22×SD1611yescharacteristic
285C4×C11C2×#13511yescharacteristic
286C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
287C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
288Dic11—82no—
289C2×#41—24no—
290C2×#41—24no—
291C2×#41—44no—
292C2×#41—44no—
293C22×Q8—221no—
294C22×Q8C22⋊D1111yescharacteristic
295C22×D4—22no—
296C22×D4—22no—
297C22×D4—21no—
298C22×D4—21no—
299C22×D4C22⋊D1111yescharacteristic
300C22×D4C22⋊D1112yes—
301C23×C4—22no—
302C23×C4—21no—
303C2×SD16—224no—
304C2×SD16—444no—
305C22×C8—221no—
306C22×C8—221no—
307C22×C8—221no—
308C4⋊Q8—112no—
309C4⋊Q8—221no—
310C4⋊Q8—221no—
311C4⋊Q8—221no—
312#127—24no—
313#127—24no—
314#127—21no—
315#127—21no—
316#127C22⋊D1112yes—
317#127C22×D1112yes—
318#121—24no—
319#121—28no—
320#121—28no—
321#121—24no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×Q8C22⋊D1112yes—
325C4×Q8C22×D1112yes—
326C4×D4—24no—
327C4×D4—24no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4C22⋊D1112yes—
331C4×D4C22×D1112yes—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4C22⋊D1111yescharacteristic
336C2×C4⋊C4C22⋊D1111yescharacteristic
337C2×C22⋊C4—22no—
338C2×C22⋊C4—21no—
339C2×C42—21no—
340C2×C42C22×D1111yescharacteristic
341#106—224no—
342C4⋊C8—112no—
343C4⋊C8—112no—
344C4⋊C8—221no—
345C4⋊C8—221no—
346#103—224no—
347#103—224no—
348#102—228no—
349C4×C8—112no—
350C4×C8—221no—
351C2×C11—82no—
352C2×C11—84no—
353C2×C11#164214yescomplemented
354C2×C11C2×#45011yescharacteristic
355C2×C11C2×#44911yescharacteristic
356C2×C11C2×#45511yescharacteristic
357C24—21no—
358C24—22no—
359#41—48no—
360#41—416no—
361#41—48no—
362C2×Q8—22no—
363C2×Q8—21no—
364C2×Q8—222no—
365C2×Q8—441no—
366C2×Q8—442no—
367C2×Q8—442no—
368C2×Q8#432414yescomplemented
369C2×Q8C2×C22⋊D1112yes—
370C2×D4—28no—
371C2×D4—28no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—21no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—48no—
381C2×D4—44no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—84no—
387C2×D4C2×C22⋊D1112yes—
388C2×D4C2×C22⋊D1114yes—
389C22×C4—21no—
390C22×C4—28no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—48no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—441no—
399C22×C4C2×C22⋊D1111yescharacteristic
400C22×C4C2×C22⋊D1111yescharacteristic
401C22×C4C2×C22⋊D1111yescharacteristic
402SD16—448no—
403C2×C8—222no—
404C2×C8—222no—
405C2×C8—222no—
406C2×C8—442no—
407C2×C8—442no—
408C2×C8—442no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—22no—
413C4⋊C4—222no—
414C4⋊C4—222no—
415C4⋊C4—441no—
416C4⋊C4—441no—
417C4⋊C4C2×C22⋊D1112yes—
418C4⋊C4C2×C22⋊D1112yes—
419C22⋊C4—28no—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C42—22no—
423C42—22no—
424C42C2×C22⋊D1111yescharacteristic
425C42C2×C22⋊D1111yescharacteristic
426C42C2×C22⋊D1111yescharacteristic
427C42C23×D1111yescharacteristic
428C11C2×#164211yescharacteristic, complemented, Sylow
429C23—22no—
430C23—24no—
431C23—44no—
432C23—42no—
433C23—42no—
434C23—44no—
435C23—44no—
436C23—42no—
437C23#6700611yescharacteristic
438Q8—22no—
439Q8—24no—
440Q8—442no—
441Q8—442no—
442Q8—882no—
443Q8C2×#432414yescomplemented
444D4—22no—
445D4—22no—
446D4—44no—
447D4—416no—
448D4—42no—
449D4—42no—
450D4—44no—
451D4—42no—
452D4—42no—
453D4—42no—
454D4—44no—
455D4—82no—
456D4—88no—
457C2×C4—24no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—416no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—44no—
468C2×C4—442no—
469C2×C4—882no—
470C2×C4#6698512yes—
471C2×C4C2×#432412yes—
472C2×C4#6700212yes—
473C2×C4#6700312yes—
474C2×C4#6700611yescharacteristic
475C2×C4#6700611yescharacteristic
476C2×C4#6700611yescharacteristic
477C2×C4C22×C22⋊D1111yescharacteristic
478C2×C4C22×C22⋊D1111yescharacteristic
479C2×C4C22×C22⋊D1111yescharacteristic
480C8—442no—
481C8—442no—
482C8—442no—
483C22—44no—
484C22—42no—
485C22—42no—
486C22—44no—
487C22—44no—
488C22—42no—
489C22—84no—
490C22—88no—
491C22#1062283112yes—
492C22#1062285112yes—
493C22#1062285512yes—
494C22C2×#6700611yescharacteristic
495C4—24no—
496C4—21no—
497C4—21no—
498C4—42no—
499C4—42no—
500C4—882no—
501C4#1062283112yes—
502C4#1062285112yes—
503C4C2×#6698511yescharacteristic
504C4C22×#432411yescharacteristic
505C4C2×#6700211yescharacteristic
506C4C2×#6700311yescharacteristic
507C2—82no—
508C2—84no—
509C2#1306781614yesdirect product factor
510C2C2×#1062283111yescharacteristic
511C2C2×#1062285111yescharacteristic
512C2C2×#1062285511yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC2×C11×#550C2
socleC23×C11#120
hypercenterC2×#550D11
hypocenterC11C2×#1642
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×#10622683C2semidirect
2. C2×#10622633C2semidirect
3. C2×#10622632C2semidirect
4. #13067816C2direct (N × H)
5. C2×#10622182C2semidirect
6. C2×Q8⋊(C11⋊C8)C2semidirect
7. C2×D4⋊(C11⋊C8)C2semidirect
26. #10622683C22semidirect
28. #10622633C22semidirect
30. #10622632C22semidirect
36. #10622182C22semidirect
37. Q8⋊(C11⋊C8)C22semidirect
38. D4⋊(C11⋊C8)C22semidirect
109. C2×Q8×C11SD16semidirect
192. Q8×C11C2×SD16semidirect
353. C2×C11#1642semidirect
368. C2×Q8#4324semidirect
428. C11C2×#1642semidirect
443. Q8C2×#4324semidirect
509. C2#13067816direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226832
C2×#106226332
C2×#106226322
#130678162
C2×#106221822
C2×Q8⋊(C11⋊C8)2
C2×D4⋊(C11⋊C8)2
C2×C11×#5502
C2×#164211