Finite Group Databasebeta

← C2×#13067813 #14729684

Subgroups — C2×#13067813 #14729684

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×#10623249C211yesmaximal, characteristic
2C2×#10622707C211yesmaximal, characteristic, complemented
3C2×#10622696C211yesmaximal, characteristic, complemented
4#13067813C218yesmaximal, direct product factor
5C2×#10622182C211yesmaximal, characteristic, complemented
6C2×#10622094C211yesmaximal, characteristic, complemented
7C2×#10622097C211yesmaximal, characteristic, complemented
8C2×C11×#486C211yesmaximal, characteristic, complemented
9C22×#4341—21no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12C22×#4325—21no—
13C2×#66993—21no—
14C2×#66992—22no—
15C2×#66991—21no—
16C2×D4×Dic11—21no—
17#10623249—22no—
18#10623249—22no—
19#10623249—22no—
20#10623249C2214yes—
21C2×C4×D44C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C11×#486—22no—
24C11×#486C2214yescomplemented
25C2×C11×#102—22no—
26C2×C4×C8×C11C2211yescharacteristic
27C2×#66899—21no—
28#10622707—22no—
29#10622707C2214yescomplemented
30#10622696—22no—
31#10622696C2214yescomplemented
32C2×#66874—21no—
33C2×#66872—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622182C2214yescomplemented
37#10622097C2214yescomplemented
38#10622094C2214yescomplemented
39C22×Q8×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11D412yes—
43C22×C22⋊D11—22no—
44C22×C22⋊D11—22no—
45C23×Dic11—22no—
46C2×#4341—24no—
47C2×#4341—24no—
48C2×#4341—44no—
49C2×#4341—44no—
50C22×D44D411yescharacteristic
51C22×C4×D11—21no—
52C22×Dic22D411yescharacteristic
53C22×C8×C11—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8C2312yes—
58C11×#127—21no—
59C11×#127—21no—
60C11×#127D412yes—
61C11×#127C2312yes—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C42×C11C2311yescharacteristic
65C2×C22⋊Dic11—22no—
66C2×#4325—24no—
67C2×#4325—44no—
68#66993—24no—
69#66993—24no—
70#66992—28no—
71#66992—28no—
72#66991—24no—
73#66991—24no—
74D4×Dic11—24no—
75D4×Dic11—24no—
76C2×(C2×D11)⋊C4—21no—
77C2×C4⋊Dic11D411yescharacteristic
78C2×C4⋊Dic11D411yescharacteristic
79C2×Dic11⋊C4—21no—
80C2×C4×Dic11—21no—
81C22×C11⋊C8—21no—
82C22×C11⋊C8—21no—
83C4×D44—21no—
84C4×D44—21no—
85C4×D44D412yes—
86C4×D44C2312yes—
87C4×Dic22—21no—
88C4×Dic22—21no—
89C4×Dic22D412yes—
90C4×Dic22C2312yes—
91C11×#102—28no—
92C4×C8×C11—21no—
93C4×C8×C11C2312yes—
94#66899—24no—
95#66874—24no—
96#66872—24no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)—21no—
99C4⋊(C11⋊C8)C2312yes—
100C4⋊(C11⋊C8)C2312yes—
101C2×#1642—111nomaximal, Sylow
102C24×C11—22no—
103C23×D11—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11—41no—
106C2×Q8×C11—42no—
107C2×Q8×C11—42no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—44no—
114C2×D4×C11—42no—
115C2×D4×C11—42no—
116C2×D4×C11—42no—
117C2×D4×C11—42no—
118C2×D4×C11C2×D414yes—
119C22×C4×C11—41no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C2×C22⋊D11—28no—
124C2×C22⋊D11—28no—
125C2×C22⋊D11—48no—
126C2×C22⋊D11—84no—
127C22×Dic11—28no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—48no—
132#4341—48no—
133#4341—416no—
134#4341—48no—
135C2×D44—21no—
136C2×D44—22no—
137C2×D44—22no—
138C2×D44C2×D412yes—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×C4×D11—42no—
142C2×C4×D11—42no—
143C2×Dic22—21no—
144C2×Dic22—22no—
145C2×Dic22SD1614yescomplemented
146C2×Dic22C2×D412yes—
147C2×C8×C11—22no—
148C2×C8×C11—42no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—41no—
152C11×C4⋊C4—41no—
153C42×C11C2×D411yescharacteristic
154C42×C11C2×D411yescharacteristic
155C42×C11C2×D411yescharacteristic
156C42×C11C2411yescharacteristic
157C22⋊Dic11—28no—
158#4325—48no—
159(C2×D11)⋊C4—22no—
160(C2×D11)⋊C4—22no—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163C4⋊Dic11C2×D412yes—
164C4⋊Dic11C2×D412yes—
165Dic11⋊C4—22no—
166Dic11⋊C4—22no—
167C4×Dic11—22no—
168C4×Dic11—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—42no—
172C2×C11⋊C8—42no—
173C2×#550—111no—
174C2×#486D1111yescharacteristic, complemented
175C2×#475—111no—
176C2×#461—111no—
177#1642—118no—
178C2×#331—111no—
179C2×Q8⋊C8—111no—
180C2×D4⋊C8—111no—
181C23×C11—24no—
182C23×C11—44no—
183C23×C11—44no—
184C23×C11—44no—
185C23×C11#12011yescharacteristic
186C22×D11—22no—
187C22×D11—42no—
188C22×D11—42no—
189C22×D11—42no—
190Q8×C11—42no—
191Q8×C11—42no—
192Q8×C11—82no—
193D4×C11—44no—
194D4×C11—42no—
195D4×C11—42no—
196D4×C11—42no—
197D4×C11—42no—
198D4×C11—44no—
199D4×C11—44no—
200D4×C11—82no—
201C2×C4×C11—22no—
202C2×C4×C11—42no—
203C2×C4×C11—82no—
204C2×C4×C11#12011yescharacteristic
205C2×C4×C11#12011yescharacteristic
206C2×C4×C11#12011yescharacteristic
207C2×C4×C11C2×SD1612yes—
208C2×C4×C11#13512yes—
209C2×C4×C11AGL(1,ℤ/8)12yes—
210C2×C4×C11AGL(1,ℤ/8)12yes—
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C22⋊D11—416no—
215C22⋊D11—88no—
216C2×Dic11—22no—
217C2×Dic11—24no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—416no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223D44—22no—
224D44—22no—
225D44—42no—
226C4×D11—42no—
227C4×D11—42no—
228C4×D11—44no—
229Dic22—22no—
230Dic22—24no—
231Dic22C2×SD1614yescomplemented
232C8×C11—42no—
233C11⋊C8—42no—
234C11⋊C8—42no—
235C22×#41—221no—
236C22×SD16—221no—
237#550—114no—
238#550—222no—
239#550—222no—
240#550—222no—
241C2×C4⋊Q8C2×D1111yescharacteristic
242C2×#127—221no—
243C2×#127C2×D1111yescharacteristic
244C2×#121—221no—
245C2×#121—222no—
246C2×C4×Q8—111no—
247C2×C4×D4—111no—
248C2×C4×D4—221no—
249#486—22no—
250#486C2×D1114yescomplemented
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—22no—
261C2×C4×C8C2×D1111yescharacteristic
262#331—114no—
263Q8⋊C8—114no—
264D4⋊C8—114no—
265C22×C11—44no—
266C22×C11—44no—
267C22×C11—44no—
268C22×C11—88no—
269C22×C11#44912yes—
270C22×C11#45012yes—
271C22×C11#45512yes—
272C22×C11C2×#12011yescharacteristic
273C2×D11—42no—
274C2×D11—42no—
275C2×D11—42no—
276C2×D11—84no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—82no—
280C4×C11#44912yes—
281C4×C11#45012yes—
282C4×C11C22×SD1611yescharacteristic
283C4×C11C2×#13511yescharacteristic
284C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
285C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
286Dic11—24no—
287Dic11—42no—
288Dic11—42no—
289C2×#41—224no—
290C2×#41—224no—
291C2×#41—444no—
292C2×#41—444no—
293C22×Q8—21no—
294C22×Q8—111no—
295C22×D4—21no—
296C22×D4—21no—
297C22×D4—111no—
298C22×D4—222no—
299C22×D4—222no—
300C22×D4C22⋊D1112yes—
301C23×C4—222no—
302C23×C4—221no—
303C2×SD16—224no—
304C2×SD16—444no—
305C22×C8—21no—
306C22×C8—221no—
307C22×C8—221no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8C22×D1112yes—
312#127—21no—
313#127—21no—
314#127—224no—
315#127—224no—
316#127C22⋊D1112yes—
317#127C22×D1112yes—
318#121—224no—
319#121—224no—
320#121—228no—
321#121—228no—
322C4×Q8—112no—
323C4×Q8—112no—
324C4×Q8—221no—
325C4×Q8—221no—
326C4×D4—112no—
327C4×D4—112no—
328C4×D4—224no—
329C4×D4—224no—
330C4×D4—221no—
331C4×D4—221no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—111no—
335C2×C4⋊C4—111no—
336C2×C4⋊C4—221no—
337C2×C22⋊C4—222no—
338C2×C22⋊C4—221no—
339C2×C42—221no—
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—28no—
349C4×C8—21no—
350C4×C8C22×D1112yes—
351C2×C11—84no—
352C2×C11#164214yescomplemented
353C2×C11C2×#45011yescharacteristic
354C2×C11C2×#44911yescharacteristic
355C2×C11C2×#45511yescharacteristic
356D11—82no—
357C24—22no—
358C24—221no—
359#41—448no—
360#41—448no—
361#41—4416no—
362C2×Q8—22no—
363C2×Q8—41no—
364C2×Q8—42no—
365C2×Q8—42no—
366C2×Q8—114no—
367C2×Q8—112no—
368C2×Q8—222no—
369C2×Q8—221no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—44no—
376C2×D4—42no—
377C2×D4—42no—
378C2×D4—42no—
379C2×D4—42no—
380C2×D4—112no—
381C2×D4—228no—
382C2×D4—228no—
383C2×D4—222no—
384C2×D4—222no—
385C2×D4—221no—
386C2×D4—448no—
387C2×D4—884no—
388C2×D4C2×C22⋊D1114yes—
389C22×C4—41no—
390C22×C4—221no—
391C22×C4—228no—
392C22×C4—221no—
393C22×C4—221no—
394C22×C4—222no—
395C22×C4—222no—
396C22×C4—448no—
397C22×C4—442no—
398C22×C4—442no—
399C22×C4D4×D1111yescharacteristic
400C22×C4D4×D1111yescharacteristic
401C22×C4C2×C22⋊D1111yescharacteristic
402SD16—448no—
403C2×C8—22no—
404C2×C8—42no—
405C2×C8—222no—
406C2×C8—222no—
407C2×C8—442no—
408C2×C8—442no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—41no—
412C4⋊C4—41no—
413C4⋊C4—112no—
414C4⋊C4—112no—
415C4⋊C4—221no—
416C4⋊C4—221no—
417C4⋊C4—222no—
418C4⋊C4—222no—
419C22⋊C4—228no—
420C22⋊C4—222no—
421C22⋊C4—222no—
422C42—222no—
423C42—222no—
424C42D4×D1111yescharacteristic
425C42D4×D1111yescharacteristic
426C42C2×C22⋊D1111yescharacteristic
427C42C23×D1111yescharacteristic
428C11C2×#164211yescharacteristic, complemented, Sylow
429C23—24no—
430C23—44no—
431C23—44no—
432C23—44no—
433C23—222no—
434C23—442no—
435C23—442no—
436C23—442no—
437C23#6699011yescharacteristic
438Q8—42no—
439Q8—42no—
440Q8—82no—
441Q8—114no—
442Q8—222no—
443Q8—224no—
444D4—44no—
445D4—44no—
446D4—42no—
447D4—42no—
448D4—42no—
449D4—42no—
450D4—44no—
451D4—82no—
452D4—222no—
453D4—222no—
454D4—4416no—
455D4—442no—
456D4—888no—
457C2×C4—22no—
458C2×C4—42no—
459C2×C4—82no—
460C2×C4—224no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—4416no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4—444no—
470C2×C4#6696412yes—
471C2×C4#6696512yes—
472C2×C4SD16×D1112yes—
473C2×C4#6696712yes—
474C2×C4#6699011yescharacteristic
475C2×C4#6699011yescharacteristic
476C2×C4#6699011yescharacteristic
477C2×C4C2×D4×D1111yescharacteristic
478C2×C4C2×D4×D1111yescharacteristic
479C2×C4C22×C22⋊D1111yescharacteristic
480C8—42no—
481C8—442no—
482C8—442no—
483C22—44no—
484C22—44no—
485C22—44no—
486C22—88no—
487C22—442no—
488C22—442no—
489C22—442no—
490C22—884no—
491C22#1062267412yes—
492C22#1062277112yes—
493C22#1062278212yes—
494C22C2×#6699011yescharacteristic
495C4—21no—
496C4—21no—
497C4—82no—
498C4—224no—
499C4—442no—
500C4—442no—
501C4#1062277112yes—
502C4#1062278212yes—
503C4C2×#6696411yescharacteristic
504C4C2×#6696511yescharacteristic
505C4C2×SD16×D1111yescharacteristic
506C4C2×#6696711yescharacteristic
507C2—84no—
508C2—882no—
509C2#1306781314yesdirect product factor
510C2C2×#1062278211yescharacteristic
511C2C2×#1062277111yescharacteristic
512C2C2×#1062267411yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#486C2
socleC23×C11#120
prime radicalC2×#10623249C2
hypercenterC2×#486D11
hypocenterC11C2×#1642
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
2. C2×#10622707C2semidirect
3. C2×#10622696C2semidirect
4. #13067813C2direct (N × H)
5. C2×#10622182C2semidirect
6. C2×#10622094C2semidirect
7. C2×#10622097C2semidirect
8. C2×C11×#486C2semidirect
24. C11×#486C22semidirect
29. #10622707C22semidirect
31. #10622696C22semidirect
36. #10622182C22semidirect
37. #10622097C22semidirect
38. #10622094C22semidirect
145. C2×Dic22SD16semidirect
174. C2×#486D11semidirect
231. Dic22C2×SD16semidirect
250. #486C2×D11semidirect
352. C2×C11#1642semidirect
428. C11C2×#1642semidirect
509. C2#13067813direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232492
C2×#106227072
C2×#106226962
#130678132
C2×#106221822
C2×#106220942
C2×#106220972
C2×C11×#4862
C2×#164211