Finite Group Databasebeta

← C2×#13067720 #14729487

Subgroups — C2×#13067720 #14729487

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×#10623258C211yesmaximal, characteristic, complemented
2C2×#10622701C211yesmaximal, characteristic, complemented
3C2×#10622461C211yesmaximal, characteristic, complemented
4C2×#10622456C211yesmaximal, characteristic
5#13067720C218yesmaximal, direct product factor
6C2×#10622122C211yesmaximal, characteristic, complemented
7C2×#10622121C211yesmaximal, characteristic, complemented
8C2×C11×#332C211yesmaximal, characteristic, complemented
9C22×Q8×D11—21no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66999—21no—
12C22×D88—21no—
13C22×#4314—21no—
14#10623258—22no—
15#10623258—22no—
16#10623258—22no—
17#10623258C2214yescomplemented
18C2×#66949—22no—
19C2×#66946—21no—
20C2×#66941—21no—
21C2×#66927C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×#66885—21no—
27C2×#66885—21no—
28#10622701—22no—
29#10622701C2214yescomplemented
30C2×#66873—22no—
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622461—22no—
33#10622461C2214yescomplemented
34#10622456—22no—
35#10622456C2214yes—
36C11×#332C2214yescomplemented
37#10622122C2214yescomplemented
38#10622121C2214yescomplemented
39C22×Q8×C11—21no—
40C2×Q8×D11—24no—
41C2×Q8×D11—24no—
42C2×Q8×D11—44no—
43C2×Q8×D11—44no—
44C22×D44—21no—
45C22×D44—21no—
46C22×D44—21no—
47C22×D44D411yescharacteristic
48C22×C4×D11—22no—
49C22×C4×D11—21no—
50C22×Dic22—22no—
51C22×Dic22D411yescharacteristic
52C22×C8×C11—21no—
53C22×C8×C11—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8D412yes—
57C11×C4⋊Q8C2312yes—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4D412yes—
60C2×C42×C11C2311yescharacteristic
61#66999—24no—
62#66999—24no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—21no—
65C2×C4⋊Dic11D411yescharacteristic
66C2×C4⋊Dic11D411yescharacteristic
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—21no—
69C2×C4×Dic11—21no—
70C22×C11⋊C8—21no—
71C2×D88—24no—
72C2×D88—44no—
73C2×#4314—24no—
74C2×#4314—44no—
75#66949—28no—
76#66949—28no—
77#66946—24no—
78#66946—24no—
79#66941—24no—
80#66941—24no—
81#66927—21no—
82#66927—21no—
83#66927—21no—
84#66927C2312yes—
85C4×D44—21no—
86C4×D44—21no—
87C4×D44D412yes—
88C4×D44C2312yes—
89C4×Dic22—21no—
90C4×Dic22—21no—
91C4×Dic22D412yes—
92C4×Dic22C2312yes—
93C11×C4⋊C8—21no—
94C11×C4⋊C8—21no—
95C11×C4⋊C8C2312yes—
96C11×C4⋊C8C2312yes—
97#66885—24no—
98#66885—24no—
99#66873—28no—
100C4×C11⋊C8—21no—
101C4×C11⋊C8C2312yes—
102C2×#1627—111nomaximal, Sylow
103C23×D11—21no—
104C23×D11—41no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—42no—
108C2×Q8×C11—42no—
109C22×C4×C11—22no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×Dic11—21no—
114C22×Dic11—21no—
115C22×Dic11—21no—
116Q8×D11—48no—
117Q8×D11—416no—
118Q8×D11—48no—
119C2×D44—21no—
120C2×D44—22no—
121C2×D44—22no—
122C2×D44—22no—
123C2×D44—22no—
124C2×D44—44no—
125C2×D44—41no—
126C2×D44—41no—
127C2×D44—41no—
128C2×D44—42no—
129C2×D44—42no—
130C2×D44—42no—
131C2×D44—42no—
132C2×D44SD1614yescomplemented
133C2×D44C2×D412yes—
134C2×C4×D11—28no—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—48no—
138C2×C4×D11—42no—
139C2×C4×D11—42no—
140C2×Dic22—28no—
141C2×Dic22—21no—
142C2×Dic22—22no—
143C2×Dic22—48no—
144C2×Dic22D814yescomplemented
145C2×Dic22C2×D412yes—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—42no—
149C2×C8×C11—42no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4C2×D414yes—
154C42×C11C2×D411yescharacteristic
155C42×C11C2×D411yescharacteristic
156C42×C11C2×D411yescharacteristic
157C42×C11C2411yescharacteristic
158(C2×D11)⋊C4—28no—
159(C2×D11)⋊C4—22no—
160(C2×D11)⋊C4—22no—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163C4⋊Dic11C2×D412yes—
164C4⋊Dic11C2×D412yes—
165Dic11⋊C4—28no—
166Dic11⋊C4—22no—
167Dic11⋊C4—22no—
168C4×Dic11—22no—
169C4×Dic11—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—42no—
172D88—48no—
173#4314—48no—
174C2×D4×Q8—111no—
175C2×#486—111no—
176C2×#460—111no—
177C2×#459—111no—
178#1627—118no—
179C2×#332D1111yescharacteristic, complemented
180C2×Q8⋊C8—111no—
181C2×D4⋊C8—111no—
182C23×C11#12011yescharacteristic
183C22×D11—22no—
184C22×D11—24no—
185C22×D11—42no—
186C22×D11—42no—
187C22×D11—42no—
188C22×D11—82no—
189C22×D11—82no—
190C22×D11—82no—
191Q8×C11—42no—
192Q8×C11—42no—
193Q8×C11—44no—
194C2×C4×C11—22no—
195C2×C4×C11—24no—
196C2×C4×C11—44no—
197C2×C4×C11#12011yescharacteristic
198C2×C4×C11#12011yescharacteristic
199C2×C4×C11#12011yescharacteristic
200C2×C4×C11C2×D812yes—
201C2×C4×C11C2×SD1612yes—
202C2×C4×C11AGL(1,ℤ/8)12yes—
203C2×C4×C11#13712yes—
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×Dic11—22no—
208C2×Dic11—24no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213D44—22no—
214D44—24no—
215D44—44no—
216D44—42no—
217D44—42no—
218D44—42no—
219D44—42no—
220D44—82no—
221D44—82no—
222D44—82no—
223D44C2×SD1614yescomplemented
224C4×D11—416no—
225C4×D11—42no—
226C4×D11—42no—
227C4×D11—44no—
228Dic22—22no—
229Dic22—24no—
230Dic22—416no—
231Dic22C2×D814yescomplemented
232C8×C11—42no—
233C8×C11—42no—
234C11⋊C8—42no—
235C23×Q8—221no—
236C22×SD16—221no—
237C22×D8—221no—
238D4×Q8—114no—
239D4×Q8—222no—
240D4×Q8—222no—
241D4×Q8—222no—
242C2×C4⋊Q8—221no—
243C2×C4⋊Q8C2×D1111yescharacteristic
244C2×#127—111no—
245C2×C22⋊Q8—221no—
246C2×C22⋊Q8—222no—
247C2×C4×Q8—111no—
248C2×C4×D4—111no—
249C2×C4×D4—221no—
250#486—114no—
251#486—222no—
252#460—114no—
253#460—222no—
254#459—114no—
255#459—222no—
256C2×C4⋊C8C2×D1111yescharacteristic
257C2×C4⋊C8C2×D1111yescharacteristic
258C2×#102—221no—
259C2×#102—221no—
260C2×#102—222no—
261C2×C4×C8—111no—
262#332C2×D1114yescomplemented
263Q8⋊C8—114no—
264D4⋊C8—114no—
265C22×C11#44712yes—
266C22×C11#44812yes—
267C22×C11#45412yes—
268C22×C11C2×#12011yescharacteristic
269C2×D11—24no—
270C2×D11—48no—
271C2×D11—42no—
272C2×D11—42no—
273C2×D11—82no—
274C2×D11—82no—
275C2×D11—82no—
276C2×D11—164no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—44no—
280C4×C11#44712yes—
281C4×C11#44812yes—
282C4×C11C22×D811yescharacteristic
283C4×C11C22×SD1611yescharacteristic
284C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
285C4×C11C2×#13711yescharacteristic
286Dic11—24no—
287Dic11—42no—
288Dic11—42no—
289C22×Q8—21no—
290C22×Q8—111no—
291C22×Q8—222no—
292C22×Q8—224no—
293C22×Q8—224no—
294C22×Q8—444no—
295C22×Q8—444no—
296C22×D4—111no—
297C22×D4—221no—
298C22×D4—221no—
299C22×D4—221no—
300C23×C4—222no—
301C23×C4—221no—
302C2×SD16—224no—
303C2×SD16—444no—
304C2×D8—224no—
305C2×D8—444no—
306C22×C8—21no—
307C22×C8—21no—
308C22×C8—221no—
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8—224no—
312C4⋊Q8—224no—
313C4⋊Q8D4412yes—
314C4⋊Q8C22×D1112yes—
315#127—112no—
316#127—221no—
317#127—221no—
318#127—221no—
319C22⋊Q8—228no—
320C22⋊Q8—224no—
321C22⋊Q8—224no—
322C22⋊Q8—228no—
323C4×Q8—112no—
324C4×Q8—112no—
325C4×Q8—221no—
326C4×Q8—221no—
327C4×D4—112no—
328C4×D4—112no—
329C4×D4—224no—
330C4×D4—224no—
331C4×D4—221no—
332C4×D4—221no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—111no—
335C2×C4⋊C4—111no—
336C2×C4⋊C4—222no—
337C2×C4⋊C4—221no—
338C2×C4⋊C4D4412yes—
339C2×C22⋊C4—222no—
340C2×C22⋊C4—221no—
341C2×C42—221no—
342C2×C42C22×D1111yescharacteristic
343C4⋊C8—21no—
344C4⋊C8—21no—
345C4⋊C8C22×D1112yes—
346C4⋊C8C22×D1112yes—
347#102—224no—
348#102—224no—
349#102—228no—
350C4×C8—112no—
351C4×C8—221no—
352C2×C11#162714yescomplemented
353C2×C11C2×#44711yescharacteristic
354C2×C11C2×#44811yescharacteristic
355C2×C11C2×#45411yescharacteristic
356D11—44no—
357D11—162no—
358C24—221no—
359C24—441no—
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8—42no—
363C2×Q8—42no—
364C2×Q8—114no—
365C2×Q8—112no—
366C2×Q8—228no—
367C2×Q8—221no—
368C2×Q8—222no—
369C2×Q8—448no—
370C2×Q8—448no—
371C2×Q8—448no—
372C2×Q8—4416no—
373C2×D4—114no—
374C2×D4—112no—
375C2×D4—221no—
376C2×D4—222no—
377C2×D4—222no—
378C2×D4—222no—
379C2×D4—222no—
380C2×D4—444no—
381C2×D4—441no—
382C2×D4—441no—
383C2×D4—441no—
384C2×D4—442no—
385C2×D4—442no—
386C2×D4—442no—
387C2×D4—442no—
388C22×C4—22no—
389C22×C4—228no—
390C22×C4—221no—
391C22×C4—221no—
392C22×C4—221no—
393C22×C4—222no—
394C22×C4—222no—
395C22×C4—448no—
396C22×C4—442no—
397C22×C4—442no—
398C22×C4C2×D4411yescharacteristic
399C22×C4D4×D1111yescharacteristic
400C22×C4D4×D1111yescharacteristic
401SD16—448no—
402D8—448no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—42no—
406C2×C8—42no—
407C2×C8—222no—
408C2×C8—442no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—112no—
413C4⋊C4—112no—
414C4⋊C4—228no—
415C4⋊C4—221no—
416C4⋊C4—221no—
417C4⋊C4—222no—
418C4⋊C4—222no—
419C4⋊C4C2×D4414yes—
420C22⋊C4—228no—
421C22⋊C4—222no—
422C22⋊C4—222no—
423C42—222no—
424C42—222no—
425C42C2×D4411yescharacteristic
426C42D4×D1111yescharacteristic
427C42D4×D1111yescharacteristic
428C42C23×D1111yescharacteristic
429C11C2×#162711yescharacteristic, complemented, Sylow
430C23—222no—
431C23—224no—
432C23—442no—
433C23—442no—
434C23—442no—
435C23—882no—
436C23—882no—
437C23—882no—
438C23#6693511yescharacteristic
439Q8—42no—
440Q8—42no—
441Q8—44no—
442Q8—114no—
443Q8—222no—
444Q8—224no—
445Q8—4416no—
446D4—114no—
447D4—222no—
448D4—224no—
449D4—444no—
450D4—442no—
451D4—442no—
452D4—442no—
453D4—442no—
454D4—882no—
455D4—882no—
456D4—882no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—44no—
460C2×C4—222no—
461C2×C4—224no—
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#6693511yescharacteristic
471C2×C4#6693511yescharacteristic
472C2×C4#6693511yescharacteristic
473C2×C4D8×D1112yes—
474C2×C4SD16×D1112yes—
475C2×C4#6696712yes—
476C2×C4#6697112yes—
477C2×C4C22×D4411yescharacteristic
478C2×C4C2×D4×D1111yescharacteristic
479C2×C4C2×D4×D1111yescharacteristic
480C8—42no—
481C8—42no—
482C8—442no—
483C22—224no—
484C22—442no—
485C22—442no—
486C22—448no—
487C22—882no—
488C22—882no—
489C22—882no—
490C22—1764no—
491C22#1062236612yes—
492C22#1062238612yes—
493C22#1062241912yes—
494C22C2×#6693511yescharacteristic
495C4—21no—
496C4—21no—
497C4—44no—
498C4—224no—
499C4—442no—
500C4—442no—
501C4#1062238612yes—
502C4#1062241912yes—
503C4C2×D8×D1111yescharacteristic
504C4C2×SD16×D1111yescharacteristic
505C4C2×#6696711yescharacteristic
506C4C2×#6697111yescharacteristic
507C2—444no—
508C2—1762no—
509C2#1306772014yesdirect product factor
510C2C2×#1062238611yescharacteristic
511C2C2×#1062241911yescharacteristic
512C2C2×#1062236611yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#332C2
socleC23×C11#120
prime radicalC2×#10622456C2
hypercenterC2×#332D11
hypocenterC11C2×#1627
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
1. C2×#10623258C2semidirect
2. C2×#10622701C2semidirect
3. C2×#10622461C2semidirect
5. #13067720C2direct (N × H)
6. C2×#10622122C2semidirect
7. C2×#10622121C2semidirect
8. C2×C11×#332C2semidirect
17. #10623258C22semidirect
29. #10622701C22semidirect
33. #10622461C22semidirect
36. C11×#332C22semidirect
37. #10622122C22semidirect
38. #10622121C22semidirect
132. C2×D44SD16semidirect
144. C2×Dic22D8semidirect
179. C2×#332D11semidirect
223. D44C2×SD16semidirect
231. Dic22C2×D8semidirect
262. #332C2×D11semidirect
352. C2×C11#1627semidirect
429. C11C2×#1627semidirect
509. C2#13067720direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232582
C2×#106227012
C2×#106224612
C2×#106224562
#130677202
C2×#106221222
C2×#106221212
C2×C11×#3322
C2×#162711