Finite Group Databasebeta

← C2×#13067718 #14729484

Subgroups — C2×#13067718 #14729484

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×D4×Dic22C211yesmaximal, characteristic, complemented
2C2×#10622683C211yesmaximal, characteristic, complemented
3C2×#10622688C211yesmaximal, characteristic, complemented
4#13067718C218yesmaximal, direct product factor
5C2×#10622124C211yesmaximal, characteristic, complemented
6C2×#10622122C211yesmaximal, characteristic, complemented
7C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
8C2×C11×#459C211yesmaximal, characteristic
9C23×Dic22—21no—
10C22×C11×D8—21no—
11C2×C11×#127C2211yescharacteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×D4×Dic11—21no—
14C22×#4324—21no—
15C2×#66977—21no—
16D4×Dic22—22no—
17D4×Dic22—22no—
18D4×Dic22—22no—
19D4×Dic22C2214yescomplemented
20C2×#66941—21no—
21C2×#66931—22no—
22C2×#66922C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C11×#459—22no—
25C11×#459C2214yes—
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#102—21no—
28C2×#66896—21no—
29C2×#66896—22no—
30#10622688—22no—
31#10622688C2214yescomplemented
32#10622683—22no—
33#10622683C2214yescomplemented
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36D4⋊(C11⋊C8)C2214yescomplemented
37#10622124C2214yescomplemented
38#10622122C2214yescomplemented
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11D411yescharacteristic
43C23×C4×C11—21no—
44C23×Dic11—22no—
45C22×Dic22—22no—
46C22×Dic22—24no—
47C22×Dic22—21no—
48C22×Dic22—24no—
49C22×Dic22—44no—
50C22×Dic22—44no—
51C22×Dic22D411yescharacteristic
52C2×C11×D8—24no—
53C2×C11×D8—44no—
54C22×C8×C11—21no—
55C11×#127—21no—
56C11×#127—21no—
57C11×#127—21no—
58C11×#127C2312yes—
59C4×D4×C11—21no—
60C4×D4×C11—21no—
61C4×D4×C11D412yes—
62C4×D4×C11C2312yes—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C22⋊C4—21no—
65C2×C42×C11C2311yescharacteristic
66C2×C22⋊Dic11—22no—
67D4×Dic11—24no—
68D4×Dic11—24no—
69C2×#4324—24no—
70C2×#4324—44no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11D411yescharacteristic
73C2×C4⋊Dic11D412yes—
74#66977—24no—
75#66977—24no—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—21no—
78C2×C4×Dic11—21no—
79C22×C11⋊C8—21no—
80C22×C11⋊C8—21no—
81#66941—24no—
82#66941—24no—
83#66931—28no—
84#66931—28no—
85#66922—21no—
86#66922—21no—
87#66922D412yes—
88#66922C2312yes—
89C4×Dic22—21no—
90C4×Dic22—21no—
91C4×Dic22D412yes—
92C4×Dic22C2312yes—
93C11×C4⋊C8—21no—
94C11×C4⋊C8C2312yes—
95C11×#102—24no—
96#66896—28no—
97#66896—24no—
98C4⋊(C11⋊C8)—21no—
99C4⋊(C11⋊C8)C2312yes—
100C4×C11⋊C8—21no—
101C4×C11⋊C8C2312yes—
102C2×#1627—111nomaximal, Sylow
103C24×C11—21no—
104C24×C11—41no—
105C2×D4×C11—21no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—44no—
111C2×D4×C11—41no—
112C2×D4×C11—41no—
113C2×D4×C11—41no—
114C2×D4×C11—42no—
115C2×D4×C11—42no—
116C2×D4×C11—42no—
117C2×D4×C11—42no—
118C2×D4×C11SD1614yescomplemented
119C2×D4×C11C2×D412yes—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—42no—
124C22×C4×C11—42no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×Dic11—28no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—22no—
132C22×Dic11—48no—
133C2×Dic22—28no—
134C2×Dic22—21no—
135C2×Dic22—22no—
136C2×Dic22—22no—
137C2×Dic22—22no—
138C2×Dic22—48no—
139C2×Dic22—416no—
140C2×Dic22—48no—
141C2×Dic22—48no—
142C2×Dic22—42no—
143C2×Dic22—42no—
144C2×Dic22D814yescomplemented
145C2×Dic22C2×D412yes—
146C11×D8—48no—
147C2×C8×C11—22no—
148C2×C8×C11—42no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4C2×D412yes—
151C11×C22⋊C4—22no—
152C11×C22⋊C4—22no—
153C42×C11C2×D411yescharacteristic
154C42×C11C2×D411yescharacteristic
155C42×C11C2×D411yescharacteristic
156C42×C11C2411yescharacteristic
157C22⋊Dic11—28no—
158#4324—48no—
159C4⋊Dic11—21no—
160C4⋊Dic11—22no—
161C4⋊Dic11—22no—
162C4⋊Dic11—22no—
163C4⋊Dic11C2×D412yes—
164C4⋊Dic11C2×D414yes—
165Dic11⋊C4—28no—
166Dic11⋊C4—22no—
167Dic11⋊C4—22no—
168C4×Dic11—22no—
169C4×Dic11—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—42no—
173C2×C11⋊C8—42no—
174C2×D4×Q8—111no—
175C2×#486—111no—
176C2×#460—111no—
177C2×#459D1111yescharacteristic
178#1627—118no—
179C2×#332—111no—
180C2×Q8⋊C8—111no—
181C2×D4⋊C8—111no—
182C23×C11—22no—
183C23×C11—24no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—82no—
188C23×C11—82no—
189C23×C11—82no—
190C23×C11#12011yescharacteristic
191D4×C11—22no—
192D4×C11—24no—
193D4×C11—44no—
194D4×C11—42no—
195D4×C11—42no—
196D4×C11—42no—
197D4×C11—42no—
198D4×C11—82no—
199D4×C11—82no—
200D4×C11—82no—
201D4×C11C2×SD1614yescomplemented
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—44no—
208C2×C4×C11#12011yescharacteristic
209C2×C4×C11#12011yescharacteristic
210C2×C4×C11#12011yescharacteristic
211C2×C4×C11C2×D812yes—
212C2×C4×C11C2×SD1612yes—
213C2×C4×C11AGL(1,ℤ/8)12yes—
214C2×C4×C11#13712yes—
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×Dic11—22no—
219C2×Dic11—24no—
220C2×Dic11—22no—
221C2×Dic11—24no—
222C2×Dic11—416no—
223C2×Dic11—44no—
224C2×Dic11—42no—
225Dic22—22no—
226Dic22—24no—
227Dic22—416no—
228Dic22—42no—
229Dic22—42no—
230Dic22—44no—
231Dic22C2×D814yescomplemented
232C8×C11—42no—
233C11⋊C8—42no—
234C11⋊C8—42no—
235C23×Q8—221no—
236C22×SD16—221no—
237C22×D8—21no—
238D4×Q8—114no—
239D4×Q8—222no—
240D4×Q8—222no—
241D4×Q8—222no—
242C2×C4⋊Q8—111no—
243C2×C4⋊Q8—221no—
244C2×#127C2×D1111yescharacteristic
245C2×C22⋊Q8—222no—
246C2×C22⋊Q8—221no—
247C2×C4×Q8—111no—
248C2×C4×D4—221no—
249C2×C4×D4C2×D1111yescharacteristic
250#486—114no—
251#486—222no—
252#460—114no—
253#460—222no—
254#459—22no—
255#459C2×D1114yes—
256C2×C4⋊C8—111no—
257C2×C4⋊C8C2×D1111yescharacteristic
258C2×#102—21no—
259C2×#102—222no—
260C2×#102—221no—
261C2×C4×C8—111no—
262#332—114no—
263Q8⋊C8—114no—
264D4⋊C8—114no—
265C22×C11—24no—
266C22×C11—48no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—82no—
270C22×C11—82no—
271C22×C11—82no—
272C22×C11—164no—
273C22×C11#44712yes—
274C22×C11#44812yes—
275C22×C11#45412yes—
276C22×C11C2×#12011yescharacteristic
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—42no—
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—44no—
288Dic11—42no—
289C22×Q8—111no—
290C22×Q8—224no—
291C22×Q8—222no—
292C22×Q8—224no—
293C22×Q8—221no—
294C22×Q8—444no—
295C22×Q8—444no—
296C22×D4—21no—
297C22×D4—21no—
298C22×D4—21no—
299C22×D4C22⋊D1111yescharacteristic
300C23×C4—21no—
301C23×C4—222no—
302C2×SD16—224no—
303C2×SD16—444no—
304C2×D8—24no—
305C2×D8—44no—
306C22×C8—21no—
307C22×C8—221no—
308C22×C8—221no—
309C4⋊Q8—112no—
310C4⋊Q8—112no—
311C4⋊Q8—224no—
312C4⋊Q8—224no—
313C4⋊Q8—221no—
314C4⋊Q8—221no—
315#127—21no—
316#127—21no—
317#127—21no—
318#127C22×D1112yes—
319C22⋊Q8—228no—
320C22⋊Q8—228no—
321C22⋊Q8—224no—
322C22⋊Q8—224no—
323C4×Q8—112no—
324C4×Q8—112no—
325C4×Q8—221no—
326C4×Q8—221no—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4—224no—
330C4×D4—224no—
331C4×D4C22⋊D1112yes—
332C4×D4C22×D1112yes—
333C2×C4⋊C4—111no—
334C2×C4⋊C4—112no—
335C2×C4⋊C4—222no—
336C2×C4⋊C4—221no—
337C2×C4⋊C4—221no—
338C2×C4⋊C4C22⋊D1111yescharacteristic
339C2×C22⋊C4—21no—
340C2×C22⋊C4—222no—
341C2×C42—221no—
342C2×C42C22×D1111yescharacteristic
343C4⋊C8—21no—
344C4⋊C8—112no—
345C4⋊C8—221no—
346C4⋊C8C22×D1112yes—
347#102—24no—
348#102—224no—
349#102—228no—
350C4×C8—112no—
351C4×C8—221no—
352C2×C11—44no—
353C2×C11—162no—
354C2×C11#162714yescomplemented
355C2×C11C2×#44711yescharacteristic
356C2×C11C2×#44811yescharacteristic
357C2×C11C2×#45411yescharacteristic
358C24—21no—
359C24—41no—
360C2×Q8—114no—
361C2×Q8—112no—
362C2×Q8—228no—
363C2×Q8—222no—
364C2×Q8—221no—
365C2×Q8—222no—
366C2×Q8—222no—
367C2×Q8—448no—
368C2×Q8—448no—
369C2×Q8—4416no—
370C2×Q8—448no—
371C2×Q8—442no—
372C2×Q8—442no—
373C2×D4—21no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—44no—
379C2×D4—42no—
380C2×D4—42no—
381C2×D4—42no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4—41no—
385C2×D4—42no—
386C2×D4#432414yescomplemented
387C2×D4C2×C22⋊D1112yes—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—221no—
394C22×C4—228no—
395C22×C4—221no—
396C22×C4—222no—
397C22×C4—448no—
398C22×C4D4×D1111yescharacteristic
399C22×C4D4×D1111yescharacteristic
400C22×C4C2×C22⋊D1111yescharacteristic
401SD16—448no—
402D8—48no—
403C2×C8—22no—
404C2×C8—42no—
405C2×C8—222no—
406C2×C8—222no—
407C2×C8—442no—
408C2×C8—442no—
409C4⋊C4—21no—
410C4⋊C4—112no—
411C4⋊C4—114no—
412C4⋊C4—228no—
413C4⋊C4—221no—
414C4⋊C4—222no—
415C4⋊C4—222no—
416C4⋊C4—222no—
417C4⋊C4—222no—
418C4⋊C4—222no—
419C4⋊C4C2×C22⋊D1112yes—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—228no—
423C42—222no—
424C42—222no—
425C42D4×D1111yescharacteristic
426C42D4×D1111yescharacteristic
427C42C2×C22⋊D1111yescharacteristic
428C42C23×D1111yescharacteristic
429C11C2×#162711yescharacteristic, complemented, Sylow
430C23—22no—
431C23—24no—
432C23—42no—
433C23—42no—
434C23—42no—
435C23—82no—
436C23—82no—
437C23—82no—
438C23#6699011yescharacteristic
439Q8—114no—
440Q8—224no—
441Q8—222no—
442Q8—4416no—
443Q8—444no—
444Q8—442no—
445Q8—442no—
446D4—22no—
447D4—24no—
448D4—44no—
449D4—42no—
450D4—42no—
451D4—42no—
452D4—42no—
453D4—82no—
454D4—82no—
455D4—82no—
456D4C2×#432414yescomplemented
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—42no—
460C2×C4—44no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—224no—
464C2×C4—222no—
465C2×C4—222no—
466C2×C4—224no—
467C2×C4—4416no—
468C2×C4—444no—
469C2×C4—442no—
470C2×C4D8×D1112yes—
471C2×C4#6696412yes—
472C2×C4C2×#432412yes—
473C2×C4#6699011yescharacteristic
474C2×C4#6699011yescharacteristic
475C2×C4#6699011yescharacteristic
476C2×C4#6700412yes—
477C2×C4C2×D4×D1111yescharacteristic
478C2×C4C2×D4×D1111yescharacteristic
479C2×C4C22×C22⋊D1111yescharacteristic
480C8—42no—
481C8—442no—
482C8—442no—
483C22—24no—
484C22—42no—
485C22—42no—
486C22—48no—
487C22—82no—
488C22—82no—
489C22—82no—
490C22—164no—
491C22#1062265312yes—
492C22#1062276912yes—
493C22#1062281412yes—
494C22C2×#6699011yescharacteristic
495C4—21no—
496C4—21no—
497C4—42no—
498C4—224no—
499C4—444no—
500C4—442no—
501C4#1062265312yes—
502C4#1062276912yes—
503C4C2×D8×D1111yescharacteristic
504C4C2×#6696411yescharacteristic
505C4C22×#432411yescharacteristic
506C4C2×#6700411yescharacteristic
507C2—44no—
508C2—162no—
509C2#1306771814yesdirect product factor
510C2C2×#1062276911yescharacteristic
511C2C2×#1062265311yescharacteristic
512C2C2×#1062281411yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC2×C11×#459C2
socleC23×C11#120
hypercenterC2×#459D11
hypocenterC11C2×#1627
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic22C2semidirect
2. C2×#10622683C2semidirect
3. C2×#10622688C2semidirect
4. #13067718C2direct (N × H)
5. C2×#10622124C2semidirect
6. C2×#10622122C2semidirect
7. C2×D4⋊(C11⋊C8)C2semidirect
19. D4×Dic22C22semidirect
31. #10622688C22semidirect
33. #10622683C22semidirect
36. D4⋊(C11⋊C8)C22semidirect
37. #10622124C22semidirect
38. #10622122C22semidirect
118. C2×D4×C11SD16semidirect
144. C2×Dic22D8semidirect
201. D4×C11C2×SD16semidirect
231. Dic22C2×D8semidirect
354. C2×C11#1627semidirect
386. C2×D4#4324semidirect
429. C11C2×#1627semidirect
456. D4C2×#4324semidirect
509. C2#13067718direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Dic222
C2×#106226832
C2×#106226882
#130677182
C2×#106221242
C2×#106221222
C2×D4⋊(C11⋊C8)2
C2×C11×#4592
C2×#162711