Finite Group Databasebeta

← C2×#13067819 #14729689

Subgroups — C2×#13067819 #14729689

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×#10623108C211yesmaximal, characteristic
2C2×#10622307C211yesmaximal, characteristic, complemented
3C2×#10622633C211yesmaximal, characteristic, complemented
4C2×#10622454C211yesmaximal, characteristic, complemented
5#13067819C218yesmaximal, direct product factor
6C2×#10622123C211yesmaximal, characteristic, complemented
7C2×#10622097C211yesmaximal, characteristic, complemented
8C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
9C22×#4343—21no—
10C2×C4×Q8×C11C2211yescharacteristic
11C22×#4314—21no—
12#10623108—22no—
13#10623108—22no—
14#10623108—22no—
15#10623108C2214yes—
16C2×#66948—22no—
17C2×#66948—21no—
18C2×#66927—21no—
19C2×#66927C2211yescharacteristic
20C2×C4×D44—21no—
21C2×C4×D44C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C2×#66899—21no—
26C2×#66885—22no—
27C2×#66880—21no—
28#10622633—22no—
29#10622633C2214yescomplemented
30C2×#66872—21no—
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32#10622454—22no—
33#10622454C2214yescomplemented
34#10622307—22no—
35#10622307C2214yescomplemented
36C11×Q8⋊C8C2214yescomplemented
37#10622123C2214yescomplemented
38#10622097C2214yescomplemented
39C22×Q8×C11D411yescharacteristic
40C2×#4343—24no—
41C2×#4343—24no—
42C2×#4343—44no—
43C2×#4343—44no—
44C22×D44—22no—
45C22×D44—21no—
46C22×D44—21no—
47C22×D44—22no—
48C22×D44D411yescharacteristic
49C22×D44D412yes—
50C22×C4×D11—22no—
51C22×C4×D11—21no—
52C22×Dic22—21no—
53C22×C8×C11—21no—
54C22×C8×C11—21no—
55C4×Q8×C11—21no—
56C4×Q8×C11—21no—
57C4×Q8×C11D412yes—
58C4×Q8×C11C2312yes—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11D411yescharacteristic
68C22×C11⋊C8—21no—
69C2×#4314—24no—
70C2×#4314—44no—
71#66948—24no—
72#66948—28no—
73#66948—28no—
74#66948—24no—
75#66927—24no—
76#66927—24no—
77#66927—21no—
78#66927—21no—
79#66927D412yes—
80#66927C2312yes—
81C4×D44—24no—
82C4×D44—21no—
83C4×D44—21no—
84C4×D44—24no—
85C4×D44D412yes—
86C4×D44C2312yes—
87#66922—21no—
88#66922—21no—
89#66922—21no—
90#66922C2312yes—
91C11×C4⋊C8—21no—
92C11×C4⋊C8C2312yes—
93C4×C8×C11—21no—
94C4×C8×C11C2312yes—
95#66899—24no—
96#66885—28no—
97#66880—24no—
98#66872—24no—
99C4⋊(C11⋊C8)—21no—
100C4⋊(C11⋊C8)C2312yes—
101C2×#1642—111nomaximal, Sylow
102C23×D11—21no—
103C23×D11—22no—
104C2×Q8×C11—21no—
105C2×Q8×C11—22no—
106C2×Q8×C11SD1614yescomplemented
107C2×Q8×C11C2×D412yes—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×Dic11—21no—
114C22×Dic11—41no—
115#4343—48no—
116#4343—416no—
117#4343—48no—
118C2×D44—28no—
119C2×D44—28no—
120C2×D44—21no—
121C2×D44—22no—
122C2×D44—22no—
123C2×D44—22no—
124C2×D44—22no—
125C2×D44—22no—
126C2×D44—22no—
127C2×D44—22no—
128C2×D44—48no—
129C2×D44—44no—
130C2×D44—42no—
131C2×D44—42no—
132C2×D44—42no—
133C2×D44—42no—
134C2×D44—84no—
135C2×D44C2×D412yes—
136C2×D44C2×D414yes—
137C2×C4×D11—28no—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—48no—
141C2×C4×D11—42no—
142C2×C4×D11—42no—
143C2×Dic22—22no—
144C2×Dic22—41no—
145C2×Dic22—42no—
146C2×Dic22—42no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—42no—
150C2×C8×C11—42no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4C2×D412yes—
155C42×C11—22no—
156C42×C11—22no—
157C42×C11C2×D411yescharacteristic
158C42×C11C2×D411yescharacteristic
159C42×C11C2×D411yescharacteristic
160C42×C11C2411yescharacteristic
161(C2×D11)⋊C4—28no—
162(C2×D11)⋊C4—22no—
163(C2×D11)⋊C4—22no—
164C4⋊Dic11—21no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167C4⋊Dic11—41no—
168C4⋊Dic11—41no—
169C4⋊Dic11C2×D412yes—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—42no—
172#4314—48no—
173C2×#550—111no—
174C2×#486—111no—
175C2×#475—111no—
176C2×#461—111no—
177#1642—118no—
178C2×#331—111no—
179C2×Q8⋊C8D1111yescharacteristic, complemented
180C2×D4⋊C8—111no—
181C23×C11#12011yescharacteristic
182C22×D11—22no—
183C22×D11—24no—
184C22×D11—42no—
185C22×D11—44no—
186C22×D11—44no—
187C22×D11—42no—
188C22×D11—44no—
189C22×D11—42no—
190Q8×C11—22no—
191Q8×C11—24no—
192Q8×C11C2×SD1614yescomplemented
193C2×C4×C11—22no—
194C2×C4×C11—24no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—42no—
198C2×C4×C11#12011yescharacteristic
199C2×C4×C11#12011yescharacteristic
200C2×C4×C11#12011yescharacteristic
201C2×C4×C11C2×SD1612yes—
202C2×C4×C11#13512yes—
203C2×C4×C11AGL(1,ℤ/8)12yes—
204C2×C4×C11AGL(1,ℤ/8)12yes—
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C2×Dic11—22no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—82no—
212D44—22no—
213D44—22no—
214D44—44no—
215D44—416no—
216D44—42no—
217D44—42no—
218D44—42no—
219D44—42no—
220D44—42no—
221D44—44no—
222D44—44no—
223D44—82no—
224D44—88no—
225C4×D11—416no—
226C4×D11—42no—
227C4×D11—42no—
228C4×D11—44no—
229Dic22—42no—
230Dic22—42no—
231Dic22—82no—
232C8×C11—42no—
233C8×C11—42no—
234C11⋊C8—42no—
235C22×#41—221no—
236C22×SD16—221no—
237#550—114no—
238#550—222no—
239#550—222no—
240#550—222no—
241C2×C4⋊Q8—111no—
242C2×#127—111no—
243C2×#127—221no—
244C2×#121—222no—
245C2×#121—221no—
246C2×C4×Q8C2×D1111yescharacteristic
247C2×C4×D4—111no—
248C2×C4×D4—221no—
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⋊C8C2×D1111yescharacteristic
258C2×#103—221no—
259C2×#103—221no—
260C2×#102—222no—
261C2×C4×C8C2×D1111yescharacteristic
262#331—114no—
263Q8⋊C8C2×D1114yescomplemented
264D4⋊C8—114no—
265C22×C11#44912yes—
266C22×C11#45012yes—
267C22×C11#45512yes—
268C22×C11C2×#12011yescharacteristic
269C2×D11—44no—
270C2×D11—42no—
271C2×D11—42no—
272C2×D11—44no—
273C2×D11—44no—
274C2×D11—42no—
275C2×D11—84no—
276C2×D11—88no—
277C4×C11—24no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—42no—
281C4×C11#44912yes—
282C4×C11#45012yes—
283C4×C11C22×SD1611yescharacteristic
284C4×C11C2×#13511yescharacteristic
285C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
286C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
287Dic11—42no—
288Dic11—82no—
289C2×#41—224no—
290C2×#41—224no—
291C2×#41—444no—
292C2×#41—444no—
293C22×Q8—221no—
294C22×Q8D4411yescharacteristic
295C22×D4—111no—
296C22×D4—112no—
297C22×D4—222no—
298C22×D4—222no—
299C22×D4—221no—
300C22×D4—221no—
301C23×C4—222no—
302C23×C4—221no—
303C2×SD16—224no—
304C2×SD16—444no—
305C22×C8—21no—
306C22×C8—21no—
307C22×C8—221no—
308C4⋊Q8—112no—
309C4⋊Q8—221no—
310C4⋊Q8—221no—
311C4⋊Q8—221no—
312#127—112no—
313#127—112no—
314#127—224no—
315#127—224no—
316#127—221no—
317#127—221no—
318#121—228no—
319#121—224no—
320#121—228no—
321#121—224no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×Q8D4412yes—
325C4×Q8C22×D1112yes—
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—111no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4—221no—
336C2×C4⋊C4D4411yescharacteristic
337C2×C22⋊C4—222no—
338C2×C22⋊C4—221no—
339C2×C42—21no—
340C2×C42C22×D1111yescharacteristic
341#106—224no—
342C4⋊C8—21no—
343C4⋊C8—112no—
344C4⋊C8—221no—
345C4⋊C8C22×D1112yes—
346#103—224no—
347#103—224no—
348#102—228no—
349C4×C8—21no—
350C4×C8C22×D1112yes—
351C2×C11#164214yescomplemented
352C2×C11C2×#45011yescharacteristic
353C2×C11C2×#44911yescharacteristic
354C2×C11C2×#45511yescharacteristic
355D11—82no—
356D11—84no—
357C24—221no—
358C24—222no—
359#41—448no—
360#41—4416no—
361#41—448no—
362C2×Q8—21no—
363C2×Q8—22no—
364C2×Q8—222no—
365C2×Q8—441no—
366C2×Q8—442no—
367C2×Q8—442no—
368C2×Q8#431414yescomplemented
369C2×Q8C2×D4412yes—
370C2×D4—112no—
371C2×D4—114no—
372C2×D4—228no—
373C2×D4—228no—
374C2×D4—222no—
375C2×D4—221no—
376C2×D4—222no—
377C2×D4—222no—
378C2×D4—222no—
379C2×D4—222no—
380C2×D4—222no—
381C2×D4—222no—
382C2×D4—448no—
383C2×D4—444no—
384C2×D4—442no—
385C2×D4—442no—
386C2×D4—442no—
387C2×D4—442no—
388C2×D4—884no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—228no—
392C22×C4—221no—
393C22×C4—222no—
394C22×C4—222no—
395C22×C4—448no—
396C22×C4—442no—
397C22×C4—442no—
398C22×C4—441no—
399C22×C4C2×D4411yescharacteristic
400C22×C4D4×D1111yescharacteristic
401C22×C4D4×D1111yescharacteristic
402SD16—448no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—42no—
406C2×C8—42no—
407C2×C8—222no—
408C2×C8—442no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—22no—
412C4⋊C4—112no—
413C4⋊C4—221no—
414C4⋊C4—222no—
415C4⋊C4—222no—
416C4⋊C4—441no—
417C4⋊C4—441no—
418C4⋊C4C2×D4412yes—
419C22⋊C4—228no—
420C22⋊C4—222no—
421C22⋊C4—222no—
422C42—22no—
423C42—22no—
424C42C2×D4411yescharacteristic
425C42D4×D1111yescharacteristic
426C42D4×D1111yescharacteristic
427C42C23×D1111yescharacteristic
428C11C2×#164211yescharacteristic, complemented, Sylow
429C23—222no—
430C23—224no—
431C23—444no—
432C23—442no—
433C23—442no—
434C23—444no—
435C23—444no—
436C23—442no—
437C23#6693511yescharacteristic
438Q8—22no—
439Q8—24no—
440Q8—442no—
441Q8—442no—
442Q8—882no—
443Q8C2×#431414yescomplemented
444D4—222no—
445D4—222no—
446D4—444no—
447D4—4416no—
448D4—442no—
449D4—442no—
450D4—442no—
451D4—442no—
452D4—444no—
453D4—442no—
454D4—444no—
455D4—882no—
456D4—888no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—42no—
462C2×C4—222no—
463C2×C4—4416no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—444no—
468C2×C4—442no—
469C2×C4—882no—
470C2×C4#6693511yescharacteristic
471C2×C4#6693511yescharacteristic
472C2×C4#6693511yescharacteristic
473C2×C4C2×#431412yes—
474C2×C4#6696112yes—
475C2×C4#6696712yes—
476C2×C4#6697212yes—
477C2×C4C22×D4411yescharacteristic
478C2×C4C2×D4×D1111yescharacteristic
479C2×C4C2×D4×D1111yescharacteristic
480C8—42no—
481C8—42no—
482C8—442no—
483C22—444no—
484C22—442no—
485C22—442no—
486C22—444no—
487C22—444no—
488C22—442no—
489C22—884no—
490C22—888no—
491C22#1062234412yes—
492C22#1062242412yes—
493C22#1062243812yes—
494C22C2×#6693511yescharacteristic
495C4—24no—
496C4—21no—
497C4—21no—
498C4—42no—
499C4—442no—
500C4—882no—
501C4#1062234412yes—
502C4#1062242412yes—
503C4C22×#431411yescharacteristic
504C4C2×#6696111yescharacteristic
505C4C2×#6696711yescharacteristic
506C4C2×#6697211yescharacteristic
507C2—882no—
508C2—884no—
509C2#1306781914yesdirect product factor
510C2C2×#1062234411yescharacteristic
511C2C2×#1062242411yescharacteristic
512C2C2×#1062243811yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×Q8⋊C8C2
socleC23×C11#120
prime radicalC2×#10623108C2
hypercenterC2×Q8⋊C8D11
hypocenterC11C2×#1642
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#10622307C2semidirect
3. C2×#10622633C2semidirect
4. C2×#10622454C2semidirect
5. #13067819C2direct (N × H)
6. C2×#10622123C2semidirect
7. C2×#10622097C2semidirect
8. C2×C11×Q8⋊C8C2semidirect
29. #10622633C22semidirect
33. #10622454C22semidirect
35. #10622307C22semidirect
36. C11×Q8⋊C8C22semidirect
37. #10622123C22semidirect
38. #10622097C22semidirect
106. C2×Q8×C11SD16semidirect
179. C2×Q8⋊C8D11semidirect
192. Q8×C11C2×SD16semidirect
263. Q8⋊C8C2×D11semidirect
351. C2×C11#1642semidirect
368. C2×Q8#4314semidirect
428. C11C2×#1642semidirect
443. Q8C2×#4314semidirect
509. C2#13067819direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231082
C2×#106223072
C2×#106226332
C2×#106224542
#130678192
C2×#106221232
C2×#106220972
C2×C11×Q8⋊C82
C2×#164211