Finite Group Databasebeta

← C2×#13067740 #14729633

Subgroups — C2×#13067740 #14729633

Order 2816.

1322 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623249C211yesmaximal, characteristic
2C2×#10622704C211yesmaximal, characteristic, complemented
3C2×#10622697C211yesmaximal, characteristic, complemented
4#13067740C218yesmaximal, direct product factor
5C2×#10622182C211yesmaximal, characteristic, complemented
6C2×#10622094C211yesmaximal, characteristic, complemented
7C2×#10622097C211yesmaximal, characteristic, complemented
8C2×C11×#492C211yesmaximal, characteristic, complemented
9C22×#4341—21no—
10C22×C11×SD16—22no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×#127C2211yescharacteristic
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×#492—22no—
24C11×#492C2214yescomplemented
25C2×C4×C8×C11C2211yescharacteristic
26#10622704—22no—
27#10622704C2214yescomplemented
28#10622697—22no—
29#10622697C2214yescomplemented
30C2×#66874—21no—
31C2×#66873—21no—
32C2×#66872—21no—
33C2×#66871—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
53C2×C11×SD16—28no—
54C2×C11×SD16—48no—
55C22×C8×C11—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8—21no—
58C11×C4⋊Q8—21no—
59C11×C4⋊Q8C2312yes—
60C11×#127—21no—
61C11×#127—21no—
62C11×#127D412yes—
63C11×#127C2312yes—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C42×C11C2311yescharacteristic
67C2×C22⋊Dic11—22no—
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—
91C4×C8×C11—21no—
92C4×C8×C11C2312yes—
93#66874—24no—
94#66873—24no—
95#66872—24no—
96#66871—24no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)—21no—
99C4⋊(C11⋊C8)C2312yes—
100C4⋊(C11⋊C8)C2312yes—
101C2×#1631—111nomaximal, Sylow
102C24×C11—22no—
103C23×D11—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11—44no—
106C2×Q8×C11—41no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—44no—
113C2×D4×C11—42no—
114C2×D4×C11—42no—
115C2×D4×C11—42no—
116C2×D4×C11—42no—
117C2×D4×C11C2×D414yes—
118C22×C4×C11—41no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C2×C22⋊D11—28no—
123C2×C22⋊D11—28no—
124C2×C22⋊D11—48no—
125C2×C22⋊D11—84no—
126C22×Dic11—28no—
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—48no—
131#4341—48no—
132#4341—416no—
133#4341—48no—
134C2×D44—21no—
135C2×D44—22no—
136C2×D44—22no—
137C2×D44C2×D412yes—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—42no—
141C2×C4×D11—42no—
142C2×Dic22—21no—
143C2×Dic22—22no—
144C2×Dic22SD1614yescomplemented
145C2×Dic22C2×D412yes—
146C11×SD16—416no—
147C2×C8×C11—24no—
148C2×C8×C11—22no—
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(C2×D11)⋊C4—22no—
159(C2×D11)⋊C4—22no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162C4⋊Dic11C2×D412yes—
163C4⋊Dic11C2×D412yes—
164Dic11⋊C4—22no—
165Dic11⋊C4—22no—
166C4×Dic11—22no—
167C4×Dic11—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—42no—
171C2×C11⋊C8—42no—
172C2×#550—111no—
173C2×#492D1111yescharacteristic, complemented
174C2×#477—111no—
175C2×#476—111no—
176#1631—118no—
177C2×#331—111no—
178C2×Q8⋊C8—111no—
179C2×D4⋊C8—111no—
180C23×C11—24no—
181C23×C11—44no—
182C23×C11—44no—
183C23×C11—44no—
184C23×C11#12011yescharacteristic
185C22×D11—22no—
186C22×D11—42no—
187C22×D11—42no—
188C22×D11—42no—
189Q8×C11—44no—
190Q8×C11—82no—
191D4×C11—44no—
192D4×C11—42no—
193D4×C11—42no—
194D4×C11—42no—
195D4×C11—42no—
196D4×C11—44no—
197D4×C11—44no—
198D4×C11—82no—
199C2×C4×C11—22no—
200C2×C4×C11—42no—
201C2×C4×C11—82no—
202C2×C4×C11#12011yescharacteristic
203C2×C4×C11#12011yescharacteristic
204C2×C4×C11#12011yescharacteristic
205C2×C4×C11C2×SD1612yes—
206C2×C4×C11#13512yes—
207C2×C4×C11AGL(1,ℤ/8)12yes—
208C2×C4×C11#13712yes—
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C22⋊D11—416no—
213C22⋊D11—88no—
214C2×Dic11—22no—
215C2×Dic11—24no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—416no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221D44—22no—
222D44—22no—
223D44—42no—
224C4×D11—42no—
225C4×D11—42no—
226C4×D11—44no—
227Dic22—22no—
228Dic22—24no—
229Dic22C2×SD1614yescomplemented
230C8×C11—24no—
231C11⋊C8—42no—
232C11⋊C8—42no—
233C22×#41—221no—
234C22×SD16—22no—
235#550—114no—
236#550—222no—
237#550—222no—
238#550—222no—
239C2×C4⋊Q8C2×D1111yescharacteristic
240C2×#127—221no—
241C2×#127C2×D1111yescharacteristic
242C2×#121—221no—
243C2×#121—222no—
244C2×C4×Q8—111no—
245C2×C4×D4—111no—
246C2×C4×D4—221no—
247#492—22no—
248#492C2×D1114yescomplemented
249#477—114no—
250#477—222no—
251#476—114no—
252#476—222no—
253C2×#107—221no—
254C2×#106—221no—
255C2×C4⋊C8—111no—
256C2×C4⋊C8—111no—
257C2×#103—221no—
258C2×#102—221no—
259C2×C4×C8C2×D1111yescharacteristic
260#331—114no—
261Q8⋊C8—114no—
262D4⋊C8—114no—
263C22×C11—44no—
264C22×C11—44no—
265C22×C11—44no—
266C22×C11—88no—
267C22×C11#45012yes—
268C22×C11#45212yes—
269C22×C11#45312yes—
270C22×C11C2×#12011yescharacteristic
271C2×D11—42no—
272C2×D11—42no—
273C2×D11—42no—
274C2×D11—84no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—82no—
278C4×C11#45012yes—
279C4×C11#45212yes—
280C4×C11C22×SD1611yescharacteristic
281C4×C11C2×#13511yescharacteristic
282C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
283C4×C11C2×#13711yescharacteristic
284Dic11—24no—
285Dic11—42no—
286Dic11—42no—
287C2×#41—224no—
288C2×#41—224no—
289C2×#41—444no—
290C2×#41—444no—
291C22×Q8—21no—
292C22×Q8—111no—
293C22×D4—21no—
294C22×D4—21no—
295C22×D4—111no—
296C22×D4—222no—
297C22×D4—222no—
298C22×D4C22⋊D1112yes—
299C23×C4—222no—
300C23×C4—221no—
301C2×SD16—28no—
302C2×SD16—48no—
303C22×C8—21no—
304C22×C8—221no—
305C22×C8—221no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8C22×D1112yes—
310#127—21no—
311#127—21no—
312#127—224no—
313#127—224no—
314#127C22⋊D1112yes—
315#127C22×D1112yes—
316#121—224no—
317#121—224no—
318#121—228no—
319#121—228no—
320C4×Q8—112no—
321C4×Q8—112no—
322C4×Q8—221no—
323C4×Q8—221no—
324C4×D4—112no—
325C4×D4—112no—
326C4×D4—224no—
327C4×D4—224no—
328C4×D4—221no—
329C4×D4—221no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—111no—
333C2×C4⋊C4—111no—
334C2×C4⋊C4—221no—
335C2×C22⋊C4—222no—
336C2×C22⋊C4—221no—
337C2×C42—221no—
338C2×C42C22×D1111yescharacteristic
339#107—224no—
340#106—224no—
341C4⋊C8—112no—
342C4⋊C8—112no—
343C4⋊C8—221no—
344C4⋊C8—221no—
345#103—224no—
346#102—224no—
347C4×C8—21no—
348C4×C8C22×D1112yes—
349C2×C11—84no—
350C2×C11#163114yescomplemented
351C2×C11C2×#45011yescharacteristic
352C2×C11C2×#45211yescharacteristic
353C2×C11C2×#45311yescharacteristic
354D11—82no—
355C24—22no—
356C24—221no—
357#41—448no—
358#41—448no—
359#41—4416no—
360C2×Q8—22no—
361C2×Q8—44no—
362C2×Q8—41no—
363C2×Q8—114no—
364C2×Q8—112no—
365C2×Q8—222no—
366C2×Q8—221no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—44no—
373C2×D4—42no—
374C2×D4—42no—
375C2×D4—42no—
376C2×D4—42no—
377C2×D4—112no—
378C2×D4—228no—
379C2×D4—228no—
380C2×D4—222no—
381C2×D4—222no—
382C2×D4—221no—
383C2×D4—448no—
384C2×D4—884no—
385C2×D4C2×C22⋊D1114yes—
386C22×C4—41no—
387C22×C4—221no—
388C22×C4—228no—
389C22×C4—221no—
390C22×C4—221no—
391C22×C4—222no—
392C22×C4—222no—
393C22×C4—448no—
394C22×C4—442no—
395C22×C4—442no—
396C22×C4D4×D1111yescharacteristic
397C22×C4D4×D1111yescharacteristic
398C22×C4C2×C22⋊D1111yescharacteristic
399SD16—416no—
400C2×C8—24no—
401C2×C8—22no—
402C2×C8—222no—
403C2×C8—222no—
404C2×C8—442no—
405C2×C8—442no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—112no—
411C4⋊C4—112no—
412C4⋊C4—221no—
413C4⋊C4—221no—
414C4⋊C4—222no—
415C4⋊C4—222no—
416C22⋊C4—228no—
417C22⋊C4—222no—
418C22⋊C4—222no—
419C42—222no—
420C42—222no—
421C42D4×D1111yescharacteristic
422C42D4×D1111yescharacteristic
423C42C2×C22⋊D1111yescharacteristic
424C42C23×D1111yescharacteristic
425C11C2×#163111yescharacteristic, complemented, Sylow
426C23—24no—
427C23—44no—
428C23—44no—
429C23—44no—
430C23—222no—
431C23—442no—
432C23—442no—
433C23—442no—
434C23#6699011yescharacteristic
435Q8—44no—
436Q8—82no—
437Q8—114no—
438Q8—222no—
439Q8—224no—
440D4—44no—
441D4—42no—
442D4—42no—
443D4—42no—
444D4—42no—
445D4—44no—
446D4—44no—
447D4—82no—
448D4—222no—
449D4—222no—
450D4—4416no—
451D4—442no—
452D4—888no—
453C2×C4—22no—
454C2×C4—42no—
455C2×C4—82no—
456C2×C4—224no—
457C2×C4—222no—
458C2×C4—222no—
459C2×C4—222no—
460C2×C4—4416no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4—444no—
466C2×C4SD16×D1112yes—
467C2×C4#6696712yes—
468C2×C4#6696812yes—
469C2×C4#6696912yes—
470C2×C4#6699011yescharacteristic
471C2×C4#6699011yescharacteristic
472C2×C4#6699011yescharacteristic
473C2×C4C2×D4×D1111yescharacteristic
474C2×C4C2×D4×D1111yescharacteristic
475C2×C4C22×C22⋊D1111yescharacteristic
476C8—24no—
477C8—442no—
478C8—442no—
479C22—44no—
480C22—44no—
481C22—44no—
482C22—88no—
483C22—442no—
484C22—442no—
485C22—442no—
486C22—884no—
487C22#1062269012yes—
488C22#1062278212yes—
489C22#1062278612yes—
490C22C2×#6699011yescharacteristic
491C4—21no—
492C4—21no—
493C4—82no—
494C4—224no—
495C4—442no—
496C4—442no—
497C4#1062278212yes—
498C4#1062278612yes—
499C4C2×SD16×D1111yescharacteristic
500C4C2×#6696711yescharacteristic
501C4C2×#6696811yescharacteristic
502C4C2×#6696911yescharacteristic
503C2—84no—
504C2—882no—
505C2#1306774014yesdirect product factor
506C2C2×#1062278211yescharacteristic
507C2C2×#1062278611yescharacteristic
508C2C2×#1062269011yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#492C2
socleC23×C11#120
prime radicalC2×#10623249C2
hypercenterC2×#492D11
hypocenterC11C2×#1631
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#492

Complements

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

NH ≅ G/Ntype
2. C2×#10622704C2semidirect
3. C2×#10622697C2semidirect
4. #13067740C2direct (N × H)
5. C2×#10622182C2semidirect
6. C2×#10622094C2semidirect
7. C2×#10622097C2semidirect
8. C2×C11×#492C2semidirect
24. C11×#492C22semidirect
27. #10622704C22semidirect
29. #10622697C22semidirect
36. #10622182C22semidirect
37. #10622097C22semidirect
38. #10622094C22semidirect
144. C2×Dic22SD16semidirect
173. C2×#492D11semidirect
229. Dic22C2×SD16semidirect
248. #492C2×D11semidirect
350. C2×C11#1631semidirect
425. C11C2×#1631semidirect
505. C2#13067740direct (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×#106227042
C2×#106226972
#130677402
C2×#106221822
C2×#106220942
C2×#106220972
C2×C11×#4922
C2×#163111