Finite Group Databasebeta

← C2×#21447775 #29833935

Subgroups — C2×#21447775 #29833935

Order 15616.

1150 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840563C211yesmaximal, characteristic, complemented
2C2×#16840198C211yesmaximal, characteristic, complemented
3C2×#16840029C211yesmaximal, characteristic, complemented
4#21447775C218yesmaximal, direct product factor
5C2×#16839575C211yesmaximal, characteristic, complemented
6C2×#16839570C211yesmaximal, characteristic, complemented
7C2×#16839545C211yesmaximal, characteristic, complemented
8C22×D16×C61C211yesmaximal, characteristic, complemented
9C2×#14519822—21no—
10#16840563—22no—
11#16840563—22no—
12#16840563—22no—
13#16840563C2214yescomplemented
14C2×#14519803—21no—
15C2×#14519803—21no—
16C2×#14519801—22no—
17C2×#14519799C2211yescharacteristic
18C2×#14519796—21no—
19C2×D8×D61—21no—
20C2×#14519783C2211yescharacteristic
21#16840198—22no—
22#16840198C2214yescomplemented
23C2×#14519721—21no—
24C2×#14519718—21no—
25C2×#14519717C2211yescharacteristic, complemented
26#16840029—22no—
27#16840029C2214yescomplemented
28C2×#14519713C2211yescharacteristic, complemented
29C2×#14519694—21no—
30#16839575C2214yescomplemented
31#16839570C2214yescomplemented
32#16839545C2214yescomplemented
33C22×D8×C61C2211yescharacteristic
34C22×D8×C61C2211yescharacteristic, complemented
35C2×D16×C61—22no—
36C2×D16×C61—22no—
37C2×D16×C61C2214yescomplemented
38C22×C16×C61C2211yescharacteristic, complemented
39#14519822—24no—
40#14519822—24no—
41#14519822—42no—
42#14519822—42no—
43C2×#11758222—21no—
44C2×#11758222D411yescharacteristic
45C2×#11758224—22no—
46C2×#11758224—41no—
47C22×C22⋊D61—42no—
48C2×D4×D61—22no—
49C2×D4×D61—41no—
50#14519803—24no—
51#14519803—24no—
52#14519803—24no—
53#14519803—42no—
54#14519801—28no—
55#14519801—28no—
56#14519799—21no—
57#14519799—21no—
58#14519799D412yes—
59#14519799C2312yes—
60#14519796—24no—
61#14519796—24no—
62C2×Dic244D411yescharacteristic
63C2×#11758190—21no—
64C2×#11758200—22no—
65C2×#11758200—41no—
66C2×D488D411yescharacteristic
67C2×#11758199—22no—
68C2×#11758199—41no—
69D8×D61—24no—
70D8×D61—24no—
71#14519783—21no—
72#14519783—21no—
73#14519783D412yes—
74#14519783C2312yes—
75C2×#11758194—21no—
76C2×#11758194D411yescharacteristic
77C2×#11758189—21no—
78C2×C8×D61—21no—
79#14519721—24no—
80#14519718—24no—
81#14519717—21no—
82#14519717C2312yescomplemented
83C2×#11758185—21no—
84#14519713—21no—
85#14519713C2312yescomplemented
86#14519694—24no—
87C22×D4×C61—21no—
88C22×D4×C61—21no—
89C2×D8×C61—21no—
90C2×D8×C61—21no—
91C2×D8×C61—21no—
92C2×D8×C61—21no—
93C2×D8×C61—21no—
94C2×D8×C61—21no—
95C2×D8×C61—21no—
96C2×D8×C61—21no—
97C2×D8×C61D412yes—
98C2×D8×C61D412yes—
99C2×D8×C61C2312yes—
100C2×D8×C61C2312yescomplemented
101C22×C8×C61C2311yescharacteristic
102D16×C61—28no—
103C2×C16×C61—21no—
104C2×C16×C61—21no—
105C2×C16×C61C2312yescomplemented
106C24×C61—41no—
107C24×C61—41no—
108C23×D61—42no—
109C2×D4×C61—22no—
110C2×D4×C61—22no—
111C2×D4×C61—22no—
112C2×D4×C61—22no—
113C2×D4×C61—41no—
114C2×D4×C61—41no—
115C2×D4×C61—41no—
116C2×D4×C61—41no—
117C2×D4×C61—41no—
118C2×D4×C61—41no—
119C2×D4×C61—41no—
120C2×D4×C61—41no—
121C22×C4×C61C2×D411yescharacteristic
122C2×C22⋊D61—21no—
123C2×C22⋊D61—42no—
124C2×C22⋊D61—48no—
125C2×C22⋊D61—48no—
126C2×C22⋊D61—42no—
127C2×C22⋊D61—41no—
128C22×Dic61—42no—
129#11758224—28no—
130#11758224—44no—
131#11758224—44no—
132#11758224—44no—
133D4×D61—28no—
134D4×D61—44no—
135D4×D61—44no—
136D4×D61—44no—
137#11758222—21no—
138#11758222—21no—
139#11758222—22no—
140#11758222—22no—
141#11758222—41no—
142#11758222—41no—
143#11758222D812yes—
144#11758222C2×D412yes—
145C2×D244—21no—
146C2×D244D811yescharacteristic
147C2×C4×D61—21no—
148C2×C4×D61—41no—
149C2×Dic122—21no—
150C2×Dic122D811yescharacteristic
151D8×C61—22no—
152D8×C61—22no—
153D8×C61—22no—
154D8×C61—22no—
155D8×C61—22no—
156D8×C61—41no—
157D8×C61—41no—
158D8×C61C2×D414yes—
159C2×C8×C61C2×D411yescharacteristic
160C2×C8×C61C2×D411yescharacteristic
161C2×C8×C61C2×D411yescharacteristic
162C2×C8×C61C2×D411yescharacteristic
163C2×C8×C61C2×D411yescharacteristic
164C2×C8×C61C2411yescharacteristic
165#11758200—28no—
166#11758200—44no—
167#11758199—28no—
168#11758199—44no—
169#11758194—21no—
170#11758194—22no—
171#11758194—41no—
172#11758194C2×D412yes—
173C2×#92418—21no—
174C2×#92418—41no—
175Dic244—21no—
176Dic244C2×D412yes—
177D488—21no—
178D488C2×D412yes—
179#11758190—22no—
180#11758190—22no—
181#11758189—22no—
182#11758189—22no—
183C8×D61—22no—
184C8×D61—22no—
185C16×C61—22no—
186#11758185—22no—
187C23×C61—42no—
188C23×C61—42no—
189C23×C61—42no—
190C23×C61—42no—
191C23×C61—81no—
192C23×C61—81no—
193C23×C61—162no—
194C23×C61—162no—
195C23×C61AGL(1,ℤ/8)11yescharacteristic
196C22×D61—21no—
197C22×D61—48no—
198C22×D61—41no—
199C22×D61—164no—
200D4×C61—24no—
201D4×C61—42no—
202D4×C61—42no—
203D4×C61—42no—
204D4×C61—42no—
205D4×C61—42no—
206D4×C61—81no—
207D4×C61—81no—
208C2×C4×C61#12011yescharacteristic
209C2×C4×C61#12011yescharacteristic
210C2×C4×C61C2×D811yescharacteristic
211C2×C4×C61C2×D811yescharacteristic
212C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
213C2×C4×C61C22×D411yescharacteristic
214C22⋊D61—22no—
215C22⋊D61—22no—
216C22⋊D61—48no—
217C22⋊D61—48no—
218C22⋊D61—42no—
219C22⋊D61—42no—
220C2×Dic61—21no—
221C2×Dic61—48no—
222C2×Dic61—41no—
223D244—22no—
224D244—21no—
225D244—41no—
226D244C2×D812yes—
227C4×D61—22no—
228C4×D61—22no—
229C4×D61—42no—
230C4×D61—42no—
231Dic122—21no—
232Dic122—22no—
233Dic122—41no—
234Dic122C2×D812yes—
235C8×C61#12011yescharacteristic
236C8×C61#12011yescharacteristic
237C8×C61C22×D411yescharacteristic
238C8×C61C22×D411yescharacteristic
239#92418—22no—
240#92418—42no—
241C2×#2192—611nomaximal, Sylow
242C22×C61—22no—
243C22×C61—44no—
244C22×C61—84no—
245C22×C61—82no—
246C22×C61—162no—
247C22×C61—162no—
248C22×C61—162no—
249C22×C61—162no—
250C22×C61—162no—
251C22×C61#44711yescharacteristic
252C22×C61#44711yescharacteristic
253C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
254C2×D61—22no—
255C2×D61—42no—
256C2×D61—42no—
257C2×D61—82no—
258C2×D61—168no—
259C4×C61#44711yescharacteristic
260C4×C61#44711yescharacteristic
261C4×C61C2×#12011yescharacteristic
262C4×C61C22×D811yescharacteristic
263Dic61—22no—
264Dic61—42no—
265C2×#576—611no—
266C2×#509—611no—
267C22×D16D6111yescharacteristic, complemented
268C2×#472—611no—
269#2192—618no—
270C2×#361—611no—
271C2×#359—611no—
272C2×#350—611no—
273C2×C61—21no—
274C2×C61—21no—
275C2×C61—84no—
276C2×C61—162no—
277C2×C61#219212yescomplemented
278C2×C61C2×#44711yescharacteristic
279D61—42no—
280D61—82no—
281C2×H(5,𝔽2)—1221no—
282#576—614no—
283#576—1222no—
284#576—1222no—
285#576—1222no—
286C2×AGL(1,ℤ/8)—1221no—
287C2×AGL(1,ℤ/8)—1222no—
288C2×AGL(1,ℤ/8)—1221no—
289C2×#135—611no—
290C2×#135—1221no—
291C22×D8—1221no—
292C22×D8C2×D6111yescharacteristic
293C22×D8C2×D6111yescharacteristic, complemented
294C2×#131—611no—
295#509—614no—
296#509—1222no—
297C2×SD32—1221no—
298C2×D16—22no—
299C2×D16—22no—
300C2×D16—1221no—
301C2×D16C2×D6114yescomplemented
302C2×M32—611no—
303C22×C16C2×D6111yescharacteristic, complemented
304#472—614no—
305#472—1222no—
306C2×#108—611no—
307C2×#100—1221no—
308#361—614no—
309#359—614no—
310#350—614no—
311C61C2×#219211yescharacteristic, complemented, Sylow
312H(5,𝔽2)—1224no—
313H(5,𝔽2)—1224no—
314H(5,𝔽2)—2442no—
315H(5,𝔽2)—2442no—
316C2×#41—611no—
317C2×#41—1222no—
318C2×#41—1221no—
319C2×#41—2441no—
320C22×D4—21no—
321C22×D4—21no—
322C22×D4—1222no—
323C22×D4—2441no—
324C22×D4—2442no—
325AGL(1,ℤ/8)—1224no—
326AGL(1,ℤ/8)—1228no—
327AGL(1,ℤ/8)—1224no—
328AGL(1,ℤ/8)—1228no—
329AGL(1,ℤ/8)—1224no—
330AGL(1,ℤ/8)—2442no—
331#135—612no—
332#135—612no—
333#135—1224no—
334#135—1224no—
335#135—1221no—
336#135—1221no—
337C2×Q16—611no—
338C2×SD16—1222no—
339C2×SD16—1221no—
340C2×SD16—2441no—
341C2×D8—21no—
342C2×D8—21no—
343C2×D8—21no—
344C2×D8—21no—
345C2×D8—21no—
346C2×D8—21no—
347C2×D8—21no—
348C2×D8—21no—
349C2×D8—611no—
350C2×D8—1224no—
351C2×D8—1224no—
352C2×D8—1222no—
353C2×D8—2441no—
354C2×D8C22⋊D6112yes—
355C2×D8C22⋊D6112yes—
356C2×D8C22×D6112yes—
357C2×D8C22×D6112yescomplemented
358#131—612no—
359#131—612no—
360#131—1221no—
361#131—1221no—
362C2×M16—611no—
363C2×M16—1221no—
364C2×M16—1221no—
365C22×C8—1221no—
366C22×C8C22×D6111yescharacteristic
367SD32—1224no—
368D16—28no—
369D16—1224no—
370M32—612no—
371M32—1221no—
372C2×C16—21no—
373C2×C16—21no—
374C2×C16—1221no—
375C2×C16C22×D6112yescomplemented
376#108—612no—
377#108—1221no—
378#100—1224no—
379C24—41no—
380C24—41no—
381C24—2442no—
382#41—612no—
383#41—612no—
384#41—1221no—
385#41—1221no—
386#41—1228no—
387#41—1222no—
388#41—1222no—
389#41—2444no—
390#41—2444no—
391#41—2444no—
392#41—2441no—
393#41—2441no—
394C2×Q8—611no—
395C2×Q8—1221no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—611no—
409C2×D4—1228no—
410C2×D4—1221no—
411C2×D4—1221no—
412C2×D4—2444no—
413C2×D4—2442no—
414C2×D4—2444no—
415C2×D4—2444no—
416C2×D4—2448no—
417C2×D4—2448no—
418C2×D4—2442no—
419C2×D4—2441no—
420C22×C4—1221no—
421C22×C4—2442no—
422C22×C4—2441no—
423C22×C4D4×D6111yescharacteristic
424Q16—612no—
425Q16—1221no—
426SD16—1228no—
427SD16—1222no—
428SD16—1222no—
429SD16—2444no—
430D8—22no—
431D8—22no—
432D8—22no—
433D8—22no—
434D8—22no—
435D8—41no—
436D8—41no—
437D8—612no—
438D8—1228no—
439D8—1221no—
440D8—2444no—
441D8C2×C22⋊D6114yes—
442M16—612no—
443M16—1221no—
444M16—1222no—
445M16—1222no—
446M16—1222no—
447M16—2441no—
448C2×C8—1221no—
449C2×C8—1222no—
450C2×C8—1222no—
451C2×C8—2441no—
452C2×C8D4×D6111yescharacteristic
453C2×C8D4×D6111yescharacteristic
454C2×C8D4×D6111yescharacteristic
455C2×C8C2×C22⋊D6111yescharacteristic
456C2×C8C2×C22⋊D6111yescharacteristic
457C2×C8C23×D6111yescharacteristic
458C16—22no—
459C16—1222no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23—81no—
465C23—81no—
466C23—162no—
467C23—162no—
468C23—1221no—
469C23—9764no—
470C23—2448no—
471C23—2441no—
472C23#1451980111yescharacteristic
473Q8—612no—
474Q8—1221no—
475Q8—1222no—
476Q8—2441no—
477D4—24no—
478D4—42no—
479D4—42no—
480D4—42no—
481D4—42no—
482D4—42no—
483D4—81no—
484D4—81no—
485D4—612no—
486D4—1222no—
487D4—1222no—
488D4—1222no—
489D4—1221no—
490D4—2448no—
491D4—2448no—
492D4—2442no—
493D4—2442no—
494D4—2441no—
495C2×C4—1221no—
496C2×C4—1222no—
497C2×C4—1222no—
498C2×C4—2448no—
499C2×C4—2441no—
500C2×C4—2442no—
501C2×C4—2442no—
502C2×C4#1451974511yescharacteristic
503C2×C4#1451974511yescharacteristic
504C2×C4D8×D6111yescharacteristic
505C2×C4D8×D6111yescharacteristic
506C2×C4#1451980111yescharacteristic
507C2×C4C2×D4×D6111yescharacteristic
508C8—1222no—
509C8—2442no—
510C8#1451974511yescharacteristic
511C8#1451974511yescharacteristic
512C8C2×D4×D6111yescharacteristic
513C8C22×C22⋊D6111yescharacteristic
514C22—22no—
515C22—44no—
516C22—84no—
517C22—82no—
518C22—162no—
519C22—162no—
520C22—162no—
521C22—162no—
522C22—162no—
523C22—1222no—
524C22—9768no—
525C22—4882no—
526C22—2442no—
527C22—2442no—
528C22#1683989411yescharacteristic
529C22#1683989411yescharacteristic
530C22C2×#1451980111yescharacteristic
531C4—1222no—
532C4—2442no—
533C4#1683989411yescharacteristic
534C4#1683989411yescharacteristic
535C4C2×#1451974511yescharacteristic
536C4C2×D8×D6111yescharacteristic
537C2—21no—
538C2—21no—
539C2—84no—
540C2—162no—
541C2—4882no—
542C2—2442no—
543C2#2144777512yesdirect product factor
544C2C2×#1683989411yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC22×D16×C61C2
socleC22×C61#447
hypercenterC22×D16D61
hypocenterC61C2×#2192
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×D16

Complements

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

NH ≅ G/Ntype
1. C2×#16840563C2semidirect
2. C2×#16840198C2semidirect
3. C2×#16840029C2semidirect
4. #21447775C2direct (N × H)
5. C2×#16839575C2semidirect
6. C2×#16839570C2semidirect
7. C2×#16839545C2semidirect
8. C22×D16×C61C2semidirect
13. #16840563C22semidirect
22. #16840198C22semidirect
25. C2×#14519717C22semidirect
27. #16840029C22semidirect
28. C2×#14519713C22semidirect
30. #16839575C22semidirect
31. #16839570C22semidirect
32. #16839545C22semidirect
34. C22×D8×C61C22semidirect
37. C2×D16×C61C22semidirect
38. C22×C16×C61C22semidirect
82. #14519717C23semidirect
85. #14519713C23semidirect
100. C2×D8×C61C23semidirect
105. C2×C16×C61C23semidirect
267. C22×D16D61semidirect
277. C2×C61#2192semidirect
293. C22×D8C2×D61semidirect
301. C2×D16C2×D61semidirect
303. C22×C16C2×D61semidirect
311. C61C2×#2192semidirect
357. C2×D8C22×D61semidirect
375. C2×C16C22×D61semidirect
543. C2#21447775direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405632
C2×#168401982
C2×#168400292
#214477752
C2×#168395752
C2×#168395702
C2×#168395452
C22×D16×C612
C2×#219261