Finite Group Databasebeta

← C2×#21447789 #29833943

Subgroups — C2×#21447789 #29833943

Order 15616.

1130 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840563C211yesmaximal, characteristic
2C2×#16840203C211yesmaximal, characteristic, complemented
3C2×#16840034C211yesmaximal, characteristic, complemented
4#21447789C218yesmaximal, direct product factor
5C2×#16839575C211yesmaximal, characteristic, complemented
6C2×#16839570C211yesmaximal, characteristic, complemented
7C2×#16839545C211yesmaximal, characteristic, complemented
8C22×SD32×C61C211yesmaximal, characteristic, complemented
9C2×#14519822—21no—
10#16840563—22no—
11#16840563—22no—
12#16840563—22no—
13#16840563C2214yes—
14C2×#14519808—21no—
15C2×#14519803—21no—
16C2×#14519801—22no—
17C2×#14519799C2211yescharacteristic
18C2×#14519796—21no—
19C2×D8×D61—21no—
20C2×#14519783C2211yescharacteristic
21#16840203—22no—
22#16840203C2214yescomplemented
23C2×#14519723—21no—
24C2×#14519720—21no—
25C2×#14519717C2211yescharacteristic, complemented
26#16840034—22no—
27#16840034C2214yescomplemented
28C2×#14519713C2211yescharacteristic, complemented
29C2×#14519696—21no—
30#16839575C2214yescomplemented
31#16839570C2214yescomplemented
32#16839545C2214yescomplemented
33C22×Q16×C61C2211yescharacteristic, complemented
34C22×D8×C61C2211yescharacteristic
35C2×SD32×C61—22no—
36C2×SD32×C61—22no—
37C2×SD32×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#14519808—24no—
51#14519808—42no—
52#14519803—24no—
53#14519803—24no—
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×#11758202—41no—
64C2×#11758190—21no—
65C2×#11758200—22no—
66C2×#11758201—41no—
67C2×D488D411yescharacteristic
68C2×#11758199—22no—
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#14519723—24no—
80#14519720—24no—
81#14519717—21no—
82#14519717C2312yescomplemented
83C2×#11758185—21no—
84#14519713—21no—
85#14519713C2312yescomplemented
86#14519696—24no—
87C22×Q8×C61—21no—
88C22×D4×C61—21no—
89C2×Q16×C61—21no—
90C2×Q16×C61—21no—
91C2×Q16×C61—21no—
92C2×Q16×C61—21no—
93C2×Q16×C61—21no—
94C2×Q16×C61C2312yescomplemented
95C2×D8×C61—21no—
96C2×D8×C61—21no—
97C2×D8×C61—21no—
98C2×D8×C61D412yes—
99C2×D8×C61D412yes—
100C2×D8×C61C2312yes—
101C22×C8×C61C2311yescharacteristic
102SD32×C61—28no—
103C2×C16×C61—21no—
104C2×C16×C61—21no—
105C2×C16×C61C2312yescomplemented
106C24×C61—41no—
107C23×D61—42no—
108C2×Q8×C61—22no—
109C2×Q8×C61—41no—
110C2×Q8×C61—41no—
111C2×Q8×C61—41no—
112C2×Q8×C61—41no—
113C2×Q8×C61—41no—
114C2×D4×C61—22no—
115C2×D4×C61—22no—
116C2×D4×C61—22no—
117C2×D4×C61—41no—
118C2×D4×C61—41no—
119C2×D4×C61—41no—
120C22×C4×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
151Q16×C61—22no—
152Q16×C61—22no—
153Q16×C61—41no—
154Q16×C61—41no—
155D8×C61—22no—
156D8×C61—22no—
157D8×C61—22no—
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#11758202—44no—
166#11758201—44no—
167#11758200—28no—
168#11758199—28no—
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—162no—
191C23×C61AGL(1,ℤ/8)11yescharacteristic
192C22×D61—21no—
193C22×D61—48no—
194C22×D61—41no—
195C22×D61—164no—
196Q8×C61—42no—
197Q8×C61—42no—
198Q8×C61—81no—
199Q8×C61—81no—
200D4×C61—24no—
201D4×C61—42no—
202D4×C61—42no—
203D4×C61—42no—
204C2×C4×C61—42no—
205C2×C4×C61—81no—
206C2×C4×C61—81no—
207C2×C4×C61#12011yescharacteristic
208C2×C4×C61#12011yescharacteristic
209C2×C4×C61C2×D811yescharacteristic
210C2×C4×C61C2×D811yescharacteristic
211C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
212C2×C4×C61C22×D411yescharacteristic
213C22⋊D61—22no—
214C22⋊D61—22no—
215C22⋊D61—48no—
216C22⋊D61—48no—
217C22⋊D61—42no—
218C22⋊D61—42no—
219C2×Dic61—21no—
220C2×Dic61—48no—
221C2×Dic61—41no—
222D244—22no—
223D244—21no—
224D244—41no—
225D244C2×D812yes—
226C4×D61—22no—
227C4×D61—22no—
228C4×D61—42no—
229C4×D61—42no—
230Dic122—21no—
231Dic122—22no—
232Dic122—41no—
233Dic122C2×D812yes—
234C8×C61#12011yescharacteristic
235C8×C61#12011yescharacteristic
236C8×C61C22×D411yescharacteristic
237C8×C61C22×D411yescharacteristic
238#92418—22no—
239#92418—42no—
240C2×#2194—611nomaximal, Sylow
241C22×C61—22no—
242C22×C61—44no—
243C22×C61—84no—
244C22×C61—162no—
245C22×C61—162no—
246C22×C61#44711yescharacteristic
247C22×C61#44711yescharacteristic
248C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
249C2×D61—22no—
250C2×D61—42no—
251C2×D61—42no—
252C2×D61—82no—
253C2×D61—168no—
254C4×C61—82no—
255C4×C61#44711yescharacteristic
256C4×C61#44711yescharacteristic
257C4×C61C2×#12011yescharacteristic
258C4×C61C22×D811yescharacteristic
259Dic61—22no—
260Dic61—42no—
261C2×#576—611no—
262C2×#510—611no—
263C22×SD32D6111yescharacteristic, complemented
264C2×#473—611no—
265#2194—618no—
266C2×#361—611no—
267C2×#359—611no—
268C2×#350—611no—
269C2×C61—21no—
270C2×C61—21no—
271C2×C61—84no—
272C2×C61#219412yescomplemented
273C2×C61C2×#44711yescharacteristic
274D61—42no—
275D61—82no—
276C2×H(5,𝔽2)—1221no—
277#576—614no—
278#576—1222no—
279#576—1222no—
280#576—1222no—
281C2×#137—1221no—
282C2×AGL(1,ℤ/8)—1221no—
283C2×AGL(1,ℤ/8)—1222no—
284C2×#135—611no—
285C2×#135—1221no—
286C22×Q16C2×D6111yescharacteristic, complemented
287C22×D8—1221no—
288C22×D8C2×D6111yescharacteristic
289C2×#131—611no—
290#510—614no—
291#510—1222no—
292C2×Q32—1221no—
293C2×SD32—22no—
294C2×SD32—22no—
295C2×SD32—1221no—
296C2×SD32C2×D6114yescomplemented
297C2×M32—611no—
298C22×C16C2×D6111yescharacteristic, complemented
299#473—614no—
300#473—1222no—
301C2×#108—611no—
302C2×#101—1221no—
303#361—614no—
304#359—614no—
305#350—614no—
306C61C2×#219411yescharacteristic, complemented, Sylow
307H(5,𝔽2)—1224no—
308H(5,𝔽2)—1224no—
309H(5,𝔽2)—2442no—
310H(5,𝔽2)—2442no—
311C2×#41—611no—
312C2×#41—1222no—
313C2×#41—1221no—
314C2×#41—2441no—
315C22×Q8—21no—
316C22×D4—21no—
317C22×D4—1222no—
318C22×D4—2441no—
319C22×D4—2442no—
320#137—1224no—
321#137—2442no—
322AGL(1,ℤ/8)—1224no—
323AGL(1,ℤ/8)—1228no—
324AGL(1,ℤ/8)—1224no—
325AGL(1,ℤ/8)—1228no—
326#135—612no—
327#135—612no—
328#135—1224no—
329#135—1224no—
330#135—1221no—
331#135—1221no—
332C2×Q16—21no—
333C2×Q16—21no—
334C2×Q16—21no—
335C2×Q16—21no—
336C2×Q16—21no—
337C2×Q16—611no—
338C2×Q16—2441no—
339C2×Q16C22×D6112yescomplemented
340C2×SD16—1222no—
341C2×SD16—1221no—
342C2×SD16—2441no—
343C2×D8—21no—
344C2×D8—21no—
345C2×D8—21no—
346C2×D8—611no—
347C2×D8—1224no—
348C2×D8—1224no—
349C2×D8—1222no—
350C2×D8C22⋊D6112yes—
351C2×D8C22⋊D6112yes—
352C2×D8C22×D6112yes—
353#131—612no—
354#131—612no—
355#131—1221no—
356#131—1221no—
357C2×M16—611no—
358C2×M16—1221no—
359C2×M16—1221no—
360C22×C8—1221no—
361C22×C8C22×D6111yescharacteristic
362Q32—1224no—
363SD32—28no—
364SD32—1224no—
365M32—612no—
366M32—1221no—
367C2×C16—21no—
368C2×C16—21no—
369C2×C16—1221no—
370C2×C16C22×D6112yescomplemented
371#108—612no—
372#108—1221no—
373#101—1224no—
374C24—41no—
375C24—2442no—
376#41—612no—
377#41—612no—
378#41—1221no—
379#41—1221no—
380#41—1228no—
381#41—1222no—
382#41—1222no—
383#41—2444no—
384#41—2444no—
385#41—2444no—
386#41—2441no—
387#41—2441no—
388C2×Q8—22no—
389C2×Q8—41no—
390C2×Q8—41no—
391C2×Q8—41no—
392C2×Q8—41no—
393C2×Q8—41no—
394C2×Q8—611no—
395C2×Q8—1221no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—611no—
403C2×D4—1228no—
404C2×D4—1221no—
405C2×D4—1221no—
406C2×D4—2444no—
407C2×D4—2442no—
408C2×D4—2444no—
409C2×D4—2444no—
410C2×D4—2448no—
411C2×D4—2448no—
412C2×D4—2442no—
413C2×D4—2441no—
414C22×C4—41no—
415C22×C4—1221no—
416C22×C4—2442no—
417C22×C4—2441no—
418C22×C4D4×D6111yescharacteristic
419Q16—22no—
420Q16—22no—
421Q16—41no—
422Q16—41no—
423Q16—612no—
424Q16—1221no—
425Q16—2444no—
426SD16—1228no—
427SD16—1222no—
428SD16—1222no—
429SD16—2444no—
430D8—22no—
431D8—22no—
432D8—22no—
433D8—612no—
434D8—1228no—
435D8—1221no—
436D8C2×C22⋊D6114yes—
437M16—612no—
438M16—1221no—
439M16—1222no—
440M16—1222no—
441M16—1222no—
442M16—2441no—
443C2×C8—1221no—
444C2×C8—1222no—
445C2×C8—1222no—
446C2×C8—2441no—
447C2×C8D4×D6111yescharacteristic
448C2×C8D4×D6111yescharacteristic
449C2×C8D4×D6111yescharacteristic
450C2×C8C2×C22⋊D6111yescharacteristic
451C2×C8C2×C22⋊D6111yescharacteristic
452C2×C8C23×D6111yescharacteristic
453C16—22no—
454C16—1222no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—162no—
459C23—1221no—
460C23—9764no—
461C23—2448no—
462C23—2441no—
463C23#1451980111yescharacteristic
464Q8—42no—
465Q8—42no—
466Q8—81no—
467Q8—81no—
468Q8—612no—
469Q8—1221no—
470Q8—1222no—
471Q8—2441no—
472D4—24no—
473D4—42no—
474D4—42no—
475D4—42no—
476D4—612no—
477D4—1222no—
478D4—1222no—
479D4—1222no—
480D4—1221no—
481D4—2448no—
482D4—2448no—
483D4—2442no—
484D4—2442no—
485D4—2441no—
486C2×C4—42no—
487C2×C4—81no—
488C2×C4—81no—
489C2×C4—1221no—
490C2×C4—1222no—
491C2×C4—1222no—
492C2×C4—2448no—
493C2×C4—2441no—
494C2×C4—2442no—
495C2×C4—2442no—
496C2×C4#1451974511yescharacteristic
497C2×C4#1451974511yescharacteristic
498C2×C4D8×D6111yescharacteristic
499C2×C4D8×D6111yescharacteristic
500C2×C4#1451980111yescharacteristic
501C2×C4C2×D4×D6111yescharacteristic
502C8—1222no—
503C8—2442no—
504C8#1451974511yescharacteristic
505C8#1451974511yescharacteristic
506C8C2×D4×D6111yescharacteristic
507C8C22×C22⋊D6111yescharacteristic
508C22—22no—
509C22—44no—
510C22—84no—
511C22—162no—
512C22—162no—
513C22—1222no—
514C22—9768no—
515C22—4882no—
516C22—2442no—
517C22—2442no—
518C22#1683989411yescharacteristic
519C22#1683989411yescharacteristic
520C22C2×#1451980111yescharacteristic
521C4—82no—
522C4—1222no—
523C4—2442no—
524C4#1683989411yescharacteristic
525C4#1683989411yescharacteristic
526C4C2×#1451974511yescharacteristic
527C4C2×D8×D6111yescharacteristic
528C2—21no—
529C2—21no—
530C2—84no—
531C2—4882no—
532C2—2442no—
533C2#2144778912yesdirect product factor
534C2C2×#1683989411yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC22×SD32×C61C2
socleC22×C61#447
prime radicalC2×#16840563C2
hypercenterC22×SD32D61
hypocenterC61C2×#2194
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×SD32

Complements

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

NH ≅ G/Ntype
2. C2×#16840203C2semidirect
3. C2×#16840034C2semidirect
4. #21447789C2direct (N × H)
5. C2×#16839575C2semidirect
6. C2×#16839570C2semidirect
7. C2×#16839545C2semidirect
8. C22×SD32×C61C2semidirect
22. #16840203C22semidirect
25. C2×#14519717C22semidirect
27. #16840034C22semidirect
28. C2×#14519713C22semidirect
30. #16839575C22semidirect
31. #16839570C22semidirect
32. #16839545C22semidirect
33. C22×Q16×C61C22semidirect
37. C2×SD32×C61C22semidirect
38. C22×C16×C61C22semidirect
82. #14519717C23semidirect
85. #14519713C23semidirect
94. C2×Q16×C61C23semidirect
105. C2×C16×C61C23semidirect
263. C22×SD32D61semidirect
272. C2×C61#2194semidirect
286. C22×Q16C2×D61semidirect
296. C2×SD32C2×D61semidirect
298. C22×C16C2×D61semidirect
306. C61C2×#2194semidirect
339. C2×Q16C22×D61semidirect
370. C2×C16C22×D61semidirect
533. C2#21447789direct (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×#168402032
C2×#168400342
#214477892
C2×#168395752
C2×#168395702
C2×#168395452
C22×SD32×C612
C2×#219461