Finite Group Databasebeta

← C4×#16840033 #29686895

Subgroups — C4×#16840033 #29686895

Order 15616.

946 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840033C211yesmaximal, characteristic
2C4×#14519805C212yesmaximal, complemented
3C2×C4×D488C211yesmaximal, characteristic, complemented
4C4×#14519783C211yesmaximal, characteristic, complemented
5#21446727C211yesmaximal, characteristic, complemented
6#21446605C211yesmaximal, characteristic, complemented
7#21446482C212yesmaximal, complemented
8#21446326C212yesmaximal, complemented
9#21445880C211yesmaximal, characteristic, complemented
10C4×#14519693C212yesmaximal, complemented
11C4×#108×C61C211yesmaximal, characteristic, complemented
12C2×#14519805C2212yes—
13C22×D488C2211yescharacteristic
14C2×#14519783C2211yescharacteristic
15C2×#14519783C2211yescharacteristic
16C4×#11758222C2211yescharacteristic
17C2×C4×D244C2212yes—
18#16840033C418yesdirect product factor
19#16839875—22no—
20#16839864—22no—
21C4×#11758190—22no—
22C4×D488—22no—
23C4×D488—21no—
24C4×D488—21no—
25C4×D488—21no—
26C4×D488—21no—
27#16839804C2212yes—
28C2×#14519711C2211yescharacteristic
29#16839768C2212yes—
30#16839764C2212yes—
31C2×#14519699C2212yes—
32C2×#14519693C2212yes—
33C2×#14519693C2212yes—
34#16839717C2211yescharacteristic
35#16839717C2211yescharacteristic
36#16839716—21no—
37#16839716—21no—
38C4×#11758194C2211yescharacteristic
39C4×#11758189—21no—
40C4×C8×D61—21no—
41#16839530C2212yes—
42#16839530C2212yes—
43C2×#108×C61C2211yescharacteristic
44C2×#108×C61C2211yescharacteristic
45C4×M16×C61C2212yes—
46C2×C4×C8×C61C2211yescharacteristic
47C61×#341C2212yes—
48C2×#11758222C2311yescharacteristic
49C22×D244C2312yes—
50C22×C4×D61—22no—
51#14519805—24no—
52#14519805C2×C418yescomplemented
53C2×#11758190—22no—
54C2×D488—22no—
55C2×D488—21no—
56C2×D488—21no—
57C2×D488—22no—
58C2×D488C2×C414yescomplemented
59#14519783—22no—
60#14519783—22no—
61#14519783—22no—
62#14519783C2×C414yescomplemented
63C2×#11758194C2311yescharacteristic
64C2×#11758194C2311yescharacteristic
65C2×#11758189—21no—
66C2×#11758189—21no—
67C2×C8×D61—21no—
68C2×C8×D61—21no—
69C4×Dic122D411yescharacteristic
70C4×Dic122D411yescharacteristic
71C4×D244—22no—
72C4×D244—22no—
73C4×D244—22no—
74C4×D244—22no—
75C4×D244D411yescharacteristic
76C4×D244D411yescharacteristic
77C4×C22⋊D61—21no—
78C4×C22⋊D61—21no—
79#14519736C2311yescharacteristic
80#14519734—21no—
81C2×C4⋊Dic61C2312yes—
82C2×#11758198—22no—
83C42×D61—21no—
84#14519711—21no—
85#14519711—21no—
86#14519711—22no—
87#14519709—22no—
88#14519702—22no—
89#14519699—22no—
90#14519699—22no—
91#14519699—22no—
92#14519699—22no—
93#14519699—22no—
94#14519693—24no—
95#14519693C2×C418yescomplemented
96#14519688—21no—
97#14519687—21no—
98#14519687—21no—
99C4×#92418—21no—
100C8×Dic61—21no—
101C8×Dic61—21no—
102C2×M16×C61C2312yes—
103C2×M16×C61C2312yes—
104C22×C8×C61C2311yescharacteristic
105C22×C8×C61C2311yescharacteristic
106C2×C42×C61C2311yescharacteristic
107#108×C61—22no—
108#108×C61C2×C414yescomplemented
109#97×C61—22no—
110C4×C8×C61—22no—
111C4×C8×C61D411yescharacteristic
112C4×C8×C61D411yescharacteristic
113C4×C8×C61D411yescharacteristic
114C4×C8×C61D411yescharacteristic
115C23×D61—22no—
116C22×C4×C61#4111yescharacteristic
117C22×C4×C61#4111yescharacteristic
118C22×C4×C61C2411yescharacteristic
119C2×C22⋊D61—21no—
120C22×Dic61—22no—
121#11758222—21no—
122#11758222—21no—
123#11758222C22×C412yes—
124#11758222#4112yes—
125C2×D244—22no—
126C2×D244—22no—
127C2×D244—22no—
128C2×D244—22no—
129C2×D244—22no—
130C2×D244C22×C414yes—
131C2×D244C2×D411yescharacteristic
132C2×C4×D61—21no—
133C2×C4×D61—21no—
134C2×C4×D61—21no—
135C2×C4×D61—42no—
136C2×C4×D61—42no—
137C2×C4×D61—84no—
138C2×Dic122C2×D411yescharacteristic
139M16×C61—22no—
140M16×C61—22no—
141M16×C61—22no—
142M16×C61C22×C414yes—
143C2×C8×C61—22no—
144C2×C8×C61—21no—
145C2×C8×C61—21no—
146C2×C8×C61—22no—
147C2×C8×C61C22×C412yes—
148C2×C8×C61C2×D411yescharacteristic
149C2×C8×C61C2×D411yescharacteristic
150C2×C8×C61C2×D411yescharacteristic
151C2×C8×C61C2×D411yescharacteristic
152C2×C8×C61#4112yes—
153C42×C61C2×D411yescharacteristic
154C42×C61C2×D411yescharacteristic
155C42×C61C2×D411yescharacteristic
156C42×C61C2×D411yescharacteristic
157C22⋊Dic61—21no—
158#11758198—21no—
159#11758198—21no—
160#11758198—42no—
161#11758198—42no—
162C4⋊Dic61—22no—
163C4⋊Dic61—22no—
164C4⋊Dic61C2×D411yescharacteristic
165C4⋊Dic61C2×D411yescharacteristic
166#11758196—21no—
167#11758196—21no—
168C4×Dic61—21no—
169C4×Dic61—21no—
170C4×Dic61—21no—
171#11758194—21no—
172#11758194—21no—
173#11758194C22×C412yes—
174#11758194#4112yes—
175C2×#92418—21no—
176C2×#92418—21no—
177D488—28no—
178D488—24no—
179D488—24no—
180#11758190—28no—
181#11758189—24no—
182#11758189—24no—
183C8×D61—24no—
184C8×D61—24no—
185C23×C61C2×#4111yescharacteristic
186C22×D61—21no—
187C22×D61—24no—
188C22×D61—42no—
189C22×D61—42no—
190C22×D61—82no—
191C22×D61—82no—
192C2×C4×C61—22no—
193C2×C4×C61—41no—
194C2×C4×C61#12111yescharacteristic
195C2×C4×C61#12111yescharacteristic
196C2×C4×C61#12111yescharacteristic
197C2×C4×C61#12111yescharacteristic
198C2×C4×C61C23×C411yescharacteristic
199C2×C4×C61C22×D411yescharacteristic
200C2×C4×C61C22×D411yescharacteristic
201C2×C4×C61C2×#4111yescharacteristic
202C2×C4×C61C2×#4111yescharacteristic
203C2×C4×C61C2×#4111yescharacteristic
204C22⋊D61—22no—
205C22⋊D61—22no—
206C2×Dic61—21no—
207C2×Dic61—21no—
208C2×Dic61—21no—
209C2×Dic61—42no—
210C2×Dic61—82no—
211D244—24no—
212D244—24no—
213D244—21no—
214D244—42no—
215D244—42no—
216D244C4×D412yes—
217C4×D61—22no—
218C4×D61—22no—
219C4×D61—42no—
220C4×D61—42no—
221C4×D61—84no—
222C4×D61—84no—
223Dic122—21no—
224Dic122C4×D412yes—
225C8×C61—24no—
226C8×C61—21no—
227C8×C61—21no—
228C8×C61—42no—
229C8×C61C4×D412yes—
230C8×C61C4×D412yes—
231#92418—22no—
232#92418—22no—
233C4×#472—611nomaximal, Sylow
234C22×C61—21no—
235C22×C61—21no—
236C22×C61C4×#4111yescharacteristic
237C22×C61C2×#12111yescharacteristic
238C22×C61#52911yescharacteristic
239C2×D61—22no—
240C2×D61—41no—
241C2×D61—41no—
242C2×D61—44no—
243C2×D61—84no—
244C2×D61—82no—
245C2×D61—82no—
246C2×D61—84no—
247C4×C61—21no—
248C4×C61—21no—
249C4×C61—21no—
250C4×C61#47212yescomplemented
251C4×C61C2×C4×D411yescharacteristic
252C4×C61C2×C4×D411yescharacteristic
253C4×C61#52511yescharacteristic
254C4×C61#53211yescharacteristic
255Dic61—22no—
256Dic61—41no—
257Dic61—41no—
258Dic61—82no—
259C2×#472—611no—
260C4×AGL(1,ℤ/8)—612no—
261C2×C4×D8—611no—
262C4×#131—611no—
263#1978—611no—
264#1952—611no—
265#1931—612no—
266#1907—612no—
267#1816—611no—
268C4×#108D6111yescharacteristic, complemented
269C4×#100—612no—
270C2×C61—21no—
271C2×C61—21no—
272C2×C61C4×#12111yescharacteristic
273C2×C61C2×#47211yescharacteristic
274C2×C61#306711yescharacteristic
275D61—42no—
276D61—84no—
277C2×AGL(1,ℤ/8)—612no—
278C22×D8—611no—
279C2×#131—611no—
280C2×#131—611no—
281C4×#41—611no—
282C2×C4×D4—612no—
283#472—618no—
284#442—1222no—
285#440—1222no—
286C4×SD16—1222no—
287C4×D8—1222no—
288C4×D8—1221no—
289C4×D8—1221no—
290C4×D8—1221no—
291C4×D8—1221no—
292C2×#108C2×D6111yescharacteristic
293C2×#108C2×D6111yescharacteristic
294#428—612no—
295C2×#107—611no—
296#418—612no—
297#417—612no—
298C2×#102—612no—
299C2×#100—612no—
300C2×#100—612no—
301#405—611no—
302#405—611no—
303#405—1221no—
304#405—1221no—
305C4×M16—611no—
306C4×M16—1221no—
307C4×M16C2×D6112yes—
308C2×C4×C8—1221no—
309C2×C4×C8C2×D6111yescharacteristic
310#343—612no—
311#343—612no—
312#341C2×D6112yes—
313C61C4×#47211yescharacteristic, complemented, Sylow
314C2×#41—611no—
315C22×D4—612no—
316C23×C4—1222no—
317AGL(1,ℤ/8)—618no—
318AGL(1,ℤ/8)—1224no—
319C2×SD16—1222no—
320C2×D8—614no—
321C2×D8—1222no—
322C2×D8—1221no—
323C2×D8—1221no—
324C2×D8—1222no—
325#131—614no—
326#131—1222no—
327#131—1222no—
328#131—1222no—
329C2×M16—611no—
330C2×M16—611no—
331C2×M16—1221no—
332C2×M16—1221no—
333C2×M16C22×D6112yes—
334C2×M16C22×D6112yes—
335C22×C8—1221no—
336C22×C8—1221no—
337C22×C8C22×D6111yescharacteristic
338C22×C8C22×D6111yescharacteristic
339C4×Q8—611no—
340C4×Q8—611no—
341C4×D4—611no—
342C4×D4—611no—
343C4×D4—1221no—
344C4×D4—1221no—
345C4×D4—1222no—
346C4×D4—1222no—
347C4×D4—1222no—
348C4×D4—1222no—
349#117—611no—
350#117—1221no—
351C2×C4⋊C4—612no—
352C2×C22⋊C4—1222no—
353C2×C42—1221no—
354C2×C42C22×D6111yescharacteristic
355#108—22no—
356#108C4×D6114yescomplemented
357#107—1222no—
358#107—1221no—
359#107—1221no—
360#106—1222no—
361#103—1222no—
362#102—1222no—
363#102—1222no—
364#102—1222no—
365#102—1222no—
366#102—1222no—
367#100—618no—
368#100—1224no—
369#97—22no—
370#97—1221no—
371#97—1221no—
372#97—1221no—
373C4×C8—22no—
374C4×C8—1221no—
375C4×C8—1221no—
376C4×C8—1221no—
377C4×C8D24411yescharacteristic
378C4×C8D24411yescharacteristic
379C4×C8D24411yescharacteristic
380C4×C8D24411yescharacteristic
381C24—1222no—
382#41—612no—
383#41—612no—
384#41—1221no—
385#41—1221no—
386C2×Q8—611no—
387C2×D4—614no—
388C2×D4—611no—
389C2×D4—1221no—
390C2×D4—1222no—
391C2×D4—1222no—
392C2×D4—1222no—
393C2×D4—1222no—
394C2×D4—1222no—
395C22×C4—1221no—
396C22×C4—1221no—
397C22×C4—1221no—
398C22×C4—1222no—
399C22×C4—4884no—
400C22×C4—2442no—
401C22×C4—2442no—
402C22×C4#1175822611yescharacteristic
403C22×C4#1175822611yescharacteristic
404C22×C4C23×D6111yescharacteristic
405SD16—1228no—
406D8—1228no—
407D8—1224no—
408D8—1224no—
409M16—22no—
410M16—22no—
411M16—22no—
412M16—612no—
413M16—612no—
414M16—1224no—
415M16—1221no—
416M16—1221no—
417M16—1224no—
418M16C2×C4×D6114yes—
419C2×C8—22no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—22no—
423C2×C8—1224no—
424C2×C8—1221no—
425C2×C8—1221no—
426C2×C8—1224no—
427C2×C8C2×C4×D6112yes—
428C2×C8C2×D24411yescharacteristic
429C2×C8C2×D24411yescharacteristic
430C2×C8C2×D24411yescharacteristic
431C2×C8C2×D24411yescharacteristic
432C2×C8#1175822212yes—
433C4⋊C4—611no—
434C4⋊C4—611no—
435C4⋊C4—1221no—
436C4⋊C4—1221no—
437C4⋊C4—1222no—
438C4⋊C4—1222no—
439C22⋊C4—1221no—
440C22⋊C4—1221no—
441C22⋊C4—1221no—
442C22⋊C4—2442no—
443C22⋊C4—2442no—
444C42—1221no—
445C42—1221no—
446C42—1221no—
447C42C2×D24411yescharacteristic
448C42C2×D24411yescharacteristic
449C42D4×D6111yescharacteristic
450C42D4×D6111yescharacteristic
451C23—1221no—
452C23—1224no—
453C23—4882no—
454C23—4882no—
455C23—2442no—
456C23—2442no—
457C23C2×#1175822611yescharacteristic
458Q8—612no—
459Q8—1221no—
460D4—612no—
461D4—1222no—
462D4—1222no—
463D4—1224no—
464D4—1224no—
465D4—1221no—
466D4—2442no—
467D4—2442no—
468C2×C4—22no—
469C2×C4—41no—
470C2×C4—1221no—
471C2×C4—1222no—
472C2×C4—1222no—
473C2×C4—1221no—
474C2×C4—1221no—
475C2×C4—4884no—
476C2×C4—4884no—
477C2×C4—4882no—
478C2×C4—2442no—
479C2×C4—2442no—
480C2×C4—2442no—
481C2×C4#1451975211yescharacteristic
482C2×C4#1451975211yescharacteristic
483C2×C4#1451975211yescharacteristic
484C2×C4#1451975211yescharacteristic
485C2×C4C22×C4×D6111yescharacteristic
486C2×C4C2×D4×D6111yescharacteristic
487C2×C4C22×D24411yescharacteristic
488C2×C4#41×D6111yescharacteristic
489C2×C4#41×D6111yescharacteristic
490C2×C4C2×#1175822211yescharacteristic
491C8—24no—
492C8—21no—
493C8—21no—
494C8—42no—
495C8—1222no—
496C8—1222no—
497C8C4×D24412yes—
498C8C4×D24412yes—
499C22—21no—
500C22—21no—
501C22—1222no—
502C22—4884no—
503C22—4884no—
504C22—4882no—
505C22—4882no—
506C22—2444no—
507C22—2441no—
508C22—2441no—
509C22C4×#1175822611yescharacteristic
510C22C2×#1451975211yescharacteristic
511C22#1684029911yescharacteristic
512C4—21no—
513C4—21no—
514C4—21no—
515C4—1222no—
516C4—4882no—
517C4—2441no—
518C4—2441no—
519C4#1684003312yesdirect product factor
520C4C4×D4×D6111yescharacteristic
521C4C2×C4×D24411yescharacteristic
522C4#1684027411yescharacteristic
523C4#1684030911yescharacteristic
524C2—21no—
525C2—21no—
526C2—4884no—
527C2—2442no—
528C2C4×#1451975211yescharacteristic
529C2C2×#1684003311yescharacteristic
530C2#2145554011yescharacteristic
subgroupG/H
centerC2×C4#14519752
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×#108×C61C2
socleC22×C61C2×#121
prime radicalC2×#16840033C2
cosocleC22×C4×C61C24
hypercenterC4×#108D61
hypocenterC61C4×#472
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#108

Complements

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

NH ≅ G/Ntype
2. C4×#14519805C2semidirect
3. C2×C4×D488C2semidirect
4. C4×#14519783C2semidirect
5. #21446727C2semidirect
6. #21446605C2semidirect
7. #21446482C2semidirect
8. #21446326C2semidirect
9. #21445880C2semidirect
10. C4×#14519693C2semidirect
11. C4×#108×C61C2semidirect
18. #16840033C4direct (N × H)
52. #14519805C2×C4semidirect
58. C2×D488C2×C4semidirect
62. #14519783C2×C4semidirect
95. #14519693C2×C4semidirect
108. #108×C61C2×C4semidirect
250. C4×C61#472semidirect
268. C4×#108D61semidirect
313. C61C4×#472semidirect
356. #108C4×D61semidirect
519. C4#16840033direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168400332
C4×#145198052
C2×C4×D4882
C4×#145197832
#214467272
#214466052
#214464822
#214463262
#214458802
C4×#145196932
C4×#108×C612
C4×#47261