Finite Group Databasebeta

← C4×#16840029 #29686887

Subgroups — C4×#16840029 #29686887

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×#16840029C211yesmaximal, characteristic
2C4×#14519803C212yesmaximal, complemented
3C4×#14519783C211yesmaximal, characteristic, complemented
4#21446730C211yesmaximal, characteristic, complemented
5#21446602C211yesmaximal, characteristic, complemented
6#21446478C212yesmaximal, complemented
7#21446330C212yesmaximal, complemented
8#21445884C211yesmaximal, characteristic, complemented
9C4×#14519713C211yesmaximal, characteristic, complemented
10C4×#14519694C212yesmaximal, complemented
11C2×C4×D8×C61C211yesmaximal, characteristic, complemented
12C2×#14519803C2212yes—
13C2×#14519783C2211yescharacteristic
14C2×#14519783C2211yescharacteristic
15C4×#11758222C2211yescharacteristic
16#16840029C418yesdirect product factor
17#16839872—22no—
18#16839862—22no—
19C4×#11758200—22no—
20C4×#11758199—22no—
21C2×#14519713C2211yescharacteristic
22C2×#14519713C2211yescharacteristic
23#16839802C2212yes—
24#16839767C2212yes—
25#16839761C2212yes—
26C2×#14519694C2212yes—
27C2×#14519694C2212yes—
28#16839717C2211yescharacteristic
29#16839717C2211yescharacteristic
30#16839716—21no—
31#16839716—21no—
32C4×#11758194C2212yes—
33C4×#11758194C2211yescharacteristic
34C4×#11758189—21no—
35C4×C8×D61—21no—
36#16839531C2212yes—
37#16839531C2212yes—
38#16839527C2212yes—
39C22×D8×C61C2211yescharacteristic
40C2×C4×D4×C61C2212yes—
41C4×D8×C61—21no—
42C4×D8×C61—21no—
43C4×D8×C61—21no—
44C4×D8×C61—21no—
45C2×#107×C61C2211yescharacteristic
46C2×#102×C61C2212yes—
47C2×C4×C8×C61C2211yescharacteristic
48C2×#11758222C2311yescharacteristic
49#14519803—24no—
50#14519803C2×C418yescomplemented
51C2×#11758200—22no—
52C2×#11758199—22no—
53#14519783—22no—
54#14519783—22no—
55#14519783—22no—
56#14519783C2×C414yescomplemented
57C2×#11758194C2312yes—
58C2×#11758194C2311yescharacteristic
59C2×#11758194C2312yes—
60C2×#11758194C2311yescharacteristic
61C2×#11758189—21no—
62C2×#11758189—21no—
63C2×C8×D61—21no—
64C2×C8×D61—21no—
65C4×Dic122D411yescharacteristic
66C4×Dic122D411yescharacteristic
67C4×D244D411yescharacteristic
68C4×D244D411yescharacteristic
69C4×C22⋊D61—21no—
70C4×C22⋊D61—21no—
71#14519736C2311yescharacteristic
72#14519734—21no—
73C42×D61—21no—
74#14519713—22no—
75#14519713C2×C414yescomplemented
76#14519710—22no—
77#14519708—22no—
78#14519700—22no—
79#14519698—22no—
80#14519698—22no—
81#14519697—22no—
82#14519694—24no—
83#14519694C2×C418yescomplemented
84#14519688—21no—
85#14519688—22no—
86#14519687—21no—
87#14519687—21no—
88C4×#92418—21no—
89C4×#92418—22no—
90C8×Dic61—21no—
91C8×Dic61—21no—
92C22×D4×C61C2312yes—
93C23×C4×C61—22no—
94C2×D8×C61—21no—
95C2×D8×C61—21no—
96C2×D8×C61—22no—
97C2×D8×C61C2×C414yescomplemented
98C22×C8×C61C2311yescharacteristic
99C22×C8×C61C2311yescharacteristic
100C4×D4×C61—22no—
101C4×D4×C61—22no—
102C4×D4×C61—22no—
103C4×D4×C61—22no—
104C2×C4⋊C4×C61C2312yes—
105C2×C22⋊C4×C61—22no—
106C2×C42×C61C2311yescharacteristic
107#107×C61—21no—
108#107×C61—21no—
109#102×C61—22no—
110#102×C61—22no—
111C4×C8×C61D411yescharacteristic
112C4×C8×C61D411yescharacteristic
113C4×C8×C61D411yescharacteristic
114C4×C8×C61D411yescharacteristic
115C24×C61—22no—
116C2×D4×C61—22no—
117C2×D4×C61—22no—
118C2×D4×C61—22no—
119C2×D4×C61—22no—
120C2×D4×C61—22no—
121C2×D4×C61C22×C414yes—
122C22×C4×C61—22no—
123C22×C4×C61—42no—
124C22×C4×C61—42no—
125C22×C4×C61—84no—
126C22×C4×C61#4111yescharacteristic
127C22×C4×C61#4111yescharacteristic
128C22×C4×C61C2411yescharacteristic
129C2×C22⋊D61—21no—
130#11758222—21no—
131#11758222—21no—
132#11758222C22×C412yes—
133#11758222#4112yes—
134C2×D244C2×D411yescharacteristic
135C2×C4×D61—21no—
136C2×C4×D61—21no—
137C2×C4×D61—21no—
138C2×Dic122C2×D411yescharacteristic
139D8×C61—24no—
140D8×C61—24no—
141C2×C8×C61—21no—
142C2×C8×C61—21no—
143C2×C8×C61C22×C412yes—
144C2×C8×C61C2×D411yescharacteristic
145C2×C8×C61C2×D411yescharacteristic
146C2×C8×C61C2×D411yescharacteristic
147C2×C8×C61C2×D411yescharacteristic
148C2×C8×C61#4112yes—
149C4⋊C4×C61—22no—
150C4⋊C4×C61—22no—
151C22⋊C4×C61—42no—
152C22⋊C4×C61—42no—
153C42×C61C2×D411yescharacteristic
154C42×C61C2×D411yescharacteristic
155C42×C61C2×D411yescharacteristic
156C42×C61C2×D411yescharacteristic
157C22⋊Dic61—21no—
158#11758200—28no—
159#11758199—28no—
160#11758198—21no—
161#11758198—21no—
162C4⋊Dic61C2×D411yescharacteristic
163C4⋊Dic61C2×D411yescharacteristic
164#11758196—21no—
165#11758196—21no—
166C4×Dic61—21no—
167C4×Dic61—21no—
168C4×Dic61—21no—
169#11758194—21no—
170#11758194—21no—
171#11758194—22no—
172#11758194—22no—
173#11758194—22no—
174#11758194C22×C412yes—
175#11758194C22×C414yes—
176#11758194#4112yes—
177C2×#92418—21no—
178C2×#92418—21no—
179C2×#92418—22no—
180C2×#92418—22no—
181#11758189—24no—
182#11758189—24no—
183C8×D61—24no—
184C8×D61—24no—
185C23×C61—24no—
186C23×C61—42no—
187C23×C61—42no—
188C23×C61—82no—
189C23×C61—82no—
190C23×C61C2×#4111yescharacteristic
191C22×D61—21no—
192D4×C61—24no—
193D4×C61—24no—
194D4×C61—42no—
195D4×C61—42no—
196C2×C4×C61—22no—
197C2×C4×C61—41no—
198C2×C4×C61—42no—
199C2×C4×C61—84no—
200C2×C4×C61—84no—
201C2×C4×C61—82no—
202C2×C4×C61#12111yescharacteristic
203C2×C4×C61#12111yescharacteristic
204C2×C4×C61#12111yescharacteristic
205C2×C4×C61#12111yescharacteristic
206C2×C4×C61C23×C411yescharacteristic
207C2×C4×C61C22×D411yescharacteristic
208C2×C4×C61C22×D411yescharacteristic
209C2×C4×C61C2×#4111yescharacteristic
210C2×C4×C61C2×#4111yescharacteristic
211C2×C4×C61C2×#4111yescharacteristic
212C22⋊D61—22no—
213C22⋊D61—22no—
214C2×Dic61—21no—
215C2×Dic61—21no—
216C2×Dic61—21no—
217D244—21no—
218D244C4×D412yes—
219C4×D61—22no—
220C4×D61—22no—
221C4×D61—42no—
222C4×D61—42no—
223Dic122—21no—
224Dic122C4×D412yes—
225C8×C61—21no—
226C8×C61—21no—
227C8×C61C4×D412yes—
228C8×C61C4×D412yes—
229#92418—22no—
230#92418—24no—
231#92418—22no—
232#92418—42no—
233C4×#472—611nomaximal, Sylow
234C22×C61—21no—
235C22×C61—21no—
236C22×C61—44no—
237C22×C61—84no—
238C22×C61—84no—
239C22×C61—82no—
240C22×C61—82no—
241C22×C61C4×#4111yescharacteristic
242C22×C61C2×#12111yescharacteristic
243C22×C61#52911yescharacteristic
244C2×D61—22no—
245C2×D61—41no—
246C2×D61—41no—
247C4×C61—21no—
248C4×C61—21no—
249C4×C61—21no—
250C4×C61—82no—
251C4×C61#47212yescomplemented
252C4×C61C2×C4×D411yescharacteristic
253C4×C61C2×C4×D411yescharacteristic
254C4×C61#52511yescharacteristic
255C4×C61#53211yescharacteristic
256Dic61—22no—
257Dic61—41no—
258Dic61—41no—
259C2×#472—611no—
260C4×AGL(1,ℤ/8)—612no—
261C2×C4×D8D6111yescharacteristic, complemented
262C4×#131—611no—
263#1978—611no—
264#1952—611no—
265#1931—612no—
266#1907—612no—
267#1816—611no—
268C4×#108—611no—
269C4×#100—612no—
270C2×C61—21no—
271C2×C61—21no—
272C2×C61—84no—
273C2×C61C4×#12111yescharacteristic
274C2×C61C2×#47211yescharacteristic
275C2×C61#306711yescharacteristic
276D61—42no—
277C2×AGL(1,ℤ/8)—612no—
278C22×D8C2×D6111yescharacteristic
279C2×#131—611no—
280C2×#131—611no—
281C4×#41—611no—
282C2×C4×D4C2×D6112yes—
283#472—618no—
284#442—1222no—
285#440—1222no—
286C4×SD16—1222no—
287C4×D8—21no—
288C4×D8—21no—
289C4×D8—21no—
290C4×D8—21no—
291C4×D8—1222no—
292C2×#108—611no—
293C2×#108—611no—
294#428—612no—
295C2×#107C2×D6111yescharacteristic
296#418—612no—
297#417—612no—
298C2×#102C2×D6112yes—
299C2×#100—612no—
300C2×#100—612no—
301#405—611no—
302#405—611no—
303#405—1221no—
304#405—1221no—
305C4×M16—611no—
306C4×M16—612no—
307C4×M16—1221no—
308C2×C4×C8—1221no—
309C2×C4×C8C2×D6111yescharacteristic
310#343—612no—
311#343—612no—
312#341—612no—
313C61C4×#47211yescharacteristic, complemented, Sylow
314C2×#41—611no—
315C22×D4C22×D6112yes—
316C23×C4—22no—
317AGL(1,ℤ/8)—618no—
318AGL(1,ℤ/8)—1224no—
319C2×SD16—1222no—
320C2×D8—22no—
321C2×D8—21no—
322C2×D8—21no—
323C2×D8—1222no—
324C2×D8C4×D6114yescomplemented
325#131—614no—
326#131—1222no—
327#131—1222no—
328#131—1222no—
329C2×M16—611no—
330C2×M16—611no—
331C2×M16—612no—
332C2×M16—612no—
333C2×M16—1221no—
334C2×M16—1221no—
335C22×C8—1221no—
336C22×C8—1221no—
337C22×C8C22×D6111yescharacteristic
338C22×C8C22×D6111yescharacteristic
339C4×Q8—611no—
340C4×Q8—611no—
341C4×D4—22no—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—22no—
345C4×D4—611no—
346C4×D4—611no—
347C4×D4—1221no—
348C4×D4—1221no—
349#117—611no—
350#117—1221no—
351C2×C4⋊C4C22×D6112yes—
352C2×C22⋊C4—22no—
353C2×C42—1221no—
354C2×C42C22×D6111yescharacteristic
355#108—614no—
356#108—1222no—
357#107—21no—
358#107—21no—
359#107—1222no—
360#106—1222no—
361#103—1222no—
362#102—22no—
363#102—22no—
364#102—1222no—
365#102—1222no—
366#102—1222no—
367#100—618no—
368#100—1224no—
369#97—1221no—
370#97—1221no—
371#97—1222no—
372#97—1221no—
373C4×C8—1221no—
374C4×C8—1221no—
375C4×C8—1222no—
376C4×C8—1221no—
377C4×C8C22⋊D6111yescharacteristic
378C4×C8C22⋊D6111yescharacteristic
379C4×C8C22⋊D6111yescharacteristic
380C4×C8C22⋊D6111yescharacteristic
381C24—22no—
382#41—612no—
383#41—612no—
384#41—1221no—
385#41—1221no—
386C2×Q8—611no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—611no—
393C2×D4—1221no—
394C2×D4C2×C4×D6114yes—
395C22×C4—22no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—84no—
399C22×C4—1221no—
400C22×C4—1221no—
401C22×C4—1221no—
402C22×C4#1175822411yescharacteristic
403C22×C4#1175822411yescharacteristic
404C22×C4C23×D6111yescharacteristic
405SD16—1228no—
406D8—24no—
407D8—24no—
408D8—1228no—
409M16—612no—
410M16—614no—
411M16—612no—
412M16—1224no—
413M16—1221no—
414M16—1222no—
415M16—1221no—
416M16—1224no—
417M16—1222no—
418M16—1222no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—1224no—
422C2×C8—1222no—
423C2×C8—1221no—
424C2×C8—1221no—
425C2×C8—1224no—
426C2×C8—1222no—
427C2×C8C2×C4×D6112yes—
428C2×C8#1175822212yes—
429C2×C8C2×C22⋊D6111yescharacteristic
430C2×C8C2×C22⋊D6111yescharacteristic
431C2×C8C2×C22⋊D6111yescharacteristic
432C2×C8C2×C22⋊D6111yescharacteristic
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—611no—
436C4⋊C4—611no—
437C4⋊C4—1221no—
438C4⋊C4—1221no—
439C22⋊C4—42no—
440C22⋊C4—42no—
441C22⋊C4—1221no—
442C22⋊C4—1221no—
443C22⋊C4—1221no—
444C42—1221no—
445C42—1221no—
446C42—1221no—
447C42D4×D6111yescharacteristic
448C42D4×D6111yescharacteristic
449C42C2×C22⋊D6111yescharacteristic
450C42C2×C22⋊D6111yescharacteristic
451C23—24no—
452C23—42no—
453C23—42no—
454C23—82no—
455C23—82no—
456C23—1221no—
457C23C2×#1175822411yescharacteristic
458Q8—612no—
459Q8—1221no—
460D4—24no—
461D4—24no—
462D4—42no—
463D4—42no—
464D4—612no—
465D4—1222no—
466D4—1222no—
467D4—1221no—
468C2×C4—22no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—84no—
472C2×C4—84no—
473C2×C4—82no—
474C2×C4—1221no—
475C2×C4—1222no—
476C2×C4—1222no—
477C2×C4—1221no—
478C2×C4—1221no—
479C2×C4—2442no—
480C2×C4—2442no—
481C2×C4#1451974811yescharacteristic
482C2×C4#1451974811yescharacteristic
483C2×C4#1451974811yescharacteristic
484C2×C4#1451974811yescharacteristic
485C2×C4C22×C4×D6111yescharacteristic
486C2×C4C2×D4×D6111yescharacteristic
487C2×C4C22×C22⋊D6111yescharacteristic
488C2×C4#41×D6111yescharacteristic
489C2×C4#41×D6111yescharacteristic
490C2×C4C2×#1175822211yescharacteristic
491C8—21no—
492C8—21no—
493C8—1224no—
494C8—1222no—
495C8—1222no—
496C8—2442no—
497C8C4×C22⋊D6112yes—
498C8C4×C22⋊D6112yes—
499C22—21no—
500C22—21no—
501C22—44no—
502C22—84no—
503C22—84no—
504C22—82no—
505C22—82no—
506C22—1222no—
507C22—2441no—
508C22—2441no—
509C22C4×#1175822411yescharacteristic
510C22C2×#1451974811yescharacteristic
511C22#1684029411yescharacteristic
512C4—21no—
513C4—21no—
514C4—21no—
515C4—82no—
516C4—1222no—
517C4—2441no—
518C4—2441no—
519C4#1684002912yesdirect product factor
520C4C4×D4×D6111yescharacteristic
521C4C2×C4×C22⋊D6111yescharacteristic
522C4#1684026911yescharacteristic
523C4#1684030911yescharacteristic
524C2—21no—
525C2—21no—
526C2—84no—
527C2—2442no—
528C2C4×#1451974811yescharacteristic
529C2C2×#1684002911yescharacteristic
530C2#2145553511yescharacteristic
subgroupG/H
centerC2×C4#14519748
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C4×D8×C61C2
socleC22×C61C2×#121
prime radicalC2×#16840029C2
cosocleC22×C4×C61C24
hypercenterC2×C4×D8D61
hypocenterC61C4×#472
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
2. C4×#14519803C2semidirect
3. C4×#14519783C2semidirect
4. #21446730C2semidirect
5. #21446602C2semidirect
6. #21446478C2semidirect
7. #21446330C2semidirect
8. #21445884C2semidirect
9. C4×#14519713C2semidirect
10. C4×#14519694C2semidirect
11. C2×C4×D8×C61C2semidirect
16. #16840029C4direct (N × H)
50. #14519803C2×C4semidirect
56. #14519783C2×C4semidirect
75. #14519713C2×C4semidirect
83. #14519694C2×C4semidirect
97. C2×D8×C61C2×C4semidirect
251. C4×C61#472semidirect
261. C2×C4×D8D61semidirect
313. C61C4×#472semidirect
324. C2×D8C4×D61semidirect
519. C4#16840029direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168400292
C4×#145198032
C4×#145197832
#214467302
#214466022
#214464782
#214463302
#214458842
C4×#145197132
C4×#145196942
C2×C4×D8×C612
C4×#47261