Finite Group Databasebeta

← C4×#16839944 #29685918

Subgroups — C4×#16839944 #29685918

Order 15616.

1358 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519825C211yesmaximal, characteristic
2C2×#16839944C211yesmaximal, characteristic
3C4×#14519808C212yesmaximal, complemented
4#21446213C211yesmaximal, characteristic, complemented
5#21446191C212yesmaximal, complemented
6#21446044C212yesmaximal, complemented
7#21446033C211yesmaximal, characteristic, complemented
8#21445777C211yesmaximal, characteristic
9C4×#14519705C212yesmaximal, complemented
10C4×#14519696C211yesmaximal, characteristic, complemented
11C4×C4⋊Q8×C61C211yesmaximal, characteristic, complemented
12C2×#14519825C2211yescharacteristic
13C2×#14519808C2212yes—
14#16840244—22no—
15#16840243—22no—
16#16840243C2212yes—
17#16840240C2211yescharacteristic
18#16840238—22no—
19C4×#11758226—22no—
20C4×#11758222—22no—
21C4×#11758222C2212yes—
22C4×Q8×D61—22no—
23#16839944C418yesdirect product factor
24#16839867—22no—
25#16839860—22no—
26C4×#11758202—22no—
27C4×#11758201—22no—
28#16839802C2212yes—
29C2×#14519705C2212yes—
30C2×#14519705C2212yes—
31#16839771C2212yes—
32#16839761C2212yes—
33C2×#14519696C2211yescharacteristic
34C2×#14519696C2211yescharacteristic
35C4×#11758194C2212yes—
36#16839531C2212yes—
37#16839522C2212yes—
38#16839522C2212yes—
39C2×C4⋊Q8×C61C2211yescharacteristic
40C2×C4×Q8×C61C2211yescharacteristic
41C2×C4×Q8×C61C2211yescharacteristic
42C61×#391C2211yescharacteristic
43C61×#391C2211yescharacteristic
44C61×#389—22no—
45C61×#384C2211yescharacteristic
46C4×C4⋊C4×C61—22no—
47C43×C61C2211yescharacteristic
48#14519825—22no—
49#14519825—24no—
50#14519825C2×C414yes—
51C2×#11758226—22no—
52C2×#11758222—22no—
53C2×#11758222C2312yes—
54C2×Q8×D61—22no—
55#14519808—24no—
56#14519808C2×C418yescomplemented
57C2×#11758202—22no—
58C2×#11758201—22no—
59C2×#11758194C2312yes—
60C2×#11758194C2312yes—
61Q8×Dic61—22no—
62Q8×Dic61—22no—
63C4×Dic122—22no—
64C4×Dic122—22no—
65C4×Dic122D412yes—
66C4×Dic122D412yes—
67#14519742—24no—
68#14519742—22no—
69C4×D244—22no—
70C4×D244—22no—
71C4×D244D412yes—
72C4×D244D412yes—
73#14519739—24no—
74#14519739—22no—
75C4×C22⋊D61—22no—
76C4×C22⋊D61—24no—
77C4×C22⋊D61—22no—
78#14519736—22no—
79#14519736C2312yes—
80#14519735—24no—
81#14519735—22no—
82#14519734—24no—
83#14519734—22no—
84C4⋊C4×D61—24no—
85C4⋊C4×D61—22no—
86C42×D61—24no—
87C42×D61—22no—
88#14519710—22no—
89#14519708—22no—
90#14519705—24no—
91#14519705C2×C418yescomplemented
92#14519701—22no—
93#14519701—22no—
94#14519700—22no—
95#14519697—22no—
96#14519696—22no—
97#14519696C2×C414yescomplemented
98#14519688—22no—
99C4×#92418—22no—
100C22×Q8×C61C2311yescharacteristic
101C22×Q8×C61C2311yescharacteristic
102C4⋊Q8×C61—22no—
103C4⋊Q8×C61C2×C414yescomplemented
104C4×Q8×C61—22no—
105C4×Q8×C61—22no—
106C4×Q8×C61—22no—
107C4×Q8×C61—22no—
108C2×C4⋊C4×C61—22no—
109C2×C4⋊C4×C61—22no—
110C2×C4⋊C4×C61—21no—
111C2×C4⋊C4×C61D412yes—
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C42×C61—21no—
115C2×C42×C61—21no—
116C2×C42×C61—21no—
117C2×C42×C61D412yes—
118C2×C42×C61C2311yescharacteristic
119C2×C42×C61C2311yescharacteristic
120C2×C42×C61C2311yescharacteristic
121#95×C61—22no—
122#95×C61—22no—
123C2×Q8×C61—22no—
124C2×Q8×C61—22no—
125C2×Q8×C61—21no—
126C2×Q8×C61—22no—
127C2×Q8×C61—22no—
128C2×Q8×C61C22×C412yes—
129C2×Q8×C61C22×C412yes—
130C2×Q8×C61#4112yes—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61C2×D412yes—
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D412yes—
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2411yescharacteristic
140C2×C22⋊D61—22no—
141#11758226—28no—
142#11758226—28no—
143Q8×D61—28no—
144Q8×D61—28no—
145#11758222—28no—
146#11758222—28no—
147#11758222—22no—
148#11758222—22no—
149#11758222C22×C414yes—
150#11758222#4114yes—
151C2×D244—22no—
152C2×D244C2×D412yes—
153C2×C4×D61—24no—
154C2×C4×D61—22no—
155C2×C4×D61—22no—
156C2×C4×D61—24no—
157C2×C4×D61—22no—
158C2×Dic122—22no—
159C2×Dic122C2×D412yes—
160C4⋊C4×C61—28no—
161C4⋊C4×C61—24no—
162C4⋊C4×C61—22no—
163C4⋊C4×C61—22no—
164C4⋊C4×C61—44no—
165C4⋊C4×C61—42no—
166C42×C61—24no—
167C42×C61—22no—
168C42×C61—22no—
169C42×C61—21no—
170C42×C61—22no—
171C42×C61—42no—
172C42×C61—41no—
173C42×C61—41no—
174C42×C61C22×C412yes—
175C42×C61C2×D412yes—
176C42×C61C2×D412yes—
177C22⋊Dic61—22no—
178#11758202—28no—
179#11758201—28no—
180#11758198—24no—
181#11758198—22no—
182#11758198—22no—
183C4⋊Dic61—22no—
184C4⋊Dic61—22no—
185C4⋊Dic61C2×D412yes—
186C4⋊Dic61C2×D412yes—
187#11758196—24no—
188#11758196—22no—
189#11758196—22no—
190C4×Dic61—24no—
191C4×Dic61—24no—
192C4×Dic61—22no—
193C4×Dic61—22no—
194C4×Dic61—22no—
195#11758194—22no—
196#11758194—22no—
197#11758194—22no—
198#11758194C22×C414yes—
199C2×#92418—22no—
200C2×#92418—22no—
201C23×C61C22×D411yescharacteristic
202C22×D61—22no—
203Q8×C61—24no—
204Q8×C61—24no—
205Q8×C61—24no—
206Q8×C61—42no—
207C2×C4×C61—22no—
208C2×C4×C61—22no—
209C2×C4×C61—22no—
210C2×C4×C61—22no—
211C2×C4×C61—22no—
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—22no—
215C2×C4×C61—22no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—42no—
222C2×C4×C61—42no—
223C2×C4×C61—41no—
224C2×C4×C61C4×D414yes—
225C2×C4×C61#12012yes—
226C2×C4×C61#12011yescharacteristic
227C2×C4×C61#12011yescharacteristic
228C2×C4×C61C23×C411yescharacteristic
229C2×C4×C61C22×D412yes—
230C2×C4×C61C2×#4112yes—
231C2×C4×C61C2×#4111yescharacteristic
232C22⋊D61—24no—
233C22⋊D61—24no—
234C2×Dic61—22no—
235C2×Dic61—22no—
236C2×Dic61—22no—
237D244—28no—
238D244—22no—
239D244C4×D414yes—
240C4×D61—216no—
241C4×D61—24no—
242C4×D61—24no—
243C4×D61—44no—
244C4×D61—82no—
245C4×D61—84no—
246Dic122—28no—
247Dic122—22no—
248Dic122C4×D414yes—
249#92418—24no—
250#92418—42no—
251C4×#456—611nomaximal, Sylow
252C22×C61—21no—
253C22×C61—21no—
254C22×C61C2×C4×D411yescharacteristic
255C22×C61C2×#12011yescharacteristic
256C22×C61#52511yescharacteristic
257C2×D61—24no—
258C2×D61—42no—
259C2×D61—42no—
260C4×C61—24no—
261C4×C61—21no—
262C4×C61—22no—
263C4×C61—24no—
264C4×C61—42no—
265C4×C61—42no—
266C4×C61—42no—
267C4×C61—81no—
268C4×C61#45612yescomplemented
269C4×C61C2×C4×D412yes—
270C4×C61#52512yes—
271Dic61—24no—
272Dic61—42no—
273Dic61—42no—
274C4×2−1+4—611no—
275C2×#456—611no—
276C4×#137—612no—
277C4×C4⋊Q8D6111yescharacteristic, complemented
278#1886—611no—
279#1882—612no—
280#1859—612no—
281#1857—611no—
282#1793—611no—
283C4×#104—612no—
284C4×#101—611no—
285C2×C61—21no—
286C2×C61—21no—
287C2×C61C4×#12011yescharacteristic
288C2×C61C2×#45611yescharacteristic
289C2×C61#301811yescharacteristic
290D61—44no—
291C2×2−1+4—611no—
292C2×#137—612no—
293C2×C4⋊Q8C2×D6111yescharacteristic
294#520—612no—
295#520—1222no—
296#520—1222no—
297#519—611no—
298#519—1222no—
299C4×#41—612no—
300C4×#41—1222no—
301C4×#41—1222no—
302C2×C4×Q8—1222no—
303C2×C4×Q8C2×D6111yescharacteristic
304C2×C4×Q8C2×D6111yescharacteristic
305#456—618no—
306#441—1222no—
307#440—1222no—
308C4×Q16—1222no—
309C4×SD16—1222no—
310#428—612no—
311C2×#104—612no—
312C2×#104—612no—
313#419—612no—
314#417—612no—
315C2×#101—611no—
316C2×#101—611no—
317C4×M16—612no—
318#391C2×D6111yescharacteristic
319#391C2×D6111yescharacteristic
320#389—22no—
321#384C2×D6111yescharacteristic
322C4×C4⋊C4—22no—
323C43C2×D6111yescharacteristic
324#343—612no—
325#339—612no—
326#339—612no—
327C61C4×#45611yescharacteristic, complemented, Sylow
3282−1+4—614no—
3292−1+4—1224no—
3302−1+4—1222no—
331C2×#41—612no—
332C2×#41—1222no—
333C2×#41—1222no—
334C22×Q8—1222no—
335C22×Q8C22×D6111yescharacteristic
336C22×Q8C22×D6111yescharacteristic
337#137—618no—
338#137—1224no—
339C2×Q16—1222no—
340C2×SD16—1222no—
341C2×M16—612no—
342C2×M16—612no—
343C4⋊Q8—22no—
344C4⋊Q8C4×D6114yescomplemented
345C4×Q8—22no—
346C4×Q8—22no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×Q8—612no—
350C4×Q8—612no—
351C4×Q8—1222no—
352C4×Q8—1222no—
353C4×Q8—1222no—
354C4×Q8—1224no—
355C4×Q8—1222no—
356C4×Q8—1222no—
357C4×D4—612no—
358C4×D4—612no—
359C4×D4—1222no—
360C4×D4—1222no—
361C4×D4—1222no—
362C4×D4—1224no—
363C4×D4—1222no—
364C4×D4—1222no—
365C4×D4—1224no—
366#117—612no—
367#117—1224no—
368#117—1222no—
369#117—1224no—
370#117—1222no—
371#117—1222no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—1222no—
376C2×C4⋊C4—1224no—
377C2×C4⋊C4C22⋊D6112yes—
378C2×C4⋊C4C22×D6111yescharacteristic
379C2×C4⋊C4C22×D6111yescharacteristic
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—1224no—
384C2×C42—1222no—
385C2×C42C22⋊D6112yes—
386C2×C42C22×D6111yescharacteristic
387C2×C42C22×D6111yescharacteristic
388C2×C42C22×D6111yescharacteristic
389#107—1222no—
390#106—1222no—
391#104—618no—
392#104—1224no—
393#103—1222no—
394#103—1222no—
395#103—1222no—
396#102—1222no—
397#101—614no—
398#101—1222no—
399#97—1222no—
400C4×C8—1222no—
401#95—22no—
402#95—22no—
403#41—614no—
404#41—614no—
405#41—1228no—
406#41—1228no—
407#41—1228no—
408#41—1222no—
409#41—1222no—
410#41—1228no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—21no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—612no—
417C2×Q8—1222no—
418C2×Q8—1228no—
419C2×Q8—1228no—
420C2×Q8C2×C4×D6112yes—
421C2×Q8C2×C4×D6112yes—
422C2×Q8#1175822212yes—
423C2×D4—612no—
424C2×D4—1222no—
425C2×D4—1222no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—1224no—
431C22×C4—1224no—
432C22×C4—1222no—
433C22×C4—1222no—
434C22×C4—1222no—
435C22×C4C2×C22⋊D6112yes—
436C22×C4C2×C22⋊D6111yescharacteristic
437C22×C4C2×C22⋊D6112yes—
438C22×C4C2×C22⋊D6111yescharacteristic
439C22×C4C23×D6111yescharacteristic
440Q16—1228no—
441SD16—1228no—
442M16—614no—
443M16—1222no—
444M16—1222no—
445M16—1222no—
446C2×C8—1222no—
447C2×C8—1222no—
448C4⋊C4—22no—
449C4⋊C4—28no—
450C4⋊C4—24no—
451C4⋊C4—22no—
452C4⋊C4—44no—
453C4⋊C4—42no—
454C4⋊C4—612no—
455C4⋊C4—612no—
456C4⋊C4—1224no—
457C4⋊C4—1222no—
458C4⋊C4—1222no—
459C4⋊C4—1222no—
460C4⋊C4—1222no—
461C22⋊C4—1224no—
462C22⋊C4—1222no—
463C22⋊C4—1222no—
464C22⋊C4—1222no—
465C42—24no—
466C42—21no—
467C42—22no—
468C42—22no—
469C42—22no—
470C42—42no—
471C42—41no—
472C42—41no—
473C42—1224no—
474C42—1224no—
475C42—1222no—
476C42—1222no—
477C42—1222no—
478C42C2×C4×D6112yes—
479C42D4×D6112yes—
480C42D4×D6112yes—
481C23—1222no—
482C23C22×C22⋊D6111yescharacteristic
483Q8—24no—
484Q8—24no—
485Q8—24no—
486Q8—42no—
487Q8—614no—
488Q8—1228no—
489Q8—1222no—
490D4—614no—
491D4—1228no—
492D4—1224no—
493D4—1224no—
494D4—1222no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—41no—
512C2×C4—12216no—
513C2×C4—1222no—
514C2×C4—1224no—
515C2×C4—1224no—
516C2×C4—1222no—
517C2×C4—1222no—
518C2×C4—4882no—
519C2×C4—4884no—
520C2×C4—2444no—
521C2×C4C4×C22⋊D6114yes—
522C2×C4#1451974511yescharacteristic
523C2×C4#1451974512yes—
524C2×C4#1451974511yescharacteristic
525C2×C4C22×C4×D6111yescharacteristic
526C2×C4C2×D4×D6112yes—
527C2×C4#41×D6112yes—
528C2×C4C2×#1175822211yescharacteristic
529C8—1224no—
530C8—2442no—
531C22—21no—
532C22—21no—
533C22—1224no—
534C22—2442no—
535C22—2442no—
536C22C2×C4×C22⋊D6111yescharacteristic
537C22C2×#1451974511yescharacteristic
538C22#1684026911yescharacteristic
539C4—24no—
540C4—21no—
541C4—22no—
542C4—24no—
543C4—42no—
544C4—42no—
545C4—42no—
546C4—81no—
547C4—1224no—
548C4—2442no—
549C4—2442no—
550C4#1683994412yesdirect product factor
551C4C4×D4×D6112yes—
552C4#1684027112yes—
553C2—21no—
554C2—21no—
555C2—2444no—
556C2C4×#1451974511yescharacteristic
557C2C2×#1683994411yescharacteristic
558C2#2145516711yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×C4⋊Q8×C61C2
socleC22×C61C2×#120
prime radicalC2×#14519825C22
cosocleC22×C4×C61C24
hypercenterC4×C4⋊Q8D61
hypocenterC61C4×#456
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. C4×#14519808C2semidirect
4. #21446213C2semidirect
5. #21446191C2semidirect
6. #21446044C2semidirect
7. #21446033C2semidirect
9. C4×#14519705C2semidirect
10. C4×#14519696C2semidirect
11. C4×C4⋊Q8×C61C2semidirect
23. #16839944C4direct (N × H)
56. #14519808C2×C4semidirect
91. #14519705C2×C4semidirect
97. #14519696C2×C4semidirect
103. C4⋊Q8×C61C2×C4semidirect
268. C4×C61#456semidirect
277. C4×C4⋊Q8D61semidirect
327. C61C4×#456semidirect
344. C4⋊Q8C4×D61semidirect
550. C4#16839944direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#145198252
C2×#168399442
C4×#145198082
#214462132
#214461912
#214460442
#214460332
#214457772
C4×#145197052
C4×#145196962
C4×C4⋊Q8×C612
C4×#45661