Finite Group Databasebeta

← C4×#16839945 #29685920

Subgroups — C4×#16839945 #29685920

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
1C2×#16839945C211yesmaximal, characteristic
2C4×#14519807C212yesmaximal, complemented
3C4×#14519775C211yesmaximal, characteristic, complemented
4#21446212C211yesmaximal, characteristic, complemented
5#21446188C212yesmaximal, complemented
6#21446045C212yesmaximal, complemented
7#21446034C211yesmaximal, characteristic, complemented
8#21445778C211yesmaximal, characteristic
9C4×#14519704C212yesmaximal, complemented
10C4×#14519696C211yesmaximal, characteristic, complemented
11C4×2−1+4×C61C211yesmaximal, characteristic
12C2×#14519807C2212yes—
13C2×#14519775C2211yescharacteristic
14C2×C4×Dic122C2211yescharacteristic
15#16839945C418yesdirect product factor
16#16839867—22no—
17#16839862—22no—
18C4×#11758202—22no—
19C4×#11758200—22no—
20#16839805C2212yes—
21C2×#14519704C2212yes—
22C2×#14519704C2212yes—
23#16839770C2212yes—
24#16839763C2212yes—
25C2×#14519696C2211yescharacteristic
26C2×#14519696C2211yescharacteristic
27C4×#11758194C2212yes—
28#16839669C2211yescharacteristic
29#16839667C2211yescharacteristic
30#16839657—22no—
31#16839631C2211yescharacteristic
32C4×#11758196—22no—
33C42×Dic61C2211yescharacteristic
34#16839531C2212yes—
35#16839521C2212yes—
36#16839521C2212yes—
37C2×2−1+4×C61C2211yescharacteristic
38C61×#520—22no—
39C61×#520—22no—
40C61×#520C2212yes—
41C61×#519—22no—
42C61×#519C2211yescharacteristic
43C4×#41×C61—22no—
44C4×#41×C61—22no—
45C4×#41×C61C2212yes—
46C2×C4×Q8×C61—22no—
47C2×C4×Q8×C61C2211yescharacteristic
48C22×Dic122C2311yescharacteristic
49#14519807—24no—
50#14519807C2×C418yescomplemented
51C2×#11758202—22no—
52C2×#11758200—22no—
53C2×#11758194C2312yes—
54C2×#11758194C2312yes—
55#14519775—22no—
56#14519775C2×C414yescomplemented
57C4×Dic122—22no—
58C4×Dic122—22no—
59C2×C4⋊Dic61C2311yescharacteristic
60C2×#11758196—22no—
61C2×#11758196—21no—
62C2×#11758196—22no—
63C2×C4×Dic61—21no—
64C2×C4×Dic61—21no—
65C2×C4×Dic61—21no—
66C2×C4×Dic61C2311yescharacteristic
67C2×C4×Dic61C2311yescharacteristic
68#14519710—22no—
69#14519708—22no—
70#14519704—24no—
71#14519704C2×C418yescomplemented
72#14519701—22no—
73#14519700—22no—
74#14519700—22no—
75#14519698—22no—
76#14519696—22no—
77#14519696C2×C414yescomplemented
78#14519688—22no—
79C4×#92418—22no—
80#14519684—22no—
81#14519684—22no—
822−1+4×C61—24no—
832−1+4×C61—22no—
842−1+4×C61C2×C414yes—
85C2×#41×C61—22no—
86C2×#41×C61—22no—
87C2×#41×C61C2312yes—
88C22×Q8×C61—22no—
89C22×Q8×C61C2311yescharacteristic
90C4×Q8×C61—22no—
91C4×Q8×C61—24no—
92C4×Q8×C61—22no—
93C4×Q8×C61—22no—
94C4×Q8×C61—22no—
95C4×Q8×C61—22no—
96C4×Q8×C61—22no—
97C4×Q8×C61—22no—
98C4×Q8×C61D412yes—
99C4×Q8×C61D412yes—
100C4×D4×C61—22no—
101C4×D4×C61—24no—
102C4×D4×C61—22no—
103C4×D4×C61—22no—
104C4×D4×C61—22no—
105C4×D4×C61—24no—
106C4×D4×C61—22no—
107C4×D4×C61D412yes—
108C4×D4×C61D412yes—
109#117×C61—24no—
110#117×C61—24no—
111#117×C61—22no—
112#117×C61—22no—
113#117×C61—22no—
114#117×C61C2312yes—
115C2×C4⋊C4×C61—24no—
116C2×C4⋊C4×C61—22no—
117C2×C4⋊C4×C61D412yes—
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C42×C61—24no—
120C2×C42×C61—22no—
121C2×C42×C61D412yes—
122C2×C42×C61C2311yescharacteristic
123#41×C61—28no—
124#41×C61—28no—
125#41×C61—28no—
126#41×C61—28no—
127#41×C61—22no—
128#41×C61—22no—
129#41×C61C22×C414yes—
130#41×C61#4114yes—
131C2×Q8×C61—22no—
132C2×Q8×C61—28no—
133C2×Q8×C61—28no—
134C2×Q8×C61—22no—
135C2×Q8×C61—22no—
136C2×Q8×C61C22×C412yes—
137C2×Q8×C61C2×D412yes—
138C2×Q8×C61#4112yes—
139C2×D4×C61—22no—
140C2×D4×C61—22no—
141C2×D4×C61C2×D412yes—
142C22×C4×C61—24no—
143C22×C4×C61—22no—
144C22×C4×C61—24no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61C2×D412yes—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D412yes—
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2411yescharacteristic
152C22×Dic61—21no—
153C22×Dic61—21no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C2×Dic122—22no—
157C2×Dic122—22no—
158C2×Dic122—21no—
159C2×Dic122C22×C412yes—
160C4⋊C4×C61—24no—
161C4⋊C4×C61—22no—
162C4⋊C4×C61—22no—
163C4⋊C4×C61—22no—
164C4⋊C4×C61—24no—
165C4⋊C4×C61—22no—
166C4⋊C4×C61—22no—
167C4⋊C4×C61C2×D412yes—
168C4⋊C4×C61C2×D412yes—
169C22⋊C4×C61—24no—
170C22⋊C4×C61—22no—
171C22⋊C4×C61—22no—
172C22⋊C4×C61—22no—
173C42×C61—24no—
174C42×C61—24no—
175C42×C61—22no—
176C42×C61—22no—
177C42×C61—22no—
178C42×C61—22no—
179C42×C61—22no—
180C42×C61C2×D412yes—
181C42×C61C2×D412yes—
182#11758202—28no—
183#11758200—28no—
184C4⋊Dic61—22no—
185#11758196—28no—
186#11758196—44no—
187#11758196—42no—
188C4×Dic61—24no—
189C4×Dic61—21no—
190C4×Dic61—22no—
191C4×Dic61—42no—
192C4×Dic61—41no—
193C4×Dic61—41no—
194C4×Dic61C22×C412yes—
195#11758194—22no—
196#11758194—22no—
197#11758194—22no—
198#11758194C22×C414yes—
199C2×#92418—22no—
200C2×#92418—22no—
201C23×C61—22no—
202C23×C61C22×D411yescharacteristic
203Q8×C61—28no—
204Q8×C61—24no—
205Q8×C61—22no—
206Q8×C61—24no—
207Q8×C61C4×D414yes—
208D4×C61—28no—
209D4×C61—24no—
210D4×C61—24no—
211D4×C61—22no—
212D4×C61C4×D414yes—
213C2×C4×C61—216no—
214C2×C4×C61—22no—
215C2×C4×C61—22no—
216C2×C4×C61—22no—
217C2×C4×C61—24no—
218C2×C4×C61—24no—
219C2×C4×C61—22no—
220C2×C4×C61—22no—
221C2×C4×C61—22no—
222C2×C4×C61—22no—
223C2×C4×C61—41no—
224C2×C4×C61—44no—
225C2×C4×C61—42no—
226C2×C4×C61—82no—
227C2×C4×C61—84no—
228C2×C4×C61C4×D414yes—
229C2×C4×C61#12011yescharacteristic
230C2×C4×C61#12012yes—
231C2×C4×C61#12011yescharacteristic
232C2×C4×C61C23×C411yescharacteristic
233C2×C4×C61C22×D412yes—
234C2×C4×C61C2×#4112yes—
235C2×C4×C61C2×#4111yescharacteristic
236C2×Dic61—22no—
237C2×Dic61—22no—
238C2×Dic61—22no—
239C2×Dic61—22no—
240C2×Dic61—22no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—42no—
246C2×Dic61—41no—
247Dic122—24no—
248Dic122—42no—
249#92418—24no—
250#92418—42no—
251C4×#456—611nomaximal, Sylow
252C22×C61—21no—
253C22×C61—21no—
254C22×C61—24no—
255C22×C61—42no—
256C22×C61—42no—
257C22×C61C2×C4×D411yescharacteristic
258C22×C61C2×#12011yescharacteristic
259C22×C61#52511yescharacteristic
260C4×C61—21no—
261C4×C61—22no—
262C4×C61—24no—
263C4×C61—24no—
264C4×C61—42no—
265C4×C61—42no—
266C4×C61—42no—
267C4×C61#45612yescomplemented
268C4×C61C2×C4×D412yes—
269C4×C61#52512yes—
270Dic61—24no—
271Dic61—42no—
272Dic61—42no—
273Dic61—81no—
274C4×2−1+4D6111yescharacteristic
275C2×#456—611no—
276C4×#137—612no—
277C4×C4⋊Q8—611no—
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×C61—44no—
288C2×C61C4×#12011yescharacteristic
289C2×C61C2×#45611yescharacteristic
290C2×C61#301811yescharacteristic
291C2×2−1+4C2×D6111yescharacteristic
292C2×#137—612no—
293C2×C4⋊Q8—611no—
294#520—22no—
295#520—22no—
296#520C2×D6112yes—
297#519—22no—
298#519C2×D6111yescharacteristic
299C4×#41—22no—
300C4×#41—22no—
301C4×#41C2×D6112yes—
302C2×C4×Q8—22no—
303C2×C4×Q8—611no—
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#391—611no—
319#391—611no—
320#389—1222no—
321#384—611no—
322C4×C4⋊C4—1222no—
323C43—611no—
324#343—612no—
325#339—612no—
326#339—612no—
327C61C4×#45611yescharacteristic, complemented, Sylow
3282−1+4—24no—
3292−1+4—22no—
3302−1+4C4×D6114yes—
331C2×#41—22no—
332C2×#41—22no—
333C2×#41C22×D6112yes—
334C22×Q8—22no—
335C22×Q8—611no—
336C22×Q8C22×D6111yescharacteristic
337#137—618no—
338#137—1224no—
339C2×Q16—1222no—
340C2×SD16—1222no—
341C2×M16—612no—
342C2×M16—612no—
343C4⋊Q8—614no—
344C4⋊Q8—1222no—
345C4×Q8—22no—
346C4×Q8—24no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×Q8—22no—
350C4×Q8—22no—
351C4×Q8—22no—
352C4×Q8—22no—
353C4×Q8—1222no—
354C4×Q8—1222no—
355C4×Q8C22⋊D6112yes—
356C4×Q8C22⋊D6112yes—
357C4×D4—22no—
358C4×D4—24no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—24no—
363C4×D4—22no—
364C4×D4C22⋊D6112yes—
365C4×D4C22⋊D6112yes—
366#117—24no—
367#117—24no—
368#117—22no—
369#117—22no—
370#117—22no—
371#117C22×D6112yes—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—611no—
375C2×C4⋊C4—1222no—
376C2×C4⋊C4—1221no—
377C2×C4⋊C4—1222no—
378C2×C4⋊C4C22⋊D6112yes—
379C2×C4⋊C4C22×D6111yescharacteristic
380C2×C42—24no—
381C2×C42—22no—
382C2×C42—611no—
383C2×C42—611no—
384C2×C42—1221no—
385C2×C42—1221no—
386C2×C42—1221no—
387C2×C42C22⋊D6112yes—
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—1222no—
402#95—1222no—
403#41—28no—
404#41—28no—
405#41—28no—
406#41—22no—
407#41—22no—
408#41—28no—
409#41C2×C4×D6114yes—
410#41#1175822214yes—
411C2×Q8—22no—
412C2×Q8—28no—
413C2×Q8—28no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—612no—
417C2×Q8—1221no—
418C2×Q8—1222no—
419C2×Q8—1222no—
420C2×Q8C2×C4×D6112yes—
421C2×Q8#1175822212yes—
422C2×Q8C2×C22⋊D6112yes—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4C2×C22⋊D6112yes—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—1221no—
432C22×C4—1221no—
433C22×C4—1221no—
434C22×C4—1221no—
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—24no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—24no—
454C4⋊C4—22no—
455C4⋊C4—1228no—
456C4⋊C4—1222no—
457C4⋊C4—2444no—
458C4⋊C4—2442no—
459C4⋊C4C2×C22⋊D6112yes—
460C4⋊C4C2×C22⋊D6112yes—
461C22⋊C4—24no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C42—24no—
466C42—24no—
467C42—22no—
468C42—22no—
469C42—22no—
470C42—22no—
471C42—22no—
472C42—612no—
473C42—1224no—
474C42—1221no—
475C42—1222no—
476C42—2442no—
477C42—2441no—
478C42—2441no—
479C42C2×C22⋊D6112yes—
480C42C2×C22⋊D6112yes—
481C23—22no—
482C23C22×C22⋊D6111yescharacteristic
483Q8—28no—
484Q8—24no—
485Q8—24no—
486Q8—22no—
487Q8—1224no—
488Q8—2442no—
489Q8C4×C22⋊D6114yes—
490D4—28no—
491D4—24no—
492D4—24no—
493D4—22no—
494D4C4×C22⋊D6114yes—
495C2×C4—216no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—41no—
506C2×C4—44no—
507C2×C4—42no—
508C2×C4—82no—
509C2×C4—84no—
510C2×C4—1222no—
511C2×C4—1222no—
512C2×C4—1222no—
513C2×C4—1222no—
514C2×C4—1222no—
515C2×C4—2442no—
516C2×C4—2441no—
517C2×C4—2441no—
518C2×C4—2441no—
519C2×C4—2441no—
520C2×C4—2441no—
521C2×C4C4×C22⋊D6114yes—
522C2×C4#1451974611yescharacteristic
523C2×C4#1451974612yes—
524C2×C4#1451974611yescharacteristic
525C2×C4C22×C4×D6111yescharacteristic
526C2×C4C22×C22⋊D6112yes—
527C2×C4C2×#1175822212yes—
528C2×C4C2×#1175822211yescharacteristic
529C8—1224no—
530C8—2442no—
531C22—21no—
532C22—21no—
533C22—24no—
534C22—42no—
535C22—42no—
536C22C2×C4×C22⋊D6111yescharacteristic
537C22C2×#1451974611yescharacteristic
538C22#1684027311yescharacteristic
539C4—21no—
540C4—22no—
541C4—24no—
542C4—24no—
543C4—42no—
544C4—42no—
545C4—42no—
546C4—1224no—
547C4—4881no—
548C4—2442no—
549C4—2442no—
550C4#1683994512yesdirect product factor
551C4C2×C4×C22⋊D6112yes—
552C4#1684027312yes—
553C2—21no—
554C2—21no—
555C2—44no—
556C2C4×#1451974611yescharacteristic
557C2C2×#1683994511yescharacteristic
558C2#2145516811yescharacteristic
subgroupG/H
centerC2×C4#14519746
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×2−1+4×C61C2
socleC22×C61C2×#120
prime radicalC2×2−1+4×C61C22
cosocleC22×C4×C61C24
hypercenterC4×2−1+4D61
hypocenterC61C4×#456
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
2. C4×#14519807C2semidirect
3. C4×#14519775C2semidirect
4. #21446212C2semidirect
5. #21446188C2semidirect
6. #21446045C2semidirect
7. #21446034C2semidirect
9. C4×#14519704C2semidirect
10. C4×#14519696C2semidirect
15. #16839945C4direct (N × H)
50. #14519807C2×C4semidirect
56. #14519775C2×C4semidirect
71. #14519704C2×C4semidirect
77. #14519696C2×C4semidirect
267. C4×C61#456semidirect
327. C61C4×#456semidirect
550. C4#16839945direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168399452
C4×#145198072
C4×#145197752
#214462122
#214461882
#214460452
#214460342
#214457782
C4×#145197042
C4×#145196962
C4×2−1+4×C612
C4×#45661