Finite Group Databasebeta

← C4×#16839986 #29686252

Subgroups — C4×#16839986 #29686252

Order 15616.

1016 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839986C211yesmaximal, characteristic
2C2×C4×#11758201C211yesmaximal, characteristic
3C4×#14519766C211yesmaximal, characteristic
4C4×Q8×Dic61C211yesmaximal, characteristic, complemented
5#21446748C211yesmaximal, characteristic
6#21446584C211yesmaximal, characteristic, complemented
7#21446456C211yesmaximal, characteristic, complemented
8#21446438C211yesmaximal, characteristic
9#21446172C211yesmaximal, characteristic
10#21446162C211yesmaximal, characteristic, complemented
11#21445832C211yesmaximal, characteristic, complemented
12C4×#14519706C211yesmaximal, characteristic, complemented
13C4×#14519701C211yesmaximal, characteristic, complemented
14C4×#14519699C211yesmaximal, characteristic
15C2×C4×Q16×C61C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C2×#14519766C2211yescharacteristic
18C2×Q8×Dic61C2211yescharacteristic
19C2×Q8×Dic61C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21#16839986C418yesdirect product factor
22C4×#11758201—24no—
23C2×#14519708C2211yescharacteristic
24C2×#14519706C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519699C2211yescharacteristic
30C2×#14519699C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×C4×#92418C2211yescharacteristic
33#16839669C2211yescharacteristic
34#16839663C2211yescharacteristic
35#16839652—21no—
36#16839652—21no—
37#16839627C2211yescharacteristic
38C4⋊C4×Dic61—21no—
39C4⋊C4×Dic61—21no—
40C4⋊C4×Dic61C2211yescharacteristic
41C4⋊C4×Dic61C2211yescharacteristic
42C4×C4⋊Dic61—21no—
43C4×C4⋊Dic61C2211yescharacteristic
44C4×#11758198—21no—
45C4×#11758198—21no—
46C42×Dic61—21no—
47C42×Dic61C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C22×Q16×C61C2211yescharacteristic
55C2×C4×Q8×C61C2211yescharacteristic
56C2×C4×Q8×C61C2211yescharacteristic
57C4×Q16×C61—24no—
58C2×#107×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C2×C4×C8×C61C2211yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C4×D61—21no—
64C2×#11758201—22no—
65C2×#11758201—22no—
66C2×#11758201C2×C414yes—
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69#14519766—22no—
70#14519766C2×C414yes—
71Q8×Dic61—22no—
72Q8×Dic61—22no—
73Q8×Dic61—22no—
74Q8×Dic61C2×C414yescomplemented
75C4×D244—22no—
76C4×D244—22no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61—21no—
89C2×C4×Dic61—21no—
90C2×C4×Dic61—21no—
91C2×C4×Dic61—21no—
92C2×C4×Dic61D411yescharacteristic
93C2×C4×Dic61D411yescharacteristic
94C2×C4×Dic61D411yescharacteristic
95C2×C4×Dic61D411yescharacteristic
96C2×C4×Dic61C2311yescharacteristic
97C2×C4×Dic61C2311yescharacteristic
98#14519708—22no—
99#14519706—22no—
100#14519706C2×C414yescomplemented
101#14519701—22no—
102#14519701—22no—
103#14519701C2×C414yescomplemented
104#14519699—22no—
105#14519699C2×C414yes—
106#14519697—22no—
107C4×#92418—22no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115C22×Q8×C61C2311yescharacteristic
116C22×Q8×C61C2311yescharacteristic
117C2×Q16×C61—22no—
118C2×Q16×C61—22no—
119C2×Q16×C61C2×C414yescomplemented
120C22×C8×C61C2311yescharacteristic
121C22×C8×C61C2311yescharacteristic
122C4×Q8×C61—22no—
123C4×Q8×C61—22no—
124C4×Q8×C61—22no—
125C4×Q8×C61D414yes—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C42×C61—21no—
131C2×C42×C61—21no—
132C2×C42×C61C2311yescharacteristic
133#107×C61—22no—
134#103×C61—22no—
135#103×C61—22no—
136C4×C8×C61—22no—
137C23×D61—21no—
138C2×Q8×C61—21no—
139C2×Q8×C61—21no—
140C2×Q8×C61—21no—
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C2×Q8×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61C22×C412yes—
147C2×Q8×C61C22×C412yes—
148C2×Q8×C61C2×D412yes—
149C2×Q8×C61#4112yes—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2411yescharacteristic
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61C2×D411yescharacteristic
161C22×Dic61C2×D411yescharacteristic
162C22×Dic61C2×D411yescharacteristic
163C22×Dic61C2×D411yescharacteristic
164C2×D244—21no—
165C2×D244—21no—
166C2×D244—21no—
167C2×D244—21no—
168C2×D244—21no—
169C2×D244C22×C412yes—
170C2×C4×D61—42no—
171C2×C4×D61—42no—
172C2×C4×D61—42no—
173Q16×C61—28no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61C22×C412yes—
180C4⋊C4×C61—24no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—42no—
185C4⋊C4×C61C2×D412yes—
186C42×C61—24no—
187C42×C61—42no—
188C42×C61C2×D412yes—
189C42×C61#4112yes—
190#11758201—28no—
191#11758198—24no—
192#11758198—24no—
193#11758198—42no—
194#11758198—42no—
195#11758198—42no—
196C4⋊Dic61—24no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—24no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61C22×C412yes—
203C4⋊Dic61#4112yes—
204C4×Dic61—24no—
205C4×Dic61—22no—
206C4×Dic61—22no—
207C4×Dic61—21no—
208C4×Dic61—21no—
209C4×Dic61—24no—
210C4×Dic61—22no—
211C4×Dic61—41no—
212C4×Dic61—42no—
213C4×Dic61—42no—
214C4×Dic61—42no—
215C4×Dic61C22×C412yes—
216C4×Dic61#4112yes—
217C2×#92418—21no—
218C2×#92418—21no—
219C2×#92418—21no—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418C22×C412yes—
223C23×C61C22×D411yescharacteristic
224C22×D61—22no—
225C22×D61—41no—
226C22×D61—41no—
227C22×D61—41no—
228C22×D61—41no—
229C22×D61—41no—
230C22×D61—41no—
231Q8×C61—22no—
232Q8×C61—22no—
233Q8×C61—22no—
234Q8×C61—22no—
235Q8×C61—22no—
236Q8×C61—41no—
237Q8×C61—41no—
238Q8×C61C4×D414yes—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—22no—
245C2×C4×C61—22no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61#12112yes—
254C2×C4×C61#12112yes—
255C2×C4×C61#13512yes—
256C2×C4×C61#13712yes—
257C2×C4×C61C23×C411yescharacteristic
258C2×C4×C61C22×D411yescharacteristic
259C2×C4×C61C2×#4111yescharacteristic
260C2×C4×C61C2×#4111yescharacteristic
261C2×C4×C61C2×#4111yescharacteristic
262C2×C4×C61C2×#4111yescharacteristic
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—22no—
270C2×Dic61—21no—
271C2×Dic61—22no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61C4×D412yes—
282C2×Dic61C4×D412yes—
283C2×Dic61#13512yes—
284D244—22no—
285D244—22no—
286D244—41no—
287D244—41no—
288C4×D61—84no—
289C8×C61—22no—
290C8×C61—41no—
291#92418—22no—
292#92418—41no—
293C4×#464—611nomaximal, Sylow
294C22×C61C2×C4×D411yescharacteristic
295C22×C61C2×#12111yescharacteristic
296C22×C61#52511yescharacteristic
297C22×C61C2×#13511yescharacteristic
298C22×C61C2×#13511yescharacteristic
299C22×C61C2×#13711yescharacteristic
300C22×C61#57511yescharacteristic
301C2×D61—42no—
302C2×D61—42no—
303C2×D61—42no—
304C2×D61—81no—
305C2×D61—81no—
306C2×D61—81no—
307C2×D61—81no—
308C4×C61—22no—
309C4×C61—24no—
310C4×C61—42no—
311C4×C61—42no—
312C4×C61—81no—
313C4×C61#46414yescomplemented
314C4×C61C2×C4×D411yescharacteristic
315C4×C61C4×#4111yescharacteristic
316C4×C61#52911yescharacteristic
317C4×C61#53211yescharacteristic
318Dic61—22no—
319Dic61—22no—
320Dic61—22no—
321Dic61—41no—
322Dic61—42no—
323Dic61—42no—
324Dic61—81no—
325C2×#464—611no—
326C2×C4×Q16D6111yescharacteristic, complemented
327C2×C4×SD16—611no—
328C4×#124—611no—
329C42×Q8—611no—
330#1983—611no—
331#1949—611no—
332#1927—611no—
333#1925—611no—
334#1880—611no—
335#1878—611no—
336#1805—611no—
337C4×C4⋊C8—611no—
338C4×#103—611no—
339C4×#102—611no—
340C2×C61C4×#12111yescharacteristic
341C2×C61C4×#13511yescharacteristic
342C2×C61C4×#13711yescharacteristic
343C2×C61C2×#46411yescharacteristic
344C2×C61#303511yescharacteristic
345C2×C61#310211yescharacteristic
346C2×C61#310811yescharacteristic
347D61—82no—
348C22×Q16C2×D6111yescharacteristic
349C22×SD16—611no—
350C2×#124—611no—
351C2×C4×Q8—611no—
352C2×C4×Q8—611no—
353C2×C4×Q8C2×D6111yescharacteristic
354C2×C4×Q8C2×D6111yescharacteristic
355C2×C4×D4—611no—
356#464—618no—
357C4×Q16—24no—
358C4×SD16—1224no—
359C2×#107C2×D6111yescharacteristic
360C2×#106—611no—
361C2×C4⋊C8—611no—
362C2×C4⋊C8—611no—
363C2×#103—611no—
364C2×#103—611no—
365C2×#103—611no—
366C2×#103C2×D6111yescharacteristic
367C2×#103C2×D6111yescharacteristic
368C2×#102—611no—
369C2×#102—611no—
370C2×#102—611no—
371C2×C4×C8—611no—
372C2×C4×C8C2×D6111yescharacteristic
373#391—611no—
374#390—611no—
375#388—1221no—
376#388—1221no—
377#382—611no—
378C4×C4⋊C4—611no—
379C4×C4⋊C4—611no—
380C4×C4⋊C4—611no—
381C4×C4⋊C4—1221no—
382C4×C4⋊C4—1221no—
383C4×C4⋊C4—1221no—
384C4×C22⋊C4—1221no—
385C4×C22⋊C4—1221no—
386C43—611no—
387C43—1221no—
388#340—611no—
389#340—611no—
390#340—611no—
391#340—611no—
392#336—611no—
393#336—611no—
394C61C4×#46411yescharacteristic, complemented, Sylow
395C22×Q8C22×D6111yescharacteristic
396C22×Q8C22×D6111yescharacteristic
397C22×D4—611no—
398C23×C4—1221no—
399C2×Q16—22no—
400C2×Q16—22no—
401C2×Q16C4×D6114yescomplemented
402C2×SD16—614no—
403C2×SD16—1222no—
404C2×SD16—1222no—
405C22×C8—611no—
406C22×C8—611no—
407C22×C8C22×D6111yescharacteristic
408C22×C8C22×D6111yescharacteristic
409#124—614no—
410#124—1222no—
411C4×Q8—22no—
412C4×Q8—22no—
413C4×Q8—22no—
414C4×Q8—614no—
415C4×Q8—1222no—
416C4×Q8—1222no—
417C4×Q8—1222no—
418C4×Q8C22⋊D6114yes—
419C4×D4—1222no—
420C4×D4—1222no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—611no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—611no—
426C2×C4⋊C4—1221no—
427C2×C4⋊C4—1221no—
428C2×C4⋊C4C22×D6111yescharacteristic
429C2×C4⋊C4C22×D6111yescharacteristic
430C2×C22⋊C4—1221no—
431C2×C22⋊C4—1221no—
432C2×C22⋊C4—1221no—
433C2×C22⋊C4—1221no—
434C2×C22⋊C4—1221no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—611no—
441C2×C42—611no—
442C2×C42—611no—
443C2×C42—1221no—
444C2×C42—1221no—
445C2×C42—1221no—
446C2×C42—1221no—
447C2×C42—1221no—
448C2×C42C22×D6111yescharacteristic
449#107—22no—
450#106—1222no—
451C4⋊C8—614no—
452C4⋊C8—1222no—
453#103—22no—
454#103—22no—
455#103—614no—
456#103—1222no—
457#103—1222no—
458#102—614no—
459#102—1222no—
460#102—1222no—
461C4×C8—22no—
462C4×C8—1222no—
463#95—1221no—
464#95—1221no—
465#95—1221no—
466#95—1221no—
467#95—1221no—
468#95—1221no—
469#95—1221no—
470C24—1221no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8C2×C4×D6112yes—
480C2×Q8C2×C4×D6112yes—
481C2×Q8#1175822212yes—
482C2×Q8C2×C22⋊D6112yes—
483C2×D4—612no—
484C2×D4—1221no—
485C2×D4—1221no—
486C2×D4—1221no—
487C2×D4—1221no—
488C2×D4—1221no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—611no—
494C22×C4—611no—
495C22×C4—611no—
496C22×C4—611no—
497C22×C4—1221no—
498C22×C4—1221no—
499C22×C4—1221no—
500C22×C4—2442no—
501C22×C4—2442no—
502C22×C4—2442no—
503C22×C4D4×D6111yescharacteristic
504C22×C4D4×D6111yescharacteristic
505C22×C4C23×D6111yescharacteristic
506Q16—28no—
507SD16—1228no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—612no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—1221no—
518C2×C8—1221no—
519C2×C8C2×C4×D6112yes—
520C4⋊C4—21no—
521C4⋊C4—24no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—42no—
525C4⋊C4—612no—
526C4⋊C4—612no—
527C4⋊C4—1224no—
528C4⋊C4—1224no—
529C4⋊C4—1221no—
530C4⋊C4—1221no—
531C4⋊C4—1221no—
532C4⋊C4—1221no—
533C4⋊C4C2×C22⋊D6112yes—
534C22⋊C4—1224no—
535C22⋊C4—1224no—
536C22⋊C4—2442no—
537C22⋊C4—2442no—
538C22⋊C4—2442no—
539C42—24no—
540C42—42no—
541C42—612no—
542C42—612no—
543C42—1222no—
544C42—1224no—
545C42—1224no—
546C42—1222no—
547C42—1221no—
548C42—1221no—
549C42—1222no—
550C42—2441no—
551C42—2442no—
552C42—2442no—
553C42—2442no—
554C42#1175822412yes—
555C42C2×C22⋊D6112yes—
556C23—1222no—
557C23—2441no—
558C23—2441no—
559C23—2441no—
560C23—2441no—
561C23—2441no—
562C23—2441no—
563C23C2×D4×D6111yescharacteristic
564Q8—22no—
565Q8—22no—
566Q8—22no—
567Q8—22no—
568Q8—22no—
569Q8—41no—
570Q8—41no—
571Q8C4×C22⋊D6114yes—
572D4—1222no—
573D4—1222no—
574D4—2441no—
575D4—2441no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—612no—
591C2×C4—612no—
592C2×C4—612no—
593C2×C4—1221no—
594C2×C4—1221no—
595C2×C4—1221no—
596C2×C4—1221no—
597C2×C4—1221no—
598C2×C4—1221no—
599C2×C4—1222no—
600C2×C4—1222no—
601C2×C4—1221no—
602C2×C4—1221no—
603C2×C4—1221no—
604C2×C4—4884no—
605C2×C4—2441no—
606C2×C4—2441no—
607C2×C4—2441no—
608C2×C4—2441no—
609C2×C4—2441no—
610C2×C4—2441no—
611C2×C4—2441no—
612C2×C4#1451974912yes—
613C2×C4#1451974912yes—
614C2×C4#1451980012yes—
615C2×C4#1451980912yes—
616C2×C4C22×C4×D6111yescharacteristic
617C2×C4C22×C22⋊D6111yescharacteristic
618C2×C4#41×D6111yescharacteristic
619C2×C4#41×D6111yescharacteristic
620C2×C4C2×#1175822411yescharacteristic
621C2×C4C2×#1175822211yescharacteristic
622C8—22no—
623C8—41no—
624C8—1222no—
625C8—2441no—
626C22—4881no—
627C22—4881no—
628C22—4881no—
629C22—4881no—
630C22—2442no—
631C22—2442no—
632C22—2442no—
633C22C4×D4×D6111yescharacteristic
634C22C2×#1451974911yescharacteristic
635C22#1684027111yescharacteristic
636C22#135×D6111yescharacteristic
637C22C2×#1451980011yescharacteristic
638C22C2×#1451980911yescharacteristic
639C22#1684055911yescharacteristic
640C4—24no—
641C4—22no—
642C4—42no—
643C4—42no—
644C4—81no—
645C4—1222no—
646C4—1222no—
647C4—1222no—
648C4—4881no—
649C4—2441no—
650C4—2442no—
651C4—2442no—
652C4#1683998614yesdirect product factor
653C4C2×C4×C22⋊D6111yescharacteristic
654C4C4×#1175822411yescharacteristic
655C4#1684029211yescharacteristic
656C4#1684030811yescharacteristic
657C2—4882no—
658C2C4×#1451974911yescharacteristic
659C2C4×#1451980011yescharacteristic
660C2C4×#1451980911yescharacteristic
661C2C2×#1683998611yescharacteristic
662C2#2145527011yescharacteristic
663C2#2145584311yescharacteristic
664C2#2145590311yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C4×Q16×C61C2
socleC23×C61C22×D4
prime radicalC22×D244C23
cosocleC22×C4×C61C24
hypercenterC2×C4×Q16D61
hypocenterC61C4×#464
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
4. C4×Q8×Dic61C2semidirect
6. #21446584C2semidirect
7. #21446456C2semidirect
10. #21446162C2semidirect
11. #21445832C2semidirect
12. C4×#14519706C2semidirect
13. C4×#14519701C2semidirect
15. C2×C4×Q16×C61C2semidirect
21. #16839986C4direct (N × H)
74. Q8×Dic61C2×C4semidirect
100. #14519706C2×C4semidirect
103. #14519701C2×C4semidirect
119. C2×Q16×C61C2×C4semidirect
313. C4×C61#464semidirect
326. C2×C4×Q16D61semidirect
394. C61C4×#464semidirect
401. C2×Q16C4×D61semidirect
652. C4#16839986direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168399862
C2×C4×#117582012
C4×#145197662
C4×Q8×Dic612
#214467482
#214465842
#214464562
#214464382
#214461722
#214461622
#214458322
C4×#145197062
C4×#145197012
C4×#145196992
C2×C4×Q16×C612
C4×#46461