Finite Group Databasebeta

← C4×#16840150 #29688553

Subgroups — C4×#16840150 #29688553

Order 15616.

1262 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×#16840150C211yesmaximal, characteristic
2C2×C4×#11758190C211yesmaximal, characteristic, complemented
3C2×C4×#11758200C211yesmaximal, characteristic, complemented
4C2×C4×#11758199C211yesmaximal, characteristic, complemented
5C4×#14519773C211yesmaximal, characteristic, complemented
6C4×#14519764C211yesmaximal, characteristic, complemented
7#21446701C211yesmaximal, characteristic, complemented
8#21446698C211yesmaximal, characteristic, complemented
9#21446696C211yesmaximal, characteristic, complemented
10#21446692C211yesmaximal, characteristic, complemented
11#21446641C211yesmaximal, characteristic, complemented
12#21446634C211yesmaximal, characteristic, complemented
13#21445986C211yesmaximal, characteristic, complemented
14C4×#14519687C211yesmaximal, characteristic, complemented
15C2×C4×D8×C61C211yesmaximal, characteristic, complemented
16C22×#11758190C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C2×#14519773C2211yescharacteristic
20C2×#14519764C2211yescharacteristic
21C2×C4×Dic122C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23C2×C4×C22⋊D61—22no—
24#16840150C418yesdirect product factor
25C4×#11758190—24no—
26C4×#11758200—24no—
27C4×#11758199—24no—
28C2×#14519710C2211yescharacteristic
29C2×#14519709C2211yescharacteristic
30C2×#14519708C2211yescharacteristic
31C2×#14519702C2211yescharacteristic
32C2×#14519700C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519687C2211yescharacteristic
38C2×#14519687C2211yescharacteristic
39C2×#14519687C2211yescharacteristic
40C2×#14519687C2211yescharacteristic
41C2×C4×#92418C2211yescharacteristic
42#16839667C2211yescharacteristic
43#16839665C2211yescharacteristic
44#16839665C2211yescharacteristic
45#16839663C2211yescharacteristic
46#16839662—22no—
47#16839656—22no—
48#16839631C2211yescharacteristic
49#16839627C2211yescharacteristic
50C4×C22⋊Dic61—22no—
51C42×Dic61C2211yescharacteristic
52C22×D8×C61C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic
55C4×D8×C61—24no—
56C2×#107×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×C4×C8×C61C2211yescharacteristic
60C22×Dic122C2311yescharacteristic
61C22×D244C2311yescharacteristic
62C22×C22⋊D61—22no—
63C22×C4×D61—21no—
64C2×#11758190—22no—
65C2×#11758190—22no—
66C2×#11758190C2×C414yescomplemented
67C2×#11758200—22no—
68C2×#11758200—22no—
69C2×#11758200C2×C414yescomplemented
70C2×#11758199—22no—
71C2×#11758199—22no—
72C2×#11758199C2×C414yescomplemented
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75#14519773—22no—
76#14519773C2×C414yescomplemented
77#14519764—22no—
78#14519764C2×C414yescomplemented
79C4×Dic122—22no—
80C4×Dic122—22no—
81C4×D244—22no—
82C4×D244—22no—
83C4×C22⋊D61—48no—
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×#11758196—21no—
87C2×#11758196—22no—
88C2×C22⋊Dic61—22no—
89C2×C22⋊Dic61—22no—
90C2×C22⋊Dic61—22no—
91C2×#11758198—21no—
92C2×#11758198—22no—
93C2×C4×Dic61—21no—
94C2×C4×Dic61D412yes—
95C2×C4×Dic61D412yes—
96C2×C4×Dic61C2311yescharacteristic
97C2×C4×Dic61C2311yescharacteristic
98#14519710—22no—
99#14519709—22no—
100#14519708—22no—
101#14519702—22no—
102#14519700—22no—
103#14519699—22no—
104#14519698—22no—
105#14519698—22no—
106#14519697—22no—
107#14519687—22no—
108#14519687—22no—
109#14519687—22no—
110#14519687C2×C414yescomplemented
111C4×#92418D414yescomplemented
112#14519684—22no—
113#14519684—22no—
114C22×D4×C61C2311yescharacteristic
115C22×D4×C61C2311yescharacteristic
116C23×C4×C61—21no—
117C23×C4×C61—21no—
118C2×D8×C61—22no—
119C2×D8×C61—22no—
120C2×D8×C61C2×C414yescomplemented
121C22×C8×C61C2311yescharacteristic
122C22×C8×C61C2311yescharacteristic
123C4×D4×C61—22no—
124C4×D4×C61—22no—
125C4×D4×C61—22no—
126C4×D4×C61—22no—
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C42×C61C2311yescharacteristic
132#107×C61—22no—
133#102×C61—22no—
134#102×C61—22no—
135C4×C8×C61D414yescomplemented
136C24×C61—21no—
137C24×C61—21no—
138C23×D61—21no—
139C2×D4×C61—21no—
140C2×D4×C61—21no—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61C22×C412yes—
150C2×D4×C61C22×C412yes—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—42no—
154C22×C4×C61—42no—
155C22×C4×C61—44no—
156C22×C4×C61—44no—
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2411yescharacteristic
160C2×C22⋊D61—28no—
161C2×C22⋊D61—44no—
162C2×C22⋊D61—44no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61C2×D412yes—
167C22×Dic61C2×D412yes—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—21no—
172C2×D244—21no—
173C2×D244C22×C412yes—
174C2×C4×D61—42no—
175C2×C4×D61—44no—
176C2×Dic122—21no—
177C2×Dic122—21no—
178C2×Dic122—21no—
179C2×Dic122—21no—
180C2×Dic122—21no—
181C2×Dic122C22×C412yes—
182D8×C61—28no—
183C2×C8×C61—21no—
184C2×C8×C61—21no—
185C2×C8×C61C22×C412yes—
186C2×C8×C61C2×D412yes—
187C2×C8×C61C2×D412yes—
188C2×C8×C61#4112yes—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C22⋊C4×C61—42no—
194C22⋊C4×C61—42no—
195C42×C61C2×D412yes—
196C42×C61C2×D412yes—
197C22⋊Dic61—28no—
198C22⋊Dic61—44no—
199C22⋊Dic61—44no—
200#11758200—28no—
201#11758199—28no—
202#11758198—44no—
203#11758198—42no—
204C4⋊Dic61—21no—
205C4⋊Dic61—21no—
206C4⋊Dic61—21no—
207C4⋊Dic61—21no—
208#11758196—44no—
209#11758196—42no—
210C4×Dic61—24no—
211C4×Dic61—21no—
212C4×Dic61—21no—
213C4×Dic61—42no—
214C4×Dic61—42no—
215C4×Dic61C22×C412yes—
216C4×Dic61#4112yes—
217C2×#92418—21no—
218C2×#92418—21no—
219C2×#92418C22×C412yes—
220C2×#92418C2×D412yes—
221C2×#92418C2×D412yes—
222C2×#92418#4112yes—
223#11758190—28no—
224C23×C61—22no—
225C23×C61—22no—
226C23×C61—41no—
227C23×C61—41no—
228C23×C61—41no—
229C23×C61—41no—
230C23×C61—42no—
231C23×C61—42no—
232C23×C61—42no—
233C23×C61—42no—
234C23×C61C22×D411yescharacteristic
235C22×D61—22no—
236C22×D61—41no—
237C22×D61—41no—
238C22×D61—42no—
239C22×D61—42no—
240D4×C61—22no—
241D4×C61—22no—
242D4×C61—22no—
243D4×C61—22no—
244D4×C61—41no—
245D4×C61—41no—
246D4×C61—41no—
247D4×C61—41no—
248C2×C4×C61—22no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—42no—
252C2×C4×C61—42no—
253C2×C4×C61—84no—
254C2×C4×C61—84no—
255C2×C4×C61#12712yes—
256C2×C4×C61#12712yes—
257C2×C4×C61AGL(1,ℤ/8)14yes—
258C2×C4×C61C23×C411yescharacteristic
259C2×C4×C61C22×D411yescharacteristic
260C2×C4×C61C22×D411yescharacteristic
261C2×C4×C61C2×#4111yescharacteristic
262C2×C4×C61C2×#4111yescharacteristic
263C2×C4×C61C2×#4111yescharacteristic
264C22⋊D61—416no—
265C2×Dic61—22no—
266C2×Dic61—22no—
267C2×Dic61—22no—
268C2×Dic61—22no—
269C2×Dic61—22no—
270C2×Dic61—22no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275C2×Dic61—42no—
276C2×Dic61—42no—
277C2×Dic61C4×D414yes—
278D244—22no—
279D244—22no—
280D244—41no—
281D244—41no—
282C4×D61—84no—
283Dic122—22no—
284Dic122—22no—
285Dic122—41no—
286Dic122—41no—
287C8×C61—22no—
288C8×C61C4×D414yescomplemented
289#92418—22no—
290#92418C4×D414yescomplemented
291C4×#496—611nomaximal, Sylow
292C22×C61—42no—
293C22×C61—42no—
294C22×C61—44no—
295C22×C61—44no—
296C22×C61—81no—
297C22×C61—81no—
298C22×C61—81no—
299C22×C61—81no—
300C22×C61—82no—
301C22×C61—82no—
302C22×C61C2×C4×D411yescharacteristic
303C22×C61C2×#12711yescharacteristic
304C22×C61#53211yescharacteristic
305C22×C61C2×AGL(1,ℤ/8)12yes—
306C22×C61#57512yes—
307C2×D61—42no—
308C2×D61—44no—
309C2×D61—81no—
310C2×D61—81no—
311C2×D61—82no—
312C4×C61—22no—
313C4×C61—81no—
314C4×C61—81no—
315C4×C61#49614yescomplemented
316C4×C61C2×C4×D411yescharacteristic
317C4×C61C2×C4×D411yescharacteristic
318C4×C61#53211yescharacteristic
319C4×C61#53211yescharacteristic
320Dic61—24no—
321Dic61—42no—
322Dic61—42no—
323Dic61—81no—
324Dic61—81no—
325C2×#496—611no—
326C2×C4×SD16—611no—
327C2×C4×SD16—611no—
328C2×C4×D8—611no—
329C2×C4×D8D6111yescharacteristic, complemented
330C4×#127—611no—
331C4×#124—611no—
332#1973—611no—
333#1973—611no—
334#1972—611no—
335#1972—611no—
336#1961—611no—
337#1959—611no—
338#1847—611no—
339C4×#97—611no—
340C2×C61—82no—
341C2×C61—82no—
342C2×C61C4×#12711yescharacteristic
343C2×C61C4×AGL(1,ℤ/8)12yes—
344C2×C61C2×#49611yescharacteristic
345C2×C61#315011yescharacteristic
346C2×C61#317112yes—
347D61—82no—
348C22×SD16—611no—
349C22×SD16—611no—
350C22×D8—611no—
351C22×D8C2×D6111yescharacteristic
352C2×#127—611no—
353C2×#124—611no—
354C2×C4×Q8—611no—
355C2×C4×D4—611no—
356C2×C4×D4—1222no—
357C2×C4×D4C2×D6111yescharacteristic
358C2×C4×D4C2×D6111yescharacteristic
359#496—618no—
360C4×SD16—1224no—
361C4×SD16—1224no—
362C4×D8—24no—
363C4×D8—1224no—
364C2×#107—611no—
365C2×#107C2×D6111yescharacteristic
366C2×#106—611no—
367C2×#106—611no—
368C2×#103—611no—
369C2×#103—611no—
370C2×#102—611no—
371C2×#102—611no—
372C2×#102—611no—
373C2×#102—611no—
374C2×#102C2×D6111yescharacteristic
375C2×#102C2×D6111yescharacteristic
376C2×#97—611no—
377C2×#97—611no—
378C2×#97—611no—
379C2×#97—611no—
380C2×C4×C8—611no—
381C2×C4×C8C2×D6111yescharacteristic
382#391—611no—
383#390—611no—
384#390—611no—
385#390—611no—
386#390—1222no—
387#388—1222no—
388#384—611no—
389#382—611no—
390C4×C22⋊C4—1222no—
391C43—611no—
392C61C4×#49611yescharacteristic, complemented, Sylow
393C22×Q8—611no—
394C22×D4—611no—
395C22×D4—1222no—
396C22×D4C22×D6111yescharacteristic
397C22×D4C22×D6111yescharacteristic
398C23×C4—21no—
399C23×C4—21no—
400C23×C4—1221no—
401C2×SD16—614no—
402C2×SD16—614no—
403C2×SD16—1222no—
404C2×SD16—1222no—
405C2×SD16—1222no—
406C2×SD16—1222no—
407C2×D8—22no—
408C2×D8—22no—
409C2×D8—614no—
410C2×D8—1222no—
411C2×D8—1222no—
412C2×D8C4×D6114yescomplemented
413C22×C8—611no—
414C22×C8—611no—
415C22×C8C22×D6111yescharacteristic
416C22×C8C22×D6111yescharacteristic
417#127—614no—
418#127—1222no—
419#124—614no—
420#124—1222no—
421C4×Q8—1222no—
422C4×Q8—1222no—
423C4×D4—22no—
424C4×D4—22no—
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—1222no—
428C4×D4—1222no—
429C4×D4—2448no—
430C2×C4⋊C4—611no—
431C2×C4⋊C4—611no—
432C2×C4⋊C4—1222no—
433C2×C4⋊C4—1221no—
434C2×C4⋊C4C22×D6111yescharacteristic
435C2×C4⋊C4C22×D6111yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—1222no—
439C2×C22⋊C4—1222no—
440C2×C22⋊C4—1222no—
441C2×C22⋊C4—1222no—
442C2×C22⋊C4—1221no—
443C2×C42—611no—
444C2×C42—612no—
445C2×C42—611no—
446C2×C42—612no—
447C2×C42—1221no—
448C2×C42C22×D6111yescharacteristic
449#107—22no—
450#107—1222no—
451#106—1222no—
452#106—1222no—
453#103—1222no—
454#103—1222no—
455#102—22no—
456#102—22no—
457#102—1222no—
458#102—1222no—
459#102—1222no—
460#102—1222no—
461#97—614no—
462#97—1222no—
463#97—1222no—
464#97—1222no—
465C4×C8—614no—
466C4×C8C22⋊D6114yescomplemented
467#95—1222no—
468#95—1222no—
469C24—21no—
470C24—21no—
471C24—1221no—
472C2×Q8—612no—
473C2×Q8—1221no—
474C2×Q8—1221no—
475C2×Q8—1221no—
476C2×Q8—1221no—
477C2×Q8—1221no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—612no—
489C2×D4—1228no—
490C2×D4—1221no—
491C2×D4—1221no—
492C2×D4—1221no—
493C2×D4—1221no—
494C2×D4—1221no—
495C2×D4—2444no—
496C2×D4—2444no—
497C2×D4C2×C4×D6112yes—
498C2×D4C2×C4×D6112yes—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—44no—
504C22×C4—44no—
505C22×C4—612no—
506C22×C4—612no—
507C22×C4—1221no—
508C22×C4—1221no—
509C22×C4—1221no—
510C22×C4—2442no—
511C22×C4—2444no—
512C22×C4D4×D6111yescharacteristic
513C22×C4D4×D6111yescharacteristic
514C22×C4C23×D6111yescharacteristic
515SD16—1228no—
516SD16—1228no—
517D8—28no—
518D8—1228no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—612no—
522C2×C8—612no—
523C2×C8—612no—
524C2×C8—612no—
525C2×C8—1221no—
526C2×C8—1221no—
527C2×C8C2×C4×D6112yes—
528C2×C8#1175822212yes—
529C2×C8C2×C22⋊D6112yes—
530C2×C8C2×C22⋊D6112yes—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—1221no—
536C4⋊C4—1221no—
537C4⋊C4—1221no—
538C4⋊C4—1221no—
539C4⋊C4—2444no—
540C4⋊C4—2442no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—1228no—
544C22⋊C4—2444no—
545C22⋊C4—2444no—
546C22⋊C4—2444no—
547C22⋊C4—2442no—
548C42—612no—
549C42—612no—
550C42—1221no—
551C42—1221no—
552C42—1224no—
553C42—2442no—
554C42—2442no—
555C42D4×D6112yes—
556C42C2×C22⋊D6112yes—
557C23—22no—
558C23—22no—
559C23—42no—
560C23—42no—
561C23—41no—
562C23—41no—
563C23—42no—
564C23—42no—
565C23—41no—
566C23—41no—
567C23—1222no—
568C23—2442no—
569C23—2441no—
570C23—2442no—
571C23—2441no—
572C23C2×D4×D6111yescharacteristic
573Q8—1222no—
574Q8—1222no—
575Q8—2441no—
576Q8—2441no—
577D4—22no—
578D4—22no—
579D4—22no—
580D4—22no—
581D4—41no—
582D4—41no—
583D4—41no—
584D4—41no—
585D4—1222no—
586D4—1222no—
587D4—24416no—
588D4—2441no—
589D4—2441no—
590C2×C4—22no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—84no—
596C2×C4—84no—
597C2×C4—614no—
598C2×C4—1222no—
599C2×C4—1222no—
600C2×C4—1222no—
601C2×C4—1222no—
602C2×C4—1222no—
603C2×C4—1222no—
604C2×C4—4884no—
605C2×C4—2442no—
606C2×C4—2441no—
607C2×C4—2441no—
608C2×C4—2442no—
609C2×C4—2441no—
610C2×C4—2441no—
611C2×C4#1451977312yes—
612C2×C4#1451977312yes—
613C2×C4#1451980114yes—
614C2×C4C22×C4×D6111yescharacteristic
615C2×C4C2×D4×D6111yescharacteristic
616C2×C4C22×C22⋊D6111yescharacteristic
617C2×C4#41×D6111yescharacteristic
618C2×C4#41×D6111yescharacteristic
619C2×C4C2×#1175822211yescharacteristic
620C8—22no—
621C8—614no—
622C8—1222no—
623C8C4×C22⋊D6114yescomplemented
624C22—44no—
625C22—44no—
626C22—42no—
627C22—42no—
628C22—82no—
629C22—82no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22—81no—
634C22—4882no—
635C22—4881no—
636C22—4881no—
637C22—2444no—
638C22—2442no—
639C22C4×D4×D6111yescharacteristic
640C22C2×#1451977311yescharacteristic
641C22#1684030911yescharacteristic
642C22C2×#1451980112yes—
643C22#1684055912yes—
644C4—22no—
645C4—81no—
646C4—81no—
647C4—1224no—
648C4—4881no—
649C4—4881no—
650C4—2442no—
651C4—2442no—
652C4#1684015014yesdirect product factor
653C4C4×D4×D6111yescharacteristic
654C4C2×C4×C22⋊D6111yescharacteristic
655C4#1684030811yescharacteristic
656C4#1684030911yescharacteristic
657C2—82no—
658C2—82no—
659C2—4882no—
660C2C4×#1451977311yescharacteristic
661C2C4×#1451980112yes—
662C2C2×#1684015011yescharacteristic
663C2#2145626211yescharacteristic
664C2#2145641212yes—
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C4×D8×C61C2
socleC23×C61C22×D4
prime radicalC2×#16840150C2
cosocleC22×C4×C61C24
hypercenterC2×C4×D8D61
hypocenterC61C4×#496
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11758190C2semidirect
3. C2×C4×#11758200C2semidirect
4. C2×C4×#11758199C2semidirect
5. C4×#14519773C2semidirect
6. C4×#14519764C2semidirect
7. #21446701C2semidirect
8. #21446698C2semidirect
9. #21446696C2semidirect
10. #21446692C2semidirect
11. #21446641C2semidirect
12. #21446634C2semidirect
13. #21445986C2semidirect
14. C4×#14519687C2semidirect
15. C2×C4×D8×C61C2semidirect
24. #16840150C4direct (N × H)
66. C2×#11758190C2×C4semidirect
69. C2×#11758200C2×C4semidirect
72. C2×#11758199C2×C4semidirect
76. #14519773C2×C4semidirect
78. #14519764C2×C4semidirect
110. #14519687C2×C4semidirect
111. C4×#92418D4semidirect
120. C2×D8×C61C2×C4semidirect
135. C4×C8×C61D4semidirect
288. C8×C61C4×D4semidirect
290. #92418C4×D4semidirect
315. C4×C61#496semidirect
329. C2×C4×D8D61semidirect
392. C61C4×#496semidirect
412. C2×D8C4×D61semidirect
466. C4×C8C22⋊D61semidirect
623. C8C4×C22⋊D61semidirect
652. C4#16840150direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168401502
C2×C4×#117581902
C2×C4×#117582002
C2×C4×#117581992
C4×#145197732
C4×#145197642
#214467012
#214466982
#214466962
#214466922
#214466412
#214466342
#214459862
C4×#145196872
C2×C4×D8×C612
C4×#49661