Finite Group Databasebeta

← C4×#16839675 #29601818

Subgroups — C4×#16839675 #29601818

Order 15616.

2158 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic122C211yesmaximal, characteristic, complemented
2C2×#16839675C211yesmaximal, characteristic
3C2×C4×#11758198C211yesmaximal, characteristic
4C2×C4×#11758198C212yesmaximal
5#21444089C211yesmaximal, characteristic, complemented
6#21444076C211yesmaximal, characteristic, complemented
7#21444074C212yesmaximal, complemented
8#21444065C211yesmaximal, characteristic
9#21444063C212yesmaximal
10C4×#14519684C212yesmaximal, complemented
11C4×#95×C61C211yesmaximal, characteristic, complemented
12C23×Dic122C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C2×C4×Dic122—28no—
15C2×C4×Dic122—24no—
16C22×C4⋊Dic61C2211yescharacteristic
17C22×#11758196C2212yes—
18C22×#11758198C2211yescharacteristic
19C22×#11758198C2212yes—
20C22×#11758198C2212yes—
21C22×#11758198C2211yescharacteristic
22C22×C4×Dic61C2211yescharacteristic
23C22×C4×Dic61C2212yes—
24#16839675C418yesdirect product factor
25C4×#11758198—28no—
26C4×#11758198—24no—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2211yescharacteristic
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2211yescharacteristic
34C2×#14519684C2212yes—
35C22×C42×C61C2212yes—
36C22×C42×C61C2211yescharacteristic
37C2×#95×C61C2212yes—
38C2×#95×C61C2211yescharacteristic
39C2×#95×C61C2211yescharacteristic
40C24×D61C2311yescharacteristic
41C22×Dic122—22no—
42C22×Dic122—22no—
43C22×Dic122—24no—
44C22×Dic122—24no—
45C22×Dic122C2×C414yescomplemented
46C23×Dic61C2311yescharacteristic
47C23×Dic61C2312yes—
48C23×Dic61C2311yescharacteristic
49C23×Dic61C2311yescharacteristic
50C23×Dic61C2312yes—
51C22×C4×D61—22no—
52C22×C4×D61—24no—
53C22×C4×D61—24no—
54C22×C4×D61—22no—
55C22×C4×D61Q814yescomplemented
56C4×Dic122—232no—
57C2×C4⋊Dic61—22no—
58C2×C4⋊Dic61—24no—
59C2×#11758196—24no—
60C2×#11758196—24no—
61C2×#11758196—24no—
62C2×#11758198—22no—
63C2×#11758198—24no—
64C2×#11758198—22no—
65C2×#11758198—22no—
66C2×#11758198—24no—
67C2×#11758198—22no—
68C2×#11758198—24no—
69C2×#11758198—24no—
70C2×#11758198—22no—
71C2×#11758198—24no—
72C2×#11758198C2×C414yes—
73C2×#11758198C2×C418yes—
74C2×C4×Dic61—24no—
75C2×C4×Dic61—24no—
76C2×C4×Dic61—22no—
77C2×C4×Dic61—24no—
78C2×C4×Dic61D418yes—
79#14519684—22no—
80#14519684—22no—
81#14519684—24no—
82#14519684—24no—
83#14519684—24no—
84#14519684—24no—
85#14519684—24no—
86#14519684C2×C418yescomplemented
87C23×C4×C61C2312yes—
88C23×C4×C61C2311yescharacteristic
89C23×C4×C61C2312yes—
90C23×C4×C61C2311yescharacteristic
91C23×C4×C61C2311yescharacteristic
92C2×C42×C61—24no—
93C2×C42×C61—24no—
94C2×C42×C61—24no—
95C2×C42×C61—24no—
96C2×C42×C61D414yes—
97#95×C61—24no—
98#95×C61—22no—
99#95×C61C2×C414yescomplemented
100C24×C61C2411yescharacteristic
101C23×D61—22no—
102C23×D61—21no—
103C23×D61—21no—
104C23×D61—22no—
105C23×D61—22no—
106C23×D61—21no—
107C23×D61—21no—
108C23×D61—22no—
109C23×D61C22×C412yes—
110C23×D61C2×Q812yes—
111C23×D61#4112yes—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61—22no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—22no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—22no—
130C22×C4×C61C22×C414yes—
131C22×C4×C61C22×C412yes—
132C22×C4×C61C2×D412yes—
133C22×C4×C61C2×D412yes—
134C22×C4×C61C2×D412yes—
135C22×C4×C61C2×D414yes—
136C22×C4×C61C2×Q812yes—
137C22×C4×C61#4114yes—
138C22×C4×C61#4112yes—
139C22×C4×C61#4114yes—
140C22×C4×C61#4112yes—
141C22×Dic61—22no—
142C22×Dic61—22no—
143C22×Dic61—22no—
144C22×Dic61—22no—
145C22×Dic61—22no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—22no—
150C22×Dic61—22no—
151C22×Dic61—21no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61—21no—
160C22×Dic61—22no—
161C22×Dic61—22no—
162C22×Dic61—21no—
163C22×Dic61C22×C412yes—
164C22×Dic61C22×C414yes—
165C22×Dic61C2×D414yes—
166C22×Dic61C2×D414yes—
167C22×Dic61C2×Q812yes—
168C22×Dic61#4112yes—
169C22×Dic61#4114yes—
170C2×C4×D61—216no—
171C2×C4×D61—28no—
172C2×C4×D61—44no—
173C2×C4×D61—48no—
174C2×C4×D61—44no—
175C2×Dic122—216no—
176C2×Dic122—28no—
177C2×Dic122—28no—
178C2×Dic122—28no—
179C2×Dic122—216no—
180C42×C61—28no—
181C42×C61—48no—
182#11758198—216no—
183#11758198—28no—
184#11758198—28no—
185#11758198—216no—
186C4⋊Dic61—28no—
187#11758196—216no—
188C4×Dic61—216no—
189C4×Dic61—44no—
190C23×C61C23×C411yescharacteristic
191C23×C61C22×D412yes—
192C23×C61C22×D411yescharacteristic
193C23×C61C22×Q811yescharacteristic
194C23×C61C2×#4112yes—
195C23×C61C2×#4111yescharacteristic
196C23×C61C2×#4111yescharacteristic
197C23×C61C2×#4111yescharacteristic
198C23×C61C2×#4112yes—
199C23×C61C2×#4111yescharacteristic
200C23×C61C2×#4112yes—
201C22×D61—24no—
202C22×D61—22no—
203C22×D61—22no—
204C22×D61—24no—
205C22×D61—24no—
206C22×D61—22no—
207C22×D61—24no—
208C22×D61—22no—
209C22×D61—24no—
210C22×D61—22no—
211C22×D61—24no—
212C22×D61—22no—
213C22×D61—41no—
214C22×D61—42no—
215C22×D61—41no—
216C22×D61—42no—
217C22×D61—41no—
218C22×D61—42no—
219C22×D61—42no—
220C22×D61—42no—
221C22×D61—42no—
222C22×D61—41no—
223C22×D61C4×Q814yescomplemented
224C2×C4×C61—24no—
225C2×C4×C61—22no—
226C2×C4×C61—22no—
227C2×C4×C61—24no—
228C2×C4×C61—24no—
229C2×C4×C61—24no—
230C2×C4×C61—24no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—24no—
234C2×C4×C61—24no—
235C2×C4×C61—24no—
236C2×C4×C61—22no—
237C2×C4×C61—42no—
238C2×C4×C61—42no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61—42no—
246C2×C4×C61—42no—
247C2×C4×C61C4×D414yes—
248C2×C4×C61#12014yes—
249C2×C4×C61C22⋊Q818yes—
250C2×C4×C61C22⋊Q814yes—
251C2×C4×C61#12418yes—
252C2×C4×C61#12414yes—
253C2×Dic61—24no—
254C2×Dic61—24no—
255C2×Dic61—24no—
256C2×Dic61—24no—
257C2×Dic61—24no—
258C2×Dic61—24no—
259C2×Dic61—22no—
260C2×Dic61—24no—
261C2×Dic61—24no—
262C2×Dic61—24no—
263C2×Dic61—22no—
264C2×Dic61—24no—
265C2×Dic61—22no—
266C2×Dic61—24no—
267C2×Dic61—24no—
268C2×Dic61—41no—
269C2×Dic61—42no—
270C2×Dic61—42no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—42no—
275C2×Dic61—41no—
276C2×Dic61—42no—
277C2×Dic61—42no—
278C2×Dic61—42no—
279C2×Dic61—42no—
280C2×Dic61—41no—
281C2×Dic61C4×D418yes—
282C4×D61—416no—
283Dic122—232no—
284C4×#393—611nomaximal, Sylow
285C22×C61C2×C4×D412yes—
286C22×C61C2×C4×D411yescharacteristic
287C22×C61C2×C4×Q811yescharacteristic
288C22×C61C4×#4111yescharacteristic
289C22×C61C4×#4112yes—
290C22×C61C2×#12011yescharacteristic
291C22×C61C2×C22⋊Q812yes—
292C22×C61C2×C22⋊Q811yescharacteristic
293C22×C61#52512yes—
294C22×C61#52512yes—
295C22×C61#52511yescharacteristic
296C22×C61#52511yescharacteristic
297C22×C61C2×#12412yes—
298C22×C61C2×#12411yescharacteristic
299C22×C61#52912yes—
300C22×C61#52912yes—
301C22×C61#52912yes—
302C22×C61#52911yescharacteristic
303C22×C61#52912yes—
304C22×C61#53212yes—
305C22×C61#53211yescharacteristic
306C22×C61#53312yes—
307C22×C61#53311yescharacteristic
308C2×D61—28no—
309C2×D61—24no—
310C2×D61—42no—
311C2×D61—42no—
312C2×D61—42no—
313C2×D61—44no—
314C2×D61—42no—
315C2×D61—44no—
316C2×D61—42no—
317C2×D61—44no—
318C2×D61—42no—
319C4×C61—24no—
320C4×C61—42no—
321C4×C61—44no—
322C4×C61—44no—
323C4×C61#39318yescomplemented
324Dic61—28no—
325Dic61—42no—
326Dic61—44no—
327Dic61—42no—
328Dic61—42no—
329C22×C4×Q8—611no—
330C2×#393—611no—
331C2×C4×C22⋊C4—612no—
332C2×C4×C22⋊C4—611no—
333#1446—611no—
334#1442—612no—
335#1442—611no—
336#1439—612no—
337#1439—611no—
338C4×#95—612no—
339C4×#95D6111yescharacteristic, complemented
340C2×C61C4×#12011yescharacteristic
341C2×C61C4×C22⋊Q812yes—
342C2×C61C4×C22⋊Q811yescharacteristic
343C2×C61C4×#12412yes—
344C2×C61C4×#12411yescharacteristic
345C2×C61C2×#39311yescharacteristic
346C2×C61#238811yescharacteristic
347C2×C61#239611yescharacteristic
348C2×C61#239612yes—
349C2×C61#239811yescharacteristic
350C2×C61#239812yes—
351D61—44no—
352C23×Q8—611no—
353C24×C4—611no—
354C2×C4×Q8—1228no—
355C2×C4×Q8—1224no—
356C22×C4⋊C4—612no—
357C22×C4⋊C4—611no—
358C22×C22⋊C4—612no—
359C22×C22⋊C4—611no—
360C22×C22⋊C4—612no—
361C22×C22⋊C4—611no—
362C22×C42—612no—
363C22×C42—611no—
364C22×C42C2×D6112yes—
365C22×C42C2×D6111yescharacteristic
366#393—618no—
367C4×C22⋊C4—1228no—
368C4×C22⋊C4—1224no—
369C2×#95—612no—
370C2×#95—612no—
371C2×#95—612no—
372C2×#95—612no—
373C2×#95—612no—
374C2×#95—611no—
375C2×#95—612no—
376C2×#95—611no—
377C2×#95C2×D6112yes—
378C2×#95C2×D6111yescharacteristic
379C2×#95C2×D6111yescharacteristic
380C61C4×#39311yescharacteristic, complemented, Sylow
381C25—611no—
382C22×Q8—614no—
383C22×Q8—1224no—
384C22×Q8—1224no—
385C22×Q8—1222no—
386C22×Q8—1222no—
387C23×C4—612no—
388C23×C4—612no—
389C23×C4—611no—
390C23×C4—611no—
391C23×C4—611no—
392C23×C4—614no—
393C23×C4—1222no—
394C23×C4—1224no—
395C23×C4—1224no—
396C23×C4—1222no—
397C23×C4C22×D6112yes—
398C23×C4C22×D6111yescharacteristic
399C23×C4C22×D6112yes—
400C23×C4C22×D6111yescharacteristic
401C23×C4C22×D6111yescharacteristic
402C4×Q8—12232no—
403C2×C4⋊C4—1224no—
404C2×C4⋊C4—1224no—
405C2×C4⋊C4—1224no—
406C2×C4⋊C4—1224no—
407C2×C4⋊C4—1222no—
408C2×C22⋊C4—618no—
409C2×C22⋊C4—614no—
410C2×C22⋊C4—1224no—
411C2×C22⋊C4—1224no—
412C2×C22⋊C4—1224no—
413C2×C22⋊C4—1222no—
414C2×C22⋊C4—1224no—
415C2×C22⋊C4—1222no—
416C2×C22⋊C4—1222no—
417C2×C22⋊C4—1222no—
418C2×C22⋊C4—1224no—
419C2×C22⋊C4—1222no—
420C2×C42—24no—
421C2×C42—24no—
422C2×C42—24no—
423C2×C42—24no—
424C2×C42—618no—
425C2×C42—1224no—
426C2×C42—1224no—
427C2×C42—1222no—
428C2×C42—1224no—
429C2×C42D24414yes—
430#95—24no—
431#95—22no—
432#95—618no—
433#95—1224no—
434#95—1224no—
435#95—1224no—
436#95—1224no—
437#95—1222no—
438#95—1222no—
439#95—1224no—
440#95C4×D6114yescomplemented
441C24—612no—
442C24—612no—
443C24—612no—
444C24—1222no—
445C24—1221no—
446C24—1222no—
447C24—1221no—
448C24—1221no—
449C24—1221no—
450C24—1222no—
451C24—1222no—
452C24C23×D6111yescharacteristic
453C2×Q8—12216no—
454C2×Q8—1228no—
455C2×Q8—12216no—
456C2×Q8—1228no—
457C2×Q8—1228no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—614no—
477C22×C4—614no—
478C22×C4—614no—
479C22×C4—612no—
480C22×C4—614no—
481C22×C4—612no—
482C22×C4—612no—
483C22×C4—1222no—
484C22×C4—1222no—
485C22×C4—1222no—
486C22×C4—1222no—
487C22×C4—1222no—
488C22×C4—1222no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4—1222no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4—1222no—
496C22×C4—1221no—
497C22×C4—1221no—
498C22×C4—1222no—
499C22×C4—1222no—
500C22×C4—1222no—
501C22×C4—1222no—
502C22×C4—1221no—
503C22×C4—1222no—
504C22×C4—1222no—
505C22×C4—12216no—
506C22×C4—1228no—
507C22×C4—2444no—
508C22×C4—2448no—
509C22×C4—2444no—
510C22×C4C2×C4×D6114yes—
511C22×C4C2×C4×D6112yes—
512C22×C4C2×D24412yes—
513C22×C4C2×D24412yes—
514C22×C4C2×D24412yes—
515C22×C4#1175822214yes—
516C22×C4#1175822212yes—
517C22×C4#1175822214yes—
518C22×C4D4×D6114yes—
519C22×C4#1175822412yes—
520C22×C4Q8×D6112yes—
521C4⋊C4—12216no—
522C4⋊C4—1228no—
523C22⋊C4—12216no—
524C22⋊C4—12216no—
525C22⋊C4—1228no—
526C22⋊C4—1228no—
527C42—28no—
528C42—48no—
529C42—12216no—
530C42—2444no—
531C23—614no—
532C23—1224no—
533C23—1222no—
534C23—1222no—
535C23—1224no—
536C23—1224no—
537C23—1222no—
538C23—1224no—
539C23—1222no—
540C23—1224no—
541C23—1222no—
542C23—1224no—
543C23—1222no—
544C23—2441no—
545C23—2442no—
546C23—2441no—
547C23—2442no—
548C23—2441no—
549C23—2442no—
550C23—2442no—
551C23—2442no—
552C23—2442no—
553C23—2441no—
554C23C22×C4×D6111yescharacteristic
555C23C2×D4×D6112yes—
556C23C22×D24411yescharacteristic
557C23C2×Q8×D6111yescharacteristic
558C23#41×D6112yes—
559C23#41×D6111yescharacteristic
560C23#41×D6111yescharacteristic
561C23C2×#1175822411yescharacteristic
562C23C2×#1175822211yescharacteristic
563C23C2×#1175822212yes—
564C23C2×#1175822212yes—
565Q8—12232no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—618no—
590C2×C4—1224no—
591C2×C4—1224no—
592C2×C4—1224no—
593C2×C4—1224no—
594C2×C4—1224no—
595C2×C4—1224no—
596C2×C4—1222no—
597C2×C4—1224no—
598C2×C4—1224no—
599C2×C4—1224no—
600C2×C4—1222no—
601C2×C4—1224no—
602C2×C4—1222no—
603C2×C4—1224no—
604C2×C4—1224no—
605C2×C4—2441no—
606C2×C4—2442no—
607C2×C4—2442no—
608C2×C4—2441no—
609C2×C4—2442no—
610C2×C4—2441no—
611C2×C4—2441no—
612C2×C4—2441no—
613C2×C4—2442no—
614C2×C4—2442no—
615C2×C4—2442no—
616C2×C4—2442no—
617C2×C4—2441no—
618C2×C4—24416no—
619C2×C4C4×D24414yes—
620C2×C4#1451974714yes—
621C2×C4#1451975518yes—
622C2×C4#1451975714yes—
623C2×C4#1451976318yes—
624C2×C4#1451976514yes—
625C22—1228no—
626C22—1224no—
627C22—2442no—
628C22—2442no—
629C22—2442no—
630C22—2442no—
631C22—2444no—
632C22—2442no—
633C22—2444no—
634C22—2444no—
635C22—2442no—
636C22C4×D4×D6112yes—
637C22C2×C4×D24411yescharacteristic
638C22C4×Q8×D6111yescharacteristic
639C22C4×#1175822411yescharacteristic
640C22C4×#1175822212yes—
641C22C2×#1451974711yescharacteristic
642C22C2×#1451975512yes—
643C22C2×#1451975711yescharacteristic
644C22#1684027112yes—
645C22#1684027112yes—
646C22#1684027411yescharacteristic
647C22#1684027411yescharacteristic
648C22C2×#1451976312yes—
649C22C2×#1451976511yescharacteristic
650C22#1684029012yes—
651C22#1684029012yes—
652C22#1684029212yes—
653C22#1684029411yescharacteristic
654C22#1684029612yes—
655C22#1684030912yes—
656C22#1684031211yescharacteristic
657C22#1684031612yes—
658C22#1684031611yescharacteristic
659C4—24no—
660C4—42no—
661C4—44no—
662C4—44no—
663C4—1228no—
664C4—2442no—
665C4—2444no—
666C4—2442no—
667C4—2442no—
668C4#1683967518yesdirect product factor
669C2—2444no—
670C2C4×#1451974711yescharacteristic
671C2C4×#1451975512yes—
672C2C4×#1451975711yescharacteristic
673C2C4×#1451976312yes—
674C2C4×#1451976511yescharacteristic
675C2C2×#1683967511yescharacteristic
676C2#2144903511yescharacteristic
677C2#2144909111yescharacteristic
678C2#2144909512yes—
679C2#2144910511yescharacteristic
680C2#2144910612yes—
subgroupG/H
centerC23×C4C22×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC4×#95×C61C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenterC4×#95D61
hypocenterC61C4×#393
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
1. C22×C4×Dic122C2semidirect
5. #21444089C2semidirect
6. #21444076C2semidirect
7. #21444074C2semidirect
10. C4×#14519684C2semidirect
11. C4×#95×C61C2semidirect
24. #16839675C4direct (N × H)
45. C22×Dic122C2×C4semidirect
55. C22×C4×D61Q8semidirect
86. #14519684C2×C4semidirect
99. #95×C61C2×C4semidirect
223. C22×D61C4×Q8semidirect
323. C4×C61#393semidirect
339. C4×#95D61semidirect
380. C61C4×#393semidirect
440. #95C4×D61semidirect
668. C4#16839675direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Dic1222
C2×#168396752
C2×C4×#117581982
#214440892
#214440762
#214440742
#214440652
#214440632
C4×#145196842
C4×#95×C612
C4×#39361