Finite Group Databasebeta

← C4×#16840105 #29687185

Subgroups — C4×#16840105 #29687185

Order 15616.

888 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840105C211yesmaximal, characteristic
2C4×#14519757C211yesmaximal, characteristic
3C4×#14519735C211yesmaximal, characteristic
4#21446459C211yesmaximal, characteristic, complemented
5#21446451C211yesmaximal, characteristic, complemented
6#21446400C211yesmaximal, characteristic, complemented
7#21446392C211yesmaximal, characteristic, complemented
8#21446130C211yesmaximal, characteristic
9#21446015C211yesmaximal, characteristic
10#21445912C211yesmaximal, characteristic
11C4×#14519708C211yesmaximal, characteristic, complemented
12C4×#14519700C211yesmaximal, characteristic, complemented
13C4×#14519702C211yesmaximal, characteristic, complemented
14C4×#14519689C211yesmaximal, characteristic
15C4×#107×C61C211yesmaximal, characteristic, complemented
16C2×#14519757C2211yescharacteristic
17C2×C4×Dic122C2211yescharacteristic
18C2×#14519735C2211yescharacteristic
19C2×#14519735C2211yescharacteristic
20C2×C42×D61C2211yescharacteristic
21#16840105C418yesdirect product factor
22C2×#14519708C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×#14519702C2211yescharacteristic
25C2×#14519702C2211yescharacteristic
26C2×#14519700C2211yescharacteristic
27C2×#14519700C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×#14519689C2211yescharacteristic
30C2×C4×#92418C2211yescharacteristic
31#16839667C2211yescharacteristic
32#16839661C2211yescharacteristic
33#16839647—21no—
34#16839636—21no—
35#16839619C2211yescharacteristic
36C4⋊C4×Dic61C2211yescharacteristic
37C4⋊C4×Dic61C2211yescharacteristic
38C4×C4⋊Dic61—21no—
39C4×C4⋊Dic61C2211yescharacteristic
40C4×#11758198—21no—
41C4×#11758198—21no—
42#16839609—21no—
43#16839607—21no—
44C42×Dic61—21no—
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53C2×#107×C61C2211yescharacteristic
54C2×#107×C61C2211yescharacteristic
55C2×C4×C8×C61C2211yescharacteristic
56C4×C4⋊C4×C61C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C22×Dic122C2311yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66#14519757—22no—
67#14519757C2×C414yes—
68C4×Dic122—22no—
69C4×Dic122—22no—
70#14519735—22no—
71#14519735—22no—
72#14519735—22no—
73#14519735C2×C414yes—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×#11758196—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61—21no—
89C2×C4×Dic61—21no—
90C2×C4×Dic61D411yescharacteristic
91C2×C4×Dic61D411yescharacteristic
92C2×C4×Dic61C2311yescharacteristic
93C42×D61—22no—
94C42×D61—22no—
95#14519708—22no—
96#14519708C2×C414yescomplemented
97#14519702—22no—
98#14519702C2×C414yescomplemented
99#14519700—22no—
100#14519700C2×C414yescomplemented
101#14519689—22no—
102#14519689C2×C414yes—
103C4×#92418—22no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111C22×C8×C61C2311yescharacteristic
112C22×C8×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C42×C61—21no—
118C2×C42×C61—21no—
119C2×C42×C61C2311yescharacteristic
120#107×C61—22no—
121#107×C61C2×C414yescomplemented
122C4×C8×C61—22no—
123#95×C61—21no—
124#95×C61—21no—
125C23×D61C2×D411yescharacteristic
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2411yescharacteristic
133C22×Dic61—21no—
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61C2×D411yescharacteristic
138C22×Dic61C2×D411yescharacteristic
139C22×Dic61C2×D411yescharacteristic
140C2×C4×D61—21no—
141C2×C4×D61—21no—
142C2×C4×D61—21no—
143C2×C4×D61—21no—
144C2×C4×D61—22no—
145C2×C4×D61—22no—
146C2×C4×D61—22no—
147C2×C4×D61—22no—
148C2×C4×D61—22no—
149C2×C4×D61—41no—
150C2×C4×D61C22×C412yes—
151C2×C4×D61#4112yes—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122—21no—
156C2×Dic122—21no—
157C2×Dic122C22×C412yes—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61C22×C412yes—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61C22×C412yes—
170C4⋊C4×C61C22×C412yes—
171C4⋊C4×C61#4112yes—
172C42×C61—42no—
173C42×C61—42no—
174C42×C61#4112yes—
175C42×C61#4112yes—
176#11758198—24no—
177#11758198—24no—
178#11758198—24no—
179#11758198—42no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—24no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—42no—
186C4⋊Dic61C22×C412yes—
187C4⋊Dic61#4112yes—
188#11758196—42no—
189C4×Dic61—24no—
190C4×Dic61—22no—
191C4×Dic61—22no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—24no—
195C4×Dic61—42no—
196C4×Dic61—42no—
197C4×Dic61—42no—
198C4×Dic61—42no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418C22×C412yes—
205C23×C61C22×D411yescharacteristic
206C22×D61—21no—
207C22×D61—21no—
208C22×D61—21no—
209C22×D61—21no—
210C22×D61—21no—
211C22×D61—21no—
212C22×D61C4×D412yes—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—22no—
216C2×C4×C61—22no—
217C2×C4×C61—22no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61#12312yes—
228C2×C4×C61#12312yes—
229C2×C4×C61#13512yes—
230C2×C4×C61#13712yes—
231C2×C4×C61C23×C411yescharacteristic
232C2×C4×C61C2×#4111yescharacteristic
233C2×C4×C61C2×#4111yescharacteristic
234C2×C4×C61C2×#4111yescharacteristic
235C2×C4×C61C2×#4111yescharacteristic
236C2×C4×C61C2×#4111yescharacteristic
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—22no—
242C2×Dic61—22no—
243C2×Dic61—21no—
244C2×Dic61—22no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61C4×D412yes—
257C2×Dic61#13512yes—
258C4×D61—22no—
259C4×D61—22no—
260C4×D61—22no—
261C4×D61—22no—
262C4×D61—44no—
263C4×D61—44no—
264Dic122—22no—
265Dic122—22no—
266Dic122—41no—
267Dic122—41no—
268C8×C61—22no—
269C8×C61—41no—
270#92418—22no—
271#92418—41no—
272C4×#485—611nomaximal, Sylow
273C22×C61C2×C4×D411yescharacteristic
274C22×C61C2×#12311yescharacteristic
275C22×C61#52511yescharacteristic
276C22×C61C2×#13511yescharacteristic
277C22×C61C2×#13511yescharacteristic
278C22×C61C2×#13711yescharacteristic
279C22×C61#57511yescharacteristic
280C2×D61—22no—
281C2×D61—22no—
282C2×D61—22no—
283C2×D61—41no—
284C2×D61—41no—
285C2×D61—41no—
286C2×D61—41no—
287C4×C61—22no—
288C4×C61—42no—
289C4×C61—42no—
290C4×C61—42no—
291C4×C61—81no—
292C4×C61#48514yescomplemented
293C4×C61C4×#4111yescharacteristic
294C4×C61C4×#4111yescharacteristic
295C4×C61#52911yescharacteristic
296C4×C61#52911yescharacteristic
297Dic61—22no—
298Dic61—22no—
299Dic61—41no—
300Dic61—42no—
301Dic61—42no—
302Dic61—42no—
303Dic61—81no—
304C2×#485—611no—
305C4×C22⋊Q8—611no—
306C4×#117—611no—
307#1928—611no—
308#1927—611no—
309#1919—611no—
310#1918—611no—
311#1873—611no—
312#1854—611no—
313#1825—611no—
314C4×#107D6111yescharacteristic, complemented
315C4×#106—611no—
316C4×#103—611no—
317C4×#103—611no—
318C4×C22⋊C8—611no—
319C2×C61C4×#12311yescharacteristic
320C2×C61C4×#13511yescharacteristic
321C2×C61C4×#13711yescharacteristic
322C2×C61C2×#48511yescharacteristic
323C2×C61#309111yescharacteristic
324C2×C61#310211yescharacteristic
325C2×C61#310711yescharacteristic
326D61—42no—
327C2×C22⋊Q8—611no—
328C2×C4×Q8—611no—
329C2×#117—611no—
330C2×#117—611no—
331C22×C42—611no—
332#485—618no—
333C2×#107C2×D6111yescharacteristic
334C2×#107C2×D6111yescharacteristic
335C2×#106—611no—
336C2×#106—611no—
337C2×#103—611no—
338C2×#103—611no—
339C2×#103—611no—
340C2×#103—611no—
341C2×C22⋊C8—611no—
342C2×C22⋊C8—611no—
343C2×C4×C8—611no—
344C2×C4×C8C2×D6111yescharacteristic
345#391—611no—
346#389—611no—
347#387—1221no—
348#385—1221no—
349#380—611no—
350C4×C4⋊C4—611no—
351C4×C4⋊C4—611no—
352C4×C4⋊C4—611no—
353C4×C4⋊C4—1221no—
354C4×C4⋊C4C2×D6111yescharacteristic
355C4×C4⋊C4C2×D6111yescharacteristic
356C4×C22⋊C4—1221no—
357C4×C22⋊C4—1221no—
358C4×C22⋊C4—1221no—
359#376—1221no—
360C43—1221no—
361#340—611no—
362#340—611no—
363#340—611no—
364#340—611no—
365#340—611no—
366#340—611no—
367#340C2×D6111yescharacteristic
368#340C2×D6111yescharacteristic
369#336—611no—
370#336—611no—
371C61C4×#48511yescharacteristic, complemented, Sylow
372C22×Q8—611no—
373C23×C4—611no—
374C23×C4—611no—
375C23×C4—611no—
376C22×C8—611no—
377C22×C8—611no—
378C22×C8C22×D6111yescharacteristic
379C22×C8C22×D6111yescharacteristic
380C22⋊Q8—614no—
381C22⋊Q8—1222no—
382C4×Q8—1222no—
383C4×Q8—1222no—
384#117—614no—
385#117—1222no—
386#117—1222no—
387#117—1222no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—611no—
390C2×C4⋊C4—611no—
391C2×C4⋊C4—1221no—
392C2×C4⋊C4—1221no—
393C2×C4⋊C4—1221no—
394C2×C4⋊C4C22×D6111yescharacteristic
395C2×C4⋊C4C22×D6111yescharacteristic
396C2×C4⋊C4C22×D6111yescharacteristic
397C2×C4⋊C4C22×D6111yescharacteristic
398C2×C22⋊C4—1221no—
399C2×C22⋊C4—1221no—
400C2×C22⋊C4—1221no—
401C2×C22⋊C4—1221no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—611no—
405C2×C42—611no—
406C2×C42—611no—
407C2×C42—1221no—
408C2×C42—1221no—
409C2×C42—1222no—
410C2×C42—1222no—
411C2×C42—1221no—
412C2×C42—1221no—
413C2×C42—1221no—
414C2×C42—1221no—
415C2×C42C22×D6111yescharacteristic
416#107—22no—
417#107C4×D6114yescomplemented
418#106—614no—
419#106—1222no—
420#103—614no—
421#103—614no—
422#103—1222no—
423#103—1222no—
424C22⋊C8—614no—
425C22⋊C8—1222no—
426C4×C8—22no—
427C4×C8—1222no—
428#95—21no—
429#95—21no—
430#95—1221no—
431#95—1221no—
432#95—1221no—
433#95—1221no—
434#95—1221no—
435#95—1221no—
436#95—1221no—
437C24—611no—
438C2×Q8—612no—
439C2×Q8—1221no—
440C2×Q8—1221no—
441C2×Q8—1221no—
442C2×Q8—1221no—
443C2×Q8—1221no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—611no—
449C22×C4—611no—
450C22×C4—612no—
451C22×C4—612no—
452C22×C4—611no—
453C22×C4—1222no—
454C22×C4—1221no—
455C22×C4—1221no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1222no—
462C22×C4—1222no—
463C22×C4—1222no—
464C22×C4—1222no—
465C22×C4—1221no—
466C22×C4—2441no—
467C22×C4D4×D6111yescharacteristic
468C22×C4D4×D6111yescharacteristic
469C22×C4C23×D6111yescharacteristic
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—612no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8C2×C4×D6112yes—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—612no—
488C4⋊C4—612no—
489C4⋊C4—1224no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4—1221no—
494C4⋊C4—2442no—
495C4⋊C4—2442no—
496C4⋊C4C2×C4×D6112yes—
497C4⋊C4C2×C4×D6112yes—
498C4⋊C4#1175822212yes—
499C22⋊C4—1224no—
500C22⋊C4—1224no—
501C22⋊C4—1224no—
502C22⋊C4—2442no—
503C42—42no—
504C42—42no—
505C42—1224no—
506C42—1224no—
507C42—1221no—
508C42—1221no—
509C42—1222no—
510C42—1222no—
511C42—2442no—
512C42—2442no—
513C42—2442no—
514C42—2442no—
515C42#1175822212yes—
516C42#1175822612yes—
517C23—612no—
518C23—1221no—
519C23—1221no—
520C23—1221no—
521C23—1221no—
522C23—1221no—
523C23—1221no—
524C23C2×D4×D6111yescharacteristic
525Q8—1222no—
526Q8—1222no—
527Q8—2441no—
528Q8—2441no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—612no—
544C2×C4—612no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—1221no—
549C2×C4—1222no—
550C2×C4—1222no—
551C2×C4—1222no—
552C2×C4—1222no—
553C2×C4—1222no—
554C2×C4—1222no—
555C2×C4—1221no—
556C2×C4—1222no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—2444no—
560C2×C4—2441no—
561C2×C4—2441no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2444no—
570C2×C4#1451976212yes—
571C2×C4#1451976212yes—
572C2×C4#1451979612yes—
573C2×C4#1451980912yes—
574C2×C4C22×C4×D6111yescharacteristic
575C2×C4#41×D6111yescharacteristic
576C2×C4#41×D6111yescharacteristic
577C2×C4C2×#1175822211yescharacteristic
578C2×C4C2×#1175822211yescharacteristic
579C2×C4C2×#1175822611yescharacteristic
580C8—22no—
581C8—41no—
582C8—1222no—
583C8—2441no—
584C22—1222no—
585C22—1222no—
586C22—1222no—
587C22—2441no—
588C22—2441no—
589C22—2441no—
590C22—2441no—
591C22C4×D4×D6111yescharacteristic
592C22C2×#1451976211yescharacteristic
593C22#1684027111yescharacteristic
594C22#135×D6111yescharacteristic
595C22C2×#1451979611yescharacteristic
596C22C2×#1451980911yescharacteristic
597C22#1684055911yescharacteristic
598C4—22no—
599C4—42no—
600C4—42no—
601C4—42no—
602C4—81no—
603C4—1222no—
604C4—1222no—
605C4—4881no—
606C4—2442no—
607C4—2442no—
608C4—2441no—
609C4—2442no—
610C4#1684010514yesdirect product factor
611C4C4×#1175822211yescharacteristic
612C4C4×#1175822611yescharacteristic
613C4#1684029011yescharacteristic
614C4#1684029911yescharacteristic
615C2—2442no—
616C2C4×#1451976211yescharacteristic
617C2C4×#1451979611yescharacteristic
618C2C4×#1451980911yescharacteristic
619C2C2×#1684010511yescharacteristic
620C2#2145573611yescharacteristic
621C2#2145583311yescharacteristic
622C2#2145588811yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×#107×C61C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
cosocleC22×C4×C61C24
hypercenterC4×#107D61
hypocenterC61C4×#485
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#107

Complements

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

NH ≅ G/Ntype
4. #21446459C2semidirect
5. #21446451C2semidirect
6. #21446400C2semidirect
7. #21446392C2semidirect
11. C4×#14519708C2semidirect
12. C4×#14519700C2semidirect
13. C4×#14519702C2semidirect
15. C4×#107×C61C2semidirect
21. #16840105C4direct (N × H)
96. #14519708C2×C4semidirect
98. #14519702C2×C4semidirect
100. #14519700C2×C4semidirect
121. #107×C61C2×C4semidirect
292. C4×C61#485semidirect
314. C4×#107D61semidirect
371. C61C4×#485semidirect
417. #107C4×D61semidirect
610. C4#16840105direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168401052
C4×#145197572
C4×#145197352
#214464592
#214464512
#214464002
#214463922
#214461302
#214460152
#214459122
C4×#145197082
C4×#145197002
C4×#145197022
C4×#145196892
C4×#107×C612
C4×#48561