Finite Group Databasebeta

← C2×#21461785 #30615510

Subgroups — C2×#21461785 #30615510

Order 15616.

1542 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×#6923C211yesmaximal, characteristic
2C22×#14519845C211yesmaximal, characteristic
3C22×#14519840C211yesmaximal, characteristic
4C2×#16840713C211yesmaximal, characteristic
5#21461785C218yesmaximal, direct product factor
6C2×#16840635C211yesmaximal, characteristic
7C2×(C2×#6923)⋊C8C211yesmaximal, characteristic
8C2×#103×D61C211yesmaximal, characteristic
9C22×D61⋊C8C2211yescharacteristic
10C2×Q8×#6923—24no—
11C2×Q8×#6923—22no—
12C2×Q8×#6923—24no—
13C2×Q8×#6923C2214yes—
14C22×C4⋊#6923—21no—
15C22×C4⋊#6923—21no—
16C22×C4⋊#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C4×#6923—21no—
19C22×C4×#6923C2211yescharacteristic
20C2×#14519845—24no—
21C2×#14519845C2214yes—
22C2×#14519840—24no—
23C2×#14519840C2214yes—
24#16840713—22no—
25#16840713C2214yes—
26C2×(C2×#6923)⋊C4—21no—
27#16840635C2214yes—
28(C2×#6923)⋊C8C2214yes—
29C22×Q8×D61C2211yescharacteristic
30C22×C8×D61C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32C2×#14519702C411yescharacteristic, complemented
33C2×#14519701C411yescharacteristic, complemented
34C2×#14519700C411yescharacteristic, complemented
35#103×D61C414yescomplemented
36#103×D61C2214yes—
37C2×#103×C61C411yescharacteristic, complemented
38C23×#6923—21no—
39C23×#6923—21no—
40C23×#6923D411yescharacteristic
41C23×#6923D411yescharacteristic
42C2×D61⋊C8—22no—
43C2×D61⋊C8—22no—
44C2×D61⋊C8—21no—
45C2×D61⋊C8C2312yes—
46C22×#92420—21no—
47Q8×#6923—216no—
48Q8×#6923—28no—
49Q8×#6923—28no—
50C2×C4⋊#6923—28no—
51C2×C4⋊#6923—24no—
52C2×C4⋊#6923—21no—
53C2×C4⋊#6923—22no—
54C2×C4⋊#6923—22no—
55C2×C4⋊#6923—22no—
56C2×C4⋊#6923—24no—
57C2×C4⋊#6923—21no—
58C2×C4⋊#6923—44no—
59C2×C4⋊#6923D414yes—
60C2×C4⋊#6923C2312yes—
61C2×C4⋊#6923C2312yes—
62C2×C4×#6923—28no—
63C2×C4×#6923—24no—
64C2×C4×#6923—22no—
65C2×C4×#6923—22no—
66C2×C4×#6923D412yes—
67C2×C4×#6923C2312yes—
68#14519845—28no—
69#14519840—28no—
70(C2×#6923)⋊C4—24no—
71C22×Dic122—21no—
72C22×Dic122C2×C411yescharacteristic
73C2×Q8×D61—21no—
74C2×Q8×D61—22no—
75C2×Q8×D61—22no—
76C2×Q8×D61—21no—
77C2×Q8×D61C2×C412yes—
78C2×Q8×D61D414yes—
79C2×Q8×D61Q814yes—
80C2×Q8×D61C2312yes—
81C22×C4×D61—21no—
82C22×C4×D61—21no—
83C22×C4×D61C2311yescharacteristic
84C22×#92418C2×C411yescharacteristic
85C2×C8×D61—22no—
86C2×C8×D61—22no—
87C2×C8×D61C2×C412yes—
88C2×C8×D61C2312yes—
89C2×C4⋊Dic61C2×C411yescharacteristic
90C2×#11758196—21no—
91C4⋊C4×D61—21no—
92C4⋊C4×D61—21no—
93C4⋊C4×D61C2×C412yes—
94C4⋊C4×D61C2312yes—
95#14519702C2×C414yescomplemented
96#14519701C2×C414yescomplemented
97#14519700C2×C414yescomplemented
98C22×Q8×C61C2×C411yescharacteristic
99C22×C8×C61C2×C411yescharacteristic
100C2×C4⋊C4×C61C2×C411yescharacteristic
101#103×C61C2×C414yescomplemented
102C23×D61C2×D411yescharacteristic
103C22×#6923—22no—
104C22×#6923—22no—
105C22×#6923—22no—
106C22×#6923—24no—
107C22×#6923—22no—
108C22×#6923—22no—
109C22×#6923—22no—
110C22×#6923—22no—
111C22×#6923—42no—
112C22×#6923—42no—
113C22×#6923—42no—
114C22×#6923—42no—
115C22×#6923—42no—
116C22×#6923SD1614yes—
117C22×#6923C2×D412yes—
118C22×#6923C2×D412yes—
119C2×Q8×C61—21no—
120C2×Q8×C61—22no—
121C2×Q8×C61C4⋊C414yescomplemented
122C2×Q8×C61C22×C412yes—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61C22×C411yescharacteristic
126C22×Dic61—21no—
127C22×Dic61—21no—
128C22×Dic61#4111yescharacteristic
129Q8×D61—24no—
130Q8×D61—24no—
131Q8×D61—24no—
132Q8×D61—24no—
133Q8×D61—24no—
134Q8×D61—22no—
135Q8×D61—22no—
136Q8×D61C4⋊C418yescomplemented
137Q8×D61C2×D414yes—
138Q8×D61C2×Q814yes—
139C2×C4×D61—22no—
140C2×C4×D61—24no—
141C2×C4×D61—24no—
142C2×C4×D61—22no—
143C2×C4×D61—22no—
144C2×C4×D61—22no—
145C2×C4×D61—42no—
146C2×C4×D61—42no—
147C2×C4×D61C22×C411yescharacteristic
148C2×C4×D61C2×D412yes—
149C2×C4×D61C2×D412yes—
150C2×C4×D61C2×D411yescharacteristic
151C2×C4×D61C2×Q812yes—
152C2×C4×D61#4112yes—
153C2×C4×D61#4111yescharacteristic
154C2×C4×D61C2411yescharacteristic
155C2×Dic122—22no—
156C2×Dic122—21no—
157C2×Dic122—22no—
158C2×Dic122—24no—
159C2×Dic122—24no—
160C2×Dic122—22no—
161C2×Dic122C4⋊C414yescomplemented
162C2×Dic122C22×C412yes—
163C2×#92420—22no—
164C2×#92420—42no—
165C4⋊#6923—216no—
166C4⋊#6923—24no—
167C4⋊#6923—22no—
168C4⋊#6923—22no—
169C4⋊#6923—22no—
170C4⋊#6923—48no—
171C4⋊#6923—42no—
172C4⋊#6923C2×D414yes—
173C4×#6923—216no—
174C4×#6923—24no—
175C4×#6923—22no—
176C4×#6923—22no—
177D61⋊C8—22no—
178D61⋊C8—22no—
179D61⋊C8—42no—
180C2×C8×C61—22no—
181C2×C8×C61C22×C412yes—
182C4⋊C4×C61—21no—
183C4⋊C4×C61C22×C412yes—
184C4⋊Dic61—21no—
185C4⋊Dic61C22×C412yes—
186#11758196—22no—
187#11758196—22no—
188C2×#92418—22no—
189C2×#92418C22×C412yes—
190C8×D61—24no—
191C8×D61—22no—
192C8×D61—22no—
193C23×C61C4×D411yescharacteristic
194C22×D61C4×D411yescharacteristic
195C22×D61#12012yes—
196C22×D61C22⋊Q812yes—
197C22×D61C2×SD1612yes—
198C22×D61#13512yes—
199C22×D61#13712yes—
200C22×D61#13712yes—
201C22×D61C22×D411yescharacteristic
202C2×#6923—22no—
203C2×#6923—22no—
204C2×#6923—28no—
205C2×#6923—22no—
206C2×#6923—24no—
207C2×#6923—22no—
208C2×#6923—22no—
209C2×#6923—42no—
210C2×#6923—42no—
211C2×#6923—44no—
212C2×#6923—48no—
213C2×#6923—42no—
214C2×#6923—42no—
215C2×#6923—42no—
216C2×#6923—84no—
217C2×#6923C2×SD1614yes—
218Q8×C61—22no—
219Q8×C61—24no—
220Q8×C61C2×C4⋊C414yescomplemented
221C2×C4×C61—22no—
222C2×C4×C61—24no—
223C2×C4×C61—22no—
224C2×C4×C61—42no—
225C2×C4×C61C2×C4⋊C412yes—
226C2×C4×C61C4×D412yes—
227C2×C4×C61C4×D411yescharacteristic
228C2×C4×C61C23×C411yescharacteristic
229C2×Dic61—22no—
230C2×Dic61—24no—
231C2×Dic61—22no—
232C2×Dic61—42no—
233C2×Dic61C4×D411yescharacteristic
234C2×Dic61C22⋊Q812yes—
235C2×Dic61#12312yes—
236C2×Dic61C2×#4111yescharacteristic
237C4×D61—24no—
238C4×D61—24no—
239C4×D61—28no—
240C4×D61—42no—
241C4×D61—42no—
242C4×D61—44no—
243C4×D61C2×C4⋊C412yes—
244C4×D61C4×D412yes—
245C4×D61#12012yes—
246C4×D61C22⋊Q812yes—
247C4×D61C22⋊Q812yes—
248C4×D61#12312yes—
249C4×D61C22×D411yescharacteristic
250C4×D61C22×D411yescharacteristic
251C4×D61C22×Q811yescharacteristic
252C4×D61C2×#4111yescharacteristic
253Dic122—22no—
254Dic122—24no—
255Dic122—24no—
256Dic122—24no—
257Dic122—28no—
258Dic122C2×C4⋊C414yescomplemented
259#92420—42no—
260C8×C61—22no—
261#92418—22no—
262C2×#1865—611nomaximal, Sylow
263C22×C61#38512yes—
264C22×C61C4×SD1612yes—
265C22×C61#44112yes—
266C22×C61C2×C4×D411yescharacteristic
267C2×D61#38512yes—
268C2×D61C4×SD1612yes—
269C2×D61#44112yes—
270C2×D61#44814yes—
271C2×D61#45214yes—
272C2×D61#47514yes—
273C2×D61#47914yes—
274C2×D61C2×#12011yescharacteristic
275C2×D61C2×C22⋊Q811yescharacteristic
276C2×D61C22×SD1611yescharacteristic
277C2×D61C2×#13511yescharacteristic
278C2×D61C2×#13711yescharacteristic
279C2×D61C2×#13711yescharacteristic
280#6923—24no—
281#6923—42no—
282#6923—44no—
283#6923—82no—
284C4×C61—24no—
285C4×C61—42no—
286C4×C61#38512yes—
287C4×C61C22×C4⋊C411yescharacteristic
288C4×C61C2×C4×D411yescharacteristic
289Dic61—24no—
290Dic61—42no—
291Dic61#38512yes—
292Dic61C2×C22⋊Q811yescharacteristic
293Dic61C2×#12311yescharacteristic
294C22×C4×Q8—611no—
295C22×#106—611no—
296C22×#103—611no—
297C22×#103—611no—
298C2×#389—611no—
299#1865—618no—
300C2×#340—611no—
301C2×#336—611no—
302C2×C61#186514yescomplemented
303C2×C61C2×#38511yescharacteristic
304C2×C61C2×C4×SD1611yescharacteristic
305C2×C61C2×#44111yescharacteristic
306D61#186514yescomplemented
307D61C2×#44811yescharacteristic
308D61C2×#45211yescharacteristic
309D61C2×#47511yescharacteristic
310D61C2×#47911yescharacteristic
311C23×Q8—611no—
312C23×C8—611no—
313C23×C8—611no—
314C2×C4×Q8—614no—
315C2×C4×Q8—1222no—
316C2×C4×Q8—1224no—
317C2×C4×Q8—1224no—
318C22×C4⋊C4—611no—
319C22×C4⋊C4—611no—
320C22×C4⋊C4—611no—
321C22×C4⋊C4—1221no—
322C22×C4⋊C4—1221no—
323C22×C42—611no—
324C22×C42—1221no—
325C2×#106—614no—
326C2×#106—1224no—
327C2×#103—611no—
328C2×#103—611no—
329C2×#103—611no—
330C2×#103—614no—
331C2×#103—614no—
332C2×#103—614no—
333C2×#103—1224no—
334C2×#103#692311yescharacteristic, complemented
335#389—614no—
336#389—1222no—
337C2×#95—1221no—
338#340—614no—
339#336—614no—
340C61C2×#186511yescharacteristic, complemented, Sylow
341C22×Q8—614no—
342C22×Q8—614no—
343C22×Q8—612no—
344C22×Q8—612no—
345C22×Q8—611no—
346C22×Q8—1221no—
347C22×Q8—1221no—
348C22×Q8—1222no—
349C22×Q8—1221no—
350C22×Q8—1222no—
351C22×Q8C2×#692311yescharacteristic
352C23×C4—611no—
353C23×C4—611no—
354C23×C4—611no—
355C23×C4—1221no—
356C23×C4—1221no—
357C23×C4—1221no—
358C23×C4—1221no—
359C22×C8—611no—
360C22×C8—612no—
361C22×C8—612no—
362C22×C8—612no—
363C22×C8—1222no—
364C22×C8—1222no—
365C22×C8—1221no—
366C22×C8—1222no—
367C22×C8—1221no—
368C22×C8—1222no—
369C22×C8C2×#692311yescharacteristic
370C4×Q8—1228no—
371C4×Q8—1228no—
372C4×Q8—12216no—
373C2×C4⋊C4—612no—
374C2×C4⋊C4—614no—
375C2×C4⋊C4—611no—
376C2×C4⋊C4—612no—
377C2×C4⋊C4—612no—
378C2×C4⋊C4—612no—
379C2×C4⋊C4—1221no—
380C2×C4⋊C4—1221no—
381C2×C4⋊C4—1221no—
382C2×C4⋊C4—1222no—
383C2×C4⋊C4—1221no—
384C2×C4⋊C4—1224no—
385C2×C4⋊C4—1228no—
386C2×C4⋊C4—1222no—
387C2×C4⋊C4—1222no—
388C2×C4⋊C4—1221no—
389C2×C4⋊C4—1224no—
390C2×C4⋊C4—2444no—
391C2×C4⋊C4C2×#692311yescharacteristic
392C2×C42—612no—
393C2×C42—612no—
394C2×C42—1224no—
395C2×C42—1222no—
396C2×C42—1222no—
397C2×C42—1228no—
398#106—1228no—
399#103—614no—
400#103—614no—
401#103—614no—
402#103—1228no—
403#103C2×#692314yescomplemented
404#95—1224no—
405C24—611no—
406C2×Q8—22no—
407C2×Q8—21no—
408C2×Q8—614no—
409C2×Q8—618no—
410C2×Q8—614no—
411C2×Q8—614no—
412C2×Q8—612no—
413C2×Q8—1224no—
414C2×Q8—1224no—
415C2×Q8—1222no—
416C2×Q8—1222no—
417C2×Q8—1224no—
418C2×Q8—1222no—
419C2×Q8—1224no—
420C2×Q8—1224no—
421C2×Q8—1224no—
422C2×Q8—1224no—
423C2×Q8—1222no—
424C2×Q8—1222no—
425C2×Q8—1221no—
426C2×Q8C4⋊#692314yescomplemented
427C2×Q8C22×#692312yes—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—611no—
431C22×C4—612no—
432C22×C4—612no—
433C22×C4—611no—
434C22×C4—612no—
435C22×C4—611no—
436C22×C4—612no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—612no—
440C22×C4—614no—
441C22×C4—612no—
442C22×C4—1224no—
443C22×C4—1222no—
444C22×C4—1224no—
445C22×C4—1222no—
446C22×C4—1222no—
447C22×C4—1222no—
448C22×C4—1222no—
449C22×C4—1222no—
450C22×C4—1221no—
451C22×C4—1224no—
452C22×C4—1222no—
453C22×C4—1222no—
454C22×C4—1222no—
455C22×C4—1222no—
456C22×C4—1221no—
457C22×C4—1222no—
458C22×C4—2442no—
459C22×C4—2442no—
460C22×C4—2442no—
461C22×C4—2442no—
462C22×C4—2442no—
463C22×C4—2442no—
464C22×C4—2442no—
465C22×C4C22×#692311yescharacteristic
466C2×C8—22no—
467C2×C8—612no—
468C2×C8—1222no—
469C2×C8—1224no—
470C2×C8—1222no—
471C2×C8—1222no—
472C2×C8—1222no—
473C2×C8—1222no—
474C2×C8—1222no—
475C2×C8—2442no—
476C2×C8—2442no—
477C2×C8C22×#692312yes—
478C4⋊C4—21no—
479C4⋊C4—614no—
480C4⋊C4—612no—
481C4⋊C4—1222no—
482C4⋊C4—1222no—
483C4⋊C4—1224no—
484C4⋊C4—1222no—
485C4⋊C4—1222no—
486C4⋊C4—1222no—
487C4⋊C4—12216no—
488C4⋊C4—1221no—
489C4⋊C4—2442no—
490C4⋊C4—2448no—
491C4⋊C4C22×#692312yes—
492C42—1224no—
493C42—1222no—
494C42—1222no—
495C42—12216no—
496C23—612no—
497C23—612no—
498C23—612no—
499C23—612no—
500C23—612no—
501C23—612no—
502C23—611no—
503C23—611no—
504C23D4×#692311yescharacteristic
505Q8—24no—
506Q8—22no—
507Q8—614no—
508Q8—1224no—
509Q8—1224no—
510Q8—1228no—
511Q8—1224no—
512Q8—1222no—
513Q8C2×C4⋊#692314yescomplemented
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—42no—
518C2×C4—612no—
519C2×C4—612no—
520C2×C4—611no—
521C2×C4—611no—
522C2×C4—612no—
523C2×C4—612no—
524C2×C4—612no—
525C2×C4—612no—
526C2×C4—612no—
527C2×C4—611no—
528C2×C4—611no—
529C2×C4—612no—
530C2×C4—611no—
531C2×C4—611no—
532C2×C4—614no—
533C2×C4—1224no—
534C2×C4—1224no—
535C2×C4—1228no—
536C2×C4—1222no—
537C2×C4—1228no—
538C2×C4—1222no—
539C2×C4—1224no—
540C2×C4—1222no—
541C2×C4—1224no—
542C2×C4—1222no—
543C2×C4—1222no—
544C2×C4—1222no—
545C2×C4—1222no—
546C2×C4—4884no—
547C2×C4—2442no—
548C2×C4—2442no—
549C2×C4—2444no—
550C2×C4—2442no—
551C2×C4—2442no—
552C2×C4—2442no—
553C2×C4—2444no—
554C2×C4—2448no—
555C2×C4—2442no—
556C2×C4—2442no—
557C2×C4—2442no—
558C2×C4C2×C4⋊#692312yes—
559C2×C4D4×#692311yescharacteristic
560C2×C4D4×#692312yes—
561C2×C4C23×#692311yescharacteristic
562C8—22no—
563C8—1222no—
564C8—2442no—
565C22—614no—
566C22—614no—
567C22—614no—
568C22—614no—
569C22—611no—
570C22—611no—
571C22—612no—
572C22—611no—
573C22—611no—
574C22—612no—
575C22—611no—
576C22—611no—
577C22—612no—
578C22#1684070912yes—
579C22SD16×#692312yes—
580C22#1684080212yes—
581C22C2×D4×#692311yescharacteristic
582C4—24no—
583C4—42no—
584C4—611no—
585C4—611no—
586C4—612no—
587C4—1224no—
588C4—1224no—
589C4—4882no—
590C4—2442no—
591C4—2444no—
592C4—2442no—
593C4#1684070912yes—
594C4C22×C4⋊#692311yescharacteristic
595C4C2×D4×#692311yescharacteristic
596C2—611no—
597C2—611no—
598C2—611no—
599C2—611no—
600C2—614no—
601C2#2146178514yesdirect product factor
602C2C2×#1684070911yescharacteristic
603C2C2×SD16×#692311yescharacteristic
604C2C2×#1684080211yescharacteristic
subgroupG/H
centerC23D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#103×C61C4
socleC23×C61C4×D4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenterC2×#103#6923
hypocenterC61C2×#1865
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
5. #21461785C2direct (N × H)
32. C2×#14519702C4semidirect
33. C2×#14519701C4semidirect
34. C2×#14519700C4semidirect
35. #103×D61C4semidirect
37. C2×#103×C61C4semidirect
95. #14519702C2×C4semidirect
96. #14519701C2×C4semidirect
97. #14519700C2×C4semidirect
101. #103×C61C2×C4semidirect
121. C2×Q8×C61C4⋊C4semidirect
136. Q8×D61C4⋊C4semidirect
161. C2×Dic122C4⋊C4semidirect
220. Q8×C61C2×C4⋊C4semidirect
258. Dic122C2×C4⋊C4semidirect
302. C2×C61#1865semidirect
306. D61#1865semidirect
334. C2×#103#6923semidirect
340. C61C2×#1865semidirect
403. #103C2×#6923semidirect
426. C2×Q8C4⋊#6923semidirect
513. Q8C2×C4⋊#6923semidirect
601. C2#21461785direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×#69232
C22×#145198452
C22×#145198402
C2×#168407132
#214617852
C2×#168406352
C2×(C2×#6923)⋊C82
C2×#103×D612
C2×#186561