Finite Group Databasebeta

← C2×#21456800 #30551238

Subgroups — C2×#21456800 #30551238

Order 15616.

2218 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840313C211yesmaximal, characteristic, complemented
2C2×#16840299C211yesmaximal, characteristic, complemented
3#21456800C2116yesmaximal, direct product factor
4C2×#16840147C212yesmaximal, complemented
5C2×#16840118C212yesmaximal, complemented
6C2×#16839962C211yesmaximal, characteristic, complemented
7C2×#16839964C211yesmaximal, characteristic, complemented
8C2×#16839958C211yesmaximal, characteristic, complemented
9C2×#16839923C212yesmaximal, complemented
10C2×#16839910C212yesmaximal, complemented
11C2×#16839814C211yesmaximal, characteristic, complemented
12C2×C61×#462C211yesmaximal, characteristic, complemented
13C22×#11758226C2212yes—
14C22×#11758201C2212yes—
15C22×#11758201C2212yes—
16C22×D488C2212yes—
17#16840313—24no—
18#16840313C2218yescomplemented
19C2×#14519774C2211yescharacteristic
20#16840299—24no—
21#16840299C2218yescomplemented
22C2×#14519772—21no—
23C2×#14519768C2211yescharacteristic
24C2×#14519766C2212yes—
25C2×#14519766C2211yescharacteristic
26C2×#14519762—21no—
27C2×#14519753C2211yescharacteristic
28C2×#14519752—21no—
29C2×#14519752—21no—
30C2×#14519752C2211yescharacteristic
31C2×C4×D244—21no—
32C2×C4×D244C2211yescharacteristic
33C2×#14519739—21no—
34C2×#14519739—21no—
35C2×#14519734—21no—
36C2×C42×D61C2211yescharacteristic
37#16840147C22116yescomplemented
38#16840118C22116yescomplemented
39#16839964C2218yescomplemented
40#16839962C2218yescomplemented
41#16839958C2218yescomplemented
42#16839923C22116yescomplemented
43#16839910C22116yescomplemented
44#16839814C2218yescomplemented
45C2×C4⋊#92418C2211yescharacteristic
46C2×#14519701C2212yes—
47C2×#14519699C2212yes—
48C2×#14519697C2212yes—
49C2×#14519689C2212yes—
50C2×C8×Dic61C2212yes—
51C22×Q16×C61C2212yes—
52C2×C4⋊Q8×C61C2211yescharacteristic
53C2×C4×Q8×C61C2211yescharacteristic
54C61×#462C2218yescomplemented
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×#103×C61C2212yes—
57C2×#11758226—24no—
58C2×#11758226—44no—
59C2×#11758226—44no—
60C2×#11758226C2318yes—
61C22×D244—21no—
62C22×D244—22no—
63C22×D244—21no—
64C22×D244—21no—
65C22×D244C2311yescharacteristic
66C22×D244C2312yes—
67C22×C4×D61—21no—
68C22×C4×D61—22no—
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61C2311yescharacteristic
72C2×#11758201—44no—
73C2×#11758201—44no—
74C2×#11758201C2318yes—
75C2×#11758201C2318yes—
76C2×D488—44no—
77C2×D488C2318yes—
78C22×#92418C2312yes—
79#14519774—22no—
80#14519774C2314yes—
81#14519772—28no—
82#14519768—22no—
83#14519768C2314yes—
84#14519766—22no—
85#14519766—24no—
86#14519766C2314yes—
87#14519766C2318yes—
88#14519762—28no—
89#14519753—22no—
90#14519753C2314yes—
91#14519752—28no—
92#14519752—28no—
93#14519752—22no—
94#14519752C2314yes—
95C4×D244—28no—
96C4×D244—22no—
97C4×D244C2314yes—
98#14519739—28no—
99#14519739—28no—
100#14519734—28no—
101C2×C4⋊Dic61—21no—
102C2×C4⋊Dic61C2311yescharacteristic
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198—22no—
110C2×#11758198—22no—
111C2×#11758198—21no—
112C2×C4×Dic61D411yescharacteristic
113C2×C4×Dic61D411yescharacteristic
114C2×C4×Dic61C2311yescharacteristic
115C42×D61D414yes—
116C42×D61C2314yes—
117C4⋊#92418C2314yes—
118#14519701C2318yes—
119#14519699C2318yes—
120#14519697C2318yes—
121#14519689C2318yes—
122C8×Dic61C2318yes—
123C22×Q8×C61C2312yes—
124C22×Q8×C61C2311yescharacteristic
125C2×Q16×C61—44no—
126C2×Q16×C61C2318yes—
127C22×C8×C61C2312yes—
128C4⋊Q8×C61—22no—
129C4⋊Q8×C61C2314yes—
130C4×Q8×C61—22no—
131C4×Q8×C61C2314yes—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C42×C61—21no—
137C2×C42×C61C2311yescharacteristic
138C4⋊C8×C61C2314yes—
139#103×C61C2318yes—
140C23×D61—22no—
141C23×D61—21no—
142C23×D61C2×D411yescharacteristic
143C2×Q8×C61—22no—
144C2×Q8×C61—21no—
145C2×Q8×C61—24no—
146C2×Q8×C61—24no—
147C2×Q8×C61—22no—
148C2×Q8×C61—22no—
149C2×Q8×C61C2414yes—
150C2×Q8×C61C2412yes—
151C22×C4×C61—22no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2411yescharacteristic
157C22×Dic61—21no—
158C22×Dic61C2×D411yescharacteristic
159C22×Dic61C2×D411yescharacteristic
160C22×Dic61C2×D411yescharacteristic
161#11758226—48no—
162#11758226—48no—
163#11758226—416no—
164C2×D244—24no—
165C2×D244—24no—
166C2×D244—22no—
167C2×D244—22no—
168C2×D244—28no—
169C2×D244—24no—
170C2×D244—24no—
171C2×D244—24no—
172C2×D244—22no—
173C2×D244—21no—
174C2×D244—44no—
175C2×D244—44no—
176C2×D244—48no—
177C2×D244—44no—
178C2×D244C2414yes—
179C2×D244C2412yes—
180C2×C4×D61—24no—
181C2×C4×D61—22no—
182C2×C4×D61—22no—
183C2×C4×D61—24no—
184C2×C4×D61—28no—
185C2×C4×D61—42no—
186C2×C4×D61—48no—
187C2×C4×D61—44no—
188C2×C4×D61C2×D414yes—
189C2×C4×D61C2×D412yes—
190C2×C4×D61C2×D414yes—
191C2×C4×D61C2412yes—
192Q16×C61—48no—
193C2×C8×C61—24no—
194C2×C8×C61C2414yes—
195C4⋊C4×C61—24no—
196C4⋊C4×C61—24no—
197C4⋊C4×C61—24no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61C2412yes—
200C42×C61—24no—
201C42×C61C2×D412yes—
202C42×C61C2412yes—
203#11758201—48no—
204#11758201—48no—
205#11758198—24no—
206#11758198—24no—
207#11758198—24no—
208#11758198—24no—
209#11758198—28no—
210#11758198—28no—
211#11758198—24no—
212C4⋊Dic61—21no—
213C4⋊Dic61—24no—
214C4⋊Dic61C2412yes—
215#11758196—24no—
216#11758196—24no—
217C4×Dic61C2×D412yes—
218C4×Dic61C2×D414yes—
219C4×Dic61C2×D414yes—
220C4×Dic61C2412yes—
221C2×#92418—24no—
222C2×#92418C2414yes—
223D488—48no—
224C23×C61C22×D411yescharacteristic
225C22×D61—22no—
226C22×D61—22no—
227C22×D61—22no—
228C22×D61—22no—
229C22×D61—24no—
230C22×D61—44no—
231C22×D61—42no—
232C22×D61—42no—
233C22×D61—44no—
234C22×D61—44no—
235C22×D61—42no—
236C22×D61C22×D412yes—
237Q8×C61—22no—
238Q8×C61—24no—
239Q8×C61—22no—
240Q8×C61—24no—
241Q8×C61—44no—
242Q8×C61—42no—
243C2×C4×C61—22no—
244C2×C4×C61—22no—
245C2×C4×C61—22no—
246C2×C4×C61—24no—
247C2×C4×C61—44no—
248C2×C4×C61—42no—
249C2×C4×C61—42no—
250C2×C4×C61#13514yes—
251C2×C4×C61C22×D412yes—
252C2×C4×C61C22×D411yescharacteristic
253C2×C4×C61C22×D412yes—
254C2×C4×C61H(5,𝔽2)12yes—
255C2×C4×C61H(5,𝔽2)12yes—
256C2×C4×C61C2511yescharacteristic
257C2×Dic61—22no—
258C2×Dic61—22no—
259C2×Dic61—22no—
260C2×Dic61—22no—
261C2×Dic61—42no—
262C2×Dic61C22×D412yes—
263C2×Dic61C22×D412yes—
264C2×Dic61C22×D412yes—
265D244—22no—
266D244—24no—
267D244—22no—
268D244—24no—
269D244—48no—
270D244—48no—
271D244—416no—
272D244—42no—
273D244—44no—
274D244—48no—
275C4×D61—24no—
276C4×D61—28no—
277C4×D61—22no—
278C4×D61—22no—
279C4×D61—44no—
280C4×D61—416no—
281C4×D61—48no—
282C8×C61—24no—
283#92418—24no—
284C2×#3212—611nomaximal, Sylow
285C22×C61#53512yes—
286C22×C61C2×#13512yes—
287C22×C61#57512yes—
288C22×C61C23×D411yescharacteristic
289C2×D61—22no—
290C2×D61—22no—
291C2×D61—22no—
292C2×D61—44no—
293C2×D61—44no—
294C2×D61—42no—
295C2×D61—42no—
296C2×D61—44no—
297C2×D61—44no—
298C2×D61—42no—
299C2×D61—88no—
300C2×D61—84no—
301C4×C61—22no—
302C4×C61—44no—
303C4×C61—42no—
304C4×C61—42no—
305C4×C61#53512yes—
306C4×C61C2×#13514yes—
307C4×C61C2×H(5,𝔽2)11yescharacteristic
308C4×C61C2×H(5,𝔽2)11yescharacteristic
309Dic61—22no—
310Dic61—22no—
311Dic61—22no—
312Dic61—42no—
313C2×#532—611no—
314C2×#529—611no—
315#3212—6116no—
316C2×#495—612no—
317C2×#488—612no—
318C2×#462D6111yescharacteristic, complemented
319C2×#460—611no—
320C2×#461—611no—
321C2×#459—611no—
322C2×#452—612no—
323C2×#449—612no—
324C2×#431—611no—
325C2×C61#321214yescomplemented
326C2×C61C2×#53511yescharacteristic
327C2×C61C22×#13511yescharacteristic
328C2×C61C2×#57511yescharacteristic
329D61—42no—
330D61—84no—
331D61—82no—
332C22×#41—612no—
333C22×Q16C2×D6112yes—
334C22×SD16—612no—
335C22×SD16—612no—
336C22×D8—612no—
337#532—618no—
338#532—1224no—
339C2×C4⋊Q8C2×D6111yescharacteristic
340C2×#127—611no—
341#529—618no—
342#529—1224no—
343C2×#126—1221no—
344C2×#125—611no—
345C2×#124—612no—
346C2×#124—611no—
347C2×#123—1221no—
348C2×C22⋊Q8—611no—
349C2×#121—611no—
350C2×#121—1221no—
351C2×#121—1221no—
352C2×C4×Q8C2×D6111yescharacteristic
353C2×C4×D4—611no—
354C2×C4×D4—1221no—
355C2×C4×D4—1221no—
356C2×C4×D4—1221no—
357C2×#117—1221no—
358C22×C42—611no—
359#495—6116no—
360#488—6116no—
361#462C2×D6118yescomplemented
362#461—618no—
363#460—618no—
364#459—618no—
365#452—6116no—
366#449—6116no—
367#431—618no—
368C2×C4⋊C8—611no—
369C2×C4⋊C8C2×D6111yescharacteristic
370C2×#103—612no—
371C2×#103C2×D6112yes—
372C2×#102—612no—
373C2×#102—612no—
374C2×C22⋊C8—612no—
375C2×C4×C8—612no—
376C61C2×#321211yescharacteristic, complemented, Sylow
377C2×#41—618no—
378C2×#41—1224no—
379C2×#41—2444no—
380C2×#41—2444no—
381C22×Q8C22×D6111yescharacteristic
382C22×Q8C22×D6112yes—
383C22×D4—611no—
384C22×D4—612no—
385C22×D4—1221no—
386C22×D4—1222no—
387C22×D4—1221no—
388C22×D4—1221no—
389C23×C4—611no—
390C23×C4—611no—
391C23×C4—611no—
392C23×C4—1222no—
393C23×C4—1221no—
394C2×Q16—44no—
395C2×Q16C22×D6118yes—
396C2×SD16—618no—
397C2×SD16—618no—
398C2×SD16—2444no—
399C2×SD16—2444no—
400C2×D8—618no—
401C2×D8—2444no—
402C22×C8—612no—
403C22×C8C22×D6112yes—
404C4⋊Q8—22no—
405C4⋊Q8C22×D6114yes—
406#127—614no—
407#127—1222no—
408#126—1228no—
409#125—614no—
410#125—1222no—
411#124—614no—
412#124—618no—
413#124—1222no—
414#124—1224no—
415#123—1228no—
416C22⋊Q8—614no—
417C22⋊Q8—1222no—
418#121—614no—
419#121—1222no—
420#121—1228no—
421#121—1228no—
422C4×Q8—22no—
423C4×Q8C22×D6114yes—
424C4×D4—614no—
425C4×D4—1228no—
426C4×D4—1228no—
427C4×D4—1228no—
428C4×D4—1222no—
429#117—1228no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—611no—
434C2×C4⋊C4—1221no—
435C2×C4⋊C4—1221no—
436C2×C4⋊C4—1221no—
437C2×C4⋊C4C22×D6111yescharacteristic
438C2×C22⋊C4—1221no—
439C2×C22⋊C4—1221no—
440C2×C22⋊C4—1222no—
441C2×C22⋊C4—1222no—
442C2×C22⋊C4—1221no—
443C2×C22⋊C4—1221no—
444C2×C22⋊C4—1221no—
445C2×C42—21no—
446C2×C42—611no—
447C2×C42—611no—
448C2×C42—611no—
449C2×C42—614no—
450C2×C42—614no—
451C2×C42C22×D6111yescharacteristic
452C4⋊C8—614no—
453C4⋊C8C22×D6114yes—
454#103—618no—
455#103C22×D6118yes—
456#102—618no—
457#102—618no—
458C22⋊C8—618no—
459C4×C8—618no—
460C24—611no—
461C24—1221no—
462C24—1222no—
463#41—2448no—
464#41—2448no—
465#41—24416no—
466C2×Q8—21no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—24no—
470C2×Q8—22no—
471C2×Q8—24no—
472C2×Q8C23×D6114yes—
473C2×Q8C23×D6112yes—
474C2×D4—614no—
475C2×D4—612no—
476C2×D4—1224no—
477C2×D4—1228no—
478C2×D4—1221no—
479C2×D4—1224no—
480C2×D4—1224no—
481C2×D4—1222no—
482C2×D4—1222no—
483C2×D4—1224no—
484C2×D4—1222no—
485C2×D4—1224no—
486C2×D4—2444no—
487C2×D4—2448no—
488C2×D4—2444no—
489C2×D4—2444no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—611no—
494C22×C4—611no—
495C22×C4—611no—
496C22×C4—614no—
497C22×C4—612no—
498C22×C4—612no—
499C22×C4—614no—
500C22×C4—1228no—
501C22×C4—1222no—
502C22×C4—1222no—
503C22×C4—1224no—
504C22×C4—1221no—
505C22×C4—1224no—
506C22×C4—2442no—
507C22×C4—2448no—
508C22×C4—2444no—
509C22×C4D4×D6111yescharacteristic
510C22×C4D4×D6111yescharacteristic
511C22×C4C23×D6111yescharacteristic
512Q16—48no—
513SD16—2448no—
514SD16—2448no—
515D8—2448no—
516C2×C8—24no—
517C2×C8—614no—
518C2×C8—1224no—
519C2×C8C23×D6114yes—
520C4⋊C4—24no—
521C4⋊C4—24no—
522C4⋊C4—24no—
523C4⋊C4—21no—
524C4⋊C4—612no—
525C4⋊C4—1224no—
526C4⋊C4—1224no—
527C4⋊C4—1224no—
528C4⋊C4—1221no—
529C4⋊C4C23×D6112yes—
530C22⋊C4—1224no—
531C22⋊C4—1224no—
532C22⋊C4—1228no—
533C22⋊C4—1228no—
534C22⋊C4—1224no—
535C22⋊C4—1224no—
536C22⋊C4—1224no—
537C42—24no—
538C42—614no—
539C42—614no—
540C42—612no—
541C42—612no—
542C42D4×D6112yes—
543C42C23×D6112yes—
544C23—612no—
545C23—1222no—
546C23—1222no—
547C23—1222no—
548C23—1222no—
549C23—1224no—
550C23—2442no—
551C23—2444no—
552C23—2444no—
553C23—2442no—
554C23—2444no—
555C23—2442no—
556C23C2×D4×D6111yescharacteristic
557Q8—22no—
558Q8—24no—
559Q8—22no—
560Q8—24no—
561Q8—42no—
562Q8—44no—
563D4—1222no—
564D4—1224no—
565D4—1222no—
566D4—1224no—
567D4—2448no—
568D4—2448no—
569D4—24416no—
570D4—2448no—
571D4—2442no—
572D4—2444no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—42no—
578C2×C4—44no—
579C2×C4—42no—
580C2×C4—612no—
581C2×C4—612no—
582C2×C4—612no—
583C2×C4—1222no—
584C2×C4—1222no—
585C2×C4—1222no—
586C2×C4—1228no—
587C2×C4—1224no—
588C2×C4—1222no—
589C2×C4—1222no—
590C2×C4—1222no—
591C2×C4—2444no—
592C2×C4—24416no—
593C2×C4—2442no—
594C2×C4—2448no—
595C2×C4#1451980014yes—
596C2×C4C2×D4×D6112yes—
597C2×C4C2×D4×D6112yes—
598C2×C4C2×D4×D6111yescharacteristic
599C2×C4#1451982212yes—
600C2×C4#1451982312yes—
601C2×C4C24×D6111yescharacteristic
602C8—24no—
603C8—1224no—
604C22—1222no—
605C22—1222no—
606C22—1222no—
607C22—4884no—
608C22—4888no—
609C22—2442no—
610C22—2444no—
611C22—2444no—
612C22—2442no—
613C22—2444no—
614C22—2442no—
615C22—2444no—
616C22#1684032812yes—
617C22C2×#1451980012yes—
618C22#1684056112yes—
619C22C22×D4×D6111yescharacteristic
620C4—22no—
621C4—42no—
622C4—44no—
623C4—42no—
624C4—1222no—
625C4—1222no—
626C4—1222no—
627C4—2442no—
628C4#1684032812yes—
629C4C2×#1451980014yes—
630C4C2×#1451982211yescharacteristic
631C4C2×#1451982311yescharacteristic
632C2—4882no—
633C2—4884no—
634C2—2442no—
635C2#2145680014yesdirect product factor
636C2C2×#1684032811yescharacteristic
637C2C22×#1451980011yescharacteristic
638C2C2×#1684056111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#462C2
socleC23×C61C22×D4
hypercenterC2×#462D61
hypocenterC61C2×#3212
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
1. C2×#16840313C2semidirect
2. C2×#16840299C2semidirect
3. #21456800C2direct (N × H)
4. C2×#16840147C2semidirect
5. C2×#16840118C2semidirect
6. C2×#16839962C2semidirect
7. C2×#16839964C2semidirect
8. C2×#16839958C2semidirect
9. C2×#16839923C2semidirect
10. C2×#16839910C2semidirect
11. C2×#16839814C2semidirect
12. C2×C61×#462C2semidirect
18. #16840313C22semidirect
21. #16840299C22semidirect
37. #16840147C22semidirect
38. #16840118C22semidirect
39. #16839964C22semidirect
40. #16839962C22semidirect
41. #16839958C22semidirect
42. #16839923C22semidirect
43. #16839910C22semidirect
44. #16839814C22semidirect
54. C61×#462C22semidirect
318. C2×#462D61semidirect
325. C2×C61#3212semidirect
361. #462C2×D61semidirect
376. C61C2×#3212semidirect
635. C2#21456800direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403132
C2×#168402992
#214568002
C2×#168401472
C2×#168401182
C2×#168399622
C2×#168399642
C2×#168399582
C2×#168399232
C2×#168399102
C2×#168398142
C2×C61×#4622
C2×#321261