Finite Group Databasebeta

← C2×#21456794 #30551232

Subgroups — C2×#21456794 #30551232

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×#16840294C211yesmaximal, characteristic, complemented
3#21456794C2116yesmaximal, direct product factor
4C2×#16840143C212yesmaximal, complemented
5C2×#16840118C212yesmaximal, complemented
6C2×#16839969C211yesmaximal, characteristic, complemented
7C2×#16839963C211yesmaximal, characteristic, complemented
8C2×#16839957C211yesmaximal, characteristic, complemented
9C2×#16839927C212yesmaximal, complemented
10C2×#16839906C212yesmaximal, complemented
11C2×#16839814C211yesmaximal, characteristic, complemented
12C2×C61×#461C211yesmaximal, characteristic, complemented
13C22×#11758226C2212yes—
14C22×#11758202C2212yes—
15C22×#11758190C2212yes—
16C22×#11758199C2212yes—
17#16840313—24no—
18#16840313C2218yescomplemented
19C2×#14519774C2211yescharacteristic
20#16840294—24no—
21#16840294C2218yescomplemented
22C2×#14519770—21no—
23C2×#14519768C2211yescharacteristic
24C2×#14519766C2212yes—
25C2×#14519764C2211yescharacteristic
26C2×#14519759—21no—
27C2×#14519757C2211yescharacteristic
28C2×#14519752—21no—
29C2×#14519752—21no—
30C2×#14519748C2211yescharacteristic
31C2×C4×Dic122C2211yescharacteristic
32C2×#14519739—21no—
33C2×#14519739—21no—
34C2×C4×C22⋊D61—21no—
35C2×#14519736—21no—
36C2×C42×D61C2211yescharacteristic
37#16840143C22116yescomplemented
38#16840118C22116yescomplemented
39#16839969C2218yescomplemented
40#16839963C2218yescomplemented
41#16839957C2218yescomplemented
42#16839927C22116yescomplemented
43#16839906C22116yescomplemented
44#16839814C2218yescomplemented
45C2×C4⋊#92418C2211yescharacteristic
46C2×#14519701C2212yes—
47C2×#14519699C2212yes—
48C2×#14519697C2212yes—
49C2×#14519689C2212yes—
50C2×C8×Dic61C2212yes—
51C22×SD16×C61C2212yes—
52C2×C4⋊Q8×C61C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C61×#461C2218yescomplemented
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×#103×C61C2212yes—
57C2×#11758226—24no—
58C2×#11758226—44no—
59C2×#11758226—44no—
60C2×#11758226C2318yes—
61C22×Dic122C2311yescharacteristic
62C22×D244—22no—
63C22×D244—21no—
64C22×D244—21no—
65C22×D244C2312yes—
66C22×C22⋊D61—21no—
67C22×C4×D61—22no—
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61C2311yescharacteristic
71C2×#11758202—44no—
72C2×#11758202C2318yes—
73C2×#11758190—44no—
74C2×#11758190C2318yes—
75C2×#11758199—44no—
76C2×#11758199C2318yes—
77C22×#92418C2312yes—
78#14519774—22no—
79#14519774C2314yes—
80#14519770—28no—
81#14519768—22no—
82#14519768C2314yes—
83#14519766—24no—
84#14519766C2318yes—
85#14519764—22no—
86#14519764C2314yes—
87#14519759—28no—
88#14519757—22no—
89#14519757C2314yes—
90#14519752—28no—
91#14519752—28no—
92#14519748—22no—
93#14519748C2314yes—
94C4×Dic122—22no—
95C4×Dic122C2314yes—
96#14519739—28no—
97#14519739—28no—
98C4×C22⋊D61—28no—
99#14519736—28no—
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61—21no—
102C2×C4⋊Dic61C2311yescharacteristic
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61—21no—
107C2×C22⋊Dic61—21no—
108C2×#11758198—21no—
109C2×#11758198—22no—
110C2×#11758198—22no—
111C2×C4×Dic61—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×D4×C61C2311yescharacteristic
125C23×C4×C61—21no—
126C2×SD16×C61—44no—
127C2×SD16×C61C2318yes—
128C22×C8×C61C2312yes—
129C4⋊Q8×C61—22no—
130C4⋊Q8×C61C2314yes—
131C4×D4×C61—22no—
132C4×D4×C61C2314yes—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C42×C61C2311yescharacteristic
138C4⋊C8×C61C2314yes—
139#103×C61C2318yes—
140C24×C61—21no—
141C23×D61—22no—
142C23×D61C2×D411yescharacteristic
143C2×Q8×C61—22no—
144C2×Q8×C61—24no—
145C2×Q8×C61—24no—
146C2×Q8×C61C2414yes—
147C2×D4×C61—21no—
148C2×D4×C61—22no—
149C2×D4×C61—22no—
150C2×D4×C61C2412yes—
151C22×C4×C61—22no—
152C22×C4×C61—21no—
153C22×C4×C61—24no—
154C22×C4×C61—44no—
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2411yescharacteristic
158C2×C22⋊D61—24no—
159C2×C22⋊D61—44no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61C2×D411yescharacteristic
163C22×Dic61C2×D411yescharacteristic
164C22×Dic61C2×D411yescharacteristic
165#11758226—48no—
166#11758226—48no—
167#11758226—416no—
168C2×D244—24no—
169C2×D244—24no—
170C2×D244—28no—
171C2×D244—24no—
172C2×D244—24no—
173C2×D244—22no—
174C2×D244—44no—
175C2×D244—48no—
176C2×D244—44no—
177C2×D244C2414yes—
178C2×C4×D61—24no—
179C2×C4×D61—22no—
180C2×C4×D61—22no—
181C2×C4×D61—28no—
182C2×C4×D61—42no—
183C2×C4×D61—48no—
184C2×C4×D61C2×D414yes—
185C2×C4×D61C2×D412yes—
186C2×C4×D61C2×D414yes—
187C2×C4×D61C2412yes—
188C2×Dic122—22no—
189C2×Dic122—22no—
190C2×Dic122—21no—
191C2×Dic122C2412yes—
192SD16×C61—48no—
193C2×C8×C61—24no—
194C2×C8×C61C2414yes—
195C4⋊C4×C61—24no—
196C4⋊C4×C61—24no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61C2412yes—
199C22⋊C4×C61—24no—
200C42×C61C2×D412yes—
201C42×C61C2412yes—
202C22⋊Dic61—24no—
203C22⋊Dic61—24no—
204C22⋊Dic61—24no—
205#11758202—48no—
206#11758199—48no—
207#11758198—24no—
208#11758198—28no—
209#11758198—28no—
210C4⋊Dic61—21no—
211C4⋊Dic61—24no—
212C4⋊Dic61—24no—
213C4⋊Dic61C2412yes—
214#11758196—24no—
215#11758196—24no—
216C4×Dic61—24no—
217C4×Dic61C2×D412yes—
218C4×Dic61C2×D414yes—
219C4×Dic61C2×D414yes—
220C4×Dic61C2412yes—
221C2×#92418—24no—
222C2×#92418C2414yes—
223#11758190—48no—
224C23×C61—22no—
225C23×C61—42no—
226C23×C61—42no—
227C23×C61—42no—
228C23×C61C22×D411yescharacteristic
229C22×D61—22no—
230C22×D61—22no—
231C22×D61—22no—
232C22×D61—24no—
233C22×D61—44no—
234C22×D61—44no—
235C22×D61—44no—
236C22×D61C22×D412yes—
237Q8×C61—24no—
238Q8×C61—24no—
239Q8×C61—44no—
240D4×C61—22no—
241D4×C61—22no—
242D4×C61—42no—
243C2×C4×C61—22no—
244C2×C4×C61—22no—
245C2×C4×C61—24no—
246C2×C4×C61—44no—
247C2×C4×C61—42no—
248C2×C4×C61—48no—
249C2×C4×C61#13514yes—
250C2×C4×C61C22×D412yes—
251C2×C4×C61C22×D411yescharacteristic
252C2×C4×C61C22×D412yes—
253C2×C4×C61H(5,𝔽2)12yes—
254C2×C4×C61H(5,𝔽2)12yes—
255C2×C4×C61C2511yescharacteristic
256C22⋊D61—48no—
257C2×Dic61—22no—
258C2×Dic61—22no—
259C2×Dic61—22no—
260C2×Dic61—22no—
261C2×Dic61—22no—
262C2×Dic61—42no—
263C2×Dic61—42no—
264C2×Dic61C22×D412yes—
265C2×Dic61C22×D412yes—
266C2×Dic61C22×D412yes—
267D244—24no—
268D244—24no—
269D244—48no—
270D244—416no—
271D244—44no—
272D244—48no—
273C4×D61—24no—
274C4×D61—28no—
275C4×D61—22no—
276C4×D61—22no—
277C4×D61—44no—
278C4×D61—416no—
279Dic122—22no—
280Dic122—22no—
281Dic122—42no—
282C8×C61—24no—
283#92418—24no—
284C2×#3212—611nomaximal, Sylow
285C22×C61—42no—
286C22×C61—42no—
287C22×C61—42no—
288C22×C61—84no—
289C22×C61#53512yes—
290C22×C61C2×#13512yes—
291C22×C61#57512yes—
292C22×C61C23×D411yescharacteristic
293C2×D61—22no—
294C2×D61—22no—
295C2×D61—22no—
296C2×D61—44no—
297C2×D61—44no—
298C2×D61—44no—
299C2×D61—44no—
300C2×D61—88no—
301C4×C61—22no—
302C4×C61—44no—
303C4×C61—42no—
304C4×C61#53512yes—
305C4×C61C2×#13514yes—
306C4×C61C2×H(5,𝔽2)11yescharacteristic
307C4×C61C2×H(5,𝔽2)11yescharacteristic
308Dic61—22no—
309Dic61—22no—
310Dic61—22no—
311Dic61—42no—
312Dic61—42no—
313C2×#532—611no—
314C2×#529—611no—
315#3212—6116no—
316C2×#495—612no—
317C2×#488—612no—
318C2×#462—611no—
319C2×#460—611no—
320C2×#461D6111yescharacteristic, complemented
321C2×#459—611no—
322C2×#452—612no—
323C2×#449—612no—
324C2×#431—611no—
325C2×C61—82no—
326C2×C61#321214yescomplemented
327C2×C61C2×#53511yescharacteristic
328C2×C61C22×#13511yescharacteristic
329C2×C61C2×#57511yescharacteristic
330D61—42no—
331D61—84no—
332C22×#41—612no—
333C22×Q16—612no—
334C22×SD16—612no—
335C22×SD16C2×D6112yes—
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×Q8—611no—
353C2×C4×D4—1221no—
354C2×C4×D4—1221no—
355C2×C4×D4—1221no—
356C2×C4×D4C2×D6111yescharacteristic
357C2×#117—1221no—
358C22×C42—611no—
359#495—6116no—
360#488—6116no—
361#462—618no—
362#461C2×D6118yescomplemented
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×Q8—611no—
382C22×Q8C22×D6112yes—
383C22×D4—612no—
384C22×D4—1222no—
385C22×D4—1221no—
386C22×D4—1221no—
387C22×D4—1221no—
388C22×D4C22×D6111yescharacteristic
389C23×C4—21no—
390C23×C4—611no—
391C23×C4—611no—
392C23×C4—611no—
393C23×C4—1222no—
394C2×Q16—618no—
395C2×Q16—2444no—
396C2×SD16—44no—
397C2×SD16—618no—
398C2×SD16—2444no—
399C2×SD16C22×D6118yes—
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—618no—
412#124—614no—
413#124—1222no—
414#124—1224no—
415#123—1228no—
416C22⋊Q8—614no—
417C22⋊Q8—1222no—
418#121—614no—
419#121—1228no—
420#121—1228no—
421#121—1222no—
422C4×Q8—614no—
423C4×Q8—1222no—
424C4×D4—22no—
425C4×D4—1228no—
426C4×D4—1228no—
427C4×D4—1228no—
428C4×D4C22×D6114yes—
429#117—1228no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—611no—
433C2×C4⋊C4—1221no—
434C2×C4⋊C4—1221no—
435C2×C4⋊C4—1221no—
436C2×C4⋊C4—1221no—
437C2×C4⋊C4C22×D6111yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4—1222no—
440C2×C22⋊C4—1222no—
441C2×C22⋊C4—1221no—
442C2×C22⋊C4—1221no—
443C2×C22⋊C4—1221no—
444C2×C22⋊C4—1221no—
445C2×C42—611no—
446C2×C42—611no—
447C2×C42—611no—
448C2×C42—614no—
449C2×C42—614no—
450C2×C42—1221no—
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—21no—
461C24—611no—
462C24—1222no—
463#41—2448no—
464#41—2448no—
465#41—24416no—
466C2×Q8—22no—
467C2×Q8—24no—
468C2×Q8—24no—
469C2×Q8—612no—
470C2×Q8—1221no—
471C2×Q8—1222no—
472C2×Q8—1222no—
473C2×Q8C23×D6114yes—
474C2×D4—21no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—614no—
478C2×D4—1228no—
479C2×D4—1224no—
480C2×D4—1224no—
481C2×D4—1224no—
482C2×D4—1222no—
483C2×D4—1224no—
484C2×D4—1224no—
485C2×D4—2444no—
486C2×D4—2448no—
487C2×D4—2444no—
488C2×D4—2444no—
489C2×D4C23×D6112yes—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—44no—
494C22×C4—611no—
495C22×C4—611no—
496C22×C4—611no—
497C22×C4—614no—
498C22×C4—612no—
499C22×C4—612no—
500C22×C4—614no—
501C22×C4—1228no—
502C22×C4—1222no—
503C22×C4—1222no—
504C22×C4—1224no—
505C22×C4—1221no—
506C22×C4—1221no—
507C22×C4—2442no—
508C22×C4—2448no—
509C22×C4D4×D6111yescharacteristic
510C22×C4D4×D6111yescharacteristic
511C22×C4C23×D6111yescharacteristic
512Q16—2448no—
513SD16—48no—
514SD16—2448no—
515D8—2448no—
516C2×C8—24no—
517C2×C8—614no—
518C2×C8—1224no—
519C2×C8C23×D6114yes—
520C4⋊C4—24no—
521C4⋊C4—24no—
522C4⋊C4—21no—
523C4⋊C4—612no—
524C4⋊C4—1224no—
525C4⋊C4—1224no—
526C4⋊C4—1224no—
527C4⋊C4—1221no—
528C4⋊C4—1224no—
529C4⋊C4C23×D6112yes—
530C22⋊C4—24no—
531C22⋊C4—1228no—
532C22⋊C4—1228no—
533C22⋊C4—1224no—
534C22⋊C4—1224no—
535C22⋊C4—1224no—
536C22⋊C4—1224no—
537C42—614no—
538C42—614no—
539C42—612no—
540C42—612no—
541C42—1224no—
542C42D4×D6112yes—
543C42C23×D6112yes—
544C23—22no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—612no—
549C23—1222no—
550C23—1222no—
551C23—1222no—
552C23—1224no—
553C23—2444no—
554C23—2444no—
555C23—2444no—
556C23C2×D4×D6111yescharacteristic
557Q8—24no—
558Q8—24no—
559Q8—44no—
560Q8—1222no—
561Q8—1222no—
562Q8—2442no—
563D4—22no—
564D4—22no—
565D4—42no—
566D4—1224no—
567D4—1224no—
568D4—2448no—
569D4—24416no—
570D4—2448no—
571D4—2448no—
572D4—2444no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—42no—
577C2×C4—44no—
578C2×C4—48no—
579C2×C4—612no—
580C2×C4—612no—
581C2×C4—612no—
582C2×C4—1222no—
583C2×C4—1222no—
584C2×C4—1222no—
585C2×C4—1228no—
586C2×C4—1224no—
587C2×C4—1222no—
588C2×C4—1222no—
589C2×C4—1222no—
590C2×C4—1222no—
591C2×C4—2444no—
592C2×C4—24416no—
593C2×C4—2442no—
594C2×C4—2442no—
595C2×C4#1451979814yes—
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—42no—
605C22—42no—
606C22—42no—
607C22—84no—
608C22—1222no—
609C22—1222no—
610C22—1222no—
611C22—4888no—
612C22—2444no—
613C22—2444no—
614C22—2444no—
615C22—2444no—
616C22#1684032812yes—
617C22C2×#1451979812yes—
618C22#1684056112yes—
619C22C22×D4×D6111yescharacteristic
620C4—22no—
621C4—42no—
622C4—44no—
623C4—1222no—
624C4—1222no—
625C4—1222no—
626C4—2442no—
627C4—2442no—
628C4#1684032812yes—
629C4C2×#1451979814yes—
630C4C2×#1451982211yescharacteristic
631C4C2×#1451982311yescharacteristic
632C2—82no—
633C2—4884no—
634C2—2442no—
635C2#2145679414yesdirect product factor
636C2C2×#1684032811yescharacteristic
637C2C22×#1451979811yescharacteristic
638C2C2×#1684056111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#461C2
socleC23×C61C22×D4
hypercenterC2×#461D61
hypocenterC61C2×#3212
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#16840313C2semidirect
2. C2×#16840294C2semidirect
3. #21456794C2direct (N × H)
4. C2×#16840143C2semidirect
5. C2×#16840118C2semidirect
6. C2×#16839969C2semidirect
7. C2×#16839963C2semidirect
8. C2×#16839957C2semidirect
9. C2×#16839927C2semidirect
10. C2×#16839906C2semidirect
11. C2×#16839814C2semidirect
12. C2×C61×#461C2semidirect
18. #16840313C22semidirect
21. #16840294C22semidirect
37. #16840143C22semidirect
38. #16840118C22semidirect
39. #16839969C22semidirect
40. #16839963C22semidirect
41. #16839957C22semidirect
42. #16839927C22semidirect
43. #16839906C22semidirect
44. #16839814C22semidirect
54. C61×#461C22semidirect
320. C2×#461D61semidirect
326. C2×C61#3212semidirect
362. #461C2×D61semidirect
376. C61C2×#3212semidirect
635. C2#21456794direct (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×#168402942
#214567942
C2×#168401432
C2×#168401182
C2×#168399692
C2×#168399632
C2×#168399572
C2×#168399272
C2×#168399062
C2×#168398142
C2×C61×#4612
C2×#321261