Finite Group Databasebeta

← C2×#21456829 #30551306

Subgroups — C2×#21456829 #30551306

Order 15616.

2166 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×#16840316C211yesmaximal, characteristic, complemented
2C2×#16840313C211yesmaximal, characteristic
3#21456829C2116yesmaximal, direct product factor
4C2×#16840155C212yesmaximal, complemented
5C2×#16840123C212yesmaximal, complemented
6C2×#16839969C211yesmaximal, characteristic, complemented
7C2×#16839963C211yesmaximal, characteristic, complemented
8C2×#16839962C211yesmaximal, characteristic, complemented
9C2×#16839927C212yesmaximal, complemented
10C2×#16839923C212yesmaximal, complemented
11C2×#16839818C211yesmaximal, characteristic, complemented
12C2×C61×#462C211yesmaximal, characteristic, complemented
13C22×#11758226C2212yes—
14C22×#11758202C2212yes—
15C22×#11758190C2212yes—
16C22×#11758201C2212yes—
17#16840316—24no—
18#16840316C2218yescomplemented
19#16840313—24no—
20#16840313C2218yes—
21C2×#14519776C2211yescharacteristic
22C2×#14519775C2211yescharacteristic
23C2×#14519774C2211yescharacteristic
24C2×#14519767—21no—
25C2×#14519766C2212yes—
26C2×#14519757C2211yescharacteristic
27C2×#14519755—21no—
28C2×#14519753C2211yescharacteristic
29C2×#14519752—21no—
30C2×#14519752—21no—
31C2×C4×Dic122—21no—
32C2×C4×Dic122C2211yescharacteristic
33C2×#14519739—21no—
34C2×#14519739—21no—
35C2×#14519734—21no—
36C2×C42×D61C2211yescharacteristic
37#16840155C22116yescomplemented
38#16840123C22116yescomplemented
39#16839969C2218yescomplemented
40#16839963C2218yescomplemented
41#16839962C2218yescomplemented
42#16839927C22116yescomplemented
43#16839923C22116yescomplemented
44#16839818C2218yescomplemented
45C2×C4⋊#92418C2211yescharacteristic
46C2×#14519701C2212yes—
47C2×#14519699C2212yes—
48C2×#14519697C2212yes—
49C2×#14519689C2212yes—
50C2×#14519687C2212yes—
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×Dic122—21no—
62C22×Dic122C2311yescharacteristic
63C22×D244—22no—
64C22×D244—21no—
65C22×D244—21no—
66C22×D244C2312yes—
67C22×C4×D61—22no—
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61C2311yescharacteristic
71C2×#11758202—44no—
72C2×#11758202C2318yes—
73C2×#11758190—44no—
74C2×#11758190C2318yes—
75C2×#11758201—44no—
76C2×#11758201C2318yes—
77C22×#92418C2312yes—
78#14519776—22no—
79#14519776C2314yes—
80#14519775—22no—
81#14519775C2314yes—
82#14519774—22no—
83#14519774C2314yes—
84#14519767—28no—
85#14519766—24no—
86#14519766C2318yes—
87#14519757—22no—
88#14519757C2314yes—
89#14519755—28no—
90#14519753—22no—
91#14519753C2314yes—
92#14519752—28no—
93#14519752—28no—
94C4×Dic122—22no—
95C4×Dic122—28no—
96C4×Dic122C2314yes—
97#14519739—28no—
98#14519739—28no—
99#14519734—28no—
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61C2311yescharacteristic
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×#11758198—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—
122#14519687C2318yes—
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×D61C2×D411yescharacteristic
142C2×Q8×C61—22no—
143C2×Q8×C61—21no—
144C2×Q8×C61—24no—
145C2×Q8×C61—24no—
146C2×Q8×C61—22no—
147C2×Q8×C61—22no—
148C2×Q8×C61C2414yes—
149C2×Q8×C61C2412yes—
150C22×C4×C61—22no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2411yescharacteristic
156C22×Dic61—21no—
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—28no—
167C2×D244—24no—
168C2×D244—24no—
169C2×D244—22no—
170C2×D244—44no—
171C2×D244—48no—
172C2×D244—44no—
173C2×D244C2414yes—
174C2×C4×D61—24no—
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—28no—
178C2×C4×D61—42no—
179C2×C4×D61—48no—
180C2×C4×D61C2×D414yes—
181C2×C4×D61C2×D412yes—
182C2×C4×D61C2×D414yes—
183C2×C4×D61C2412yes—
184C2×Dic122—22no—
185C2×Dic122—22no—
186C2×Dic122—21no—
187C2×Dic122—24no—
188C2×Dic122—44no—
189C2×Dic122C2412yes—
190Q16×C61—48no—
191C2×C8×C61—24no—
192C2×C8×C61C2414yes—
193C4⋊C4×C61—24no—
194C4⋊C4×C61—24no—
195C4⋊C4×C61—24no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61C2412yes—
198C42×C61—24no—
199C42×C61C2×D412yes—
200C42×C61C2412yes—
201#11758202—48no—
202#11758201—48no—
203#11758198—24no—
204#11758198—24no—
205#11758198—28no—
206#11758198—28no—
207C4⋊Dic61—21no—
208C4⋊Dic61—24no—
209C4⋊Dic61C2412yes—
210#11758196—24no—
211#11758196—24no—
212#11758196—24no—
213#11758196—24no—
214#11758196—24no—
215C4×Dic61—24no—
216C4×Dic61C2×D412yes—
217C4×Dic61C2×D414yes—
218C4×Dic61C2×D414yes—
219C4×Dic61C2412yes—
220C2×#92418—24no—
221C2×#92418C2414yes—
222#11758190—48no—
223C23×C61C22×D411yescharacteristic
224C22×D61—22no—
225C22×D61—22no—
226C22×D61—22no—
227C22×D61—24no—
228C22×D61—44no—
229C22×D61—44no—
230C22×D61—44no—
231C22×D61C22×D412yes—
232Q8×C61—22no—
233Q8×C61—24no—
234Q8×C61—22no—
235Q8×C61—24no—
236Q8×C61—44no—
237Q8×C61—42no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—24no—
242C2×C4×C61—44no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61#13714yes—
246C2×C4×C61C22×D412yes—
247C2×C4×C61C22×D411yescharacteristic
248C2×C4×C61C22×D412yes—
249C2×C4×C61H(5,𝔽2)12yes—
250C2×C4×C61H(5,𝔽2)12yes—
251C2×C4×C61C2511yescharacteristic
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—22no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—42no—
258C2×Dic61—42no—
259C2×Dic61C22×D412yes—
260C2×Dic61C22×D412yes—
261C2×Dic61C22×D412yes—
262D244—24no—
263D244—24no—
264D244—48no—
265D244—416no—
266D244—44no—
267D244—48no—
268C4×D61—24no—
269C4×D61—28no—
270C4×D61—22no—
271C4×D61—22no—
272C4×D61—44no—
273C4×D61—416no—
274Dic122—22no—
275Dic122—22no—
276Dic122—48no—
277Dic122—42no—
278C8×C61—24no—
279#92418—24no—
280C2×#3216—611nomaximal, Sylow
281C22×C61#53512yes—
282C22×C61C2×#13712yes—
283C22×C61#57512yes—
284C22×C61C23×D411yescharacteristic
285C2×D61—22no—
286C2×D61—22no—
287C2×D61—22no—
288C2×D61—44no—
289C2×D61—44no—
290C2×D61—44no—
291C2×D61—44no—
292C2×D61—88no—
293C4×C61—22no—
294C4×C61—44no—
295C4×C61—42no—
296C4×C61—42no—
297C4×C61#53512yes—
298C4×C61C2×#13714yes—
299C4×C61C2×H(5,𝔽2)11yescharacteristic
300C4×C61C2×H(5,𝔽2)11yescharacteristic
301Dic61—22no—
302Dic61—22no—
303Dic61—22no—
304Dic61—42no—
305Dic61—42no—
306C2×#533—611no—
307C2×#532—611no—
308#3216—6116no—
309C2×#497—612no—
310C2×#489—612no—
311C2×#462—611no—
312C2×#462D6111yescharacteristic, complemented
313C2×#460—611no—
314C2×#460—611no—
315C2×#452—612no—
316C2×#452—612no—
317C2×#432—611no—
318C2×C61#321614yescomplemented
319C2×C61C2×#53511yescharacteristic
320C2×C61C22×#13711yescharacteristic
321C2×C61C2×#57511yescharacteristic
322D61—42no—
323D61—84no—
324C22×#41—612no—
325C22×Q16—612no—
326C22×Q16C2×D6112yes—
327C22×SD16—612no—
328C22×SD16—612no—
329#533—618no—
330#533—1224no—
331#532—618no—
332#532—1224no—
333C2×C4⋊Q8—611no—
334C2×C4⋊Q8—611no—
335C2×C4⋊Q8C2×D6111yescharacteristic
336C2×#127—611no—
337C2×#125—1221no—
338C2×#124—612no—
339C2×C22⋊Q8—611no—
340C2×C22⋊Q8—611no—
341C2×C22⋊Q8—1221no—
342C2×#121—1221no—
343C2×#121—1221no—
344C2×C4×Q8—611no—
345C2×C4×Q8—1221no—
346C2×C4×Q8C2×D6111yescharacteristic
347C2×C4×D4—1221no—
348C2×C4×D4—1221no—
349C2×#117—1221no—
350C22×C42—611no—
351#497—6116no—
352#489—6116no—
353#462—618no—
354#462C2×D6118yescomplemented
355#460—618no—
356#460—618no—
357#452—6116no—
358#452—6116no—
359#432—618no—
360C2×C4⋊C8—611no—
361C2×C4⋊C8C2×D6111yescharacteristic
362C2×#103—612no—
363C2×#103C2×D6112yes—
364C2×#102—612no—
365C2×#102—612no—
366C2×C22⋊C8—612no—
367C2×#97—612no—
368C61C2×#321611yescharacteristic, complemented, Sylow
369C2×#41—618no—
370C2×#41—1224no—
371C2×#41—2444no—
372C2×#41—2444no—
373C22×Q8—611no—
374C22×Q8—1221no—
375C22×Q8C22×D6111yescharacteristic
376C22×Q8C22×D6112yes—
377C22×D4—612no—
378C22×D4—1222no—
379C22×D4—1221no—
380C22×D4—1221no—
381C23×C4—611no—
382C23×C4—611no—
383C23×C4—611no—
384C23×C4—1222no—
385C2×Q16—44no—
386C2×Q16—618no—
387C2×Q16—2444no—
388C2×Q16C22×D6118yes—
389C2×SD16—618no—
390C2×SD16—618no—
391C2×SD16—2444no—
392C2×SD16—2444no—
393C22×C8—612no—
394C22×C8C22×D6112yes—
395C4⋊Q8—22no—
396C4⋊Q8—614no—
397C4⋊Q8—614no—
398C4⋊Q8—1222no—
399C4⋊Q8—1222no—
400C4⋊Q8C22×D6114yes—
401#127—614no—
402#127—1222no—
403#125—1228no—
404#124—618no—
405#124—1224no—
406C22⋊Q8—614no—
407C22⋊Q8—614no—
408C22⋊Q8—1222no—
409C22⋊Q8—1228no—
410C22⋊Q8—1222no—
411#121—1228no—
412#121—1228no—
413C4×Q8—22no—
414C4×Q8—614no—
415C4×Q8—1228no—
416C4×Q8—1222no—
417C4×Q8C22×D6114yes—
418C4×D4—1228no—
419C4×D4—1228no—
420#117—1228no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—1221no—
426C2×C4⋊C4—1221no—
427C2×C4⋊C4—1221no—
428C2×C4⋊C4—1221no—
429C2×C4⋊C4—1221no—
430C2×C4⋊C4—1221no—
431C2×C4⋊C4C22×D6111yescharacteristic
432C2×C22⋊C4—1222no—
433C2×C22⋊C4—1222no—
434C2×C22⋊C4—1221no—
435C2×C22⋊C4—1221no—
436C2×C42—21no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—614no—
441C2×C42—614no—
442C2×C42—1221no—
443C2×C42C22×D6111yescharacteristic
444C4⋊C8—614no—
445C4⋊C8C22×D6114yes—
446#103—618no—
447#103C22×D6118yes—
448#102—618no—
449#102—618no—
450C22⋊C8—618no—
451#97—618no—
452C24—611no—
453C24—1222no—
454#41—2448no—
455#41—2448no—
456#41—24416no—
457C2×Q8—21no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—24no—
461C2×Q8—22no—
462C2×Q8—24no—
463C2×Q8—612no—
464C2×Q8—1224no—
465C2×Q8—1221no—
466C2×Q8—1222no—
467C2×Q8—1222no—
468C2×Q8—2444no—
469C2×Q8C23×D6114yes—
470C2×Q8C23×D6112yes—
471C2×D4—614no—
472C2×D4—1228no—
473C2×D4—1224no—
474C2×D4—1224no—
475C2×D4—1222no—
476C2×D4—1224no—
477C2×D4—1224no—
478C2×D4—2444no—
479C2×D4—2448no—
480C2×D4—2444no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—614no—
488C22×C4—612no—
489C22×C4—612no—
490C22×C4—614no—
491C22×C4—1228no—
492C22×C4—1224no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4—1221no—
496C22×C4—1221no—
497C22×C4—2442no—
498C22×C4—2448no—
499C22×C4D4×D6111yescharacteristic
500C22×C4D4×D6111yescharacteristic
501C22×C4C23×D6111yescharacteristic
502Q16—48no—
503Q16—2448no—
504SD16—2448no—
505SD16—2448no—
506C2×C8—24no—
507C2×C8—614no—
508C2×C8—1224no—
509C2×C8C23×D6114yes—
510C4⋊C4—24no—
511C4⋊C4—24no—
512C4⋊C4—24no—
513C4⋊C4—21no—
514C4⋊C4—612no—
515C4⋊C4—1224no—
516C4⋊C4—1224no—
517C4⋊C4—1224no—
518C4⋊C4—1224no—
519C4⋊C4—1224no—
520C4⋊C4—1221no—
521C4⋊C4—1224no—
522C4⋊C4C23×D6112yes—
523C22⋊C4—1228no—
524C22⋊C4—1228no—
525C22⋊C4—1224no—
526C22⋊C4—1224no—
527C42—24no—
528C42—614no—
529C42—614no—
530C42—612no—
531C42—612no—
532C42—1224no—
533C42D4×D6112yes—
534C42C23×D6112yes—
535C23—612no—
536C23—1222no—
537C23—1222no—
538C23—1222no—
539C23—1224no—
540C23—2444no—
541C23—2444no—
542C23—2444no—
543C23C2×D4×D6111yescharacteristic
544Q8—22no—
545Q8—24no—
546Q8—22no—
547Q8—24no—
548Q8—42no—
549Q8—44no—
550Q8—1222no—
551Q8—1222no—
552Q8—2448no—
553Q8—2442no—
554D4—1224no—
555D4—1224no—
556D4—2448no—
557D4—24416no—
558D4—2448no—
559D4—2444no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—42no—
565C2×C4—44no—
566C2×C4—42no—
567C2×C4—612no—
568C2×C4—612no—
569C2×C4—612no—
570C2×C4—1222no—
571C2×C4—1222no—
572C2×C4—1222no—
573C2×C4—1228no—
574C2×C4—1224no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—1222no—
579C2×C4—2444no—
580C2×C4—24416no—
581C2×C4—2442no—
582C2×C4—2442no—
583C2×C4#1451980914yes—
584C2×C4C2×D4×D6112yes—
585C2×C4C2×D4×D6112yes—
586C2×C4C2×D4×D6111yescharacteristic
587C2×C4#1451982212yes—
588C2×C4#1451982312yes—
589C2×C4C24×D6111yescharacteristic
590C8—24no—
591C8—1224no—
592C22—1222no—
593C22—1222no—
594C22—1222no—
595C22—4888no—
596C22—2444no—
597C22—2444no—
598C22—2444no—
599C22—2444no—
600C22#1684032812yes—
601C22C2×#1451980912yes—
602C22#1684056112yes—
603C22C22×D4×D6111yescharacteristic
604C4—22no—
605C4—42no—
606C4—44no—
607C4—42no—
608C4—1222no—
609C4—1222no—
610C4—1222no—
611C4—2442no—
612C4—2442no—
613C4#1684032812yes—
614C4C2×#1451980914yes—
615C4C2×#1451982211yescharacteristic
616C4C2×#1451982311yescharacteristic
617C2—4884no—
618C2—2442no—
619C2#2145682914yesdirect product factor
620C2C2×#1684032811yescharacteristic
621C2C22×#1451980911yescharacteristic
622C2C2×#1684056111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#462C2
socleC23×C61C22×D4
prime radicalC2×#16840313C2
hypercenterC2×#462D61
hypocenterC61C2×#3216
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×#16840316C2semidirect
3. #21456829C2direct (N × H)
4. C2×#16840155C2semidirect
5. C2×#16840123C2semidirect
6. C2×#16839969C2semidirect
7. C2×#16839963C2semidirect
8. C2×#16839962C2semidirect
9. C2×#16839927C2semidirect
10. C2×#16839923C2semidirect
11. C2×#16839818C2semidirect
12. C2×C61×#462C2semidirect
18. #16840316C22semidirect
37. #16840155C22semidirect
38. #16840123C22semidirect
39. #16839969C22semidirect
40. #16839963C22semidirect
41. #16839962C22semidirect
42. #16839927C22semidirect
43. #16839923C22semidirect
44. #16839818C22semidirect
54. C61×#462C22semidirect
312. C2×#462D61semidirect
318. C2×C61#3216semidirect
354. #462C2×D61semidirect
368. C61C2×#3216semidirect
619. C2#21456829direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403162
C2×#168403132
#214568292
C2×#168401552
C2×#168401232
C2×#168399692
C2×#168399632
C2×#168399622
C2×#168399272
C2×#168399232
C2×#168398182
C2×C61×#4622
C2×#321661