Finite Group Databasebeta

← C2×#21456946 #30552053

Subgroups — C2×#21456946 #30552053

Order 15616.

2286 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840309C211yesmaximal, characteristic
2C2×C4⋊Q8×D61C211yesmaximal, characteristic, complemented
3#21456946C2116yesmaximal, direct product factor
4C2×#16840159C212yesmaximal, complemented
5C2×#16840107C212yesmaximal, complemented
6C2×#16840082C212yesmaximal, complemented
7C2×#16840079C212yesmaximal, complemented
8C2×#16840053C211yesmaximal, characteristic, complemented
9C2×#16840052C211yesmaximal, characteristic, complemented
10C2×#16840049C211yesmaximal, characteristic, complemented
11C2×#16839814C211yesmaximal, characteristic, complemented
12C2×C61×#476C211yesmaximal, characteristic, complemented
13C22×#11758222—21no—
14C22×Q8×D61—21no—
15#16840309—24no—
16#16840309C2218yes—
17C2×#14519777C2211yescharacteristic
18C2×#14519776—21no—
19C2×#14519776C2212yes—
20C2×#14519776C2211yescharacteristic
21C2×#14519775—21no—
22C4⋊Q8×D61—24no—
23C4⋊Q8×D61C2218yescomplemented
24C2×#14519773C2211yescharacteristic
25C2×#14519763—21no—
26C2×#14519752C2211yescharacteristic
27C2×#14519750—21no—
28C2×#14519748C2211yescharacteristic
29C2×C4×D244C2211yescharacteristic
30C2×C4×C22⋊D61—21no—
31C2×C4⋊C4×D61—21no—
32C2×C4⋊C4×D61C2212yes—
33C2×C42×D61C2211yescharacteristic
34#16840159C22116yescomplemented
35#16840107C22116yescomplemented
36#16840082C22116yescomplemented
37#16840079C22116yescomplemented
38#16840053C2218yescomplemented
39#16840052C2218yescomplemented
40#16840049C2218yescomplemented
41#16839814C2218yescomplemented
42C2×#14519709C2212yes—
43C2×#14519708C2212yes—
44C2×#14519708C2212yes—
45C2×C4⋊#92418C2211yescharacteristic
46C2×#14519699C2212yes—
47C2×#14519698C2212yes—
48C2×#14519697C2212yes—
49C2×#14519689C2212yes—
50C2×C8×Dic61C2212yes—
51C2×C4⋊Q8×C61C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C61×#476C2218yescomplemented
54C2×#106×C61C2212yes—
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×#102×C61C2212yes—
57C2×#11758222—28no—
58C2×#11758222—48no—
59C22×Dic122—21no—
60C22×Dic122—21no—
61C22×Dic122—22no—
62C2×Q8×D61—28no—
63C2×Q8×D61—48no—
64C22×D244—21no—
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C22×C22⋊D61—21no—
68C22×C22⋊D61—21no—
69C22×C4×D61—22no—
70C22×C4×D61—21no—
71C22×C4×D61D411yescharacteristic
72C22×C4×D61D411yescharacteristic
73C22×C4×D61C2311yescharacteristic
74C22×#92418C2312yes—
75#14519777—22no—
76#14519777C2314yes—
77#14519776—24no—
78#14519776—28no—
79#14519776—22no—
80#14519776C2318yes—
81#14519776C2314yes—
82#14519775—28no—
83#14519773—22no—
84#14519773C2314yes—
85#14519763—28no—
86#14519752—22no—
87#14519752C2314yes—
88#14519750—28no—
89#14519748—22no—
90#14519748C2314yes—
91C4×D244—22no—
92C4×D244C2314yes—
93C4×C22⋊D61—28no—
94C2×C4⋊Dic61—21no—
95C2×C4⋊Dic61C2312yes—
96C2×C4⋊Dic61C2311yescharacteristic
97C2×#11758196—22no—
98C2×#11758196—22no—
99C2×#11758196—21no—
100C4⋊C4×D61—28no—
101C4⋊C4×D61—24no—
102C4⋊C4×D61C2318yes—
103C2×C22⋊Dic61—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×C4×Dic61D411yescharacteristic
107C2×C4×Dic61D411yescharacteristic
108C2×C4×Dic61C2311yescharacteristic
109C42×D61D414yes—
110C42×D61C2314yes—
111#14519709C2318yes—
112#14519708C2318yes—
113#14519708C2318yes—
114C4⋊#92418C2314yes—
115#14519699C2318yes—
116#14519698C2318yes—
117#14519697C2318yes—
118#14519689C2318yes—
119C8×Dic61C2318yes—
120C22×Q8×C61—21no—
121C22×D4×C61C2311yescharacteristic
122C23×C4×C61—21no—
123C22×C8×C61C2312yes—
124C4⋊Q8×C61—22no—
125C4⋊Q8×C61C2314yes—
126C4×D4×C61—22no—
127C4×D4×C61C2314yes—
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61C2312yes—
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C22⋊C4×C61—21no—
132C2×C42×C61C2311yescharacteristic
133#106×C61C2318yes—
134C4⋊C8×C61C2314yes—
135#102×C61C2318yes—
136C24×C61—21no—
137C23×D61—21no—
138C23×D61C2×D411yescharacteristic
139C2×Q8×C61—24no—
140C2×Q8×C61—44no—
141C2×D4×C61—21no—
142C2×D4×C61—22no—
143C2×D4×C61—22no—
144C2×D4×C61C2412yes—
145C22×C4×C61—22no—
146C22×C4×C61—21no—
147C22×C4×C61—24no—
148C22×C4×C61—44no—
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2411yescharacteristic
152C2×C22⋊D61—24no—
153C2×C22⋊D61—24no—
154C2×C22⋊D61—24no—
155C2×C22⋊D61—44no—
156C2×C22⋊D61—44no—
157C2×C22⋊D61—44no—
158C22×Dic61—21no—
159C22×Dic61—22no—
160C22×Dic61C2×D411yescharacteristic
161C22×Dic61C2×D411yescharacteristic
162C22×Dic61C2×D411yescharacteristic
163Q8×D61—432no—
164#11758222—432no—
165C2×D244—22no—
166C2×D244—22no—
167C2×D244—24no—
168C2×D244—21no—
169C2×D244—44no—
170C2×D244C2412yes—
171C2×C4×D61—22no—
172C2×C4×D61—22no—
173C2×C4×D61—24no—
174C2×C4×D61—28no—
175C2×C4×D61—24no—
176C2×C4×D61—48no—
177C2×C4×D61—44no—
178C2×C4×D61SD1618yes—
179C2×C4×D61C2×D414yes—
180C2×C4×D61C2×D412yes—
181C2×C4×D61C2×D414yes—
182C2×C4×D61C2412yes—
183C2×Dic122—24no—
184C2×Dic122—28no—
185C2×Dic122—24no—
186C2×Dic122—44no—
187C2×Dic122—44no—
188C2×Dic122—48no—
189C2×C8×C61—24no—
190C2×C8×C61C2414yes—
191C4⋊C4×C61—24no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—22no—
194C4⋊C4×C61C2414yes—
195C4⋊C4×C61C2412yes—
196C22⋊C4×C61—24no—
197C42×C61C2×D412yes—
198C42×C61C2412yes—
199C22⋊Dic61—24no—
200#11758198—24no—
201#11758198—24no—
202C4⋊Dic61—24no—
203C4⋊Dic61—22no—
204C4⋊Dic61—21no—
205C4⋊Dic61C2414yes—
206C4⋊Dic61C2412yes—
207#11758196—28no—
208#11758196—28no—
209#11758196—24no—
210C4×Dic61C2×D412yes—
211C4×Dic61C2×D414yes—
212C4×Dic61C2×D414yes—
213C4×Dic61C2412yes—
214C2×#92418—24no—
215C2×#92418C2414yes—
216C23×C61—22no—
217C23×C61—42no—
218C23×C61—42no—
219C23×C61—42no—
220C23×C61C22×D411yescharacteristic
221C22×D61—22no—
222C22×D61—22no—
223C22×D61—22no—
224C22×D61—42no—
225C22×D61—42no—
226C22×D61—42no—
227C22×D61C2×SD1614yes—
228C22×D61C22×D412yes—
229Q8×C61—48no—
230D4×C61—22no—
231D4×C61—22no—
232D4×C61—42no—
233C2×C4×C61—22no—
234C2×C4×C61—24no—
235C2×C4×C61—22no—
236C2×C4×C61—42no—
237C2×C4×C61—44no—
238C2×C4×C61—48no—
239C2×C4×C61C2×SD1614yes—
240C2×C4×C61C22×D412yes—
241C2×C4×C61C22×D411yescharacteristic
242C2×C4×C61C22×D412yes—
243C2×C4×C612−1+412yes—
244C2×C4×C612−1+412yes—
245C2×C4×C61C2511yescharacteristic
246C22⋊D61—48no—
247C22⋊D61—48no—
248C22⋊D61—48no—
249C2×Dic61—22no—
250C2×Dic61—24no—
251C2×Dic61—22no—
252C2×Dic61—42no—
253C2×Dic61—44no—
254C2×Dic61C2×SD1614yes—
255C2×Dic61AGL(1,ℤ/8)14yes—
256C2×Dic61C22×D412yes—
257C2×Dic61C22×D412yes—
258C2×Dic61C22×D412yes—
259D244—22no—
260D244—22no—
261D244—48no—
262D244—42no—
263C4×D61—24no—
264C4×D61—22no—
265C4×D61—22no—
266C4×D61—28no—
267C4×D61—416no—
268C4×D61—48no—
269C4×D61C2×SD16116yes—
270Dic122—48no—
271Dic122—48no—
272Dic122—416no—
273C8×C61—24no—
274#92418—24no—
275C2×#3227—611nomaximal, Sylow
276C22×C61—42no—
277C22×C61—42no—
278C22×C61—42no—
279C22×C61—84no—
280C22×C61#53612yes—
281C22×C61C22×SD1612yes—
282C22×C61C2×AGL(1,ℤ/8)12yes—
283C22×C61C23×D411yescharacteristic
284C2×D61—22no—
285C2×D61—28no—
286C2×D61—22no—
287C2×D61—42no—
288C2×D61—42no—
289C2×D61—42no—
290C2×D61—84no—
291C2×D61C22×SD1614yes—
292C4×C61—22no—
293C4×C61—42no—
294C4×C61—44no—
295C4×C61#53612yes—
296C4×C61C22×SD1614yes—
297C4×C61C2×2−1+411yescharacteristic
298C4×C61C2×2−1+411yescharacteristic
299Dic61—22no—
300Dic61—42no—
301Dic61—44no—
302Dic61C22×SD1614yes—
303Dic61C2×AGL(1,ℤ/8)14yes—
304C2×#532—611no—
305C22×C4⋊Q8—611no—
306#3227—6116no—
307C2×#498—612no—
308C2×#486—612no—
309C2×#481—612no—
310C2×#481—612no—
311C2×#476—611no—
312C2×#476—611no—
313C2×#476—611no—
314C2×#476D6111yescharacteristic, complemented
315C2×#431—611no—
316C2×C61—82no—
317C2×C61#322714yescomplemented
318C2×C61C2×#53611yescharacteristic
319C2×C61C23×SD1611yescharacteristic
320C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
321D61—24no—
322D61—82no—
323C22×#41—1221no—
324C23×Q8—1221no—
325#532—618no—
326#532—1224no—
327C2×C4⋊Q8—618no—
328C2×C4⋊Q8—612no—
329C2×C4⋊Q8—611no—
330C2×C4⋊Q8—611no—
331C2×C4⋊Q8—1221no—
332C2×C4⋊Q8—1224no—
333C2×C4⋊Q8—1221no—
334C2×C4⋊Q8C2×D6111yescharacteristic
335C2×#127—611no—
336C2×#124—1221no—
337C2×#121—611no—
338C2×#121—611no—
339C2×#121—1221no—
340C2×C4×D4—611no—
341C2×C4×D4—1221no—
342C2×C4×D4C2×D6111yescharacteristic
343C22×C4⋊C4—612no—
344C22×C4⋊C4—1221no—
345C22×C42—611no—
346#498—6116no—
347#486—6116no—
348#481—6116no—
349#481—6116no—
350#476—618no—
351#476—618no—
352#476—618no—
353#476C2×D6118yescomplemented
354#431—618no—
355C2×#106—612no—
356C2×#106—612no—
357C2×#106—612no—
358C2×#106C2×D6112yes—
359C2×C4⋊C8—611no—
360C2×C4⋊C8C2×D6111yescharacteristic
361C2×#102—612no—
362C2×#102—612no—
363C2×#102—612no—
364C2×#102C2×D6112yes—
365C2×C22⋊C8—612no—
366C2×C4×C8—612no—
367C61C2×#322711yescharacteristic, complemented, Sylow
368C2×#41—1228no—
369C2×#41—2448no—
370C22×Q8—21no—
371C22×Q8—1221no—
372C22×Q8—1222no—
373C22×Q8—1228no—
374C22×Q8—1221no—
375C22×Q8—2448no—
376C22×D4—611no—
377C22×D4—1221no—
378C22×D4—1221no—
379C22×D4—1221no—
380C22×D4—1221no—
381C22×D4C22×D6111yescharacteristic
382C23×C4—21no—
383C23×C4—611no—
384C23×C4—611no—
385C23×C4—611no—
386C23×C4—1222no—
387C23×C4—1221no—
388C22×C8—612no—
389C22×C8C22×D6112yes—
390C4⋊Q8—22no—
391C4⋊Q8—618no—
392C4⋊Q8—614no—
393C4⋊Q8—614no—
394C4⋊Q8—1228no—
395C4⋊Q8—1224no—
396C4⋊Q8—1222no—
397C4⋊Q8—1228no—
398C4⋊Q8—1222no—
399C4⋊Q8C22×D6114yes—
400#127—614no—
401#127—1222no—
402#124—1228no—
403#121—614no—
404#121—614no—
405#121—1228no—
406#121—1222no—
407#121—1222no—
408C4×D4—22no—
409C4×D4—614no—
410C4×D4—1228no—
411C4×D4—1222no—
412C4×D4C22×D6114yes—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—612no—
415C2×C4⋊C4—611no—
416C2×C4⋊C4—618no—
417C2×C4⋊C4—1224no—
418C2×C4⋊C4—1228no—
419C2×C4⋊C4—1222no—
420C2×C4⋊C4—1222no—
421C2×C4⋊C4—1221no—
422C2×C4⋊C4—1221no—
423C2×C4⋊C4C22×D6112yes—
424C2×C4⋊C4C22×D6111yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—1221no—
427C2×C22⋊C4—1221no—
428C2×C22⋊C4—1221no—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—614no—
433C2×C42—614no—
434C2×C42C22×D6111yescharacteristic
435#106—618no—
436#106—618no—
437#106—618no—
438#106C22×D6118yes—
439C4⋊C8—614no—
440C4⋊C8C22×D6114yes—
441#102—618no—
442#102—618no—
443#102—618no—
444#102C22×D6118yes—
445C22⋊C8—618no—
446C4×C8—618no—
447C24—21no—
448C24—611no—
449C24—1221no—
450#41—24432no—
451C2×Q8—24no—
452C2×Q8—44no—
453C2×Q8—1224no—
454C2×Q8—1228no—
455C2×Q8—1224no—
456C2×Q8—2444no—
457C2×Q8—2448no—
458C2×Q8—2444no—
459C2×Q8—24432no—
460C2×D4—21no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—612no—
464C2×D4—1224no—
465C2×D4—1224no—
466C2×D4—1224no—
467C2×D4—1224no—
468C2×D4—1221no—
469C2×D4—1222no—
470C2×D4—1222no—
471C2×D4—2444no—
472C2×D4—2444no—
473C2×D4—2444no—
474C2×D4—2444no—
475C2×D4C23×D6112yes—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—44no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—614no—
483C22×C4—618no—
484C22×C4—611no—
485C22×C4—612no—
486C22×C4—614no—
487C22×C4—612no—
488C22×C4—1224no—
489C22×C4—1228no—
490C22×C4—1222no—
491C22×C4—1222no—
492C22×C4—1221no—
493C22×C4—1222no—
494C22×C4—1224no—
495C22×C4—2448no—
496C22×C4—2444no—
497C22×C4D4×D6111yescharacteristic
498C22×C4D4×D6111yescharacteristic
499C22×C4C23×D6111yescharacteristic
500C2×C8—24no—
501C2×C8—614no—
502C2×C8—1224no—
503C2×C8C23×D6114yes—
504C4⋊C4—24no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—614no—
508C4⋊C4—612no—
509C4⋊C4—1228no—
510C4⋊C4—1228no—
511C4⋊C4—1224no—
512C4⋊C4—1222no—
513C4⋊C4—1221no—
514C4⋊C4—1224no—
515C4⋊C4C23×D6114yes—
516C4⋊C4C23×D6112yes—
517C22⋊C4—24no—
518C22⋊C4—1224no—
519C22⋊C4—1224no—
520C22⋊C4—1224no—
521C42—614no—
522C42—614no—
523C42—612no—
524C42—612no—
525C42D4×D6112yes—
526C42C23×D6112yes—
527C23—22no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—614no—
532C23—612no—
533C23—1222no—
534C23—1222no—
535C23—1222no—
536C23—2442no—
537C23—2442no—
538C23—2442no—
539C23C2×D4×D6111yescharacteristic
540Q8—48no—
541Q8—2448no—
542Q8—24416no—
543Q8—2448no—
544D4—22no—
545D4—22no—
546D4—42no—
547D4—1222no—
548D4—1222no—
549D4—2448no—
550D4—2448no—
551D4—2448no—
552D4—2448no—
553D4—2442no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—42no—
558C2×C4—44no—
559C2×C4—48no—
560C2×C4—614no—
561C2×C4—614no—
562C2×C4—612no—
563C2×C4—612no—
564C2×C4—6116no—
565C2×C4—612no—
566C2×C4—1228no—
567C2×C4—1222no—
568C2×C4—1224no—
569C2×C4—1222no—
570C2×C4—1222no—
571C2×C4—1222no—
572C2×C4—1224no—
573C2×C4—24416no—
574C2×C4—2442no—
575C2×C4—2444no—
576C2×C4—2448no—
577C2×C4SD16×D6114yes—
578C2×C4C2×D4×D6112yes—
579C2×C4C2×D4×D6112yes—
580C2×C4C2×D4×D6111yescharacteristic
581C2×C4#1451982412yes—
582C2×C4#1451982512yes—
583C2×C4C24×D6111yescharacteristic
584C8—24no—
585C8—1224no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—84no—
590C22—614no—
591C22—1228no—
592C22—1222no—
593C22—1222no—
594C22—4884no—
595C22—2442no—
596C22—2442no—
597C22—2442no—
598C22#1684033512yes—
599C22C2×SD16×D6112yes—
600C22AGL(1,ℤ/8)×D6112yes—
601C22C22×D4×D6111yescharacteristic
602C4—22no—
603C4—42no—
604C4—44no—
605C4—614no—
606C4—614no—
607C4—1222no—
608C4—2442no—
609C4—2444no—
610C4#1684033512yes—
611C4C2×SD16×D6114yes—
612C4C2×#1451982411yescharacteristic
613C4C2×#1451982511yescharacteristic
614C2—82no—
615C2—1224no—
616C2—4882no—
617C2#2145694614yesdirect product factor
618C2C2×#1684033511yescharacteristic
619C2C22×SD16×D6111yescharacteristic
620C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#476C2
socleC23×C61C22×D4
prime radicalC2×#16840309C2
hypercenterC2×#476D61
hypocenterC61C2×#3227
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊Q8×D61C2semidirect
3. #21456946C2direct (N × H)
4. C2×#16840159C2semidirect
5. C2×#16840107C2semidirect
6. C2×#16840082C2semidirect
7. C2×#16840079C2semidirect
8. C2×#16840053C2semidirect
9. C2×#16840052C2semidirect
10. C2×#16840049C2semidirect
11. C2×#16839814C2semidirect
12. C2×C61×#476C2semidirect
23. C4⋊Q8×D61C22semidirect
34. #16840159C22semidirect
35. #16840107C22semidirect
36. #16840082C22semidirect
37. #16840079C22semidirect
38. #16840053C22semidirect
39. #16840052C22semidirect
40. #16840049C22semidirect
41. #16839814C22semidirect
53. C61×#476C22semidirect
314. C2×#476D61semidirect
317. C2×C61#3227semidirect
353. #476C2×D61semidirect
367. C61C2×#3227semidirect
617. C2#21456946direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403092
C2×C4⋊Q8×D612
#214569462
C2×#168401592
C2×#168401072
C2×#168400822
C2×#168400792
C2×#168400532
C2×#168400522
C2×#168400492
C2×#168398142
C2×C61×#4762
C2×#322761