Finite Group Databasebeta

← C2×#21455915 #30548179

Subgroups — C2×#21455915 #30548179

Order 15616.

2550 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
1C2×#16840314C211yesmaximal, characteristic, complemented
2C22×#14519739C211yesmaximal, characteristic
3#21455915C2116yesmaximal, direct product factor
4C2×#16840097C211yesmaximal, characteristic, complemented
5C2×#16840041C212yesmaximal, complemented
6C2×#16839966C212yesmaximal, complemented
7C2×#16839915C211yesmaximal, characteristic
8C2×#16839912C211yesmaximal, characteristic
9C2×#16839865C212yesmaximal, complemented
10C2×#16839861C212yesmaximal, complemented
11C2×#16839816C211yesmaximal, characteristic, complemented
12C2×C61×#484C211yesmaximal, characteristic, complemented
13C23×D244C2211yescharacteristic
14C23×C4×D61—21no—
15C22×#11758190C2212yes—
16C22×#11758201C2212yes—
17#16840314—24no—
18#16840314C2218yescomplemented
19C2×#14519776C2211yescharacteristic, complemented
20C2×#14519775C2211yescharacteristic, complemented
21C2×#14519767—21no—
22C2×#14519756C2211yescharacteristic
23C2×#14519754—21no—
24C2×Q8×Dic61C2211yescharacteristic, complemented
25C2×#14519742—21no—
26C2×#14519742C2211yescharacteristic, complemented
27C2×#14519739—21no—
28C2×#14519739—21no—
29C2×#14519739—24no—
30C2×#14519739C2212yes—
31C2×#14519739C2218yes—
32C2×#14519739C2212yes—
33C2×#14519733—21no—
34C22×#11758198—21no—
35C22×C4×Dic61C2211yescharacteristic
36#16840097C2218yescomplemented
37#16840041C22116yescomplemented
38#16839966C22116yescomplemented
39#16839915C2218yes—
40#16839912C2218yes—
41#16839865C22116yescomplemented
42#16839861C22116yescomplemented
43#16839816C2218yescomplemented
44C2×#14519710C2212yescomplemented
45C2×#14519706C2212yescomplemented
46C2×#14519700C2212yescomplemented
47C2×#14519699C2212yes—
48C2×#14519697C2212yes—
49C2×C22⋊#92418C2211yescharacteristic
50C2×#14519687C2212yescomplemented
51C2×C22⋊Q8×C61C2211yescharacteristic
52C22×C4⋊C4×C61C2211yescharacteristic
53C61×#484C2218yescomplemented
54C2×#107×C61C2212yescomplemented
55C2×#103×C61C2212yescomplemented
56C2×C22⋊C8×C61C2211yescharacteristic
57C24×D61—21no—
58C22×Dic122—21no—
59C22×Dic122C2311yescharacteristic
60C22×D244—21no—
61C22×D244—22no—
62C22×D244—28no—
63C22×D244C2314yes—
64C22×D244C2312yes—
65C23×Dic61D411yescharacteristic
66C23×Dic61D411yescharacteristic
67C22×C4×D61—22no—
68C22×C4×D61—28no—
69C22×C4×D61—22no—
70C22×C4×D61—48no—
71C2×#11758190—28no—
72C2×#11758190C2318yes—
73C2×#11758201—28no—
74C2×#11758201C2318yes—
75C22×#92418C2312yes—
76#14519776—22no—
77#14519776C2314yescomplemented
78#14519775—22no—
79#14519775C2314yescomplemented
80#14519767—28no—
81#14519756—22no—
82#14519756C2314yes—
83#14519754—28no—
84Q8×Dic61—22no—
85Q8×Dic61C2314yescomplemented
86#14519742—28no—
87#14519742—22no—
88#14519742C2314yescomplemented
89#14519739—28no—
90#14519739—24no—
91#14519739—28no—
92#14519739—24no—
93#14519739C2318yes—
94#14519739C2318yes—
95#14519733—28no—
96C2×C4⋊Dic61—21no—
97C2×C4⋊Dic61C2311yescharacteristic
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×C22⋊Dic61—21no—
104C2×#11758198—22no—
105C2×#11758198—22no—
106C2×#11758198—28no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61—21no—
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61D414yes—
112C2×C4×Dic61C2311yescharacteristic
113C2×C4×Dic61C2311yescharacteristic
114C2×C4×Dic61C2314yes—
115#14519710C2318yescomplemented
116#14519706C2318yescomplemented
117#14519700C2318yescomplemented
118#14519699C2318yes—
119#14519697C2318yes—
120C22⋊#92418C2314yes—
121#14519687C2318yescomplemented
122C22×Q8×C61C2311yescharacteristic
123C23×C4×C61—21no—
124C23×C4×C61C2311yescharacteristic
125C22×C8×C61C2312yes—
126C22⋊Q8×C61—22no—
127C22⋊Q8×C61C2314yes—
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61—22no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61C2312yes—
132C2×C4⋊C4×C61C2314yes—
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C22⋊C4×C61—21no—
135#107×C61C2318yescomplemented
136#103×C61C2318yescomplemented
137C22⋊C8×C61C2314yes—
138C24×C61C2×D411yescharacteristic
139C23×D61—28no—
140C23×D61—24no—
141C23×D61—22no—
142C23×D61—44no—
143C23×D61—44no—
144C2×Q8×C61—21no—
145C2×Q8×C61—24no—
146C2×Q8×C61C2412yes—
147C22×C4×C61—24no—
148C22×C4×C61—24no—
149C22×C4×C61—22no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—44no—
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D412yes—
155C22×C4×C61C2412yes—
156C22×C4×C61C2411yescharacteristic
157C22×Dic61—24no—
158C22×Dic61—24no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61C2×D411yescharacteristic
162C22×Dic61C2×D414yes—
163C22×Dic61C2×D411yescharacteristic
164C22×Dic61C2×D411yescharacteristic
165C22×Dic61C2×D414yes—
166C22×Dic61C2×D411yescharacteristic
167C2×D244—28no—
168C2×D244—216no—
169C2×D244—24no—
170C2×D244—22no—
171C2×D244—24no—
172C2×D244—216no—
173C2×D244#4118yes—
174C2×D244C2414yes—
175C2×C4×D61—28no—
176C2×C4×D61—28no—
177C2×C4×D61—48no—
178C2×C4×D61—432no—
179C2×C4×D61—48no—
180C2×Dic122—24no—
181C2×Dic122—21no—
182C2×Dic122—24no—
183C2×Dic122—44no—
184C2×Dic122C2412yes—
185C2×C8×C61—24no—
186C2×C8×C61C2414yes—
187C4⋊C4×C61—24no—
188C4⋊C4×C61—22no—
189C4⋊C4×C61—24no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61C2414yes—
192C4⋊C4×C61C2412yes—
193C22⋊C4×C61—24no—
194C22⋊Dic61—24no—
195#11758201—216no—
196#11758198—28no—
197#11758198—28no—
198C4⋊Dic61—21no—
199C4⋊Dic61—24no—
200C4⋊Dic61C2412yes—
201#11758196—24no—
202#11758196—24no—
203#11758196—24no—
204#11758196—24no—
205#11758196—24no—
206C4×Dic61—24no—
207C4×Dic61—24no—
208C4×Dic61C2×D414yes—
209C4×Dic61C2×D412yes—
210C4×Dic61C2×D414yes—
211C4×Dic61C2×D412yes—
212C4×Dic61C2412yes—
213C4×Dic61C2412yes—
214C2×#92418—24no—
215C2×#92418C2414yes—
216#11758190—216no—
217C23×C61—22no—
218C23×C61—22no—
219C23×C61#13714yes—
220C23×C61C22×D412yes—
221C23×C61C22×D411yescharacteristic
222C22×D61—216no—
223C22×D61—28no—
224C22×D61—24no—
225C22×D61—48no—
226C22×D61—432no—
227C22×D61—44no—
228C22×D61—48no—
229C22×D61—44no—
230Q8×C61—24no—
231Q8×C61—42no—
232C2×C4×C61—22no—
233C2×C4×C61—24no—
234C2×C4×C61—24no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—24no—
238C2×C4×C61—48no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61—44no—
242C2×C4×C61C22×D412yes—
243C2×C4×C61C22×D411yescharacteristic
244C2×C4×C61C2×#4114yes—
245C2×C4×C61C2511yescharacteristic
246C2×Dic61—22no—
247C2×Dic61—28no—
248C2×Dic61—22no—
249C2×Dic61—22no—
250C2×Dic61—28no—
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—42no—
254C2×Dic61—42no—
255C2×Dic61AGL(1,ℤ/8)14yes—
256C2×Dic61C22×D412yes—
257C2×Dic61C22×D412yes—
258C2×Dic61C22×D412yes—
259C2×Dic61C22×D412yes—
260D244—216no—
261D244—28no—
262D244—24no—
263D244C2×#4118yes—
264C4×D61—416no—
265C4×D61—416no—
266Dic122—24no—
267Dic122—42no—
268Dic122—48no—
269C8×C61—24no—
270#92418—24no—
271C2×#3110—611nomaximal, Sylow
272C22×C61—28no—
273C22×C61—22no—
274C22×C61—22no—
275C22×C61#52512yes—
276C22×C61C2×AGL(1,ℤ/8)12yes—
277C22×C61C2×#13714yes—
278C22×C61C2×#13712yes—
279C22×C61C23×D411yescharacteristic
280C2×D61—28no—
281C2×D61—432no—
282C2×D61—416no—
283C2×D61—44no—
284C2×D61—44no—
285C4×C61—22no—
286C4×C61—42no—
287C4×C61—42no—
288C4×C61—44no—
289C4×C61#52512yes—
290C4×C61C22×#4112yes—
291Dic61—22no—
292Dic61—22no—
293Dic61—22no—
294Dic61—42no—
295Dic61—42no—
296Dic61C2×AGL(1,ℤ/8)14yes—
297C2×#533—611no—
298C22×C4×D4—611no—
299#3110—6116no—
300C2×#484—611no—
301C2×#484D6111yescharacteristic, complemented
302C2×#474—612no—
303C2×#461—612no—
304C2×#450—611no—
305C2×#450—611no—
306C2×#440—612no—
307C2×#440—612no—
308C2×#432—611no—
309C2×C61—24no—
310C2×C61#311014yescomplemented
311C2×C61C2×#52511yescharacteristic
312C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
313C2×C61C22×#13711yescharacteristic
314D61—48no—
315C23×D4—611no—
316C24×C4—1221no—
317C22×SD16—612no—
318C22×SD16—612no—
319#533—618no—
320#533—1224no—
321C2×C4⋊Q8—611no—
322C2×C4⋊Q8—611no—
323C2×#125—1221no—
324C2×C22⋊Q8—611no—
325C2×C22⋊Q8—1221no—
326C2×C22⋊Q8C2×D6111yescharacteristic
327C2×C4×Q8—611no—
328C2×C4×Q8—611no—
329C2×C4×Q8—1221no—
330C2×C4×D4—618no—
331C2×C4×D4—612no—
332C2×C4×D4—612no—
333C2×C4×D4—1221no—
334C2×C4×D4—1221no—
335C2×C4×D4—1224no—
336C2×#117—1221no—
337C22×C4⋊C4C2×D6111yescharacteristic
338C22×C22⋊C4—1221no—
339C22×C42—611no—
340#484—618no—
341#484C2×D6118yescomplemented
342#474—6116no—
343#461—6116no—
344#450—618no—
345#450—618no—
346#440—6116no—
347#440—6116no—
348#432—618no—
349C2×#107—612no—
350C2×#107C2×D6112yescomplemented
351C2×C4⋊C8—612no—
352C2×#103—612no—
353C2×#103C2×D6112yescomplemented
354C2×#102—612no—
355C2×#102—612no—
356C2×C22⋊C8—611no—
357C2×C22⋊C8C2×D6111yescharacteristic
358C2×#97—612no—
359C61C2×#311011yescharacteristic, complemented, Sylow
360C25—1221no—
361C22×Q8—611no—
362C22×Q8—1221no—
363C22×Q8C22×D6111yescharacteristic
364C22×D4—612no—
365C22×D4—614no—
366C22×D4—1228no—
367C22×D4—1222no—
368C22×D4—1221no—
369C23×C4—21no—
370C23×C4—611no—
371C23×C4—611no—
372C23×C4—1228no—
373C23×C4—1222no—
374C23×C4—1222no—
375C23×C4—2448no—
376C23×C4C22×D6111yescharacteristic
377C2×SD16—618no—
378C2×SD16—618no—
379C2×SD16—1228no—
380C2×SD16—1228no—
381C22×C8—612no—
382C22×C8C22×D6112yes—
383C4⋊Q8—614no—
384C4⋊Q8—614no—
385C4⋊Q8—1222no—
386C4⋊Q8—1222no—
387#125—1228no—
388C22⋊Q8—22no—
389C22⋊Q8—614no—
390C22⋊Q8—1228no—
391C22⋊Q8—1222no—
392C22⋊Q8C22×D6114yes—
393C4×Q8—614no—
394C4×Q8—614no—
395C4×Q8—1222no—
396C4×Q8—1228no—
397C4×Q8—1222no—
398C4×D4—618no—
399C4×D4—618no—
400C4×D4—1228no—
401C4×D4—1224no—
402C4×D4—1228no—
403C4×D4—1224no—
404#117—1228no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—611no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4—1221no—
415C2×C4⋊C4C22×D6112yes—
416C2×C4⋊C4C22×D6114yes—
417C2×C4⋊C4C22×D6111yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—1228no—
420C2×C22⋊C4—1222no—
421C2×C22⋊C4—1222no—
422C2×C22⋊C4—1221no—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—614no—
426C2×C42—611no—
427C2×C42—611no—
428C2×C42—614no—
429C2×C42—1221no—
430C2×C42—1221no—
431#107—618no—
432#107C22×D6118yescomplemented
433C4⋊C8—618no—
434#103—618no—
435#103C22×D6118yescomplemented
436#102—618no—
437#102—618no—
438C22⋊C8—614no—
439C22⋊C8C22×D6114yes—
440#97—618no—
441C24—1228no—
442C24—1224no—
443C24—1222no—
444C24—2444no—
445C24—2444no—
446C24D4×D6111yescharacteristic
447C2×Q8—21no—
448C2×Q8—24no—
449C2×Q8—612no—
450C2×Q8—1224no—
451C2×Q8—1221no—
452C2×Q8—1224no—
453C2×Q8—2444no—
454C2×Q8C23×D6112yes—
455C2×D4—618no—
456C2×D4—614no—
457C2×D4—12216no—
458C2×D4—1228no—
459C2×D4—12216no—
460C2×D4—1224no—
461C2×D4—1222no—
462C2×D4—1224no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—44no—
469C22×C4—611no—
470C22×C4—614no—
471C22×C4—614no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—1228no—
476C22×C4—1228no—
477C22×C4—1224no—
478C22×C4—1224no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—2448no—
482C22×C4—24432no—
483C22×C4—2448no—
484C22×C4D4×D6112yes—
485C22×C4D4×D6111yescharacteristic
486C22×C4C23×D6112yes—
487C22×C4C23×D6111yescharacteristic
488SD16—12216no—
489SD16—12216no—
490C2×C8—24no—
491C2×C8—614no—
492C2×C8—1224no—
493C2×C8C23×D6114yes—
494C4⋊C4—24no—
495C4⋊C4—22no—
496C4⋊C4—24no—
497C4⋊C4—21no—
498C4⋊C4—612no—
499C4⋊C4—1224no—
500C4⋊C4—1224no—
501C4⋊C4—1224no—
502C4⋊C4—1224no—
503C4⋊C4—1224no—
504C4⋊C4—1221no—
505C4⋊C4—1224no—
506C4⋊C4C23×D6112yes—
507C4⋊C4C23×D6114yes—
508C22⋊C4—24no—
509C22⋊C4—1228no—
510C22⋊C4—1228no—
511C22⋊C4—1224no—
512C42—614no—
513C42—612no—
514C42—614no—
515C42—612no—
516C42—612no—
517C42—612no—
518C42—1224no—
519C42—1224no—
520C23—22no—
521C23—22no—
522C23—12216no—
523C23—1228no—
524C23—1224no—
525C23—2448no—
526C23—24432no—
527C23—2444no—
528C23—2448no—
529C23—2444no—
530C23#1451980914yes—
531C23C2×D4×D6112yes—
532C23C2×D4×D6111yescharacteristic
533Q8—24no—
534Q8—42no—
535Q8—1224no—
536Q8—2448no—
537Q8—2442no—
538D4—618no—
539D4—12216no—
540D4—1228no—
541D4—1224no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—48no—
549C2×C4—42no—
550C2×C4—44no—
551C2×C4—42no—
552C2×C4—614no—
553C2×C4—612no—
554C2×C4—612no—
555C2×C4—612no—
556C2×C4—612no—
557C2×C4—1228no—
558C2×C4—1222no—
559C2×C4—1228no—
560C2×C4—1222no—
561C2×C4—1222no—
562C2×C4—1222no—
563C2×C4—1222no—
564C2×C4—24416no—
565C2×C4—24416no—
566C2×C4—2442no—
567C2×C4—2442no—
568C2×C4C2×D4×D6112yes—
569C2×C4C2×D4×D6111yescharacteristic
570C2×C4#41×D6114yes—
571C2×C4C24×D6111yescharacteristic
572C8—24no—
573C8—1224no—
574C22—28no—
575C22—22no—
576C22—22no—
577C22—1228no—
578C22—24432no—
579C22—24416no—
580C22—2444no—
581C22—2444no—
582C22#1684027012yes—
583C22AGL(1,ℤ/8)×D6112yes—
584C22C2×#1451980914yes—
585C22C2×#1451980912yes—
586C22C22×D4×D6111yescharacteristic
587C4—22no—
588C4—44no—
589C4—42no—
590C4—42no—
591C4—614no—
592C4—1222no—
593C4—1222no—
594C4—1222no—
595C4—2442no—
596C4—2442no—
597C4#1684027012yes—
598C4C2×#41×D6112yes—
599C2—24no—
600C2—2448no—
601C2#2145591514yesdirect product factor
602C2C2×#1684027011yescharacteristic
603C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
604C2C22×#1451980911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#484C2
socleC23×C61C22×D4
prime radicalC23×D244C22
hypercenterC2×#484D61
hypocenterC61C2×#3110
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
1. C2×#16840314C2semidirect
3. #21455915C2direct (N × H)
4. C2×#16840097C2semidirect
5. C2×#16840041C2semidirect
6. C2×#16839966C2semidirect
9. C2×#16839865C2semidirect
10. C2×#16839861C2semidirect
11. C2×#16839816C2semidirect
12. C2×C61×#484C2semidirect
18. #16840314C22semidirect
19. C2×#14519776C22semidirect
20. C2×#14519775C22semidirect
24. C2×Q8×Dic61C22semidirect
26. C2×#14519742C22semidirect
36. #16840097C22semidirect
37. #16840041C22semidirect
38. #16839966C22semidirect
41. #16839865C22semidirect
42. #16839861C22semidirect
43. #16839816C22semidirect
44. C2×#14519710C22semidirect
45. C2×#14519706C22semidirect
46. C2×#14519700C22semidirect
50. C2×#14519687C22semidirect
53. C61×#484C22semidirect
54. C2×#107×C61C22semidirect
55. C2×#103×C61C22semidirect
77. #14519776C23semidirect
79. #14519775C23semidirect
85. Q8×Dic61C23semidirect
88. #14519742C23semidirect
115. #14519710C23semidirect
116. #14519706C23semidirect
117. #14519700C23semidirect
121. #14519687C23semidirect
135. #107×C61C23semidirect
136. #103×C61C23semidirect
301. C2×#484D61semidirect
310. C2×C61#3110semidirect
341. #484C2×D61semidirect
350. C2×#107C2×D61semidirect
353. C2×#103C2×D61semidirect
359. C61C2×#3110semidirect
432. #107C22×D61semidirect
435. #103C22×D61semidirect
601. C2#21455915direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403142
C22×#145197392
#214559152
C2×#168400972
C2×#168400412
C2×#168399662
C2×#168399152
C2×#168399122
C2×#168398652
C2×#168398612
C2×#168398162
C2×C61×#4842
C2×#311061