Finite Group Databasebeta

← C2×#21455629 #30547539

Subgroups — C2×#21455629 #30547539

Order 15616.

2358 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D61C211yesmaximal, characteristic, complemented
2C2×C4×#11758226C211yesmaximal, characteristic
3#21455629C2116yesmaximal, direct product factor
4C2×#16840055C212yesmaximal, complemented
5C2×#16840047C211yesmaximal, characteristic, complemented
6C2×#16840051C212yesmaximal, complemented
7C2×#16840043C211yesmaximal, characteristic, complemented
8C2×#16840039C211yesmaximal, characteristic, complemented
9C2×#16839801C212yesmaximal, complemented
10C2×#16839784C211yesmaximal, characteristic, complemented
11C2×#16839762C212yesmaximal
12C2×C61×#475C211yesmaximal, characteristic, complemented
13C22×#11758226C2211yescharacteristic
14C22×Q8×D61—21no—
15C22×#11758189C2212yes—
16C2×#14519777C2211yescharacteristic
17C2×#14519776—21no—
18C2×#14519776C2212yes—
19C2×#14519775—21no—
20C4⋊Q8×D61—24no—
21C4⋊Q8×D61C2218yescomplemented
22C4×#11758226—24no—
23C4×#11758226C2218yes—
24C2×Q8×Dic61C2211yescharacteristic
25C2×C4×D244—21no—
26C2×C4×D244C2211yescharacteristic
27C2×#14519739—21no—
28C2×#14519739C2211yescharacteristic
29C2×#14519735—21no—
30C2×#14519735C2211yescharacteristic
31C2×C4⋊C4×D61—21no—
32C2×C4⋊C4×D61C2212yes—
33C2×C42×D61—21no—
34C2×C42×D61C2211yescharacteristic
35#16840055C22116yescomplemented
36#16840051C22116yescomplemented
37#16840047C2218yescomplemented
38#16840043C2218yescomplemented
39#16840039C2218yescomplemented
40#16839801C22116yescomplemented
41C2×#14519711C2212yes—
42C2×#14519710C2212yes—
43C2×#14519708C2212yes—
44#16839784C2218yescomplemented
45C2×C4⋊#92418C2211yescharacteristic
46C2×#14519706C2212yes—
47#16839762C22116yes—
48C2×#14519701C2212yes—
49C2×#14519699C2212yes—
50C2×#14519697C2212yes—
51C2×C4⋊Q8×C61C2211yescharacteristic
52C2×C4×Q8×C61C2211yescharacteristic
53C61×#475C2218yescomplemented
54C2×#106×C61C2212yes—
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×#103×C61C2212yes—
57C2×#11758226—22no—
58C2×#11758226—24no—
59C2×#11758226Q818yescomplemented
60C2×#11758226C2314yes—
61C22×Dic122—21no—
62C22×Dic122—22no—
63C2×Q8×D61—28no—
64C2×Q8×D61—48no—
65C22×D244—21no—
66C22×D244C2311yescharacteristic
67C22×C4×D61—21no—
68C22×C4×D61—22no—
69C22×C4×D61—21no—
70C22×C4×D61—21no—
71C22×C4×D61D411yescharacteristic
72C22×C4×D61D411yescharacteristic
73C22×C4×D61C2311yescharacteristic
74C2×#11758189—28no—
75C2×#11758189C2318yes—
76C22×#92418C2312yes—
77#14519777—22no—
78#14519777C2314yes—
79#14519776—24no—
80#14519776—28no—
81#14519776C2318yes—
82#14519775—28no—
83Q8×Dic61—22no—
84Q8×Dic61C2314yes—
85C4×D244—28no—
86C4×D244—22no—
87C4×D244C2314yes—
88#14519739—28no—
89#14519739—22no—
90#14519739C2314yes—
91#14519735—22no—
92#14519735—28no—
93#14519735C2314yes—
94C2×C4⋊Dic61—21no—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61C2312yes—
97C2×C4⋊Dic61C2311yescharacteristic
98C2×#11758196—22no—
99C2×#11758196—22no—
100C4⋊C4×D61—28no—
101C4⋊C4×D61—24no—
102C4⋊C4×D61C2318yes—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×C4×Dic61—21no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61D411yescharacteristic
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111C42×D61—28no—
112C42×D61D414yes—
113C42×D61C2314yes—
114#14519711C2318yes—
115#14519710C2318yes—
116#14519708C2318yes—
117C4⋊#92418C2314yes—
118#14519706C2318yes—
119#14519701C2318yes—
120#14519699C2318yes—
121#14519697C2318yes—
122C22×Q8×C61—21no—
123C22×Q8×C61C2311yescharacteristic
124C22×C8×C61C2312yes—
125C4⋊Q8×C61—22no—
126C4⋊Q8×C61C2314yes—
127C4×Q8×C61—22no—
128C4×Q8×C61C2314yes—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61C2312yes—
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C42×C61—21no—
134C2×C42×C61C2311yescharacteristic
135#106×C61C2318yes—
136C4⋊C8×C61C2314yes—
137#103×C61C2318yes—
138C23×D61—21no—
139C23×D61C2×D411yescharacteristic
140C2×Q8×C61—21no—
141C2×Q8×C61—24no—
142C2×Q8×C61—22no—
143C2×Q8×C61—44no—
144C2×Q8×C61C2×Q814yescomplemented
145C2×Q8×C61C2412yes—
146C22×C4×C61—21no—
147C22×C4×C61—22no—
148C22×C4×C61—21no—
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2411yescharacteristic
152C22×Dic61—22no—
153C22×Dic61—21no—
154C22×Dic61C2×D411yescharacteristic
155C22×Dic61C2×D411yescharacteristic
156C22×Dic61C2×D411yescharacteristic
157#11758226—216no—
158#11758226—28no—
159#11758226C2×Q8116yescomplemented
160Q8×D61—432no—
161C2×D244—28no—
162C2×D244—24no—
163C2×D244—21no—
164C2×D244—22no—
165C2×D244C2×Q814yescomplemented
166C2×D244C2412yes—
167C2×C4×D61—24no—
168C2×C4×D61—28no—
169C2×C4×D61—24no—
170C2×C4×D61—24no—
171C2×C4×D61—28no—
172C2×C4×D61—24no—
173C2×C4×D61—24no—
174C2×C4×D61—48no—
175C2×C4×D61—44no—
176C2×C4×D61—44no—
177C2×C4×D61C2×D414yes—
178C2×C4×D61C2×D414yes—
179C2×C4×D61C2×D412yes—
180C2×C4×D61C2×Q814yes—
181C2×C4×D61#4114yes—
182C2×C4×D61C2412yes—
183C2×Dic122—24no—
184C2×Dic122—28no—
185C2×Dic122—48no—
186C2×Dic122—44no—
187C2×C8×C61—24no—
188C2×C8×C61C2414yes—
189C4⋊C4×C61—24no—
190C4⋊C4×C61—24no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—22no—
193C4⋊C4×C61C2414yes—
194C4⋊C4×C61C2412yes—
195C42×C61—24no—
196C42×C61C2×D412yes—
197C42×C61C2412yes—
198#11758198—24no—
199#11758198—24no—
200#11758198—24no—
201C4⋊Dic61—24no—
202C4⋊Dic61—22no—
203C4⋊Dic61—21no—
204C4⋊Dic61—24no—
205C4⋊Dic61C2414yes—
206C4⋊Dic61C2412yes—
207#11758196—28no—
208#11758196—28no—
209C4×Dic61—24no—
210C4×Dic61—24no—
211C4×Dic61C2×D414yes—
212C4×Dic61C2×D412yes—
213C4×Dic61C2×D414yes—
214C4×Dic61C2412yes—
215C2×#92418—24no—
216C2×#92418C2414yes—
217#11758189—216no—
218C23×C61C22×D411yescharacteristic
219C22×D61—22no—
220C22×D61—22no—
221C22×D61—24no—
222C22×D61—22no—
223C22×D61—42no—
224C22×D61—42no—
225C22×D61C22⋊Q814yes—
226C22×D61C22×D412yes—
227Q8×C61—24no—
228Q8×C61—22no—
229Q8×C61—48no—
230Q8×C61C22×Q814yescomplemented
231C2×C4×C61—24no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—24no—
236C2×C4×C61—44no—
237C2×C4×C61—42no—
238C2×C4×C61AGL(1,ℤ/8)14yes—
239C2×C4×C61C22×D412yes—
240C2×C4×C61C22×D411yescharacteristic
241C2×C4×C61C22×D412yes—
242C2×C4×C61C22×Q812yes—
243C2×C4×C61C2×#4112yes—
244C2×C4×C61C2511yescharacteristic
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—24no—
248C2×Dic61—44no—
249C2×Dic61—42no—
250C2×Dic61C22⋊Q814yes—
251C2×Dic61#13714yes—
252C2×Dic61C22×D412yes—
253C2×Dic61C22×D412yes—
254C2×Dic61C22×D412yes—
255D244—216no—
256D244—24no—
257D244—22no—
258D244C22×Q814yescomplemented
259C4×D61—28no—
260C4×D61—216no—
261C4×D61—28no—
262C4×D61—416no—
263C4×D61—48no—
264C4×D61—48no—
265C4×D61C22⋊Q818yes—
266C4×D61C22×Q814yes—
267C4×D61C2×#4114yes—
268Dic122—416no—
269Dic122—48no—
270C8×C61—24no—
271#92418—24no—
272C2×#3079—611nomaximal, Sylow
273C22×C61C2×C22⋊Q812yes—
274C22×C61C2×AGL(1,ℤ/8)12yes—
275C22×C61C2×#13712yes—
276C22×C61C23×D411yescharacteristic
277C2×D61—28no—
278C2×D61—22no—
279C2×D61—22no—
280C2×D61—24no—
281C2×D61—48no—
282C2×D61—42no—
283C2×D61—42no—
284C2×D61C2×C22⋊Q814yes—
285C4×C61—24no—
286C4×C61—22no—
287C4×C61—44no—
288C4×C61—42no—
289C4×C61C2×C22⋊Q812yes—
290C4×C61C2×AGL(1,ℤ/8)14yes—
291C4×C61C23×Q811yescharacteristic
292C4×C61C22×#4111yescharacteristic
293Dic61—22no—
294Dic61—44no—
295Dic61—42no—
296Dic61C2×C22⋊Q814yes—
297Dic61C2×#13714yes—
298C22×C4⋊Q8—611no—
299C2×C4×#41—611no—
300#3079—6116no—
301C2×#477—612no—
302C2×#475—611no—
303C2×#475D6111yescharacteristic, complemented
304C2×#476—612no—
305C2×#474—611no—
306C2×#474—611no—
307C2×#428—612no—
308C2×#423—611no—
309C2×#417—612no—
310C2×C61#307914yescomplemented
311C2×C61C22×C22⋊Q811yescharacteristic
312C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
313C2×C61C22×#13711yescharacteristic
314D61—24no—
315D61—44no—
316C22×#41—611no—
317C23×Q8—1221no—
318C22×M16—612no—
319C2×C4⋊Q8—618no—
320C2×C4⋊Q8—612no—
321C2×C4⋊Q8—611no—
322C2×C4⋊Q8—1221no—
323C2×C4⋊Q8—1224no—
324C2×C4⋊Q8—1221no—
325C2×C4⋊Q8C2×D6111yescharacteristic
326C4×#41—618no—
327C4×#41—1224no—
328C2×C4×Q8—611no—
329C2×C4×Q8C2×D6111yescharacteristic
330C2×C4×D4—611no—
331C2×C4×D4—611no—
332C2×C4×D4—1221no—
333C2×C4×D4—1221no—
334C2×#117—611no—
335C2×#117—1221no—
336C22×C4⋊C4—612no—
337C22×C4⋊C4—1221no—
338C22×C42—611no—
339C22×C42—1221no—
340#477—6116no—
341#476—6116no—
342#475—618no—
343#475C2×D6118yescomplemented
344#474—618no—
345#474—618no—
346#428—6116no—
347C2×#107—612no—
348C2×#107—612no—
349C2×#106—612no—
350C2×#106C2×D6112yes—
351#423—618no—
352C2×C4⋊C8—612no—
353C2×C4⋊C8—611no—
354C2×C4⋊C8C2×D6111yescharacteristic
355#417—6116no—
356C2×#103—612no—
357C2×#103C2×D6112yes—
358C2×#102—612no—
359C2×#102—612no—
360C61C2×#307911yescharacteristic, complemented, Sylow
361C2×#41—618no—
362C2×#41—614no—
363C2×#41—1222no—
364C2×#41—1224no—
365C22×Q8—21no—
366C22×Q8—1222no—
367C22×Q8—1228no—
368C22×Q8—1221no—
369C22×Q8—2448no—
370C22×Q8C22×D6111yescharacteristic
371C22×D4—611no—
372C22×D4—1221no—
373C23×C4—611no—
374C23×C4—611no—
375C23×C4—611no—
376C23×C4—1221no—
377C23×C4—1221no—
378C23×C4—1222no—
379C23×C4—1221no—
380C2×M16—618no—
381C2×M16—1228no—
382C22×C8—612no—
383C22×C8C22×D6112yes—
384C4⋊Q8—22no—
385C4⋊Q8—618no—
386C4⋊Q8—614no—
387C4⋊Q8—1228no—
388C4⋊Q8—1224no—
389C4⋊Q8—1228no—
390C4⋊Q8—1222no—
391C4⋊Q8C22×D6114yes—
392C4×Q8—22no—
393C4×Q8—614no—
394C4×Q8—1222no—
395C4×Q8C22×D6114yes—
396C4×D4—614no—
397C4×D4—614no—
398C4×D4—1228no—
399C4×D4—1222no—
400C4×D4—1228no—
401C4×D4—1222no—
402#117—614no—
403#117—1228no—
404#117—1222no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—612no—
408C2×C4⋊C4—611no—
409C2×C4⋊C4—618no—
410C2×C4⋊C4—1224no—
411C2×C4⋊C4—1228no—
412C2×C4⋊C4—1222no—
413C2×C4⋊C4—1222no—
414C2×C4⋊C4—1221no—
415C2×C4⋊C4—1221no—
416C2×C4⋊C4C22×D6112yes—
417C2×C4⋊C4C22×D6111yescharacteristic
418C2×C22⋊C4—1221no—
419C2×C22⋊C4—1221no—
420C2×C22⋊C4—1221no—
421C2×C42—21no—
422C2×C42—611no—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—614no—
426C2×C42—614no—
427C2×C42—1228no—
428C2×C42—1221no—
429C2×C42—1221no—
430C2×C42C22×D6111yescharacteristic
431#107—618no—
432#107—618no—
433#106—618no—
434#106C22×D6118yes—
435C4⋊C8—618no—
436C4⋊C8—614no—
437C4⋊C8C22×D6114yes—
438#103—618no—
439#103C22×D6118yes—
440#102—618no—
441#102—618no—
442C24—611no—
443C24—1221no—
444#41—6116no—
445#41—12216no—
446#41—1228no—
447C2×Q8—21no—
448C2×Q8—24no—
449C2×Q8—22no—
450C2×Q8—44no—
451C2×Q8—1228no—
452C2×Q8—1224no—
453C2×Q8—2448no—
454C2×Q8—24432no—
455C2×Q8—2444no—
456C2×Q8Q8×D6114yescomplemented
457C2×Q8C23×D6112yes—
458C2×D4—614no—
459C2×D4—612no—
460C2×D4—1224no—
461C2×D4—1228no—
462C2×D4—1221no—
463C2×D4—1222no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—612no—
470C22×C4—614no—
471C22×C4—614no—
472C22×C4—612no—
473C22×C4—611no—
474C22×C4—614no—
475C22×C4—614no—
476C22×C4—1224no—
477C22×C4—1224no—
478C22×C4—1228no—
479C22×C4—1224no—
480C22×C4—1228no—
481C22×C4—1224no—
482C22×C4—1221no—
483C22×C4—1222no—
484C22×C4—1224no—
485C22×C4—2444no—
486C22×C4—2448no—
487C22×C4—2444no—
488C22×C4D4×D6111yescharacteristic
489C22×C4D4×D6111yescharacteristic
490C22×C4C23×D6111yescharacteristic
491M16—12216no—
492C2×C8—24no—
493C2×C8—614no—
494C2×C8—1224no—
495C2×C8C23×D6114yes—
496C4⋊C4—24no—
497C4⋊C4—24no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—614no—
501C4⋊C4—612no—
502C4⋊C4—1228no—
503C4⋊C4—1228no—
504C4⋊C4—1224no—
505C4⋊C4—1222no—
506C4⋊C4—1221no—
507C4⋊C4—1224no—
508C4⋊C4C23×D6114yes—
509C4⋊C4C23×D6112yes—
510C22⋊C4—1224no—
511C22⋊C4—1224no—
512C22⋊C4—1224no—
513C42—24no—
514C42—614no—
515C42—614no—
516C42—612no—
517C42—612no—
518C42—1224no—
519C42—1224no—
520C42D4×D6112yes—
521C42C23×D6112yes—
522C23—614no—
523C23—612no—
524C23—1222no—
525C23—1222no—
526C23—1224no—
527C23—1222no—
528C23—2442no—
529C23—2442no—
530C23C2×D4×D6111yescharacteristic
531Q8—24no—
532Q8—22no—
533Q8—48no—
534Q8—24416no—
535Q8—2448no—
536Q8C2×Q8×D6114yescomplemented
537D4—614no—
538D4—12216no—
539D4—1224no—
540D4—1222no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—44no—
547C2×C4—42no—
548C2×C4—614no—
549C2×C4—614no—
550C2×C4—612no—
551C2×C4—612no—
552C2×C4—618no—
553C2×C4—614no—
554C2×C4—614no—
555C2×C4—612no—
556C2×C4—1228no—
557C2×C4—12216no—
558C2×C4—1222no—
559C2×C4—1228no—
560C2×C4—1222no—
561C2×C4—1224no—
562C2×C4—2448no—
563C2×C4—24416no—
564C2×C4—2442no—
565C2×C4—2444no—
566C2×C4—2448no—
567C2×C4#1451980414yes—
568C2×C4C2×D4×D6112yes—
569C2×C4C2×D4×D6111yescharacteristic
570C2×C4C2×D4×D6112yes—
571C2×C4C2×Q8×D6112yes—
572C2×C4#41×D6112yes—
573C2×C4C24×D6111yescharacteristic
574C8—24no—
575C8—1224no—
576C22—614no—
577C22—1228no—
578C22—1222no—
579C22—1222no—
580C22—1224no—
581C22—2448no—
582C22—2442no—
583C22—2442no—
584C22C22⋊Q8×D6112yes—
585C22C2×#1451980412yes—
586C22#137×D6112yes—
587C22C22×D4×D6111yescharacteristic
588C4—22no—
589C4—24no—
590C4—44no—
591C4—42no—
592C4—614no—
593C4—614no—
594C4—1222no—
595C4—2442no—
596C4—2444no—
597C4C22⋊Q8×D6112yes—
598C4C2×#1451980414yes—
599C4C22×Q8×D6111yescharacteristic
600C4C2×#41×D6111yescharacteristic
601C2—1224no—
602C2—2444no—
603C2#2145562914yesdirect product factor
604C2C2×C22⋊Q8×D6111yescharacteristic
605C2C22×#1451980411yescharacteristic
606C2C2×#137×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#475C2
socleC23×C61C22×D4
prime radicalC22×#11758226C22
hypercenterC2×#475D61
hypocenterC61C2×#3079
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊Q8×D61C2semidirect
3. #21455629C2direct (N × H)
4. C2×#16840055C2semidirect
5. C2×#16840047C2semidirect
6. C2×#16840051C2semidirect
7. C2×#16840043C2semidirect
8. C2×#16840039C2semidirect
9. C2×#16839801C2semidirect
10. C2×#16839784C2semidirect
12. C2×C61×#475C2semidirect
21. C4⋊Q8×D61C22semidirect
35. #16840055C22semidirect
36. #16840051C22semidirect
37. #16840047C22semidirect
38. #16840043C22semidirect
39. #16840039C22semidirect
40. #16839801C22semidirect
44. #16839784C22semidirect
53. C61×#475C22semidirect
59. C2×#11758226Q8semidirect
144. C2×Q8×C61C2×Q8semidirect
159. #11758226C2×Q8semidirect
165. C2×D244C2×Q8semidirect
230. Q8×C61C22×Q8semidirect
258. D244C22×Q8semidirect
303. C2×#475D61semidirect
310. C2×C61#3079semidirect
343. #475C2×D61semidirect
360. C61C2×#3079semidirect
456. C2×Q8Q8×D61semidirect
536. Q8C2×Q8×D61semidirect
603. C2#21455629direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D612
C2×C4×#117582262
#214556292
C2×#168400552
C2×#168400472
C2×#168400512
C2×#168400432
C2×#168400392
C2×#168398012
C2×#168397842
C2×#168397622
C2×C61×#4752
C2×#307961