Finite Group Databasebeta

← C2×#21462070 #30623902

Subgroups — C2×#21462070 #30623902

Order 15616.

1398 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840748C211yesmaximal, characteristic, complemented
2C2×#16840741C211yesmaximal, characteristic, complemented
3#21462070C218yesmaximal, direct product factor
4C2×#16840664C212yesmaximal, complemented
5C2×#16840662C212yesmaximal, complemented
6C2×#16840273C211yesmaximal, characteristic
7C2×D61⋊M16—21no—
8C2×#14519856—21no—
9#16840748—22no—
10#16840748C2214yescomplemented
11C2×#14519838—21no—
12C2×#14519837C2212yes—
13#16840741—22no—
14#16840741C2214yescomplemented
15C2×#14519836—21no—
16C2×#14519835C2212yes—
17#16840664C2218yescomplemented
18#16840662C2218yescomplemented
19C22×#11758222C2211yescharacteristic
20#16840273—22no—
21#16840273—22no—
22#16840273C414yescomplemented
23#16840273C2214yes—
24C2×#14519760C411yescharacteristic, complemented
25C2×#14519760C2211yescharacteristic
26C2×#14519756—21no—
27C2×#14519751—21no—
28C2×#14519746C411yescharacteristic, complemented
29C2×#14519746C2211yescharacteristic
30C2×C4×C22⋊D61—21no—
31C2×C4×C22⋊D61—21no—
32C2×#14519736C411yescharacteristic, complemented
33C24×C4×C61C411yescharacteristic, complemented
34C2×#11758213—41no—
35D61⋊M16—24no—
36D61⋊M16—42no—
37C2×#11758217—22no—
38C2×D61⋊C8—41no—
39#14519856—24no—
40#14519856—42no—
41C2×C4⋊#6923—41no—
42C2×C22⋊#6923—22no—
43C2×C4×#6923—41no—
44#14519838—24no—
45#14519837—22no—
46#14519837C2314yes—
47#14519836—24no—
48#14519835—22no—
49#14519835C2314yes—
50C2×#11758222—41no—
51C2×#11758222—41no—
52C2×#11758222—42no—
53C2×#11758222C2×C412yes—
54C2×#11758222D412yes—
55C2×#11758222D412yes—
56C2×#11758222C2312yes—
57C22×Dic122D411yescharacteristic
58C22×D244D411yescharacteristic
59C22×C22⋊D61—21no—
60C22×C22⋊D61—21no—
61C22×C22⋊D61C2×C411yescharacteristic
62C22×C22⋊D61C2311yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65#14519760—22no—
66#14519760—21no—
67#14519760—21no—
68#14519760C2×C412yes—
69#14519760C2×C414yescomplemented
70#14519760C2312yes—
71#14519756—24no—
72#14519756—24no—
73#14519751—24no—
74#14519751—24no—
75#14519746—22no—
76#14519746—21no—
77#14519746—21no—
78#14519746C2×C412yes—
79#14519746C2×C414yescomplemented
80#14519746C2312yes—
81C4×C22⋊D61—24no—
82C4×C22⋊D61—24no—
83C4×C22⋊D61—24no—
84C4×C22⋊D61—24no—
85#14519736—22no—
86#14519736C2×C414yescomplemented
87C2×C4⋊Dic61—21no—
88C2×#11758196—21no—
89C2×#11758196—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61C2×C411yescharacteristic
93C2×C22⋊Dic61C2×C411yescharacteristic
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×C4×Dic61—21no—
97C25×C61C2×C411yescharacteristic
98C23×C4×C61—21no—
99C23×C4×C61—21no—
100C23×C4×C61—22no—
101C23×C4×C61—42no—
102C23×C4×C61—41no—
103C23×C4×C61—41no—
104C23×C4×C61C2×C411yescharacteristic
105C23×C4×C61C2×C411yescharacteristic
106C23×C4×C61C2×C414yescomplemented
107C24×C61—21no—
108C24×C61—21no—
109C24×C61—41no—
110C24×C61—41no—
111C24×C61—44no—
112C24×C61C22×C411yescharacteristic
113C24×C61C22×C412yes—
114C23×D61C22⋊C411yescharacteristic
115C23×D61C2×D411yescharacteristic
116C22×#6923—42no—
117C22×C4×C61—22no—
118C22×C4×C61—21no—
119C22×C4×C61—21no—
120C22×C4×C61—21no—
121C22×C4×C61—21no—
122C22×C4×C61—24no—
123C22×C4×C61—24no—
124C22×C4×C61—42no—
125C22×C4×C61—42no—
126C22×C4×C61—44no—
127C22×C4×C61—44no—
128C22×C4×C61—44no—
129C22×C4×C61—44no—
130C22×C4×C61—42no—
131C22×C4×C61—41no—
132C22×C4×C61—41no—
133C22×C4×C61—41no—
134C22×C4×C61—41no—
135C22×C4×C61C22⋊C411yescharacteristic
136C22×C4×C61C22⋊C412yes—
137C22×C4×C61C22⋊C411yescharacteristic
138C22×C4×C61C22×C412yes—
139C22×C4×C61C22×C412yes—
140C2×C22⋊D61—22no—
141C2×C22⋊D61—24no—
142C2×C22⋊D61—22no—
143C2×C22⋊D61—41no—
144C2×C22⋊D61—41no—
145C2×C22⋊D61—41no—
146C2×C22⋊D61—41no—
147C2×C22⋊D61—44no—
148C2×C22⋊D61—44no—
149C2×C22⋊D61C22⋊C412yes—
150C2×C22⋊D61C22×C412yes—
151C2×C22⋊D61C22×C411yescharacteristic
152C2×C22⋊D61C2×D411yescharacteristic
153C2×C22⋊D61C2×D411yescharacteristic
154C2×C22⋊D61C2411yescharacteristic
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61C22⋊C411yescharacteristic
158C22×Dic61C2×D411yescharacteristic
159#11758222—42no—
160#11758222—42no—
161#11758222—42no—
162#11758222—42no—
163#11758222—42no—
164#11758222—42no—
165#11758222—42no—
166#11758222—42no—
167C2×D244—41no—
168C2×D244—41no—
169C2×D244C22⋊C412yes—
170C2×D244C2×D412yes—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—22no—
174C2×C4×D61—21no—
175C2×C4×D61—22no—
176C2×C4×D61—21no—
177C2×C4×D61C22⋊C412yes—
178C2×C4×D61C22⋊C412yes—
179C2×C4×D61C2×D412yes—
180C2×C4×D61C2×D412yes—
181C2×Dic122—41no—
182C2×Dic122—41no—
183C2×Dic122C22⋊C412yes—
184C2×Dic122C2×D412yes—
185C22⋊#6923—24no—
186C22⋊#6923—42no—
187#11758217—24no—
188#11758217—42no—
189C2×#92420—42no—
190C4⋊#6923—44no—
191C4×#6923—44no—
192#11758213—44no—
193D61⋊C8—44no—
194C22⋊Dic61—21no—
195C22⋊Dic61—21no—
196C22⋊Dic61—22no—
197C22⋊Dic61—24no—
198C22⋊Dic61—22no—
199C22⋊Dic61C22×C412yes—
200C22⋊Dic61C22×C412yes—
201#11758198—22no—
202#11758198—24no—
203#11758198—22no—
204C4⋊Dic61—24no—
205#11758196—22no—
206#11758196—24no—
207#11758196—22no—
208C4×Dic61—24no—
209C23×C61—24no—
210C23×C61—22no—
211C23×C61—21no—
212C23×C61—21no—
213C23×C61—42no—
214C23×C61—42no—
215C23×C61—44no—
216C23×C61—42no—
217C23×C61—42no—
218C23×C61—44no—
219C23×C61—48no—
220C23×C61—44no—
221C23×C61—41no—
222C23×C61—41no—
223C23×C61—44no—
224C23×C61C2×C22⋊C411yescharacteristic
225C23×C61C2×C22⋊C411yescharacteristic
226C23×C61C23×C411yescharacteristic
227C22×D61—21no—
228C22×D61—21no—
229C22×D61—21no—
230C22×D61—21no—
231C22×D61—42no—
232C22×D61—42no—
233C22×D61C2×C22⋊C411yescharacteristic
234C22×D61C2×C22⋊C412yes—
235C22×D61C22×D411yescharacteristic
236C2×#6923—44no—
237C2×#6923—84no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—22no—
244C2×C4×C61—22no—
245C2×C4×C61—48no—
246C2×C4×C61—42no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—44no—
250C2×C4×C61—44no—
251C2×C4×C61—42no—
252C2×C4×C61#9912yes—
253C2×C4×C61#9911yescharacteristic
254C2×C4×C61#9911yescharacteristic
255C2×C4×C61C2×C22⋊C412yes—
256C2×C4×C61C2×C22⋊C412yes—
257C22⋊D61—42no—
258C22⋊D61—41no—
259C22⋊D61—42no—
260C22⋊D61—41no—
261C22⋊D61—41no—
262C22⋊D61—41no—
263C22⋊D61—44no—
264C22⋊D61—48no—
265C22⋊D61—44no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—22no—
271C2×Dic61—22no—
272C2×Dic61—42no—
273C2×Dic61—42no—
274C2×Dic61C2×C22⋊C411yescharacteristic
275C2×Dic61C2×C22⋊C412yes—
276C2×Dic61C22×D411yescharacteristic
277D244—42no—
278D244—42no—
279C4×D61—22no—
280C4×D61—22no—
281C4×D61—22no—
282C4×D61—22no—
283C4×D61—22no—
284C4×D61—22no—
285C4×D61—22no—
286C4×D61—22no—
287Dic122—42no—
288Dic122—42no—
289#92420—44no—
290C2×#2120—611nomaximal, Sylow
291C22×C61—22no—
292C22×C61—24no—
293C22×C61—21no—
294C22×C61—21no—
295C22×C61—41no—
296C22×C61—41no—
297C22×C61—42no—
298C22×C61—44no—
299C22×C61—42no—
300C22×C61—44no—
301C22×C61—48no—
302C22×C61—44no—
303C22×C61—42no—
304C22×C61—44no—
305C22×C61—42no—
306C22×C61C2×#9911yescharacteristic
307C22×C61C2×#9911yescharacteristic
308C22×C61C22×C22⋊C411yescharacteristic
309C2×D61—21no—
310C2×D61—22no—
311C2×D61—21no—
312C2×D61—42no—
313C2×D61—42no—
314C2×D61—42no—
315C2×D61—41no—
316C2×D61—41no—
317C2×D61—81no—
318C2×D61—81no—
319#6923—84no—
320C4×C61—22no—
321C4×C61—42no—
322C4×C61C2×#9912yes—
323C4×C61C2×#9912yes—
324Dic61—21no—
325Dic61—21no—
326Dic61—22no—
327Dic61—42no—
328Dic61—42no—
329C2×#525—611no—
330C2×#413—611no—
331C2×#410—611no—
332#2120—618no—
333C2×#352—612no—
334C2×AΣL(1,𝔽16)—612no—
335C2×C61—21no—
336C2×C61—21no—
337C2×C61—44no—
338C2×C61—41no—
339C2×C61—41no—
340C2×C61#212012yescomplemented
341C2×C61C22×#9911yescharacteristic
342D61—41no—
343D61—41no—
344D61—42no—
345C22×#41—611no—
346C24×C4#692311yescharacteristic, complemented
347C22×M16—1221no—
348#525—614no—
349#525—614no—
350#525—1222no—
351#525—1222no—
352C2×#123—611no—
353C2×#123—611no—
354C2×C22⋊Q8—1221no—
355C2×#121—1221no—
356C2×#120—611no—
357C2×#120—611no—
358C2×C4×D4—1221no—
359C2×C4×D4—1221no—
360C2×#117—611no—
361C2×#117—1221no—
362#413—614no—
363#413—1222no—
364C2×#101—1221no—
365C2×#100—612no—
366#410—614no—
367#410—1222no—
368C2×#99—612no—
369C2×#99—1221no—
370#352—618no—
371AΣL(1,𝔽16)—618no—
372C61C2×#212011yescharacteristic, complemented, Sylow
373C25C2×#692311yescharacteristic
374C2×#41—612no—
375C2×#41—612no—
376C2×#41—612no—
377C2×#41—612no—
378C2×#41—2441no—
379C2×#41—2442no—
380C2×#41—2441no—
381C22×Q8—611no—
382C22×D4—611no—
383C22×D4—611no—
384C22×D4—611no—
385C22×D4—1221no—
386C22×D4—1221no—
387C23×C4—21no—
388C23×C4—22no—
389C23×C4—21no—
390C23×C4—41no—
391C23×C4—42no—
392C23×C4—41no—
393C23×C4—611no—
394C23×C4—611no—
395C23×C4C2×#692311yescharacteristic
396C23×C4C2×#692311yescharacteristic
397C23×C4C2×#692314yescomplemented
398C2×M16—1222no—
399C2×M16—1224no—
400C2×M16—2442no—
401C2×M16—2441no—
402C22×C8—2441no—
403#123—612no—
404#123—612no—
405#123—614no—
406#123—1221no—
407#123—1221no—
408#123—1222no—
409C22⋊Q8—1224no—
410C22⋊Q8—1224no—
411#121—1224no—
412#121—1224no—
413#120—612no—
414#120—612no—
415#120—614no—
416#120—1221no—
417#120—1221no—
418#120—1222no—
419C4×D4—1224no—
420C4×D4—1224no—
421C4×D4—1224no—
422C4×D4—1224no—
423#117—614no—
424#117—1222no—
425#117—1224no—
426#117—2442no—
427C2×C4⋊C4—1221no—
428C2×C4⋊C4—1221no—
429C2×C4⋊C4—1221no—
430C2×C4⋊C4—2441no—
431C2×C22⋊C4—611no—
432C2×C22⋊C4—611no—
433C2×C22⋊C4—1221no—
434C2×C22⋊C4—1221no—
435C2×C22⋊C4—1221no—
436C2×C22⋊C4—1221no—
437C2×C22⋊C4—1222no—
438C2×C42—1221no—
439C2×C42—2441no—
440#101—1224no—
441#100—614no—
442#100—1222no—
443#99—614no—
444#99—1222no—
445#99—1224no—
446C24—21no—
447C24—21no—
448C24—41no—
449C24—41no—
450C24—44no—
451C24—611no—
452C24—611no—
453C24C22×#692311yescharacteristic
454C24C22×#692312yes—
455#41—2442no—
456#41—2442no—
457#41—2442no—
458#41—2442no—
459#41—2442no—
460#41—2442no—
461#41—2442no—
462#41—2442no—
463C2×Q8—612no—
464C2×Q8—612no—
465C2×Q8—2441no—
466C2×Q8—2441no—
467C2×D4—611no—
468C2×D4—611no—
469C2×D4—612no—
470C2×D4—611no—
471C2×D4—611no—
472C2×D4—612no—
473C2×D4—612no—
474C2×D4—612no—
475C2×D4—1222no—
476C2×D4—1224no—
477C2×D4—1222no—
478C2×D4—2441no—
479C2×D4—2441no—
480C2×D4—2441no—
481C2×D4—2441no—
482C2×D4—2441no—
483C2×D4—2441no—
484C2×D4—2444no—
485C2×D4—2444no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—44no—
496C22×C4—44no—
497C22×C4—44no—
498C22×C4—44no—
499C22×C4—42no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—611no—
505C22×C4—611no—
506C22×C4—612no—
507C22×C4—612no—
508C22×C4—612no—
509C22×C4—612no—
510C22×C4—1221no—
511C22×C4—1222no—
512C22×C4—1221no—
513C22×C4—1222no—
514C22×C4—1221no—
515C22×C4—1221no—
516C22×C4—1221no—
517C22×C4—1221no—
518C22×C4—2442no—
519C22×C4C22⋊#692311yescharacteristic
520C22×C4C22⋊#692312yes—
521C22×C4C22⋊#692311yescharacteristic
522C22×C4C22×#692312yes—
523C22×C4C22×#692312yes—
524M16—1224no—
525M16—2444no—
526M16—2442no—
527C2×C8—2444no—
528C2×C8—2442no—
529C4⋊C4—1222no—
530C4⋊C4—1224no—
531C4⋊C4—1222no—
532C4⋊C4—1224no—
533C4⋊C4—2444no—
534C22⋊C4—612no—
535C22⋊C4—612no—
536C22⋊C4—1222no—
537C22⋊C4—1224no—
538C22⋊C4—1222no—
539C22⋊C4—1222no—
540C22⋊C4—1224no—
541C22⋊C4—1222no—
542C22⋊C4—1221no—
543C22⋊C4—1221no—
544C22⋊C4—1224no—
545C22⋊C4—2442no—
546C42—1224no—
547C42—2444no—
548C23—24no—
549C23—21no—
550C23—21no—
551C23—22no—
552C23—42no—
553C23—42no—
554C23—44no—
555C23—42no—
556C23—42no—
557C23—44no—
558C23—44no—
559C23—48no—
560C23—44no—
561C23—41no—
562C23—41no—
563C23—611no—
564C23—612no—
565C23—611no—
566C23—1221no—
567C23—1221no—
568C23—1221no—
569C23—1221no—
570C23—2442no—
571C23—2442no—
572C23C2×C22⋊#692311yescharacteristic
573C23C2×C22⋊#692311yescharacteristic
574C23C23×#692311yescharacteristic
575Q8—2442no—
576Q8—2442no—
577D4—2442no—
578D4—2442no—
579D4—2441no—
580D4—2441no—
581D4—2441no—
582D4—2442no—
583D4—2441no—
584D4—2442no—
585D4—2444no—
586D4—2444no—
587D4—2448no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—48no—
596C2×C4—42no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—44no—
600C2×C4—44no—
601C2×C4—42no—
602C2×C4—611no—
603C2×C4—612no—
604C2×C4—611no—
605C2×C4—1221no—
606C2×C4—1221no—
607C2×C4—1221no—
608C2×C4—1221no—
609C2×C4—1222no—
610C2×C4—1222no—
611C2×C4—1222no—
612C2×C4—1222no—
613C2×C4—1222no—
614C2×C4—1222no—
615C2×C4—1222no—
616C2×C4—1222no—
617C2×C4—1222no—
618C2×C4—1222no—
619C2×C4—4884no—
620C2×C4—2444no—
621C2×C4—2442no—
622C2×C4—2442no—
623C2×C4#1451983511yescharacteristic
624C2×C4#1451983512yes—
625C2×C4#1451983511yescharacteristic
626C2×C4C2×C22⋊#692312yes—
627C2×C4C2×C22⋊#692312yes—
628C8—2444no—
629C22—22no—
630C22—24no—
631C22—21no—
632C22—21no—
633C22—41no—
634C22—41no—
635C22—42no—
636C22—44no—
637C22—42no—
638C22—44no—
639C22—44no—
640C22—48no—
641C22—44no—
642C22—42no—
643C22—42no—
644C22—1221no—
645C22—1222no—
646C22—1221no—
647C22—4881no—
648C22—4881no—
649C22—2441no—
650C22—2441no—
651C22—2442no—
652C22—2442no—
653C22—2442no—
654C22C2×#1451983511yescharacteristic
655C22C2×#1451983511yescharacteristic
656C22C22×C22⋊#692311yescharacteristic
657C4—22no—
658C4—42no—
659C4—1221no—
660C4—1221no—
661C4—1222no—
662C4—4884no—
663C4—2442no—
664C4—2442no—
665C4C2×#1451983512yes—
666C4C2×#1451983512yes—
667C2—21no—
668C2—21no—
669C2—44no—
670C2—41no—
671C2—41no—
672C2—2441no—
673C2—2441no—
674C2—2442no—
675C2#2146207012yesdirect product factor
676C2C22×#1451983511yescharacteristic
subgroupG/H
centerC2×C4#14519835
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC24×C4×C61C4
socleC22×C61C2×#99
prime radicalC2×#16840273C2
cosocleC2×C22⋊D61C24
hypercenterC24×C4#6923
hypocenterC61C2×#2120
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
1. C2×#16840748C2semidirect
2. C2×#16840741C2semidirect
3. #21462070C2direct (N × H)
4. C2×#16840664C2semidirect
5. C2×#16840662C2semidirect
10. #16840748C22semidirect
14. #16840741C22semidirect
17. #16840664C22semidirect
18. #16840662C22semidirect
22. #16840273C4semidirect
24. C2×#14519760C4semidirect
28. C2×#14519746C4semidirect
32. C2×#14519736C4semidirect
33. C24×C4×C61C4semidirect
69. #14519760C2×C4semidirect
79. #14519746C2×C4semidirect
86. #14519736C2×C4semidirect
106. C23×C4×C61C2×C4semidirect
340. C2×C61#2120semidirect
346. C24×C4#6923semidirect
372. C61C2×#2120semidirect
397. C23×C4C2×#6923semidirect
675. C2#21462070direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407482
C2×#168407412
#214620702
C2×#168406642
C2×#168406622
C2×#168402732
C2×#212061