Finite Group Databasebeta

← C2×#21461843 #30615714

Subgroups — C2×#21461843 #30615714

Order 15616.

2066 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519856C211yesmaximal, characteristic, complemented
2C22×#14519836C212yesmaximal
3C2×#16840705C211yesmaximal, characteristic, complemented
4#21461843C218yesmaximal, direct product factor
5C2×#16840640C212yesmaximal, complemented
6C22×#14519762C211yesmaximal, characteristic
7C2×#14519856—28no—
8C2×#14519856—22no—
9C2×#14519856C2214yescomplemented
10C22×C4⋊#6923—21no—
11C22×C22⋊#6923C2212yes—
12C22×C22⋊#6923C2212yes—
13C22×C4×#6923—21no—
14C2×#14519836—28no—
15C2×#14519836C2218yes—
16#16840705—22no—
17#16840705C2214yescomplemented
18C2×(C2×#6923)⋊C4—21no—
19C2×(C2×#6923)⋊C4—21no—
20#16840640C2218yescomplemented
21C23×D244C2211yescharacteristic
22C23×C4×D61C2211yescharacteristic
23C2×#14519762—22no—
24C2×#14519762—21no—
25C2×#14519762—21no—
26C2×#14519762—22no—
27C2×#14519762—21no—
28C2×#14519762—21no—
29C2×#14519762C414yescomplemented
30C2×#14519762C2214yes—
31C22×#11758196C411yescharacteristic, complemented
32C22×#11758198C411yescharacteristic, complemented
33C22×#11758198C411yescharacteristic, complemented
34C22×#11758198C2211yescharacteristic
35C22×C4⋊C4×C61C411yescharacteristic, complemented
36C23×#6923—22no—
37C23×#6923—22no—
38#14519856—216no—
39#14519856—216no—
40C2×C4⋊#6923—28no—
41C2×C4⋊#6923—24no—
42C2×C22⋊#6923—22no—
43C2×C22⋊#6923—24no—
44C2×C22⋊#6923—24no—
45C2×C22⋊#6923—24no—
46C2×C22⋊#6923—22no—
47C2×C22⋊#6923D418yes—
48C2×C22⋊#6923C2314yes—
49C2×C22⋊#6923C2314yes—
50C2×C4×#6923—28no—
51C2×C4×#6923—24no—
52#14519836—216no—
53(C2×#6923)⋊C4—24no—
54(C2×#6923)⋊C4—24no—
55C24×D61C2×C411yescharacteristic
56C24×D61C2311yescharacteristic
57C22×D244—24no—
58C22×D244—21no—
59C22×D244—21no—
60C22×D244—21no—
61C22×D244—21no—
62C22×D244—24no—
63C22×D244C2×C412yes—
64C22×D244C2312yes—
65C23×Dic61C2×C411yescharacteristic
66C23×Dic61C2×C411yescharacteristic
67C22×C4×D61—24no—
68C22×C4×D61—24no—
69C22×C4×D61C2×C412yes—
70C22×C4×D61D412yes—
71C22×C4×D61D411yescharacteristic
72C22×C4×D61D411yescharacteristic
73C22×C4×D61D412yes—
74C22×C4×D61D411yescharacteristic
75C22×C4×D61D411yescharacteristic
76C22×C4×D61C2312yes—
77#14519762—24no—
78#14519762—24no—
79#14519762—24no—
80#14519762—24no—
81#14519762—24no—
82#14519762—24no—
83#14519762—24no—
84#14519762—24no—
85C2×#11758196—22no—
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×#11758196C2×C414yescomplemented
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—22no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—22no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198C2×C412yes—
100C2×#11758198C2×C414yescomplemented
101C2×#11758198C2×C414yescomplemented
102C2×#11758198C2312yes—
103C23×C4×C61C2×C411yescharacteristic
104C23×C4×C61C2×C411yescharacteristic
105C23×C4×C61C2×C411yescharacteristic
106C2×C4⋊C4×C61—22no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61C2×C414yescomplemented
110C24×C61C22×C411yescharacteristic
111C23×D61—21no—
112C23×D61—21no—
113C23×D61—24no—
114C23×D61—42no—
115C23×D61—42no—
116C23×D61—42no—
117C23×D61—42no—
118C23×D61C22×C412yes—
119C23×D61C22×C411yescharacteristic
120C23×D61C2×D411yescharacteristic
121C23×D61C2×D411yescharacteristic
122C23×D61C2×D411yescharacteristic
123C23×D61C2×D411yescharacteristic
124C23×D61C2×D414yes—
125C23×D61#4114yes—
126C23×D61C2411yescharacteristic
127C22×#6923—28no—
128C22×#6923—24no—
129C22×#6923—24no—
130C22×#6923—44no—
131C22×#6923—44no—
132C22×#6923—44no—
133C22×#6923—44no—
134C22×#6923—44no—
135C22×C4×C61—24no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—24no—
141C22×C4×C61—42no—
142C22×C4×C61C22⋊C412yes—
143C22×C4×C61C22⋊C411yescharacteristic
144C22×C4×C61C22⋊C411yescharacteristic
145C22×C4×C61C22×C412yes—
146C22×C4×C61C22×C412yes—
147C22×C4×C61C22×C412yes—
148C22×Dic61—24no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61—42no—
152C22×Dic61C22⋊C412yes—
153C22×Dic61C22⋊C411yescharacteristic
154C22×Dic61C22⋊C411yescharacteristic
155C22×Dic61C22×C412yes—
156C22×Dic61C22×C412yes—
157C2×D244—22no—
158C2×D244—22no—
159C2×D244—28no—
160C2×D244—24no—
161C2×D244—22no—
162C2×D244—22no—
163C2×D244—24no—
164C2×D244—42no—
165C2×D244—42no—
166C2×D244—44no—
167C2×D244—44no—
168C2×D244—42no—
169C2×D244—42no—
170C2×C4×D61—28no—
171C2×C4×D61—22no—
172C2×C4×D61—22no—
173C2×C4×D61—24no—
174C2×C4×D61—24no—
175C2×C4×D61—24no—
176C2×C4×D61—28no—
177C2×C4×D61—22no—
178C2×C4×D61—22no—
179C2×C4×D61—24no—
180C2×C4×D61—24no—
181C2×C4×D61—24no—
182C2×C4×D61C22⋊C412yes—
183C2×C4×D61C22⋊C412yes—
184C2×C4×D61C22⋊C412yes—
185C2×C4×D61C22⋊C412yes—
186C2×C4×D61C2×D412yes—
187C2×C4×D61C2×D412yes—
188C2×C4×D61C2×D412yes—
189C2×C4×D61C2×D412yes—
190C22⋊#6923—28no—
191C22⋊#6923—24no—
192C22⋊#6923—24no—
193C22⋊#6923—24no—
194C22⋊#6923—44no—
195C22⋊#6923C2×D418yes—
196C4⋊#6923—216no—
197C4×#6923—216no—
198C4⋊C4×C61—24no—
199C4⋊C4×C61—24no—
200#11758198—22no—
201#11758198—22no—
202#11758198—22no—
203#11758198—22no—
204#11758198—24no—
205#11758198—24no—
206#11758198—24no—
207#11758198—24no—
208#11758196—24no—
209#11758196—24no—
210C23×C61—22no—
211C23×C61—22no—
212C23×C61C2×C22⋊C411yescharacteristic
213C23×C61C2×C22⋊C411yescharacteristic
214C23×C61C4×D414yes—
215C23×C61C23×C411yescharacteristic
216C22×D61—22no—
217C22×D61—22no—
218C22×D61—22no—
219C22×D61—22no—
220C22×D61—22no—
221C22×D61—24no—
222C22×D61—41no—
223C22×D61—41no—
224C22×D61—41no—
225C22×D61—41no—
226C22×D61—41no—
227C22×D61—41no—
228C22×D61—48no—
229C22×D61—48no—
230C22×D61—41no—
231C22×D61—41no—
232C22×D61—42no—
233C22×D61—42no—
234C22×D61—42no—
235C22×D61—42no—
236C22×D61—42no—
237C22×D61—42no—
238C22×D61—42no—
239C22×D61—42no—
240C22×D61—88no—
241C22×D61C2×C22⋊C411yescharacteristic
242C22×D61C2×C22⋊C411yescharacteristic
243C22×D61C4×D414yes—
244C22×D61#12012yes—
245C22×D61#12012yes—
246C22×D61#12114yes—
247C22×D61#12114yes—
248C22×D61#12312yes—
249C22×D61#12312yes—
250C22×D61C22×D411yescharacteristic
251C22×D61C22×D411yescharacteristic
252C22×D61C22×D412yes—
253C22×D61C2×#4112yes—
254C2×#6923—28no—
255C2×#6923—44no—
256C2×#6923—44no—
257C2×#6923—416no—
258C2×#6923—44no—
259C2×#6923—44no—
260C2×#6923—44no—
261C2×#6923—88no—
262C2×C4×C61—24no—
263C2×C4×C61—24no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—24no—
269C2×C4×C61—42no—
270C2×C4×C61—42no—
271C2×C4×C61—42no—
272C2×C4×C61—42no—
273C2×C4×C61—42no—
274C2×C4×C61C2×C22⋊C412yes—
275C2×C4×C61C2×C22⋊C412yes—
276C2×Dic61—24no—
277C2×Dic61—24no—
278C2×Dic61—22no—
279C2×Dic61—22no—
280C2×Dic61—22no—
281C2×Dic61—42no—
282C2×Dic61—42no—
283C2×Dic61—42no—
284C2×Dic61C2×C22⋊C412yes—
285C2×Dic61C2×C22⋊C412yes—
286D244—42no—
287D244—44no—
288D244—42no—
289D244—44no—
290D244—44no—
291C4×D61—22no—
292C4×D61—22no—
293C4×D61—24no—
294C4×D61—24no—
295C4×D61—22no—
296C4×D61—22no—
297C4×D61—24no—
298C4×D61—24no—
299C4×D61—24no—
300C4×D61—24no—
301C2×#1899—611nomaximal, Sylow
302C22×C61—21no—
303C22×C61—21no—
304C22×C61—21no—
305C22×C61—21no—
306C22×C61—28no—
307C22×C61#38612yes—
308C22×C61#38612yes—
309C22×C61#41012yes—
310C22×C61#41012yes—
311C22×C61C22×C22⋊C411yescharacteristic
312C22×C61C2×C4×D412yes—
313C2×D61—21no—
314C2×D61—21no—
315C2×D61—21no—
316C2×D61—21no—
317C2×D61—21no—
318C2×D61—21no—
319C2×D61—21no—
320C2×D61—21no—
321C2×D61—24no—
322C2×D61—28no—
323C2×D61—24no—
324C2×D61—44no—
325C2×D61—42no—
326C2×D61—44no—
327C2×D61—42no—
328C2×D61—42no—
329C2×D61—42no—
330C2×D61—42no—
331C2×D61—42no—
332C2×D61—42no—
333C2×D61—84no—
334C2×D61—84no—
335C2×D61—84no—
336C2×D61#38612yes—
337C2×D61#38612yes—
338C2×D61C2×#12011yescharacteristic
339C2×D61C2×#12112yes—
340C2×D61C2×#12311yescharacteristic
341#6923—48no—
342#6923—84no—
343C4×C61—22no—
344C4×C61—22no—
345C4×C61—42no—
346C4×C61—42no—
347Dic61—22no—
348Dic61—22no—
349Dic61—42no—
350C22×#123—611no—
351C22×#117—611no—
352C22×#99—612no—
353C2×#381—611no—
354#1899—618no—
355C2×#342—612no—
356C2×C61—22no—
357C2×C61—22no—
358C2×C61#189914yescomplemented
359C2×C61C2×#38611yescharacteristic
360C2×C61C2×#41011yescharacteristic
361C2×C61C2×#41011yescharacteristic
362D61—21no—
363D61—22no—
364D61—21no—
365D61—22no—
366D61—22no—
367D61—82no—
368C23×D4—611no—
369C24×C4—611no—
370C2×#123—614no—
371C2×#123—614no—
372C2×#123—1221no—
373C2×#123—1222no—
374C2×#123—1221no—
375C2×#123—1221no—
376C2×#123—1222no—
377C2×#123—1221no—
378C2×#117—614no—
379C2×#117—1228no—
380C2×#117—1222no—
381C22×C4⋊C4—611no—
382C22×C4⋊C4—1221no—
383C22×C4⋊C4#692311yescharacteristic, complemented
384C22×C22⋊C4—612no—
385C22×C22⋊C4—611no—
386C22×C22⋊C4—611no—
387C22×C22⋊C4—611no—
388C22×C22⋊C4—612no—
389C22×C42—1221no—
390C2×#99—618no—
391C2×#99—1228no—
392#381—614no—
393#381—1222no—
394C2×#95—1221no—
395C2×#95—1221no—
396#342—618no—
397C61C2×#189911yescharacteristic, complemented, Sylow
398C25—611no—
399C25—611no—
400C22×D4—612no—
401C22×D4—612no—
402C22×D4—1221no—
403C22×D4—1221no—
404C22×D4—1221no—
405C22×D4—1221no—
406C22×D4—1224no—
407C22×D4—1224no—
408C23×C4—611no—
409C23×C4—611no—
410C23×C4—612no—
411C23×C4—611no—
412C23×C4—611no—
413C23×C4—612no—
414C23×C4—611no—
415C23×C4—612no—
416C23×C4—612no—
417C23×C4—611no—
418C23×C4—1224no—
419C23×C4—1224no—
420C23×C4—1222no—
421C23×C4—1222no—
422C23×C4C2×#692311yescharacteristic
423C23×C4C2×#692311yescharacteristic
424C23×C4C2×#692311yescharacteristic
425#123—1224no—
426#123—1224no—
427#123—1224no—
428#123—1224no—
429#123—1224no—
430#123—1224no—
431#123—1224no—
432#123—1224no—
433#117—12216no—
434#117—12216no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—614no—
439C2×C4⋊C4—1222no—
440C2×C4⋊C4—1221no—
441C2×C4⋊C4—1221no—
442C2×C4⋊C4—1224no—
443C2×C4⋊C4—1228no—
444C2×C4⋊C4C2×#692314yescomplemented
445C2×C22⋊C4—614no—
446C2×C22⋊C4—618no—
447C2×C22⋊C4—612no—
448C2×C22⋊C4—612no—
449C2×C22⋊C4—614no—
450C2×C22⋊C4—614no—
451C2×C22⋊C4—614no—
452C2×C22⋊C4—1222no—
453C2×C22⋊C4—1221no—
454C2×C22⋊C4—1221no—
455C2×C22⋊C4—1221no—
456C2×C22⋊C4—1221no—
457C2×C22⋊C4—1221no—
458C2×C22⋊C4—1221no—
459C2×C22⋊C4—1222no—
460C2×C22⋊C4—1224no—
461C2×C22⋊C4—1222no—
462C2×C22⋊C4—1221no—
463C2×C22⋊C4—1221no—
464C2×C22⋊C4—1224no—
465C2×C22⋊C4—1224no—
466C2×C22⋊C4—1222no—
467C2×C42—1224no—
468C2×C42—1228no—
469#99—12216no—
470#95—1224no—
471#95—1224no—
472C24—611no—
473C24—611no—
474C24—611no—
475C24—611no—
476C24—614no—
477C24—614no—
478C24—611no—
479C24—611no—
480C24—612no—
481C24—1224no—
482C24—1221no—
483C24—1221no—
484C24—2442no—
485C24—2442no—
486C24—2442no—
487C24—2442no—
488C24C22×#692311yescharacteristic
489C2×D4—1224no—
490C2×D4—1222no—
491C2×D4—1222no—
492C2×D4—1222no—
493C2×D4—1222no—
494C2×D4—1228no—
495C2×D4—1224no—
496C2×D4—2442no—
497C2×D4—2444no—
498C2×D4—2442no—
499C2×D4—2442no—
500C2×D4—2444no—
501C2×D4—2442no—
502C22×C4—24no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—24no—
508C22×C4—42no—
509C22×C4—612no—
510C22×C4—611no—
511C22×C4—611no—
512C22×C4—612no—
513C22×C4—612no—
514C22×C4—612no—
515C22×C4—612no—
516C22×C4—612no—
517C22×C4—612no—
518C22×C4—612no—
519C22×C4—612no—
520C22×C4—612no—
521C22×C4—612no—
522C22×C4—1222no—
523C22×C4—1222no—
524C22×C4—1224no—
525C22×C4—1224no—
526C22×C4—1224no—
527C22×C4—1224no—
528C22×C4—1222no—
529C22×C4—1222no—
530C22×C4—1228no—
531C22×C4—1224no—
532C22×C4—1228no—
533C22×C4—1224no—
534C22×C4—1224no—
535C22×C4—1228no—
536C22×C4—1224no—
537C22×C4—1221no—
538C22×C4—1221no—
539C22×C4—1224no—
540C22×C4—2444no—
541C22×C4—2444no—
542C22×C4—2444no—
543C22×C4—2444no—
544C22×C4—2444no—
545C22×C4—2442no—
546C22×C4C22⋊#692312yes—
547C22×C4C22⋊#692311yescharacteristic
548C22×C4C22⋊#692311yescharacteristic
549C22×C4C22×#692312yes—
550C22×C4C22×#692312yes—
551C22×C4C22×#692312yes—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—1224no—
555C4⋊C4—1224no—
556C4⋊C4—12216no—
557C22⋊C4—618no—
558C22⋊C4—1224no—
559C22⋊C4—1224no—
560C22⋊C4—1222no—
561C22⋊C4—1222no—
562C22⋊C4—1222no—
563C22⋊C4—1222no—
564C22⋊C4—1228no—
565C22⋊C4—1224no—
566C22⋊C4—1224no—
567C22⋊C4—1224no—
568C22⋊C4—1224no—
569C22⋊C4—1224no—
570C22⋊C4—2444no—
571C42—12216no—
572C23—22no—
573C23—22no—
574C23—612no—
575C23—614no—
576C23—612no—
577C23—611no—
578C23—611no—
579C23—611no—
580C23—611no—
581C23—612no—
582C23—614no—
583C23—612no—
584C23—614no—
585C23—612no—
586C23—612no—
587C23—1222no—
588C23—1222no—
589C23—1222no—
590C23—1222no—
591C23—1224no—
592C23—1222no—
593C23—4888no—
594C23—2448no—
595C23—2448no—
596C23—2441no—
597C23—2441no—
598C23—2441no—
599C23—2441no—
600C23—2441no—
601C23—2441no—
602C23—2441no—
603C23—2441no—
604C23—2442no—
605C23—2442no—
606C23—2442no—
607C23—2442no—
608C23—2442no—
609C23—2442no—
610C23—2442no—
611C23—2442no—
612C23C2×C22⋊#692311yescharacteristic
613C23C2×C22⋊#692311yescharacteristic
614C23D4×#692314yes—
615C23C23×#692311yescharacteristic
616D4—2442no—
617D4—2444no—
618D4—2442no—
619D4—2444no—
620D4—2444no—
621C2×C4—24no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—24no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—612no—
634C2×C4—612no—
635C2×C4—1222no—
636C2×C4—1222no—
637C2×C4—1224no—
638C2×C4—1224no—
639C2×C4—1222no—
640C2×C4—1222no—
641C2×C4—1224no—
642C2×C4—1224no—
643C2×C4—1224no—
644C2×C4—1224no—
645C2×C4—1224no—
646C2×C4—1222no—
647C2×C4—1222no—
648C2×C4—1224no—
649C2×C4—1228no—
650C2×C4—1222no—
651C2×C4—4888no—
652C2×C4—2444no—
653C2×C4—2444no—
654C2×C4—2444no—
655C2×C4—2442no—
656C2×C4—24416no—
657C2×C4—2444no—
658C2×C4—2444no—
659C2×C4—2442no—
660C2×C4—2442no—
661C2×C4C2×C22⋊#692312yes—
662C2×C4C2×C22⋊#692312yes—
663C22—28no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—611no—
669C22—612no—
670C22—611no—
671C22—612no—
672C22—612no—
673C22—1228no—
674C22—1224no—
675C22—1224no—
676C22—1221no—
677C22—1221no—
678C22—1221no—
679C22—1221no—
680C22—1221no—
681C22—1221no—
682C22—1221no—
683C22—1221no—
684C22—4884no—
685C22—4884no—
686C22—4884no—
687C22—2444no—
688C22—2442no—
689C22—2442no—
690C22—2442no—
691C22—2442no—
692C22—2444no—
693C22—2442no—
694C22—2442no—
695C22—2442no—
696C22#1684071012yes—
697C22#1684071012yes—
698C22#1684074112yes—
699C22#1684074312yes—
700C22C22×C22⋊#692311yescharacteristic
701C22C2×D4×#692312yes—
702C4—22no—
703C4—22no—
704C4—42no—
705C4—42no—
706C4—1222no—
707C4—1222no—
708C4—4884no—
709C4—2448no—
710C4—2442no—
711C2—22no—
712C2—22no—
713C2—1222no—
714C2—1221no—
715C2—1221no—
716C2—1222no—
717C2—1222no—
718C2—4882no—
719C2#2146184314yesdirect product factor
720C2C2×#1684071011yescharacteristic
721C2C2×#1684074111yescharacteristic
722C2C2×#1684074311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D244C22
cosocleC23×D61C24
hypercenterC22×C4⋊C4#6923
hypocenterC61C2×#1899
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#14519856C2semidirect
3. C2×#16840705C2semidirect
4. #21461843C2direct (N × H)
5. C2×#16840640C2semidirect
9. C2×#14519856C22semidirect
17. #16840705C22semidirect
20. #16840640C22semidirect
29. C2×#14519762C4semidirect
31. C22×#11758196C4semidirect
32. C22×#11758198C4semidirect
33. C22×#11758198C4semidirect
35. C22×C4⋊C4×C61C4semidirect
88. C2×#11758196C2×C4semidirect
100. C2×#11758198C2×C4semidirect
101. C2×#11758198C2×C4semidirect
109. C2×C4⋊C4×C61C2×C4semidirect
358. C2×C61#1899semidirect
383. C22×C4⋊C4#6923semidirect
397. C61C2×#1899semidirect
444. C2×C4⋊C4C2×#6923semidirect
719. C2#21461843direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198562
C22×#145198362
C2×#168407052
#214618432
C2×#168406402
C22×#145197622
C2×#189961