Finite Group Databasebeta

← C2×#21444374 #29647346

Subgroups — C2×#21444374 #29647346

Order 15616.

1498 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840275C211yesmaximal, characteristic
2C2×C22⋊C8×D61C211yesmaximal, characteristic, complemented
3C2×#16839624C211yesmaximal, characteristic, complemented
4#21444374C218yesmaximal, direct product factor
5C2×#16839499C211yesmaximal, characteristic, complemented
6C2×#16839497C211yesmaximal, characteristic, complemented
7C2×#16839495C211yesmaximal, characteristic, complemented
8C2×C61×#328C211yesmaximal, characteristic, complemented
9C22×#11758226C411yescharacteristic, complemented
10C23×C4×D61C2211yescharacteristic
11C22×C8×D61—21no—
12#16840275—22no—
13#16840275—22no—
14#16840275C414yescomplemented
15#16840275C2214yes—
16C2×#14519762—21no—
17C2×#14519753C411yescharacteristic, complemented
18C2×#14519752C411yescharacteristic, complemented
19C2×#14519751C2211yescharacteristic
20C2×#14519747—21no—
21C2×#14519739—21no—
22C2×#14519737—21no—
23C2×#14519735C411yescharacteristic, complemented
24C22×#11758198—21no—
25C2×C22⋊#92418C2211yescharacteristic
26C2×#14519689—21no—
27C22⋊C8×D61—22no—
28C22⋊C8×D61C2214yescomplemented
29#16839624—22no—
30#16839624C2214yescomplemented
31C2×#14519684—21no—
32C2×#14519684C2211yescharacteristic
33#16839499C2214yescomplemented
34#16839497C2214yescomplemented
35#16839495C2214yescomplemented
36C2×C22⋊Q8×C61C2211yescharacteristic
37C2×C22⋊C8×C61C2211yescharacteristic
38C2×#95×C61C2211yescharacteristic
39C61×#328C2214yescomplemented
40C24×D61D411yescharacteristic
41C2×#11758226—22no—
42C2×#11758226—44no—
43C2×#11758226C2×C414yescomplemented
44C22×D244—21no—
45C22×D244—21no—
46C22×D244C2×C411yescharacteristic
47C22×C22⋊D61—21no—
48C23×Dic61—21no—
49C23×Dic61D411yescharacteristic
50C22×C4×D61—21no—
51C22×C4×D61—44no—
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61C2×C412yes—
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D412yes—
57C22×C4×D61D411yescharacteristic
58C22×C4×D61D412yes—
59C22×C4×D61C2312yes—
60C22×#92418—21no—
61C2×C8×D61—24no—
62C2×C8×D61—44no—
63#14519762—24no—
64#14519762—24no—
65#14519753—22no—
66#14519753C2×C414yescomplemented
67#14519752—22no—
68#14519752C2×C414yescomplemented
69#14519751—21no—
70#14519751—21no—
71#14519751C2×C412yes—
72#14519751C2312yes—
73#14519747—24no—
74#14519747—24no—
75#14519739—24no—
76#14519739—24no—
77#14519737—24no—
78#14519737—24no—
79#14519735—22no—
80#14519735C2×C414yescomplemented
81C2×C4⋊Dic61C2×C411yescharacteristic
82C2×#11758196—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198—24no—
88C2×#11758198—44no—
89C2×C4×Dic61—21no—
90C22⋊#92418—21no—
91C22⋊#92418C2312yes—
92#14519689—24no—
93#14519684—21no—
94#14519684—24no—
95#14519684C2312yes—
96C22×Q8×C61C2×C411yescharacteristic
97C23×C4×C61—21no—
98C23×C4×C61C2311yescharacteristic
99C22×C8×C61—21no—
100C22⋊Q8×C61—21no—
101C22⋊Q8×C61—21no—
102C22⋊Q8×C61C2×C412yes—
103C22⋊Q8×C61C2312yes—
104C2×C4⋊C4×C61—21no—
105C2×C4⋊C4×C61C2×C411yescharacteristic
106C2×C22⋊C4×C61—21no—
107C22⋊C8×C61—21no—
108C22⋊C8×C61C2312yes—
109#95×C61—21no—
110#95×C61C2312yes—
111C24×C61C2×D411yescharacteristic
112C23×D61—22no—
113C23×D61—22no—
114C23×D61—24no—
115C23×D61—21no—
116C23×D61—42no—
117C23×D61C22⋊C411yescharacteristic
118C23×D61C22⋊C412yes—
119C23×D61C22⋊C411yescharacteristic
120C23×D61C2×D412yes—
121C2×Q8×C61—21no—
122C2×Q8×C61—42no—
123C2×Q8×C61C22×C412yes—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—22no—
127C22×C4×C61—42no—
128C22×C4×C61—42no—
129C22×C4×C61—42no—
130C22×C4×C61—42no—
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2411yescharacteristic
137C2×C22⋊D61—22no—
138C2×C22⋊D61—22no—
139C2×C22⋊D61—42no—
140C2×C22⋊D61—42no—
141C22×Dic61—21no—
142C22×Dic61—22no—
143C22×Dic61—42no—
144C22×Dic61—42no—
145C22×Dic61—42no—
146C22×Dic61—42no—
147C22×Dic61C22⋊C411yescharacteristic
148C22×Dic61C22⋊C411yescharacteristic
149C22×Dic61C22⋊C412yes—
150C22×Dic61C2×D412yes—
151#11758226—48no—
152#11758226—48no—
153C2×D244—24no—
154C2×D244—24no—
155C2×D244—21no—
156C2×D244—42no—
157C2×D244—44no—
158C2×D244—44no—
159C2×D244C22×C412yes—
160C2×C4×D61—24no—
161C2×C4×D61—24no—
162C2×C4×D61—24no—
163C2×C4×D61—44no—
164C2×C4×D61—44no—
165C2×C4×D61—44no—
166C2×C4×D61—44no—
167C2×C4×D61—42no—
168C2×C4×D61—42no—
169C2×C4×D61—44no—
170C2×C4×D61C22⋊C412yes—
171C2×C4×D61C22⋊C412yes—
172C2×C4×D61C22⋊C412yes—
173C2×C4×D61C22⋊C412yes—
174C2×C4×D61C22×C412yes—
175C2×C4×D61C22×C412yes—
176C2×C4×D61C2×D412yes—
177C2×C4×D61C2×D412yes—
178C2×C8×C61—22no—
179C2×C8×C61—42no—
180C4⋊C4×C61—22no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—22no—
183C4⋊C4×C61C22×C412yes—
184C22⋊C4×C61—22no—
185C22⋊C4×C61—22no—
186#11758198—24no—
187#11758198—24no—
188#11758198—22no—
189#11758198—22no—
190#11758198—24no—
191#11758198—48no—
192C4⋊Dic61—21no—
193C4⋊Dic61C22×C412yes—
194#11758196—24no—
195C4×Dic61—24no—
196C2×#92418—22no—
197C2×#92418—42no—
198C8×D61—48no—
199C23×C61—22no—
200C23×C61—22no—
201C23×C61C2×C22⋊C411yescharacteristic
202C23×C61C2×C22⋊C411yescharacteristic
203C23×C61#13512yes—
204C23×C61#13512yes—
205C23×C61C22×D411yescharacteristic
206C22×D61—22no—
207C22×D61—22no—
208C22×D61—22no—
209C22×D61—22no—
210C22×D61—22no—
211C22×D61—24no—
212C22×D61—22no—
213C22×D61—22no—
214C22×D61—24no—
215C22×D61—24no—
216C22×D61—22no—
217C22×D61—42no—
218C22×D61—42no—
219C22×D61—48no—
220C22×D61—48no—
221C22×D61—42no—
222C22×D61—42no—
223C22×D61—42no—
224C22×D61#9914yes—
225C22×D61C2×C22⋊C412yes—
226C22×D61C2×C22⋊C412yes—
227Q8×C61—42no—
228Q8×C61—42no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—42no—
238C2×C4×C61—42no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61—42no—
242C2×C4×C61—84no—
243C2×C4×C61C2×C22⋊C411yescharacteristic
244C2×C4×C61C2×C22⋊C411yescharacteristic
245C2×C4×C61C23×C411yescharacteristic
246C2×C4×C61C22×D411yescharacteristic
247C22⋊D61—42no—
248C22⋊D61—42no—
249C22⋊D61—44no—
250C2×Dic61—22no—
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—42no—
254C2×Dic61—42no—
255C2×Dic61—42no—
256C2×Dic61—42no—
257C2×Dic61—42no—
258C2×Dic61—42no—
259C2×Dic61—84no—
260C2×Dic61C2×C22⋊C412yes—
261C2×Dic61C2×C22⋊C412yes—
262D244—42no—
263D244—42no—
264D244—48no—
265D244—48no—
266C4×D61—24no—
267C4×D61—24no—
268C4×D61—24no—
269C4×D61—24no—
270C4×D61—42no—
271C4×D61—42no—
272C4×D61—42no—
273C4×D61—42no—
274C4×D61—48no—
275C8×C61—42no—
276#92418—42no—
277C2×#1516—611nomaximal, Sylow
278C22×C61—21no—
279C22×C61—21no—
280C22×C61—21no—
281C22×C61—21no—
282C22×C61—24no—
283C22×C61—24no—
284C22×C61C2×#9912yes—
285C22×C61#41612yes—
286C22×C61#41612yes—
287C22×C61#42112yes—
288C22×C61C22×C22⋊C411yescharacteristic
289C22×C61C2×#13511yescharacteristic
290C22×C61C2×#13511yescharacteristic
291C2×D61—22no—
292C2×D61—22no—
293C2×D61—28no—
294C2×D61—22no—
295C2×D61—22no—
296C2×D61—22no—
297C2×D61—44no—
298C2×D61—44no—
299C2×D61—48no—
300C2×D61—44no—
301C2×D61—42no—
302C2×D61—42no—
303C2×D61—42no—
304C2×D61—84no—
305C2×D61C2×#9914yes—
306C4×C61—21no—
307C4×C61—21no—
308C4×C61—21no—
309C4×C61—21no—
310C4×C61—42no—
311C4×C61—42no—
312C4×C61—82no—
313Dic61—22no—
314Dic61—22no—
315Dic61—42no—
316Dic61—82no—
317C2×#525—611no—
318C22×C22⋊C8—611no—
319C2×#381—611no—
320#1516—618no—
321C2×#328—611no—
322C2×#328D6111yescharacteristic, complemented
323C2×#327—611no—
324C2×#327—611no—
325C2×C61—21no—
326C2×C61—21no—
327C2×C61—22no—
328C2×C61#151614yescomplemented
329C2×C61C22×#9911yescharacteristic
330C2×C61C2×#41611yescharacteristic
331C2×C61C2×#42111yescharacteristic
332D61—24no—
333D61—42no—
334D61—82no—
335C22×#41—611no—
336C24×C4—611no—
337C23×C8—1221no—
338#525—614no—
339#525—614no—
340#525—1222no—
341#525—1222no—
342C2×#123—1221no—
343C2×C22⋊Q8—611no—
344C2×C22⋊Q8C2×D6111yescharacteristic
345C2×#121—611no—
346C2×#121—611no—
347C2×#120—1221no—
348C2×C4×D4—1221no—
349C2×C4×D4—1221no—
350C2×#117—611no—
351C22×C22⋊C4—1221no—
352C2×C22⋊C8—611no—
353C2×C22⋊C8—614no—
354C2×C22⋊C8—1222no—
355C2×C22⋊C8—1221no—
356C2×C22⋊C8C2×D6111yescharacteristic
357#381—614no—
358#381—1222no—
359C2×#95—611no—
360C2×#95—1221no—
361C2×#95C2×D6111yescharacteristic
362#328—614no—
363#328C2×D6114yescomplemented
364#327—614no—
365#327—614no—
366C61C2×#151611yescharacteristic, complemented, Sylow
367C25—611no—
368C2×#41—614no—
369C2×#41—1222no—
370C2×#41—2444no—
371C22×Q8C4×D6111yescharacteristic
372C22×D4—611no—
373C22×D4—1221no—
374C22×D4—1221no—
375C22×D4—1221no—
376C23×C4—21no—
377C23×C4—611no—
378C23×C4—611no—
379C23×C4—611no—
380C23×C4—611no—
381C23×C4—612no—
382C23×C4—611no—
383C23×C4—612no—
384C23×C4—612no—
385C23×C4—612no—
386C23×C4—1221no—
387C23×C4—1221no—
388C23×C4—2444no—
389C23×C4C22×D6111yescharacteristic
390C22×C8—21no—
391C22×C8—1224no—
392C22×C8—1221no—
393C22×C8—2444no—
394#123—1224no—
395#123—1224no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—614no—
399C22⋊Q8—1222no—
400C22⋊Q8C4×D6112yes—
401C22⋊Q8C22×D6112yes—
402#121—612no—
403#121—612no—
404#121—614no—
405#121—1222no—
406#121—1221no—
407#121—1221no—
408#120—1224no—
409#120—1224no—
410C4×D4—1224no—
411C4×D4—1224no—
412C4×D4—1224no—
413C4×D4—1224no—
414#117—614no—
415#117—1222no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4—1221no—
419C2×C4⋊C4C4×D6111yescharacteristic
420C2×C22⋊C4—21no—
421C2×C22⋊C4—1221no—
422C2×C22⋊C4—1221no—
423C2×C22⋊C4—1221no—
424C2×C22⋊C4—1221no—
425C2×C22⋊C4—1224no—
426C2×C22⋊C4—2444no—
427C2×C42—1221no—
428C22⋊C8—21no—
429C22⋊C8—612no—
430C22⋊C8—1224no—
431C22⋊C8—1221no—
432C22⋊C8C22×D6112yes—
433#95—21no—
434#95—612no—
435#95—1224no—
436#95—1221no—
437#95C22×D6112yes—
438C24—611no—
439C24—611no—
440C24—612no—
441C24—612no—
442C24—1224no—
443C24—1222no—
444C24—1222no—
445C24—1221no—
446C24—2442no—
447C24D4×D6111yescharacteristic
448#41—2448no—
449#41—2448no—
450C2×Q8—21no—
451C2×Q8—42no—
452C2×Q8C2×C4×D6112yes—
453C2×D4—612no—
454C2×D4—1224no—
455C2×D4—1224no—
456C2×D4—1222no—
457C2×D4—1222no—
458C2×D4—1221no—
459C2×D4—2442no—
460C2×D4—2444no—
461C2×D4—2444no—
462C2×D4—2442no—
463C2×D4—2442no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—612no—
474C22×C4—612no—
475C22×C4—612no—
476C22×C4—612no—
477C22×C4—612no—
478C22×C4—612no—
479C22×C4—612no—
480C22×C4—612no—
481C22×C4—612no—
482C22×C4—612no—
483C22×C4—1224no—
484C22×C4—1224no—
485C22×C4—1224no—
486C22×C4—1221no—
487C22×C4—1222no—
488C22×C4—2442no—
489C22×C4—2442no—
490C22×C4—2444no—
491C22×C4—2444no—
492C22×C4—2444no—
493C22×C4—2444no—
494C22×C4—2444no—
495C22×C4—2442no—
496C22×C4—2442no—
497C22×C4—2442no—
498C22×C4—2442no—
499C22×C4C2×C4×D6111yescharacteristic
500C22×C4C2×C4×D6111yescharacteristic
501C22×C4D4×D6111yescharacteristic
502C22×C4D4×D6111yescharacteristic
503C22×C4D4×D6111yescharacteristic
504C22×C4C23×D6111yescharacteristic
505C2×C8—22no—
506C2×C8—42no—
507C2×C8—1222no—
508C2×C8—2448no—
509C2×C8—2442no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—21no—
513C4⋊C4—612no—
514C4⋊C4—1224no—
515C4⋊C4—1221no—
516C4⋊C4C2×C4×D6112yes—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—1224no—
520C22⋊C4—1224no—
521C22⋊C4—1224no—
522C22⋊C4—1222no—
523C22⋊C4—1222no—
524C22⋊C4—2448no—
525C42—1224no—
526C23—22no—
527C23—22no—
528C23—612no—
529C23—614no—
530C23—612no—
531C23—1224no—
532C23—1224no—
533C23—1222no—
534C23—1222no—
535C23—1222no—
536C23—1224no—
537C23—1222no—
538C23—1222no—
539C23—1222no—
540C23—1222no—
541C23—1222no—
542C23—2442no—
543C23—2442no—
544C23—2448no—
545C23—2448no—
546C23—2442no—
547C23—2442no—
548C23—2442no—
549C23C22⋊C4×D6111yescharacteristic
550C23C22⋊C4×D6111yescharacteristic
551C23#1451979812yes—
552C23#1451980012yes—
553C23C2×D4×D6111yescharacteristic
554Q8—42no—
555Q8—42no—
556D4—2442no—
557D4—2442no—
558D4—2448no—
559D4—2448no—
560D4—2444no—
561D4—2442no—
562D4—2442no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—84no—
577C2×C4—612no—
578C2×C4—612no—
579C2×C4—1224no—
580C2×C4—1224no—
581C2×C4—1224no—
582C2×C4—1224no—
583C2×C4—1222no—
584C2×C4—1222no—
585C2×C4—1222no—
586C2×C4—4884no—
587C2×C4—2442no—
588C2×C4—2442no—
589C2×C4—2442no—
590C2×C4—2442no—
591C2×C4—2448no—
592C2×C4—2442no—
593C2×C4—2442no—
594C2×C4—2442no—
595C2×C4—2442no—
596C2×C4—2442no—
597C2×C4—2442no—
598C2×C4C22⋊C4×D6111yescharacteristic
599C2×C4C22⋊C4×D6111yescharacteristic
600C2×C4C22×C4×D6111yescharacteristic
601C2×C4C2×D4×D6111yescharacteristic
602C8—42no—
603C8—2442no—
604C22—24no—
605C22—24no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—614no—
611C22—1228no—
612C22—1222no—
613C22—1222no—
614C22—1222no—
615C22—1222no—
616C22—1222no—
617C22—4884no—
618C22—2444no—
619C22—2444no—
620C22—2448no—
621C22—2442no—
622C22—2442no—
623C22—2442no—
624C22—2444no—
625C22#99×D6112yes—
626C22#1683975712yes—
627C22#1683975712yes—
628C22#1683977712yes—
629C22C2×C22⋊C4×D6111yescharacteristic
630C22C2×#1451979811yescharacteristic
631C22C2×#1451980011yescharacteristic
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—42no—
637C4—42no—
638C4—82no—
639C4—1222no—
640C4—1222no—
641C4—4882no—
642C4—2442no—
643C2—21no—
644C2—21no—
645C2—22no—
646C2—1224no—
647C2—4882no—
648C2—2442no—
649C2#2144437414yesdirect product factor
650C2C2×#99×D6111yescharacteristic
651C2C2×#1683975711yescharacteristic
652C2C2×#1683977711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#328C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#16840275C2
cosocleC22×C4×C61C24
hypercenterC2×#328D61
hypocenterC61C2×#1516
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C8×D61C2semidirect
3. C2×#16839624C2semidirect
4. #21444374C2direct (N × H)
5. C2×#16839499C2semidirect
6. C2×#16839497C2semidirect
7. C2×#16839495C2semidirect
8. C2×C61×#328C2semidirect
9. C22×#11758226C4semidirect
14. #16840275C4semidirect
17. C2×#14519753C4semidirect
18. C2×#14519752C4semidirect
23. C2×#14519735C4semidirect
28. C22⋊C8×D61C22semidirect
30. #16839624C22semidirect
33. #16839499C22semidirect
34. #16839497C22semidirect
35. #16839495C22semidirect
39. C61×#328C22semidirect
43. C2×#11758226C2×C4semidirect
66. #14519753C2×C4semidirect
68. #14519752C2×C4semidirect
80. #14519735C2×C4semidirect
322. C2×#328D61semidirect
328. C2×C61#1516semidirect
363. #328C2×D61semidirect
366. C61C2×#1516semidirect
649. C2#21444374direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402752
C2×C22⋊C8×D612
C2×#168396242
#214443742
C2×#168394992
C2×#168394972
C2×#168394952
C2×C61×#3282
C2×#151661