Finite Group Databasebeta

← C2×#21444177 #29645977

Subgroups — C2×#21444177 #29645977

Order 15616.

1770 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519750C211yesmaximal, characteristic
2C2×#16839724C211yesmaximal, characteristic, complemented
3C2×C22⋊C8×D61C211yesmaximal, characteristic, complemented
4#21444177C218yesmaximal, direct product factor
5C2×#16839486C211yesmaximal, characteristic, complemented
6C2×#16839485C211yesmaximal, characteristic, complemented
7C2×#16839485C211yesmaximal, characteristic, complemented
8C2×C61×#323C211yesmaximal, characteristic, complemented
9C23×D244C411yescharacteristic
10C23×C22⋊D61C411yescharacteristic
11C23×C22⋊D61C411yescharacteristic
12C23×C4×D61C2211yescharacteristic
13C22×#11758189—21no—
14C22×C8×D61—21no—
15C2×#14519750—21no—
16C2×#14519750—21no—
17C2×#14519750—22no—
18C2×#14519750—21no—
19C2×#14519750—21no—
20C2×#14519750—22no—
21C2×#14519750C414yes—
22C2×#14519750C2214yes—
23C22×#11758196C411yescharacteristic
24C22×#11758198C2211yescharacteristic
25#16839724—22no—
26#16839724C2214yescomplemented
27C2×C22⋊#92418C2211yescharacteristic
28C2×C22⋊#92418C2211yescharacteristic
29C2×#14519689—21no—
30C2×#14519689—21no—
31C22⋊C8×D61—22no—
32C22⋊C8×D61C2214yescomplemented
33#16839486C2214yescomplemented
34#16839485C2214yescomplemented
35#16839485C2214yescomplemented
36C22×C22⋊C4×C61C2211yescharacteristic
37C2×C22⋊C8×C61C2211yescharacteristic
38C2×C22⋊C8×C61C2211yescharacteristic
39C61×#323C2214yescomplemented
40C24×D61C2×C411yescharacteristic
41C24×D61C2×C411yescharacteristic
42C22×D244—21no—
43C22×D244—22no—
44C22×D244—21no—
45C22×D244—44no—
46C22×D244C2×C414yes—
47C22×C22⋊D61—21no—
48C22×C22⋊D61—22no—
49C22×C22⋊D61—21no—
50C22×C22⋊D61—22no—
51C22×C22⋊D61—21no—
52C22×C22⋊D61—21no—
53C22×C22⋊D61—44no—
54C22×C22⋊D61—44no—
55C22×C22⋊D61C2×C414yes—
56C22×C22⋊D61C2×C414yes—
57C23×Dic61C2×C411yescharacteristic
58C23×Dic61C2×C411yescharacteristic
59C22×C4×D61—44no—
60C22×C4×D61C2×C412yes—
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61D412yes—
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×C4×D61D412yes—
67C22×C4×D61C2312yes—
68C2×#11758189—24no—
69C2×#11758189—44no—
70C22×#92418—21no—
71C22×#92418—21no—
72C2×C8×D61—24no—
73C2×C8×D61—44no—
74#14519750—24no—
75#14519750—24no—
76#14519750—24no—
77#14519750—24no—
78#14519750—24no—
79#14519750—24no—
80#14519750—24no—
81#14519750—24no—
82C2×#11758196—22no—
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×#11758196C2×C414yes—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198C2×C412yes—
91C2×#11758198C2312yes—
92C22⋊#92418—21no—
93C22⋊#92418—21no—
94C22⋊#92418C2312yes—
95C22⋊#92418C2312yes—
96#14519689—24no—
97#14519689—24no—
98C25×C61C2×C411yescharacteristic
99C23×C4×C61C2×C411yescharacteristic
100C23×C4×C61C2311yescharacteristic
101C22×C8×C61—21no—
102C22×C8×C61—21no—
103C2×C22⋊C4×C61—21no—
104C2×C22⋊C4×C61—21no—
105C2×C22⋊C4×C61—21no—
106C2×C22⋊C4×C61—21no—
107C2×C22⋊C4×C61C2×C412yes—
108C2×C22⋊C4×C61C2312yes—
109C22⋊C8×C61—21no—
110C22⋊C8×C61—21no—
111C22⋊C8×C61C2312yes—
112C22⋊C8×C61C2312yes—
113C24×C61—21no—
114C24×C61—21no—
115C24×C61—22no—
116C24×C61—22no—
117C24×C61—42no—
118C24×C61—42no—
119C24×C61C22×C411yescharacteristic
120C24×C61C22×C412yes—
121C23×D61—22no—
122C23×D61—22no—
123C23×D61—24no—
124C23×D61—21no—
125C23×D61—21no—
126C23×D61—22no—
127C23×D61—22no—
128C23×D61—42no—
129C23×D61—42no—
130C23×D61—42no—
131C23×D61C22⋊C411yescharacteristic
132C23×D61C22⋊C412yes—
133C23×D61C22⋊C411yescharacteristic
134C23×D61C22×C412yes—
135C23×D61C22×C412yes—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—42no—
139C22×C4×C61—42no—
140C22×C4×C61C22×C412yes—
141C22×C4×C61C22×C411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2411yescharacteristic
147C2×C22⋊D61—24no—
148C2×C22⋊D61—24no—
149C2×C22⋊D61—24no—
150C2×C22⋊D61—24no—
151C2×C22⋊D61—44no—
152C2×C22⋊D61—48no—
153C2×C22⋊D61—48no—
154C2×C22⋊D61—48no—
155C2×C22⋊D61—44no—
156C2×C22⋊D61—44no—
157C2×C22⋊D61—48no—
158C2×C22⋊D61—44no—
159C22×Dic61—24no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—42no—
163C22×Dic61C22⋊C411yescharacteristic
164C22×Dic61C22⋊C412yes—
165C22×Dic61C22⋊C411yescharacteristic
166C22×Dic61C22×C412yes—
167C22×Dic61C22×C412yes—
168C2×D244—24no—
169C2×D244—24no—
170C2×D244—44no—
171C2×D244—48no—
172C2×D244—44no—
173C2×D244—48no—
174C2×C4×D61—24no—
175C2×C4×D61—24no—
176C2×C4×D61—44no—
177C2×C4×D61—44no—
178C2×C4×D61—44no—
179C2×C4×D61—44no—
180C2×C4×D61—42no—
181C2×C4×D61—42no—
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—
190C2×C8×C61—22no—
191C2×C8×C61—22no—
192C2×C8×C61—42no—
193C2×C8×C61—42no—
194C22⋊C4×C61—22no—
195C22⋊C4×C61—22no—
196C22⋊C4×C61—22no—
197C22⋊C4×C61—22no—
198#11758198—22no—
199#11758198—22no—
200#11758198—22no—
201#11758198—22no—
202#11758196—24no—
203#11758196—24no—
204C2×#92418—22no—
205C2×#92418—22no—
206C2×#92418—42no—
207C2×#92418—42no—
208#11758189—48no—
209C8×D61—48no—
210C23×C61—22no—
211C23×C61—22no—
212C23×C61—22no—
213C23×C61—22no—
214C23×C61—22no—
215C23×C61—42no—
216C23×C61—42no—
217C23×C61—42no—
218C23×C61—42no—
219C23×C61—42no—
220C23×C61—42no—
221C23×C61—42no—
222C23×C61—42no—
223C23×C61—84no—
224C23×C61—84no—
225C23×C61C2×C22⋊C411yescharacteristic
226C23×C61C2×C22⋊C411yescharacteristic
227C23×C61#13112yes—
228C23×C61#13112yes—
229C23×C61C23×C411yescharacteristic
230C22×D61—22no—
231C22×D61—22no—
232C22×D61—22no—
233C22×D61—22no—
234C22×D61—24no—
235C22×D61—22no—
236C22×D61—22no—
237C22×D61—22no—
238C22×D61—24no—
239C22×D61—24no—
240C22×D61—22no—
241C22×D61—22no—
242C22×D61—22no—
243C22×D61—42no—
244C22×D61—42no—
245C22×D61—48no—
246C22×D61—48no—
247C22×D61—42no—
248C22×D61—42no—
249C22×D61—42no—
250C22×D61—42no—
251C22×D61—42no—
252C22×D61—42no—
253C22×D61—42no—
254C22×D61—42no—
255C22×D61—84no—
256C22×D61—84no—
257C22×D61#10014yes—
258C22×D61C2×C22⋊C412yes—
259C22×D61C2×C22⋊C412yes—
260C2×C4×C61—22no—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—42no—
268C2×C4×C61—42no—
269C2×C4×C61—42no—
270C2×C4×C61C2×C22⋊C411yescharacteristic
271C2×C4×C61C2×C22⋊C411yescharacteristic
272C2×C4×C61C22×D411yescharacteristic
273C2×C4×C61C22×D411yescharacteristic
274C22⋊D61—48no—
275C22⋊D61—48no—
276C22⋊D61—48no—
277C22⋊D61—48no—
278C2×Dic61—22no—
279C2×Dic61—24no—
280C2×Dic61—24no—
281C2×Dic61—22no—
282C2×Dic61—42no—
283C2×Dic61—42no—
284C2×Dic61—42no—
285C2×Dic61#9914yes—
286C2×Dic61C2×C22⋊C412yes—
287C2×Dic61C2×C22⋊C412yes—
288D244—48no—
289D244—48no—
290C4×D61—24no—
291C4×D61—24no—
292C4×D61—24no—
293C4×D61—24no—
294C4×D61—42no—
295C4×D61—42no—
296C4×D61—42no—
297C4×D61—42no—
298C8×C61—42no—
299C8×C61—42no—
300#92418—42no—
301#92418—42no—
302C2×#1471—611nomaximal, Sylow
303C22×C61—21no—
304C22×C61—21no—
305C22×C61—21no—
306C22×C61—21no—
307C22×C61—24no—
308C22×C61—24no—
309C22×C61—42no—
310C22×C61—42no—
311C22×C61—42no—
312C22×C61—82no—
313C22×C61—82no—
314C22×C61—84no—
315C22×C61—84no—
316C22×C61#40812yes—
317C22×C61#40812yes—
318C22×C61C2×#9912yes—
319C22×C61C2×#10012yes—
320C22×C61C22×C22⋊C411yescharacteristic
321C22×C61C2×#13111yescharacteristic
322C22×C61C2×#13111yescharacteristic
323C2×D61—22no—
324C2×D61—22no—
325C2×D61—28no—
326C2×D61—22no—
327C2×D61—22no—
328C2×D61—22no—
329C2×D61—44no—
330C2×D61—44no—
331C2×D61—48no—
332C2×D61—44no—
333C2×D61—42no—
334C2×D61—42no—
335C2×D61—42no—
336C2×D61—84no—
337C2×D61—84no—
338C2×D61—82no—
339C2×D61—82no—
340C2×D61C2×#10014yes—
341C4×C61—21no—
342C4×C61—21no—
343C4×C61—21no—
344C4×C61—21no—
345C4×C61—42no—
346Dic61—22no—
347Dic61—42no—
348Dic61C2×#9914yes—
349C22×#121—611no—
350C2×#407—611no—
351C22×C22⋊C8—611no—
352#1471—618no—
353C2×#323—611no—
354C2×#323—611no—
355C2×#323—611no—
356C2×#323D6111yescharacteristic, complemented
357C2×C61—21no—
358C2×C61—21no—
359C2×C61—22no—
360C2×C61—82no—
361C2×C61#147114yescomplemented
362C2×C61C2×#40811yescharacteristic
363C2×C61C22×#9911yescharacteristic
364C2×C61C22×#10011yescharacteristic
365D61—24no—
366D61—42no—
367D61—82no—
368C23×D4—611no—
369C23×D4—611no—
370C23×D4—611no—
371C24×C4—611no—
372C22×M16—1221no—
373C23×C8—1221no—
374C2×#121—614no—
375C2×#121—614no—
376C2×#121—1221no—
377C2×#121—1221no—
378C2×#121—1222no—
379C2×#121—1221no—
380C2×#121—1221no—
381C2×#121—1222no—
382C22×C4⋊C4—611no—
383C22×C22⋊C4—611no—
384C22×C22⋊C4C2×D6111yescharacteristic
385#407—614no—
386#407—1222no—
387C2×C22⋊C8—611no—
388C2×C22⋊C8—611no—
389C2×C22⋊C8—614no—
390C2×C22⋊C8—1222no—
391C2×C22⋊C8—1221no—
392C2×C22⋊C8—1221no—
393C2×C22⋊C8C2×D6111yescharacteristic
394C2×C22⋊C8C2×D6111yescharacteristic
395#323—614no—
396#323—614no—
397#323—614no—
398#323C2×D6114yescomplemented
399C61C2×#147111yescharacteristic, complemented, Sylow
400C25—611no—
401C25—611no—
402C25C4×D6111yescharacteristic
403C22×D4—614no—
404C22×D4—614no—
405C22×D4—614no—
406C22×D4—1222no—
407C22×D4—1221no—
408C22×D4—1221no—
409C22×D4—1221no—
410C22×D4—1222no—
411C22×D4—1221no—
412C22×D4—1222no—
413C22×D4—1221no—
414C22×D4—1221no—
415C22×D4—2444no—
416C22×D4—2444no—
417C22×D4—2444no—
418C23×C4—611no—
419C23×C4—611no—
420C23×C4—611no—
421C23×C4—612no—
422C23×C4—612no—
423C23×C4—611no—
424C23×C4—611no—
425C23×C4—612no—
426C23×C4—612no—
427C23×C4—611no—
428C23×C4—2444no—
429C23×C4C4×D6111yescharacteristic
430C23×C4C22×D6111yescharacteristic
431C2×M16—1224no—
432C2×M16—2444no—
433C22×C8—21no—
434C22×C8—21no—
435C22×C8—1224no—
436C22×C8—1221no—
437C22×C8—1221no—
438C22×C8—2444no—
439#121—1224no—
440#121—1224no—
441#121—1224no—
442#121—1224no—
443#121—1224no—
444#121—1224no—
445#121—1224no—
446#121—1224no—
447C2×C4⋊C4—614no—
448C2×C4⋊C4—1222no—
449C2×C4⋊C4—1221no—
450C2×C4⋊C4—1221no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—612no—
456C2×C22⋊C4—612no—
457C2×C22⋊C4—1221no—
458C2×C22⋊C4—1221no—
459C2×C22⋊C4—1221no—
460C2×C22⋊C4—1221no—
461C2×C22⋊C4C4×D6112yes—
462C2×C22⋊C4C22×D6112yes—
463C22⋊C8—21no—
464C22⋊C8—21no—
465C22⋊C8—612no—
466C22⋊C8—612no—
467C22⋊C8—1224no—
468C22⋊C8—1224no—
469C22⋊C8—1221no—
470C22⋊C8—1221no—
471C22⋊C8C22×D6112yes—
472C22⋊C8C22×D6112yes—
473C24—21no—
474C24—21no—
475C24—22no—
476C24—22no—
477C24—42no—
478C24—42no—
479C24—611no—
480C24—611no—
481C24—612no—
482C24—612no—
483C24—612no—
484C24—1224no—
485C24—1222no—
486C24—1222no—
487C24—1222no—
488C24—1222no—
489C24—1221no—
490C24—1221no—
491C24—2442no—
492C24—2442no—
493C24—2442no—
494C24C2×C4×D6111yescharacteristic
495C24C2×C4×D6112yes—
496C2×D4—1224no—
497C2×D4—1224no—
498C2×D4—1224no—
499C2×D4—1224no—
500C2×D4—1224no—
501C2×D4—1224no—
502C2×D4—2444no—
503C2×D4—2448no—
504C2×D4—2444no—
505C2×D4—2448no—
506C2×D4—2444no—
507C2×D4—2448no—
508C2×D4—2444no—
509C2×D4—2448no—
510C2×D4—2444no—
511C2×D4—2448no—
512C2×D4—2444no—
513C2×D4—2448no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—611no—
519C22×C4—612no—
520C22×C4—612no—
521C22×C4—611no—
522C22×C4—612no—
523C22×C4—612no—
524C22×C4—612no—
525C22×C4—612no—
526C22×C4—612no—
527C22×C4—612no—
528C22×C4—612no—
529C22×C4—612no—
530C22×C4—612no—
531C22×C4—1224no—
532C22×C4—1224no—
533C22×C4—1224no—
534C22×C4—1221no—
535C22×C4—1221no—
536C22×C4—2442no—
537C22×C4—2442no—
538C22×C4—2444no—
539C22×C4—2444no—
540C22×C4—2444no—
541C22×C4—2444no—
542C22×C4—2442no—
543C22×C4C2×C4×D6112yes—
544C22×C4C2×C4×D6111yescharacteristic
545C22×C4D4×D6111yescharacteristic
546C22×C4D4×D6111yescharacteristic
547C22×C4D4×D6111yescharacteristic
548C22×C4D4×D6111yescharacteristic
549C22×C4C23×D6111yescharacteristic
550M16—2448no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—42no—
554C2×C8—42no—
555C2×C8—1222no—
556C2×C8—1222no—
557C2×C8—2448no—
558C2×C8—2442no—
559C2×C8—2442no—
560C4⋊C4—1224no—
561C4⋊C4—1224no—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—1222no—
567C22⋊C4—1222no—
568C22⋊C4—1222no—
569C22⋊C4—1222no—
570C23—22no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—84no—
584C23—84no—
585C23—612no—
586C23—614no—
587C23—612no—
588C23—1224no—
589C23—1224no—
590C23—1222no—
591C23—1222no—
592C23—1224no—
593C23—1222no—
594C23—1222no—
595C23—1222no—
596C23—1222no—
597C23—1222no—
598C23—1222no—
599C23—1222no—
600C23—1222no—
601C23—4884no—
602C23—4884no—
603C23—2442no—
604C23—2442no—
605C23—2448no—
606C23—2448no—
607C23—2442no—
608C23—2442no—
609C23—2442no—
610C23—2442no—
611C23—2442no—
612C23—2442no—
613C23—2442no—
614C23—2442no—
615C23C22⋊C4×D6111yescharacteristic
616C23C22⋊C4×D6111yescharacteristic
617C23#1451978312yes—
618C23#1451978512yes—
619C23C22×C4×D6111yescharacteristic
620D4—2448no—
621D4—2448no—
622D4—2448no—
623D4—2448no—
624D4—2448no—
625D4—2448no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—612no—
637C2×C4—614no—
638C2×C4—612no—
639C2×C4—1224no—
640C2×C4—1224no—
641C2×C4—1224no—
642C2×C4—1224no—
643C2×C4—1224no—
644C2×C4—1224no—
645C2×C4—1222no—
646C2×C4—1222no—
647C2×C4—2442no—
648C2×C4—2442no—
649C2×C4—2442no—
650C2×C4—2442no—
651C2×C4—2442no—
652C2×C4—2442no—
653C2×C4—2442no—
654C2×C4C22⋊C4×D6111yescharacteristic
655C2×C4C22⋊C4×D6111yescharacteristic
656C2×C4C2×D4×D6111yescharacteristic
657C2×C4C2×D4×D6111yescharacteristic
658C8—42no—
659C8—42no—
660C8—2442no—
661C8—2442no—
662C22—24no—
663C22—24no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—82no—
672C22—82no—
673C22—84no—
674C22—84no—
675C22—614no—
676C22—1228no—
677C22—1222no—
678C22—1222no—
679C22—1222no—
680C22—1222no—
681C22—1222no—
682C22—4882no—
683C22—4882no—
684C22—4884no—
685C22—4884no—
686C22—2448no—
687C22—2444no—
688C22—2444no—
689C22—2442no—
690C22—2442no—
691C22—2442no—
692C22—2444no—
693C22#1683972712yes—
694C22#1683972712yes—
695C22#99×D6112yes—
696C22#100×D6112yes—
697C22C2×C22⋊C4×D6111yescharacteristic
698C22C2×#1451978311yescharacteristic
699C22C2×#1451978511yescharacteristic
700C4—21no—
701C4—21no—
702C4—21no—
703C4—21no—
704C4—42no—
705C4—614no—
706C4—1222no—
707C4—2442no—
708C2—22no—
709C2—21no—
710C2—21no—
711C2—82no—
712C2—1224no—
713C2—4882no—
714C2—2442no—
715C2#2144417714yesdirect product factor
716C2C2×#1683972711yescharacteristic
717C2C2×#99×D6111yescharacteristic
718C2C2×#100×D6111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#323C2
socleC23×C61C2×C22⋊C4
prime radicalC22×#14519750C2
cosocleC22×C4×C61C24
hypercenterC2×#323D61
hypocenterC61C2×#1471
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. C2×#16839724C2semidirect
3. C2×C22⋊C8×D61C2semidirect
4. #21444177C2direct (N × H)
5. C2×#16839486C2semidirect
6. C2×#16839485C2semidirect
7. C2×#16839485C2semidirect
8. C2×C61×#323C2semidirect
26. #16839724C22semidirect
32. C22⋊C8×D61C22semidirect
33. #16839486C22semidirect
34. #16839485C22semidirect
35. #16839485C22semidirect
39. C61×#323C22semidirect
356. C2×#323D61semidirect
361. C2×C61#1471semidirect
398. #323C2×D61semidirect
399. C61C2×#1471semidirect
715. C2#21444177direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197502
C2×#168397242
C2×C22⋊C8×D612
#214441772
C2×#168394862
C2×#168394852
C2×C61×#3232
C2×#147161