Finite Group Databasebeta

← #29679482

Subgroups — #29679482

Order 15616.

1514 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758226C211yesmaximal, characteristic
2C2×C4⋊C8×D61C211yesmaximal, characteristic, complemented
3C2×#16839757C212yesmaximal
4#21448224C211yesmaximal, characteristic, complemented
5#21445832C212yesmaximal, complemented
6#21445828C212yesmaximal, complemented
7#21445824C211yesmaximal, characteristic, complemented
8#21445820C211yesmaximal, characteristic, complemented
9#21445816C211yesmaximal, characteristic, complemented
10#21445534C212yesmaximal, complemented
11C61×#1803C211yesmaximal, characteristic, complemented
12C22×#11758226C2211yescharacteristic
13C22×C8×D61C2212yes—
14C4×#11758226—24no—
15C4×#11758226C418yescomplemented
16C2×Q8×Dic61C2211yescharacteristic
17C2×C4×D244—21no—
18C2×C4×D244C2211yescharacteristic
19C2×#14519739—21no—
20C2×#14519739C2211yescharacteristic
21C2×#14519735—21no—
22C2×#14519735C2212yes—
23C2×#14519735C2211yescharacteristic
24C2×C42×D61—21no—
25C2×C42×D61C2211yescharacteristic
26C2×C4⋊#92418C2211yescharacteristic
27C2×#14519706C2212yes—
28C4⋊C8×D61—24no—
29#16839757—28no—
30C2×#14519701C2212yes—
31C2×#14519699C2212yes—
32C2×#14519697C2212yes—
33#16839632C2211yescharacteristic
34#16839627C2212yes—
35#16839619—21no—
36#16839619—21no—
37C4⋊C4×Dic61—21no—
38C4⋊C4×Dic61—21no—
39#16839525C2212yes—
40#16839524C2212yes—
41#16839524C2212yes—
42C2×C4×Q8×C61C2211yescharacteristic
43C2×C4⋊C8×C61C2211yescharacteristic
44C2×#103×C61C2212yes—
45C61×#384C2211yescharacteristic
46C61×#340C2212yes—
47C2×#11758226—22no—
48C2×#11758226—22no—
49C2×#11758226—22no—
50C2×#11758226C2×C414yes—
51C2×#11758226D414yes—
52C2×#11758226Q814yes—
53C22×D244—21no—
54C22×D244C2311yescharacteristic
55C22×C4×D61—21no—
56C22×C4×D61—21no—
57C22×C4×D61—21no—
58C22×C4×D61D411yescharacteristic
59C22×C4×D61D411yescharacteristic
60C22×C4×D61C2311yescharacteristic
61C22×#92418C2312yes—
62C2×C8×D61—24no—
63C2×C8×D61—24no—
64C2×C8×D61—24no—
65Q8×Dic61—22no—
66Q8×Dic61C2×C414yes—
67C4×D244—28no—
68C4×D244—22no—
69C4×D244C2×C414yes—
70#14519739—28no—
71#14519739—22no—
72#14519739C2×C414yes—
73#14519735—22no—
74#14519735—28no—
75#14519735—24no—
76#14519735—24no—
77#14519735C2×C414yes—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61—21no—
81C2×C4⋊Dic61C2312yes—
82C2×C4⋊Dic61C2311yescharacteristic
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—22no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61—21no—
89C2×C4×Dic61—22no—
90C2×C4×Dic61D411yescharacteristic
91C2×C4×Dic61D411yescharacteristic
92C2×C4×Dic61C2311yescharacteristic
93C42×D61—28no—
94C42×D61C2×C414yes—
95C42×D61D414yes—
96C4⋊#92418—22no—
97#14519706—24no—
98#14519701—24no—
99#14519699—24no—
100#14519697—24no—
101#14519684—22no—
102#14519684—22no—
103C22×Q8×C61C2311yescharacteristic
104C22×C8×C61C2312yes—
105C4×Q8×C61—22no—
106C4×Q8×C61C2×C414yes—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61C2312yes—
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C42×C61—21no—
113C2×C42×C61C2311yescharacteristic
114C4⋊C8×C61—22no—
115#103×C61—24no—
116C23×D61—21no—
117C23×D61C2×D411yescharacteristic
118C2×Q8×C61—21no—
119C2×Q8×C61—21no—
120C2×Q8×C61—21no—
121C2×Q8×C61C22×C412yes—
122C2×Q8×C61C2×D412yes—
123C2×Q8×C61C2×Q812yes—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—22no—
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2411yescharacteristic
130C22×Dic61—21no—
131C22×Dic61—22no—
132C22×Dic61C2×D411yescharacteristic
133C22×Dic61C2×D411yescharacteristic
134C22×Dic61C2×D411yescharacteristic
135#11758226—28no—
136#11758226—28no—
137#11758226—28no—
138#11758226C4⋊C4116yescomplemented
139C2×D244—24no—
140C2×D244—24no—
141C2×D244—24no—
142C2×D244—21no—
143C2×D244—21no—
144C2×D244—21no—
145C2×D244C22×C412yes—
146C2×D244C2×D412yes—
147C2×D244C2×Q812yes—
148C2×C4×D61—22no—
149C2×C4×D61—22no—
150C2×C4×D61—24no—
151C2×C4×D61—24no—
152C2×C4×D61—24no—
153C2×C4×D61—24no—
154C2×C4×D61—24no—
155C2×C4×D61—41no—
156C2×C4×D61—41no—
157C2×C4×D61—42no—
158C2×C4×D61—42no—
159C2×C4×D61—42no—
160C2×C4×D61—42no—
161C2×C4×D61C22⋊C414yes—
162C2×C4×D61C22⋊C414yes—
163C2×C4×D61C22×C412yes—
164C2×C4×D61C2×D412yes—
165C2×C4×D61C2×D412yes—
166C2×C4×D61C2×Q812yes—
167C2×C4×D61#4112yes—
168C2×C4×D61#4112yes—
169C2×C8×C61—22no—
170C2×C8×C61—22no—
171C2×C8×C61—22no—
172C4⋊C4×C61—24no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—22no—
175C4⋊C4×C61—22no—
176C4⋊C4×C61—42no—
177C4⋊C4×C61—42no—
178C4⋊C4×C61C22×C412yes—
179C42×C61—24no—
180C42×C61C22×C412yes—
181C42×C61C2×D412yes—
182#11758198—24no—
183#11758198—24no—
184#11758198—24no—
185#11758198—44no—
186C4⋊Dic61—21no—
187C4⋊Dic61—24no—
188C4⋊Dic61—22no—
189C4⋊Dic61—22no—
190C4⋊Dic61—42no—
191C4⋊Dic61—42no—
192C4⋊Dic61C22×C412yes—
193C4×Dic61—24no—
194C4×Dic61—24no—
195C4×Dic61—44no—
196C4×Dic61C22⋊C414yes—
197C4×Dic61C22⋊C414yes—
198C4×Dic61C22×C412yes—
199C4×Dic61C2×D412yes—
200C2×#92418—22no—
201C2×#92418—22no—
202C2×#92418—22no—
203C8×D61—48no—
204C23×C61C22×D411yescharacteristic
205C22×D61—21no—
206C22×D61—21no—
207C22×D61—21no—
208C22×D61—21no—
209C22×D61—22no—
210C22×D61—22no—
211C22×D61—22no—
212C22×D61—41no—
213C22×D61—41no—
214C22×D61—41no—
215C22×D61—41no—
216C22×D61C2×C22⋊C412yes—
217C22×D61#12112yes—
218C22×D61C22⋊Q812yes—
219Q8×C61—22no—
220Q8×C61—22no—
221Q8×C61—22no—
222Q8×C61C2×C4⋊C414yes—
223C2×C4×C61—22no—
224C2×C4×C61—22no—
225C2×C4×C61—22no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—22no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—42no—
232C2×C4×C61—42no—
233C2×C4×C61—42no—
234C2×C4×C61C2×C22⋊C412yes—
235C2×C4×C61C2×C22⋊C412yes—
236C2×C4×C61#13512yes—
237C2×C4×C61#13512yes—
238C2×C4×C61C23×C411yescharacteristic
239C2×C4×C61C22×D411yescharacteristic
240C2×C4×C61C22×D411yescharacteristic
241C2×C4×C61C22×Q811yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—22no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—42no—
252C2×Dic61—42no—
253C2×Dic61—42no—
254C2×Dic61C2×C22⋊C412yes—
255C2×Dic61C2×C22⋊C412yes—
256C2×Dic61C2×C22⋊C412yes—
257C2×Dic61#12112yes—
258C2×Dic61C22⋊Q812yes—
259D244—216no—
260D244—22no—
261D244—22no—
262D244—22no—
263D244C2×C4⋊C414yes—
264C4×D61—28no—
265C4×D61—216no—
266C4×D61—44no—
267C4×D61—48no—
268C4×D61—48no—
269C4×D61C2×C4⋊C414yes—
270C4×D61#11714yes—
271C4×D61#12114yes—
272C4×D61C22⋊Q814yes—
273C8×C61—42no—
274#92418—42no—
275#20645—611nomaximal, Sylow
276C22×C61C22×C22⋊C411yescharacteristic
277C22×C61C2×#12111yescharacteristic
278C22×C61C2×C22⋊Q811yescharacteristic
279C22×C61C2×#13511yescharacteristic
280C22×C61C2×#13511yescharacteristic
281C22×C61#57511yescharacteristic
282C22×C61#57511yescharacteristic
283C2×D61—22no—
284C2×D61—22no—
285C2×D61—22no—
286C2×D61—22no—
287C2×D61—22no—
288C2×D61—22no—
289C2×D61—24no—
290C2×D61—42no—
291C2×D61—42no—
292C2×D61—42no—
293C2×D61—42no—
294C2×D61—42no—
295C2×D61—42no—
296C2×D61#38014yes—
297C4×C61—22no—
298C4×C61—24no—
299C4×C61—42no—
300C4×C61—82no—
301C4×C61#41614yescomplemented
302C4×C61C22×C4⋊C411yescharacteristic
303C4×C61C2×#11711yescharacteristic
304C4×C61C2×#12111yescharacteristic
305C4×C61C2×C22⋊Q811yescharacteristic
306Dic61—22no—
307Dic61—22no—
308Dic61—42no—
309Dic61—82no—
310Dic61#38014yes—
311C2×C4×#41—611no—
312C22×C4⋊C8—611no—
313C2×#416—612no—
314#2285—611no—
315#1805—612no—
316#1804—612no—
317#1803—611no—
318#1803D6111yescharacteristic, complemented
319#1802—611no—
320#1802—611no—
321#1735—612no—
322C2×C61C2×#38011yescharacteristic
323C2×C61C2×#41611yescharacteristic
324C2×C61#289611yescharacteristic
325C2×C61#303511yescharacteristic
326C2×C61#303511yescharacteristic
327C2×C61#307611yescharacteristic
328C2×C61#307611yescharacteristic
329D61—24no—
330D61—44no—
331C22×#41—611no—
332C23×C8—612no—
333C4×#41—618no—
334C4×#41—1224no—
335C2×C4×Q8—611no—
336C2×C4×Q8C2×D6111yescharacteristic
337C2×C4×D4—611no—
338C2×C4×D4—611no—
339C2×C4×D4—1221no—
340C2×C4×D4—1221no—
341C2×#117—611no—
342C2×#117—612no—
343C2×#117—1221no—
344C22×C42—611no—
345C22×C42—1221no—
346C2×C4⋊C8—612no—
347C2×C4⋊C8—611no—
348C2×C4⋊C8—1224no—
349C2×C4⋊C8C2×D6111yescharacteristic
350#416—1228no—
351C2×#103—612no—
352C2×#103C2×D6112yes—
353C2×#102—612no—
354C2×#102—612no—
355#384—611no—
356#384C2×D6111yescharacteristic
357#382—612no—
358#380—1221no—
359#380—1221no—
360C4×C4⋊C4—1221no—
361C4×C4⋊C4—1221no—
362#340—612no—
363#340—612no—
364#340—612no—
365#340C2×D6112yes—
366C61#2064511yescharacteristic, complemented, Sylow
367C2×#41—614no—
368C2×#41—614no—
369C2×#41—614no—
370C2×#41—1222no—
371C2×#41—1222no—
372C2×#41—1222no—
373C22×Q8C22×D6111yescharacteristic
374C22×D4—611no—
375C22×D4—1221no—
376C23×C4—611no—
377C23×C4—611no—
378C23×C4—611no—
379C23×C4—1221no—
380C23×C4—1221no—
381C23×C4—1221no—
382C22×C8—612no—
383C22×C8—1224no—
384C22×C8—1224no—
385C22×C8—1224no—
386C22×C8C22×D6112yes—
387C4×Q8—22no—
388C4×Q8—614no—
389C4×Q8—1222no—
390C4×Q8C4×D6114yes—
391C4×D4—614no—
392C4×D4—614no—
393C4×D4—1228no—
394C4×D4—1222no—
395C4×D4—1228no—
396C4×D4—1222no—
397#117—614no—
398#117—1228no—
399#117—1222no—
400#117—1224no—
401#117—1224no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—611no—
406C2×C4⋊C4—612no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4C22×D6112yes—
411C2×C4⋊C4C22×D6111yescharacteristic
412C2×C22⋊C4—1221no—
413C2×C22⋊C4—1221no—
414C2×C22⋊C4—1221no—
415C2×C22⋊C4—1222no—
416C2×C42—21no—
417C2×C42—611no—
418C2×C42—611no—
419C2×C42—611no—
420C2×C42—614no—
421C2×C42—614no—
422C2×C42—1228no—
423C2×C42—1221no—
424C2×C42—1221no—
425C2×C42—1222no—
426C2×C42C22×D6111yescharacteristic
427C4⋊C8—22no—
428C4⋊C8—1224no—
429C4⋊C8—1222no—
430#103—24no—
431#103—1224no—
432#102—1224no—
433#102—1224no—
434#95—1222no—
435#95—1222no—
436C24—611no—
437C24—1221no—
438#41—6116no—
439#41—1228no—
440#41—1228no—
441#41—1228no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8C2×C4×D6112yes—
446C2×Q8D4×D6112yes—
447C2×Q8Q8×D6112yes—
448C2×D4—612no—
449C2×D4—612no—
450C2×D4—612no—
451C2×D4—1224no—
452C2×D4—1224no—
453C2×D4—1224no—
454C2×D4—1221no—
455C2×D4—1221no—
456C2×D4—1221no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—611no—
461C22×C4—612no—
462C22×C4—612no—
463C22×C4—612no—
464C22×C4—612no—
465C22×C4—612no—
466C22×C4—612no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—614no—
470C22×C4—614no—
471C22×C4—1224no—
472C22×C4—1224no—
473C22×C4—1224no—
474C22×C4—1224no—
475C22×C4—1222no—
476C22×C4—1222no—
477C22×C4—1221no—
478C22×C4—1224no—
479C22×C4—1222no—
480C22×C4—2441no—
481C22×C4—2441no—
482C22×C4—2442no—
483C22×C4—2442no—
484C22×C4—2442no—
485C22×C4—2442no—
486C22×C4D4×D6111yescharacteristic
487C22×C4D4×D6111yescharacteristic
488C22×C4C23×D6111yescharacteristic
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—1222no—
493C2×C8—1222no—
494C2×C8—1222no—
495C2×C8—2448no—
496C4⋊C4—21no—
497C4⋊C4—24no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—42no—
501C4⋊C4—42no—
502C4⋊C4—612no—
503C4⋊C4—1224no—
504C4⋊C4—1221no—
505C4⋊C4—1222no—
506C4⋊C4—1222no—
507C4⋊C4—2442no—
508C4⋊C4—2442no—
509C4⋊C4C2×C4×D6112yes—
510C22⋊C4—1224no—
511C22⋊C4—1224no—
512C22⋊C4—1224no—
513C22⋊C4—2444no—
514C42—24no—
515C42—612no—
516C42—612no—
517C42—614no—
518C42—614no—
519C42—1224no—
520C42—1224no—
521C42—2444no—
522C42C2×C4×D6112yes—
523C42D4×D6112yes—
524C23—612no—
525C23—612no—
526C23—612no—
527C23—1221no—
528C23—1221no—
529C23—1221no—
530C23—1221no—
531C23—1222no—
532C23—1222no—
533C23—1222no—
534C23—2441no—
535C23—2441no—
536C23—2441no—
537C23—2441no—
538C23C2×D4×D6111yescharacteristic
539Q8—22no—
540Q8—22no—
541Q8—22no—
542Q8C4⋊C4×D6114yes—
543D4—614no—
544D4—12216no—
545D4—1222no—
546D4—1222no—
547D4—1222no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—612no—
560C2×C4—612no—
561C2×C4—612no—
562C2×C4—614no—
563C2×C4—614no—
564C2×C4—614no—
565C2×C4—614no—
566C2×C4—612no—
567C2×C4—612no—
568C2×C4—12216no—
569C2×C4—1221no—
570C2×C4—1221no—
571C2×C4—1221no—
572C2×C4—1221no—
573C2×C4—1228no—
574C2×C4—1222no—
575C2×C4—2444no—
576C2×C4—2448no—
577C2×C4—2442no—
578C2×C4—2442no—
579C2×C4—2442no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2448no—
583C2×C4C22⋊C4×D6112yes—
584C2×C4C22⋊C4×D6112yes—
585C2×C4#1451979812yes—
586C2×C4#1451980012yes—
587C2×C4C22×C4×D6111yescharacteristic
588C2×C4C2×D4×D6111yescharacteristic
589C2×C4C2×D4×D6111yescharacteristic
590C2×C4C2×Q8×D6111yescharacteristic
591C2×C4#41×D6111yescharacteristic
592C2×C4#41×D6111yescharacteristic
593C8—42no—
594C8—2442no—
595C22—614no—
596C22—1222no—
597C22—1222no—
598C22—1222no—
599C22—1222no—
600C22—1222no—
601C22—1222no—
602C22—1224no—
603C22—2442no—
604C22—2442no—
605C22—2442no—
606C22—2442no—
607C22—2442no—
608C22—2442no—
609C22C2×C22⋊C4×D6111yescharacteristic
610C22#121×D6111yescharacteristic
611C22C22⋊Q8×D6111yescharacteristic
612C22C2×#1451979811yescharacteristic
613C22C2×#1451980011yescharacteristic
614C22#1684055811yescharacteristic
615C22#1684056111yescharacteristic
616C4—24no—
617C4—22no—
618C4—42no—
619C4—82no—
620C4—614no—
621C4—1222no—
622C4—1222no—
623C4—4882no—
624C4—2442no—
625C4#1683975714yescomplemented
626C4C2×C4⋊C4×D6111yescharacteristic
627C4#117×D6111yescharacteristic
628C4#121×D6111yescharacteristic
629C4C22⋊Q8×D6111yescharacteristic
630C2—1224no—
631C2—2444no—
632C2#380×D6111yescharacteristic
633C2C2×#1683975711yescharacteristic
634C2#2145433511yescharacteristic
635C2#2145526911yescharacteristic
636C2#2145527711yescharacteristic
637C2#2145560211yescharacteristic
638C2#2145561011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1803C2
socleC23×C61C22×D4
prime radicalC22×#11758226C22
cosocleC22×C4×C61C24
hypercenter#1803D61
hypocenterC61#20645
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C8×D61C2semidirect
4. #21448224C2semidirect
5. #21445832C2semidirect
6. #21445828C2semidirect
7. #21445824C2semidirect
8. #21445820C2semidirect
9. #21445816C2semidirect
10. #21445534C2semidirect
11. C61×#1803C2semidirect
15. C4×#11758226C4semidirect
138. #11758226C4⋊C4semidirect
301. C4×C61#416semidirect
318. #1803D61semidirect
366. C61#20645semidirect
625. C4#16839757semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582262
C2×C4⋊C8×D612
C2×#168397572
#214482242
#214458322
#214458282
#214458242
#214458202
#214458162
#214455342
C61×#18032
#2064561