Finite Group Databasebeta

← #29646557

Subgroups — #29646557

Order 15616.

988 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D61C211yesmaximal, characteristic
2#21454447C211yesmaximal, characteristic
3C2×#16839814C211yesmaximal, characteristic
4#21444238C214yesmaximal, complemented
5#21444223C211yesmaximal, characteristic, complemented
6#21444222C211yesmaximal, characteristic, complemented
7#21444221C211yesmaximal, characteristic, complemented
8#21444212C214yesmaximal, complemented
9C61×#1481C211yesmaximal, characteristic, complemented
10#16840319C2211yescharacteristic
11#16840318—21no—
12#16840317C411yescharacteristic
13#16840317C411yescharacteristic
14#16840316—21no—
15#16840316C2212yes—
16#16840315—21no—
17#16840314—21no—
18#16840314C412yes—
19C4⋊Q8×D61C411yescharacteristic
20C4⋊Q8×D61C411yescharacteristic
21#125×D61—21no—
22C22⋊Q8×D61—21no—
23C22⋊Q8×D61C412yes—
24C4×Q8×D61—21no—
25C4×Q8×D61C2212yes—
26#117×D61—21no—
27C2×C42×D61C2211yescharacteristic
28#16839818—21no—
29#16839816—21no—
30#16839815C2211yescharacteristic
31#16839814—21no—
32#16839814—21no—
33#16839814C2212yes—
34#16839814C2212yes—
35#16839813C2212yes—
36#16839784—21no—
37C2×C4⋊#92418C2211yescharacteristic
38#16839724—21no—
39C2×#14519689—21no—
40C4×#11758189C2212yes—
41C2×C8×Dic61—21no—
42#16839494C2214yescomplemented
43Q8⋊#92418C2214yescomplemented
44#16839492C2214yescomplemented
45C61×#533C2211yescharacteristic
46C61×#431C2211yescharacteristic
47C2×C4⋊C8×C61C2211yescharacteristic
48C61×Q8⋊C8C2214yescomplemented
49C2×Q8×D61—21no—
50C2×Q8×D61C2×C412yes—
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C2×#11758189—22no—
55C22×#92418—21no—
56#14519777C2×C411yescharacteristic
57#14519777C2×C411yescharacteristic
58#14519776—21no—
59#14519776—21no—
60#14519776—21no—
61#14519776C2×C412yes—
62#14519775—21no—
63#14519775C2×C412yes—
64#14519769—21no—
65#14519768—21no—
66#14519768—21no—
67#14519767—22no—
68#14519767—22no—
69#14519757—21no—
70#14519757C2×C412yes—
71#14519756—21no—
72#14519756C2×C412yes—
73#14519755—22no—
74#14519755—22no—
75#14519754—22no—
76#14519754—22no—
77#14519753—21no—
78#14519753C2×C412yes—
79Q8×Dic61—21no—
80Q8×Dic61C2×C412yes—
81C4×Dic122—21no—
82C4×Dic122—22no—
83C4×Dic122—22no—
84C4×Dic122C2312yes—
85#14519742—21no—
86#14519742—22no—
87#14519742—22no—
88#14519742C2×C412yes—
89#14519736—21no—
90#14519735—21no—
91#14519735—21no—
92#14519734—22no—
93#14519733—22no—
94C4⋊C4×D61—21no—
95C4⋊C4×D61—21no—
96C4⋊C4×D61—21no—
97C4⋊C4×D61—22no—
98C4⋊C4×D61—22no—
99C4⋊C4×D61C2×C412yes—
100C22⋊C4×D61—22no—
101C2×C4×Dic61C2×C411yescharacteristic
102C2×C4×Dic61D411yescharacteristic
103C2×C4×Dic61D411yescharacteristic
104C42×D61—22no—
105C42×D61C2×C411yescharacteristic
106C42×D61C2×C411yescharacteristic
107C42×D61D411yescharacteristic
108C42×D61D411yescharacteristic
109C42×D61D411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61C2311yescharacteristic
112C42×D61C2311yescharacteristic
113C4⋊#92418—21no—
114C4⋊#92418—21no—
115C4⋊#92418C2312yes—
116#14519706—22no—
117C22⋊#92418—21no—
118#14519689—22no—
119#14519689—22no—
120#14519689—22no—
121#14519687—22no—
122C4×#92418C2312yes—
123C8×Dic61—22no—
124C8×Dic61—22no—
125C22×C8×C61—21no—
126C4⋊Q8×C61C2×C411yescharacteristic
127C4⋊Q8×C61C2×C411yescharacteristic
128#125×C61—21no—
129C22⋊Q8×C61—21no—
130C22⋊Q8×C61C2×C412yes—
131C4×Q8×C61—21no—
132C4×Q8×C61C2312yes—
133#117×C61—21no—
134C2×C42×C61C2311yescharacteristic
135C4⋊C8×C61—21no—
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2312yes—
138C22⋊C8×C61—21no—
139C4×C8×C61C2312yes—
140C23×D61C22⋊C411yescharacteristic
141C2×Q8×C61—21no—
142C2×Q8×C61C22×C412yes—
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×Dic61C22⋊C411yescharacteristic
147C22×Dic61C22⋊C411yescharacteristic
148C22×Dic61C22⋊C411yescharacteristic
149Q8×D61—28no—
150Q8×D61—44no—
151C2×C4×D61—22no—
152C2×C4×D61—22no—
153C2×C4×D61—24no—
154C2×C4×D61—22no—
155C2×C4×D61—22no—
156C2×C4×D61—42no—
157C2×C4×D61C22⋊C411yescharacteristic
158C2×C4×D61C22⋊C411yescharacteristic
159C2×C4×D61C22⋊C411yescharacteristic
160C2×C4×D61C22⋊C411yescharacteristic
161C2×C4×D61C22⋊C411yescharacteristic
162C2×C4×D61C22⋊C411yescharacteristic
163C2×C4×D61C22×C411yescharacteristic
164C2×C4×D61C22×C411yescharacteristic
165C2×C4×D61C2×D411yescharacteristic
166C2×C4×D61C2×D411yescharacteristic
167C2×C4×D61C2×D411yescharacteristic
168C2×C4×D61C2×D411yescharacteristic
169C2×Dic122—21no—
170C2×Dic122—22no—
171C2×Dic122—22no—
172C2×Dic122C22×C412yes—
173C2×C8×C61—22no—
174C2×C8×C61—22no—
175C2×C8×C61—42no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—22no—
180C4⋊C4×C61—22no—
181C4⋊C4×C61C22×C412yes—
182C22⋊C4×C61—22no—
183C42×C61—22no—
184C42×C61C22×C411yescharacteristic
185C42×C61C2×D411yescharacteristic
186C42×C61C2×D411yescharacteristic
187C42×C61C2411yescharacteristic
188C22⋊Dic61—22no—
189#11758198—22no—
190#11758198—22no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—22no—
195C4⋊Dic61—22no—
196C4⋊Dic61C22×C412yes—
197#11758196—22no—
198#11758196—22no—
199#11758196—22no—
200#11758196—22no—
201#11758196—22no—
202#11758196—22no—
203#11758196—22no—
204#11758196—22no—
205C4×Dic61—22no—
206C4×Dic61—22no—
207C4×Dic61—22no—
208C4×Dic61C22⋊C411yescharacteristic
209C4×Dic61C22⋊C411yescharacteristic
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22×C411yescharacteristic
215C4×Dic61C22×C411yescharacteristic
216C4×Dic61C2×D411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C2×#92418—22no—
221C2×#92418—22no—
222C2×#92418—42no—
223#11758189—44no—
224C23×C61C2×C22⋊C411yescharacteristic
225C22×D61—22no—
226C22×D61—22no—
227C22×D61—41no—
228C22×D61C2×C22⋊C411yescharacteristic
229C22×D61C2×C22⋊C411yescharacteristic
230Q8×C61—24no—
231Q8×C61—42no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—41no—
236C2×C4×C61C2×C22⋊C411yescharacteristic
237C2×C4×C61C2×C22⋊C411yescharacteristic
238C2×C4×C61C2×C22⋊C411yescharacteristic
239C2×C4×C61#13712yes—
240C2×C4×C61#13712yes—
241C2×C4×C61C23×C411yescharacteristic
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C61C22×D411yescharacteristic
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61C2×C22⋊C411yescharacteristic
250C2×Dic61C2×C22⋊C411yescharacteristic
251C2×Dic61C2×C22⋊C411yescharacteristic
252C2×Dic61C2×C22⋊C411yescharacteristic
253C2×Dic61C2×C22⋊C411yescharacteristic
254C2×Dic61C2×C22⋊C411yescharacteristic
255C4×D61—22no—
256C4×D61—22no—
257C4×D61—21no—
258C4×D61—21no—
259C4×D61—21no—
260C4×D61—21no—
261C4×D61—22no—
262C4×D61—22no—
263C4×D61—22no—
264C4×D61—22no—
265C4×D61—22no—
266C4×D61—41no—
267C4×D61—41no—
268C4×D61—44no—
269C4×D61—44no—
270C4×D61#13114yes—
271Dic122—24no—
272Dic122—42no—
273Dic122—44no—
274Dic122—44no—
275C8×C61—42no—
276C8×C61—42no—
277#92418—42no—
278#92418—42no—
279#17464—611nomaximal, Sylow
280C22×C61—21no—
281C22×C61—21no—
282C22×C61#41912yes—
283C22×C61C22×C22⋊C411yescharacteristic
284C2×D61—21no—
285C2×D61—21no—
286C2×D61—21no—
287C2×D61—21no—
288C2×D61—21no—
289C2×D61—44no—
290C2×D61#40812yes—
291C4×C61—21no—
292C4×C61—21no—
293C4×C61—21no—
294C4×C61—42no—
295C4×C61—42no—
296C4×C61#41912yes—
297C4×C61C2×#13112yes—
298C4×C61C2×#13711yescharacteristic
299C4×C61C2×#13711yescharacteristic
300Dic61—21no—
301Dic61—21no—
302Dic61—21no—
303Dic61—21no—
304Dic61—42no—
305Dic61—42no—
306Dic61#40812yes—
307Dic61#42112yes—
308C2×#533—611no—
309#2920—611no—
310C2×#431—611no—
311#1485—614no—
312#1481—611no—
313#1481—611no—
314#1481—611no—
315#1481D6111yescharacteristic, complemented
316#1479—614no—
317C2×C61—22no—
318C2×C61C2×#40811yescharacteristic
319C2×C61C2×#41911yescharacteristic
320C2×C61C2×#42111yescharacteristic
321D61—22no—
322D61—41no—
323#533—611no—
324#533—611no—
325#533—612no—
326#533—612no—
327#533—611no—
328#533—1221no—
329#533—1221no—
330#533—1221no—
331#533—1221no—
332#533C2×D6111yescharacteristic
333C2×C4⋊Q8—611no—
334C2×C4⋊Q8—611no—
335C2×#125—1221no—
336C2×C22⋊Q8—612no—
337C2×C22⋊Q8—1221no—
338C2×C4×Q8—612no—
339C2×C4×Q8—1221no—
340C2×#117—1221no—
341C22×C42—611no—
342#432—1221no—
343#432—1221no—
344#431—611no—
345#431—612no—
346#431—612no—
347#431—612no—
348#431—1221no—
349#431—1221no—
350#431C2×D6111yescharacteristic
351#423—1221no—
352C2×C4⋊C8—611no—
353C2×C4⋊C8C2×D6111yescharacteristic
354#407—1221no—
355C2×C22⋊C8—1221no—
356C4×M16—612no—
357C2×C4×C8—1221no—
358Q8⋊C8—614no—
359Q8⋊C8—614no—
360Q8⋊C8—614no—
361Q8⋊C8C2×D6114yescomplemented
362C61#1746411yescharacteristic, complemented, Sylow
363C22×Q8—612no—
364C22×Q8—1221no—
365C23×C4—611no—
366C23×C4—611no—
367C23×C4—611no—
368C2×M16—1222no—
369C22×C8—21no—
370C22×C8—1221no—
371C4⋊Q8—612no—
372C4⋊Q8—612no—
373C4⋊Q8—611no—
374C4⋊Q8—611no—
375C4⋊Q8—1221no—
376C4⋊Q8—1221no—
377C4⋊Q8—1221no—
378C4⋊Q8—1221no—
379C4⋊Q8C4×D6111yescharacteristic
380C4⋊Q8C4×D6111yescharacteristic
381#125—21no—
382#125—1222no—
383#125—1222no—
384#125—1221no—
385#125—1221no—
386#125—1221no—
387C22⋊Q8—21no—
388C22⋊Q8—612no—
389C22⋊Q8—612no—
390C22⋊Q8—612no—
391C22⋊Q8—1222no—
392C22⋊Q8—1222no—
393C22⋊Q8—1222no—
394C22⋊Q8—1222no—
395C22⋊Q8—1221no—
396C22⋊Q8—1221no—
397C22⋊Q8—1221no—
398C22⋊Q8C4×D6112yes—
399C4×Q8—21no—
400C4×Q8—612no—
401C4×Q8—612no—
402C4×Q8—612no—
403C4×Q8—1222no—
404C4×Q8—1222no—
405C4×Q8—1222no—
406C4×Q8—1221no—
407C4×Q8—1222no—
408C4×Q8—1221no—
409C4×Q8—1221no—
410C4×Q8C22×D6112yes—
411#117—21no—
412#117—1222no—
413#117—1222no—
414#117—1221no—
415#117—1221no—
416#117—1221no—
417C2×C4⋊C4—612no—
418C2×C4⋊C4—1221no—
419C2×C4⋊C4—1221no—
420C2×C4⋊C4—1222no—
421C2×C4⋊C4—1222no—
422C2×C4⋊C4—1221no—
423C2×C22⋊C4—1222no—
424C2×C42—611no—
425C2×C42—611no—
426C2×C42—611no—
427C2×C42—611no—
428C2×C42—611no—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—1222no—
436C2×C42C22×D6111yescharacteristic
437C4⋊C8—21no—
438C4⋊C8—21no—
439C4⋊C8—612no—
440C4⋊C8—1222no—
441C4⋊C8—1221no—
442C4⋊C8—1221no—
443C4⋊C8C22×D6112yes—
444C22⋊C8—21no—
445C22⋊C8—1222no—
446C22⋊C8—1222no—
447C22⋊C8—1222no—
448C22⋊C8—1221no—
449#97—1222no—
450C4×C8—612no—
451C4×C8—1222no—
452C4×C8—1222no—
453C4×C8C22×D6112yes—
454C24—611no—
455C2×Q8—21no—
456C2×Q8—612no—
457C2×Q8—1222no—
458C2×Q8—1222no—
459C2×Q8—1228no—
460C2×Q8—1221no—
461C2×Q8—2444no—
462C2×Q8C2×C4×D6112yes—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—1224no—
479C22×C4—1222no—
480C22×C4—1222no—
481C22×C4—1222no—
482C22×C4—1222no—
483C22×C4—2442no—
484C22×C4C2×C4×D6111yescharacteristic
485C22×C4D4×D6111yescharacteristic
486C22×C4D4×D6111yescharacteristic
487M16—2444no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—42no—
491C2×C8—1222no—
492C2×C8—1222no—
493C2×C8—2442no—
494C4⋊C4—22no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—22no—
499C4⋊C4—612no—
500C4⋊C4—1222no—
501C4⋊C4—1222no—
502C4⋊C4—1222no—
503C4⋊C4—1222no—
504C4⋊C4—1222no—
505C4⋊C4—1222no—
506C4⋊C4—1222no—
507C4⋊C4—1222no—
508C4⋊C4—1222no—
509C4⋊C4—1222no—
510C4⋊C4—1221no—
511C4⋊C4—1221no—
512C4⋊C4—1221no—
513C4⋊C4C2×C4×D6112yes—
514C22⋊C4—22no—
515C22⋊C4—1222no—
516C22⋊C4—1222no—
517C22⋊C4—1222no—
518C42—22no—
519C42—611no—
520C42—611no—
521C42—611no—
522C42—611no—
523C42—611no—
524C42—611no—
525C42—611no—
526C42—611no—
527C42—611no—
528C42—611no—
529C42—611no—
530C42—611no—
531C42—1222no—
532C42—1222no—
533C42—1222no—
534C42C2×C4×D6111yescharacteristic
535C42D4×D6111yescharacteristic
536C42D4×D6111yescharacteristic
537C42C23×D6111yescharacteristic
538C23—611no—
539C23—611no—
540C23—1222no—
541C23—1222no—
542C23—2441no—
543C23C22⋊C4×D6111yescharacteristic
544Q8—24no—
545Q8—42no—
546Q8—1224no—
547Q8—2442no—
548Q8—2444no—
549Q8—2444no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—41no—
554C2×C4—611no—
555C2×C4—611no—
556C2×C4—614no—
557C2×C4—611no—
558C2×C4—611no—
559C2×C4—611no—
560C2×C4—611no—
561C2×C4—1222no—
562C2×C4—1222no—
563C2×C4—1222no—
564C2×C4—1222no—
565C2×C4—1222no—
566C2×C4—1222no—
567C2×C4—1222no—
568C2×C4—1222no—
569C2×C4—1222no—
570C2×C4—1222no—
571C2×C4—1221no—
572C2×C4—1221no—
573C2×C4—1221no—
574C2×C4—1221no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4—2444no—
580C2×C4—2444no—
581C2×C4C22⋊C4×D6111yescharacteristic
582C2×C4C22⋊C4×D6111yescharacteristic
583C2×C4C22⋊C4×D6111yescharacteristic
584C2×C4#1451980612yes—
585C2×C4#1451980912yes—
586C2×C4C22×C4×D6111yescharacteristic
587C2×C4C2×D4×D6111yescharacteristic
588C2×C4C2×D4×D6111yescharacteristic
589C8—42no—
590C8—42no—
591C8—2442no—
592C8—2442no—
593C22—21no—
594C22—21no—
595C22—612no—
596C22—1221no—
597C22—1221no—
598C22—1221no—
599C22—1221no—
600C22—1221no—
601C22—2444no—
602C22#1683976912yes—
603C22C2×C22⋊C4×D6111yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—42no—
608C4—42no—
609C4—612no—
610C4—612no—
611C4—1221no—
612C4—1221no—
613C4—1221no—
614C4—1221no—
615C4—2442no—
616C4—2442no—
617C4#1683976912yes—
618C4#131×D6112yes—
619C4C2×#1451980611yescharacteristic
620C4C2×#1451980911yescharacteristic
621C2—22no—
622C2—1222no—
623C2—2441no—
624C2#408×D6111yescharacteristic
625C2C2×#1683976911yescharacteristic
626C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1481C2
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC42×C61C24
hypercenter#1481D61
hypocenterC61#17464
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
4. #21444238C2semidirect
5. #21444223C2semidirect
6. #21444222C2semidirect
7. #21444221C2semidirect
8. #21444212C2semidirect
9. C61×#1481C2semidirect
42. #16839494C22semidirect
43. Q8⋊#92418C22semidirect
44. #16839492C22semidirect
48. C61×Q8⋊C8C22semidirect
315. #1481D61semidirect
361. Q8⋊C8C2×D61semidirect
362. C61#17464semidirect

Maximal subgroups

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

subgroupindex
#533×D612
#214544472
C2×#168398142
#214442382
#214442232
#214442222
#214442212
#214442122
C61×#14812
#1746461