Finite Group Databasebeta

← #29648108

Subgroups — #29648108

Order 15616.

1232 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840311C211yesmaximal, characteristic
2#21454450C211yesmaximal, characteristic, complemented
3#432×D61C211yesmaximal, characteristic, complemented
4#21444452C214yesmaximal, complemented
5#21444428C214yesmaximal, complemented
6#21444418C211yesmaximal, characteristic, complemented
7#21444417C211yesmaximal, characteristic, complemented
8#21444416C211yesmaximal, characteristic, complemented
9C61×#1527C211yesmaximal, characteristic, complemented
10C22×#11758226C411yescharacteristic
11C22×#11758224C411yescharacteristic
12#16840311—21no—
13#16840311—21no—
14#16840311—21no—
15#16840311—21no—
16#16840311C412yes—
17#16840311C412yes—
18#16840311C2212yes—
19#16840311C2212yes—
20C2×#14519775C411yescharacteristic
21C2×#14519773C411yescharacteristic
22C2×#14519765C2211yescharacteristic
23C2×#14519750—21no—
24C2×#14519750—21no—
25C2×#14519737—21no—
26C2×#14519737—21no—
27C2×C42×D61C2211yescharacteristic
28#16839819C2211yescharacteristic
29#16839818—21no—
30#16839817C2212yescomplemented
31#16839817C2212yescomplemented
32#16839817C2212yescomplemented
33#16839816—21no—
34#16839813—21no—
35#16839813—21no—
36#16839785—21no—
37C4⋊C8×D61—21no—
38#16839725—21no—
39C22⋊C8×D61—21no—
40C4×#11758194C2211yescharacteristic
41#97×D61C2212yescomplemented
42#16839502C2214yescomplemented
43#16839501C2214yescomplemented
44#16839501C2214yescomplemented
45C2×#124×C61C2211yescharacteristic
46C61×#432C2211yescharacteristic
47C4×M16×C61C2211yescharacteristic
48C61×#329C2214yescomplemented
49C2×#11758226—21no—
50C2×#11758226—21no—
51C2×#11758226—44no—
52C2×#11758226C2×C412yes—
53C2×#11758226C2×C412yes—
54C2×#11758224—21no—
55C2×#11758224—21no—
56C2×#11758224—44no—
57C2×#11758224C2×C412yes—
58C2×#11758224C2×C412yes—
59C22×Dic122C2×C411yescharacteristic
60C22×D244—21no—
61C22×D244C2×C411yescharacteristic
62C22×C22⋊D61—21no—
63C22×C22⋊D61—21no—
64C22×C22⋊D61—21no—
65C23×Dic61—21no—
66C22×C4×D61—21no—
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C2×#11758194—21no—
71C2×C8×D61—22no—
72#14519775—21no—
73#14519775—21no—
74#14519775C2×C412yes—
75#14519775C2×C412yes—
76#14519773—21no—
77#14519773—21no—
78#14519773C2×C412yes—
79#14519773C2×C412yes—
80#14519765—21no—
81#14519765—21no—
82#14519765C2×C412yes—
83#14519765C2312yes—
84#14519750—22no—
85#14519750—22no—
86#14519750—22no—
87#14519750—22no—
88#14519750—22no—
89#14519750—22no—
90#14519750—22no—
91#14519750—22no—
92#14519737—22no—
93#14519737—22no—
94#14519737—22no—
95#14519737—22no—
96#14519737—22no—
97#14519737—22no—
98#14519737—22no—
99#14519737—22no—
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×C4×Dic61C2×C411yescharacteristic
105C2×C4×Dic61D411yescharacteristic
106C2×C4×Dic61D411yescharacteristic
107C42×D61C2×C411yescharacteristic
108C42×D61C2×C411yescharacteristic
109C42×D61D411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61D411yescharacteristic
112C42×D61D411yescharacteristic
113C42×D61C2311yescharacteristic
114C42×D61C2311yescharacteristic
115C4⋊#92418—21no—
116#14519706—22no—
117#14519706—22no—
118#14519706—22no—
119C22⋊#92418—21no—
120#14519689—22no—
121#14519689—22no—
122#14519689—22no—
123#14519688C2312yes—
124#14519688C2312yes—
125#14519687—22no—
126C4×#92418—21no—
127C22×Q8×C61C2×C411yescharacteristic
128C22×D4×C61C2×C411yescharacteristic
129C2×M16×C61—21no—
130#124×C61—21no—
131#124×C61—21no—
132#124×C61C2×C412yes—
133#124×C61C2312yes—
134C2×C22⋊C4×C61—21no—
135C2×C22⋊C4×C61—21no—
136C2×C42×C61C2311yescharacteristic
137C4⋊C8×C61—21no—
138C22⋊C8×C61—21no—
139#97×C61C2312yes—
140#97×C61C2312yes—
141C4×C8×C61—21no—
142C24×C61—21no—
143C23×D61—21no—
144C23×D61C22⋊C411yescharacteristic
145C2×Q8×C61—21no—
146C2×Q8×C61—42no—
147C2×Q8×C61C22×C412yes—
148C2×D4×C61—21no—
149C2×D4×C61—42no—
150C2×D4×C61C22×C412yes—
151C22×C4×C61—21no—
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C2×C22⋊D61—22no—
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—22no—
159C2×C22⋊D61—22no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61—44no—
162C2×C22⋊D61—44no—
163C2×C22⋊D61—44no—
164C22×Dic61—21no—
165C22×Dic61—22no—
166C22×Dic61—22no—
167C22×Dic61—44no—
168C22×Dic61C22⋊C411yescharacteristic
169C22×Dic61C22⋊C411yescharacteristic
170C22×Dic61C22⋊C411yescharacteristic
171#11758226—44no—
172#11758226—44no—
173#11758226—44no—
174#11758226—44no—
175#11758224—44no—
176#11758224—44no—
177#11758224—44no—
178#11758224—44no—
179C2×D244—22no—
180C2×D244—22no—
181C2×D244—21no—
182C2×D244—44no—
183C2×D244—42no—
184C2×D244C22×C412yes—
185C2×C4×D61—24no—
186C2×C4×D61—22no—
187C2×C4×D61—22no—
188C2×C4×D61—42no—
189C2×C4×D61—42no—
190C2×C4×D61—44no—
191C2×C4×D61C22⋊C411yescharacteristic
192C2×C4×D61C22⋊C411yescharacteristic
193C2×C4×D61C22⋊C411yescharacteristic
194C2×C4×D61C22⋊C411yescharacteristic
195C2×C4×D61C22⋊C411yescharacteristic
196C2×C4×D61C22⋊C411yescharacteristic
197C2×C4×D61C22×C411yescharacteristic
198C2×C4×D61C22×C411yescharacteristic
199C2×C4×D61C2×D411yescharacteristic
200C2×C4×D61C2×D411yescharacteristic
201C2×C4×D61C2×D411yescharacteristic
202C2×C4×D61C2×D411yescharacteristic
203C2×Dic122—21no—
204C2×Dic122—42no—
205C2×Dic122C22×C412yes—
206M16×C61—42no—
207C2×C8×C61—22no—
208C2×C8×C61—22no—
209C22⋊C4×C61—22no—
210C22⋊C4×C61—22no—
211C22⋊C4×C61—22no—
212C22⋊C4×C61—22no—
213C42×C61C22×C411yescharacteristic
214C42×C61C2×D411yescharacteristic
215C42×C61C2×D411yescharacteristic
216C42×C61C2411yescharacteristic
217#11758198—22no—
218#11758198—22no—
219#11758198—22no—
220#11758198—22no—
221#11758196—22no—
222#11758196—22no—
223#11758196—22no—
224#11758196—22no—
225C4×Dic61C22⋊C411yescharacteristic
226C4×Dic61C22⋊C411yescharacteristic
227C4×Dic61C22⋊C411yescharacteristic
228C4×Dic61C22⋊C411yescharacteristic
229C4×Dic61C22⋊C411yescharacteristic
230C4×Dic61C22⋊C411yescharacteristic
231C4×Dic61C22×C411yescharacteristic
232C4×Dic61C22×C411yescharacteristic
233C4×Dic61C2×D411yescharacteristic
234C4×Dic61C2×D411yescharacteristic
235C4×Dic61C2×D411yescharacteristic
236C4×Dic61C2×D411yescharacteristic
237#11758194—42no—
238C2×#92418—22no—
239C2×#92418—22no—
240C8×D61—44no—
241C23×C61—22no—
242C23×C61—42no—
243C23×C61—42no—
244C23×C61—42no—
245C23×C61C2×C22⋊C411yescharacteristic
246C22×D61—22no—
247C22×D61—22no—
248C22×D61—22no—
249C22×D61—41no—
250C22×D61—42no—
251C22×D61—42no—
252C22×D61—42no—
253C22×D61C2×C22⋊C411yescharacteristic
254C22×D61C2×C22⋊C411yescharacteristic
255Q8×C61—42no—
256Q8×C61—42no—
257D4×C61—42no—
258D4×C61—42no—
259C2×C4×C61—22no—
260C2×C4×C61—22no—
261C2×C4×C61—22no—
262C2×C4×C61—41no—
263C2×C4×C61—42no—
264C2×C4×C61C2×C22⋊C411yescharacteristic
265C2×C4×C61C2×C22⋊C411yescharacteristic
266C2×C4×C61C2×C22⋊C411yescharacteristic
267C2×C4×C61C23×C411yescharacteristic
268C2×C4×C61C22×D411yescharacteristic
269C2×C4×C61C22×D411yescharacteristic
270C22⋊D61—44no—
271C22⋊D61—44no—
272C22⋊D61—44no—
273C22⋊D61—44no—
274C22⋊D61—44no—
275C22⋊D61—44no—
276C2×Dic61—22no—
277C2×Dic61—22no—
278C2×Dic61—22no—
279C2×Dic61—22no—
280C2×Dic61—44no—
281C2×Dic61—42no—
282C2×Dic61—44no—
283C2×Dic61C2×C22⋊C411yescharacteristic
284C2×Dic61C2×C22⋊C411yescharacteristic
285C2×Dic61C2×C22⋊C411yescharacteristic
286C2×Dic61C2×C22⋊C411yescharacteristic
287C2×Dic61C2×C22⋊C411yescharacteristic
288C2×Dic61C2×C22⋊C411yescharacteristic
289D244—42no—
290D244—44no—
291D244—44no—
292D244—42no—
293C4×D61—22no—
294C4×D61—22no—
295C4×D61—22no—
296C4×D61—22no—
297C4×D61—22no—
298C4×D61—41no—
299C4×D61—41no—
300C4×D61—41no—
301C4×D61—41no—
302C4×D61—41no—
303C4×D61—41no—
304C4×D61—44no—
305C4×D61—44no—
306C4×D61#10014yes—
307Dic122—42no—
308Dic122—42no—
309C8×C61—42no—
310C8×C61—42no—
311#92418—42no—
312#92418—42no—
313#17671—611nomaximal, Sylow
314C22×C61—21no—
315C22×C61—21no—
316C22×C61—42no—
317C22×C61—42no—
318C22×C61—42no—
319C22×C61—84no—
320C22×C61#42112yes—
321C22×C61C22×C22⋊C411yescharacteristic
322C2×D61—21no—
323C2×D61—21no—
324C2×D61—21no—
325C2×D61—21no—
326C2×D61—21no—
327C2×D61—44no—
328C2×D61—42no—
329C2×D61—42no—
330C2×D61—42no—
331C2×D61—84no—
332C2×D61C2×#10012yes—
333C4×C61—21no—
334C4×C61—21no—
335C4×C61—21no—
336C4×C61—21no—
337C4×C61—21no—
338C4×C61—42no—
339C4×C61C2×#10012yes—
340Dic61—21no—
341Dic61—21no—
342Dic61—21no—
343Dic61—21no—
344Dic61—42no—
345Dic61C2×#10012yes—
346Dic61#42112yes—
347C2×#532—611no—
348#2920—611no—
349C2×#432—611no—
350#1536—614no—
351#1530—614no—
352#1527—611no—
353#1527—611no—
354#1527—611no—
355#1527D6111yescharacteristic, complemented
356C2×C61—22no—
357C2×C61—82no—
358C2×C61C22×#10011yescharacteristic
359C2×C61C2×#42111yescharacteristic
360C2×C61C2×#42111yescharacteristic
361D61—22no—
362D61—41no—
363D61—82no—
364C22×#41—611no—
365C22×#41—611no—
366#532—612no—
367#532—612no—
368#532—612no—
369#532—612no—
370#532—1221no—
371#532—1221no—
372#532—1221no—
373#532—1221no—
374C2×C4⋊Q8—611no—
375C2×#127—611no—
376C2×#124—611no—
377C2×#124C2×D6111yescharacteristic
378C2×#121—1221no—
379C2×#121—1221no—
380C2×C4×D4—1221no—
381C2×C4×D4—1221no—
382C22×C42—611no—
383#432—611no—
384#432—612no—
385#432—612no—
386#432—612no—
387#432—1221no—
388#432—1221no—
389#432C2×D6111yescharacteristic
390#431—1221no—
391#431—1221no—
392#423—1221no—
393C2×C4⋊C8—1221no—
394#407—1221no—
395C2×C22⋊C8—1221no—
396C4×M16—611no—
397C4×M16C2×D6111yescharacteristic
398C2×#97—612no—
399#329—614no—
400#329—614no—
401#329—614no—
402#329C2×D6114yescomplemented
403C61#1767111yescharacteristic, complemented, Sylow
404C2×#41—612no—
405C2×#41—612no—
406C2×#41—612no—
407C2×#41—612no—
408C2×#41—1221no—
409C2×#41—1221no—
410C2×#41—1221no—
411C2×#41—1221no—
412C2×#41—2444no—
413C2×#41—2444no—
414C22×Q8—611no—
415C22×Q8C4×D6111yescharacteristic
416C22×D4—611no—
417C22×D4—1221no—
418C22×D4—1221no—
419C22×D4—1221no—
420C22×D4—1221no—
421C22×D4C4×D6111yescharacteristic
422C23×C4—611no—
423C23×C4—611no—
424C23×C4—611no—
425C23×C4—1221no—
426C23×C4—1221no—
427C2×M16—21no—
428C2×M16—1221no—
429C22×C8—1222no—
430C4⋊Q8—612no—
431C4⋊Q8—612no—
432C4⋊Q8—1221no—
433C4⋊Q8—1221no—
434#127—612no—
435#127—612no—
436#127—1221no—
437#127—1221no—
438#124—21no—
439#124—21no—
440#124—612no—
441#124—612no—
442#124—1221no—
443#124—1221no—
444#124C4×D6112yes—
445#124C22×D6112yes—
446#121—1222no—
447#121—1222no—
448#121—1222no—
449#121—1222no—
450#121—1222no—
451#121—1222no—
452#121—1222no—
453#121—1222no—
454C4×D4—1222no—
455C4×D4—1222no—
456C4×D4—1222no—
457C4×D4—1222no—
458C4×D4—1222no—
459C4×D4—1222no—
460C4×D4—1222no—
461C4×D4—1222no—
462C2×C4⋊C4—1221no—
463C2×C4⋊C4—1221no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—1221no—
467C2×C22⋊C4—1221no—
468C2×C42—611no—
469C2×C42—611no—
470C2×C42—611no—
471C2×C42—611no—
472C2×C42—611no—
473C2×C42—611no—
474C2×C42—611no—
475C2×C42—611no—
476C2×C42—611no—
477C2×C42—611no—
478C2×C42—611no—
479C2×C42C22×D6111yescharacteristic
480C4⋊C8—21no—
481C4⋊C8—1222no—
482C4⋊C8—1222no—
483C4⋊C8—1222no—
484C4⋊C8—1221no—
485C22⋊C8—21no—
486C22⋊C8—1222no—
487C22⋊C8—1222no—
488C22⋊C8—1222no—
489C22⋊C8—1221no—
490#97—612no—
491#97—612no—
492#97—1222no—
493#97C22×D6112yes—
494#97C22×D6112yes—
495C4×C8—21no—
496C4×C8—1221no—
497C24—21no—
498C24—611no—
499C24—1221no—
500#41—2444no—
501#41—2444no—
502#41—2444no—
503#41—2444no—
504#41—2444no—
505#41—2444no—
506#41—2444no—
507#41—2444no—
508C2×Q8—21no—
509C2×Q8—42no—
510C2×Q8—612no—
511C2×Q8—1221no—
512C2×Q8—2442no—
513C2×Q8C2×C4×D6112yes—
514C2×D4—21no—
515C2×D4—42no—
516C2×D4—612no—
517C2×D4—1222no—
518C2×D4—1222no—
519C2×D4—1222no—
520C2×D4—1222no—
521C2×D4—1222no—
522C2×D4—1222no—
523C2×D4—1222no—
524C2×D4—1222no—
525C2×D4—1221no—
526C2×D4—2442no—
527C2×D4—2444no—
528C2×D4—2444no—
529C2×D4—2444no—
530C2×D4—2444no—
531C2×D4C2×C4×D6112yes—
532C22×C4—21no—
533C22×C4—611no—
534C22×C4—611no—
535C22×C4—611no—
536C22×C4—611no—
537C22×C4—611no—
538C22×C4—611no—
539C22×C4—611no—
540C22×C4—611no—
541C22×C4—611no—
542C22×C4—611no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—611no—
546C22×C4—611no—
547C22×C4—611no—
548C22×C4—1224no—
549C22×C4—1222no—
550C22×C4—1222no—
551C22×C4—1222no—
552C22×C4—1222no—
553C22×C4—1221no—
554C22×C4—2442no—
555C22×C4—2442no—
556C22×C4—2444no—
557C22×C4—2444no—
558C22×C4C2×C4×D6111yescharacteristic
559C22×C4D4×D6111yescharacteristic
560C22×C4D4×D6111yescharacteristic
561M16—42no—
562M16—2442no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—1222no—
566C2×C8—1222no—
567C2×C8—2444no—
568C4⋊C4—1222no—
569C4⋊C4—1222no—
570C4⋊C4—1222no—
571C4⋊C4—1222no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—1222no—
577C22⋊C4—1222no—
578C22⋊C4—1222no—
579C22⋊C4—1222no—
580C42—611no—
581C42—611no—
582C42—611no—
583C42—611no—
584C42—611no—
585C42—611no—
586C42—611no—
587C42—611no—
588C42—611no—
589C42—611no—
590C42—611no—
591C42—611no—
592C42C2×C4×D6111yescharacteristic
593C42D4×D6111yescharacteristic
594C42D4×D6111yescharacteristic
595C42C23×D6111yescharacteristic
596C23—22no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—611no—
601C23—611no—
602C23—1222no—
603C23—1222no—
604C23—1222no—
605C23—2441no—
606C23—2442no—
607C23—2442no—
608C23—2442no—
609C23C22⋊C4×D6111yescharacteristic
610Q8—42no—
611Q8—42no—
612Q8—2442no—
613Q8—2442no—
614D4—42no—
615D4—42no—
616D4—2442no—
617D4—2444no—
618D4—2444no—
619D4—2444no—
620D4—2444no—
621D4—2444no—
622D4—2444no—
623D4—2444no—
624D4—2444no—
625D4—2442no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—41no—
630C2×C4—42no—
631C2×C4—611no—
632C2×C4—611no—
633C2×C4—614no—
634C2×C4—611no—
635C2×C4—611no—
636C2×C4—611no—
637C2×C4—611no—
638C2×C4—1222no—
639C2×C4—1222no—
640C2×C4—1222no—
641C2×C4—1222no—
642C2×C4—1222no—
643C2×C4—1222no—
644C2×C4—1222no—
645C2×C4—1222no—
646C2×C4—1222no—
647C2×C4—2441no—
648C2×C4—2441no—
649C2×C4—2441no—
650C2×C4—2441no—
651C2×C4—2441no—
652C2×C4—2441no—
653C2×C4—2444no—
654C2×C4—2444no—
655C2×C4—2444no—
656C2×C4—2444no—
657C2×C4—2442no—
658C2×C4C22⋊C4×D6111yescharacteristic
659C2×C4C22⋊C4×D6111yescharacteristic
660C2×C4C22⋊C4×D6111yescharacteristic
661C2×C4C22×C4×D6111yescharacteristic
662C2×C4C2×D4×D6111yescharacteristic
663C2×C4C2×D4×D6111yescharacteristic
664C8—42no—
665C8—42no—
666C8—2442no—
667C8—2442no—
668C22—21no—
669C22—21no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—84no—
674C22—612no—
675C22—1221no—
676C22—1221no—
677C22—1221no—
678C22—1221no—
679C22—1221no—
680C22—4884no—
681C22—2444no—
682C22—2442no—
683C22—2442no—
684C22—2442no—
685C22#1683977712yes—
686C22C2×C22⋊C4×D6111yescharacteristic
687C4—21no—
688C4—21no—
689C4—21no—
690C4—21no—
691C4—21no—
692C4—42no—
693C4—612no—
694C4—612no—
695C4—1221no—
696C4—1221no—
697C4—1221no—
698C4—1221no—
699C4—2442no—
700C4#100×D6112yes—
701C2—22no—
702C2—82no—
703C2—1222no—
704C2—4882no—
705C2—2441no—
706C2C2×#100×D6111yescharacteristic
707C2#421×D6111yescharacteristic
708C2C2×#1683977711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1527C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840311C2
cosocleC42×C61C24
hypercenter#1527D61
hypocenterC61#17671
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1527

Complements

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

NH ≅ G/Ntype
2. #21454450C2semidirect
3. #432×D61C2semidirect
4. #21444452C2semidirect
5. #21444428C2semidirect
6. #21444418C2semidirect
7. #21444417C2semidirect
8. #21444416C2semidirect
9. C61×#1527C2semidirect
30. #16839817C22semidirect
31. #16839817C22semidirect
32. #16839817C22semidirect
41. #97×D61C22semidirect
42. #16839502C22semidirect
43. #16839501C22semidirect
44. #16839501C22semidirect
48. C61×#329C22semidirect
355. #1527D61semidirect
402. #329C2×D61semidirect
403. C61#17671semidirect

Maximal subgroups

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

subgroupindex
C2×#168403112
#214544502
#432×D612
#214444522
#214444282
#214444182
#214444172
#214444162
C61×#15272
#1767161