Finite Group Databasebeta

← #29646020

Subgroups — #29646020

Order 15616.

1268 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840311C211yesmaximal, characteristic
2#21454449C211yesmaximal, characteristic, complemented
3#431×D61C211yesmaximal, characteristic, complemented
4#21444177C214yesmaximal, complemented
5#21444172C211yesmaximal, characteristic, complemented
6#21444171C211yesmaximal, characteristic, complemented
7#21444170C211yesmaximal, characteristic, complemented
8#21444138C214yesmaximal, complemented
9C61×#1469C211yesmaximal, characteristic, complemented
10C22×#11758226C411yescharacteristic
11C22×#11758224C411yescharacteristic
12#16840311—21no—
13#16840311—21no—
14#16840311—21no—
15#16840311—21no—
16#16840311—21no—
17#16840311—21no—
18#16840311—21no—
19#16840311—21no—
20C2×#14519775C411yescharacteristic
21C2×#14519773C411yescharacteristic
22C2×#14519765C2211yescharacteristic
23C2×#14519750C412yes—
24C2×#14519750C2212yes—
25C2×#14519737C412yes—
26C2×#14519737C2212yes—
27C2×C42×D61C2211yescharacteristic
28#16839819C2211yescharacteristic
29#16839817—21no—
30#16839815C2211yescharacteristic
31#16839814—21no—
32#16839814—21no—
33#16839813—21no—
34#16839812C2212yes—
35#16839812C2212yes—
36#16839784—21no—
37C4⋊C8×D61—21no—
38#16839724C2212yes—
39C22⋊C8×D61C2212yes—
40#16839714—21no—
41C4×C8×D61—21no—
42#16839486C2214yes—
43#16839485C2214yes—
44#16839485C2214yes—
45C2×#124×C61C2211yescharacteristic
46C61×#432C2211yescharacteristic
47C61×#431C2211yescharacteristic
48C61×#323C2214yes—
49C2×#11758226—21no—
50C2×#11758226—21no—
51C2×#11758226—21no—
52C2×#11758226—21no—
53C2×#11758226—44no—
54C2×#11758224—21no—
55C2×#11758224—21no—
56C2×#11758224—21no—
57C2×#11758224—21no—
58C2×#11758224—44no—
59C22×Dic122C2×C411yescharacteristic
60C22×D244C2×C412yes—
61C22×D244C2×C411yescharacteristic
62C22×C22⋊D61C2×C412yes—
63C22×C22⋊D61C2×C412yes—
64C22×C22⋊D61C2×C412yes—
65C23×Dic61C2×C412yes—
66C22×C4×D61C2×C411yescharacteristic
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61C2×C412yes—
69C22×C4×D61C2311yescharacteristic
70C2×#11758189—22no—
71C2×C8×D61—22no—
72#14519775—21no—
73#14519775—21no—
74#14519775—21no—
75#14519775—21no—
76#14519773—21no—
77#14519773—21no—
78#14519773—21no—
79#14519773—21no—
80#14519765—21no—
81#14519765—21no—
82#14519765—21no—
83#14519765—21no—
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×#11758196C2×C412yes—
101C2×#11758196C2×C412yes—
102C2×#11758198C2×C412yes—
103C2×#11758198C2312yes—
104C2×C4×Dic61C2×C411yescharacteristic
105C2×C4×Dic61C2×C411yescharacteristic
106C2×C4×Dic61C2311yescharacteristic
107C42×D61D411yescharacteristic
108C42×D61D411yescharacteristic
109C42×D61D411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61D411yescharacteristic
112C42×D61D411yescharacteristic
113C42×D61D411yescharacteristic
114C42×D61D411yescharacteristic
115C4⋊#92418—21no—
116C4⋊#92418—21no—
117#14519706—22no—
118#14519706—22no—
119C22⋊#92418C2312yes—
120C22⋊#92418C2312yes—
121#14519689—22no—
122#14519689—22no—
123#14519688—21no—
124C4×#92418—21no—
125C8×Dic61—22no—
126C8×Dic61—22no—
127C22×Q8×C61C2×C411yescharacteristic
128C22×D4×C61C2×C411yescharacteristic
129#124×C61—21no—
130#124×C61—21no—
131#124×C61—21no—
132#124×C61—21no—
133C2×C22⋊C4×C61C2×C412yes—
134C2×C22⋊C4×C61C2312yes—
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61—21no—
138C22⋊C8×C61C2312yes—
139C22⋊C8×C61C2312yes—
140#97×C61—21no—
141C4×C8×C61—21no—
142C24×C61C22×C412yes—
143C23×D61C22×C411yescharacteristic
144C23×D61C22×C412yes—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—42no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—42no—
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C412yes—
154C22×C4×C61C2411yescharacteristic
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—28no—
162C2×C22⋊D61—44no—
163C2×C22⋊D61—44no—
164C22×Dic61—22no—
165C22×Dic61—22no—
166C22×Dic61—44no—
167C22×Dic61C22×C411yescharacteristic
168C22×Dic61C22×C411yescharacteristic
169C22×Dic61C22×C412yes—
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—21no—
183C2×D244—42no—
184C2×D244—44no—
185C2×C4×D61—24no—
186C2×C4×D61—24no—
187C2×C4×D61—22no—
188C2×C4×D61—22no—
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—21no—
205C2×Dic122—42no—
206C2×C8×C61—22no—
207C2×C8×C61—22no—
208C22⋊C4×C61—22no—
209C22⋊C4×C61—22no—
210C22⋊C4×C61—22no—
211C22⋊C4×C61—22no—
212C42×C61C2×D411yescharacteristic
213C42×C61C2×D411yescharacteristic
214C42×C61C2×D411yescharacteristic
215C42×C61C2×D411yescharacteristic
216#11758198—22no—
217#11758198—22no—
218#11758198—22no—
219#11758198—22no—
220#11758196—22no—
221#11758196—22no—
222#11758196—22no—
223#11758196—22no—
224C4×Dic61C22⋊C411yescharacteristic
225C4×Dic61C22⋊C411yescharacteristic
226C4×Dic61C22⋊C411yescharacteristic
227C4×Dic61C22⋊C411yescharacteristic
228C4×Dic61C22⋊C411yescharacteristic
229C4×Dic61C22⋊C411yescharacteristic
230C4×Dic61C22⋊C411yescharacteristic
231C4×Dic61C22⋊C411yescharacteristic
232C4×Dic61C2×D411yescharacteristic
233C4×Dic61C2×D411yescharacteristic
234C4×Dic61C2×D411yescharacteristic
235C4×Dic61C2×D411yescharacteristic
236C2×#92418—22no—
237C2×#92418—22no—
238#11758189—44no—
239C8×D61—44no—
240C23×C61—22no—
241C23×C61—24no—
242C23×C61—42no—
243C23×C61—42no—
244C23×C61C23×C411yescharacteristic
245C22×D61—22no—
246C22×D61—22no—
247C22×D61—22no—
248C22×D61—24no—
249C22×D61—41no—
250C22×D61—42no—
251C22×D61—42no—
252C22×D61C2×C22⋊C411yescharacteristic
253C22×D61C2×C22⋊C411yescharacteristic
254Q8×C61—42no—
255Q8×C61—42no—
256D4×C61—42no—
257D4×C61—42no—
258C2×C4×C61—22no—
259C2×C4×C61—22no—
260C2×C4×C61—22no—
261C2×C4×C61—41no—
262C2×C4×C61—42no—
263C2×C4×C61C2×C22⋊C411yescharacteristic
264C2×C4×C61C2×C22⋊C411yescharacteristic
265C2×C4×C61C2×C22⋊C411yescharacteristic
266C2×C4×C61C2×C22⋊C411yescharacteristic
267C2×C4×C61C22×D411yescharacteristic
268C2×C4×C61C22×D411yescharacteristic
269C22⋊D61—44no—
270C22⋊D61—44no—
271C22⋊D61—44no—
272C22⋊D61—44no—
273C22⋊D61—44no—
274C22⋊D61—44no—
275C2×Dic61—22no—
276C2×Dic61—22no—
277C2×Dic61—22no—
278C2×Dic61—44no—
279C2×Dic61—44no—
280C2×Dic61—42no—
281C2×Dic61C2×C22⋊C411yescharacteristic
282C2×Dic61C2×C22⋊C411yescharacteristic
283C2×Dic61C2×C22⋊C411yescharacteristic
284C2×Dic61C2×C22⋊C411yescharacteristic
285C2×Dic61C2×C22⋊C411yescharacteristic
286C2×Dic61C2×C22⋊C411yescharacteristic
287C2×Dic61#13114yes—
288D244—42no—
289D244—44no—
290D244—44no—
291D244—42no—
292C4×D61—22no—
293C4×D61—22no—
294C4×D61—22no—
295C4×D61—22no—
296C4×D61—22no—
297C4×D61—22no—
298C4×D61—22no—
299C4×D61—22no—
300C4×D61—22no—
301C4×D61—41no—
302C4×D61—41no—
303C4×D61—44no—
304C4×D61—44no—
305C4×D61#10014yes—
306Dic122—42no—
307Dic122—42no—
308C8×C61—42no—
309C8×C61—42no—
310#92418—42no—
311#92418—42no—
312#17384—611nomaximal, Sylow
313C22×C61—21no—
314C22×C61—21no—
315C22×C61—42no—
316C22×C61—42no—
317C22×C61—42no—
318C22×C61—84no—
319C22×C61C22×C22⋊C411yescharacteristic
320C22×C61C2×#13112yes—
321C2×D61—21no—
322C2×D61—21no—
323C2×D61—21no—
324C2×D61—21no—
325C2×D61—21no—
326C2×D61—44no—
327C2×D61—42no—
328C2×D61—42no—
329C2×D61—42no—
330C2×D61—84no—
331C2×D61C2×#10012yes—
332C4×C61—21no—
333C4×C61—21no—
334C4×C61—21no—
335C4×C61—21no—
336C4×C61—21no—
337C4×C61—42no—
338C4×C61C2×#10012yes—
339Dic61—21no—
340Dic61—21no—
341Dic61—42no—
342Dic61#40812yes—
343Dic61#40812yes—
344Dic61#41012yes—
345Dic61C2×#10012yes—
346C2×#532—611no—
347#2920—611no—
348C2×#431—611no—
349#1471—614no—
350#1469—611no—
351#1469—611no—
352#1469—611no—
353#1469D6111yescharacteristic, complemented
354#1460—614no—
355C2×C61—22no—
356C2×C61—82no—
357C2×C61C2×#40811yescharacteristic
358C2×C61C2×#41011yescharacteristic
359C2×C61C22×#10011yescharacteristic
360D61—22no—
361D61—41no—
362D61—82no—
363C22×#41—611no—
364C22×#41—611no—
365#532—1221no—
366#532—1221no—
367#532—1221no—
368#532—1221no—
369#532—1221no—
370#532—1221no—
371#532—1221no—
372#532—1221no—
373C2×C4⋊Q8—611no—
374C2×#127—611no—
375C2×#124—611no—
376C2×#124C2×D6111yescharacteristic
377C2×#121—612no—
378C2×#121—612no—
379C2×C4×D4—612no—
380C2×C4×D4—612no—
381C22×C42—611no—
382#432—611no—
383#432—1221no—
384#432C2×D6111yescharacteristic
385#431—611no—
386#431—612no—
387#431—612no—
388#431—1221no—
389#431—1221no—
390#431—1221no—
391#431C2×D6111yescharacteristic
392#423—1221no—
393C2×C4⋊C8—1221no—
394#407—612no—
395C2×C22⋊C8—612no—
396C4×M16—1221no—
397C2×C4×C8—1221no—
398#323—614no—
399#323—614no—
400#323—614no—
401#323C2×D6114yes—
402C61#1738411yescharacteristic, complemented, Sylow
403C2×#41—1221no—
404C2×#41—1221no—
405C2×#41—1221no—
406C2×#41—1221no—
407C2×#41—1221no—
408C2×#41—1221no—
409C2×#41—1221no—
410C2×#41—1221no—
411C2×#41—2444no—
412C2×#41—2444no—
413C22×Q8—611no—
414C22×Q8C4×D6111yescharacteristic
415C22×D4—612no—
416C22×D4—612no—
417C22×D4—612no—
418C22×D4—612no—
419C22×D4—611no—
420C22×D4C4×D6111yescharacteristic
421C23×C4—611no—
422C23×C4—611no—
423C23×C4—611no—
424C23×C4—612no—
425C23×C4—612no—
426C2×M16—1222no—
427C22×C8—1222no—
428C4⋊Q8—1221no—
429C4⋊Q8—1221no—
430C4⋊Q8—1221no—
431C4⋊Q8—1221no—
432#127—1221no—
433#127—1221no—
434#127—1221no—
435#127—1221no—
436#124—21no—
437#124—21no—
438#124—21no—
439#124—21no—
440#124—1221no—
441#124—1221no—
442#124—1221no—
443#124—1221no—
444#121—1222no—
445#121—1222no—
446#121—1222no—
447#121—1222no—
448#121—1222no—
449#121—1222no—
450#121—1222no—
451#121—1222no—
452C4×D4—1222no—
453C4×D4—1222no—
454C4×D4—1222no—
455C4×D4—1222no—
456C4×D4—1222no—
457C4×D4—1222no—
458C4×D4—1222no—
459C4×D4—1222no—
460C2×C4⋊C4—612no—
461C2×C4⋊C4—612no—
462C2×C22⋊C4—612no—
463C2×C22⋊C4—612no—
464C2×C22⋊C4C4×D6112yes—
465C2×C22⋊C4C22×D6112yes—
466C2×C42—611no—
467C2×C42—611no—
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×C42C22×D6111yescharacteristic
478C4⋊C8—21no—
479C4⋊C8—21no—
480C4⋊C8—1222no—
481C4⋊C8—1222no—
482C4⋊C8—1221no—
483C4⋊C8—1221no—
484C22⋊C8—612no—
485C22⋊C8—612no—
486C22⋊C8—1222no—
487C22⋊C8—1222no—
488C22⋊C8C22×D6112yes—
489C22⋊C8C22×D6112yes—
490#97—21no—
491#97—1221no—
492C4×C8—21no—
493C4×C8—1222no—
494C4×C8—1222no—
495C4×C8—1221no—
496C24—611no—
497C24—612no—
498C24C2×C4×D6112yes—
499#41—2444no—
500#41—2444no—
501#41—2444no—
502#41—2444no—
503#41—2444no—
504#41—2444no—
505#41—2444no—
506#41—2444no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—42no—
510C2×Q8—1221no—
511C2×Q8—1221no—
512C2×Q8—2442no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—42no—
516C2×D4—1222no—
517C2×D4—1222no—
518C2×D4—1222no—
519C2×D4—1222no—
520C2×D4—1222no—
521C2×D4—1222no—
522C2×D4—1228no—
523C2×D4—1222no—
524C2×D4—1222no—
525C2×D4—1221no—
526C2×D4—1221no—
527C2×D4—2442no—
528C2×D4—2444no—
529C2×D4—2444no—
530C2×D4—2444no—
531C22×C4—611no—
532C22×C4—611no—
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—612no—
547C22×C4—1224no—
548C22×C4—1224no—
549C22×C4—1222no—
550C22×C4—1222no—
551C22×C4—1222no—
552C22×C4—1222no—
553C22×C4—2442no—
554C22×C4—2444no—
555C22×C4—2444no—
556C22×C4C2×C4×D6111yescharacteristic
557C22×C4C2×C4×D6111yescharacteristic
558C22×C4C2×C4×D6112yes—
559C22×C4C23×D6111yescharacteristic
560M16—2444no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—1222no—
564C2×C8—1222no—
565C2×C8—2444no—
566C4⋊C4—1222no—
567C4⋊C4—1222no—
568C4⋊C4—1222no—
569C4⋊C4—1222no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—1222no—
575C22⋊C4—1222no—
576C22⋊C4—1222no—
577C22⋊C4—1222no—
578C42—611no—
579C42—611no—
580C42—611no—
581C42—611no—
582C42—611no—
583C42—611no—
584C42—611no—
585C42—611no—
586C42—611no—
587C42—611no—
588C42—611no—
589C42—611no—
590C42D4×D6111yescharacteristic
591C42D4×D6111yescharacteristic
592C42D4×D6111yescharacteristic
593C42D4×D6111yescharacteristic
594C23—22no—
595C23—24no—
596C23—42no—
597C23—42no—
598C23—611no—
599C23—611no—
600C23—1222no—
601C23—1222no—
602C23—1224no—
603C23—1222no—
604C23—2441no—
605C23—2442no—
606C23—2442no—
607C23C22×C4×D6111yescharacteristic
608Q8—42no—
609Q8—42no—
610Q8—2442no—
611Q8—2442no—
612D4—42no—
613D4—42no—
614D4—2442no—
615D4—2444no—
616D4—2444no—
617D4—2444no—
618D4—2444no—
619D4—2444no—
620D4—2444no—
621D4—2444no—
622D4—2444no—
623D4—2442no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—611no—
630C2×C4—611no—
631C2×C4—611no—
632C2×C4—611no—
633C2×C4—614no—
634C2×C4—614no—
635C2×C4—611no—
636C2×C4—611no—
637C2×C4—1222no—
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—1222no—
648C2×C4—1222no—
649C2×C4—2441no—
650C2×C4—2441no—
651C2×C4—2444no—
652C2×C4—2444no—
653C2×C4—2444no—
654C2×C4—2444no—
655C2×C4—2442no—
656C2×C4C22⋊C4×D6111yescharacteristic
657C2×C4C22⋊C4×D6111yescharacteristic
658C2×C4C22⋊C4×D6111yescharacteristic
659C2×C4C22⋊C4×D6111yescharacteristic
660C2×C4C2×D4×D6111yescharacteristic
661C2×C4C2×D4×D6111yescharacteristic
662C8—42no—
663C8—42no—
664C8—2442no—
665C8—2442no—
666C22—21no—
667C22—21no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—84no—
672C22—612no—
673C22—1221no—
674C22—1221no—
675C22—1221no—
676C22—1221no—
677C22—1221no—
678C22—4884no—
679C22—2444no—
680C22—2442no—
681C22—2442no—
682C22—2442no—
683C22C2×C22⋊C4×D6111yescharacteristic
684C22#131×D6112yes—
685C4—21no—
686C4—21no—
687C4—21no—
688C4—21no—
689C4—21no—
690C4—42no—
691C4—612no—
692C4—612no—
693C4—612no—
694C4—612no—
695C4—1221no—
696C4—1221no—
697C4—2442no—
698C4#100×D6112yes—
699C2—22no—
700C2—82no—
701C2—1222no—
702C2—4882no—
703C2—2441no—
704C2#408×D6111yescharacteristic
705C2#410×D6111yescharacteristic
706C2C2×#100×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1469C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840311C2
cosocleC22×C4×C61C24
hypercenter#1469D61
hypocenterC61#17384
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1469

Complements

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

NH ≅ G/Ntype
2. #21454449C2semidirect
3. #431×D61C2semidirect
4. #21444177C2semidirect
5. #21444172C2semidirect
6. #21444171C2semidirect
7. #21444170C2semidirect
8. #21444138C2semidirect
9. C61×#1469C2semidirect
353. #1469D61semidirect
402. C61#17384semidirect

Maximal subgroups

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

subgroupindex
C2×#168403112
#214544492
#431×D612
#214441772
#214441722
#214441712
#214441702
#214441382
C61×#14692
#1738461