Finite Group Databasebeta

← #29646552

Subgroups — #29646552

Order 15616.

1268 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×#16840309C211yesmaximal, characteristic
2#21454447C211yesmaximal, characteristic, complemented
3#431×D61C211yesmaximal, characteristic, complemented
4#21444234C214yesmaximal, complemented
5#21444216C214yesmaximal, complemented
6#21444211C211yesmaximal, characteristic, complemented
7#21444210C211yesmaximal, characteristic, complemented
8#21444209C211yesmaximal, characteristic, complemented
9C61×#1478C211yesmaximal, characteristic, complemented
10C22×#11758222—21no—
11#16840309—21no—
12#16840309—21no—
13#16840309—21no—
14#16840309—21no—
15#16840309C412yes—
16#16840309C412yes—
17#16840309C2212yes—
18#16840309C2212yes—
19C2×#14519776C411yescharacteristic
20C2×#14519773C411yescharacteristic
21C2×#14519763—21no—
22C2×#14519752C411yescharacteristic
23C2×#14519750—21no—
24C2×#14519748C411yescharacteristic
25C2×C4×D244C2211yescharacteristic
26C2×C4×C22⋊D61—21no—
27C2×C42×D61C2211yescharacteristic
28#16839818—21no—
29#16839816—21no—
30#16839815C2211yescharacteristic
31#16839815C2211yescharacteristic
32#16839814C2212yescomplemented
33#16839813—21no—
34#16839813C2212yescomplemented
35#16839812—21no—
36#16839784—21no—
37C4⋊C8×D61C2212yescomplemented
38#16839724—21no—
39C22⋊C8×D61—21no—
40C4×#11758189C2212yescomplemented
41C4×C8×D61—21no—
42#16839491C2214yescomplemented
43D4⋊#92418C2214yescomplemented
44#16839489C2214yescomplemented
45C2×C4×D4×C61C2211yescharacteristic
46C61×#431C2211yescharacteristic
47C61×#431C2211yescharacteristic
48C61×D4⋊C8C2214yescomplemented
49C2×#11758222—22no—
50C2×#11758222—22no—
51C2×#11758222—22no—
52C2×#11758222—22no—
53C2×#11758222—48no—
54C22×Dic122—21no—
55C22×D244—21no—
56C22×D244C2×C411yescharacteristic
57C22×C22⋊D61—21no—
58C22×C22⋊D61—21no—
59C22×C22⋊D61—21no—
60C22×C4×D61—21no—
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C2×#11758189—22no—
65C2×C8×D61—22no—
66#14519776—21no—
67#14519776—21no—
68#14519776C2×C412yes—
69#14519776C2×C412yes—
70#14519773—21no—
71#14519773—21no—
72#14519773C2×C412yes—
73#14519773C2×C412yes—
74#14519763—22no—
75#14519763—22no—
76#14519763—22no—
77#14519763—22no—
78#14519752—21no—
79#14519752—21no—
80#14519752C2×C412yes—
81#14519752C2×C412yes—
82#14519750—22no—
83#14519750—22no—
84#14519750—22no—
85#14519750—22no—
86#14519748—21no—
87#14519748—21no—
88#14519748C2×C412yes—
89#14519748C2×C412yes—
90C4×D244—21no—
91C4×D244—21no—
92C4×D244C2×C412yes—
93C4×D244C2312yes—
94C4×C22⋊D61—22no—
95C4×C22⋊D61—22no—
96C4×C22⋊D61—22no—
97C4×C22⋊D61—22no—
98C2×C4⋊Dic61C2×C411yescharacteristic
99C2×#11758196—21no—
100C2×C22⋊Dic61—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×C4×Dic61C2×C411yescharacteristic
104C2×C4×Dic61D411yescharacteristic
105C2×C4×Dic61D411yescharacteristic
106C42×D61C2×C411yescharacteristic
107C42×D61C2×C411yescharacteristic
108C42×D61D411yescharacteristic
109C42×D61D411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61D411yescharacteristic
112C42×D61C2311yescharacteristic
113C42×D61C2311yescharacteristic
114C4⋊#92418—21no—
115C4⋊#92418C2312yes—
116#14519706—22no—
117#14519706—22no—
118C22⋊#92418—21no—
119C22⋊#92418—21no—
120#14519689—22no—
121#14519689—22no—
122#14519687—22no—
123C4×#92418—21no—
124C4×#92418C2312yes—
125C8×Dic61—22no—
126C22×D4×C61C2×C411yescharacteristic
127C23×C4×C61—21no—
128C4×D4×C61—21no—
129C4×D4×C61—21no—
130C4×D4×C61C2×C412yes—
131C4×D4×C61C2312yes—
132C2×C4⋊C4×C61C2×C411yescharacteristic
133C2×C22⋊C4×C61—21no—
134C2×C42×C61C2311yescharacteristic
135C4⋊C8×C61—21no—
136C4⋊C8×C61C2312yes—
137C22⋊C8×C61—21no—
138C22⋊C8×C61—21no—
139C4×C8×C61—21no—
140C4×C8×C61C2312yes—
141C24×C61—21no—
142C23×D61—21no—
143C23×D61C22⋊C411yescharacteristic
144C2×D4×C61—21no—
145C2×D4×C61—22no—
146C2×D4×C61—22no—
147C2×D4×C61C22×C412yes—
148C22×C4×C61—21no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—44no—
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×Dic61C22⋊C411yescharacteristic
166C22×Dic61C22⋊C411yescharacteristic
167C22×Dic61C22⋊C411yescharacteristic
168#11758222—48no—
169#11758222—48no—
170#11758222—48no—
171#11758222—48no—
172C2×D244—22no—
173C2×D244—22no—
174C2×D244—22no—
175C2×D244—22no—
176C2×D244—21no—
177C2×D244—44no—
178C2×D244C22×C412yes—
179C2×C4×D61—22no—
180C2×C4×D61—22no—
181C2×C4×D61—24no—
182C2×C4×D61—22no—
183C2×C4×D61—22no—
184C2×C4×D61—42no—
185C2×C4×D61—44no—
186C2×C4×D61C22⋊C411yescharacteristic
187C2×C4×D61C22⋊C411yescharacteristic
188C2×C4×D61C22⋊C411yescharacteristic
189C2×C4×D61C22⋊C411yescharacteristic
190C2×C4×D61C22⋊C411yescharacteristic
191C2×C4×D61C22⋊C411yescharacteristic
192C2×C4×D61C22×C411yescharacteristic
193C2×C4×D61C22×C411yescharacteristic
194C2×C4×D61C2×D411yescharacteristic
195C2×C4×D61C2×D411yescharacteristic
196C2×C4×D61C2×D411yescharacteristic
197C2×C4×D61C2×D411yescharacteristic
198C2×Dic122—22no—
199C2×Dic122—22no—
200C2×Dic122—44no—
201C2×C8×C61—22no—
202C2×C8×C61—22no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61C22×C412yes—
205C22⋊C4×C61—22no—
206C22⋊C4×C61—22no—
207C42×C61C22×C411yescharacteristic
208C42×C61C2×D411yescharacteristic
209C42×C61C2×D411yescharacteristic
210C42×C61C2411yescharacteristic
211C22⋊Dic61—22no—
212C22⋊Dic61—22no—
213#11758198—22no—
214#11758198—22no—
215#11758198—22no—
216#11758198—22no—
217C4⋊Dic61—21no—
218C4⋊Dic61C22×C412yes—
219#11758196—22no—
220#11758196—22no—
221C4×Dic61C22⋊C411yescharacteristic
222C4×Dic61C22⋊C411yescharacteristic
223C4×Dic61C22⋊C411yescharacteristic
224C4×Dic61C22⋊C411yescharacteristic
225C4×Dic61C22⋊C411yescharacteristic
226C4×Dic61C22⋊C411yescharacteristic
227C4×Dic61C22×C411yescharacteristic
228C4×Dic61C22×C411yescharacteristic
229C4×Dic61C2×D411yescharacteristic
230C4×Dic61C2×D411yescharacteristic
231C4×Dic61C2×D411yescharacteristic
232C4×Dic61C2×D411yescharacteristic
233C2×#92418—22no—
234C2×#92418—22no—
235#11758189—44no—
236C8×D61—44no—
237C23×C61—22no—
238C23×C61—42no—
239C23×C61—42no—
240C23×C61—42no—
241C23×C61C2×C22⋊C411yescharacteristic
242C22×D61—22no—
243C22×D61—22no—
244C22×D61—22no—
245C22×D61—41no—
246C22×D61—42no—
247C22×D61—42no—
248C22×D61—42no—
249C22×D61C2×C22⋊C411yescharacteristic
250C22×D61C2×C22⋊C411yescharacteristic
251D4×C61—22no—
252D4×C61—22no—
253D4×C61—42no—
254C2×C4×C61—22no—
255C2×C4×C61—22no—
256C2×C4×C61—41no—
257C2×C4×C61—44no—
258C2×C4×C61—42no—
259C2×C4×C61—44no—
260C2×C4×C61C2×C22⋊C411yescharacteristic
261C2×C4×C61C2×C22⋊C411yescharacteristic
262C2×C4×C61C2×C22⋊C411yescharacteristic
263C2×C4×C61#13112yes—
264C2×C4×C61#13112yes—
265C2×C4×C61C23×C411yescharacteristic
266C2×C4×C61C22×D411yescharacteristic
267C2×C4×C61C22×D411yescharacteristic
268C22⋊D61—44no—
269C22⋊D61—44no—
270C22⋊D61—44no—
271C22⋊D61—44no—
272C22⋊D61—44no—
273C22⋊D61—44no—
274C2×Dic61—22no—
275C2×Dic61—22no—
276C2×Dic61—22no—
277C2×Dic61—22no—
278C2×Dic61—42no—
279C2×Dic61C2×C22⋊C411yescharacteristic
280C2×Dic61C2×C22⋊C411yescharacteristic
281C2×Dic61C2×C22⋊C411yescharacteristic
282C2×Dic61C2×C22⋊C411yescharacteristic
283C2×Dic61C2×C22⋊C411yescharacteristic
284C2×Dic61C2×C22⋊C411yescharacteristic
285D244—22no—
286D244—22no—
287D244—44no—
288D244—44no—
289D244—42no—
290C4×D61—22no—
291C4×D61—21no—
292C4×D61—21no—
293C4×D61—21no—
294C4×D61—21no—
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×D61AGL(1,ℤ/8)14yes—
306Dic122—44no—
307Dic122—44no—
308C8×C61—42no—
309C8×C61—42no—
310#92418—42no—
311#92418—42no—
312#17463—611nomaximal, Sylow
313C22×C61—21no—
314C22×C61—21no—
315C22×C61—42no—
316C22×C61—42no—
317C22×C61—42no—
318C22×C61—84no—
319C22×C61#40812yes—
320C22×C61C22×C22⋊C411yescharacteristic
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×D61#41812yes—
332C4×C61—21no—
333C4×C61—21no—
334C4×C61—21no—
335C4×C61—42no—
336C4×C61#40812yes—
337C4×C61C2×#13111yescharacteristic
338C4×C61C2×#13111yescharacteristic
339C4×C61C2×AGL(1,ℤ/8)12yes—
340Dic61—21no—
341Dic61—21no—
342Dic61—21no—
343Dic61—21no—
344Dic61—42no—
345Dic61#41812yes—
346Dic61#42112yes—
347C2×#532—611no—
348#2920—611no—
349C2×#431—611no—
350#1484—614no—
351#1480—614no—
352#1478—611no—
353#1478—611no—
354#1478—611no—
355#1478D6111yescharacteristic, complemented
356C2×C61—22no—
357C2×C61—82no—
358C2×C61C2×#40811yescharacteristic
359C2×C61C2×#41811yescharacteristic
360C2×C61C2×#42111yescharacteristic
361D61—22no—
362D61—41no—
363D61—82no—
364C22×#41—1221no—
365#532—612no—
366#532—612no—
367#532—612no—
368#532—612no—
369#532—1221no—
370#532—1221no—
371#532—1221no—
372#532—1221no—
373C2×C4⋊Q8—611no—
374C2×#127—611no—
375C2×#124—1221no—
376C2×#121—611no—
377C2×#121—611no—
378C2×#121—1221no—
379C2×C4×D4—611no—
380C2×C4×D4—1221no—
381C2×C4×D4C2×D6111yescharacteristic
382C22×C42—611no—
383#432—1221no—
384#432—1221no—
385#431—611no—
386#431—612no—
387#431—611no—
388#431—612no—
389#431—1221no—
390#431—1221no—
391#431C2×D6111yescharacteristic
392#431C2×D6111yescharacteristic
393#423—1221no—
394C2×C4⋊C8—612no—
395#407—1221no—
396C2×C22⋊C8—1221no—
397C4×M16—612no—
398C2×C4×C8—1221no—
399D4⋊C8—614no—
400D4⋊C8—614no—
401D4⋊C8—614no—
402D4⋊C8C2×D6114yescomplemented
403C61#1746311yescharacteristic, complemented, Sylow
404C2×#41—1222no—
405C2×#41—1222no—
406C2×#41—1222no—
407C2×#41—1222no—
408C2×#41—2448no—
409C22×Q8—1221no—
410C22×D4—611no—
411C22×D4—1221no—
412C22×D4—1221no—
413C22×D4—1221no—
414C22×D4—1221no—
415C22×D4C4×D6111yescharacteristic
416C23×C4—21no—
417C23×C4—611no—
418C23×C4—611no—
419C23×C4—611no—
420C23×C4—1221no—
421C2×M16—1222no—
422C22×C8—1222no—
423C4⋊Q8—612no—
424C4⋊Q8—612no—
425C4⋊Q8—1221no—
426C4⋊Q8—1221no—
427#127—612no—
428#127—612no—
429#127—1221no—
430#127—1221no—
431#124—1222no—
432#124—1222no—
433#124—1222no—
434#124—1222no—
435#121—612no—
436#121—612no—
437#121—612no—
438#121—612no—
439#121—1222no—
440#121—1222no—
441#121—1222no—
442#121—1222no—
443#121—1221no—
444#121—1221no—
445#121—1221no—
446#121—1221no—
447C4×D4—21no—
448C4×D4—21no—
449C4×D4—612no—
450C4×D4—612no—
451C4×D4—1222no—
452C4×D4—1222no—
453C4×D4—1222no—
454C4×D4—1222no—
455C4×D4—1221no—
456C4×D4—1221no—
457C4×D4C4×D6112yes—
458C4×D4C22×D6112yes—
459C2×C4⋊C4—611no—
460C2×C4⋊C4—1221no—
461C2×C4⋊C4C4×D6111yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—1221no—
464C2×C22⋊C4—1221no—
465C2×C22⋊C4—1221no—
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—612no—
480C4⋊C8—1222no—
481C4⋊C8—1222no—
482C4⋊C8—1221no—
483C4⋊C8C22×D6112yes—
484C22⋊C8—21no—
485C22⋊C8—21no—
486C22⋊C8—1222no—
487C22⋊C8—1222no—
488C22⋊C8—1221no—
489C22⋊C8—1221no—
490#97—1222no—
491C4×C8—21no—
492C4×C8—612no—
493C4×C8—1222no—
494C4×C8—1221no—
495C4×C8C22×D6112yes—
496C24—21no—
497C24—611no—
498C24—1221no—
499#41—2448no—
500#41—2448no—
501#41—2448no—
502#41—2448no—
503C2×Q8—1222no—
504C2×Q8—1222no—
505C2×Q8—2444no—
506C2×D4—21no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—612no—
510C2×D4—1222no—
511C2×D4—1222no—
512C2×D4—1222no—
513C2×D4—1222no—
514C2×D4—1222no—
515C2×D4—1222no—
516C2×D4—1222no—
517C2×D4—1222no—
518C2×D4—1221no—
519C2×D4—1222no—
520C2×D4—1222no—
521C2×D4—2444no—
522C2×D4—2444no—
523C2×D4—2444no—
524C2×D4—2444no—
525C2×D4C2×C4×D6112yes—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—44no—
530C22×C4—611no—
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—1224no—
546C22×C4—1222no—
547C22×C4—1222no—
548C22×C4—1221no—
549C22×C4—1222no—
550C22×C4—1222no—
551C22×C4—2444no—
552C22×C4—2442no—
553C22×C4C2×C4×D6111yescharacteristic
554C22×C4D4×D6111yescharacteristic
555C22×C4D4×D6111yescharacteristic
556M16—2444no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—1222no—
560C2×C8—1222no—
561C2×C8—2444no—
562C4⋊C4—21no—
563C4⋊C4—612no—
564C4⋊C4—1222no—
565C4⋊C4—1222no—
566C4⋊C4—1221no—
567C4⋊C4C2×C4×D6112yes—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—1222no—
571C22⋊C4—1222no—
572C22⋊C4—1222no—
573C22⋊C4—1222no—
574C22⋊C4—1222no—
575C22⋊C4—1222no—
576C42—611no—
577C42—611no—
578C42—611no—
579C42—611no—
580C42—611no—
581C42—611no—
582C42—611no—
583C42—611no—
584C42—611no—
585C42—611no—
586C42—611no—
587C42—611no—
588C42C2×C4×D6111yescharacteristic
589C42D4×D6111yescharacteristic
590C42D4×D6111yescharacteristic
591C42C23×D6111yescharacteristic
592C23—22no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—611no—
597C23—611no—
598C23—1222no—
599C23—1222no—
600C23—1222no—
601C23—2441no—
602C23—2442no—
603C23—2442no—
604C23—2442no—
605C23C22⋊C4×D6111yescharacteristic
606Q8—2444no—
607Q8—2444no—
608D4—22no—
609D4—22no—
610D4—42no—
611D4—1222no—
612D4—1222no—
613D4—2444no—
614D4—2444no—
615D4—2444no—
616D4—2444no—
617D4—2444no—
618D4—2444no—
619D4—2444no—
620D4—2444no—
621D4—2442no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—41no—
625C2×C4—44no—
626C2×C4—42no—
627C2×C4—44no—
628C2×C4—611no—
629C2×C4—611no—
630C2×C4—614no—
631C2×C4—611no—
632C2×C4—611no—
633C2×C4—611no—
634C2×C4—611no—
635C2×C4—1222no—
636C2×C4—1222no—
637C2×C4—1222no—
638C2×C4—1222no—
639C2×C4—1222no—
640C2×C4—1222no—
641C2×C4—1222no—
642C2×C4—1222no—
643C2×C4—1222no—
644C2×C4—1221no—
645C2×C4—1221no—
646C2×C4—1221no—
647C2×C4—1221no—
648C2×C4—1222no—
649C2×C4—1222no—
650C2×C4—2441no—
651C2×C4—2441no—
652C2×C4—2444no—
653C2×C4—2442no—
654C2×C4—2444no—
655C2×C4C22⋊C4×D6111yescharacteristic
656C2×C4C22⋊C4×D6111yescharacteristic
657C2×C4C22⋊C4×D6111yescharacteristic
658C2×C4#1451978312yes—
659C2×C4#1451978512yes—
660C2×C4C22×C4×D6111yescharacteristic
661C2×C4C2×D4×D6111yescharacteristic
662C2×C4C2×D4×D6111yescharacteristic
663C8—42no—
664C8—42no—
665C8—2442no—
666C8—2442no—
667C22—21no—
668C22—21no—
669C22—42no—
670C22—42no—
671C22—42no—
672C22—84no—
673C22—612no—
674C22—1221no—
675C22—1221no—
676C22—1221no—
677C22—1221no—
678C22—1221no—
679C22—4884no—
680C22—2444no—
681C22—2442no—
682C22—2442no—
683C22—2442no—
684C22#1683972712yes—
685C22C2×C22⋊C4×D6111yescharacteristic
686C4—21no—
687C4—21no—
688C4—21no—
689C4—42no—
690C4—612no—
691C4—612no—
692C4—1221no—
693C4—1221no—
694C4—1221no—
695C4—1221no—
696C4—2442no—
697C4#1683972712yes—
698C4C2×#1451978311yescharacteristic
699C4C2×#1451978511yescharacteristic
700C4AGL(1,ℤ/8)×D6112yes—
701C2—22no—
702C2—82no—
703C2—1222no—
704C2—4882no—
705C2—2441no—
706C2C2×#1683972711yescharacteristic
707C2#418×D6111yescharacteristic
708C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1478C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840309C2
cosocleC42×C61C24
hypercenter#1478D61
hypocenterC61#17463
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
2. #21454447C2semidirect
3. #431×D61C2semidirect
4. #21444234C2semidirect
5. #21444216C2semidirect
6. #21444211C2semidirect
7. #21444210C2semidirect
8. #21444209C2semidirect
9. C61×#1478C2semidirect
32. #16839814C22semidirect
34. #16839813C22semidirect
37. C4⋊C8×D61C22semidirect
40. C4×#11758189C22semidirect
42. #16839491C22semidirect
43. D4⋊#92418C22semidirect
44. #16839489C22semidirect
48. C61×D4⋊C8C22semidirect
355. #1478D61semidirect
402. D4⋊C8C2×D61semidirect
403. C61#17463semidirect

Maximal subgroups

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

subgroupindex
C2×#168403092
#214544472
#431×D612
#214442342
#214442162
#214442112
#214442102
#214442092
C61×#14782
#1746361