Finite Group Databasebeta

← #29653590

Subgroups — #29653590

Order 15616.

1192 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455052C211yesmaximal, characteristic, complemented
2C2×#16839900C211yesmaximal, characteristic, complemented
3#21449464C211yesmaximal, characteristic, complemented
4#21444788C214yesmaximal, complemented
5#21444782C214yesmaximal, complemented
6#21444335C211yesmaximal, characteristic, complemented
7#21444310C211yesmaximal, characteristic, complemented
8#21444183C211yesmaximal, characteristic, complemented
9C61×#3536C211yesmaximal, characteristic
10C23×Dic122C2211yescharacteristic
11C2×#14519807—21no—
12C22×#11758200—21no—
13C2×#14519775—21no—
14#16839917—21no—
15#16839917C2212yescomplemented
16#16839900—22no—
17#16839900—21no—
18#16839900C2214yes—
19#16839900C2212yescomplemented
20#16839770—21no—
21C2×#14519700—21no—
22#16839726C2211yescharacteristic
23C2×C22⋊#92418C2211yescharacteristic
24#16839682C2214yescomplemented
25#16839667—21no—
26#16839634—22no—
27C4×C22⋊Dic61C2211yescharacteristic
28#16839499C2212yescomplemented
29#16839496C2214yes—
30#16839496C2212yescomplemented
31#16839488C2214yescomplemented
32C61×#562—22no—
33C61×#554—21no—
34C61×#548—21no—
35C61×#547—21no—
36C61×#546—21no—
37C61×#546—22no—
38C61×#543—21no—
39C61×#542—21no—
40C61×#539C2212yes—
41C61×#538—21no—
42C61×#537—21no—
43C61×#537C2212yes—
44C61×#525C2211yescharacteristic
45C2×C22⋊Q8×C61C2211yescharacteristic
46C2×#121×C61C2211yescharacteristic
47C22×Dic122—21no—
48C22×Dic122—21no—
49C22×Dic122—21no—
50C22×Dic122—21no—
51C22×Dic122—21no—
52C22×Dic122—44no—
53C22×Dic122C2312yes—
54C23×Dic61—21no—
55#14519807—44no—
56C2×#11758202—22no—
57C2×#11758200—24no—
58C2×#11758200—22no—
59C2×#11758200—44no—
60C2×#11758194—21no—
61C22×#92418—21no—
62#14519775—44no—
63C2×#11758196—24no—
64C2×C22⋊Dic61—21no—
65C2×C4×Dic61—21no—
66#14519700—24no—
67#14519700—22no—
68#14519700—22no—
69C22⋊#92418—21no—
70C22⋊#92418—21no—
71C22⋊#92418C2312yes—
72C22⋊#92418C2312yes—
73#14519684—24no—
74#14519684C2312yes—
75C2×#41×C61—21no—
76C2×#41×C61—22no—
77C2×#41×C61D411yescharacteristic
78C22×Q8×C61D411yescharacteristic
79C22×D4×C61—21no—
80C22×D4×C61D411yescharacteristic
81C23×C4×C61C2311yescharacteristic
82C4⋊Q8×C61—21no—
83#126×C61—22no—
84#125×C61—22no—
85#124×C61—22no—
86#124×C61—21no—
87#124×C61—22no—
88#123×C61—22no—
89#123×C61—22no—
90#123×C61—22no—
91#123×C61—22no—
92#123×C61—21no—
93C22⋊Q8×C61—21no—
94C22⋊Q8×C61—22no—
95C22⋊Q8×C61—22no—
96C22⋊Q8×C61—22no—
97C22⋊Q8×C61—22no—
98C22⋊Q8×C61—21no—
99C22⋊Q8×C61—21no—
100C22⋊Q8×C61—21no—
101C22⋊Q8×C61—21no—
102C22⋊Q8×C61—22no—
103C22⋊Q8×C61—22no—
104C22⋊Q8×C61D411yescharacteristic
105C22⋊Q8×C61C2311yescharacteristic
106#121×C61—21no—
107#121×C61—22no—
108#121×C61—22no—
109#121×C61—22no—
110#121×C61—22no—
111#121×C61—21no—
112#121×C61—22no—
113#121×C61—21no—
114#121×C61D411yescharacteristic
115#121×C61D412yes—
116#121×C61C2311yescharacteristic
117#121×C61C2312yes—
118#120×C61—22no—
119#120×C61—21no—
120C4×Q8×C61—21no—
121C4×D4×C61—22no—
122C4×D4×C61—21no—
123C4×D4×C61—22no—
124C4×D4×C61—21no—
125C4×D4×C61—21no—
126#117×C61D411yescharacteristic
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61D411yescharacteristic
129C2×C4⋊C4×C61D411yescharacteristic
130C2×C4⋊C4×C61C2312yes—
131C2×C22⋊C4×C61—22no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61D412yes—
134C24×C61—21no—
135C24×C61C2×D411yescharacteristic
136#41×C61—42no—
137#41×C61—84no—
138#41×C61—82no—
139C2×Q8×C61—22no—
140C2×Q8×C61—21no—
141C2×Q8×C61—21no—
142C2×Q8×C61—42no—
143C2×Q8×C61C2×D411yescharacteristic
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—22no—
147C2×D4×C61—22no—
148C2×D4×C61—22no—
149C2×D4×C61—21no—
150C2×D4×C61—22no—
151C2×D4×C61—21no—
152C2×D4×C61—42no—
153C2×D4×C61—82no—
154C2×D4×C61C2×D411yescharacteristic
155C2×D4×C61C2×D412yes—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—42no—
162C22×C4×C61C2×D412yes—
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D412yes—
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2411yescharacteristic
170C22×Dic61—22no—
171C22×Dic61—22no—
172C22×Dic61—44no—
173C22×Dic61—41no—
174C22×Dic61—41no—
175C2×Dic122—24no—
176C2×Dic122—24no—
177C2×Dic122—22no—
178C2×Dic122—22no—
179C2×Dic122—24no—
180C2×Dic122—44no—
181C2×Dic122—44no—
182C2×Dic122—44no—
183C2×Dic122—42no—
184C2×Dic122—42no—
185C2×Dic122—42no—
186C2×Dic122—41no—
187C2×Dic122—41no—
188C4⋊C4×C61—22no—
189C4⋊C4×C61—22no—
190C4⋊C4×C61—22no—
191C4⋊C4×C61—22no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—22no—
197C4⋊C4×C61—22no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61C2×D412yes—
200C4⋊C4×C61C2×D411yescharacteristic
201C4⋊C4×C61C2×D411yescharacteristic
202C22⋊C4×C61—22no—
203C22⋊C4×C61—22no—
204C22⋊C4×C61—22no—
205C22⋊C4×C61—22no—
206C22⋊C4×C61—22no—
207C22⋊C4×C61—21no—
208C22⋊C4×C61—22no—
209C22⋊C4×C61—22no—
210C22⋊C4×C61—21no—
211C22⋊C4×C61—21no—
212C22⋊C4×C61—22no—
213C22⋊C4×C61—21no—
214C22⋊C4×C61—22no—
215C22⋊C4×C61—21no—
216C42×C61—22no—
217C42×C61—21no—
218C22⋊Dic61—24no—
219#11758202—44no—
220#11758200—48no—
221#11758200—44no—
222#11758196—48no—
223C4×Dic61—42no—
224#11758194—42no—
225C2×#92418—22no—
226C2×#92418—22no—
227C2×#92418—42no—
228C23×C61—22no—
229C23×C61—22no—
230C23×C61—22no—
231C23×C61—21no—
232C23×C61—41no—
233C23×C61—42no—
234C23×C61—81no—
235C23×C61—81no—
236C23×C61#12011yescharacteristic
237C23×C61#12011yescharacteristic
238C23×C61C22×D411yescharacteristic
239Q8×C61—41no—
240Q8×C61—42no—
241Q8×C61—81no—
242Q8×C61—82no—
243D4×C61—42no—
244D4×C61—41no—
245D4×C61—44no—
246D4×C61—42no—
247D4×C61—42no—
248D4×C61—42no—
249D4×C61—82no—
250D4×C61—81no—
251D4×C61—82no—
252D4×C61—82no—
253C2×C4×C61—22no—
254C2×C4×C61—22no—
255C2×C4×C61—22no—
256C2×C4×C61—21no—
257C2×C4×C61—22no—
258C2×C4×C61—21no—
259C2×C4×C61—22no—
260C2×C4×C61—21no—
261C2×C4×C61—22no—
262C2×C4×C61—24no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—42no—
267C2×C4×C61—42no—
268C2×C4×C61—81no—
269C2×C4×C61—82no—
270C2×C4×C61—82no—
271C2×C4×C61—82no—
272C2×C4×C61#12011yescharacteristic
273C2×C4×C61#12011yescharacteristic
274C2×C4×C61C22×D411yescharacteristic
275C2×C4×C61C22×D411yescharacteristic
276C2×Dic61—24no—
277C2×Dic61—24no—
278C2×Dic61—42no—
279C2×Dic61—44no—
280C2×Dic61—44no—
281C2×Dic61—42no—
282C2×Dic61—42no—
283C2×Dic61—42no—
284Dic122—24no—
285Dic122—24no—
286Dic122—42no—
287Dic122—42no—
288Dic122—44no—
289Dic122—44no—
290#92418—42no—
291#92418—42no—
292#18261—611nomaximal, Sylow
293C22×C61—21no—
294C22×C61—21no—
295C22×C61—21no—
296C22×C61—21no—
297C22×C61—21no—
298C22×C61—21no—
299C22×C61—21no—
300C22×C61—44no—
301C22×C61—41no—
302C22×C61—42no—
303C22×C61—41no—
304C22×C61—42no—
305C22×C61—41no—
306C22×C61—42no—
307C22×C61—162no—
308C22×C61#45612yes—
309C22×C61C2×#12011yescharacteristic
310C22×C61#57712yes—
311C4×C61—21no—
312C4×C61—21no—
313C4×C61—21no—
314C4×C61—42no—
315C4×C61—42no—
316C4×C61—41no—
317C4×C61—41no—
318C4×C61—41no—
319C4×C61—42no—
320C4×C61B(4,𝔽2)12yes—
321Dic61—44no—
322Dic61—44no—
323#3536D6111yescharacteristic
324#3004—611no—
325C2×#448—611no—
326#2434—611no—
327#1604—614no—
328#1603—614no—
329#1507—611no—
330#1501—611no—
331#1472—611no—
332C2×C61—22no—
333C2×C61—22no—
334C2×C61—41no—
335C2×C61—81no—
336C2×C61—82no—
337C2×C61#300911yescharacteristic
338C2×C61C2×#45611yescharacteristic
339C2×C61C2×B(4,𝔽2)11yescharacteristic
340C23×Q8—611no—
341C2×#137—1221no—
342C22×SD16—1221no—
343#562—22no—
344#554—21no—
345#548—21no—
346#547—21no—
347#546—21no—
348#546—22no—
349#543—21no—
350#542—21no—
351#539C2×D6112yes—
352#538—21no—
353#537—21no—
354#537C2×D6112yes—
355C2×C4⋊Q8—1221no—
356#525C2×D6111yescharacteristic
357C2×C22⋊Q8C2×D6111yescharacteristic
358C2×#121C2×D6111yescharacteristic
359#451—612no—
360#451—1221no—
361#448—614no—
362#448—612no—
363#448—1222no—
364#448—1221no—
365#419—1221no—
366C2×#103—1221no—
367#407—611no—
368C2×C22⋊C8—611no—
369#395—614no—
370#391—1221no—
371#385—1222no—
372C4×C22⋊C4—611no—
373#328—612no—
374#327—614no—
375#327—612no—
376#324—614no—
377C61#1826111yescharacteristic, complemented, Sylow
378C2×#41—21no—
379C2×#41—22no—
380C2×#41C22⋊D6111yescharacteristic
381C22×Q8—612no—
382C22×Q8—1221no—
383C22×Q8—1221no—
384C22×Q8—1221no—
385C22×Q8—1221no—
386C22×Q8—1221no—
387C22×Q8—2444no—
388C22×Q8C22⋊D6111yescharacteristic
389C22×D4—21no—
390C22×D4C22⋊D6111yescharacteristic
391C23×C4—1221no—
392C23×C4C22×D6111yescharacteristic
393#137—2444no—
394C2×Q16—1222no—
395C2×SD16—1224no—
396C2×SD16—1222no—
397C2×SD16—2444no—
398C2×M16—1221no—
399C22×C8—1221no—
400C4⋊Q8—21no—
401C4⋊Q8—2444no—
402#126—22no—
403#125—22no—
404#124—22no—
405#124—21no—
406#124—22no—
407#123—22no—
408#123—22no—
409#123—22no—
410#123—21no—
411#123—22no—
412C22⋊Q8—21no—
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—22no—
417C22⋊Q8—21no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8—21no—
421C22⋊Q8—22no—
422C22⋊Q8—22no—
423C22⋊Q8C22⋊D6111yescharacteristic
424C22⋊Q8C22×D6111yescharacteristic
425#121—21no—
426#121—22no—
427#121—22no—
428#121—22no—
429#121—22no—
430#121—21no—
431#121—21no—
432#121—22no—
433#121C22⋊D6112yes—
434#121C22⋊D6111yescharacteristic
435#121C22×D6112yes—
436#121C22×D6111yescharacteristic
437#120—22no—
438#120—21no—
439C4×Q8—21no—
440C4×D4—22no—
441C4×D4—21no—
442C4×D4—21no—
443C4×D4—21no—
444C4×D4—22no—
445#117C22⋊D6111yescharacteristic
446C2×C4⋊C4—21no—
447C2×C4⋊C4—1224no—
448C2×C4⋊C4C22⋊D6111yescharacteristic
449C2×C4⋊C4C22⋊D6111yescharacteristic
450C2×C4⋊C4C22×D6112yes—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—1221no—
454C2×C22⋊C4C22⋊D6112yes—
455C2×C42—1221no—
456#103—1224no—
457#103—1222no—
458#103—1222no—
459C22⋊C8—612no—
460C22⋊C8—612no—
461C22⋊C8—1221no—
462C22⋊C8—1221no—
463#95—612no—
464#95—1224no—
465C24—21no—
466C24C2×C22⋊D6111yescharacteristic
467#41—42no—
468#41—84no—
469#41—82no—
470C2×Q8—22no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—42no—
474C2×Q8—1224no—
475C2×Q8—1224no—
476C2×Q8—1224no—
477C2×Q8—1222no—
478C2×Q8—1222no—
479C2×Q8—2442no—
480C2×Q8—2442no—
481C2×Q8—2442no—
482C2×Q8—2444no—
483C2×Q8—2444no—
484C2×Q8—2444no—
485C2×Q8—2441no—
486C2×Q8—2441no—
487C2×Q8C2×C22⋊D6111yescharacteristic
488C2×D4—21no—
489C2×D4—22no—
490C2×D4—21no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—21no—
494C2×D4—22no—
495C2×D4—21no—
496C2×D4—42no—
497C2×D4—82no—
498C2×D4C2×C22⋊D6111yescharacteristic
499C2×D4C2×C22⋊D6112yes—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—42no—
506C22×C4—1222no—
507C22×C4—1222no—
508C22×C4—2444no—
509C22×C4—2441no—
510C22×C4—2441no—
511C22×C4C2×C22⋊D6112yes—
512C22×C4C2×C22⋊D6111yescharacteristic
513C22×C4C2×C22⋊D6111yescharacteristic
514C22×C4C2×C22⋊D6111yescharacteristic
515C22×C4C2×C22⋊D6112yes—
516C22×C4C2×C22⋊D6111yescharacteristic
517C22×C4C2×C22⋊D6111yescharacteristic
518C22×C4C23×D6111yescharacteristic
519Q16—2444no—
520SD16—2448no—
521SD16—2444no—
522M16—2442no—
523C2×C8—1222no—
524C2×C8—1222no—
525C2×C8—2442no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—2448no—
538C4⋊C4C2×C22⋊D6112yes—
539C4⋊C4C2×C22⋊D6111yescharacteristic
540C4⋊C4C2×C22⋊D6111yescharacteristic
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—21no—
547C22⋊C4—21no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—21no—
551C22⋊C4—22no—
552C22⋊C4—21no—
553C22⋊C4—22no—
554C22⋊C4—21no—
555C22⋊C4—1224no—
556C42—22no—
557C42—21no—
558C42—2442no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—21no—
563C23—41no—
564C23—42no—
565C23—81no—
566C23—81no—
567C23#1451974611yescharacteristic
568C23#1451974611yescharacteristic
569C23C22×C22⋊D6111yescharacteristic
570Q8—41no—
571Q8—42no—
572Q8—81no—
573Q8—82no—
574Q8—1224no—
575Q8—1224no—
576Q8—2442no—
577Q8—2442no—
578Q8—2444no—
579Q8—2444no—
580D4—42no—
581D4—41no—
582D4—42no—
583D4—44no—
584D4—42no—
585D4—42no—
586D4—82no—
587D4—81no—
588D4—82no—
589D4—82no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—24no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—81no—
606C2×C4—82no—
607C2×C4—82no—
608C2×C4—82no—
609C2×C4—1224no—
610C2×C4—1224no—
611C2×C4—2442no—
612C2×C4—2442no—
613C2×C4—2444no—
614C2×C4—2444no—
615C2×C4—2442no—
616C2×C4—2442no—
617C2×C4#1451974611yescharacteristic
618C2×C4#1451974611yescharacteristic
619C2×C4C22×C22⋊D6111yescharacteristic
620C2×C4C22×C22⋊D6111yescharacteristic
621C8—2442no—
622C8—2442no—
623C22—21no—
624C22—21no—
625C22—21no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—21no—
630C22—44no—
631C22—41no—
632C22—42no—
633C22—41no—
634C22—42no—
635C22—41no—
636C22—42no—
637C22—162no—
638C22#1683994512yes—
639C22C2×#1451974611yescharacteristic
640C22#1684057312yes—
641C4—21no—
642C4—21no—
643C4—21no—
644C4—41no—
645C4—41no—
646C4—42no—
647C4—42no—
648C4—42no—
649C4—41no—
650C4—2444no—
651C4—2444no—
652C4#1683994912yes—
653C2—22no—
654C2—22no—
655C2—41no—
656C2—82no—
657C2—81no—
658C2#2145509611yescharacteristic
659C2C2×#1683994511yescharacteristic
660C2C2×#1683994911yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#3536C2
socleC22×C61C2×#120
hypercenter#3536D61
hypocenterC61#18261
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3536

Complements

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

NH ≅ G/Ntype
1. #21455052C2semidirect
2. C2×#16839900C2semidirect
3. #21449464C2semidirect
4. #21444788C2semidirect
5. #21444782C2semidirect
6. #21444335C2semidirect
7. #21444310C2semidirect
8. #21444183C2semidirect
15. #16839917C22semidirect
19. #16839900C22semidirect
24. #16839682C22semidirect
28. #16839499C22semidirect
30. #16839496C22semidirect
31. #16839488C22semidirect
377. C61#18261semidirect

Maximal subgroups

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

subgroupindex
#214550522
C2×#168399002
#214494642
#214447882
#214447822
#214443352
#214443102
#214441832
C61×#35362
#1826161