Finite Group Databasebeta

← #29653638

Subgroups — #29653638

Order 15616.

1124 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455739C211yesmaximal, characteristic, complemented
2C2×#16840078C211yesmaximal, characteristic, complemented
3#21450291C211yesmaximal, characteristic, complemented
4#21444867C214yesmaximal, complemented
5#21444839C214yesmaximal, complemented
6#21444335C211yesmaximal, characteristic, complemented
7#21444310C211yesmaximal, characteristic, complemented
8#21444179C211yesmaximal, characteristic, complemented
9C61×#3537C211yesmaximal, characteristic
10C2×#14519758—22no—
11C22×C4⋊Dic61C2211yescharacteristic, complemented
12#16840095C2212yescomplemented
13#16840090—21no—
14#16840078—22no—
15#16840078C2214yescomplemented
16#16840078C2212yescomplemented
17#16840073—21no—
18#16839805—21no—
19C2×#14519708—21no—
20#16839763—21no—
21C2×#14519698—21no—
22#16839726C2211yescharacteristic, complemented
23C2×C22⋊#92418C2211yescharacteristic, complemented
24#16839698C2214yescomplemented
25#16839665—21no—
26#16839631—21no—
27C4×C22⋊Dic61C2211yescharacteristic, complemented
28#16839499C2212yescomplemented
29#16839496C2214yescomplemented
30#16839496C2212yescomplemented
31#16839486C2214yescomplemented
32C61×#560—22no—
33C61×#553—21no—
34C61×#553—21no—
35D42×C61—22no—
36D42×C61—21no—
37D42×C61—21no—
38C61×#540—21no—
39C61×#538—21no—
40C61×#538C2212yes—
41C61×#535—21no—
42C61×#534—21no—
43C61×#534C2212yes—
44C61×#525C2211yescharacteristic
45C2×#121×C61C2211yescharacteristic
46C2×#121×C61C2211yescharacteristic
47C23×Dic61—21no—
48C2×#11758194—21no—
49C22×#92418—21no—
50#14519758—48no—
51C2×C4⋊Dic61—21no—
52C2×C4⋊Dic61—21no—
53C2×C4⋊Dic61—21no—
54C2×C4⋊Dic61—21no—
55C2×C4⋊Dic61—21no—
56C2×C4⋊Dic61C2312yes—
57C2×#11758196—24no—
58C2×C22⋊Dic61—21no—
59C2×C22⋊Dic61—24no—
60C2×C4×Dic61—21no—
61#14519710—22no—
62#14519708—24no—
63#14519708—22no—
64#14519701—22no—
65#14519698—24no—
66#14519698—22no—
67C22⋊#92418—21no—
68C22⋊#92418—21no—
69C22⋊#92418C2312yes—
70C22⋊#92418C2312yes—
71#14519684C2312yes—
72C2×#41×C61D411yescharacteristic
73C22×D4×C61—22no—
74C22×D4×C61—21no—
75C22×D4×C61—22no—
76C22×D4×C61—21no—
77C22×D4×C61D412yes—
78C22×D4×C61D411yescharacteristic
79C22×D4×C61D411yescharacteristic
80C23×C4×C61C2311yescharacteristic
81#127×C61—22no—
82#127×C61—21no—
83#126×C61—22no—
84#126×C61—22no—
85#125×C61—21no—
86#124×C61—22no—
87#123×C61—22no—
88#123×C61—21no—
89#123×C61—22no—
90#123×C61—22no—
91#123×C61—22no—
92C22⋊Q8×C61D411yescharacteristic
93C22⋊Q8×C61C2311yescharacteristic
94#121×C61—22no—
95#121×C61—21no—
96#121×C61—21no—
97#121×C61—22no—
98#121×C61—22no—
99#121×C61—22no—
100#121×C61—22no—
101#121×C61—21no—
102#121×C61—22no—
103#121×C61—21no—
104#121×C61—21no—
105#121×C61—21no—
106#121×C61—21no—
107#121×C61—21no—
108#121×C61D411yescharacteristic
109#121×C61D412yes—
110#121×C61C2311yescharacteristic
111#121×C61C2312yes—
112#120×C61—22no—
113#120×C61—22no—
114#120×C61—22no—
115#120×C61—22no—
116#120×C61—21no—
117#120×C61—22no—
118#120×C61—22no—
119C4×D4×C61—22no—
120C4×D4×C61—21no—
121C4×D4×C61—21no—
122C4×D4×C61—22no—
123C4×D4×C61—21no—
124C4×D4×C61—21no—
125#117×C61—21no—
126#117×C61D411yescharacteristic
127C2×C4⋊C4×C61D411yescharacteristic
128C2×C4⋊C4×C61D411yescharacteristic
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61C2312yes—
131C24×C61—22no—
132C24×C61—21no—
133C24×C61C2×D411yescharacteristic
134C24×C61C2×D412yes—
135#41×C61—42no—
136C2×Q8×C61C2×D411yescharacteristic
137C2×D4×C61—22no—
138C2×D4×C61—21no—
139C2×D4×C61—22no—
140C2×D4×C61—21no—
141C2×D4×C61—22no—
142C2×D4×C61—22no—
143C2×D4×C61—22no—
144C2×D4×C61—22no—
145C2×D4×C61—22no—
146C2×D4×C61—21no—
147C2×D4×C61—22no—
148C2×D4×C61—22no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—42no—
153C2×D4×C61—42no—
154C2×D4×C61—44no—
155C2×D4×C61—82no—
156C2×D4×C61—82no—
157C2×D4×C61—84no—
158C2×D4×C61—84no—
159C2×D4×C61C2×D411yescharacteristic
160C2×D4×C61C2×D412yes—
161C22×C4×C61—22no—
162C22×C4×C61—22no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—42no—
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D412yes—
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2411yescharacteristic
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—44no—
176C22×Dic61—41no—
177C22×Dic61—41no—
178C4⋊C4×C61—22no—
179C4⋊C4×C61—22no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61C2×D412yes—
186C4⋊C4×C61C2×D411yescharacteristic
187C4⋊C4×C61C2×D411yescharacteristic
188C22⋊C4×C61—22no—
189C22⋊C4×C61—22no—
190C22⋊C4×C61—22no—
191C22⋊C4×C61—22no—
192C22⋊C4×C61—22no—
193C22⋊C4×C61—21no—
194C22⋊C4×C61—21no—
195C22⋊C4×C61—21no—
196C22⋊C4×C61—22no—
197C22⋊C4×C61—21no—
198C22⋊C4×C61—22no—
199C22⋊C4×C61—22no—
200C22⋊C4×C61—22no—
201C22⋊C4×C61—21no—
202C42×C61—22no—
203C42×C61—21no—
204C22⋊Dic61—24no—
205C22⋊Dic61—48no—
206C4⋊Dic61—22no—
207C4⋊Dic61—22no—
208C4⋊Dic61—41no—
209C4⋊Dic61—41no—
210#11758196—48no—
211C4×Dic61—42no—
212#11758194—42no—
213C2×#92418—22no—
214C2×#92418—22no—
215C2×#92418—42no—
216C23×C61—22no—
217C23×C61—22no—
218C23×C61—22no—
219C23×C61—22no—
220C23×C61—21no—
221C23×C61—24no—
222C23×C61—41no—
223C23×C61—42no—
224C23×C61—42no—
225C23×C61—42no—
226C23×C61—81no—
227C23×C61—81no—
228C23×C61—82no—
229C23×C61—82no—
230C23×C61—82no—
231C23×C61#12011yescharacteristic
232C23×C61#12011yescharacteristic
233C23×C61C22×D411yescharacteristic
234Q8×C61—41no—
235D4×C61—42no—
236D4×C61—41no—
237D4×C61—44no—
238D4×C61—42no—
239D4×C61—44no—
240D4×C61—42no—
241D4×C61—42no—
242D4×C61—42no—
243D4×C61—81no—
244D4×C61—82no—
245D4×C61—82no—
246D4×C61—81no—
247D4×C61—82no—
248D4×C61—82no—
249D4×C61—82no—
250D4×C61—82no—
251D4×C61—82no—
252C2×C4×C61—22no—
253C2×C4×C61—22no—
254C2×C4×C61—22no—
255C2×C4×C61—21no—
256C2×C4×C61—22no—
257C2×C4×C61—22no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61—42no—
264C2×C4×C61—42no—
265C2×C4×C61—81no—
266C2×C4×C61—82no—
267C2×C4×C61—82no—
268C2×C4×C61#12011yescharacteristic
269C2×C4×C61#12011yescharacteristic
270C2×C4×C61C22×D411yescharacteristic
271C2×C4×C61C22×D411yescharacteristic
272C2×Dic61—24no—
273C2×Dic61—42no—
274C2×Dic61—42no—
275C2×Dic61—44no—
276C2×Dic61—42no—
277C2×Dic61—82no—
278C2×Dic61—82no—
279#92418—42no—
280#92418—42no—
281#18265—611nomaximal, Sylow
282C22×C61—21no—
283C22×C61—21no—
284C22×C61—21no—
285C22×C61—21no—
286C22×C61—21no—
287C22×C61—21no—
288C22×C61—21no—
289C22×C61—44no—
290C22×C61—42no—
291C22×C61—42no—
292C22×C61—41no—
293C22×C61—42no—
294C22×C61—42no—
295C22×C61—41no—
296C22×C61—41no—
297C22×C61—42no—
298C22×C61—42no—
299C22×C61—84no—
300C22×C61—162no—
301C22×C61—164no—
302C22×C61#45312yes—
303C22×C61C2×#12011yescharacteristic
304C22×C61#57712yes—
305C4×C61—21no—
306C4×C61—21no—
307C4×C61—21no—
308C4×C61—42no—
309C4×C61—41no—
310C4×C61—42no—
311C4×C61—41no—
312C4×C61—41no—
313C4×C61#45812yes—
314Dic61—44no—
315Dic61—82no—
316#3537D6111yescharacteristic
317#3092—611no—
318C2×#481—611no—
319#2501—611no—
320#1618—614no—
321#1613—614no—
322#1507—611no—
323#1501—611no—
324#1471—611no—
325C2×C61—22no—
326C2×C61—22no—
327C2×C61—41no—
328C2×C61—82no—
329C2×C61—82no—
330C2×C61—81no—
331C2×C61#300911yescharacteristic
332C2×C61C2×#45311yescharacteristic
333C2×C61C2×#45811yescharacteristic
334#560—22no—
335#553—21no—
336#553—21no—
337D42—22no—
338D42—21no—
339D42—21no—
340#540—21no—
341#538—21no—
342#538C2×D6112yes—
343#535—21no—
344#534—21no—
345#534C2×D6112yes—
346#525C2×D6111yescharacteristic
347C2×#123—1222no—
348C2×#121C2×D6111yescharacteristic
349C2×#121C2×D6111yescharacteristic
350C22×C4⋊C4—611no—
351#484—612no—
352#483—1221no—
353#481—614no—
354#481—612no—
355#481—1222no—
356#480—1221no—
357#428—1221no—
358C2×#106—1221no—
359#417—1221no—
360C2×#102—1221no—
361#407—611no—
362C2×C22⋊C8—611no—
363#399—614no—
364#390—1221no—
365#384—1221no—
366C4×C22⋊C4—611no—
367#328—612no—
368#327—612no—
369#327—614no—
370#323—614no—
371C61#1826511yescharacteristic, complemented, Sylow
372C2×#41C22⋊D6111yescharacteristic
373C22×D4—22no—
374C22×D4—21no—
375C22×D4—21no—
376C22×D4—22no—
377C22×D4C22⋊D6112yes—
378C22×D4C22⋊D6111yescharacteristic
379C22×D4C22⋊D6111yescharacteristic
380C23×C4—1221no—
381C23×C4C22×D6111yescharacteristic
382C2×M16—1221no—
383C22×C8—1221no—
384#127—22no—
385#127—21no—
386#126—22no—
387#126—22no—
388#125—21no—
389#124—22no—
390#123—22no—
391#123—21no—
392#123—22no—
393#123—22no—
394#123—22no—
395#123—2448no—
396C22⋊Q8C22⋊D6111yescharacteristic
397C22⋊Q8C22×D6111yescharacteristic
398#121—22no—
399#121—21no—
400#121—21no—
401#121—22no—
402#121—22no—
403#121—22no—
404#121—22no—
405#121—21no—
406#121—21no—
407#121—21no—
408#121—21no—
409#121—21no—
410#121—21no—
411#121—22no—
412#121C22⋊D6112yes—
413#121C22⋊D6111yescharacteristic
414#121C22×D6112yes—
415#121C22×D6111yescharacteristic
416#120—22no—
417#120—22no—
418#120—22no—
419#120—21no—
420#120—22no—
421#120—22no—
422#120—22no—
423C4×D4—22no—
424C4×D4—21no—
425C4×D4—21no—
426C4×D4—21no—
427C4×D4—21no—
428C4×D4—22no—
429#117—21no—
430#117C22⋊D6111yescharacteristic
431C2×C4⋊C4—612no—
432C2×C4⋊C4—1221no—
433C2×C4⋊C4—1221no—
434C2×C4⋊C4—1221no—
435C2×C4⋊C4—1221no—
436C2×C4⋊C4—1221no—
437C2×C4⋊C4—1224no—
438C2×C4⋊C4C22⋊D6111yescharacteristic
439C2×C4⋊C4C22⋊D6111yescharacteristic
440C2×C22⋊C4—21no—
441C2×C22⋊C4—1221no—
442C2×C22⋊C4—1224no—
443C2×C22⋊C4C22×D6112yes—
444C2×C42—1221no—
445#107—1222no—
446#106—1224no—
447#106—1222no—
448#103—1222no—
449#102—1224no—
450#102—1222no—
451C22⋊C8—612no—
452C22⋊C8—612no—
453C22⋊C8—1221no—
454C22⋊C8—1221no—
455#95—612no—
456C24—22no—
457C24—21no—
458C24C2×C22⋊D6111yescharacteristic
459C24C2×C22⋊D6112yes—
460#41—42no—
461C2×Q8C2×C22⋊D6111yescharacteristic
462C2×D4—21no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—21no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—21no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—44no—
480C2×D4—82no—
481C2×D4—82no—
482C2×D4—84no—
483C2×D4—84no—
484C2×D4C2×C22⋊D6111yescharacteristic
485C2×D4C2×C22⋊D6112yes—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—42no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—2444no—
494C22×C4—2441no—
495C22×C4—2441no—
496C22×C4C2×C22⋊D6111yescharacteristic
497C22×C4C2×C22⋊D6111yescharacteristic
498C22×C4C2×C22⋊D6111yescharacteristic
499C22×C4C2×C22⋊D6112yes—
500C22×C4C2×C22⋊D6111yescharacteristic
501C22×C4C2×C22⋊D6111yescharacteristic
502C22×C4C23×D6111yescharacteristic
503M16—2442no—
504C2×C8—1222no—
505C2×C8—1222no—
506C2×C8—2442no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—1222no—
515C4⋊C4—1222no—
516C4⋊C4—2448no—
517C4⋊C4—2441no—
518C4⋊C4—2441no—
519C4⋊C4C2×C22⋊D6112yes—
520C4⋊C4C2×C22⋊D6111yescharacteristic
521C4⋊C4C2×C22⋊D6111yescharacteristic
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—21no—
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—21no—
534C22⋊C4—22no—
535C22⋊C4—21no—
536C22⋊C4—1224no—
537C22⋊C4—2448no—
538C42—22no—
539C42—21no—
540C42—2442no—
541C23—22no—
542C23—22no—
543C23—22no—
544C23—22no—
545C23—21no—
546C23—24no—
547C23—41no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—81no—
552C23—81no—
553C23—82no—
554C23—82no—
555C23—82no—
556C23#1451974611yescharacteristic
557C23#1451974611yescharacteristic
558C23C22×C22⋊D6111yescharacteristic
559Q8—41no—
560D4—42no—
561D4—41no—
562D4—44no—
563D4—42no—
564D4—44no—
565D4—42no—
566D4—42no—
567D4—42no—
568D4—81no—
569D4—82no—
570D4—82no—
571D4—81no—
572D4—82no—
573D4—82no—
574D4—82no—
575D4—82no—
576D4—82no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—81no—
591C2×C4—82no—
592C2×C4—82no—
593C2×C4—1224no—
594C2×C4—4882no—
595C2×C4—4882no—
596C2×C4—2444no—
597C2×C4—2442no—
598C2×C4—2442no—
599C2×C4—2442no—
600C2×C4#1451974611yescharacteristic
601C2×C4#1451974611yescharacteristic
602C2×C4C22×C22⋊D6111yescharacteristic
603C2×C4C22×C22⋊D6111yescharacteristic
604C8—2442no—
605C8—2442no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—44no—
614C22—42no—
615C22—42no—
616C22—41no—
617C22—41no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—41no—
623C22—84no—
624C22—162no—
625C22—164no—
626C22#1683993012yes—
627C22C2×#1451974611yescharacteristic
628C22#1684057312yes—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—42no—
633C4—41no—
634C4—41no—
635C4—42no—
636C4—41no—
637C4—4882no—
638C4—2444no—
639C4#1683995212yes—
640C2—22no—
641C2—22no—
642C2—41no—
643C2—82no—
644C2—82no—
645C2—81no—
646C2#2145509611yescharacteristic
647C2C2×#1683993011yescharacteristic
648C2C2×#1683995211yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#3537C2
socleC22×C61C2×#120
hypercenter#3537D61
hypocenterC61#18265
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3537

Complements

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

NH ≅ G/Ntype
1. #21455739C2semidirect
2. C2×#16840078C2semidirect
3. #21450291C2semidirect
4. #21444867C2semidirect
5. #21444839C2semidirect
6. #21444335C2semidirect
7. #21444310C2semidirect
8. #21444179C2semidirect
11. C22×C4⋊Dic61C22semidirect
12. #16840095C22semidirect
15. #16840078C22semidirect
16. #16840078C22semidirect
22. #16839726C22semidirect
23. C2×C22⋊#92418C22semidirect
24. #16839698C22semidirect
27. C4×C22⋊Dic61C22semidirect
28. #16839499C22semidirect
29. #16839496C22semidirect
30. #16839496C22semidirect
31. #16839486C22semidirect
371. C61#18265semidirect

Maximal subgroups

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

subgroupindex
#214557392
C2×#168400782
#214502912
#214448672
#214448392
#214443352
#214443102
#214441792
C61×#35372
#1826561