Finite Group Databasebeta

← #29708158

Subgroups — #29708158

Order 15616.

1520 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758199C212yesmaximal, complemented
2C4×#14519751C211yesmaximal, characteristic, complemented
3#21447144C211yesmaximal, characteristic, complemented
4#21447050C211yesmaximal, characteristic, complemented
5#21446998C212yesmaximal, complemented
6#21446952C211yesmaximal, characteristic, complemented
7#21446890C211yesmaximal, characteristic, complemented
8#21446815C212yesmaximal, complemented
9C4×#14519698C212yesmaximal, complemented
10C4×C22⋊#92418C211yesmaximal, characteristic, complemented
11C2×C61×#532C211yesmaximal, characteristic, complemented
12C22×#11758199C2212yes—
13C2×#14519751C2211yescharacteristic
14C2×C4×D244C2211yescharacteristic
15C2×C4×C22⋊D61—21no—
16C4×#11758199—28no—
17C2×#14519710C2212yes—
18C2×#14519698C2212yes—
19C2×#14519698C2212yes—
20C2×#14519698C2212yes—
21C2×#14519697C2212yes—
22C2×C22⋊#92418C2212yes—
23C2×C4×#92418C2212yes—
24#16839664C2211yescharacteristic
25#16839660C2211yescharacteristic
26#16839653—21no—
27#16839641—21no—
28#16839622C2211yescharacteristic
29C4×C4⋊Dic61C2211yescharacteristic
30C4×#11758198—21no—
31#16839524C2212yes—
32#16839524C2212yes—
33#16839517C2211yescharacteristic
34#16839517C2211yescharacteristic
35C22×#41×C61—21no—
36C61×#532—28no—
37C2×C4⋊Q8×C61C2211yescharacteristic
38C2×#127×C61C2211yescharacteristic
39C2×#124×C61—21no—
40C2×#121×C61—21no—
41C2×#121×C61C2212yes—
42C2×C4×D4×C61—21no—
43C2×C4×D4×C61C2212yes—
44C22×C42×C61C2211yescharacteristic
45C22×D244C2311yescharacteristic
46C22×C22⋊D61—21no—
47C22×C4×D61—21no—
48C2×#11758199—24no—
49C2×#11758199—24no—
50C2×#11758199—24no—
51C22×#92418C2312yes—
52C22×#92418C2312yes—
53#14519751—22no—
54#14519751—22no—
55C4×D244—24no—
56C4×C22⋊D61—44no—
57C2×C4⋊Dic61C2311yescharacteristic
58C2×C4⋊Dic61C2311yescharacteristic
59C2×C4⋊Dic61C2311yescharacteristic
60C2×#11758196—21no—
61C2×C22⋊Dic61—21no—
62C2×#11758198—21no—
63C2×#11758198—21no—
64C2×#11758198—21no—
65C2×#11758198—21no—
66C2×C4×Dic61—21no—
67#14519710—24no—
68#14519698—24no—
69#14519698—24no—
70#14519698—24no—
71#14519697—24no—
72C22⋊#92418—24no—
73C4×#92418—24no—
74#14519684—21no—
75#14519684—21no—
76#14519684—21no—
77C2×#41×C61—28no—
78C2×#41×C61—44no—
79C2×#41×C61—44no—
80C22×Q8×C61—21no—
81C22×D4×C61—22no—
82C22×D4×C61—21no—
83C22×D4×C61—21no—
84C22×D4×C61C2312yes—
85C23×C4×C61—22no—
86C23×C4×C61D411yescharacteristic
87C23×C4×C61D411yescharacteristic
88C23×C4×C61C2311yescharacteristic
89C4⋊Q8×C61—24no—
90#127×C61—24no—
91#124×C61—28no—
92#121×C61—28no—
93#121×C61—24no—
94#121×C61—24no—
95C4×D4×C61—28no—
96C4×D4×C61—24no—
97C4×D4×C61D418yescomplemented
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61C2312yes—
100C2×C22⋊C4×C61—22no—
101C2×C22⋊C4×C61—22no—
102C2×C42×C61—24no—
103C2×C42×C61D411yescharacteristic
104C2×C42×C61D411yescharacteristic
105C2×C42×C61C2311yescharacteristic
106C2×C42×C61C2311yescharacteristic
107C24×C61—22no—
108C24×C61C2×D411yescharacteristic
109C23×D61—21no—
110#41×C61—432no—
111C2×Q8×C61—24no—
112C2×Q8×C61—42no—
113C2×Q8×C61—42no—
114C2×D4×C61—24no—
115C2×D4×C61—28no—
116C2×D4×C61—24no—
117C2×D4×C61—22no—
118C2×D4×C61—22no—
119C2×D4×C61—22no—
120C2×D4×C61—22no—
121C2×D4×C61—22no—
122C2×D4×C61—42no—
123C2×D4×C61—42no—
124C2×D4×C61—44no—
125C2×D4×C61—44no—
126C2×D4×C61—42no—
127C2×D4×C61—42no—
128C2×D4×C61C2×D414yes—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—28no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—41no—
140C22×C4×C61—44no—
141C22×C4×C61—44no—
142C22×C4×C61D814yescomplemented
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2411yescharacteristic
149C2×C22⋊D61—24no—
150C2×C22⋊D61—42no—
151C2×C22⋊D61—42no—
152C22×Dic61—21no—
153C22×Dic61—21no—
154C22×Dic61—21no—
155C2×D244—22no—
156C2×D244—22no—
157C2×D244—21no—
158C2×D244#4112yescomplemented
159C2×C4×D61—42no—
160C2×C4×D61—42no—
161C2×C4×D61—42no—
162C4⋊C4×C61—24no—
163C4⋊C4×C61—22no—
164C4⋊C4×C61C2×D414yes—
165C22⋊C4×C61—28no—
166C22⋊C4×C61—28no—
167C42×C61—22no—
168C42×C61—22no—
169C42×C61—22no—
170C42×C61C2×D414yes—
171C22⋊Dic61—42no—
172#11758199—216no—
173#11758198—24no—
174#11758198—42no—
175#11758198—42no—
176#11758198—42no—
177C4⋊Dic61—21no—
178C4⋊Dic61—22no—
179C4⋊Dic61—22no—
180C4⋊Dic61#4112yescomplemented
181#11758196—42no—
182C4×Dic61—42no—
183C2×#92418—22no—
184C2×#92418—22no—
185C2×#92418—22no—
186C2×#92418—22no—
187C2×#92418—22no—
188C2×#92418#4114yescomplemented
189C23×C61—21no—
190C23×C61—21no—
191C23×C61—21no—
192C23×C61—21no—
193C23×C61—21no—
194C23×C61—21no—
195C23×C61—24no—
196C23×C61—42no—
197C23×C61—42no—
198C23×C61—42no—
199C23×C61—42no—
200C23×C61—42no—
201C23×C61—42no—
202C23×C61C2×D812yes—
203C23×C61C22×D411yescharacteristic
204C22×D61—22no—
205C22×D61—41no—
206C22×D61—41no—
207C22×D61—41no—
208C22×D61—41no—
209C22×D61—41no—
210C22×D61—41no—
211Q8×C61—48no—
212D4×C61—24no—
213D4×C61—24no—
214D4×C61—48no—
215D4×C61—48no—
216D4×C61—416no—
217D4×C61—42no—
218D4×C61—42no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—28no—
226C2×C4×C61—21no—
227C2×C4×C61—24no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—44no—
231C2×C4×C61—42no—
232C2×C4×C61—42no—
233C2×C4×C61—42no—
234C2×C4×C61—42no—
235C2×C4×C61—416no—
236C2×C4×C61#12012yes—
237C2×C4×C61#12012yes—
238C2×C4×C61C2×D812yes—
239C2×C4×C61C2×D812yes—
240C2×C4×C61#13512yes—
241C2×C4×C61AGL(1,ℤ/8)12yes—
242C2×C4×C61C22×D412yes—
243C2×C4×C61C2×#4111yescharacteristic
244C2×C4×C61C2×#4112yes—
245C2×C4×C61C2×#4111yescharacteristic
246C22⋊D61—48no—
247C2×Dic61—22no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256D244—24no—
257D244—42no—
258C4×D61—84no—
259#92418—24no—
260#92418—42no—
261#23567—611nomaximal, Sylow
262C22×C61—22no—
263C22×C61—22no—
264C22×C61—22no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61—41no—
269C22×C61—44no—
270C22×C61—44no—
271C22×C61—44no—
272C22×C61—82no—
273C22×C61—82no—
274C22×C61—82no—
275C22×C61—82no—
276C22×C61C2×#12011yescharacteristic
277C22×C61#52511yescharacteristic
278C22×C61#53211yescharacteristic
279C22×C61C22×D811yescharacteristic
280C22×C61C2×#13511yescharacteristic
281C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
282C22×C61#57511yescharacteristic
283C2×D61—42no—
284C2×D61—42no—
285C2×D61—42no—
286C2×D61—81no—
287C2×D61—81no—
288C2×D61—81no—
289C2×D61—81no—
290C4×C61—22no—
291C4×C61—22no—
292C4×C61—22no—
293C4×C61—41no—
294C4×C61—44no—
295C4×C61#44714yes—
296C4×C61#52512yes—
297C4×C61#53212yes—
298Dic61—42no—
299Dic61—81no—
300Dic61—81no—
301C2×#532D6111yescharacteristic, complemented
302C2×C4×D8—612no—
303C4×#121—611no—
304#2057—611no—
305#2041—611no—
306#2033—612no—
307#2023—611no—
308#2011—611no—
309#1999—612no—
310C4×#102—612no—
311C4×C22⋊C8—611no—
312C2×C61—42no—
313C2×C61—84no—
314C2×C61#238811yescharacteristic
315C2×C61C2×#44711yescharacteristic
316C2×C61#300211yescharacteristic
317C2×C61#310011yescharacteristic
318C2×C61#310611yescharacteristic
319C2×C61#316911yescharacteristic
320C2×C61#317111yescharacteristic
321D61—82no—
322C22×#41—21no—
323C22×D8—612no—
324#532—28no—
325C2×C4⋊Q8C2×D6111yescharacteristic
326C2×#127C2×D6111yescharacteristic
327C2×#124—21no—
328C2×#121—21no—
329C2×#121—611no—
330C2×#121C2×D6112yes—
331C2×C4×D4—21no—
332C2×C4×D4—611no—
333C2×C4×D4—1221no—
334C2×C4×D4C2×D6112yes—
335C22×C42C2×D6111yescharacteristic
336C4×D8—1228no—
337C2×#107—612no—
338C2×#102—612no—
339C2×#102—612no—
340C2×#102—612no—
341C2×#102—612no—
342C2×C22⋊C8—612no—
343C2×C4×C8—612no—
344#390—611no—
345#389—611no—
346#388—1221no—
347#386—1221no—
348#380—611no—
349C4×C4⋊C4—611no—
350C4×C22⋊C4—1221no—
351#340—612no—
352#340—612no—
353#336—611no—
354#336—611no—
355C61#2356711yescharacteristic, complemented, Sylow
356C2×#41—28no—
357C2×#41—44no—
358C2×#41—44no—
359C22×Q8—21no—
360C22×D4—22no—
361C22×D4—21no—
362C22×D4—21no—
363C22×D4—611no—
364C22×D4—1221no—
365C22×D4C22×D6112yes—
366C23×C4—22no—
367C23×C4—1221no—
368C23×C4C22⋊D6111yescharacteristic
369C23×C4C22⋊D6111yescharacteristic
370C23×C4C22×D6111yescharacteristic
371C2×D8—1224no—
372C2×D8—1224no—
373C2×D8—1224no—
374C22×C8—612no—
375C22×C8—612no—
376C4⋊Q8—24no—
377#127—24no—
378#124—28no—
379#121—28no—
380#121—24no—
381#121—24no—
382#121—1222no—
383#121—1222no—
384C4×D4—28no—
385C4×D4—24no—
386C4×D4—1224no—
387C4×D4—2444no—
388C4×D4C22⋊D6118yescomplemented
389C2×C4⋊C4—21no—
390C2×C4⋊C4—611no—
391C2×C4⋊C4—611no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4—1221no—
394C2×C4⋊C4C22×D6112yes—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—1221no—
398C2×C22⋊C4—1221no—
399C2×C22⋊C4—1221no—
400C2×C22⋊C4—1221no—
401C2×C22⋊C4—1221no—
402C2×C42—24no—
403C2×C42—1221no—
404C2×C42C22⋊D6111yescharacteristic
405C2×C42C22⋊D6111yescharacteristic
406C2×C42C22×D6111yescharacteristic
407C2×C42C22×D6111yescharacteristic
408#107—1224no—
409#102—1224no—
410#102—1224no—
411#102—1224no—
412#102—1224no—
413C22⋊C8—1224no—
414C4×C8—1224no—
415#95—1221no—
416#95—1221no—
417#95—1221no—
418C24—22no—
419C24—1221no—
420C24C2×C22⋊D6111yescharacteristic
421#41—432no—
422C2×Q8—24no—
423C2×Q8—42no—
424C2×Q8—42no—
425C2×D4—24no—
426C2×D4—28no—
427C2×D4—24no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—42no—
434C2×D4—42no—
435C2×D4—44no—
436C2×D4—44no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—612no—
440C2×D4—1224no—
441C2×D4—1222no—
442C2×D4—1222no—
443C2×D4—1221no—
444C2×D4—2442no—
445C2×D4—2442no—
446C2×D4C2×C22⋊D6114yes—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—28no—
456C22×C4—22no—
457C22×C4—41no—
458C22×C4—44no—
459C22×C4—44no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—2442no—
464C22×C4—2442no—
465C22×C4—2442no—
466C22×C4#1175819914yescomplemented
467C22×C4C2×C22⋊D6111yescharacteristic
468C22×C4C2×C22⋊D6111yescharacteristic
469C22×C4C2×C22⋊D6111yescharacteristic
470C22×C4C2×C22⋊D6111yescharacteristic
471C22×C4C2×C22⋊D6111yescharacteristic
472C22×C4C23×D6111yescharacteristic
473D8—12216no—
474C2×C8—614no—
475C2×C8—1222no—
476C2×C8—1222no—
477C2×C8—1222no—
478C2×C8—1222no—
479C2×C8—1222no—
480C4⋊C4—24no—
481C4⋊C4—22no—
482C4⋊C4—612no—
483C4⋊C4—1221no—
484C4⋊C4—1222no—
485C4⋊C4—1222no—
486C4⋊C4—2442no—
487C4⋊C4C2×C22⋊D6114yes—
488C22⋊C4—28no—
489C22⋊C4—28no—
490C22⋊C4—1224no—
491C22⋊C4—2442no—
492C22⋊C4—2442no—
493C22⋊C4—2442no—
494C22⋊C4—2442no—
495C42—22no—
496C42—22no—
497C42—22no—
498C42—2442no—
499C42C2×C22⋊D6114yes—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—24no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—1222no—
514C23—2441no—
515C23—2441no—
516C23—2441no—
517C23—2441no—
518C23—2441no—
519C23—2441no—
520C23C2×#1175819912yes—
521C23C22×C22⋊D6111yescharacteristic
522Q8—48no—
523D4—24no—
524D4—24no—
525D4—48no—
526D4—48no—
527D4—416no—
528D4—42no—
529D4—42no—
530D4—1224no—
531D4—2448no—
532D4—2442no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—28no—
540C2×C4—21no—
541C2×C4—24no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—44no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—416no—
550C2×C4—1222no—
551C2×C4—4884no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4—2441no—
558C2×C4—2441no—
559C2×C4—2441no—
560C2×C4#1451974612yes—
561C2×C4#1451974612yes—
562C2×C4C2×#1175819912yes—
563C2×C4C2×#1175819912yes—
564C2×C4#1451979712yes—
565C2×C4#1451980312yes—
566C2×C4C22×C22⋊D6112yes—
567C2×C4#41×D6111yescharacteristic
568C2×C4#41×D6112yes—
569C2×C4#41×D6111yescharacteristic
570C8—1224no—
571C8—2442no—
572C22—22no—
573C22—22no—
574C22—22no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—44no—
580C22—44no—
581C22—44no—
582C22—82no—
583C22—82no—
584C22—82no—
585C22—82no—
586C22—4881no—
587C22—4881no—
588C22—4881no—
589C22—4881no—
590C22—2442no—
591C22—2442no—
592C22—2442no—
593C22C2×#1451974611yescharacteristic
594C22#1684026911yescharacteristic
595C22#1684030811yescharacteristic
596C22C22×#1175819911yescharacteristic
597C22C2×#1451979711yescharacteristic
598C22C2×#1451980311yescharacteristic
599C22#1684056011yescharacteristic
600C4—22no—
601C4—22no—
602C4—22no—
603C4—41no—
604C4—44no—
605C4—4881no—
606C4—4881no—
607C4—2442no—
608C4#1683989614yes—
609C4#1684026912yes—
610C4#1684030812yes—
611C2—42no—
612C2—84no—
613C2—4882no—
614C2#2144903211yescharacteristic
615C2C2×#1683989611yescharacteristic
616C2#2145503711yescharacteristic
617C2#2145581511yescharacteristic
618C2#2145587311yescharacteristic
619C2#2145639411yescharacteristic
620C2#2145640811yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#532C2
socleC23×C61C22×D4
hypercenterC2×#532D61
hypocenterC61#23567
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. C2×C4×#11758199C2semidirect
2. C4×#14519751C2semidirect
3. #21447144C2semidirect
4. #21447050C2semidirect
5. #21446998C2semidirect
6. #21446952C2semidirect
7. #21446890C2semidirect
8. #21446815C2semidirect
9. C4×#14519698C2semidirect
10. C4×C22⋊#92418C2semidirect
11. C2×C61×#532C2semidirect
97. C4×D4×C61D4semidirect
142. C22×C4×C61D8semidirect
158. C2×D244#41semidirect
180. C4⋊Dic61#41semidirect
188. C2×#92418#41semidirect
301. C2×#532D61semidirect
355. C61#23567semidirect
388. C4×D4C22⋊D61semidirect
466. C22×C4#11758199semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117581992
C4×#145197512
#214471442
#214470502
#214469982
#214469522
#214468902
#214468152
C4×#145196982
C4×C22⋊#924182
C2×C61×#5322
#2356761