Finite Group Databasebeta

← #29709203

Subgroups — #29709203

Order 15616.

956 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758190C211yesmaximal, characteristic, complemented
2C2×C4×#11758199C211yesmaximal, characteristic
3C4×#14519764C211yesmaximal, characteristic, complemented
4#21448280C211yesmaximal, characteristic, complemented
5#21447305C211yesmaximal, characteristic, complemented
6#21447236C211yesmaximal, characteristic, complemented
7#21447215C211yesmaximal, characteristic, complemented
8#21447191C211yesmaximal, characteristic, complemented
9#21447138C211yesmaximal, characteristic, complemented
10#21447128C211yesmaximal, characteristic
11#21447058C211yesmaximal, characteristic, complemented
12#21446898C211yesmaximal, characteristic
13C4×#14519706C211yesmaximal, characteristic, complemented
14C4×#14519700C211yesmaximal, characteristic, complemented
15C4×#102×C61C211yesmaximal, characteristic, complemented
16C22×#11758190C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519764C2211yescharacteristic
19C2×C4×Dic122C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×#14519734—21no—
22C4×#11758190—24no—
23C4×#11758199—24no—
24C2×#14519710C2211yescharacteristic
25C2×#14519709C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519702C2211yescharacteristic
29C2×#14519700C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519699C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×C4×#92418C2211yescharacteristic
35#16839667C2211yescharacteristic
36#16839665C2211yescharacteristic
37#16839663C2211yescharacteristic
38#16839663C2211yescharacteristic
39#16839658C2211yescharacteristic
40#16839658C2211yescharacteristic
41#16839656—21no—
42#16839656—21no—
43#16839651—21no—
44#16839651—21no—
45#16839627C2211yescharacteristic
46C4×#11758198—21no—
47C4×C22⋊Dic61—21no—
48C4×C22⋊Dic61—21no—
49C42×Dic61C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C2×C4×C8×C61C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×Dic122C2311yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C4×D61—21no—
64C2×#11758190—22no—
65C2×#11758190—22no—
66C2×#11758190—22no—
67C2×#11758199—22no—
68C2×#11758199—22no—
69C2×#11758199—22no—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72#14519764—22no—
73#14519764—22no—
74C4×Dic122—22no—
75C4×Dic122—22no—
76C4×D244—22no—
77C4×D244D414yes—
78#14519734—44no—
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×C4×Dic61—21no—
94C2×C4×Dic61D411yescharacteristic
95C2×C4×Dic61D411yescharacteristic
96C2×C4×Dic61D411yescharacteristic
97C2×C4×Dic61D411yescharacteristic
98C2×C4×Dic61C2311yescharacteristic
99C2×C4×Dic61C2311yescharacteristic
100#14519710—22no—
101#14519709—22no—
102#14519706—22no—
103#14519706—22no—
104#14519702—22no—
105#14519700—22no—
106#14519700—22no—
107#14519699—22no—
108#14519698—22no—
109#14519697—22no—
110C4×#92418—22no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117C22×D4×C61C2311yescharacteristic
118C23×C4×C61—21no—
119C22×C8×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C4×D4×C61—22no—
122C4×D4×C61—22no—
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C22⋊C4×C61—21no—
127C2×C42×C61—21no—
128C2×C42×C61C2311yescharacteristic
129#102×C61—22no—
130#102×C61—22no—
131C4×C8×C61—22no—
132#95×C61—21no—
133C24×C61—21no—
134C23×D61—21no—
135C2×D4×C61—21no—
136C2×D4×C61—21no—
137C2×D4×C61—21no—
138C2×D4×C61—21no—
139C2×D4×C61—21no—
140C2×D4×C61#4112yes—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—42no—
145C22×C4×C61—42no—
146C22×C4×C61—42no—
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2411yescharacteristic
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61C2×D411yescharacteristic
154C22×Dic61C2×D411yescharacteristic
155C22×Dic61C2×D411yescharacteristic
156C22×Dic61C2×D411yescharacteristic
157C2×D244—21no—
158C2×D244—21no—
159C2×D244—21no—
160C2×D244—21no—
161C2×D244—21no—
162C2×D244C2×D412yes—
163C2×C4×D61—24no—
164C2×C4×D61—42no—
165C2×C4×D61—42no—
166C2×Dic122—21no—
167C2×Dic122—21no—
168C2×Dic122—21no—
169C2×Dic122—21no—
170C2×Dic122—21no—
171C2×Dic122#4112yes—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61#4112yes—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C22⋊C4×C61—42no—
185C42×C61—42no—
186C42×C61C2×D412yes—
187C42×C61#4112yes—
188C22⋊Dic61—24no—
189C22⋊Dic61—24no—
190C22⋊Dic61—42no—
191C22⋊Dic61—42no—
192#11758199—28no—
193#11758198—24no—
194#11758198—42no—
195#11758198—42no—
196#11758198—42no—
197#11758198—42no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61C2×D412yes—
202#11758196—42no—
203#11758196—42no—
204#11758196—42no—
205C4×Dic61—22no—
206C4×Dic61—22no—
207C4×Dic61—21no—
208C4×Dic61—21no—
209C4×Dic61—21no—
210C4×Dic61—21no—
211C4×Dic61—22no—
212C4×Dic61—41no—
213C4×Dic61—42no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418—21no—
219C2×#92418#4112yes—
220#11758190—28no—
221C23×C61—22no—
222C23×C61—41no—
223C23×C61—41no—
224C23×C61—41no—
225C23×C61—41no—
226C23×C61—41no—
227C23×C61—41no—
228C23×C61C22×D411yescharacteristic
229C22×D61—22no—
230C22×D61—41no—
231C22×D61—41no—
232C22×D61—41no—
233C22×D61—41no—
234C22×D61—41no—
235C22×D61—41no—
236D4×C61—22no—
237D4×C61—22no—
238D4×C61—41no—
239D4×C61—41no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—84no—
252C2×C4×C61#12112yes—
253C2×C4×C61#12112yes—
254C2×C4×C61#13512yes—
255C2×C4×C61AGL(1,ℤ/8)12yes—
256C2×C4×C61C22×D411yescharacteristic
257C2×C4×C61C2×#4111yescharacteristic
258C2×C4×C61C2×#4111yescharacteristic
259C2×C4×C61C2×#4111yescharacteristic
260C2×C4×C61C2×#4111yescharacteristic
261C2×C4×C61C2×#4111yescharacteristic
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—22no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—22no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61#13512yes—
283D244—22no—
284D244—22no—
285D244—41no—
286D244—41no—
287C4×D61—48no—
288Dic122—22no—
289Dic122—22no—
290Dic122—41no—
291Dic122—41no—
292C8×C61—22no—
293C8×C61—41no—
294#92418—22no—
295#92418—41no—
296#23680—611nomaximal, Sylow
297C22×C61—42no—
298C22×C61—42no—
299C22×C61—42no—
300C22×C61—81no—
301C22×C61—81no—
302C22×C61—81no—
303C22×C61—81no—
304C22×C61C2×#12111yescharacteristic
305C22×C61#52511yescharacteristic
306C22×C61#53211yescharacteristic
307C22×C61C2×#13511yescharacteristic
308C22×C61C2×#13511yescharacteristic
309C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
310C22×C61#57511yescharacteristic
311C2×D61—42no—
312C2×D61—42no—
313C2×D61—42no—
314C2×D61—81no—
315C2×D61—81no—
316C2×D61—81no—
317C2×D61—81no—
318C4×C61—22no—
319C4×C61—81no—
320C4×C61—81no—
321C4×C61—81no—
322C4×C61#46314yes—
323C4×C61#52511yescharacteristic
324C4×C61#52511yescharacteristic
325C4×C61#52911yescharacteristic
326C4×C61#52911yescharacteristic
327Dic61—22no—
328Dic61—41no—
329Dic61—41no—
330Dic61—42no—
331Dic61—41no—
332Dic61—42no—
333Dic61—81no—
334C2×C4×SD16—611no—
335C2×C4×D8—611no—
336C4×#124—611no—
337#2293—611no—
338#2085—611no—
339#2073—611no—
340#2068—611no—
341#2065—611no—
342#2055—611no—
343#2054—611no—
344#2042—611no—
345#2012—611no—
346C4×C4⋊C8—611no—
347C4×#103—611no—
348C4×#102D6111yescharacteristic, complemented
349C2×C61—82no—
350C2×C61#239211yescharacteristic
351C2×C61C2×#46311yescharacteristic
352C2×C61#303511yescharacteristic
353C2×C61#310211yescharacteristic
354C2×C61#310611yescharacteristic
355C2×C61#316811yescharacteristic
356C2×C61#317111yescharacteristic
357D61—82no—
358C22×SD16—611no—
359C22×D8—611no—
360C2×#124—611no—
361C2×C4×Q8—611no—
362C2×C4×D4—611no—
363C2×C4×D4C2×D6111yescharacteristic
364C2×#117—1221no—
365C4×SD16—1224no—
366C4×D8—1224no—
367C2×#107—611no—
368C2×#106—611no—
369C2×C4⋊C8—611no—
370C2×C4⋊C8—611no—
371C2×#103—611no—
372C2×#103—611no—
373C2×#103—611no—
374C2×#102—611no—
375C2×#102—611no—
376C2×#102—611no—
377C2×#102C2×D6111yescharacteristic
378C2×#102C2×D6111yescharacteristic
379C2×C4×C8—611no—
380C2×C4×C8C2×D6111yescharacteristic
381#391—611no—
382#390—611no—
383#390—611no—
384#390—611no—
385#389—611no—
386#389—611no—
387#388—1221no—
388#388—1221no—
389#388—1221no—
390#388—1221no—
391#382—611no—
392C4×C4⋊C4C2×D6111yescharacteristic
393C4×C22⋊C4—1221no—
394C4×C22⋊C4—1221no—
395C4×C22⋊C4—1221no—
396C43—611no—
397#340—611no—
398#340—611no—
399#340C2×D6111yescharacteristic
400#340C2×D6111yescharacteristic
401#336—611no—
402#336—611no—
403C61#2368011yescharacteristic, complemented, Sylow
404C22×Q8—611no—
405C22×D4—611no—
406C22×D4C22×D6111yescharacteristic
407C23×C4—21no—
408C23×C4—1221no—
409C2×SD16—1222no—
410C2×SD16—1222no—
411C2×SD16—1222no—
412C2×D8—1222no—
413C2×D8—1222no—
414C2×D8—1222no—
415C22×C8—611no—
416C22×C8—611no—
417C22×C8C22×D6111yescharacteristic
418C22×C8C22×D6111yescharacteristic
419#124—1222no—
420#124—1222no—
421C4×Q8—1222no—
422C4×Q8—1222no—
423C4×D4—22no—
424C4×D4—22no—
425C4×D4—614no—
426C4×D4—1222no—
427#117—2444no—
428C2×C4⋊C4—611no—
429C2×C4⋊C4—611no—
430C2×C4⋊C4—1221no—
431C2×C4⋊C4—1221no—
432C2×C4⋊C4—1221no—
433C2×C4⋊C4C22×D6111yescharacteristic
434C2×C4⋊C4C22×D6111yescharacteristic
435C2×C4⋊C4C22×D6111yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—1221no—
438C2×C22⋊C4—1221no—
439C2×C22⋊C4—1221no—
440C2×C22⋊C4—1221no—
441C2×C22⋊C4—1221no—
442C2×C22⋊C4—1221no—
443C2×C22⋊C4—1221no—
444C2×C22⋊C4—1221no—
445C2×C22⋊C4—1221no—
446C2×C42—21no—
447C2×C42—611no—
448C2×C42—611no—
449C2×C42—611no—
450C2×C42—611no—
451C2×C42—611no—
452C2×C42—611no—
453C2×C42—1221no—
454C2×C42C22×D6111yescharacteristic
455#107—1222no—
456#106—1222no—
457C4⋊C8—1222no—
458C4⋊C8—1222no—
459#103—1222no—
460#103—1222no—
461#103—1222no—
462#102—22no—
463#102—22no—
464#102—1222no—
465#102—1222no—
466#102—1222no—
467C4×C8—22no—
468C4×C8—1222no—
469#95—21no—
470#95—1221no—
471#95—1221no—
472#95—1221no—
473#95—1221no—
474#95—1221no—
475#95—1221no—
476C24—21no—
477C24—1221no—
478C2×Q8—612no—
479C2×Q8—1221no—
480C2×Q8—1221no—
481C2×Q8—1221no—
482C2×Q8—1221no—
483C2×Q8—1221no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—612no—
490C2×D4—1221no—
491C2×D4—1221no—
492C2×D4—1221no—
493C2×D4—1221no—
494C2×D4—1221no—
495C2×D4#1175822212yes—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—611no—
503C22×C4—611no—
504C22×C4—611no—
505C22×C4—611no—
506C22×C4—1221no—
507C22×C4—1221no—
508C22×C4—1224no—
509C22×C4—1221no—
510C22×C4—2442no—
511C22×C4—2442no—
512C22×C4D4×D6111yescharacteristic
513C22×C4D4×D6111yescharacteristic
514C22×C4C23×D6111yescharacteristic
515SD16—1228no—
516D8—1228no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—612no—
523C2×C8—1221no—
524C2×C8—1221no—
525C2×C8—1221no—
526C2×C8—1221no—
527C2×C8—1221no—
528C2×C8#1175822212yes—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—612no—
536C4⋊C4—1221no—
537C4⋊C4—1221no—
538C4⋊C4—1221no—
539C4⋊C4—2442no—
540C4⋊C4—2442no—
541C4⋊C4—2442no—
542C22⋊C4—42no—
543C22⋊C4—1224no—
544C22⋊C4—1224no—
545C22⋊C4—1224no—
546C22⋊C4—2442no—
547C22⋊C4—2442no—
548C22⋊C4—2442no—
549C22⋊C4—2442no—
550C22⋊C4—2442no—
551C22⋊C4—2442no—
552C42—42no—
553C42—1222no—
554C42—1221no—
555C42—1221no—
556C42—1221no—
557C42—1221no—
558C42—1222no—
559C42—1222no—
560C42—2441no—
561C42—2442no—
562C42#1175822212yes—
563C42D4×D6112yes—
564C23—22no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—1222no—
572C23—2441no—
573C23—2441no—
574C23—2441no—
575C23—2441no—
576C23—2441no—
577C23—2441no—
578C23C2×D4×D6111yescharacteristic
579Q8—1222no—
580Q8—1222no—
581Q8—2441no—
582Q8—2441no—
583D4—22no—
584D4—22no—
585D4—41no—
586D4—41no—
587D4—1222no—
588D4—1222no—
589D4—2441no—
590D4—2441no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—84no—
603C2×C4—612no—
604C2×C4—1221no—
605C2×C4—1221no—
606C2×C4—1222no—
607C2×C4—1221no—
608C2×C4—1221no—
609C2×C4—1222no—
610C2×C4—1221no—
611C2×C4—1221no—
612C2×C4—1221no—
613C2×C4—1221no—
614C2×C4—1221no—
615C2×C4—1221no—
616C2×C4—1221no—
617C2×C4—2441no—
618C2×C4—2441no—
619C2×C4—2441no—
620C2×C4—2441no—
621C2×C4—2441no—
622C2×C4—2441no—
623C2×C4—2441no—
624C2×C4—2448no—
625C2×C4#1451975012yes—
626C2×C4#1451975012yes—
627C2×C4#1451979812yes—
628C2×C4#1451980112yes—
629C2×C4C2×D4×D6111yescharacteristic
630C2×C4#41×D6111yescharacteristic
631C2×C4#41×D6111yescharacteristic
632C2×C4C2×#1175822211yescharacteristic
633C2×C4C2×#1175822211yescharacteristic
634C2×C4C2×#1175822211yescharacteristic
635C8—22no—
636C8—41no—
637C8—1222no—
638C8—2441no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—4881no—
647C22—4881no—
648C22—4881no—
649C22—4881no—
650C22—2442no—
651C22—2442no—
652C22—2442no—
653C22C2×#1451975011yescharacteristic
654C22#1684027111yescharacteristic
655C22#1684030911yescharacteristic
656C22#135×D6111yescharacteristic
657C22C2×#1451979811yescharacteristic
658C22C2×#1451980111yescharacteristic
659C22#1684055911yescharacteristic
660C4—22no—
661C4—81no—
662C4—81no—
663C4—81no—
664C4—1222no—
665C4—4881no—
666C4—2441no—
667C4—2441no—
668C4—2442no—
669C4—2442no—
670C4—2441no—
671C4#1683997614yes—
672C4#1684027111yescharacteristic
673C4#1684027111yescharacteristic
674C4#1684029011yescharacteristic
675C4#1684029611yescharacteristic
676C2—82no—
677C2—4882no—
678C2#2144906311yescharacteristic
679C2C2×#1683997611yescharacteristic
680C2#2145527211yescharacteristic
681C2#2145584111yescharacteristic
682C2#2145587511yescharacteristic
683C2#2145638511yescharacteristic
684C2#2145641211yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC4×#102×C61C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
hypercenterC4×#102D61
hypocenterC61#23680
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
1. C2×C4×#11758190C2semidirect
3. C4×#14519764C2semidirect
4. #21448280C2semidirect
5. #21447305C2semidirect
6. #21447236C2semidirect
7. #21447215C2semidirect
8. #21447191C2semidirect
9. #21447138C2semidirect
11. #21447058C2semidirect
13. C4×#14519706C2semidirect
14. C4×#14519700C2semidirect
15. C4×#102×C61C2semidirect
348. C4×#102D61semidirect
403. C61#23680semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117581902
C2×C4×#117581992
C4×#145197642
#214482802
#214473052
#214472362
#214472152
#214471912
#214471382
#214471282
#214470582
#214468982
C4×#145197062
C4×#145197002
C4×#102×C612
#2368061