Finite Group Databasebeta

← #29709553

Subgroups — #29709553

Order 15616.

876 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×Dic61C211yesmaximal, characteristic, complemented
2C2×#16839822C211yesmaximal, characteristic, complemented
3#21448515C211yesmaximal, characteristic
4#21448504C211yesmaximal, characteristic, complemented
5#21447317C211yesmaximal, characteristic, complemented
6#21447254C211yesmaximal, characteristic, complemented
7#21447200C211yesmaximal, characteristic, complemented
8#21447193C211yesmaximal, characteristic, complemented
9#21447013C211yesmaximal, characteristic, complemented
10#21447006C211yesmaximal, characteristic
11#21446819C211yesmaximal, characteristic
12#21445707C211yesmaximal, characteristic, complemented
13#21445651C211yesmaximal, characteristic, complemented
14#21445646C211yesmaximal, characteristic, complemented
15C61×#2055C211yesmaximal, characteristic, complemented
16C2×#14519753C2211yescharacteristic
17C2×#14519748C2211yescharacteristic
18C2×Q8×Dic61C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic
20C2×#14519734C2211yescharacteristic
21SD16×Dic61—24no—
22#16839822—24no—
23C2×#14519709C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26C2×C4⋊#92418C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519687C2211yescharacteristic
34C2×C8×Dic61C2211yescharacteristic
35#16839662—21no—
36#16839660C2211yescharacteristic
37#16839660C2211yescharacteristic
38#16839659—21no—
39#16839654—21no—
40#16839651—21no—
41#16839650—21no—
42#16839644—21no—
43#16839639—21no—
44#16839634—21no—
45#16839619C2211yescharacteristic
46#16839619C2211yescharacteristic
47C4⋊C4×Dic61C2211yescharacteristic
48C4⋊C4×Dic61C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54C22×SD16×C61C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×#103×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C61×#391C2211yescharacteristic
59C61×#390C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×C22⋊D61—21no—
62C23×Dic61—21no—
63C22×C4×D61C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66#14519753—22no—
67#14519753—22no—
68#14519748—22no—
69#14519748—22no—
70Q8×Dic61—22no—
71Q8×Dic61—22no—
72D4×Dic61—22no—
73D4×Dic61—22no—
74#14519734—22no—
75#14519734—22no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×#11758196D411yescharacteristic
85C2×#11758196D411yescharacteristic
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198D411yescharacteristic
92C2×#11758198D411yescharacteristic
93C2×C4×Dic61—21no—
94C2×C4×Dic61—21no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61C2311yescharacteristic
97#14519709—22no—
98#14519708—22no—
99#14519708—22no—
100C4⋊#92418—22no—
101#14519701—22no—
102#14519701—22no—
103#14519698—22no—
104#14519698—22no—
105#14519689—22no—
106#14519689—22no—
107#14519687—22no—
108C8×Dic61D414yescomplemented
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115C22×Q8×C61C2311yescharacteristic
116C22×D4×C61C2311yescharacteristic
117C2×SD16×C61—22no—
118C2×SD16×C61—22no—
119C2×SD16×C61—22no—
120C22×C8×C61C2311yescharacteristic
121C22×C8×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C42×C61C2311yescharacteristic
127C4⋊C8×C61—22no—
128#103×C61—22no—
129#102×C61—22no—
130#95×C61—21no—
131#95×C61—21no—
132C24×C61—21no—
133C23×D61C2×D411yescharacteristic
134C2×Q8×C61—21no—
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61—21no—
138C2×Q8×C61—21no—
139C2×Q8×C61#4112yes—
140C2×D4×C61—21no—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61#4112yes—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2411yescharacteristic
152C2×C22⋊D61—24no—
153C2×C22⋊D61—81no—
154C2×C22⋊D61—81no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—42no—
160C22×Dic61—81no—
161C22×Dic61—81no—
162C22×Dic61C2×D411yescharacteristic
163C22×Dic61C2×D411yescharacteristic
164C22×Dic61C2×D411yescharacteristic
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171SD16×C61—28no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61C2×D412yes—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C22⋊C4×C61—81no—
183C22⋊C4×C61—81no—
184C42×C61—21no—
185C42×C61—21no—
186C22⋊Dic61—24no—
187C22⋊Dic61—42no—
188#11758198—24no—
189#11758198—22no—
190#11758198—22no—
191#11758198—81no—
192#11758198—81no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—42no—
200C4⋊Dic61#4112yes—
201C4⋊Dic61#4112yes—
202#11758196—24no—
203#11758196—22no—
204#11758196—22no—
205#11758196—81no—
206#11758196—81no—
207C4×Dic61—42no—
208C4×Dic61—81no—
209C4×Dic61—81no—
210C4×Dic61C2×D412yes—
211C4×Dic61#4112yes—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418C2×D412yes—
218C23×C61—22no—
219C23×C61—41no—
220C23×C61—41no—
221C23×C61—41no—
222C23×C61—41no—
223C23×C61—41no—
224C23×C61—41no—
225C23×C61C22×D411yescharacteristic
226C22×D61—21no—
227C22×D61—21no—
228C22×D61—21no—
229C22×D61—21no—
230C22×D61—21no—
231C22×D61—21no—
232C22×D61—21no—
233Q8×C61—22no—
234Q8×C61—22no—
235Q8×C61—41no—
236Q8×C61—41no—
237D4×C61—22no—
238D4×C61—22no—
239D4×C61—41no—
240D4×C61—41no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—22no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61C22×D411yescharacteristic
257C2×C4×C61C2×#4111yescharacteristic
258C2×C4×C61C2×#4111yescharacteristic
259C2×C4×C61C2×#4111yescharacteristic
260C2×C4×C61C2×#4111yescharacteristic
261C2×C4×C61C2×#4111yescharacteristic
262C22⋊D61—84no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—22no—
270C2×Dic61—22no—
271C2×Dic61—21no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—84no—
283C2×Dic61#12112yes—
284C2×Dic61#12112yes—
285C4×D61—41no—
286C4×D61—41no—
287C4×D61—41no—
288C4×D61—41no—
289C8×C61—22no—
290C8×C61—41no—
291#92418—22no—
292#92418—41no—
293#23707—611nomaximal, Sylow
294C22×C61—42no—
295C22×C61—42no—
296C22×C61—42no—
297C22×C61—81no—
298C22×C61—81no—
299C22×C61—81no—
300C22×C61—81no—
301C22×C61C2×#12111yescharacteristic
302C22×C61#52511yescharacteristic
303C22×C61#52511yescharacteristic
304C22×C61#57711yescharacteristic
305C22×C61#57711yescharacteristic
306C22×C61#57711yescharacteristic
307C22×C61#57711yescharacteristic
308C2×D61—41no—
309C2×D61—41no—
310C2×D61—41no—
311C2×D61—41no—
312C2×D61—41no—
313C2×D61—41no—
314C2×D61—41no—
315C4×C61—42no—
316C4×C61—41no—
317C4×C61—41no—
318C4×C61—81no—
319C4×C61—81no—
320C4×C61#52511yescharacteristic
321C4×C61#52911yescharacteristic
322C4×C61#52911yescharacteristic
323C4×C61#53211yescharacteristic
324Dic61—22no—
325Dic61—22no—
326Dic61—42no—
327Dic61—42no—
328Dic61—41no—
329Dic61—81no—
330Dic61—81no—
331C2×C4×SD16—611no—
332C2×#433—611no—
333#2324—611no—
334#2323—611no—
335#2088—611no—
336#2077—611no—
337#2066—611no—
338#2065—611no—
339#2055D6111yescharacteristic, complemented
340#2035—611no—
341#2034—611no—
342#2000—611no—
343C4×#106—611no—
344#1763—611no—
345#1762—611no—
346C2×C61—82no—
347C2×C61#239211yescharacteristic
348C2×C61#305711yescharacteristic
349C2×C61#306011yescharacteristic
350C2×C61#312311yescharacteristic
351C2×C61#312511yescharacteristic
352C2×C61#312511yescharacteristic
353C2×C61#312611yescharacteristic
354D61—81no—
355C22×SD16C2×D6111yescharacteristic
356C2×C22⋊Q8—611no—
357C2×#121—611no—
358C2×C4×Q8—611no—
359C2×C4×D4—611no—
360C2×#117—611no—
361C4×SD16—1224no—
362#433—1224no—
363C2×#106—611no—
364C2×#106—611no—
365C2×#106—611no—
366C2×C4⋊C8—611no—
367C2×C4⋊C8C2×D6111yescharacteristic
368C2×#103—611no—
369C2×#103—611no—
370C2×#103C2×D6111yescharacteristic
371C2×#102—611no—
372C2×#102—611no—
373C2×#102C2×D6111yescharacteristic
374C2×C22⋊C8—611no—
375C2×C22⋊C8—611no—
376C2×#97—611no—
377C2×C4×C8—611no—
378#391C2×D6111yescharacteristic
379#390—1221no—
380#390C2×D6111yescharacteristic
381#389—611no—
382#389—611no—
383#389—1221no—
384#388—1221no—
385#388—1221no—
386#388—1221no—
387#387—1221no—
388#386—1221no—
389#385—1221no—
390#380—611no—
391#380—611no—
392C4×C4⋊C4—611no—
393C4×C4⋊C4—611no—
394#340—611no—
395#340—611no—
396#340—611no—
397#340—611no—
398#340—611no—
399#340C2×D6111yescharacteristic
400C61#2370711yescharacteristic, complemented, Sylow
401C22×Q8C22×D6111yescharacteristic
402C22×D4—1221no—
403C22×D4C22×D6111yescharacteristic
404C23×C4—611no—
405C23×C4—1221no—
406C2×SD16—22no—
407C2×SD16—22no—
408C2×SD16—22no—
409C22×C8—611no—
410C22×C8—611no—
411C22×C8C22×D6111yescharacteristic
412C22×C8C22×D6111yescharacteristic
413C22⋊Q8—1222no—
414C22⋊Q8—1222no—
415#121—1222no—
416#121—1222no—
417C4×Q8—1222no—
418C4×Q8—1222no—
419C4×D4—1222no—
420C4×D4—1222no—
421#117—1222no—
422#117—1222no—
423C2×C4⋊C4—611no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—611no—
426C2×C4⋊C4—611no—
427C2×C4⋊C4—611no—
428C2×C4⋊C4—611no—
429C2×C4⋊C4—1221no—
430C2×C4⋊C4—1221no—
431C2×C4⋊C4—1221no—
432C2×C4⋊C4—1221no—
433C2×C4⋊C4C22×D6111yescharacteristic
434C2×C4⋊C4C22×D6111yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—611no—
438C2×C22⋊C4—611no—
439C2×C22⋊C4—1221no—
440C2×C22⋊C4—1221no—
441C2×C22⋊C4—1221no—
442C2×C22⋊C4—1221no—
443C2×C22⋊C4—1221no—
444C2×C42—611no—
445C2×C42—1221no—
446C2×C42—1221no—
447C2×C42—1221no—
448C2×C42C22×D6111yescharacteristic
449#106—1222no—
450#106—1222no—
451#106—1222no—
452C4⋊C8—22no—
453C4⋊C8—1222no—
454#103—22no—
455#103—1222no—
456#103—1222no—
457#102—22no—
458#102—1222no—
459#102—1222no—
460C22⋊C8—1222no—
461C22⋊C8—1222no—
462#97—1222no—
463C4×C8—614no—
464#95—21no—
465#95—21no—
466#95—1221no—
467#95—1221no—
468#95—1221no—
469#95—1221no—
470#95—1221no—
471#95—1221no—
472C24—21no—
473C24—611no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8#1175822412yes—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—1224no—
486C2×D4—4881no—
487C2×D4—4881no—
488C2×D4#1175822412yes—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—611no—
493C22×C4—611no—
494C22×C4—611no—
495C22×C4—1221no—
496C22×C4—1221no—
497C22×C4—1221no—
498C22×C4—1221no—
499C22×C4—1221no—
500C22×C4—1221no—
501C22×C4—1221no—
502C22×C4—1221no—
503C22×C4—1221no—
504C22×C4—1221no—
505C22×C4—4881no—
506C22×C4—4881no—
507C22×C4—2442no—
508C22×C4D4×D6111yescharacteristic
509C22×C4D4×D6111yescharacteristic
510C22×C4C23×D6111yescharacteristic
511SD16—28no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—612no—
518C2×C8—1221no—
519C2×C8—1221no—
520C2×C8—1221no—
521C2×C8—1221no—
522C2×C8—1221no—
523C2×C8D4×D6112yes—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—612no—
529C4⋊C4—612no—
530C4⋊C4—1222no—
531C4⋊C4—1222no—
532C4⋊C4—1224no—
533C4⋊C4—1221no—
534C4⋊C4—1221no—
535C4⋊C4—1221no—
536C4⋊C4—1221no—
537C4⋊C4—1221no—
538C4⋊C4—1221no—
539C4⋊C4—4881no—
540C4⋊C4—4881no—
541C4⋊C4—2442no—
542C22⋊C4—81no—
543C22⋊C4—81no—
544C22⋊C4—1222no—
545C22⋊C4—1222no—
546C22⋊C4—1224no—
547C22⋊C4—1224no—
548C22⋊C4—4881no—
549C22⋊C4—4881no—
550C22⋊C4—2442no—
551C42—21no—
552C42—21no—
553C42—612no—
554C42—612no—
555C42—4881no—
556C42—4881no—
557C42—2442no—
558C23—22no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—1221no—
566C23—1221no—
567C23—1221no—
568C23—1221no—
569C23—1221no—
570C23—1221no—
571C23—1221no—
572C23C2×D4×D6111yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577D4—22no—
578D4—22no—
579D4—41no—
580D4—41no—
581D4—4884no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—612no—
598C2×C4—612no—
599C2×C4—1221no—
600C2×C4—1221no—
601C2×C4—1221no—
602C2×C4—1221no—
603C2×C4—1221no—
604C2×C4—1221no—
605C2×C4—1222no—
606C2×C4—1222no—
607C2×C4—1221no—
608C2×C4—4884no—
609C2×C4—2441no—
610C2×C4—2441no—
611C2×C4—2441no—
612C2×C4—2441no—
613C2×C4—2441no—
614C2×C4—2441no—
615C2×C4—2441no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4—2441no—
619C2×C4—2441no—
620C2×C4—2441no—
621C2×C4—2441no—
622C2×C4—2441no—
623C2×C4C2×D4×D6111yescharacteristic
624C2×C4#41×D6111yescharacteristic
625C2×C4#41×D6111yescharacteristic
626C2×C4#41×D6111yescharacteristic
627C2×C4C2×#1175822411yescharacteristic
628C2×C4C2×#1175822411yescharacteristic
629C8—22no—
630C8—41no—
631C8—1222no—
632C8—2441no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—2441no—
641C22—2441no—
642C22—2441no—
643C22—2441no—
644C22—2441no—
645C22—2441no—
646C22—2441no—
647C22#121×D6111yescharacteristic
648C22#1684027211yescharacteristic
649C22#1684027211yescharacteristic
650C22#1684056811yescharacteristic
651C22#1684056911yescharacteristic
652C22#1684057111yescharacteristic
653C22#1684057211yescharacteristic
654C4—41no—
655C4—42no—
656C4—41no—
657C4—81no—
658C4—81no—
659C4—1222no—
660C4—1222no—
661C4—4881no—
662C4—4881no—
663C4—2441no—
664C4—2442no—
665C4—2442no—
666C4#1684026811yescharacteristic
667C4#1684028911yescharacteristic
668C4#1684028911yescharacteristic
669C4#1684031111yescharacteristic
670C2—82no—
671C2—4881no—
672C2#2144905811yescharacteristic
673C2#2145545611yescharacteristic
674C2#2145547611yescharacteristic
675C2#2145606911yescharacteristic
676C2#2145609311yescharacteristic
677C2#2145609511yescharacteristic
678C2#2145610811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2055C2
socleC23×C61C22×D4
prime radicalC2×#14519748C22
hypercenter#2055D61
hypocenterC61#23707
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2055

Complements

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

NH ≅ G/Ntype
1. C2×SD16×Dic61C2semidirect
2. C2×#16839822C2semidirect
4. #21448504C2semidirect
5. #21447317C2semidirect
6. #21447254C2semidirect
7. #21447200C2semidirect
8. #21447193C2semidirect
9. #21447013C2semidirect
12. #21445707C2semidirect
13. #21445651C2semidirect
14. #21445646C2semidirect
15. C61×#2055C2semidirect
108. C8×Dic61D4semidirect
339. #2055D61semidirect
400. C61#23707semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×Dic612
C2×#168398222
#214485152
#214485042
#214473172
#214472542
#214472002
#214471932
#214470132
#214470062
#214468192
#214457072
#214456512
#214456462
C61×#20552
#2370761