Finite Group Databasebeta

← #29707962

Subgroups — #29707962

Order 15616.

1494 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519797C211yesmaximal, characteristic
2C22×C4⋊#92418C211yesmaximal, characteristic, complemented
3C2×#16839758C211yesmaximal, characteristic, complemented
4C2×#16839756C211yesmaximal, characteristic, complemented
5#21448309C211yesmaximal, characteristic, complemented
6#21447141C212yesmaximal, complemented
7#21447136C212yesmaximal, complemented
8#21447134C212yesmaximal, complemented
9#21447129C212yesmaximal, complemented
10#21445535C211yesmaximal, characteristic, complemented
11C61×#2297C211yesmaximal, characteristic, complemented
12C22×#11758222C2211yescharacteristic
13C2×#14519797—24no—
14C2×#14519797—24no—
15C2×#14519797—24no—
16C22×#11758202C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C22×#11758199C2211yescharacteristic
20C23×#92418C2211yescharacteristic
21C23×#92418C2211yescharacteristic
22C2×#14519736C2211yescharacteristic
23C2×C4⋊#92418—24no—
24C2×C4⋊#92418C2212yes—
25C2×C4⋊#92418C2212yes—
26#16839758—24no—
27#16839756—24no—
28C2×#14519701C2212yes—
29C2×#14519700C2212yes—
30C2×#14519698C2212yes—
31C2×#14519697C2212yes—
32#16839668C2212yes—
33#16839664C2212yes—
34#16839641—21no—
35#16839641—21no—
36C4×#11758198—22no—
37#16839524C2212yes—
38#16839524C2212yes—
39C22×#41×C61C2211yescharacteristic
40C2×#117×C61C2211yescharacteristic
41C22×C42×C61C2211yescharacteristic
42C61×#391C2212yes—
43C61×#390C2212yes—
44C61×#386—21no—
45C61×#386—21no—
46C4×C22⋊C4×C61—22no—
47C2×#11758222—22no—
48C2×#11758222—22no—
49C2×#11758222—22no—
50C2×#11758222—22no—
51C2×#11758222—22no—
52C2×#11758222D414yes—
53C22×Dic122C2311yescharacteristic
54C22×D244C2311yescharacteristic
55C22×C22⋊D61—21no—
56C22×C4×D61—21no—
57#14519797—232no—
58C2×#11758202—22no—
59C2×#11758202—22no—
60C2×#11758202—22no—
61C2×#11758200—22no—
62C2×#11758200—22no—
63C2×#11758200—22no—
64C2×#11758201—22no—
65C2×#11758201—22no—
66C2×#11758201—22no—
67C2×#11758199—22no—
68C2×#11758199—22no—
69C2×#11758199—22no—
70C22×#92418—22no—
71C22×#92418—22no—
72C22×#92418—22no—
73C22×#92418—22no—
74C22×#92418—22no—
75C22×#92418D414yes—
76C22×#92418C2312yes—
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79#14519736—22no—
80#14519736—22no—
81C2×C4⋊Dic61C2312yes—
82C2×C22⋊Dic61—21no—
83C2×#11758198—22no—
84C2×#11758198—22no—
85C2×C4×Dic61—21no—
86C4⋊#92418—24no—
87C4⋊#92418—24no—
88#14519701—24no—
89#14519700—24no—
90#14519698—24no—
91#14519697—24no—
92#14519684—22no—
93#14519684—22no—
94C2×#41×C61—22no—
95C2×#41×C61—22no—
96C2×#41×C61—22no—
97C2×#41×C61—22no—
98C2×#41×C61—22no—
99C2×#41×C61D414yes—
100C22×Q8×C61C2311yescharacteristic
101C22×D4×C61—21no—
102C22×D4×C61C2311yescharacteristic
103C23×C4×C61—21no—
104C23×C4×C61D411yescharacteristic
105C23×C4×C61D411yescharacteristic
106C23×C4×C61C2311yescharacteristic
107#117×C61—22no—
108#117×C61—22no—
109C2×C4⋊C4×C61C2312yes—
110C2×C22⋊C4×C61—21no—
111C2×C22⋊C4×C61—22no—
112C2×C22⋊C4×C61—22no—
113C2×C42×C61—22no—
114C2×C42×C61—22no—
115C2×C42×C61—21no—
116C2×C42×C61D412yes—
117C2×C42×C61C2312yes—
118#95×C61—22no—
119#95×C61—22no—
120C24×C61—21no—
121C24×C61C2×D411yescharacteristic
122C23×D61—21no—
123#41×C61—28no—
124#41×C61—28no—
125#41×C61—44no—
126#41×C61—44no—
127C2×Q8×C61—21no—
128C2×Q8×C61—21no—
129C2×Q8×C61—21no—
130C2×Q8×C61—21no—
131C2×Q8×C61—21no—
132C2×Q8×C61C2×D412yes—
133C2×D4×C61—24no—
134C2×D4×C61—21no—
135C2×D4×C61—21no—
136C2×D4×C61—21no—
137C2×D4×C61—21no—
138C2×D4×C61—21no—
139C2×D4×C61—42no—
140C2×D4×C61—42no—
141C2×D4×C61C2×D412yes—
142C22×C4×C61—22no—
143C22×C4×C61—24no—
144C22×C4×C61—22no—
145C22×C4×C61—21no—
146C22×C4×C61—24no—
147C22×C4×C61—22no—
148C22×C4×C61—42no—
149C22×C4×C61—42no—
150C22×C4×C61—42no—
151C22×C4×C61C2×D412yes—
152C22×C4×C61C2×D412yes—
153C22×C4×C61C2×D412yes—
154C22×C4×C61C2×D412yes—
155C22×C4×C61C2×D412yes—
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61#4112yes—
158C22×C4×C61#4112yes—
159C22×C4×C61#4112yes—
160C22×C4×C61C2411yescharacteristic
161C2×C22⋊D61—24no—
162C2×C22⋊D61—42no—
163C2×C22⋊D61—42no—
164C22×Dic61—21no—
165C22×Dic61—22no—
166#11758222—28no—
167#11758222—28no—
168#11758222—44no—
169#11758222—44no—
170C2×D244—21no—
171C2×D244—21no—
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244C2×D412yes—
176C2×C4×D61—24no—
177C2×C4×D61—42no—
178C2×C4×D61—42no—
179C2×Dic122—21no—
180C2×Dic122—21no—
181C2×Dic122—21no—
182C2×Dic122—21no—
183C2×Dic122—21no—
184C2×Dic122C2×D412yes—
185C4⋊C4×C61—22no—
186C4⋊C4×C61—22no—
187C22⋊C4×C61—44no—
188C22⋊C4×C61—42no—
189C22⋊C4×C61—44no—
190C42×C61—24no—
191C42×C61—22no—
192C42×C61—22no—
193C42×C61—42no—
194C22⋊Dic61—42no—
195#11758202—28no—
196#11758201—28no—
197#11758200—28no—
198#11758199—28no—
199#11758198—44no—
200#11758198—44no—
201C4⋊Dic61—22no—
202C4⋊Dic61—22no—
203C4×Dic61—42no—
204C2×#92418—28no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—22no—
210C2×#92418—22no—
211C2×#92418—22no—
212C2×#92418—44no—
213C2×#92418C2×D412yes—
214C2×#92418C2×D412yes—
215C23×C61—22no—
216C23×C61—22no—
217C23×C61—22no—
218C23×C61—41no—
219C23×C61—41no—
220C23×C61—42no—
221C23×C61—42no—
222C23×C61#12112yes—
223C23×C61#12112yes—
224C23×C61#12112yes—
225C23×C61C22×D411yescharacteristic
226C22×D61—22no—
227C22×D61—41no—
228C22×D61—41no—
229C22×D61—42no—
230C22×D61—42no—
231Q8×C61—22no—
232Q8×C61—22no—
233Q8×C61—41no—
234Q8×C61—41no—
235D4×C61—22no—
236D4×C61—22no—
237D4×C61—48no—
238D4×C61—41no—
239D4×C61—41no—
240C2×C4×C61—28no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—22no—
244C2×C4×C61—22no—
245C2×C4×C61—22no—
246C2×C4×C61—22no—
247C2×C4×C61—44no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—48no—
251C2×C4×C61—42no—
252C2×C4×C61—42no—
253C2×C4×C61—42no—
254C2×C4×C61#12014yes—
255C2×C4×C61#12112yes—
256C2×C4×C61#12112yes—
257C2×C4×C61#12112yes—
258C2×C4×C61#12314yes—
259C2×C4×C61#12314yes—
260C2×C4×C61#12414yes—
261C2×C4×C61#13514yescomplemented
262C2×C4×C61C22×D411yescharacteristic
263C2×C4×C61C22×D411yescharacteristic
264C2×C4×C61C22×D411yescharacteristic
265C2×C4×C61C2×#4111yescharacteristic
266C2×C4×C61C2×#4111yescharacteristic
267C2×C4×C61C2×#4111yescharacteristic
268C22⋊D61—48no—
269C2×Dic61—22no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—42no—
273C2×Dic61—42no—
274C2×Dic61—42no—
275D244—22no—
276D244—22no—
277D244—41no—
278D244—41no—
279C4×D61—48no—
280Dic122—22no—
281Dic122—22no—
282Dic122—41no—
283Dic122—41no—
284#92418—22no—
285#92418—22no—
286#92418—42no—
287#23539—611nomaximal, Sylow
288C22×C61—24no—
289C22×C61—24no—
290C22×C61—22no—
291C22×C61—22no—
292C22×C61—42no—
293C22×C61—44no—
294C22×C61—82no—
295C22×C61—81no—
296C22×C61—81no—
297C22×C61#39414yes—
298C22×C61C2×#12111yescharacteristic
299C22×C61C2×#12111yescharacteristic
300C22×C61C2×#12111yescharacteristic
301C22×C61C2×#13512yes—
302C22×C61#57512yes—
303C2×D61—42no—
304C2×D61—44no—
305C2×D61—82no—
306C2×D61—81no—
307C2×D61—81no—
308C4×C61—24no—
309C4×C61—42no—
310C4×C61—42no—
311C4×C61—82no—
312C4×C61#39414yes—
313C4×C61C2×#12011yescharacteristic
314C4×C61C2×#12311yescharacteristic
315C4×C61C2×#12311yescharacteristic
316C4×C61C2×#12411yescharacteristic
317Dic61—42no—
318Dic61—82no—
319C22×#135—611no—
320C22×C4⋊C8—611no—
321C2×#416—611no—
322C2×#416—611no—
323#2297—611no—
324#2297D6111yescharacteristic, complemented
325#2056—612no—
326#2055—612no—
327#2055—612no—
328#2054—612no—
329#1735—611no—
330C2×C61—24no—
331C2×C61—82no—
332C2×C61C2×#39411yescharacteristic
333C2×C61#303512yes—
334C2×C61#303512yes—
335C2×C61#305011yescharacteristic
336C2×C61#305411yescharacteristic
337D61—82no—
338C22×#41—611no—
339C22×#41C2×D6111yescharacteristic
340C2×#135—1224no—
341C2×#135—1224no—
342C2×#135—1224no—
343C22×Q16—611no—
344C22×SD16—611no—
345C22×SD16—611no—
346C22×D8—611no—
347C23×C8—611no—
348C23×C8—611no—
349C2×#117—611no—
350C2×#117C2×D6111yescharacteristic
351C22×C42C2×D6111yescharacteristic
352C2×C4⋊C8—612no—
353C2×C4⋊C8—612no—
354C2×C4⋊C8—1224no—
355#416—1224no—
356#416—1224no—
357C2×#103—612no—
358C2×#103—612no—
359C2×#102—612no—
360C2×#102—612no—
361#391—612no—
362#391C2×D6112yes—
363#390—612no—
364#390C2×D6112yes—
365#386—21no—
366#386—21no—
367#386—1221no—
368#386—1221no—
369C4×C22⋊C4—22no—
370C4×C22⋊C4—1222no—
371#340—612no—
372#340—612no—
373C61#2353911yescharacteristic, complemented, Sylow
374C2×#41—22no—
375C2×#41—22no—
376C2×#41—22no—
377C2×#41—22no—
378C2×#41—22no—
379C2×#41—614no—
380C2×#41—1222no—
381C2×#41—1222no—
382C2×#41—1222no—
383C2×#41—1222no—
384C2×#41—1222no—
385C2×#41D24414yes—
386C22×Q8—611no—
387C22×Q8C22×D6111yescharacteristic
388C22×D4—21no—
389C22×D4—611no—
390C22×D4—1221no—
391C22×D4C22×D6111yescharacteristic
392C23×C4—21no—
393C23×C4—1221no—
394C23×C4C22⋊D6111yescharacteristic
395C23×C4C22⋊D6111yescharacteristic
396C23×C4C22×D6111yescharacteristic
397#135—12232no—
398C2×Q16—1222no—
399C2×Q16—1222no—
400C2×Q16—1222no—
401C2×SD16—1222no—
402C2×SD16—1222no—
403C2×SD16—1222no—
404C2×SD16—1222no—
405C2×SD16—1222no—
406C2×SD16—1222no—
407C2×D8—1222no—
408C2×D8—1222no—
409C2×D8—1222no—
410C22×C8—614no—
411C22×C8—611no—
412C22×C8—611no—
413C22×C8—612no—
414C22×C8—1222no—
415C22×C8—1222no—
416C22×C8—1222no—
417C22×C8—1222no—
418C22×C8—1222no—
419#117—22no—
420#117—22no—
421#117—1222no—
422#117—1222no—
423C2×C4⋊C4—612no—
424C2×C4⋊C4C22×D6112yes—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—1221no—
429C2×C22⋊C4—1222no—
430C2×C22⋊C4—1222no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—21no—
434C2×C42—1221no—
435C2×C42C22⋊D6112yes—
436C2×C42C22×D6112yes—
437C4⋊C8—1224no—
438C4⋊C8—1224no—
439#103—1224no—
440#103—1224no—
441#102—1224no—
442#102—1224no—
443#95—22no—
444#95—22no—
445#95—1222no—
446#95—1222no—
447C24—21no—
448C24—1221no—
449C24C2×C22⋊D6111yescharacteristic
450#41—28no—
451#41—28no—
452#41—44no—
453#41—44no—
454#41—1228no—
455#41—1228no—
456#41—2444no—
457#41—2444no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—612no—
464C2×Q8—1221no—
465C2×Q8—1221no—
466C2×Q8—1221no—
467C2×Q8—1221no—
468C2×Q8—1221no—
469C2×Q8C2×D24412yes—
470C2×D4—24no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—612no—
479C2×D4—1224no—
480C2×D4—1221no—
481C2×D4—1221no—
482C2×D4—1221no—
483C2×D4—1221no—
484C2×D4—1221no—
485C2×D4—2442no—
486C2×D4—2442no—
487C2×D4C2×D24412yes—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—1221no—
498C22×C4—1224no—
499C22×C4—1222no—
500C22×C4—2442no—
501C22×C4—2442no—
502C22×C4C2×D24412yes—
503C22×C4#1175822212yes—
504C22×C4D4×D6112yes—
505C22×C4D4×D6112yes—
506C22×C4#1175822412yes—
507C22×C4#1175822412yes—
508C22×C4C2×C22⋊D6112yes—
509C22×C4C2×C22⋊D6112yes—
510C22×C4C2×C22⋊D6111yescharacteristic
511C22×C4C23×D6111yescharacteristic
512Q16—1228no—
513SD16—1228no—
514SD16—1228no—
515D8—1228no—
516C2×C8—612no—
517C2×C8—612no—
518C2×C8—1221no—
519C2×C8—1221no—
520C2×C8—1221no—
521C2×C8—1221no—
522C2×C8—1228no—
523C2×C8—1222no—
524C2×C8—1222no—
525C2×C8—1222no—
526C2×C8—2444no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—1222no—
530C4⋊C4—1222no—
531C22⋊C4—44no—
532C22⋊C4—42no—
533C22⋊C4—44no—
534C22⋊C4—2444no—
535C22⋊C4—2442no—
536C22⋊C4—2444no—
537C42—22no—
538C42—22no—
539C42—24no—
540C42—42no—
541C42—2442no—
542C23—22no—
543C23—22no—
544C23—22no—
545C23—41no—
546C23—41no—
547C23—42no—
548C23—42no—
549C23—1222no—
550C23—2441no—
551C23—2441no—
552C23—2442no—
553C23—2442no—
554C23#1451974812yes—
555C23#1451974912yes—
556C23#1451975112yes—
557C23C22×C22⋊D6111yescharacteristic
558Q8—22no—
559Q8—22no—
560Q8—41no—
561Q8—41no—
562Q8—1222no—
563Q8—1222no—
564Q8—2441no—
565Q8—2441no—
566D4—22no—
567D4—22no—
568D4—48no—
569D4—41no—
570D4—41no—
571D4—1222no—
572D4—1222no—
573D4—2448no—
574D4—2441no—
575D4—2441no—
576C2×C4—28no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—44no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—48no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—1222no—
591C2×C4—2442no—
592C2×C4—2442no—
593C2×C4—2442no—
594C2×C4—2441no—
595C2×C4—2441no—
596C2×C4—2448no—
597C2×C4#1451974714yes—
598C2×C4#1451974812yes—
599C2×C4#1451974912yes—
600C2×C4#1451975112yes—
601C2×C4#1451975914yes—
602C2×C4#1451976114yes—
603C2×C4#1451976314yes—
604C2×C4#1451979714yescomplemented
605C2×C4C2×D4×D6111yescharacteristic
606C2×C4C2×D4×D6111yescharacteristic
607C2×C4C22×D24411yescharacteristic
608C2×C4C2×#1175822411yescharacteristic
609C2×C4C2×#1175822411yescharacteristic
610C2×C4C2×#1175822211yescharacteristic
611C8—1222no—
612C8—1222no—
613C8—2442no—
614C22—22no—
615C22—22no—
616C22—24no—
617C22—24no—
618C22—42no—
619C22—44no—
620C22—81no—
621C22—81no—
622C22—82no—
623C22—4881no—
624C22—4881no—
625C22—4882no—
626C22—2442no—
627C22—2444no—
628C22#1683967814yes—
629C22C2×#1451974811yescharacteristic
630C22C2×#1451974911yescharacteristic
631C22C2×#1451975111yescharacteristic
632C22C2×#1451979712yes—
633C22#1684056012yes—
634C4—24no—
635C4—42no—
636C4—42no—
637C4—82no—
638C4—4882no—
639C4—2442no—
640C4#1683967814yes—
641C4C2×#1451974711yescharacteristic
642C4C2×#1451975911yescharacteristic
643C4C2×#1451976111yescharacteristic
644C4C2×#1451976311yescharacteristic
645C2—24no—
646C2—82no—
647C2—4882no—
648C2C2×#1683967811yescharacteristic
649C2#2145526812yes—
650C2#2145527412yes—
651C2#2145539711yescharacteristic
652C2#2145542511yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2297C2
socleC23×C61C22×D4
prime radicalC22×#14519797C2
hypercenter#2297D61
hypocenterC61#23539
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ #2297

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊#92418C2semidirect
3. C2×#16839758C2semidirect
4. C2×#16839756C2semidirect
5. #21448309C2semidirect
6. #21447141C2semidirect
7. #21447136C2semidirect
8. #21447134C2semidirect
9. #21447129C2semidirect
10. #21445535C2semidirect
11. C61×#2297C2semidirect
261. C2×C4×C61#135semidirect
324. #2297D61semidirect
373. C61#23539semidirect
604. C2×C4#14519797semidirect

Maximal subgroups

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

subgroupindex
C22×#145197972
C22×C4⋊#924182
C2×#168397582
C2×#168397562
#214483092
#214471412
#214471362
#214471342
#214471292
#214455352
C61×#22972
#2353961