Finite Group Databasebeta

← #29709329

Subgroups — #29709329

Order 15616.

908 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839862C211yesmaximal, characteristic, complemented
2C2×C4×#11758200C211yesmaximal, characteristic, complemented
3#21448471C211yesmaximal, characteristic, complemented
4#21447301C211yesmaximal, characteristic, complemented
5#21447238C211yesmaximal, characteristic, complemented
6#21447207C211yesmaximal, characteristic, complemented
7#21447193C211yesmaximal, characteristic, complemented
8#21447136C211yesmaximal, characteristic, complemented
9#21447136C211yesmaximal, characteristic, complemented
10#21447050C211yesmaximal, characteristic
11#21446907C211yesmaximal, characteristic
12#21445676C211yesmaximal, characteristic, complemented
13#21445644C211yesmaximal, characteristic, complemented
14C4×#14519698C211yesmaximal, characteristic, complemented
15C61×#2328C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C2×C4×Dic122C2211yescharacteristic
19#16839862—24no—
20C4×#11758200—24no—
21C2×#14519710C2211yescharacteristic
22C2×#14519708C2211yescharacteristic
23C2×C4⋊#92418C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×#14519700C2211yescharacteristic
26C2×#14519700C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519688C2211yescharacteristic
34C2×C4×#92418C2211yescharacteristic
35#16839668C2211yescharacteristic
36#16839668C2211yescharacteristic
37#16839660C2211yescharacteristic
38#16839660C2211yescharacteristic
39#16839644—21no—
40#16839644—21no—
41#16839629—21no—
42#16839626—21no—
43C4×C4⋊Dic61C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C2×#127×C61C2211yescharacteristic
51C2×C4×D4×C61C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C61×#390C2211yescharacteristic
54C61×#390C2211yescharacteristic
55C61×#386—21no—
56C61×#386—21no—
57C61×#386—21no—
58C61×#386—21no—
59C61×#382C2211yescharacteristic
60C61×#376C2211yescharacteristic
61C22×Dic122C2311yescharacteristic
62C2×#11758200—22no—
63C2×#11758200—22no—
64C2×#11758200—22no—
65C2×#11758200—22no—
66C2×#11758200—22no—
67C2×#11758200—22no—
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C4×Dic122—22no—
73C4×Dic122D414yescomplemented
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×C4×Dic61—21no—
81C2×C4×Dic61—21no—
82#14519710—22no—
83#14519708—22no—
84C4⋊#92418—22no—
85C4⋊#92418—22no—
86#14519700—22no—
87#14519700—22no—
88#14519698—22no—
89#14519698—22no—
90#14519698—22no—
91#14519698—22no—
92#14519698—22no—
93#14519698—22no—
94#14519688—22no—
95C4×#92418—22no—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103C22×D4×C61—21no—
104C22×D4×C61—21no—
105C22×D4×C61C2311yescharacteristic
106C22×D4×C61C2311yescharacteristic
107C23×C4×C61—21no—
108C23×C4×C61—21no—
109#127×C61—22no—
110#127×C61—22no—
111C4×D4×C61—22no—
112C4×D4×C61—22no—
113C4×D4×C61—22no—
114C4×D4×C61—22no—
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61—21no—
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61—21no—
121C2×C22⋊C4×C61—21no—
122C2×C22⋊C4×C61—21no—
123C2×C42×C61C2311yescharacteristic
124C2×C42×C61C2311yescharacteristic
125C2×C42×C61C2311yescharacteristic
126#95×C61—21no—
127#95×C61—21no—
128#95×C61D411yescharacteristic
129#95×C61D411yescharacteristic
130#95×C61D411yescharacteristic
131#95×C61D411yescharacteristic
132C24×C61—21no—
133C24×C61—21no—
134C2×D4×C61—24no—
135C2×D4×C61—24no—
136C2×D4×C61—21no—
137C2×D4×C61—21no—
138C2×D4×C61—21no—
139C2×D4×C61—21no—
140C2×D4×C61—21no—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—81no—
147C2×D4×C61—81no—
148C2×D4×C61—81no—
149C2×D4×C61—81no—
150C2×D4×C61#4112yes—
151C2×D4×C61#4112yes—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—42no—
155C22×C4×C61—42no—
156C22×C4×C61—81no—
157C22×C4×C61—81no—
158C22×C4×C61—81no—
159C22×C4×C61—81no—
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2411yescharacteristic
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C2×Dic122—21no—
172C2×Dic122—21no—
173C2×Dic122—21no—
174C2×Dic122—21no—
175C2×Dic122—21no—
176C2×Dic122C2×D412yes—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C22⋊C4×C61—42no—
182C22⋊C4×C61—42no—
183C22⋊C4×C61—81no—
184C22⋊C4×C61—81no—
185C22⋊C4×C61—81no—
186C22⋊C4×C61—81no—
187C42×C61—21no—
188C42×C61—21no—
189C42×C61—21no—
190C42×C61—21no—
191C42×C61C2×D412yes—
192C42×C61#4112yes—
193#11758200—28no—
194#11758200—28no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61C2×D412yes—
201#11758196—24no—
202#11758196—81no—
203#11758196—81no—
204C4×Dic61—24no—
205C4×Dic61—81no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418#4112yes—
217C2×#92418#4112yes—
218C23×C61—22no—
219C23×C61—22no—
220C23×C61—41no—
221C23×C61—41no—
222C23×C61—41no—
223C23×C61—41no—
224C23×C61—41no—
225C23×C61—41no—
226C23×C61—41no—
227C23×C61—41no—
228C23×C61—41no—
229C23×C61—41no—
230C23×C61—41no—
231C23×C61—41no—
232C23×C61C22×D411yescharacteristic
233D4×C61—22no—
234D4×C61—22no—
235D4×C61—22no—
236D4×C61—22no—
237D4×C61—41no—
238D4×C61—41no—
239D4×C61—41no—
240D4×C61—41no—
241D4×C61—84no—
242D4×C61—84no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—84no—
266C2×C4×C61—84no—
267C2×C4×C61#12112yes—
268C2×C4×C61#12112yes—
269C2×C4×C61C22×D411yescharacteristic
270C2×C4×C61C2×#4111yescharacteristic
271C2×C4×C61C2×#4111yescharacteristic
272C2×C4×C61C2×#4111yescharacteristic
273C2×C4×C61C2×#4111yescharacteristic
274C2×C4×C61C2×#4111yescharacteristic
275C2×Dic61—22no—
276C2×Dic61—22no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—41no—
287Dic122—22no—
288Dic122—22no—
289Dic122—41no—
290Dic122—41no—
291#92418—22no—
292#92418—22no—
293#92418—41no—
294#92418—41no—
295#23690—611nomaximal, Sylow
296C22×C61—42no—
297C22×C61—42no—
298C22×C61—42no—
299C22×C61—42no—
300C22×C61—42no—
301C22×C61—42no—
302C22×C61—81no—
303C22×C61—81no—
304C22×C61—81no—
305C22×C61—81no—
306C22×C61—81no—
307C22×C61—81no—
308C22×C61—81no—
309C22×C61—81no—
310C22×C61C2×#12111yescharacteristic
311C22×C61#52511yescharacteristic
312C22×C61#53211yescharacteristic
313C22×C61#57611yescharacteristic
314C22×C61#57711yescharacteristic
315C22×C61#57711yescharacteristic
316C22×C61#57711yescharacteristic
317C4×C61—22no—
318C4×C61—22no—
319C4×C61—41no—
320C4×C61—41no—
321C4×C61—41no—
322C4×C61—41no—
323C4×C61—81no—
324C4×C61—81no—
325C4×C61#52511yescharacteristic
326C4×C61#52511yescharacteristic
327C4×C61#52911yescharacteristic
328C4×C61#52911yescharacteristic
329Dic61—42no—
330Dic61—42no—
331Dic61—81no—
332Dic61—81no—
333C2×#440—611no—
334C2×C4×SD16—611no—
335#2328D6111yescharacteristic
336#2320—611no—
337#2085—611no—
338#2074—611no—
339#2067—611no—
340#2065—611no—
341#2055—611no—
342#2055—611no—
343#2041—611no—
344#2014—611no—
345#1768—611no—
346#1762—611no—
347C4×#102—611no—
348C2×C61—82no—
349C2×C61—82no—
350C2×C61#239211yescharacteristic
351C2×C61#304311yescharacteristic
352C2×C61#304511yescharacteristic
353C2×C61#311811yescharacteristic
354C2×C61#312311yescharacteristic
355C2×C61#317411yescharacteristic
356C2×C61#317911yescharacteristic
357C22×SD16—611no—
358C22×SD16—611no—
359C2×#127C2×D6111yescharacteristic
360C2×C4×Q8—611no—
361C2×C4×D4C2×D6111yescharacteristic
362C2×C4×D4C2×D6111yescharacteristic
363#440—1224no—
364C4×SD16—1224no—
365C2×#107—611no—
366C2×#106—611no—
367C2×C4⋊C8—611no—
368C2×C4⋊C8—611no—
369C2×#103—611no—
370C2×#103—611no—
371C2×#102—611no—
372C2×#102—611no—
373C2×#102—611no—
374C2×#102—611no—
375C2×#102—611no—
376C2×#102—611no—
377C2×#97—611no—
378C2×C4×C8—611no—
379#391—611no—
380#391—611no—
381#390C2×D6111yescharacteristic
382#390C2×D6111yescharacteristic
383#389—611no—
384#389—611no—
385#387—1221no—
386#387—1221no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#383—1221no—
392#382—1221no—
393#382C2×D6111yescharacteristic
394C4×C4⋊C4—611no—
395#376C2×D6111yescharacteristic
396#340—611no—
397#340—611no—
398#340—611no—
399#340—611no—
400#336—611no—
401#336—611no—
402C61#2369011yescharacteristic, complemented, Sylow
403C22×Q8—611no—
404C22×D4—21no—
405C22×D4—21no—
406C22×D4C22×D6111yescharacteristic
407C22×D4C22×D6111yescharacteristic
408C23×C4—21no—
409C23×C4—21no—
410C2×SD16—1222no—
411C2×SD16—1222no—
412C2×SD16—1222no—
413C2×SD16—1222no—
414C2×SD16—1222no—
415C2×SD16—1222no—
416C22×C8—611no—
417C22×C8—611no—
418C22×C8—611no—
419C22×C8—611no—
420#127—22no—
421#127—22no—
422C4×Q8—614no—
423C4×Q8—1222no—
424C4×D4—22no—
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—22no—
428C2×C4⋊C4—611no—
429C2×C4⋊C4—611no—
430C2×C4⋊C4—611no—
431C2×C4⋊C4—1221no—
432C2×C4⋊C4—1221no—
433C2×C4⋊C4—1221no—
434C2×C4⋊C4C22×D6111yescharacteristic
435C2×C4⋊C4C22×D6111yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C42—1221no—
443C2×C42—1221no—
444C2×C42C22×D6111yescharacteristic
445C2×C42C22×D6111yescharacteristic
446C2×C42C22×D6111yescharacteristic
447#107—1222no—
448#106—1222no—
449C4⋊C8—1222no—
450C4⋊C8—1222no—
451#103—1222no—
452#103—1222no—
453#102—1222no—
454#102—1222no—
455#102—1222no—
456#102—1222no—
457#102—1222no—
458#102—1222no—
459#97—1222no—
460C4×C8—1222no—
461#95—21no—
462#95—21no—
463#95—1221no—
464#95—1221no—
465#95—1221no—
466#95—1221no—
467#95—1221no—
468#95—1221no—
469#95—1221no—
470#95C22⋊D6111yescharacteristic
471#95C22⋊D6111yescharacteristic
472#95C22⋊D6111yescharacteristic
473#95C22⋊D6111yescharacteristic
474C24—21no—
475C24—21no—
476C2×Q8—612no—
477C2×Q8—1221no—
478C2×Q8—1221no—
479C2×Q8—1221no—
480C2×Q8—1221no—
481C2×Q8—1221no—
482C2×D4—24no—
483C2×D4—24no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—81no—
495C2×D4—81no—
496C2×D4—81no—
497C2×D4—81no—
498C2×D4#1175822212yes—
499C2×D4#1175822212yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—81no—
505C22×C4—81no—
506C22×C4—81no—
507C22×C4—81no—
508C22×C4—1221no—
509C22×C4—1221no—
510C22×C4—1221no—
511C22×C4—1221no—
512C22×C4C2×C22⋊D6111yescharacteristic
513C22×C4C2×C22⋊D6111yescharacteristic
514C22×C4C2×C22⋊D6111yescharacteristic
515C22×C4C2×C22⋊D6111yescharacteristic
516C22×C4C2×C22⋊D6111yescharacteristic
517C22×C4C2×C22⋊D6111yescharacteristic
518C22×C4C23×D6111yescharacteristic
519SD16—1228no—
520SD16—1228no—
521C2×C8—612no—
522C2×C8—612no—
523C2×C8—1221no—
524C2×C8—1221no—
525C2×C8—1221no—
526C2×C8—1221no—
527C2×C8—1221no—
528C2×C8—1221no—
529C2×C8—1221no—
530C2×C8—1221no—
531C2×C8—1221no—
532C2×C8—1221no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—612no—
538C4⋊C4—1221no—
539C4⋊C4—1224no—
540C4⋊C4—1221no—
541C4⋊C4—1221no—
542C4⋊C4—1221no—
543C4⋊C4—1221no—
544C4⋊C4—4881no—
545C4⋊C4—4881no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—81no—
549C22⋊C4—81no—
550C22⋊C4—81no—
551C22⋊C4—81no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—1224no—
557C42—4881no—
558C42D4×D6112yes—
559C42#1175822412yes—
560C23—22no—
561C23—22no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23C22×C22⋊D6111yescharacteristic
575Q8—1222no—
576Q8—1222no—
577Q8—2441no—
578Q8—2441no—
579D4—22no—
580D4—22no—
581D4—22no—
582D4—22no—
583D4—41no—
584D4—41no—
585D4—41no—
586D4—41no—
587D4—84no—
588D4—84no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—84no—
612C2×C4—84no—
613C2×C4—1222no—
614C2×C4—1222no—
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×C4—2441no—
624C2×C4—2441no—
625C2×C4#1451974812yes—
626C2×C4#1451974812yes—
627C2×C4C2×D4×D6111yescharacteristic
628C2×C4#41×D6111yescharacteristic
629C2×C4#41×D6111yescharacteristic
630C2×C4C2×#1175822411yescharacteristic
631C2×C4C2×#1175822211yescharacteristic
632C2×C4C2×#1175822211yescharacteristic
633C8—1222no—
634C8—1222no—
635C8—2441no—
636C8—2441no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22C2×#1451974811yescharacteristic
652C22#1684027311yescharacteristic
653C22#1684030811yescharacteristic
654C22#1684056511yescharacteristic
655C22#1684057311yescharacteristic
656C22#1684057311yescharacteristic
657C22#1684057311yescharacteristic
658C4—22no—
659C4—22no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4—41no—
664C4—81no—
665C4—81no—
666C4—4881no—
667C4—4881no—
668C4—2442no—
669C4—2442no—
670C4#1684027111yescharacteristic
671C4#1684027111yescharacteristic
672C4#1684029211yescharacteristic
673C4#1684029211yescharacteristic
674C2—82no—
675C2—82no—
676C2#2144905711yescharacteristic
677C2#2145533611yescharacteristic
678C2#2145535411yescharacteristic
679C2#2145600311yescharacteristic
680C2#2145607111yescharacteristic
681C2#2145644111yescharacteristic
682C2#2145650411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2328C2
socleC23×C61C22×D4
prime radicalC2×#127×C61C22
hypercenter#2328D61
hypocenterC61#23690
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ #376 ◁ #2328

Complements

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

NH ≅ G/Ntype
1. C2×#16839862C2semidirect
2. C2×C4×#11758200C2semidirect
3. #21448471C2semidirect
4. #21447301C2semidirect
5. #21447238C2semidirect
6. #21447207C2semidirect
7. #21447193C2semidirect
8. #21447136C2semidirect
9. #21447136C2semidirect
12. #21445676C2semidirect
13. #21445644C2semidirect
14. C4×#14519698C2semidirect
73. C4×Dic122D4semidirect
402. C61#23690semidirect

Maximal subgroups

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

subgroupindex
C2×#168398622
C2×C4×#117582002
#214484712
#214473012
#214472382
#214472072
#214471932
#214471362
#214470502
#214469072
#214456762
#214456442
C4×#145196982
C61×#23282
#2369061