Finite Group Databasebeta

← #29729520

Subgroups — #29729520

Order 15616.

850 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839966C211yesmaximal, characteristic
2C2×#16839886C211yesmaximal, characteristic, complemented
3#21451033C211yesmaximal, characteristic, complemented
4#21450740C211yesmaximal, characteristic
5#21447201C211yesmaximal, characteristic, complemented
6#21447137C211yesmaximal, characteristic
7#21447133C211yesmaximal, characteristic
8#21446676C211yesmaximal, characteristic
9#21446671C211yesmaximal, characteristic
10#21446619C211yesmaximal, characteristic, complemented
11#21446579C211yesmaximal, characteristic, complemented
12#21446494C211yesmaximal, characteristic, complemented
13#21446492C211yesmaximal, characteristic, complemented
14#21445633C211yesmaximal, characteristic
15C61×#2066C211yesmaximal, characteristic, complemented
16C22×#11758190C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C2×#14519775C2211yescharacteristic
19C2×#14519755—21no—
20C2×C4×Dic122C2211yescharacteristic
21C2×#14519739C2211yescharacteristic
22#16839966—24no—
23#16839886—24no—
24C2×#14519708C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519702C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519700C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519699C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×C4×#92418C2211yescharacteristic
34C2×C8×Dic61C2211yescharacteristic
35C2×C8×Dic61C2211yescharacteristic
36#16839704—21no—
37#16839703—21no—
38#16839686—21no—
39#16839684—21no—
40#16839669C2211yescharacteristic
41#16839668C2211yescharacteristic
42#16839667C2211yescharacteristic
43#16839666—21no—
44#16839664C2211yescharacteristic
45#16839663C2211yescharacteristic
46#16839658C2211yescharacteristic
47#16839631C2211yescharacteristic
48#16839626—21no—
49#16839621—21no—
50C4⋊C4×Dic61C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54C2×#106×C61C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×#103×C61C2211yescharacteristic
57C2×#103×C61C2211yescharacteristic
58C61×#391C2211yescharacteristic
59C61×#389C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×Dic122D411yescharacteristic
62C22×Dic122C2311yescharacteristic
63C22×D244C2311yescharacteristic
64C22×C4×D61—21no—
65C2×#11758190—22no—
66C2×#11758190—22no—
67C2×#11758190—41no—
68C2×#11758201—22no—
69C2×#11758201—22no—
70C2×#11758201—41no—
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73#14519775—22no—
74#14519775—22no—
75#14519755—44no—
76C4×Dic122—22no—
77C4×Dic122—22no—
78#14519739—22no—
79#14519739—22no—
80C2×C4⋊Dic61D411yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×#11758196D411yescharacteristic
89C2×#11758196D411yescharacteristic
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61C2311yescharacteristic
97C2×C4×Dic61C2311yescharacteristic
98#14519708—41no—
99#14519706—22no—
100#14519706D414yes—
101#14519702—41no—
102#14519701—22no—
103#14519700—22no—
104#14519700—22no—
105#14519699—22no—
106#14519697—22no—
107C4×#92418—22no—
108C8×Dic61—22no—
109C8×Dic61—22no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118C22×Q8×C61C2311yescharacteristic
119C22×C8×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C2×C4⋊C4×C61—21no—
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C42×C61C2311yescharacteristic
126#106×C61—41no—
127C4⋊C8×C61—22no—
128#103×C61—22no—
129#103×C61—41no—
130#95×C61—21no—
131#95×C61—21no—
132#95×C61—21no—
133C23×D61—21no—
134C2×Q8×C61—21no—
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61—21no—
138C2×Q8×C61—21no—
139C2×Q8×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2411yescharacteristic
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61C2×D411yescharacteristic
151C22×Dic61C2×D411yescharacteristic
152C22×Dic61C2×D411yescharacteristic
153C22×Dic61C2×D411yescharacteristic
154C2×D244—21no—
155C2×D244—21no—
156C2×D244—21no—
157C2×D244—21no—
158C2×D244—21no—
159C2×D244#4112yes—
160C2×C4×D61—42no—
161C2×C4×D61—42no—
162C2×C4×D61—42no—
163C2×Dic122—22no—
164C2×Dic122—22no—
165C2×Dic122—21no—
166C2×Dic122—21no—
167C2×Dic122—21no—
168C2×Dic122—21no—
169C2×Dic122—21no—
170C2×Dic122—21no—
171C2×Dic122SD1614yescomplemented
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—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—42no—
185C42×C61—21no—
186C42×C61—21no—
187#11758201—44no—
188#11758198—42no—
189#11758198—42no—
190#11758198—42no—
191#11758198—81no—
192#11758198—81no—
193C4⋊Dic61—22no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198#11758196—22no—
199#11758196—22no—
200#11758196—42no—
201#11758196—42no—
202#11758196—42no—
203#11758196—42no—
204#11758196—81no—
205C4×Dic61—21no—
206C4×Dic61—21no—
207C4×Dic61—42no—
208C4×Dic61C2×D412yes—
209C4×Dic61#4112yes—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418C2×D412yes—
215C2×#92418#4112yes—
216#11758190—44no—
217C23×C61C22×D411yescharacteristic
218C22×D61—22no—
219C22×D61—41no—
220C22×D61—41no—
221C22×D61—41no—
222C22×D61—41no—
223C22×D61—41no—
224C22×D61—41no—
225Q8×C61—41no—
226Q8×C61—41no—
227Q8×C61—41no—
228Q8×C61—41no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61C2×SD1612yes—
247C2×C4×C61C22×D411yescharacteristic
248C2×C4×C61C2×#4111yescharacteristic
249C2×C4×C61C2×#4111yescharacteristic
250C2×C4×C61C2×#4111yescharacteristic
251C2×C4×C61H(5,𝔽2)11yescharacteristic
252C2×C4×C612−1+411yescharacteristic
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61#12112yes—
270C2×Dic61#12112yes—
271C2×Dic61C2×SD1612yes—
272C2×Dic61C2×SD1612yes—
273C2×Dic61#13512yes—
274D244—22no—
275D244—22no—
276D244—41no—
277D244—41no—
278C4×D61—84no—
279Dic122—28no—
280Dic122—41no—
281Dic122—41no—
282Dic122—41no—
283Dic122—41no—
284C8×C61—22no—
285C8×C61—41no—
286#92418—22no—
287#92418—22no—
288#25293—611nomaximal, Sylow
289C22×C61C2×#12111yescharacteristic
290C22×C61#54811yescharacteristic
291C22×C61#55011yescharacteristic
292C22×C61C22×SD1611yescharacteristic
293C22×C61C2×#13511yescharacteristic
294C22×C61#57711yescharacteristic
295C22×C61#57811yescharacteristic
296C2×D61—42no—
297C2×D61—42no—
298C2×D61—42no—
299C2×D61—81no—
300C2×D61—81no—
301C2×D61—81no—
302C2×D61—81no—
303C4×C61—22no—
304C4×C61—41no—
305C4×C61—81no—
306C4×C61—81no—
307C4×C61—81no—
308C4×C61—81no—
309C4×C61#52911yescharacteristic
310C4×C61#54211yescharacteristic
311C4×C61#54611yescharacteristic
312C4×C61#54811yescharacteristic
313Dic61—22no—
314Dic61—22no—
315Dic61—41no—
316Dic61—81no—
317Dic61—81no—
318Dic61—81no—
319Dic61#46514yes—
320C2×#461—611no—
321C2×C8×Q8—611no—
322#2568—611no—
323#2538—611no—
324#2066—611no—
325#2066D6111yescharacteristic, complemented
326#2055—611no—
327#2055—611no—
328#1968—611no—
329#1968—611no—
330#1956—611no—
331#1948—611no—
332#1933—611no—
333#1933—611no—
334C4×#102—611no—
335C2×C61#242611yescharacteristic
336C2×C61C2×#46511yescharacteristic
337C2×C61#306311yescharacteristic
338C2×C61#335911yescharacteristic
339C2×C61#336011yescharacteristic
340C2×C61#339211yescharacteristic
341C2×C61#339311yescharacteristic
342D61—82no—
343C22×SD16—611no—
344C22×SD16—611no—
345C2×C4⋊Q8—611no—
346C2×C22⋊Q8—1221no—
347C2×C4×Q8—611no—
348C2×C4×D4—611no—
349#461—1224no—
350C8×Q8—1224no—
351C2×#106—611no—
352C2×#106C2×D6111yescharacteristic
353C2×C4⋊C8—611no—
354C2×C4⋊C8—611no—
355C2×C4⋊C8C2×D6111yescharacteristic
356C2×#103—611no—
357C2×#103—611no—
358C2×#103—611no—
359C2×#103—611no—
360C2×#103C2×D6111yescharacteristic
361C2×#103C2×D6111yescharacteristic
362C2×#102—611no—
363C2×#102—611no—
364C2×C4×C8—611no—
365C2×C4×C8—611no—
366C2×C4×C8—611no—
367#400—1221no—
368#400—1221no—
369#396—1221no—
370#396—1221no—
371#391—611no—
372#391—611no—
373#391—611no—
374#391—1221no—
375#391C2×D6111yescharacteristic
376#390—611no—
377#390—611no—
378#389—611no—
379#389C2×D6111yescharacteristic
380#384—611no—
381#382—1221no—
382#380—1221no—
383C4×C4⋊C4—611no—
384#340—611no—
385#340—611no—
386#340—611no—
387#340C2×D6111yescharacteristic
388C61#2529311yescharacteristic, complemented, Sylow
389C22×Q8—611no—
390C22×Q8—611no—
391C22×Q8C22×D6111yescharacteristic
392C22×D4—611no—
393C23×C4—1221no—
394C2×SD16—1222no—
395C2×SD16—1222no—
396C2×SD16—1222no—
397C2×SD16—1222no—
398C2×SD16—2441no—
399C2×SD16—2441no—
400C22×C8—611no—
401C22×C8—611no—
402C22×C8C22×D6111yescharacteristic
403C22×C8C22×D6111yescharacteristic
404C4⋊Q8—1222no—
405C4⋊Q8—1222no—
406C22⋊Q8—2444no—
407C4×Q8—1222no—
408C4×Q8—1222no—
409C4×D4—1222no—
410C4×D4—1222no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—611no—
413C2×C4⋊C4—611no—
414C2×C4⋊C4—611no—
415C2×C4⋊C4—611no—
416C2×C4⋊C4—611no—
417C2×C4⋊C4—1221no—
418C2×C4⋊C4—1221no—
419C2×C4⋊C4—1221no—
420C2×C4⋊C4—1221no—
421C2×C4⋊C4—1221no—
422C2×C4⋊C4C22×D6111yescharacteristic
423C2×C4⋊C4C22×D6111yescharacteristic
424C2×C4⋊C4C22×D6111yescharacteristic
425C2×C22⋊C4—1221no—
426C2×C22⋊C4—1221no—
427C2×C22⋊C4—1221no—
428C2×C22⋊C4—1221no—
429C2×C22⋊C4—1221no—
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—1221no—
433C2×C42C22×D6111yescharacteristic
434#106—41no—
435#106—2441no—
436C4⋊C8—22no—
437C4⋊C8—614no—
438C4⋊C8—1222no—
439#103—22no—
440#103—41no—
441#103—1222no—
442#103—1222no—
443#103—1222no—
444#103—2441no—
445#102—1222no—
446#102—1222no—
447C4×C8—1222no—
448C4×C8—1222no—
449C4×C8—1222no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—1221no—
454#95—1221no—
455#95—1221no—
456#95—1221no—
457#95—1221no—
458#95—1221no—
459#95—1221no—
460#95—1221no—
461C24—1221no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—614no—
469C2×Q8—1222no—
470C2×Q8—1222no—
471C2×Q8—1221no—
472C2×Q8—1221no—
473C2×Q8—1221no—
474C2×Q8—1221no—
475C2×Q8—1221no—
476C2×Q8—1221no—
477C2×D4—612no—
478C2×D4—1221no—
479C2×D4—1221no—
480C2×D4—1221no—
481C2×D4—1221no—
482C2×D4—1221no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—611no—
490C22×C4—611no—
491C22×C4—1221no—
492C22×C4—1221no—
493C22×C4—1221no—
494C22×C4—2442no—
495C22×C4—2442no—
496C22×C4—2442no—
497C22×C4D4×D6111yescharacteristic
498C22×C4D4×D6111yescharacteristic
499C22×C4C23×D6111yescharacteristic
500SD16—2444no—
501SD16—2444no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—612no—
508C2×C8—612no—
509C2×C8—1221no—
510C2×C8—1221no—
511C2×C8—1221no—
512C2×C8—1221no—
513C2×C8D4×D6112yes—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—42no—
521C4⋊C4—1222no—
522C4⋊C4—1222no—
523C4⋊C4—1222no—
524C4⋊C4—1221no—
525C4⋊C4—1221no—
526C4⋊C4—1221no—
527C4⋊C4—1221no—
528C4⋊C4—4881no—
529C4⋊C4—2442no—
530C4⋊C4—2442no—
531C4⋊C4—2442no—
532C4⋊C4—2442no—
533C22⋊C4—4881no—
534C22⋊C4—4881no—
535C22⋊C4—2442no—
536C22⋊C4—2442no—
537C22⋊C4—2442no—
538C42—21no—
539C42—21no—
540C42—612no—
541C42—612no—
542C42—1221no—
543C42—1221no—
544C42—2442no—
545C23—1222no—
546C23—2441no—
547C23—2441no—
548C23—2441no—
549C23—2441no—
550C23—2441no—
551C23—2441no—
552C23C2×D4×D6111yescharacteristic
553Q8—41no—
554Q8—41no—
555Q8—41no—
556Q8—41no—
557Q8—1228no—
558Q8—2441no—
559Q8—2441no—
560Q8—2441no—
561Q8—2441no—
562D4—1222no—
563D4—1222no—
564D4—2441no—
565D4—2441no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—612no—
584C2×C4—612no—
585C2×C4—612no—
586C2×C4—612no—
587C2×C4—612no—
588C2×C4—1221no—
589C2×C4—1221no—
590C2×C4—1221no—
591C2×C4—1221no—
592C2×C4—1221no—
593C2×C4—1221no—
594C2×C4—1221no—
595C2×C4—4884no—
596C2×C4—2441no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4—2441no—
604C2×C4—2441no—
605C2×C4SD16×D6112yes—
606C2×C4C2×D4×D6111yescharacteristic
607C2×C4#41×D6111yescharacteristic
608C2×C4#41×D6111yescharacteristic
609C2×C4#41×D6111yescharacteristic
610C2×C4#1451982211yescharacteristic
611C2×C4#1451982511yescharacteristic
612C8—22no—
613C8—41no—
614C8—1222no—
615C8—1222no—
616C22—4881no—
617C22—4881no—
618C22—4881no—
619C22—4881no—
620C22—2442no—
621C22—2442no—
622C22—2442no—
623C22#121×D6111yescharacteristic
624C22#1684042211yescharacteristic
625C22#1684043011yescharacteristic
626C22C2×SD16×D6111yescharacteristic
627C22#135×D6111yescharacteristic
628C22#1684057111yescharacteristic
629C22#1684057811yescharacteristic
630C4—22no—
631C4—41no—
632C4—81no—
633C4—81no—
634C4—81no—
635C4—81no—
636C4—614no—
637C4—1222no—
638C4—1222no—
639C4—4881no—
640C4—4881no—
641C4—4881no—
642C4—2441no—
643C4#1684029511yescharacteristic
644C4#1684038211yescharacteristic
645C4#1684040111yescharacteristic
646C4#1684042211yescharacteristic
647C2—4882no—
648C2#2144938011yescharacteristic
649C2#465×D6111yescharacteristic
650C2#2145550711yescharacteristic
651C2#2145846011yescharacteristic
652C2#2145847111yescharacteristic
653C2#2145879511yescharacteristic
654C2#2145880211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2066C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenter#2066D61
hypocenterC61#25293
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2066

Complements

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

NH ≅ G/Ntype
2. C2×#16839886C2semidirect
3. #21451033C2semidirect
5. #21447201C2semidirect
10. #21446619C2semidirect
11. #21446579C2semidirect
12. #21446494C2semidirect
13. #21446492C2semidirect
15. C61×#2066C2semidirect
171. C2×Dic122SD16semidirect
325. #2066D61semidirect
388. C61#25293semidirect

Maximal subgroups

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

subgroupindex
C2×#168399662
C2×#168398862
#214510332
#214507402
#214472012
#214471372
#214471332
#214466762
#214466712
#214466192
#214465792
#214464942
#214464922
#214456332
C61×#20662
#2529361