Finite Group Databasebeta

← #29721334

Subgroups — #29721334

Order 15616.

828 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840056C211yesmaximal, characteristic, complemented
2C2×#16839816C211yesmaximal, characteristic
3#21454169C211yesmaximal, characteristic
4#21448347C211yesmaximal, characteristic
5#21447245C211yesmaximal, characteristic
6#21447016C211yesmaximal, characteristic
7#21447015C211yesmaximal, characteristic
8#21446765C211yesmaximal, characteristic, complemented
9#21446581C211yesmaximal, characteristic, complemented
10#21446561C211yesmaximal, characteristic, complemented
11#21446560C211yesmaximal, characteristic, complemented
12#21446510C211yesmaximal, characteristic, complemented
13#21446507C211yesmaximal, characteristic, complemented
14#21445823C211yesmaximal, characteristic, complemented
15C61×#2075C211yesmaximal, characteristic
16C2×#14519776C2211yescharacteristic
17C2×#14519756C2211yescharacteristic
18C2×#14519754—21no—
19C2×#14519742C2211yescharacteristic
20C22×C4×Dic61C2211yescharacteristic
21#16840056—24no—
22#16839816—24no—
23C2×#14519710C2211yescharacteristic
24C2×#14519709C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519702C2211yescharacteristic
29C2×#14519702C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33C2×#14519687C2211yescharacteristic
34C2×#14519687C2211yescharacteristic
35#16839667C2211yescharacteristic
36#16839666—21no—
37#16839661C2211yescharacteristic
38#16839659—21no—
39#16839658C2211yescharacteristic
40#16839658C2211yescharacteristic
41#16839644—21no—
42#16839634—21no—
43#16839631C2211yescharacteristic
44#16839622C2211yescharacteristic
45#16839620—21no—
46C4⋊C4×Dic61C2211yescharacteristic
47#16839613—21no—
48C22⋊C4×Dic61—21no—
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54C2×#107×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C61×#380C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×Dic122—21no—
62C22×Dic122C2311yescharacteristic
63C23×Dic61D411yescharacteristic
64C23×Dic61D411yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67#14519776—22no—
68#14519776—22no—
69#14519756—22no—
70#14519756—22no—
71#14519754—44no—
72#14519742—22no—
73#14519742—22no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C4×Dic61—22no—
88C2×C4×Dic61—22no—
89C2×C4×Dic61—21no—
90C2×C4×Dic61—21no—
91C2×C4×Dic61D411yescharacteristic
92C2×C4×Dic61D411yescharacteristic
93C2×C4×Dic61C2311yescharacteristic
94C2×C4×Dic61C2311yescharacteristic
95#14519710—22no—
96#14519709—22no—
97#14519708—22no—
98#14519706—22no—
99#14519706D414yes—
100#14519702—22no—
101#14519702—22no—
102#14519700—22no—
103#14519700—22no—
104C22⋊#92418—22no—
105#14519687—22no—
106#14519687—22no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114C23×C4×C61C2311yescharacteristic
115C22×C8×C61C2311yescharacteristic
116C22×C8×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C22⋊C4×C61—21no—
122C2×C22⋊C4×C61—21no—
123#107×C61—22no—
124C22⋊C8×C61—22no—
125#95×C61—21no—
126#95×C61—21no—
127C24×C61C2×D411yescharacteristic
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2411yescharacteristic
140C22×Dic61—22no—
141C22×Dic61—21no—
142C22×Dic61—21no—
143C22×Dic61—22no—
144C22×Dic61—22no—
145C22×Dic61—22no—
146C22×Dic61—22no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—41no—
150C22×Dic61C2×D411yescharacteristic
151C22×Dic61C2×D411yescharacteristic
152C22×Dic61C2×D411yescharacteristic
153C22×Dic61C2×D411yescharacteristic
154C2×Dic122—21no—
155C2×Dic122—21no—
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122—42no—
160C2×Dic122—42no—
161C2×Dic122—42no—
162C2×Dic122#4112yes—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61C2×D412yes—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C22⋊C4×C61—42no—
178C22⋊C4×C61—42no—
179C22⋊Dic61—24no—
180C22⋊Dic61—42no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—42no—
187C4⋊Dic61#4112yes—
188#11758196—24no—
189#11758196—42no—
190#11758196—42no—
191#11758196—42no—
192#11758196—42no—
193#11758196—42no—
194#11758196—42no—
195C4×Dic61—21no—
196C4×Dic61—21no—
197C4×Dic61—22no—
198C4×Dic61—22no—
199C4×Dic61—42no—
200C4×Dic61—42no—
201C4×Dic61C2×D412yes—
202C4×Dic61#4112yes—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418C2×D412yes—
209C23×C61—21no—
210C23×C61—21no—
211C23×C61—21no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61AGL(1,ℤ/8)12yes—
216C23×C61C22×D411yescharacteristic
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61C22×D411yescharacteristic
237C2×C4×C61C2×#4111yescharacteristic
238C2×C4×C61C2×#4111yescharacteristic
239C2×C4×C61C2×#4111yescharacteristic
240C2×C4×C612−1+411yescharacteristic
241C2×C4×C612−1+411yescharacteristic
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—44no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—44no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61#12112yes—
265C2×Dic61#12112yes—
266C2×Dic61#13712yes—
267C2×Dic61#13712yes—
268Dic122—22no—
269Dic122—22no—
270Dic122—41no—
271Dic122—41no—
272Dic122—84no—
273C8×C61—22no—
274C8×C61—41no—
275#92418—22no—
276#92418—41no—
277#24711—611nomaximal, Sylow
278C22×C61—22no—
279C22×C61—22no—
280C22×C61—22no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61C2×#12111yescharacteristic
286C22×C61#52511yescharacteristic
287C22×C61#53611yescharacteristic
288C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
289C22×C61C2×#13711yescharacteristic
290C22×C61C2×#13711yescharacteristic
291C22×C61#57511yescharacteristic
292C4×C61—41no—
293C4×C61—81no—
294C4×C61—81no—
295C4×C61—81no—
296C4×C61—81no—
297C4×C61#54711yescharacteristic
298C4×C61#54811yescharacteristic
299C4×C61#55211yescharacteristic
300C4×C61#55611yescharacteristic
301Dic61—22no—
302Dic61—42no—
303Dic61—42no—
304Dic61—41no—
305Dic61—41no—
306Dic61—81no—
307Dic61—81no—
308Dic61#47014yes—
309C2×#477—611no—
310C2×#432—611no—
311#2857—611no—
312C4×C22⋊Q8—611no—
313#2075—611no—
314#2075D6111yescharacteristic
315#2035—611no—
316#2035—611no—
317#1987—611no—
318#1948—611no—
319#1944—611no—
320#1944—611no—
321#1935—611no—
322#1935—611no—
323#1803—611no—
324C2×C61—42no—
325C2×C61#241511yescharacteristic
326C2×C61C2×#47011yescharacteristic
327C2×C61#305511yescharacteristic
328C2×C61#311211yescharacteristic
329C2×C61#311611yescharacteristic
330C2×C61#323711yescharacteristic
331C2×C61#323811yescharacteristic
332C2×C4⋊Q8—611no—
333C2×C22⋊Q8—611no—
334C2×C22⋊Q8—1221no—
335C2×C4×Q8—611no—
336C22×C42—611no—
337#477—1224no—
338#432—1224no—
339C2×#107—611no—
340C2×#107C2×D6111yescharacteristic
341C2×#106—611no—
342C2×#106—611no—
343C2×C4⋊C8—611no—
344C2×C4⋊C8—611no—
345C2×#103—611no—
346C2×#103—611no—
347C2×#103—611no—
348C2×#103—611no—
349C2×C22⋊C8—611no—
350C2×C22⋊C8C2×D6111yescharacteristic
351C2×#97—611no—
352C2×#97—611no—
353#391—611no—
354#391—1221no—
355#389—611no—
356#389—611no—
357#389—611no—
358#389—1221no—
359#387—1221no—
360#385—1221no—
361#384—611no—
362#380—611no—
363#380—1221no—
364#380C2×D6111yescharacteristic
365#380C2×D6111yescharacteristic
366C4×C4⋊C4—611no—
367C4×C4⋊C4—1221no—
368C4×C22⋊C4—1221no—
369#340—611no—
370#340—611no—
371#340—611no—
372#340—611no—
373#340—611no—
374#340C2×D6111yescharacteristic
375#340C2×D6111yescharacteristic
376#340C2×D6111yescharacteristic
377C61#2471111yescharacteristic, complemented, Sylow
378C22×Q8—611no—
379C22×Q8—1221no—
380C23×C4—611no—
381C23×C4—611no—
382C23×C4C22×D6111yescharacteristic
383C22×C8—611no—
384C22×C8—611no—
385C22×C8C22×D6111yescharacteristic
386C22×C8C22×D6111yescharacteristic
387C4⋊Q8—1222no—
388C4⋊Q8—1222no—
389C22⋊Q8—1222no—
390C22⋊Q8—1222no—
391C22⋊Q8—2444no—
392C4×Q8—1222no—
393C4×Q8—1222no—
394C2×C4⋊C4—611no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4—611no—
397C2×C4⋊C4—1221no—
398C2×C4⋊C4—1221no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4—1221no—
403C2×C4⋊C4—1221no—
404C2×C4⋊C4—1221no—
405C2×C4⋊C4C22×D6111yescharacteristic
406C2×C4⋊C4C22×D6111yescharacteristic
407C2×C4⋊C4C22×D6111yescharacteristic
408C2×C4⋊C4C22×D6111yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—1221no—
412C2×C22⋊C4—1221no—
413C2×C42—611no—
414C2×C42—611no—
415C2×C42—611no—
416C2×C42—611no—
417C2×C42—1222no—
418C2×C42—1222no—
419C2×C42—1221no—
420C2×C42—1221no—
421#107—22no—
422#107—1222no—
423#106—1222no—
424#106—1222no—
425C4⋊C8—614no—
426C4⋊C8—1222no—
427#103—1222no—
428#103—1222no—
429#103—1222no—
430#103—1222no—
431C22⋊C8—22no—
432C22⋊C8—1222no—
433#97—1222no—
434#97—1222no—
435#95—21no—
436#95—21no—
437#95—1221no—
438#95—1221no—
439#95—1221no—
440#95—1221no—
441#95—1221no—
442#95—1221no—
443#95—1221no—
444C24D4×D6111yescharacteristic
445C2×Q8—612no—
446C2×Q8—1221no—
447C2×Q8—1221no—
448C2×Q8—1221no—
449C2×Q8—1221no—
450C2×Q8—1221no—
451C2×Q8—2442no—
452C2×Q8—2442no—
453C2×Q8—2442no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—1222no—
469C22×C4—1222no—
470C22×C4—1222no—
471C22×C4—1222no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1222no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—2441no—
478C22×C4D4×D6111yescharacteristic
479C22×C4C23×D6111yescharacteristic
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—612no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8D4×D6112yes—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—612no—
501C4⋊C4—1224no—
502C4⋊C4—1221no—
503C4⋊C4—1221no—
504C4⋊C4—1221no—
505C4⋊C4—1221no—
506C4⋊C4—1221no—
507C4⋊C4—2442no—
508C4⋊C4—2442no—
509C4⋊C4—2442no—
510C4⋊C4—2442no—
511C4⋊C4—2442no—
512C4⋊C4—2442no—
513C4⋊C4—2442no—
514C22⋊C4—42no—
515C22⋊C4—42no—
516C22⋊C4—1224no—
517C22⋊C4—2442no—
518C42—612no—
519C42—612no—
520C42—1222no—
521C42—1222no—
522C42—1221no—
523C42—1221no—
524C42—2442no—
525C42—2442no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23#1451980112yes—
533C23C2×D4×D6111yescharacteristic
534Q8—1222no—
535Q8—1222no—
536Q8—4884no—
537Q8—2441no—
538Q8—2441no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—612no—
559C2×C4—612no—
560C2×C4—612no—
561C2×C4—612no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—1221no—
566C2×C4—1222no—
567C2×C4—1222no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—1221no—
571C2×C4—1221no—
572C2×C4—2444no—
573C2×C4—2444no—
574C2×C4—2441no—
575C2×C4—2441no—
576C2×C4—2441no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4C2×D4×D6111yescharacteristic
585C2×C4#41×D6111yescharacteristic
586C2×C4#41×D6111yescharacteristic
587C2×C4#41×D6111yescharacteristic
588C2×C4#1451982411yescharacteristic
589C2×C4#1451982411yescharacteristic
590C8—22no—
591C8—41no—
592C8—1222no—
593C8—2441no—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22#121×D6111yescharacteristic
602C22#1684027011yescharacteristic
603C22#1684033411yescharacteristic
604C22C2×#1451980111yescharacteristic
605C22#137×D6111yescharacteristic
606C22#137×D6111yescharacteristic
607C22#1684055911yescharacteristic
608C4—41no—
609C4—81no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4—614no—
614C4—1222no—
615C4—4881no—
616C4—4881no—
617C4—2442no—
618C4—2441no—
619C4—2441no—
620C4—2442no—
621C4#1684041011yescharacteristic
622C4#1684042011yescharacteristic
623C4#1684044811yescharacteristic
624C4#1684047911yescharacteristic
625C2—42no—
626C2#2144924311yescharacteristic
627C2#470×D6111yescharacteristic
628C2#2145543511yescharacteristic
629C2#2145593811yescharacteristic
630C2#2145597611yescharacteristic
631C2#2145703011yescharacteristic
632C2#2145703811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2075C2
socleC23×C61C22×D4
prime radicalC24×C61C2×D4
hypercenter#2075D61
hypocenterC61#24711
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2075

Complements

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

NH ≅ G/Ntype
1. C2×#16840056C2semidirect
8. #21446765C2semidirect
9. #21446581C2semidirect
10. #21446561C2semidirect
11. #21446560C2semidirect
12. #21446510C2semidirect
13. #21446507C2semidirect
14. #21445823C2semidirect
377. C61#24711semidirect

Maximal subgroups

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

subgroupindex
C2×#168400562
C2×#168398162
#214541692
#214483472
#214472452
#214470162
#214470152
#214467652
#214465812
#214465612
#214465602
#214465102
#214465072
#214458232
C61×#20752
#2471161