Finite Group Databasebeta

← #30615840

Subgroups — #30615840

Order 15616.

906 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840765C211yesmaximal, characteristic
2C2×#16840726C211yesmaximal, characteristic
3#21461879C211yesmaximal, characteristic, complemented
4#21461878C211yesmaximal, characteristic, complemented
5#21461877C211yesmaximal, characteristic, complemented
6#21461876C211yesmaximal, characteristic, complemented
7#21461875C211yesmaximal, characteristic, complemented
8#21461874C211yesmaximal, characteristic, complemented
9#21461873C211yesmaximal, characteristic, complemented
10#21461872C211yesmaximal, characteristic, complemented
11#21461485C211yesmaximal, characteristic
12#21461485C211yesmaximal, characteristic
13#21461485C211yesmaximal, characteristic
14C2×#16840628C211yesmaximal, characteristic
15#21448298C211yesmaximal, characteristic
16C22×#11758217C2211yescharacteristic
17C22×#11758217C2211yescharacteristic
18C23×#92420C2211yescharacteristic
19C23×#92420C2211yescharacteristic
20#16840765—24no—
21C2×#14519844C2211yescharacteristic
22C2×#14519844C2211yescharacteristic
23C2×C4⋊#92420C2211yescharacteristic
24C2×C4⋊#92420C2211yescharacteristic
25#16840726—24no—
26C2×#14519832C2211yescharacteristic
27C2×#14519832C2211yescharacteristic
28C2×C4×#92420C2211yescharacteristic
29C2×C4×#92420C2211yescharacteristic
30#16840628C2211yescharacteristic
31#16840628C2211yescharacteristic
32#16840628C2211yescharacteristic
33#16840628C2211yescharacteristic
34#16840628C2211yescharacteristic
35#16840628C2211yescharacteristic
36#16840628C2211yescharacteristic
37#16840628C2211yescharacteristic
38#16840628C2211yescharacteristic
39#16840628C2211yescharacteristic
40#16840628C2211yescharacteristic
41#16840628C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46C2×#14519733C2211yescharacteristic
47C2×#14519733C2211yescharacteristic
48C22×C4×Dic61C2211yescharacteristic
49#16839659C411yescharacteristic
50#16839659C411yescharacteristic
51#16839657C411yescharacteristic
52#16839657C411yescharacteristic
53#16839637C411yescharacteristic
54#16839635C411yescharacteristic
55#16839634C411yescharacteristic
56C4⋊C4×Dic61C2211yescharacteristic
57C4⋊C4×Dic61C2211yescharacteristic
58#16839613C2211yescharacteristic
59#16839613C2211yescharacteristic
60C61×#385C411yescharacteristic
61C2×#11758217—22no—
62C2×#11758217—22no—
63C2×#11758217—22no—
64C2×#11758217—22no—
65C2×#11758217—22no—
66C2×#11758217D414yes—
67C22×#92420—22no—
68C22×#92420—22no—
69C22×#92420—22no—
70C22×#92420—22no—
71C22×#92420—22no—
72C22×#92420Q814yes—
73C22×#92420C2311yescharacteristic
74C22×#92420C2311yescharacteristic
75C22×#92420C2311yescharacteristic
76C22×#92420C2311yescharacteristic
77C22×#92420C2311yescharacteristic
78C22×#92420C2311yescharacteristic
79C22×#92420C2311yescharacteristic
80C22×#92420C2311yescharacteristic
81#14519844—22no—
82#14519844—22no—
83C4⋊#92420—22no—
84C4⋊#92420—22no—
85#14519832—22no—
86#14519832—22no—
87C4×#92420—22no—
88C4×#92420—22no—
89C23×Dic61C2×C411yescharacteristic
90C23×Dic61C2311yescharacteristic
91#14519733—22no—
92#14519733—22no—
93#14519733—22no—
94#14519733—22no—
95C2×C4⋊Dic61C2×C411yescharacteristic
96C2×C4⋊Dic61C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×#11758196C2×C411yescharacteristic
99C2×#11758196C2×C411yescharacteristic
100C2×#11758196C2×C411yescharacteristic
101C2×#11758196C2×C411yescharacteristic
102C2×#11758196C2×C411yescharacteristic
103C2×#11758196C2×C411yescharacteristic
104C2×#11758196C2×C411yescharacteristic
105C2×C22⋊Dic61C2×C411yescharacteristic
106C2×C22⋊Dic61C2×C411yescharacteristic
107C2×C4×Dic61—22no—
108C2×C4×Dic61—22no—
109C2×C4×Dic61C2×C411yescharacteristic
110C2×C4×Dic61C2×C411yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112C2×C4×Dic61C2311yescharacteristic
113C2×C4×Dic61C2311yescharacteristic
114C2×C4×Dic61C2311yescharacteristic
115C2×C4×Dic61C2311yescharacteristic
116C2×C4×Dic61C2311yescharacteristic
117#14519684C2×C411yescharacteristic
118#14519684C2×C411yescharacteristic
119#14519684C2×C411yescharacteristic
120#14519684C2×C411yescharacteristic
121#14519684C2×C411yescharacteristic
122#14519684C2×C411yescharacteristic
123C23×C4×C61C2×C411yescharacteristic
124C2×C4⋊C4×C61C2×C411yescharacteristic
125C2×C4⋊C4×C61C2×C411yescharacteristic
126C2×C22⋊C4×C61C2×C411yescharacteristic
127C2×C22⋊C4×C61C2×C411yescharacteristic
128#95×C61C2×C411yescharacteristic
129#95×C61C2×C411yescharacteristic
130C24×C61C22×C411yescharacteristic
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—41no—
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C22×C411yescharacteristic
139C22×C4×C61C22×C411yescharacteristic
140C22×Dic61—22no—
141C22×Dic61—22no—
142C22×Dic61—41no—
143C22×Dic61C22×C411yescharacteristic
144C22×Dic61C22×C411yescharacteristic
145C22×Dic61C22×C411yescharacteristic
146C22×Dic61C22×C411yescharacteristic
147C22×Dic61C22×C411yescharacteristic
148C22×Dic61C22×C411yescharacteristic
149C22×Dic61C22×C411yescharacteristic
150C22×Dic61C2×D412yes—
151C22×Dic61C2×Q812yes—
152C22×Dic61#4112yes—
153C22×Dic61#4112yes—
154C22×Dic61#4112yes—
155C22×Dic61#4112yes—
156C22×Dic61C2411yescharacteristic
157#11758217—28no—
158#11758217—44no—
159C2×#92420—28no—
160C2×#92420—21no—
161C2×#92420—21no—
162C2×#92420—21no—
163C2×#92420—21no—
164C2×#92420—21no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420—21no—
174C2×#92420—21no—
175C2×#92420—21no—
176C2×#92420—21no—
177C2×#92420—21no—
178C2×#92420—21no—
179C2×#92420—21no—
180C2×#92420—44no—
181C2×#92420C2×D412yes—
182C2×#92420C2×D412yes—
183C2×#92420C2×Q812yes—
184C2×#92420C2×Q812yes—
185C4⋊C4×C61—22no—
186C4⋊C4×C61—41no—
187C22⋊C4×C61—22no—
188C22⋊C4×C61—22no—
189C22⋊Dic61—22no—
190C22⋊Dic61—22no—
191C4⋊Dic61—22no—
192C4⋊Dic61—41no—
193#11758196—22no—
194#11758196—22no—
195#11758196—22no—
196#11758196—22no—
197#11758196—22no—
198#11758196—22no—
199#11758196—41no—
200#11758196—41no—
201C4×Dic61—22no—
202C4×Dic61—22no—
203C4×Dic61—21no—
204C4×Dic61—21no—
205C4×Dic61—21no—
206C4×Dic61—21no—
207C4×Dic61—21no—
208C4×Dic61—21no—
209C4×Dic61—21no—
210C4×Dic61—21no—
211C4×Dic61—21no—
212C4×Dic61—21no—
213C4×Dic61—21no—
214C4×Dic61—21no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61#11712yes—
220C23×C61C4×D412yes—
221C23×C61C4×Q812yes—
222C23×C61C23×C411yescharacteristic
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—44no—
241C2×C4×C61#13112yes—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—44no—
260C2×Dic61#11712yes—
261C2×Dic61C4×D412yes—
262C2×Dic61C4×Q812yes—
263C2×Dic61C22⋊Q814yes—
264C2×Dic61#12314yes—
265C2×Dic61#12514yes—
266C2×Dic61#12614yes—
267C2×Dic61#13112yes—
268C2×Dic61C22×D411yescharacteristic
269C2×Dic61C22×Q811yescharacteristic
270C2×Dic61C2×#4111yescharacteristic
271C2×Dic61C2×#4111yescharacteristic
272C2×Dic61C2×#4111yescharacteristic
273C2×Dic61C2×#4111yescharacteristic
274#92420—22no—
275#92420—22no—
276#92420—22no—
277#92420—22no—
278#92420—41no—
279#92420—41no—
280#92420—41no—
281#92420—41no—
282#21027—611nomaximal, Sylow
283C22×C61—22no—
284C22×C61—22no—
285C22×C61—22no—
286C22×C61—22no—
287C22×C61—22no—
288C22×C61—22no—
289C22×C61#38714yes—
290C22×C61C2×#11711yescharacteristic
291C22×C61C2×C4×D411yescharacteristic
292C22×C61C2×C4×Q811yescharacteristic
293C22×C61C2×#13111yescharacteristic
294C22×C61C2×#13111yescharacteristic
295C22×C61#56811yescharacteristic
296C22×C61#56811yescharacteristic
297C4×C61—22no—
298C4×C61—41no—
299C4×C61—41no—
300C4×C61—41no—
301C4×C61—41no—
302C4×C61—41no—
303Dic61—22no—
304Dic61—41no—
305Dic61—41no—
306Dic61—41no—
307Dic61—41no—
308Dic61—41no—
309Dic61#38714yes—
310Dic61C2×C22⋊Q811yescharacteristic
311Dic61C2×#12311yescharacteristic
312Dic61C2×#12511yescharacteristic
313Dic61C2×#12611yescharacteristic
314C2×#423—611no—
315C2×#405—611no—
316#2296—611no—
317#1917—611no—
318#1917—611no—
319#1917—611no—
320#1917—611no—
321#1916—611no—
322#1916—611no—
323#1916—611no—
324#1916—611no—
325#1729—611no—
326#1729—611no—
327#1729—611no—
328C2×#336—611no—
329C2×C61—24no—
330C2×C61C2×#38711yescharacteristic
331C2×C61#292511yescharacteristic
332C2×C61#292511yescharacteristic
333C2×C61#293311yescharacteristic
334C2×C61#293311yescharacteristic
335C2×C61#296011yescharacteristic
336C2×C61#296111yescharacteristic
337C22×M16—611no—
338C22×M16—611no—
339C23×C8—611no—
340C23×C8—611no—
341C2×#117—611no—
342C2×#117—611no—
343C22×C42—611no—
344#423—1224no—
345C2×C4⋊C8—611no—
346C2×C4⋊C8—611no—
347C2×C4⋊C8—611no—
348C2×C4⋊C8—611no—
349#405—1224no—
350C2×#97—611no—
351C2×#97—611no—
352C2×C4×C8—611no—
353C2×C4×C8—611no—
354#389—611no—
355#389—611no—
356#389—611no—
357#389—611no—
358#385—611no—
359#385—611no—
360#385—611no—
361#385#692311yescharacteristic
362C4×C4⋊C4—611no—
363C4×C4⋊C4—611no—
364C4×C4⋊C4—611no—
365C4×C4⋊C4—611no—
366#336—611no—
367#336—611no—
368#336—611no—
369#336—611no—
370#336—611no—
371#336—611no—
372#336—611no—
373#336—611no—
374#336—611no—
375#336—611no—
376#336—611no—
377#336—611no—
378#336—611no—
379#336—611no—
380#336—611no—
381#336—611no—
382C61#2102711yescharacteristic, complemented, Sylow
383C23×C4—611no—
384C23×C4—611no—
385C23×C4C2×#692311yescharacteristic
386C2×M16—614no—
387C2×M16—1222no—
388C2×M16—1222no—
389C2×M16—1222no—
390C2×M16—1222no—
391C2×M16—1222no—
392C22×C8—614no—
393C22×C8—611no—
394C22×C8—611no—
395C22×C8—611no—
396C22×C8—611no—
397C22×C8—611no—
398C22×C8—611no—
399C22×C8—611no—
400C22×C8—611no—
401C22×C8—1222no—
402C22×C8—1222no—
403C22×C8—1222no—
404C22×C8—1222no—
405C22×C8—1222no—
406#117—1222no—
407#117—1222no—
408#117—1222no—
409#117—1222no—
410C2×C4⋊C4—611no—
411C2×C4⋊C4—611no—
412C2×C4⋊C4—611no—
413C2×C4⋊C4—611no—
414C2×C4⋊C4—611no—
415C2×C4⋊C4—611no—
416C2×C4⋊C4—611no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4C2×#692311yescharacteristic
421C2×C4⋊C4C2×#692311yescharacteristic
422C2×C22⋊C4—611no—
423C2×C22⋊C4—611no—
424C2×C22⋊C4C2×#692311yescharacteristic
425C2×C22⋊C4C2×#692311yescharacteristic
426C2×C42—611no—
427C2×C42—611no—
428C2×C42—611no—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—1222no—
435C2×C42—1222no—
436C4⋊C8—1222no—
437C4⋊C8—1222no—
438C4⋊C8—1222no—
439C4⋊C8—1222no—
440#97—1222no—
441#97—1222no—
442C4×C8—1222no—
443C4×C8—1222no—
444#95—611no—
445#95—611no—
446#95—611no—
447#95—611no—
448#95—611no—
449#95—611no—
450#95C2×#692311yescharacteristic
451#95C2×#692311yescharacteristic
452C24C22×#692311yescharacteristic
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—41no—
456C22×C4—612no—
457C22×C4—612no—
458C22×C4—612no—
459C22×C4—612no—
460C22×C4—612no—
461C22×C4—612no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—1222no—
471C22×C4—1222no—
472C22×C4—2441no—
473C22×C4C22×#692311yescharacteristic
474C22×C4C22×#692311yescharacteristic
475C22×C4C22×#692311yescharacteristic
476C22×C4C22×#692311yescharacteristic
477C22×C4C22×#692311yescharacteristic
478C22×C4C22×#692311yescharacteristic
479M16—1228no—
480M16—2444no—
481C2×C8—612no—
482C2×C8—612no—
483C2×C8—612no—
484C2×C8—612no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—1228no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8—1221no—
496C2×C8—1221no—
497C2×C8—1221no—
498C2×C8—1221no—
499C2×C8—1221no—
500C2×C8—1221no—
501C2×C8—1221no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8—2444no—
507C4⋊C4—22no—
508C4⋊C4—41no—
509C4⋊C4—1222no—
510C4⋊C4—1222no—
511C4⋊C4—1222no—
512C4⋊C4—1222no—
513C4⋊C4—1222no—
514C4⋊C4—1222no—
515C4⋊C4—1222no—
516C4⋊C4—2441no—
517C4⋊C4—2441no—
518C4⋊C4—2441no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—1222no—
522C22⋊C4—1222no—
523C42—1221no—
524C42—1221no—
525C42—1221no—
526C42—1221no—
527C42—1222no—
528C42—1221no—
529C42—1222no—
530C42—1221no—
531C42—1221no—
532C42—1221no—
533C42—1221no—
534C42—1221no—
535C42—1221no—
536C42—1221no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23#1451985612yes—
542C23D4×#692312yes—
543C23Q8×#692312yes—
544C23C23×#692311yescharacteristic
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—44no—
563C2×C4—614no—
564C2×C4—614no—
565C2×C4—614no—
566C2×C4—614no—
567C2×C4—612no—
568C2×C4—611no—
569C2×C4—611no—
570C2×C4—612no—
571C2×C4—611no—
572C2×C4—611no—
573C2×C4—612no—
574C2×C4—611no—
575C2×C4—611no—
576C2×C4—612no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4—1221no—
581C2×C4—1221no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—1221no—
590C2×C4—1221no—
591C2×C4—1221no—
592C2×C4—1221no—
593C2×C4—1221no—
594C2×C4—2444no—
595C2×C4#1451986412yes—
596C8—1222no—
597C8—1222no—
598C8—1222no—
599C8—1222no—
600C8—2441no—
601C8—2441no—
602C8—2441no—
603C8—2441no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22#1684071114yes—
611C22C2×#1451985611yescharacteristic
612C22C2×D4×#692311yescharacteristic
613C22C2×Q8×#692311yescharacteristic
614C22C2×#1451986411yescharacteristic
615C22D61⋊#13111yescharacteristic
616C22#1684084011yescharacteristic
617C22#1684084111yescharacteristic
618C4—22no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—611no—
625C4—611no—
626C4—611no—
627C4—611no—
628C4—614no—
629C4—1222no—
630C4—2441no—
631C4—2441no—
632C4—2441no—
633C4—2441no—
634C4—2441no—
635C2—24no—
636C2C2×#1684071111yescharacteristic
637C2#2146251411yescharacteristic
638C2#2146251711yescharacteristic
639C2#2146255111yescharacteristic
640C2#2146255311yescharacteristic
641C2#2146260711yescharacteristic
642C2#2146261011yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#385C4
prime radicalC24×C61C22×C4
cosocleC22×Dic61C24
hypercenter#385#6923
hypocenterC61#21027
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
3. #21461879C2semidirect
4. #21461878C2semidirect
5. #21461877C2semidirect
6. #21461876C2semidirect
7. #21461875C2semidirect
8. #21461874C2semidirect
9. #21461873C2semidirect
10. #21461872C2semidirect
382. C61#21027semidirect

Maximal subgroups

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

subgroupindex
C2×#168407652
C2×#168407262
#214618792
#214618782
#214618772
#214618762
#214618752
#214618742
#214618732
#214618722
#214614852
C2×#168406282
#214482982
#2102761