Finite Group Databasebeta

← #29748132

Subgroups — #29748132

Order 15616.

764 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450193C211yesmaximal, characteristic
2#21448822C211yesmaximal, characteristic
3#21447142C211yesmaximal, characteristic, complemented
4#21447023C211yesmaximal, characteristic
5#21446961C211yesmaximal, characteristic, complemented
6#21446829C211yesmaximal, characteristic
7#21446766C211yesmaximal, characteristic, complemented
8#21446495C211yesmaximal, characteristic, complemented
9#21446461C211yesmaximal, characteristic, complemented
10#21446412C211yesmaximal, characteristic, complemented
11#21446159C211yesmaximal, characteristic, complemented
12#21446124C211yesmaximal, characteristic
13#21445910C211yesmaximal, characteristic
14C4×#14519702C211yesmaximal, characteristic, complemented
15C61×#1923C211yesmaximal, characteristic
16C22×Dic244C2211yescharacteristic
17C2×#14519777C2211yescharacteristic
18C2×#14519756C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20C2×C4×Dic122C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22C2×#14519711C2211yescharacteristic
23C2×#14519702C2211yescharacteristic
24C2×#14519702C2211yescharacteristic
25C2×#14519702C2211yescharacteristic
26C2×#14519702C2211yescharacteristic
27C2×#14519702C2211yescharacteristic
28C2×#14519702C2211yescharacteristic
29#16839704—21no—
30#16839674—21no—
31#16839668C2211yescharacteristic
32#16839668C2211yescharacteristic
33#16839668C2211yescharacteristic
34#16839666—21no—
35#16839660C2211yescharacteristic
36#16839659—21no—
37#16839655—21no—
38#16839649—21no—
39#16839634—21no—
40#16839622C2211yescharacteristic
41C4×C4⋊Dic61C2211yescharacteristic
42C4×C4⋊Dic61C2211yescharacteristic
43C22⋊C4×Dic61—21no—
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52C2×C4⋊C8×C61C2211yescharacteristic
53C2×C22⋊C8×C61C2211yescharacteristic
54C2×C22⋊C8×C61C2211yescharacteristic
55C2×C4×C8×C61C2211yescharacteristic
56C4×C22⋊C4×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×Dic122—21no—
60C22×Dic122C2311yescharacteristic
61C22×Dic122C2311yescharacteristic
62C23×Dic61—21no—
63C2×Dic244—22no—
64C2×Dic244—41no—
65C2×Dic244—41no—
66#14519777—22no—
67#14519777—41no—
68#14519756—22no—
69#14519756—22no—
70#14519756—22no—
71#14519756—41no—
72C4×Dic122—22no—
73C4×Dic122—41no—
74C2×C4⋊Dic61—22no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—41no—
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C4×Dic61—21no—
92C2×C4×Dic61—21no—
93C2×C4×Dic61—21no—
94#14519711—22no—
95#14519702—22no—
96#14519702—22no—
97#14519702—22no—
98#14519702—22no—
99#14519702—41no—
100#14519702—41no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111C23×C4×C61C2311yescharacteristic
112C22×C8×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C22×C8×C61C2311yescharacteristic
116C2×C22⋊C4×C61D411yescharacteristic
117C2×C22⋊C4×C61D411yescharacteristic
118C2×C42×C61C2311yescharacteristic
119C2×C42×C61C2311yescharacteristic
120C4⋊C8×C61—41no—
121C22⋊C8×C61—41no—
122C22⋊C8×C61—41no—
123C4×C8×C61—41no—
124#95×C61D411yescharacteristic
125#95×C61D411yescharacteristic
126C24×C61C2×D411yescharacteristic
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2411yescharacteristic
139C22×Dic61—21no—
140C22×Dic61—21no—
141C22×Dic61—21no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—42no—
148C22×Dic61—42no—
149C22×Dic61—81no—
150C2×Dic122—21no—
151C2×Dic122—21no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122—21no—
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—42no—
162C2×Dic122—42no—
163C2×Dic122—81no—
164C2×Dic122#4112yes—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C22⋊C4×C61—41no—
178C22⋊C4×C61Q1614yescomplemented
179C42×C61—21no—
180C42×C61—21no—
181C42×C61—21no—
182C42×C61—21no—
183C22⋊Dic61—24no—
184C22⋊Dic61—42no—
185C22⋊Dic61—81no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—42no—
196C4⋊Dic61—42no—
197C4⋊Dic61#4112yes—
198C4⋊Dic61#4112yes—
199C4⋊Dic61#4112yes—
200#11758196—24no—
201#11758196—42no—
202#11758196—42no—
203#11758196—81no—
204C4×Dic61—42no—
205C4×Dic61—81no—
206C4×Dic61—81no—
207Dic244—44no—
208C23×C61—21no—
209C23×C61—21no—
210C23×C61—21no—
211C23×C61—21no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61C2×Q1612yes—
215C23×C61C22×D411yescharacteristic
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
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—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61C2×Q1612yes—
234C2×C4×C61C2×Q1612yes—
235C2×C4×C61C2×#4111yescharacteristic
236C2×C4×C61C2×#4111yescharacteristic
237C2×C4×C61C2×#4111yescharacteristic
238C2×C4×C61C2×#4111yescharacteristic
239C2×C4×C61H(5,𝔽2)11yescharacteristic
240C2×C4×C61H(5,𝔽2)11yescharacteristic
241C2×Dic61—22no—
242C2×Dic61—22no—
243C2×Dic61—22no—
244C2×Dic61—22no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—84no—
266Dic122—22no—
267Dic122—22no—
268Dic122—41no—
269Dic122—41no—
270Dic122—41no—
271Dic122—41no—
272Dic122—41no—
273Dic122—41no—
274Dic122—84no—
275C8×C61—41no—
276C8×C61—41no—
277C8×C61—41no—
278C8×C61—41no—
279#26726—611nomaximal, Sylow
280C22×C61—22no—
281C22×C61—22no—
282C22×C61—22no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61#52511yescharacteristic
288C22×C61#54611yescharacteristic
289C22×C61#54611yescharacteristic
290C22×C61C22×Q1611yescharacteristic
291C22×C61#57511yescharacteristic
292C22×C61#57711yescharacteristic
293C22×C61#57711yescharacteristic
294C4×C61—22no—
295C4×C61—22no—
296C4×C61—41no—
297C4×C61—41no—
298C4×C61—41no—
299C4×C61#52911yescharacteristic
300C4×C61#53811yescharacteristic
301C4×C61#55511yescharacteristic
302C4×C61#55911yescharacteristic
303Dic61—42no—
304Dic61—42no—
305Dic61—42no—
306Dic61—42no—
307Dic61—81no—
308Dic61—81no—
309Dic61—81no—
310Dic61—81no—
311#2492—611no—
312#2360—611no—
313#2056—611no—
314#2036—611no—
315#2024—611no—
316#2001—611no—
317#1987—611no—
318#1933—611no—
319#1928—611no—
320#1923D6111yescharacteristic
321#1921—611no—
322#1878—611no—
323#1872—611no—
324#1824—611no—
325C4×#103—611no—
326C2×C61—42no—
327C2×C61#245911yescharacteristic
328C2×C61#310411yescharacteristic
329C2×C61#312511yescharacteristic
330C2×C61#329911yescharacteristic
331C2×C61#329911yescharacteristic
332C2×C61#331111yescharacteristic
333C2×C61#332311yescharacteristic
334C22×Q16—611no—
335C2×C4⋊Q8—611no—
336C2×C22⋊Q8—611no—
337C2×C22⋊Q8—611no—
338C2×C4×Q8—611no—
339C22×C4⋊C4—611no—
340C2×#107—611no—
341C2×C4⋊C8C2×D6111yescharacteristic
342C2×#103—611no—
343C2×#103—611no—
344C2×#103—611no—
345C2×#103—611no—
346C2×#103—611no—
347C2×#103—611no—
348C2×C22⋊C8C2×D6111yescharacteristic
349C2×C22⋊C8C2×D6111yescharacteristic
350C2×C4×C8C2×D6111yescharacteristic
351#400—1221no—
352#393—1221no—
353#391—611no—
354#391—611no—
355#391—611no—
356#391—1221no—
357#389—611no—
358#389—1221no—
359#388—1221no—
360#387—1221no—
361#385—1221no—
362#380—611no—
363C4×C4⋊C4—611no—
364C4×C4⋊C4—611no—
365C4×C22⋊C4—1221no—
366C4×C22⋊C4C2×D6111yescharacteristic
367#340—611no—
368#340—611no—
369#340—611no—
370#340—611no—
371#340—611no—
372#340—611no—
373#340—611no—
374#340—611no—
375#336C2×D6111yescharacteristic
376#336C2×D6111yescharacteristic
377C61#2672611yescharacteristic, complemented, Sylow
378C22×Q8—611no—
379C22×Q8—611no—
380C22×Q8—1221no—
381C23×C4—1221no—
382C23×C4C22×D6111yescharacteristic
383C2×Q16—1222no—
384C2×Q16—2441no—
385C2×Q16—2441no—
386C22×C8C22×D6111yescharacteristic
387C22×C8C22×D6111yescharacteristic
388C22×C8C22×D6111yescharacteristic
389C22×C8C22×D6111yescharacteristic
390C4⋊Q8—1222no—
391C4⋊Q8—2441no—
392C22⋊Q8—1222no—
393C22⋊Q8—1222no—
394C22⋊Q8—1222no—
395C22⋊Q8—2441no—
396C4×Q8—1222no—
397C4×Q8—2441no—
398C2×C4⋊C4—611no—
399C2×C4⋊C4—611no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—611no—
402C2×C4⋊C4—611no—
403C2×C4⋊C4—611no—
404C2×C4⋊C4—1222no—
405C2×C4⋊C4—1221no—
406C2×C4⋊C4—1221no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—2441no—
412C2×C22⋊C4—1221no—
413C2×C22⋊C4—1221no—
414C2×C22⋊C4—1221no—
415C2×C22⋊C4D24411yescharacteristic
416C2×C22⋊C4D24411yescharacteristic
417C2×C42—1221no—
418C2×C42—1221no—
419C2×C42—1221no—
420C2×C42C22×D6111yescharacteristic
421C2×C42C22×D6111yescharacteristic
422#107—1222no—
423C4⋊C8—41no—
424#103—1222no—
425#103—1222no—
426#103—1222no—
427#103—1222no—
428#103—2441no—
429#103—2441no—
430C22⋊C8—41no—
431C22⋊C8—41no—
432C4×C8—41no—
433#95—1221no—
434#95—1221no—
435#95—1221no—
436#95—1221no—
437#95—1221no—
438#95—1221no—
439#95—1221no—
440#95—1221no—
441#95—1221no—
442#95—1221no—
443#95D24411yescharacteristic
444#95D24411yescharacteristic
445C24C2×D24411yescharacteristic
446C2×Q8—612no—
447C2×Q8—1221no—
448C2×Q8—1221no—
449C2×Q8—1221no—
450C2×Q8—1221no—
451C2×Q8—1221no—
452C2×Q8—1221no—
453C2×Q8—1221no—
454C2×Q8—1221no—
455C2×Q8—1221no—
456C2×Q8—1221no—
457C2×Q8—1221no—
458C2×Q8—4881no—
459C2×Q8—2442no—
460C2×Q8—2442no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—1221no—
468C22×C4—1221no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—1221no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—4881no—
476C22×C4—2442no—
477C22×C4—2442no—
478C22×C4C2×D24411yescharacteristic
479C22×C4C2×D24411yescharacteristic
480C22×C4C2×D24411yescharacteristic
481C22×C4C2×D24411yescharacteristic
482C22×C4C2×D24411yescharacteristic
483C22×C4C23×D6111yescharacteristic
484Q16—2444no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C4⋊C4—612no—
498C4⋊C4—612no—
499C4⋊C4—612no—
500C4⋊C4—1224no—
501C4⋊C4—1221no—
502C4⋊C4—1221no—
503C4⋊C4—1221no—
504C4⋊C4—1221no—
505C4⋊C4—1221no—
506C4⋊C4—1221no—
507C4⋊C4—1221no—
508C4⋊C4—1221no—
509C4⋊C4—1221no—
510C4⋊C4—4881no—
511C4⋊C4—2442no—
512C4⋊C4—2442no—
513C4⋊C4—2442no—
514C4⋊C4—2442no—
515C22⋊C4—41no—
516C22⋊C4—1224no—
517C22⋊C4—4881no—
518C22⋊C4—2442no—
519C22⋊C4Dic24414yescomplemented
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—4881no—
525C42—4881no—
526C42—2442no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23C2×Dic24412yes—
534C23C22×D24411yescharacteristic
535Q8—1222no—
536Q8—1222no—
537Q8—4884no—
538Q8—2441no—
539Q8—2441no—
540Q8—2441no—
541Q8—2441no—
542Q8—2441no—
543Q8—2441no—
544C2×C4—21no—
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—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—1222no—
562C2×C4—1222no—
563C2×C4—1222no—
564C2×C4—1222no—
565C2×C4—4884no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2441no—
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×C4—2441no—
585C2×C4—2441no—
586C2×C4C2×Dic24412yes—
587C2×C4C2×Dic24412yes—
588C2×C4#41×D6111yescharacteristic
589C2×C4#41×D6111yescharacteristic
590C2×C4#41×D6111yescharacteristic
591C2×C4#41×D6111yescharacteristic
592C2×C4#1451982211yescharacteristic
593C2×C4#1451982211yescharacteristic
594C8—41no—
595C8—41no—
596C8—41no—
597C8—41no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22#1684027411yescharacteristic
606C22#1684040711yescharacteristic
607C22#1684040711yescharacteristic
608C22C22×Dic24411yescharacteristic
609C22#1684056211yescharacteristic
610C22#1684057411yescharacteristic
611C22#1684057411yescharacteristic
612C4—22no—
613C4—22no—
614C4—41no—
615C4—41no—
616C4—41no—
617C4—4881no—
618C4—4881no—
619C4—4881no—
620C4—4881no—
621C4—2442no—
622C4—2442no—
623C4—2442no—
624C4—2442no—
625C4#1684029511yescharacteristic
626C4#1684034411yescharacteristic
627C4#1684047411yescharacteristic
628C4#1684049611yescharacteristic
629C2—42no—
630C2#2144975411yescharacteristic
631C2#2145585911yescharacteristic
632C2#2145609811yescharacteristic
633C2#2145769611yescharacteristic
634C2#2145769611yescharacteristic
635C2#2145785711yescharacteristic
636C2#2145803711yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1923C2
socleC23×C61C22×D4
prime radicalC24×C61C2×D4
hypercenter#1923D61
hypocenterC61#26726
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
3. #21447142C2semidirect
5. #21446961C2semidirect
7. #21446766C2semidirect
8. #21446495C2semidirect
9. #21446461C2semidirect
10. #21446412C2semidirect
11. #21446159C2semidirect
14. C4×#14519702C2semidirect
178. C22⋊C4×C61Q16semidirect
377. C61#26726semidirect
519. C22⋊C4Dic244semidirect

Maximal subgroups

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

subgroupindex
#214501932
#214488222
#214471422
#214470232
#214469612
#214468292
#214467662
#214464952
#214464612
#214464122
#214461592
#214461242
#214459102
C4×#145197022
C61×#19232
#2672661