Finite Group Databasebeta

← #29683099

Subgroups — #29683099

Order 15616.

938 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839873C211yesmaximal, characteristic
2#21448458C211yesmaximal, characteristic, complemented
3#21448179C211yesmaximal, characteristic, complemented
4#21446446C211yesmaximal, characteristic, complemented
5#21446437C211yesmaximal, characteristic, complemented
6#21446399C211yesmaximal, characteristic, complemented
7#21446168C211yesmaximal, characteristic
8#21446166C211yesmaximal, characteristic
9#21446081C211yesmaximal, characteristic, complemented
10#21446065C211yesmaximal, characteristic, complemented
11#21445715C211yesmaximal, characteristic, complemented
12#21445633C211yesmaximal, characteristic, complemented
13#21445633C211yesmaximal, characteristic, complemented
14#21445569C211yesmaximal, characteristic, complemented
15C61×#1920C211yesmaximal, characteristic, complemented
16C22×D488C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18C2×#14519739C2211yescharacteristic
19C2×#14519739C2211yescharacteristic
20C2×#14519739C2211yescharacteristic
21#16839873C418yescomplemented
22C2×#14519710C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×#14519687C2211yescharacteristic
31C2×C8×Dic61C2211yescharacteristic
32#16839664C2211yescharacteristic
33#16839663C2211yescharacteristic
34#16839661C2211yescharacteristic
35#16839654—21no—
36#16839652—21no—
37#16839624—21no—
38#16839619—21no—
39C4⋊C4×Dic61C2211yescharacteristic
40C4⋊C4×Dic61C2211yescharacteristic
41C4⋊C4×Dic61C2211yescharacteristic
42C4×#11758198—21no—
43C4×#11758198—21no—
44#16839609—21no—
45#16839608C2211yescharacteristic
46#95×D61—21no—
47#16839525C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53C2×#106×C61C2211yescharacteristic
54C61×#389C2211yescharacteristic
55C4×C4⋊C4×C61C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C22×D244C2311yescharacteristic
61C22×D244C2311yescharacteristic
62C22×C4×D61—21no—
63C22×C4×D61—21no—
64C22×C4×D61—21no—
65C22×C4×D61—21no—
66C2×D488—22no—
67C2×D488—22no—
68C2×D488C2×C414yes—
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C4×D244—22no—
72C4×D244—22no—
73#14519739—22no—
74#14519739—22no—
75#14519739—22no—
76#14519739—22no—
77#14519739C2×C414yes—
78#14519739C2×C414yescomplemented
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×C4×Dic61—21no—
91C2×C4×Dic61—21no—
92C2×C4×Dic61—21no—
93C2×C4×Dic61C2311yescharacteristic
94C2×C4×Dic61C2311yescharacteristic
95#14519710—22no—
96#14519708—22no—
97#14519699—22no—
98#14519699—22no—
99#14519697—22no—
100#14519697—22no—
101#14519697C2×C414yes—
102#14519697C2×C414yescomplemented
103#14519687C2×C414yescomplemented
104C8×Dic61—22no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684D411yescharacteristic
110#14519684D411yescharacteristic
111#14519684D411yescharacteristic
112#14519684D411yescharacteristic
113C22×C8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C42×C61—21no—
121C2×C42×C61C2311yescharacteristic
122#106×C61C2×C414yescomplemented
123#95×C61—21no—
124#95×C61—21no—
125C23×D61—21no—
126C23×D61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2411yescharacteristic
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61C2×D411yescharacteristic
137C22×Dic61C2×D411yescharacteristic
138C22×Dic61C2×D411yescharacteristic
139C22×Dic61C2×D411yescharacteristic
140C2×D244—21no—
141C2×D244—21no—
142C2×D244—21no—
143C2×D244—21no—
144C2×D244—21no—
145C2×D244—21no—
146C2×D244—21no—
147C2×D244—21no—
148C2×D244C22×C412yes—
149C2×D244C22×C412yes—
150C2×D244#4112yes—
151C2×D244#4112yes—
152C2×C4×D61—24no—
153C2×C4×D61—24no—
154C2×C4×D61—24no—
155C2×C4×D61—24no—
156C2×C4×D61—81no—
157C2×C4×D61—81no—
158C2×C4×D61—81no—
159C2×C4×D61—81no—
160C2×C4×D61—81no—
161C2×C4×D61—81no—
162C2×C4×D61—81no—
163C2×C4×D61—81no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61C22×C412yes—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—81no—
176C4⋊C4×C61C22×C412yes—
177C4⋊C4×C61C22×C412yes—
178C4⋊C4×C61#4112yes—
179C42×C61—21no—
180C42×C61—21no—
181C42×C61—81no—
182#11758198—24no—
183#11758198—24no—
184#11758198—24no—
185#11758198—24no—
186#11758198—81no—
187#11758198—81no—
188#11758198—81no—
189#11758198—81no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—81no—
194C4⋊Dic61#4112yes—
195C4×Dic61—21no—
196C4×Dic61—21no—
197C4×Dic61—81no—
198C4×Dic61—81no—
199C4×Dic61—81no—
200C4×Dic61C22×C412yes—
201C4×Dic61#4112yes—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418C22×C412yes—
208D488—28no—
209C23×C61C22×D411yescharacteristic
210C22×D61—22no—
211C22×D61—22no—
212C22×D61—22no—
213C22×D61—22no—
214C22×D61—41no—
215C22×D61—41no—
216C22×D61—41no—
217C22×D61—41no—
218C22×D61—41no—
219C22×D61—41no—
220C22×D61—41no—
221C22×D61—41no—
222C22×D61—41no—
223C22×D61—41no—
224C2×C4×C61—22no—
225C2×C4×C61—22no—
226C2×C4×C61—21no—
227C2×C4×C61—22no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—41no—
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×C61C23×C411yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C2×C4×C61C2×#4111yescharacteristic
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—22no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61C4×D412yes—
265C2×Dic61C4×D412yes—
266D244—22no—
267D244—22no—
268D244—22no—
269D244—22no—
270D244—22no—
271D244—41no—
272D244—41no—
273D244#11714yes—
274C4×D61—84no—
275C4×D61—84no—
276C4×D61—84no—
277C4×D61—84no—
278C8×C61—22no—
279C8×C61—41no—
280#92418—22no—
281#92418—41no—
282#21126—611nomaximal, Sylow
283C22×C61C2×C4×D411yescharacteristic
284C22×C61#52511yescharacteristic
285C22×C61#52511yescharacteristic
286C22×C61#57611yescharacteristic
287C22×C61#57611yescharacteristic
288C22×C61#57711yescharacteristic
289C22×C61#57711yescharacteristic
290C2×D61—24no—
291C2×D61—42no—
292C2×D61—42no—
293C2×D61—42no—
294C2×D61—42no—
295C2×D61—42no—
296C2×D61—42no—
297C2×D61—42no—
298C2×D61—42no—
299C2×D61—42no—
300C2×D61—81no—
301C2×D61—81no—
302C2×D61—81no—
303C2×D61—81no—
304C4×C61—42no—
305C4×C61—41no—
306C4×C61—41no—
307C4×C61—42no—
308C4×C61—42no—
309C4×C61—81no—
310C4×C61C2×#11711yescharacteristic
311C4×C61C4×#4111yescharacteristic
312C4×C61#52911yescharacteristic
313C4×C61#52911yescharacteristic
314Dic61—22no—
315Dic61—22no—
316Dic61—41no—
317Dic61—41no—
318Dic61—42no—
319Dic61—81no—
320C2×#442—611no—
321#2319—611no—
322#2275—611no—
323#1926—611no—
324#1925—611no—
325#1920D6111yescharacteristic, complemented
326#1919—611no—
327#1879—611no—
328#1879—611no—
329#1864—611no—
330#1862—611no—
331#1776—611no—
332C4×#102—611no—
333C4×#102—611no—
334#1746—611no—
335C2×C61#229011yescharacteristic
336C2×C61#294611yescharacteristic
337C2×C61#294611yescharacteristic
338C2×C61#311811yescharacteristic
339C2×C61#311911yescharacteristic
340C2×C61#312211yescharacteristic
341C2×C61#312511yescharacteristic
342D61—44no—
343D61—82no—
344C22×D8—611no—
345C2×C4×D4—611no—
346C2×C4×D4—611no—
347C2×C4×D4—611no—
348C2×C4×D4—611no—
349#442—618no—
350C2×#107—611no—
351C2×#106—611no—
352C2×#106C2×D6111yescharacteristic
353C2×#102—611no—
354C2×#102—611no—
355C2×#102—611no—
356C2×#102—611no—
357C2×#102—611no—
358C2×#102—611no—
359C2×#97—611no—
360C2×C4×C8—611no—
361#390—611no—
362#390—611no—
363#389—611no—
364#389C2×D6111yescharacteristic
365#388—1221no—
366#388—1221no—
367#381—1221no—
368#380—1221no—
369C4×C4⋊C4—611no—
370C4×C4⋊C4—611no—
371C4×C4⋊C4—611no—
372C4×C4⋊C4C2×D6111yescharacteristic
373C4×C22⋊C4—1221no—
374C4×C22⋊C4—1221no—
375C4×C22⋊C4—1221no—
376#376—611no—
377C2×#95—1221no—
378#340—611no—
379#340—611no—
380#340—611no—
381#340C2×D6111yescharacteristic
382#340C2×D6111yescharacteristic
383#340C2×D6111yescharacteristic
384#336—611no—
385#336—611no—
386#336—611no—
387#336C2×D6111yescharacteristic
388C61#2112611yescharacteristic, complemented, Sylow
389C22×D4—611no—
390C22×D4—611no—
391C23×C4—1221no—
392C23×C4—1221no—
393C23×C4—1221no—
394C23×C4—1221no—
395C2×D8—614no—
396C2×D8—1222no—
397C2×D8—1222no—
398C22×C8—611no—
399C22×C8—611no—
400C22×C8C22×D6111yescharacteristic
401C22×C8C22×D6111yescharacteristic
402C4×D4—614no—
403C4×D4—614no—
404C4×D4—1222no—
405C4×D4—1222no—
406C4×D4—1222no—
407C4×D4—1222no—
408C4×D4—1222no—
409C4×D4—1222no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—611no—
412C2×C4⋊C4—611no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4C22×D6111yescharacteristic
415C2×C4⋊C4C22×D6111yescharacteristic
416C2×C4⋊C4C22×D6111yescharacteristic
417C2×C4⋊C4C22×D6111yescharacteristic
418C2×C22⋊C4—1221no—
419C2×C22⋊C4—1221no—
420C2×C22⋊C4—1221no—
421C2×C22⋊C4—1221no—
422C2×C22⋊C4—1221no—
423C2×C22⋊C4—1221no—
424C2×C22⋊C4—1221no—
425C2×C22⋊C4—1221no—
426C2×C42—21no—
427C2×C42—611no—
428C2×C42—611no—
429C2×C42—1221no—
430C2×C42—1221no—
431C2×C42—1221no—
432C2×C42C22×D6111yescharacteristic
433#107—1222no—
434#106—1222no—
435#106C4×D6114yescomplemented
436#102—614no—
437#102—614no—
438#102—1222no—
439#102—1222no—
440#102—1222no—
441#102—1222no—
442#97—614no—
443C4×C8—1222no—
444#95—21no—
445#95—21no—
446#95—611no—
447#95—611no—
448#95—611no—
449#95—611no—
450#95—1221no—
451#95—1221no—
452#95—1221no—
453#95—1221no—
454C24—1221no—
455C24—1221no—
456C2×D4—612no—
457C2×D4—612no—
458C2×D4—612no—
459C2×D4—612no—
460C2×D4—1221no—
461C2×D4—1221no—
462C2×D4—1221no—
463C2×D4—1221no—
464C2×D4—1221no—
465C2×D4—1221no—
466C2×D4—1221no—
467C2×D4—1221no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—1224no—
477C22×C4—1224no—
478C22×C4—1224no—
479C22×C4—1224no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—4881no—
483C22×C4—4881no—
484C22×C4—4881no—
485C22×C4—4881no—
486C22×C4—4881no—
487C22×C4—4881no—
488C22×C4—4881no—
489C22×C4—4881no—
490C22×C4D4×D6111yescharacteristic
491C22×C4D4×D6111yescharacteristic
492C22×C4C23×D6111yescharacteristic
493D8—1228no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—612no—
500C2×C8—1221no—
501C2×C8—1221no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8C2×C4×D6112yes—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—81no—
512C4⋊C4—612no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C4⋊C4—4881no—
517C4⋊C4C2×C4×D6112yes—
518C4⋊C4C2×C4×D6112yes—
519C4⋊C4#1175822612yes—
520C22⋊C4—1224no—
521C22⋊C4—1224no—
522C22⋊C4—1224no—
523C22⋊C4—1224no—
524C22⋊C4—4881no—
525C22⋊C4—4881no—
526C22⋊C4—4881no—
527C22⋊C4—4881no—
528C42—21no—
529C42—21no—
530C42—81no—
531C42—612no—
532C42—612no—
533C42—1221no—
534C42—1221no—
535C42—4881no—
536C42—4881no—
537C42—4881no—
538C23—1222no—
539C23—1222no—
540C23—1222no—
541C23—1222no—
542C23—2441no—
543C23—2441no—
544C23—2441no—
545C23—2441no—
546C23—2441no—
547C23—2441no—
548C23—2441no—
549C23—2441no—
550C23—2441no—
551C23—2441no—
552C23C2×D4×D6111yescharacteristic
553D4—614no—
554D4—1222no—
555D4—1222no—
556D4—1222no—
557D4—1222no—
558D4—1222no—
559D4—2441no—
560D4—2441no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
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—612no—
580C2×C4—612no—
581C2×C4—1221no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1222no—
586C2×C4—1221no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—1221no—
590C2×C4—1221no—
591C2×C4—1221no—
592C2×C4—4884no—
593C2×C4—4884no—
594C2×C4—4884no—
595C2×C4—4884no—
596C2×C4—2441no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4C22×C4×D6111yescharacteristic
602C2×C4#41×D6111yescharacteristic
603C2×C4#41×D6111yescharacteristic
604C2×C4#41×D6111yescharacteristic
605C2×C4#41×D6111yescharacteristic
606C2×C4C2×#1175822611yescharacteristic
607C8—22no—
608C8—41no—
609C8—1222no—
610C8—2441no—
611C22—1224no—
612C22—4881no—
613C22—4881no—
614C22—4881no—
615C22—4881no—
616C22—2442no—
617C22—2442no—
618C22—2442no—
619C22—2442no—
620C22—2442no—
621C22—2442no—
622C22—2442no—
623C22—2442no—
624C22—2442no—
625C22C4×D4×D6111yescharacteristic
626C22#1684027011yescharacteristic
627C22#1684027511yescharacteristic
628C22#1684056411yescharacteristic
629C22#1684056611yescharacteristic
630C22#1684056811yescharacteristic
631C22#1684057111yescharacteristic
632C4—42no—
633C4—42no—
634C4—42no—
635C4—41no—
636C4—41no—
637C4—81no—
638C4—1222no—
639C4—1222no—
640C4—4881no—
641C4—2441no—
642C4—2441no—
643C4—2442no—
644C4#117×D6111yescharacteristic
645C4C4×#1175822611yescharacteristic
646C4#1684029511yescharacteristic
647C4#1684029711yescharacteristic
648C2—4882no—
649C2—2444no—
650C2#2144825711yescharacteristic
651C2#2145464611yescharacteristic
652C2#2145465011yescharacteristic
653C2#2145600811yescharacteristic
654C2#2145602511yescharacteristic
655C2#2145605811yescharacteristic
656C2#2145609111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1920C2
socleC23×C61C22×D4
prime radicalC22×D488C22
cosocleC22×C4×C61C24
hypercenter#1920D61
hypocenterC61#21126
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1920

Complements

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

NH ≅ G/Ntype
2. #21448458C2semidirect
3. #21448179C2semidirect
4. #21446446C2semidirect
5. #21446437C2semidirect
6. #21446399C2semidirect
9. #21446081C2semidirect
10. #21446065C2semidirect
11. #21445715C2semidirect
12. #21445633C2semidirect
13. #21445633C2semidirect
14. #21445569C2semidirect
15. C61×#1920C2semidirect
21. #16839873C4semidirect
78. #14519739C2×C4semidirect
102. #14519697C2×C4semidirect
103. #14519687C2×C4semidirect
122. #106×C61C2×C4semidirect
325. #1920D61semidirect
388. C61#21126semidirect
435. #106C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398732
#214484582
#214481792
#214464462
#214464372
#214463992
#214461682
#214461662
#214460812
#214460652
#214457152
#214456332
#214455692
C61×#19202
#2112661