Finite Group Databasebeta

← #29683106

Subgroups — #29683106

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×#16839875C211yesmaximal, characteristic
2#21448463C211yesmaximal, characteristic, complemented
3#21448181C211yesmaximal, characteristic, complemented
4#21446447C211yesmaximal, characteristic, complemented
5#21446440C211yesmaximal, characteristic, complemented
6#21446405C211yesmaximal, characteristic, complemented
7#21446398C211yesmaximal, characteristic, complemented
8#21446166C211yesmaximal, characteristic
9#21446166C211yesmaximal, characteristic
10#21446083C211yesmaximal, characteristic, complemented
11#21446069C211yesmaximal, characteristic, complemented
12#21445716C211yesmaximal, characteristic, complemented
13C4×#14519699C211yesmaximal, characteristic, complemented
14C4×#14519699C211yesmaximal, characteristic, complemented
15C61×#1746C211yesmaximal, characteristic, complemented
16C22×D488C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21#16839875C418yescomplemented
22C2×#14519711C2211yescharacteristic
23C2×#14519709C2211yescharacteristic
24C2×#14519709C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519699C2211yescharacteristic
27C2×#14519699C2211yescharacteristic
28C2×#14519699C2211yescharacteristic
29C2×#14519699C2211yescharacteristic
30C2×#14519699C2211yescharacteristic
31#16839664C2211yescharacteristic
32#16839664C2211yescharacteristic
33#16839660C2211yescharacteristic
34#16839660C2211yescharacteristic
35#16839651—21no—
36#16839651—21no—
37#16839624—21no—
38#16839621—21no—
39C4×C4⋊Dic61C2211yescharacteristic
40C4×C4⋊Dic61C2211yescharacteristic
41C4×C4⋊Dic61C2211yescharacteristic
42C4×C4⋊Dic61C2211yescharacteristic
43#16839609—21no—
44#16839609—21no—
45#16839609—21no—
46#95×D61—21no—
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53C2×#97×C61C2211yescharacteristic
54C2×C4×C8×C61C2211yescharacteristic
55C61×#376C2211yescharacteristic
56C61×#336C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
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—
69C4×D244—22no—
70C4×D244—22no—
71C4×D244—22no—
72C4×D244—22no—
73C4×D244—22no—
74C4×D244—22no—
75C4×D244C2×C414yes—
76C4×D244C2×C414yescomplemented
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×C4×Dic61—21no—
94C2×C4×Dic61—21no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61—21no—
97#14519711—22no—
98#14519709—22no—
99#14519709C2×C414yescomplemented
100#14519699—22no—
101#14519699—22no—
102#14519699—22no—
103#14519699—22no—
104#14519699C2×C414yes—
105#14519699C2×C414yescomplemented
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112C22×C8×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C22×C8×C61C2311yescharacteristic
116C2×C42×C61C2311yescharacteristic
117C2×C42×C61C2311yescharacteristic
118C2×C42×C61C2311yescharacteristic
119#97×C61C2×C414yescomplemented
120C4×C8×C61—22no—
121#95×C61D411yescharacteristic
122#95×C61D411yescharacteristic
123#95×C61D411yescharacteristic
124#95×C61D411yescharacteristic
125C23×D61—21no—
126C23×D61—21no—
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2411yescharacteristic
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61—21no—
138C22×Dic61—21no—
139C22×Dic61—21no—
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×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61C22×C412yes—
175C2×C8×C61C22×C412yes—
176C42×C61—21no—
177C42×C61—21no—
178C42×C61—21no—
179C42×C61—21no—
180C42×C61C22×C412yes—
181C42×C61#4112yes—
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—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61C22×C412yes—
199C4⋊Dic61C22×C412yes—
200C4⋊Dic61#4112yes—
201C4⋊Dic61#4112yes—
202#11758196—81no—
203#11758196—81no—
204C4×Dic61—81no—
205C4×Dic61—81no—
206C4×Dic61—81no—
207C4×Dic61—81no—
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—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×C61C4×D412yes—
241C2×C4×C61C4×D412yes—
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—22no—
249C2×Dic61—22no—
250C2×Dic61—22no—
251C2×Dic61—22no—
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—41no—
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—22no—
280C8×C61—41no—
281C8×C61—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—22no—
305C4×C61—22no—
306C4×C61—41no—
307C4×C61—41no—
308C4×C61—41no—
309C4×C61—41no—
310C4×C61C2×#11711yescharacteristic
311C4×C61C4×#4111yescharacteristic
312C4×C61#52911yescharacteristic
313C4×C61#52911yescharacteristic
314Dic61—42no—
315Dic61—42no—
316Dic61—42no—
317Dic61—42no—
318Dic61—81no—
319Dic61—81no—
320C2×#442—611no—
321#2319—611no—
322#2275—611no—
323#1926—611no—
324#1925—611no—
325#1920—611no—
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#1746D6111yescharacteristic, complemented
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×#106—611no—
353C2×#102—611no—
354C2×#102—611no—
355C2×#102—611no—
356C2×#102—611no—
357C2×#102—611no—
358C2×#102—611no—
359C2×#97C2×D6111yescharacteristic
360C2×C4×C8C2×D6111yescharacteristic
361#390—611no—
362#390—611no—
363#389—611no—
364#389—611no—
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⋊C4—611no—
373C4×C22⋊C4—1221no—
374C4×C22⋊C4—1221no—
375C4×C22⋊C4—1221no—
376#376C2×D6111yescharacteristic
377C2×#95—1221no—
378#340—611no—
379#340—611no—
380#340—611no—
381#340—611no—
382#340—611no—
383#340—611no—
384#336C2×D6111yescharacteristic
385#336C2×D6111yescharacteristic
386#336C2×D6111yescharacteristic
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×C8C22×D6111yescharacteristic
399C22×C8C22×D6111yescharacteristic
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—611no—
411C2×C4⋊C4—611no—
412C2×C4⋊C4—611no—
413C2×C4⋊C4—611no—
414C2×C4⋊C4—611no—
415C2×C4⋊C4—611no—
416C2×C4⋊C4—1221no—
417C2×C4⋊C4—1221no—
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—1221no—
427C2×C42—1221no—
428C2×C42—1221no—
429C2×C42—1221no—
430C2×C42C22×D6111yescharacteristic
431C2×C42C22×D6111yescharacteristic
432C2×C42C22×D6111yescharacteristic
433#107—1222no—
434#106—614no—
435#106—1222no—
436#102—614no—
437#102—614no—
438#102—1222no—
439#102—1222no—
440#102—1222no—
441#102—1222no—
442#97C4×D6114yescomplemented
443C4×C8—22no—
444#95—1221no—
445#95—1221no—
446#95—1221no—
447#95—1221no—
448#95—1221no—
449#95—1221no—
450#95D24411yescharacteristic
451#95D24411yescharacteristic
452#95D24411yescharacteristic
453#95D24411yescharacteristic
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—1224no—
469C22×C4—1224no—
470C22×C4—1221no—
471C22×C4—1221no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1224no—
475C22×C4—1224no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—4881no—
479C22×C4—4881no—
480C22×C4—4881no—
481C22×C4—4881no—
482C22×C4—4881no—
483C22×C4—4881no—
484C22×C4—4881no—
485C22×C4—4881no—
486C22×C4C2×D24411yescharacteristic
487C22×C4C2×D24411yescharacteristic
488C22×C4C2×D24411yescharacteristic
489C22×C4C2×D24411yescharacteristic
490C22×C4C2×D24411yescharacteristic
491C22×C4C2×D24411yescharacteristic
492C22×C4C23×D6111yescharacteristic
493D8—1228no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8C2×C4×D6112yes—
505C2×C8C2×C4×D6112yes—
506C4⋊C4—612no—
507C4⋊C4—612no—
508C4⋊C4—612no—
509C4⋊C4—612no—
510C4⋊C4—1221no—
511C4⋊C4—1221no—
512C4⋊C4—1221no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C4⋊C4—1221no—
517C4⋊C4—1221no—
518C4⋊C4—4881no—
519C4⋊C4—4881no—
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—21no—
531C42—21no—
532C42—4881no—
533C42—4881no—
534C42—4881no—
535C42—4881no—
536C42C2×C4×D6112yes—
537C42#1175822212yes—
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—
552C23C22×D24411yescharacteristic
553D4—614no—
554D4—1222no—
555D4—1222no—
556D4—1222no—
557D4—1222no—
558D4—1222no—
559D4—2441no—
560D4—2441no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—1222no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—1222no—
581C2×C4—4884no—
582C2×C4—4884no—
583C2×C4—4884no—
584C2×C4—4884no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4—2441no—
596C2×C4—2441no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4C4×D24412yes—
600C2×C4C4×D24412yes—
601C2×C4C22×C4×D6111yescharacteristic
602C2×C4#41×D6111yescharacteristic
603C2×C4#41×D6111yescharacteristic
604C2×C4#41×D6111yescharacteristic
605C2×C4#41×D6111yescharacteristic
606C2×C4C2×#1175822211yescharacteristic
607C8—22no—
608C8—22no—
609C8—41no—
610C8—41no—
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—
625C22C2×C4×D24411yescharacteristic
626C22#1684027411yescharacteristic
627C22#1684027411yescharacteristic
628C22#1684056711yescharacteristic
629C22#1684056711yescharacteristic
630C22#1684057411yescharacteristic
631C22#1684057411yescharacteristic
632C4—22no—
633C4—22no—
634C4—41no—
635C4—41no—
636C4—41no—
637C4—41no—
638C4—4881no—
639C4—4881no—
640C4—2442no—
641C4—2442no—
642C4—2442no—
643C4—2442no—
644C4#117×D6111yescharacteristic
645C4#1684023011yescharacteristic
646C4#1684029011yescharacteristic
647C4#1684029011yescharacteristic
648C2—4882no—
649C2—2444no—
650C2#2144826311yescharacteristic
651C2#2145465311yescharacteristic
652C2#2145465311yescharacteristic
653C2#2145600511yescharacteristic
654C2#2145602011yescharacteristic
655C2#2145606311yescharacteristic
656C2#2145609811yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1746C2
socleC23×C61C22×D4
prime radicalC22×D488C22
cosocleC22×C4×C61C24
hypercenter#1746D61
hypocenterC61#21126
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ #376 ◁ #1746

Complements

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

NH ≅ G/Ntype
2. #21448463C2semidirect
3. #21448181C2semidirect
4. #21446447C2semidirect
5. #21446440C2semidirect
6. #21446405C2semidirect
7. #21446398C2semidirect
10. #21446083C2semidirect
11. #21446069C2semidirect
12. #21445716C2semidirect
13. C4×#14519699C2semidirect
14. C4×#14519699C2semidirect
15. C61×#1746C2semidirect
21. #16839875C4semidirect
76. C4×D244C2×C4semidirect
99. #14519709C2×C4semidirect
105. #14519699C2×C4semidirect
119. #97×C61C2×C4semidirect
334. #1746D61semidirect
388. C61#21126semidirect
442. #97C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398752
#214484632
#214481812
#214464472
#214464402
#214464052
#214463982
#214461662
#214460832
#214460692
#214457162
C4×#145196992
C61×#17462
#2112661