Finite Group Databasebeta

← #29687777

Subgroups — #29687777

Order 15616.

876 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840049C211yesmaximal, characteristic
2#21448181C211yesmaximal, characteristic
3#21446772C211yesmaximal, characteristic, complemented
4#21446585C211yesmaximal, characteristic, complemented
5#21446401C211yesmaximal, characteristic, complemented
6#21446394C211yesmaximal, characteristic, complemented
7#21446079C211yesmaximal, characteristic
8#21446065C211yesmaximal, characteristic
9#21445826C211yesmaximal, characteristic
10#21445717C211yesmaximal, characteristic, complemented
11C4×#14519708C211yesmaximal, characteristic, complemented
12#21445676C211yesmaximal, characteristic, complemented
13#21445647C211yesmaximal, characteristic
14C4×#14519697C211yesmaximal, characteristic
15C61×#2331C211yesmaximal, characteristic, complemented
16C2×C4×D244C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19#16840049C418yescomplemented
20C2×#14519710C2211yescharacteristic
21C2×#14519708C2211yescharacteristic
22C2×#14519708C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×#14519688C2211yescharacteristic
31C2×C4×#92418C2211yescharacteristic
32C4×C4⋊Dic61C2211yescharacteristic
33C4×C4⋊Dic61C2211yescharacteristic
34C4×C4⋊Dic61C2211yescharacteristic
35#16839609—21no—
36#16839609—21no—
37#16839609—21no—
38#95×D61—21no—
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839517C2211yescharacteristic
48#16839517C2211yescharacteristic
49C2×C4⋊Q8×C61C2211yescharacteristic
50C61×#391—21no—
51C61×#391—21no—
52C61×#389C2211yescharacteristic
53C61×#389C2211yescharacteristic
54C61×#387—21no—
55C61×#387—21no—
56C61×#382C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C61×#376C2211yescharacteristic
60C22×D244C2311yescharacteristic
61C22×C4×D61—21no—
62C22×C4×D61—21no—
63C22×C4×D61—21no—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C4×D244—22no—
69C4×D244—22no—
70C4×D244—22no—
71C4×D244—22no—
72C4×D244C2×C414yes—
73C4×D244Q814yescomplemented
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×#11758198—21no—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×C4×Dic61—21no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61—21no—
83#14519710—22no—
84#14519708—22no—
85#14519708C2×C414yescomplemented
86#14519708C2×C414yescomplemented
87C4⋊#92418—22no—
88C4⋊#92418C2×C414yescomplemented
89#14519697—22no—
90#14519697—22no—
91#14519697C2×C414yes—
92#14519697C2×C414yes—
93#14519688—22no—
94C4×#92418—22no—
95#14519684—21no—
96#14519684—21no—
97#14519684—21no—
98C22×Q8×C61—21no—
99C4⋊Q8×C61—22no—
100C4⋊Q8×C61C2×C414yescomplemented
101C2×C4⋊C4×C61—21no—
102C2×C4⋊C4×C61—21no—
103C2×C4⋊C4×C61—21no—
104C2×C4⋊C4×C61C2311yescharacteristic
105C2×C4⋊C4×C61C2311yescharacteristic
106C2×C4⋊C4×C61C2311yescharacteristic
107C2×C4⋊C4×C61C2311yescharacteristic
108C2×C42×C61—21no—
109C2×C42×C61—21no—
110C2×C42×C61C2311yescharacteristic
111C2×C42×C61C2311yescharacteristic
112C2×C42×C61C2311yescharacteristic
113#95×C61—21no—
114#95×C61—21no—
115#95×C61—21no—
116#95×C61—21no—
117#95×C61—21no—
118#95×C61—21no—
119#95×C61D411yescharacteristic
120#95×C61D411yescharacteristic
121#95×C61D411yescharacteristic
122#95×C61D411yescharacteristic
123C23×D61—21no—
124C2×Q8×C61—24no—
125C2×Q8×C61—81no—
126C2×Q8×C61—81no—
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×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2411yescharacteristic
138C22×Dic61—21no—
139C22×Dic61—21no—
140C22×Dic61—21no—
141C2×D244—21no—
142C2×D244—21no—
143C2×D244—21no—
144C2×D244C22×C412yes—
145C2×D244C2×Q812yes—
146C2×D244#4112yes—
147C2×C4×D61—24no—
148C2×C4×D61—24no—
149C2×C4×D61—24no—
150C2×C4×D61—81no—
151C2×C4×D61—81no—
152C2×C4×D61—81no—
153C2×C4×D61—81no—
154C2×C4×D61—81no—
155C2×C4×D61—81no—
156C4⋊C4×C61—24no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—81no—
164C4⋊C4×C61—81no—
165C4⋊C4×C61C22×C412yes—
166C4⋊C4×C61C22×C412yes—
167C42×C61—21no—
168C42×C61—21no—
169C42×C61—81no—
170C42×C61—81no—
171C42×C61C22×C412yes—
172C42×C61C2×Q812yes—
173C42×C61#4112yes—
174C42×C61#4112yes—
175#11758198—24no—
176#11758198—24no—
177#11758198—24no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61C22×C412yes—
182C4⋊Dic61C2×Q812yes—
183C4⋊Dic61#4112yes—
184C4×Dic61—81no—
185C4×Dic61—81no—
186C4×Dic61—81no—
187C2×#92418—21no—
188C2×#92418—21no—
189C2×#92418—21no—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418C22×C412yes—
198C2×#92418C22×C412yes—
199C23×C61C22×D411yescharacteristic
200C22×D61—22no—
201C22×D61—22no—
202C22×D61—22no—
203C22×D61—41no—
204C22×D61—41no—
205C22×D61—41no—
206C22×D61—41no—
207Q8×C61—84no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—22no—
217C2×C4×C61—22no—
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—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×C61C4×D412yes—
235C2×C4×C61C4×D412yes—
236C2×C4×C61C22⋊Q812yes—
237C2×C4×C61C22⋊Q812yes—
238C2×C4×C61C23×C411yescharacteristic
239C2×C4×C61C22×Q811yescharacteristic
240C2×C4×C61C2×#4111yescharacteristic
241C2×C4×C61C2×#4111yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253D244—22no—
254D244—22no—
255D244—22no—
256D244C4×Q814yes—
257C4×D61—84no—
258C4×D61—84no—
259C4×D61—84no—
260#92418—22no—
261#92418—22no—
262#92418—41no—
263#92418—41no—
264#21623—611nomaximal, Sylow
265C22×C61C2×C4×D411yescharacteristic
266C22×C61C2×C22⋊Q811yescharacteristic
267C22×C61#52511yescharacteristic
268C22×C61#57611yescharacteristic
269C22×C61#57711yescharacteristic
270C22×C61#57711yescharacteristic
271C22×C61#57711yescharacteristic
272C2×D61—24no—
273C2×D61—42no—
274C2×D61—42no—
275C2×D61—42no—
276C2×D61—42no—
277C2×D61—42no—
278C2×D61—42no—
279C4×C61—22no—
280C4×C61—22no—
281C4×C61—22no—
282C4×C61—22no—
283C4×C61—41no—
284C4×C61—41no—
285C4×C61—42no—
286C4×C61—42no—
287C4×C61—81no—
288C4×C61—81no—
289C4×C61C2×C4×Q811yescharacteristic
290C4×C61C4×#4111yescharacteristic
291C4×C61#52911yescharacteristic
292C4×C61#53311yescharacteristic
293Dic61—42no—
294Dic61—42no—
295Dic61—42no—
296C2×#476—611no—
297#2331D6111yescharacteristic, complemented
298#2275—611no—
299#1988—611no—
300#1949—611no—
301#1920—611no—
302#1919—611no—
303#1864—611no—
304#1862—611no—
305#1804—611no—
306#1776—611no—
307C4×#106—611no—
308#1768—611no—
309#1762—611no—
310C4×#102—611no—
311C2×C61C4×C22⋊Q811yescharacteristic
312C2×C61#294611yescharacteristic
313C2×C61#294911yescharacteristic
314C2×C61#308111yescharacteristic
315C2×C61#308411yescharacteristic
316C2×C61#311811yescharacteristic
317C2×C61#312511yescharacteristic
318D61—44no—
319C2×C4⋊Q8C2×D6111yescharacteristic
320C2×C4×D4—611no—
321C2×C4×D4—611no—
322C2×C4×D4—611no—
323#476—618no—
324C2×#107—611no—
325C2×#106—611no—
326C2×#106—611no—
327C2×#106—611no—
328C2×C4⋊C8—611no—
329C2×C4⋊C8—611no—
330C2×#102—611no—
331C2×#102—611no—
332C2×#102—611no—
333C2×#102—611no—
334C2×#97—611no—
335C2×C4×C8—611no—
336#391—21no—
337#391—21no—
338#389C2×D6111yescharacteristic
339#389C2×D6111yescharacteristic
340#387—21no—
341#387—21no—
342#382C2×D6111yescharacteristic
343C4×C4⋊C4—611no—
344C4×C4⋊C4—611no—
345C4×C4⋊C4—611no—
346C4×C4⋊C4C2×D6111yescharacteristic
347C4×C4⋊C4C2×D6111yescharacteristic
348C4×C22⋊C4—1221no—
349C4×C22⋊C4—1221no—
350C4×C22⋊C4—1221no—
351#376C2×D6111yescharacteristic
352C2×#95—1221no—
353#340—611no—
354#340—611no—
355#340—611no—
356#340—611no—
357#340—611no—
358#340—611no—
359#340—611no—
360#340—611no—
361#336—611no—
362#336—611no—
363C61#2162311yescharacteristic, complemented, Sylow
364C22×Q8—21no—
365C22×D4—611no—
366C23×C4—1221no—
367C23×C4—1221no—
368C23×C4—1221no—
369C22×C8—611no—
370C22×C8—611no—
371C22×C8—611no—
372C22×C8—611no—
373C4⋊Q8—22no—
374C4⋊Q8C4×D6114yescomplemented
375C4×D4—614no—
376C4×D4—614no—
377C4×D4—1222no—
378C4×D4—1222no—
379C4×D4—1222no—
380C4×D4—1222no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—611no—
385C2×C4⋊C4—611no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4C22×D6111yescharacteristic
388C2×C4⋊C4C22×D6111yescharacteristic
389C2×C4⋊C4C22×D6111yescharacteristic
390C2×C4⋊C4C22×D6111yescharacteristic
391C2×C22⋊C4—1221no—
392C2×C22⋊C4—1221no—
393C2×C22⋊C4—1221no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—1221no—
397C2×C42—1221no—
398C2×C42—1221no—
399C2×C42C22×D6111yescharacteristic
400C2×C42C22×D6111yescharacteristic
401C2×C42C22×D6111yescharacteristic
402#107—1222no—
403#106—614no—
404#106—614no—
405#106—1222no—
406C4⋊C8—614no—
407C4⋊C8—1222no—
408#102—614no—
409#102—614no—
410#102—1222no—
411#102—1222no—
412#97—1222no—
413C4×C8—1222no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—1221no—
421#95—1221no—
422#95—1221no—
423#95C22⋊D6111yescharacteristic
424#95C22⋊D6111yescharacteristic
425#95C22⋊D6111yescharacteristic
426#95C22⋊D6111yescharacteristic
427C24—1221no—
428C2×Q8—24no—
429C2×Q8—81no—
430C2×Q8—81no—
431C2×D4—612no—
432C2×D4—612no—
433C2×D4—612no—
434C2×D4—1221no—
435C2×D4—1221no—
436C2×D4—1221no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—1224no—
442C22×C4—1221no—
443C22×C4—1221no—
444C22×C4—1221no—
445C22×C4—1224no—
446C22×C4—1224no—
447C22×C4—4881no—
448C22×C4—4881no—
449C22×C4—4881no—
450C22×C4—4881no—
451C22×C4—4881no—
452C22×C4—4881no—
453C22×C4C2×C22⋊D6111yescharacteristic
454C22×C4C2×C22⋊D6111yescharacteristic
455C22×C4C2×C22⋊D6111yescharacteristic
456C22×C4C2×C22⋊D6111yescharacteristic
457C22×C4C2×C22⋊D6111yescharacteristic
458C22×C4C2×C22⋊D6111yescharacteristic
459C22×C4C23×D6111yescharacteristic
460C2×C8—612no—
461C2×C8—612no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—24no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—81no—
480C4⋊C4—81no—
481C4⋊C4—612no—
482C4⋊C4—612no—
483C4⋊C4—612no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4C2×C4×D6112yes—
488C4⋊C4C2×C4×D6112yes—
489C22⋊C4—1224no—
490C22⋊C4—1224no—
491C22⋊C4—1224no—
492C42—21no—
493C42—21no—
494C42—81no—
495C42—81no—
496C42—4881no—
497C42—4881no—
498C42—4881no—
499C42C2×C4×D6112yes—
500C42#1175822212yes—
501C42Q8×D6112yes—
502C42#1175822612yes—
503C23—1222no—
504C23—1222no—
505C23—1222no—
506C23—2441no—
507C23—2441no—
508C23—2441no—
509C23—2441no—
510C23C22×C22⋊D6111yescharacteristic
511Q8—84no—
512D4—614no—
513D4—1222no—
514D4—1222no—
515D4—1222no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—1222no—
543C2×C4—1222no—
544C2×C4—1222no—
545C2×C4—4884no—
546C2×C4—4884no—
547C2×C4—4884no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4C4×C22⋊D6112yes—
555C2×C4C4×C22⋊D6112yes—
556C2×C4#1451975312yes—
557C2×C4#1451975312yes—
558C2×C4C22×C4×D6111yescharacteristic
559C2×C4C2×Q8×D6111yescharacteristic
560C2×C4#41×D6111yescharacteristic
561C2×C4#41×D6111yescharacteristic
562C2×C4C2×#1175822211yescharacteristic
563C2×C4C2×#1175822611yescharacteristic
564C8—1222no—
565C8—1222no—
566C8—2441no—
567C8—2441no—
568C22—1224no—
569C22—2442no—
570C22—2442no—
571C22—2442no—
572C22—2442no—
573C22—2442no—
574C22—2442no—
575C22C2×C4×C22⋊D6111yescharacteristic
576C22C2×#1451975311yescharacteristic
577C22#1684026911yescharacteristic
578C22#1684056511yescharacteristic
579C22#1684057011yescharacteristic
580C22#1684057011yescharacteristic
581C22#1684057311yescharacteristic
582C4—22no—
583C4—22no—
584C4—22no—
585C4—22no—
586C4—42no—
587C4—42no—
588C4—41no—
589C4—41no—
590C4—81no—
591C4—81no—
592C4—2442no—
593C4—2442no—
594C4—2442no—
595C4C4×Q8×D6111yescharacteristic
596C4C4×#1175822611yescharacteristic
597C4#1684029911yescharacteristic
598C4#1684031611yescharacteristic
599C2—2444no—
600C2C4×#1451975311yescharacteristic
601C2#2145465111yescharacteristic
602C2#2145467811yescharacteristic
603C2#2145564411yescharacteristic
604C2#2145567711yescharacteristic
605C2#2145599711yescharacteristic
606C2#2145609011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2331C2
socleC23×C61C22×D4
prime radicalC22×D244C23
cosocleC22×C4×C61C24
hypercenter#2331D61
hypocenterC61#21623
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ #376 ◁ #2331

Complements

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

NH ≅ G/Ntype
3. #21446772C2semidirect
4. #21446585C2semidirect
5. #21446401C2semidirect
6. #21446394C2semidirect
10. #21445717C2semidirect
11. C4×#14519708C2semidirect
12. #21445676C2semidirect
15. C61×#2331C2semidirect
19. #16840049C4semidirect
73. C4×D244Q8semidirect
85. #14519708C2×C4semidirect
86. #14519708C2×C4semidirect
88. C4⋊#92418C2×C4semidirect
100. C4⋊Q8×C61C2×C4semidirect
297. #2331D61semidirect
363. C61#21623semidirect
374. C4⋊Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168400492
#214481812
#214467722
#214465852
#214464012
#214463942
#214460792
#214460652
#214458262
#214457172
C4×#145197082
#214456762
#214456472
C4×#145196972
C61×#23312
#2162361