Finite Group Databasebeta

← #29683083

Subgroups — #29683083

Order 15616.

890 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839860C211yesmaximal, characteristic
2#21448181C211yesmaximal, characteristic
3#21446457C211yesmaximal, characteristic, complemented
4#21446450C211yesmaximal, characteristic, complemented
5#21446408C211yesmaximal, characteristic, complemented
6#21446387C211yesmaximal, characteristic, complemented
7#21446156C211yesmaximal, characteristic
8#21446156C211yesmaximal, characteristic
9#21446079C211yesmaximal, characteristic
10#21446065C211yesmaximal, characteristic
11#21445717C211yesmaximal, characteristic, complemented
12C4×#14519701C211yesmaximal, characteristic, complemented
13C4×#14519697C211yesmaximal, characteristic
14#21445571C211yesmaximal, characteristic, complemented
15C61×#2320C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20#16839860C418yescomplemented
21C2×#14519710C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×#14519701C2211yescharacteristic
25C2×#14519701C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
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#16839517C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48#16839517C2211yescharacteristic
49C2×C4×Q8×C61C2211yescharacteristic
50C61×#391C2211yescharacteristic
51C61×#391C2211yescharacteristic
52C61×#389C2211yescharacteristic
53C61×#389C2211yescharacteristic
54C61×#387—21no—
55C61×#387—21no—
56C61×#383—21no—
57C61×#382—21no—
58C4×C4⋊C4×C61C2211yescharacteristic
59C61×#376C2211yescharacteristic
60C22×D244C2311yescharacteristic
61C22×C4×D61—21no—
62C22×C4×D61—21no—
63C22×C4×D61—21no—
64C2×#11758201—22no—
65C2×#11758201—22no—
66C2×#11758201C2×C414yes—
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C4×D244—22no—
72C4×D244—22no—
73C4×D244—22no—
74C4×D244—22no—
75C4×D244—22no—
76C4×D244C2×C414yes—
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86#14519710—22no—
87#14519710C2×C414yescomplemented
88#14519708—22no—
89#14519701—22no—
90#14519701—22no—
91#14519701C2×C414yescomplemented
92#14519697—22no—
93#14519697—22no—
94#14519697C2×C414yes—
95#14519688C2×C414yescomplemented
96C4×#92418—22no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100C22×Q8×C61C2311yescharacteristic
101C4×Q8×C61—22no—
102C4×Q8×C61C2×C414yescomplemented
103C2×C4⋊C4×C61—21no—
104C2×C4⋊C4×C61—21no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61C2311yescharacteristic
107C2×C4⋊C4×C61C2311yescharacteristic
108C2×C4⋊C4×C61C2311yescharacteristic
109C2×C42×C61—21no—
110C2×C42×C61—21no—
111C2×C42×C61C2311yescharacteristic
112C2×C42×C61C2311yescharacteristic
113C2×C42×C61C2311yescharacteristic
114#95×C61—21no—
115#95×C61—21no—
116#95×C61—21no—
117#95×C61—21no—
118#95×C61—21no—
119#95×C61—21no—
120#95×C61—21no—
121#95×C61D411yescharacteristic
122#95×C61D411yescharacteristic
123#95×C61D411yescharacteristic
124#95×C61D411yescharacteristic
125C23×D61—21no—
126C2×Q8×C61—21no—
127C2×Q8×C61—21no—
128C2×Q8×C61—21no—
129C2×Q8×C61—21no—
130C2×Q8×C61—21no—
131C2×Q8×C61C22×C412yes—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2411yescharacteristic
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C2×D244—21no—
147C2×D244—21no—
148C2×D244—21no—
149C2×D244C22×C412yes—
150C2×D244#4112yes—
151C2×D244#4112yes—
152C2×C4×D61—24no—
153C2×C4×D61—24no—
154C2×C4×D61—24no—
155C2×C4×D61—81no—
156C2×C4×D61—81no—
157C2×C4×D61—81no—
158C2×C4×D61—81no—
159C2×C4×D61—81no—
160C2×C4×D61—81no—
161C4⋊C4×C61—24no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—81no—
168C4⋊C4×C61—81no—
169C4⋊C4×C61C22×C412yes—
170C42×C61—24no—
171C42×C61—21no—
172C42×C61—21no—
173C42×C61—21no—
174C42×C61—21no—
175C42×C61—81no—
176C42×C61C22×C412yes—
177C42×C61#4112yes—
178#11758201—28no—
179#11758198—24no—
180#11758198—24no—
181#11758198—24no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61C22×C412yes—
186C4⋊Dic61#4112yes—
187C4⋊Dic61#4112yes—
188C4×Dic61—81no—
189C4×Dic61—81no—
190C4×Dic61—81no—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418C22×C412yes—
202C2×#92418C22×C412yes—
203C23×C61C22×D411yescharacteristic
204C22×D61—22no—
205C22×D61—22no—
206C22×D61—22no—
207C22×D61—41no—
208C22×D61—41no—
209C22×D61—41no—
210C22×D61—41no—
211Q8×C61—22no—
212Q8×C61—22no—
213Q8×C61—41no—
214Q8×C61—41no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—22no—
220C2×C4×C61—22no—
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—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×C61—41no—
243C2×C4×C61C4×D412yes—
244C2×C4×C61C4×D412yes—
245C2×C4×C61C23×C411yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C61C2×#4111yescharacteristic
249C2×C4×C61C2×#4111yescharacteristic
250C2×C4×C61C2×#4111yescharacteristic
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260D244—22no—
261D244—22no—
262D244—22no—
263D244#11714yes—
264C4×D61—84no—
265C4×D61—84no—
266C4×D61—84no—
267#92418—22no—
268#92418—22no—
269#92418—41no—
270#92418—41no—
271#21125—611nomaximal, Sylow
272C22×C61C2×C4×D411yescharacteristic
273C22×C61#52511yescharacteristic
274C22×C61#52511yescharacteristic
275C22×C61#57611yescharacteristic
276C22×C61#57711yescharacteristic
277C22×C61#57711yescharacteristic
278C22×C61#57811yescharacteristic
279C2×D61—24no—
280C2×D61—42no—
281C2×D61—42no—
282C2×D61—42no—
283C2×D61—42no—
284C2×D61—42no—
285C2×D61—42no—
286C4×C61—22no—
287C4×C61—22no—
288C4×C61—41no—
289C4×C61—41no—
290C4×C61—41no—
291C4×C61—41no—
292C4×C61—42no—
293C4×C61—42no—
294C4×C61—81no—
295C4×C61—81no—
296C4×C61C2×#11711yescharacteristic
297C4×C61C4×#4111yescharacteristic
298C4×C61#52911yescharacteristic
299C4×C61#52911yescharacteristic
300Dic61—42no—
301Dic61—42no—
302Dic61—42no—
303C2×#440—611no—
304#2320D6111yescharacteristic, complemented
305#2275—611no—
306#1928—611no—
307#1927—611no—
308#1921—611no—
309#1918—611no—
310#1877—611no—
311#1877—611no—
312#1864—611no—
313#1862—611no—
314#1776—611no—
315C4×#103—611no—
316C4×#102—611no—
317#1746—611no—
318C2×C61#229011yescharacteristic
319C2×C61#294611yescharacteristic
320C2×C61#294711yescharacteristic
321C2×C61#311811yescharacteristic
322C2×C61#312011yescharacteristic
323C2×C61#312311yescharacteristic
324C2×C61#312411yescharacteristic
325D61—44no—
326C22×SD16—611no—
327C2×C4×Q8C2×D6111yescharacteristic
328C2×C4×D4—611no—
329C2×C4×D4—611no—
330C2×C4×D4—611no—
331#440—618no—
332C2×#107—611no—
333C2×#107—611no—
334C2×#106—611no—
335C2×#103—611no—
336C2×#103—611no—
337C2×#103—611no—
338C2×#102—611no—
339C2×#102—611no—
340C2×#102—611no—
341C2×#97—611no—
342C2×C4×C8—611no—
343#391C2×D6111yescharacteristic
344#391C2×D6111yescharacteristic
345#389C2×D6111yescharacteristic
346#389C2×D6111yescharacteristic
347#387—21no—
348#387—21no—
349#383—21no—
350#382—21no—
351C4×C4⋊C4—611no—
352C4×C4⋊C4—611no—
353C4×C4⋊C4—611no—
354C4×C4⋊C4C2×D6111yescharacteristic
355C4×C22⋊C4—1221no—
356C4×C22⋊C4—1221no—
357C4×C22⋊C4—1221no—
358#376C2×D6111yescharacteristic
359C2×#95—1221no—
360#340—611no—
361#340—611no—
362#340—611no—
363#340—611no—
364#340—611no—
365#340—611no—
366#336—611no—
367#336—611no—
368#336—611no—
369#336—611no—
370C61#2112511yescharacteristic, complemented, Sylow
371C22×Q8C22×D6111yescharacteristic
372C22×D4—611no—
373C23×C4—1221no—
374C23×C4—1221no—
375C23×C4—1221no—
376C2×SD16—614no—
377C2×SD16—1222no—
378C2×SD16—1222no—
379C22×C8—611no—
380C22×C8—611no—
381C22×C8—611no—
382C22×C8—611no—
383C4×Q8—22no—
384C4×Q8C4×D6114yescomplemented
385C4×D4—614no—
386C4×D4—1222no—
387C4×D4—1222no—
388C4×D4—1222no—
389C4×D4—1222no—
390C4×D4—1222no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—611no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4—611no—
397C2×C4⋊C4C22×D6111yescharacteristic
398C2×C4⋊C4C22×D6111yescharacteristic
399C2×C4⋊C4C22×D6111yescharacteristic
400C2×C22⋊C4—1221no—
401C2×C22⋊C4—1221no—
402C2×C22⋊C4—1221no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—1221no—
406C2×C42—1221no—
407C2×C42—1221no—
408C2×C42C22×D6111yescharacteristic
409C2×C42C22×D6111yescharacteristic
410C2×C42C22×D6111yescharacteristic
411#107—614no—
412#107—1222no—
413#106—1222no—
414#103—614no—
415#103—1222no—
416#103—1222no—
417#102—614no—
418#102—1222no—
419#102—1222no—
420#97—614no—
421C4×C8—1222no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—1221no—
430#95—1221no—
431#95—1221no—
432#95C22⋊D6111yescharacteristic
433#95C22⋊D6111yescharacteristic
434#95C22⋊D6111yescharacteristic
435#95C22⋊D6111yescharacteristic
436C24—1221no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C2×C4×D6112yes—
443C2×D4—612no—
444C2×D4—612no—
445C2×D4—612no—
446C2×D4—1221no—
447C2×D4—1221no—
448C2×D4—1221no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—1224no—
454C22×C4—1224no—
455C22×C4—1221no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4—1224no—
459C22×C4—4881no—
460C22×C4—4881no—
461C22×C4—4881no—
462C22×C4—4881no—
463C22×C4—4881no—
464C22×C4—4881no—
465C22×C4C2×C22⋊D6111yescharacteristic
466C22×C4C2×C22⋊D6111yescharacteristic
467C22×C4C2×C22⋊D6111yescharacteristic
468C22×C4C2×C22⋊D6111yescharacteristic
469C22×C4C2×C22⋊D6111yescharacteristic
470C22×C4C2×C22⋊D6111yescharacteristic
471C22×C4C23×D6111yescharacteristic
472SD16—1228no—
473C2×C8—612no—
474C2×C8—612no—
475C2×C8—1221no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C4⋊C4—21no—
486C4⋊C4—24no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—81no—
492C4⋊C4—81no—
493C4⋊C4—612no—
494C4⋊C4—612no—
495C4⋊C4—612no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4C2×C4×D6112yes—
500C22⋊C4—1224no—
501C22⋊C4—1224no—
502C22⋊C4—1224no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—24no—
508C42—81no—
509C42—4881no—
510C42—4881no—
511C42—4881no—
512C42C2×C4×D6112yes—
513C42#1175822212yes—
514C23—1222no—
515C23—1222no—
516C23—1222no—
517C23—2441no—
518C23—2441no—
519C23—2441no—
520C23—2441no—
521C23C22×C22⋊D6111yescharacteristic
522Q8—22no—
523Q8—22no—
524Q8—41no—
525Q8—41no—
526D4—614no—
527D4—1222no—
528D4—1222no—
529D4—1222no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—1222no—
559C2×C4—1222no—
560C2×C4—1222no—
561C2×C4—4884no—
562C2×C4—4884no—
563C2×C4—4884no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4C4×C22⋊D6112yes—
571C2×C4C4×C22⋊D6112yes—
572C2×C4C22×C4×D6111yescharacteristic
573C2×C4#41×D6111yescharacteristic
574C2×C4#41×D6111yescharacteristic
575C2×C4#41×D6111yescharacteristic
576C2×C4#41×D6111yescharacteristic
577C2×C4C2×#1175822211yescharacteristic
578C8—1222no—
579C8—1222no—
580C8—2441no—
581C8—2441no—
582C22—1224no—
583C22—2442no—
584C22—2442no—
585C22—2442no—
586C22—2442no—
587C22—2442no—
588C22—2442no—
589C22C2×C4×C22⋊D6111yescharacteristic
590C22#1684026911yescharacteristic
591C22#1684026911yescharacteristic
592C22#1684056511yescharacteristic
593C22#1684057011yescharacteristic
594C22#1684057011yescharacteristic
595C22#1684057711yescharacteristic
596C4—22no—
597C4—22no—
598C4—42no—
599C4—42no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4—2442no—
607C4—2442no—
608C4—2442no—
609C4#117×D6111yescharacteristic
610C4#1684023011yescharacteristic
611C4#1684029011yescharacteristic
612C4#1684029011yescharacteristic
613C2—2444no—
614C2#2144825611yescharacteristic
615C2#2145464711yescharacteristic
616C2#2145466211yescharacteristic
617C2#2145599711yescharacteristic
618C2#2145602711yescharacteristic
619C2#2145606611yescharacteristic
620C2#2145607511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2320C2
socleC23×C61C22×D4
prime radicalC22×D244C23
cosocleC22×C4×C61C24
hypercenter#2320D61
hypocenterC61#21125
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ #376 ◁ #2320

Complements

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

NH ≅ G/Ntype
3. #21446457C2semidirect
4. #21446450C2semidirect
5. #21446408C2semidirect
6. #21446387C2semidirect
11. #21445717C2semidirect
12. C4×#14519701C2semidirect
14. #21445571C2semidirect
15. C61×#2320C2semidirect
20. #16839860C4semidirect
87. #14519710C2×C4semidirect
91. #14519701C2×C4semidirect
95. #14519688C2×C4semidirect
102. C4×Q8×C61C2×C4semidirect
304. #2320D61semidirect
370. C61#21125semidirect
384. C4×Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398602
#214481812
#214464572
#214464502
#214464082
#214463872
#214461562
#214460792
#214460652
#214457172
C4×#145197012
C4×#145196972
#214455712
C61×#23202
#2112561