Finite Group Databasebeta

← #29699364

Subgroups — #29699364

Order 15616.

838 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×#16839864C211yesmaximal, characteristic
2#21448790C211yesmaximal, characteristic
3C4⋊C4×Dic122C211yesmaximal, characteristic, complemented
4#21446516C211yesmaximal, characteristic
5#21446502C211yesmaximal, characteristic
6#21446412C211yesmaximal, characteristic, complemented
7#21446391C211yesmaximal, characteristic, complemented
8#21446173C211yesmaximal, characteristic
9#21446173C211yesmaximal, characteristic
10#21445953C211yesmaximal, characteristic, complemented
11#21445835C211yesmaximal, characteristic, complemented
12#21445820C211yesmaximal, characteristic
13#21445650C211yesmaximal, characteristic, complemented
14C4×#14519702C211yesmaximal, characteristic, complemented
15C61×#1771C211yesmaximal, characteristic, complemented
16C22×#11758190C2211yescharacteristic
17C2×C4×Dic122C2211yescharacteristic
18C2×C4×Dic122C2211yescharacteristic
19C2×C4×Dic122C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21#16839864C418yescomplemented
22C2×#14519711C2211yescharacteristic
23C2×#14519702C2211yescharacteristic
24C2×#14519702C2211yescharacteristic
25C2×#14519702C2211yescharacteristic
26C2×#14519699C2211yescharacteristic
27C2×#14519699C2211yescharacteristic
28C2×#14519699C2211yescharacteristic
29#16839664C2211yescharacteristic
30#16839664C2211yescharacteristic
31#16839660C2211yescharacteristic
32#16839660C2211yescharacteristic
33#16839659—21no—
34#16839659—21no—
35#16839652—21no—
36#16839652—21no—
37#16839632C2211yescharacteristic
38#16839631—21no—
39#16839628C2211yescharacteristic
40#16839624—21no—
41C4⋊C4×Dic61—21no—
42C4×C4⋊Dic61C2211yescharacteristic
43C4×C4⋊Dic61C2211yescharacteristic
44#16839609—21no—
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53C2×C4⋊C8×C61C2211yescharacteristic
54C2×#97×C61C2211yescharacteristic
55C2×#97×C61C2211yescharacteristic
56C2×C4×C8×C61C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C22×Dic122C2311yescharacteristic
61C22×D244C2311yescharacteristic
62C22×C4×D61—21no—
63C2×#11758190—22no—
64C2×#11758190—22no—
65C2×#11758190C2×C414yes—
66C4×Dic122—22no—
67C4×Dic122—22no—
68C4×Dic122—22no—
69C4×Dic122—41no—
70C4×Dic122—41no—
71C4×Dic122C2×C414yes—
72C4×D244—22no—
73C4×D244C2×C414yes—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×#11758196—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×C4×Dic61—21no—
93C2×C4×Dic61—21no—
94C2×C4×Dic61—21no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61—21no—
97#14519711C2×C414yes—
98#14519702—22no—
99#14519702—22no—
100#14519702C2×C414yes—
101#14519699—41no—
102#14519699—41no—
103#14519699C2×C414yes—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110C22×C8×C61C2311yescharacteristic
111C22×C8×C61C2311yescharacteristic
112C22×C8×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114C2×C4⋊C4×C61D411yescharacteristic
115C2×C4⋊C4×C61D411yescharacteristic
116C2×C42×C61C2311yescharacteristic
117C2×C42×C61C2311yescharacteristic
118C2×C42×C61C2311yescharacteristic
119C4⋊C8×C61—22no—
120#97×C61—41no—
121#97×C61C2×C414yes—
122C4×C8×C61—41no—
123#95×C61D411yescharacteristic
124#95×C61D411yescharacteristic
125C23×D61—21no—
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2411yescharacteristic
133C22×Dic61—21no—
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×D244C22×C412yes—
146C2×C4×D61—24no—
147C2×C4×D61—81no—
148C2×C4×D61—81no—
149C2×Dic122—21no—
150C2×Dic122—21no—
151C2×Dic122—21no—
152C2×Dic122C22×C412yes—
153C2×Dic122#4112yes—
154C2×Dic122#4112yes—
155C2×C8×C61—21no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61C22×C412yes—
166C2×C8×C61C22×C412yes—
167C4⋊C4×C61—22no—
168C4⋊C4×C61—41no—
169C42×C61—21no—
170C42×C61—21no—
171C42×C61—21no—
172C42×C61—21no—
173C42×C61C22×C412yes—
174C42×C61#4112yes—
175#11758198—24no—
176#11758198—42no—
177#11758198—42no—
178#11758198—81no—
179#11758198—81no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—42no—
191C4⋊Dic61—81no—
192C4⋊Dic61C22×C412yes—
193C4⋊Dic61C22×C412yes—
194#11758196—24no—
195#11758196—42no—
196#11758196—42no—
197#11758196—81no—
198#11758196—81no—
199C4×Dic61—24no—
200C4×Dic61—42no—
201C4×Dic61—42no—
202C4×Dic61—81no—
203C4×Dic61—81no—
204#11758190—28no—
205C23×C61C22×D411yescharacteristic
206C22×D61—22no—
207C22×D61—41no—
208C22×D61—41no—
209C22×D61—41no—
210C22×D61—41no—
211C22×D61—41no—
212C22×D61—41no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
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×C61C4×D412yes—
229C2×C4×C61C4×D412yes—
230C2×C4×C61#13712yes—
231C2×C4×C61C23×C411yescharacteristic
232C2×C4×C61C2×#4111yescharacteristic
233C2×C4×C61C2×#4111yescharacteristic
234C2×C4×C61C2×#4111yescharacteristic
235C2×C4×C61H(5,𝔽2)11yescharacteristic
236C2×C4×C612−1+411yescharacteristic
237C2×Dic61—22no—
238C2×Dic61—22no—
239C2×Dic61—22no—
240C2×Dic61—22no—
241C2×Dic61—22no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
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—
258D244—22no—
259D244—22no—
260D244—41no—
261D244—41no—
262C4×D61—84no—
263Dic122—22no—
264Dic122—22no—
265Dic122—22no—
266Dic122#11714yes—
267C8×C61—22no—
268C8×C61—22no—
269C8×C61—41no—
270C8×C61—41no—
271#22775—611nomaximal, Sylow
272C22×C61C2×C4×D411yescharacteristic
273C22×C61#54611yescharacteristic
274C22×C61#54811yescharacteristic
275C22×C61C2×#13711yescharacteristic
276C22×C61#57511yescharacteristic
277C22×C61#57611yescharacteristic
278C22×C61#57711yescharacteristic
279C2×D61—42no—
280C2×D61—42no—
281C2×D61—42no—
282C2×D61—81no—
283C2×D61—81no—
284C2×D61—81no—
285C2×D61—81no—
286C4×C61—22no—
287C4×C61—22no—
288C4×C61—22no—
289C4×C61—41no—
290C4×C61—41no—
291C4×C61—41no—
292C4×C61C2×#11711yescharacteristic
293C4×C61#52011yescharacteristic
294C4×C61#55211yescharacteristic
295C4×C61#55311yescharacteristic
296Dic61—24no—
297Dic61—42no—
298Dic61—42no—
299Dic61—81no—
300Dic61—81no—
301Dic61—81no—
302Dic61—81no—
303C2×#440—611no—
304#2357—611no—
305Q8×C4⋊C4—611no—
306#1936—611no—
307#1934—611no—
308#1921—611no—
309#1918—611no—
310#1880—611no—
311#1880—611no—
312#1836—611no—
313#1805—611no—
314#1802—611no—
315#1771D6111yescharacteristic, complemented
316#1763—611no—
317C4×#103—611no—
318C2×C61#235211yescharacteristic
319C2×C61C4×#13711yescharacteristic
320C2×C61#294611yescharacteristic
321C2×C61#330911yescharacteristic
322C2×C61#332011yescharacteristic
323C2×C61#337111yescharacteristic
324C2×C61#337511yescharacteristic
325D61—82no—
326C22×SD16—611no—
327C2×C4×Q8—611no—
328C2×C4×Q8—611no—
329C2×C4×Q8—611no—
330C2×C4×D4—611no—
331#440—618no—
332C2×#107—611no—
333C2×C4⋊C8C2×D6111yescharacteristic
334C2×#103—611no—
335C2×#103—611no—
336C2×#103—611no—
337C2×#102—611no—
338C2×#102—611no—
339C2×#102—611no—
340C2×#97C2×D6111yescharacteristic
341C2×#97C2×D6111yescharacteristic
342C2×C4×C8C2×D6111yescharacteristic
343#390—611no—
344#390—611no—
345#389—611no—
346#389—611no—
347#389—1221no—
348#389—1221no—
349#388—1221no—
350#388—1221no—
351#384—611no—
352#384—1221no—
353#382—611no—
354#381—1221no—
355C4×C4⋊C4—611no—
356C4×C4⋊C4—611no—
357C4×C4⋊C4—1221no—
358C4×C4⋊C4C2×D6111yescharacteristic
359C4×C22⋊C4—1221no—
360#340—611no—
361#340—611no—
362#340—611no—
363#340—611no—
364#340—611no—
365#340—611no—
366#340—611no—
367#340—611no—
368#336C2×D6111yescharacteristic
369#336C2×D6111yescharacteristic
370C61#2277511yescharacteristic, complemented, Sylow
371C22×Q8—611no—
372C22×D4—611no—
373C23×C4—1221no—
374C2×SD16—614no—
375C2×SD16—1222no—
376C2×SD16—1222no—
377C22×C8C22×D6111yescharacteristic
378C22×C8C22×D6111yescharacteristic
379C22×C8C22×D6111yescharacteristic
380C22×C8C22×D6111yescharacteristic
381C4×Q8—614no—
382C4×Q8—1222no—
383C4×Q8—1222no—
384C4×Q8—1222no—
385C4×Q8—2441no—
386C4×Q8—2441no—
387C4×D4—614no—
388C4×D4—1222no—
389C2×C4⋊C4—611no—
390C2×C4⋊C4—611no—
391C2×C4⋊C4—611no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4—611no—
394C2×C4⋊C4—611no—
395C2×C4⋊C4—1221no—
396C2×C4⋊C4—1221no—
397C2×C4⋊C4—1221no—
398C2×C4⋊C4—1221no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4D24411yescharacteristic
403C2×C4⋊C4D24411yescharacteristic
404C2×C22⋊C4—1221no—
405C2×C22⋊C4—1221no—
406C2×C22⋊C4—1221no—
407C2×C22⋊C4—1221no—
408C2×C22⋊C4—1221no—
409C2×C42—1221no—
410C2×C42—1221no—
411C2×C42—1221no—
412C2×C42—1221no—
413C2×C42—1221no—
414C2×C42C22×D6111yescharacteristic
415C2×C42C22×D6111yescharacteristic
416C2×C42C22×D6111yescharacteristic
417#107—614no—
418C4⋊C8—22no—
419#103—614no—
420#103—1222no—
421#103—1222no—
422#102—614no—
423#102—2441no—
424#102—2441no—
425#97—41no—
426#97C4×D6114yes—
427C4×C8—41no—
428#95—1221no—
429#95—1221no—
430#95—1221no—
431#95—1221no—
432#95—1221no—
433#95—1221no—
434#95D24411yescharacteristic
435#95D24411yescharacteristic
436C24—1221no—
437C2×Q8—612no—
438C2×Q8—612no—
439C2×Q8—612no—
440C2×Q8—1221no—
441C2×Q8—1221no—
442C2×Q8—1221no—
443C2×D4—612no—
444C2×D4—1221no—
445C2×D4—1221no—
446C2×D4—1221no—
447C2×D4—1221no—
448C2×D4—1221no—
449C22×C4—1221no—
450C22×C4—1221no—
451C22×C4—1221no—
452C22×C4—1224no—
453C22×C4—1221no—
454C22×C4—1221no—
455C22×C4—1221no—
456C22×C4—1221no—
457C22×C4—4881no—
458C22×C4—4881no—
459C22×C4C2×D24411yescharacteristic
460C22×C4C2×D24411yescharacteristic
461C22×C4C2×D24411yescharacteristic
462C22×C4C2×D24411yescharacteristic
463C22×C4C2×D24411yescharacteristic
464C22×C4C2×D24411yescharacteristic
465C22×C4C23×D6111yescharacteristic
466SD16—1228no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8C2×C4×D6112yes—
478C2×C8C2×C4×D6112yes—
479C4⋊C4—22no—
480C4⋊C4—41no—
481C4⋊C4—612no—
482C4⋊C4—612no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—1224no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4—1221no—
494C4⋊C4—4881no—
495C4⋊C4—4881no—
496C4⋊C4—4881no—
497C4⋊C4—2442no—
498C4⋊C4—2442no—
499C4⋊C4—2442no—
500C22⋊C4—1224no—
501C22⋊C4—4881no—
502C22⋊C4—4881no—
503C22⋊C4—2442no—
504C22⋊C4—2442no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—1224no—
510C42—4881no—
511C42—4881no—
512C42—2442no—
513C42—2442no—
514C42C2×C4×D6112yes—
515C42#1175822212yes—
516C23—1222no—
517C23—2441no—
518C23—2441no—
519C23—2441no—
520C23—2441no—
521C23—2441no—
522C23—2441no—
523C23C22×D24411yescharacteristic
524Q8—614no—
525Q8—1222no—
526Q8—1222no—
527Q8—1222no—
528D4—1222no—
529D4—1222no—
530D4—2441no—
531D4—2441no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
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—1222no—
548C2×C4—1222no—
549C2×C4—1222no—
550C2×C4—1222no—
551C2×C4—1222no—
552C2×C4—4884no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4—2441no—
558C2×C4—2441no—
559C2×C4—2441no—
560C2×C4—2441no—
561C2×C4—2441no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4C4×D24412yes—
570C2×C4C4×D24412yes—
571C2×C4#1451981012yes—
572C2×C4C22×C4×D6111yescharacteristic
573C2×C4#41×D6111yescharacteristic
574C2×C4#41×D6111yescharacteristic
575C2×C4C2×#1175822211yescharacteristic
576C2×C4#1451982211yescharacteristic
577C2×C4#1451982511yescharacteristic
578C8—22no—
579C8—22no—
580C8—41no—
581C8—41no—
582C22—4881no—
583C22—4881no—
584C22—4881no—
585C22—4881no—
586C22—2442no—
587C22—2442no—
588C22—2442no—
589C22C2×C4×D24411yescharacteristic
590C22#1684040711yescharacteristic
591C22#1684042411yescharacteristic
592C22C2×#1451981011yescharacteristic
593C22#1684056211yescharacteristic
594C22#1684056711yescharacteristic
595C22#1684057411yescharacteristic
596C4—22no—
597C4—22no—
598C4—22no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—1224no—
603C4—4881no—
604C4—4881no—
605C4—4881no—
606C4—4881no—
607C4—2442no—
608C4—2442no—
609C4#117×D6111yescharacteristic
610C4#1684024311yescharacteristic
611C4#1684045311yescharacteristic
612C4#1684046211yescharacteristic
613C2—4882no—
614C2#2144875111yescharacteristic
615C2C4×#1451981011yescharacteristic
616C2#2145465311yescharacteristic
617C2#2145782711yescharacteristic
618C2#2145799211yescharacteristic
619C2#2145858911yescharacteristic
620C2#2145863511yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1771C2
socleC23×C61C22×D4
prime radicalC22×D244C23
cosocleC22×C4×C61C24
hypercenter#1771D61
hypocenterC61#22775
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
3. C4⋊C4×Dic122C2semidirect
6. #21446412C2semidirect
7. #21446391C2semidirect
10. #21445953C2semidirect
11. #21445835C2semidirect
13. #21445650C2semidirect
14. C4×#14519702C2semidirect
15. C61×#1771C2semidirect
21. #16839864C4semidirect
315. #1771D61semidirect
370. C61#22775semidirect

Maximal subgroups

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

subgroupindex
C2×#168398642
#214487902
C4⋊C4×Dic1222
#214465162
#214465022
#214464122
#214463912
#214461732
#214459532
#214458352
#214458202
#214456502
C4×#145197022
C61×#17712
#2277561