Finite Group Databasebeta

← #29743126

Subgroups — #29743126

Order 15616.

828 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840066C211yesmaximal, characteristic, complemented
2C2×C4×#11758200C211yesmaximal, characteristic
3C4⋊C4×Dic122C211yesmaximal, characteristic, complemented
4#21447347C211yesmaximal, characteristic
5#21447295C211yesmaximal, characteristic, complemented
6#21447207C211yesmaximal, characteristic
7#21447154C211yesmaximal, characteristic, complemented
8#21446549C211yesmaximal, characteristic, complemented
9#21446378C211yesmaximal, characteristic, complemented
10#21446177C211yesmaximal, characteristic
11#21446177C211yesmaximal, characteristic
12#21446080C211yesmaximal, characteristic
13#21446072C211yesmaximal, characteristic, complemented
14#21446072C211yesmaximal, characteristic, complemented
15C61×#2454C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C2×C4×Dic122C2211yescharacteristic
18C2×C4×Dic122C2211yescharacteristic
19C2×C4×Dic122C2211yescharacteristic
20#16840066—24no—
21C4×#11758200—24no—
22C2×#14519710C2211yescharacteristic
23C2×#14519710C2211yescharacteristic
24C2×#14519710C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26C2×#14519708C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic
28C2×#14519700C2211yescharacteristic
29C2×#14519700C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×C4×#92418C2211yescharacteristic
35#16839660C2211yescharacteristic
36#16839660C2211yescharacteristic
37#16839659—21no—
38#16839659—21no—
39#16839632C2211yescharacteristic
40#16839631—21no—
41C4⋊C4×Dic61—21no—
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C2×#125×C61C2211yescharacteristic
51C2×C4×D4×C61C2211yescharacteristic
52C61×#399—21no—
53C61×#396—21no—
54C61×#390C2211yescharacteristic
55C61×#390C2211yescharacteristic
56C61×#389C2211yescharacteristic
57C61×#389C2211yescharacteristic
58C61×#385—21no—
59C61×#380—21no—
60C4×C4⋊C4×C61C2211yescharacteristic
61C22×Dic122C2311yescharacteristic
62C2×#11758200—22no—
63C2×#11758200—22no—
64C2×#11758200Q814yes—
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C4×Dic122—22no—
70C4×Dic122—22no—
71C4×Dic122—22no—
72C4×Dic122—22no—
73C4×Dic122—41no—
74C4×Dic122—41no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61—21no—
88#14519710—22no—
89#14519710—22no—
90#14519710—41no—
91#14519708—22no—
92#14519708—22no—
93C4⋊#92418—22no—
94#14519700—22no—
95#14519700—22no—
96#14519700D414yes—
97#14519698—22no—
98#14519698—22no—
99#14519698—41no—
100C4×#92418—22no—
101#14519684—21no—
102#14519684—21no—
103C22×D4×C61C2311yescharacteristic
104C23×C4×C61—21no—
105#125×C61—22no—
106#125×C61—41no—
107C4×D4×C61—22no—
108C4×D4×C61—41no—
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61—21no—
111C2×C4⋊C4×C61—21no—
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61D411yescharacteristic
114C2×C4⋊C4×C61D411yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C22⋊C4×C61—21no—
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61—21no—
121C2×C22⋊C4×C61—21no—
122C2×C22⋊C4×C61—21no—
123C2×C42×C61C2311yescharacteristic
124C2×C42×C61C2311yescharacteristic
125C2×C42×C61C2311yescharacteristic
126#95×C61—21no—
127#95×C61—21no—
128#95×C61D411yescharacteristic
129#95×C61D411yescharacteristic
130C24×C61—21no—
131C2×D4×C61—21no—
132C2×D4×C61—21no—
133C2×D4×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61—21no—
136C2×D4×C61C2×Q812yes—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—42no—
141C22×C4×C61—42no—
142C22×C4×C61—81no—
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2411yescharacteristic
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—21no—
154C2×Dic122—21no—
155C2×Dic122—21no—
156C2×Dic122—21no—
157C2×Dic122C2×D412yes—
158C2×Dic122C2×Q812yes—
159C2×Dic122#4112yes—
160C4⋊C4×C61—22no—
161C4⋊C4×C61—22no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—42no—
168C4⋊C4×C61—42no—
169C4⋊C4×C61—81no—
170C4⋊C4×C61—81no—
171C4⋊C4×C61C2×D412yes—
172C22⋊C4×C61—42no—
173C22⋊C4×C61—42no—
174C22⋊C4×C61—81no—
175C22⋊C4×C61—81no—
176C22⋊C4×C61—81no—
177C42×C61—21no—
178C42×C61—21no—
179C42×C61—21no—
180C42×C61—21no—
181C42×C61—21no—
182C42×C61—21no—
183#11758200—28no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—42no—
190C4⋊Dic61—81no—
191C4⋊Dic61#4112yes—
192#11758196—24no—
193#11758196—42no—
194#11758196—42no—
195#11758196—81no—
196#11758196—81no—
197C4×Dic61—24no—
198C4×Dic61—42no—
199C4×Dic61—42no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418C2×D412yes—
211C2×#92418C2×Q812yes—
212C23×C61—22no—
213C23×C61—41no—
214C23×C61—41no—
215C23×C61—41no—
216C23×C61—41no—
217C23×C61—41no—
218C23×C61—41no—
219C23×C61C22×D411yescharacteristic
220D4×C61—22no—
221D4×C61—22no—
222D4×C61—41no—
223D4×C61—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—22no—
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×C61—21no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—84no—
250C2×C4×C61#13512yes—
251C2×C4×C61#13712yes—
252C2×C4×C61C22×D411yescharacteristic
253C2×C4×C61C22×Q811yescharacteristic
254C2×C4×C61C2×#4111yescharacteristic
255C2×C4×C61C2×#4111yescharacteristic
256C2×C4×C61H(5,𝔽2)11yescharacteristic
257C2×C4×C612−1+411yescharacteristic
258C2×Dic61—22no—
259C2×Dic61—22no—
260C2×Dic61—22no—
261C2×Dic61—22no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270Dic122—22no—
271Dic122—22no—
272Dic122—22no—
273Dic122C22⋊Q814yes—
274#92418—22no—
275#92418—22no—
276#92418—41no—
277#92418—41no—
278#26379—611nomaximal, Sylow
279C22×C61—42no—
280C22×C61—42no—
281C22×C61—42no—
282C22×C61—81no—
283C22×C61—81no—
284C22×C61—81no—
285C22×C61—81no—
286C22×C61#52511yescharacteristic
287C22×C61D4211yescharacteristic
288C22×C61D4×Q811yescharacteristic
289C22×C61C2×#13511yescharacteristic
290C22×C61C2×#13711yescharacteristic
291C22×C61#57611yescharacteristic
292C22×C61#57711yescharacteristic
293C4×C61—22no—
294C4×C61—22no—
295C4×C61—41no—
296C4×C61—41no—
297C4×C61—42no—
298C4×C61—41no—
299C4×C61—41no—
300C4×C61—81no—
301C4×C61—81no—
302C4×C61C2×C22⋊Q811yescharacteristic
303C4×C61#53911yescharacteristic
304C4×C61#54711yescharacteristic
305C4×C61#55411yescharacteristic
306Dic61—24no—
307Dic61—42no—
308Dic61—81no—
309Dic61—81no—
310C2×#479—611no—
311C2×C4×SD16—611no—
312#2454D6111yescharacteristic
313Q8×C4⋊C4—611no—
314#2093—611no—
315#2084—611no—
316#2067—611no—
317#2059—611no—
318#1942—611no—
319#1916—611no—
320#1880—611no—
321#1880—611no—
322#1864—611no—
323#1863—611no—
324#1863—611no—
325C2×C61—82no—
326C2×C61#244911yescharacteristic
327C2×C61#310811yescharacteristic
328C2×C61#311911yescharacteristic
329C2×C61#326611yescharacteristic
330C2×C61#328711yescharacteristic
331C2×C61#338111yescharacteristic
332C2×C61#338511yescharacteristic
333C22×SD16—611no—
334C2×#125C2×D6111yescharacteristic
335C2×C4×Q8—611no—
336C2×C4×Q8—611no—
337C2×C4×Q8—611no—
338C2×C4×D4C2×D6111yescharacteristic
339#479—1224no—
340C4×SD16—1224no—
341C2×#107—611no—
342C2×#107—611no—
343C2×#107—611no—
344C2×#106—611no—
345C2×#106—611no—
346C2×C4⋊C8—611no—
347C2×#103—611no—
348C2×#103—611no—
349C2×#103—611no—
350C2×#102—611no—
351C2×#102—611no—
352C2×#102—611no—
353C2×C4×C8—611no—
354#399—21no—
355#396—21no—
356#390C2×D6111yescharacteristic
357#390C2×D6111yescharacteristic
358#389—611no—
359#389—611no—
360#389—1221no—
361#389—1221no—
362#389C2×D6111yescharacteristic
363#389C2×D6111yescharacteristic
364#385—21no—
365#384—611no—
366#384—1221no—
367#380—21no—
368C4×C4⋊C4—1221no—
369C4×C4⋊C4C2×D6111yescharacteristic
370#340—611no—
371#340—611no—
372#340—611no—
373#340—611no—
374#336—611no—
375#336—611no—
376#336—611no—
377#336—611no—
378C61#2637911yescharacteristic, complemented, Sylow
379C22×Q8—611no—
380C22×D4C22×D6111yescharacteristic
381C23×C4—21no—
382C2×SD16—614no—
383C2×SD16—1222no—
384C2×SD16—1222no—
385C22×C8—611no—
386C22×C8—611no—
387C22×C8—611no—
388C22×C8—611no—
389#125—22no—
390#125—41no—
391C4×Q8—1222no—
392C4×Q8—1222no—
393C4×Q8—1222no—
394C4×Q8—1222no—
395C4×Q8—2441no—
396C4×Q8—2441no—
397C4×D4—22no—
398C4×D4—41no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—611no—
404C2×C4⋊C4—611no—
405C2×C4⋊C4—611no—
406C2×C4⋊C4—1221no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4C22⋊D6111yescharacteristic
414C2×C4⋊C4C22⋊D6111yescharacteristic
415C2×C4⋊C4C22×D6111yescharacteristic
416C2×C4⋊C4C22×D6111yescharacteristic
417C2×C4⋊C4C22×D6111yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C42—1221no—
424C2×C42—1221no—
425C2×C42—1221no—
426C2×C42C22×D6111yescharacteristic
427C2×C42C22×D6111yescharacteristic
428C2×C42C22×D6111yescharacteristic
429#107—1222no—
430#107—1222no—
431#107—2441no—
432#106—1222no—
433#106—1222no—
434C4⋊C8—1222no—
435#103—614no—
436#103—1222no—
437#103—1222no—
438#102—1222no—
439#102—1222no—
440#102—2441no—
441C4×C8—1222no—
442#95—21no—
443#95—21no—
444#95—1221no—
445#95—1221no—
446#95C22⋊D6111yescharacteristic
447#95C22⋊D6111yescharacteristic
448C24—21no—
449C2×Q8—612no—
450C2×Q8—612no—
451C2×Q8—612no—
452C2×Q8—1221no—
453C2×Q8—1221no—
454C2×Q8—1221no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4Q8×D6112yes—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—81no—
467C22×C4—1221no—
468C22×C4—1221no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4C2×C22⋊D6111yescharacteristic
472C22×C4C2×C22⋊D6111yescharacteristic
473C22×C4C2×C22⋊D6111yescharacteristic
474C22×C4C2×C22⋊D6111yescharacteristic
475C22×C4C2×C22⋊D6111yescharacteristic
476C22×C4C2×C22⋊D6111yescharacteristic
477C22×C4C23×D6111yescharacteristic
478SD16—1228no—
479C2×C8—612no—
480C2×C8—612no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4—81no—
501C4⋊C4—81no—
502C4⋊C4—612no—
503C4⋊C4—1224no—
504C4⋊C4—1221no—
505C4⋊C4—1221no—
506C4⋊C4—1221no—
507C4⋊C4—1221no—
508C4⋊C4—1221no—
509C4⋊C4—4881no—
510C4⋊C4—4881no—
511C4⋊C4—4881no—
512C4⋊C4—2442no—
513C4⋊C4—2442no—
514C4⋊C4—2442no—
515C4⋊C4D4×D6112yes—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—81no—
519C22⋊C4—81no—
520C22⋊C4—81no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—1224no—
528C42—2442no—
529C42—2442no—
530C23—22no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23C22×C22⋊D6111yescharacteristic
538Q8—614no—
539Q8—1222no—
540Q8—1222no—
541Q8—1222no—
542D4—22no—
543D4—22no—
544D4—41no—
545D4—41no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—84no—
572C2×C4—1222no—
573C2×C4—1222no—
574C2×C4—1222no—
575C2×C4—1222no—
576C2×C4—2441no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4#1451979712yes—
585C2×C4#1451980712yes—
586C2×C4C2×D4×D6111yescharacteristic
587C2×C4C2×Q8×D6111yescharacteristic
588C2×C4#41×D6111yescharacteristic
589C2×C4#41×D6111yescharacteristic
590C2×C4#1451982211yescharacteristic
591C2×C4#1451982511yescharacteristic
592C8—1222no—
593C8—1222no—
594C8—2441no—
595C8—2441no—
596C22—42no—
597C22—42no—
598C22—42no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22#1684026911yescharacteristic
604C22D4×C22⋊D6111yescharacteristic
605C22Q8×C22⋊D6111yescharacteristic
606C22C2×#1451979711yescharacteristic
607C22C2×#1451980711yescharacteristic
608C22#1684056511yescharacteristic
609C22#1684057311yescharacteristic
610C4—22no—
611C4—22no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—42no—
617C4—81no—
618C4—81no—
619C4—1224no—
620C4—4881no—
621C4—4881no—
622C4—2442no—
623C4C22⋊Q8×D6111yescharacteristic
624C4#1684035811yescharacteristic
625C4#1684041411yescharacteristic
626C4#1684046611yescharacteristic
627C2—82no—
628C2#2144962511yescharacteristic
629C2#2145589511yescharacteristic
630C2#2145601211yescharacteristic
631C2#2145732511yescharacteristic
632C2#2145757511yescharacteristic
633C2#2145869411yescharacteristic
634C2#2145872911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2454C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
hypercenter#2454D61
hypocenterC61#26379
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2454

Complements

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

NH ≅ G/Ntype
1. C2×#16840066C2semidirect
3. C4⋊C4×Dic122C2semidirect
5. #21447295C2semidirect
7. #21447154C2semidirect
8. #21446549C2semidirect
9. #21446378C2semidirect
13. #21446072C2semidirect
14. #21446072C2semidirect
378. C61#26379semidirect

Maximal subgroups

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

subgroupindex
C2×#168400662
C2×C4×#117582002
C4⋊C4×Dic1222
#214473472
#214472952
#214472072
#214471542
#214465492
#214463782
#214461772
#214460802
#214460722
C61×#24542
#2637961