Finite Group Databasebeta

← #30616079

Subgroups — #30616079

Order 15616.

938 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462302C211yesmaximal, characteristic, complemented
2#21462258C211yesmaximal, characteristic, complemented
3#21461897C212yesmaximal, complemented
4#21461880C212yesmaximal, complemented
5#21461814C212yesmaximal
6#21461784C212yesmaximal, complemented
7C4×#14519845C211yesmaximal, characteristic, complemented
8#21461589C211yesmaximal, characteristic, complemented
9#21461589C211yesmaximal, characteristic, complemented
10#21461537C211yesmaximal, characteristic, complemented
11C4×D8×D61C211yesmaximal, characteristic
12C2×D4×#6923C2212yes—
13C2×#14519845C2212yes—
14C2×#14519839C2212yes—
15C2×#14519839C2212yes—
16#16840721C2211yescharacteristic
17#16840714C2212yes—
18#16840713C2212yes—
19#16840712—22no—
20#16840705—21no—
21#16840704—21no—
22C4⋊C4×#6923C2212yes—
23C4×C4⋊#6923C2211yescharacteristic
24C4×C4⋊#6923C2211yescharacteristic
25C22⋊C4×#6923—22no—
26C4×C22⋊#6923—21no—
27#16840698C2211yescharacteristic
28C2×(C2×#6923)⋊C4—21no—
29#16840636C2212yes—
30#16840635C2212yes—
31#16840635C2212yes—
32(C2×#6923)⋊C8C2212yes—
33(C2×#6923)⋊C8C2212yes—
34C2×D8×D61C2211yescharacteristic
35C4×D4×D61C2211yescharacteristic
36C4×D4×D61C2211yescharacteristic
37C4×D488C411yescharacteristic, complemented
38D8×Dic61C411yescharacteristic, complemented
39#16839844C411yescharacteristic, complemented
40C4×#11758199C411yescharacteristic, complemented
41C4×#11758199C411yescharacteristic, complemented
42#16839842C411yescharacteristic, complemented
43#16839842C411yescharacteristic, complemented
44#107×D61C2211yescharacteristic
45#102×D61C2211yescharacteristic
46#102×D61C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48C4×D8×C61C411yescharacteristic, complemented
49C23×#6923—22no—
50C2×D61⋊C8C2312yes—
51D4×#6923—24no—
52D4×#6923—24no—
53C2×C4⋊#6923—22no—
54C2×C4⋊#6923C2312yes—
55C2×C4⋊#6923C2312yes—
56C2×C22⋊#6923—22no—
57C2×C22⋊#6923—22no—
58C2×C22⋊#6923—22no—
59C2×C4×#6923—22no—
60C2×C4×#6923—21no—
61C2×C4×#6923—21no—
62C2×C4×#6923C2312yes—
63#14519845—24no—
64#14519839—24no—
65#14519839—24no—
66#14519832—21no—
67#14519832—21no—
68(C2×#6923)⋊C4—22no—
69(C2×#6923)⋊C4—22no—
70(C2×#6923)⋊C4—21no—
71(C2×#6923)⋊C4—21no—
72(C2×#6923)⋊C4D411yescharacteristic
73(C2×#6923)⋊C4D411yescharacteristic
74(C2×#6923)⋊C4D412yes—
75C2×D4×D61C2311yescharacteristic
76C2×D4×D61C2311yescharacteristic
77C22×C4×D61—21no—
78C22×C4×D61—21no—
79C2×D488C2×C411yescharacteristic
80C2×#11758199C2×C411yescharacteristic
81C2×#11758199C2×C411yescharacteristic
82D8×D61—24no—
83C2×C8×D61C2311yescharacteristic
84C2×C8×D61C2311yescharacteristic
85C4×D244C2×C411yescharacteristic
86C4×D244C2×C411yescharacteristic, complemented
87D4×Dic61C2×C411yescharacteristic
88D4×Dic61C2×C411yescharacteristic, complemented
89#14519739C2×C411yescharacteristic
90#14519739C2×C411yescharacteristic, complemented
91C4×C22⋊D61—21no—
92C4×C22⋊D61—21no—
93#14519737—21no—
94#14519737—21no—
95C4⋊C4×D61C2311yescharacteristic
96C4⋊C4×D61C2311yescharacteristic
97C22⋊C4×D61—21no—
98C22⋊C4×D61—21no—
99C42×D61C2311yescharacteristic
100#14519711C2×C411yescharacteristic, complemented
101#14519710C2×C411yescharacteristic, complemented
102#14519710C2×C411yescharacteristic, complemented
103#14519699C2×C411yescharacteristic
104#14519699C2×C411yescharacteristic, complemented
105#14519698C2×C411yescharacteristic
106#14519698C2×C411yescharacteristic, complemented
107#14519697C2×C411yescharacteristic
108#14519697C2×C411yescharacteristic, complemented
109C4×#92418C2×C411yescharacteristic, complemented
110C8×Dic61C2×C411yescharacteristic, complemented
111C8×Dic61C2×C411yescharacteristic, complemented
112C2×D8×C61C2×C411yescharacteristic
113C4×D4×C61C2×C411yescharacteristic
114C4×D4×C61C2×C411yescharacteristic, complemented
115#107×C61C2×C411yescharacteristic, complemented
116#102×C61C2×C411yescharacteristic
117#102×C61C2×C411yescharacteristic, complemented
118C4×C8×C61C2×C411yescharacteristic, complemented
119C23×D61—21no—
120C23×D61—21no—
121C22×#6923—22no—
122C22×#6923—28no—
123C22×#6923—22no—
124C22×#6923—82no—
125C22×#6923—82no—
126C22×#6923C2×D412yes—
127C22×#6923C2×D412yes—
128C2×D4×C61C22×C411yescharacteristic
129C2×D4×C61C22×C411yescharacteristic
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C2×C22⋊D61—21no—
133C2×C22⋊D61—21no—
134C22×Dic61—21no—
135C22×Dic61—21no—
136D4×D61—22no—
137D4×D61—22no—
138D4×D61—22no—
139D4×D61#4114yes—
140C2×D244C22×C411yescharacteristic
141C2×D244C22×C411yescharacteristic
142C2×C4×D61—21no—
143C2×C4×D61—21no—
144C2×C4×D61—21no—
145C2×C4×D61—21no—
146C2×C4×D61—21no—
147C2×C4×D61—21no—
148C2×C4×D61—82no—
149C2×C4×D61—82no—
150C2×C4×D61C2×D411yescharacteristic
151C2×C4×D61C2×D411yescharacteristic
152C2×C4×D61C2411yescharacteristic
153C22⋊#6923—28no—
154C22⋊#6923—82no—
155C22⋊#6923—82no—
156C2×#92420—22no—
157C4⋊#6923—22no—
158C4⋊#6923—22no—
159C4⋊#6923—22no—
160C4⋊#6923—82no—
161C4⋊#6923#4114yes—
162C4×#6923—22no—
163C4×#6923—22no—
164C4×#6923—81no—
165C4×#6923—81no—
166C4×#6923—82no—
167D61⋊C8—22no—
168D61⋊C8—22no—
169D8×C61—22no—
170C2×C8×C61C22×C411yescharacteristic
171C2×C8×C61C22×C411yescharacteristic
172C4⋊C4×C61C22×C411yescharacteristic
173C4⋊C4×C61C22×C411yescharacteristic
174C22⋊C4×C61—21no—
175C22⋊C4×C61—21no—
176C42×C61C22×C411yescharacteristic
177C22⋊Dic61—21no—
178C22⋊Dic61—21no—
179#11758199—22no—
180#11758199—22no—
181#11758198—21no—
182#11758198—21no—
183#11758198—21no—
184#11758198—21no—
185C4⋊Dic61C22×C411yescharacteristic
186C4⋊Dic61C22×C411yescharacteristic
187#11758196—21no—
188#11758196—21no—
189C4×Dic61C22×C411yescharacteristic
190C4×Dic61#4111yescharacteristic
191C4×Dic61#4111yescharacteristic
192C2×#92418C22×C411yescharacteristic
193C2×#92418C22×C411yescharacteristic
194D488—22no—
195C8×D61—22no—
196C8×D61—22no—
197C23×C61—21no—
198C23×C61—21no—
199C22×D61—21no—
200C22×D61—24no—
201C22×D61—21no—
202C22×D61—42no—
203C22×D61—41no—
204C22×D61—41no—
205C22×D61—42no—
206C22×D61—42no—
207C22×D61—41no—
208C22×D61—41no—
209C22×D61C22×D411yescharacteristic
210C2×#6923—22no—
211C2×#6923—22no—
212C2×#6923—24no—
213C2×#6923—22no—
214C2×#6923—22no—
215C2×#6923—22no—
216C2×#6923—22no—
217C2×#6923—42no—
218C2×#6923—42no—
219C2×#6923—42no—
220C2×#6923—42no—
221C2×#6923—42no—
222C2×#6923—88no—
223D4×C61—21no—
224D4×C61—21no—
225D4×C61—21no—
226D4×C61#11712yes—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—81no—
230C2×C4×C61—81no—
231C2×C4×C61C4×D411yescharacteristic
232C2×C4×C61C4×D411yescharacteristic
233C2×C4×C61C23×C411yescharacteristic
234C22⋊D61—24no—
235C22⋊D61—42no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—81no—
239C2×Dic61—81no—
240C2×Dic61C4×D411yescharacteristic
241C2×Dic61C4×D411yescharacteristic
242C2×Dic61C2×#4111yescharacteristic
243D244—21no—
244D244—21no—
245D244—21no—
246D244#11712yes—
247C4×D61—22no—
248C4×D61—21no—
249C4×D61—21no—
250C4×D61—42no—
251C4×D61—42no—
252C4×D61—81no—
253C4×D61—81no—
254C4×D61—81no—
255C4×D61—81no—
256C4×D61C2×#4112yes—
257C4×D61C2×#4112yes—
258#92420—42no—
259C8×C61—21no—
260C8×C61—21no—
261#92418—21no—
262#92418—21no—
263#21134—611nomaximal, Sylow
264C22×C61—22no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61—41no—
269C22×C61—41no—
270C22×C61C2×C4×D411yescharacteristic
271C2×D61—22no—
272C2×D61—41no—
273C2×D61—41no—
274C2×D61—44no—
275C2×D61—44no—
276C2×D61—41no—
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—82no—
280C2×D61—82no—
281C2×D61#52512yes—
282C2×D61#57612yes—
283C2×D61#57711yescharacteristic
284C2×D61#57711yescharacteristic
285#6923—42no—
286#6923—44no—
287#6923—42no—
288#6923—82no—
289C4×C61—21no—
290C4×C61—21no—
291C4×C61—41no—
292C4×C61—41no—
293C4×C61C2×#11711yescharacteristic
294C4×C61C4×#4111yescharacteristic
295Dic61—21no—
296Dic61—21no—
297Dic61—41no—
298Dic61—41no—
299Dic61#52912yes—
300C2×C4×D8—611no—
301#2319—611no—
302#2275—611no—
303#1926—612no—
304#1918—612no—
305#1879—612no—
306#1864—612no—
307C4×#106—611no—
308#1762—611no—
309#1762—611no—
310#1746—611no—
311C2×C61—42no—
312C2×C61—81no—
313C2×C61#229011yescharacteristic
314C2×C61#294811yescharacteristic
315C2×C61#295211yescharacteristic
316D61—42no—
317D61—81no—
318D61#311812yes—
319D61#311912yes—
320C22×D8—611no—
321C2×C4×D4—611no—
322C2×C4×D4—611no—
323C2×C4×D4—612no—
324C4×D8—611no—
325C4×D8—611no—
326C4×D8—611no—
327C4×D8—611no—
328C4×D8—611no—
329C4×D8—611no—
330C4×D8—611no—
331C4×D8#692311yescharacteristic, complemented
332C2×#107—611no—
333C2×#106—612no—
334C2×#102—611no—
335C2×#102—611no—
336C2×#102—612no—
337C2×#102—612no—
338C2×#97—611no—
339C2×C4×C8—611no—
340#390—612no—
341#389—612no—
342#388—1222no—
343#381—1221no—
344#380—1221no—
345C4×C4⋊C4—611no—
346C4×C4⋊C4—612no—
347C4×C4⋊C4—611no—
348C4×C22⋊C4—1221no—
349C4×C22⋊C4—1222no—
350#376—611no—
351C2×#95—1221no—
352#340—612no—
353#340—612no—
354#340—612no—
355#336—612no—
356#336—612no—
357C61#2113411yescharacteristic, complemented, Sylow
358C22×D4—611no—
359C22×D4—611no—
360C23×C4—1221no—
361C23×C4—1221no—
362C23×C4—1222no—
363C2×D8—611no—
364C2×D8—611no—
365C2×D8—611no—
366C2×D8—1224no—
367C2×D8C2×#692311yescharacteristic
368C22×C8—611no—
369C22×C8—611no—
370C22×C8—612no—
371C4×D4—611no—
372C4×D4—611no—
373C4×D4—611no—
374C4×D4—611no—
375C4×D4—611no—
376C4×D4—611no—
377C4×D4—1221no—
378C4×D4—1221no—
379C4×D4—1221no—
380C4×D4—1221no—
381C4×D4—1224no—
382C4×D4—1224no—
383C4×D4C2×#692311yescharacteristic
384C4×D4C2×#692311yescharacteristic, complemented
385C2×C4⋊C4—612no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4—611no—
388C2×C4⋊C4—612no—
389C2×C4⋊C4—1222no—
390C2×C22⋊C4—1221no—
391C2×C22⋊C4—1221no—
392C2×C22⋊C4—1222no—
393C2×C22⋊C4—1222no—
394C2×C22⋊C4—1222no—
395C2×C42—611no—
396C2×C42—612no—
397C2×C42—1221no—
398C2×C42—1222no—
399C2×C42—1221no—
400#107—611no—
401#107—611no—
402#107—611no—
403#107C2×#692311yescharacteristic, complemented
404#106—1224no—
405#102—611no—
406#102—611no—
407#102—611no—
408#102—611no—
409#102—611no—
410#102—611no—
411#102—1224no—
412#102—1224no—
413#102C2×#692311yescharacteristic
414#102C2×#692311yescharacteristic, complemented
415#97—1221no—
416#97—1221no—
417C4×C8—611no—
418C4×C8—611no—
419C4×C8—611no—
420C4×C8C2×#692311yescharacteristic, complemented
421#95—611no—
422#95—611no—
423#95—612no—
424#95—1221no—
425#95—1222no—
426#95—1221no—
427#95—1222no—
428C24—1221no—
429C24—1221no—
430C2×D4—614no—
431C2×D4—611no—
432C2×D4—611no—
433C2×D4—1222no—
434C2×D4—1222no—
435C2×D4—1222no—
436C2×D4—1221no—
437C2×D4—1221no—
438C2×D4C22×#692311yescharacteristic
439C2×D4C22×#692311yescharacteristic
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—611no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—612no—
446C22×C4—612no—
447C22×C4—1221no—
448C22×C4—1221no—
449C22×C4—1221no—
450C22×C4—1221no—
451C22×C4—1221no—
452C22×C4—1221no—
453C22×C4—1228no—
454C22×C4—1222no—
455C22×C4—1221no—
456C22×C4—1221no—
457C22×C4—1222no—
458C22×C4—4882no—
459C22×C4—4882no—
460C22×C4—4882no—
461C22×C4—4882no—
462D8—22no—
463D8—1222no—
464D8—1222no—
465D8—1222no—
466C2×C8—611no—
467C2×C8—611no—
468C2×C8—1222no—
469C2×C8—1222no—
470C2×C8—1222no—
471C2×C8—1222no—
472C2×C8—1222no—
473C2×C8C22×#692311yescharacteristic
474C2×C8C22×#692311yescharacteristic
475C4⋊C4—614no—
476C4⋊C4—611no—
477C4⋊C4—611no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—1222no—
481C4⋊C4—1222no—
482C4⋊C4—1222no—
483C4⋊C4—4882no—
484C4⋊C4C22×#692311yescharacteristic
485C4⋊C4C22×#692311yescharacteristic
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—1221no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C22⋊C4—1221no—
492C22⋊C4—1228no—
493C22⋊C4—1221no—
494C22⋊C4—1221no—
495C22⋊C4—4882no—
496C22⋊C4—4882no—
497C42—611no—
498C42—611no—
499C42—611no—
500C42—1222no—
501C42—1222no—
502C42—4881no—
503C42—4881no—
504C42—4882no—
505C42C22×#692311yescharacteristic
506C23—21no—
507C23—21no—
508C23—611no—
509C23—1224no—
510C23—1221no—
511C23—1221no—
512C23—2441no—
513C23—2442no—
514C23—2442no—
515C23—2441no—
516C23—2442no—
517C23—2441no—
518C23—2441no—
519D4—21no—
520D4—21no—
521D4—21no—
522D4—612no—
523D4—1224no—
524D4—1221no—
525D4—1221no—
526D4—1221no—
527D4—2442no—
528D4#1451985612yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—611no—
534C2×C4—612no—
535C2×C4—612no—
536C2×C4—611no—
537C2×C4—611no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1222no—
541C2×C4—1222no—
542C2×C4—1222no—
543C2×C4—1222no—
544C2×C4—1224no—
545C2×C4—1222no—
546C2×C4—1222no—
547C2×C4—1222no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—4881no—
551C2×C4—4881no—
552C2×C4—4881no—
553C2×C4—4881no—
554C2×C4—4881no—
555C2×C4—4881no—
556C2×C4—4888no—
557C2×C4—2442no—
558C2×C4—2442no—
559C2×C4—2442no—
560C2×C4—2442no—
561C2×C4—2442no—
562C2×C4—2442no—
563C2×C4—2442no—
564C2×C4D4×#692311yescharacteristic
565C2×C4D4×#692311yescharacteristic
566C2×C4C23×#692311yescharacteristic
567C8—21no—
568C8—21no—
569C8—1221no—
570C8—1221no—
571C8—2442no—
572C22—22no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—612no—
579C22—612no—
580C22—611no—
581C22—611no—
582C22—1222no—
583C22—4882no—
584C22—4882no—
585C22—2444no—
586C22—2444no—
587C22—2441no—
588C22—2441no—
589C22—2441no—
590C22—2441no—
591C22—2441no—
592C22C2×D4×#692311yescharacteristic
593C4—21no—
594C4—21no—
595C4—41no—
596C4—41no—
597C4—612no—
598C4—1221no—
599C4—1221no—
600C4—4882no—
601C4—2442no—
602C4—2442no—
603C4—2444no—
604C4—2441no—
605C4—2441no—
606C4C2×#1451985611yescharacteristic
607C4#41×#692311yescharacteristic
608C2—42no—
609C2—81no—
610C2—612no—
611C2—612no—
612C2—4881no—
613C2—2442no—
614C2#2146227311yescharacteristic
615C2#2146257811yescharacteristic
616C2#2146258211yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC4×D8×C61C4
socleC22×C61C2×C4×D4
prime radicalC2×D8×D61C22
cosocleC2×C4×D61C24
hypercenterC4×D8#6923
hypocenterC61#21134
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #21462302C2semidirect
2. #21462258C2semidirect
3. #21461897C2semidirect
4. #21461880C2semidirect
6. #21461784C2semidirect
7. C4×#14519845C2semidirect
8. #21461589C2semidirect
9. #21461589C2semidirect
10. #21461537C2semidirect
37. C4×D488C4semidirect
38. D8×Dic61C4semidirect
39. #16839844C4semidirect
40. C4×#11758199C4semidirect
41. C4×#11758199C4semidirect
42. #16839842C4semidirect
43. #16839842C4semidirect
48. C4×D8×C61C4semidirect
86. C4×D244C2×C4semidirect
88. D4×Dic61C2×C4semidirect
90. #14519739C2×C4semidirect
100. #14519711C2×C4semidirect
101. #14519710C2×C4semidirect
102. #14519710C2×C4semidirect
104. #14519699C2×C4semidirect
106. #14519698C2×C4semidirect
108. #14519697C2×C4semidirect
109. C4×#92418C2×C4semidirect
110. C8×Dic61C2×C4semidirect
111. C8×Dic61C2×C4semidirect
114. C4×D4×C61C2×C4semidirect
115. #107×C61C2×C4semidirect
117. #102×C61C2×C4semidirect
118. C4×C8×C61C2×C4semidirect
331. C4×D8#6923semidirect
357. C61#21134semidirect
384. C4×D4C2×#6923semidirect
403. #107C2×#6923semidirect
414. #102C2×#6923semidirect
420. C4×C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623022
#214622582
#214618972
#214618802
#214618142
#214617842
C4×#145198452
#214615892
#214615372
C4×D8×D612
#2113461