Finite Group Databasebeta

← #29651043

Subgroups — #29651043

Order 15616.

670 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455866C211yesmaximal, characteristic
2#21454817C211yesmaximal, characteristic, complemented
3D4×#11758194C211yesmaximal, characteristic, complemented
4#21444730C211yesmaximal, characteristic, complemented
5#21444712C211yesmaximal, characteristic, complemented
6#21444700C211yesmaximal, characteristic, complemented
7#21444680C211yesmaximal, characteristic, complemented
8#21444652C211yesmaximal, characteristic, complemented
9#21444651C211yesmaximal, characteristic, complemented
10#21444628C211yesmaximal, characteristic, complemented
11#21444611C211yesmaximal, characteristic, complemented
12#21444607C211yesmaximal, characteristic, complemented
13#21444285C211yesmaximal, characteristic, complemented
14#21444114C211yesmaximal, characteristic, complemented
15C61×#1478C211yesmaximal, characteristic, complemented
16C22×#11758194—21no—
17#16840296C2211yescharacteristic
18#16840097C411yescharacteristic
19#16840080C411yescharacteristic
20#16840062C411yescharacteristic
21#16840062C411yescharacteristic
22#16839977C411yescharacteristic
23#16839977C411yescharacteristic
24#16839913C411yescharacteristic
25#16839896C411yescharacteristic
26#16839889C2211yescharacteristic, complemented
27#16839886C2211yescharacteristic, complemented
28C4×#11758200C2211yescharacteristic
29C4×#11758200C2211yescharacteristic
30C4×#11758199C2211yescharacteristic
31C4×#11758199C2211yescharacteristic
32#16839840C2211yescharacteristic
33#16839840C2211yescharacteristic
34#16839839C2211yescharacteristic, complemented
35#16839837—21no—
36#16839836—21no—
37#16839834—21no—
38#16839834—21no—
39D4×#92418C2211yescharacteristic
40D4×#92418C2211yescharacteristic
41#16839827C2211yescharacteristic, complemented
42#16839821—21no—
43#16839815C2211yescharacteristic
44#16839786C2211yescharacteristic
45#16839726—21no—
46#16839716—21no—
47C4×#11758194C2211yescharacteristic
48#16839514C2211yescharacteristic, complemented
49#16839514C2211yescharacteristic, complemented
50#16839512C2211yescharacteristic, complemented
51#16839512C2211yescharacteristic, complemented
52#16839494C2211yescharacteristic, complemented
53#16839494C2211yescharacteristic, complemented
54#16839491C2211yescharacteristic, complemented
55#16839491C2211yescharacteristic, complemented
56#16839484C2211yescharacteristic, complemented
57#16839484C2211yescharacteristic, complemented
58#16839483C2211yescharacteristic, complemented
59C8×#92418C2211yescharacteristic, complemented
60C2×C4×D4×C61C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C61×#431C2211yescharacteristic
63C61×D4⋊C8C2211yescharacteristic
64C61×D4⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×D4⋊C8C2211yescharacteristic
67C2×#11758200C2×C411yescharacteristic
68C2×#11758200C2×C411yescharacteristic
69C2×#11758199C2×C411yescharacteristic
70C2×#11758199C2×C411yescharacteristic
71C2×#11758194—21no—
72C2×#11758194—21no—
73C2×#11758194—21no—
74C2×#11758194—44no—
75C2×#11758194D411yescharacteristic
76C2×#11758194D411yescharacteristic
77C2×#11758189—21no—
78C22×#92418—21no—
79C22×#92418—21no—
80C2×C8×D61—21no—
81#14519771—21no—
82#14519769C2×C411yescharacteristic
83#14519765C2×C411yescharacteristic
84#14519760—21no—
85#14519756C2×C411yescharacteristic
86#14519751C2×C411yescharacteristic
87C4×Dic122C2311yescharacteristic
88C4×D244C2311yescharacteristic
89C4×C22⋊D61—21no—
90#14519734—21no—
91#14519710C2×C411yescharacteristic
92#14519710C2×C411yescharacteristic
93#14519708C2×C411yescharacteristic
94#14519708C2×C411yescharacteristic
95C4⋊#92418—21no—
96C4⋊#92418C2×C411yescharacteristic
97C4⋊#92418C2×C411yescharacteristic
98C4⋊#92418C2311yescharacteristic
99C4⋊#92418C2311yescharacteristic
100#14519706—21no—
101#14519706—21no—
102#14519700C2×C411yescharacteristic
103#14519700C2×C411yescharacteristic
104#14519698C2×C411yescharacteristic
105#14519698C2×C411yescharacteristic
106#14519698C2×C411yescharacteristic
107#14519698C2×C411yescharacteristic
108#14519697C2×C411yescharacteristic
109#14519697C2×C411yescharacteristic
110C22⋊#92418—21no—
111C22⋊#92418—21no—
112C22⋊#92418—21no—
113C22⋊#92418—21no—
114C22⋊#92418C2×C411yescharacteristic
115C22⋊#92418C2×C411yescharacteristic
116#14519689—21no—
117#14519689—21no—
118#14519688D411yescharacteristic
119#14519688D411yescharacteristic
120#14519687—21no—
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C4×#92418C2311yescharacteristic
124C4×#92418C2311yescharacteristic
125C8×Dic61—21no—
126C22×D4×C61C2×C411yescharacteristic
127C23×C4×C61—21no—
128C4×D4×C61—21no—
129C4×D4×C61—21no—
130C4×D4×C61C2×C411yescharacteristic
131C4×D4×C61C2×C411yescharacteristic
132C4×D4×C61C2311yescharacteristic
133C4×D4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2×C411yescharacteristic
135C2×C22⋊C4×C61—21no—
136C2×C42×C61C2311yescharacteristic
137C4⋊C8×C61—21no—
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140C22⋊C8×C61—21no—
141C22⋊C8×C61—21no—
142C4×C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C4×C8×C61C2311yescharacteristic
145C24×C61—21no—
146C2×D4×C61—22no—
147C2×D4×C61—21no—
148C2×D4×C61—41no—
149C2×D4×C61C22×C411yescharacteristic
150C2×D4×C61C22×C411yescharacteristic
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—42no—
157C22×C4×C61—42no—
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61#4111yescharacteristic
161C2×C22⋊D61—21no—
162C2×D244C22×C411yescharacteristic
163C2×C4×D61—21no—
164C2×Dic122C22×C411yescharacteristic
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61C22×C411yescharacteristic
171C4⋊C4×C61C22×C411yescharacteristic
172C22⋊C4×C61—21no—
173C22⋊C4×C61—21no—
174C22⋊C4×C61—21no—
175C22⋊C4×C61—21no—
176C42×C61C22×C411yescharacteristic
177C42×C61C2×D411yescharacteristic
178C42×C61#4111yescharacteristic
179C42×C61C2411yescharacteristic
180C22⋊Dic61—21no—
181#11758200—22no—
182#11758200—41no—
183#11758199—22no—
184#11758199—41no—
185#11758198—21no—
186#11758198—21no—
187#11758198—21no—
188#11758198—21no—
189C4⋊Dic61C22×C411yescharacteristic
190C4⋊Dic61C22×C411yescharacteristic
191#11758196—21no—
192#11758196—21no—
193#11758196—21no—
194#11758196—21no—
195C4×Dic61—21no—
196#11758194—22no—
197#11758194—41no—
198#11758194—42no—
199#11758194—42no—
200#11758194—42no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—42no—
204C2×#92418—42no—
205C2×#92418C22×C411yescharacteristic
206C2×#92418C22×C411yescharacteristic
207C2×#92418C22×C411yescharacteristic
208C2×#92418C22×C411yescharacteristic
209C2×#92418C2×D411yescharacteristic
210C2×#92418C2×D411yescharacteristic
211C2×#92418C2×D411yescharacteristic
212C2×#92418C2×D411yescharacteristic
213#11758189—42no—
214C8×D61—42no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61—42no—
218C23×C61—42no—
219C23×C61—81no—
220C23×C61C4×D411yescharacteristic
221C22×D61—21no—
222D4×C61—21no—
223D4×C61—21no—
224D4×C61—21no—
225D4×C61—42no—
226D4×C61#13112yes—
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—42no—
235C2×C4×C61—42no—
236C2×C4×C61—42no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61C4×D411yescharacteristic
242C2×C4×C61C4×D411yescharacteristic
243C2×C4×C61C4×D411yescharacteristic
244C2×C4×C61C23×C411yescharacteristic
245C2×C4×C61C22×D411yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C22⋊D61—81no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251D244—21no—
252D244—21no—
253C4×D61—41no—
254C4×D61—41no—
255Dic122—21no—
256Dic122—21no—
257C8×C61—41no—
258C8×C61—41no—
259C8×C61—41no—
260C8×C61—41no—
261#92418—21no—
262#92418—21no—
263#92418—21no—
264#92418—21no—
265#92418—21no—
266#92418—21no—
267#92418—21no—
268#92418—41no—
269#92418—41no—
270#92418AGL(1,ℤ/8)12yes—
271#18006—611nomaximal, Sylow
272C22×C61—21no—
273C22×C61—22no—
274C22×C61—21no—
275C22×C61—21no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—84no—
282C22×C61C2×C4×D411yescharacteristic
283C2×D61—41no—
284C2×D61—41no—
285C2×D61—41no—
286C4×C61—21no—
287C4×C61—21no—
288C4×C61—21no—
289C4×C61—21no—
290C4×C61—41no—
291C4×C61—41no—
292C4×C61C2×#13111yescharacteristic
293C4×C61#56811yescharacteristic
294C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
295C4×C61#57511yescharacteristic
296Dic61—41no—
297Dic61—41no—
298Dic61—41no—
299#3105—611no—
300#2969—611no—
301D4×M16—611no—
302#1594—611no—
303#1590—611no—
304#1588—611no—
305#1586—611no—
306#1582—611no—
307#1581—611no—
308SD16⋊C8—611no—
309C8×D8—611no—
310#1574—611no—
311#1495—611no—
312#1478D6111yescharacteristic, complemented
313#1453—611no—
314C2×C61—41no—
315C2×C61—42no—
316C2×C61—81no—
317C2×C61#293311yescharacteristic
318C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
319C2×C61#295711yescharacteristic
320D61—81no—
321C22×M16—1221no—
322#529—611no—
323C2×C4×D4C2×D6111yescharacteristic
324#484—611no—
325#481—611no—
326#478—611no—
327#478—611no—
328#463—611no—
329#463—611no—
330#450—611no—
331#447—611no—
332#446—611no—
333C8×Q8—611no—
334C4×SD16—611no—
335C4×SD16—611no—
336C4×D8—611no—
337C4×D8—611no—
338#436—611no—
339#436—611no—
340#436—611no—
341#436—1221no—
342#435—1221no—
343#435—1221no—
344#435—1221no—
345C8×D4—611no—
346C8×D4—611no—
347C8×D4—611no—
348#433—1221no—
349#431—611no—
350#431C2×D6111yescharacteristic
351#431C2×D6111yescharacteristic
352#423—611no—
353#407—1221no—
354#405—1221no—
355C4×M16—611no—
356#335—611no—
357#335—611no—
358#334—611no—
359#334—611no—
360Q8⋊C8—611no—
361Q8⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364D4⋊C8C2×D6111yescharacteristic
365D4⋊C8C2×D6111yescharacteristic
366D4⋊C8C2×D6111yescharacteristic
367D4⋊C8C2×D6111yescharacteristic
368#322—611no—
369#322—611no—
370#322—611no—
371C82—611no—
372C61#1800611yescharacteristic, complemented, Sylow
373C22×D4C4×D6111yescharacteristic
374C23×C4—21no—
375C2×SD16—611no—
376C2×SD16—611no—
377C2×D8—611no—
378C2×D8—611no—
379C2×M16—611no—
380C2×M16—611no—
381C2×M16—1221no—
382C2×M16—1221no—
383C2×M16—1221no—
384C2×M16—1221no—
385C2×M16—2444no—
386C22×C8—1221no—
387C22×C8—1221no—
388C22×C8—1221no—
389#126—1221no—
390#125—611no—
391#124—611no—
392#123—1221no—
393C22⋊Q8—611no—
394#121—611no—
395C4×Q8—611no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—611no—
399C4×D4—1221no—
400C4×D4C4×D6111yescharacteristic
401C4×D4C4×D6111yescharacteristic
402C4×D4C22×D6111yescharacteristic
403C4×D4C22×D6111yescharacteristic
404#117—1221no—
405C2×C4⋊C4C4×D6111yescharacteristic
406C2×C22⋊C4—21no—
407C2×C42C22×D6111yescharacteristic
408#107—611no—
409#107—611no—
410#106—611no—
411#106—611no—
412C4⋊C8—21no—
413C4⋊C8—611no—
414C4⋊C8—611no—
415C4⋊C8—611no—
416C4⋊C8—611no—
417C4⋊C8—1221no—
418C4⋊C8—1221no—
419C4⋊C8—1221no—
420C4⋊C8C22×D6111yescharacteristic
421C4⋊C8C22×D6111yescharacteristic
422#103—611no—
423#103—611no—
424#102—611no—
425#102—611no—
426#102—611no—
427#102—611no—
428#102—611no—
429#102—611no—
430C22⋊C8—21no—
431C22⋊C8—21no—
432C22⋊C8—611no—
433C22⋊C8—611no—
434C22⋊C8—1221no—
435C22⋊C8—1221no—
436C22⋊C8—1221no—
437C22⋊C8—1221no—
438C22⋊C8—1221no—
439C22⋊C8—1221no—
440#97—611no—
441#97—611no—
442#97—1221no—
443C4×C8—21no—
444C4×C8—611no—
445C4×C8—611no—
446C4×C8—611no—
447C4×C8—611no—
448C4×C8—1221no—
449C4×C8C22×D6111yescharacteristic
450C4×C8C22×D6111yescharacteristic
451C24—21no—
452C2×Q8—611no—
453C2×D4—22no—
454C2×D4—21no—
455C2×D4—41no—
456C2×D4—611no—
457C2×D4—1221no—
458C2×D4C2×C4×D6111yescharacteristic
459C2×D4C2×C4×D6111yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—1221no—
468C22×C4C2×C4×D6111yescharacteristic
469C22×C4D4×D6111yescharacteristic
470C22×C4#1175822411yescharacteristic
471SD16—1222no—
472SD16—2441no—
473D8—1222no—
474D8—2441no—
475M16—1222no—
476M16—2442no—
477M16—2442no—
478M16—2441no—
479M16—2442no—
480M16—2442no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—611no—
486C2×C8—611no—
487C2×C8—611no—
488C2×C8—611no—
489C2×C8—611no—
490C2×C8—611no—
491C2×C8—611no—
492C2×C8—611no—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8—2442no—
496C2×C8—2442no—
497C2×C8—2442no—
498C4⋊C4—21no—
499C4⋊C4—611no—
500C4⋊C4—611no—
501C4⋊C4—1221no—
502C4⋊C4—1221no—
503C4⋊C4—1221no—
504C4⋊C4—1221no—
505C4⋊C4C2×C4×D6111yescharacteristic
506C4⋊C4C2×C4×D6111yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—1221no—
512C22⋊C4—1221no—
513C22⋊C4—1221no—
514C22⋊C4—1221no—
515C22⋊C4—1221no—
516C42—1221no—
517C42C2×C4×D6111yescharacteristic
518C42D4×D6111yescharacteristic
519C42#1175822411yescharacteristic
520C42C23×D6111yescharacteristic
521C23—21no—
522C23—21no—
523C23—42no—
524C23—42no—
525C23—81no—
526C23—1221no—
527C23#1451973711yescharacteristic
528Q8—1221no—
529Q8—1221no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—42no—
534D4—1221no—
535D4—1221no—
536D4—4881no—
537D4#1451978312yes—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—1221no—
553C2×C4—1221no—
554C2×C4—1221no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4#1451973711yescharacteristic
558C2×C4#1451973711yescharacteristic
559C2×C4#1451973711yescharacteristic
560C2×C4C22×C4×D6111yescharacteristic
561C2×C4C2×D4×D6111yescharacteristic
562C2×C4C2×#1175822411yescharacteristic
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8—612no—
568C8—1221no—
569C8—1221no—
570C8—1221no—
571C8—1221no—
572C8—1221no—
573C8—1221no—
574C8—1221no—
575C8—2441no—
576C8—2441no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—22no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—84no—
587C22—2441no—
588C22—2441no—
589C22—2441no—
590C22C2×#1451973711yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—41no—
596C4—41no—
597C4—2441no—
598C4—2441no—
599C4—2441no—
600C4C2×#1451978311yescharacteristic
601C4#1684052811yescharacteristic
602C4AGL(1,ℤ/8)×D6111yescharacteristic
603C4#1684055811yescharacteristic
604C2—41no—
605C2—42no—
606C2—81no—
607C2—4881no—
608C2#2145454011yescharacteristic
609C2#2145462311yescharacteristic
610C2#2145473211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1478C2
socleC22×C61C2×C4×D4
prime radical#16839896C4
cosocleC42×C61C24
hypercenter#1478D61
hypocenterC61#18006
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
2. #21454817C2semidirect
3. D4×#11758194C2semidirect
4. #21444730C2semidirect
5. #21444712C2semidirect
6. #21444700C2semidirect
7. #21444680C2semidirect
8. #21444652C2semidirect
9. #21444651C2semidirect
10. #21444628C2semidirect
11. #21444611C2semidirect
12. #21444607C2semidirect
13. #21444285C2semidirect
14. #21444114C2semidirect
15. C61×#1478C2semidirect
26. #16839889C22semidirect
27. #16839886C22semidirect
34. #16839839C22semidirect
41. #16839827C22semidirect
48. #16839514C22semidirect
49. #16839514C22semidirect
50. #16839512C22semidirect
51. #16839512C22semidirect
52. #16839494C22semidirect
53. #16839494C22semidirect
54. #16839491C22semidirect
55. #16839491C22semidirect
56. #16839484C22semidirect
57. #16839484C22semidirect
58. #16839483C22semidirect
59. C8×#92418C22semidirect
312. #1478D61semidirect
372. C61#18006semidirect

Maximal subgroups

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

subgroupindex
#214558662
#214548172
D4×#117581942
#214447302
#214447122
#214447002
#214446802
#214446522
#214446512
#214446282
#214446112
#214446072
#214442852
#214441142
C61×#14782
#1800661