Finite Group Databasebeta

← #29721278

Subgroups — #29721278

Order 15616.

868 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840059C211yesmaximal, characteristic, complemented
2C2×#16839819C211yesmaximal, characteristic, complemented
3C4×#14519751C211yesmaximal, characteristic
4#21447256C211yesmaximal, characteristic, complemented
5#21447245C211yesmaximal, characteristic, complemented
6#21447008C211yesmaximal, characteristic
7#21447001C211yesmaximal, characteristic
8#21446777C211yesmaximal, characteristic, complemented
9#21446585C211yesmaximal, characteristic, complemented
10#21446559C211yesmaximal, characteristic, complemented
11#21446554C211yesmaximal, characteristic, complemented
12#21446515C211yesmaximal, characteristic, complemented
13#21446515C211yesmaximal, characteristic, complemented
14#21445826C211yesmaximal, characteristic, complemented
15C61×#2851C211yesmaximal, characteristic, complemented
16C2×#14519751C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18C2×C4×C22⋊D61—21no—
19#16840059—24no—
20#16839819—24no—
21C2×#14519710C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26C2×C4⋊#92418C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31C2×C22⋊#92418C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33C2×#14519688C2211yescharacteristic
34C2×#14519688C2211yescharacteristic
35#16839664C2211yescharacteristic
36#16839660C2211yescharacteristic
37#16839653—21no—
38#16839641—21no—
39#16839622C2211yescharacteristic
40C4×C4⋊Dic61C2211yescharacteristic
41C4×#11758198—21no—
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50C2×#125×C61C2211yescharacteristic
51C22×C42×C61C2211yescharacteristic
52C61×#389C2211yescharacteristic
53C61×#389C2211yescharacteristic
54C61×#387—21no—
55C61×#387—21no—
56C61×#385—21no—
57C61×#385—21no—
58C61×#382C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C61×#380C2211yescharacteristic
61C22×D244C2311yescharacteristic
62C22×C22⋊D61—21no—
63C22×C4×D61—21no—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68#14519751—22no—
69#14519751—22no—
70C4×D244—22no—
71C4×D244—22no—
72C4×C22⋊D61—44no—
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×#11758196—21no—
77C2×C22⋊Dic61—21no—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×C4×Dic61—21no—
83#14519710—22no—
84#14519710—22no—
85#14519708—22no—
86#14519708—22no—
87C4⋊#92418—22no—
88C4⋊#92418D414yescomplemented
89#14519697—22no—
90#14519697—22no—
91#14519697—22no—
92#14519697—22no—
93C22⋊#92418—22no—
94C22⋊#92418—22no—
95#14519688—22no—
96#14519688—22no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100C23×C4×C61D411yescharacteristic
101C23×C4×C61D411yescharacteristic
102C23×C4×C61C2311yescharacteristic
103#125×C61—22no—
104#125×C61—22no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61C2311yescharacteristic
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C22⋊C4×C61—21no—
114C2×C22⋊C4×C61—21no—
115C2×C42×C61—22no—
116C2×C42×C61—22no—
117C2×C42×C61D411yescharacteristic
118C2×C42×C61D411yescharacteristic
119C2×C42×C61C2311yescharacteristic
120C2×C42×C61C2311yescharacteristic
121#95×C61—21no—
122#95×C61—21no—
123#95×C61—21no—
124#95×C61—21no—
125#95×C61—21no—
126#95×C61—21no—
127C24×C61C2×D411yescharacteristic
128C23×D61—21no—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—41no—
143C22×C4×C61—41no—
144C22×C4×C61—41no—
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2411yescharacteristic
151C2×C22⋊D61—24no—
152C2×C22⋊D61—42no—
153C2×C22⋊D61—42no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C2×D244—21no—
158C2×D244—21no—
159C2×D244—21no—
160C2×D244—21no—
161C2×D244—21no—
162C2×D244#4112yes—
163C2×C4×D61—42no—
164C2×C4×D61—42no—
165C2×C4×D61—42no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—42no—
175C4⋊C4×C61—42no—
176C4⋊C4×C61—42no—
177C4⋊C4×C61—42no—
178C22⋊C4×C61—42no—
179C22⋊C4×C61—42no—
180C42×C61—22no—
181C42×C61—22no—
182C42×C61—21no—
183C42×C61—21no—
184C42×C61C2×D412yes—
185C42×C61#4112yes—
186C22⋊Dic61—42no—
187#11758198—24no—
188#11758198—42no—
189#11758198—42no—
190#11758198—42no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61#4112yes—
197#11758196—42no—
198C4×Dic61—42no—
199C2×#92418—21no—
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×#92418C2×D412yes—
210C2×#92418C2×D412yes—
211C23×C61—21no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61AGL(1,ℤ/8)12yes—
218C23×C61C22×D411yescharacteristic
219C22×D61—22no—
220C22×D61—41no—
221C22×D61—41no—
222C22×D61—41no—
223C22×D61—41no—
224C22×D61—41no—
225C22×D61—41no—
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—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—44no—
240C2×C4×C61—44no—
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—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61#12112yes—
258C2×C4×C61#12112yes—
259C2×C4×C61C22×D411yescharacteristic
260C2×C4×C61C2×#4111yescharacteristic
261C2×C4×C61C2×#4111yescharacteristic
262C2×C4×C61C2×#4111yescharacteristic
263C2×C4×C612−1+411yescharacteristic
264C2×C4×C612−1+411yescharacteristic
265C22⋊D61—48no—
266C2×Dic61—22no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275D244—22no—
276D244—22no—
277D244—41no—
278D244—41no—
279C4×D61—84no—
280#92418—22no—
281#92418—22no—
282#92418—41no—
283#92418—41no—
284#24706—611nomaximal, Sylow
285C22×C61—22no—
286C22×C61—22no—
287C22×C61—22no—
288C22×C61—41no—
289C22×C61—41no—
290C22×C61—41no—
291C22×C61—41no—
292C22×C61C2×#12111yescharacteristic
293C22×C61#52511yescharacteristic
294C22×C61#53611yescharacteristic
295C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
296C22×C61#57511yescharacteristic
297C22×C61#57511yescharacteristic
298C22×C61#57511yescharacteristic
299C2×D61—42no—
300C2×D61—42no—
301C2×D61—42no—
302C2×D61—81no—
303C2×D61—81no—
304C2×D61—81no—
305C2×D61—81no—
306C4×C61—22no—
307C4×C61—22no—
308C4×C61—41no—
309C4×C61—41no—
310C4×C61—41no—
311C4×C61—81no—
312C4×C61—81no—
313C4×C61—81no—
314C4×C61—81no—
315C4×C61#54711yescharacteristic
316C4×C61#54811yescharacteristic
317C4×C61#55211yescharacteristic
318C4×C61#55611yescharacteristic
319Dic61—42no—
320Dic61—81no—
321Dic61—81no—
322C2×#478—611no—
323C2×#432—611no—
324#2851D6111yescharacteristic, complemented
325C4×#121—611no—
326#2077—611no—
327#2075—611no—
328#2034—611no—
329#2033—611no—
330#1989—611no—
331#1949—611no—
332#1944—611no—
333#1943—611no—
334#1936—611no—
335#1936—611no—
336#1804—611no—
337C2×C61—42no—
338C2×C61#241511yescharacteristic
339C2×C61#305411yescharacteristic
340C2×C61#305511yescharacteristic
341C2×C61#311111yescharacteristic
342C2×C61#311411yescharacteristic
343C2×C61#323411yescharacteristic
344C2×C61#324011yescharacteristic
345D61—82no—
346C2×#125C2×D6111yescharacteristic
347C2×#121—611no—
348C2×C4×D4—611no—
349C2×C4×D4—1221no—
350C22×C42C2×D6111yescharacteristic
351#478—1224no—
352#432—1224no—
353C2×#107—611no—
354C2×#107—611no—
355C2×#106—611no—
356C2×#106—611no—
357C2×C4⋊C8—611no—
358C2×C4⋊C8—611no—
359C2×#102—611no—
360C2×#102—611no—
361C2×#102—611no—
362C2×#102—611no—
363C2×C22⋊C8—611no—
364C2×C22⋊C8—611no—
365C2×#97—611no—
366C2×#97—611no—
367#390—611no—
368#389—611no—
369#389C2×D6111yescharacteristic
370#389C2×D6111yescharacteristic
371#388—1221no—
372#387—21no—
373#387—21no—
374#386—1221no—
375#385—21no—
376#385—21no—
377#382C2×D6111yescharacteristic
378#380—611no—
379#380C2×D6111yescharacteristic
380#380C2×D6111yescharacteristic
381C4×C4⋊C4—611no—
382C4×C22⋊C4—1221no—
383#340—611no—
384#340—611no—
385#340—611no—
386#340—611no—
387#340—611no—
388#340—611no—
389#340—611no—
390#340—611no—
391C61#2470611yescharacteristic, complemented, Sylow
392C22×D4—611no—
393C22×D4—1221no—
394C23×C4—1221no—
395C23×C4C22⋊D6111yescharacteristic
396C23×C4C22⋊D6111yescharacteristic
397C23×C4C22×D6111yescharacteristic
398C22×C8—611no—
399C22×C8—611no—
400C22×C8—611no—
401C22×C8—611no—
402#125—22no—
403#125—22no—
404#121—1222no—
405#121—1222no—
406C4×D4—1222no—
407C4×D4—1222no—
408C4×D4—2444no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—611no—
414C2×C4⋊C4—611no—
415C2×C4⋊C4—611no—
416C2×C4⋊C4—1221no—
417C2×C4⋊C4C22×D6111yescharacteristic
418C2×C4⋊C4C22×D6111yescharacteristic
419C2×C4⋊C4C22×D6111yescharacteristic
420C2×C4⋊C4C22×D6111yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—1221no—
424C2×C22⋊C4—1221no—
425C2×C22⋊C4—1221no—
426C2×C22⋊C4—1221no—
427C2×C22⋊C4—1221no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—1221no—
431C2×C42C22⋊D6111yescharacteristic
432C2×C42C22⋊D6111yescharacteristic
433C2×C42C22×D6111yescharacteristic
434C2×C42C22×D6111yescharacteristic
435#107—1222no—
436#107—1222no—
437#106—1222no—
438#106—1222no—
439C4⋊C8—614no—
440C4⋊C8—1222no—
441#102—1222no—
442#102—1222no—
443#102—1222no—
444#102—1222no—
445C22⋊C8—1222no—
446C22⋊C8—1222no—
447#97—1222no—
448#97—1222no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—1221no—
456#95—1221no—
457#95—1221no—
458C24—1221no—
459C24C2×C22⋊D6111yescharacteristic
460C2×D4—612no—
461C2×D4—1224no—
462C2×D4—1221no—
463C2×D4—1221no—
464C2×D4—1221no—
465C2×D4—1221no—
466C2×D4—1221no—
467C2×D4—2442no—
468C2×D4—2442no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—1221no—
486C22×C4—1221no—
487C22×C4—1221no—
488C22×C4—2442no—
489C22×C4—2442no—
490C22×C4—2442no—
491C22×C4C2×C22⋊D6111yescharacteristic
492C22×C4C2×C22⋊D6111yescharacteristic
493C22×C4C2×C22⋊D6111yescharacteristic
494C22×C4C2×C22⋊D6111yescharacteristic
495C22×C4C2×C22⋊D6111yescharacteristic
496C22×C4C23×D6111yescharacteristic
497C2×C8—612no—
498C2×C8—612no—
499C2×C8—1221no—
500C2×C8—1221no—
501C2×C8—1221no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8—1221no—
507C2×C8—1221no—
508C2×C8—1221no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—42no—
518C4⋊C4—42no—
519C4⋊C4—42no—
520C4⋊C4—42no—
521C4⋊C4—612no—
522C4⋊C4—1221no—
523C4⋊C4—1221no—
524C4⋊C4—1221no—
525C4⋊C4—1221no—
526C4⋊C4—1221no—
527C4⋊C4—2442no—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C22⋊C4—1224no—
531C22⋊C4—2442no—
532C22⋊C4—2442no—
533C22⋊C4—2442no—
534C22⋊C4—2442no—
535C42—21no—
536C42—21no—
537C42—22no—
538C42—22no—
539C42—2442no—
540C42D4×D6112yes—
541C42#1175822412yes—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—1222no—
549C23—2441no—
550C23—2441no—
551C23—2441no—
552C23—2441no—
553C23—2441no—
554C23—2441no—
555C23#1451980212yes—
556C23C22×C22⋊D6111yescharacteristic
557D4—1222no—
558D4—1222no—
559D4—2448no—
560D4—2441no—
561D4—2441no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—44no—
576C2×C4—44no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—1222no—
594C2×C4—4884no—
595C2×C4—2441no—
596C2×C4—2441no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4#1451974912yes—
604C2×C4#1451974912yes—
605C2×C4C2×D4×D6111yescharacteristic
606C2×C4#41×D6111yescharacteristic
607C2×C4#41×D6111yescharacteristic
608C2×C4C2×#1175822411yescharacteristic
609C2×C4#1451982511yescharacteristic
610C2×C4#1451982511yescharacteristic
611C8—1222no—
612C8—1222no—
613C8—2441no—
614C8—2441no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—4881no—
623C22—4881no—
624C22—4881no—
625C22—4881no—
626C22—2442no—
627C22—2442no—
628C22—2442no—
629C22C2×#1451974911yescharacteristic
630C22#1684026911yescharacteristic
631C22#1684033611yescharacteristic
632C22C2×#1451980211yescharacteristic
633C22#1684056011yescharacteristic
634C22#1684056011yescharacteristic
635C22#1684056011yescharacteristic
636C4—22no—
637C4—22no—
638C4—41no—
639C4—41no—
640C4—41no—
641C4—81no—
642C4—81no—
643C4—81no—
644C4—81no—
645C4—4881no—
646C4—4881no—
647C4—2442no—
648C4#1684041411yescharacteristic
649C4#1684042211yescharacteristic
650C4#1684044611yescharacteristic
651C4#1684048311yescharacteristic
652C2—42no—
653C2—4882no—
654C2#2144924911yescharacteristic
655C2#2145542511yescharacteristic
656C2#2145544011yescharacteristic
657C2#2145592211yescharacteristic
658C2#2145595311yescharacteristic
659C2#2145700911yescharacteristic
660C2#2145705911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2851C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenter#2851D61
hypocenterC61#24706
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2851

Complements

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

NH ≅ G/Ntype
1. C2×#16840059C2semidirect
2. C2×#16839819C2semidirect
4. #21447256C2semidirect
5. #21447245C2semidirect
8. #21446777C2semidirect
9. #21446585C2semidirect
10. #21446559C2semidirect
11. #21446554C2semidirect
12. #21446515C2semidirect
13. #21446515C2semidirect
14. #21445826C2semidirect
15. C61×#2851C2semidirect
88. C4⋊#92418D4semidirect
324. #2851D61semidirect
391. C61#24706semidirect

Maximal subgroups

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

subgroupindex
C2×#168400592
C2×#168398192
C4×#145197512
#214472562
#214472452
#214470082
#214470012
#214467772
#214465852
#214465592
#214465542
#214465152
#214458262
C61×#28512
#2470661