Finite Group Databasebeta

← #29721280

Subgroups — #29721280

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×#16840062C211yesmaximal, characteristic, complemented
2C2×#16839818C211yesmaximal, characteristic, complemented
3#21454130C211yesmaximal, characteristic, complemented
4C4×#14519748C211yesmaximal, characteristic
5#21447257C211yesmaximal, characteristic, complemented
6#21447246C211yesmaximal, characteristic, complemented
7#21447006C211yesmaximal, characteristic
8#21446999C211yesmaximal, characteristic
9#21446774C211yesmaximal, characteristic, complemented
10#21446585C211yesmaximal, characteristic, complemented
11#21446561C211yesmaximal, characteristic, complemented
12#21446556C211yesmaximal, characteristic, complemented
13#21446518C211yesmaximal, characteristic, complemented
14#21446518C211yesmaximal, characteristic, complemented
15C61×#1804C211yesmaximal, characteristic, complemented
16C2×#14519769C2211yescharacteristic
17C2×#14519748C2211yescharacteristic
18C2×C4×C22⋊D61—21no—
19C2×C42×D61C2211yescharacteristic
20#16840062—24no—
21#16839818—24no—
22C2×#14519710C2211yescharacteristic
23C2×#14519710C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26C2×C4⋊#92418C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519689C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519687C2211yescharacteristic
32C2×#14519687C2211yescharacteristic
33#16839665C2211yescharacteristic
34#16839661C2211yescharacteristic
35#16839661C2211yescharacteristic
36#16839658C2211yescharacteristic
37#16839650—21no—
38#16839647—21no—
39#16839647—21no—
40#16839638—21no—
41#16839636—21no—
42#16839636—21no—
43#16839619C2211yescharacteristic
44#16839619C2211yescharacteristic
45#16839619C2211yescharacteristic
46C4×C4⋊Dic61C2211yescharacteristic
47C4×C22⋊Dic61—21no—
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C61×#382C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×C22⋊D61—21no—
62C22×C4×D61D411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67#14519769—22no—
68#14519769—22no—
69#14519748—22no—
70#14519748—22no—
71C4×C22⋊D61—44no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×C22⋊Dic61—21no—
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61D411yescharacteristic
89C2×C4×Dic61D411yescharacteristic
90C2×C4×Dic61C2311yescharacteristic
91C42×D61—22no—
92C42×D61—22no—
93#14519710—22no—
94#14519710—22no—
95#14519708—22no—
96#14519708—22no—
97C4⋊#92418D414yescomplemented
98#14519698—22no—
99#14519698—22no—
100#14519689—22no—
101#14519689—22no—
102#14519687—22no—
103#14519687—22no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111C22×D4×C61C2311yescharacteristic
112C23×C4×C61—21no—
113C22×C8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C4×D4×C61—22no—
116C4×D4×C61—22no—
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C22⋊C4×C61—21no—
121C2×C42×C61C2311yescharacteristic
122C4⋊C8×C61—22no—
123#102×C61—22no—
124#102×C61—22no—
125#95×C61—21no—
126#95×C61—21no—
127C24×C61—21no—
128C23×D61C2×D411yescharacteristic
129C2×D4×C61—21no—
130C2×D4×C61—21no—
131C2×D4×C61—21no—
132C2×D4×C61—21no—
133C2×D4×C61—21no—
134C2×D4×C61#4112yes—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—42no—
139C22×C4×C61—42no—
140C22×C4×C61—42no—
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2411yescharacteristic
144C2×C22⋊D61—24no—
145C2×C22⋊D61—42no—
146C2×C22⋊D61—42no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61C2×D411yescharacteristic
152C22×Dic61C2×D411yescharacteristic
153C22×Dic61C2×D411yescharacteristic
154C2×C4×D61—22no—
155C2×C4×D61—22no—
156C2×C4×D61—22no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61—41no—
164C2×C4×D61—41no—
165C2×C4×D61—41no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C22⋊C4×C61—42no—
179C42×C61C2×D412yes—
180C42×C61#4112yes—
181C22⋊Dic61—24no—
182C22⋊Dic61—42no—
183C22⋊Dic61—42no—
184#11758198—42no—
185#11758198—42no—
186#11758198—42no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—42no—
195C4⋊Dic61—42no—
196C4⋊Dic61#4112yes—
197#11758196—42no—
198#11758196—42no—
199#11758196—42no—
200C4×Dic61—22no—
201C4×Dic61—22no—
202C4×Dic61—21no—
203C4×Dic61—21no—
204C4×Dic61—42no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418C2×D412yes—
210C2×#92418C2×D412yes—
211C23×C61—22no—
212C23×C61—41no—
213C23×C61—41no—
214C23×C61—41no—
215C23×C61—41no—
216C23×C61—41no—
217C23×C61—41no—
218C23×C61C22×D411yescharacteristic
219C22×D61—21no—
220C22×D61—21no—
221C22×D61—21no—
222C22×D61—21no—
223C22×D61—21no—
224C22×D61—21no—
225C22×D61AGL(1,ℤ/8)12yes—
226D4×C61—22no—
227D4×C61—22no—
228D4×C61—41no—
229D4×C61—41no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—84no—
244C2×C4×C61#12112yes—
245C2×C4×C61#12112yes—
246C2×C4×C61C22×D411yescharacteristic
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C61C2×#4111yescharacteristic
249C2×C4×C61C2×#4111yescharacteristic
250C2×C4×C612−1+411yescharacteristic
251C2×C4×C612−1+411yescharacteristic
252C22⋊D61—48no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—22no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C4×D61—44no—
275C4×D61—44no—
276C4×D61—41no—
277C4×D61—41no—
278C4×D61—41no—
279C4×D61—41no—
280C8×C61—41no—
281C8×C61—41no—
282#92418—22no—
283#92418—22no—
284#24706—611nomaximal, Sylow
285C22×C61—42no—
286C22×C61—42no—
287C22×C61—42no—
288C22×C61—81no—
289C22×C61—81no—
290C22×C61—81no—
291C22×C61—81no—
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—22no—
300C2×D61—22no—
301C2×D61—22no—
302C2×D61—41no—
303C2×D61—41no—
304C2×D61—41no—
305C2×D61—41no—
306C4×C61—22no—
307C4×C61—22no—
308C4×C61—81no—
309C4×C61—81no—
310C4×C61—81no—
311C4×C61#54711yescharacteristic
312C4×C61#54811yescharacteristic
313C4×C61#55211yescharacteristic
314C4×C61#55611yescharacteristic
315Dic61—42no—
316Dic61—41no—
317Dic61—41no—
318Dic61—41no—
319Dic61—81no—
320Dic61—81no—
321Dic61—81no—
322C2×#478—611no—
323C2×#432—611no—
324#2851—611no—
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#1804D6111yescharacteristic, complemented
337C2×C61—82no—
338C2×C61#241511yescharacteristic
339C2×C61#305411yescharacteristic
340C2×C61#305511yescharacteristic
341C2×C61#311111yescharacteristic
342C2×C61#311411yescharacteristic
343C2×C61#323411yescharacteristic
344C2×C61#324011yescharacteristic
345D61—42no—
346C2×#125—611no—
347C2×#121—611no—
348C2×C4×D4—1221no—
349C2×C4×D4C2×D6111yescharacteristic
350C22×C42—611no—
351#478—1224no—
352#432—1224no—
353C2×#107—611no—
354C2×#107—611no—
355C2×#106—611no—
356C2×#106—611no—
357C2×C4⋊C8—611no—
358C2×C4⋊C8C2×D6111yescharacteristic
359C2×#102—611no—
360C2×#102—611no—
361C2×#102C2×D6111yescharacteristic
362C2×#102C2×D6111yescharacteristic
363C2×C22⋊C8—611no—
364C2×C22⋊C8—611no—
365C2×#97—611no—
366C2×#97—611no—
367#390—611no—
368#389—611no—
369#389—611no—
370#389—611no—
371#388—1221no—
372#387—1221no—
373#387—1221no—
374#386—1221no—
375#385—1221no—
376#385—1221no—
377#382C2×D6111yescharacteristic
378#380—611no—
379#380—611no—
380#380—611no—
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#340C2×D6111yescharacteristic
390#340C2×D6111yescharacteristic
391C61#2470611yescharacteristic, complemented, Sylow
392C22×D4—1221no—
393C22×D4C22×D6111yescharacteristic
394C23×C4—21no—
395C23×C4—611no—
396C23×C4—611no—
397C23×C4—611no—
398C22×C8—611no—
399C22×C8—611no—
400C22×C8C22×D6111yescharacteristic
401C22×C8C22×D6111yescharacteristic
402#125—1222no—
403#125—1222no—
404#121—1222no—
405#121—1222no—
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—2444no—
409C2×C4⋊C4—611no—
410C2×C4⋊C4—611no—
411C2×C4⋊C4—611no—
412C2×C4⋊C4—611no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4—1221no—
415C2×C4⋊C4—1221no—
416C2×C4⋊C4—1221no—
417C2×C4⋊C4—1221no—
418C2×C4⋊C4C22×D6111yescharacteristic
419C2×C4⋊C4C22×D6111yescharacteristic
420C2×C4⋊C4C22×D6111yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—1221no—
423C2×C22⋊C4—1221no—
424C2×C22⋊C4—1221no—
425C2×C22⋊C4—1221no—
426C2×C22⋊C4—1221no—
427C2×C22⋊C4—1221no—
428C2×C42—611no—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—1222no—
432C2×C42—1222no—
433C2×C42—1221no—
434C2×C42C22×D6111yescharacteristic
435#107—1222no—
436#107—1222no—
437#106—1222no—
438#106—1222no—
439C4⋊C8—22no—
440C4⋊C8—614no—
441#102—22no—
442#102—22no—
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—1221no—
452#95—1221no—
453#95—1221no—
454#95—1221no—
455#95—1221no—
456#95—1221no—
457#95—1221no—
458C24—21no—
459C24—611no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—1224no—
466C2×D4—2442no—
467C2×D4—2442no—
468C2×D4#1175822412yes—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—1222no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1221no—
484C22×C4—1221no—
485C22×C4—1221no—
486C22×C4—1222no—
487C22×C4—1222no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4—2441no—
492C22×C4—2441no—
493C22×C4—2441no—
494C22×C4D4×D6111yescharacteristic
495C22×C4D4×D6111yescharacteristic
496C22×C4C23×D6111yescharacteristic
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—612no—
504C2×C8—612no—
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—612no—
516C4⋊C4—1221no—
517C4⋊C4—1221no—
518C4⋊C4—1221no—
519C4⋊C4—1221no—
520C4⋊C4—1221no—
521C4⋊C4—1221no—
522C4⋊C4—1221no—
523C4⋊C4—2442no—
524C4⋊C4—2442no—
525C4⋊C4—2442no—
526C4⋊C4—2442no—
527C4⋊C4—2442no—
528C22⋊C4—42no—
529C22⋊C4—1224no—
530C22⋊C4—2442no—
531C22⋊C4—2442no—
532C22⋊C4—2442no—
533C22⋊C4—2442no—
534C22⋊C4—2442no—
535C42—1221no—
536C42—1221no—
537C42—1222no—
538C42—1222no—
539C42—2442no—
540C42#1175822212yes—
541C42D4×D6112yes—
542C23—22no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—612no—
550C23—1221no—
551C23—1221no—
552C23—1221no—
553C23—1221no—
554C23—1221no—
555C23—1221no—
556C23C2×D4×D6111yescharacteristic
557D4—22no—
558D4—22no—
559D4—41no—
560D4—41no—
561D4—2448no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—84no—
576C2×C4—1221no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4—1222no—
581C2×C4—1221no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—2444no—
587C2×C4—2444no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4—2441no—
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#1451975012yes—
604C2×C4#1451975012yes—
605C2×C4C2×D4×D6111yescharacteristic
606C2×C4#41×D6111yescharacteristic
607C2×C4C2×#1175822411yescharacteristic
608C2×C4C2×#1175822211yescharacteristic
609C2×C4#1451982411yescharacteristic
610C2×C4#1451982511yescharacteristic
611C8—41no—
612C8—41no—
613C8—1222no—
614C8—1222no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22—1222no—
623C22—1222no—
624C22—1222no—
625C22—2441no—
626C22—2441no—
627C22—2441no—
628C22—2441no—
629C22C2×#1451975011yescharacteristic
630C22#1684027211yescharacteristic
631C22#1684033511yescharacteristic
632C22AGL(1,ℤ/8)×D6111yescharacteristic
633C22#1684055811yescharacteristic
634C22#1684055911yescharacteristic
635C22#1684055911yescharacteristic
636C4—22no—
637C4—22no—
638C4—81no—
639C4—81no—
640C4—81no—
641C4—4881no—
642C4—4881no—
643C4—4881no—
644C4—2441no—
645C4—2441no—
646C4—2441no—
647C4—2442no—
648C4#1684041411yescharacteristic
649C4#1684041811yescharacteristic
650C4#1684044711yescharacteristic
651C4#1684048011yescharacteristic
652C2—82no—
653C2—2442no—
654C2#2144925011yescharacteristic
655C2#2145542711yescharacteristic
656C2#2145543611yescharacteristic
657C2#2145592511yescharacteristic
658C2#2145595611yescharacteristic
659C2#2145700711yescharacteristic
660C2#2145705811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1804C2
socleC23×C61C22×D4
prime radicalC2×#14519748C22
hypercenter#1804D61
hypocenterC61#24706
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
1. C2×#16840062C2semidirect
2. C2×#16839818C2semidirect
3. #21454130C2semidirect
5. #21447257C2semidirect
6. #21447246C2semidirect
9. #21446774C2semidirect
10. #21446585C2semidirect
11. #21446561C2semidirect
12. #21446556C2semidirect
13. #21446518C2semidirect
14. #21446518C2semidirect
15. C61×#1804C2semidirect
97. C4⋊#92418D4semidirect
336. #1804D61semidirect
391. C61#24706semidirect

Maximal subgroups

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

subgroupindex
C2×#168400622
C2×#168398182
#214541302
C4×#145197482
#214472572
#214472462
#214470062
#214469992
#214467742
#214465852
#214465612
#214465562
#214465182
C61×#18042
#2470661