Finite Group Databasebeta

← #29603113

Subgroups — #29603113

Order 15616.

1802 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839659C211yesmaximal, characteristic, complemented
2C2×#16839654C211yesmaximal, characteristic
3C2×#16839653C211yesmaximal, characteristic
4C2×#16839621C211yesmaximal, characteristic
5C2×#16839621C211yesmaximal, characteristic
6C2×C4×#11758196C211yesmaximal, characteristic, complemented
7C2×#16839609C211yesmaximal, characteristic
8#21444077C211yesmaximal, characteristic, complemented
9#21444076C211yesmaximal, characteristic, complemented
10#21444067C211yesmaximal, characteristic
11#21444067C211yesmaximal, characteristic
12#21444047C211yesmaximal, characteristic, complemented
13#21444047C211yesmaximal, characteristic, complemented
14#21444043C211yesmaximal, characteristic, complemented
15C61×#1434C211yesmaximal, characteristic, complemented
16C23×C4×D61C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×#11758196C2211yescharacteristic
19C22×#11758196C2211yescharacteristic
20C22×#11758196C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×C4×Dic61C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32#16839659—24no—
33#16839654—24no—
34#16839653—24no—
35#16839621—24no—
36#16839621C418yescomplemented
37C4×#11758196—24no—
38#16839609—24no—
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C22×C42×C61C2211yescharacteristic
52C2×#95×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C24×D61C2311yescharacteristic
59C23×Dic61C2311yescharacteristic
60C23×Dic61C2311yescharacteristic
61C23×Dic61C2311yescharacteristic
62C23×Dic61C2311yescharacteristic
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2311yescharacteristic
65C23×Dic61C2311yescharacteristic
66C22×C4×D61—22no—
67C22×C4×D61—22no—
68C22×C4×D61—22no—
69C22×C4×D61—22no—
70C22×C4×D61—22no—
71C22×C4×D61—22no—
72C22×C4×D61C2×C414yes—
73C2×C4⋊Dic61—22no—
74C2×C4⋊Dic61—22no—
75C2×C4⋊Dic61—41no—
76C2×#11758196—22no—
77C2×#11758196—22no—
78C2×#11758196—22no—
79C2×#11758196—22no—
80C2×#11758196—22no—
81C2×#11758196—22no—
82C2×#11758196—22no—
83C2×#11758196—22no—
84C2×#11758196—22no—
85C2×#11758196—22no—
86C2×#11758196—22no—
87C2×#11758196—41no—
88C2×#11758196C2×C414yes—
89C2×#11758196C2×C414yes—
90C2×#11758196D414yes—
91C2×#11758198—22no—
92C2×#11758198—22no—
93C2×#11758198—22no—
94C2×#11758198—22no—
95C2×#11758198—22no—
96C2×#11758198—22no—
97C2×#11758198—22no—
98C2×#11758198—22no—
99C2×#11758198—22no—
100C2×#11758198—22no—
101C2×#11758198—22no—
102C2×#11758198—22no—
103C2×#11758198—22no—
104C2×#11758198—41no—
105C2×#11758198—41no—
106C2×#11758198C2×C414yes—
107C2×#11758198C2×C414yes—
108C2×#11758198D414yes—
109C2×C4×Dic61—22no—
110C2×C4×Dic61—22no—
111C2×C4×Dic61—22no—
112C2×C4×Dic61—22no—
113C2×C4×Dic61—22no—
114C2×C4×Dic61—22no—
115C2×C4×Dic61—22no—
116C2×C4×Dic61—22no—
117C2×C4×Dic61D414yes—
118#14519684—22no—
119#14519684—22no—
120#14519684—22no—
121#14519684—22no—
122#14519684—22no—
123#14519684—22no—
124#14519684—22no—
125#14519684—22no—
126#14519684—22no—
127#14519684—41no—
128#14519684—41no—
129#14519684C2×C414yes—
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C2×C42×C61—22no—
138C2×C42×C61—22no—
139C2×C42×C61—22no—
140#95×C61—22no—
141#95×C61—22no—
142#95×C61—22no—
143#95×C61—22no—
144#95×C61—22no—
145#95×C61C2×C414yes—
146C24×C61C2411yescharacteristic
147C23×D61—21no—
148C23×D61—21no—
149C23×D61—21no—
150C23×D61—21no—
151C23×D61—21no—
152C23×D61—21no—
153C23×D61—21no—
154C23×D61—21no—
155C23×D61—21no—
156C23×D61—21no—
157C23×D61—21no—
158C23×D61—21no—
159C23×D61C22×C412yes—
160C23×D61C2×D412yes—
161C23×D61#4112yes—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61C22×C412yes—
204C22×C4×C61C22×C412yes—
205C22×C4×C61C22×C412yes—
206C22×C4×C61C2×D412yes—
207C22×C4×C61C2×D412yes—
208C22×C4×C61C2×D412yes—
209C22×C4×C61#4112yes—
210C22×C4×C61#4112yes—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61C22×C412yes—
249C22×Dic61C22×C412yes—
250C22×Dic61C22×C412yes—
251C22×Dic61C2×D412yes—
252C22×Dic61C2×D412yes—
253C22×Dic61C2×D412yes—
254C22×Dic61C2×D412yes—
255C22×Dic61C2×D412yes—
256C22×Dic61#4112yes—
257C22×Dic61#4112yes—
258C22×Dic61#4112yes—
259C22×Dic61#4112yes—
260C2×C4×D61—28no—
261C2×C4×D61—28no—
262C2×C4×D61—28no—
263C2×C4×D61—44no—
264C2×C4×D61—44no—
265C2×C4×D61—44no—
266C2×C4×D61—44no—
267C42×C61—44no—
268#11758198—28no—
269#11758198—28no—
270#11758198—28no—
271#11758198—28no—
272#11758198—44no—
273#11758198—44no—
274C4⋊Dic61—44no—
275#11758196—28no—
276#11758196—28no—
277#11758196—28no—
278#11758196—44no—
279#11758196—44no—
280C4×Dic61—28no—
281C4×Dic61—44no—
282C4×Dic61—44no—
283C23×C61C23×C411yescharacteristic
284C23×C61C22×D411yescharacteristic
285C23×C61C22×D411yescharacteristic
286C23×C61C22×D411yescharacteristic
287C23×C61C2×#4111yescharacteristic
288C23×C61C2×#4111yescharacteristic
289C23×C61C2×#4111yescharacteristic
290C23×C61C2×#4111yescharacteristic
291C23×C61C2×#4111yescharacteristic
292C23×C61C2×#4111yescharacteristic
293C23×C61C2×#4111yescharacteristic
294C23×C61H(5,𝔽2)11yescharacteristic
295C23×C612−1+411yescharacteristic
296C23×C612−1+411yescharacteristic
297C23×C612−1+411yescharacteristic
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—22no—
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—22no—
305C22×D61—22no—
306C22×D61—22no—
307C22×D61—22no—
308C22×D61—22no—
309C22×D61—22no—
310C22×D61—22no—
311C22×D61—22no—
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—22no—
316C22×D61—41no—
317C22×D61—41no—
318C22×D61—41no—
319C22×D61—41no—
320C22×D61—41no—
321C22×D61—41no—
322C22×D61—41no—
323C22×D61—41no—
324C22×D61—41no—
325C22×D61—41no—
326C22×D61—41no—
327C22×D61—41no—
328C22×D61—41no—
329C22×D61—41no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61C4×D414yes—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61#12114yes—
382C2×Dic61—22no—
383C2×Dic61—22no—
384C2×Dic61—22no—
385C2×Dic61—22no—
386C2×Dic61—22no—
387C2×Dic61—22no—
388C2×Dic61—22no—
389C2×Dic61—22no—
390C2×Dic61—22no—
391C2×Dic61—22no—
392C2×Dic61—22no—
393C2×Dic61—22no—
394C2×Dic61—22no—
395C2×Dic61—22no—
396C2×Dic61—22no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—41no—
403C2×Dic61—41no—
404C2×Dic61—41no—
405C2×Dic61—41no—
406C2×Dic61—41no—
407C2×Dic61—41no—
408C2×Dic61—41no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411C2×Dic61—41no—
412C2×Dic61—41no—
413C2×Dic61—41no—
414C2×Dic61—41no—
415C2×Dic61—41no—
416C2×Dic61—41no—
417C2×Dic61—41no—
418C2×Dic61—41no—
419C2×Dic61—41no—
420C2×Dic61—41no—
421C2×Dic61—41no—
422C2×Dic61—41no—
423C2×Dic61—41no—
424C2×Dic61#11714yes—
425C2×Dic61C4×D414yes—
426C2×Dic61C4×D414yes—
427C2×Dic61#12114yes—
428C2×Dic61#12314yes—
429C2×Dic61#12414yes—
430C2×Dic61#12614yes—
431C4×D61—416no—
432#13994—611nomaximal, Sylow
433C22×C61C2×#11711yescharacteristic
434C22×C61C2×C4×D411yescharacteristic
435C22×C61C2×C4×D411yescharacteristic
436C22×C61C2×C4×D411yescharacteristic
437C22×C61C4×#4111yescharacteristic
438C22×C61#51911yescharacteristic
439C22×C61#52011yescharacteristic
440C22×C61C2×#12111yescharacteristic
441C22×C61C2×#12111yescharacteristic
442C22×C61C2×#12311yescharacteristic
443C22×C61#52511yescharacteristic
444C22×C61C2×#12411yescharacteristic
445C22×C61C2×#12611yescharacteristic
446C22×C61#52911yescharacteristic
447C22×C61#53211yescharacteristic
448C22×C61#53611yescharacteristic
449C22×C61#53711yescharacteristic
450C22×C61#54111yescharacteristic
451C22×C61#54211yescharacteristic
452C22×C61D4211yescharacteristic
453C22×C61#54711yescharacteristic
454C22×C61#54711yescharacteristic
455C22×C61#54711yescharacteristic
456C22×C61#54711yescharacteristic
457C22×C61#54811yescharacteristic
458C22×C61#54811yescharacteristic
459C22×C61#55211yescharacteristic
460C22×C61#55211yescharacteristic
461C22×C61#55211yescharacteristic
462C22×C61#55211yescharacteristic
463C22×C61#55211yescharacteristic
464C22×C61#55311yescharacteristic
465C22×C61#55511yescharacteristic
466C22×C61#55511yescharacteristic
467C22×C61#55611yescharacteristic
468C2×D61—24no—
469C2×D61—24no—
470C2×D61—24no—
471C2×D61—42no—
472C2×D61—42no—
473C2×D61—42no—
474C2×D61—42no—
475C2×D61—42no—
476C2×D61—42no—
477C2×D61—42no—
478C2×D61—42no—
479C2×D61—42no—
480C2×D61—42no—
481C2×D61—42no—
482C2×D61—42no—
483C4×C61—24no—
484C4×C61—42no—
485C4×C61—42no—
486C4×C61—42no—
487C4×C61—42no—
488C4×C61—42no—
489C4×C61—81no—
490Dic61—42no—
491Dic61—42no—
492Dic61—42no—
493Dic61—42no—
494Dic61—42no—
495Dic61—81no—
496Dic61#38818yescomplemented
497C2×#389—611no—
498C2×#388—611no—
499C2×#388—611no—
500C2×#380—611no—
501C2×#380—611no—
502C2×C4×C4⋊C4—611no—
503C2×C4×C22⋊C4—611no—
504#1442—611no—
505#1442—611no—
506#1440—611no—
507#1440—611no—
508C4⋊#95—611no—
509C4⋊#95—611no—
510#1434—611no—
511#1434D6111yescharacteristic, complemented
512C2×C61C2×#38811yescharacteristic
513C2×C61C4×#12111yescharacteristic
514C2×C61#232311yescharacteristic
515C2×C61#234411yescharacteristic
516C2×C61#234611yescharacteristic
517C2×C61#236111yescharacteristic
518C2×C61#236211yescharacteristic
519C2×C61#248511yescharacteristic
520C2×C61#248611yescharacteristic
521C2×C61#248911yescharacteristic
522C2×C61#249111yescharacteristic
523C2×C61#249511yescharacteristic
524C2×C61#249611yescharacteristic
525C2×C61#253611yescharacteristic
526C2×C61#253711yescharacteristic
527D61—44no—
528C24×C4—611no—
529C22×C4⋊C4—611no—
530C22×C4⋊C4—611no—
531C22×C4⋊C4—611no—
532C22×C4⋊C4—611no—
533C22×C4⋊C4—611no—
534C22×C4⋊C4—611no—
535C22×C22⋊C4—611no—
536C22×C22⋊C4—611no—
537C22×C22⋊C4—611no—
538C22×C22⋊C4—611no—
539C22×C22⋊C4—611no—
540C22×C22⋊C4—611no—
541C22×C42—611no—
542C22×C42—611no—
543C22×C42—611no—
544C22×C42C2×D6111yescharacteristic
545#389—1224no—
546#388—1224no—
547#388—1224no—
548#380—618no—
549#380—1224no—
550C4×C4⋊C4—1224no—
551C4×C22⋊C4—1224no—
552C2×#95—611no—
553C2×#95—611no—
554C2×#95—611no—
555C2×#95—611no—
556C2×#95—611no—
557C2×#95—611no—
558C2×#95—611no—
559C2×#95—611no—
560C2×#95—611no—
561C2×#95—611no—
562C2×#95—611no—
563C2×#95—611no—
564C2×#95C2×D6111yescharacteristic
565C2×#95C2×D6111yescharacteristic
566C2×#95C2×D6111yescharacteristic
567C2×#95C2×D6111yescharacteristic
568C2×#95C2×D6111yescharacteristic
569C2×#95C2×D6111yescharacteristic
570C61#1399411yescharacteristic, complemented, Sylow
571C25—611no—
572C23×C4—611no—
573C23×C4—611no—
574C23×C4—611no—
575C23×C4—611no—
576C23×C4—611no—
577C23×C4—611no—
578C23×C4—614no—
579C23×C4—611no—
580C23×C4—1222no—
581C23×C4—1222no—
582C23×C4—1222no—
583C23×C4—1222no—
584C23×C4—1222no—
585C23×C4—1222no—
586C23×C4C22×D6111yescharacteristic
587C23×C4C22×D6111yescharacteristic
588C23×C4C22×D6111yescharacteristic
589C23×C4C22×D6111yescharacteristic
590C23×C4C22×D6111yescharacteristic
591C23×C4C22×D6111yescharacteristic
592C23×C4C22×D6111yescharacteristic
593C2×C4⋊C4—614no—
594C2×C4⋊C4—614no—
595C2×C4⋊C4—614no—
596C2×C4⋊C4—1222no—
597C2×C4⋊C4—1222no—
598C2×C4⋊C4—1222no—
599C2×C4⋊C4—1222no—
600C2×C4⋊C4—1222no—
601C2×C4⋊C4—1222no—
602C2×C4⋊C4—1222no—
603C2×C4⋊C4—1222no—
604C2×C4⋊C4—1222no—
605C2×C4⋊C4—1222no—
606C2×C4⋊C4—1222no—
607C2×C4⋊C4—1222no—
608C2×C4⋊C4—1222no—
609C2×C4⋊C4—2441no—
610C2×C4⋊C4—2441no—
611C2×C22⋊C4—614no—
612C2×C22⋊C4—614no—
613C2×C22⋊C4—614no—
614C2×C22⋊C4—1222no—
615C2×C22⋊C4—1222no—
616C2×C22⋊C4—1222no—
617C2×C22⋊C4—1222no—
618C2×C22⋊C4—1222no—
619C2×C22⋊C4—1222no—
620C2×C22⋊C4—1222no—
621C2×C22⋊C4—1222no—
622C2×C22⋊C4—1222no—
623C2×C22⋊C4—1222no—
624C2×C22⋊C4—1222no—
625C2×C22⋊C4—1222no—
626C2×C22⋊C4—1222no—
627C2×C22⋊C4—2441no—
628C2×C22⋊C4—2441no—
629C2×C42—22no—
630C2×C42—22no—
631C2×C42—22no—
632C2×C42—614no—
633C2×C42—1222no—
634C2×C42—1222no—
635C2×C42—1222no—
636C2×C42—1222no—
637C2×C42—1222no—
638C2×C42—1222no—
639C2×C42—1222no—
640C2×C42—1222no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—614no—
647#95—1222no—
648#95—1222no—
649#95—1222no—
650#95—1222no—
651#95—1222no—
652#95—1222no—
653#95—1222no—
654#95—1222no—
655#95—1222no—
656#95—2441no—
657#95—2441no—
658#95C4×D6114yes—
659C24—612no—
660C24—612no—
661C24—612no—
662C24—1221no—
663C24—1221no—
664C24—1221no—
665C24—1221no—
666C24—1221no—
667C24—1221no—
668C24—1221no—
669C24—1221no—
670C24—1221no—
671C24—1221no—
672C24—1221no—
673C24—1221no—
674C24C23×D6111yescharacteristic
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—612no—
717C22×C4—612no—
718C22×C4—612no—
719C22×C4—612no—
720C22×C4—612no—
721C22×C4—612no—
722C22×C4—612no—
723C22×C4—612no—
724C22×C4—612no—
725C22×C4—612no—
726C22×C4—612no—
727C22×C4—612no—
728C22×C4—1228no—
729C22×C4—1228no—
730C22×C4—1228no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—1221no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—1221no—
760C22×C4—1221no—
761C22×C4—1221no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—2444no—
769C22×C4—2444no—
770C22×C4—2444no—
771C22×C4—2444no—
772C22×C4C2×C4×D6112yes—
773C22×C4C2×C4×D6112yes—
774C22×C4C2×C4×D6112yes—
775C22×C4#1175822212yes—
776C22×C4#1175822212yes—
777C22×C4D4×D6112yes—
778C22×C4D4×D6112yes—
779C22×C4D4×D6112yes—
780C4⋊C4—1228no—
781C4⋊C4—1228no—
782C4⋊C4—1228no—
783C4⋊C4—2444no—
784C4⋊C4—2444no—
785C4⋊C4—2444no—
786C22⋊C4—1228no—
787C22⋊C4—1228no—
788C22⋊C4—1228no—
789C22⋊C4—1228no—
790C22⋊C4—2444no—
791C22⋊C4—2444no—
792C42—44no—
793C42—1228no—
794C42—2444no—
795C42—2444no—
796C23—614no—
797C23—1222no—
798C23—1222no—
799C23—1222no—
800C23—1222no—
801C23—1222no—
802C23—1222no—
803C23—1222no—
804C23—1222no—
805C23—1222no—
806C23—1222no—
807C23—1222no—
808C23—1222no—
809C23—1222no—
810C23—1222no—
811C23—1222no—
812C23—1222no—
813C23—1222no—
814C23—1222no—
815C23—2441no—
816C23—2441no—
817C23—2441no—
818C23—2441no—
819C23—2441no—
820C23—2441no—
821C23—2441no—
822C23—2441no—
823C23—2441no—
824C23—2441no—
825C23—2441no—
826C23—2441no—
827C23—2441no—
828C23—2441no—
829C23—2441no—
830C23—2441no—
831C23C22×C4×D6111yescharacteristic
832C23C2×D4×D6111yescharacteristic
833C23C2×D4×D6111yescharacteristic
834C23C2×D4×D6111yescharacteristic
835C23#41×D6111yescharacteristic
836C23#41×D6111yescharacteristic
837C23#41×D6111yescharacteristic
838C23#41×D6111yescharacteristic
839C23#41×D6111yescharacteristic
840C23C2×#1175822211yescharacteristic
841C23C2×#1175822211yescharacteristic
842C23#1451982311yescharacteristic
843C23#1451982411yescharacteristic
844C23#1451982411yescharacteristic
845C23#1451982511yescharacteristic
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—614no—
895C2×C4—614no—
896C2×C4—614no—
897C2×C4—614no—
898C2×C4—614no—
899C2×C4—614no—
900C2×C4—614no—
901C2×C4—1222no—
902C2×C4—1222no—
903C2×C4—1222no—
904C2×C4—1222no—
905C2×C4—1222no—
906C2×C4—1222no—
907C2×C4—1222no—
908C2×C4—1222no—
909C2×C4—1222no—
910C2×C4—1222no—
911C2×C4—1222no—
912C2×C4—1222no—
913C2×C4—1222no—
914C2×C4—1222no—
915C2×C4—1222no—
916C2×C4—24416no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4—2441no—
920C2×C4—2441no—
921C2×C4—2441no—
922C2×C4—2441no—
923C2×C4—2441no—
924C2×C4—2441no—
925C2×C4—2441no—
926C2×C4—2441no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4—2441no—
940C2×C4—2441no—
941C2×C4—2441no—
942C2×C4—2441no—
943C2×C4—2441no—
944C2×C4#1451975014yes—
945C22—1224no—
946C22—1224no—
947C22—1224no—
948C22—2442no—
949C22—2442no—
950C22—2442no—
951C22—2442no—
952C22—2442no—
953C22—2442no—
954C22—2442no—
955C22—2442no—
956C22—2442no—
957C22—2442no—
958C22—2442no—
959C22—2442no—
960C22#117×D6111yescharacteristic
961C22C4×D4×D6111yescharacteristic
962C22C4×D4×D6111yescharacteristic
963C22C4×D4×D6111yescharacteristic
964C22C4×#1175822211yescharacteristic
965C22#1684023811yescharacteristic
966C22#1684024211yescharacteristic
967C22#121×D6111yescharacteristic
968C22C2×#1451975011yescharacteristic
969C22#123×D6111yescharacteristic
970C22#1684027111yescharacteristic
971C22#124×D6111yescharacteristic
972C22#126×D6111yescharacteristic
973C22#1684029011yescharacteristic
974C22#1684030911yescharacteristic
975C22#1684033411yescharacteristic
976C22#1684034211yescharacteristic
977C22#1684037111yescharacteristic
978C22#1684037811yescharacteristic
979C22#1684039611yescharacteristic
980C22#1684041011yescharacteristic
981C22#1684041011yescharacteristic
982C22#1684041311yescharacteristic
983C22#1684041411yescharacteristic
984C22#1684042011yescharacteristic
985C22#1684042111yescharacteristic
986C22#1684044411yescharacteristic
987C22#1684044511yescharacteristic
988C22#1684044511yescharacteristic
989C22#1684044511yescharacteristic
990C22#1684044811yescharacteristic
991C22#1684046311yescharacteristic
992C22#1684047511yescharacteristic
993C22#1684047511yescharacteristic
994C22#1684048411yescharacteristic
995C4—24no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—81no—
1002C4—618no—
1003C4—4881no—
1004C4—2442no—
1005C4—2442no—
1006C4—2442no—
1007C4—2442no—
1008C4—2442no—
1009C2—2444no—
1010C2#388×D6111yescharacteristic
1011C2C4×#1451975011yescharacteristic
1012C2#2144850011yescharacteristic
1013C2#2144868511yescharacteristic
1014C2#2144870511yescharacteristic
1015C2#2144883211yescharacteristic
1016C2#2144884711yescharacteristic
1017C2#2145011511yescharacteristic
1018C2#2145012611yescharacteristic
1019C2#2145015911yescharacteristic
1020C2#2145018111yescharacteristic
1021C2#2145022911yescharacteristic
1022C2#2145024011yescharacteristic
1023C2#2145072711yescharacteristic
1024C2#2145073411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1434C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenter#1434D61
hypocenterC61#13994
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
1. C2×#16839659C2semidirect
6. C2×C4×#11758196C2semidirect
8. #21444077C2semidirect
9. #21444076C2semidirect
12. #21444047C2semidirect
13. #21444047C2semidirect
14. #21444043C2semidirect
15. C61×#1434C2semidirect
36. #16839621C4semidirect
496. Dic61#388semidirect
511. #1434D61semidirect
570. C61#13994semidirect

Maximal subgroups

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

subgroupindex
C2×#168396592
C2×#168396542
C2×#168396532
C2×#168396212
C2×C4×#117581962
C2×#168396092
#214440772
#214440762
#214440672
#214440472
#214440432
C61×#14342
#1399461