Finite Group Databasebeta

← #29608255

Subgroups — #29608255

Order 15616.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839655C211yesmaximal, characteristic, complemented
2C2×#16839639C211yesmaximal, characteristic
3C2×#16839638C211yesmaximal, characteristic
4#21444080C211yesmaximal, characteristic, complemented
5#21444079C211yesmaximal, characteristic, complemented
6#21444075C211yesmaximal, characteristic, complemented
7#21444065C211yesmaximal, characteristic, complemented
8#21444058C211yesmaximal, characteristic
9#21444055C211yesmaximal, characteristic, complemented
10#21444044C211yesmaximal, characteristic, complemented
11#21444041C211yesmaximal, characteristic, complemented
12#21444041C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×#1440C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C24×Dic61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×C22⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×C4×Dic61C2211yescharacteristic
28#16839655—24no—
29#16839639C418yescomplemented
30#16839638—24no—
31C2×#14519684C2211yescharacteristic
32C2×#14519684C2211yescharacteristic
33C2×#14519684C2211yescharacteristic
34C2×#14519684C2211yescharacteristic
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C22×C22⋊C4×C61C2211yescharacteristic
48C22×C22⋊C4×C61C2211yescharacteristic
49C22×C22⋊C4×C61C2211yescharacteristic
50C2×#95×C61C2211yescharacteristic
51C2×#95×C61C2211yescharacteristic
52C2×#95×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C24×D61C2311yescharacteristic
55C22×C22⋊D61—22no—
56C22×C22⋊D61—22no—
57C22×C22⋊D61—22no—
58C22×C22⋊D61—22no—
59C22×C22⋊D61—41no—
60C22×C22⋊D61—41no—
61C22×C22⋊D61C2×C414yes—
62C23×Dic61—41no—
63C23×Dic61—41no—
64C23×Dic61—41no—
65C23×Dic61—41no—
66C23×Dic61—41no—
67C23×Dic61—41no—
68C23×Dic61C2×C414yescomplemented
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C22×C4×D61—22no—
77C22×C4×D61—22no—
78C22×C4×D61—22no—
79C22×C4×D61—41no—
80C22×C4×D61—41no—
81C22×C4×D61—41no—
82C22×C4×D61—41no—
83C2×C4⋊Dic61—22no—
84C2×C4⋊Dic61—41no—
85C2×C4⋊Dic61—41no—
86C2×C22⋊Dic61—22no—
87C2×C22⋊Dic61—22no—
88C2×C22⋊Dic61—41no—
89C2×C22⋊Dic61—41no—
90C2×C22⋊Dic61—41no—
91C2×C22⋊Dic61D414yes—
92C2×#11758198—22no—
93C2×#11758198—22no—
94C2×#11758198—22no—
95C2×#11758198—22no—
96C2×#11758198—22no—
97C2×#11758198—41no—
98C2×#11758198—41no—
99C2×#11758198—41no—
100C2×#11758198—41no—
101C2×#11758198—41no—
102C2×#11758198—41no—
103C2×#11758198—41no—
104C2×#11758198—41no—
105C2×#11758198C2×C414yes—
106C2×#11758198C2×C414yes—
107C2×C4×Dic61—22no—
108C2×C4×Dic61—22no—
109C2×C4×Dic61—41no—
110#14519684—22no—
111#14519684—22no—
112#14519684—22no—
113#14519684—22no—
114#14519684—41no—
115#14519684—41no—
116#14519684—41no—
117#14519684—41no—
118#14519684—41no—
119#14519684—41no—
120#14519684—41no—
121#14519684—41no—
122#14519684—41no—
123#14519684—41no—
124#14519684C2×C414yescomplemented
125#14519684C2×C414yescomplemented
126C25×C61C2311yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C2×C22⋊C4×C61—22no—
134C2×C22⋊C4×C61—22no—
135C2×C22⋊C4×C61—22no—
136C2×C22⋊C4×C61—22no—
137C2×C22⋊C4×C61—22no—
138C2×C22⋊C4×C61—41no—
139C2×C22⋊C4×C61—41no—
140C2×C22⋊C4×C61—41no—
141C2×C22⋊C4×C61C2×C414yescomplemented
142#95×C61—22no—
143#95×C61—41no—
144#95×C61—41no—
145#95×C61—41no—
146C24×C61—21no—
147C24×C61—21no—
148C24×C61—21no—
149C24×C61—21no—
150C24×C61—21no—
151C24×C61—21no—
152C24×C61—21no—
153C24×C61—21no—
154C24×C61—21no—
155C24×C61—21no—
156C24×C61—21no—
157C24×C61—21no—
158C24×C61C22×C412yes—
159C24×C61C2×D412yes—
160C24×C61#4112yes—
161C24×C61C2411yescharacteristic
162C23×D61—21no—
163C23×D61—21no—
164C23×D61—21no—
165C23×D61—21no—
166C23×D61—21no—
167C23×D61—21no—
168C23×D61—21no—
169C23×D61—21no—
170C23×D61—21no—
171C23×D61—21no—
172C23×D61—21no—
173C23×D61—21no—
174C23×D61C22×C412yes—
175C23×D61#4112yes—
176C23×D61#4112yes—
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×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61C22×C412yes—
217C22×C4×C61C22×C412yes—
218C22×C4×C61#4112yes—
219C2×C22⋊D61—28no—
220C2×C22⋊D61—28no—
221C2×C22⋊D61—44no—
222C2×C22⋊D61—44no—
223C2×C22⋊D61—44no—
224C2×C22⋊D61—44no—
225C2×C22⋊D61—44no—
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×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—21no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255C22×Dic61—21no—
256C22×Dic61—21no—
257C22×Dic61—21no—
258C22×Dic61—21no—
259C22×Dic61—21no—
260C22×Dic61—21no—
261C22×Dic61—21no—
262C22×Dic61—21no—
263C22×Dic61—21no—
264C22×Dic61—21no—
265C22×Dic61—21no—
266C22×Dic61—21no—
267C22×Dic61—21no—
268C22×Dic61—21no—
269C22×Dic61—44no—
270C22×Dic61—44no—
271C22×Dic61—44no—
272C22×Dic61—44no—
273C22×Dic61—44no—
274C22×Dic61—44no—
275C22×Dic61—44no—
276C22×Dic61C22×C412yes—
277C22×Dic61C22×C412yes—
278C22×Dic61C22×C412yes—
279C22×Dic61C2×D412yes—
280C22×Dic61C2×D412yes—
281C22×Dic61#4112yes—
282C2×C4×D61—44no—
283C2×C4×D61—44no—
284C2×C4×D61—44no—
285C2×C4×D61—44no—
286C2×C4×D61—44no—
287C2×C4×D61—44no—
288C2×C4×D61—44no—
289C22⋊C4×C61—28no—
290C22⋊C4×C61—44no—
291C22⋊C4×C61—44no—
292C22⋊Dic61—44no—
293C22⋊Dic61—44no—
294#11758198—44no—
295#11758198—44no—
296#11758198—44no—
297#11758198—44no—
298#11758198—44no—
299C4⋊Dic61—44no—
300C4×Dic61—44no—
301C23×C61—22no—
302C23×C61—22no—
303C23×C61—22no—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—22no—
312C23×C61—22no—
313C23×C61—22no—
314C23×C61—22no—
315C23×C61—22no—
316C23×C61—22no—
317C23×C61—22no—
318C23×C61—22no—
319C23×C61—41no—
320C23×C61—41no—
321C23×C61—41no—
322C23×C61—41no—
323C23×C61—41no—
324C23×C61—41no—
325C23×C61—41no—
326C23×C61—41no—
327C23×C61—41no—
328C23×C61—41no—
329C23×C61—41no—
330C23×C61—41no—
331C23×C61—41no—
332C23×C61—41no—
333C23×C61—41no—
334C23×C61—41no—
335C23×C61C4×D414yes—
336C23×C61C23×C411yescharacteristic
337C23×C61C22×D411yescharacteristic
338C23×C61C2×#4111yescharacteristic
339C23×C61C2×#4111yescharacteristic
340C23×C61C2×#4111yescharacteristic
341C23×C61C2×#4111yescharacteristic
342C23×C61C2×#4111yescharacteristic
343C23×C61H(5,𝔽2)11yescharacteristic
344C23×C61H(5,𝔽2)11yescharacteristic
345C23×C61H(5,𝔽2)11yescharacteristic
346C23×C61H(5,𝔽2)11yescharacteristic
347C23×C61H(5,𝔽2)11yescharacteristic
348C23×C61H(5,𝔽2)11yescharacteristic
349C23×C61H(5,𝔽2)11yescharacteristic
350C23×C612−1+411yescharacteristic
351C22×D61—22no—
352C22×D61—22no—
353C22×D61—22no—
354C22×D61—22no—
355C22×D61—22no—
356C22×D61—22no—
357C22×D61—22no—
358C22×D61—22no—
359C22×D61—22no—
360C22×D61—22no—
361C22×D61—22no—
362C22×D61—22no—
363C22×D61—22no—
364C22×D61—22no—
365C22×D61—22no—
366C22×D61—22no—
367C22×D61—22no—
368C22×D61—22no—
369C22×D61—41no—
370C22×D61—41no—
371C22×D61—41no—
372C22×D61—41no—
373C22×D61—41no—
374C22×D61—41no—
375C22×D61—41no—
376C22×D61—41no—
377C22×D61—41no—
378C22×D61—41no—
379C22×D61—41no—
380C22×D61—41no—
381C22×D61—41no—
382C22×D61—41no—
383C22×D61—41no—
384C22×D61—41no—
385C22×D61#11714yes—
386C2×C4×C61—22no—
387C2×C4×C61—22no—
388C2×C4×C61—22no—
389C2×C4×C61—22no—
390C2×C4×C61—22no—
391C2×C4×C61—22no—
392C2×C4×C61—22no—
393C2×C4×C61—22no—
394C2×C4×C61—22no—
395C2×C4×C61—41no—
396C2×C4×C61—41no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61—41no—
400C2×C4×C61—41no—
401C2×C4×C61—41no—
402C2×C4×C61—41no—
403C2×C4×C61—41no—
404C2×C4×C61—41no—
405C2×C4×C61—41no—
406C2×C4×C61—41no—
407C2×C4×C61—41no—
408C2×C4×C61—41no—
409C2×C4×C61—41no—
410C2×C4×C61—41no—
411C2×C4×C61—41no—
412C2×C4×C61—41no—
413C2×C4×C61—41no—
414C2×C4×C61—41no—
415C2×C4×C61—41no—
416C2×C4×C61—41no—
417C2×C4×C61—41no—
418C2×C4×C61—41no—
419C2×C4×C61—41no—
420C2×C4×C61—41no—
421C2×C4×C61—41no—
422C2×C4×C61—41no—
423C2×C4×C61—41no—
424C2×C4×C61—41no—
425C2×C4×C61—41no—
426C2×C4×C61—41no—
427C2×C4×C61—41no—
428C22⋊D61—416no—
429C2×Dic61—22no—
430C2×Dic61—22no—
431C2×Dic61—22no—
432C2×Dic61—22no—
433C2×Dic61—22no—
434C2×Dic61—22no—
435C2×Dic61—22no—
436C2×Dic61—22no—
437C2×Dic61—22no—
438C2×Dic61—22no—
439C2×Dic61—22no—
440C2×Dic61—22no—
441C2×Dic61—22no—
442C2×Dic61—22no—
443C2×Dic61—22no—
444C2×Dic61—22no—
445C2×Dic61—22no—
446C2×Dic61—22no—
447C2×Dic61—416no—
448C2×Dic61—41no—
449C2×Dic61—41no—
450C2×Dic61—41no—
451C2×Dic61—41no—
452C2×Dic61—41no—
453C2×Dic61—41no—
454C2×Dic61—41no—
455C2×Dic61—41no—
456C2×Dic61—41no—
457C2×Dic61—41no—
458C2×Dic61—41no—
459C2×Dic61—41no—
460C2×Dic61—41no—
461C2×Dic61—41no—
462C2×Dic61—41no—
463C2×Dic61—41no—
464C2×Dic61—41no—
465C2×Dic61—41no—
466C2×Dic61—41no—
467C2×Dic61—41no—
468C2×Dic61—41no—
469C2×Dic61—41no—
470C2×Dic61—41no—
471C2×Dic61—41no—
472C2×Dic61—41no—
473C2×Dic61—41no—
474C2×Dic61—41no—
475C2×Dic61—41no—
476C2×Dic61—41no—
477C2×Dic61—41no—
478C2×Dic61—41no—
479C4×D61—416no—
480#14427—611nomaximal, Sylow
481C22×C61—24no—
482C22×C61—24no—
483C22×C61—24no—
484C22×C61—42no—
485C22×C61—42no—
486C22×C61—42no—
487C22×C61—42no—
488C22×C61—42no—
489C22×C61—42no—
490C22×C61—42no—
491C22×C61—42no—
492C22×C61—42no—
493C22×C61—42no—
494C22×C61—42no—
495C22×C61—42no—
496C22×C61C2×#11711yescharacteristic
497C22×C61C2×C4×D411yescharacteristic
498C22×C61C4×#4111yescharacteristic
499C22×C61#51811yescharacteristic
500C22×C61#51811yescharacteristic
501C22×C61#51811yescharacteristic
502C22×C61#52011yescharacteristic
503C22×C61#53411yescharacteristic
504C22×C61#53711yescharacteristic
505C22×C61#53811yescharacteristic
506C22×C61#53811yescharacteristic
507C22×C61#53811yescharacteristic
508C22×C61#53811yescharacteristic
509C22×C61#53911yescharacteristic
510C22×C61#53911yescharacteristic
511C22×C61#53911yescharacteristic
512C22×C61#53911yescharacteristic
513C22×C61#54011yescharacteristic
514C22×C61#54211yescharacteristic
515C22×C61#54611yescharacteristic
516C22×C61#54611yescharacteristic
517C22×C61#54611yescharacteristic
518C22×C61#54611yescharacteristic
519C22×C61#55111yescharacteristic
520C22×C61#55111yescharacteristic
521C22×C61#55111yescharacteristic
522C22×C61#55111yescharacteristic
523C22×C61#55311yescharacteristic
524C22×C61#55311yescharacteristic
525C22×C61#55311yescharacteristic
526C22×C61#55311yescharacteristic
527C22×C61#56011yescharacteristic
528C22×C61#56011yescharacteristic
529C22×C61#56011yescharacteristic
530C22×C61H(3,𝔽4)11yescharacteristic
531C2×D61—24no—
532C2×D61—24no—
533C2×D61—24no—
534C2×D61—42no—
535C2×D61—42no—
536C2×D61—42no—
537C2×D61—42no—
538C2×D61—42no—
539C2×D61—42no—
540C2×D61—42no—
541C2×D61—42no—
542C2×D61—42no—
543C2×D61—42no—
544C2×D61—42no—
545C2×D61—42no—
546C4×C61—42no—
547C4×C61—42no—
548C4×C61—42no—
549C4×C61—81no—
550C4×C61—81no—
551C4×C61—81no—
552Dic61—42no—
553Dic61—42no—
554Dic61—42no—
555Dic61—42no—
556Dic61—42no—
557Dic61—42no—
558Dic61—81no—
559C2×#388—611no—
560C2×#386—611no—
561C2×#386—611no—
562#1443—611no—
563#1443—611no—
564#1442—611no—
565#1440D6111yescharacteristic, complemented
566#1439—611no—
567#1438—611no—
568#1437—611no—
569#1434—611no—
570C22⋊#95—611no—
571C22⋊#95—611no—
572C22⋊#95—611no—
573C22⋊#95—611no—
574C2×C61—44no—
575C2×C61#231811yescharacteristic
576C2×C61#232511yescharacteristic
577C2×C61#233511yescharacteristic
578C2×C61#234211yescharacteristic
579C2×C61#235311yescharacteristic
580C2×C61#236411yescharacteristic
581C2×C61#237511yescharacteristic
582C2×C61#268411yescharacteristic
583C2×C61#268811yescharacteristic
584C2×C61#269111yescharacteristic
585C2×C61#269311yescharacteristic
586C2×C61#274611yescharacteristic
587C2×C61#274911yescharacteristic
588C2×C61#277811yescharacteristic
589C2×C61#278211yescharacteristic
590D61—44no—
591C23×D4—611no—
592C24×C4—611no—
593C24×C4—611no—
594C22×C4⋊C4—611no—
595C22×C22⋊C4—611no—
596C22×C22⋊C4—611no—
597C22×C22⋊C4—611no—
598C22×C22⋊C4—611no—
599C22×C22⋊C4—611no—
600C22×C22⋊C4—611no—
601C22×C22⋊C4—611no—
602C22×C22⋊C4C2×D6111yescharacteristic
603C22×C22⋊C4C2×D6111yescharacteristic
604C22×C22⋊C4C2×D6111yescharacteristic
605C22×C42—611no—
606#388—1224no—
607#386—618no—
608#386—1224no—
609C2×#95—611no—
610C2×#95—611no—
611C2×#95—611no—
612C2×#95—611no—
613C2×#95—611no—
614C2×#95—611no—
615C2×#95—611no—
616C2×#95—611no—
617C2×#95—611no—
618C2×#95—611no—
619C2×#95—611no—
620C2×#95—611no—
621C2×#95—611no—
622C2×#95—611no—
623C2×#95—611no—
624C2×#95—611no—
625C2×#95C2×D6111yescharacteristic
626C2×#95C2×D6111yescharacteristic
627C2×#95C2×D6111yescharacteristic
628C2×#95C2×D6111yescharacteristic
629C61#1442711yescharacteristic, complemented, Sylow
630C25—611no—
631C25C22×D6111yescharacteristic
632C22×D4—614no—
633C22×D4—1222no—
634C22×D4—1222no—
635C22×D4—1222no—
636C22×D4—1222no—
637C22×D4—2441no—
638C22×D4—2441no—
639C23×C4—611no—
640C23×C4—611no—
641C23×C4—611no—
642C23×C4—611no—
643C23×C4—611no—
644C23×C4—611no—
645C23×C4—614no—
646C23×C4—611no—
647C23×C4—1222no—
648C23×C4—1222no—
649C23×C4—1222no—
650C23×C4—2441no—
651C23×C4—2441no—
652C23×C4—2441no—
653C23×C4—2441no—
654C23×C4—2441no—
655C23×C4—2441no—
656C23×C4—2441no—
657C23×C4—2441no—
658C23×C4—2441no—
659C23×C4—2441no—
660C23×C4C22×D6111yescharacteristic
661C23×C4C22×D6111yescharacteristic
662C23×C4C22×D6111yescharacteristic
663C23×C4C22×D6111yescharacteristic
664C23×C4C22×D6111yescharacteristic
665C23×C4C22×D6111yescharacteristic
666C2×C4⋊C4—1222no—
667C2×C4⋊C4—2441no—
668C2×C4⋊C4—2441no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—41no—
675C2×C22⋊C4—41no—
676C2×C22⋊C4—41no—
677C2×C22⋊C4—614no—
678C2×C22⋊C4—614no—
679C2×C22⋊C4—614no—
680C2×C22⋊C4—1222no—
681C2×C22⋊C4—1222no—
682C2×C22⋊C4—1222no—
683C2×C22⋊C4—1222no—
684C2×C22⋊C4—1222no—
685C2×C22⋊C4—1222no—
686C2×C22⋊C4—1222no—
687C2×C22⋊C4—2441no—
688C2×C22⋊C4—2441no—
689C2×C22⋊C4—2441no—
690C2×C22⋊C4—2441no—
691C2×C22⋊C4—2441no—
692C2×C22⋊C4—2441no—
693C2×C22⋊C4—2441no—
694C2×C22⋊C4—2441no—
695C2×C22⋊C4—2441no—
696C2×C22⋊C4—2441no—
697C2×C22⋊C4—2441no—
698C2×C22⋊C4C4×D6114yescomplemented
699C2×C42—1222no—
700C2×C42—1222no—
701C2×C42—2441no—
702#95—22no—
703#95—41no—
704#95—41no—
705#95—41no—
706#95—614no—
707#95—614no—
708#95—1222no—
709#95—1222no—
710#95—1222no—
711#95—1222no—
712#95—2441no—
713#95—2441no—
714#95—2441no—
715#95—2441no—
716#95—2441no—
717#95—2441no—
718#95—2441no—
719#95—2441no—
720#95—2441no—
721#95—2441no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—612no—
735C24—612no—
736C24—612no—
737C24—1221no—
738C24—1221no—
739C24—1221no—
740C24—1221no—
741C24—1221no—
742C24—1221no—
743C24—1221no—
744C24—1221no—
745C24—1221no—
746C24—1221no—
747C24—1221no—
748C24—1221no—
749C24C2×C4×D6112yes—
750C24D4×D6112yes—
751C24#1175822412yes—
752C24C23×D6111yescharacteristic
753C2×D4—1228no—
754C2×D4—1228no—
755C2×D4—2444no—
756C2×D4—2444no—
757C2×D4—2444no—
758C2×D4—2444no—
759C2×D4—2444no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—612no—
800C22×C4—612no—
801C22×C4—612no—
802C22×C4—612no—
803C22×C4—612no—
804C22×C4—612no—
805C22×C4—1221no—
806C22×C4—1221no—
807C22×C4—1221no—
808C22×C4—1221no—
809C22×C4—1221no—
810C22×C4—1221no—
811C22×C4—1221no—
812C22×C4—1221no—
813C22×C4—1221no—
814C22×C4—1221no—
815C22×C4—1221no—
816C22×C4—1221no—
817C22×C4—1221no—
818C22×C4—1221no—
819C22×C4—1221no—
820C22×C4—1221no—
821C22×C4—1221no—
822C22×C4—1221no—
823C22×C4—1221no—
824C22×C4—1221no—
825C22×C4—1221no—
826C22×C4—1221no—
827C22×C4—1221no—
828C22×C4—1221no—
829C22×C4—1221no—
830C22×C4—1221no—
831C22×C4—1221no—
832C22×C4—1221no—
833C22×C4—1221no—
834C22×C4—1221no—
835C22×C4—1221no—
836C22×C4—1221no—
837C22×C4—1221no—
838C22×C4—1221no—
839C22×C4—1221no—
840C22×C4—1221no—
841C22×C4—1221no—
842C22×C4—1221no—
843C22×C4—1221no—
844C22×C4—1221no—
845C22×C4—1221no—
846C22×C4—1221no—
847C22×C4—1221no—
848C22×C4—2444no—
849C22×C4—2444no—
850C22×C4—2444no—
851C22×C4—2444no—
852C22×C4—2444no—
853C22×C4—2444no—
854C22×C4—2444no—
855C22×C4—2444no—
856C22×C4—2444no—
857C22×C4—2444no—
858C22×C4—2444no—
859C22×C4—2444no—
860C22×C4—2444no—
861C22×C4—2444no—
862C22×C4C2×C4×D6112yes—
863C22×C4C2×C4×D6112yes—
864C22×C4#1175822412yes—
865C4⋊C4—2444no—
866C22⋊C4—28no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C22⋊C4—2444no—
870C22⋊C4—2444no—
871C22⋊C4—2444no—
872C22⋊C4—2444no—
873C22⋊C4—2444no—
874C22⋊C4—2444no—
875C22⋊C4—2444no—
876C42—2444no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—614no—
912C23—1222no—
913C23—1222no—
914C23—1222no—
915C23—1222no—
916C23—1222no—
917C23—1222no—
918C23—1222no—
919C23—1222no—
920C23—1222no—
921C23—1222no—
922C23—1222no—
923C23—1222no—
924C23—1222no—
925C23—1222no—
926C23—1222no—
927C23—1222no—
928C23—1222no—
929C23—1222no—
930C23—2441no—
931C23—2441no—
932C23—2441no—
933C23—2441no—
934C23—2441no—
935C23—2441no—
936C23—2441no—
937C23—2441no—
938C23—2441no—
939C23—2441no—
940C23—2441no—
941C23—2441no—
942C23—2441no—
943C23—2441no—
944C23—2441no—
945C23—2441no—
946C23#1451973714yes—
947C23C22×C4×D6111yescharacteristic
948C23C2×D4×D6111yescharacteristic
949C23#41×D6111yescharacteristic
950C23#41×D6111yescharacteristic
951C23#41×D6111yescharacteristic
952C23C2×#1175822411yescharacteristic
953C23C2×#1175822411yescharacteristic
954C23#1451982211yescharacteristic
955C23#1451982211yescharacteristic
956C23#1451982211yescharacteristic
957C23#1451982311yescharacteristic
958C23#1451982311yescharacteristic
959C23#1451982311yescharacteristic
960C23#1451982311yescharacteristic
961C23#1451982411yescharacteristic
962D4—24416no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—1222no—
1006C2×C4—1222no—
1007C2×C4—1222no—
1008C2×C4—1222no—
1009C2×C4—1222no—
1010C2×C4—1222no—
1011C2×C4—1222no—
1012C2×C4—1222no—
1013C2×C4—1222no—
1014C2×C4—1222no—
1015C2×C4—1222no—
1016C2×C4—1222no—
1017C2×C4—1222no—
1018C2×C4—1222no—
1019C2×C4—1222no—
1020C2×C4—1222no—
1021C2×C4—1222no—
1022C2×C4—1222no—
1023C2×C4—24416no—
1024C2×C4—2441no—
1025C2×C4—2441no—
1026C2×C4—2441no—
1027C2×C4—2441no—
1028C2×C4—2441no—
1029C2×C4—2441no—
1030C2×C4—2441no—
1031C2×C4—24416no—
1032C2×C4—2441no—
1033C2×C4—2441no—
1034C2×C4—2441no—
1035C2×C4—2441no—
1036C2×C4—2441no—
1037C2×C4—2441no—
1038C2×C4—2441no—
1039C2×C4—2441no—
1040C2×C4—2441no—
1041C2×C4—2441no—
1042C2×C4—2441no—
1043C2×C4—2441no—
1044C2×C4—2441no—
1045C2×C4—2441no—
1046C2×C4—2441no—
1047C2×C4—2441no—
1048C2×C4—2441no—
1049C2×C4—2441no—
1050C2×C4—2441no—
1051C2×C4—2441no—
1052C2×C4—2441no—
1053C2×C4—2441no—
1054C2×C4—2441no—
1055C2×C4—2441no—
1056C22—24no—
1057C22—24no—
1058C22—24no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—1224no—
1072C22—1224no—
1073C22—1224no—
1074C22—2442no—
1075C22—2442no—
1076C22—2442no—
1077C22—2442no—
1078C22—2442no—
1079C22—2442no—
1080C22—2442no—
1081C22—2442no—
1082C22—2442no—
1083C22—2442no—
1084C22—2442no—
1085C22—2442no—
1086C22#117×D6111yescharacteristic
1087C22C2×#1451973711yescharacteristic
1088C22C4×#1175822411yescharacteristic
1089C22#1684023411yescharacteristic
1090C22#1684023411yescharacteristic
1091C22#1684023611yescharacteristic
1092C22#1684024111yescharacteristic
1093C22#1684032011yescharacteristic
1094C22#1684033911yescharacteristic
1095C22#1684034411yescharacteristic
1096C22#1684034611yescharacteristic
1097C22#1684034711yescharacteristic
1098C22#1684034911yescharacteristic
1099C22#1684035311yescharacteristic
1100C22#1684035311yescharacteristic
1101C22#1684035511yescharacteristic
1102C22#1684035611yescharacteristic
1103C22#1684036411yescharacteristic
1104C22#1684038111yescharacteristic
1105C22#1684039911yescharacteristic
1106C22#1684040411yescharacteristic
1107C22#1684040411yescharacteristic
1108C22#1684040411yescharacteristic
1109C22#1684043511yescharacteristic
1110C22#1684043511yescharacteristic
1111C22#1684043511yescharacteristic
1112C22#1684044211yescharacteristic
1113C22#1684045511yescharacteristic
1114C22#1684045911yescharacteristic
1115C22#1684046311yescharacteristic
1116C22#1684046411yescharacteristic
1117C22#1684050011yescharacteristic
1118C22#1684050211yescharacteristic
1119C22#1684050311yescharacteristic
1120C22#1684050411yescharacteristic
1121C4—42no—
1122C4—42no—
1123C4—42no—
1124C4—81no—
1125C4—81no—
1126C4—81no—
1127C4—4881no—
1128C4—2442no—
1129C4—2442no—
1130C4—2442no—
1131C4—2442no—
1132C4—2442no—
1133C4—2442no—
1134C2—44no—
1135C2—2444no—
1136C2#2144844911yescharacteristic
1137C2#2144852011yescharacteristic
1138C2#2144860211yescharacteristic
1139C2#2144866111yescharacteristic
1140C2#2144875411yescharacteristic
1141C2#2144886711yescharacteristic
1142C2#2144895911yescharacteristic
1143C2#2145219411yescharacteristic
1144C2#2145224811yescharacteristic
1145C2#2145229911yescharacteristic
1146C2#2145232311yescharacteristic
1147C2#2145301011yescharacteristic
1148C2#2145303511yescharacteristic
1149C2#2145343911yescharacteristic
1150C2#2145349011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1440C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenter#1440D61
hypocenterC61#14427
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
1. C2×#16839655C2semidirect
4. #21444080C2semidirect
5. #21444079C2semidirect
6. #21444075C2semidirect
7. #21444065C2semidirect
9. #21444055C2semidirect
10. #21444044C2semidirect
11. #21444041C2semidirect
12. #21444041C2semidirect
13. #21444040C2semidirect
14. #21444040C2semidirect
15. C61×#1440C2semidirect
29. #16839639C4semidirect
68. C23×Dic61C2×C4semidirect
124. #14519684C2×C4semidirect
125. #14519684C2×C4semidirect
141. C2×C22⋊C4×C61C2×C4semidirect
565. #1440D61semidirect
629. C61#14427semidirect
698. C2×C22⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396552
C2×#168396392
C2×#168396382
#214440802
#214440792
#214440752
#214440652
#214440582
#214440552
#214440442
#214440412
#214440402
C61×#14402
#1442761