Finite Group Databasebeta

← #29610078

Subgroups — #29610078

Order 15616.

1858 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839680C211yesmaximal, characteristic
2C2×#16839663C211yesmaximal, characteristic
3C2×#16839652C211yesmaximal, characteristic, complemented
4C2×#16839643C211yesmaximal, characteristic, complemented
5C2×#16839640C211yesmaximal, characteristic
6#21444067C211yesmaximal, characteristic, complemented
7#21444061C211yesmaximal, characteristic, complemented
8#21444061C211yesmaximal, characteristic, complemented
9#21444061C211yesmaximal, characteristic, complemented
10#21444055C211yesmaximal, characteristic, complemented
11#21444054C211yesmaximal, characteristic, complemented
12#21444044C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×#1444C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C22×#11758196C2211yescharacteristic
19C22×#11758198C2211yescharacteristic
20C22×#11758198C2211yescharacteristic
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32#16839680C418yescomplemented
33#16839663—24no—
34#16839652—24no—
35#16839643—24no—
36#16839640—24no—
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C22×C4⋊C4×C61C2211yescharacteristic
50C22×C4⋊C4×C61C2211yescharacteristic
51C22×C4⋊C4×C61C2211yescharacteristic
52C2×#95×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C24×D61C2311yescharacteristic
57C24×D61C2311yescharacteristic
58C22×D244—22no—
59C22×D244—22no—
60C22×D244—22no—
61C22×D244—22no—
62C22×D244—41no—
63C22×D244—41no—
64C22×D244C2×C414yes—
65C23×Dic61C2311yescharacteristic
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C22×C4×D61—22no—
72C22×C4×D61—22no—
73C22×C4×D61—22no—
74C22×C4×D61—41no—
75C22×C4×D61—41no—
76C22×C4×D61—41no—
77C22×C4×D61—41no—
78C2×#11758196—22no—
79C2×#11758196—22no—
80C2×#11758196C2×C414yescomplemented
81C2×#11758198—22no—
82C2×#11758198—22no—
83C2×#11758198—22no—
84C2×#11758198—22no—
85C2×#11758198—22no—
86C2×#11758198—22no—
87C2×#11758198—22no—
88C2×#11758198—22no—
89C2×#11758198—22no—
90C2×#11758198—22no—
91C2×#11758198—22no—
92C2×#11758198—22no—
93C2×#11758198—41no—
94C2×#11758198—41no—
95C2×#11758198—41no—
96C2×#11758198—41no—
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×#11758198—41no—
106C2×#11758198—41no—
107C2×#11758198—41no—
108C2×#11758198—41no—
109C2×#11758198C2×C414yes—
110C2×#11758198C2×C414yes—
111C2×#11758198C2×C414yescomplemented
112C2×#11758198C2×C414yescomplemented
113C2×#11758198D414yes—
114C2×C4×Dic61—22no—
115C2×C4×Dic61—22no—
116C2×C4×Dic61—22no—
117C2×C4×Dic61—22no—
118C2×C4×Dic61—41no—
119C2×C4×Dic61—41no—
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#14519684—41no—
130#14519684—41no—
131#14519684D414yes—
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C2×C4⋊C4×C61—22no—
140C2×C4⋊C4×C61—22no—
141C2×C4⋊C4×C61—22no—
142C2×C4⋊C4×C61—41no—
143C2×C4⋊C4×C61—41no—
144C2×C4⋊C4×C61—41no—
145C2×C4⋊C4×C61—41no—
146C2×C4⋊C4×C61—41no—
147C2×C4⋊C4×C61—41no—
148#95×C61—22no—
149#95×C61—41no—
150#95×C61—41no—
151#95×C61C2×C414yescomplemented
152C24×C61C2411yescharacteristic
153C23×D61—21no—
154C23×D61—21no—
155C23×D61—21no—
156C23×D61—21no—
157C23×D61—21no—
158C23×D61—21no—
159C23×D61—21no—
160C23×D61—21no—
161C23×D61—21no—
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×D61—21no—
175C23×D61—21no—
176C23×D61—21no—
177C23×D61—21no—
178C23×D61—21no—
179C23×D61C22×C412yes—
180C23×D61C22×C412yes—
181C23×D61C2×D412yes—
182C23×D61#4112yes—
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×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61C22×C412yes—
226C22×C4×C61C22×C412yes—
227C22×C4×C61C22×C412yes—
228C22×C4×C61C2×D412yes—
229C22×C4×C61C2×D412yes—
230C22×C4×C61#4112yes—
231C22×C4×C61#4112yes—
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×Dic61C22×C412yes—
269C22×Dic61C22×C412yes—
270C22×Dic61C2×D412yes—
271C22×Dic61C2×D412yes—
272C22×Dic61C2×D412yes—
273C22×Dic61#4112yes—
274C2×D244—28no—
275C2×D244—28no—
276C2×D244—44no—
277C2×D244—44no—
278C2×D244—44no—
279C2×D244—44no—
280C2×D244—44no—
281C2×C4×D61—44no—
282C2×C4×D61—44no—
283C2×C4×D61—44no—
284C2×C4×D61—44no—
285C2×C4×D61—44no—
286C2×C4×D61—44no—
287C2×C4×D61—44no—
288C4⋊C4×C61—44no—
289C4⋊C4×C61—44no—
290C4⋊C4×C61—44no—
291#11758198—28no—
292#11758198—44no—
293#11758198—44no—
294#11758198—44no—
295#11758198—44no—
296#11758198—44no—
297#11758198—44no—
298#11758198—44no—
299#11758198—44no—
300#11758198—44no—
301#11758198—44no—
302#11758196—28no—
303C4×Dic61—44no—
304C4×Dic61—44no—
305C23×C61C23×C411yescharacteristic
306C23×C61C22×D411yescharacteristic
307C23×C61C22×D411yescharacteristic
308C23×C61C2×#4111yescharacteristic
309C23×C61C2×#4111yescharacteristic
310C23×C61C2×#4111yescharacteristic
311C23×C61C2×#4111yescharacteristic
312C23×C61H(5,𝔽2)11yescharacteristic
313C23×C61H(5,𝔽2)11yescharacteristic
314C23×C61H(5,𝔽2)11yescharacteristic
315C23×C61H(5,𝔽2)11yescharacteristic
316C23×C61H(5,𝔽2)11yescharacteristic
317C23×C61H(5,𝔽2)11yescharacteristic
318C23×C612−1+411yescharacteristic
319C23×C612−1+411yescharacteristic
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—22no—
323C22×D61—22no—
324C22×D61—22no—
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—22no—
328C22×D61—22no—
329C22×D61—22no—
330C22×D61—22no—
331C22×D61—22no—
332C22×D61—22no—
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—22no—
343C22×D61—22no—
344C22×D61—22no—
345C22×D61—41no—
346C22×D61—41no—
347C22×D61—41no—
348C22×D61—41no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—41no—
353C22×D61—41no—
354C22×D61—41no—
355C22×D61—41no—
356C22×D61—41no—
357C22×D61—41no—
358C22×D61—41no—
359C22×D61—41no—
360C22×D61—41no—
361C22×D61—41no—
362C22×D61—41no—
363C22×D61—41no—
364C22×D61—41no—
365C22×D61—41no—
366C22×D61—41no—
367C22×D61—41no—
368C22×D61—41no—
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—41no—
386C22×D61—41no—
387C22×D61—41no—
388C22×D61—41no—
389C22×D61C4×D414yes—
390C2×C4×C61—22no—
391C2×C4×C61—22no—
392C2×C4×C61—22no—
393C2×C4×C61—22no—
394C2×C4×C61—22no—
395C2×C4×C61—22no—
396C2×C4×C61—22no—
397C2×C4×C61—22no—
398C2×C4×C61—22no—
399C2×C4×C61—22no—
400C2×C4×C61—22no—
401C2×C4×C61—22no—
402C2×C4×C61—22no—
403C2×C4×C61—22no—
404C2×C4×C61—22no—
405C2×C4×C61—22no—
406C2×C4×C61—22no—
407C2×C4×C61—22no—
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—
428C2×C4×C61—41no—
429C2×C4×C61—41no—
430C2×C4×C61—41no—
431C2×C4×C61—41no—
432C2×C4×C61—41no—
433C2×C4×C61—41no—
434C2×C4×C61—41no—
435C2×C4×C61—41no—
436C2×C4×C61—41no—
437C2×C4×C61—41no—
438C2×C4×C61C4×D414yes—
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—22no—
448C2×Dic61—22no—
449C2×Dic61—22no—
450C2×Dic61—22no—
451C2×Dic61—22no—
452C2×Dic61—22no—
453C2×Dic61—22no—
454C2×Dic61—22no—
455C2×Dic61—22no—
456C2×Dic61—22no—
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—
479C2×Dic61—41no—
480C2×Dic61—41no—
481D244—416no—
482C4×D61—416no—
483#14573—611nomaximal, Sylow
484C22×C61C2×C4×D411yescharacteristic
485C22×C61C2×C4×D411yescharacteristic
486C22×C61C4×#4111yescharacteristic
487C22×C61#51811yescharacteristic
488C22×C61#51811yescharacteristic
489C22×C61#52011yescharacteristic
490C22×C61#52011yescharacteristic
491C22×C61#53411yescharacteristic
492C22×C61#53511yescharacteristic
493C22×C61#53611yescharacteristic
494C22×C61#53711yescharacteristic
495C22×C61#53811yescharacteristic
496C22×C61#53811yescharacteristic
497C22×C61#53911yescharacteristic
498C22×C61#53911yescharacteristic
499C22×C61#54011yescharacteristic
500C22×C61#54211yescharacteristic
501C22×C61#54211yescharacteristic
502C22×C61#54211yescharacteristic
503C22×C61D4211yescharacteristic
504C22×C61#54611yescharacteristic
505C22×C61#54611yescharacteristic
506C22×C61#54611yescharacteristic
507C22×C61#54611yescharacteristic
508C22×C61#54711yescharacteristic
509C22×C61#55011yescharacteristic
510C22×C61#55111yescharacteristic
511C22×C61#55111yescharacteristic
512C22×C61#55211yescharacteristic
513C22×C61#55311yescharacteristic
514C22×C61#55511yescharacteristic
515C22×C61#56011yescharacteristic
516C22×C61#56011yescharacteristic
517C22×C61#56211yescharacteristic
518C22×C61#56211yescharacteristic
519C2×D61—24no—
520C2×D61—24no—
521C2×D61—24no—
522C2×D61—42no—
523C2×D61—42no—
524C2×D61—42no—
525C2×D61—42no—
526C2×D61—42no—
527C2×D61—42no—
528C2×D61—42no—
529C2×D61—42no—
530C2×D61—42no—
531C2×D61—42no—
532C2×D61—42no—
533C2×D61—42no—
534C2×D61—42no—
535C2×D61—42no—
536C2×D61—42no—
537C2×D61—42no—
538C2×D61—42no—
539C2×D61—42no—
540C2×D61—42no—
541C2×D61—81no—
542C2×D61—81no—
543C2×D61—81no—
544C2×D61—81no—
545C2×D61—81no—
546C2×D61—81no—
547C2×D61—81no—
548C2×D61—81no—
549C4×C61—24no—
550C4×C61—42no—
551C4×C61—42no—
552C4×C61—42no—
553C4×C61—42no—
554C4×C61—81no—
555C4×C61—81no—
556Dic61—42no—
557Dic61—42no—
558Dic61—42no—
559Dic61—42no—
560Dic61—42no—
561Dic61—42no—
562C2×#394—611no—
563C2×#390—611no—
564C2×#388—611no—
565C2×#387—611no—
566C2×#386—611no—
567#1444D6111yescharacteristic, complemented
568#1440—611no—
569#1439—611no—
570#1439—611no—
571#1439—611no—
572#1437—611no—
573#1436—611no—
574#1434—611no—
575C22⋊#95—611no—
576C22⋊#95—611no—
577C2×C61#232511yescharacteristic
578C2×C61#232611yescharacteristic
579C2×C61#233511yescharacteristic
580C2×C61#235811yescharacteristic
581C2×C61#235911yescharacteristic
582C2×C61#236311yescharacteristic
583C2×C61#237711yescharacteristic
584C2×C61#267211yescharacteristic
585C2×C61#267311yescharacteristic
586C2×C61#268511yescharacteristic
587C2×C61#268611yescharacteristic
588C2×C61#269111yescharacteristic
589C2×C61#269411yescharacteristic
590C2×C61#273711yescharacteristic
591C2×C61#276111yescharacteristic
592D61—44no—
593D61—82no—
594C23×D4—611no—
595C24×C4—611no—
596C22×C4⋊C4—611no—
597C22×C4⋊C4C2×D6111yescharacteristic
598C22×C4⋊C4C2×D6111yescharacteristic
599C22×C4⋊C4C2×D6111yescharacteristic
600C22×C22⋊C4—611no—
601C22×C22⋊C4—611no—
602C22×C22⋊C4—611no—
603C22×C22⋊C4—611no—
604C22×C22⋊C4—611no—
605C22×C22⋊C4—611no—
606C22×C22⋊C4—611no—
607C22×C22⋊C4—611no—
608C22×C22⋊C4—611no—
609C22×C22⋊C4—611no—
610C22×C22⋊C4—611no—
611C22×C42—611no—
612C22×C42—611no—
613#394—618no—
614#390—1224no—
615#388—1224no—
616#387—1224no—
617#386—1224no—
618C2×#95—611no—
619C2×#95—611no—
620C2×#95—611no—
621C2×#95—611no—
622C2×#95—611no—
623C2×#95—611no—
624C2×#95—611no—
625C2×#95—611no—
626C2×#95—611no—
627C2×#95—611no—
628C2×#95—611no—
629C2×#95—611no—
630C2×#95C2×D6111yescharacteristic
631C2×#95C2×D6111yescharacteristic
632C2×#95C2×D6111yescharacteristic
633C2×#95C2×D6111yescharacteristic
634C61#1457311yescharacteristic, complemented, Sylow
635C25—611no—
636C25—611no—
637C22×D4—614no—
638C22×D4—1222no—
639C22×D4—1222no—
640C22×D4—1222no—
641C22×D4—1222no—
642C22×D4—2441no—
643C22×D4—2441no—
644C23×C4—611no—
645C23×C4—611no—
646C23×C4—611no—
647C23×C4—611no—
648C23×C4—611no—
649C23×C4—611no—
650C23×C4—1222no—
651C23×C4—1222no—
652C23×C4—1222no—
653C23×C4—2441no—
654C23×C4—2441no—
655C23×C4—2441no—
656C23×C4—2441no—
657C23×C4C22×D6111yescharacteristic
658C23×C4C22×D6111yescharacteristic
659C23×C4C22×D6111yescharacteristic
660C23×C4C22×D6111yescharacteristic
661C23×C4C22×D6111yescharacteristic
662C23×C4C22×D6111yescharacteristic
663C23×C4C22×D6111yescharacteristic
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—41no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—41no—
672C2×C4⋊C4—41no—
673C2×C4⋊C4—614no—
674C2×C4⋊C4—1222no—
675C2×C4⋊C4—1222no—
676C2×C22⋊C4—614no—
677C2×C22⋊C4—614no—
678C2×C22⋊C4—614no—
679C2×C22⋊C4—614no—
680C2×C22⋊C4—614no—
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—1222no—
688C2×C22⋊C4—1222no—
689C2×C22⋊C4—1222no—
690C2×C22⋊C4—1222no—
691C2×C22⋊C4—1222no—
692C2×C22⋊C4—1222no—
693C2×C22⋊C4—2441no—
694C2×C22⋊C4—2441no—
695C2×C22⋊C4—2441no—
696C2×C22⋊C4—2441no—
697C2×C22⋊C4—2441no—
698C2×C22⋊C4—2441no—
699C2×C22⋊C4—2441no—
700C2×C22⋊C4—2441no—
701C2×C22⋊C4—2441no—
702C2×C22⋊C4—2441no—
703C2×C22⋊C4—2441no—
704C2×C22⋊C4—2441no—
705C2×C22⋊C4—2441no—
706C2×C22⋊C4—2441no—
707C2×C22⋊C4—2441no—
708C2×C22⋊C4—2441no—
709C2×C42—1222no—
710C2×C42—1222no—
711C2×C42—1222no—
712C2×C42—1222no—
713C2×C42—2441no—
714C2×C42—2441no—
715#95—22no—
716#95—41no—
717#95—41no—
718#95—614no—
719#95—1222no—
720#95—1222no—
721#95—1222no—
722#95—1222no—
723#95—1222no—
724#95—1222no—
725#95—1222no—
726#95—2441no—
727#95—2441no—
728#95—2441no—
729#95—2441no—
730#95C4×D6114yescomplemented
731C24—612no—
732C24—612no—
733C24—612no—
734C24—612no—
735C24—1221no—
736C24—1221no—
737C24—1221no—
738C24—1221no—
739C24—1221no—
740C24—1221no—
741C24—1221no—
742C24—1221no—
743C24—1221no—
744C24—1221no—
745C24—1221no—
746C24—1221no—
747C24—1221no—
748C24—1221no—
749C24—1221no—
750C24—1221no—
751C24—1221no—
752C24—1221no—
753C24—1221no—
754C24—1221no—
755C24—1221no—
756C24—1221no—
757C24—1221no—
758C24—1221no—
759C24—1221no—
760C24—1221no—
761C24C23×D6111yescharacteristic
762C2×D4—1228no—
763C2×D4—1228no—
764C2×D4—2444no—
765C2×D4—2444no—
766C2×D4—2444no—
767C2×D4—2444no—
768C2×D4—2444no—
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—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—612no—
812C22×C4—612no—
813C22×C4—612no—
814C22×C4—612no—
815C22×C4—612no—
816C22×C4—612no—
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—1221no—
849C22×C4—1221no—
850C22×C4—1221no—
851C22×C4—1221no—
852C22×C4—1221no—
853C22×C4—2444no—
854C22×C4—2444no—
855C22×C4—2444no—
856C22×C4—2444no—
857C22×C4—2444no—
858C22×C4—2444no—
859C22×C4—2444no—
860C22×C4C2×C4×D6112yes—
861C22×C4C2×C4×D6112yes—
862C22×C4C2×C4×D6112yes—
863C22×C4D4×D6112yes—
864C22×C4D4×D6112yes—
865C22×C4#1175822612yes—
866C22×C4#1175822612yes—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—1228no—
871C22⋊C4—1228no—
872C22⋊C4—2444no—
873C22⋊C4—2444no—
874C22⋊C4—2444no—
875C22⋊C4—2444no—
876C22⋊C4—2444no—
877C22⋊C4—2444no—
878C22⋊C4—2444no—
879C22⋊C4—2444no—
880C22⋊C4—2444no—
881C22⋊C4—2444no—
882C42—2444no—
883C42—2444no—
884C23—614no—
885C23—1222no—
886C23—1222no—
887C23—1222no—
888C23—1222no—
889C23—1222no—
890C23—1222no—
891C23—1222no—
892C23—1222no—
893C23—1222no—
894C23—1222no—
895C23—1222no—
896C23—1222no—
897C23—1222no—
898C23—1222no—
899C23—1222no—
900C23—1222no—
901C23—1222no—
902C23—1222no—
903C23—1222no—
904C23—1222no—
905C23—1222no—
906C23—1222no—
907C23—1222no—
908C23—1222no—
909C23—1222no—
910C23—2441no—
911C23—2441no—
912C23—2441no—
913C23—2441no—
914C23—2441no—
915C23—2441no—
916C23—2441no—
917C23—2441no—
918C23—2441no—
919C23—2441no—
920C23—2441no—
921C23—2441no—
922C23—2441no—
923C23—2441no—
924C23—2441no—
925C23—2441no—
926C23—2441no—
927C23—2441no—
928C23—2441no—
929C23—2441no—
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—2441no—
947C23—2441no—
948C23—2441no—
949C23—2441no—
950C23—2441no—
951C23—2441no—
952C23—2441no—
953C23—2441no—
954C23C22×C4×D6111yescharacteristic
955C23C2×D4×D6111yescharacteristic
956C23C2×D4×D6111yescharacteristic
957C23#41×D6111yescharacteristic
958C23#41×D6111yescharacteristic
959C23C2×#1175822611yescharacteristic
960C23C2×#1175822611yescharacteristic
961C23#1451982211yescharacteristic
962C23#1451982211yescharacteristic
963C23#1451982211yescharacteristic
964C23#1451982211yescharacteristic
965C23#1451982311yescharacteristic
966C23#1451982311yescharacteristic
967C23#1451982511yescharacteristic
968C23#1451982511yescharacteristic
969D4—24416no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
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—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—1222no—
1019C2×C4—1222no—
1020C2×C4—1222no—
1021C2×C4—1222no—
1022C2×C4—1222no—
1023C2×C4—1222no—
1024C2×C4—1222no—
1025C2×C4—1222no—
1026C2×C4—1222no—
1027C2×C4—1222no—
1028C2×C4—1222no—
1029C2×C4—1222no—
1030C2×C4—1222no—
1031C2×C4—1222no—
1032C2×C4—1222no—
1033C2×C4—1222no—
1034C2×C4—1222no—
1035C2×C4—1222no—
1036C2×C4—24416no—
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—
1056C2×C4—2441no—
1057C2×C4—2441no—
1058C2×C4—2441no—
1059C2×C4—2441no—
1060C2×C4—2441no—
1061C2×C4#1451973914yes—
1062C22—1224no—
1063C22—1224no—
1064C22—1224no—
1065C22—4881no—
1066C22—4881no—
1067C22—4881no—
1068C22—4881no—
1069C22—4881no—
1070C22—4881no—
1071C22—4881no—
1072C22—4881no—
1073C22—2442no—
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—2442no—
1087C22—2442no—
1088C22—2442no—
1089C22—2442no—
1090C22—2442no—
1091C22—2442no—
1092C22C4×D4×D6111yescharacteristic
1093C22C2×#1451973911yescharacteristic
1094C22C4×#1175822611yescharacteristic
1095C22#1684023411yescharacteristic
1096C22#1684023411yescharacteristic
1097C22#1684024311yescharacteristic
1098C22#1684024311yescharacteristic
1099C22#1684032211yescharacteristic
1100C22#1684032511yescharacteristic
1101C22#1684033711yescharacteristic
1102C22#1684034211yescharacteristic
1103C22#1684034811yescharacteristic
1104C22#1684035211yescharacteristic
1105C22#1684035811yescharacteristic
1106C22#1684036011yescharacteristic
1107C22#1684036211yescharacteristic
1108C22#1684038611yescharacteristic
1109C22#1684038611yescharacteristic
1110C22#1684038611yescharacteristic
1111C22#1684039411yescharacteristic
1112C22#1684040111yescharacteristic
1113C22#1684040311yescharacteristic
1114C22#1684040311yescharacteristic
1115C22#1684040411yescharacteristic
1116C22#1684041511yescharacteristic
1117C22#1684043011yescharacteristic
1118C22#1684043911yescharacteristic
1119C22#1684043911yescharacteristic
1120C22#1684044411yescharacteristic
1121C22#1684046511yescharacteristic
1122C22#1684047811yescharacteristic
1123C22#1684050111yescharacteristic
1124C22#1684050211yescharacteristic
1125C22#1684050811yescharacteristic
1126C22#1684050811yescharacteristic
1127C4—24no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—81no—
1133C4—81no—
1134C4—2442no—
1135C4—2442no—
1136C4—2442no—
1137C4—2442no—
1138C4—2442no—
1139C4—2442no—
1140C2—4882no—
1141C2—2444no—
1142C2#2144851611yescharacteristic
1143C2#2144852711yescharacteristic
1144C2#2144861211yescharacteristic
1145C2#2144879511yescharacteristic
1146C2#2144880611yescharacteristic
1147C2#2144885611yescharacteristic
1148C2#2144897511yescharacteristic
1149C2#2145206911yescharacteristic
1150C2#2145208711yescharacteristic
1151C2#2145220311yescharacteristic
1152C2#2145223211yescharacteristic
1153C2#2145230711yescharacteristic
1154C2#2145233211yescharacteristic
1155C2#2145288111yescharacteristic
1156C2#2145319911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1444C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1444D61
hypocenterC61#14573
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
3. C2×#16839652C2semidirect
4. C2×#16839643C2semidirect
6. #21444067C2semidirect
7. #21444061C2semidirect
8. #21444061C2semidirect
9. #21444061C2semidirect
10. #21444055C2semidirect
11. #21444054C2semidirect
12. #21444044C2semidirect
13. #21444040C2semidirect
14. #21444040C2semidirect
15. C61×#1444C2semidirect
32. #16839680C4semidirect
80. C2×#11758196C2×C4semidirect
111. C2×#11758198C2×C4semidirect
112. C2×#11758198C2×C4semidirect
151. #95×C61C2×C4semidirect
567. #1444D61semidirect
634. C61#14573semidirect
730. #95C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396802
C2×#168396632
C2×#168396522
C2×#168396432
C2×#168396402
#214440672
#214440612
#214440552
#214440542
#214440442
#214440402
C61×#14442
#1457361