Finite Group Databasebeta

← #29609333

Subgroups — #29609333

Order 15616.

1958 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839679C211yesmaximal, characteristic
2C2×#16839664C211yesmaximal, characteristic
3C2×#16839661C211yesmaximal, characteristic, complemented
4C2×#16839651C211yesmaximal, characteristic, complemented
5C2×#16839640C211yesmaximal, characteristic
6C2×#16839636C211yesmaximal, characteristic, complemented
7C2×#16839636C211yesmaximal, characteristic, complemented
8#21444083C211yesmaximal, characteristic, complemented
9#21444067C211yesmaximal, characteristic, complemented
10#21444065C211yesmaximal, characteristic, complemented
11#21444065C211yesmaximal, characteristic, complemented
12#21444063C211yesmaximal, characteristic, complemented
13#21444055C211yesmaximal, characteristic, complemented
14#21444046C211yesmaximal, characteristic, complemented
15C61×#1436C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35#16839679C418yescomplemented
36#16839664—24no—
37#16839661—24no—
38#16839651—24no—
39#16839640—24no—
40#16839636—24no—
41#16839636—24no—
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C22×C4⋊C4×C61C2211yescharacteristic
52C22×C42×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C24×D61C2311yescharacteristic
59C24×D61C2311yescharacteristic
60C22×D244—22no—
61C22×D244—22no—
62C22×D244—22no—
63C22×D244—22no—
64C22×D244—41no—
65C22×D244—41no—
66C22×D244C2×C414yes—
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C22×C4×D61—22no—
74C22×C4×D61—22no—
75C22×C4×D61—22no—
76C22×C4×D61—41no—
77C22×C4×D61—41no—
78C22×C4×D61—41no—
79C22×C4×D61—41no—
80C2×C4⋊Dic61—22no—
81C2×C4⋊Dic61—22no—
82C2×C4⋊Dic61—22no—
83C2×C4⋊Dic61—22no—
84C2×C4⋊Dic61—22no—
85C2×C4⋊Dic61—22no—
86C2×C4⋊Dic61—41no—
87C2×C4⋊Dic61—41no—
88C2×C4⋊Dic61—41no—
89C2×#11758196—22no—
90C2×#11758196—22no—
91C2×#11758196—22no—
92C2×#11758196—41no—
93C2×#11758196—41no—
94C2×#11758196—41no—
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—22no—
105C2×#11758198—22no—
106C2×#11758198—22no—
107C2×#11758198—22no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×#11758198—22no—
111C2×#11758198—41no—
112C2×#11758198—41no—
113C2×#11758198—41no—
114C2×#11758198—41no—
115C2×#11758198—41no—
116C2×#11758198—41no—
117C2×#11758198—41no—
118C2×#11758198—41no—
119C2×#11758198—41no—
120C2×#11758198—41no—
121C2×#11758198—41no—
122C2×#11758198—41no—
123C2×#11758198C2×C414yes—
124C2×#11758198C2×C414yes—
125C2×#11758198C2×C414yescomplemented
126C2×#11758198C2×C414yescomplemented
127C2×#11758198D414yes—
128C2×C4×Dic61—22no—
129C2×C4×Dic61—22no—
130C2×C4×Dic61—41no—
131#14519684—22no—
132#14519684—22no—
133#14519684—22no—
134#14519684—22no—
135#14519684—41no—
136#14519684—41no—
137#14519684—41no—
138#14519684C2×C414yescomplemented
139#14519684D414yes—
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C2×C4⋊C4×C61—22no—
148C2×C4⋊C4×C61—22no—
149C2×C4⋊C4×C61C2×C414yescomplemented
150C2×C42×C61—22no—
151C2×C42×C61—22no—
152C2×C42×C61—41no—
153#95×C61—22no—
154#95×C61—22no—
155#95×C61—22no—
156#95×C61—41no—
157#95×C61D414yescomplemented
158C24×C61C2411yescharacteristic
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×D61—21no—
180C23×D61—21no—
181C23×D61—21no—
182C23×D61—21no—
183C23×D61—21no—
184C23×D61—21no—
185C23×D61C22×C412yes—
186C23×D61C22×C412yes—
187C23×D61C2×D412yes—
188C23×D61#4112yes—
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×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61C22×C412yes—
229C22×C4×C61C22×C412yes—
230C22×C4×C61C22×C412yes—
231C22×C4×C61C2×D412yes—
232C22×C4×C61C2×D412yes—
233C22×C4×C61C2×D412yes—
234C22×C4×C61C2×D412yes—
235C22×C4×C61C2×D412yes—
236C22×C4×C61#4112yes—
237C22×C4×C61#4112yes—
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—21no—
270C22×Dic61—21no—
271C22×Dic61—21no—
272C22×Dic61—21no—
273C22×Dic61—21no—
274C22×Dic61—21no—
275C22×Dic61C22×C412yes—
276C22×Dic61C22×C412yes—
277C22×Dic61C2×D412yes—
278C22×Dic61C2×D412yes—
279C22×Dic61C2×D412yes—
280C2×D244—28no—
281C2×D244—28no—
282C2×D244—44no—
283C2×D244—44no—
284C2×D244—44no—
285C2×D244—44no—
286C2×D244—44no—
287C2×C4×D61—44no—
288C2×C4×D61—44no—
289C2×C4×D61—44no—
290C2×C4×D61—44no—
291C2×C4×D61—44no—
292C2×C4×D61—44no—
293C2×C4×D61—44no—
294C4⋊C4×C61—28no—
295C42×C61—44no—
296#11758198—28no—
297#11758198—28no—
298#11758198—28no—
299#11758198—44no—
300#11758198—44no—
301#11758198—44no—
302#11758198—44no—
303#11758198—44no—
304#11758198—44no—
305#11758198—44no—
306#11758198—44no—
307C4⋊Dic61—44no—
308C4⋊Dic61—44no—
309C4⋊Dic61—44no—
310#11758196—44no—
311#11758196—44no—
312C4×Dic61—44no—
313C23×C61C23×C411yescharacteristic
314C23×C61C22×D411yescharacteristic
315C23×C61C22×D411yescharacteristic
316C23×C61C22×D411yescharacteristic
317C23×C61C2×#4111yescharacteristic
318C23×C61C2×#4111yescharacteristic
319C23×C61C2×#4111yescharacteristic
320C23×C61H(5,𝔽2)11yescharacteristic
321C23×C61H(5,𝔽2)11yescharacteristic
322C23×C61H(5,𝔽2)11yescharacteristic
323C23×C61H(5,𝔽2)11yescharacteristic
324C23×C61H(5,𝔽2)11yescharacteristic
325C23×C612−1+411yescharacteristic
326C23×C612−1+411yescharacteristic
327C23×C612−1+411yescharacteristic
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—22no—
346C22×D61—22no—
347C22×D61—22no—
348C22×D61—22no—
349C22×D61—22no—
350C22×D61—22no—
351C22×D61—22no—
352C22×D61—22no—
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×D61—41no—
390C22×D61—41no—
391C22×D61—41no—
392C22×D61—41no—
393C22×D61—41no—
394C22×D61—41no—
395C22×D61—41no—
396C22×D61—41no—
397C22×D61C4×D414yes—
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—22no—
409C2×C4×C61—22no—
410C2×C4×C61—22no—
411C2×C4×C61—22no—
412C2×C4×C61—22no—
413C2×C4×C61—22no—
414C2×C4×C61—22no—
415C2×C4×C61—22no—
416C2×C4×C61—22no—
417C2×C4×C61—22no—
418C2×C4×C61—22no—
419C2×C4×C61—22no—
420C2×C4×C61—22no—
421C2×C4×C61—22no—
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×C61—41no—
439C2×C4×C61—41no—
440C2×C4×C61—41no—
441C2×C4×C61—41no—
442C2×C4×C61—41no—
443C2×C4×C61—41no—
444C2×C4×C61—41no—
445C2×C4×C61C4×D414yes—
446C2×C4×C61C4×D414yes—
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—22no—
458C2×Dic61—22no—
459C2×Dic61—22no—
460C2×Dic61—22no—
461C2×Dic61—22no—
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—
481C2×Dic61—41no—
482C2×Dic61—41no—
483C2×Dic61—41no—
484C2×Dic61—41no—
485C2×Dic61—41no—
486C2×Dic61—41no—
487C2×Dic61—41no—
488C2×Dic61—41no—
489D244—416no—
490C4×D61—416no—
491#14518—611nomaximal, Sylow
492C22×C61C2×C4×D411yescharacteristic
493C22×C61C2×C4×D411yescharacteristic
494C22×C61C2×C4×D411yescharacteristic
495C22×C61#51811yescharacteristic
496C22×C61#52011yescharacteristic
497C22×C61#52011yescharacteristic
498C22×C61#52011yescharacteristic
499C22×C61#53411yescharacteristic
500C22×C61#53511yescharacteristic
501C22×C61#53511yescharacteristic
502C22×C61#53611yescharacteristic
503C22×C61#53611yescharacteristic
504C22×C61#53711yescharacteristic
505C22×C61#53911yescharacteristic
506C22×C61#53911yescharacteristic
507C22×C61#54011yescharacteristic
508C22×C61#54211yescharacteristic
509C22×C61#54211yescharacteristic
510C22×C61#54211yescharacteristic
511C22×C61D4211yescharacteristic
512C22×C61D4211yescharacteristic
513C22×C61D4211yescharacteristic
514C22×C61#54611yescharacteristic
515C22×C61#54611yescharacteristic
516C22×C61#54711yescharacteristic
517C22×C61#54711yescharacteristic
518C22×C61#54811yescharacteristic
519C22×C61#54811yescharacteristic
520C22×C61#55111yescharacteristic
521C22×C61#55311yescharacteristic
522C22×C61#55311yescharacteristic
523C22×C61#56011yescharacteristic
524C22×C61#56211yescharacteristic
525C22×C61#56211yescharacteristic
526C22×C61#56311yescharacteristic
527C2×D61—24no—
528C2×D61—24no—
529C2×D61—24no—
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—42no—
542C2×D61—42no—
543C2×D61—42no—
544C2×D61—42no—
545C2×D61—42no—
546C2×D61—42no—
547C2×D61—42no—
548C2×D61—42no—
549C2×D61—81no—
550C2×D61—81no—
551C2×D61—81no—
552C2×D61—81no—
553C2×D61—81no—
554C2×D61—81no—
555C2×D61—81no—
556C2×D61—81no—
557C4×C61—24no—
558C4×C61—24no—
559C4×C61—42no—
560C4×C61—42no—
561C4×C61—42no—
562C4×C61—42no—
563C4×C61—81no—
564Dic61—42no—
565Dic61—42no—
566Dic61—42no—
567Dic61—42no—
568Dic61—42no—
569Dic61—81no—
570C2×#394—611no—
571C2×#390—611no—
572C2×#389—611no—
573C2×#388—611no—
574C2×#386—611no—
575C2×#385—611no—
576C2×#385—611no—
577#1444—611no—
578#1440—611no—
579#1439—611no—
580#1439—611no—
581#1439—611no—
582#1437—611no—
583#1436D6111yescharacteristic, complemented
584#1434—611no—
585C2×C61#232211yescharacteristic
586C2×C61#232411yescharacteristic
587C2×C61#232611yescharacteristic
588C2×C61#235811yescharacteristic
589C2×C61#236111yescharacteristic
590C2×C61#236111yescharacteristic
591C2×C61#237611yescharacteristic
592C2×C61#266911yescharacteristic
593C2×C61#267211yescharacteristic
594C2×C61#267411yescharacteristic
595C2×C61#268111yescharacteristic
596C2×C61#270111yescharacteristic
597C2×C61#271111yescharacteristic
598C2×C61#272311yescharacteristic
599C2×C61#275711yescharacteristic
600D61—44no—
601D61—82no—
602C23×D4—611no—
603C24×C4—611no—
604C22×C4⋊C4—611no—
605C22×C4⋊C4—611no—
606C22×C4⋊C4—611no—
607C22×C4⋊C4—611no—
608C22×C4⋊C4—611no—
609C22×C4⋊C4C2×D6111yescharacteristic
610C22×C22⋊C4—611no—
611C22×C22⋊C4—611no—
612C22×C22⋊C4—611no—
613C22×C22⋊C4—611no—
614C22×C22⋊C4—611no—
615C22×C22⋊C4—611no—
616C22×C22⋊C4—611no—
617C22×C22⋊C4—611no—
618C22×C22⋊C4—611no—
619C22×C22⋊C4—611no—
620C22×C22⋊C4—611no—
621C22×C42—611no—
622C22×C42C2×D6111yescharacteristic
623#394—618no—
624#390—1224no—
625#389—1224no—
626#388—1224no—
627#386—1224no—
628#385—1224no—
629#385—1224no—
630C2×#95—611no—
631C2×#95—611no—
632C2×#95—611no—
633C2×#95—611no—
634C2×#95—611no—
635C2×#95—611no—
636C2×#95—611no—
637C2×#95—611no—
638C2×#95—611no—
639C2×#95C2×D6111yescharacteristic
640C2×#95C2×D6111yescharacteristic
641C2×#95C2×D6111yescharacteristic
642C2×#95C2×D6111yescharacteristic
643C2×#95C2×D6111yescharacteristic
644C61#1451811yescharacteristic, complemented, Sylow
645C25—611no—
646C25—611no—
647C22×D4—614no—
648C22×D4—1222no—
649C22×D4—1222no—
650C22×D4—1222no—
651C22×D4—1222no—
652C22×D4—2441no—
653C22×D4—2441no—
654C23×C4—611no—
655C23×C4—611no—
656C23×C4—611no—
657C23×C4—611no—
658C23×C4—611no—
659C23×C4—611no—
660C23×C4—1222no—
661C23×C4—1222no—
662C23×C4—1222no—
663C23×C4—2441no—
664C23×C4—2441no—
665C23×C4—2441no—
666C23×C4—2441no—
667C23×C4C22×D6111yescharacteristic
668C23×C4C22×D6111yescharacteristic
669C23×C4C22×D6111yescharacteristic
670C23×C4C22×D6111yescharacteristic
671C23×C4C22×D6111yescharacteristic
672C23×C4C22×D6111yescharacteristic
673C23×C4C22×D6111yescharacteristic
674C2×C4⋊C4—22no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—1222no—
677C2×C4⋊C4—1222no—
678C2×C4⋊C4—1222no—
679C2×C4⋊C4—1222no—
680C2×C4⋊C4—1222no—
681C2×C4⋊C4—1222no—
682C2×C4⋊C4—1222no—
683C2×C4⋊C4—1222no—
684C2×C4⋊C4—1222no—
685C2×C4⋊C4—2441no—
686C2×C4⋊C4—2441no—
687C2×C4⋊C4—2441no—
688C2×C4⋊C4—2441no—
689C2×C4⋊C4—2441no—
690C2×C4⋊C4—2441no—
691C2×C4⋊C4C4×D6114yescomplemented
692C2×C22⋊C4—614no—
693C2×C22⋊C4—614no—
694C2×C22⋊C4—614no—
695C2×C22⋊C4—614no—
696C2×C22⋊C4—614no—
697C2×C22⋊C4—1222no—
698C2×C22⋊C4—1222no—
699C2×C22⋊C4—1222no—
700C2×C22⋊C4—1222no—
701C2×C22⋊C4—1222no—
702C2×C22⋊C4—1222no—
703C2×C22⋊C4—1222no—
704C2×C22⋊C4—1222no—
705C2×C22⋊C4—1222no—
706C2×C22⋊C4—1222no—
707C2×C22⋊C4—1222no—
708C2×C22⋊C4—1222no—
709C2×C22⋊C4—1222no—
710C2×C22⋊C4—1222no—
711C2×C22⋊C4—1222no—
712C2×C22⋊C4—1222no—
713C2×C22⋊C4—2441no—
714C2×C22⋊C4—2441no—
715C2×C22⋊C4—2441no—
716C2×C22⋊C4—2441no—
717C2×C22⋊C4—2441no—
718C2×C22⋊C4—2441no—
719C2×C22⋊C4—2441no—
720C2×C22⋊C4—2441no—
721C2×C22⋊C4—2441no—
722C2×C22⋊C4—2441no—
723C2×C22⋊C4—2441no—
724C2×C22⋊C4—2441no—
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—41no—
728C2×C42—1222no—
729C2×C42—1222no—
730C2×C42—2441no—
731#95—22no—
732#95—22no—
733#95—22no—
734#95—41no—
735#95—614no—
736#95—614no—
737#95—1222no—
738#95—1222no—
739#95—1222no—
740#95—1222no—
741#95—2441no—
742#95—2441no—
743#95—2441no—
744#95D24414yescomplemented
745C24—612no—
746C24—612no—
747C24—612no—
748C24—612no—
749C24—1221no—
750C24—1221no—
751C24—1221no—
752C24—1221no—
753C24—1221no—
754C24—1221no—
755C24—1221no—
756C24—1221no—
757C24—1221no—
758C24—1221no—
759C24—1221no—
760C24—1221no—
761C24—1221no—
762C24—1221no—
763C24—1221no—
764C24—1221no—
765C24—1221no—
766C24—1221no—
767C24—1221no—
768C24—1221no—
769C24—1221no—
770C24—1221no—
771C24—1221no—
772C24—1221no—
773C24—1221no—
774C24—1221no—
775C24C23×D6111yescharacteristic
776C2×D4—1228no—
777C2×D4—1228no—
778C2×D4—2444no—
779C2×D4—2444no—
780C2×D4—2444no—
781C2×D4—2444no—
782C2×D4—2444no—
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—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—612no—
823C22×C4—612no—
824C22×C4—612no—
825C22×C4—612no—
826C22×C4—612no—
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—1221no—
854C22×C4—1221no—
855C22×C4—1221no—
856C22×C4—1221no—
857C22×C4—1221no—
858C22×C4—1221no—
859C22×C4—1221no—
860C22×C4—1221no—
861C22×C4—1221no—
862C22×C4—1221no—
863C22×C4—1221no—
864C22×C4—2444no—
865C22×C4—2444no—
866C22×C4—2444no—
867C22×C4—2444no—
868C22×C4—2444no—
869C22×C4—2444no—
870C22×C4—2444no—
871C22×C4C2×C4×D6112yes—
872C22×C4C2×C4×D6112yes—
873C22×C4C2×C4×D6112yes—
874C22×C4C2×D24412yes—
875C22×C4C2×D24412yes—
876C22×C4C2×D24412yes—
877C22×C4#1175822212yes—
878C22×C4D4×D6112yes—
879C22×C4D4×D6112yes—
880C22×C4#1175822412yes—
881C4⋊C4—28no—
882C4⋊C4—2444no—
883C4⋊C4—2444no—
884C4⋊C4—2444no—
885C4⋊C4—2444no—
886C4⋊C4—2444no—
887C22⋊C4—1228no—
888C22⋊C4—1228no—
889C22⋊C4—1228no—
890C22⋊C4—2444no—
891C22⋊C4—2444no—
892C22⋊C4—2444no—
893C22⋊C4—2444no—
894C22⋊C4—2444no—
895C22⋊C4—2444no—
896C22⋊C4—2444no—
897C22⋊C4—2444no—
898C42—44no—
899C42—2444no—
900C23—614no—
901C23—1222no—
902C23—1222no—
903C23—1222no—
904C23—1222no—
905C23—1222no—
906C23—1222no—
907C23—1222no—
908C23—1222no—
909C23—1222no—
910C23—1222no—
911C23—1222no—
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—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—
954C23—2441no—
955C23—2441no—
956C23—2441no—
957C23—2441no—
958C23—2441no—
959C23—2441no—
960C23—2441no—
961C23—2441no—
962C23—2441no—
963C23—2441no—
964C23—2441no—
965C23—2441no—
966C23—2441no—
967C23—2441no—
968C23—2441no—
969C23—2441no—
970C23C22×C4×D6111yescharacteristic
971C23C2×D4×D6111yescharacteristic
972C23C2×D4×D6111yescharacteristic
973C23C22×D24411yescharacteristic
974C23#41×D6111yescharacteristic
975C23C2×#1175822411yescharacteristic
976C23C2×#1175822211yescharacteristic
977C23#1451982211yescharacteristic
978C23#1451982311yescharacteristic
979C23#1451982311yescharacteristic
980C23#1451982311yescharacteristic
981C23#1451982311yescharacteristic
982C23#1451982411yescharacteristic
983C23#1451982511yescharacteristic
984C23#1451982511yescharacteristic
985D4—24416no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
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—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—1222no—
1034C2×C4—1222no—
1035C2×C4—1222no—
1036C2×C4—1222no—
1037C2×C4—1222no—
1038C2×C4—1222no—
1039C2×C4—1222no—
1040C2×C4—1222no—
1041C2×C4—1222no—
1042C2×C4—1222no—
1043C2×C4—1222no—
1044C2×C4—1222no—
1045C2×C4—1222no—
1046C2×C4—1222no—
1047C2×C4—1222no—
1048C2×C4—24416no—
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—2441no—
1062C2×C4—2441no—
1063C2×C4—2441no—
1064C2×C4—2441no—
1065C2×C4—2441no—
1066C2×C4—2441no—
1067C2×C4—2441no—
1068C2×C4—2441no—
1069C2×C4—2441no—
1070C2×C4—2441no—
1071C2×C4—2441no—
1072C2×C4—2441no—
1073C2×C4—2441no—
1074C2×C4—2441no—
1075C2×C4—2441no—
1076C2×C4#1451973714yes—
1077C2×C4C4×D24414yes—
1078C22—1224no—
1079C22—1224no—
1080C22—1224no—
1081C22—4881no—
1082C22—4881no—
1083C22—4881no—
1084C22—4881no—
1085C22—4881no—
1086C22—4881no—
1087C22—4881no—
1088C22—4881no—
1089C22—2442no—
1090C22—2442no—
1091C22—2442no—
1092C22—2442no—
1093C22—2442no—
1094C22—2442no—
1095C22—2442no—
1096C22—2442no—
1097C22—2442no—
1098C22—2442no—
1099C22—2442no—
1100C22—2442no—
1101C22—2442no—
1102C22—2442no—
1103C22—2442no—
1104C22—2442no—
1105C22—2442no—
1106C22—2442no—
1107C22—2442no—
1108C22C4×D4×D6111yescharacteristic
1109C22C2×#1451973711yescharacteristic
1110C22C2×C4×D24411yescharacteristic
1111C22#1684023411yescharacteristic
1112C22#1684024211yescharacteristic
1113C22#1684024411yescharacteristic
1114C22#1684024411yescharacteristic
1115C22#1684032311yescharacteristic
1116C22#1684033011yescharacteristic
1117C22#1684033111yescharacteristic
1118C22#1684033511yescharacteristic
1119C22#1684033711yescharacteristic
1120C22#1684034311yescharacteristic
1121C22#1684035311yescharacteristic
1122C22#1684036011yescharacteristic
1123C22#1684036311yescharacteristic
1124C22#1684038411yescharacteristic
1125C22#1684038511yescharacteristic
1126C22#1684038511yescharacteristic
1127C22#1684039611yescharacteristic
1128C22D4×D24411yescharacteristic
1129C22D4×D24411yescharacteristic
1130C22#1684039911yescharacteristic
1131C22#1684040111yescharacteristic
1132C22#1684041311yescharacteristic
1133C22#1684041611yescharacteristic
1134C22#1684042111yescharacteristic
1135C22#1684042411yescharacteristic
1136C22#1684043511yescharacteristic
1137C22#1684045611yescharacteristic
1138C22#1684045811yescharacteristic
1139C22#1684050311yescharacteristic
1140C22#1684050811yescharacteristic
1141C22#1684050911yescharacteristic
1142C22#1684051611yescharacteristic
1143C4—24no—
1144C4—24no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—42no—
1149C4—81no—
1150C4—4881no—
1151C4—2442no—
1152C4—2442no—
1153C4—2442no—
1154C4—2442no—
1155C4—2442no—
1156C2—4882no—
1157C2—2444no—
1158C2#2144849211yescharacteristic
1159C2#2144851311yescharacteristic
1160C2#2144853311yescharacteristic
1161C2#2144879911yescharacteristic
1162C2#2144883311yescharacteristic
1163C2#2144883711yescharacteristic
1164C2#2144896611yescharacteristic
1165C2#2145203411yescharacteristic
1166C2#2145207311yescharacteristic
1167C2#2145210111yescharacteristic
1168C2#2145216611yescharacteristic
1169C2#2145243611yescharacteristic
1170C2#2145257311yescharacteristic
1171C2#2145273611yescharacteristic
1172C2#2145316011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1436C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1436D61
hypocenterC61#14518
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C2×#16839661C2semidirect
4. C2×#16839651C2semidirect
6. C2×#16839636C2semidirect
7. C2×#16839636C2semidirect
8. #21444083C2semidirect
9. #21444067C2semidirect
10. #21444065C2semidirect
11. #21444065C2semidirect
12. #21444063C2semidirect
13. #21444055C2semidirect
14. #21444046C2semidirect
15. C61×#1436C2semidirect
35. #16839679C4semidirect
125. C2×#11758198C2×C4semidirect
126. C2×#11758198C2×C4semidirect
138. #14519684C2×C4semidirect
149. C2×C4⋊C4×C61C2×C4semidirect
157. #95×C61D4semidirect
583. #1436D61semidirect
644. C61#14518semidirect
691. C2×C4⋊C4C4×D61semidirect
744. #95D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168396792
C2×#168396642
C2×#168396612
C2×#168396512
C2×#168396402
C2×#168396362
#214440832
#214440672
#214440652
#214440632
#214440552
#214440462
C61×#14362
#1451861