Finite Group Databasebeta

← #29603039

Subgroups — #29603039

Order 15616.

2170 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839651C211yesmaximal, characteristic, complemented
2C2×#16839640C211yesmaximal, characteristic
3C2×#16839640C211yesmaximal, characteristic
4C2×#16839633C211yesmaximal, characteristic, complemented
5C2×#16839619C211yesmaximal, characteristic, complemented
6C2×#16839609C211yesmaximal, characteristic, complemented
7C2×#16839609C211yesmaximal, characteristic, complemented
8#21444067C211yesmaximal, characteristic, complemented
9#21444065C211yesmaximal, characteristic, complemented
10#21444059C211yesmaximal, characteristic
11#21444055C211yesmaximal, characteristic, complemented
12#21444053C211yesmaximal, characteristic, complemented
13#21444050C211yesmaximal, characteristic, complemented
14#21444045C211yesmaximal, characteristic, complemented
15C61×#1442C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×#11758196C2211yescharacteristic
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34#16839651—24no—
35#16839640—24no—
36#16839640C418yescomplemented
37#16839633—24no—
38#16839619—24no—
39#16839609—24no—
40#16839609—24no—
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C22×C4⋊C4×C61C2211yescharacteristic
52C2×#95×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—22no—
77C22×C4×D61—22no—
78C22×C4×D61—22no—
79C22×C4×D61—22no—
80C22×C4×D61—22no—
81C22×C4×D61—22no—
82C22×C4×D61—41no—
83C22×C4×D61—41no—
84C22×C4×D61—41no—
85C22×C4×D61—41no—
86C22×C4×D61C2×C414yescomplemented
87C2×C4⋊Dic61—22no—
88C2×C4⋊Dic61—22no—
89C2×C4⋊Dic61—41no—
90C2×#11758196—22no—
91C2×#11758196—22no—
92C2×#11758196—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—22no—
105C2×#11758198—22no—
106C2×#11758198—22no—
107C2×#11758198—22no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×#11758198—22no—
111C2×#11758198—22no—
112C2×#11758198—22no—
113C2×#11758198—22no—
114C2×#11758198—22no—
115C2×#11758198—41no—
116C2×#11758198—41no—
117C2×#11758198—41no—
118C2×#11758198—41no—
119C2×#11758198C2×C414yes—
120C2×#11758198C2×C414yes—
121C2×#11758198C2×C414yescomplemented
122C2×#11758198D414yes—
123C2×C4×Dic61—22no—
124C2×C4×Dic61—22no—
125C2×C4×Dic61—22no—
126C2×C4×Dic61—22no—
127C2×C4×Dic61—22no—
128C2×C4×Dic61—22no—
129C2×C4×Dic61—41no—
130C2×C4×Dic61—41no—
131C2×C4×Dic61—41no—
132#14519684—22no—
133#14519684—22no—
134#14519684—22no—
135#14519684—22no—
136#14519684—22no—
137#14519684—41no—
138#14519684—41no—
139#14519684C2×C414yescomplemented
140#14519684D414yescomplemented
141#14519684D414yescomplemented
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149C2×C4⋊C4×C61—22no—
150C2×C4⋊C4×C61—22no—
151C2×C4⋊C4×C61—41no—
152#95×C61—22no—
153#95×C61—22no—
154#95×C61—22no—
155#95×C61—22no—
156#95×C61—41no—
157#95×C61C2×C414yescomplemented
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×D61C22×C412yes—
184C23×D61C22×C412yes—
185C23×D61C2×D412yes—
186C23×D61#4112yes—
187C23×D61#4112yes—
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×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61C22×C412yes—
231C22×C4×C61C22×C412yes—
232C22×C4×C61C22×C412yes—
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×Dic61C22×C412yes—
272C22×Dic61C22×C412yes—
273C22×Dic61C2×D412yes—
274C22×Dic61C2×D412yes—
275C22×Dic61C2×D412yes—
276C22×Dic61C2×D412yes—
277C22×Dic61C2×D412yes—
278C22×Dic61#4112yes—
279C22×Dic61#4112yes—
280C2×D244—28no—
281C2×D244—28no—
282C2×D244—44no—
283C2×D244—44no—
284C2×D244—44no—
285C2×D244—44no—
286C2×D244—44no—
287C2×C4×D61—28no—
288C2×C4×D61—28no—
289C2×C4×D61—28no—
290C2×C4×D61—44no—
291C2×C4×D61—44no—
292C2×C4×D61—44no—
293C2×C4×D61—44no—
294C2×C4×D61—44no—
295C2×C4×D61—44no—
296C2×C4×D61—44no—
297C2×C4×D61—44no—
298C2×C4×D61—44no—
299C2×C4×D61—44no—
300C2×C4×D61—44no—
301C4⋊C4×C61—44no—
302#11758198—28no—
303#11758198—28no—
304#11758198—28no—
305#11758198—28no—
306#11758198—28no—
307#11758198—28no—
308#11758198—44no—
309#11758198—44no—
310#11758198—44no—
311#11758198—44no—
312C4⋊Dic61—44no—
313#11758196—44no—
314C4×Dic61—44no—
315C4×Dic61—44no—
316C4×Dic61—44no—
317C23×C61C23×C411yescharacteristic
318C23×C61C22×D411yescharacteristic
319C23×C61C22×D411yescharacteristic
320C23×C61C22×D411yescharacteristic
321C23×C61C2×#4111yescharacteristic
322C23×C61C2×#4111yescharacteristic
323C23×C61C2×#4111yescharacteristic
324C23×C61C2×#4111yescharacteristic
325C23×C61C2×#4111yescharacteristic
326C23×C61C2×#4111yescharacteristic
327C23×C61C2×#4111yescharacteristic
328C23×C61H(5,𝔽2)11yescharacteristic
329C23×C61H(5,𝔽2)11yescharacteristic
330C23×C61H(5,𝔽2)11yescharacteristic
331C23×C612−1+411yescharacteristic
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—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—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×D61—41no—
398C22×D61—41no—
399C22×D61—41no—
400C22×D61#11714yes—
401C22×D61C4×D414yes—
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—22no—
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×C61—41no—
446C2×C4×C61—41no—
447C2×C4×C61—41no—
448C2×C4×C61—41no—
449C2×C4×C61—41no—
450C2×C4×C61C4×D414yes—
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—22no—
463C2×Dic61—22no—
464C2×Dic61—22no—
465C2×Dic61—22no—
466C2×Dic61—22no—
467C2×Dic61—22no—
468C2×Dic61—22no—
469C2×Dic61—22no—
470C2×Dic61—22no—
471C2×Dic61—22no—
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—
489C2×Dic61—41no—
490C2×Dic61—41no—
491C2×Dic61C4×D414yes—
492C2×Dic61#12114yes—
493D244—416no—
494C4×D61—416no—
495C4×D61—416no—
496#13988—611nomaximal, Sylow
497C22×C61C2×#11711yescharacteristic
498C22×C61C2×C4×D411yescharacteristic
499C22×C61C2×C4×D411yescharacteristic
500C22×C61C2×C4×D411yescharacteristic
501C22×C61C4×#4111yescharacteristic
502C22×C61#51811yescharacteristic
503C22×C61#52011yescharacteristic
504C22×C61C2×#12111yescharacteristic
505C22×C61#52511yescharacteristic
506C22×C61#52511yescharacteristic
507C22×C61#52511yescharacteristic
508C22×C61#52911yescharacteristic
509C22×C61#52911yescharacteristic
510C22×C61#52911yescharacteristic
511C22×C61#53211yescharacteristic
512C22×C61#53811yescharacteristic
513C22×C61#53911yescharacteristic
514C22×C61#54011yescharacteristic
515C22×C61#54211yescharacteristic
516C22×C61D4211yescharacteristic
517C22×C61D4211yescharacteristic
518C22×C61#54611yescharacteristic
519C22×C61#54611yescharacteristic
520C22×C61#54611yescharacteristic
521C22×C61#54611yescharacteristic
522C22×C61#54611yescharacteristic
523C22×C61#54711yescharacteristic
524C22×C61#54811yescharacteristic
525C22×C61#54811yescharacteristic
526C22×C61#55111yescharacteristic
527C22×C61#55111yescharacteristic
528C22×C61#55111yescharacteristic
529C22×C61#55211yescharacteristic
530C22×C61#55311yescharacteristic
531C22×C61#55311yescharacteristic
532C2×D61—24no—
533C2×D61—24no—
534C2×D61—24no—
535C2×D61—24no—
536C2×D61—24no—
537C2×D61—24no—
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—42no—
550C2×D61—42no—
551C2×D61—42no—
552C2×D61—42no—
553C2×D61—42no—
554C2×D61—42no—
555C2×D61—42no—
556C2×D61—42no—
557C2×D61—42no—
558C2×D61—42no—
559C2×D61—42no—
560C2×D61—42no—
561C2×D61—42no—
562C4×C61—24no—
563C4×C61—42no—
564C4×C61—42no—
565C4×C61—42no—
566C4×C61—42no—
567C4×C61—42no—
568C4×C61—81no—
569Dic61—24no—
570Dic61—24no—
571Dic61—42no—
572Dic61—42no—
573Dic61—42no—
574Dic61—81no—
575C2×#388—611no—
576C2×#386—611no—
577C2×#386—611no—
578C2×#385—611no—
579C2×#380—611no—
580C2×C4×C22⋊C4—611no—
581C2×C4×C22⋊C4—611no—
582#1442D6111yescharacteristic, complemented
583#1440—611no—
584#1439—611no—
585#1438—611no—
586#1437—611no—
587#1436—611no—
588#1436—611no—
589#1434—611no—
590C2×C61#229011yescharacteristic
591C2×C61C4×#12111yescharacteristic
592C2×C61#233511yescharacteristic
593C2×C61#234211yescharacteristic
594C2×C61#235211yescharacteristic
595C2×C61#235811yescharacteristic
596C2×C61#236111yescharacteristic
597C2×C61#242411yescharacteristic
598C2×C61#242711yescharacteristic
599C2×C61#245711yescharacteristic
600C2×C61#246311yescharacteristic
601C2×C61#246411yescharacteristic
602C2×C61#247711yescharacteristic
603C2×C61#255311yescharacteristic
604C2×C61#257811yescharacteristic
605D61—44no—
606D61—44no—
607C23×D4—611no—
608C24×C4—611no—
609C24×C4—611no—
610C22×C4⋊C4—611no—
611C22×C4⋊C4—611no—
612C22×C4⋊C4C2×D6111yescharacteristic
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×C22⋊C4—611no—
622C22×C22⋊C4—611no—
623C22×C42—611no—
624C22×C42—611no—
625C22×C42—611no—
626#388—1224no—
627#386—618no—
628#386—1224no—
629#385—1224no—
630#380—1224no—
631C4×C22⋊C4—1224no—
632C4×C22⋊C4—1224no—
633C2×#95—611no—
634C2×#95—611no—
635C2×#95—611no—
636C2×#95—611no—
637C2×#95—611no—
638C2×#95—611no—
639C2×#95—611no—
640C2×#95—611no—
641C2×#95—611no—
642C2×#95—611no—
643C2×#95C2×D6111yescharacteristic
644C2×#95C2×D6111yescharacteristic
645C2×#95C2×D6111yescharacteristic
646C2×#95C2×D6111yescharacteristic
647C2×#95C2×D6111yescharacteristic
648C2×#95C2×D6111yescharacteristic
649C61#1398811yescharacteristic, complemented, Sylow
650C25—611no—
651C25—611no—
652C22×D4—614no—
653C22×D4—1222no—
654C22×D4—1222no—
655C22×D4—1222no—
656C22×D4—1222no—
657C22×D4—2441no—
658C22×D4—2441no—
659C23×C4—611no—
660C23×C4—611no—
661C23×C4—611no—
662C23×C4—611no—
663C23×C4—611no—
664C23×C4—614no—
665C23×C4—611no—
666C23×C4—1222no—
667C23×C4—1222no—
668C23×C4—1222no—
669C23×C4—1222no—
670C23×C4—1222no—
671C23×C4—1222no—
672C23×C4—1222no—
673C23×C4—1222no—
674C23×C4—1222no—
675C23×C4—2441no—
676C23×C4—2441no—
677C23×C4—2441no—
678C23×C4—2441no—
679C23×C4C22×D6111yescharacteristic
680C23×C4C22×D6111yescharacteristic
681C23×C4C22×D6111yescharacteristic
682C23×C4C22×D6111yescharacteristic
683C23×C4C22×D6111yescharacteristic
684C23×C4C22×D6111yescharacteristic
685C23×C4C22×D6111yescharacteristic
686C2×C4⋊C4—22no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4—41no—
689C2×C4⋊C4—1222no—
690C2×C4⋊C4—1222no—
691C2×C4⋊C4—1222no—
692C2×C4⋊C4—1222no—
693C2×C4⋊C4—1222no—
694C2×C4⋊C4—2441no—
695C2×C22⋊C4—614no—
696C2×C22⋊C4—614no—
697C2×C22⋊C4—614no—
698C2×C22⋊C4—614no—
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—1222no—
714C2×C22⋊C4—1222no—
715C2×C22⋊C4—1222no—
716C2×C22⋊C4—1222no—
717C2×C22⋊C4—1222no—
718C2×C22⋊C4—1222no—
719C2×C22⋊C4—1222no—
720C2×C22⋊C4—1222no—
721C2×C22⋊C4—2441no—
722C2×C22⋊C4—2441no—
723C2×C22⋊C4—2441no—
724C2×C22⋊C4—2441no—
725C2×C42—1222no—
726C2×C42—1222no—
727C2×C42—1222no—
728C2×C42—1222no—
729C2×C42—1222no—
730C2×C42—1222no—
731C2×C42—2441no—
732C2×C42—2441no—
733C2×C42—2441no—
734#95—22no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—41no—
739#95—614no—
740#95—614no—
741#95—614no—
742#95—1222no—
743#95—1222no—
744#95—1222no—
745#95—1222no—
746#95—1222no—
747#95—2441no—
748#95—2441no—
749#95C4×D6114yescomplemented
750C24—612no—
751C24—612no—
752C24—612no—
753C24—612no—
754C24—612no—
755C24—612no—
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—
775C24—1221no—
776C24—1221no—
777C24—1221no—
778C24—1221no—
779C24—1221no—
780C24C23×D6111yescharacteristic
781C2×D4—1228no—
782C2×D4—1228no—
783C2×D4—2444no—
784C2×D4—2444no—
785C2×D4—2444no—
786C2×D4—2444no—
787C2×D4—2444no—
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—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—612no—
830C22×C4—612no—
831C22×C4—612no—
832C22×C4—612no—
833C22×C4—612no—
834C22×C4—612no—
835C22×C4—612no—
836C22×C4—612no—
837C22×C4—612no—
838C22×C4—1228no—
839C22×C4—1228no—
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—1221no—
865C22×C4—1221no—
866C22×C4—1228no—
867C22×C4—1221no—
868C22×C4—1221no—
869C22×C4—1221no—
870C22×C4—1221no—
871C22×C4—1221no—
872C22×C4—1221no—
873C22×C4—1221no—
874C22×C4—2444no—
875C22×C4—2444no—
876C22×C4—2444no—
877C22×C4—2444no—
878C22×C4—2444no—
879C22×C4—2444no—
880C22×C4—2444no—
881C22×C4—2444no—
882C22×C4—2444no—
883C22×C4—2444no—
884C22×C4—2444no—
885C22×C4C2×C4×D6112yes—
886C22×C4C2×C4×D6112yes—
887C22×C4C2×C4×D6112yes—
888C22×C4D4×D6112yes—
889C22×C4D4×D6112yes—
890C22×C4D4×D6112yes—
891C22×C4#1175822612yes—
892C22×C4#1175822612yes—
893C4⋊C4—44no—
894C4⋊C4—2444no—
895C4⋊C4—2444no—
896C22⋊C4—1228no—
897C22⋊C4—1228no—
898C22⋊C4—1228no—
899C22⋊C4—1228no—
900C22⋊C4—1228no—
901C22⋊C4—1228no—
902C22⋊C4—2444no—
903C22⋊C4—2444no—
904C22⋊C4—2444no—
905C22⋊C4—2444no—
906C42—2444no—
907C42—2444no—
908C42—2444no—
909C23—614no—
910C23—614no—
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—1222no—
927C23—1222no—
928C23—1222no—
929C23—1222no—
930C23—1222no—
931C23—1222no—
932C23—1222no—
933C23—1222no—
934C23—1222no—
935C23—1222no—
936C23—1222no—
937C23—1222no—
938C23—1222no—
939C23—1222no—
940C23—1222no—
941C23—1222no—
942C23—1222no—
943C23—1222no—
944C23—1222no—
945C23—1222no—
946C23—1222no—
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—
970C23—2441no—
971C23—2441no—
972C23—2441no—
973C23—2441no—
974C23—2441no—
975C23—2441no—
976C23—2441no—
977C23—2441no—
978C23—2441no—
979C23C22×C4×D6111yescharacteristic
980C23C2×D4×D6111yescharacteristic
981C23C2×D4×D6111yescharacteristic
982C23C2×D4×D6111yescharacteristic
983C23#41×D6111yescharacteristic
984C23#41×D6111yescharacteristic
985C23#41×D6111yescharacteristic
986C23#41×D6111yescharacteristic
987C23#41×D6111yescharacteristic
988C23C2×#1175822611yescharacteristic
989C23C2×#1175822611yescharacteristic
990C23#1451982211yescharacteristic
991C23#1451982311yescharacteristic
992C23#1451982311yescharacteristic
993C23#1451982411yescharacteristic
994D4—24416no—
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—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
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—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—614no—
1044C2×C4—614no—
1045C2×C4—1222no—
1046C2×C4—1222no—
1047C2×C4—1222no—
1048C2×C4—1222no—
1049C2×C4—1222no—
1050C2×C4—1222no—
1051C2×C4—1222no—
1052C2×C4—1222no—
1053C2×C4—1222no—
1054C2×C4—1222no—
1055C2×C4—1222no—
1056C2×C4—1222no—
1057C2×C4—1222no—
1058C2×C4—1222no—
1059C2×C4—1222no—
1060C2×C4—1222no—
1061C2×C4—1222no—
1062C2×C4—1222no—
1063C2×C4—1222no—
1064C2×C4—1222no—
1065C2×C4—1222no—
1066C2×C4—24416no—
1067C2×C4—24416no—
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—2441no—
1077C2×C4—2441no—
1078C2×C4—2441no—
1079C2×C4—2441no—
1080C2×C4—2441no—
1081C2×C4—2441no—
1082C2×C4—2441no—
1083C2×C4—2441no—
1084C2×C4—2441no—
1085C2×C4—2441no—
1086C2×C4—2441no—
1087C2×C4#1451973914yes—
1088C22—1224no—
1089C22—1224no—
1090C22—1224no—
1091C22—1224no—
1092C22—1224no—
1093C22—1224no—
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—
1108C22—2442no—
1109C22—2442no—
1110C22—2442no—
1111C22—2442no—
1112C22—2442no—
1113C22—2442no—
1114C22—2442no—
1115C22—2442no—
1116C22—2442no—
1117C22—2442no—
1118C22#117×D6111yescharacteristic
1119C22C4×D4×D6111yescharacteristic
1120C22C4×D4×D6111yescharacteristic
1121C22C2×#1451973911yescharacteristic
1122C22C4×#1175822611yescharacteristic
1123C22#1684023411yescharacteristic
1124C22#1684024211yescharacteristic
1125C22#121×D6111yescharacteristic
1126C22#1684027011yescharacteristic
1127C22#1684027511yescharacteristic
1128C22#1684027511yescharacteristic
1129C22#1684029511yescharacteristic
1130C22#1684029711yescharacteristic
1131C22#1684029711yescharacteristic
1132C22#1684031311yescharacteristic
1133C22#1684034811yescharacteristic
1134C22#1684036111yescharacteristic
1135C22#1684036811yescharacteristic
1136C22#1684037811yescharacteristic
1137C22#1684039411yescharacteristic
1138C22#1684039611yescharacteristic
1139C22#1684040311yescharacteristic
1140C22#1684040411yescharacteristic
1141C22#1684040411yescharacteristic
1142C22#1684040511yescharacteristic
1143C22#1684040911yescharacteristic
1144C22#1684041011yescharacteristic
1145C22#1684042011yescharacteristic
1146C22#1684042011yescharacteristic
1147C22#1684043711yescharacteristic
1148C22#1684043911yescharacteristic
1149C22#1684044211yescharacteristic
1150C22#1684045011yescharacteristic
1151C22#1684046311yescharacteristic
1152C22#1684046511yescharacteristic
1153C4—24no—
1154C4—42no—
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—42no—
1159C4—81no—
1160C4—1224no—
1161C4—1224no—
1162C4—4881no—
1163C4—2442no—
1164C4—2442no—
1165C4—2442no—
1166C2—2444no—
1167C2—2444no—
1168C2#2144825711yescharacteristic
1169C2#2144832711yescharacteristic
1170C2#2144860811yescharacteristic
1171C2#2144866311yescharacteristic
1172C2#2144874511yescharacteristic
1173C2#2144879511yescharacteristic
1174C2#2144883211yescharacteristic
1175C2#2144934811yescharacteristic
1176C2#2144939111yescharacteristic
1177C2#2144972911yescharacteristic
1178C2#2144981611yescharacteristic
1179C2#2144982811yescharacteristic
1180C2#2145001511yescharacteristic
1181C2#2145086711yescharacteristic
1182C2#2145114811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1442C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1442D61
hypocenterC61#13988
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
1. C2×#16839651C2semidirect
4. C2×#16839633C2semidirect
5. C2×#16839619C2semidirect
6. C2×#16839609C2semidirect
7. C2×#16839609C2semidirect
8. #21444067C2semidirect
9. #21444065C2semidirect
11. #21444055C2semidirect
12. #21444053C2semidirect
13. #21444050C2semidirect
14. #21444045C2semidirect
15. C61×#1442C2semidirect
36. #16839640C4semidirect
86. C22×C4×D61C2×C4semidirect
121. C2×#11758198C2×C4semidirect
139. #14519684C2×C4semidirect
140. #14519684D4semidirect
141. #14519684D4semidirect
157. #95×C61C2×C4semidirect
582. #1442D61semidirect
649. C61#13988semidirect
749. #95C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396512
C2×#168396402
C2×#168396332
C2×#168396192
C2×#168396092
#214440672
#214440652
#214440592
#214440552
#214440532
#214440502
#214440452
C61×#14422
#1398861