Finite Group Databasebeta

← #29603624

Subgroups — #29603624

Order 15616.

2062 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×#16839664C211yesmaximal, characteristic
2C2×#16839654C211yesmaximal, characteristic, complemented
3C2×#16839651C211yesmaximal, characteristic, complemented
4C2×#16839640C211yesmaximal, characteristic
5C2×#16839636C211yesmaximal, characteristic, complemented
6C2×C4×C4⋊Dic61C211yesmaximal, characteristic, complemented
7C2×#16839609C211yesmaximal, characteristic, complemented
8#21444071C211yesmaximal, characteristic, complemented
9#21444065C211yesmaximal, characteristic, complemented
10#21444065C211yesmaximal, characteristic, complemented
11#21444059C211yesmaximal, characteristic
12#21444055C211yesmaximal, characteristic, complemented
13#21444055C211yesmaximal, characteristic, complemented
14#21444053C211yesmaximal, characteristic, complemented
15C61×#1434C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36#16839664C418yescomplemented
37#16839654—24no—
38#16839651—24no—
39#16839640—24no—
40#16839636—24no—
41C4×C4⋊Dic61—24no—
42#16839609—24no—
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C22×C42×C61C2211yescharacteristic
52C2×#95×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C24×D61C2311yescharacteristic
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—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—41no—
86C2×C4⋊Dic61—41no—
87C2×C4⋊Dic61C2×C414yescomplemented
88C2×C4⋊Dic61D414yescomplemented
89C2×#11758196—22no—
90C2×#11758196—22no—
91C2×#11758196—41no—
92C2×#11758198—22no—
93C2×#11758198—22no—
94C2×#11758198—22no—
95C2×#11758198—22no—
96C2×#11758198—22no—
97C2×#11758198—22no—
98C2×#11758198—22no—
99C2×#11758198—22no—
100C2×#11758198—22no—
101C2×#11758198—22no—
102C2×#11758198—22no—
103C2×#11758198—22no—
104C2×#11758198—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×#11758198—41no—
120C2×#11758198—41no—
121C2×#11758198C2×C414yes—
122C2×#11758198C2×C414yes—
123C2×#11758198C2×C414yescomplemented
124C2×#11758198C2×C414yescomplemented
125C2×C4×Dic61—22no—
126C2×C4×Dic61—22no—
127C2×C4×Dic61—22no—
128C2×C4×Dic61—22no—
129C2×C4×Dic61—22no—
130C2×C4×Dic61—22no—
131C2×C4×Dic61—41no—
132C2×C4×Dic61—41no—
133C2×C4×Dic61—41no—
134#14519684—22no—
135#14519684—22no—
136#14519684—22no—
137#14519684—22no—
138#14519684—22no—
139#14519684—41no—
140#14519684—41no—
141#14519684D414yes—
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149C2×C42×C61—22no—
150C2×C42×C61—22no—
151C2×C42×C61C2×C414yescomplemented
152#95×C61—22no—
153#95×C61—22no—
154#95×C61—22no—
155#95×C61—22no—
156#95×C61—22no—
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×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×C61C22×C412yes—
228C22×C4×C61C22×C412yes—
229C22×C4×C61C22×C412yes—
230C22×C4×C61C2×D412yes—
231C22×C4×C61C2×D412yes—
232C22×C4×C61C2×D412yes—
233C22×C4×C61C2×D412yes—
234C22×C4×C61C2×D412yes—
235C22×C4×C61#4112yes—
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×Dic61C22×C412yes—
273C22×Dic61C22×C412yes—
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—44no—
289C2×C4×D61—44no—
290C2×C4×D61—44no—
291C2×C4×D61—44no—
292C2×C4×D61—44no—
293C2×C4×D61—44no—
294C42×C61—28no—
295#11758198—28no—
296#11758198—28no—
297#11758198—28no—
298#11758198—28no—
299#11758198—28no—
300#11758198—44no—
301#11758198—44no—
302#11758198—44no—
303#11758198—44no—
304#11758198—44no—
305#11758198—44no—
306C4⋊Dic61—28no—
307C4⋊Dic61—28no—
308C4⋊Dic61—44no—
309#11758196—44no—
310C4×Dic61—44no—
311C4×Dic61—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×C61C2×#4111yescharacteristic
321C23×C61C2×#4111yescharacteristic
322C23×C61C2×#4111yescharacteristic
323C23×C61C2×#4111yescharacteristic
324C23×C61H(5,𝔽2)11yescharacteristic
325C23×C61H(5,𝔽2)11yescharacteristic
326C23×C61H(5,𝔽2)11yescharacteristic
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×D61#11714yes—
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×C61C4×D414yes—
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—22no—
463C2×Dic61—22no—
464C2×Dic61—22no—
465C2×Dic61—22no—
466C2×Dic61—22no—
467C2×Dic61—22no—
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#12114yes—
489D244—416no—
490C4×D61—416no—
491#14036—611nomaximal, Sylow
492C22×C61C2×#11711yescharacteristic
493C22×C61C2×C4×D411yescharacteristic
494C22×C61C2×C4×D411yescharacteristic
495C22×C61C2×C4×D411yescharacteristic
496C22×C61C4×#4111yescharacteristic
497C22×C61#51811yescharacteristic
498C22×C61#52011yescharacteristic
499C22×C61C2×#12111yescharacteristic
500C22×C61#52511yescharacteristic
501C22×C61#52511yescharacteristic
502C22×C61#52511yescharacteristic
503C22×C61#52911yescharacteristic
504C22×C61#52911yescharacteristic
505C22×C61#52911yescharacteristic
506C22×C61#53211yescharacteristic
507C22×C61#53811yescharacteristic
508C22×C61#53811yescharacteristic
509C22×C61#54211yescharacteristic
510C22×C61#54211yescharacteristic
511C22×C61D4211yescharacteristic
512C22×C61D4211yescharacteristic
513C22×C61#54611yescharacteristic
514C22×C61#54611yescharacteristic
515C22×C61#54611yescharacteristic
516C22×C61#54711yescharacteristic
517C22×C61#54811yescharacteristic
518C22×C61#54811yescharacteristic
519C22×C61#55011yescharacteristic
520C22×C61#55011yescharacteristic
521C22×C61#55111yescharacteristic
522C22×C61#55111yescharacteristic
523C22×C61#55211yescharacteristic
524C22×C61#55311yescharacteristic
525C22×C61#55311yescharacteristic
526C22×C61#55911yescharacteristic
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—24no—
560C4×C61—42no—
561C4×C61—42no—
562C4×C61—81no—
563C4×C61—81no—
564Dic61—24no—
565Dic61—42no—
566Dic61—42no—
567Dic61—42no—
568Dic61—42no—
569Dic61—42no—
570C2×#390—611no—
571C2×#388—611no—
572C2×#388—611no—
573C2×#386—611no—
574C2×#385—611no—
575C2×C4×C4⋊C4—611no—
576C2×C4×C22⋊C4—611no—
577#1441—611no—
578#1439—611no—
579#1439—611no—
580#1438—611no—
581#1437—611no—
582#1437—611no—
583#1436—611no—
584#1434D6111yescharacteristic, complemented
585C2×C61#229011yescharacteristic
586C2×C61C4×#12111yescharacteristic
587C2×C61#233711yescharacteristic
588C2×C61#234211yescharacteristic
589C2×C61#235211yescharacteristic
590C2×C61#236111yescharacteristic
591C2×C61#236611yescharacteristic
592C2×C61#242411yescharacteristic
593C2×C61#242611yescharacteristic
594C2×C61#245611yescharacteristic
595C2×C61#245811yescharacteristic
596C2×C61#246111yescharacteristic
597C2×C61#247911yescharacteristic
598C2×C61#255411yescharacteristic
599C2×C61#259711yescharacteristic
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×C22⋊C4—611no—
609C22×C22⋊C4—611no—
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×C42—611no—
620C22×C42—611no—
621C22×C42—611no—
622C22×C42C2×D6111yescharacteristic
623#390—618no—
624#388—1224no—
625#388—1224no—
626#386—1224no—
627#385—1224no—
628C4×C4⋊C4—1224no—
629C4×C22⋊C4—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×#95C2×D6111yescharacteristic
639C2×#95C2×D6111yescharacteristic
640C2×#95C2×D6111yescharacteristic
641C2×#95C2×D6111yescharacteristic
642C2×#95C2×D6111yescharacteristic
643C2×#95C2×D6111yescharacteristic
644C61#1403611yescharacteristic, 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—1222no—
664C23×C4—1222no—
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—614no—
675C2×C4⋊C4—614no—
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—2441no—
684C2×C4⋊C4—2441no—
685C2×C4⋊C4—2441no—
686C2×C22⋊C4—614no—
687C2×C22⋊C4—614no—
688C2×C22⋊C4—614no—
689C2×C22⋊C4—614no—
690C2×C22⋊C4—1222no—
691C2×C22⋊C4—1222no—
692C2×C22⋊C4—1222no—
693C2×C22⋊C4—1222no—
694C2×C22⋊C4—1222no—
695C2×C22⋊C4—1222no—
696C2×C22⋊C4—1222no—
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×C42—22no—
720C2×C42—22no—
721C2×C42—1222no—
722C2×C42—1222no—
723C2×C42—1222no—
724C2×C42—1222no—
725C2×C42—1222no—
726C2×C42—1222no—
727C2×C42—2441no—
728C2×C42—2441no—
729C2×C42—2441no—
730C2×C42C4×D6114yescomplemented
731#95—22no—
732#95—22no—
733#95—22no—
734#95—22no—
735#95—22no—
736#95—614no—
737#95—1222no—
738#95—1222no—
739#95—1222no—
740#95—1222no—
741#95—1222no—
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—612no—
822C22×C4—612no—
823C22×C4—612no—
824C22×C4—612no—
825C22×C4—612no—
826C22×C4—612no—
827C22×C4—612no—
828C22×C4—612no—
829C22×C4—1228no—
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×C4C2×C4×D6112yes—
871C22×C4C2×C4×D6112yes—
872C22×C4C2×C4×D6112yes—
873C22×C4C2×D24412yes—
874C22×C4C2×D24412yes—
875C22×C4C2×D24412yes—
876C22×C4#1175822212yes—
877C22×C4D4×D6112yes—
878C22×C4D4×D6112yes—
879C22×C4#1175822412yes—
880C22×C4#1175822612yes—
881C4⋊C4—1228no—
882C4⋊C4—1228no—
883C4⋊C4—2444no—
884C4⋊C4—2444no—
885C22⋊C4—1228no—
886C22⋊C4—1228no—
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—
896C42—28no—
897C42—2444no—
898C42—2444no—
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
975C23#41×D6111yescharacteristic
976C23#41×D6111yescharacteristic
977C23#41×D6111yescharacteristic
978C23C2×#1175822411yescharacteristic
979C23C2×#1175822211yescharacteristic
980C23C2×#1175822611yescharacteristic
981C23#1451982311yescharacteristic
982C23#1451982311yescharacteristic
983C23#1451982311yescharacteristic
984C23#1451982411yescharacteristic
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—614no—
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—1222no—
1049C2×C4—1222no—
1050C2×C4—1222no—
1051C2×C4—1222no—
1052C2×C4—1222no—
1053C2×C4—1222no—
1054C2×C4—24416no—
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#1451973714yes—
1076C2×C4#1451973914yes—
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—
1108C22#117×D6111yescharacteristic
1109C22C2×#1451973711yescharacteristic
1110C22C2×#1451973911yescharacteristic
1111C22C2×C4×D24411yescharacteristic
1112C22#1684023011yescharacteristic
1113C22#1684023611yescharacteristic
1114C22#1684024211yescharacteristic
1115C22#121×D6111yescharacteristic
1116C22#1684027411yescharacteristic
1117C22#1684027411yescharacteristic
1118C22#1684027511yescharacteristic
1119C22#1684029011yescharacteristic
1120C22#1684029011yescharacteristic
1121C22#1684029811yescharacteristic
1122C22#1684030711yescharacteristic
1123C22#1684035111yescharacteristic
1124C22#1684035111yescharacteristic
1125C22#1684037811yescharacteristic
1126C22#1684037811yescharacteristic
1127C22D4×D24411yescharacteristic
1128C22D4×D24411yescharacteristic
1129C22#1684040411yescharacteristic
1130C22#1684040411yescharacteristic
1131C22#1684040511yescharacteristic
1132C22#1684041611yescharacteristic
1133C22#1684042011yescharacteristic
1134C22#1684042111yescharacteristic
1135C22#1684043311yescharacteristic
1136C22#1684043411yescharacteristic
1137C22#1684043511yescharacteristic
1138C22#1684043511yescharacteristic
1139C22#1684045011yescharacteristic
1140C22#1684045811yescharacteristic
1141C22#1684046511yescharacteristic
1142C22#1684049711yescharacteristic
1143C4—24no—
1144C4—24no—
1145C4—24no—
1146C4—42no—
1147C4—42no—
1148C4—81no—
1149C4—81no—
1150C4—1224no—
1151C4—2442no—
1152C4—2442no—
1153C4—2442no—
1154C4—2442no—
1155C4—2442no—
1156C2—4882no—
1157C2—2444no—
1158C2#2144826311yescharacteristic
1159C2#2144832511yescharacteristic
1160C2#2144862911yescharacteristic
1161C2#2144866111yescharacteristic
1162C2#2144874511yescharacteristic
1163C2#2144883311yescharacteristic
1164C2#2144888311yescharacteristic
1165C2#2144936011yescharacteristic
1166C2#2144938411yescharacteristic
1167C2#2144970911yescharacteristic
1168C2#2144974811yescharacteristic
1169C2#2144978411yescharacteristic
1170C2#2145004811yescharacteristic
1171C2#2145087811yescharacteristic
1172C2#2145136611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1434C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1434D61
hypocenterC61#14036
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C2×#16839654C2semidirect
3. C2×#16839651C2semidirect
5. C2×#16839636C2semidirect
6. C2×C4×C4⋊Dic61C2semidirect
7. C2×#16839609C2semidirect
8. #21444071C2semidirect
9. #21444065C2semidirect
10. #21444065C2semidirect
12. #21444055C2semidirect
13. #21444055C2semidirect
14. #21444053C2semidirect
15. C61×#1434C2semidirect
36. #16839664C4semidirect
87. C2×C4⋊Dic61C2×C4semidirect
88. C2×C4⋊Dic61D4semidirect
123. C2×#11758198C2×C4semidirect
124. C2×#11758198C2×C4semidirect
151. C2×C42×C61C2×C4semidirect
157. #95×C61D4semidirect
584. #1434D61semidirect
644. C61#14036semidirect
730. C2×C42C4×D61semidirect
744. #95D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168396642
C2×#168396542
C2×#168396512
C2×#168396402
C2×#168396362
C2×C4×C4⋊Dic612
C2×#168396092
#214440712
#214440652
#214440592
#214440552
#214440532
C61×#14342
#1403661