Finite Group Databasebeta

← #29603429

Subgroups — #29603429

Order 15616.

2178 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839640C211yesmaximal, characteristic
2C2×#16839640C211yesmaximal, characteristic
3C2×#16839640C211yesmaximal, characteristic
4C2×C4×#11758198C211yesmaximal, characteristic, complemented
5C2×#95×D61C211yesmaximal, characteristic, complemented
6#21444081C211yesmaximal, characteristic, complemented
7#21444080C211yesmaximal, characteristic, complemented
8#21444067C211yesmaximal, characteristic, complemented
9#21444067C211yesmaximal, characteristic, complemented
10#21444057C211yesmaximal, characteristic, complemented
11#21444055C211yesmaximal, characteristic, complemented
12#21444045C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×#1434C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C22×#11758198C2211yescharacteristic
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×C4×Dic61C2211yescharacteristic
30#16839640—24no—
31#16839640—24no—
32#16839640C418yescomplemented
33C4×#11758198—24no—
34C2×#14519684C2211yescharacteristic
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48#95×D61—24no—
49C22×C42×C61C2211yescharacteristic
50C2×#95×C61C2211yescharacteristic
51C2×#95×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—22no—
63C22×D244—22no—
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—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×D61—41no—
87C22×C4×D61—41no—
88C22×C4×D61—41no—
89C22×C4×D61—41no—
90C22×C4×D61C2×C414yes—
91C22×C4×D61D414yes—
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—41no—
108C2×#11758198—41no—
109C2×#11758198—41no—
110C2×#11758198—41no—
111C2×#11758198—41no—
112C2×#11758198—41no—
113C2×#11758198—41no—
114C2×#11758198—41no—
115C2×#11758198C2×C414yes—
116C2×#11758198C2×C414yescomplemented
117C2×#11758198C2×C414yescomplemented
118C2×#11758198D414yes—
119C2×C4×Dic61—22no—
120C2×C4×Dic61—22no—
121C2×C4×Dic61—41no—
122#14519684—22no—
123#14519684—22no—
124#14519684—22no—
125#14519684—22no—
126#14519684—22no—
127#14519684—22no—
128#14519684—22no—
129#14519684—22no—
130#14519684—41no—
131#14519684—41no—
132#14519684—41no—
133#14519684—41no—
134#14519684—41no—
135#14519684C2×C414yescomplemented
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C2×C42×C61—22no—
144C2×C42×C61—22no—
145C2×C42×C61—41no—
146#95×C61—22no—
147#95×C61—22no—
148#95×C61—22no—
149#95×C61—22no—
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×D61C22×C412yes—
176C23×D61C22×C412yes—
177C23×D61C2×D412yes—
178C23×D61C2×D412yes—
179C23×D61#4112yes—
180C23×D61#4112yes—
181C23×D61#4112yes—
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×C61C22×C412yes—
225C22×C4×C61C22×C412yes—
226C22×C4×C61C22×C412yes—
227C22×C4×C61C2×D412yes—
228C22×C4×C61C2×D412yes—
229C22×C4×C61#4112yes—
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×Dic61—21no—
269C22×Dic61C22×C412yes—
270C22×Dic61C22×C412yes—
271C22×Dic61C2×D412yes—
272C22×Dic61C2×D412yes—
273C22×Dic61#4112yes—
274C2×D244—28no—
275C2×D244—28no—
276C2×D244—28no—
277C2×D244—44no—
278C2×D244—44no—
279C2×D244—44no—
280C2×D244—44no—
281C2×C4×D61—28no—
282C2×C4×D61—28no—
283C2×C4×D61—28no—
284C2×C4×D61—28no—
285C2×C4×D61—44no—
286C2×C4×D61—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—
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—
301C2×C4×D61—44no—
302C42×C61—44no—
303#11758198—28no—
304#11758198—28no—
305#11758198—44no—
306#11758198—44no—
307#11758198—44no—
308#11758198—44no—
309#11758198—44no—
310#11758198—44no—
311#11758198—44no—
312C4×Dic61—44no—
313C23×C61C23×C411yescharacteristic
314C23×C61C22×D411yescharacteristic
315C23×C61C22×D411yescharacteristic
316C23×C61C2×#4111yescharacteristic
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×C61H(5,𝔽2)11yescharacteristic
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—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—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#11714yes—
392C22×D61C4×D414yes—
393C22×D61C4×D414yes—
394C22×D61#12114yes—
395C22×D61#12314yes—
396C22×D61#12414yes—
397C22×D61#12614yes—
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—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×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#12314yes—
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—
491C4×D61—416no—
492C4×D61—416no—
493#14020—611nomaximal, Sylow
494C22×C61C2×#11711yescharacteristic
495C22×C61C2×C4×D411yescharacteristic
496C22×C61C2×C4×D411yescharacteristic
497C22×C61C4×#4111yescharacteristic
498C22×C61C4×#4111yescharacteristic
499C22×C61#51811yescharacteristic
500C22×C61#51811yescharacteristic
501C22×C61C2×#12111yescharacteristic
502C22×C61C2×#12311yescharacteristic
503C22×C61C2×#12311yescharacteristic
504C22×C61#52511yescharacteristic
505C22×C61C2×#12411yescharacteristic
506C22×C61C2×#12611yescharacteristic
507C22×C61#52911yescharacteristic
508C22×C61#52911yescharacteristic
509C22×C61#53411yescharacteristic
510C22×C61#53511yescharacteristic
511C22×C61#53811yescharacteristic
512C22×C61#53811yescharacteristic
513C22×C61#54611yescharacteristic
514C22×C61#54611yescharacteristic
515C22×C61#54611yescharacteristic
516C22×C61#54611yescharacteristic
517C22×C61#55111yescharacteristic
518C22×C61#55111yescharacteristic
519C22×C61#55111yescharacteristic
520C22×C61#55111yescharacteristic
521C22×C61#55311yescharacteristic
522C22×C61#55311yescharacteristic
523C22×C61#55311yescharacteristic
524C22×C61#55311yescharacteristic
525C22×C61#55311yescharacteristic
526C22×C61#55311yescharacteristic
527C22×C61#55311yescharacteristic
528C22×C61#55311yescharacteristic
529C2×D61—24no—
530C2×D61—24no—
531C2×D61—24no—
532C2×D61—24no—
533C2×D61—24no—
534C2×D61—24no—
535C2×D61—24no—
536C2×D61—24no—
537C2×D61—24no—
538C2×D61—24no—
539C2×D61—24no—
540C2×D61—24no—
541C2×D61—24no—
542C2×D61—24no—
543C2×D61—42no—
544C2×D61—42no—
545C2×D61—42no—
546C2×D61—42no—
547C2×D61—42no—
548C2×D61—42no—
549C2×D61—42no—
550C2×D61—81no—
551C2×D61—81no—
552C2×D61—81no—
553C2×D61—81no—
554C2×D61—81no—
555C2×D61—81no—
556C2×D61—81no—
557C2×D61—81no—
558C2×D61#38818yes—
559C4×C61—24no—
560C4×C61—42no—
561C4×C61—42no—
562C4×C61—42no—
563C4×C61—42no—
564C4×C61—42no—
565C4×C61—81no—
566Dic61—42no—
567Dic61—42no—
568Dic61—42no—
569Dic61—42no—
570Dic61—42no—
571Dic61—81no—
572C2×#386—611no—
573C2×#386—611no—
574C2×#386—611no—
575C2×C4×C22⋊C4—611no—
576C22×#95—611no—
577#1443—611no—
578#1443—611no—
579#1440—611no—
580#1440—611no—
581#1437—611no—
582#1437—611no—
583#1434—611no—
584#1434D6111yescharacteristic, complemented
585C22⋊#95—611no—
586C22⋊#95—611no—
587C2×C61C2×#38811yescharacteristic
588C2×C61C4×#12311yescharacteristic
589C2×C61#232111yescharacteristic
590C2×C61#235311yescharacteristic
591C2×C61#235311yescharacteristic
592C2×C61#236411yescharacteristic
593C2×C61#236411yescharacteristic
594C2×C61#241111yescharacteristic
595C2×C61#241211yescharacteristic
596C2×C61#244411yescharacteristic
597C2×C61#244411yescharacteristic
598C2×C61#250411yescharacteristic
599C2×C61#251011yescharacteristic
600C2×C61#251011yescharacteristic
601C2×C61#259111yescharacteristic
602D61—28no—
603D61—82no—
604C23×D4—611no—
605C24×C4—611no—
606C24×C4—611no—
607C24×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×C42—611no—
618C22×C42C2×D6111yescharacteristic
619#386—618no—
620#386—1224no—
621#386—1224no—
622C4×C22⋊C4—1224no—
623C2×#95—611no—
624C2×#95—611no—
625C2×#95—611no—
626C2×#95—611no—
627C2×#95—611no—
628C2×#95—611no—
629C2×#95—611no—
630C2×#95—611no—
631C2×#95—611no—
632C2×#95—611no—
633C2×#95—611no—
634C2×#95—611no—
635C2×#95—611no—
636C2×#95—611no—
637C2×#95—1224no—
638C2×#95C2×D6111yescharacteristic
639C2×#95C2×D6111yescharacteristic
640C2×#95C2×D6111yescharacteristic
641C2×#95C2×D6111yescharacteristic
642C2×#95C2×D6111yescharacteristic
643C2×#95C2×D6111yescharacteristic
644C61#1402011yescharacteristic, complemented, Sylow
645C25—611no—
646C25—611no—
647C22×D4—614no—
648C22×D4—1222no—
649C22×D4—1222no—
650C22×D4—1222no—
651C22×D4—1222no—
652C22×D4—1222no—
653C22×D4—1222no—
654C23×C4—611no—
655C23×C4—611no—
656C23×C4—611no—
657C23×C4—611no—
658C23×C4—611no—
659C23×C4—614no—
660C23×C4—614no—
661C23×C4—611no—
662C23×C4—1222no—
663C23×C4—1222no—
664C23×C4—1222no—
665C23×C4—1222no—
666C23×C4—1222no—
667C23×C4—1222no—
668C23×C4—1222no—
669C23×C4—1222no—
670C23×C4—1222no—
671C23×C4—1222no—
672C23×C4—1222no—
673C23×C4—2441no—
674C23×C4—2441no—
675C23×C4—2441no—
676C23×C4—2441no—
677C23×C4—2441no—
678C23×C4—2441no—
679C23×C4—2441no—
680C23×C4—2441no—
681C23×C4C22×D6111yescharacteristic
682C23×C4C22×D6111yescharacteristic
683C23×C4C22×D6111yescharacteristic
684C23×C4C22×D6111yescharacteristic
685C23×C4C22×D6111yescharacteristic
686C23×C4C22×D6111yescharacteristic
687C23×C4C22×D6111yescharacteristic
688C2×C22⋊C4—614no—
689C2×C22⋊C4—614no—
690C2×C22⋊C4—614no—
691C2×C22⋊C4—614no—
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—2441no—
708C2×C22⋊C4—2441no—
709C2×C22⋊C4—2441no—
710C2×C22⋊C4—2441no—
711C2×C22⋊C4—2441no—
712C2×C22⋊C4—2441no—
713C2×C22⋊C4—2441no—
714C2×C22⋊C4—2441no—
715C2×C42—22no—
716C2×C42—22no—
717C2×C42—41no—
718C2×C42—1222no—
719C2×C42—1222no—
720C2×C42—2441no—
721#95—22no—
722#95—22no—
723#95—22no—
724#95—22no—
725#95—41no—
726#95—614no—
727#95—1222no—
728#95—1222no—
729#95—1222no—
730#95—1222no—
731#95—1222no—
732#95—1222no—
733#95—1222no—
734#95—1222no—
735#95—2441no—
736#95—2441no—
737#95—2441no—
738#95—2441no—
739#95—2441no—
740#95C4×D6114yescomplemented
741C24—612no—
742C24—612no—
743C24—612no—
744C24—612no—
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—
771C24C23×D6111yescharacteristic
772C2×D4—1228no—
773C2×D4—1228no—
774C2×D4—1228no—
775C2×D4—2444no—
776C2×D4—2444no—
777C2×D4—2444no—
778C2×D4—2444no—
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—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—612no—
821C22×C4—612no—
822C22×C4—612no—
823C22×C4—612no—
824C22×C4—612no—
825C22×C4—1228no—
826C22×C4—1228no—
827C22×C4—1228no—
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—1228no—
859C22×C4—1221no—
860C22×C4—1221no—
861C22×C4—1221no—
862C22×C4—1221no—
863C22×C4—1221no—
864C22×C4—1221no—
865C22×C4—1221no—
866C22×C4—2444no—
867C22×C4—2444no—
868C22×C4—2444no—
869C22×C4—2444no—
870C22×C4—2444no—
871C22×C4—2444no—
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—
882C22×C4—2444no—
883C22×C4C2×C4×D6112yes—
884C22×C4C2×C4×D6112yes—
885C22×C4C2×C4×D6112yes—
886C22×C4#1175822212yes—
887C22×C4#1175822212yes—
888C22×C4D4×D6112yes—
889C22×C4D4×D6112yes—
890C22×C4#1175822612yes—
891C22⋊C4—1228no—
892C22⋊C4—1228no—
893C22⋊C4—2444no—
894C22⋊C4—2444no—
895C22⋊C4—2444no—
896C22⋊C4—2444no—
897C22⋊C4—2444no—
898C22⋊C4—2444no—
899C22⋊C4—2444no—
900C42—44no—
901C42—2444no—
902C23—614no—
903C23—614no—
904C23—614no—
905C23—614no—
906C23—614no—
907C23—614no—
908C23—614no—
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—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—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—
970C23—2441no—
971C23—2441no—
972C23C22×C4×D6111yescharacteristic
973C23C2×D4×D6111yescharacteristic
974C23C2×D4×D6111yescharacteristic
975C23#41×D6111yescharacteristic
976C23#41×D6111yescharacteristic
977C23#41×D6111yescharacteristic
978C23#41×D6111yescharacteristic
979C23#41×D6111yescharacteristic
980C23C2×#1175822211yescharacteristic
981C23C2×#1175822211yescharacteristic
982C23C2×#1175822611yescharacteristic
983C23#1451982211yescharacteristic
984C23#1451982311yescharacteristic
985C23#1451982311yescharacteristic
986C23#1451982311yescharacteristic
987D4—24416no—
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—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—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—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—24416no—
1052C2×C4—24416no—
1053C2×C4—24416no—
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—2441no—
1077C2×C4—2441no—
1078C2×C4—2441no—
1079C2×C4—2441no—
1080C2×C4—2441no—
1081C2×C4#1451976214yes—
1082C22—618no—
1083C22—1224no—
1084C22—1224no—
1085C22—1224no—
1086C22—1224no—
1087C22—1224no—
1088C22—1224no—
1089C22—1224no—
1090C22—1224no—
1091C22—1224no—
1092C22—1224no—
1093C22—1224no—
1094C22—1224no—
1095C22—1224no—
1096C22—1224no—
1097C22—4881no—
1098C22—4881no—
1099C22—4881no—
1100C22—4881no—
1101C22—4881no—
1102C22—4881no—
1103C22—4881no—
1104C22—4881no—
1105C22—2442no—
1106C22—2442no—
1107C22—2442no—
1108C22—2442no—
1109C22—2442no—
1110C22—2442no—
1111C22—2442no—
1112C22#117×D6111yescharacteristic
1113C22C4×D4×D6111yescharacteristic
1114C22C4×D4×D6111yescharacteristic
1115C22C4×#1175822211yescharacteristic
1116C22C4×#1175822611yescharacteristic
1117C22#1684023411yescharacteristic
1118C22#1684023611yescharacteristic
1119C22#121×D6111yescharacteristic
1120C22#123×D6111yescharacteristic
1121C22C2×#1451976211yescharacteristic
1122C22#1684027111yescharacteristic
1123C22#124×D6111yescharacteristic
1124C22#126×D6111yescharacteristic
1125C22#1684029011yescharacteristic
1126C22#1684029911yescharacteristic
1127C22#1684032011yescharacteristic
1128C22#1684033011yescharacteristic
1129C22#1684034811yescharacteristic
1130C22#1684035111yescharacteristic
1131C22#1684040211yescharacteristic
1132C22#1684040311yescharacteristic
1133C22#1684040411yescharacteristic
1134C22#1684040811yescharacteristic
1135C22#1684043611yescharacteristic
1136C22#1684043611yescharacteristic
1137C22#1684043711yescharacteristic
1138C22#1684043911yescharacteristic
1139C22#1684045611yescharacteristic
1140C22#1684045611yescharacteristic
1141C22#1684045611yescharacteristic
1142C22#1684045711yescharacteristic
1143C22#1684046211yescharacteristic
1144C22#1684046311yescharacteristic
1145C22#1684046511yescharacteristic
1146C22#1684046511yescharacteristic
1147C4—24no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—81no—
1154C4—4881no—
1155C4—2442no—
1156C4—2442no—
1157C4—2442no—
1158C4—2442no—
1159C4—2442no—
1160C2—1228no—
1161C2—4882no—
1162C2#388×D6111yescharacteristic
1163C2C4×#1451976211yescharacteristic
1164C2#2144847211yescharacteristic
1165C2#2144875811yescharacteristic
1166C2#2144876011yescharacteristic
1167C2#2144886511yescharacteristic
1168C2#2144887011yescharacteristic
1169C2#2144920311yescharacteristic
1170C2#2144921211yescharacteristic
1171C2#2144956811yescharacteristic
1172C2#2144957411yescharacteristic
1173C2#2145030811yescharacteristic
1174C2#2145037611yescharacteristic
1175C2#2145038611yescharacteristic
1176C2#2145129711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1434C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1434D61
hypocenterC61#14020
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
4. C2×C4×#11758198C2semidirect
5. C2×#95×D61C2semidirect
6. #21444081C2semidirect
7. #21444080C2semidirect
8. #21444067C2semidirect
9. #21444067C2semidirect
10. #21444057C2semidirect
11. #21444055C2semidirect
12. #21444045C2semidirect
13. #21444040C2semidirect
14. #21444040C2semidirect
15. C61×#1434C2semidirect
32. #16839640C4semidirect
116. C2×#11758198C2×C4semidirect
117. C2×#11758198C2×C4semidirect
135. #14519684C2×C4semidirect
151. #95×C61C2×C4semidirect
584. #1434D61semidirect
644. C61#14020semidirect
740. #95C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396402
C2×C4×#117581982
C2×#95×D612
#214440812
#214440802
#214440672
#214440572
#214440552
#214440452
#214440402
C61×#14342
#1402061