Finite Group Databasebeta

← #29603370

Subgroups — #29603370

Order 15616.

2950 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519739C211yesmaximal, characteristic
2C22×C4⋊C4×D61C211yesmaximal, characteristic, complemented
3C2×#16839640C211yesmaximal, characteristic
4C2×#16839640C211yesmaximal, characteristic
5C2×#16839636C211yesmaximal, characteristic, complemented
6C2×#16839633C211yesmaximal, characteristic, complemented
7C2×#16839633C211yesmaximal, characteristic, complemented
8#21444082C211yesmaximal, characteristic, complemented
9#21444063C211yesmaximal, characteristic, complemented
10#21444061C211yesmaximal, characteristic, complemented
11#21444053C211yesmaximal, characteristic, complemented
12#21444050C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×#1444C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C2×#14519739—24no—
22C2×#14519739—24no—
23C2×#14519739—24no—
24C22×C4⋊Dic61C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C2×C4⋊C4×D61—24no—
29C2×C4⋊C4×D61—24no—
30C2×C4⋊C4×D61—24no—
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic
40#16839640—24no—
41#16839640C418yescomplemented
42#16839636—24no—
43#16839633—24no—
44#16839633—24no—
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C22×C4⋊C4×C61C2211yescharacteristic
56C22×C4⋊C4×C61C2211yescharacteristic
57C22×C4⋊C4×C61C2211yescharacteristic
58C2×#95×C61C2211yescharacteristic
59C2×#95×C61C2211yescharacteristic
60C2×#95×C61C2211yescharacteristic
61C2×#95×C61C2211yescharacteristic
62C24×D61C2311yescharacteristic
63C24×D61C2311yescharacteristic
64C22×D244—22no—
65C22×D244—22no—
66C22×D244—22no—
67C22×D244—22no—
68C22×D244C2×C414yes—
69C22×D244D414yes—
70C22×D244Q814yes—
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C22×C4×D61—22no—
78C22×C4×D61—22no—
79C22×C4×D61—22no—
80C22×C4×D61—22no—
81C22×C4×D61—22no—
82C22×C4×D61—22no—
83C22×C4×D61—22no—
84C22×C4×D61—22no—
85C22×C4×D61—22no—
86C22×C4×D61—22no—
87C22×C4×D61—22no—
88C22×C4×D61—22no—
89C22×C4×D61—22no—
90C22×C4×D61—22no—
91C22×C4×D61—22no—
92C22×C4×D61—22no—
93C22×C4×D61—22no—
94C22×C4×D61—22no—
95C22×C4×D61—22no—
96C22×C4×D61—22no—
97C22×C4×D61—41no—
98C22×C4×D61—41no—
99C22×C4×D61—41no—
100C22×C4×D61—41no—
101C22×C4×D61—41no—
102C22×C4×D61—41no—
103C22×C4×D61C2×C414yescomplemented
104C22×C4×D61D414yes—
105#14519739—232no—
106C2×C4⋊Dic61—22no—
107C2×C4⋊Dic61—22no—
108C2×C4⋊Dic61D414yescomplemented
109C2×#11758196—22no—
110C2×#11758196—22no—
111C2×#11758196—22no—
112C2×#11758196—22no—
113C2×#11758196—22no—
114C2×#11758196—22no—
115C2×#11758196—22no—
116C2×#11758196—41no—
117C2×#11758196D414yescomplemented
118C4⋊C4×D61—232no—
119C2×#11758198—22no—
120C2×#11758198—22no—
121C2×#11758198—22no—
122C2×#11758198—22no—
123C2×#11758198—22no—
124C2×#11758198—22no—
125C2×#11758198—22no—
126C2×#11758198—22no—
127C2×#11758198—22no—
128C2×#11758198—22no—
129C2×#11758198—22no—
130C2×#11758198—22no—
131C2×#11758198—22no—
132C2×#11758198—22no—
133C2×#11758198—22no—
134C2×#11758198—22no—
135C2×#11758198—22no—
136C2×#11758198—22no—
137C2×#11758198—41no—
138C2×#11758198—41no—
139C2×#11758198C2×C414yescomplemented
140C2×#11758198C2×C414yescomplemented
141C2×#11758198C2×C414yescomplemented
142C2×#11758198D414yes—
143C2×C4×Dic61—22no—
144C2×C4×Dic61—22no—
145C2×C4×Dic61—22no—
146#14519684—22no—
147#14519684—22no—
148#14519684—22no—
149#14519684—22no—
150#14519684—22no—
151#14519684—22no—
152#14519684—22no—
153#14519684—22no—
154#14519684—41no—
155#14519684C2×C414yescomplemented
156C23×C4×C61C2311yescharacteristic
157C23×C4×C61C2311yescharacteristic
158C23×C4×C61C2311yescharacteristic
159C23×C4×C61C2311yescharacteristic
160C23×C4×C61C2311yescharacteristic
161C23×C4×C61C2311yescharacteristic
162C23×C4×C61C2311yescharacteristic
163C2×C4⋊C4×C61—22no—
164C2×C4⋊C4×C61—22no—
165C2×C4⋊C4×C61—22no—
166C2×C4⋊C4×C61—22no—
167C2×C4⋊C4×C61—22no—
168C2×C4⋊C4×C61—22no—
169C2×C4⋊C4×C61—22no—
170C2×C4⋊C4×C61—22no—
171C2×C4⋊C4×C61—41no—
172#95×C61—22no—
173#95×C61—22no—
174#95×C61—41no—
175#95×C61C2×C414yescomplemented
176C24×C61C2411yescharacteristic
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×D61—21no—
186C23×D61—21no—
187C23×D61—21no—
188C23×D61—21no—
189C23×D61—21no—
190C23×D61—21no—
191C23×D61—21no—
192C23×D61—21no—
193C23×D61—21no—
194C23×D61—21no—
195C23×D61—21no—
196C23×D61—21no—
197C23×D61C22×C412yes—
198C23×D61C22×C412yes—
199C23×D61C2×D412yes—
200C23×D61C2×D412yes—
201C23×D61C2×D412yes—
202C23×D61C2×D412yes—
203C23×D61C2×Q812yes—
204C23×D61C2×Q812yes—
205C23×D61#4112yes—
206C23×D61#4112yes—
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×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61C22×C412yes—
247C22×C4×C61C22×C412yes—
248C22×C4×C61C22×C412yes—
249C22×C4×C61C2×D412yes—
250C22×C4×C61C2×D412yes—
251C22×C4×C61C2×D412yes—
252C22×C4×C61C2×D412yes—
253C22×C4×C61C2×D412yes—
254C22×C4×C61C2×Q812yes—
255C22×C4×C61#4112yes—
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×Dic61—21no—
276C22×Dic61—21no—
277C22×Dic61—21no—
278C22×Dic61—21no—
279C22×Dic61—21no—
280C22×Dic61—21no—
281C22×Dic61—21no—
282C22×Dic61—21no—
283C22×Dic61—21no—
284C22×Dic61—21no—
285C22×Dic61—21no—
286C22×Dic61—21no—
287C22×Dic61—21no—
288C22×Dic61—21no—
289C22×Dic61C22×C412yes—
290C22×Dic61C22×C412yes—
291C22×Dic61C2×D412yes—
292C22×Dic61C2×D412yes—
293C22×Dic61C2×D412yes—
294C22×Dic61C2×D412yes—
295C22×Dic61C2×D412yes—
296C22×Dic61C2×D412yes—
297C22×Dic61#4112yes—
298C2×D244—28no—
299C2×D244—28no—
300C2×D244—28no—
301C2×D244—28no—
302C2×D244—28no—
303C2×D244—28no—
304C2×D244C4⋊C4116yescomplemented
305C2×C4×D61—28no—
306C2×C4×D61—28no—
307C2×C4×D61—28no—
308C2×C4×D61—28no—
309C2×C4×D61—28no—
310C2×C4×D61—28no—
311C2×C4×D61—28no—
312C2×C4×D61—28no—
313C2×C4×D61—28no—
314C2×C4×D61—28no—
315C2×C4×D61—28no—
316C2×C4×D61—44no—
317C2×C4×D61—44no—
318C2×C4×D61—44no—
319C2×C4×D61—44no—
320C2×C4×D61—44no—
321C2×C4×D61—44no—
322C2×C4×D61—44no—
323C2×C4×D61—44no—
324C2×C4×D61—44no—
325C2×C4×D61—44no—
326C2×C4×D61—44no—
327C2×C4×D61—44no—
328C2×C4×D61—44no—
329C2×C4×D61—44no—
330C2×C4×D61—44no—
331C2×C4×D61—44no—
332C2×C4×D61—44no—
333C4⋊C4×C61—28no—
334C4⋊C4×C61—28no—
335C4⋊C4×C61—44no—
336#11758198—28no—
337#11758198—28no—
338#11758198—28no—
339#11758198—28no—
340#11758198—28no—
341#11758198—44no—
342#11758198—44no—
343#11758198—44no—
344C4⋊Dic61—28no—
345#11758196—28no—
346#11758196—28no—
347#11758196—44no—
348C4×Dic61—28no—
349C23×C61C23×C411yescharacteristic
350C23×C61C22×D411yescharacteristic
351C23×C61C22×D411yescharacteristic
352C23×C61C22×D411yescharacteristic
353C23×C61C22×D411yescharacteristic
354C23×C61C22×D411yescharacteristic
355C23×C61C22×Q811yescharacteristic
356C23×C61C2×#4111yescharacteristic
357C23×C61C2×#4111yescharacteristic
358C23×C61C2×#4111yescharacteristic
359C23×C61C2×#4111yescharacteristic
360C23×C61H(5,𝔽2)11yescharacteristic
361C23×C61H(5,𝔽2)11yescharacteristic
362C23×C612−1+411yescharacteristic
363C23×C612−1+411yescharacteristic
364C22×D61—22no—
365C22×D61—22no—
366C22×D61—22no—
367C22×D61—22no—
368C22×D61—22no—
369C22×D61—22no—
370C22×D61—22no—
371C22×D61—22no—
372C22×D61—22no—
373C22×D61—22no—
374C22×D61—22no—
375C22×D61—22no—
376C22×D61—22no—
377C22×D61—22no—
378C22×D61—22no—
379C22×D61—22no—
380C22×D61—22no—
381C22×D61—22no—
382C22×D61—22no—
383C22×D61—22no—
384C22×D61—22no—
385C22×D61—22no—
386C22×D61—22no—
387C22×D61—22no—
388C22×D61—22no—
389C22×D61—22no—
390C22×D61—22no—
391C22×D61—22no—
392C22×D61—22no—
393C22×D61—22no—
394C22×D61—22no—
395C22×D61—22no—
396C22×D61—22no—
397C22×D61—22no—
398C22×D61—22no—
399C22×D61—22no—
400C22×D61—22no—
401C22×D61—22no—
402C22×D61—22no—
403C22×D61—22no—
404C22×D61—22no—
405C22×D61—22no—
406C22×D61—22no—
407C22×D61—22no—
408C22×D61—22no—
409C22×D61—22no—
410C22×D61—41no—
411C22×D61—41no—
412C22×D61—41no—
413C22×D61—41no—
414C22×D61—41no—
415C22×D61—41no—
416C22×D61—41no—
417C22×D61—41no—
418C22×D61—41no—
419C22×D61—41no—
420C22×D61—41no—
421C22×D61—41no—
422C22×D61—41no—
423C22×D61—41no—
424C22×D61—41no—
425C22×D61—41no—
426C22×D61C2×C4⋊C414yes—
427C22×D61C2×C4⋊C414yescomplemented
428C22×D61C4×D414yes—
429C22×D61C4×D414yes—
430C22×D61#12014yes—
431C22×D61C22⋊Q814yes—
432C22×D61C22⋊Q814yes—
433C22×D61#12314yes—
434C2×C4×C61—22no—
435C2×C4×C61—22no—
436C2×C4×C61—22no—
437C2×C4×C61—22no—
438C2×C4×C61—22no—
439C2×C4×C61—22no—
440C2×C4×C61—22no—
441C2×C4×C61—22no—
442C2×C4×C61—22no—
443C2×C4×C61—22no—
444C2×C4×C61—22no—
445C2×C4×C61—22no—
446C2×C4×C61—22no—
447C2×C4×C61—22no—
448C2×C4×C61—22no—
449C2×C4×C61—22no—
450C2×C4×C61—22no—
451C2×C4×C61—22no—
452C2×C4×C61—22no—
453C2×C4×C61—22no—
454C2×C4×C61—22no—
455C2×C4×C61—22no—
456C2×C4×C61—22no—
457C2×C4×C61—22no—
458C2×C4×C61—41no—
459C2×C4×C61—41no—
460C2×C4×C61—41no—
461C2×C4×C61—41no—
462C2×C4×C61—41no—
463C2×C4×C61—41no—
464C2×C4×C61—41no—
465C2×C4×C61—41no—
466C2×C4×C61—41no—
467C2×C4×C61—41no—
468C2×C4×C61—41no—
469C2×C4×C61—41no—
470C2×C4×C61—41no—
471C2×C4×C61—41no—
472C2×C4×C61—41no—
473C2×C4×C61—41no—
474C2×C4×C61—41no—
475C2×C4×C61—41no—
476C2×C4×C61—41no—
477C2×C4×C61—41no—
478C2×C4×C61—41no—
479C2×C4×C61—41no—
480C2×C4×C61—41no—
481C2×C4×C61C2×C4⋊C414yescomplemented
482C2×C4×C61C4×D414yescomplemented
483C2×Dic61—22no—
484C2×Dic61—22no—
485C2×Dic61—22no—
486C2×Dic61—22no—
487C2×Dic61—22no—
488C2×Dic61—22no—
489C2×Dic61—22no—
490C2×Dic61—22no—
491C2×Dic61—22no—
492C2×Dic61—22no—
493C2×Dic61—22no—
494C2×Dic61—22no—
495C2×Dic61—22no—
496C2×Dic61—22no—
497C2×Dic61—22no—
498C2×Dic61—22no—
499C2×Dic61—22no—
500C2×Dic61—22no—
501C2×Dic61—22no—
502C2×Dic61—22no—
503C2×Dic61—22no—
504C2×Dic61—41no—
505C2×Dic61—41no—
506C2×Dic61—41no—
507C2×Dic61—41no—
508C2×Dic61—41no—
509C2×Dic61—41no—
510C2×Dic61—41no—
511C2×Dic61—41no—
512C2×Dic61—41no—
513C2×Dic61—41no—
514C2×Dic61—41no—
515C2×Dic61—41no—
516C2×Dic61—41no—
517C2×Dic61—41no—
518C2×Dic61—41no—
519C2×Dic61—41no—
520C2×Dic61—41no—
521C2×Dic61—41no—
522C2×Dic61—41no—
523C2×Dic61C4×D414yescomplemented
524C2×Dic61#12014yes—
525D244—232no—
526C4×D61—232no—
527C4×D61—416no—
528C4×D61—416no—
529C4×D61—416no—
530#14015—611nomaximal, Sylow
531C22×C61C22×C4⋊C411yescharacteristic
532C22×C61C2×C4×D411yescharacteristic
533C22×C61C2×C4×D411yescharacteristic
534C22×C61C2×C4×D411yescharacteristic
535C22×C61C2×C4×D411yescharacteristic
536C22×C61#52011yescharacteristic
537C22×C61#52011yescharacteristic
538C22×C61C2×#12011yescharacteristic
539C22×C61C2×#12011yescharacteristic
540C22×C61C2×C22⋊Q811yescharacteristic
541C22×C61C2×C22⋊Q811yescharacteristic
542C22×C61C2×#12311yescharacteristic
543C22×C61#52511yescharacteristic
544C22×C61#52511yescharacteristic
545C22×C61#52511yescharacteristic
546C22×C61#53411yescharacteristic
547C22×C61#53611yescharacteristic
548C22×C61#53911yescharacteristic
549C22×C61#53911yescharacteristic
550C22×C61D4211yescharacteristic
551C22×C61D4211yescharacteristic
552C22×C61D4211yescharacteristic
553C22×C61D4211yescharacteristic
554C22×C61#54711yescharacteristic
555C22×C61#54711yescharacteristic
556C22×C61#54711yescharacteristic
557C22×C61#54711yescharacteristic
558C22×C61#54811yescharacteristic
559C22×C61#54811yescharacteristic
560C22×C61D4×Q811yescharacteristic
561C22×C61D4×Q811yescharacteristic
562C22×C61#55311yescharacteristic
563C22×C61#55311yescharacteristic
564C22×C61#55411yescharacteristic
565C22×C61#55411yescharacteristic
566C2×D61—24no—
567C2×D61—24no—
568C2×D61—24no—
569C2×D61—24no—
570C2×D61—24no—
571C2×D61—24no—
572C2×D61—24no—
573C2×D61—24no—
574C2×D61—24no—
575C2×D61—24no—
576C2×D61—24no—
577C2×D61—24no—
578C2×D61—24no—
579C2×D61—24no—
580C2×D61—24no—
581C2×D61—24no—
582C2×D61—24no—
583C2×D61—42no—
584C2×D61—42no—
585C2×D61—42no—
586C2×D61—42no—
587C2×D61—42no—
588C2×D61—42no—
589C2×D61—42no—
590C2×D61—42no—
591C2×D61—42no—
592C2×D61—42no—
593C2×D61—42no—
594C2×D61—42no—
595C2×D61#38518yescomplemented
596C4×C61—24no—
597C4×C61—24no—
598C4×C61—42no—
599C4×C61—42no—
600C4×C61—42no—
601C4×C61—42no—
602C4×C61—81no—
603Dic61—24no—
604Dic61—24no—
605Dic61—42no—
606Dic61—42no—
607Dic61—42no—
608Dic61—81no—
609C22×C4×D4—611no—
610C23×C4⋊C4—611no—
611C2×#386—611no—
612C2×#386—611no—
613C2×#385—611no—
614C2×#385—611no—
615C2×#385—611no—
616#1444—611no—
617#1444D6111yescharacteristic, complemented
618#1439—611no—
619#1439—611no—
620#1436—611no—
621#1436—611no—
622C22⋊#95—611no—
623C22⋊#95—611no—
624C2×C61C2×#38511yescharacteristic
625C2×C61C4×#12011yescharacteristic
626C2×C61#232211yescharacteristic
627C2×C61D4×C4⋊C411yescharacteristic
628C2×C61D4×C4⋊C411yescharacteristic
629C2×C61#236111yescharacteristic
630C2×C61#236111yescharacteristic
631C2×C61#240311yescharacteristic
632C2×C61#240611yescharacteristic
633C2×C61#240911yescharacteristic
634C2×C61#244311yescharacteristic
635C2×C61#244311yescharacteristic
636C2×C61#244911yescharacteristic
637C2×C61#244911yescharacteristic
638C2×C61#257911yescharacteristic
639D61—28no—
640D61—44no—
641C23×D4—611no—
642C24×C4—611no—
643C24×C4—611no—
644C24×C4—611no—
645C24×C4—611no—
646C2×C4×D4—1224no—
647C2×C4×D4—1224no—
648C2×C4×D4—1224no—
649C22×C4⋊C4—611no—
650C22×C4⋊C4—611no—
651C22×C4⋊C4—611no—
652C22×C4⋊C4—611no—
653C22×C4⋊C4—1224no—
654C22×C4⋊C4—1224no—
655C22×C4⋊C4—1224no—
656C22×C4⋊C4C2×D6111yescharacteristic
657C22×C4⋊C4C2×D6111yescharacteristic
658C22×C4⋊C4C2×D6111yescharacteristic
659C22×C22⋊C4—611no—
660C22×C22⋊C4—611no—
661C22×C22⋊C4—611no—
662C22×C22⋊C4—611no—
663C22×C22⋊C4—611no—
664C22×C22⋊C4—611no—
665C22×C22⋊C4—611no—
666C22×C22⋊C4—611no—
667C22×C42—611no—
668#386—618no—
669#386—1224no—
670#385—1224no—
671#385—1224no—
672#385—1224no—
673C2×#95—611no—
674C2×#95—611no—
675C2×#95—611no—
676C2×#95—611no—
677C2×#95—611no—
678C2×#95—611no—
679C2×#95—611no—
680C2×#95—611no—
681C2×#95—611no—
682C2×#95—611no—
683C2×#95C2×D6111yescharacteristic
684C2×#95C2×D6111yescharacteristic
685C2×#95C2×D6111yescharacteristic
686C2×#95C2×D6111yescharacteristic
687C61#1401511yescharacteristic, complemented, Sylow
688C25—611no—
689C25—611no—
690C22×D4—614no—
691C22×D4—614no—
692C22×D4—614no—
693C22×D4—1222no—
694C22×D4—1222no—
695C22×D4—1222no—
696C22×D4—1222no—
697C23×C4—611no—
698C23×C4—611no—
699C23×C4—611no—
700C23×C4—611no—
701C23×C4—611no—
702C23×C4—614no—
703C23×C4—614no—
704C23×C4—611no—
705C23×C4—1222no—
706C23×C4—1222no—
707C23×C4—1222no—
708C23×C4—1222no—
709C23×C4—1222no—
710C23×C4—1222no—
711C23×C4—1222no—
712C23×C4—1222no—
713C23×C4—1222no—
714C23×C4—1222no—
715C23×C4—1222no—
716C23×C4—1222no—
717C23×C4—1222no—
718C23×C4—1222no—
719C23×C4—1222no—
720C23×C4—1222no—
721C23×C4—1222no—
722C23×C4—1222no—
723C23×C4—1222no—
724C23×C4—1222no—
725C23×C4—2441no—
726C23×C4—2441no—
727C23×C4—2441no—
728C23×C4—2441no—
729C23×C4—2441no—
730C23×C4—2441no—
731C23×C4C22×D6111yescharacteristic
732C23×C4C22×D6111yescharacteristic
733C23×C4C22×D6111yescharacteristic
734C23×C4C22×D6111yescharacteristic
735C23×C4C22×D6111yescharacteristic
736C23×C4C22×D6111yescharacteristic
737C23×C4C22×D6111yescharacteristic
738C4×D4—12232no—
739C2×C4⋊C4—22no—
740C2×C4⋊C4—22no—
741C2×C4⋊C4—22no—
742C2×C4⋊C4—22no—
743C2×C4⋊C4—22no—
744C2×C4⋊C4—22no—
745C2×C4⋊C4—22no—
746C2×C4⋊C4—22no—
747C2×C4⋊C4—41no—
748C2×C4⋊C4—614no—
749C2×C4⋊C4—614no—
750C2×C4⋊C4—12232no—
751C2×C4⋊C4—1222no—
752C2×C4⋊C4—1222no—
753C2×C4⋊C4—1222no—
754C2×C4⋊C4—1222no—
755C2×C4⋊C4—1222no—
756C2×C4⋊C4—1222no—
757C2×C4⋊C4—1222no—
758C2×C4⋊C4—1222no—
759C2×C4⋊C4—1222no—
760C2×C4⋊C4—2441no—
761C2×C22⋊C4—614no—
762C2×C22⋊C4—614no—
763C2×C22⋊C4—614no—
764C2×C22⋊C4—614no—
765C2×C22⋊C4—1222no—
766C2×C22⋊C4—1222no—
767C2×C22⋊C4—1222no—
768C2×C22⋊C4—1222no—
769C2×C22⋊C4—1222no—
770C2×C22⋊C4—1222no—
771C2×C22⋊C4—1222no—
772C2×C22⋊C4—1222no—
773C2×C22⋊C4—1222no—
774C2×C22⋊C4—1222no—
775C2×C22⋊C4—1222no—
776C2×C22⋊C4—1222no—
777C2×C22⋊C4—1222no—
778C2×C22⋊C4—1222no—
779C2×C22⋊C4—1222no—
780C2×C22⋊C4—1222no—
781C2×C22⋊C4—1222no—
782C2×C22⋊C4—1222no—
783C2×C22⋊C4—2441no—
784C2×C22⋊C4—2441no—
785C2×C42—1222no—
786C2×C42—1222no—
787C2×C42—1222no—
788#95—22no—
789#95—22no—
790#95—41no—
791#95—614no—
792#95—1222no—
793#95—1222no—
794#95—1222no—
795#95—1222no—
796#95—1222no—
797#95—1222no—
798#95—1222no—
799#95—1222no—
800#95—2441no—
801#95C4×D6114yescomplemented
802C24—612no—
803C24—612no—
804C24—612no—
805C24—612no—
806C24—612no—
807C24—612no—
808C24—612no—
809C24—612no—
810C24—612no—
811C24—612no—
812C24—1221no—
813C24—1221no—
814C24—1221no—
815C24—1221no—
816C24—1221no—
817C24—1221no—
818C24—1221no—
819C24—1221no—
820C24—1221no—
821C24—1221no—
822C24—1221no—
823C24—1221no—
824C24—1221no—
825C24—1221no—
826C24—1221no—
827C24—1221no—
828C24—1221no—
829C24—1221no—
830C24—1221no—
831C24—1221no—
832C24C23×D6111yescharacteristic
833C2×D4—6116no—
834C2×D4—1228no—
835C2×D4—1228no—
836C2×D4—1228no—
837C2×D4—1228no—
838C2×D4—1228no—
839C2×D4—1228no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—612no—
880C22×C4—612no—
881C22×C4—612no—
882C22×C4—612no—
883C22×C4—612no—
884C22×C4—612no—
885C22×C4—612no—
886C22×C4—612no—
887C22×C4—612no—
888C22×C4—1228no—
889C22×C4—1228no—
890C22×C4—1228no—
891C22×C4—1228no—
892C22×C4—1228no—
893C22×C4—1228no—
894C22×C4—1228no—
895C22×C4—1228no—
896C22×C4—1228no—
897C22×C4—1228no—
898C22×C4—1221no—
899C22×C4—1221no—
900C22×C4—1221no—
901C22×C4—1221no—
902C22×C4—1221no—
903C22×C4—1221no—
904C22×C4—1221no—
905C22×C4—1221no—
906C22×C4—1228no—
907C22×C4—1221no—
908C22×C4—1221no—
909C22×C4—1221no—
910C22×C4—1221no—
911C22×C4—1221no—
912C22×C4—1221no—
913C22×C4—1221no—
914C22×C4—1221no—
915C22×C4—1221no—
916C22×C4—1221no—
917C22×C4—1221no—
918C22×C4—1221no—
919C22×C4—1221no—
920C22×C4—1221no—
921C22×C4—1221no—
922C22×C4—1221no—
923C22×C4—1221no—
924C22×C4—1221no—
925C22×C4—1221no—
926C22×C4—1221no—
927C22×C4—1221no—
928C22×C4—1221no—
929C22×C4—1221no—
930C22×C4—1221no—
931C22×C4—1221no—
932C22×C4—2444no—
933C22×C4—2444no—
934C22×C4—2444no—
935C22×C4—2444no—
936C22×C4—2444no—
937C22×C4—2444no—
938C22×C4—2444no—
939C22×C4—2444no—
940C22×C4—2444no—
941C22×C4—2444no—
942C22×C4—2444no—
943C22×C4—2444no—
944C22×C4—2444no—
945C22×C4—2444no—
946C22×C4—2444no—
947C22×C4—2444no—
948C22×C4—2444no—
949C22×C4C2×C4×D6112yes—
950C22×C4C2×C4×D6112yes—
951C22×C4C2×C4×D6112yes—
952C22×C4D4×D6112yes—
953C22×C4D4×D6112yes—
954C22×C4D4×D6112yes—
955C22×C4D4×D6112yes—
956C22×C4D4×D6112yes—
957C22×C4Q8×D6112yes—
958C22×C4#1175822612yes—
959C4⋊C4—28no—
960C4⋊C4—28no—
961C4⋊C4—44no—
962C4⋊C4—1228no—
963C4⋊C4—1228no—
964C4⋊C4—1228no—
965C4⋊C4—2444no—
966C22⋊C4—1228no—
967C22⋊C4—1228no—
968C22⋊C4—1228no—
969C22⋊C4—1228no—
970C22⋊C4—1228no—
971C22⋊C4—2444no—
972C22⋊C4—2444no—
973C22⋊C4—2444no—
974C42—1228no—
975C23—614no—
976C23—614no—
977C23—614no—
978C23—614no—
979C23—614no—
980C23—614no—
981C23—614no—
982C23—614no—
983C23—1222no—
984C23—1222no—
985C23—1222no—
986C23—1222no—
987C23—1222no—
988C23—1222no—
989C23—1222no—
990C23—1222no—
991C23—1222no—
992C23—1222no—
993C23—1222no—
994C23—1222no—
995C23—1222no—
996C23—1222no—
997C23—1222no—
998C23—1222no—
999C23—1222no—
1000C23—1222no—
1001C23—1222no—
1002C23—1222no—
1003C23—1222no—
1004C23—1222no—
1005C23—1222no—
1006C23—1222no—
1007C23—1222no—
1008C23—1222no—
1009C23—1222no—
1010C23—1222no—
1011C23—1222no—
1012C23—1222no—
1013C23—1222no—
1014C23—1222no—
1015C23—1222no—
1016C23—1222no—
1017C23—1222no—
1018C23—1222no—
1019C23—1222no—
1020C23—1222no—
1021C23—1222no—
1022C23—1222no—
1023C23—1222no—
1024C23—1222no—
1025C23—1222no—
1026C23—1222no—
1027C23—1222no—
1028C23—1222no—
1029C23—2441no—
1030C23—2441no—
1031C23—2441no—
1032C23—2441no—
1033C23—2441no—
1034C23—2441no—
1035C23—2441no—
1036C23—2441no—
1037C23—2441no—
1038C23—2441no—
1039C23—2441no—
1040C23—2441no—
1041C23—2441no—
1042C23—2441no—
1043C23—2441no—
1044C23—2441no—
1045C23C22×C4×D6111yescharacteristic
1046C23C2×D4×D6111yescharacteristic
1047C23C2×D4×D6111yescharacteristic
1048C23C2×D4×D6111yescharacteristic
1049C23C2×D4×D6111yescharacteristic
1050C23C2×D4×D6111yescharacteristic
1051C23C2×Q8×D6111yescharacteristic
1052C23#41×D6111yescharacteristic
1053C23#41×D6111yescharacteristic
1054C23#41×D6111yescharacteristic
1055C23C2×#1175822611yescharacteristic
1056C23#1451982211yescharacteristic
1057C23#1451982311yescharacteristic
1058C23#1451982511yescharacteristic
1059C23#1451982511yescharacteristic
1060D4—12232no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—614no—
1109C2×C4—614no—
1110C2×C4—12232no—
1111C2×C4—1222no—
1112C2×C4—1222no—
1113C2×C4—1222no—
1114C2×C4—1222no—
1115C2×C4—1222no—
1116C2×C4—1222no—
1117C2×C4—1222no—
1118C2×C4—1222no—
1119C2×C4—1222no—
1120C2×C4—1222no—
1121C2×C4—1222no—
1122C2×C4—1222no—
1123C2×C4—1222no—
1124C2×C4—1222no—
1125C2×C4—1222no—
1126C2×C4—1222no—
1127C2×C4—1222no—
1128C2×C4—1222no—
1129C2×C4—1222no—
1130C2×C4—1222no—
1131C2×C4—1222no—
1132C2×C4—24416no—
1133C2×C4—24416no—
1134C2×C4—24416no—
1135C2×C4—2441no—
1136C2×C4—2441no—
1137C2×C4—2441no—
1138C2×C4—2441no—
1139C2×C4—2441no—
1140C2×C4—2441no—
1141C2×C4—2441no—
1142C2×C4—2441no—
1143C2×C4—2441no—
1144C2×C4—2441no—
1145C2×C4—2441no—
1146C2×C4—2441no—
1147C2×C4—2441no—
1148C2×C4—2441no—
1149C2×C4—2441no—
1150C2×C4—2441no—
1151C2×C4—2441no—
1152C2×C4—2441no—
1153C2×C4—2441no—
1154C2×C4C4⋊C4×D6114yescomplemented
1155C2×C4#1451973914yescomplemented
1156C22—618no—
1157C22—1224no—
1158C22—1224no—
1159C22—1224no—
1160C22—1224no—
1161C22—1224no—
1162C22—1224no—
1163C22—1224no—
1164C22—1224no—
1165C22—1224no—
1166C22—1224no—
1167C22—1224no—
1168C22—1224no—
1169C22—1224no—
1170C22—1224no—
1171C22—1224no—
1172C22—1224no—
1173C22—1224no—
1174C22—2442no—
1175C22—2442no—
1176C22—2442no—
1177C22—2442no—
1178C22—2442no—
1179C22—2442no—
1180C22—2442no—
1181C22—2442no—
1182C22—2442no—
1183C22—2442no—
1184C22—2442no—
1185C22—2442no—
1186C22C2×C4⋊C4×D6111yescharacteristic
1187C22C4×D4×D6111yescharacteristic
1188C22C4×D4×D6111yescharacteristic
1189C22C4×D4×D6111yescharacteristic
1190C22C2×#1451973911yescharacteristic
1191C22#1684024311yescharacteristic
1192C22#1684024411yescharacteristic
1193C22#120×D6111yescharacteristic
1194C22#120×D6111yescharacteristic
1195C22C22⋊Q8×D6111yescharacteristic
1196C22C22⋊Q8×D6111yescharacteristic
1197C22#123×D6111yescharacteristic
1198C22#1684027011yescharacteristic
1199C22#1684027511yescharacteristic
1200C22#1684027511yescharacteristic
1201C22#1684032011yescharacteristic
1202C22#1684033711yescharacteristic
1203C22#1684035811yescharacteristic
1204C22#1684036011yescharacteristic
1205C22#1684039411yescharacteristic
1206C22#1684039611yescharacteristic
1207C22#1684039611yescharacteristic
1208C22#1684039711yescharacteristic
1209C22#1684041411yescharacteristic
1210C22#1684041411yescharacteristic
1211C22#1684041511yescharacteristic
1212C22#1684041511yescharacteristic
1213C22#1684042211yescharacteristic
1214C22#1684042211yescharacteristic
1215C22#1684042711yescharacteristic
1216C22#1684042711yescharacteristic
1217C22#1684045711yescharacteristic
1218C22#1684046511yescharacteristic
1219C22#1684046811yescharacteristic
1220C22#1684047311yescharacteristic
1221C4—24no—
1222C4—24no—
1223C4—42no—
1224C4—42no—
1225C4—42no—
1226C4—42no—
1227C4—81no—
1228C4—1224no—
1229C4—1224no—
1230C4—4881no—
1231C4—2442no—
1232C4—2442no—
1233C4—2442no—
1234C2—1228no—
1235C2—2444no—
1236C2#385×D6111yescharacteristic
1237C2#2144832011yescharacteristic
1238C2#2144848311yescharacteristic
1239C2#2144871911yescharacteristic
1240C2#2144872011yescharacteristic
1241C2#2144883411yescharacteristic
1242C2#2144883811yescharacteristic
1243C2#2144912811yescharacteristic
1244C2#2144915511yescharacteristic
1245C2#2144917911yescharacteristic
1246C2#2144955511yescharacteristic
1247C2#2144955711yescharacteristic
1248C2#2144962111yescharacteristic
1249C2#2144962311yescharacteristic
1250C2#2145116711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1444C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1444D61
hypocenterC61#14015
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D61C2semidirect
5. C2×#16839636C2semidirect
6. C2×#16839633C2semidirect
7. C2×#16839633C2semidirect
8. #21444082C2semidirect
9. #21444063C2semidirect
10. #21444061C2semidirect
11. #21444053C2semidirect
12. #21444050C2semidirect
13. #21444040C2semidirect
14. #21444040C2semidirect
15. C61×#1444C2semidirect
41. #16839640C4semidirect
103. C22×C4×D61C2×C4semidirect
108. C2×C4⋊Dic61D4semidirect
117. C2×#11758196D4semidirect
139. C2×#11758198C2×C4semidirect
140. C2×#11758198C2×C4semidirect
141. C2×#11758198C2×C4semidirect
155. #14519684C2×C4semidirect
175. #95×C61C2×C4semidirect
304. C2×D244C4⋊C4semidirect
427. C22×D61C2×C4⋊C4semidirect
481. C2×C4×C61C2×C4⋊C4semidirect
482. C2×C4×C61C4×D4semidirect
523. C2×Dic61C4×D4semidirect
595. C2×D61#385semidirect
617. #1444D61semidirect
687. C61#14015semidirect
801. #95C4×D61semidirect
1154. C2×C4C4⋊C4×D61semidirect
1155. C2×C4#14519739semidirect

Maximal subgroups

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

subgroupindex
C22×#145197392
C22×C4⋊C4×D612
C2×#168396402
C2×#168396362
C2×#168396332
#214440822
#214440632
#214440612
#214440532
#214440502
#214440402
C61×#14442
#1401561