Finite Group Databasebeta

← #29603376

Subgroups — #29603376

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×#14519737C211yesmaximal, characteristic
2C22×C4⋊C4×D61C211yesmaximal, characteristic, complemented
3C2×#16839638C211yesmaximal, characteristic
4C2×#16839638C211yesmaximal, characteristic
5C2×#16839637C211yesmaximal, characteristic, complemented
6C2×#16839636C211yesmaximal, characteristic, complemented
7C2×#16839634C211yesmaximal, characteristic, complemented
8#21444083C211yesmaximal, characteristic, complemented
9#21444082C211yesmaximal, characteristic, complemented
10#21444062C211yesmaximal, characteristic, complemented
11#21444053C211yesmaximal, characteristic, complemented
12#21444050C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C24×Dic61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C2×#14519737—24no—
22C2×#14519737—24no—
23C2×#14519737—24no—
24C22×C4⋊Dic61C2211yescharacteristic
25C22×C4⋊Dic61C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C2×C4⋊C4×D61—24no—
31C2×C4⋊C4×D61—24no—
32C2×C4⋊C4×D61—24no—
33C22×C22⋊Dic61C2211yescharacteristic
34C22×C22⋊Dic61C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×C4×Dic61C2211yescharacteristic
39#16839638—24no—
40#16839638C418yescomplemented
41#16839637—24no—
42#16839636—24no—
43#16839634—24no—
44C2×#14519684C2211yescharacteristic
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×C22⋊C4×C61C2211yescharacteristic
57C22×C22⋊C4×C61C2211yescharacteristic
58C22×C22⋊C4×C61C2211yescharacteristic
59C2×#95×C61C2211yescharacteristic
60C2×#95×C61C2211yescharacteristic
61C2×#95×C61C2211yescharacteristic
62C24×D61C2311yescharacteristic
63C22×C22⋊D61—22no—
64C22×C22⋊D61—22no—
65C22×C22⋊D61—22no—
66C22×C22⋊D61—22no—
67C22×C22⋊D61C2×C414yes—
68C22×C22⋊D61D414yes—
69C22×C22⋊D61Q814yes—
70C23×Dic61—22no—
71C23×Dic61—22no—
72C23×Dic61—22no—
73C23×Dic61—22no—
74C23×Dic61—22no—
75C23×Dic61—41no—
76C23×Dic61—41no—
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
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—22no—
98C22×C4×D61—22no—
99C22×C4×D61—41no—
100C22×C4×D61—41no—
101C22×C4×D61—41no—
102C22×C4×D61—41no—
103C22×C4×D61C2×C414yescomplemented
104C22×C4×D61D414yes—
105#14519737—232no—
106C2×C4⋊Dic61—22no—
107C2×C4⋊Dic61—22no—
108C2×C4⋊Dic61—22no—
109C2×C4⋊Dic61—22no—
110C2×C4⋊Dic61—41no—
111C2×C4⋊Dic61D414yescomplemented
112C2×#11758196—22no—
113C2×#11758196—22no—
114C2×#11758196—22no—
115C2×#11758196—22no—
116C2×#11758196—22no—
117C2×#11758196—22no—
118C2×#11758196—22no—
119C2×#11758196—22no—
120C2×#11758196—22no—
121C2×#11758196—22no—
122C2×#11758196—41no—
123C2×#11758196D414yescomplemented
124C4⋊C4×D61—232no—
125C2×C22⋊Dic61—22no—
126C2×C22⋊Dic61—22no—
127C2×C22⋊Dic61—22no—
128C2×C22⋊Dic61—22no—
129C2×C22⋊Dic61—41no—
130C2×C22⋊Dic61C2×C414yescomplemented
131C2×#11758198—22no—
132C2×#11758198—22no—
133C2×#11758198—22no—
134C2×#11758198—22no—
135C2×#11758198—22no—
136C2×#11758198—22no—
137C2×#11758198—22no—
138C2×#11758198C2×C414yescomplemented
139C2×#11758198D414yes—
140C2×C4×Dic61—22no—
141C2×C4×Dic61—22no—
142C2×C4×Dic61—22no—
143#14519684—22no—
144#14519684—22no—
145#14519684—22no—
146#14519684—22no—
147#14519684—22no—
148#14519684—22no—
149#14519684—22no—
150#14519684—22no—
151#14519684—41no—
152#14519684C2×C414yescomplemented
153#14519684C2×C414yescomplemented
154C25×C61C2311yescharacteristic
155C23×C4×C61C2311yescharacteristic
156C23×C4×C61C2311yescharacteristic
157C23×C4×C61C2311yescharacteristic
158C23×C4×C61C2311yescharacteristic
159C23×C4×C61C2311yescharacteristic
160C23×C4×C61C2311yescharacteristic
161C2×C4⋊C4×C61—22no—
162C2×C4⋊C4×C61—22no—
163C2×C4⋊C4×C61—22no—
164C2×C22⋊C4×C61—22no—
165C2×C22⋊C4×C61—22no—
166C2×C22⋊C4×C61—22no—
167C2×C22⋊C4×C61—22no—
168C2×C22⋊C4×C61—22no—
169C2×C22⋊C4×C61—22no—
170C2×C22⋊C4×C61—22no—
171C2×C22⋊C4×C61—41no—
172C2×C22⋊C4×C61C2×C414yescomplemented
173#95×C61—22no—
174#95×C61—22no—
175#95×C61—41no—
176C24×C61—21no—
177C24×C61—21no—
178C24×C61—21no—
179C24×C61—21no—
180C24×C61—21no—
181C24×C61—21no—
182C24×C61—21no—
183C24×C61—21no—
184C24×C61—21no—
185C24×C61—21no—
186C24×C61—21no—
187C24×C61—21no—
188C24×C61C22×C412yes—
189C24×C61C2×D412yes—
190C24×C61C2×Q812yes—
191C24×C61C2411yescharacteristic
192C23×D61—21no—
193C23×D61—21no—
194C23×D61—21no—
195C23×D61—21no—
196C23×D61—21no—
197C23×D61—21no—
198C23×D61—21no—
199C23×D61—21no—
200C23×D61C22×C412yes—
201C23×D61C2×D412yes—
202C23×D61C2×D412yes—
203C23×D61C2×D412yes—
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×C61C22×C412yes—
243C22×C4×C61C22×C412yes—
244C22×C4×C61C2×D412yes—
245C22×C4×C61C2×D412yes—
246C22×C4×C61C2×D412yes—
247C22×C4×C61C2×D412yes—
248C22×C4×C61#4112yes—
249C2×C22⋊D61—28no—
250C2×C22⋊D61—28no—
251C2×C22⋊D61—28no—
252C2×C22⋊D61—28no—
253C2×C22⋊D61—28no—
254C2×C22⋊D61—28no—
255C2×C22⋊D61C4⋊C4116yescomplemented
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—28no—
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×Dic61—21no—
290C22×Dic61—21no—
291C22×Dic61—21no—
292C22×Dic61—21no—
293C22×Dic61—21no—
294C22×Dic61—44no—
295C22×Dic61—44no—
296C22×Dic61—44no—
297C22×Dic61—44no—
298C22×Dic61—44no—
299C22×Dic61—44no—
300C22×Dic61C22×C412yes—
301C22×Dic61C22×C412yes—
302C22×Dic61C22×C412yes—
303C22×Dic61C2×D412yes—
304C22×Dic61C2×D412yes—
305C22×Dic61C2×D412yes—
306C22×Dic61C2×D412yes—
307C22×Dic61C2×D412yes—
308C22×Dic61C2×D412yes—
309C22×Dic61C2×D412yes—
310C22×Dic61C2×Q812yes—
311C22×Dic61#4112yes—
312C2×C4×D61—28no—
313C2×C4×D61—28no—
314C2×C4×D61—28no—
315C2×C4×D61—28no—
316C2×C4×D61—28no—
317C2×C4×D61—28no—
318C2×C4×D61—28no—
319C2×C4×D61—28no—
320C2×C4×D61—28no—
321C2×C4×D61—28no—
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—
334C22⋊C4×C61—28no—
335C22⋊C4×C61—28no—
336C22⋊C4×C61—44no—
337C22⋊Dic61—28no—
338C22⋊Dic61—44no—
339#11758198—28no—
340#11758198—28no—
341#11758198—44no—
342C4⋊Dic61—28no—
343C4⋊Dic61—44no—
344#11758196—28no—
345#11758196—28no—
346#11758196—28no—
347#11758196—44no—
348C4×Dic61—28no—
349C23×C61—22no—
350C23×C61—22no—
351C23×C61—22no—
352C23×C61—22no—
353C23×C61—22no—
354C23×C61—22no—
355C23×C61—22no—
356C23×C61—22no—
357C23×C61—22no—
358C23×C61—22no—
359C23×C61—22no—
360C23×C61—22no—
361C23×C61—22no—
362C23×C61—22no—
363C23×C61—22no—
364C23×C61—22no—
365C23×C61—22no—
366C23×C61—22no—
367C23×C61—41no—
368C23×C61—41no—
369C23×C61—41no—
370C23×C61—41no—
371C23×C61—41no—
372C23×C61—41no—
373C23×C61—41no—
374C23×C61—41no—
375C23×C61—41no—
376C23×C61—41no—
377C23×C61—41no—
378C23×C61—41no—
379C23×C61—41no—
380C23×C61—41no—
381C23×C61—41no—
382C23×C61—41no—
383C23×C61C2×C4⋊C414yescomplemented
384C23×C61C23×C411yescharacteristic
385C23×C61C22×D411yescharacteristic
386C23×C61C22×D411yescharacteristic
387C23×C61C22×D411yescharacteristic
388C23×C61C22×D411yescharacteristic
389C23×C61C22×D411yescharacteristic
390C23×C61C22×Q811yescharacteristic
391C23×C61C2×#4111yescharacteristic
392C23×C61C2×#4111yescharacteristic
393C23×C61C2×#4111yescharacteristic
394C23×C61C2×#4111yescharacteristic
395C23×C61H(5,𝔽2)11yescharacteristic
396C23×C61H(5,𝔽2)11yescharacteristic
397C23×C612−1+411yescharacteristic
398C23×C612−1+411yescharacteristic
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—22no—
411C22×D61—22no—
412C22×D61—22no—
413C22×D61—22no—
414C22×D61—22no—
415C22×D61—22no—
416C22×D61—22no—
417C22×D61—22no—
418C22×D61—22no—
419C22×D61—22no—
420C22×D61—22no—
421C22×D61—22no—
422C22×D61—22no—
423C22×D61—22no—
424C22×D61—22no—
425C22×D61—22no—
426C22×D61—22no—
427C22×D61C2×C4⋊C414yes—
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—41no—
453C2×C4×C61—41no—
454C2×C4×C61—41no—
455C2×C4×C61—41no—
456C2×C4×C61—41no—
457C2×C4×C61—41no—
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×C61C4×D414yescomplemented
476C22⋊D61—232no—
477C2×Dic61—22no—
478C2×Dic61—22no—
479C2×Dic61—22no—
480C2×Dic61—22no—
481C2×Dic61—22no—
482C2×Dic61—22no—
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—416no—
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×Dic61—41no—
524C2×Dic61C2×C4⋊C414yescomplemented
525C2×Dic61C4×D414yescomplemented
526C2×Dic61#12014yes—
527C4×D61—232no—
528C4×D61—416no—
529C4×D61—416no—
530#14015—611nomaximal, Sylow
531C22×C61—24no—
532C22×C61—24no—
533C22×C61—24no—
534C22×C61—42no—
535C22×C61—42no—
536C22×C61—42no—
537C22×C61—42no—
538C22×C61—42no—
539C22×C61—42no—
540C22×C61—42no—
541C22×C61—42no—
542C22×C61—42no—
543C22×C61—42no—
544C22×C61—42no—
545C22×C61—42no—
546C22×C61C22×C4⋊C411yescharacteristic
547C22×C61C2×C4×D411yescharacteristic
548C22×C61C2×C4×D411yescharacteristic
549C22×C61C2×C4×D411yescharacteristic
550C22×C61C2×C4×D411yescharacteristic
551C22×C61#52011yescharacteristic
552C22×C61#52011yescharacteristic
553C22×C61C2×#12011yescharacteristic
554C22×C61C2×#12011yescharacteristic
555C22×C61C2×C22⋊Q811yescharacteristic
556C22×C61C2×C22⋊Q811yescharacteristic
557C22×C61C2×#12311yescharacteristic
558C22×C61#52511yescharacteristic
559C22×C61#52511yescharacteristic
560C22×C61#52511yescharacteristic
561C22×C61#53411yescharacteristic
562C22×C61#53611yescharacteristic
563C22×C61#53911yescharacteristic
564C22×C61#53911yescharacteristic
565C22×C61D4211yescharacteristic
566C22×C61D4211yescharacteristic
567C22×C61D4211yescharacteristic
568C22×C61D4211yescharacteristic
569C22×C61#54711yescharacteristic
570C22×C61#54711yescharacteristic
571C22×C61#54711yescharacteristic
572C22×C61#54711yescharacteristic
573C22×C61#54811yescharacteristic
574C22×C61#54811yescharacteristic
575C22×C61D4×Q811yescharacteristic
576C22×C61D4×Q811yescharacteristic
577C22×C61#55311yescharacteristic
578C22×C61#55311yescharacteristic
579C22×C61#55411yescharacteristic
580C22×C61#55411yescharacteristic
581C2×D61—24no—
582C2×D61—24no—
583C2×D61—24no—
584C2×D61—24no—
585C2×D61—24no—
586C2×D61—24no—
587C2×D61—24no—
588C2×D61—24no—
589C2×D61—24no—
590C2×D61—24no—
591C2×D61—24no—
592C2×D61—24no—
593C2×D61—24no—
594C2×D61—24no—
595C2×D61#38518yescomplemented
596C4×C61—24no—
597C4×C61—42no—
598C4×C61—42no—
599C4×C61—42no—
600C4×C61—42no—
601C4×C61—81no—
602Dic61—24no—
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#1444—611no—
618#1439—611no—
619#1439D6111yescharacteristic, complemented
620#1436—611no—
621#1436—611no—
622C22⋊#95—611no—
623C22⋊#95—611no—
624C2×C61—44no—
625C2×C61C2×#38511yescharacteristic
626C2×C61C4×#12011yescharacteristic
627C2×C61#232211yescharacteristic
628C2×C61D4×C4⋊C411yescharacteristic
629C2×C61D4×C4⋊C411yescharacteristic
630C2×C61#236111yescharacteristic
631C2×C61#236111yescharacteristic
632C2×C61#240311yescharacteristic
633C2×C61#240611yescharacteristic
634C2×C61#240911yescharacteristic
635C2×C61#244311yescharacteristic
636C2×C61#244311yescharacteristic
637C2×C61#244911yescharacteristic
638C2×C61#244911yescharacteristic
639C2×C61#257911yescharacteristic
640D61—28no—
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—611no—
654C22×C4⋊C4—611no—
655C22×C4⋊C4—1224no—
656C22×C4⋊C4—1224no—
657C22×C4⋊C4—1224no—
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⋊C4C2×D6111yescharacteristic
665C22×C22⋊C4C2×D6111yescharacteristic
666C22×C22⋊C4C2×D6111yescharacteristic
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×#95—611no—
684C2×#95C2×D6111yescharacteristic
685C2×#95C2×D6111yescharacteristic
686C2×#95C2×D6111yescharacteristic
687C61#1401511yescharacteristic, complemented, Sylow
688C25—611no—
689C25C22×D6111yescharacteristic
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—611no—
703C23×C4—614no—
704C23×C4—614no—
705C23×C4—611no—
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—1222no—
726C23×C4—2441no—
727C23×C4—2441no—
728C23×C4—2441no—
729C23×C4—2441no—
730C23×C4—2441no—
731C23×C4—2441no—
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—614no—
743C2×C4⋊C4—614no—
744C2×C4⋊C4—12232no—
745C2×C4⋊C4—1222no—
746C2×C4⋊C4—1222no—
747C2×C4⋊C4—1222no—
748C2×C4⋊C4—1222no—
749C2×C4⋊C4—1222no—
750C2×C4⋊C4—1222no—
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—2441no—
760C2×C4⋊C4—2441no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—41no—
769C2×C22⋊C4—614no—
770C2×C22⋊C4—614no—
771C2×C22⋊C4—614no—
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⋊C4C4×D6114yescomplemented
785C2×C42—1222no—
786C2×C42—1222no—
787C2×C42—1222no—
788#95—22no—
789#95—22no—
790#95—41no—
791#95—614no—
792#95—614no—
793#95—1222no—
794#95—1222no—
795#95—1222no—
796#95—1222no—
797#95—1222no—
798#95—1222no—
799#95—1222no—
800#95—1222no—
801#95—2441no—
802C24—21no—
803C24—21no—
804C24—21no—
805C24—21no—
806C24—21no—
807C24—21no—
808C24—21no—
809C24—21no—
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—612no—
815C24—612no—
816C24—612no—
817C24—612no—
818C24—612no—
819C24—612no—
820C24—612no—
821C24—1221no—
822C24—1221no—
823C24—1221no—
824C24—1221no—
825C24—1221no—
826C24—1221no—
827C24—1221no—
828C24—1221no—
829C24C2×C4×D6112yes—
830C24D4×D6112yes—
831C24Q8×D6112yes—
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—612no—
876C22×C4—612no—
877C22×C4—612no—
878C22×C4—612no—
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—1228no—
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—1221no—
897C22×C4—1221no—
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—1221no—
907C22×C4—1221no—
908C22×C4—1228no—
909C22×C4—1228no—
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—1221no—
933C22×C4—1221no—
934C22×C4—1221no—
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×C4—2444no—
950C22×C4—2444no—
951C22×C4—2444no—
952C22×C4C2×C4×D6112yes—
953C22×C4C2×C4×D6112yes—
954C22×C4D4×D6112yes—
955C22×C4D4×D6112yes—
956C22×C4D4×D6112yes—
957C22×C4D4×D6112yes—
958C22×C4#1175822412yes—
959C4⋊C4—28no—
960C4⋊C4—1228no—
961C4⋊C4—1228no—
962C4⋊C4—1228no—
963C4⋊C4—1228no—
964C4⋊C4—2444no—
965C4⋊C4—2444no—
966C22⋊C4—28no—
967C22⋊C4—28no—
968C22⋊C4—44no—
969C22⋊C4—1228no—
970C22⋊C4—1228no—
971C22⋊C4—1228no—
972C22⋊C4—2444no—
973C22⋊C4—2444no—
974C42—1228no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—614no—
1010C23—614no—
1011C23—614no—
1012C23—614no—
1013C23—614no—
1014C23—614no—
1015C23—614no—
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—1222no—
1030C23—1222no—
1031C23—1222no—
1032C23—1222no—
1033C23—1222no—
1034C23—1222no—
1035C23—1222no—
1036C23—1222no—
1037C23—1222no—
1038C23—1222no—
1039C23—1222no—
1040C23—1222no—
1041C23—1222no—
1042C23—1222no—
1043C23—1222no—
1044C23C4⋊C4×D6114yescomplemented
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×#1175822411yescharacteristic
1056C23#1451982211yescharacteristic
1057C23#1451982311yescharacteristic
1058C23#1451982411yescharacteristic
1059C23#1451982411yescharacteristic
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—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
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—614no—
1103C2×C4—614no—
1104C2×C4—614no—
1105C2×C4—12232no—
1106C2×C4—1222no—
1107C2×C4—1222no—
1108C2×C4—1222no—
1109C2×C4—1222no—
1110C2×C4—1222no—
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—1222no—
1133C2×C4—24416no—
1134C2×C4—24416no—
1135C2×C4—24416no—
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×C4—2441no—
1155C2×C4#1451973714yescomplemented
1156C22—24no—
1157C22—24no—
1158C22—24no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22—42no—
1168C22—42no—
1169C22—42no—
1170C22—42no—
1171C22—618no—
1172C22—1224no—
1173C22—1224no—
1174C22—1224no—
1175C22—1224no—
1176C22—1224no—
1177C22—1224no—
1178C22—1224no—
1179C22—1224no—
1180C22—1224no—
1181C22—1224no—
1182C22—1224no—
1183C22—1224no—
1184C22—1224no—
1185C22—1224no—
1186C22C2×C4⋊C4×D6111yescharacteristic
1187C22C4×D4×D6111yescharacteristic
1188C22C4×D4×D6111yescharacteristic
1189C22C4×D4×D6111yescharacteristic
1190C22C2×#1451973711yescharacteristic
1191C22#1684024111yescharacteristic
1192C22#1684024211yescharacteristic
1193C22#120×D6111yescharacteristic
1194C22#120×D6111yescharacteristic
1195C22C22⋊Q8×D6111yescharacteristic
1196C22C22⋊Q8×D6111yescharacteristic
1197C22#123×D6111yescharacteristic
1198C22#1684027011yescharacteristic
1199C22#1684027211yescharacteristic
1200C22#1684027211yescharacteristic
1201C22#1684032011yescharacteristic
1202C22#1684033211yescharacteristic
1203C22#1684035311yescharacteristic
1204C22#1684035511yescharacteristic
1205C22#1684039411yescharacteristic
1206C22#1684039611yescharacteristic
1207C22#1684039611yescharacteristic
1208C22#1684039711yescharacteristic
1209C22#1684041011yescharacteristic
1210C22#1684041011yescharacteristic
1211C22#1684041211yescharacteristic
1212C22#1684041211yescharacteristic
1213C22#1684042011yescharacteristic
1214C22#1684042011yescharacteristic
1215C22#1684042511yescharacteristic
1216C22#1684042511yescharacteristic
1217C22#1684045911yescharacteristic
1218C22#1684046311yescharacteristic
1219C22#1684046611yescharacteristic
1220C22#1684047011yescharacteristic
1221C4—24no—
1222C4—42no—
1223C4—42no—
1224C4—42no—
1225C4—42no—
1226C4—81no—
1227C4—1224no—
1228C4—1224no—
1229C4—1224no—
1230C4—4881no—
1231C4—2442no—
1232C4—2442no—
1233C4—2442no—
1234C2—44no—
1235C2—1228no—
1236C2#385×D6111yescharacteristic
1237C2#2144832411yescharacteristic
1238C2#2144848911yescharacteristic
1239C2#2144871511yescharacteristic
1240C2#2144871711yescharacteristic
1241C2#2144883211yescharacteristic
1242C2#2144884011yescharacteristic
1243C2#2144912811yescharacteristic
1244C2#2144914911yescharacteristic
1245C2#2144917711yescharacteristic
1246C2#2144954711yescharacteristic
1247C2#2144954911yescharacteristic
1248C2#2144962911yescharacteristic
1249C2#2144963111yescharacteristic
1250C2#2145116111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1439C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenter#1439D61
hypocenterC61#14015
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D61C2semidirect
5. C2×#16839637C2semidirect
6. C2×#16839636C2semidirect
7. C2×#16839634C2semidirect
8. #21444083C2semidirect
9. #21444082C2semidirect
10. #21444062C2semidirect
11. #21444053C2semidirect
12. #21444050C2semidirect
13. #21444040C2semidirect
14. #21444040C2semidirect
15. C61×#1439C2semidirect
40. #16839638C4semidirect
103. C22×C4×D61C2×C4semidirect
111. C2×C4⋊Dic61D4semidirect
123. C2×#11758196D4semidirect
130. C2×C22⋊Dic61C2×C4semidirect
138. C2×#11758198C2×C4semidirect
152. #14519684C2×C4semidirect
153. #14519684C2×C4semidirect
172. C2×C22⋊C4×C61C2×C4semidirect
255. C2×C22⋊D61C4⋊C4semidirect
383. C23×C61C2×C4⋊C4semidirect
475. C2×C4×C61C4×D4semidirect
524. C2×Dic61C2×C4⋊C4semidirect
525. C2×Dic61C4×D4semidirect
595. C2×D61#385semidirect
619. #1439D61semidirect
687. C61#14015semidirect
784. C2×C22⋊C4C4×D61semidirect
1044. C23C4⋊C4×D61semidirect
1155. C2×C4#14519737semidirect

Maximal subgroups

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

subgroupindex
C22×#145197372
C22×C4⋊C4×D612
C2×#168396382
C2×#168396372
C2×#168396362
C2×#168396342
#214440832
#214440822
#214440622
#214440532
#214440502
#214440402
C61×#14392
#1401561