Finite Group Databasebeta

← #29603465

Subgroups — #29603465

Order 15616.

3166 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519751C211yesmaximal, characteristic
2C22×C4×C22⋊D61C211yesmaximal, characteristic, complemented
3C2×#16839641C211yesmaximal, characteristic, complemented
4C2×#16839641C211yesmaximal, characteristic, complemented
5C2×#16839641C211yesmaximal, characteristic, complemented
6C2×#16839640C211yesmaximal, characteristic, complemented
7#21444071C211yesmaximal, characteristic, complemented
8#21444067C211yesmaximal, characteristic, complemented
9#21444063C211yesmaximal, characteristic, complemented
10#21444059C211yesmaximal, characteristic, complemented
11#21444055C211yesmaximal, characteristic, complemented
12#21444053C211yesmaximal, characteristic, complemented
13#21444042C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C22×#95×C61C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C22⋊D61C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519751—24no—
21C2×#14519751—24no—
22C2×#14519751C418yescomplemented
23C2×C4×C22⋊D61—24no—
24C2×C4×C22⋊D61—24no—
25C2×C4×C22⋊D61—24no—
26C22×C4⋊Dic61C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic
40#16839641—24no—
41#16839641—24no—
42#16839641—24no—
43#16839640—24no—
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C24×C4×C61C2211yescharacteristic
55C24×C4×C61C2211yescharacteristic
56C24×C4×C61C2211yescharacteristic
57C2×#95×C61—24no—
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×D244—41no—
69C22×D244—41no—
70C22×D244C2×C414yescomplemented
71C22×C22⋊D61—22no—
72C22×C22⋊D61—22no—
73C22×C22⋊D61—22no—
74C22×C22⋊D61—22no—
75C22×C22⋊D61—22no—
76C22×C22⋊D61—22no—
77C22×C22⋊D61—22no—
78C22×C22⋊D61—22no—
79C22×C22⋊D61—22no—
80C22×C22⋊D61—22no—
81C22×C22⋊D61C2×C414yes—
82C22×C22⋊D61C2×C414yescomplemented
83C22×C22⋊D61D414yes—
84C22×C22⋊D61D414yes—
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89C23×Dic61C2311yescharacteristic
90C23×Dic61C2311yescharacteristic
91C22×C4×D61—22no—
92C22×C4×D61—22no—
93C22×C4×D61—22no—
94C22×C4×D61—22no—
95C22×C4×D61—22no—
96C22×C4×D61—41no—
97C22×C4×D61—41no—
98#14519751—232no—
99C4×C22⋊D61—232no—
100C2×C4⋊Dic61—22no—
101C2×C4⋊Dic61—22no—
102C2×C4⋊Dic61C2×C414yescomplemented
103C2×#11758196—22no—
104C2×#11758196—22no—
105C2×#11758196—22no—
106C2×C22⋊Dic61—22no—
107C2×C22⋊Dic61—22no—
108C2×C22⋊Dic61—22no—
109C2×C22⋊Dic61—22no—
110C2×C22⋊Dic61—22no—
111C2×C22⋊Dic61D414yescomplemented
112C2×#11758198—22no—
113C2×#11758198—22no—
114C2×#11758198—22no—
115C2×#11758198—22no—
116C2×#11758198—22no—
117C2×#11758198—22no—
118C2×#11758198—22no—
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—41no—
132C2×#11758198—41no—
133C2×#11758198—41no—
134C2×#11758198—41no—
135C2×#11758198—41no—
136C2×#11758198—41no—
137C2×#11758198C2×C414yescomplemented
138C2×#11758198C2×C414yescomplemented
139C2×C4×Dic61—22no—
140C2×C4×Dic61—22no—
141C2×C4×Dic61—22no—
142#14519684—22no—
143#14519684—22no—
144#14519684—22no—
145#14519684—22no—
146#14519684—22no—
147#14519684—22no—
148#14519684—22no—
149#14519684—22no—
150#14519684—41no—
151#14519684—41no—
152C25×C61C2311yescharacteristic
153C23×C4×C61—22no—
154C23×C4×C61—22no—
155C23×C4×C61—22no—
156C23×C4×C61—22no—
157C23×C4×C61—22no—
158C23×C4×C61—22no—
159C23×C4×C61—22no—
160C23×C4×C61—22no—
161C23×C4×C61—22no—
162C23×C4×C61—22no—
163C23×C4×C61—22no—
164C23×C4×C61—22no—
165C23×C4×C61—22no—
166C23×C4×C61—41no—
167C23×C4×C61—41no—
168C23×C4×C61—41no—
169C23×C4×C61—41no—
170C23×C4×C61—41no—
171C23×C4×C61—41no—
172C23×C4×C61C2×C414yescomplemented
173C23×C4×C61D414yescomplemented
174C23×C4×C61C2311yescharacteristic
175C23×C4×C61C2311yescharacteristic
176C23×C4×C61C2311yescharacteristic
177C23×C4×C61C2311yescharacteristic
178C23×C4×C61C2311yescharacteristic
179C23×C4×C61C2311yescharacteristic
180#95×C61—22no—
181#95×C61—22no—
182#95×C61—22no—
183#95×C61D414yescomplemented
184C24×C61—21no—
185C24×C61—21no—
186C24×C61—21no—
187C24×C61—21no—
188C24×C61—21no—
189C24×C61—21no—
190C24×C61—21no—
191C24×C61—21no—
192C24×C61C22×C412yes—
193C24×C61C2×D412yes—
194C24×C61C2×D412yes—
195C24×C61C2×D412yes—
196C24×C61C2×D412yes—
197C24×C61#4112yes—
198C24×C61#4112yes—
199C24×C61C2411yescharacteristic
200C23×D61—21no—
201C23×D61—21no—
202C23×D61—21no—
203C23×D61—21no—
204C23×D61—21no—
205C23×D61—21no—
206C23×D61—21no—
207C23×D61—21no—
208C23×D61—21no—
209C23×D61—21no—
210C23×D61—21no—
211C23×D61—21no—
212C23×D61—21no—
213C23×D61—21no—
214C23×D61—21no—
215C23×D61—21no—
216C23×D61—21no—
217C23×D61—21no—
218C23×D61—21no—
219C23×D61—21no—
220C23×D61—21no—
221C23×D61—21no—
222C23×D61—21no—
223C23×D61—21no—
224C23×D61—21no—
225C23×D61—21no—
226C23×D61C22×C412yes—
227C23×D61C22×C412yes—
228C23×D61C2×D412yes—
229C23×D61C2×D412yes—
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—28no—
239C22×C4×C61—28no—
240C22×C4×C61—28no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61—21no—
252C22×C4×C61—21no—
253C22×C4×C61—21no—
254C22×C4×C61—21no—
255C22×C4×C61—21no—
256C22×C4×C61—21no—
257C22×C4×C61—21no—
258C22×C4×C61—21no—
259C22×C4×C61—21no—
260C22×C4×C61—21no—
261C22×C4×C61—21no—
262C22×C4×C61—21no—
263C22×C4×C61—21no—
264C22×C4×C61—21no—
265C22×C4×C61—28no—
266C22×C4×C61—28no—
267C22×C4×C61—44no—
268C22×C4×C61—44no—
269C22×C4×C61—44no—
270C22×C4×C61—44no—
271C22×C4×C61—44no—
272C22×C4×C61—44no—
273C22×C4×C61—44no—
274C22×C4×C61—44no—
275C22×C4×C61—44no—
276C22×C4×C61—44no—
277C22×C4×C61—44no—
278C22×C4×C61—44no—
279C22×C4×C61—44no—
280C22×C4×C61—44no—
281C22×C4×C61—44no—
282C22×C4×C61—44no—
283C22×C4×C61C22×C412yes—
284C22×C4×C61C22×C412yes—
285C22×C4×C61C2×D412yes—
286C22×C4×C61C2×D412yes—
287C22×C4×C61C2×D412yes—
288C22×C4×C61C2×D412yes—
289C22×C4×C61C2×D412yes—
290C22×C4×C61#4112yes—
291C22×C4×C61#4112yes—
292C22×C4×C61#4112yes—
293C2×C22⋊D61—28no—
294C2×C22⋊D61—28no—
295C2×C22⋊D61—28no—
296C2×C22⋊D61—28no—
297C2×C22⋊D61—28no—
298C2×C22⋊D61—28no—
299C2×C22⋊D61—28no—
300C2×C22⋊D61—28no—
301C2×C22⋊D61—28no—
302C2×C22⋊D61—44no—
303C2×C22⋊D61—44no—
304C2×C22⋊D61—44no—
305C2×C22⋊D61—44no—
306C2×C22⋊D61C22⋊C4116yescomplemented
307C22×Dic61—21no—
308C22×Dic61—21no—
309C22×Dic61—21no—
310C22×Dic61—21no—
311C22×Dic61—21no—
312C22×Dic61—21no—
313C22×Dic61—21no—
314C22×Dic61—21no—
315C22×Dic61—21no—
316C22×Dic61—21no—
317C22×Dic61—21no—
318C22×Dic61—21no—
319C22×Dic61—21no—
320C22×Dic61—21no—
321C22×Dic61—21no—
322C22×Dic61—21no—
323C22×Dic61—21no—
324C22×Dic61—21no—
325C22×Dic61—21no—
326C22×Dic61—21no—
327C22×Dic61—21no—
328C22×Dic61—21no—
329C22×Dic61—21no—
330C22×Dic61—21no—
331C22×Dic61—21no—
332C22×Dic61—21no—
333C22×Dic61—21no—
334C22×Dic61—21no—
335C22×Dic61—21no—
336C22×Dic61—21no—
337C22×Dic61—21no—
338C22×Dic61—21no—
339C22×Dic61—21no—
340C22×Dic61—21no—
341C22×Dic61—21no—
342C22×Dic61—21no—
343C22×Dic61C22×C412yes—
344C22×Dic61C22×C412yes—
345C22×Dic61C2×D412yes—
346C22×Dic61C2×D412yes—
347C22×Dic61C2×D412yes—
348C22×Dic61C2×D412yes—
349C2×D244—28no—
350C2×D244—28no—
351C2×D244—44no—
352C2×D244—44no—
353C2×D244—44no—
354C2×D244—44no—
355C2×D244—44no—
356C2×C4×D61—28no—
357C2×C4×D61—44no—
358C2×C4×D61—44no—
359C2×C4×D61—44no—
360C2×C4×D61—44no—
361C2×C4×D61—44no—
362C2×C4×D61—44no—
363C22⋊Dic61—28no—
364C22⋊Dic61—44no—
365#11758198—28no—
366#11758198—28no—
367#11758198—28no—
368#11758198—44no—
369#11758198—44no—
370#11758198—44no—
371#11758198—44no—
372#11758198—44no—
373#11758198—44no—
374C4⋊Dic61—28no—
375#11758196—28no—
376C4×Dic61—28no—
377C23×C61—22no—
378C23×C61—22no—
379C23×C61—22no—
380C23×C61—22no—
381C23×C61—22no—
382C23×C61—22no—
383C23×C61—22no—
384C23×C61—22no—
385C23×C61—22no—
386C23×C61—22no—
387C23×C61—22no—
388C23×C61—22no—
389C23×C61—22no—
390C23×C61—22no—
391C23×C61—22no—
392C23×C61—22no—
393C23×C61—22no—
394C23×C61—22no—
395C23×C61—22no—
396C23×C61—22no—
397C23×C61—22no—
398C23×C61—22no—
399C23×C61—22no—
400C23×C61—22no—
401C23×C61—22no—
402C23×C61—22no—
403C23×C61—22no—
404C23×C61—22no—
405C23×C61C2×C22⋊C414yes—
406C23×C61C4×D414yes—
407C23×C61C4×D414yes—
408C23×C61#12014yes—
409C23×C61#12114yes—
410C23×C61#12114yes—
411C23×C61#12314yes—
412C23×C61C23×C411yescharacteristic
413C23×C61C22×D411yescharacteristic
414C23×C61C22×D411yescharacteristic
415C23×C61C22×D411yescharacteristic
416C23×C61C22×D411yescharacteristic
417C23×C61C22×D411yescharacteristic
418C23×C61C2×#4111yescharacteristic
419C23×C61C2×#4111yescharacteristic
420C23×C61C2×#4111yescharacteristic
421C23×C61C2×#4111yescharacteristic
422C23×C61C2×#4111yescharacteristic
423C23×C61H(5,𝔽2)11yescharacteristic
424C23×C61H(5,𝔽2)11yescharacteristic
425C23×C61H(5,𝔽2)11yescharacteristic
426C23×C612−1+411yescharacteristic
427C22×D61—22no—
428C22×D61—22no—
429C22×D61—22no—
430C22×D61—22no—
431C22×D61—22no—
432C22×D61—22no—
433C22×D61—22no—
434C22×D61—22no—
435C22×D61—22no—
436C22×D61—22no—
437C22×D61—22no—
438C22×D61—22no—
439C22×D61—22no—
440C22×D61—22no—
441C22×D61—22no—
442C22×D61—22no—
443C22×D61—22no—
444C22×D61—22no—
445C22×D61—22no—
446C22×D61—22no—
447C22×D61—22no—
448C22×D61—22no—
449C22×D61—22no—
450C22×D61—22no—
451C22×D61—22no—
452C22×D61—41no—
453C22×D61—41no—
454C22×D61—41no—
455C22×D61—41no—
456C22×D61—41no—
457C22×D61—41no—
458C22×D61—41no—
459C22×D61—41no—
460C22×D61—41no—
461C22×D61—41no—
462C22×D61—41no—
463C22×D61—41no—
464C22×D61—41no—
465C22×D61—41no—
466C22×D61—41no—
467C22×D61—41no—
468C22×D61—41no—
469C22×D61—41no—
470C22×D61—41no—
471C22×D61—41no—
472C22×D61—41no—
473C22×D61—41no—
474C22×D61—41no—
475C22×D61—41no—
476C22×D61—41no—
477C22×D61—41no—
478C22×D61—41no—
479C22×D61—41no—
480C22×D61—41no—
481C22×D61—41no—
482C22×D61—41no—
483C22×D61—41no—
484C22×D61—41no—
485C22×D61—41no—
486C22×D61—41no—
487C22×D61—41no—
488C22×D61—41no—
489C22×D61—41no—
490C22×D61—41no—
491C22×D61—41no—
492C22×D61—41no—
493C22×D61—41no—
494C22×D61—41no—
495C22×D61—41no—
496C22×D61C2×C22⋊C414yes—
497C2×C4×C61—22no—
498C2×C4×C61—22no—
499C2×C4×C61—22no—
500C2×C4×C61—22no—
501C2×C4×C61—22no—
502C2×C4×C61—22no—
503C2×C4×C61—22no—
504C2×C4×C61—22no—
505C2×C4×C61—22no—
506C2×C4×C61—22no—
507C2×C4×C61—22no—
508C2×C4×C61—22no—
509C2×C4×C61—22no—
510C2×C4×C61—22no—
511C2×C4×C61—22no—
512C2×C4×C61—22no—
513C2×C4×C61—22no—
514C2×C4×C61—22no—
515C2×C4×C61—22no—
516C2×C4×C61—22no—
517C2×C4×C61—22no—
518C2×C4×C61—22no—
519C2×C4×C61—22no—
520C2×C4×C61—22no—
521C2×C4×C61—416no—
522C2×C4×C61—416no—
523C2×C4×C61—416no—
524C2×C4×C61—41no—
525C2×C4×C61—41no—
526C2×C4×C61—41no—
527C2×C4×C61—41no—
528C2×C4×C61—41no—
529C2×C4×C61—41no—
530C2×C4×C61—41no—
531C2×C4×C61—41no—
532C2×C4×C61—41no—
533C2×C4×C61—41no—
534C2×C4×C61—41no—
535C2×C4×C61—41no—
536C2×C4×C61—41no—
537C2×C4×C61—41no—
538C2×C4×C61—41no—
539C2×C4×C61—41no—
540C2×C4×C61C4×D414yescomplemented
541C2×C4×C61#12114yescomplemented
542C22⋊D61—232no—
543C22⋊D61—416no—
544C2×Dic61—22no—
545C2×Dic61—22no—
546C2×Dic61—22no—
547C2×Dic61—22no—
548C2×Dic61—22no—
549C2×Dic61—22no—
550C2×Dic61—22no—
551C2×Dic61—22no—
552C2×Dic61—22no—
553C2×Dic61—22no—
554C2×Dic61—22no—
555C2×Dic61—22no—
556C2×Dic61—22no—
557C2×Dic61—22no—
558C2×Dic61—22no—
559C2×Dic61—41no—
560C2×Dic61—41no—
561C2×Dic61—41no—
562C2×Dic61—41no—
563C2×Dic61—41no—
564C2×Dic61—41no—
565C2×Dic61—41no—
566C2×Dic61—41no—
567C2×Dic61—41no—
568C2×Dic61—41no—
569C2×Dic61—41no—
570C2×Dic61—41no—
571C2×Dic61—41no—
572C2×Dic61—41no—
573C2×Dic61—41no—
574C2×Dic61—41no—
575C2×Dic61—41no—
576C2×Dic61—41no—
577C2×Dic61—41no—
578C2×Dic61—41no—
579C2×Dic61—41no—
580C2×Dic61—41no—
581C2×Dic61—41no—
582C2×Dic61—41no—
583C2×Dic61—41no—
584C2×Dic61—41no—
585C2×Dic61C2×C22⋊C414yes—
586D244—416no—
587C4×D61—416no—
588#14023—611nomaximal, Sylow
589C22×C61—24no—
590C22×C61—24no—
591C22×C61—24no—
592C22×C61—24no—
593C22×C61—24no—
594C22×C61—24no—
595C22×C61—24no—
596C22×C61—24no—
597C22×C61—24no—
598C22×C61—24no—
599C22×C61—24no—
600C22×C61—24no—
601C22×C61—24no—
602C22×C61—24no—
603C22×C61#38618yescomplemented
604C22×C61C22×C22⋊C411yescharacteristic
605C22×C61C2×C4×D411yescharacteristic
606C22×C61C2×C4×D411yescharacteristic
607C22×C61C2×C4×D411yescharacteristic
608C22×C61C4×#4111yescharacteristic
609C22×C61#51811yescharacteristic
610C22×C61#52011yescharacteristic
611C22×C61C2×#12011yescharacteristic
612C22×C61C2×#12111yescharacteristic
613C22×C61C2×#12111yescharacteristic
614C22×C61C2×#12111yescharacteristic
615C22×C61C2×#12311yescharacteristic
616C22×C61#52511yescharacteristic
617C22×C61#52911yescharacteristic
618C22×C61#53211yescharacteristic
619C22×C61#53411yescharacteristic
620C22×C61#53711yescharacteristic
621C22×C61#53811yescharacteristic
622C22×C61#53911yescharacteristic
623C22×C61D4211yescharacteristic
624C22×C61D4211yescharacteristic
625C22×C61D4211yescharacteristic
626C22×C61#54611yescharacteristic
627C22×C61#54611yescharacteristic
628C22×C61#54611yescharacteristic
629C22×C61#54611yescharacteristic
630C22×C61#54611yescharacteristic
631C22×C61#54611yescharacteristic
632C22×C61#54711yescharacteristic
633C22×C61#54711yescharacteristic
634C22×C61#54711yescharacteristic
635C22×C61#54811yescharacteristic
636C22×C61#55311yescharacteristic
637C22×C61#55311yescharacteristic
638C22×C61#55311yescharacteristic
639C2×D61—24no—
640C2×D61—24no—
641C2×D61—24no—
642C2×D61—42no—
643C2×D61—42no—
644C2×D61—42no—
645C2×D61—42no—
646C2×D61—42no—
647C2×D61—42no—
648C2×D61—42no—
649C2×D61—42no—
650C2×D61—42no—
651C2×D61—42no—
652C2×D61—42no—
653C2×D61—42no—
654C2×D61—42no—
655C2×D61—42no—
656C2×D61—42no—
657C2×D61—42no—
658C2×D61—42no—
659C2×D61—42no—
660C2×D61—42no—
661C2×D61—81no—
662C2×D61—81no—
663C2×D61—81no—
664C2×D61—81no—
665C2×D61—81no—
666C2×D61—81no—
667C2×D61—81no—
668C2×D61—81no—
669C4×C61—24no—
670C4×C61—24no—
671C4×C61—42no—
672C4×C61—42no—
673C4×C61—42no—
674C4×C61—42no—
675Dic61—24no—
676Dic61—42no—
677Dic61—42no—
678Dic61—42no—
679Dic61—81no—
680Dic61—81no—
681C22×#121—611no—
682C22×C4×D4—611no—
683C2×#386—611no—
684C2×#386—611no—
685C2×#386—611no—
686C2×#386—611no—
687C22×#95D6111yescharacteristic, complemented
688#1441—611no—
689#1440—611no—
690#1439—611no—
691#1438—611no—
692#1437—611no—
693#1436—611no—
694C22⋊#95—611no—
695C22⋊#95—611no—
696C2×C61—28no—
697C2×C61C2×#38611yescharacteristic
698C2×C61C4×#12111yescharacteristic
699C2×C61#232511yescharacteristic
700C2×C61D4×C22⋊C411yescharacteristic
701C2×C61#233911yescharacteristic
702C2×C61#236111yescharacteristic
703C2×C61#236411yescharacteristic
704C2×C61#241011yescharacteristic
705C2×C61#241611yescharacteristic
706C2×C61#242411yescharacteristic
707C2×C61#242511yescharacteristic
708C2×C61#243011yescharacteristic
709C2×C61#244311yescharacteristic
710C2×C61#244411yescharacteristic
711C2×C61#254311yescharacteristic
712D61—44no—
713D61—82no—
714C23×D4—611no—
715C23×D4—611no—
716C23×D4—611no—
717C24×C4—611no—
718C24×C4C2×D6111yescharacteristic
719C24×C4C2×D6111yescharacteristic
720C24×C4C2×D6111yescharacteristic
721C2×#121—618no—
722C2×#121—1224no—
723C2×#121—1224no—
724C2×C4×D4—1224no—
725C2×C4×D4—1224no—
726C2×C4×D4—1224no—
727C22×C4⋊C4—611no—
728C22×C4⋊C4—611no—
729C22×C22⋊C4—611no—
730C22×C22⋊C4—611no—
731C22×C22⋊C4—611no—
732C22×C22⋊C4—611no—
733C22×C22⋊C4—611no—
734C22×C22⋊C4—611no—
735C22×C22⋊C4—611no—
736C22×C22⋊C4—611no—
737C22×C22⋊C4—611no—
738C22×C22⋊C4—611no—
739C22×C22⋊C4—611no—
740C22×C42—611no—
741#386—1224no—
742#386—1224no—
743#386—1224no—
744#386—1224no—
745C2×#95—24no—
746C2×#95—611no—
747C2×#95—611no—
748C2×#95—611no—
749C2×#95—611no—
750C2×#95—611no—
751C2×#95—611no—
752C2×#95—611no—
753C2×#95—611no—
754C2×#95—611no—
755C2×#95—611no—
756C2×#95C2×D6111yescharacteristic
757C2×#95C2×D6111yescharacteristic
758C2×#95C2×D6111yescharacteristic
759C2×#95C2×D6111yescharacteristic
760C61#1402311yescharacteristic, complemented, Sylow
761C25—611no—
762C25—611no—
763C25C22×D6111yescharacteristic
764C22×D4—614no—
765C22×D4—614no—
766C22×D4—614no—
767C22×D4—614no—
768C22×D4—614no—
769C22×D4—1222no—
770C22×D4—1222no—
771C22×D4—1222no—
772C22×D4—1222no—
773C22×D4—1222no—
774C22×D4—1222no—
775C22×D4—1222no—
776C22×D4—1222no—
777C22×D4—1222no—
778C22×D4—1222no—
779C22×D4—1222no—
780C22×D4—1222no—
781C22×D4—1222no—
782C22×D4—1222no—
783C22×D4—2441no—
784C22×D4—2441no—
785C23×C4—22no—
786C23×C4—22no—
787C23×C4—22no—
788C23×C4—22no—
789C23×C4—22no—
790C23×C4—22no—
791C23×C4—22no—
792C23×C4—22no—
793C23×C4—22no—
794C23×C4—22no—
795C23×C4—22no—
796C23×C4—22no—
797C23×C4—22no—
798C23×C4—41no—
799C23×C4—41no—
800C23×C4—41no—
801C23×C4—41no—
802C23×C4—41no—
803C23×C4—41no—
804C23×C4—611no—
805C23×C4—611no—
806C23×C4—611no—
807C23×C4—611no—
808C23×C4—611no—
809C23×C4—611no—
810C23×C4—1222no—
811C23×C4—1222no—
812C23×C4—1222no—
813C23×C4—1222no—
814C23×C4—1222no—
815C23×C4—2441no—
816C23×C4—2441no—
817C23×C4C4×D6114yescomplemented
818C23×C4D24414yescomplemented
819C23×C4C22×D6111yescharacteristic
820C23×C4C22×D6111yescharacteristic
821C23×C4C22×D6111yescharacteristic
822C23×C4C22×D6111yescharacteristic
823C23×C4C22×D6111yescharacteristic
824C23×C4C22×D6111yescharacteristic
825#121—12232no—
826C4×D4—12232no—
827C2×C4⋊C4—614no—
828C2×C4⋊C4—1222no—
829C2×C4⋊C4—1222no—
830C2×C4⋊C4—1222no—
831C2×C4⋊C4—1222no—
832C2×C4⋊C4—1222no—
833C2×C22⋊C4—614no—
834C2×C22⋊C4—614no—
835C2×C22⋊C4—614no—
836C2×C22⋊C4—1222no—
837C2×C22⋊C4—1222no—
838C2×C22⋊C4—1222no—
839C2×C22⋊C4—1222no—
840C2×C22⋊C4—1222no—
841C2×C22⋊C4—1222no—
842C2×C22⋊C4—1222no—
843C2×C22⋊C4—1222no—
844C2×C22⋊C4—1222no—
845C2×C22⋊C4—1222no—
846C2×C22⋊C4—1222no—
847C2×C22⋊C4—1222no—
848C2×C22⋊C4—1222no—
849C2×C22⋊C4—1222no—
850C2×C22⋊C4—1222no—
851C2×C22⋊C4—1222no—
852C2×C22⋊C4—1222no—
853C2×C22⋊C4—1222no—
854C2×C22⋊C4—1222no—
855C2×C22⋊C4—1222no—
856C2×C22⋊C4—1222no—
857C2×C22⋊C4—1222no—
858C2×C22⋊C4—1222no—
859C2×C22⋊C4—1222no—
860C2×C22⋊C4—2441no—
861C2×C22⋊C4—2441no—
862C2×C22⋊C4—2441no—
863C2×C22⋊C4—2441no—
864C2×C22⋊C4—2441no—
865C2×C22⋊C4—2441no—
866C2×C42—1222no—
867C2×C42—1222no—
868C2×C42—1222no—
869#95—22no—
870#95—22no—
871#95—22no—
872#95—1222no—
873#95—1222no—
874#95—1222no—
875#95—1222no—
876#95—1222no—
877#95—1222no—
878#95—1222no—
879#95—1222no—
880#95—2441no—
881#95—2441no—
882#95C22⋊D6114yescomplemented
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—612no—
892C24—612no—
893C24—612no—
894C24—612no—
895C24—1221no—
896C24—1221no—
897C24—1221no—
898C24—1221no—
899C24—1221no—
900C24—1221no—
901C24—1221no—
902C24—1221no—
903C24—1221no—
904C24—1221no—
905C24—1221no—
906C24—1221no—
907C24—1221no—
908C24—1221no—
909C24—1221no—
910C24—1221no—
911C24—1221no—
912C24—1221no—
913C24—1221no—
914C24—1221no—
915C24—1221no—
916C24—1221no—
917C24—1221no—
918C24—1221no—
919C24—1221no—
920C24—1221no—
921C24C2×C4×D6112yes—
922C24C2×D24412yes—
923C24#1175822212yes—
924C24D4×D6112yes—
925C24D4×D6112yes—
926C24D4×D6112yes—
927C24#1175822612yes—
928C24C23×D6111yescharacteristic
929C2×D4—6116no—
930C2×D4—1228no—
931C2×D4—1228no—
932C2×D4—1228no—
933C2×D4—1228no—
934C2×D4—1228no—
935C2×D4—1228no—
936C2×D4—1228no—
937C2×D4—1228no—
938C2×D4—1228no—
939C2×D4—1228no—
940C2×D4—1228no—
941C2×D4—2444no—
942C2×D4—2444no—
943C2×D4—2444no—
944C2×D4—2444no—
945C2×D4—2444no—
946C2×D4—2444no—
947C2×D4—2444no—
948C2×D4—2444no—
949C2×D4—2444no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—28no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—28no—
984C22×C4—28no—
985C22×C4—28no—
986C22×C4—28no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—612no—
1004C22×C4—612no—
1005C22×C4—612no—
1006C22×C4—612no—
1007C22×C4—612no—
1008C22×C4—612no—
1009C22×C4—1228no—
1010C22×C4—1221no—
1011C22×C4—1221no—
1012C22×C4—1221no—
1013C22×C4—1221no—
1014C22×C4—1221no—
1015C22×C4—1221no—
1016C22×C4—1221no—
1017C22×C4—1221no—
1018C22×C4—1221no—
1019C22×C4—1221no—
1020C22×C4—1221no—
1021C22×C4—1221no—
1022C22×C4—1221no—
1023C22×C4—1221no—
1024C22×C4—1221no—
1025C22×C4—1221no—
1026C22×C4—1221no—
1027C22×C4—1221no—
1028C22×C4—1221no—
1029C22×C4—1221no—
1030C22×C4—1221no—
1031C22×C4—1221no—
1032C22×C4—1221no—
1033C22×C4—1221no—
1034C22×C4—1221no—
1035C22×C4—1221no—
1036C22×C4—1221no—
1037C22×C4—1221no—
1038C22×C4—1221no—
1039C22×C4—1221no—
1040C22×C4—1221no—
1041C22×C4—1221no—
1042C22×C4—1221no—
1043C22×C4—1221no—
1044C22×C4—1221no—
1045C22×C4—1221no—
1046C22×C4—2444no—
1047C22×C4—2444no—
1048C22×C4—2444no—
1049C22×C4—2444no—
1050C22×C4—2444no—
1051C22×C4—2444no—
1052C22×C4C2×C4×D6112yes—
1053C22×C4C2×C4×D6112yes—
1054C22×C4C2×D24412yes—
1055C22×C4C2×D24412yes—
1056C22×C4#1175822212yes—
1057C22×C4#1175822212yes—
1058C22×C4#1175822212yes—
1059C22×C4C2×C22⋊D6112yes—
1060C22×C4C2×C22⋊D6112yes—
1061C22×C4C2×C22⋊D6112yes—
1062C4⋊C4—1228no—
1063C4⋊C4—1228no—
1064C22⋊C4—1228no—
1065C22⋊C4—1228no—
1066C22⋊C4—1228no—
1067C22⋊C4—1228no—
1068C22⋊C4—2444no—
1069C22⋊C4—2444no—
1070C22⋊C4—2444no—
1071C22⋊C4—2444no—
1072C22⋊C4—2444no—
1073C22⋊C4—2444no—
1074C22⋊C4—2444no—
1075C42—1228no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—22no—
1104C23—614no—
1105C23—1222no—
1106C23—1222no—
1107C23—1222no—
1108C23—1222no—
1109C23—1222no—
1110C23—1222no—
1111C23—1222no—
1112C23—1222no—
1113C23—1222no—
1114C23—1222no—
1115C23—1222no—
1116C23—1222no—
1117C23—1222no—
1118C23—1222no—
1119C23—1222no—
1120C23—1222no—
1121C23—1222no—
1122C23—1222no—
1123C23—1222no—
1124C23—1222no—
1125C23—1222no—
1126C23—1222no—
1127C23—1222no—
1128C23—1222no—
1129C23—1222no—
1130C23—2441no—
1131C23—2441no—
1132C23—2441no—
1133C23—2441no—
1134C23—2441no—
1135C23—2441no—
1136C23—2441no—
1137C23—2441no—
1138C23—2441no—
1139C23—2441no—
1140C23—2441no—
1141C23—2441no—
1142C23—2441no—
1143C23—2441no—
1144C23—2441no—
1145C23—2441no—
1146C23—2441no—
1147C23—2441no—
1148C23—2441no—
1149C23—2441no—
1150C23—2441no—
1151C23—2441no—
1152C23—2441no—
1153C23—2441no—
1154C23—2441no—
1155C23—2441no—
1156C23—2441no—
1157C23—2441no—
1158C23—2441no—
1159C23—2441no—
1160C23—2441no—
1161C23—2441no—
1162C23—2441no—
1163C23—2441no—
1164C23—2441no—
1165C23—2441no—
1166C23—2441no—
1167C23—2441no—
1168C23—2441no—
1169C23—2441no—
1170C23—2441no—
1171C23—2441no—
1172C23—2441no—
1173C23—2441no—
1174C23C22⋊C4×D6114yes—
1175C23#1451973914yes—
1176C23C4×D24414yes—
1177C23#1451974714yes—
1178C23#1451975014yes—
1179C23#1451975214yes—
1180C23#1451976214yes—
1181C23C22×C4×D6111yescharacteristic
1182C23C2×D4×D6111yescharacteristic
1183C23C2×D4×D6111yescharacteristic
1184C23C2×D4×D6111yescharacteristic
1185C23C22×C22⋊D6111yescharacteristic
1186C23C22×D24411yescharacteristic
1187C23C2×#1175822211yescharacteristic
1188C23C2×#1175822211yescharacteristic
1189C23C2×#1175822211yescharacteristic
1190C23C2×#1175822211yescharacteristic
1191C23C2×#1175822611yescharacteristic
1192C23#1451982211yescharacteristic
1193C23#1451982211yescharacteristic
1194C23#1451982211yescharacteristic
1195C23#1451982511yescharacteristic
1196D4—12232no—
1197D4—24416no—
1198D4—24416no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—416no—
1224C2×C4—416no—
1225C2×C4—416no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—614no—
1243C2×C4—1222no—
1244C2×C4—1222no—
1245C2×C4—1222no—
1246C2×C4—1222no—
1247C2×C4—1222no—
1248C2×C4—1222no—
1249C2×C4—1222no—
1250C2×C4—1222no—
1251C2×C4—1222no—
1252C2×C4—1222no—
1253C2×C4—1222no—
1254C2×C4—1222no—
1255C2×C4—1222no—
1256C2×C4—1222no—
1257C2×C4—1222no—
1258C2×C4—24416no—
1259C2×C4—2441no—
1260C2×C4—2441no—
1261C2×C4—2441no—
1262C2×C4—2441no—
1263C2×C4—2441no—
1264C2×C4—2441no—
1265C2×C4—2441no—
1266C2×C4—2441no—
1267C2×C4—2441no—
1268C2×C4—2441no—
1269C2×C4—2441no—
1270C2×C4—2441no—
1271C2×C4—2441no—
1272C2×C4—2441no—
1273C2×C4—2441no—
1274C2×C4—2441no—
1275C2×C4—2441no—
1276C2×C4—2441no—
1277C2×C4—2441no—
1278C2×C4—2441no—
1279C2×C4—2441no—
1280C2×C4—2441no—
1281C2×C4—2441no—
1282C2×C4—2441no—
1283C2×C4—2441no—
1284C2×C4—2441no—
1285C2×C4C4×C22⋊D6114yescomplemented
1286C2×C4#1451975114yescomplemented
1287C22—24no—
1288C22—24no—
1289C22—24no—
1290C22—24no—
1291C22—24no—
1292C22—24no—
1293C22—24no—
1294C22—24no—
1295C22—24no—
1296C22—24no—
1297C22—24no—
1298C22—24no—
1299C22—24no—
1300C22—24no—
1301C22—1224no—
1302C22—1224no—
1303C22—1224no—
1304C22—4881no—
1305C22—4881no—
1306C22—4881no—
1307C22—4881no—
1308C22—4881no—
1309C22—4881no—
1310C22—4881no—
1311C22—4881no—
1312C22—2442no—
1313C22—2442no—
1314C22—2442no—
1315C22—2442no—
1316C22—2442no—
1317C22—2442no—
1318C22—2442no—
1319C22—2442no—
1320C22—2442no—
1321C22—2442no—
1322C22—2442no—
1323C22—2442no—
1324C22—2442no—
1325C22—2442no—
1326C22—2442no—
1327C22—2442no—
1328C22—2442no—
1329C22—2442no—
1330C22—2442no—
1331C22#1683964018yescomplemented
1332C22C2×C22⋊C4×D6111yescharacteristic
1333C22C2×C4×C22⋊D6111yescharacteristic
1334C22C2×#1451973911yescharacteristic
1335C22C2×C4×D24411yescharacteristic
1336C22C4×#1175822211yescharacteristic
1337C22#1684023511yescharacteristic
1338C22#1684024311yescharacteristic
1339C22C2×#1451974711yescharacteristic
1340C22C2×#1451975011yescharacteristic
1341C22C2×#1451975111yescharacteristic
1342C22C2×#1451975211yescharacteristic
1343C22C2×#1451976211yescharacteristic
1344C22#1684027311yescharacteristic
1345C22#1684029611yescharacteristic
1346C22#1684031211yescharacteristic
1347C22#1684032411yescharacteristic
1348C22#1684034311yescharacteristic
1349C22#1684035011yescharacteristic
1350C22#1684035911yescharacteristic
1351C22D4×C22⋊D6111yescharacteristic
1352C22D4×C22⋊D6111yescharacteristic
1353C22D4×C22⋊D6111yescharacteristic
1354C22#1684040211yescharacteristic
1355C22#1684040211yescharacteristic
1356C22#1684040211yescharacteristic
1357C22#1684040211yescharacteristic
1358C22#1684040211yescharacteristic
1359C22#1684040211yescharacteristic
1360C22#1684041311yescharacteristic
1361C22#1684041311yescharacteristic
1362C22#1684041311yescharacteristic
1363C22#1684042311yescharacteristic
1364C22#1684046011yescharacteristic
1365C22#1684046011yescharacteristic
1366C22#1684046011yescharacteristic
1367C4—24no—
1368C4—24no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—42no—
1373C4—1224no—
1374C4—4881no—
1375C4—4881no—
1376C4—2442no—
1377C4—2442no—
1378C4—2442no—
1379C2—28no—
1380C2—4882no—
1381C2—2444no—
1382C2C2×#1683964011yescharacteristic
1383C2C4×#1451975111yescharacteristic
1384C2#2144852211yescharacteristic
1385C2C22⋊C4×C22⋊D6111yescharacteristic
1386C2#2144864611yescharacteristic
1387C2#2144883511yescharacteristic
1388C2#2144886611yescharacteristic
1389C2#2144918711yescharacteristic
1390C2#2144925311yescharacteristic
1391C2#2144935511yescharacteristic
1392C2#2144937011yescharacteristic
1393C2#2144942911yescharacteristic
1394C2#2144955411yescharacteristic
1395C2#2144956911yescharacteristic
1396C2#2145077911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC22×#95×C61C2
socle, cosocleC24×C61C24
prime radicalC22×#14519751C2
hypercenterC22×#95D61
hypocenterC61#14023
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D61C2semidirect
3. C2×#16839641C2semidirect
4. C2×#16839641C2semidirect
5. C2×#16839641C2semidirect
6. C2×#16839640C2semidirect
7. #21444071C2semidirect
8. #21444067C2semidirect
9. #21444063C2semidirect
10. #21444059C2semidirect
11. #21444055C2semidirect
12. #21444053C2semidirect
13. #21444042C2semidirect
14. #21444040C2semidirect
15. C22×#95×C61C2semidirect
22. C2×#14519751C4semidirect
70. C22×D244C2×C4semidirect
82. C22×C22⋊D61C2×C4semidirect
102. C2×C4⋊Dic61C2×C4semidirect
111. C2×C22⋊Dic61D4semidirect
137. C2×#11758198C2×C4semidirect
138. C2×#11758198C2×C4semidirect
172. C23×C4×C61C2×C4semidirect
173. C23×C4×C61D4semidirect
183. #95×C61D4semidirect
306. C2×C22⋊D61C22⋊C4semidirect
540. C2×C4×C61C4×D4semidirect
541. C2×C4×C61#121semidirect
603. C22×C61#386semidirect
687. C22×#95D61semidirect
760. C61#14023semidirect
817. C23×C4C4×D61semidirect
818. C23×C4D244semidirect
882. #95C22⋊D61semidirect
1285. C2×C4C4×C22⋊D61semidirect
1286. C2×C4#14519751semidirect
1331. C22#16839640semidirect

Maximal subgroups

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

subgroupindex
C22×#145197512
C22×C4×C22⋊D612
C2×#168396412
C2×#168396402
#214440712
#214440672
#214440632
#214440592
#214440552
#214440532
#214440422
#214440402
C22×#95×C612
#1402361