Finite Group Databasebeta

← #29603461

Subgroups — #29603461

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×#14519737C211yesmaximal, characteristic, complemented
3C2×#16839640C211yesmaximal, characteristic, complemented
4C2×#16839639C211yesmaximal, characteristic, complemented
5C2×#16839639C211yesmaximal, characteristic, complemented
6C2×#16839639C211yesmaximal, characteristic, complemented
7C22×#14519684C211yesmaximal, characteristic, complemented
8#21444071C211yesmaximal, characteristic, complemented
9#21444067C211yesmaximal, characteristic, complemented
10#21444063C211yesmaximal, characteristic, complemented
11#21444059C211yesmaximal, characteristic, complemented
12#21444055C211yesmaximal, characteristic, complemented
13#21444053C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C22⋊D61C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C24×Dic61C2211yescharacteristic
20C24×Dic61C2211yescharacteristic
21C23×C4×D61C2211yescharacteristic
22C2×#14519751—24no—
23C2×#14519751—24no—
24C2×#14519751C418yescomplemented
25C2×#14519737—24no—
26C2×#14519737—24no—
27C2×#14519737—24no—
28C22×C4⋊Dic61C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic
40#16839640—24no—
41#16839639—24no—
42#16839639—24no—
43#16839639—24no—
44C2×#14519684—24no—
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C24×C4×C61C2211yescharacteristic
56C22×C22⋊C4×C61C2211yescharacteristic
57C22×C22⋊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×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×Dic61—22no—
86C23×Dic61—22no—
87C23×Dic61—22no—
88C23×Dic61—22no—
89C23×Dic61—22no—
90C23×Dic61—22no—
91C23×Dic61—22no—
92C23×Dic61—22no—
93C23×Dic61—22no—
94C23×Dic61—41no—
95C23×Dic61—41no—
96C23×Dic61—41no—
97C23×Dic61—41no—
98C23×Dic61D414yescomplemented
99C23×Dic61C2311yescharacteristic
100C23×Dic61C2311yescharacteristic
101C23×Dic61C2311yescharacteristic
102C23×Dic61C2311yescharacteristic
103C23×Dic61C2311yescharacteristic
104C23×Dic61C2311yescharacteristic
105C22×C4×D61—22no—
106C22×C4×D61—22no—
107C22×C4×D61—22no—
108C22×C4×D61—22no—
109C22×C4×D61—22no—
110C22×C4×D61—41no—
111C22×C4×D61—41no—
112#14519751—232no—
113#14519737—232no—
114C2×C4⋊Dic61—22no—
115C2×C4⋊Dic61—22no—
116C2×C4⋊Dic61C2×C414yescomplemented
117C2×#11758196—22no—
118C2×#11758196—22no—
119C2×#11758196—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—22no—
138C2×#11758198—22no—
139C2×#11758198—41no—
140C2×#11758198—41no—
141C2×#11758198—41no—
142C2×#11758198—41no—
143C2×#11758198—41no—
144C2×#11758198—41no—
145C2×#11758198C2×C414yescomplemented
146C2×#11758198C2×C414yescomplemented
147C2×C4×Dic61—22no—
148C2×C4×Dic61—22no—
149C2×C4×Dic61—22no—
150#14519684—22no—
151#14519684—22no—
152#14519684—22no—
153#14519684—22no—
154#14519684—22no—
155#14519684—22no—
156#14519684—22no—
157#14519684—22no—
158#14519684—22no—
159#14519684D414yescomplemented
160C25×C61C2311yescharacteristic
161C23×C4×C61—22no—
162C23×C4×C61—22no—
163C23×C4×C61—22no—
164C23×C4×C61—22no—
165C23×C4×C61—41no—
166C23×C4×C61—41no—
167C23×C4×C61C2×C414yescomplemented
168C23×C4×C61C2311yescharacteristic
169C23×C4×C61C2311yescharacteristic
170C23×C4×C61C2311yescharacteristic
171C23×C4×C61C2311yescharacteristic
172C23×C4×C61C2311yescharacteristic
173C23×C4×C61C2311yescharacteristic
174C2×C22⋊C4×C61—22no—
175C2×C22⋊C4×C61—22no—
176C2×C22⋊C4×C61—22no—
177C2×C22⋊C4×C61—22no—
178C2×C22⋊C4×C61—22no—
179C2×C22⋊C4×C61D414yescomplemented
180#95×C61—22no—
181#95×C61—22no—
182#95×C61—41no—
183#95×C61—41no—
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—28no—
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×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—28no—
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—21no—
266C22×C4×C61—21no—
267C22×C4×C61—21no—
268C22×C4×C61—44no—
269C22×C4×C61—44no—
270C22×C4×C61—44no—
271C22×C4×C61—44no—
272C22×C4×C61—44no—
273C22×C4×C61C22×C412yes—
274C22×C4×C61C22×C412yes—
275C22×C4×C61C2×D412yes—
276C22×C4×C61C2×D412yes—
277C22×C4×C61C2×D412yes—
278C22×C4×C61#4112yes—
279C2×C22⋊D61—28no—
280C2×C22⋊D61—28no—
281C2×C22⋊D61—28no—
282C2×C22⋊D61—28no—
283C2×C22⋊D61—28no—
284C2×C22⋊D61—28no—
285C2×C22⋊D61—28no—
286C2×C22⋊D61—28no—
287C2×C22⋊D61—28no—
288C2×C22⋊D61—44no—
289C2×C22⋊D61—44no—
290C2×C22⋊D61—44no—
291C2×C22⋊D61—44no—
292C2×C22⋊D61C22⋊C4116yescomplemented
293C22×Dic61—21no—
294C22×Dic61—21no—
295C22×Dic61—21no—
296C22×Dic61—21no—
297C22×Dic61—21no—
298C22×Dic61—21no—
299C22×Dic61—21no—
300C22×Dic61—21no—
301C22×Dic61—28no—
302C22×Dic61—28no—
303C22×Dic61—21no—
304C22×Dic61—21no—
305C22×Dic61—21no—
306C22×Dic61—21no—
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—28no—
328C22×Dic61—44no—
329C22×Dic61—44no—
330C22×Dic61—44no—
331C22×Dic61—44no—
332C22×Dic61—44no—
333C22×Dic61—44no—
334C22×Dic61—44no—
335C22×Dic61—44no—
336C22×Dic61—44no—
337C22×Dic61—44no—
338C22×Dic61—44no—
339C22×Dic61C22×C412yes—
340C22×Dic61C22×C412yes—
341C22×Dic61C2×D412yes—
342C22×Dic61C2×D412yes—
343C22×Dic61C2×D412yes—
344C22×Dic61C2×D412yes—
345C22×Dic61C2×D412yes—
346C22×Dic61C2×D412yes—
347C22×Dic61#4112yes—
348C22×Dic61#4112yes—
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⋊C4×C61—28no—
364C22⋊C4×C61—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—416no—
513C2×C4×C61—41no—
514C2×C4×C61—41no—
515C2×C4×C61—41no—
516C2×C4×C61—41no—
517C2×C4×C61—41no—
518C2×C4×C61—41no—
519C2×C4×C61—41no—
520C2×C4×C61—41no—
521C2×C4×C61—41no—
522C2×C4×C61—41no—
523C2×C4×C61—41no—
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×C61C4×D414yescomplemented
540C22⋊D61—232no—
541C22⋊D61—416no—
542C2×Dic61—22no—
543C2×Dic61—22no—
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—22no—
560C2×Dic61—22no—
561C2×Dic61—22no—
562C2×Dic61—22no—
563C2×Dic61—22no—
564C2×Dic61—22no—
565C2×Dic61—22no—
566C2×Dic61—416no—
567C2×Dic61—416no—
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×Dic61C2×C22⋊C414yes—
585C2×Dic61#12114yescomplemented
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—42no—
671C4×C61—42no—
672C4×C61—42no—
673C4×C61—81no—
674C4×C61—81no—
675Dic61—24no—
676Dic61—24no—
677Dic61—42no—
678Dic61—42no—
679Dic61—42no—
680Dic61—42no—
681C22×#121—611no—
682C22×C4×D4—611no—
683C2×#386—611no—
684C2×#386—611no—
685C2×#386—611no—
686C2×#386—611no—
687C22×#95—611no—
688#1441—611no—
689#1440—611no—
690#1439—611no—
691#1438—611no—
692#1437—611no—
693#1436—611no—
694C22⋊#95—611no—
695C22⋊#95D6111yescharacteristic, complemented
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×C4—611no—
719C24×C4—611no—
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⋊C4C2×D6111yescharacteristic
739C22×C22⋊C4C2×D6111yescharacteristic
740C22×C42—611no—
741#386—1224no—
742#386—1224no—
743#386—1224no—
744#386—1224no—
745C2×#95—611no—
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—1224no—
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—41no—
790C23×C4—41no—
791C23×C4—611no—
792C23×C4—611no—
793C23×C4—611no—
794C23×C4—611no—
795C23×C4—611no—
796C23×C4—611no—
797C23×C4—614no—
798C23×C4—1222no—
799C23×C4—1222no—
800C23×C4—1222no—
801C23×C4—1222no—
802C23×C4—1222no—
803C23×C4—1222no—
804C23×C4—1222no—
805C23×C4—1222no—
806C23×C4—1222no—
807C23×C4—1222no—
808C23×C4—1222no—
809C23×C4—1222no—
810C23×C4—1222no—
811C23×C4—1222no—
812C23×C4—2441no—
813C23×C4—2441no—
814C23×C4—2441no—
815C23×C4—2441no—
816C23×C4—2441no—
817C23×C4—2441no—
818C23×C4C4×D6114yescomplemented
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—22no—
834C2×C22⋊C4—22no—
835C2×C22⋊C4—22no—
836C2×C22⋊C4—22no—
837C2×C22⋊C4—22no—
838C2×C22⋊C4—614no—
839C2×C22⋊C4—614no—
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—2441no—
860C2×C22⋊C4—2441no—
861C2×C22⋊C4—2441no—
862C2×C22⋊C4—2441no—
863C2×C22⋊C4—2441no—
864C2×C22⋊C4—2441no—
865C2×C22⋊C4D24414yescomplemented
866C2×C42—1222no—
867C2×C42—1222no—
868C2×C42—1222no—
869#95—22no—
870#95—22no—
871#95—41no—
872#95—41no—
873#95—614no—
874#95—1222no—
875#95—1222no—
876#95—1222no—
877#95—1222no—
878#95—1222no—
879#95—1222no—
880#95—1222no—
881#95—1222no—
882#95—1222no—
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—21no—
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—28no—
973C22×C4—28no—
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—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—612no—
994C22×C4—612no—
995C22×C4—612no—
996C22×C4—612no—
997C22×C4—612no—
998C22×C4—612no—
999C22×C4—612no—
1000C22×C4—612no—
1001C22×C4—612no—
1002C22×C4—612no—
1003C22×C4—1228no—
1004C22×C4—1228no—
1005C22×C4—1221no—
1006C22×C4—1221no—
1007C22×C4—1221no—
1008C22×C4—1221no—
1009C22×C4—1221no—
1010C22×C4—1221no—
1011C22×C4—1221no—
1012C22×C4—1221no—
1013C22×C4—1228no—
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—1228no—
1039C22×C4—2444no—
1040C22×C4—2444no—
1041C22×C4—2444no—
1042C22×C4—2444no—
1043C22×C4—2444no—
1044C22×C4—2444no—
1045C22×C4—2444no—
1046C22×C4—2444no—
1047C22×C4—2444no—
1048C22×C4—2444no—
1049C22×C4—2444no—
1050C22×C4—2444no—
1051C22×C4—2444no—
1052C22×C4—2444no—
1053C22×C4—2444no—
1054C22×C4—2444no—
1055C22×C4—2444no—
1056C22×C4C2×C4×D6112yes—
1057C22×C4C2×C4×D6112yes—
1058C22×C4C2×D24412yes—
1059C22×C4C2×D24412yes—
1060C22×C4D4×D6112yes—
1061C22×C4#1175822412yes—
1062C4⋊C4—1228no—
1063C4⋊C4—1228no—
1064C22⋊C4—28no—
1065C22⋊C4—44no—
1066C22⋊C4—1228no—
1067C22⋊C4—1228no—
1068C22⋊C4—1228no—
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
1185C23C2×D4×D6111yescharacteristic
1186C23C22×D24411yescharacteristic
1187C23#41×D6111yescharacteristic
1188C23#41×D6111yescharacteristic
1189C23C2×#1175822411yescharacteristic
1190C23C2×#1175822211yescharacteristic
1191C23C2×#1175822611yescharacteristic
1192C23#1451982211yescharacteristic
1193C23#1451982211yescharacteristic
1194C23#1451982311yescharacteristic
1195C23#1451982411yescharacteristic
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—416no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
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—614no—
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—1222no—
1259C2×C4—1222no—
1260C2×C4—1222no—
1261C2×C4—1222no—
1262C2×C4—1222no—
1263C2×C4—1222no—
1264C2×C4—1222no—
1265C2×C4—1222no—
1266C2×C4—1222no—
1267C2×C4—24416no—
1268C2×C4—24416no—
1269C2×C4—24416no—
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×C4—2441no—
1286C2×C4#1451973714yescomplemented
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×#1451973711yescharacteristic
1334C22C2×#1451973911yescharacteristic
1335C22C2×C4×D24411yescharacteristic
1336C22#1684023011yescharacteristic
1337C22#1684023511yescharacteristic
1338C22#1684024211yescharacteristic
1339C22C2×#1451974711yescharacteristic
1340C22#121×D6111yescharacteristic
1341C22C2×#1451975011yescharacteristic
1342C22C2×#1451975211yescharacteristic
1343C22C2×#1451976211yescharacteristic
1344C22#1684027511yescharacteristic
1345C22#1684029811yescharacteristic
1346C22#1684030711yescharacteristic
1347C22#1684032011yescharacteristic
1348C22#1684033911yescharacteristic
1349C22#1684035211yescharacteristic
1350C22#1684036111yescharacteristic
1351C22#1684039411yescharacteristic
1352C22#1684039411yescharacteristic
1353C22D4×D24411yescharacteristic
1354C22#1684039911yescharacteristic
1355C22#1684039911yescharacteristic
1356C22#1684040411yescharacteristic
1357C22#1684040411yescharacteristic
1358C22#1684040711yescharacteristic
1359C22#1684040711yescharacteristic
1360C22#1684041011yescharacteristic
1361C22#1684041011yescharacteristic
1362C22#1684041611yescharacteristic
1363C22#1684042111yescharacteristic
1364C22#1684045811yescharacteristic
1365C22#1684046111yescharacteristic
1366C22#1684046111yescharacteristic
1367C4—24no—
1368C4—42no—
1369C4—42no—
1370C4—42no—
1371C4—81no—
1372C4—81no—
1373C4—1224no—
1374C4—1224no—
1375C4—2442no—
1376C4—2442no—
1377C4—2442no—
1378C4—2442no—
1379C2—28no—
1380C2—4882no—
1381C2—2444no—
1382C2C2×#1683964011yescharacteristic
1383C2#2144832511yescharacteristic
1384C2#2144851911yescharacteristic
1385C2#2144863511yescharacteristic
1386C2#2144864311yescharacteristic
1387C2#2144883311yescharacteristic
1388C2#2144886911yescharacteristic
1389C2#2144919211yescharacteristic
1390C2#2144925811yescharacteristic
1391C2#2144935311yescharacteristic
1392C2#2144936811yescharacteristic
1393C2#2144942711yescharacteristic
1394C2#2144955811yescharacteristic
1395C2#2144957311yescharacteristic
1396C2#2145078311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C22⋊#95C2
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×#14519737C2semidirect
3. C2×#16839640C2semidirect
4. C2×#16839639C2semidirect
5. C2×#16839639C2semidirect
6. C2×#16839639C2semidirect
7. C22×#14519684C2semidirect
8. #21444071C2semidirect
9. #21444067C2semidirect
10. #21444063C2semidirect
11. #21444059C2semidirect
12. #21444055C2semidirect
13. #21444053C2semidirect
14. #21444040C2semidirect
15. C61×C22⋊#95C2semidirect
24. C2×#14519751C4semidirect
70. C22×D244C2×C4semidirect
82. C22×C22⋊D61C2×C4semidirect
98. C23×Dic61D4semidirect
116. C2×C4⋊Dic61C2×C4semidirect
145. C2×#11758198C2×C4semidirect
146. C2×#11758198C2×C4semidirect
159. #14519684D4semidirect
167. C23×C4×C61C2×C4semidirect
179. C2×C22⋊C4×C61D4semidirect
292. C2×C22⋊D61C22⋊C4semidirect
539. C2×C4×C61C4×D4semidirect
585. C2×Dic61#121semidirect
603. C22×C61#386semidirect
695. C22⋊#95D61semidirect
760. C61#14023semidirect
818. C23×C4C4×D61semidirect
865. C2×C22⋊C4D244semidirect
1286. C2×C4#14519737semidirect
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×#145197372
C2×#168396402
C2×#168396392
C22×#145196842
#214440712
#214440672
#214440632
#214440592
#214440552
#214440532
#214440402
C61×C22⋊#952
#1402361