Finite Group Databasebeta

← #29603472

Subgroups — #29603472

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×#14519750C211yesmaximal, characteristic
2C22×C4×D244C211yesmaximal, characteristic, complemented
3C2×#16839640C211yesmaximal, characteristic, complemented
4C2×#16839638C211yesmaximal, characteristic, complemented
5C2×#16839638C211yesmaximal, characteristic, complemented
6C2×#16839638C211yesmaximal, characteristic, complemented
7C2×#95×D61C211yesmaximal, characteristic, complemented
8#21444073C211yesmaximal, characteristic, complemented
9#21444067C211yesmaximal, characteristic, complemented
10#21444064C211yesmaximal, characteristic, complemented
11#21444058C211yesmaximal, characteristic, complemented
12#21444052C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×#1437C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C22⋊D61C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C23×C4×D61C2211yescharacteristic
22C23×C4×D61C2211yescharacteristic
23C2×#14519750—24no—
24C2×#14519750—24no—
25C2×#14519750C418yescomplemented
26C2×C4×D244—24no—
27C2×C4×D244—24no—
28C2×C4×D244—24no—
29C22×C4⋊Dic61C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×C22⋊Dic61C2211yescharacteristic
32C22×C22⋊Dic61C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39#16839640—24no—
40#16839638—24no—
41#16839638—24no—
42#16839638—24no—
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54#95×D61—24no—
55C22×C22⋊C4×C61C2211yescharacteristic
56C22×C22⋊C4×C61C2211yescharacteristic
57C22×C22⋊C4×C61C2211yescharacteristic
58C22×C42×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×D244D414yes—
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⋊D61—41no—
82C22×C22⋊D61—41no—
83C22×C22⋊D61C2×C414yescomplemented
84C22×C22⋊D61C2×C414yescomplemented
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—22no—
97C22×C4×D61—22no—
98C22×C4×D61—22no—
99C22×C4×D61—22no—
100C22×C4×D61—22no—
101C22×C4×D61—22no—
102C22×C4×D61—22no—
103C22×C4×D61—22no—
104C22×C4×D61—22no—
105C22×C4×D61—22no—
106C22×C4×D61—22no—
107C22×C4×D61—22no—
108C22×C4×D61—22no—
109C22×C4×D61—41no—
110C22×C4×D61—41no—
111C22×C4×D61—41no—
112C22×C4×D61—41no—
113C22×C4×D61—41no—
114C22×C4×D61—41no—
115C22×C4×D61—41no—
116C22×C4×D61—41no—
117C22×C4×D61C2×C414yescomplemented
118C22×C4×D61D414yescomplemented
119#14519750—232no—
120C4×D244—232no—
121C2×C4⋊Dic61—22no—
122C2×C4⋊Dic61—22no—
123C2×C4⋊Dic61—22no—
124C2×#11758196—22no—
125C2×#11758196—22no—
126C2×#11758196C2×C414yescomplemented
127C2×C22⋊Dic61—22no—
128C2×C22⋊Dic61—22no—
129C2×C22⋊Dic61—22no—
130C2×C22⋊Dic61—41no—
131C2×C22⋊Dic61—41no—
132C2×C22⋊Dic61—41no—
133C2×#11758198—22no—
134C2×#11758198—22no—
135C2×#11758198—22no—
136C2×#11758198—22no—
137C2×#11758198—22no—
138C2×#11758198—22no—
139C2×#11758198—22no—
140C2×#11758198—22no—
141C2×#11758198—22no—
142C2×#11758198—22no—
143C2×#11758198—22no—
144C2×#11758198—22no—
145C2×#11758198—22no—
146C2×#11758198—22no—
147C2×#11758198—41no—
148C2×#11758198—41no—
149C2×#11758198C2×C414yescomplemented
150C2×#11758198D414yescomplemented
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#14519684—22no—
160#14519684—41no—
161#14519684D414yescomplemented
162C25×C61C2311yescharacteristic
163C23×C4×C61C2311yescharacteristic
164C23×C4×C61C2311yescharacteristic
165C23×C4×C61C2311yescharacteristic
166C23×C4×C61C2311yescharacteristic
167C23×C4×C61C2311yescharacteristic
168C23×C4×C61C2311yescharacteristic
169C2×C22⋊C4×C61—22no—
170C2×C22⋊C4×C61—22no—
171C2×C22⋊C4×C61—22no—
172C2×C22⋊C4×C61—22no—
173C2×C22⋊C4×C61—22no—
174C2×C22⋊C4×C61—22no—
175C2×C22⋊C4×C61—22no—
176C2×C22⋊C4×C61—41no—
177C2×C22⋊C4×C61C2×C414yescomplemented
178C2×C42×C61—22no—
179C2×C42×C61—22no—
180C2×C42×C61—22no—
181#95×C61—22no—
182#95×C61—22no—
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×C61—21no—
193C24×C61—21no—
194C24×C61—21no—
195C24×C61—21no—
196C24×C61—21no—
197C24×C61—21no—
198C24×C61C22×C412yes—
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×D61C22×C412yes—
221C23×D61C22×C412yes—
222C23×D61C2×D412yes—
223C23×D61C2×D412yes—
224C23×D61C2×D412yes—
225C23×D61C2×D412yes—
226C23×D61C2×D412yes—
227C23×D61C2×D412yes—
228C23×D61#4112yes—
229C23×D61#4112yes—
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×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×C61C22×C412yes—
264C22×C4×C61C22×C412yes—
265C22×C4×C61C2×D412yes—
266C22×C4×C61C2×D412yes—
267C22×C4×C61C2×D412yes—
268C22×C4×C61C2×D412yes—
269C22×C4×C61C2×D412yes—
270C22×C4×C61#4112yes—
271C22×C4×C61#4112yes—
272C2×C22⋊D61—28no—
273C2×C22⋊D61—28no—
274C2×C22⋊D61—28no—
275C2×C22⋊D61—28no—
276C2×C22⋊D61—28no—
277C2×C22⋊D61—44no—
278C2×C22⋊D61—44no—
279C2×C22⋊D61—44no—
280C2×C22⋊D61—44no—
281C2×C22⋊D61—44no—
282C2×C22⋊D61—44no—
283C2×C22⋊D61—44no—
284C2×C22⋊D61—44no—
285C2×C22⋊D61—44no—
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—21no—
295C22×Dic61—21no—
296C22×Dic61—21no—
297C22×Dic61—21no—
298C22×Dic61—21no—
299C22×Dic61—21no—
300C22×Dic61—21no—
301C22×Dic61—21no—
302C22×Dic61—21no—
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×Dic61C22×C412yes—
322C22×Dic61C22×C412yes—
323C22×Dic61C2×D412yes—
324C22×Dic61C2×D412yes—
325C22×Dic61C2×D412yes—
326C22×Dic61C2×D412yes—
327C22×Dic61#4112yes—
328C2×D244—28no—
329C2×D244—28no—
330C2×D244—28no—
331C2×D244—28no—
332C2×D244—28no—
333C2×D244—28no—
334C2×D244C22⋊C4116yescomplemented
335C2×C4×D61—28no—
336C2×C4×D61—28no—
337C2×C4×D61—28no—
338C2×C4×D61—28no—
339C2×C4×D61—28no—
340C2×C4×D61—28no—
341C2×C4×D61—44no—
342C2×C4×D61—44no—
343C2×C4×D61—44no—
344C2×C4×D61—44no—
345C2×C4×D61—44no—
346C2×C4×D61—44no—
347C2×C4×D61—44no—
348C2×C4×D61—44no—
349C2×C4×D61—44no—
350C2×C4×D61—44no—
351C2×C4×D61—44no—
352C2×C4×D61—44no—
353C2×C4×D61—44no—
354C2×C4×D61—44no—
355C2×C4×D61—44no—
356C2×C4×D61—44no—
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—
365C22⋊C4×C61—44no—
366C42×C61—28no—
367C22⋊Dic61—44no—
368C22⋊Dic61—44no—
369#11758198—28no—
370#11758198—28no—
371#11758198—28no—
372#11758198—44no—
373#11758198—44no—
374#11758198—44no—
375C4⋊Dic61—28no—
376#11758196—28no—
377C23×C61—22no—
378C23×C61—22no—
379C23×C61—22no—
380C23×C61—22no—
381C23×C61—22no—
382C23×C61—22no—
383C23×C61—22no—
384C23×C61—41no—
385C23×C61—41no—
386C23×C61—41no—
387C23×C61—41no—
388C23×C61—41no—
389C23×C61—41no—
390C23×C61—41no—
391C23×C61—41no—
392C23×C61—41no—
393C23×C61—41no—
394C23×C61—41no—
395C23×C61—41no—
396C23×C61—41no—
397C23×C61—41no—
398C23×C61—41no—
399C23×C61—41no—
400C23×C61—41no—
401C23×C61—41no—
402C23×C61—41no—
403C23×C61—41no—
404C23×C61—41no—
405C23×C61—41no—
406C23×C61—41no—
407C23×C61—41no—
408C23×C61—41no—
409C23×C61—41no—
410C23×C61—41no—
411C23×C61—41no—
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—22no—
453C22×D61—22no—
454C22×D61—22no—
455C22×D61—22no—
456C22×D61—22no—
457C22×D61—22no—
458C22×D61—22no—
459C22×D61—22no—
460C22×D61—22no—
461C22×D61—22no—
462C22×D61—22no—
463C22×D61—22no—
464C22×D61—22no—
465C22×D61—22no—
466C22×D61—22no—
467C22×D61—22no—
468C22×D61—22no—
469C22×D61—22no—
470C22×D61—22no—
471C22×D61—22no—
472C22×D61—22no—
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×D61C2×C22⋊C414yes—
490C22×D61C2×C22⋊C414yes—
491C22×D61C4×D414yes—
492C22×D61C4×D414yes—
493C22×D61#12014yes—
494C22×D61#12114yes—
495C22×D61#12114yes—
496C22×D61#12314yes—
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—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×C61C2×C22⋊C414yes—
538C2×C4×C61#12114yescomplemented
539C22⋊D61—416no—
540C22⋊D61—416no—
541C2×Dic61—22no—
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—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×Dic61C4×D414yescomplemented
583D244—232no—
584C4×D61—416no—
585C4×D61—416no—
586C4×D61—416no—
587C4×D61—416no—
588#14023—611nomaximal, Sylow
589C22×C61—42no—
590C22×C61—42no—
591C22×C61—42no—
592C22×C61—42no—
593C22×C61—42no—
594C22×C61—42no—
595C22×C61—42no—
596C22×C61—81no—
597C22×C61—81no—
598C22×C61—81no—
599C22×C61—81no—
600C22×C61—81no—
601C22×C61—81no—
602C22×C61—81no—
603C22×C61—81no—
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—24no—
643C2×D61—24no—
644C2×D61—24no—
645C2×D61—24no—
646C2×D61—24no—
647C2×D61—24no—
648C2×D61—24no—
649C2×D61—24no—
650C2×D61—24no—
651C2×D61—24no—
652C2×D61—24no—
653C2×D61—24no—
654C2×D61—24no—
655C2×D61—24no—
656C2×D61—42no—
657C2×D61—42no—
658C2×D61—42no—
659C2×D61—42no—
660C2×D61—42no—
661C2×D61—42no—
662C2×D61—42no—
663C2×D61—42no—
664C2×D61—42no—
665C2×D61—42no—
666C2×D61—42no—
667C2×D61—42no—
668C2×D61#38618yescomplemented
669C4×C61—24no—
670C4×C61—24no—
671C4×C61—42no—
672C4×C61—42no—
673C4×C61—42no—
674C4×C61—81no—
675Dic61—24no—
676Dic61—42no—
677Dic61—42no—
678Dic61—42no—
679Dic61—42no—
680Dic61—81no—
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#1437D6111yescharacteristic, complemented
693#1436—611no—
694C22⋊#95—611no—
695C22⋊#95—611no—
696C2×C61—82no—
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—28no—
713D61—44no—
714C23×D4—611no—
715C23×D4—611no—
716C23×D4—611no—
717C24×C4—611no—
718C24×C4—611no—
719C24×C4—611no—
720C24×C4—611no—
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⋊C4C2×D6111yescharacteristic
738C22×C22⋊C4C2×D6111yescharacteristic
739C22×C22⋊C4C2×D6111yescharacteristic
740C22×C42C2×D6111yescharacteristic
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—611no—
756C2×#95—1224no—
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—611no—
786C23×C4—611no—
787C23×C4—611no—
788C23×C4—611no—
789C23×C4—611no—
790C23×C4—614no—
791C23×C4—614no—
792C23×C4—611no—
793C23×C4—1222no—
794C23×C4—1222no—
795C23×C4—1222no—
796C23×C4—1222no—
797C23×C4—1222no—
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—2441no—
812C23×C4—2441no—
813C23×C4—2441no—
814C23×C4—2441no—
815C23×C4—2441no—
816C23×C4—2441no—
817C23×C4—2441no—
818C23×C4—2441no—
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—22no—
839C2×C22⋊C4—22no—
840C2×C22⋊C4—41no—
841C2×C22⋊C4—614no—
842C2×C22⋊C4—614no—
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⋊C4C4×D6114yescomplemented
866C2×C42—22no—
867C2×C42—22no—
868C2×C42—22no—
869#95—22no—
870#95—22no—
871#95—41no—
872#95—614no—
873#95—1222no—
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—2441no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24—21no—
896C24—21no—
897C24—612no—
898C24—612no—
899C24—612no—
900C24—612no—
901C24—612no—
902C24—612no—
903C24—612no—
904C24—612no—
905C24—612no—
906C24—612no—
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—
921C24—1221no—
922C24—1221no—
923C24—1221no—
924C24—1221no—
925C24—1221no—
926C24—1221no—
927C24C2×C4×D6112yes—
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—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—612no—
984C22×C4—612no—
985C22×C4—612no—
986C22×C4—612no—
987C22×C4—612no—
988C22×C4—612no—
989C22×C4—612no—
990C22×C4—1228no—
991C22×C4—1228no—
992C22×C4—1228no—
993C22×C4—1228no—
994C22×C4—1228no—
995C22×C4—1221no—
996C22×C4—1221no—
997C22×C4—1221no—
998C22×C4—1221no—
999C22×C4—1221no—
1000C22×C4—1221no—
1001C22×C4—1221no—
1002C22×C4—1221no—
1003C22×C4—1221no—
1004C22×C4—1221no—
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—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—1228no—
1024C22×C4—1221no—
1025C22×C4—1221no—
1026C22×C4—1221no—
1027C22×C4—1221no—
1028C22×C4—1221no—
1029C22×C4—1221no—
1030C22×C4—1221no—
1031C22×C4—2444no—
1032C22×C4—2444no—
1033C22×C4—2444no—
1034C22×C4—2444no—
1035C22×C4—2444no—
1036C22×C4—2444no—
1037C22×C4—2444no—
1038C22×C4—2444no—
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×C4C2×C4×D6112yes—
1054C22×C4C2×C4×D6112yes—
1055C22×C4#1175822212yes—
1056C22×C4#1175822212yes—
1057C22×C4D4×D6112yes—
1058C22×C4D4×D6112yes—
1059C22×C4D4×D6112yes—
1060C22×C4D4×D6112yes—
1061C22×C4D4×D6112yes—
1062C4⋊C4—1228no—
1063C4⋊C4—1228no—
1064C22⋊C4—28no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—1228no—
1068C22⋊C4—1228no—
1069C22⋊C4—1228no—
1070C22⋊C4—2444no—
1071C22⋊C4—2444no—
1072C22⋊C4—2444no—
1073C22⋊C4—2444no—
1074C22⋊C4—2444no—
1075C42—28no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—614no—
1112C23—614no—
1113C23—614no—
1114C23—614no—
1115C23—614no—
1116C23—614no—
1117C23—614no—
1118C23—614no—
1119C23—1222no—
1120C23—1222no—
1121C23—1222no—
1122C23—1222no—
1123C23—1222no—
1124C23—1222no—
1125C23—1222no—
1126C23—1222no—
1127C23—1222no—
1128C23—1222no—
1129C23—1222no—
1130C23—1222no—
1131C23—1222no—
1132C23—1222no—
1133C23—1222no—
1134C23—1222no—
1135C23—1222no—
1136C23—1222no—
1137C23—1222no—
1138C23—1222no—
1139C23—1222no—
1140C23—1222no—
1141C23—1222no—
1142C23—1222no—
1143C23—1222no—
1144C23—1222no—
1145C23—1222no—
1146C23—1222no—
1147C23—1222no—
1148C23—1222no—
1149C23—1222no—
1150C23—1222no—
1151C23—1222no—
1152C23—1222no—
1153C23—1222no—
1154C23—1222no—
1155C23—1222no—
1156C23—1222no—
1157C23—1222no—
1158C23—1222no—
1159C23—1222no—
1160C23—1222no—
1161C23—1222no—
1162C23—1222no—
1163C23—1222no—
1164C23—1222no—
1165C23—2441no—
1166C23—2441no—
1167C23—2441no—
1168C23—2441no—
1169C23—2441no—
1170C23—2441no—
1171C23—2441no—
1172C23—2441no—
1173C23—2441no—
1174C23—2441no—
1175C23—2441no—
1176C23—2441no—
1177C23—2441no—
1178C23—2441no—
1179C23—2441no—
1180C23—2441no—
1181C23C22×C4×D6111yescharacteristic
1182C23C2×D4×D6111yescharacteristic
1183C23C2×D4×D6111yescharacteristic
1184C23C2×D4×D6111yescharacteristic
1185C23C2×D4×D6111yescharacteristic
1186C23C2×D4×D6111yescharacteristic
1187C23#41×D6111yescharacteristic
1188C23#41×D6111yescharacteristic
1189C23#41×D6111yescharacteristic
1190C23C2×#1175822211yescharacteristic
1191C23C2×#1175822211yescharacteristic
1192C23#1451982211yescharacteristic
1193C23#1451982311yescharacteristic
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—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
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—614no—
1240C2×C4—1222no—
1241C2×C4—1222no—
1242C2×C4—1222no—
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—24416no—
1260C2×C4—24416no—
1261C2×C4—24416no—
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×C4C22⋊C4×D6114yes—
1286C2×C4#1451975014yescomplemented
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—618no—
1303C22—1224no—
1304C22—1224no—
1305C22—1224no—
1306C22—1224no—
1307C22—1224no—
1308C22—1224no—
1309C22—1224no—
1310C22—1224no—
1311C22—1224no—
1312C22—1224no—
1313C22—1224no—
1314C22—1224no—
1315C22—1224no—
1316C22—1224no—
1317C22—1224no—
1318C22—1224no—
1319C22—1224no—
1320C22—2442no—
1321C22—2442no—
1322C22—2442no—
1323C22—2442no—
1324C22—2442no—
1325C22—2442no—
1326C22—2442no—
1327C22—2442no—
1328C22—2442no—
1329C22—2442no—
1330C22—2442no—
1331C22—2442no—
1332C22C2×C22⋊C4×D6111yescharacteristic
1333C22C4×D4×D6111yescharacteristic
1334C22C4×D4×D6111yescharacteristic
1335C22C4×D4×D6111yescharacteristic
1336C22C4×#1175822211yescharacteristic
1337C22#1684023411yescharacteristic
1338C22#1684024211yescharacteristic
1339C22#120×D6111yescharacteristic
1340C22#121×D6111yescharacteristic
1341C22#121×D6111yescharacteristic
1342C22C2×#1451975011yescharacteristic
1343C22#123×D6111yescharacteristic
1344C22#1684027111yescharacteristic
1345C22#1684029011yescharacteristic
1346C22#1684030911yescharacteristic
1347C22#1684032311yescharacteristic
1348C22#1684034111yescharacteristic
1349C22#1684034611yescharacteristic
1350C22#1684035311yescharacteristic
1351C22#1684039611yescharacteristic
1352C22#1684039611yescharacteristic
1353C22#1684039711yescharacteristic
1354C22#1684040211yescharacteristic
1355C22#1684040511yescharacteristic
1356C22#1684040811yescharacteristic
1357C22#1684040811yescharacteristic
1358C22#1684040811yescharacteristic
1359C22#1684040911yescharacteristic
1360C22#1684041011yescharacteristic
1361C22#1684041711yescharacteristic
1362C22#1684041711yescharacteristic
1363C22#1684042011yescharacteristic
1364C22#1684045611yescharacteristic
1365C22#1684046211yescharacteristic
1366C22#1684046311yescharacteristic
1367C4—24no—
1368C4—24no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—81no—
1373C4—1224no—
1374C4—4881no—
1375C4—2442no—
1376C4—2442no—
1377C4—2442no—
1378C4—2442no—
1379C2—82no—
1380C2—1228no—
1381C2—2444no—
1382C2#386×D6111yescharacteristic
1383C2C4×#1451975011yescharacteristic
1384C2#2144852311yescharacteristic
1385C2#2144864011yescharacteristic
1386C2#2144865011yescharacteristic
1387C2#2144883211yescharacteristic
1388C2#2144887011yescharacteristic
1389C2#2144919611yescharacteristic
1390C2#2144926211yescharacteristic
1391C2#2144936211yescharacteristic
1392C2#2144937511yescharacteristic
1393C2#2144942611yescharacteristic
1394C2#2144956111yescharacteristic
1395C2#2144957611yescharacteristic
1396C2#2145078411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1437C2
socle, cosocleC24×C61C24
prime radicalC22×#14519750C2
hypercenter#1437D61
hypocenterC61#14023
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C22×C4×D244C2semidirect
3. C2×#16839640C2semidirect
4. C2×#16839638C2semidirect
5. C2×#16839638C2semidirect
6. C2×#16839638C2semidirect
7. C2×#95×D61C2semidirect
8. #21444073C2semidirect
9. #21444067C2semidirect
10. #21444064C2semidirect
11. #21444058C2semidirect
12. #21444052C2semidirect
13. #21444040C2semidirect
14. #21444040C2semidirect
15. C61×#1437C2semidirect
25. C2×#14519750C4semidirect
83. C22×C22⋊D61C2×C4semidirect
84. C22×C22⋊D61C2×C4semidirect
117. C22×C4×D61C2×C4semidirect
118. C22×C4×D61D4semidirect
126. C2×#11758196C2×C4semidirect
149. C2×#11758198C2×C4semidirect
150. C2×#11758198D4semidirect
161. #14519684D4semidirect
177. C2×C22⋊C4×C61C2×C4semidirect
334. C2×D244C22⋊C4semidirect
538. C2×C4×C61#121semidirect
582. C2×Dic61C4×D4semidirect
668. C2×D61#386semidirect
692. #1437D61semidirect
760. C61#14023semidirect
865. C2×C22⋊C4C4×D61semidirect
1286. C2×C4#14519750semidirect

Maximal subgroups

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

subgroupindex
C22×#145197502
C22×C4×D2442
C2×#168396402
C2×#168396382
C2×#95×D612
#214440732
#214440672
#214440642
#214440582
#214440522
#214440402
C61×#14372
#1402361