Finite Group Databasebeta

← #29604518

Subgroups — #29604518

Order 15616.

2690 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519750C211yesmaximal, characteristic
2C2×#16839664C211yesmaximal, characteristic, complemented
3C2×#16839655C211yesmaximal, characteristic, complemented
4C2×#16839641C211yesmaximal, characteristic, complemented
5C2×#16839641C211yesmaximal, characteristic, complemented
6C2×C4×#11758198C211yesmaximal, characteristic, complemented
7#21444073C211yesmaximal, characteristic, complemented
8#21444059C211yesmaximal, characteristic, complemented
9#21444058C211yesmaximal, characteristic, complemented
10#21444058C211yesmaximal, characteristic, complemented
11#21444057C211yesmaximal, characteristic, complemented
12#21444055C211yesmaximal, characteristic, complemented
13#21444052C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C22⋊D61C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519750—24no—
21C2×#14519750—24no—
22C2×#14519750C418yescomplemented
23C22×C4⋊Dic61C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37#16839664—24no—
38#16839655—24no—
39#16839641—24no—
40#16839641—24no—
41C4×#11758198—24no—
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C24×C4×C61C2211yescharacteristic
53C22×C22⋊C4×C61C2211yescharacteristic
54C22×C22⋊C4×C61C2211yescharacteristic
55C22×C42×C61C2211yescharacteristic
56C22×C42×C61C2211yescharacteristic
57C4×C22⋊C4×C61—24no—
58C2×#95×C61C2211yescharacteristic
59C2×#95×C61C2211yescharacteristic
60C24×D61C2311yescharacteristic
61C24×D61C2311yescharacteristic
62C22×D244—22no—
63C22×D244—22no—
64C22×D244—22no—
65C22×D244—22no—
66C22×D244—41no—
67C22×D244—41no—
68C22×D244C2×C414yescomplemented
69C22×C22⋊D61—22no—
70C22×C22⋊D61—22no—
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—41no—
78C22×C22⋊D61—41no—
79C22×C22⋊D61—41no—
80C22×C22⋊D61—41no—
81C22×C22⋊D61C2×C414yes—
82C22×C22⋊D61C2×C414yes—
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89C22×C4×D61—22no—
90C22×C4×D61—22no—
91C22×C4×D61—22no—
92C22×C4×D61—22no—
93C22×C4×D61—41no—
94C22×C4×D61—41no—
95C22×C4×D61C2×C414yescomplemented
96#14519750—232no—
97C2×C4⋊Dic61—22no—
98C2×C4⋊Dic61—22no—
99C2×C4⋊Dic61—41no—
100C2×#11758196—22no—
101C2×#11758196—22no—
102C2×#11758196C2×C414yescomplemented
103C2×C22⋊Dic61—22no—
104C2×C22⋊Dic61—22no—
105C2×C22⋊Dic61—22no—
106C2×C22⋊Dic61—22no—
107C2×C22⋊Dic61—41no—
108C2×C22⋊Dic61—41no—
109C2×#11758198—22no—
110C2×#11758198—22no—
111C2×#11758198—22no—
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—41no—
129C2×#11758198—41no—
130C2×#11758198—41no—
131C2×#11758198—41no—
132C2×#11758198—41no—
133C2×#11758198—41no—
134C2×#11758198C2×C414yescomplemented
135C2×#11758198D414yescomplemented
136C2×C4×Dic61—22no—
137C2×C4×Dic61—22no—
138C2×C4×Dic61—41no—
139#14519684—22no—
140#14519684—22no—
141#14519684—22no—
142#14519684—22no—
143#14519684—22no—
144#14519684—22no—
145#14519684—22no—
146#14519684—41no—
147#14519684—41no—
148#14519684D414yescomplemented
149C25×C61C2311yescharacteristic
150C23×C4×C61—22no—
151C23×C4×C61—22no—
152C23×C4×C61—22no—
153C23×C4×C61—22no—
154C23×C4×C61—22no—
155C23×C4×C61—41no—
156C23×C4×C61—41no—
157C23×C4×C61C2311yescharacteristic
158C23×C4×C61C2311yescharacteristic
159C23×C4×C61C2311yescharacteristic
160C23×C4×C61C2311yescharacteristic
161C23×C4×C61C2311yescharacteristic
162C23×C4×C61C2311yescharacteristic
163C2×C22⋊C4×C61—22no—
164C2×C22⋊C4×C61—22no—
165C2×C22⋊C4×C61—22no—
166C2×C22⋊C4×C61C2×C414yes—
167C2×C22⋊C4×C61D414yes—
168C2×C22⋊C4×C61D414yes—
169C2×C42×C61—22no—
170C2×C42×C61—22no—
171C2×C42×C61—22no—
172C2×C42×C61—22no—
173C2×C42×C61—41no—
174C2×C42×C61—41no—
175#95×C61—22no—
176#95×C61—22no—
177C24×C61—21no—
178C24×C61—21no—
179C24×C61—21no—
180C24×C61—21no—
181C24×C61—21no—
182C24×C61—21no—
183C24×C61—21no—
184C24×C61—21no—
185C24×C61—21no—
186C24×C61—21no—
187C24×C61—21no—
188C24×C61—21no—
189C24×C61C22×C412yes—
190C24×C61C2×D412yes—
191C24×C61C2×D412yes—
192C24×C61C2411yescharacteristic
193C23×D61—21no—
194C23×D61—21no—
195C23×D61—21no—
196C23×D61—21no—
197C23×D61—21no—
198C23×D61—21no—
199C23×D61—21no—
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×D61C22×C412yes—
220C23×D61C22×C412yes—
221C23×D61C2×D412yes—
222C23×D61#4112yes—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—28no—
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—44no—
255C22×C4×C61—44no—
256C22×C4×C61—44no—
257C22×C4×C61—44no—
258C22×C4×C61—44no—
259C22×C4×C61—44no—
260C22×C4×C61C22×C412yes—
261C22×C4×C61C22×C412yes—
262C22×C4×C61C2×D412yes—
263C22×C4×C61C2×D412yes—
264C22×C4×C61C2×D412yes—
265C22×C4×C61C2×D412yes—
266C22×C4×C61C2×D412yes—
267C22×C4×C61C2×D412yes—
268C22×C4×C61#4112yes—
269C22×C4×C61#4112yes—
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—44no—
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×Dic61—21no—
322C22×Dic61C22×C412yes—
323C22×Dic61C22×C412yes—
324C22×Dic61C2×D412yes—
325C22×Dic61C2×D412yes—
326C22×Dic61C2×D412yes—
327C22×Dic61#4112yes—
328C2×D244—28no—
329C2×D244—28no—
330C2×D244—44no—
331C2×D244—44no—
332C2×D244—44no—
333C2×D244—44no—
334C2×D244—44no—
335C2×C4×D61—28no—
336C2×C4×D61—28no—
337C2×C4×D61—44no—
338C2×C4×D61—44no—
339C2×C4×D61—44no—
340C2×C4×D61—44no—
341C2×C4×D61—44no—
342C22⋊C4×C61—28no—
343C22⋊C4×C61C22⋊C4116yescomplemented
344C42×C61—44no—
345C42×C61—44no—
346C22⋊Dic61—44no—
347C22⋊Dic61—44no—
348#11758198—28no—
349#11758198—28no—
350#11758198—28no—
351#11758198—44no—
352#11758198—44no—
353#11758198—44no—
354#11758198—44no—
355#11758198—44no—
356#11758198—44no—
357C4⋊Dic61—44no—
358#11758196—28no—
359C4×Dic61—44no—
360C23×C61—22no—
361C23×C61—22no—
362C23×C61—22no—
363C23×C61—22no—
364C23×C61—22no—
365C23×C61—22no—
366C23×C61—22no—
367C23×C61—22no—
368C23×C61—22no—
369C23×C61—22no—
370C23×C61—22no—
371C23×C61—22no—
372C23×C61—22no—
373C23×C61—22no—
374C23×C61—22no—
375C23×C61—22no—
376C23×C61—22no—
377C23×C61—22no—
378C23×C61—41no—
379C23×C61—41no—
380C23×C61—41no—
381C23×C61—41no—
382C23×C61—41no—
383C23×C61—41no—
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×C61C2×C22⋊C414yes—
395C23×C61C23×C411yescharacteristic
396C23×C61C22×D411yescharacteristic
397C23×C61C22×D411yescharacteristic
398C23×C61C22×D411yescharacteristic
399C23×C61C22×D411yescharacteristic
400C23×C61C2×#4111yescharacteristic
401C23×C61C2×#4111yescharacteristic
402C23×C61C2×#4111yescharacteristic
403C23×C61C2×#4111yescharacteristic
404C23×C61C2×#4111yescharacteristic
405C23×C61C2×#4111yescharacteristic
406C23×C61H(5,𝔽2)11yescharacteristic
407C23×C61H(5,𝔽2)11yescharacteristic
408C23×C61H(5,𝔽2)11yescharacteristic
409C23×C61H(5,𝔽2)11yescharacteristic
410C22×D61—22no—
411C22×D61—22no—
412C22×D61—22no—
413C22×D61—22no—
414C22×D61—22no—
415C22×D61—22no—
416C22×D61—22no—
417C22×D61—22no—
418C22×D61—22no—
419C22×D61—22no—
420C22×D61—22no—
421C22×D61—22no—
422C22×D61—22no—
423C22×D61—22no—
424C22×D61—22no—
425C22×D61—22no—
426C22×D61—22no—
427C22×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—41no—
436C22×D61—41no—
437C22×D61—41no—
438C22×D61—41no—
439C22×D61—41no—
440C22×D61—41no—
441C22×D61—41no—
442C22×D61—41no—
443C22×D61—41no—
444C22×D61—41no—
445C22×D61—41no—
446C22×D61—41no—
447C22×D61—41no—
448C22×D61—41no—
449C22×D61—41no—
450C22×D61—41no—
451C22×D61—41no—
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×D61C4×D414yes—
480C2×C4×C61—22no—
481C2×C4×C61—22no—
482C2×C4×C61—22no—
483C2×C4×C61—22no—
484C2×C4×C61—22no—
485C2×C4×C61—22no—
486C2×C4×C61—22no—
487C2×C4×C61—22no—
488C2×C4×C61—22no—
489C2×C4×C61—22no—
490C2×C4×C61—22no—
491C2×C4×C61—22no—
492C2×C4×C61—22no—
493C2×C4×C61—22no—
494C2×C4×C61—22no—
495C2×C4×C61—22no—
496C2×C4×C61—22no—
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—416no—
508C2×C4×C61—41no—
509C2×C4×C61—41no—
510C2×C4×C61—41no—
511C2×C4×C61—41no—
512C2×C4×C61—41no—
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×C61C2×C22⋊C414yes—
521C2×C4×C61C2×C22⋊C414yes—
522C2×C4×C61#12114yescomplemented
523C22⋊D61—416no—
524C22⋊D61—416no—
525C2×Dic61—22no—
526C2×Dic61—22no—
527C2×Dic61—22no—
528C2×Dic61—22no—
529C2×Dic61—22no—
530C2×Dic61—22no—
531C2×Dic61—22no—
532C2×Dic61—22no—
533C2×Dic61—22no—
534C2×Dic61—22no—
535C2×Dic61—22no—
536C2×Dic61—22no—
537C2×Dic61—22no—
538C2×Dic61—22no—
539C2×Dic61—22no—
540C2×Dic61—41no—
541C2×Dic61—41no—
542C2×Dic61—41no—
543C2×Dic61—41no—
544C2×Dic61—41no—
545C2×Dic61—41no—
546C2×Dic61—41no—
547C2×Dic61—41no—
548C2×Dic61—41no—
549C2×Dic61—41no—
550C2×Dic61—41no—
551C2×Dic61—41no—
552C2×Dic61—41no—
553C2×Dic61—41no—
554C2×Dic61—41no—
555C2×Dic61—41no—
556C2×Dic61—41no—
557C2×Dic61—41no—
558C2×Dic61—41no—
559C2×Dic61—41no—
560C2×Dic61—41no—
561C2×Dic61—41no—
562C2×Dic61—41no—
563C2×Dic61—41no—
564C2×Dic61—41no—
565C2×Dic61—41no—
566C2×Dic61C4×D414yes—
567D244—416no—
568C4×D61—416no—
569#14100—611nomaximal, Sylow
570C22×C61—24no—
571C22×C61—24no—
572C22×C61—24no—
573C22×C61—42no—
574C22×C61—42no—
575C22×C61—42no—
576C22×C61—42no—
577C22×C61—42no—
578C22×C61—42no—
579C22×C61—42no—
580C22×C61—42no—
581C22×C61—42no—
582C22×C61—42no—
583C22×C61—42no—
584C22×C61—42no—
585C22×C61C22×C22⋊C411yescharacteristic
586C22×C61C2×C4×D411yescharacteristic
587C22×C61C2×C4×D411yescharacteristic
588C22×C61C4×#4111yescharacteristic
589C22×C61C4×#4111yescharacteristic
590C22×C61#51811yescharacteristic
591C22×C61#51811yescharacteristic
592C22×C61C2×#12111yescharacteristic
593C22×C61#52511yescharacteristic
594C22×C61#52511yescharacteristic
595C22×C61#52511yescharacteristic
596C22×C61#52911yescharacteristic
597C22×C61#53211yescharacteristic
598C22×C61#53211yescharacteristic
599C22×C61#53211yescharacteristic
600C22×C61#53811yescharacteristic
601C22×C61#53811yescharacteristic
602C22×C61#54011yescharacteristic
603C22×C61#54011yescharacteristic
604C22×C61D4211yescharacteristic
605C22×C61D4211yescharacteristic
606C22×C61D4211yescharacteristic
607C22×C61D4211yescharacteristic
608C22×C61#54611yescharacteristic
609C22×C61#54611yescharacteristic
610C22×C61#54611yescharacteristic
611C22×C61#54611yescharacteristic
612C22×C61#54611yescharacteristic
613C22×C61#54611yescharacteristic
614C22×C61#54611yescharacteristic
615C22×C61#55011yescharacteristic
616C22×C61#55311yescharacteristic
617C22×C61#55311yescharacteristic
618C22×C61#55311yescharacteristic
619C22×C61#55511yescharacteristic
620C2×D61—24no—
621C2×D61—24no—
622C2×D61—24no—
623C2×D61—42no—
624C2×D61—42no—
625C2×D61—42no—
626C2×D61—42no—
627C2×D61—42no—
628C2×D61—42no—
629C2×D61—42no—
630C2×D61—42no—
631C2×D61—42no—
632C2×D61—42no—
633C2×D61—42no—
634C2×D61—42no—
635C2×D61—42no—
636C2×D61—42no—
637C2×D61—42no—
638C2×D61—42no—
639C2×D61—42no—
640C2×D61—42no—
641C2×D61—42no—
642C2×D61—81no—
643C2×D61—81no—
644C2×D61—81no—
645C2×D61—81no—
646C2×D61—81no—
647C2×D61—81no—
648C2×D61—81no—
649C2×D61—81no—
650C4×C61—24no—
651C4×C61—24no—
652C4×C61—24no—
653C4×C61—42no—
654C4×C61—42no—
655C4×C61—42no—
656Dic61—24no—
657Dic61—42no—
658Dic61—42no—
659Dic61—42no—
660Dic61—81no—
661Dic61—81no—
662C22×#121—611no—
663C2×#390—611no—
664C2×#388—611no—
665C2×#386—611no—
666C2×#386—611no—
667C2×C4×C22⋊C4—611no—
668C2×C4×C22⋊C4D6111yescharacteristic, complemented
669#1441—611no—
670#1438—611no—
671#1438—611no—
672#1438—611no—
673#1437—611no—
674#1437—611no—
675#1436—611no—
676C22⋊#95—611no—
677C2×C61—44no—
678C2×C61#229711yescharacteristic
679C2×C61C4×#12111yescharacteristic
680C2×C61#233311yescharacteristic
681C2×C61D4×C22⋊C411yescharacteristic
682C2×C61D4×C22⋊C411yescharacteristic
683C2×C61#236311yescharacteristic
684C2×C61#236411yescharacteristic
685C2×C61#242411yescharacteristic
686C2×C61#242811yescharacteristic
687C2×C61#245611yescharacteristic
688C2×C61#246411yescharacteristic
689C2×C61#246411yescharacteristic
690C2×C61#247611yescharacteristic
691C2×C61#255511yescharacteristic
692C2×C61#255911yescharacteristic
693D61—44no—
694D61—82no—
695C23×D4—611no—
696C23×D4—611no—
697C23×D4—611no—
698C24×C4—611no—
699C24×C4C2×D6111yescharacteristic
700C2×#121—618no—
701C2×#121—1224no—
702C2×#121—1224no—
703C22×C4⋊C4—611no—
704C22×C4⋊C4—611no—
705C22×C22⋊C4—611no—
706C22×C22⋊C4—611no—
707C22×C22⋊C4—611no—
708C22×C22⋊C4—611no—
709C22×C22⋊C4—611no—
710C22×C22⋊C4—611no—
711C22×C22⋊C4—611no—
712C22×C22⋊C4—611no—
713C22×C22⋊C4—611no—
714C22×C22⋊C4—611no—
715C22×C22⋊C4—611no—
716C22×C22⋊C4C2×D6111yescharacteristic
717C22×C22⋊C4C2×D6111yescharacteristic
718C22×C42—611no—
719C22×C42C2×D6111yescharacteristic
720C22×C42C2×D6111yescharacteristic
721#390—1224no—
722#388—1224no—
723#386—1224no—
724#386—1224no—
725C4×C22⋊C4—24no—
726C4×C22⋊C4—1224no—
727C2×#95—611no—
728C2×#95—611no—
729C2×#95—611no—
730C2×#95—611no—
731C2×#95—611no—
732C2×#95—611no—
733C2×#95—611no—
734C2×#95—611no—
735C2×#95—611no—
736C2×#95—611no—
737C2×#95C2×D6111yescharacteristic
738C2×#95C2×D6111yescharacteristic
739C61#1410011yescharacteristic, complemented, Sylow
740C25—611no—
741C25—611no—
742C25C22×D6111yescharacteristic
743C22×D4—614no—
744C22×D4—614no—
745C22×D4—614no—
746C22×D4—1222no—
747C22×D4—1222no—
748C22×D4—1222no—
749C22×D4—1222no—
750C22×D4—1222no—
751C22×D4—1222no—
752C22×D4—1222no—
753C22×D4—1222no—
754C22×D4—1222no—
755C22×D4—1222no—
756C22×D4—1222no—
757C22×D4—1222no—
758C22×D4—2441no—
759C22×D4—2441no—
760C22×D4—2441no—
761C22×D4—2441no—
762C22×D4—2441no—
763C22×D4—2441no—
764C23×C4—22no—
765C23×C4—22no—
766C23×C4—22no—
767C23×C4—22no—
768C23×C4—22no—
769C23×C4—41no—
770C23×C4—41no—
771C23×C4—611no—
772C23×C4—611no—
773C23×C4—611no—
774C23×C4—611no—
775C23×C4—614no—
776C23×C4—611no—
777C23×C4—611no—
778C23×C4—1222no—
779C23×C4—1222no—
780C23×C4—1222no—
781C23×C4—1222no—
782C23×C4—2441no—
783C23×C4—2441no—
784C23×C4C22×D6111yescharacteristic
785C23×C4C22×D6111yescharacteristic
786C23×C4C22×D6111yescharacteristic
787C23×C4C22×D6111yescharacteristic
788C23×C4C22×D6111yescharacteristic
789C23×C4C22×D6111yescharacteristic
790#121—12232no—
791C2×C4⋊C4—614no—
792C2×C4⋊C4—1222no—
793C2×C4⋊C4—1222no—
794C2×C4⋊C4—1222no—
795C2×C4⋊C4—1222no—
796C2×C4⋊C4—2441no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—614no—
801C2×C22⋊C4—614no—
802C2×C22⋊C4—1222no—
803C2×C22⋊C4—1222no—
804C2×C22⋊C4—1222no—
805C2×C22⋊C4—1222no—
806C2×C22⋊C4—1222no—
807C2×C22⋊C4—1222no—
808C2×C22⋊C4—1222no—
809C2×C22⋊C4—1222no—
810C2×C22⋊C4—1222no—
811C2×C22⋊C4—1222no—
812C2×C22⋊C4—1222no—
813C2×C22⋊C4—1222no—
814C2×C22⋊C4—1222no—
815C2×C22⋊C4—1222no—
816C2×C22⋊C4—1222no—
817C2×C22⋊C4—1222no—
818C2×C22⋊C4—1222no—
819C2×C22⋊C4—1222no—
820C2×C22⋊C4—1222no—
821C2×C22⋊C4—1222no—
822C2×C22⋊C4—1222no—
823C2×C22⋊C4—1222no—
824C2×C22⋊C4—1222no—
825C2×C22⋊C4—2441no—
826C2×C22⋊C4—2441no—
827C2×C22⋊C4—2441no—
828C2×C22⋊C4—2441no—
829C2×C22⋊C4—2441no—
830C2×C22⋊C4—2441no—
831C2×C22⋊C4—2441no—
832C2×C22⋊C4—2441no—
833C2×C22⋊C4C4×D6114yes—
834C2×C22⋊C4D24414yes—
835C2×C22⋊C4C22⋊D6114yes—
836C2×C42—22no—
837C2×C42—22no—
838C2×C42—22no—
839C2×C42—22no—
840C2×C42—41no—
841C2×C42—41no—
842C2×C42—1222no—
843C2×C42—1222no—
844C2×C42—2441no—
845#95—22no—
846#95—22no—
847#95—614no—
848#95—1222no—
849#95—1222no—
850#95—1222no—
851#95—1222no—
852#95—1222no—
853#95—1222no—
854#95—1222no—
855#95—2441no—
856#95—2441no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—612no—
870C24—612no—
871C24—612no—
872C24—612no—
873C24—1221no—
874C24—1221no—
875C24—1221no—
876C24—1221no—
877C24—1221no—
878C24—1221no—
879C24—1221no—
880C24—1221no—
881C24—1221no—
882C24—1221no—
883C24—1221no—
884C24—1221no—
885C24—1221no—
886C24—1221no—
887C24—1221no—
888C24—1221no—
889C24—1221no—
890C24—1221no—
891C24—1221no—
892C24—1221no—
893C24—1221no—
894C24—1221no—
895C24—1221no—
896C24—1221no—
897C24—1221no—
898C24—1221no—
899C24C2×C4×D6112yes—
900C24C2×D24412yes—
901C24C2×C22⋊D6112yes—
902C24C23×D6111yescharacteristic
903C2×D4—1228no—
904C2×D4—1228no—
905C2×D4—1228no—
906C2×D4—1228no—
907C2×D4—1228no—
908C2×D4—1228no—
909C2×D4—2444no—
910C2×D4—2444no—
911C2×D4—2444no—
912C2×D4—2444no—
913C2×D4—2444no—
914C2×D4—2444no—
915C2×D4—2444no—
916C2×D4—2444no—
917C2×D4—2444no—
918C2×D4—2444no—
919C2×D4—2444no—
920C2×D4—2444no—
921C2×D4—2444no—
922C2×D4—2444no—
923C2×D4—2444no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—28no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—44no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—612no—
962C22×C4—612no—
963C22×C4—612no—
964C22×C4—612no—
965C22×C4—612no—
966C22×C4—612no—
967C22×C4—1228no—
968C22×C4—1221no—
969C22×C4—1221no—
970C22×C4—1221no—
971C22×C4—1221no—
972C22×C4—1221no—
973C22×C4—1221no—
974C22×C4—1221no—
975C22×C4—1221no—
976C22×C4—1221no—
977C22×C4—1221no—
978C22×C4—1221no—
979C22×C4—1221no—
980C22×C4—1221no—
981C22×C4—1221no—
982C22×C4—1221no—
983C22×C4—1221no—
984C22×C4—1221no—
985C22×C4—1221no—
986C22×C4—1221no—
987C22×C4—1221no—
988C22×C4—1221no—
989C22×C4—1221no—
990C22×C4—1228no—
991C22×C4—1221no—
992C22×C4—1221no—
993C22×C4—1221no—
994C22×C4—1221no—
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—2444no—
1006C22×C4—2444no—
1007C22×C4—2444no—
1008C22×C4—2444no—
1009C22×C4—2444no—
1010C22×C4C2×C4×D6112yes—
1011C22×C4C2×C4×D6112yes—
1012C22×C4C2×D24412yes—
1013C22×C4C2×D24412yes—
1014C22×C4#1175822212yes—
1015C22×C4#1175822212yes—
1016C22×C4#1175822212yes—
1017C22×C4#1175822212yes—
1018C22×C4D4×D6112yes—
1019C22×C4D4×D6112yes—
1020C22×C4C2×C22⋊D6112yes—
1021C22×C4C2×C22⋊D6112yes—
1022C4⋊C4—1228no—
1023C4⋊C4—2444no—
1024C22⋊C4—28no—
1025C22⋊C4—1228no—
1026C22⋊C4—1228no—
1027C22⋊C4—1228no—
1028C22⋊C4—2444no—
1029C22⋊C4—2444no—
1030C22⋊C4—2444no—
1031C22⋊C4—2444no—
1032C22⋊C4—2444no—
1033C22⋊C4—2444no—
1034C22⋊C4—2444no—
1035C22⋊C4—2444no—
1036C22⋊C4#11758198116yescomplemented
1037C42—44no—
1038C42—44no—
1039C42—2444no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—614no—
1075C23—1222no—
1076C23—1222no—
1077C23—1222no—
1078C23—1222no—
1079C23—1222no—
1080C23—1222no—
1081C23—1222no—
1082C23—1222no—
1083C23—1222no—
1084C23—1222no—
1085C23—1222no—
1086C23—1222no—
1087C23—1222no—
1088C23—1222no—
1089C23—1222no—
1090C23—1222no—
1091C23—1222no—
1092C23—1222no—
1093C23—1222no—
1094C23—1222no—
1095C23—1222no—
1096C23—1222no—
1097C23—1222no—
1098C23—1222no—
1099C23—1222no—
1100C23—2441no—
1101C23—2441no—
1102C23—2441no—
1103C23—2441no—
1104C23—2441no—
1105C23—2441no—
1106C23—2441no—
1107C23—2441no—
1108C23—2441no—
1109C23—2441no—
1110C23—2441no—
1111C23—2441no—
1112C23—2441no—
1113C23—2441no—
1114C23—2441no—
1115C23—2441no—
1116C23—2441no—
1117C23—2441no—
1118C23—2441no—
1119C23—2441no—
1120C23—2441no—
1121C23—2441no—
1122C23—2441no—
1123C23—2441no—
1124C23—2441no—
1125C23—2441no—
1126C23—2441no—
1127C23—2441no—
1128C23—2441no—
1129C23—2441no—
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—
1144C23C2×#1175819814yes—
1145C23C22×C4×D6111yescharacteristic
1146C23C2×D4×D6111yescharacteristic
1147C23C2×D4×D6111yescharacteristic
1148C23C22×C22⋊D6111yescharacteristic
1149C23C22×D24411yescharacteristic
1150C23#41×D6111yescharacteristic
1151C23#41×D6111yescharacteristic
1152C23C2×#1175822211yescharacteristic
1153C23C2×#1175822211yescharacteristic
1154C23C2×#1175822211yescharacteristic
1155C23C2×#1175822211yescharacteristic
1156C23#1451982211yescharacteristic
1157C23#1451982211yescharacteristic
1158C23#1451982311yescharacteristic
1159C23#1451982311yescharacteristic
1160D4—24416no—
1161D4—24416no—
1162D4—24416no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—416no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—614no—
1204C2×C4—1222no—
1205C2×C4—1222no—
1206C2×C4—1222no—
1207C2×C4—1222no—
1208C2×C4—1222no—
1209C2×C4—1222no—
1210C2×C4—1222no—
1211C2×C4—1222no—
1212C2×C4—1222no—
1213C2×C4—1222no—
1214C2×C4—1222no—
1215C2×C4—1222no—
1216C2×C4—1222no—
1217C2×C4—1222no—
1218C2×C4—1222no—
1219C2×C4—24416no—
1220C2×C4—2441no—
1221C2×C4—2441no—
1222C2×C4—2441no—
1223C2×C4—2441no—
1224C2×C4—2441no—
1225C2×C4—2441no—
1226C2×C4—2441no—
1227C2×C4—2441no—
1228C2×C4—2441no—
1229C2×C4—2441no—
1230C2×C4—2441no—
1231C2×C4—2441no—
1232C2×C4—2441no—
1233C2×C4—2441no—
1234C2×C4—2441no—
1235C2×C4—2441no—
1236C2×C4—2441no—
1237C2×C4—2441no—
1238C2×C4—2441no—
1239C2×C4—2441no—
1240C2×C4—2441no—
1241C2×C4—2441no—
1242C2×C4—2441no—
1243C2×C4—2441no—
1244C2×C4—2441no—
1245C2×C4—2441no—
1246C2×C4C2×#1175819814yes—
1247C2×C4C2×#1175819814yes—
1248C2×C4#1451975014yescomplemented
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—1224no—
1265C22—1224no—
1266C22—1224no—
1267C22—4881no—
1268C22—4881no—
1269C22—4881no—
1270C22—4881no—
1271C22—4881no—
1272C22—4881no—
1273C22—4881no—
1274C22—4881no—
1275C22—2442no—
1276C22—2442no—
1277C22—2442no—
1278C22—2442no—
1279C22—2442no—
1280C22—2442no—
1281C22—2442no—
1282C22—2442no—
1283C22—2442no—
1284C22—2442no—
1285C22—2442no—
1286C22—2442no—
1287C22—2442no—
1288C22—2442no—
1289C22—2442no—
1290C22—2442no—
1291C22—2442no—
1292C22—2442no—
1293C22—2442no—
1294C22C22×#1175819811yescharacteristic
1295C22C4×D4×D6111yescharacteristic
1296C22C4×D4×D6111yescharacteristic
1297C22C4×#1175822211yescharacteristic
1298C22C4×#1175822211yescharacteristic
1299C22#1684023411yescharacteristic
1300C22#1684023411yescharacteristic
1301C22C2×#1451975011yescharacteristic
1302C22#1684027111yescharacteristic
1303C22#1684027311yescharacteristic
1304C22#1684027311yescharacteristic
1305C22#1684029011yescharacteristic
1306C22#1684030911yescharacteristic
1307C22#1684031211yescharacteristic
1308C22#1684031211yescharacteristic
1309C22#1684034511yescharacteristic
1310C22#1684035011yescharacteristic
1311C22#1684036311yescharacteristic
1312C22#1684036711yescharacteristic
1313C22D4×C22⋊D6111yescharacteristic
1314C22D4×C22⋊D6111yescharacteristic
1315C22D4×D24411yescharacteristic
1316C22D4×D24411yescharacteristic
1317C22#1684040011yescharacteristic
1318C22#1684040011yescharacteristic
1319C22#1684040211yescharacteristic
1320C22#1684040211yescharacteristic
1321C22#1684040711yescharacteristic
1322C22#1684040711yescharacteristic
1323C22#1684040811yescharacteristic
1324C22#1684043311yescharacteristic
1325C22#1684045611yescharacteristic
1326C22#1684046111yescharacteristic
1327C22#1684046211yescharacteristic
1328C22#1684047511yescharacteristic
1329C4—24no—
1330C4—24no—
1331C4—24no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—1224no—
1336C4—4881no—
1337C4—4881no—
1338C4—2442no—
1339C4—2442no—
1340C4—2442no—
1341C2—44no—
1342C2—4882no—
1343C2—2444no—
1344C2#2144830911yescharacteristic
1345C2C4×#1451975011yescharacteristic
1346C2#2144857911yescharacteristic
1347C2D4×#1175819811yescharacteristic
1348C2D4×#1175819811yescharacteristic
1349C2#2144885811yescharacteristic
1350C2#2144887011yescharacteristic
1351C2#2144935511yescharacteristic
1352C2#2144940711yescharacteristic
1353C2#2144971111yescharacteristic
1354C2#2144981911yescharacteristic
1355C2#2144982511yescharacteristic
1356C2#2144999911yescharacteristic
1357C2#2145088811yescharacteristic
1358C2#2145094211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C4×C22⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC22×#14519750C2
hypercenterC2×C4×C22⋊C4D61
hypocenterC61#14100
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16839664C2semidirect
3. C2×#16839655C2semidirect
4. C2×#16839641C2semidirect
5. C2×#16839641C2semidirect
6. C2×C4×#11758198C2semidirect
7. #21444073C2semidirect
8. #21444059C2semidirect
9. #21444058C2semidirect
10. #21444058C2semidirect
11. #21444057C2semidirect
12. #21444055C2semidirect
13. #21444052C2semidirect
14. #21444040C2semidirect
15. C2×C4×C22⋊C4×C61C2semidirect
22. C2×#14519750C4semidirect
68. C22×D244C2×C4semidirect
95. C22×C4×D61C2×C4semidirect
102. C2×#11758196C2×C4semidirect
134. C2×#11758198C2×C4semidirect
135. C2×#11758198D4semidirect
148. #14519684D4semidirect
343. C22⋊C4×C61C22⋊C4semidirect
522. C2×C4×C61#121semidirect
668. C2×C4×C22⋊C4D61semidirect
739. C61#14100semidirect
1036. C22⋊C4#11758198semidirect
1248. 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
C2×#168396642
C2×#168396552
C2×#168396412
C2×C4×#117581982
#214440732
#214440592
#214440582
#214440572
#214440552
#214440522
#214440402
C2×C4×C22⋊C4×C612
#1410061