Finite Group Databasebeta

← #29601576

Subgroups — #29601576

Order 15616.

2666 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519737C211yesmaximal, characteristic
2C2×#16839662C211yesmaximal, characteristic
3C2×#16839662C211yesmaximal, characteristic
4C2×C4×#11758196C211yesmaximal, characteristic, complemented
5C2×#16839613C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
7C2×C4×#11758198C211yesmaximal, characteristic, complemented
8#21444056C211yesmaximal, characteristic, complemented
9#21444055C211yesmaximal, characteristic, complemented
10#21444055C211yesmaximal, characteristic, complemented
11#21444047C211yesmaximal, characteristic, complemented
12#21444041C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic, complemented
14#95×Dic61C211yesmaximal, characteristic, complemented
15C61×#1437C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C24×Dic61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C2×#14519737—24no—
20C2×#14519737—24no—
21C2×#14519737C418yescomplemented
22C22×#11758196C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37C22×C4×Dic61C2211yescharacteristic
38#16839662C418yescomplemented
39#16839662C418yescomplemented
40C4×#11758196—24no—
41#16839613—24no—
42C22⋊C4×Dic61—24no—
43C4×#11758198—24no—
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C22×C22⋊C4×C61C2211yescharacteristic
54C22×C22⋊C4×C61C2211yescharacteristic
55C22×C22⋊C4×C61C2211yescharacteristic
56C22×C42×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C2×#95×C61C2211yescharacteristic
59C2×#95×C61C2211yescharacteristic
60C24×D61C2311yescharacteristic
61C22×C22⋊D61—22no—
62C22×C22⋊D61—22no—
63C22×C22⋊D61—22no—
64C22×C22⋊D61—22no—
65C22×C22⋊D61C2×C414yes—
66C22×C22⋊D61C2×C414yes—
67C22×C22⋊D61C2×C414yes—
68C23×Dic61—22no—
69C23×Dic61—22no—
70C23×Dic61—22no—
71C23×Dic61—22no—
72C23×Dic61—41no—
73C23×Dic61—41no—
74C23×Dic61C2×C414yes—
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C22×C4×D61—22no—
83C22×C4×D61—22no—
84C22×C4×D61—22no—
85C22×C4×D61—22no—
86C22×C4×D61—41no—
87C22×C4×D61—41no—
88C22×C4×D61C2×C414yes—
89#14519737—232no—
90C2×#11758196—22no—
91C2×#11758196—22no—
92C2×#11758196—22no—
93C2×#11758196—22no—
94C2×#11758196C2×C414yes—
95C2×#11758196C2×C414yescomplemented
96C2×#11758196C2×C414yescomplemented
97C2×#11758196D414yes—
98C2×#11758196D414yes—
99C2×C22⋊Dic61—22no—
100C2×C22⋊Dic61—22no—
101C2×C22⋊Dic61—41no—
102C2×C22⋊Dic61—41no—
103C2×C22⋊Dic61C2×C414yescomplemented
104C2×C22⋊Dic61C2×C414yescomplemented
105C2×#11758198—22no—
106C2×#11758198—22no—
107C2×#11758198—22no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×#11758198—22no—
111C2×#11758198—41no—
112C2×#11758198—41no—
113C2×#11758198—41no—
114C2×#11758198—41no—
115C2×#11758198C2×C414yes—
116C2×#11758198C2×C414yescomplemented
117C2×#11758198C2×C414yescomplemented
118C2×#11758198C2×C414yescomplemented
119C2×#11758198C2×C414yescomplemented
120C2×C4×Dic61—22no—
121C2×C4×Dic61—22no—
122C2×C4×Dic61—22no—
123C2×C4×Dic61—22no—
124C2×C4×Dic61—22no—
125C2×C4×Dic61—22no—
126C2×C4×Dic61—22no—
127C2×C4×Dic61—22no—
128C2×C4×Dic61—22no—
129C2×C4×Dic61—22no—
130C2×C4×Dic61—22no—
131C2×C4×Dic61—22no—
132C2×C4×Dic61—41no—
133C2×C4×Dic61—41no—
134C2×C4×Dic61—41no—
135C2×C4×Dic61C2×C414yes—
136C2×C4×Dic61C2×C414yescomplemented
137C2×C4×Dic61C2×C414yescomplemented
138#14519684—22no—
139#14519684—22no—
140#14519684—22no—
141#14519684—22no—
142#14519684—22no—
143#14519684—22no—
144#14519684—22no—
145#14519684—41no—
146#14519684D414yescomplemented
147C25×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149C23×C4×C61C2311yescharacteristic
150C23×C4×C61C2311yescharacteristic
151C23×C4×C61C2311yescharacteristic
152C23×C4×C61C2311yescharacteristic
153C23×C4×C61C2311yescharacteristic
154C2×C22⋊C4×C61—22no—
155C2×C22⋊C4×C61—22no—
156C2×C22⋊C4×C61—22no—
157C2×C22⋊C4×C61—22no—
158C2×C22⋊C4×C61—41no—
159C2×C22⋊C4×C61—41no—
160C2×C22⋊C4×C61C2×C414yes—
161C2×C22⋊C4×C61C2×C414yescomplemented
162C2×C22⋊C4×C61C2×C414yescomplemented
163C2×C42×C61—22no—
164C2×C42×C61—22no—
165C2×C42×C61—41no—
166#95×C61—22no—
167#95×C61—22no—
168#95×C61—41no—
169C24×C61—21no—
170C24×C61—21no—
171C24×C61—21no—
172C24×C61—21no—
173C24×C61—21no—
174C24×C61—21no—
175C24×C61—21no—
176C24×C61—21no—
177C24×C61—21no—
178C24×C61—21no—
179C24×C61—21no—
180C24×C61—21no—
181C24×C61C22×C412yes—
182C24×C61C22×C412yes—
183C24×C61C22×C412yes—
184C24×C61C2411yescharacteristic
185C23×D61—21no—
186C23×D61—21no—
187C23×D61—21no—
188C23×D61—21no—
189C23×D61—21no—
190C23×D61—21no—
191C23×D61—21no—
192C23×D61—21no—
193C23×D61—21no—
194C23×D61—21no—
195C23×D61—21no—
196C23×D61—21no—
197C23×D61C22×C412yes—
198C23×D61C22×C412yes—
199C23×D61C22×C412yes—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61C22×C412yes—
233C22×C4×C61C22×C412yes—
234C22×C4×C61C22×C412yes—
235C22×C4×C61C22×C412yes—
236C22×C4×C61C22×C412yes—
237C22×C4×C61C22×C412yes—
238C22×C4×C61C2×D412yes—
239C22×C4×C61C2×D412yes—
240C22×C4×C61C2×D412yes—
241C22×C4×C61#4112yes—
242C2×C22⋊D61—28no—
243C2×C22⋊D61—28no—
244C2×C22⋊D61—28no—
245C2×C22⋊D61—28no—
246C2×C22⋊D61—28no—
247C2×C22⋊D61—28no—
248C2×C22⋊D61C42116yescomplemented
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—21no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255C22×Dic61—21no—
256C22×Dic61—21no—
257C22×Dic61—21no—
258C22×Dic61—21no—
259C22×Dic61—21no—
260C22×Dic61—21no—
261C22×Dic61—21no—
262C22×Dic61—21no—
263C22×Dic61—21no—
264C22×Dic61—21no—
265C22×Dic61—21no—
266C22×Dic61—21no—
267C22×Dic61—21no—
268C22×Dic61—21no—
269C22×Dic61—21no—
270C22×Dic61—21no—
271C22×Dic61—21no—
272C22×Dic61—21no—
273C22×Dic61—21no—
274C22×Dic61—21no—
275C22×Dic61—21no—
276C22×Dic61—21no—
277C22×Dic61—21no—
278C22×Dic61—21no—
279C22×Dic61—28no—
280C22×Dic61—28no—
281C22×Dic61—44no—
282C22×Dic61—44no—
283C22×Dic61—44no—
284C22×Dic61—44no—
285C22×Dic61—44no—
286C22×Dic61C22×C412yes—
287C22×Dic61C22×C412yes—
288C22×Dic61C22×C412yes—
289C22×Dic61C22×C412yes—
290C22×Dic61C22×C412yes—
291C22×Dic61C22×C412yes—
292C22×Dic61C22×C412yes—
293C22×Dic61C22×C412yes—
294C22×Dic61C22×C412yes—
295C22×Dic61C2×D412yes—
296C22×Dic61C2×D412yes—
297C22×Dic61C2×D412yes—
298C22×Dic61C2×D412yes—
299C22×Dic61C2×D412yes—
300C22×Dic61C2×D412yes—
301C22×Dic61#4112yes—
302C22×Dic61#4112yes—
303C22×Dic61#4112yes—
304C22×Dic61#4112yes—
305C2×C4×D61—28no—
306C2×C4×D61—28no—
307C2×C4×D61—44no—
308C2×C4×D61—44no—
309C2×C4×D61—44no—
310C2×C4×D61—44no—
311C2×C4×D61—44no—
312C22⋊C4×C61—28no—
313C22⋊C4×C61—28no—
314C22⋊C4×C61—44no—
315C42×C61—44no—
316C22⋊Dic61—28no—
317C22⋊Dic61—44no—
318#11758198—28no—
319#11758198—28no—
320#11758198—28no—
321#11758198—44no—
322#11758198—44no—
323#11758196—28no—
324#11758196—28no—
325#11758196C22⋊C4116yescomplemented
326C4×Dic61—28no—
327C4×Dic61—28no—
328C4×Dic61—28no—
329C4×Dic61—44no—
330C4×Dic61—44no—
331C4×Dic61—44no—
332C23×C61—22no—
333C23×C61—22no—
334C23×C61—22no—
335C23×C61—22no—
336C23×C61—22no—
337C23×C61—22no—
338C23×C61—22no—
339C23×C61—22no—
340C23×C61—22no—
341C23×C61—22no—
342C23×C61—22no—
343C23×C61—22no—
344C23×C61—22no—
345C23×C61—22no—
346C23×C61—22no—
347C23×C61—22no—
348C23×C61—22no—
349C23×C61—22no—
350C23×C61—41no—
351C23×C61—41no—
352C23×C61—41no—
353C23×C61—41no—
354C23×C61—41no—
355C23×C61—41no—
356C23×C61—41no—
357C23×C61—41no—
358C23×C61—41no—
359C23×C61—41no—
360C23×C61—41no—
361C23×C61—41no—
362C23×C61—41no—
363C23×C61—41no—
364C23×C61—41no—
365C23×C61—41no—
366C23×C61C2×C4214yes—
367C23×C61C23×C411yescharacteristic
368C23×C61C23×C411yescharacteristic
369C23×C61C23×C411yescharacteristic
370C23×C61C22×D411yescharacteristic
371C23×C61C22×D411yescharacteristic
372C23×C61C22×D411yescharacteristic
373C23×C61C2×#4111yescharacteristic
374C23×C61C2×#4111yescharacteristic
375C23×C61C2×#4111yescharacteristic
376C23×C61C2×#4111yescharacteristic
377C23×C61C2×#4111yescharacteristic
378C23×C61H(5,𝔽2)11yescharacteristic
379C23×C61H(5,𝔽2)11yescharacteristic
380C23×C61H(5,𝔽2)11yescharacteristic
381C23×C612−1+411yescharacteristic
382C22×D61—22no—
383C22×D61—22no—
384C22×D61—22no—
385C22×D61—22no—
386C22×D61—22no—
387C22×D61—22no—
388C22×D61—22no—
389C22×D61—22no—
390C22×D61—22no—
391C22×D61—22no—
392C22×D61—22no—
393C22×D61—22no—
394C22×D61—22no—
395C22×D61—22no—
396C22×D61—22no—
397C22×D61—22no—
398C22×D61—22no—
399C22×D61—22no—
400C22×D61—41no—
401C22×D61—41no—
402C22×D61—41no—
403C22×D61—41no—
404C22×D61—41no—
405C22×D61—41no—
406C22×D61—41no—
407C22×D61—41no—
408C22×D61—41no—
409C22×D61—41no—
410C22×D61—41no—
411C22×D61—41no—
412C22×D61—41no—
413C22×D61—41no—
414C22×D61—41no—
415C22×D61—41no—
416C22×D61C2×C4214yes—
417C2×C4×C61—22no—
418C2×C4×C61—22no—
419C2×C4×C61—22no—
420C2×C4×C61—22no—
421C2×C4×C61—22no—
422C2×C4×C61—22no—
423C2×C4×C61—22no—
424C2×C4×C61—22no—
425C2×C4×C61—22no—
426C2×C4×C61—22no—
427C2×C4×C61—22no—
428C2×C4×C61—22no—
429C2×C4×C61—22no—
430C2×C4×C61—22no—
431C2×C4×C61—22no—
432C2×C4×C61—22no—
433C2×C4×C61—22no—
434C2×C4×C61—22no—
435C2×C4×C61—22no—
436C2×C4×C61—22no—
437C2×C4×C61—22no—
438C2×C4×C61—22no—
439C2×C4×C61—22no—
440C2×C4×C61—22no—
441C2×C4×C61—41no—
442C2×C4×C61—41no—
443C2×C4×C61—41no—
444C2×C4×C61—41no—
445C2×C4×C61—41no—
446C2×C4×C61—41no—
447C2×C4×C61—41no—
448C2×C4×C61—41no—
449C2×C4×C61—41no—
450C2×C4×C61—41no—
451C2×C4×C61—41no—
452C2×C4×C61—41no—
453C2×C4×C61—41no—
454C2×C4×C61—41no—
455C2×C4×C61—41no—
456C2×C4×C61—41no—
457C2×C4×C61C2×C22⋊C414yes—
458C2×C4×C61C4×D414yescomplemented
459C22⋊D61—232no—
460C2×Dic61—22no—
461C2×Dic61—22no—
462C2×Dic61—22no—
463C2×Dic61—22no—
464C2×Dic61—22no—
465C2×Dic61—22no—
466C2×Dic61—22no—
467C2×Dic61—22no—
468C2×Dic61—22no—
469C2×Dic61—22no—
470C2×Dic61—22no—
471C2×Dic61—22no—
472C2×Dic61—22no—
473C2×Dic61—22no—
474C2×Dic61—22no—
475C2×Dic61—22no—
476C2×Dic61—22no—
477C2×Dic61—22no—
478C2×Dic61—22no—
479C2×Dic61—22no—
480C2×Dic61—22no—
481C2×Dic61—22no—
482C2×Dic61—22no—
483C2×Dic61—22no—
484C2×Dic61—22no—
485C2×Dic61—22no—
486C2×Dic61—22no—
487C2×Dic61—416no—
488C2×Dic61—41no—
489C2×Dic61—41no—
490C2×Dic61—41no—
491C2×Dic61—41no—
492C2×Dic61—41no—
493C2×Dic61—41no—
494C2×Dic61—41no—
495C2×Dic61—41no—
496C2×Dic61—41no—
497C2×Dic61—41no—
498C2×Dic61—41no—
499C2×Dic61—41no—
500C2×Dic61C2×C4214yes—
501C2×Dic61C2×C22⋊C414yes—
502C2×Dic61C2×C22⋊C414yes—
503C2×Dic61#11714yes—
504C2×Dic61C4×D414yes—
505C2×Dic61C4×D414yes—
506C2×Dic61C4×D414yes—
507C2×Dic61C4×D414yes—
508C2×Dic61C4×D414yes—
509C2×Dic61C4×D414yescomplemented
510C4×D61—416no—
511#13820—611nomaximal, Sylow
512C22×C61—24no—
513C22×C61—24no—
514C22×C61—24no—
515C22×C61—42no—
516C22×C61—42no—
517C22×C61—42no—
518C22×C61—42no—
519C22×C61—42no—
520C22×C61—42no—
521C22×C61—42no—
522C22×C61—42no—
523C22×C61—42no—
524C22×C61—42no—
525C22×C61—42no—
526C22×C61—42no—
527C22×C61C22×C4211yescharacteristic
528C22×C61C22×C22⋊C411yescharacteristic
529C22×C61C2×#11711yescharacteristic
530C22×C61C2×C4×D411yescharacteristic
531C22×C61C2×C4×D411yescharacteristic
532C22×C61C2×C4×D411yescharacteristic
533C22×C61C2×C4×D411yescharacteristic
534C22×C61C2×C4×D411yescharacteristic
535C22×C61C2×C4×D411yescharacteristic
536C22×C61C2×C4×D411yescharacteristic
537C22×C61C4×#4111yescharacteristic
538C22×C61C4×#4111yescharacteristic
539C22×C61C4×#4111yescharacteristic
540C22×C61#51811yescharacteristic
541C22×C61#51811yescharacteristic
542C22×C61#51811yescharacteristic
543C22×C61#52011yescharacteristic
544C22×C61#52011yescharacteristic
545C22×C61#52011yescharacteristic
546C22×C61D4211yescharacteristic
547C22×C61D4211yescharacteristic
548C22×C61#54611yescharacteristic
549C22×C61#54611yescharacteristic
550C22×C61#54711yescharacteristic
551C22×C61#54811yescharacteristic
552C22×C61#54811yescharacteristic
553C22×C61#55011yescharacteristic
554C22×C61#55011yescharacteristic
555C22×C61#55011yescharacteristic
556C22×C61#55311yescharacteristic
557C22×C61#55311yescharacteristic
558C22×C61#55511yescharacteristic
559C22×C61#55611yescharacteristic
560C22×C61#55911yescharacteristic
561C22×C61#55911yescharacteristic
562C2×D61—24no—
563C2×D61—24no—
564C2×D61—24no—
565C2×D61—42no—
566C2×D61—42no—
567C2×D61—42no—
568C2×D61—42no—
569C2×D61—42no—
570C2×D61—42no—
571C2×D61—42no—
572C2×D61—42no—
573C2×D61—42no—
574C2×D61—42no—
575C2×D61—42no—
576C2×D61—42no—
577C4×C61—24no—
578C4×C61—24no—
579C4×C61—42no—
580C4×C61—42no—
581C4×C61—42no—
582C4×C61—42no—
583Dic61—24no—
584Dic61—24no—
585Dic61—24no—
586Dic61—42no—
587Dic61—42no—
588Dic61—42no—
589Dic61C4×C22⋊C418yescomplemented
590C22×C4×D4—611no—
591C2×#390—611no—
592C2×#390—611no—
593C2×C4×C4⋊C4—611no—
594C2×C4×C4⋊C4—611no—
595C2×C4×C22⋊C4—611no—
596C2×C4×C22⋊C4—611no—
597#1437—611no—
598#1437—611no—
599#1437—611no—
600#1437D6111yescharacteristic, complemented
601C4⋊#95—611no—
602C22⋊#95—611no—
603C22⋊#95—611no—
604C4×#95—611no—
605C2×C61—44no—
606C2×C61C2×C4×C22⋊C411yescharacteristic
607C2×C61C42×D411yescharacteristic
608C2×C61#227511yescharacteristic
609C2×C61D4×C22⋊C411yescharacteristic
610C2×C61#234111yescharacteristic
611C2×C61#235411yescharacteristic
612C2×C61#235711yescharacteristic
613C2×C61#236111yescharacteristic
614C2×C61#236111yescharacteristic
615C2×C61#236311yescharacteristic
616C2×C61#236311yescharacteristic
617C2×C61#236611yescharacteristic
618C2×C61#236611yescharacteristic
619C2×C61#236711yescharacteristic
620C2×C61#236711yescharacteristic
621D61—44no—
622C23×D4—611no—
623C24×C4—611no—
624C24×C4—611no—
625C2×C4×D4—618no—
626C2×C4×D4—1224no—
627C2×C4×D4—1224no—
628C22×C4⋊C4—611no—
629C22×C4⋊C4—611no—
630C22×C4⋊C4—611no—
631C22×C22⋊C4—611no—
632C22×C22⋊C4—611no—
633C22×C22⋊C4—611no—
634C22×C22⋊C4—611no—
635C22×C22⋊C4—611no—
636C22×C22⋊C4—611no—
637C22×C22⋊C4—611no—
638C22×C22⋊C4C2×D6111yescharacteristic
639C22×C22⋊C4C2×D6111yescharacteristic
640C22×C22⋊C4C2×D6111yescharacteristic
641C22×C42—611no—
642C22×C42—611no—
643C22×C42—611no—
644C22×C42—611no—
645C22×C42—611no—
646C22×C42—611no—
647C22×C42C2×D6111yescharacteristic
648#390—618no—
649#390—618no—
650C4×C4⋊C4—1224no—
651C4×C4⋊C4—1224no—
652C4×C22⋊C4—1224no—
653C4×C22⋊C4—1224no—
654C2×#95—611no—
655C2×#95—611no—
656C2×#95—611no—
657C2×#95—611no—
658C2×#95—611no—
659C2×#95—611no—
660C2×#95—611no—
661C2×#95—611no—
662C2×#95—611no—
663C2×#95C2×D6111yescharacteristic
664C2×#95C2×D6111yescharacteristic
665C2×#95C2×D6111yescharacteristic
666C61#1382011yescharacteristic, complemented, Sylow
667C25—611no—
668C25C22×D6111yescharacteristic
669C22×D4—614no—
670C22×D4—614no—
671C22×D4—614no—
672C22×D4—1222no—
673C22×D4—1222no—
674C22×D4—1222no—
675C22×D4—1222no—
676C23×C4—611no—
677C23×C4—611no—
678C23×C4—611no—
679C23×C4—611no—
680C23×C4—611no—
681C23×C4—611no—
682C23×C4—611no—
683C23×C4—614no—
684C23×C4—614no—
685C23×C4—1222no—
686C23×C4—1222no—
687C23×C4—1222no—
688C23×C4—1222no—
689C23×C4—1222no—
690C23×C4—1222no—
691C23×C4—1222no—
692C23×C4—1222no—
693C23×C4—2441no—
694C23×C4—2441no—
695C23×C4—2441no—
696C23×C4—2441no—
697C23×C4C22×D6111yescharacteristic
698C23×C4C22×D6111yescharacteristic
699C23×C4C22×D6111yescharacteristic
700C23×C4C22×D6111yescharacteristic
701C23×C4C22×D6111yescharacteristic
702C23×C4C22×D6111yescharacteristic
703C4×D4—12232no—
704C2×C4⋊C4—614no—
705C2×C4⋊C4—614no—
706C2×C4⋊C4—614no—
707C2×C4⋊C4—614no—
708C2×C4⋊C4—614no—
709C2×C4⋊C4—1222no—
710C2×C4⋊C4—1222no—
711C2×C4⋊C4—1222no—
712C2×C4⋊C4—1222no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—41no—
718C2×C22⋊C4—41no—
719C2×C22⋊C4—614no—
720C2×C22⋊C4—614no—
721C2×C22⋊C4—614no—
722C2×C22⋊C4—614no—
723C2×C22⋊C4—614no—
724C2×C22⋊C4—614no—
725C2×C22⋊C4—614no—
726C2×C22⋊C4—1222no—
727C2×C22⋊C4—1222no—
728C2×C22⋊C4—1222no—
729C2×C22⋊C4—1222no—
730C2×C22⋊C4—1222no—
731C2×C22⋊C4—1222no—
732C2×C22⋊C4—1222no—
733C2×C22⋊C4—1222no—
734C2×C22⋊C4—2441no—
735C2×C22⋊C4—2441no—
736C2×C22⋊C4—2441no—
737C2×C22⋊C4—2441no—
738C2×C22⋊C4—2441no—
739C2×C22⋊C4—2441no—
740C2×C22⋊C4C4×D6114yes—
741C2×C22⋊C4C4×D6114yescomplemented
742C2×C22⋊C4C4×D6114yescomplemented
743C2×C42—22no—
744C2×C42—22no—
745C2×C42—41no—
746C2×C42—614no—
747C2×C42—614no—
748C2×C42—614no—
749C2×C42—1222no—
750C2×C42—1222no—
751C2×C42—1222no—
752C2×C42—1222no—
753C2×C42—1222no—
754C2×C42—1222no—
755C2×C42—1222no—
756C2×C42—1222no—
757C2×C42—1222no—
758C2×C42—1222no—
759C2×C42—1222no—
760C2×C42—1222no—
761C2×C42—2441no—
762C2×C42—2441no—
763C2×C42—2441no—
764#95—22no—
765#95—22no—
766#95—41no—
767#95—614no—
768#95—1222no—
769#95—1222no—
770#95—1222no—
771#95—1222no—
772#95—1222no—
773#95—1222no—
774#95—1222no—
775#95—2441no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—612no—
789C24—612no—
790C24—612no—
791C24—1221no—
792C24—1221no—
793C24—1221no—
794C24—1221no—
795C24—1221no—
796C24—1221no—
797C24—1221no—
798C24—1221no—
799C24—1221no—
800C24—1221no—
801C24—1221no—
802C24—1221no—
803C24C2×C4×D6112yes—
804C24C2×C4×D6112yes—
805C24C2×C4×D6112yes—
806C24C23×D6111yescharacteristic
807C2×D4—6116no—
808C2×D4—1228no—
809C2×D4—1228no—
810C2×D4—1228no—
811C2×D4—1228no—
812C2×D4—1228no—
813C2×D4—1228no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—612no—
847C22×C4—612no—
848C22×C4—612no—
849C22×C4—612no—
850C22×C4—612no—
851C22×C4—612no—
852C22×C4—612no—
853C22×C4—612no—
854C22×C4—612no—
855C22×C4—612no—
856C22×C4—612no—
857C22×C4—612no—
858C22×C4—612no—
859C22×C4—612no—
860C22×C4—612no—
861C22×C4—612no—
862C22×C4—612no—
863C22×C4—612no—
864C22×C4—612no—
865C22×C4—1228no—
866C22×C4—1228no—
867C22×C4—1228no—
868C22×C4—1221no—
869C22×C4—1221no—
870C22×C4—1221no—
871C22×C4—1221no—
872C22×C4—1221no—
873C22×C4—1221no—
874C22×C4—1221no—
875C22×C4—1221no—
876C22×C4—1221no—
877C22×C4—1221no—
878C22×C4—1221no—
879C22×C4—1221no—
880C22×C4—1221no—
881C22×C4—1221no—
882C22×C4—1221no—
883C22×C4—1221no—
884C22×C4—1221no—
885C22×C4—1221no—
886C22×C4—1221no—
887C22×C4—1221no—
888C22×C4—1221no—
889C22×C4—1221no—
890C22×C4—1221no—
891C22×C4—1221no—
892C22×C4—1221no—
893C22×C4—1221no—
894C22×C4—1221no—
895C22×C4—1221no—
896C22×C4—1221no—
897C22×C4—1221no—
898C22×C4—1228no—
899C22×C4—2444no—
900C22×C4—2444no—
901C22×C4—2444no—
902C22×C4—2444no—
903C22×C4—2444no—
904C22×C4—2444no—
905C22×C4—2444no—
906C22×C4—2444no—
907C22×C4—2444no—
908C22×C4—2444no—
909C22×C4C2×C4×D6112yes—
910C22×C4C2×C4×D6112yes—
911C22×C4C2×C4×D6112yes—
912C22×C4C2×C4×D6112yes—
913C22×C4C2×C4×D6112yes—
914C22×C4C2×C4×D6112yes—
915C22×C4D4×D6112yes—
916C22×C4D4×D6112yes—
917C22×C4D4×D6112yes—
918C22×C4#1175822412yes—
919C4⋊C4—6116no—
920C4⋊C4—1228no—
921C4⋊C4—1228no—
922C22⋊C4—28no—
923C22⋊C4—28no—
924C22⋊C4—44no—
925C22⋊C4—1228no—
926C22⋊C4—1228no—
927C22⋊C4—1228no—
928C22⋊C4—1228no—
929C22⋊C4—2444no—
930C22⋊C4—2444no—
931C22⋊C4—2444no—
932C42—44no—
933C42—1228no—
934C42—1228no—
935C42—1228no—
936C42—2444no—
937C42—2444no—
938C42—2444no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—614no—
974C23—1222no—
975C23—1222no—
976C23—1222no—
977C23—1222no—
978C23—1222no—
979C23—1222no—
980C23—1222no—
981C23—1222no—
982C23—1222no—
983C23—1222no—
984C23—1222no—
985C23—1222no—
986C23—1222no—
987C23—1222no—
988C23—1222no—
989C23—1222no—
990C23—1222no—
991C23—1222no—
992C23—2441no—
993C23—2441no—
994C23—2441no—
995C23—2441no—
996C23—2441no—
997C23—2441no—
998C23—2441no—
999C23—2441no—
1000C23—2441no—
1001C23—2441no—
1002C23—2441no—
1003C23—2441no—
1004C23—2441no—
1005C23—2441no—
1006C23—2441no—
1007C23—2441no—
1008C23C42×D6114yes—
1009C23C22×C4×D6111yescharacteristic
1010C23C22×C4×D6111yescharacteristic
1011C23C22×C4×D6111yescharacteristic
1012C23C2×D4×D6111yescharacteristic
1013C23C2×D4×D6111yescharacteristic
1014C23C2×D4×D6111yescharacteristic
1015C23#41×D6111yescharacteristic
1016C23#41×D6111yescharacteristic
1017C23#41×D6111yescharacteristic
1018C23#41×D6111yescharacteristic
1019C23C2×#1175822411yescharacteristic
1020C23#1451982211yescharacteristic
1021C23#1451982211yescharacteristic
1022C23#1451982311yescharacteristic
1023C23#1451982411yescharacteristic
1024D4—12232no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—614no—
1066C2×C4—614no—
1067C2×C4—614no—
1068C2×C4—614no—
1069C2×C4—614no—
1070C2×C4—614no—
1071C2×C4—614no—
1072C2×C4—614no—
1073C2×C4—614no—
1074C2×C4—614no—
1075C2×C4—1222no—
1076C2×C4—1222no—
1077C2×C4—1222no—
1078C2×C4—1222no—
1079C2×C4—1222no—
1080C2×C4—1222no—
1081C2×C4—1222no—
1082C2×C4—1222no—
1083C2×C4—1222no—
1084C2×C4—1222no—
1085C2×C4—1222no—
1086C2×C4—1222no—
1087C2×C4—1222no—
1088C2×C4—1222no—
1089C2×C4—1222no—
1090C2×C4—1222no—
1091C2×C4—1222no—
1092C2×C4—1222no—
1093C2×C4—1222no—
1094C2×C4—1222no—
1095C2×C4—1222no—
1096C2×C4—1222no—
1097C2×C4—1222no—
1098C2×C4—1222no—
1099C2×C4—1222no—
1100C2×C4—1222no—
1101C2×C4—1222no—
1102C2×C4—24416no—
1103C2×C4—24416no—
1104C2×C4—2441no—
1105C2×C4—2441no—
1106C2×C4—2441no—
1107C2×C4—2441no—
1108C2×C4—2441no—
1109C2×C4—2441no—
1110C2×C4—2441no—
1111C2×C4—2441no—
1112C2×C4—2441no—
1113C2×C4—2441no—
1114C2×C4—2441no—
1115C2×C4—2441no—
1116C2×C4C22⋊C4×D6114yes—
1117C2×C4#1451973714yescomplemented
1118C22—24no—
1119C22—24no—
1120C22—24no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—1224no—
1134C22—1224no—
1135C22—1224no—
1136C22—2442no—
1137C22—2442no—
1138C22—2442no—
1139C22—2442no—
1140C22—2442no—
1141C22—2442no—
1142C22—2442no—
1143C22—2442no—
1144C22—2442no—
1145C22—2442no—
1146C22—2442no—
1147C22—2442no—
1148C22C2×C42×D6111yescharacteristic
1149C22C2×C22⋊C4×D6111yescharacteristic
1150C22#117×D6111yescharacteristic
1151C22C4×D4×D6111yescharacteristic
1152C22C4×D4×D6111yescharacteristic
1153C22C4×D4×D6111yescharacteristic
1154C22C4×D4×D6111yescharacteristic
1155C22C4×D4×D6111yescharacteristic
1156C22C4×D4×D6111yescharacteristic
1157C22C2×#1451973711yescharacteristic
1158C22C4×#1175822411yescharacteristic
1159C22C4×#1175822411yescharacteristic
1160C22#1684023011yescharacteristic
1161C22#1684023411yescharacteristic
1162C22#1684023411yescharacteristic
1163C22#1684023511yescharacteristic
1164C22#1684024111yescharacteristic
1165C22#1684024111yescharacteristic
1166C22#1684024211yescharacteristic
1167C22#1684039411yescharacteristic
1168C22#1684039611yescharacteristic
1169C22#1684040111yescharacteristic
1170C22#1684040411yescharacteristic
1171C22#1684041011yescharacteristic
1172C22#1684041811yescharacteristic
1173C22#1684042011yescharacteristic
1174C22#1684043011yescharacteristic
1175C22#1684043011yescharacteristic
1176C22#1684043211yescharacteristic
1177C22#1684045511yescharacteristic
1178C22#1684046311yescharacteristic
1179C22#1684047411yescharacteristic
1180C22#1684047911yescharacteristic
1181C22#1684049411yescharacteristic
1182C22#1684049611yescharacteristic
1183C4—24no—
1184C4—24no—
1185C4—42no—
1186C4—42no—
1187C4—42no—
1188C4—42no—
1189C4—618no—
1190C4—1224no—
1191C4—1224no—
1192C4—1224no—
1193C4—2442no—
1194C4—2442no—
1195C4—2442no—
1196C2—44no—
1197C2—2444no—
1198C2C4×C22⋊C4×D6111yescharacteristic
1199C2C4×#1451973711yescharacteristic
1200C2#2144817811yescharacteristic
1201C2#2144863711yescharacteristic
1202C2#2144865811yescharacteristic
1203C2#2144876511yescharacteristic
1204C2#2144878911yescharacteristic
1205C2#2144883011yescharacteristic
1206C2#2144883211yescharacteristic
1207C2#2144885211yescharacteristic
1208C2#2144885411yescharacteristic
1209C2#2144888011yescharacteristic
1210C2#2144888211yescharacteristic
1211C2#2144888511yescharacteristic
1212C2#2144889311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC61×#1437C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenter#1437D61
hypocenterC61#13820
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
4. C2×C4×#11758196C2semidirect
5. C2×#16839613C2semidirect
6. C2×C22⋊C4×Dic61C2semidirect
7. C2×C4×#11758198C2semidirect
8. #21444056C2semidirect
9. #21444055C2semidirect
10. #21444055C2semidirect
11. #21444047C2semidirect
12. #21444041C2semidirect
13. #21444040C2semidirect
14. #95×Dic61C2semidirect
15. C61×#1437C2semidirect
21. C2×#14519737C4semidirect
38. #16839662C4semidirect
39. #16839662C4semidirect
95. C2×#11758196C2×C4semidirect
96. C2×#11758196C2×C4semidirect
103. C2×C22⋊Dic61C2×C4semidirect
104. C2×C22⋊Dic61C2×C4semidirect
116. C2×#11758198C2×C4semidirect
117. C2×#11758198C2×C4semidirect
118. C2×#11758198C2×C4semidirect
119. C2×#11758198C2×C4semidirect
136. C2×C4×Dic61C2×C4semidirect
137. C2×C4×Dic61C2×C4semidirect
146. #14519684D4semidirect
161. C2×C22⋊C4×C61C2×C4semidirect
162. C2×C22⋊C4×C61C2×C4semidirect
248. C2×C22⋊D61C42semidirect
325. #11758196C22⋊C4semidirect
458. C2×C4×C61C4×D4semidirect
509. C2×Dic61C4×D4semidirect
589. Dic61C4×C22⋊C4semidirect
600. #1437D61semidirect
666. C61#13820semidirect
741. C2×C22⋊C4C4×D61semidirect
742. C2×C22⋊C4C4×D61semidirect
1117. C2×C4#14519737semidirect

Maximal subgroups

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

subgroupindex
C22×#145197372
C2×#168396622
C2×C4×#117581962
C2×#168396132
C2×C22⋊C4×Dic612
C2×C4×#117581982
#214440562
#214440552
#214440472
#214440412
#214440402
#95×Dic612
C61×#14372
#1382061