Finite Group Databasebeta

← #29601507

Subgroups — #29601507

Order 15616.

2882 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519737C211yesmaximal, characteristic
2C2×#16839638C211yesmaximal, characteristic
3C2×#16839638C211yesmaximal, characteristic
4C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
5C2×C4×#11758198C211yesmaximal, characteristic, complemented
6C2×#16839609C211yesmaximal, characteristic, complemented
7C2×#95×D61C211yesmaximal, characteristic, complemented
8#21444056C211yesmaximal, characteristic, complemented
9#21444050C211yesmaximal, characteristic, complemented
10#21444050C211yesmaximal, characteristic, complemented
11#21444043C211yesmaximal, characteristic, complemented
12#21444041C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic, complemented
14C4×#14519684C211yesmaximal, characteristic, complemented
15C61×#1437C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C24×Dic61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C2×#14519737—24no—
22C2×#14519737—24no—
23C2×#14519737C418yescomplemented
24C22×#11758196C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34#16839638C418yescomplemented
35#16839638C418yescomplemented
36C22⋊C4×Dic61—24no—
37C4×#11758198—24no—
38#16839609—24no—
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52#95×D61—24no—
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×C414yescomplemented
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—22no—
87C22×C4×D61—22no—
88C22×C4×D61—22no—
89C22×C4×D61—22no—
90C22×C4×D61—22no—
91C22×C4×D61—22no—
92C22×C4×D61—22no—
93C22×C4×D61—22no—
94C22×C4×D61—41no—
95C22×C4×D61—41no—
96C22×C4×D61—41no—
97C22×C4×D61—41no—
98C22×C4×D61—41no—
99C22×C4×D61—41no—
100C22×C4×D61C2×C414yes—
101C22×C4×D61C2×C414yescomplemented
102C22×C4×D61C2×C414yescomplemented
103#14519737—232no—
104C2×#11758196—22no—
105C2×#11758196—22no—
106C2×#11758196C2×C414yescomplemented
107C2×C22⋊Dic61—22no—
108C2×C22⋊Dic61—22no—
109C2×C22⋊Dic61—41no—
110C2×C22⋊Dic61—41no—
111C2×C22⋊Dic61C2×C414yescomplemented
112C2×C22⋊Dic61C2×C414yescomplemented
113C2×#11758198—22no—
114C2×#11758198—22no—
115C2×#11758198—22no—
116C2×#11758198—22no—
117C2×#11758198C2×C414yes—
118C2×#11758198C2×C414yescomplemented
119C2×#11758198C2×C414yescomplemented
120C2×#11758198D414yes—
121C2×#11758198D414yes—
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—41no—
131C2×C4×Dic61—41no—
132C2×C4×Dic61—41no—
133C2×C4×Dic61C2×C414yescomplemented
134#14519684—22no—
135#14519684—22no—
136#14519684—22no—
137#14519684—22no—
138#14519684—22no—
139#14519684—22no—
140#14519684—22no—
141#14519684—41no—
142#14519684C2×C414yescomplemented
143#14519684C2×C414yescomplemented
144#14519684C2×C414yescomplemented
145#14519684C2×C414yescomplemented
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×C414yescomplemented
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×D61C22×C412yes—
194C23×D61C22×C412yes—
195C23×D61C22×C412yes—
196C23×D61C2×D412yes—
197C23×D61C2×D412yes—
198C23×D61#4112yes—
199C23×D61#4112yes—
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—21no—
280C22×Dic61—21no—
281C22×Dic61—21no—
282C22×Dic61—21no—
283C22×Dic61—28no—
284C22×Dic61—28no—
285C22×Dic61—44no—
286C22×Dic61—44no—
287C22×Dic61—44no—
288C22×Dic61—44no—
289C22×Dic61—44no—
290C22×Dic61C22×C412yes—
291C22×Dic61C22×C412yes—
292C22×Dic61C22×C412yes—
293C22×Dic61C22×C412yes—
294C22×Dic61C22×C412yes—
295C22×Dic61C22×C412yes—
296C22×Dic61C22×C412yes—
297C22×Dic61C22×C412yes—
298C22×Dic61C22×C412yes—
299C22×Dic61C2×D412yes—
300C22×Dic61C2×D412yes—
301C22×Dic61C2×D412yes—
302C22×Dic61C2×D412yes—
303C22×Dic61#4112yes—
304C22×Dic61#4112yes—
305C2×C4×D61—28no—
306C2×C4×D61—28no—
307C2×C4×D61—28no—
308C2×C4×D61—28no—
309C2×C4×D61—28no—
310C2×C4×D61—28no—
311C2×C4×D61—44no—
312C2×C4×D61—44no—
313C2×C4×D61—44no—
314C2×C4×D61—44no—
315C2×C4×D61—44no—
316C2×C4×D61—44no—
317C2×C4×D61—44no—
318C2×C4×D61—44no—
319C2×C4×D61—44no—
320C2×C4×D61—44no—
321C2×C4×D61—44no—
322C2×C4×D61—44no—
323C2×C4×D61—44no—
324C2×C4×D61—44no—
325C2×C4×D61—44no—
326C22⋊C4×C61—28no—
327C22⋊C4×C61—28no—
328C22⋊C4×C61—44no—
329C42×C61—44no—
330C22⋊Dic61—28no—
331C22⋊Dic61—44no—
332#11758198—28no—
333#11758198—28no—
334#11758198C22⋊C4116yescomplemented
335#11758196—28no—
336C4×Dic61—28no—
337C4×Dic61—44no—
338C4×Dic61—44no—
339C4×Dic61—44no—
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—22no—
351C23×C61—22no—
352C23×C61—22no—
353C23×C61—22no—
354C23×C61—22no—
355C23×C61—22no—
356C23×C61—22no—
357C23×C61—22no—
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×C61—41no—
367C23×C61—41no—
368C23×C61—41no—
369C23×C61—41no—
370C23×C61—41no—
371C23×C61—41no—
372C23×C61—41no—
373C23×C61—41no—
374C23×C61C2×C4214yes—
375C23×C61C23×C411yescharacteristic
376C23×C61C23×C411yescharacteristic
377C23×C61C23×C411yescharacteristic
378C23×C61C22×D411yescharacteristic
379C23×C61C22×D411yescharacteristic
380C23×C61C22×D411yescharacteristic
381C23×C61C2×#4111yescharacteristic
382C23×C61C2×#4111yescharacteristic
383C23×C61C2×#4111yescharacteristic
384C23×C61C2×#4111yescharacteristic
385C23×C61C2×#4111yescharacteristic
386C23×C61H(5,𝔽2)11yescharacteristic
387C23×C61H(5,𝔽2)11yescharacteristic
388C23×C61H(5,𝔽2)11yescharacteristic
389C23×C612−1+411yescharacteristic
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—22no—
401C22×D61—22no—
402C22×D61—22no—
403C22×D61—22no—
404C22×D61—22no—
405C22×D61—22no—
406C22×D61—22no—
407C22×D61—22no—
408C22×D61—22no—
409C22×D61—22no—
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×D61C2×C4214yes—
419C22×D61C2×C22⋊C414yes—
420C22×D61#11714yes—
421C22×D61C4×D414yes—
422C22×D61C4×D414yes—
423C22×D61C4×D414yes—
424C22×D61C4×D414yes—
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—22no—
442C2×C4×C61—22no—
443C2×C4×C61—22no—
444C2×C4×C61—22no—
445C2×C4×C61—22no—
446C2×C4×C61—22no—
447C2×C4×C61—22no—
448C2×C4×C61—22no—
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×C61—41no—
458C2×C4×C61—41no—
459C2×C4×C61—41no—
460C2×C4×C61—41no—
461C2×C4×C61—41no—
462C2×C4×C61—41no—
463C2×C4×C61—41no—
464C2×C4×C61—41no—
465C2×C4×C61C2×C22⋊C414yes—
466C2×C4×C61C4×D414yescomplemented
467C22⋊D61—232no—
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—22no—
488C2×Dic61—22no—
489C2×Dic61—22no—
490C2×Dic61—22no—
491C2×Dic61—22no—
492C2×Dic61—22no—
493C2×Dic61—22no—
494C2×Dic61—22no—
495C2×Dic61—22no—
496C2×Dic61—22no—
497C2×Dic61—22no—
498C2×Dic61—22no—
499C2×Dic61—22no—
500C2×Dic61—22no—
501C2×Dic61—416no—
502C2×Dic61—41no—
503C2×Dic61—41no—
504C2×Dic61—41no—
505C2×Dic61—41no—
506C2×Dic61—41no—
507C2×Dic61—41no—
508C2×Dic61—41no—
509C2×Dic61—41no—
510C2×Dic61—41no—
511C2×Dic61—41no—
512C2×Dic61—41no—
513C2×Dic61—41no—
514C2×Dic61C2×C4214yes—
515C2×Dic61C2×C22⋊C414yes—
516C2×Dic61C4×D414yes—
517C2×Dic61C4×D414yescomplemented
518C4×D61—416no—
519C4×D61—416no—
520C4×D61—416no—
521#13813—611nomaximal, Sylow
522C22×C61—24no—
523C22×C61—24no—
524C22×C61—24no—
525C22×C61—42no—
526C22×C61—42no—
527C22×C61—42no—
528C22×C61—42no—
529C22×C61—42no—
530C22×C61—42no—
531C22×C61—42no—
532C22×C61—42no—
533C22×C61—42no—
534C22×C61—42no—
535C22×C61—42no—
536C22×C61—42no—
537C22×C61C22×C4211yescharacteristic
538C22×C61C22×C22⋊C411yescharacteristic
539C22×C61C2×#11711yescharacteristic
540C22×C61C2×C4×D411yescharacteristic
541C22×C61C2×C4×D411yescharacteristic
542C22×C61C2×C4×D411yescharacteristic
543C22×C61C2×C4×D411yescharacteristic
544C22×C61C2×C4×D411yescharacteristic
545C22×C61C2×C4×D411yescharacteristic
546C22×C61C2×C4×D411yescharacteristic
547C22×C61C4×#4111yescharacteristic
548C22×C61C4×#4111yescharacteristic
549C22×C61C4×#4111yescharacteristic
550C22×C61#51811yescharacteristic
551C22×C61#51811yescharacteristic
552C22×C61#51811yescharacteristic
553C22×C61#52011yescharacteristic
554C22×C61#52011yescharacteristic
555C22×C61#52011yescharacteristic
556C22×C61D4211yescharacteristic
557C22×C61D4211yescharacteristic
558C22×C61#54611yescharacteristic
559C22×C61#54611yescharacteristic
560C22×C61#54611yescharacteristic
561C22×C61#54611yescharacteristic
562C22×C61#54611yescharacteristic
563C22×C61#54711yescharacteristic
564C22×C61#54711yescharacteristic
565C22×C61#54811yescharacteristic
566C22×C61#55111yescharacteristic
567C22×C61#55111yescharacteristic
568C22×C61#55211yescharacteristic
569C22×C61#55311yescharacteristic
570C22×C61#55311yescharacteristic
571C22×C61#55311yescharacteristic
572C2×D61—24no—
573C2×D61—24no—
574C2×D61—24no—
575C2×D61—24no—
576C2×D61—24no—
577C2×D61—24no—
578C2×D61—24no—
579C2×D61—24no—
580C2×D61—24no—
581C2×D61—24no—
582C2×D61—24no—
583C2×D61—24no—
584C2×D61—24no—
585C2×D61—24no—
586C2×D61C4×C22⋊C418yescomplemented
587C4×C61—24no—
588C4×C61—24no—
589C4×C61—42no—
590C4×C61—42no—
591C4×C61—42no—
592C4×C61—42no—
593Dic61—24no—
594Dic61—24no—
595Dic61—24no—
596Dic61—24no—
597Dic61—42no—
598Dic61—42no—
599Dic61—42no—
600C22×C4×D4—611no—
601C2×#386—611no—
602C2×#386—611no—
603C2×C4×C22⋊C4—611no—
604C2×C4×C22⋊C4—611no—
605C2×C4×C22⋊C4—611no—
606C22×#95—611no—
607#1437—611no—
608#1437D6111yescharacteristic, complemented
609#1436—611no—
610#1436—611no—
611#1434—611no—
612C22⋊#95—611no—
613C22⋊#95—611no—
614C4×#95—611no—
615C2×C61—44no—
616C2×C61C2×C4×C22⋊C411yescharacteristic
617C2×C61C42×D411yescharacteristic
618C2×C61#227511yescharacteristic
619C2×C61D4×C22⋊C411yescharacteristic
620C2×C61#233911yescharacteristic
621C2×C61#235211yescharacteristic
622C2×C61#235311yescharacteristic
623C2×C61#235811yescharacteristic
624C2×C61#235811yescharacteristic
625C2×C61#235911yescharacteristic
626C2×C61#235911yescharacteristic
627C2×C61#236111yescharacteristic
628C2×C61#236111yescharacteristic
629C2×C61#236411yescharacteristic
630C2×C61#236411yescharacteristic
631D61—28no—
632C23×D4—611no—
633C24×C4—611no—
634C24×C4—611no—
635C24×C4—611no—
636C24×C4—611no—
637C2×C4×D4—618no—
638C2×C4×D4—1224no—
639C2×C4×D4—1224no—
640C22×C4⋊C4—611no—
641C22×C22⋊C4—611no—
642C22×C22⋊C4—611no—
643C22×C22⋊C4—611no—
644C22×C22⋊C4—611no—
645C22×C22⋊C4—611no—
646C22×C22⋊C4C2×D6111yescharacteristic
647C22×C22⋊C4C2×D6111yescharacteristic
648C22×C22⋊C4C2×D6111yescharacteristic
649C22×C42—611no—
650C22×C42—611no—
651C22×C42—611no—
652C22×C42—611no—
653C22×C42C2×D6111yescharacteristic
654#386—618no—
655#386—618no—
656C4×C22⋊C4—1224no—
657C4×C22⋊C4—1224no—
658C4×C22⋊C4—1224no—
659C2×#95—611no—
660C2×#95—611no—
661C2×#95—611no—
662C2×#95—611no—
663C2×#95—611no—
664C2×#95—611no—
665C2×#95—611no—
666C2×#95—611no—
667C2×#95—611no—
668C2×#95—611no—
669C2×#95—611no—
670C2×#95—611no—
671C2×#95—611no—
672C2×#95—1224no—
673C2×#95C2×D6111yescharacteristic
674C2×#95C2×D6111yescharacteristic
675C2×#95C2×D6111yescharacteristic
676C61#1381311yescharacteristic, complemented, Sylow
677C25—611no—
678C25C22×D6111yescharacteristic
679C22×D4—614no—
680C22×D4—614no—
681C22×D4—614no—
682C22×D4—1222no—
683C22×D4—1222no—
684C22×D4—1222no—
685C22×D4—1222no—
686C23×C4—611no—
687C23×C4—611no—
688C23×C4—611no—
689C23×C4—611no—
690C23×C4—611no—
691C23×C4—611no—
692C23×C4—611no—
693C23×C4—614no—
694C23×C4—614no—
695C23×C4—614no—
696C23×C4—614no—
697C23×C4—1222no—
698C23×C4—1222no—
699C23×C4—1222no—
700C23×C4—1222no—
701C23×C4—1222no—
702C23×C4—1222no—
703C23×C4—1222no—
704C23×C4—1222no—
705C23×C4—1222no—
706C23×C4—1222no—
707C23×C4—1222no—
708C23×C4—1222no—
709C23×C4—1222no—
710C23×C4—1222no—
711C23×C4—1222no—
712C23×C4—1222no—
713C23×C4—2441no—
714C23×C4—2441no—
715C23×C4—2441no—
716C23×C4—2441no—
717C23×C4—2441no—
718C23×C4—2441no—
719C23×C4—2441no—
720C23×C4—2441no—
721C23×C4C22×D6111yescharacteristic
722C23×C4C22×D6111yescharacteristic
723C23×C4C22×D6111yescharacteristic
724C23×C4C22×D6111yescharacteristic
725C23×C4C22×D6111yescharacteristic
726C23×C4C22×D6111yescharacteristic
727C4×D4—12232no—
728C2×C4⋊C4—614no—
729C2×C4⋊C4—1222no—
730C2×C4⋊C4—1222no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—22no—
735C2×C22⋊C4—41no—
736C2×C22⋊C4—41no—
737C2×C22⋊C4—614no—
738C2×C22⋊C4—614no—
739C2×C22⋊C4—614no—
740C2×C22⋊C4—614no—
741C2×C22⋊C4—614no—
742C2×C22⋊C4—614no—
743C2×C22⋊C4—614no—
744C2×C22⋊C4—1222no—
745C2×C22⋊C4—1222no—
746C2×C22⋊C4—1222no—
747C2×C22⋊C4—1222no—
748C2×C22⋊C4—1222no—
749C2×C22⋊C4—1222no—
750C2×C22⋊C4—2441no—
751C2×C22⋊C4—2441no—
752C2×C22⋊C4C4×D6114yescomplemented
753C2×C22⋊C4C4×D6114yescomplemented
754C2×C22⋊C4C4×D6114yescomplemented
755C2×C42—22no—
756C2×C42—22no—
757C2×C42—41no—
758C2×C42—614no—
759C2×C42—1222no—
760C2×C42—1222no—
761C2×C42—1222no—
762C2×C42—1222no—
763C2×C42—1222no—
764C2×C42—1222no—
765C2×C42—1222no—
766C2×C42—1222no—
767C2×C42—2441no—
768C2×C42—2441no—
769C2×C42—2441no—
770#95—22no—
771#95—22no—
772#95—41no—
773#95—614no—
774#95—614no—
775#95—614no—
776#95—614no—
777#95—614no—
778#95—1222no—
779#95—1222no—
780#95—1222no—
781#95—1222no—
782#95—1222no—
783#95—1222no—
784#95—1222no—
785#95—2441no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—612no—
799C24—612no—
800C24—612no—
801C24—612no—
802C24—612no—
803C24—612no—
804C24—612no—
805C24—1221no—
806C24—1221no—
807C24—1221no—
808C24—1221no—
809C24—1221no—
810C24—1221no—
811C24—1221no—
812C24—1221no—
813C24C2×C4×D6112yes—
814C24C2×C4×D6112yes—
815C24C2×C4×D6112yes—
816C24C23×D6111yescharacteristic
817C2×D4—6116no—
818C2×D4—1228no—
819C2×D4—1228no—
820C2×D4—1228no—
821C2×D4—1228no—
822C2×D4—1228no—
823C2×D4—1228no—
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—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
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—612no—
866C22×C4—612no—
867C22×C4—612no—
868C22×C4—612no—
869C22×C4—612no—
870C22×C4—612no—
871C22×C4—1228no—
872C22×C4—1228no—
873C22×C4—1228no—
874C22×C4—1228no—
875C22×C4—1228no—
876C22×C4—1228no—
877C22×C4—1228no—
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—1221no—
899C22×C4—1221no—
900C22×C4—1221no—
901C22×C4—1221no—
902C22×C4—1221no—
903C22×C4—1221no—
904C22×C4—1221no—
905C22×C4—1221no—
906C22×C4—1221no—
907C22×C4—1221no—
908C22×C4—1221no—
909C22×C4—1221no—
910C22×C4—1221no—
911C22×C4—1221no—
912C22×C4—1228no—
913C22×C4—2444no—
914C22×C4—2444no—
915C22×C4—2444no—
916C22×C4—2444no—
917C22×C4—2444no—
918C22×C4—2444no—
919C22×C4—2444no—
920C22×C4—2444no—
921C22×C4—2444no—
922C22×C4—2444no—
923C22×C4—2444no—
924C22×C4—2444no—
925C22×C4—2444no—
926C22×C4—2444no—
927C22×C4—2444no—
928C22×C4—2444no—
929C22×C4—2444no—
930C22×C4—2444no—
931C22×C4—2444no—
932C22×C4—2444no—
933C22×C4C2×C4×D6112yes—
934C22×C4C2×C4×D6112yes—
935C22×C4C2×C4×D6112yes—
936C22×C4C2×C4×D6112yes—
937C22×C4C2×C4×D6112yes—
938C22×C4C2×C4×D6112yes—
939C22×C4D4×D6112yes—
940C22×C4D4×D6112yes—
941C22×C4D4×D6112yes—
942C22×C4#1175822412yes—
943C4⋊C4—1228no—
944C22⋊C4—28no—
945C22⋊C4—28no—
946C22⋊C4—44no—
947C22⋊C4—6116no—
948C22⋊C4—1228no—
949C22⋊C4—1228no—
950C22⋊C4—1228no—
951C22⋊C4—2444no—
952C42—44no—
953C42—1228no—
954C42—2444no—
955C42—2444no—
956C42—2444no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—614no—
992C23—614no—
993C23—614no—
994C23—614no—
995C23—614no—
996C23—614no—
997C23—614no—
998C23—1222no—
999C23—1222no—
1000C23—1222no—
1001C23—1222no—
1002C23—1222no—
1003C23—1222no—
1004C23—1222no—
1005C23—1222no—
1006C23—1222no—
1007C23—1222no—
1008C23—1222no—
1009C23—1222no—
1010C23—1222no—
1011C23—1222no—
1012C23—1222no—
1013C23—1222no—
1014C23—1222no—
1015C23—1222no—
1016C23—1222no—
1017C23—1222no—
1018C23—1222no—
1019C23—1222no—
1020C23—1222no—
1021C23—1222no—
1022C23—1222no—
1023C23—1222no—
1024C23—1222no—
1025C23—1222no—
1026C23C42×D6114yes—
1027C23C22×C4×D6111yescharacteristic
1028C23C22×C4×D6111yescharacteristic
1029C23C22×C4×D6111yescharacteristic
1030C23C2×D4×D6111yescharacteristic
1031C23C2×D4×D6111yescharacteristic
1032C23C2×D4×D6111yescharacteristic
1033C23#41×D6111yescharacteristic
1034C23#41×D6111yescharacteristic
1035C23#41×D6111yescharacteristic
1036C23#41×D6111yescharacteristic
1037C23C2×#1175822411yescharacteristic
1038C23#1451982211yescharacteristic
1039C23#1451982211yescharacteristic
1040C23#1451982311yescharacteristic
1041C23#1451982411yescharacteristic
1042D4—12232no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—614no—
1084C2×C4—614no—
1085C2×C4—614no—
1086C2×C4—614no—
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—1222no—
1103C2×C4—1222no—
1104C2×C4—1222no—
1105C2×C4—1222no—
1106C2×C4—1222no—
1107C2×C4—1222no—
1108C2×C4—1222no—
1109C2×C4—1222no—
1110C2×C4—1222no—
1111C2×C4—1222no—
1112C2×C4—1222no—
1113C2×C4—1222no—
1114C2×C4—1222no—
1115C2×C4—1222no—
1116C2×C4—1222no—
1117C2×C4—1222no—
1118C2×C4—1222no—
1119C2×C4—1222no—
1120C2×C4—24416no—
1121C2×C4—24416no—
1122C2×C4—24416no—
1123C2×C4—24416no—
1124C2×C4—2441no—
1125C2×C4—2441no—
1126C2×C4—2441no—
1127C2×C4—2441no—
1128C2×C4—2441no—
1129C2×C4—2441no—
1130C2×C4—2441no—
1131C2×C4—2441no—
1132C2×C4—2441no—
1133C2×C4—2441no—
1134C2×C4—2441no—
1135C2×C4—2441no—
1136C2×C4C22⋊C4×D6114yes—
1137C2×C4#1451973714yescomplemented
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—42no—
1148C22—42no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—618no—
1154C22—1224no—
1155C22—1224no—
1156C22—1224no—
1157C22—1224no—
1158C22—1224no—
1159C22—1224no—
1160C22—1224no—
1161C22—1224no—
1162C22—1224no—
1163C22—1224no—
1164C22—1224no—
1165C22—1224no—
1166C22—1224no—
1167C22—1224no—
1168C22C2×C42×D6111yescharacteristic
1169C22C2×C22⋊C4×D6111yescharacteristic
1170C22#117×D6111yescharacteristic
1171C22C4×D4×D6111yescharacteristic
1172C22C4×D4×D6111yescharacteristic
1173C22C4×D4×D6111yescharacteristic
1174C22C4×D4×D6111yescharacteristic
1175C22C4×D4×D6111yescharacteristic
1176C22C4×D4×D6111yescharacteristic
1177C22C2×#1451973711yescharacteristic
1178C22C4×#1175822411yescharacteristic
1179C22C4×#1175822411yescharacteristic
1180C22#1684023011yescharacteristic
1181C22#1684023411yescharacteristic
1182C22#1684023411yescharacteristic
1183C22#1684023511yescharacteristic
1184C22#1684024111yescharacteristic
1185C22#1684024111yescharacteristic
1186C22#1684024211yescharacteristic
1187C22#1684039611yescharacteristic
1188C22#1684039711yescharacteristic
1189C22#1684039911yescharacteristic
1190C22#1684040111yescharacteristic
1191C22#1684040111yescharacteristic
1192C22#1684040511yescharacteristic
1193C22#1684040911yescharacteristic
1194C22#1684041011yescharacteristic
1195C22#1684041211yescharacteristic
1196C22#1684042011yescharacteristic
1197C22#1684043511yescharacteristic
1198C22#1684044211yescharacteristic
1199C22#1684044811yescharacteristic
1200C22#1684045711yescharacteristic
1201C22#1684045911yescharacteristic
1202C22#1684046311yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—1224no—
1210C4—1224no—
1211C4—1224no—
1212C4—1224no—
1213C4—2442no—
1214C4—2442no—
1215C4—2442no—
1216C2—44no—
1217C2—1228no—
1218C2C4×C22⋊C4×D6111yescharacteristic
1219C2C4×#1451973711yescharacteristic
1220C2#2144817811yescharacteristic
1221C2#2144864011yescharacteristic
1222C2#2144864511yescharacteristic
1223C2#2144874711yescharacteristic
1224C2#2144875411yescharacteristic
1225C2#2144879911yescharacteristic
1226C2#2144880011yescharacteristic
1227C2#2144880811yescharacteristic
1228C2#2144881011yescharacteristic
1229C2#2144883211yescharacteristic
1230C2#2144884011yescharacteristic
1231C2#2144886311yescharacteristic
1232C2#2144886811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC61×#1437C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenter#1437D61
hypocenterC61#13813
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
4. C2×C22⋊C4×Dic61C2semidirect
5. C2×C4×#11758198C2semidirect
6. C2×#16839609C2semidirect
7. C2×#95×D61C2semidirect
8. #21444056C2semidirect
9. #21444050C2semidirect
10. #21444050C2semidirect
11. #21444043C2semidirect
12. #21444041C2semidirect
13. #21444040C2semidirect
14. C4×#14519684C2semidirect
15. C61×#1437C2semidirect
23. C2×#14519737C4semidirect
34. #16839638C4semidirect
35. #16839638C4semidirect
74. C23×Dic61C2×C4semidirect
101. C22×C4×D61C2×C4semidirect
102. C22×C4×D61C2×C4semidirect
106. C2×#11758196C2×C4semidirect
111. C2×C22⋊Dic61C2×C4semidirect
112. C2×C22⋊Dic61C2×C4semidirect
118. C2×#11758198C2×C4semidirect
119. C2×#11758198C2×C4semidirect
133. C2×C4×Dic61C2×C4semidirect
142. #14519684C2×C4semidirect
143. #14519684C2×C4semidirect
144. #14519684C2×C4semidirect
145. #14519684C2×C4semidirect
146. #14519684D4semidirect
160. C2×C22⋊C4×C61C2×C4semidirect
161. C2×C22⋊C4×C61C2×C4semidirect
162. C2×C22⋊C4×C61C2×C4semidirect
248. C2×C22⋊D61C42semidirect
334. #11758198C22⋊C4semidirect
466. C2×C4×C61C4×D4semidirect
517. C2×Dic61C4×D4semidirect
586. C2×D61C4×C22⋊C4semidirect
608. #1437D61semidirect
676. C61#13813semidirect
752. C2×C22⋊C4C4×D61semidirect
753. C2×C22⋊C4C4×D61semidirect
754. C2×C22⋊C4C4×D61semidirect
1137. 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×#168396382
C2×C22⋊C4×Dic612
C2×C4×#117581982
C2×#168396092
C2×#95×D612
#214440562
#214440502
#214440432
#214440412
#214440402
C4×#145196842
C61×#14372
#1381361