Finite Group Databasebeta

← #29602877

Subgroups — #29602877

Order 15616.

2690 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×D4×Dic61C211yesmaximal, characteristic
2C2×#16839642C211yesmaximal, characteristic
3C2×#16839637C211yesmaximal, characteristic, complemented
4C2×#16839637C211yesmaximal, characteristic, complemented
5C2×#16839622C211yesmaximal, characteristic, complemented
6C22×#14519684C211yesmaximal, characteristic, complemented
7#21444084C211yesmaximal, characteristic, complemented
8#21444076C211yesmaximal, characteristic, complemented
9#21444064C211yesmaximal, characteristic, complemented
10#21444064C211yesmaximal, characteristic, complemented
11#21444053C211yesmaximal, characteristic, complemented
12#21444053C211yesmaximal, characteristic, complemented
13#21444041C211yesmaximal, characteristic, complemented
14#21444041C211yesmaximal, characteristic, complemented
15C2×C61×#386C211yesmaximal, characteristic
16C24×Dic61C2211yescharacteristic
17C24×Dic61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C2×D4×Dic61—24no—
20C2×D4×Dic61—24no—
21C2×D4×Dic61—24no—
22C22×C4⋊Dic61C2211yescharacteristic
23C22×C4⋊Dic61C2211yescharacteristic
24C22×C4⋊Dic61C2211yescharacteristic
25C22×C4⋊Dic61C2211yescharacteristic
26C22×C4⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×C22⋊Dic61C2211yescharacteristic
31C22×C22⋊Dic61C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33#16839642—24no—
34#16839637—24no—
35#16839637—24no—
36#16839622—24no—
37C2×#14519684—24no—
38C2×#14519684C2211yescharacteristic
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
52C23×D4×C61C2211yescharacteristic
53C24×C4×C61C2211yescharacteristic
54C22×C22⋊C4×C61C2211yescharacteristic
55C22×C22⋊C4×C61C2211yescharacteristic
56C22×C22⋊C4×C61C2211yescharacteristic
57C61×#386C418yescomplemented
58C2×#95×C61C2211yescharacteristic
59C2×#95×C61C2211yescharacteristic
60C23×Dic61—22no—
61C23×Dic61—22no—
62C23×Dic61—22no—
63C23×Dic61—22no—
64C23×Dic61—22no—
65C23×Dic61—22no—
66C23×Dic61—22no—
67C23×Dic61—22no—
68C23×Dic61—22no—
69C23×Dic61—22no—
70C23×Dic61—22no—
71C23×Dic61—22no—
72C23×Dic61—22no—
73C23×Dic61—22no—
74C23×Dic61—41no—
75C23×Dic61—41no—
76C23×Dic61—41no—
77C23×Dic61—41no—
78C23×Dic61—41no—
79C23×Dic61—41no—
80C23×Dic61D414yes—
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89D4×Dic61—232no—
90C2×C4⋊Dic61—22no—
91C2×C4⋊Dic61—22no—
92C2×C4⋊Dic61—22no—
93C2×C4⋊Dic61—22no—
94C2×C4⋊Dic61—22no—
95C2×C4⋊Dic61—22no—
96C2×C4⋊Dic61—22no—
97C2×C4⋊Dic61—22no—
98C2×C4⋊Dic61—22no—
99C2×C4⋊Dic61—22no—
100C2×C4⋊Dic61—22no—
101C2×C4⋊Dic61—41no—
102C2×C4⋊Dic61—41no—
103C2×C4⋊Dic61—41no—
104C2×C4⋊Dic61—41no—
105C2×C22⋊Dic61—22no—
106C2×C22⋊Dic61—22no—
107C2×C22⋊Dic61—22no—
108C2×C22⋊Dic61—22no—
109C2×C22⋊Dic61—22no—
110C2×C22⋊Dic61—22no—
111C2×C22⋊Dic61—22no—
112C2×C22⋊Dic61—22no—
113C2×C22⋊Dic61—22no—
114C2×C22⋊Dic61—22no—
115C2×C22⋊Dic61—22no—
116C2×C22⋊Dic61—22no—
117C2×C22⋊Dic61—41no—
118C2×C22⋊Dic61—41no—
119C2×C22⋊Dic61D414yes—
120C2×C4×Dic61—22no—
121C2×C4×Dic61—22no—
122C2×C4×Dic61—22no—
123#14519684—22no—
124#14519684—22no—
125#14519684—22no—
126#14519684—22no—
127#14519684—22no—
128#14519684—22no—
129#14519684—22no—
130#14519684—22no—
131#14519684—22no—
132#14519684—22no—
133#14519684—22no—
134#14519684—41no—
135#14519684—41no—
136#14519684D414yescomplemented
137C25×C61C2311yescharacteristic
138C25×C61C2311yescharacteristic
139C22×D4×C61—22no—
140C22×D4×C61—22no—
141C22×D4×C61—22no—
142C22×D4×C61—22no—
143C22×D4×C61C2×C414yes—
144C22×D4×C61D414yes—
145C22×D4×C61Q814yes—
146C23×C4×C61—22no—
147C23×C4×C61—22no—
148C23×C4×C61—22no—
149C23×C4×C61—22no—
150C23×C4×C61—41no—
151C23×C4×C61—41no—
152C23×C4×C61C2×C414yescomplemented
153C23×C4×C61C2311yescharacteristic
154C23×C4×C61C2311yescharacteristic
155C23×C4×C61C2311yescharacteristic
156C23×C4×C61C2311yescharacteristic
157C23×C4×C61C2311yescharacteristic
158C2×C22⋊C4×C61—22no—
159C2×C22⋊C4×C61—22no—
160C2×C22⋊C4×C61—22no—
161C2×C22⋊C4×C61—22no—
162C2×C22⋊C4×C61—41no—
163C2×C22⋊C4×C61—41no—
164C2×C22⋊C4×C61C2×C414yescomplemented
165C2×C22⋊C4×C61C2×C414yescomplemented
166C2×C22⋊C4×C61C2×C414yescomplemented
167#95×C61C2×C414yescomplemented
168#95×C61C2×C414yescomplemented
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×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×C61C22×C412yes—
191C24×C61C2×D412yes—
192C24×C61C2×D412yes—
193C24×C61C2×D412yes—
194C24×C61C2×D412yes—
195C24×C61C2×Q812yes—
196C24×C61C2×Q812yes—
197C24×C61#4112yes—
198C24×C61#4112yes—
199C24×C61C2411yescharacteristic
200C2×D4×C61—28no—
201C2×D4×C61—28no—
202C2×D4×C61—28no—
203C2×D4×C61—28no—
204C2×D4×C61—28no—
205C2×D4×C61—28no—
206C2×D4×C61C4⋊C4116yescomplemented
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—28no—
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×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—28no—
235C22×C4×C61—44no—
236C22×C4×C61—44no—
237C22×C4×C61—44no—
238C22×C4×C61—44no—
239C22×C4×C61—44no—
240C22×C4×C61C22×C412yes—
241C22×C4×C61C22×C412yes—
242C22×C4×C61C22×C412yes—
243C22×C4×C61C22×C412yes—
244C22×C4×C61C22×C412yes—
245C22×C4×C61C2×D412yes—
246C22×C4×C61C2×D412yes—
247C22×C4×C61C2×Q812yes—
248C22×C4×C61#4112yes—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—21no—
253C22×Dic61—28no—
254C22×Dic61—28no—
255C22×Dic61—28no—
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—21no—
284C22×Dic61—21no—
285C22×Dic61—21no—
286C22×Dic61—28no—
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—44no—
302C22×Dic61—44no—
303C22×Dic61—44no—
304C22×Dic61—44no—
305C22×Dic61—44no—
306C22×Dic61—44no—
307C22×Dic61—44no—
308C22×Dic61—44no—
309C22×Dic61—44no—
310C22×Dic61—44no—
311C22×Dic61—44no—
312C22×Dic61—44no—
313C22×Dic61—44no—
314C22×Dic61—44no—
315C22×Dic61—44no—
316C22×Dic61—44no—
317C22×Dic61—44no—
318C22×Dic61C2×D412yes—
319C22×Dic61C2×D412yes—
320C22×Dic61C2×D412yes—
321C22×Dic61C2×D412yes—
322C22×Dic61C2×D412yes—
323C22×Dic61C2×D412yes—
324C22×Dic61#4112yes—
325C22×Dic61#4112yes—
326C22⋊C4×C61—28no—
327C22⋊C4×C61—28no—
328C22⋊C4×C61—44no—
329C22⋊Dic61—28no—
330C22⋊Dic61—28no—
331C22⋊Dic61—44no—
332C22⋊Dic61—44no—
333C22⋊Dic61—44no—
334C4⋊Dic61—28no—
335C4⋊Dic61—44no—
336C4⋊Dic61—44no—
337C4⋊Dic61—44no—
338C4⋊Dic61—44no—
339C4×Dic61—28no—
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—22no—
359C23×C61—22no—
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—22no—
379C23×C61—22no—
380C23×C61—22no—
381C23×C61—22no—
382C23×C61—22no—
383C23×C61—22no—
384C23×C61—22no—
385C23×C61—22no—
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×C61C2×C4⋊C414yes—
403C23×C61C2×C4⋊C414yes—
404C23×C61C4×D414yes—
405C23×C61C4×D414yes—
406C23×C61#12014yes—
407C23×C61C22⋊Q814yes—
408C23×C61C22⋊Q814yes—
409C23×C61#12314yes—
410C23×C61C23×C411yescharacteristic
411C23×C61C22×D411yescharacteristic
412C23×C61C22×D411yescharacteristic
413C23×C61C22×D411yescharacteristic
414C23×C61C22×D411yescharacteristic
415C23×C61C22×Q811yescharacteristic
416C23×C61C2×#4111yescharacteristic
417C23×C61C2×#4111yescharacteristic
418C23×C61C2×#4111yescharacteristic
419C23×C61C2×#4111yescharacteristic
420C23×C61C2×#4111yescharacteristic
421C23×C61H(5,𝔽2)11yescharacteristic
422C23×C61H(5,𝔽2)11yescharacteristic
423C23×C61H(5,𝔽2)11yescharacteristic
424C23×C612−1+411yescharacteristic
425D4×C61—232no—
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—416no—
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×C61—41no—
458C2×C4×C61—41no—
459C2×C4×C61—41no—
460C2×C4×C61C2×C4⋊C414yes—
461C2×C4×C61C4×D414yescomplemented
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—416no—
484C2×Dic61—416no—
485C2×Dic61—416no—
486C2×Dic61—41no—
487C2×Dic61—41no—
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×Dic61—41no—
501C2×Dic61—41no—
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×Dic61—41no—
515C2×Dic61—41no—
516C2×Dic61—41no—
517C2×Dic61—41no—
518C2×Dic61—41no—
519C2×Dic61—41no—
520C2×Dic61#12114yes—
521#13975—611nomaximal, Sylow
522C22×C61—24no—
523C22×C61—24no—
524C22×C61—24no—
525C22×C61—24no—
526C22×C61—24no—
527C22×C61—24no—
528C22×C61—24no—
529C22×C61—24no—
530C22×C61—24no—
531C22×C61—24no—
532C22×C61—24no—
533C22×C61—24no—
534C22×C61—24no—
535C22×C61—24no—
536C22×C61—24no—
537C22×C61—24no—
538C22×C61—24no—
539C22×C61—42no—
540C22×C61—42no—
541C22×C61—42no—
542C22×C61—42no—
543C22×C61—42no—
544C22×C61—42no—
545C22×C61—42no—
546C22×C61—42no—
547C22×C61—42no—
548C22×C61—42no—
549C22×C61—42no—
550C22×C61—42no—
551C22×C61#38518yescomplemented
552C22×C61C22×C4⋊C411yescharacteristic
553C22×C61C2×C4×D411yescharacteristic
554C22×C61C2×C4×D411yescharacteristic
555C22×C61C2×C4×D411yescharacteristic
556C22×C61C4×#4111yescharacteristic
557C22×C61#51811yescharacteristic
558C22×C61#52011yescharacteristic
559C22×C61C2×#12011yescharacteristic
560C22×C61C2×#12111yescharacteristic
561C22×C61C2×C22⋊Q811yescharacteristic
562C22×C61C2×C22⋊Q811yescharacteristic
563C22×C61C2×#12311yescharacteristic
564C22×C61#52511yescharacteristic
565C22×C61#52911yescharacteristic
566C22×C61#53211yescharacteristic
567C22×C61#53411yescharacteristic
568C22×C61#53711yescharacteristic
569C22×C61#53811yescharacteristic
570C22×C61#53911yescharacteristic
571C22×C61D4211yescharacteristic
572C22×C61D4211yescharacteristic
573C22×C61#54611yescharacteristic
574C22×C61#54611yescharacteristic
575C22×C61#54611yescharacteristic
576C22×C61#54611yescharacteristic
577C22×C61#54611yescharacteristic
578C22×C61#54711yescharacteristic
579C22×C61#54711yescharacteristic
580C22×C61D4×Q811yescharacteristic
581C22×C61#55111yescharacteristic
582C22×C61#55111yescharacteristic
583C22×C61#55211yescharacteristic
584C22×C61#55411yescharacteristic
585C22×C61#55411yescharacteristic
586C22×C61#55411yescharacteristic
587C4×C61—24no—
588C4×C61—24no—
589C4×C61—42no—
590C4×C61—42no—
591C4×C61—42no—
592Dic61—24no—
593Dic61—42no—
594Dic61—42no—
595Dic61—42no—
596Dic61—42no—
597Dic61—42no—
598Dic61—81no—
599Dic61—81no—
600C22×C4×D4—611no—
601C2×#386—611no—
602C2×#386D6111yescharacteristic
603C2×#385—611no—
604C2×#385—611no—
605C2×#380—611no—
606C22×#95—611no—
607#1444—611no—
608#1442—611no—
609#1439—611no—
610#1439—611no—
611#1436—611no—
612#1436—611no—
613C22⋊#95—611no—
614C22⋊#95—611no—
615C2×C61—28no—
616C2×C61—44no—
617C2×C61C2×#38511yescharacteristic
618C2×C61C4×#12111yescharacteristic
619C2×C61#232511yescharacteristic
620C2×C61D4×C4⋊C411yescharacteristic
621C2×C61#234911yescharacteristic
622C2×C61#235811yescharacteristic
623C2×C61#235911yescharacteristic
624C2×C61#241011yescharacteristic
625C2×C61#241711yescharacteristic
626C2×C61#241811yescharacteristic
627C2×C61#241911yescharacteristic
628C2×C61#243011yescharacteristic
629C2×C61#244911yescharacteristic
630C2×C61#245011yescharacteristic
631C2×C61#256411yescharacteristic
632C23×D4C2×D6111yescharacteristic
633C24×C4—611no—
634C24×C4—611no—
635C24×C4—611no—
636C24×C4C2×D6111yescharacteristic
637C2×C4×D4—1224no—
638C2×C4×D4—1224no—
639C2×C4×D4—1224no—
640C22×C4⋊C4—611no—
641C22×C4⋊C4—611no—
642C22×C4⋊C4—611no—
643C22×C4⋊C4—611no—
644C22×C4⋊C4—611no—
645C22×C22⋊C4—611no—
646C22×C22⋊C4—611no—
647C22×C22⋊C4—611no—
648C22×C22⋊C4—611no—
649C22×C22⋊C4—611no—
650C22×C22⋊C4C2×D6111yescharacteristic
651C22×C22⋊C4C2×D6111yescharacteristic
652C22×C22⋊C4C2×D6111yescharacteristic
653C22×C42—611no—
654#386—1224no—
655#386Dic6118yescomplemented
656#385—1224no—
657#385—1224no—
658#380—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—611no—
673C2×#95—1224no—
674C2×#95C2×D6111yescharacteristic
675C2×#95C2×D6111yescharacteristic
676C61#1397511yescharacteristic, complemented, Sylow
677C25C22×D6111yescharacteristic
678C25C22×D6111yescharacteristic
679C22×D4—22no—
680C22×D4—22no—
681C22×D4—22no—
682C22×D4—22no—
683C22×D4Dic12214yes—
684C22×D4D24414yes—
685C22×D4C2×Dic6114yes—
686C23×C4—22no—
687C23×C4—22no—
688C23×C4—22no—
689C23×C4—22no—
690C23×C4—41no—
691C23×C4—41no—
692C23×C4—611no—
693C23×C4—611no—
694C23×C4—611no—
695C23×C4—611no—
696C23×C4—611no—
697C23×C4—611no—
698C23×C4—614no—
699C23×C4—611no—
700C23×C4—611no—
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—1222no—
714C23×C4—1222no—
715C23×C4—2441no—
716C23×C4—2441no—
717C23×C4—2441no—
718C23×C4—2441no—
719C23×C4—2441no—
720C23×C4—2441no—
721C23×C4C2×Dic6114yescomplemented
722C23×C4C22×D6111yescharacteristic
723C23×C4C22×D6111yescharacteristic
724C23×C4C22×D6111yescharacteristic
725C23×C4C22×D6111yescharacteristic
726C23×C4C22×D6111yescharacteristic
727C4×D4—12232no—
728C2×C4⋊C4—1222no—
729C2×C4⋊C4—1222no—
730C2×C4⋊C4—1222no—
731C2×C4⋊C4—1222no—
732C2×C4⋊C4—1222no—
733C2×C4⋊C4—1222no—
734C2×C4⋊C4—1222no—
735C2×C4⋊C4—1222no—
736C2×C4⋊C4—1222no—
737C2×C4⋊C4—1222no—
738C2×C4⋊C4—1222no—
739C2×C4⋊C4—2441no—
740C2×C4⋊C4—2441no—
741C2×C4⋊C4—2441no—
742C2×C4⋊C4—2441no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—41no—
748C2×C22⋊C4—41no—
749C2×C22⋊C4—614no—
750C2×C22⋊C4—1222no—
751C2×C22⋊C4—1222no—
752C2×C22⋊C4—1222no—
753C2×C22⋊C4—1222no—
754C2×C22⋊C4—1222no—
755C2×C22⋊C4—1222no—
756C2×C22⋊C4—1222no—
757C2×C22⋊C4—1222no—
758C2×C22⋊C4—1222no—
759C2×C22⋊C4—1222no—
760C2×C22⋊C4—1222no—
761C2×C22⋊C4—1222no—
762C2×C22⋊C4—2441no—
763C2×C22⋊C4—2441no—
764C2×C22⋊C4C2×Dic6114yescomplemented
765C2×C22⋊C4C2×Dic6114yescomplemented
766C2×C22⋊C4C2×Dic6114yescomplemented
767C2×C42—1222no—
768C2×C42—1222no—
769C2×C42—1222no—
770#95—614no—
771#95—1222no—
772#95—1222no—
773#95—1222no—
774#95—1222no—
775#95—1222no—
776#95—1222no—
777#95—1222no—
778#95—1222no—
779#95—1222no—
780#95—1222no—
781#95—1222no—
782#95—2441no—
783#95—2441no—
784#95C2×Dic6114yescomplemented
785#95C2×Dic6114yescomplemented
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—21no—
799C24—21no—
800C24—21no—
801C24—21no—
802C24—21no—
803C24—21no—
804C24—21no—
805C24—21no—
806C24C2×Dic12212yes—
807C24C2×Dic12212yes—
808C24C2×D24412yes—
809C24C2×D24412yes—
810C24D4×D6112yes—
811C24D4×D6112yes—
812C24#1175822412yes—
813C24#1175822412yes—
814C24C22×Dic6112yes—
815C24C22×Dic6112yes—
816C24C23×D6111yescharacteristic
817C2×D4—28no—
818C2×D4—28no—
819C2×D4—28no—
820C2×D4—28no—
821C2×D4—28no—
822C2×D4—28no—
823C2×D4C4⋊Dic61116yescomplemented
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—28no—
851C22×C4—28no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
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—1221no—
867C22×C4—1221no—
868C22×C4—1221no—
869C22×C4—1221no—
870C22×C4—1228no—
871C22×C4—1228no—
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—1221no—
899C22×C4—1221no—
900C22×C4—1221no—
901C22×C4—1221no—
902C22×C4—1228no—
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—1221no—
913C22×C4—1221no—
914C22×C4—1221no—
915C22×C4—1221no—
916C22×C4—1221no—
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×C4—2444no—
934C22×C4C2×Dic12212yes—
935C22×C4C2×D24412yes—
936C22×C4D4×D6112yes—
937C22×C4#1175822412yes—
938C22×C4C22×Dic6112yes—
939C22×C4C22×Dic6112yes—
940C22×C4C22×Dic6112yes—
941C22×C4C22×Dic6112yes—
942C22×C4C22×Dic6112yes—
943C4⋊C4—1228no—
944C4⋊C4—2444no—
945C4⋊C4—2444no—
946C4⋊C4—2444no—
947C4⋊C4—2444no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—44no—
951C22⋊C4—1228no—
952C22⋊C4—1228no—
953C22⋊C4—2444no—
954C22⋊C4—2444no—
955C22⋊C4—2444no—
956C42—1228no—
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—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23C2×C4⋊Dic6114yes—
1020C23C2×C4⋊Dic6114yes—
1021C23D4×Dic6114yes—
1022C23D4×Dic6114yes—
1023C23#1451974714yes—
1024C23#1451975414yes—
1025C23#1451975414yes—
1026C23#1451976114yes—
1027C23C23×Dic6111yescharacteristic
1028C23C2×D4×D6111yescharacteristic
1029C23C2×D4×D6111yescharacteristic
1030C23C2×D4×D6111yescharacteristic
1031C23C22×D24411yescharacteristic
1032C23C22×Dic12211yescharacteristic
1033C23#41×D6111yescharacteristic
1034C23#41×D6111yescharacteristic
1035C23C2×#1175822411yescharacteristic
1036C23C2×#1175822411yescharacteristic
1037C23C2×#1175822411yescharacteristic
1038C23#1451982211yescharacteristic
1039C23#1451982211yescharacteristic
1040C23#1451982311yescharacteristic
1041C23#1451982411yescharacteristic
1042D4—232no—
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—416no—
1065C2×C4—41no—
1066C2×C4—41no—
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—614no—
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—24416no—
1100C2×C4—24416no—
1101C2×C4—2441no—
1102C2×C4—2441no—
1103C2×C4—2441no—
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—24416no—
1116C2×C4—2441no—
1117C2×C4—2441no—
1118C2×C4—2441no—
1119C2×C4—2441no—
1120C2×C4—2441no—
1121C2×C4—2441no—
1122C2×C4—2441no—
1123C2×C4—2441no—
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×C4C2×C4⋊Dic6114yes—
1137C2×C4D4×Dic6114yescomplemented
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—24no—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—24no—
1151C22—24no—
1152C22—24no—
1153C22—24no—
1154C22—24no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22#1683963718yescomplemented
1168C22C22×C4⋊Dic6111yescharacteristic
1169C22C2×D4×Dic6111yescharacteristic
1170C22C2×D4×Dic6111yescharacteristic
1171C22C2×D4×Dic6111yescharacteristic
1172C22#41×Dic6111yescharacteristic
1173C22#1684023711yescharacteristic
1174C22#1684024511yescharacteristic
1175C22C2×#1451974711yescharacteristic
1176C22#121×D6111yescharacteristic
1177C22C2×#1451975411yescharacteristic
1178C22C2×#1451975411yescharacteristic
1179C22C2×#1451976111yescharacteristic
1180C22#1684027211yescharacteristic
1181C22#1684029311yescharacteristic
1182C22#1684030711yescharacteristic
1183C22#1684032011yescharacteristic
1184C22#1684033911yescharacteristic
1185C22#1684034911yescharacteristic
1186C22#1684035711yescharacteristic
1187C22#1684039411yescharacteristic
1188C22D4×D24411yescharacteristic
1189C22#1684039911yescharacteristic
1190C22#1684039911yescharacteristic
1191C22#1684040411yescharacteristic
1192C22#1684040711yescharacteristic
1193C22#1684040711yescharacteristic
1194C22#1684041011yescharacteristic
1195C22#1684041611yescharacteristic
1196C22D4×Dic12211yescharacteristic
1197C22#1684043511yescharacteristic
1198C22#1684044311yescharacteristic
1199C22#1684044911yescharacteristic
1200C22#1684046911yescharacteristic
1201C22#1684047111yescharacteristic
1202C22#1684047111yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—1224no—
1209C4—4881no—
1210C4—4881no—
1211C4—2442no—
1212C4—2442no—
1213C4—2442no—
1214C4—2442no—
1215C4—2442no—
1216C2—28no—
1217C2—44no—
1218C2C2×#1683963711yescharacteristic
1219C2#121×Dic6111yescharacteristic
1220C2#2144852411yescharacteristic
1221C2D4×C4⋊Dic6111yescharacteristic
1222C2#2144872911yescharacteristic
1223C2#2144880311yescharacteristic
1224C2#2144881511yescharacteristic
1225C2#2144919211yescharacteristic
1226C2#2144926711yescharacteristic
1227C2#2144927911yescharacteristic
1228C2#2144929411yescharacteristic
1229C2#2144942711yescharacteristic
1230C2#2144963211yescharacteristic
1231C2#2144964711yescharacteristic
1232C2#2145100311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#386C2
socle, cosocleC24×C61C24
prime radicalC23×D4×C61C22
hypercenterC2×#386D61
hypocenterC61#13975
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×#16839637C2semidirect
4. C2×#16839637C2semidirect
5. C2×#16839622C2semidirect
6. C22×#14519684C2semidirect
7. #21444084C2semidirect
8. #21444076C2semidirect
9. #21444064C2semidirect
10. #21444064C2semidirect
11. #21444053C2semidirect
12. #21444053C2semidirect
13. #21444041C2semidirect
14. #21444041C2semidirect
57. C61×#386C4semidirect
136. #14519684D4semidirect
152. C23×C4×C61C2×C4semidirect
164. C2×C22⋊C4×C61C2×C4semidirect
165. C2×C22⋊C4×C61C2×C4semidirect
166. C2×C22⋊C4×C61C2×C4semidirect
167. #95×C61C2×C4semidirect
168. #95×C61C2×C4semidirect
206. C2×D4×C61C4⋊C4semidirect
461. C2×C4×C61C4×D4semidirect
551. C22×C61#385semidirect
655. #386Dic61semidirect
676. C61#13975semidirect
721. C23×C4C2×Dic61semidirect
764. C2×C22⋊C4C2×Dic61semidirect
765. C2×C22⋊C4C2×Dic61semidirect
766. C2×C22⋊C4C2×Dic61semidirect
784. #95C2×Dic61semidirect
785. #95C2×Dic61semidirect
823. C2×D4C4⋊Dic61semidirect
1137. C2×C4D4×Dic61semidirect
1167. C22#16839637semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic612
C2×#168396422
C2×#168396372
C2×#168396222
C22×#145196842
#214440842
#214440762
#214440642
#214440532
#214440412
C2×C61×#3862
#1397561