Finite Group Databasebeta

← #29602200

Subgroups — #29602200

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×#14519737C211yesmaximal, characteristic
2C2×#16839641C211yesmaximal, characteristic
3C2×#16839639C211yesmaximal, characteristic
4C2×#16839637C211yesmaximal, characteristic, complemented
5C2×#16839619C211yesmaximal, characteristic, complemented
6C22×#14519684C211yesmaximal, characteristic, complemented
7#21444073C211yesmaximal, characteristic, complemented
8#21444069C211yesmaximal, characteristic, complemented
9#21444065C211yesmaximal, characteristic, complemented
10#21444061C211yesmaximal, characteristic, complemented
11#21444048C211yesmaximal, characteristic, complemented
12#21444043C211yesmaximal, characteristic, complemented
13#21444041C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C2×C61×#385C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C24×Dic61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519737—24no—
21C2×#14519737—24no—
22C2×#14519737C418yescomplemented
23C22×C4⋊Dic61C2211yescharacteristic
24C22×C4⋊Dic61C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33#16839641—24no—
34#16839639—24no—
35#16839637—24no—
36#16839619—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
52C24×C4×C61C2211yescharacteristic
53C22×C4⋊C4×C61C2211yescharacteristic
54C22×C4⋊C4×C61C2211yescharacteristic
55C22×C22⋊C4×C61C2211yescharacteristic
56C22×C22⋊C4×C61C2211yescharacteristic
57C61×#385—24no—
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⋊D61D414yes—
67C22×C22⋊D61Q814yes—
68C23×Dic61—22no—
69C23×Dic61—22no—
70C23×Dic61—22no—
71C23×Dic61—22no—
72C23×Dic61—22no—
73C23×Dic61—22no—
74C23×Dic61—22no—
75C23×Dic61—22no—
76C23×Dic61—22no—
77C23×Dic61—41no—
78C23×Dic61—41no—
79C23×Dic61—41no—
80C23×Dic61—41no—
81C23×Dic61C2×C414yes—
82C23×Dic61C2311yescharacteristic
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#14519737—232no—
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×#11758196—22no—
104C2×#11758196—22no—
105C2×#11758196C2×C414yescomplemented
106C2×C22⋊Dic61—22no—
107C2×C22⋊Dic61—22no—
108C2×C22⋊Dic61—22no—
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—41no—
120C2×#11758198—41no—
121C2×#11758198—41no—
122C2×#11758198—41no—
123C2×#11758198C2×C414yescomplemented
124C2×C4×Dic61—22no—
125C2×C4×Dic61—22no—
126C2×C4×Dic61C2×C414yescomplemented
127#14519684—22no—
128#14519684—22no—
129#14519684—22no—
130#14519684—22no—
131#14519684—22no—
132#14519684—22no—
133#14519684—22no—
134#14519684—22no—
135#14519684—22no—
136#14519684—22no—
137#14519684—22no—
138#14519684—41no—
139#14519684—41no—
140#14519684D414yescomplemented
141C25×C61C2311yescharacteristic
142C23×C4×C61—22no—
143C23×C4×C61—22no—
144C23×C4×C61—22no—
145C23×C4×C61—22no—
146C23×C4×C61—22no—
147C23×C4×C61—41no—
148C23×C4×C61—41no—
149C23×C4×C61C2311yescharacteristic
150C23×C4×C61C2311yescharacteristic
151C23×C4×C61C2311yescharacteristic
152C23×C4×C61C2311yescharacteristic
153C23×C4×C61C2311yescharacteristic
154C23×C4×C61C2311yescharacteristic
155C2×C4⋊C4×C61—22no—
156C2×C4⋊C4×C61—22no—
157C2×C4⋊C4×C61—22no—
158C2×C4⋊C4×C61—22no—
159C2×C4⋊C4×C61—41no—
160C2×C4⋊C4×C61—41no—
161C2×C22⋊C4×C61—22no—
162C2×C22⋊C4×C61—22no—
163C2×C22⋊C4×C61—22no—
164C2×C22⋊C4×C61C2×C414yes—
165C2×C22⋊C4×C61D414yes—
166C2×C22⋊C4×C61D414yes—
167#95×C61—22no—
168#95×C61—22no—
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×C61C22×C412yes—
178C24×C61C2×D412yes—
179C24×C61C2×D412yes—
180C24×C61C2×D412yes—
181C24×C61C2×Q812yes—
182C24×C61#4112yes—
183C24×C61#4112yes—
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×D61C2×D412yes—
199C23×D61C2×Q812yes—
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—28no—
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×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—44no—
236C22×C4×C61—44no—
237C22×C4×C61—44no—
238C22×C4×C61—44no—
239C22×C4×C61—44no—
240C22×C4×C61—44no—
241C22×C4×C61C22×C412yes—
242C22×C4×C61C22×C412yes—
243C22×C4×C61C2×D412yes—
244C22×C4×C61C2×D412yes—
245C22×C4×C61C2×D412yes—
246C22×C4×C61C2×D412yes—
247C22×C4×C61C2×D412yes—
248C22×C4×C61#4112yes—
249C2×C22⋊D61—28no—
250C2×C22⋊D61—28no—
251C2×C22⋊D61—28no—
252C2×C22⋊D61—28no—
253C2×C22⋊D61—28no—
254C2×C22⋊D61—28no—
255C2×C22⋊D61C4⋊C4116yescomplemented
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—28no—
265C22×Dic61—28no—
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—28no—
285C22×Dic61—21no—
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—44no—
300C22×Dic61—44no—
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×Dic61C22×C412yes—
311C22×Dic61C22×C412yes—
312C22×Dic61C22×C412yes—
313C22×Dic61C2×D412yes—
314C22×Dic61C2×D412yes—
315C22×Dic61C2×D412yes—
316C22×Dic61C2×Q812yes—
317C22×Dic61#4112yes—
318C22×Dic61#4112yes—
319C2×C4×D61—28no—
320C2×C4×D61—28no—
321C2×C4×D61—44no—
322C2×C4×D61—44no—
323C2×C4×D61—44no—
324C2×C4×D61—44no—
325C2×C4×D61—44no—
326C4⋊C4×C61—44no—
327C4⋊C4×C61—44no—
328C22⋊C4×C61—44no—
329C22⋊C4×C61C22⋊C4116yescomplemented
330C22⋊Dic61—44no—
331#11758198—28no—
332#11758198—44no—
333#11758198—44no—
334#11758198—44no—
335#11758198—44no—
336C4⋊Dic61—44no—
337C4⋊Dic61—44no—
338#11758196—28no—
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×C61C2×C22⋊C414yes—
369C23×C61C2×C4⋊C414yes—
370C23×C61#11714yes—
371C23×C61#12114yes—
372C23×C61#12114yes—
373C23×C61C22⋊Q814yes—
374C23×C61C22⋊Q814yes—
375C23×C61C23×C411yescharacteristic
376C23×C61C22×D411yescharacteristic
377C23×C61C22×D411yescharacteristic
378C23×C61C22×D411yescharacteristic
379C23×C61C22×D411yescharacteristic
380C23×C61C22×Q811yescharacteristic
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—41no—
409C22×D61—41no—
410C22×D61—41no—
411C22×D61—41no—
412C22×D61—41no—
413C22×D61—41no—
414C22×D61—41no—
415C22×D61—41no—
416C22×D61—41no—
417C22×D61—41no—
418C22×D61—41no—
419C22×D61—41no—
420C22×D61—41no—
421C22×D61—41no—
422C22×D61—41no—
423C22×D61—41no—
424C22×D61C2×C4⋊C414yes—
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—416no—
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×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×C61—41no—
466C2×C4×C61C2×C22⋊C414yes—
467C2×C4×C61C2×C22⋊C414yes—
468C22⋊D61—232no—
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—416no—
491C2×Dic61—416no—
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×Dic61C2×C4⋊C414yes—
519C2×Dic61C4×D414yes—
520C4×D61—416no—
521#13899—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#38018yescomplemented
537C22×C61C22×C22⋊C411yescharacteristic
538C22×C61C22×C4⋊C411yescharacteristic
539C22×C61C2×#11711yescharacteristic
540C22×C61C2×C4×D411yescharacteristic
541C22×C61C4×#4111yescharacteristic
542C22×C61#51811yescharacteristic
543C22×C61#52011yescharacteristic
544C22×C61C2×#12111yescharacteristic
545C22×C61C2×#12111yescharacteristic
546C22×C61C2×C22⋊Q811yescharacteristic
547C22×C61C2×C22⋊Q811yescharacteristic
548C22×C61#52511yescharacteristic
549C22×C61#52511yescharacteristic
550C22×C61#52911yescharacteristic
551C22×C61#52911yescharacteristic
552C22×C61#53811yescharacteristic
553C22×C61#53811yescharacteristic
554C22×C61#53911yescharacteristic
555C22×C61#53911yescharacteristic
556C22×C61D4211yescharacteristic
557C22×C61D4211yescharacteristic
558C22×C61D4211yescharacteristic
559C22×C61#54611yescharacteristic
560C22×C61#54611yescharacteristic
561C22×C61#54611yescharacteristic
562C22×C61#54611yescharacteristic
563C22×C61#54611yescharacteristic
564C22×C61#54611yescharacteristic
565C22×C61#54711yescharacteristic
566C22×C61#54711yescharacteristic
567C22×C61#54711yescharacteristic
568C22×C61D4×Q811yescharacteristic
569C22×C61#55411yescharacteristic
570C22×C61#55411yescharacteristic
571C22×C61#55411yescharacteristic
572C2×D61—24no—
573C2×D61—24no—
574C2×D61—24no—
575C2×D61—42no—
576C2×D61—42no—
577C2×D61—42no—
578C2×D61—42no—
579C2×D61—42no—
580C2×D61—42no—
581C2×D61—42no—
582C2×D61—42no—
583C2×D61—42no—
584C2×D61—42no—
585C2×D61—42no—
586C2×D61—42no—
587C4×C61—24no—
588C4×C61—24no—
589C4×C61—42no—
590C4×C61—42no—
591C4×C61—81no—
592C4×C61—81no—
593Dic61—24no—
594Dic61—24no—
595Dic61—42no—
596Dic61—42no—
597Dic61—42no—
598Dic61—81no—
599Dic61—81no—
600C22×C4×D4—611no—
601C2×#386—611no—
602C2×#386—611no—
603C2×#385—611no—
604C2×#385D6111yescharacteristic, complemented
605C2×#380—611no—
606C22×#95—611no—
607#1441—611no—
608#1441—611no—
609#1439—611no—
610#1439—611no—
611C4⋊#95—611no—
612#1434—611no—
613C22⋊#95—611no—
614C22⋊#95—611no—
615C2×C61—28no—
616C2×C61C2×#38011yescharacteristic
617C2×C61#229011yescharacteristic
618C2×C61#231811yescharacteristic
619C2×C61D4×C22⋊C411yescharacteristic
620C2×C61#233911yescharacteristic
621C2×C61D4×C4⋊C411yescharacteristic
622C2×C61#234911yescharacteristic
623C2×C61#242411yescharacteristic
624C2×C61#242411yescharacteristic
625C2×C61#242511yescharacteristic
626C2×C61#242511yescharacteristic
627C2×C61#244911yescharacteristic
628C2×C61#244911yescharacteristic
629C2×C61#245011yescharacteristic
630C2×C61#245011yescharacteristic
631D61—44no—
632C23×D4—611no—
633C24×C4—611no—
634C24×C4—611no—
635C24×C4—611no—
636C24×C4C2×D6111yescharacteristic
637C2×C4×D4—618no—
638C2×C4×D4—1224no—
639C2×C4×D4—1224no—
640C22×C4⋊C4—611no—
641C22×C4⋊C4—611no—
642C22×C4⋊C4—611no—
643C22×C4⋊C4C2×D6111yescharacteristic
644C22×C4⋊C4C2×D6111yescharacteristic
645C22×C22⋊C4—611no—
646C22×C22⋊C4—611no—
647C22×C22⋊C4—611no—
648C22×C22⋊C4—611no—
649C22×C22⋊C4—611no—
650C22×C22⋊C4—611no—
651C22×C22⋊C4C2×D6111yescharacteristic
652C22×C22⋊C4C2×D6111yescharacteristic
653C22×C42—611no—
654#386—1224no—
655#386—1224no—
656#385—24no—
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#1389911yescharacteristic, 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—22no—
687C23×C4—22no—
688C23×C4—22no—
689C23×C4—22no—
690C23×C4—22no—
691C23×C4—41no—
692C23×C4—41no—
693C23×C4—611no—
694C23×C4—611no—
695C23×C4—611no—
696C23×C4—611no—
697C23×C4—611no—
698C23×C4—614no—
699C23×C4—614no—
700C23×C4—611no—
701C23×C4—611no—
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×C4C22×D6111yescharacteristic
722C23×C4C22×D6111yescharacteristic
723C23×C4C22×D6111yescharacteristic
724C23×C4C22×D6111yescharacteristic
725C23×C4C22×D6111yescharacteristic
726C23×C4C22×D6111yescharacteristic
727C4×D4—12232no—
728C2×C4⋊C4—22no—
729C2×C4⋊C4—22no—
730C2×C4⋊C4—22no—
731C2×C4⋊C4—22no—
732C2×C4⋊C4—41no—
733C2×C4⋊C4—41no—
734C2×C4⋊C4—614no—
735C2×C4⋊C4—1222no—
736C2×C4⋊C4—1222no—
737C2×C4⋊C4—1222no—
738C2×C4⋊C4—1222no—
739C2×C4⋊C4—1222no—
740C2×C4⋊C4—1222no—
741C2×C4⋊C4—2441no—
742C2×C4⋊C4—2441no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—614no—
747C2×C22⋊C4—1222no—
748C2×C22⋊C4—1222no—
749C2×C22⋊C4—1222no—
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—2441no—
761C2×C22⋊C4—2441no—
762C2×C22⋊C4—2441no—
763C2×C22⋊C4—2441no—
764C2×C22⋊C4C4×D6114yes—
765C2×C22⋊C4D24414yes—
766C2×C22⋊C4C22⋊D6114yes—
767C2×C42—614no—
768C2×C42—1222no—
769C2×C42—1222no—
770#95—22no—
771#95—22no—
772#95—614no—
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—1222no—
783#95—1222no—
784#95—2441no—
785#95—2441no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—612no—
795C24—612no—
796C24—612no—
797C24—1221no—
798C24—1221no—
799C24—1221no—
800C24—1221no—
801C24—1221no—
802C24—1221no—
803C24—1221no—
804C24—1221no—
805C24—1221no—
806C24—1221no—
807C24—1221no—
808C24—1221no—
809C24C2×C4×D6112yes—
810C24C2×D24412yes—
811C24D4×D6112yes—
812C24#1175822412yes—
813C24Q8×D6112yes—
814C24#1175822612yes—
815C24C2×C22⋊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—28no—
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—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—612no—
866C22×C4—612no—
867C22×C4—612no—
868C22×C4—612no—
869C22×C4—612no—
870C22×C4—612no—
871C22×C4—612no—
872C22×C4—612no—
873C22×C4—612no—
874C22×C4—1228no—
875C22×C4—1228no—
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—1228no—
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—1228no—
904C22×C4—1228no—
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—1221no—
918C22×C4—1221no—
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×C4—2444no—
935C22×C4C2×C4×D6112yes—
936C22×C4C2×C4×D6112yes—
937C22×C4C2×D24412yes—
938C22×C4C2×D24412yes—
939C22×C4D4×D6112yes—
940C22×C4#1175822412yes—
941C22×C4C2×C22⋊D6112yes—
942C22×C4C2×C22⋊D6112yes—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C4⋊C4—1228no—
946C4⋊C4—2444no—
947C4⋊C4—2444no—
948C22⋊C4—44no—
949C22⋊C4—1228no—
950C22⋊C4—2444no—
951C22⋊C4—2444no—
952C22⋊C4—2444no—
953C22⋊C4—2444no—
954C22⋊C4—2444no—
955C22⋊C4#11758198116yescomplemented
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—614no—
986C23—1222no—
987C23—1222no—
988C23—1222no—
989C23—1222no—
990C23—1222no—
991C23—1222no—
992C23—1222no—
993C23—1222no—
994C23—1222no—
995C23—1222no—
996C23—1222no—
997C23—1222no—
998C23—1222no—
999C23—1222no—
1000C23—1222no—
1001C23—1222no—
1002C23—1222no—
1003C23—1222no—
1004C23—2441no—
1005C23—2441no—
1006C23—2441no—
1007C23—2441no—
1008C23—2441no—
1009C23—2441no—
1010C23—2441no—
1011C23—2441no—
1012C23—2441no—
1013C23—2441no—
1014C23—2441no—
1015C23—2441no—
1016C23—2441no—
1017C23—2441no—
1018C23—2441no—
1019C23—2441no—
1020C23C2×#1175819814yes—
1021C23C4⋊C4×D6114yes—
1022C23#1451973514yes—
1023C23#1451974814yes—
1024C23#1451975214yes—
1025C23#1451975314yes—
1026C23#1451975714yes—
1027C23C22×C4×D6111yescharacteristic
1028C23C2×D4×D6111yescharacteristic
1029C23C2×D4×D6111yescharacteristic
1030C23C22×C22⋊D6111yescharacteristic
1031C23C22×D24411yescharacteristic
1032C23C2×Q8×D6111yescharacteristic
1033C23#41×D6111yescharacteristic
1034C23#41×D6111yescharacteristic
1035C23C2×#1175822411yescharacteristic
1036C23C2×#1175822411yescharacteristic
1037C23C2×#1175822611yescharacteristic
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—416no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
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—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—614no—
1085C2×C4—614no—
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—1222no—
1103C2×C4—1222no—
1104C2×C4—1222no—
1105C2×C4—1222no—
1106C2×C4—1222no—
1107C2×C4—24416no—
1108C2×C4—24416no—
1109C2×C4—2441no—
1110C2×C4—2441no—
1111C2×C4—2441no—
1112C2×C4—2441no—
1113C2×C4—2441no—
1114C2×C4—2441no—
1115C2×C4—2441no—
1116C2×C4—2441no—
1117C2×C4—2441no—
1118C2×C4—2441no—
1119C2×C4—2441no—
1120C2×C4—2441no—
1121C2×C4—2441no—
1122C2×C4—2441no—
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×C4C2×#1175819814yes—
1137C2×C4C2×#1175819814yes—
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—1224no—
1153C22—1224no—
1154C22—1224no—
1155C22—2442no—
1156C22—2442no—
1157C22—2442no—
1158C22—2442no—
1159C22—2442no—
1160C22—2442no—
1161C22—2442no—
1162C22—2442no—
1163C22—2442no—
1164C22—2442no—
1165C22—2442no—
1166C22—2442no—
1167C22#1683961918yescomplemented
1168C22C22×#1175819811yescharacteristic
1169C22C2×C4⋊C4×D6111yescharacteristic
1170C22C2×#1451973511yescharacteristic
1171C22C4×D4×D6111yescharacteristic
1172C22C4×#1175822411yescharacteristic
1173C22#1684023411yescharacteristic
1174C22#1684024111yescharacteristic
1175C22C2×#1451974811yescharacteristic
1176C22C2×#1451975211yescharacteristic
1177C22C2×#1451975311yescharacteristic
1178C22C2×#1451975711yescharacteristic
1179C22#1684026811yescharacteristic
1180C22#1684027511yescharacteristic
1181C22#1684028911yescharacteristic
1182C22#1684029811yescharacteristic
1183C22#1684034711yescharacteristic
1184C22#1684035211yescharacteristic
1185C22#1684035611yescharacteristic
1186C22#1684036111yescharacteristic
1187C22#1684039411yescharacteristic
1188C22D4×C22⋊D6111yescharacteristic
1189C22D4×D24411yescharacteristic
1190C22#1684039911yescharacteristic
1191C22#1684040011yescharacteristic
1192C22#1684040411yescharacteristic
1193C22#1684040611yescharacteristic
1194C22#1684040711yescharacteristic
1195C22#1684040711yescharacteristic
1196C22#1684041011yescharacteristic
1197C22#1684041111yescharacteristic
1198C22#1684041611yescharacteristic
1199C22#1684042511yescharacteristic
1200C22#1684046611yescharacteristic
1201C22#1684046611yescharacteristic
1202C22#1684047011yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—42no—
1206C4—42no—
1207C4—81no—
1208C4—81no—
1209C4—1224no—
1210C4—1224no—
1211C4—4881no—
1212C4—4881no—
1213C4—2442no—
1214C4—2442no—
1215C4—2442no—
1216C2—28no—
1217C2—2444no—
1218C2C2×#1683961911yescharacteristic
1219C2#2144825511yescharacteristic
1220C2#2144844711yescharacteristic
1221C2D4×#1175819811yescharacteristic
1222C2#2144864411yescharacteristic
1223C2#2144871711yescharacteristic
1224C2#2144872511yescharacteristic
1225C2#2144935111yescharacteristic
1226C2#2144935311yescharacteristic
1227C2#2144936611yescharacteristic
1228C2#2144936811yescharacteristic
1229C2#2144962411yescharacteristic
1230C2#2144962611yescharacteristic
1231C2#2144963911yescharacteristic
1232C2#2144964111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#385C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×#385D61
hypocenterC61#13899
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C2×#16839637C2semidirect
5. C2×#16839619C2semidirect
6. C22×#14519684C2semidirect
7. #21444073C2semidirect
8. #21444069C2semidirect
9. #21444065C2semidirect
10. #21444061C2semidirect
11. #21444048C2semidirect
12. #21444043C2semidirect
13. #21444041C2semidirect
14. #21444040C2semidirect
15. C2×C61×#385C2semidirect
22. C2×#14519737C4semidirect
95. C22×C4×D61C2×C4semidirect
105. C2×#11758196C2×C4semidirect
123. C2×#11758198C2×C4semidirect
126. C2×C4×Dic61C2×C4semidirect
140. #14519684D4semidirect
255. C2×C22⋊D61C4⋊C4semidirect
329. C22⋊C4×C61C22⋊C4semidirect
536. C22×C61#380semidirect
604. C2×#385D61semidirect
676. C61#13899semidirect
955. C22⋊C4#11758198semidirect
1167. C22#16839619semidirect

Maximal subgroups

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

subgroupindex
C22×#145197372
C2×#168396412
C2×#168396392
C2×#168396372
C2×#168396192
C22×#145196842
#214440732
#214440692
#214440652
#214440612
#214440482
#214440432
#214440412
#214440402
C2×C61×#3852
#1389961