Finite Group Databasebeta

← #29609351

Subgroups — #29609351

Order 15616.

2390 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839671C211yesmaximal, characteristic
2C2×#16839663C211yesmaximal, characteristic, complemented
3C2×#16839641C211yesmaximal, characteristic, complemented
4C2×#16839641C211yesmaximal, characteristic, complemented
5C2×#16839640C211yesmaximal, characteristic, complemented
6C2×#16839638C211yesmaximal, characteristic, complemented
7#21444078C211yesmaximal, characteristic, complemented
8#21444067C211yesmaximal, characteristic, complemented
9#21444061C211yesmaximal, characteristic, complemented
10#21444061C211yesmaximal, characteristic, complemented
11#21444058C211yesmaximal, characteristic, complemented
12#21444056C211yesmaximal, characteristic, complemented
13#21444044C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C2×C61×#385C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C22⋊D61C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C22×C22⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32#16839671C418yescomplemented
33#16839663—24no—
34#16839641—24no—
35#16839641—24no—
36#16839640—24no—
37#16839638—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
50C24×C4×C61C2211yescharacteristic
51C22×C4⋊C4×C61C2211yescharacteristic
52C22×C4⋊C4×C61C2211yescharacteristic
53C22×C22⋊C4×C61C2211yescharacteristic
54C22×C22⋊C4×C61C2211yescharacteristic
55C61×#385—24no—
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C24×D61C2311yescharacteristic
59C24×D61C2311yescharacteristic
60C22×D244—22no—
61C22×D244—22no—
62C22×D244—22no—
63C22×D244—22no—
64C22×D244—41no—
65C22×D244—41no—
66C22×D244C2×C414yescomplemented
67C22×C22⋊D61—22no—
68C22×C22⋊D61—22no—
69C22×C22⋊D61—22no—
70C22×C22⋊D61—22no—
71C22×C22⋊D61—22no—
72C22×C22⋊D61—22no—
73C22×C22⋊D61—41no—
74C22×C22⋊D61—41no—
75C22×C22⋊D61—41no—
76C22×C22⋊D61—41no—
77C22×C22⋊D61—41no—
78C22×C22⋊D61—41no—
79C22×C22⋊D61C2×C414yes—
80C22×C22⋊D61C2×C414yescomplemented
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C22×C4×D61—22no—
88C22×C4×D61—22no—
89C22×C4×D61—22no—
90C22×C4×D61—41no—
91C22×C4×D61—41no—
92C22×C4×D61—41no—
93C22×C4×D61—41no—
94C2×C22⋊Dic61—22no—
95C2×C22⋊Dic61—22no—
96C2×C22⋊Dic61—41no—
97C2×C22⋊Dic61—41no—
98C2×C22⋊Dic61—41no—
99C2×C22⋊Dic61D414yescomplemented
100C2×#11758198—22no—
101C2×#11758198—22no—
102C2×#11758198—22no—
103C2×#11758198—22no—
104C2×#11758198—22no—
105C2×#11758198—22no—
106C2×#11758198—22no—
107C2×#11758198—22no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×#11758198—41no—
111C2×#11758198—41no—
112C2×#11758198—41no—
113C2×#11758198—41no—
114C2×#11758198—41no—
115C2×#11758198—41no—
116C2×#11758198—41no—
117C2×#11758198—41no—
118C2×#11758198—41no—
119C2×#11758198—41no—
120C2×#11758198—41no—
121C2×#11758198—41no—
122C2×#11758198—41no—
123C2×#11758198—41no—
124C2×#11758198C2×C414yescomplemented
125C2×#11758198C2×C414yescomplemented
126C2×#11758198D414yescomplemented
127C2×C4×Dic61—22no—
128C2×C4×Dic61—22no—
129C2×C4×Dic61—41no—
130#14519684—22no—
131#14519684—22no—
132#14519684—22no—
133#14519684—22no—
134#14519684—22no—
135#14519684—22no—
136#14519684—22no—
137#14519684—41no—
138#14519684—41no—
139#14519684—41no—
140#14519684—41no—
141#14519684C2×C414yescomplemented
142C25×C61C2311yescharacteristic
143C23×C4×C61—22no—
144C23×C4×C61—22no—
145C23×C4×C61—22no—
146C23×C4×C61—41no—
147C23×C4×C61—41no—
148C23×C4×C61—41no—
149C23×C4×C61—41no—
150C23×C4×C61C2311yescharacteristic
151C23×C4×C61C2311yescharacteristic
152C23×C4×C61C2311yescharacteristic
153C23×C4×C61C2311yescharacteristic
154C23×C4×C61C2311yescharacteristic
155C23×C4×C61C2311yescharacteristic
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×C4⋊C4×C61—41no—
162C2×C22⋊C4×C61—22no—
163C2×C22⋊C4×C61—22no—
164C2×C22⋊C4×C61—22no—
165C2×C22⋊C4×C61—22no—
166C2×C22⋊C4×C61—41no—
167C2×C22⋊C4×C61C2×C414yescomplemented
168#95×C61—22no—
169#95×C61D414yescomplemented
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×C61C22×C412yes—
183C24×C61C2×D412yes—
184C24×C61#4112yes—
185C24×C61C2411yescharacteristic
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×D61—21no—
198C23×D61—21no—
199C23×D61—21no—
200C23×D61—21no—
201C23×D61—21no—
202C23×D61—21no—
203C23×D61—21no—
204C23×D61—21no—
205C23×D61—21no—
206C23×D61—21no—
207C23×D61—21no—
208C23×D61—21no—
209C23×D61—21no—
210C23×D61—21no—
211C23×D61—21no—
212C23×D61C22×C412yes—
213C23×D61C22×C412yes—
214C23×D61C2×D412yes—
215C23×D61#4112yes—
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—21no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61—44no—
252C22×C4×C61—44no—
253C22×C4×C61—44no—
254C22×C4×C61—44no—
255C22×C4×C61—44no—
256C22×C4×C61—44no—
257C22×C4×C61—44no—
258C22×C4×C61C22×C412yes—
259C22×C4×C61C22×C412yes—
260C22×C4×C61C2×D412yes—
261C22×C4×C61C2×D412yes—
262C22×C4×C61C2×D412yes—
263C22×C4×C61C2×D412yes—
264C22×C4×C61#4112yes—
265C2×C22⋊D61—28no—
266C2×C22⋊D61—28no—
267C2×C22⋊D61—28no—
268C2×C22⋊D61—44no—
269C2×C22⋊D61—44no—
270C2×C22⋊D61—44no—
271C2×C22⋊D61—44no—
272C2×C22⋊D61—44no—
273C2×C22⋊D61—44no—
274C2×C22⋊D61—44no—
275C2×C22⋊D61—44no—
276C2×C22⋊D61—44no—
277C2×C22⋊D61—44no—
278C2×C22⋊D61—44no—
279C22×Dic61—21no—
280C22×Dic61—21no—
281C22×Dic61—21no—
282C22×Dic61—21no—
283C22×Dic61—21no—
284C22×Dic61—21no—
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—21no—
300C22×Dic61—21no—
301C22×Dic61—21no—
302C22×Dic61—21no—
303C22×Dic61—21no—
304C22×Dic61—21no—
305C22×Dic61—21no—
306C22×Dic61—21no—
307C22×Dic61—21no—
308C22×Dic61—21no—
309C22×Dic61—21no—
310C22×Dic61—21no—
311C22×Dic61—21no—
312C22×Dic61—21no—
313C22×Dic61—21no—
314C22×Dic61—21no—
315C22×Dic61—21no—
316C22×Dic61C22×C412yes—
317C22×Dic61C22×C412yes—
318C22×Dic61C2×D412yes—
319C22×Dic61C2×D412yes—
320C22×Dic61C2×D412yes—
321C2×D244—28no—
322C2×D244—28no—
323C2×D244—44no—
324C2×D244—44no—
325C2×D244—44no—
326C2×D244—44no—
327C2×D244—44no—
328C2×C4×D61—44no—
329C2×C4×D61—44no—
330C2×C4×D61—44no—
331C2×C4×D61—44no—
332C2×C4×D61—44no—
333C2×C4×D61—44no—
334C2×C4×D61—44no—
335C4⋊C4×C61—44no—
336C4⋊C4×C61—44no—
337C22⋊C4×C61—28no—
338C22⋊C4×C61—44no—
339C22⋊Dic61—44no—
340C22⋊Dic61—44no—
341#11758198—44no—
342#11758198—44no—
343#11758198—44no—
344#11758198—44no—
345#11758198—44no—
346#11758198—44no—
347#11758198—44no—
348#11758198—44no—
349#11758198—44no—
350C4×Dic61—44no—
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—41no—
370C23×C61—41no—
371C23×C61—41no—
372C23×C61—41no—
373C23×C61—41no—
374C23×C61—41no—
375C23×C61—41no—
376C23×C61—41no—
377C23×C61—41no—
378C23×C61—41no—
379C23×C61—41no—
380C23×C61—41no—
381C23×C61—41no—
382C23×C61—41no—
383C23×C61—41no—
384C23×C61—41no—
385C23×C61C4×D414yes—
386C23×C61C23×C411yescharacteristic
387C23×C61C22×D411yescharacteristic
388C23×C61C22×D411yescharacteristic
389C23×C61C22×D411yescharacteristic
390C23×C61C2×#4111yescharacteristic
391C23×C61C2×#4111yescharacteristic
392C23×C61C2×#4111yescharacteristic
393C23×C61H(5,𝔽2)11yescharacteristic
394C23×C61H(5,𝔽2)11yescharacteristic
395C23×C61H(5,𝔽2)11yescharacteristic
396C23×C61H(5,𝔽2)11yescharacteristic
397C23×C61H(5,𝔽2)11yescharacteristic
398C23×C61H(5,𝔽2)11yescharacteristic
399C23×C61H(5,𝔽2)11yescharacteristic
400C23×C612−1+411yescharacteristic
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×D61—22no—
419C22×D61—22no—
420C22×D61—22no—
421C22×D61—22no—
422C22×D61—22no—
423C22×D61—22no—
424C22×D61—22no—
425C22×D61—22no—
426C22×D61—41no—
427C22×D61—41no—
428C22×D61—41no—
429C22×D61—41no—
430C22×D61—41no—
431C22×D61—41no—
432C22×D61—41no—
433C22×D61—41no—
434C22×D61—41no—
435C22×D61—41no—
436C22×D61—41no—
437C22×D61—41no—
438C22×D61—41no—
439C22×D61—41no—
440C22×D61—41no—
441C22×D61—41no—
442C22×D61—41no—
443C22×D61—41no—
444C22×D61—41no—
445C22×D61—41no—
446C22×D61—41no—
447C22×D61—41no—
448C22×D61—41no—
449C22×D61—41no—
450C22×D61—41no—
451C22×D61—41no—
452C22×D61—41no—
453C22×D61—41no—
454C22×D61—41no—
455C22×D61—41no—
456C22×D61—41no—
457C22×D61—41no—
458C22×D61—41no—
459C22×D61—41no—
460C22×D61—41no—
461C22×D61—41no—
462C22×D61—41no—
463C22×D61—41no—
464C22×D61—41no—
465C22×D61—41no—
466C22×D61—41no—
467C22×D61—41no—
468C22×D61—41no—
469C22×D61—41no—
470C22×D61C4×D414yes—
471C2×C4×C61—22no—
472C2×C4×C61—22no—
473C2×C4×C61—22no—
474C2×C4×C61—22no—
475C2×C4×C61—22no—
476C2×C4×C61—22no—
477C2×C4×C61—22no—
478C2×C4×C61—22no—
479C2×C4×C61—22no—
480C2×C4×C61—22no—
481C2×C4×C61—22no—
482C2×C4×C61—22no—
483C2×C4×C61—22no—
484C2×C4×C61—22no—
485C2×C4×C61—22no—
486C2×C4×C61—22no—
487C2×C4×C61—22no—
488C2×C4×C61—22no—
489C2×C4×C61—416no—
490C2×C4×C61—41no—
491C2×C4×C61—41no—
492C2×C4×C61—41no—
493C2×C4×C61—41no—
494C2×C4×C61—41no—
495C2×C4×C61—41no—
496C2×C4×C61—41no—
497C2×C4×C61—41no—
498C2×C4×C61—41no—
499C2×C4×C61—41no—
500C2×C4×C61—41no—
501C2×C4×C61—41no—
502C2×C4×C61—41no—
503C2×C4×C61—41no—
504C2×C4×C61—41no—
505C2×C4×C61—41no—
506C2×C4×C61—41no—
507C2×C4×C61—41no—
508C2×C4×C61—41no—
509C2×C4×C61—41no—
510C2×C4×C61—41no—
511C2×C4×C61—41no—
512C2×C4×C61—41no—
513C2×C4×C61C4×D414yes—
514C22⋊D61—416no—
515C22⋊D61—416no—
516C2×Dic61—22no—
517C2×Dic61—22no—
518C2×Dic61—22no—
519C2×Dic61—22no—
520C2×Dic61—22no—
521C2×Dic61—22no—
522C2×Dic61—22no—
523C2×Dic61—22no—
524C2×Dic61—22no—
525C2×Dic61—22no—
526C2×Dic61—22no—
527C2×Dic61—22no—
528C2×Dic61—22no—
529C2×Dic61—22no—
530C2×Dic61—22no—
531C2×Dic61—41no—
532C2×Dic61—41no—
533C2×Dic61—41no—
534C2×Dic61—41no—
535C2×Dic61—41no—
536C2×Dic61—41no—
537C2×Dic61—41no—
538C2×Dic61—41no—
539C2×Dic61—41no—
540C2×Dic61—41no—
541C2×Dic61—41no—
542C2×Dic61—41no—
543C2×Dic61—41no—
544C2×Dic61—41no—
545C2×Dic61—41no—
546C2×Dic61—41no—
547C2×Dic61—41no—
548C2×Dic61—41no—
549C2×Dic61—41no—
550C2×Dic61—41no—
551C2×Dic61—41no—
552C2×Dic61—41no—
553C2×Dic61—41no—
554C2×Dic61—41no—
555C2×Dic61—41no—
556C2×Dic61—41no—
557C2×Dic61—41no—
558D244—416no—
559C4×D61—416no—
560#14519—611nomaximal, Sylow
561C22×C61—24no—
562C22×C61—24no—
563C22×C61—24no—
564C22×C61—42no—
565C22×C61—42no—
566C22×C61—42no—
567C22×C61—42no—
568C22×C61—42no—
569C22×C61—42no—
570C22×C61—42no—
571C22×C61—42no—
572C22×C61—42no—
573C22×C61—42no—
574C22×C61—42no—
575C22×C61—42no—
576C22×C61C2×C4×D411yescharacteristic
577C22×C61C2×C4×D411yescharacteristic
578C22×C61C2×C4×D411yescharacteristic
579C22×C61#51811yescharacteristic
580C22×C61#51811yescharacteristic
581C22×C61#51811yescharacteristic
582C22×C61#52011yescharacteristic
583C22×C61#53411yescharacteristic
584C22×C61#53411yescharacteristic
585C22×C61#53511yescharacteristic
586C22×C61#53511yescharacteristic
587C22×C61#53511yescharacteristic
588C22×C61#53711yescharacteristic
589C22×C61#53811yescharacteristic
590C22×C61#53811yescharacteristic
591C22×C61#53811yescharacteristic
592C22×C61#53911yescharacteristic
593C22×C61#54011yescharacteristic
594C22×C61#54011yescharacteristic
595C22×C61D4211yescharacteristic
596C22×C61D4211yescharacteristic
597C22×C61D4211yescharacteristic
598C22×C61#54611yescharacteristic
599C22×C61#54611yescharacteristic
600C22×C61#54611yescharacteristic
601C22×C61#54611yescharacteristic
602C22×C61#54711yescharacteristic
603C22×C61#54811yescharacteristic
604C22×C61#55111yescharacteristic
605C22×C61#55111yescharacteristic
606C22×C61#55311yescharacteristic
607C22×C61#56011yescharacteristic
608C22×C61#56011yescharacteristic
609C22×C61#56211yescharacteristic
610C22×C61#56211yescharacteristic
611C2×D61—24no—
612C2×D61—24no—
613C2×D61—24no—
614C2×D61—42no—
615C2×D61—42no—
616C2×D61—42no—
617C2×D61—42no—
618C2×D61—42no—
619C2×D61—42no—
620C2×D61—42no—
621C2×D61—42no—
622C2×D61—42no—
623C2×D61—42no—
624C2×D61—42no—
625C2×D61—42no—
626C2×D61—42no—
627C2×D61—42no—
628C2×D61—42no—
629C2×D61—42no—
630C2×D61—42no—
631C2×D61—42no—
632C2×D61—42no—
633C2×D61—81no—
634C2×D61—81no—
635C2×D61—81no—
636C2×D61—81no—
637C2×D61—81no—
638C2×D61—81no—
639C2×D61—81no—
640C2×D61—81no—
641C4×C61—24no—
642C4×C61—42no—
643C4×C61—42no—
644C4×C61—42no—
645C4×C61—42no—
646C4×C61—81no—
647Dic61—42no—
648Dic61—42no—
649Dic61—42no—
650Dic61—42no—
651Dic61—42no—
652Dic61—81no—
653C2×#392—611no—
654C2×#390—611no—
655C2×#386—611no—
656C2×#386—611no—
657C2×#386—611no—
658C2×#386—611no—
659C2×#385D6111yescharacteristic, complemented
660#1442—611no—
661#1440—611no—
662#1439—611no—
663#1439—611no—
664#1438—611no—
665#1437—611no—
666#1434—611no—
667C22⋊#95—611no—
668C2×C61—44no—
669C2×C61#232111yescharacteristic
670C2×C61#232511yescharacteristic
671C2×C61#232811yescharacteristic
672C2×C61#235811yescharacteristic
673C2×C61#235811yescharacteristic
674C2×C61#236111yescharacteristic
675C2×C61#237711yescharacteristic
676C2×C61#266911yescharacteristic
677C2×C61#267111yescharacteristic
678C2×C61#267611yescharacteristic
679C2×C61#267811yescharacteristic
680C2×C61#268811yescharacteristic
681C2×C61#269611yescharacteristic
682C2×C61#270611yescharacteristic
683C2×C61#274911yescharacteristic
684D61—44no—
685D61—82no—
686C23×D4—611no—
687C23×D4—611no—
688C23×D4—611no—
689C24×C4—611no—
690C24×C4C2×D6111yescharacteristic
691C22×C4⋊C4C2×D6111yescharacteristic
692C22×C4⋊C4C2×D6111yescharacteristic
693C22×C22⋊C4—611no—
694C22×C22⋊C4—611no—
695C22×C22⋊C4—611no—
696C22×C22⋊C4—611no—
697C22×C22⋊C4—611no—
698C22×C22⋊C4—611no—
699C22×C22⋊C4—611no—
700C22×C22⋊C4—611no—
701C22×C22⋊C4—611no—
702C22×C22⋊C4—611no—
703C22×C22⋊C4—611no—
704C22×C22⋊C4C2×D6111yescharacteristic
705C22×C22⋊C4C2×D6111yescharacteristic
706C22×C42—611no—
707#392—618no—
708#390—1224no—
709#386—1224no—
710#386—1224no—
711#386—1224no—
712#386—1224no—
713#385—24no—
714C2×#95—611no—
715C2×#95—611no—
716C2×#95—611no—
717C2×#95—611no—
718C2×#95—611no—
719C2×#95—611no—
720C2×#95—611no—
721C2×#95—611no—
722C2×#95—611no—
723C2×#95—611no—
724C2×#95—611no—
725C2×#95—611no—
726C2×#95C2×D6111yescharacteristic
727C2×#95C2×D6111yescharacteristic
728C61#1451911yescharacteristic, complemented, Sylow
729C25—611no—
730C25—611no—
731C25C22×D6111yescharacteristic
732C22×D4—614no—
733C22×D4—614no—
734C22×D4—614no—
735C22×D4—1222no—
736C22×D4—1222no—
737C22×D4—1222no—
738C22×D4—1222no—
739C22×D4—1222no—
740C22×D4—1222no—
741C22×D4—1222no—
742C22×D4—1222no—
743C22×D4—1222no—
744C22×D4—1222no—
745C22×D4—2441no—
746C22×D4—2441no—
747C22×D4—2441no—
748C22×D4—2441no—
749C22×D4—2441no—
750C22×D4—2441no—
751C22×D4—2441no—
752C22×D4—2441no—
753C23×C4—22no—
754C23×C4—22no—
755C23×C4—22no—
756C23×C4—41no—
757C23×C4—41no—
758C23×C4—41no—
759C23×C4—41no—
760C23×C4—611no—
761C23×C4—611no—
762C23×C4—611no—
763C23×C4—611no—
764C23×C4—611no—
765C23×C4—611no—
766C23×C4—1222no—
767C23×C4—1222no—
768C23×C4—1222no—
769C23×C4—2441no—
770C23×C4—2441no—
771C23×C4—2441no—
772C23×C4—2441no—
773C23×C4C22×D6111yescharacteristic
774C23×C4C22×D6111yescharacteristic
775C23×C4C22×D6111yescharacteristic
776C23×C4C22×D6111yescharacteristic
777C23×C4C22×D6111yescharacteristic
778C23×C4C22×D6111yescharacteristic
779C2×C4⋊C4—22no—
780C2×C4⋊C4—22no—
781C2×C4⋊C4—22no—
782C2×C4⋊C4—41no—
783C2×C4⋊C4—41no—
784C2×C4⋊C4—41no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—614no—
791C2×C22⋊C4—614no—
792C2×C22⋊C4—614no—
793C2×C22⋊C4—614no—
794C2×C22⋊C4—1222no—
795C2×C22⋊C4—1222no—
796C2×C22⋊C4—1222no—
797C2×C22⋊C4—1222no—
798C2×C22⋊C4—1222no—
799C2×C22⋊C4—1222no—
800C2×C22⋊C4—1222no—
801C2×C22⋊C4—1222no—
802C2×C22⋊C4—1222no—
803C2×C22⋊C4—1222no—
804C2×C22⋊C4—1222no—
805C2×C22⋊C4—1222no—
806C2×C22⋊C4—2441no—
807C2×C22⋊C4—2441no—
808C2×C22⋊C4—2441no—
809C2×C22⋊C4—2441no—
810C2×C22⋊C4—2441no—
811C2×C22⋊C4—2441no—
812C2×C22⋊C4—2441no—
813C2×C22⋊C4—2441no—
814C2×C22⋊C4—2441no—
815C2×C22⋊C4—2441no—
816C2×C22⋊C4—2441no—
817C2×C22⋊C4—2441no—
818C2×C22⋊C4—2441no—
819C2×C22⋊C4—2441no—
820C2×C22⋊C4—2441no—
821C2×C22⋊C4—2441no—
822C2×C22⋊C4—2441no—
823C2×C22⋊C4C4×D6114yescomplemented
824C2×C42—1222no—
825C2×C42—1222no—
826C2×C42—2441no—
827#95—22no—
828#95—614no—
829#95—1222no—
830#95—1222no—
831#95—1222no—
832#95—1222no—
833#95—1222no—
834#95—1222no—
835#95—1222no—
836#95—2441no—
837#95—2441no—
838#95—2441no—
839#95—2441no—
840#95C22⋊D6114yescomplemented
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—612no—
854C24—612no—
855C24—612no—
856C24—612no—
857C24—1221no—
858C24—1221no—
859C24—1221no—
860C24—1221no—
861C24—1221no—
862C24—1221no—
863C24—1221no—
864C24—1221no—
865C24—1221no—
866C24—1221no—
867C24—1221no—
868C24—1221no—
869C24—1221no—
870C24—1221no—
871C24—1221no—
872C24—1221no—
873C24—1221no—
874C24—1221no—
875C24—1221no—
876C24—1221no—
877C24—1221no—
878C24—1221no—
879C24—1221no—
880C24—1221no—
881C24—1221no—
882C24—1221no—
883C24C2×C4×D6112yes—
884C24D4×D6112yes—
885C24#1175822612yes—
886C24C23×D6111yescharacteristic
887C2×D4—1228no—
888C2×D4—1228no—
889C2×D4—1228no—
890C2×D4—1228no—
891C2×D4—1228no—
892C2×D4—2444no—
893C2×D4—2444no—
894C2×D4—2444no—
895C2×D4—2444no—
896C2×D4—2444no—
897C2×D4—2444no—
898C2×D4—2444no—
899C2×D4—2444no—
900C2×D4—2444no—
901C2×D4—2444no—
902C2×D4—2444no—
903C2×D4—2444no—
904C2×D4—2444no—
905C2×D4—2444no—
906C2×D4—2444no—
907C2×D4—2444no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—44no—
950C22×C4—612no—
951C22×C4—612no—
952C22×C4—612no—
953C22×C4—612no—
954C22×C4—612no—
955C22×C4—1221no—
956C22×C4—1221no—
957C22×C4—1221no—
958C22×C4—1221no—
959C22×C4—1221no—
960C22×C4—1221no—
961C22×C4—1221no—
962C22×C4—1221no—
963C22×C4—1221no—
964C22×C4—1221no—
965C22×C4—1221no—
966C22×C4—1221no—
967C22×C4—1221no—
968C22×C4—1221no—
969C22×C4—1221no—
970C22×C4—1221no—
971C22×C4—1221no—
972C22×C4—1221no—
973C22×C4—1221no—
974C22×C4—1221no—
975C22×C4—1221no—
976C22×C4—1221no—
977C22×C4—1221no—
978C22×C4—1221no—
979C22×C4—1221no—
980C22×C4—1221no—
981C22×C4—1221no—
982C22×C4—1221no—
983C22×C4—1221no—
984C22×C4—1221no—
985C22×C4—1221no—
986C22×C4—1221no—
987C22×C4—1221no—
988C22×C4—1221no—
989C22×C4—1221no—
990C22×C4—1221no—
991C22×C4—1221no—
992C22×C4—2444no—
993C22×C4—2444no—
994C22×C4—2444no—
995C22×C4—2444no—
996C22×C4—2444no—
997C22×C4—2444no—
998C22×C4—2444no—
999C22×C4C2×C4×D6112yes—
1000C22×C4C2×C4×D6112yes—
1001C22×C4#1175822212yes—
1002C22×C4D4×D6112yes—
1003C22×C4C2×C22⋊D6112yes—
1004C22×C4C2×C22⋊D6112yes—
1005C22×C4C2×C22⋊D6112yes—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C22⋊C4—28no—
1009C22⋊C4—44no—
1010C22⋊C4—2444no—
1011C22⋊C4—2444no—
1012C22⋊C4—2444no—
1013C22⋊C4—2444no—
1014C22⋊C4—2444no—
1015C22⋊C4—2444no—
1016C22⋊C4—2444no—
1017C22⋊C4—2444no—
1018C22⋊C4—2444no—
1019C22⋊C4—2444no—
1020C22⋊C4—2444no—
1021C42—2444no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—614no—
1057C23—1222no—
1058C23—1222no—
1059C23—1222no—
1060C23—1222no—
1061C23—1222no—
1062C23—1222no—
1063C23—1222no—
1064C23—1222no—
1065C23—1222no—
1066C23—1222no—
1067C23—1222no—
1068C23—1222no—
1069C23—1222no—
1070C23—1222no—
1071C23—1222no—
1072C23—1222no—
1073C23—1222no—
1074C23—1222no—
1075C23—1222no—
1076C23—1222no—
1077C23—1222no—
1078C23—1222no—
1079C23—1222no—
1080C23—1222no—
1081C23—1222no—
1082C23—2441no—
1083C23—2441no—
1084C23—2441no—
1085C23—2441no—
1086C23—2441no—
1087C23—2441no—
1088C23—2441no—
1089C23—2441no—
1090C23—2441no—
1091C23—2441no—
1092C23—2441no—
1093C23—2441no—
1094C23—2441no—
1095C23—2441no—
1096C23—2441no—
1097C23—2441no—
1098C23—2441no—
1099C23—2441no—
1100C23—2441no—
1101C23—2441no—
1102C23—2441no—
1103C23—2441no—
1104C23—2441no—
1105C23—2441no—
1106C23—2441no—
1107C23—2441no—
1108C23—2441no—
1109C23—2441no—
1110C23—2441no—
1111C23—2441no—
1112C23—2441no—
1113C23—2441no—
1114C23—2441no—
1115C23—2441no—
1116C23—2441no—
1117C23—2441no—
1118C23—2441no—
1119C23—2441no—
1120C23—2441no—
1121C23—2441no—
1122C23—2441no—
1123C23—2441no—
1124C23—2441no—
1125C23—2441no—
1126C23#1451973914yes—
1127C23C22×C4×D6111yescharacteristic
1128C23C2×D4×D6111yescharacteristic
1129C23C2×D4×D6111yescharacteristic
1130C23C22×C22⋊D6111yescharacteristic
1131C23#41×D6111yescharacteristic
1132C23C2×#1175822211yescharacteristic
1133C23C2×#1175822611yescharacteristic
1134C23#1451982211yescharacteristic
1135C23#1451982211yescharacteristic
1136C23#1451982211yescharacteristic
1137C23#1451982211yescharacteristic
1138C23#1451982311yescharacteristic
1139C23#1451982311yescharacteristic
1140C23#1451982311yescharacteristic
1141C23#1451982511yescharacteristic
1142D4—24416no—
1143D4—24416no—
1144D4—24416no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—416no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—1222no—
1188C2×C4—1222no—
1189C2×C4—1222no—
1190C2×C4—1222no—
1191C2×C4—1222no—
1192C2×C4—1222no—
1193C2×C4—1222no—
1194C2×C4—1222no—
1195C2×C4—1222no—
1196C2×C4—1222no—
1197C2×C4—1222no—
1198C2×C4—1222no—
1199C2×C4—1222no—
1200C2×C4—1222no—
1201C2×C4—1222no—
1202C2×C4—24416no—
1203C2×C4—2441no—
1204C2×C4—2441no—
1205C2×C4—2441no—
1206C2×C4—2441no—
1207C2×C4—2441no—
1208C2×C4—2441no—
1209C2×C4—2441no—
1210C2×C4—2441no—
1211C2×C4—2441no—
1212C2×C4—2441no—
1213C2×C4—2441no—
1214C2×C4—2441no—
1215C2×C4—2441no—
1216C2×C4—2441no—
1217C2×C4—2441no—
1218C2×C4—2441no—
1219C2×C4—2441no—
1220C2×C4—2441no—
1221C2×C4—2441no—
1222C2×C4—2441no—
1223C2×C4—2441no—
1224C2×C4—2441no—
1225C2×C4—2441no—
1226C2×C4—2441no—
1227C2×C4—2441no—
1228C2×C4—2441no—
1229C2×C4—2441no—
1230C2×C4C4×C22⋊D6114yes—
1231C22—24no—
1232C22—24no—
1233C22—24no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—1224no—
1247C22—1224no—
1248C22—1224no—
1249C22—4881no—
1250C22—4881no—
1251C22—4881no—
1252C22—4881no—
1253C22—4881no—
1254C22—4881no—
1255C22—4881no—
1256C22—4881no—
1257C22—2442no—
1258C22—2442no—
1259C22—2442no—
1260C22—2442no—
1261C22—2442no—
1262C22—2442no—
1263C22—2442no—
1264C22—2442no—
1265C22—2442no—
1266C22—2442no—
1267C22—2442no—
1268C22—2442no—
1269C22—2442no—
1270C22—2442no—
1271C22—2442no—
1272C22—2442no—
1273C22—2442no—
1274C22—2442no—
1275C22—2442no—
1276C22C4×D4×D6111yescharacteristic
1277C22C2×C4×C22⋊D6111yescharacteristic
1278C22C2×#1451973911yescharacteristic
1279C22#1684023411yescharacteristic
1280C22#1684023411yescharacteristic
1281C22#1684023411yescharacteristic
1282C22#1684024311yescharacteristic
1283C22#1684032211yescharacteristic
1284C22#1684032311yescharacteristic
1285C22#1684032611yescharacteristic
1286C22#1684032711yescharacteristic
1287C22#1684032911yescharacteristic
1288C22#1684034211yescharacteristic
1289C22#1684034811yescharacteristic
1290C22#1684035211yescharacteristic
1291C22#1684035211yescharacteristic
1292C22#1684035811yescharacteristic
1293C22#1684036311yescharacteristic
1294C22#1684036311yescharacteristic
1295C22#1684039411yescharacteristic
1296C22D4×C22⋊D6111yescharacteristic
1297C22D4×C22⋊D6111yescharacteristic
1298C22#1684040011yescharacteristic
1299C22#1684040311yescharacteristic
1300C22#1684040411yescharacteristic
1301C22#1684040811yescharacteristic
1302C22#1684041311yescharacteristic
1303C22#1684042311yescharacteristic
1304C22#1684043911yescharacteristic
1305C22#1684044111yescharacteristic
1306C22#1684046011yescharacteristic
1307C22#1684050111yescharacteristic
1308C22#1684050211yescharacteristic
1309C22#1684050811yescharacteristic
1310C22#1684050811yescharacteristic
1311C4—24no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—42no—
1316C4—81no—
1317C4—4881no—
1318C4—2442no—
1319C4—2442no—
1320C4—2442no—
1321C4—2442no—
1322C4—2442no—
1323C2—44no—
1324C2—4882no—
1325C2—2444no—
1326C2#2144847611yescharacteristic
1327C2#2144851611yescharacteristic
1328C2#2144854111yescharacteristic
1329C2#2144879511yescharacteristic
1330C2#2144879611yescharacteristic
1331C2#2144883511yescharacteristic
1332C2#2144897511yescharacteristic
1333C2#2145203311yescharacteristic
1334C2#2145205911yescharacteristic
1335C2#2145211611yescharacteristic
1336C2#2145213811yescharacteristic
1337C2#2145225811yescharacteristic
1338C2#2145236311yescharacteristic
1339C2#2145250811yescharacteristic
1340C2#2145304311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#385C2
socle, cosocleC24×C61C24
prime radicalC2×#16839671C2
hypercenterC2×#385D61
hypocenterC61#14519
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×#16839663C2semidirect
3. C2×#16839641C2semidirect
4. C2×#16839641C2semidirect
5. C2×#16839640C2semidirect
6. C2×#16839638C2semidirect
7. #21444078C2semidirect
8. #21444067C2semidirect
9. #21444061C2semidirect
10. #21444061C2semidirect
11. #21444058C2semidirect
12. #21444056C2semidirect
13. #21444044C2semidirect
14. #21444040C2semidirect
15. C2×C61×#385C2semidirect
32. #16839671C4semidirect
66. C22×D244C2×C4semidirect
80. C22×C22⋊D61C2×C4semidirect
99. C2×C22⋊Dic61D4semidirect
124. C2×#11758198C2×C4semidirect
125. C2×#11758198C2×C4semidirect
126. C2×#11758198D4semidirect
141. #14519684C2×C4semidirect
167. C2×C22⋊C4×C61C2×C4semidirect
169. #95×C61D4semidirect
659. C2×#385D61semidirect
728. C61#14519semidirect
823. C2×C22⋊C4C4×D61semidirect
840. #95C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396712
C2×#168396632
C2×#168396412
C2×#168396402
C2×#168396382
#214440782
#214440672
#214440612
#214440582
#214440562
#214440442
#214440402
C2×C61×#3852
#1451961