Finite Group Databasebeta

← #29608281

Subgroups — #29608281

Order 15616.

1866 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839665C211yesmaximal, characteristic
2C2×#16839656C211yesmaximal, characteristic, complemented
3C2×#16839647C211yesmaximal, characteristic, complemented
4C2×#16839642C211yesmaximal, characteristic
5C2×#16839634C211yesmaximal, characteristic, complemented
6#21444088C211yesmaximal, characteristic, complemented
7#21444066C211yesmaximal, characteristic, complemented
8#21444062C211yesmaximal, characteristic, complemented
9#21444062C211yesmaximal, characteristic, complemented
10#21444062C211yesmaximal, characteristic, complemented
11#21444056C211yesmaximal, characteristic, complemented
12#21444047C211yesmaximal, characteristic, complemented
13#21444044C211yesmaximal, characteristic, complemented
14#21444041C211yesmaximal, characteristic, complemented
15C61×#1438C211yesmaximal, characteristic
16C24×Dic61C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×#11758196C2211yescharacteristic
19C22×#11758196C2211yescharacteristic
20C22×#11758196C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×C22⋊Dic61C2211yescharacteristic
23C22×C22⋊Dic61C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C4×Dic61C2211yescharacteristic
29C22×C4×Dic61C2211yescharacteristic
30#16839665C418yescomplemented
31#16839656—24no—
32#16839647—24no—
33#16839642—24no—
34#16839634—24no—
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C23×D4×C61C2211yescharacteristic
50C22×C22⋊C4×C61C2211yescharacteristic
51C22×C22⋊C4×C61C2211yescharacteristic
52C22×C22⋊C4×C61C2211yescharacteristic
53C22×C22⋊C4×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C23×Dic61—22no—
57C23×Dic61—22no—
58C23×Dic61—22no—
59C23×Dic61—41no—
60C23×Dic61—41no—
61C23×Dic61—41no—
62C23×Dic61—41no—
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2311yescharacteristic
65C23×Dic61C2311yescharacteristic
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C2×C4⋊Dic61—22no—
72C2×C4⋊Dic61—22no—
73C2×C4⋊Dic61C2×C414yescomplemented
74C2×#11758196—22no—
75C2×#11758196—22no—
76C2×#11758196—22no—
77C2×#11758196—41no—
78C2×#11758196—41no—
79C2×#11758196—41no—
80C2×#11758196—41no—
81C2×#11758196—41no—
82C2×#11758196D414yescomplemented
83C2×C22⋊Dic61—22no—
84C2×C22⋊Dic61—22no—
85C2×C22⋊Dic61—22no—
86C2×C22⋊Dic61—22no—
87C2×C22⋊Dic61—22no—
88C2×C22⋊Dic61—22no—
89C2×C22⋊Dic61—22no—
90C2×C22⋊Dic61—22no—
91C2×C22⋊Dic61—22no—
92C2×C22⋊Dic61—41no—
93C2×C22⋊Dic61—41no—
94C2×C22⋊Dic61—41no—
95C2×C22⋊Dic61—41no—
96C2×C22⋊Dic61—41no—
97C2×C22⋊Dic61—41no—
98C2×C22⋊Dic61—41no—
99C2×C22⋊Dic61—41no—
100C2×C22⋊Dic61C2×C414yes—
101C2×C22⋊Dic61C2×C414yes—
102C2×C22⋊Dic61C2×C414yescomplemented
103C2×C22⋊Dic61C2×C414yescomplemented
104C2×C4×Dic61—22no—
105C2×C4×Dic61—22no—
106C2×C4×Dic61—41no—
107C2×C4×Dic61—41no—
108C2×C4×Dic61—41no—
109C2×C4×Dic61C2×C414yescomplemented
110#14519684—22no—
111#14519684—22no—
112#14519684—22no—
113#14519684—22no—
114#14519684—22no—
115#14519684—22no—
116#14519684—22no—
117#14519684—41no—
118#14519684—41no—
119#14519684—41no—
120#14519684—41no—
121#14519684—41no—
122#14519684—41no—
123#14519684D414yes—
124C25×C61C2311yescharacteristic
125C25×C61C2311yescharacteristic
126C22×D4×C61—22no—
127C22×D4×C61—22no—
128C22×D4×C61—22no—
129C22×D4×C61—22no—
130C22×D4×C61—41no—
131C22×D4×C61—41no—
132C22×D4×C61C2×C414yes—
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61—22no—
139C2×C22⋊C4×C61—22no—
140C2×C22⋊C4×C61—22no—
141C2×C22⋊C4×C61—22no—
142C2×C22⋊C4×C61—41no—
143C2×C22⋊C4×C61—41no—
144C2×C22⋊C4×C61—41no—
145C2×C22⋊C4×C61—41no—
146C2×C22⋊C4×C61—41no—
147C2×C22⋊C4×C61—41no—
148C2×C22⋊C4×C61—41no—
149C2×C22⋊C4×C61—41no—
150#95×C61—22no—
151#95×C61—22no—
152C24×C61—21no—
153C24×C61—21no—
154C24×C61—21no—
155C24×C61—21no—
156C24×C61—21no—
157C24×C61—21no—
158C24×C61—21no—
159C24×C61—21no—
160C24×C61—21no—
161C24×C61—21no—
162C24×C61—21no—
163C24×C61—21no—
164C24×C61—21no—
165C24×C61—21no—
166C24×C61—21no—
167C24×C61—21no—
168C24×C61—21no—
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×C61C22×C412yes—
179C24×C61C22×C412yes—
180C24×C61#4112yes—
181C24×C61#4112yes—
182C24×C61C2411yescharacteristic
183C2×D4×C61—28no—
184C2×D4×C61—28no—
185C2×D4×C61—44no—
186C2×D4×C61—44no—
187C2×D4×C61—44no—
188C2×D4×C61—44no—
189C2×D4×C61—44no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
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×C61C22×C412yes—
222C22×C4×C61C2×D412yes—
223C22×C4×C61C2×D412yes—
224C22×C4×C61#4112yes—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—21no—
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—44no—
273C22×Dic61—44no—
274C22×Dic61—44no—
275C22×Dic61—44no—
276C22×Dic61—44no—
277C22×Dic61—44no—
278C22×Dic61—44no—
279C22×Dic61C22×C412yes—
280C22×Dic61C22×C412yes—
281C22×Dic61C22×C412yes—
282C22×Dic61C22×C412yes—
283C22×Dic61C2×D412yes—
284C22×Dic61C2×D412yes—
285C22×Dic61C2×D412yes—
286C22×Dic61C2×D412yes—
287C22×Dic61#4112yes—
288C22⋊C4×C61—44no—
289C22⋊C4×C61—44no—
290C22⋊C4×C61—44no—
291C22⋊C4×C61—44no—
292C22⋊Dic61—28no—
293C22⋊Dic61—28no—
294C22⋊Dic61—44no—
295C22⋊Dic61—44no—
296C22⋊Dic61—44no—
297C22⋊Dic61—44no—
298C22⋊Dic61—44no—
299C4⋊Dic61—28no—
300#11758196—44no—
301#11758196—44no—
302#11758196—44no—
303C4×Dic61—44no—
304C4×Dic61—44no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—22no—
312C23×C61—22no—
313C23×C61—22no—
314C23×C61—22no—
315C23×C61—22no—
316C23×C61—22no—
317C23×C61—22no—
318C23×C61—22no—
319C23×C61—22no—
320C23×C61—22no—
321C23×C61—22no—
322C23×C61—22no—
323C23×C61—22no—
324C23×C61—22no—
325C23×C61—22no—
326C23×C61—22no—
327C23×C61—22no—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—41no—
331C23×C61—41no—
332C23×C61—41no—
333C23×C61—41no—
334C23×C61—41no—
335C23×C61—41no—
336C23×C61—41no—
337C23×C61—41no—
338C23×C61—41no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—41no—
348C23×C61—41no—
349C23×C61—41no—
350C23×C61—41no—
351C23×C61—41no—
352C23×C61—41no—
353C23×C61—41no—
354C23×C61—41no—
355C23×C61—41no—
356C23×C61—41no—
357C23×C61—41no—
358C23×C61—41no—
359C23×C61—41no—
360C23×C61—41no—
361C23×C61—41no—
362C23×C61—41no—
363C23×C61—41no—
364C23×C61—41no—
365C23×C61—41no—
366C23×C61—41no—
367C23×C61—41no—
368C23×C61—41no—
369C23×C61—41no—
370C23×C61—41no—
371C23×C61—41no—
372C23×C61—41no—
373C23×C61—41no—
374C23×C61#11714yes—
375C23×C61C23×C411yescharacteristic
376C23×C61C22×D411yescharacteristic
377C23×C61C22×D411yescharacteristic
378C23×C61C2×#4111yescharacteristic
379C23×C61C2×#4111yescharacteristic
380C23×C61C2×#4111yescharacteristic
381C23×C61C2×#4111yescharacteristic
382C23×C61H(5,𝔽2)11yescharacteristic
383C23×C61H(5,𝔽2)11yescharacteristic
384C23×C61H(5,𝔽2)11yescharacteristic
385C23×C61H(5,𝔽2)11yescharacteristic
386C23×C61H(5,𝔽2)11yescharacteristic
387C23×C61H(5,𝔽2)11yescharacteristic
388C23×C612−1+411yescharacteristic
389C23×C612−1+411yescharacteristic
390D4×C61—416no—
391C2×C4×C61—22no—
392C2×C4×C61—22no—
393C2×C4×C61—22no—
394C2×C4×C61—22no—
395C2×C4×C61—22no—
396C2×C4×C61—22no—
397C2×C4×C61—22no—
398C2×C4×C61—22no—
399C2×C4×C61—22no—
400C2×C4×C61—41no—
401C2×C4×C61—41no—
402C2×C4×C61—41no—
403C2×C4×C61—41no—
404C2×C4×C61—41no—
405C2×C4×C61—41no—
406C2×C4×C61—41no—
407C2×C4×C61—41no—
408C2×C4×C61—41no—
409C2×C4×C61—41no—
410C2×C4×C61—41no—
411C2×C4×C61—41no—
412C2×C4×C61—41no—
413C2×C4×C61—41no—
414C2×C4×C61—41no—
415C2×C4×C61—41no—
416C2×C4×C61—41no—
417C2×C4×C61—41no—
418C2×C4×C61—41no—
419C2×C4×C61—41no—
420C2×C4×C61—41no—
421C2×C4×C61—41no—
422C2×C4×C61—41no—
423C2×C4×C61—41no—
424C2×C4×C61—41no—
425C2×C4×C61C4×D414yes—
426C2×Dic61—22no—
427C2×Dic61—22no—
428C2×Dic61—22no—
429C2×Dic61—22no—
430C2×Dic61—22no—
431C2×Dic61—22no—
432C2×Dic61—22no—
433C2×Dic61—22no—
434C2×Dic61—22no—
435C2×Dic61—22no—
436C2×Dic61—22no—
437C2×Dic61—22no—
438C2×Dic61—22no—
439C2×Dic61—22no—
440C2×Dic61—22no—
441C2×Dic61—22no—
442C2×Dic61—22no—
443C2×Dic61—22no—
444C2×Dic61—22no—
445C2×Dic61—22no—
446C2×Dic61—22no—
447C2×Dic61—22no—
448C2×Dic61—22no—
449C2×Dic61—22no—
450C2×Dic61—416no—
451C2×Dic61—41no—
452C2×Dic61—41no—
453C2×Dic61—41no—
454C2×Dic61—41no—
455C2×Dic61—41no—
456C2×Dic61—41no—
457C2×Dic61—41no—
458C2×Dic61—41no—
459C2×Dic61—41no—
460C2×Dic61—41no—
461C2×Dic61—41no—
462C2×Dic61—41no—
463C2×Dic61—41no—
464C2×Dic61—41no—
465C2×Dic61—41no—
466C2×Dic61—41no—
467C2×Dic61—41no—
468C2×Dic61—41no—
469C2×Dic61—41no—
470C2×Dic61—41no—
471C2×Dic61—41no—
472C2×Dic61—41no—
473C2×Dic61—41no—
474C2×Dic61—41no—
475C2×Dic61—41no—
476C2×Dic61—41no—
477C2×Dic61—41no—
478C2×Dic61—41no—
479C2×Dic61—41no—
480C2×Dic61—41no—
481C2×Dic61—41no—
482C2×Dic61C4×D414yes—
483#14429—611nomaximal, Sylow
484C22×C61—24no—
485C22×C61—24no—
486C22×C61—24no—
487C22×C61—42no—
488C22×C61—42no—
489C22×C61—42no—
490C22×C61—42no—
491C22×C61—42no—
492C22×C61—42no—
493C22×C61—42no—
494C22×C61—42no—
495C22×C61—42no—
496C22×C61—42no—
497C22×C61—42no—
498C22×C61—42no—
499C22×C61—42no—
500C22×C61—42no—
501C22×C61—42no—
502C22×C61—42no—
503C22×C61—42no—
504C22×C61—42no—
505C22×C61—42no—
506C22×C61—81no—
507C22×C61—81no—
508C22×C61—81no—
509C22×C61—81no—
510C22×C61—81no—
511C22×C61—81no—
512C22×C61—81no—
513C22×C61—81no—
514C22×C61C2×#11711yescharacteristic
515C22×C61C2×C4×D411yescharacteristic
516C22×C61C2×C4×D411yescharacteristic
517C22×C61#51811yescharacteristic
518C22×C61#51811yescharacteristic
519C22×C61#52011yescharacteristic
520C22×C61#52011yescharacteristic
521C22×C61#53411yescharacteristic
522C22×C61#53511yescharacteristic
523C22×C61#53611yescharacteristic
524C22×C61#53711yescharacteristic
525C22×C61#53811yescharacteristic
526C22×C61#53811yescharacteristic
527C22×C61#53811yescharacteristic
528C22×C61#53911yescharacteristic
529C22×C61#53911yescharacteristic
530C22×C61#53911yescharacteristic
531C22×C61#54211yescharacteristic
532C22×C61#54211yescharacteristic
533C22×C61D4211yescharacteristic
534C22×C61#54611yescharacteristic
535C22×C61#54611yescharacteristic
536C22×C61#54611yescharacteristic
537C22×C61#54811yescharacteristic
538C22×C61#55011yescharacteristic
539C22×C61#55011yescharacteristic
540C22×C61#55111yescharacteristic
541C22×C61#55111yescharacteristic
542C22×C61#55211yescharacteristic
543C22×C61#55311yescharacteristic
544C22×C61#55911yescharacteristic
545C22×C61#56011yescharacteristic
546C22×C61#56011yescharacteristic
547C22×C61#56211yescharacteristic
548C22×C61#56211yescharacteristic
549C4×C61—24no—
550C4×C61—42no—
551C4×C61—81no—
552C4×C61—81no—
553C4×C61—81no—
554Dic61—24no—
555Dic61—42no—
556Dic61—42no—
557Dic61—42no—
558Dic61—42no—
559Dic61—42no—
560Dic61—42no—
561Dic61—81no—
562C2×#390—611no—
563C2×#388—611no—
564C2×#387—611no—
565C2×#386—611no—
566C2×#385—611no—
567#1445—611no—
568#1440—611no—
569#1439—611no—
570#1439—611no—
571#1439—611no—
572#1438D6111yescharacteristic
573#1437—611no—
574C4⋊#95—611no—
575#1434—611no—
576C22⋊#95—611no—
577C2×C61—44no—
578C2×C61—82no—
579C2×C61#231811yescharacteristic
580C2×C61#232511yescharacteristic
581C2×C61#232611yescharacteristic
582C2×C61#234211yescharacteristic
583C2×C61#235211yescharacteristic
584C2×C61#236611yescharacteristic
585C2×C61#237711yescharacteristic
586C2×C61#267811yescharacteristic
587C2×C61#268111yescharacteristic
588C2×C61#269411yescharacteristic
589C2×C61#270511yescharacteristic
590C2×C61#271411yescharacteristic
591C2×C61#273011yescharacteristic
592C2×C61#275111yescharacteristic
593C2×C61#279611yescharacteristic
594C23×D4C2×D6111yescharacteristic
595C24×C4—611no—
596C22×C4⋊C4—611no—
597C22×C4⋊C4—611no—
598C22×C4⋊C4—611no—
599C22×C4⋊C4—611no—
600C22×C22⋊C4—611no—
601C22×C22⋊C4—611no—
602C22×C22⋊C4—611no—
603C22×C22⋊C4—611no—
604C22×C22⋊C4—611no—
605C22×C22⋊C4—611no—
606C22×C22⋊C4—611no—
607C22×C22⋊C4C2×D6111yescharacteristic
608C22×C22⋊C4C2×D6111yescharacteristic
609C22×C22⋊C4C2×D6111yescharacteristic
610C22×C22⋊C4C2×D6111yescharacteristic
611C22×C42—611no—
612C22×C42—611no—
613#390—618no—
614#388—1224no—
615#387—1224no—
616#386—1224no—
617#385—1224no—
618C2×#95—611no—
619C2×#95—611no—
620C2×#95—611no—
621C2×#95—611no—
622C2×#95—611no—
623C2×#95—611no—
624C2×#95—611no—
625C2×#95—611no—
626C2×#95—611no—
627C2×#95—611no—
628C2×#95—611no—
629C2×#95—611no—
630C2×#95—611no—
631C2×#95—611no—
632C2×#95C2×D6111yescharacteristic
633C2×#95C2×D6111yescharacteristic
634C61#1442911yescharacteristic, complemented, Sylow
635C25C22×D6111yescharacteristic
636C25C22×D6111yescharacteristic
637C22×D4—22no—
638C22×D4—22no—
639C22×D4—22no—
640C22×D4—22no—
641C22×D4—41no—
642C22×D4—41no—
643C22×D4C4×D6114yes—
644C23×C4—611no—
645C23×C4—611no—
646C23×C4—611no—
647C23×C4—611no—
648C23×C4—611no—
649C23×C4—611no—
650C23×C4—611no—
651C23×C4—611no—
652C23×C4—1222no—
653C23×C4—1222no—
654C23×C4—1222no—
655C23×C4—2441no—
656C23×C4—2441no—
657C23×C4—2441no—
658C23×C4—2441no—
659C23×C4C22×D6111yescharacteristic
660C23×C4C22×D6111yescharacteristic
661C23×C4C22×D6111yescharacteristic
662C23×C4C22×D6111yescharacteristic
663C23×C4C22×D6111yescharacteristic
664C2×C4⋊C4—614no—
665C2×C4⋊C4—614no—
666C2×C4⋊C4—1222no—
667C2×C4⋊C4—1222no—
668C2×C4⋊C4—1222no—
669C2×C4⋊C4—1222no—
670C2×C4⋊C4—1222no—
671C2×C4⋊C4—2441no—
672C2×C4⋊C4—2441no—
673C2×C4⋊C4—2441no—
674C2×C4⋊C4—2441no—
675C2×C4⋊C4—2441no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—41no—
681C2×C22⋊C4—41no—
682C2×C22⋊C4—41no—
683C2×C22⋊C4—41no—
684C2×C22⋊C4—41no—
685C2×C22⋊C4—41no—
686C2×C22⋊C4—41no—
687C2×C22⋊C4—41no—
688C2×C22⋊C4—614no—
689C2×C22⋊C4—614no—
690C2×C22⋊C4—614no—
691C2×C22⋊C4—614no—
692C2×C22⋊C4—1222no—
693C2×C22⋊C4—1222no—
694C2×C22⋊C4—1222no—
695C2×C22⋊C4—1222no—
696C2×C22⋊C4—1222no—
697C2×C22⋊C4—1222no—
698C2×C22⋊C4—1222no—
699C2×C22⋊C4—1222no—
700C2×C22⋊C4—1222no—
701C2×C22⋊C4—2441no—
702C2×C22⋊C4—2441no—
703C2×C22⋊C4—2441no—
704C2×C22⋊C4—2441no—
705C2×C22⋊C4—2441no—
706C2×C22⋊C4—2441no—
707C2×C22⋊C4—2441no—
708C2×C22⋊C4—2441no—
709C2×C42—614no—
710C2×C42—1222no—
711C2×C42—1222no—
712C2×C42—2441no—
713C2×C42—2441no—
714C2×C42—2441no—
715#95—22no—
716#95—22no—
717#95—614no—
718#95—1222no—
719#95—1222no—
720#95—1222no—
721#95—1222no—
722#95—1222no—
723#95—1222no—
724#95—1222no—
725#95—2441no—
726#95—2441no—
727#95—2441no—
728#95—2441no—
729#95—2441no—
730#95—2441no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24C2×C4×D6112yes—
758C24C2×C4×D6112yes—
759C24#1175822412yes—
760C24#1175822412yes—
761C24C23×D6111yescharacteristic
762C2×D4—28no—
763C2×D4—28no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—44no—
768C2×D4—44no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—612no—
801C22×C4—612no—
802C22×C4—612no—
803C22×C4—612no—
804C22×C4—612no—
805C22×C4—612no—
806C22×C4—612no—
807C22×C4—612no—
808C22×C4—612no—
809C22×C4—1221no—
810C22×C4—1221no—
811C22×C4—1221no—
812C22×C4—1221no—
813C22×C4—1221no—
814C22×C4—1221no—
815C22×C4—1221no—
816C22×C4—1221no—
817C22×C4—1221no—
818C22×C4—1221no—
819C22×C4—1221no—
820C22×C4—1221no—
821C22×C4—1221no—
822C22×C4—1221no—
823C22×C4—1221no—
824C22×C4—1221no—
825C22×C4—1221no—
826C22×C4—1221no—
827C22×C4—1221no—
828C22×C4—1221no—
829C22×C4—1221no—
830C22×C4—1221no—
831C22×C4—1221no—
832C22×C4—1221no—
833C22×C4—1221no—
834C22×C4—1221no—
835C22×C4—1221no—
836C22×C4—1221no—
837C22×C4—1221no—
838C22×C4—1221no—
839C22×C4—1221no—
840C22×C4—1221no—
841C22×C4—1221no—
842C22×C4—1221no—
843C22×C4—1221no—
844C22×C4—1221no—
845C22×C4—1221no—
846C22×C4—1221no—
847C22×C4—1221no—
848C22×C4—1221no—
849C22×C4—1221no—
850C22×C4—1221no—
851C22×C4—1221no—
852C22×C4—1221no—
853C22×C4—1221no—
854C22×C4—1221no—
855C22×C4—1221no—
856C22×C4—2444no—
857C22×C4—2444no—
858C22×C4—2444no—
859C22×C4—2444no—
860C22×C4—2444no—
861C22×C4—2444no—
862C22×C4—2444no—
863C22×C4C2×C4×D6112yes—
864C22×C4D4×D6112yes—
865C22×C4D4×D6112yes—
866C22×C4#1175822412yes—
867C4⋊C4—1228no—
868C4⋊C4—2444no—
869C4⋊C4—2444no—
870C4⋊C4—2444no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—1228no—
876C22⋊C4—1228no—
877C22⋊C4—2444no—
878C22⋊C4—2444no—
879C22⋊C4—2444no—
880C22⋊C4—2444no—
881C22⋊C4—2444no—
882C42—2444no—
883C42—2444no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23#1451973314yes—
954C23C22×C4×D6111yescharacteristic
955C23C2×D4×D6111yescharacteristic
956C23C2×D4×D6111yescharacteristic
957C23#41×D6111yescharacteristic
958C23C2×#1175822411yescharacteristic
959C23C2×#1175822411yescharacteristic
960C23C2×#1175822411yescharacteristic
961C23#1451982211yescharacteristic
962C23#1451982211yescharacteristic
963C23#1451982211yescharacteristic
964C23#1451982211yescharacteristic
965C23#1451982211yescharacteristic
966C23#1451982311yescharacteristic
967C23#1451982411yescharacteristic
968C23#1451982411yescharacteristic
969D4—416no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—614no—
1005C2×C4—1222no—
1006C2×C4—1222no—
1007C2×C4—1222no—
1008C2×C4—1222no—
1009C2×C4—1222no—
1010C2×C4—1222no—
1011C2×C4—1222no—
1012C2×C4—1222no—
1013C2×C4—1222no—
1014C2×C4—1222no—
1015C2×C4—1222no—
1016C2×C4—1222no—
1017C2×C4—1222no—
1018C2×C4—1222no—
1019C2×C4—1222no—
1020C2×C4—1222no—
1021C2×C4—1222no—
1022C2×C4—1222no—
1023C2×C4—1222no—
1024C2×C4—1222no—
1025C2×C4—1222no—
1026C2×C4—1222no—
1027C2×C4—1222no—
1028C2×C4—1222no—
1029C2×C4—2441no—
1030C2×C4—2441no—
1031C2×C4—2441no—
1032C2×C4—2441no—
1033C2×C4—2441no—
1034C2×C4—2441no—
1035C2×C4—2441no—
1036C2×C4—24416no—
1037C2×C4—2441no—
1038C2×C4—2441no—
1039C2×C4—2441no—
1040C2×C4—2441no—
1041C2×C4—2441no—
1042C2×C4—2441no—
1043C2×C4—2441no—
1044C2×C4—2441no—
1045C2×C4—2441no—
1046C2×C4—2441no—
1047C2×C4—2441no—
1048C2×C4—2441no—
1049C2×C4—2441no—
1050C2×C4—2441no—
1051C2×C4—2441no—
1052C2×C4—2441no—
1053C2×C4—2441no—
1054C2×C4—2441no—
1055C2×C4—2441no—
1056C2×C4—2441no—
1057C2×C4—2441no—
1058C2×C4—2441no—
1059C2×C4—2441no—
1060C2×C4—2441no—
1061C2×C4#1451973714yes—
1062C22—24no—
1063C22—24no—
1064C22—24no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22C2×#1451973311yescharacteristic
1093C22C4×D4×D6111yescharacteristic
1094C22C2×#1451973711yescharacteristic
1095C22#1684023411yescharacteristic
1096C22#1684023511yescharacteristic
1097C22#1684024111yescharacteristic
1098C22#1684024111yescharacteristic
1099C22#1684032211yescharacteristic
1100C22#1684032511yescharacteristic
1101C22#1684033211yescharacteristic
1102C22#1684034111yescharacteristic
1103C22#1684034411yescharacteristic
1104C22#1684034711yescharacteristic
1105C22#1684034911yescharacteristic
1106C22#1684035511yescharacteristic
1107C22#1684035611yescharacteristic
1108C22#1684035711yescharacteristic
1109C22#1684037911yescharacteristic
1110C22#1684037911yescharacteristic
1111C22#1684039611yescharacteristic
1112C22#1684039911yescharacteristic
1113C22#1684039911yescharacteristic
1114C22#1684039911yescharacteristic
1115C22#1684041811yescharacteristic
1116C22#1684043011yescharacteristic
1117C22#1684043211yescharacteristic
1118C22#1684044311yescharacteristic
1119C22#1684044311yescharacteristic
1120C22#1684044911yescharacteristic
1121C22#1684045511yescharacteristic
1122C22#1684049411yescharacteristic
1123C22#1684050011yescharacteristic
1124C22#1684050111yescharacteristic
1125C22#1684050711yescharacteristic
1126C22#1684050911yescharacteristic
1127C4—24no—
1128C4—42no—
1129C4—81no—
1130C4—81no—
1131C4—81no—
1132C4—1224no—
1133C4—4881no—
1134C4—2442no—
1135C4—2442no—
1136C4—2442no—
1137C4—2442no—
1138C4—2442no—
1139C4—2442no—
1140C2—44no—
1141C2—82no—
1142C2#2144844511yescharacteristic
1143C2#2144852111yescharacteristic
1144C2#2144852911yescharacteristic
1145C2#2144867011yescharacteristic
1146C2#2144874611yescharacteristic
1147C2#2144888011yescharacteristic
1148C2#2144897111yescharacteristic
1149C2#2145213711yescharacteristic
1150C2#2145217011yescharacteristic
1151C2#2145233811yescharacteristic
1152C2#2145249911yescharacteristic
1153C2#2145260811yescharacteristic
1154C2#2145281811yescharacteristic
1155C2#2145307411yescharacteristic
1156C2#2145366311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1438C2
socle, cosocleC24×C61C24
prime radicalC23×D4×C61C22
hypercenter#1438D61
hypocenterC61#14429
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#16839656C2semidirect
3. C2×#16839647C2semidirect
5. C2×#16839634C2semidirect
6. #21444088C2semidirect
7. #21444066C2semidirect
8. #21444062C2semidirect
9. #21444062C2semidirect
10. #21444062C2semidirect
11. #21444056C2semidirect
12. #21444047C2semidirect
13. #21444044C2semidirect
14. #21444041C2semidirect
30. #16839665C4semidirect
73. C2×C4⋊Dic61C2×C4semidirect
82. C2×#11758196D4semidirect
102. C2×C22⋊Dic61C2×C4semidirect
103. C2×C22⋊Dic61C2×C4semidirect
109. C2×C4×Dic61C2×C4semidirect
634. C61#14429semidirect

Maximal subgroups

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

subgroupindex
C2×#168396652
C2×#168396562
C2×#168396472
C2×#168396422
C2×#168396342
#214440882
#214440662
#214440622
#214440562
#214440472
#214440442
#214440412
C61×#14382
#1442961