Finite Group Databasebeta

← #29609324

Subgroups — #29609324

Order 15616.

1966 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839680C211yesmaximal, characteristic
2C2×#16839651C211yesmaximal, characteristic, complemented
3C2×#16839640C211yesmaximal, characteristic
4C2×#16839640C211yesmaximal, characteristic
5C2×#16839636C211yesmaximal, characteristic, complemented
6#21444085C211yesmaximal, characteristic, complemented
7#21444070C211yesmaximal, characteristic, complemented
8#21444067C211yesmaximal, characteristic, complemented
9#21444065C211yesmaximal, characteristic, complemented
10#21444055C211yesmaximal, characteristic, complemented
11#21444053C211yesmaximal, characteristic, complemented
12#21444040C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×#1443C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×#11758196C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33#16839680C418yescomplemented
34#16839651—24no—
35#16839640—24no—
36#16839640—24no—
37#16839636—24no—
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#95×C61C2211yescharacteristic
50C2×#95×C61C2211yescharacteristic
51C2×#95×C61C2211yescharacteristic
52C2×#95×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C24×D61C2311yescharacteristic
57C24×D61C2311yescharacteristic
58C22×D244—22no—
59C22×D244—22no—
60C22×D244—22no—
61C22×D244—22no—
62C22×D244—41no—
63C22×D244—41no—
64C22×D244C2×C414yes—
65C23×Dic61C2311yescharacteristic
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C22×C4×D61—22no—
72C22×C4×D61—22no—
73C22×C4×D61—22no—
74C22×C4×D61—22no—
75C22×C4×D61—22no—
76C22×C4×D61—22no—
77C22×C4×D61—41no—
78C22×C4×D61—41no—
79C22×C4×D61—41no—
80C22×C4×D61—41no—
81C22×C4×D61—41no—
82C22×C4×D61—41no—
83C22×C4×D61—41no—
84C22×C4×D61—41no—
85C2×C4⋊Dic61—22no—
86C2×C4⋊Dic61—22no—
87C2×C4⋊Dic61—41no—
88C2×#11758196—22no—
89C2×#11758196—22no—
90C2×#11758196—41no—
91C2×#11758196—41no—
92C2×#11758196—41no—
93C2×#11758196C2×C414yescomplemented
94C2×#11758198—22no—
95C2×#11758198—22no—
96C2×#11758198—22no—
97C2×#11758198—22no—
98C2×#11758198—22no—
99C2×#11758198—22no—
100C2×#11758198—22no—
101C2×#11758198—22no—
102C2×#11758198—22no—
103C2×#11758198—22no—
104C2×#11758198—22no—
105C2×#11758198—22no—
106C2×#11758198—41no—
107C2×#11758198—41no—
108C2×#11758198—41no—
109C2×#11758198—41no—
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×#11758198C2×C414yescomplemented
119C2×#11758198C2×C414yescomplemented
120C2×#11758198C2×C414yescomplemented
121C2×#11758198C2×C414yescomplemented
122C2×#11758198D414yes—
123C2×#11758198D414yes—
124C2×C4×Dic61—22no—
125C2×C4×Dic61—41no—
126C2×C4×Dic61—41no—
127#14519684—22no—
128#14519684—22no—
129#14519684—22no—
130#14519684—22no—
131#14519684—22no—
132#14519684—41no—
133#14519684—41no—
134#14519684—41no—
135#14519684—41no—
136#14519684—41no—
137#14519684—41no—
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145#95×C61—22no—
146#95×C61—22no—
147#95×C61—22no—
148#95×C61—22no—
149#95×C61—41no—
150#95×C61—41no—
151#95×C61C2×C414yescomplemented
152C24×C61C2411yescharacteristic
153C23×D61—21no—
154C23×D61—21no—
155C23×D61—21no—
156C23×D61—21no—
157C23×D61—21no—
158C23×D61—21no—
159C23×D61—21no—
160C23×D61—21no—
161C23×D61—21no—
162C23×D61—21no—
163C23×D61—21no—
164C23×D61—21no—
165C23×D61—21no—
166C23×D61—21no—
167C23×D61—21no—
168C23×D61—21no—
169C23×D61—21no—
170C23×D61—21no—
171C23×D61—21no—
172C23×D61—21no—
173C23×D61—21no—
174C23×D61—21no—
175C23×D61—21no—
176C23×D61—21no—
177C23×D61C22×C412yes—
178C23×D61C22×C412yes—
179C23×D61C2×D412yes—
180C23×D61C2×D412yes—
181C23×D61#4112yes—
182C23×D61#4112yes—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
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×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61C22×C412yes—
228C22×C4×C61C22×C412yes—
229C22×C4×C61C22×C412yes—
230C22×C4×C61C2×D412yes—
231C22×C4×C61C2×D412yes—
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×Dic61C22×C412yes—
269C22×Dic61C22×C412yes—
270C22×Dic61C2×D412yes—
271C22×Dic61C2×D412yes—
272C22×Dic61#4112yes—
273C22×Dic61#4112yes—
274C2×D244—28no—
275C2×D244—28no—
276C2×D244—44no—
277C2×D244—44no—
278C2×D244—44no—
279C2×D244—44no—
280C2×D244—44no—
281C2×C4×D61—44no—
282C2×C4×D61—44no—
283C2×C4×D61—44no—
284C2×C4×D61—44no—
285C2×C4×D61—44no—
286C2×C4×D61—44no—
287C2×C4×D61—44no—
288C2×C4×D61—44no—
289C2×C4×D61—44no—
290C2×C4×D61—44no—
291C2×C4×D61—44no—
292C2×C4×D61—44no—
293C2×C4×D61—44no—
294C2×C4×D61—44no—
295#11758198—28no—
296#11758198—28no—
297#11758198—44no—
298#11758198—44no—
299#11758198—44no—
300#11758198—44no—
301#11758198—44no—
302#11758198—44no—
303#11758198—44no—
304#11758198—44no—
305C4⋊Dic61—44no—
306#11758196—44no—
307#11758196—44no—
308C4×Dic61—44no—
309C23×C61C23×C411yescharacteristic
310C23×C61C22×D411yescharacteristic
311C23×C61C22×D411yescharacteristic
312C23×C61C2×#4111yescharacteristic
313C23×C61C2×#4111yescharacteristic
314C23×C61C2×#4111yescharacteristic
315C23×C61C2×#4111yescharacteristic
316C23×C61H(5,𝔽2)11yescharacteristic
317C23×C61H(5,𝔽2)11yescharacteristic
318C23×C61H(5,𝔽2)11yescharacteristic
319C23×C61H(5,𝔽2)11yescharacteristic
320C23×C61H(5,𝔽2)11yescharacteristic
321C23×C61H(5,𝔽2)11yescharacteristic
322C23×C612−1+411yescharacteristic
323C23×C612−1+411yescharacteristic
324C22×D61—22no—
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—22no—
328C22×D61—22no—
329C22×D61—22no—
330C22×D61—22no—
331C22×D61—22no—
332C22×D61—22no—
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—22no—
343C22×D61—22no—
344C22×D61—22no—
345C22×D61—22no—
346C22×D61—22no—
347C22×D61—22no—
348C22×D61—22no—
349C22×D61—22no—
350C22×D61—22no—
351C22×D61—22no—
352C22×D61—22no—
353C22×D61—22no—
354C22×D61—22no—
355C22×D61—22no—
356C22×D61—22no—
357C22×D61—22no—
358C22×D61—22no—
359C22×D61—22no—
360C22×D61—41no—
361C22×D61—41no—
362C22×D61—41no—
363C22×D61—41no—
364C22×D61—41no—
365C22×D61—41no—
366C22×D61—41no—
367C22×D61—41no—
368C22×D61—41no—
369C22×D61—41no—
370C22×D61—41no—
371C22×D61—41no—
372C22×D61—41no—
373C22×D61—41no—
374C22×D61—41no—
375C22×D61—41no—
376C22×D61—41no—
377C22×D61—41no—
378C22×D61—41no—
379C22×D61—41no—
380C22×D61—41no—
381C22×D61—41no—
382C22×D61—41no—
383C22×D61—41no—
384C22×D61—41no—
385C22×D61—41no—
386C22×D61—41no—
387C22×D61—41no—
388C22×D61—41no—
389C22×D61—41no—
390C22×D61—41no—
391C22×D61—41no—
392C22×D61C4×D414yes—
393C22×D61C4×D414yes—
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—22no—
401C2×C4×C61—22no—
402C2×C4×C61—22no—
403C2×C4×C61—22no—
404C2×C4×C61—22no—
405C2×C4×C61—22no—
406C2×C4×C61—22no—
407C2×C4×C61—22no—
408C2×C4×C61—22no—
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×C61—41no—
426C2×C4×C61—41no—
427C2×C4×C61—41no—
428C2×C4×C61—41no—
429C2×C4×C61—41no—
430C2×C4×C61—41no—
431C2×C4×C61—41no—
432C2×C4×C61—41no—
433C2×C4×C61—41no—
434C2×C4×C61—41no—
435C2×C4×C61—41no—
436C2×C4×C61—41no—
437C2×C4×C61—41no—
438C2×C4×C61—41no—
439C2×C4×C61—41no—
440C2×C4×C61—41no—
441C2×C4×C61—41no—
442C2×C4×C61—41no—
443C2×Dic61—22no—
444C2×Dic61—22no—
445C2×Dic61—22no—
446C2×Dic61—22no—
447C2×Dic61—22no—
448C2×Dic61—22no—
449C2×Dic61—22no—
450C2×Dic61—22no—
451C2×Dic61—22no—
452C2×Dic61—22no—
453C2×Dic61—22no—
454C2×Dic61—22no—
455C2×Dic61—22no—
456C2×Dic61—22no—
457C2×Dic61—22no—
458C2×Dic61—22no—
459C2×Dic61—22no—
460C2×Dic61—22no—
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×Dic61—41no—
483C2×Dic61—41no—
484C2×Dic61—41no—
485D244—416no—
486C4×D61—416no—
487C4×D61—416no—
488#14517—611nomaximal, Sylow
489C22×C61C2×C4×D411yescharacteristic
490C22×C61C2×C4×D411yescharacteristic
491C22×C61C4×#4111yescharacteristic
492C22×C61#51811yescharacteristic
493C22×C61#51811yescharacteristic
494C22×C61#52011yescharacteristic
495C22×C61#52011yescharacteristic
496C22×C61#53411yescharacteristic
497C22×C61#53411yescharacteristic
498C22×C61#53611yescharacteristic
499C22×C61#53711yescharacteristic
500C22×C61#53811yescharacteristic
501C22×C61#53811yescharacteristic
502C22×C61#53811yescharacteristic
503C22×C61#53911yescharacteristic
504C22×C61#53911yescharacteristic
505C22×C61#53911yescharacteristic
506C22×C61#54211yescharacteristic
507C22×C61#54211yescharacteristic
508C22×C61D4211yescharacteristic
509C22×C61#54611yescharacteristic
510C22×C61#54611yescharacteristic
511C22×C61#54611yescharacteristic
512C22×C61#54611yescharacteristic
513C22×C61#54611yescharacteristic
514C22×C61#54711yescharacteristic
515C22×C61#55111yescharacteristic
516C22×C61#55111yescharacteristic
517C22×C61#55211yescharacteristic
518C22×C61#55311yescharacteristic
519C22×C61#55311yescharacteristic
520C22×C61#56011yescharacteristic
521C22×C61#56011yescharacteristic
522C22×C61#56211yescharacteristic
523C22×C61#56211yescharacteristic
524C2×D61—24no—
525C2×D61—24no—
526C2×D61—24no—
527C2×D61—24no—
528C2×D61—24no—
529C2×D61—24no—
530C2×D61—42no—
531C2×D61—42no—
532C2×D61—42no—
533C2×D61—42no—
534C2×D61—42no—
535C2×D61—42no—
536C2×D61—42no—
537C2×D61—42no—
538C2×D61—42no—
539C2×D61—42no—
540C2×D61—42no—
541C2×D61—42no—
542C2×D61—42no—
543C2×D61—42no—
544C2×D61—42no—
545C2×D61—42no—
546C2×D61—42no—
547C2×D61—42no—
548C2×D61—42no—
549C2×D61—42no—
550C2×D61—42no—
551C2×D61—42no—
552C2×D61—42no—
553C2×D61—42no—
554C4×C61—42no—
555C4×C61—42no—
556C4×C61—42no—
557C4×C61—42no—
558C4×C61—42no—
559C4×C61—81no—
560C4×C61—81no—
561Dic61—42no—
562Dic61—42no—
563Dic61—42no—
564Dic61—42no—
565Dic61—42no—
566Dic61—42no—
567C2×#394—611no—
568C2×#388—611no—
569C2×#386—611no—
570C2×#386—611no—
571C2×#385—611no—
572#1445—611no—
573#1443D6111yescharacteristic, complemented
574#1441—611no—
575#1440—611no—
576#1439—611no—
577#1437—611no—
578#1436—611no—
579C22⋊#95—611no—
580C22⋊#95—611no—
581C22⋊#95—611no—
582C2×C61#232211yescharacteristic
583C2×C61#232511yescharacteristic
584C2×C61#233711yescharacteristic
585C2×C61#235811yescharacteristic
586C2×C61#235911yescharacteristic
587C2×C61#236411yescharacteristic
588C2×C61#237711yescharacteristic
589C2×C61#266811yescharacteristic
590C2×C61#267211yescharacteristic
591C2×C61#268711yescharacteristic
592C2×C61#269111yescharacteristic
593C2×C61#269711yescharacteristic
594C2×C61#270811yescharacteristic
595C2×C61#274611yescharacteristic
596C2×C61#275011yescharacteristic
597D61—44no—
598D61—44no—
599C23×D4—611no—
600C24×C4—611no—
601C24×C4—611no—
602C22×C4⋊C4—611no—
603C22×C4⋊C4—611no—
604C22×C4⋊C4—611no—
605C22×C22⋊C4—611no—
606C22×C22⋊C4—611no—
607C22×C22⋊C4—611no—
608C22×C22⋊C4—611no—
609C22×C22⋊C4—611no—
610C22×C22⋊C4—611no—
611C22×C22⋊C4—611no—
612C22×C22⋊C4—611no—
613C22×C22⋊C4—611no—
614C22×C22⋊C4—611no—
615C22×C42—611no—
616#394—618no—
617#388—1224no—
618#386—1224no—
619#386—1224no—
620#385—1224no—
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
634C2×#95C2×D6111yescharacteristic
635C2×#95C2×D6111yescharacteristic
636C2×#95C2×D6111yescharacteristic
637C2×#95C2×D6111yescharacteristic
638C2×#95C2×D6111yescharacteristic
639C61#1451711yescharacteristic, complemented, Sylow
640C25—611no—
641C25—611no—
642C22×D4—614no—
643C22×D4—1222no—
644C22×D4—1222no—
645C22×D4—1222no—
646C22×D4—1222no—
647C22×D4—2441no—
648C22×D4—2441no—
649C23×C4—611no—
650C23×C4—611no—
651C23×C4—611no—
652C23×C4—611no—
653C23×C4—611no—
654C23×C4—611no—
655C23×C4—1222no—
656C23×C4—1222no—
657C23×C4—1222no—
658C23×C4—1222no—
659C23×C4—1222no—
660C23×C4—1222no—
661C23×C4—2441no—
662C23×C4—2441no—
663C23×C4—2441no—
664C23×C4—2441no—
665C23×C4—2441no—
666C23×C4—2441no—
667C23×C4—2441no—
668C23×C4—2441no—
669C23×C4C22×D6111yescharacteristic
670C23×C4C22×D6111yescharacteristic
671C23×C4C22×D6111yescharacteristic
672C23×C4C22×D6111yescharacteristic
673C23×C4C22×D6111yescharacteristic
674C23×C4C22×D6111yescharacteristic
675C23×C4C22×D6111yescharacteristic
676C2×C4⋊C4—614no—
677C2×C4⋊C4—1222no—
678C2×C4⋊C4—1222no—
679C2×C4⋊C4—1222no—
680C2×C4⋊C4—1222no—
681C2×C4⋊C4—2441no—
682C2×C4⋊C4—2441no—
683C2×C4⋊C4—2441no—
684C2×C4⋊C4—2441no—
685C2×C22⋊C4—614no—
686C2×C22⋊C4—614no—
687C2×C22⋊C4—614no—
688C2×C22⋊C4—614no—
689C2×C22⋊C4—614no—
690C2×C22⋊C4—614no—
691C2×C22⋊C4—1222no—
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—1222no—
702C2×C22⋊C4—1222no—
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×C22⋊C4—2441no—
710C2×C22⋊C4—2441no—
711C2×C22⋊C4—2441no—
712C2×C22⋊C4—2441no—
713C2×C22⋊C4—2441no—
714C2×C22⋊C4—2441no—
715C2×C42—1222no—
716C2×C42—2441no—
717C2×C42—2441no—
718#95—22no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—41no—
723#95—41no—
724#95—1222no—
725#95—1222no—
726#95—1222no—
727#95—1222no—
728#95—1222no—
729#95—2441no—
730#95—2441no—
731#95—2441no—
732#95—2441no—
733#95—2441no—
734#95—2441no—
735#95C4×D6114yescomplemented
736C24—612no—
737C24—612no—
738C24—612no—
739C24—612no—
740C24—612no—
741C24—612no—
742C24—1221no—
743C24—1221no—
744C24—1221no—
745C24—1221no—
746C24—1221no—
747C24—1221no—
748C24—1221no—
749C24—1221no—
750C24—1221no—
751C24—1221no—
752C24—1221no—
753C24—1221no—
754C24—1221no—
755C24—1221no—
756C24—1221no—
757C24—1221no—
758C24—1221no—
759C24—1221no—
760C24—1221no—
761C24—1221no—
762C24—1221no—
763C24—1221no—
764C24—1221no—
765C24—1221no—
766C24C23×D6111yescharacteristic
767C2×D4—1228no—
768C2×D4—1228no—
769C2×D4—2444no—
770C2×D4—2444no—
771C2×D4—2444no—
772C2×D4—2444no—
773C2×D4—2444no—
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—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—612no—
819C22×C4—612no—
820C22×C4—612no—
821C22×C4—612no—
822C22×C4—612no—
823C22×C4—612no—
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—1221no—
857C22×C4—1221no—
858C22×C4—1221no—
859C22×C4—1221no—
860C22×C4—2444no—
861C22×C4—2444no—
862C22×C4—2444no—
863C22×C4—2444no—
864C22×C4—2444no—
865C22×C4—2444no—
866C22×C4—2444no—
867C22×C4—2444no—
868C22×C4—2444no—
869C22×C4—2444no—
870C22×C4—2444no—
871C22×C4—2444no—
872C22×C4—2444no—
873C22×C4—2444no—
874C22×C4C2×C4×D6112yes—
875C22×C4C2×C4×D6112yes—
876C22×C4C2×C4×D6112yes—
877C22×C4D4×D6112yes—
878C22×C4D4×D6112yes—
879C4⋊C4—2444no—
880C4⋊C4—2444no—
881C4⋊C4—2444no—
882C22⋊C4—1228no—
883C22⋊C4—1228no—
884C22⋊C4—2444no—
885C22⋊C4—2444no—
886C22⋊C4—2444no—
887C22⋊C4—2444no—
888C22⋊C4—2444no—
889C22⋊C4—2444no—
890C22⋊C4—2444no—
891C22⋊C4—2444no—
892C42—2444no—
893C23—614no—
894C23—614no—
895C23—1222no—
896C23—1222no—
897C23—1222no—
898C23—1222no—
899C23—1222no—
900C23—1222no—
901C23—1222no—
902C23—1222no—
903C23—1222no—
904C23—1222no—
905C23—1222no—
906C23—1222no—
907C23—1222no—
908C23—1222no—
909C23—1222no—
910C23—1222no—
911C23—1222no—
912C23—1222no—
913C23—1222no—
914C23—1222no—
915C23—1222no—
916C23—1222no—
917C23—1222no—
918C23—1222no—
919C23—1222no—
920C23—1222no—
921C23—1222no—
922C23—1222no—
923C23—1222no—
924C23—1222no—
925C23—1222no—
926C23—1222no—
927C23—1222no—
928C23—1222no—
929C23—1222no—
930C23—1222no—
931C23—2441no—
932C23—2441no—
933C23—2441no—
934C23—2441no—
935C23—2441no—
936C23—2441no—
937C23—2441no—
938C23—2441no—
939C23—2441no—
940C23—2441no—
941C23—2441no—
942C23—2441no—
943C23—2441no—
944C23—2441no—
945C23—2441no—
946C23—2441no—
947C23—2441no—
948C23—2441no—
949C23—2441no—
950C23—2441no—
951C23—2441no—
952C23—2441no—
953C23—2441no—
954C23—2441no—
955C23—2441no—
956C23—2441no—
957C23—2441no—
958C23—2441no—
959C23—2441no—
960C23—2441no—
961C23—2441no—
962C23—2441no—
963C23C22×C4×D6111yescharacteristic
964C23C2×D4×D6111yescharacteristic
965C23C2×D4×D6111yescharacteristic
966C23#41×D6111yescharacteristic
967C23#41×D6111yescharacteristic
968C23#41×D6111yescharacteristic
969C23#41×D6111yescharacteristic
970C23#1451982211yescharacteristic
971C23#1451982311yescharacteristic
972C23#1451982311yescharacteristic
973C23#1451982311yescharacteristic
974C23#1451982311yescharacteristic
975C23#1451982311yescharacteristic
976C23#1451982411yescharacteristic
977C23#1451982511yescharacteristic
978D4—24416no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
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—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—1222no—
1029C2×C4—1222no—
1030C2×C4—1222no—
1031C2×C4—1222no—
1032C2×C4—1222no—
1033C2×C4—1222no—
1034C2×C4—1222no—
1035C2×C4—1222no—
1036C2×C4—1222no—
1037C2×C4—1222no—
1038C2×C4—1222no—
1039C2×C4—1222no—
1040C2×C4—1222no—
1041C2×C4—1222no—
1042C2×C4—1222no—
1043C2×C4—1222no—
1044C2×C4—1222no—
1045C2×C4—1222no—
1046C2×C4—24416no—
1047C2×C4—24416no—
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—2441no—
1062C2×C4—2441no—
1063C2×C4—2441no—
1064C2×C4—2441no—
1065C2×C4—2441no—
1066C2×C4—2441no—
1067C2×C4—2441no—
1068C2×C4—2441no—
1069C2×C4—2441no—
1070C2×C4—2441no—
1071C2×C4—2441no—
1072C22—1224no—
1073C22—1224no—
1074C22—1224no—
1075C22—1224no—
1076C22—1224no—
1077C22—1224no—
1078C22—2442no—
1079C22—2442no—
1080C22—2442no—
1081C22—2442no—
1082C22—2442no—
1083C22—2442no—
1084C22—2442no—
1085C22—2442no—
1086C22—2442no—
1087C22—2442no—
1088C22—2442no—
1089C22—2442no—
1090C22—2442no—
1091C22—2442no—
1092C22—2442no—
1093C22—2442no—
1094C22—2442no—
1095C22—2442no—
1096C22—2442no—
1097C22—2442no—
1098C22—2442no—
1099C22—2442no—
1100C22—2442no—
1101C22—2442no—
1102C22C4×D4×D6111yescharacteristic
1103C22C4×D4×D6111yescharacteristic
1104C22#1684023011yescharacteristic
1105C22#1684023411yescharacteristic
1106C22#1684023611yescharacteristic
1107C22#1684024211yescharacteristic
1108C22#1684024411yescharacteristic
1109C22#1684032311yescharacteristic
1110C22#1684032311yescharacteristic
1111C22#1684033511yescharacteristic
1112C22#1684034111yescharacteristic
1113C22#1684034611yescharacteristic
1114C22#1684035111yescharacteristic
1115C22#1684035111yescharacteristic
1116C22#1684035311yescharacteristic
1117C22#1684035311yescharacteristic
1118C22#1684036011yescharacteristic
1119C22#1684037811yescharacteristic
1120C22#1684037811yescharacteristic
1121C22#1684039611yescharacteristic
1122C22#1684040111yescharacteristic
1123C22#1684040411yescharacteristic
1124C22#1684040411yescharacteristic
1125C22#1684040511yescharacteristic
1126C22#1684040511yescharacteristic
1127C22#1684041411yescharacteristic
1128C22#1684043711yescharacteristic
1129C22#1684043711yescharacteristic
1130C22#1684044411yescharacteristic
1131C22#1684045711yescharacteristic
1132C22#1684046311yescharacteristic
1133C22#1684050211yescharacteristic
1134C22#1684050311yescharacteristic
1135C22#1684050811yescharacteristic
1136C22#1684051011yescharacteristic
1137C4—42no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—81no—
1143C4—81no—
1144C4—2442no—
1145C4—2442no—
1146C4—2442no—
1147C4—2442no—
1148C4—2442no—
1149C4—2442no—
1150C2—2444no—
1151C2—2444no—
1152C2#2144849211yescharacteristic
1153C2#2144852311yescharacteristic
1154C2#2144862911yescharacteristic
1155C2#2144879711yescharacteristic
1156C2#2144880411yescharacteristic
1157C2#2144886311yescharacteristic
1158C2#2144897411yescharacteristic
1159C2#2145202911yescharacteristic
1160C2#2145207711yescharacteristic
1161C2#2145224511yescharacteristic
1162C2#2145230211yescharacteristic
1163C2#2145238411yescharacteristic
1164C2#2145254211yescharacteristic
1165C2#2145299611yescharacteristic
1166C2#2145306411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1443C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1443D61
hypocenterC61#14517
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
2. C2×#16839651C2semidirect
5. C2×#16839636C2semidirect
6. #21444085C2semidirect
7. #21444070C2semidirect
8. #21444067C2semidirect
9. #21444065C2semidirect
10. #21444055C2semidirect
11. #21444053C2semidirect
12. #21444040C2semidirect
13. #21444040C2semidirect
14. #21444040C2semidirect
15. C61×#1443C2semidirect
33. #16839680C4semidirect
93. C2×#11758196C2×C4semidirect
118. C2×#11758198C2×C4semidirect
119. C2×#11758198C2×C4semidirect
120. C2×#11758198C2×C4semidirect
121. C2×#11758198C2×C4semidirect
151. #95×C61C2×C4semidirect
573. #1443D61semidirect
639. C61#14517semidirect
735. #95C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396802
C2×#168396512
C2×#168396402
C2×#168396362
#214440852
#214440702
#214440672
#214440652
#214440552
#214440532
#214440402
C61×#14432
#1451761