Finite Group Databasebeta

← #29602974

Subgroups — #29602974

Order 15616.

2070 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×#16839640C211yesmaximal, characteristic
2C2×#16839640C211yesmaximal, characteristic
3C2×#16839624C211yesmaximal, characteristic, complemented
4C2×C4×#11758198C211yesmaximal, characteristic, complemented
5C2×#16839609C211yesmaximal, characteristic, complemented
6#21444079C211yesmaximal, characteristic, complemented
7#21444065C211yesmaximal, characteristic, complemented
8#21444065C211yesmaximal, characteristic, complemented
9#21444059C211yesmaximal, characteristic
10#21444057C211yesmaximal, characteristic, complemented
11#21444055C211yesmaximal, characteristic, complemented
12#21444053C211yesmaximal, characteristic, complemented
13#21444043C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×#1434C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×#11758198C2211yescharacteristic
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32#16839640—24no—
33#16839640C418yescomplemented
34#16839624—24no—
35C4×#11758198—24no—
36#16839609—24no—
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C22×C42×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—22no—
78C22×C4×D61—22no—
79C22×C4×D61—22no—
80C22×C4×D61—41no—
81C22×C4×D61—41no—
82C22×C4×D61—41no—
83C22×C4×D61—41no—
84C22×C4×D61C2×C414yescomplemented
85C2×C4⋊Dic61—22no—
86C2×C4⋊Dic61—41no—
87C2×C4⋊Dic61—41no—
88C2×#11758198—22no—
89C2×#11758198—22no—
90C2×#11758198—22no—
91C2×#11758198—22no—
92C2×#11758198—22no—
93C2×#11758198—22no—
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×#11758198C2×C414yes—
115C2×#11758198C2×C414yes—
116C2×#11758198C2×C414yescomplemented
117C2×#11758198D414yes—
118C2×C4×Dic61—22no—
119C2×C4×Dic61—22no—
120C2×C4×Dic61—22no—
121C2×C4×Dic61—22no—
122C2×C4×Dic61—41no—
123C2×C4×Dic61—41no—
124#14519684—22no—
125#14519684—22no—
126#14519684—22no—
127#14519684—22no—
128#14519684—22no—
129#14519684—22no—
130#14519684—22no—
131#14519684—22no—
132#14519684—22no—
133#14519684—41no—
134#14519684—41no—
135#14519684C2×C414yescomplemented
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C2×C42×C61—22no—
144C2×C42×C61—22no—
145C2×C42×C61—41no—
146#95×C61—22no—
147#95×C61—41no—
148#95×C61—41no—
149#95×C61—41no—
150#95×C61C2×C414yescomplemented
151#95×C61D414yescomplemented
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×D61#4112yes—
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×C61C22×C412yes—
224C22×C4×C61C22×C412yes—
225C22×C4×C61C22×C412yes—
226C22×C4×C61C2×D412yes—
227C22×C4×C61C2×D412yes—
228C22×C4×C61C2×D412yes—
229C22×C4×C61C2×D412yes—
230C22×C4×C61#4112yes—
231C22×C4×C61#4112yes—
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×Dic61#4112yes—
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—28no—
282C2×C4×D61—28no—
283C2×C4×D61—28no—
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—
295C42×C61—44no—
296#11758198—28no—
297#11758198—28no—
298#11758198—28no—
299#11758198—28no—
300#11758198—44no—
301#11758198—44no—
302#11758198—44no—
303#11758198—44no—
304#11758198—44no—
305#11758198—44no—
306C4⋊Dic61—44no—
307C4×Dic61—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×C61C2×#4111yescharacteristic
317C23×C61C2×#4111yescharacteristic
318C23×C61C2×#4111yescharacteristic
319C23×C61C2×#4111yescharacteristic
320C23×C61H(5,𝔽2)11yescharacteristic
321C23×C61H(5,𝔽2)11yescharacteristic
322C23×C61H(5,𝔽2)11yescharacteristic
323C23×C61H(5,𝔽2)11yescharacteristic
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×D61#11714yes—
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—22no—
410C2×C4×C61—22no—
411C2×C4×C61—22no—
412C2×C4×C61—22no—
413C2×C4×C61—22no—
414C2×C4×C61—22no—
415C2×C4×C61—22no—
416C2×C4×C61—22no—
417C2×C4×C61—22no—
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×C61C4×D414yes—
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—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×Dic61—41no—
483C2×Dic61—41no—
484C2×Dic61#12314yes—
485D244—416no—
486C4×D61—416no—
487C4×D61—416no—
488#13984—611nomaximal, Sylow
489C22×C61C2×#11711yescharacteristic
490C22×C61C2×C4×D411yescharacteristic
491C22×C61C2×C4×D411yescharacteristic
492C22×C61C4×#4111yescharacteristic
493C22×C61C4×#4111yescharacteristic
494C22×C61#51811yescharacteristic
495C22×C61#51811yescharacteristic
496C22×C61C2×#12311yescharacteristic
497C22×C61#52511yescharacteristic
498C22×C61#52511yescharacteristic
499C22×C61#52511yescharacteristic
500C22×C61#52911yescharacteristic
501C22×C61#52911yescharacteristic
502C22×C61#52911yescharacteristic
503C22×C61#52911yescharacteristic
504C22×C61#53811yescharacteristic
505C22×C61#53811yescharacteristic
506C22×C61#54011yescharacteristic
507C22×C61#54011yescharacteristic
508C22×C61D4211yescharacteristic
509C22×C61#54611yescharacteristic
510C22×C61#54611yescharacteristic
511C22×C61#54611yescharacteristic
512C22×C61#54611yescharacteristic
513C22×C61#54611yescharacteristic
514C22×C61#55011yescharacteristic
515C22×C61#55111yescharacteristic
516C22×C61#55111yescharacteristic
517C22×C61#55111yescharacteristic
518C22×C61#55111yescharacteristic
519C22×C61#55111yescharacteristic
520C22×C61#55311yescharacteristic
521C22×C61#55311yescharacteristic
522C22×C61#55311yescharacteristic
523C22×C61#55511yescharacteristic
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—24no—
555C4×C61—42no—
556C4×C61—42no—
557C4×C61—42no—
558C4×C61—42no—
559C4×C61—42no—
560C4×C61—42no—
561Dic61—24no—
562Dic61—42no—
563Dic61—42no—
564Dic61—42no—
565Dic61—81no—
566Dic61—81no—
567C2×#386—611no—
568C2×#386—611no—
569C2×#381—611no—
570C2×C4×C22⋊C4—611no—
571C2×C4×C22⋊C4—611no—
572#1443—611no—
573#1439—611no—
574#1439—611no—
575#1438—611no—
576#1437—611no—
577#1437—611no—
578#1436—611no—
579#1434—611no—
580#1434D6111yescharacteristic, complemented
581C22⋊#95—611no—
582C2×C61#229011yescharacteristic
583C2×C61C4×#12311yescharacteristic
584C2×C61#233311yescharacteristic
585C2×C61#234211yescharacteristic
586C2×C61#235311yescharacteristic
587C2×C61#235811yescharacteristic
588C2×C61#236311yescharacteristic
589C2×C61#241811yescharacteristic
590C2×C61#242011yescharacteristic
591C2×C61#245611yescharacteristic
592C2×C61#245711yescharacteristic
593C2×C61#245711yescharacteristic
594C2×C61#247111yescharacteristic
595C2×C61#257211yescharacteristic
596C2×C61#257611yescharacteristic
597D61—44no—
598D61—44no—
599C23×D4—611no—
600C24×C4—611no—
601C24×C4—611no—
602C22×C4⋊C4—611no—
603C22×C22⋊C4—611no—
604C22×C22⋊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×C42—611no—
614C22×C42—611no—
615C22×C42C2×D6111yescharacteristic
616#386—618no—
617#386—1224no—
618#381—1224no—
619C4×C22⋊C4—1224no—
620C4×C22⋊C4—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×#95—611no—
633C2×#95C2×D6111yescharacteristic
634C2×#95C2×D6111yescharacteristic
635C2×#95C2×D6111yescharacteristic
636C2×#95C2×D6111yescharacteristic
637C2×#95C2×D6111yescharacteristic
638C2×#95C2×D6111yescharacteristic
639C61#1398411yescharacteristic, 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—614no—
654C23×C4—611no—
655C23×C4—611no—
656C23×C4—1222no—
657C23×C4—1222no—
658C23×C4—1222no—
659C23×C4—1222no—
660C23×C4—1222no—
661C23×C4—1222no—
662C23×C4—1222no—
663C23×C4—1222no—
664C23×C4—1222no—
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—1222no—
677C2×C4⋊C4—2441no—
678C2×C4⋊C4—2441no—
679C2×C22⋊C4—614no—
680C2×C22⋊C4—614no—
681C2×C22⋊C4—614no—
682C2×C22⋊C4—614no—
683C2×C22⋊C4—1222no—
684C2×C22⋊C4—1222no—
685C2×C22⋊C4—1222no—
686C2×C22⋊C4—1222no—
687C2×C22⋊C4—1222no—
688C2×C22⋊C4—1222no—
689C2×C22⋊C4—1222no—
690C2×C22⋊C4—1222no—
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—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—22no—
710C2×C42—22no—
711C2×C42—41no—
712C2×C42—1222no—
713C2×C42—1222no—
714C2×C42—1222no—
715C2×C42—1222no—
716C2×C42—2441no—
717C2×C42—2441no—
718#95—22no—
719#95—41no—
720#95—41no—
721#95—41no—
722#95—614no—
723#95—1222no—
724#95—1222no—
725#95—1222no—
726#95—1222no—
727#95—1222no—
728#95—1222no—
729#95—1222no—
730#95—1222no—
731#95—1222no—
732#95—2441no—
733#95—2441no—
734#95C4×D6114yescomplemented
735#95D24414yescomplemented
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—612no—
815C22×C4—612no—
816C22×C4—612no—
817C22×C4—612no—
818C22×C4—612no—
819C22×C4—612no—
820C22×C4—1228no—
821C22×C4—1228no—
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—1228no—
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—2444no—
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×C4C2×C4×D6112yes—
871C22×C4C2×C4×D6112yes—
872C22×C4C2×C4×D6112yes—
873C22×C4C2×D24412yes—
874C22×C4C2×D24412yes—
875C22×C4C2×D24412yes—
876C22×C4#1175822212yes—
877C22×C4D4×D6112yes—
878C22×C4#1175822612yes—
879C4⋊C4—2444no—
880C22⋊C4—1228no—
881C22⋊C4—1228no—
882C22⋊C4—1228no—
883C22⋊C4—1228no—
884C22⋊C4—2444no—
885C22⋊C4—2444no—
886C22⋊C4—2444no—
887C22⋊C4—2444no—
888C22⋊C4—2444no—
889C22⋊C4—2444no—
890C42—44no—
891C42—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
965C23C22×D24411yescharacteristic
966C23#41×D6111yescharacteristic
967C23#41×D6111yescharacteristic
968C23#41×D6111yescharacteristic
969C23#41×D6111yescharacteristic
970C23#41×D6111yescharacteristic
971C23#41×D6111yescharacteristic
972C23C2×#1175822211yescharacteristic
973C23C2×#1175822611yescharacteristic
974C23#1451982211yescharacteristic
975C23#1451982211yescharacteristic
976C23#1451982311yescharacteristic
977C23#1451982311yescharacteristic
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—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
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—614no—
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—24416no—
1044C2×C4—24416no—
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—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×C4C4×D24414yes—
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—
1102C22#117×D6111yescharacteristic
1103C22C4×D4×D6111yescharacteristic
1104C22C2×C4×D24411yescharacteristic
1105C22#1684023011yescharacteristic
1106C22C4×#1175822611yescharacteristic
1107C22#1684023411yescharacteristic
1108C22#1684023411yescharacteristic
1109C22#123×D6111yescharacteristic
1110C22#1684027411yescharacteristic
1111C22#1684027411yescharacteristic
1112C22#1684027511yescharacteristic
1113C22#1684029011yescharacteristic
1114C22#1684029011yescharacteristic
1115C22#1684029511yescharacteristic
1116C22#1684029711yescharacteristic
1117C22#1684034611yescharacteristic
1118C22#1684035111yescharacteristic
1119C22#1684036211yescharacteristic
1120C22#1684036411yescharacteristic
1121C22D4×D24411yescharacteristic
1122C22#1684040211yescharacteristic
1123C22#1684040411yescharacteristic
1124C22#1684040711yescharacteristic
1125C22#1684040711yescharacteristic
1126C22#1684040911yescharacteristic
1127C22#1684043411yescharacteristic
1128C22#1684043611yescharacteristic
1129C22#1684043711yescharacteristic
1130C22#1684043711yescharacteristic
1131C22#1684043911yescharacteristic
1132C22#1684044211yescharacteristic
1133C22#1684045711yescharacteristic
1134C22#1684046011yescharacteristic
1135C22#1684046511yescharacteristic
1136C22#1684047511yescharacteristic
1137C4—24no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4—42no—
1144C4—1224no—
1145C4—4881no—
1146C4—4881no—
1147C4—2442no—
1148C4—2442no—
1149C4—2442no—
1150C2—2444no—
1151C2—2444no—
1152C2#2144826311yescharacteristic
1153C2#2144834011yescharacteristic
1154C2#2144858211yescharacteristic
1155C2#2144866311yescharacteristic
1156C2#2144875811yescharacteristic
1157C2#2144880111yescharacteristic
1158C2#2144885911yescharacteristic
1159C2#2144928611yescharacteristic
1160C2#2144931011yescharacteristic
1161C2#2144970911yescharacteristic
1162C2#2144972411yescharacteristic
1163C2#2144973311yescharacteristic
1164C2#2144992811yescharacteristic
1165C2#2145106711yescharacteristic
1166C2#2145112111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1434C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1434D61
hypocenterC61#13984
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. C2×#16839624C2semidirect
4. C2×C4×#11758198C2semidirect
5. C2×#16839609C2semidirect
6. #21444079C2semidirect
7. #21444065C2semidirect
8. #21444065C2semidirect
10. #21444057C2semidirect
11. #21444055C2semidirect
12. #21444053C2semidirect
13. #21444043C2semidirect
14. #21444040C2semidirect
15. C61×#1434C2semidirect
33. #16839640C4semidirect
84. C22×C4×D61C2×C4semidirect
116. C2×#11758198C2×C4semidirect
135. #14519684C2×C4semidirect
150. #95×C61C2×C4semidirect
151. #95×C61D4semidirect
580. #1434D61semidirect
639. C61#13984semidirect
734. #95C4×D61semidirect
735. #95D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168396402
C2×#168396242
C2×C4×#117581982
C2×#168396092
#214440792
#214440652
#214440592
#214440572
#214440552
#214440532
#214440432
#214440402
C61×#14342
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