Finite Group Databasebeta

← #29604172

Subgroups — #29604172

Order 15616.

1578 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839659C211yesmaximal, characteristic, complemented
2C2×#16839654C211yesmaximal, characteristic
3C2×#16839651C211yesmaximal, characteristic
4C2×#16839651C211yesmaximal, characteristic
5C2×#16839613C211yesmaximal, characteristic, complemented
6#21444070C211yesmaximal, characteristic, complemented
7#21444063C211yesmaximal, characteristic
8#21444063C211yesmaximal, characteristic
9#21444055C211yesmaximal, characteristic
10#21444055C211yesmaximal, characteristic
11#21444054C211yesmaximal, characteristic, complemented
12#21444053C211yesmaximal, characteristic, complemented
13#21444044C211yesmaximal, characteristic, complemented
14#95×Dic61C211yesmaximal, characteristic, complemented
15C61×#1443C211yesmaximal, characteristic, complemented
16C22×C4⋊Dic61C2211yescharacteristic
17C22×#11758196C2211yescharacteristic
18C22×#11758196C2211yescharacteristic
19C22×#11758196C2211yescharacteristic
20C22×#11758196C2211yescharacteristic
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×C4×Dic61C2211yescharacteristic
29C22×C4×Dic61C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33#16839659—24no—
34#16839654—24no—
35#16839651—24no—
36#16839651C418yescomplemented
37#16839613—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
57C23×Dic61C2311yescharacteristic
58C23×Dic61C2311yescharacteristic
59C23×Dic61C2311yescharacteristic
60C23×Dic61C2311yescharacteristic
61C23×Dic61C2311yescharacteristic
62C23×Dic61C2311yescharacteristic
63C23×Dic61C2311yescharacteristic
64C2×C4⋊Dic61—22no—
65C2×C4⋊Dic61—22no—
66C2×C4⋊Dic61—22no—
67C2×#11758196—22no—
68C2×#11758196—22no—
69C2×#11758196—22no—
70C2×#11758196—22no—
71C2×#11758196—22no—
72C2×#11758196—22no—
73C2×#11758196—22no—
74C2×#11758196—22no—
75C2×#11758196—22no—
76C2×#11758196—41no—
77C2×#11758196C2×C414yes—
78C2×#11758196D414yes—
79C2×#11758198—22no—
80C2×#11758198—22no—
81C2×#11758198—22no—
82C2×#11758198—22no—
83C2×#11758198—22no—
84C2×#11758198—22no—
85C2×#11758198—22no—
86C2×#11758198—22no—
87C2×#11758198—22no—
88C2×#11758198—22no—
89C2×#11758198—22no—
90C2×#11758198—22no—
91C2×#11758198—22no—
92C2×#11758198—22no—
93C2×#11758198—41no—
94C2×#11758198—41no—
95C2×#11758198—41no—
96C2×#11758198—41no—
97C2×#11758198C2×C414yes—
98C2×#11758198C2×C414yes—
99C2×#11758198C2×C414yes—
100C2×C4×Dic61—22no—
101C2×C4×Dic61—22no—
102C2×C4×Dic61—22no—
103C2×C4×Dic61—22no—
104C2×C4×Dic61—22no—
105C2×C4×Dic61—22no—
106C2×C4×Dic61—22no—
107C2×C4×Dic61—41no—
108C2×C4×Dic61—41no—
109C2×C4×Dic61—41no—
110C2×C4×Dic61—41no—
111C2×C4×Dic61—41no—
112C2×C4×Dic61—41no—
113C2×C4×Dic61C2×C414yes—
114C2×C4×Dic61D414yes—
115#14519684—22no—
116#14519684—22no—
117#14519684—22no—
118#14519684—22no—
119#14519684—22no—
120#14519684—22no—
121#14519684—22no—
122#14519684—22no—
123#14519684—22no—
124#14519684—41no—
125#14519684C2×C414yes—
126C23×C4×C61C2311yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133#95×C61—22no—
134#95×C61—22no—
135#95×C61—22no—
136#95×C61—22no—
137#95×C61—22no—
138#95×C61—22no—
139#95×C61C2×C414yes—
140C24×C61C2411yescharacteristic
141C23×D61—21no—
142C23×D61—21no—
143C23×D61—21no—
144C23×D61—21no—
145C23×D61—21no—
146C23×D61—21no—
147C23×D61—21no—
148C23×D61—21no—
149C23×D61—21no—
150C23×D61—21no—
151C23×D61—21no—
152C23×D61—21no—
153C23×D61—21no—
154C23×D61—21no—
155C23×D61C22×C412yes—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
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×C61C22×C412yes—
200C22×C4×C61C22×C412yes—
201C22×C4×C61C22×C412yes—
202C22×C4×C61C2×D412yes—
203C22×C4×C61C2×D412yes—
204C22×C4×C61#4112yes—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
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×Dic61C22×C412yes—
241C22×Dic61C22×C412yes—
242C22×Dic61C22×C412yes—
243C22×Dic61C2×D412yes—
244C22×Dic61C2×D412yes—
245C22×Dic61C2×D412yes—
246C22×Dic61C2×D412yes—
247C22×Dic61#4112yes—
248C22×Dic61#4112yes—
249C22×Dic61#4112yes—
250C22×Dic61#4112yes—
251C22×Dic61#4112yes—
252C22×Dic61#4112yes—
253C22×Dic61#4112yes—
254#11758198—28no—
255#11758198—28no—
256#11758198—28no—
257#11758198—44no—
258#11758198—44no—
259#11758198—44no—
260#11758198—44no—
261C4⋊Dic61—44no—
262#11758196—28no—
263#11758196—28no—
264#11758196—28no—
265#11758196—44no—
266C4×Dic61—28no—
267C4×Dic61—44no—
268C4×Dic61—44no—
269C4×Dic61—44no—
270C4×Dic61—44no—
271C23×C61C23×C411yescharacteristic
272C23×C61C22×D411yescharacteristic
273C23×C61C22×D411yescharacteristic
274C23×C61C2×#4111yescharacteristic
275C23×C61C2×#4111yescharacteristic
276C23×C61C2×#4111yescharacteristic
277C23×C61C2×#4111yescharacteristic
278C23×C61C2×#4111yescharacteristic
279C23×C61C2×#4111yescharacteristic
280C23×C61C2×#4111yescharacteristic
281C23×C61C2×#4111yescharacteristic
282C23×C61H(5,𝔽2)11yescharacteristic
283C23×C61H(5,𝔽2)11yescharacteristic
284C23×C612−1+411yescharacteristic
285C23×C612−1+411yescharacteristic
286C22×D61—22no—
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61—41no—
300C22×D61—41no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61—41no—
304C22×D61—41no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61—41no—
314C22×D61—41no—
315C22×D61—41no—
316C22×D61—41no—
317C22×D61—41no—
318C22×D61—41no—
319C22×D61—41no—
320C22×D61—41no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×Dic61—22no—
371C2×Dic61—22no—
372C2×Dic61—22no—
373C2×Dic61—22no—
374C2×Dic61—22no—
375C2×Dic61—22no—
376C2×Dic61—22no—
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—22no—
380C2×Dic61—22no—
381C2×Dic61—22no—
382C2×Dic61—22no—
383C2×Dic61—22no—
384C2×Dic61—22no—
385C2×Dic61—22no—
386C2×Dic61—22no—
387C2×Dic61—22no—
388C2×Dic61—22no—
389C2×Dic61—22no—
390C2×Dic61—22no—
391C2×Dic61—22no—
392C2×Dic61—22no—
393C2×Dic61—22no—
394C2×Dic61—22no—
395C2×Dic61—22no—
396C2×Dic61—22no—
397C2×Dic61—22no—
398C2×Dic61—22no—
399C2×Dic61—22no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—41no—
403C2×Dic61—41no—
404C2×Dic61—41no—
405C2×Dic61—41no—
406C2×Dic61—41no—
407C2×Dic61—41no—
408C2×Dic61—41no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411C2×Dic61—41no—
412C2×Dic61—41no—
413C2×Dic61—41no—
414C2×Dic61—41no—
415C2×Dic61#11714yes—
416C2×Dic61C4×D414yes—
417C2×Dic61C4×D414yes—
418C2×Dic61#12114yes—
419#14077—611nomaximal, Sylow
420C22×C61C2×#11711yescharacteristic
421C22×C61C2×C4×D411yescharacteristic
422C22×C61C2×C4×D411yescharacteristic
423C22×C61C4×#4111yescharacteristic
424C22×C61C4×#4111yescharacteristic
425C22×C61#52011yescharacteristic
426C22×C61#52011yescharacteristic
427C22×C61C2×#12111yescharacteristic
428C22×C61#52511yescharacteristic
429C22×C61#52911yescharacteristic
430C22×C61#52911yescharacteristic
431C22×C61#52911yescharacteristic
432C22×C61#53211yescharacteristic
433C22×C61#53211yescharacteristic
434C22×C61#53211yescharacteristic
435C22×C61#53411yescharacteristic
436C22×C61#53611yescharacteristic
437C22×C61#53911yescharacteristic
438C22×C61#53911yescharacteristic
439C22×C61#54611yescharacteristic
440C22×C61#54611yescharacteristic
441C22×C61#54811yescharacteristic
442C22×C61#54811yescharacteristic
443C22×C61#55111yescharacteristic
444C22×C61#55211yescharacteristic
445C22×C61#55211yescharacteristic
446C22×C61#55311yescharacteristic
447C22×C61#55311yescharacteristic
448C22×C61#55311yescharacteristic
449C22×C61#55311yescharacteristic
450C22×C61#55611yescharacteristic
451C22×C61#55611yescharacteristic
452C22×C61#55611yescharacteristic
453C22×C61#55611yescharacteristic
454C22×C61#55911yescharacteristic
455C2×D61—42no—
456C2×D61—42no—
457C2×D61—42no—
458C2×D61—42no—
459C2×D61—42no—
460C2×D61—42no—
461C2×D61—42no—
462C2×D61—81no—
463C2×D61—81no—
464C2×D61—81no—
465C2×D61—81no—
466C2×D61—81no—
467C2×D61—81no—
468C2×D61—81no—
469C2×D61—81no—
470C4×C61—42no—
471C4×C61—42no—
472C4×C61—42no—
473C4×C61—42no—
474C4×C61—42no—
475C4×C61—42no—
476C4×C61—81no—
477Dic61—24no—
478Dic61—24no—
479Dic61—24no—
480Dic61—24no—
481Dic61—42no—
482Dic61—42no—
483Dic61—81no—
484C2×#389—611no—
485C2×#388—611no—
486C2×#388—611no—
487C2×#388—611no—
488C2×C4×C4⋊C4—611no—
489#1443D6111yescharacteristic, complemented
490#1441—611no—
491#1439—611no—
492#1439—611no—
493#1437—611no—
494#1437—611no—
495#1436—611no—
496#1436—611no—
497#1434—611no—
498C4×#95—611no—
499C2×C61#229311yescharacteristic
500C2×C61C4×#12111yescharacteristic
501C2×C61#232211yescharacteristic
502C2×C61#234711yescharacteristic
503C2×C61#235211yescharacteristic
504C2×C61#236711yescharacteristic
505C2×C61#237311yescharacteristic
506C2×C61#254311yescharacteristic
507C2×C61#254511yescharacteristic
508C2×C61#255811yescharacteristic
509C2×C61#256011yescharacteristic
510C2×C61#259411yescharacteristic
511C2×C61#259611yescharacteristic
512C2×C61#260211yescharacteristic
513C2×C61#260411yescharacteristic
514D61—82no—
515C22×C4⋊C4—611no—
516C22×C4⋊C4—611no—
517C22×C4⋊C4—611no—
518C22×C4⋊C4—611no—
519C22×C4⋊C4—611no—
520C22×C22⋊C4—611no—
521C22×C22⋊C4—611no—
522C22×C22⋊C4—611no—
523C22×C22⋊C4—611no—
524C22×C22⋊C4—611no—
525C22×C22⋊C4—611no—
526C22×C22⋊C4—611no—
527C22×C42—611no—
528C22×C42—611no—
529C22×C42—611no—
530C22×C42—611no—
531C22×C42—611no—
532#389—1224no—
533#388—618no—
534#388—1224no—
535#388—1224no—
536C4×C4⋊C4—1224no—
537C2×#95—611no—
538C2×#95—611no—
539C2×#95—611no—
540C2×#95—611no—
541C2×#95—611no—
542C2×#95—611no—
543C2×#95—611no—
544C2×#95—611no—
545C2×#95—611no—
546C2×#95—611no—
547C2×#95—611no—
548C2×#95C2×D6111yescharacteristic
549C2×#95C2×D6111yescharacteristic
550C2×#95C2×D6111yescharacteristic
551C2×#95C2×D6111yescharacteristic
552C2×#95C2×D6111yescharacteristic
553C2×#95C2×D6111yescharacteristic
554C2×#95C2×D6111yescharacteristic
555C61#1407711yescharacteristic, complemented, Sylow
556C25—611no—
557C23×C4—611no—
558C23×C4—611no—
559C23×C4—611no—
560C23×C4—611no—
561C23×C4—611no—
562C23×C4—611no—
563C23×C4—611no—
564C23×C4C22×D6111yescharacteristic
565C23×C4C22×D6111yescharacteristic
566C23×C4C22×D6111yescharacteristic
567C23×C4C22×D6111yescharacteristic
568C23×C4C22×D6111yescharacteristic
569C23×C4C22×D6111yescharacteristic
570C23×C4C22×D6111yescharacteristic
571C2×C4⋊C4—614no—
572C2×C4⋊C4—614no—
573C2×C4⋊C4—1222no—
574C2×C4⋊C4—1222no—
575C2×C4⋊C4—1222no—
576C2×C4⋊C4—1222no—
577C2×C4⋊C4—1222no—
578C2×C4⋊C4—1222no—
579C2×C4⋊C4—1222no—
580C2×C4⋊C4—1222no—
581C2×C4⋊C4—1222no—
582C2×C4⋊C4—1222no—
583C2×C4⋊C4—1222no—
584C2×C4⋊C4—1222no—
585C2×C4⋊C4—2441no—
586C2×C22⋊C4—614no—
587C2×C22⋊C4—614no—
588C2×C22⋊C4—614no—
589C2×C22⋊C4—1222no—
590C2×C22⋊C4—1222no—
591C2×C22⋊C4—1222no—
592C2×C22⋊C4—1222no—
593C2×C22⋊C4—1222no—
594C2×C22⋊C4—1222no—
595C2×C22⋊C4—1222no—
596C2×C22⋊C4—1222no—
597C2×C22⋊C4—1222no—
598C2×C22⋊C4—1222no—
599C2×C22⋊C4—1222no—
600C2×C22⋊C4—1222no—
601C2×C22⋊C4—1222no—
602C2×C22⋊C4—1222no—
603C2×C22⋊C4—2441no—
604C2×C22⋊C4—2441no—
605C2×C22⋊C4—2441no—
606C2×C22⋊C4—2441no—
607C2×C42—614no—
608C2×C42—614no—
609C2×C42—1222no—
610C2×C42—1222no—
611C2×C42—1222no—
612C2×C42—1222no—
613C2×C42—1222no—
614C2×C42—1222no—
615C2×C42—1222no—
616C2×C42—2441no—
617C2×C42—2441no—
618C2×C42—2441no—
619C2×C42—2441no—
620C2×C42—2441no—
621C2×C42—2441no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—614no—
629#95—1222no—
630#95—1222no—
631#95—1222no—
632#95—1222no—
633#95—1222no—
634#95—1222no—
635#95—1222no—
636#95—1222no—
637#95—1222no—
638#95—2441no—
639#95C4×D6114yes—
640C24—612no—
641C24—1221no—
642C24—1221no—
643C24—1221no—
644C24—1221no—
645C24—1221no—
646C24—1221no—
647C24—1221no—
648C24—1221no—
649C24—1221no—
650C24—1221no—
651C24—1221no—
652C24—1221no—
653C24—1221no—
654C24—1221no—
655C24C23×D6111yescharacteristic
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—612no—
700C22×C4—612no—
701C22×C4—612no—
702C22×C4—612no—
703C22×C4—612no—
704C22×C4—612no—
705C22×C4—612no—
706C22×C4—612no—
707C22×C4—612no—
708C22×C4—612no—
709C22×C4—612no—
710C22×C4—612no—
711C22×C4—612no—
712C22×C4—612no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4C2×C4×D6112yes—
749C22×C4C2×C4×D6112yes—
750C22×C4C2×C4×D6112yes—
751C22×C4D4×D6112yes—
752C22×C4D4×D6112yes—
753C22×C4#1175822412yes—
754C4⋊C4—1228no—
755C4⋊C4—1228no—
756C4⋊C4—1228no—
757C4⋊C4—2444no—
758C4⋊C4—2444no—
759C22⋊C4—1228no—
760C22⋊C4—1228no—
761C22⋊C4—1228no—
762C22⋊C4—2444no—
763C22⋊C4—2444no—
764C22⋊C4—2444no—
765C22⋊C4—2444no—
766C42—1228no—
767C42—2444no—
768C42—2444no—
769C42—2444no—
770C42—2444no—
771C23—1222no—
772C23—1222no—
773C23—1222no—
774C23—1222no—
775C23—1222no—
776C23—1222no—
777C23—1222no—
778C23—2441no—
779C23—2441no—
780C23—2441no—
781C23—2441no—
782C23—2441no—
783C23—2441no—
784C23—2441no—
785C23—2441no—
786C23—2441no—
787C23—2441no—
788C23—2441no—
789C23—2441no—
790C23—2441no—
791C23—2441no—
792C23—2441no—
793C23—2441no—
794C23—2441no—
795C23—2441no—
796C23—2441no—
797C23—2441no—
798C23—2441no—
799C23—2441no—
800C23—2441no—
801C23—2441no—
802C23—2441no—
803C23—2441no—
804C23—2441no—
805C23—2441no—
806C23C22×C4×D6111yescharacteristic
807C23C2×D4×D6111yescharacteristic
808C23C2×D4×D6111yescharacteristic
809C23#41×D6111yescharacteristic
810C23#41×D6111yescharacteristic
811C23#41×D6111yescharacteristic
812C23#41×D6111yescharacteristic
813C23#41×D6111yescharacteristic
814C23#41×D6111yescharacteristic
815C23#41×D6111yescharacteristic
816C23C2×#1175822411yescharacteristic
817C23#1451982311yescharacteristic
818C23#1451982311yescharacteristic
819C23#1451982411yescharacteristic
820C23#1451982511yescharacteristic
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—614no—
871C2×C4—614no—
872C2×C4—614no—
873C2×C4—614no—
874C2×C4—1222no—
875C2×C4—1222no—
876C2×C4—1222no—
877C2×C4—1222no—
878C2×C4—1222no—
879C2×C4—1222no—
880C2×C4—1222no—
881C2×C4—1222no—
882C2×C4—1222no—
883C2×C4—1222no—
884C2×C4—1222no—
885C2×C4—1222no—
886C2×C4—1222no—
887C2×C4—1222no—
888C2×C4—1222no—
889C2×C4—1222no—
890C2×C4—1222no—
891C2×C4—1222no—
892C2×C4—1222no—
893C2×C4—1222no—
894C2×C4—1222no—
895C2×C4—1222no—
896C2×C4—1222no—
897C2×C4—1222no—
898C2×C4—1222no—
899C2×C4—1222no—
900C2×C4—1222no—
901C2×C4—1222no—
902C2×C4—1222no—
903C2×C4—1222no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4—2441no—
916C2×C4—2441no—
917C2×C4—2441no—
918C2×C4—2441no—
919C22—4881no—
920C22—4881no—
921C22—4881no—
922C22—4881no—
923C22—4881no—
924C22—4881no—
925C22—4881no—
926C22—4881no—
927C22—2442no—
928C22—2442no—
929C22—2442no—
930C22—2442no—
931C22—2442no—
932C22—2442no—
933C22—2442no—
934C22#117×D6111yescharacteristic
935C22C4×D4×D6111yescharacteristic
936C22C4×D4×D6111yescharacteristic
937C22C4×#1175822411yescharacteristic
938C22#1684023011yescharacteristic
939C22#1684024211yescharacteristic
940C22#1684024411yescharacteristic
941C22#121×D6111yescharacteristic
942C22#1684027011yescharacteristic
943C22#1684028911yescharacteristic
944C22#1684029511yescharacteristic
945C22#1684029511yescharacteristic
946C22#1684030711yescharacteristic
947C22#1684031111yescharacteristic
948C22#1684031111yescharacteristic
949C22#1684032311yescharacteristic
950C22#1684033511yescharacteristic
951C22#1684035311yescharacteristic
952C22#1684036011yescharacteristic
953C22#1684040411yescharacteristic
954C22#1684040411yescharacteristic
955C22#1684041811yescharacteristic
956C22#1684042211yescharacteristic
957C22#1684043511yescharacteristic
958C22#1684044411yescharacteristic
959C22#1684044411yescharacteristic
960C22#1684046311yescharacteristic
961C22#1684046311yescharacteristic
962C22#1684046311yescharacteristic
963C22#1684046311yescharacteristic
964C22#1684047911yescharacteristic
965C22#1684047911yescharacteristic
966C22#1684047911yescharacteristic
967C22#1684048311yescharacteristic
968C22#1684049411yescharacteristic
969C4—42no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—42no—
974C4—42no—
975C4—81no—
976C4—1224no—
977C4—1224no—
978C4—1224no—
979C4—1224no—
980C4—4881no—
981C4—2442no—
982C4—2442no—
983C2—4882no—
984C2#2144827911yescharacteristic
985C2#2144833111yescharacteristic
986C2#2144849211yescharacteristic
987C2#2144870711yescharacteristic
988C2#2144874311yescharacteristic
989C2#2144889311yescharacteristic
990C2#2144893211yescharacteristic
991C2#2145077611yescharacteristic
992C2#2145079411yescharacteristic
993C2#2145093611yescharacteristic
994C2#2145096411yescharacteristic
995C2#2145132011yescharacteristic
996C2#2145134811yescharacteristic
997C2#2145142611yescharacteristic
998C2#2145146011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1443C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenter#1443D61
hypocenterC61#14077
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
1. C2×#16839659C2semidirect
5. C2×#16839613C2semidirect
6. #21444070C2semidirect
11. #21444054C2semidirect
12. #21444053C2semidirect
13. #21444044C2semidirect
14. #95×Dic61C2semidirect
15. C61×#1443C2semidirect
36. #16839651C4semidirect
489. #1443D61semidirect
555. C61#14077semidirect

Maximal subgroups

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

subgroupindex
C2×#168396592
C2×#168396542
C2×#168396512
C2×#168396132
#214440702
#214440632
#214440552
#214440542
#214440532
#214440442
#95×Dic612
C61×#14432
#1407761