Finite Group Databasebeta

← #29610907

Subgroups — #29610907

Order 15616.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839677C211yesmaximal, characteristic
2#21444085C211yesmaximal, characteristic, complemented
3#21444080C211yesmaximal, characteristic, complemented
4#21444073C211yesmaximal, characteristic, complemented
5#21444067C211yesmaximal, characteristic, complemented
6#21444066C211yesmaximal, characteristic, complemented
7#21444065C211yesmaximal, characteristic, complemented
8#21444064C211yesmaximal, characteristic, complemented
9#21444063C211yesmaximal, characteristic, complemented
10#21444062C211yesmaximal, characteristic, complemented
11#21444058C211yesmaximal, characteristic
12#21444058C211yesmaximal, characteristic
13#21444057C211yesmaximal, characteristic, complemented
14#21444052C211yesmaximal, characteristic, complemented
15C61×#1437C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×#11758196C2211yescharacteristic
19C22×#11758196C2211yescharacteristic
20C22×C22⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×C22⋊Dic61C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29#16839677C418yescomplemented
30C2×#14519684C2211yescharacteristic
31C2×#14519684C2211yescharacteristic
32C2×#14519684C2211yescharacteristic
33C2×#14519684C2211yescharacteristic
34C2×#14519684C2211yescharacteristic
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C22×C22⋊C4×C61C2211yescharacteristic
46C22×C22⋊C4×C61C2211yescharacteristic
47C22×C22⋊C4×C61C2211yescharacteristic
48C22×C42×C61C2211yescharacteristic
49C2×#95×C61C2211yescharacteristic
50C2×#95×C61C2211yescharacteristic
51C2×#95×C61C2211yescharacteristic
52C24×D61C2311yescharacteristic
53C22×C22⋊D61—41no—
54C22×C22⋊D61—41no—
55C22×C22⋊D61—41no—
56C22×C22⋊D61—41no—
57C22×C22⋊D61—41no—
58C22×C22⋊D61—41no—
59C22×C22⋊D61C2×C414yes—
60C23×Dic61C2311yescharacteristic
61C23×Dic61C2311yescharacteristic
62C23×Dic61C2311yescharacteristic
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2311yescharacteristic
65C23×Dic61C2311yescharacteristic
66C23×Dic61C2311yescharacteristic
67C2×C4⋊Dic61—41no—
68C2×C4⋊Dic61—41no—
69C2×C4⋊Dic61—41no—
70C2×#11758196—22no—
71C2×#11758196—41no—
72C2×#11758196—41no—
73C2×#11758196—41no—
74C2×#11758196—41no—
75C2×#11758196C2×C414yes—
76C2×C22⋊Dic61—41no—
77C2×C22⋊Dic61—41no—
78C2×C22⋊Dic61—41no—
79C2×C22⋊Dic61—41no—
80C2×C22⋊Dic61—41no—
81C2×C22⋊Dic61—41no—
82C2×C22⋊Dic61—41no—
83C2×C22⋊Dic61—41no—
84C2×C22⋊Dic61C2×C414yes—
85C2×#11758198—22no—
86C2×#11758198—22no—
87C2×#11758198—41no—
88C2×#11758198—41no—
89C2×#11758198—41no—
90C2×#11758198—41no—
91C2×#11758198—41no—
92C2×#11758198—41no—
93C2×#11758198—41no—
94C2×#11758198—41no—
95C2×#11758198—41no—
96C2×#11758198—41no—
97C2×#11758198—41no—
98C2×#11758198—41no—
99C2×#11758198—41no—
100C2×#11758198—41no—
101C2×#11758198C2×C414yes—
102C2×#11758198C2×C414yes—
103#14519684—22no—
104#14519684—41no—
105#14519684—41no—
106#14519684—41no—
107#14519684—41no—
108#14519684—41no—
109#14519684—41no—
110#14519684—41no—
111#14519684—41no—
112#14519684—41no—
113#14519684—41no—
114#14519684—41no—
115#14519684—41no—
116#14519684—41no—
117#14519684C2×C414yes—
118C25×C61C2311yescharacteristic
119C23×C4×C61C2311yescharacteristic
120C23×C4×C61C2311yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C23×C4×C61C2311yescharacteristic
123C23×C4×C61C2311yescharacteristic
124C23×C4×C61C2311yescharacteristic
125C2×C22⋊C4×C61—22no—
126C2×C22⋊C4×C61—22no—
127C2×C22⋊C4×C61—41no—
128C2×C22⋊C4×C61—41no—
129C2×C22⋊C4×C61—41no—
130C2×C22⋊C4×C61—41no—
131C2×C22⋊C4×C61—41no—
132C2×C22⋊C4×C61—41no—
133C2×C22⋊C4×C61C2×C414yes—
134C2×C42×C61—41no—
135C2×C42×C61—41no—
136C2×C42×C61—41no—
137#95×C61—41no—
138#95×C61—41no—
139#95×C61—41no—
140C24×C61—21no—
141C24×C61—21no—
142C24×C61—21no—
143C24×C61—21no—
144C24×C61—21no—
145C24×C61—21no—
146C24×C61—21no—
147C24×C61—21no—
148C24×C61—21no—
149C24×C61—21no—
150C24×C61—21no—
151C24×C61—21no—
152C24×C61—21no—
153C24×C61—21no—
154C24×C61C22×C412yes—
155C24×C61C2411yescharacteristic
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×D61C22×C412yes—
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×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×C61C22×C412yes—
210C22×C4×C61C22×C412yes—
211C22×C4×C61#4112yes—
212C22×C4×C61#4112yes—
213C2×C22⋊D61—44no—
214C2×C22⋊D61—44no—
215C2×C22⋊D61—44no—
216C2×C22⋊D61—44no—
217C2×C22⋊D61—44no—
218C2×C22⋊D61—44no—
219C2×C22⋊D61—44no—
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×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×Dic61C22×C412yes—
267C22×Dic61C22×C412yes—
268C22×Dic61C22×C412yes—
269C22⋊C4×C61—44no—
270C22⋊C4×C61—44no—
271C22⋊C4×C61—44no—
272C42×C61—44no—
273C22⋊Dic61—44no—
274C22⋊Dic61—44no—
275C22⋊Dic61—44no—
276#11758198—44no—
277#11758198—44no—
278#11758198—44no—
279#11758198—44no—
280#11758198—44no—
281#11758198—44no—
282C4⋊Dic61—44no—
283#11758196—44no—
284#11758196—44no—
285C23×C61—22no—
286C23×C61—22no—
287C23×C61—22no—
288C23×C61—22no—
289C23×C61—22no—
290C23×C61—22no—
291C23×C61—22no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—41no—
307C23×C61—41no—
308C23×C61—41no—
309C23×C61—41no—
310C23×C61—41no—
311C23×C61—41no—
312C23×C61—41no—
313C23×C61—41no—
314C23×C61—41no—
315C23×C61—41no—
316C23×C61—41no—
317C23×C61—41no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61C23×C411yescharacteristic
321C23×C61C2×#4111yescharacteristic
322C23×C61C2×#4111yescharacteristic
323C23×C61H(5,𝔽2)11yescharacteristic
324C23×C61H(5,𝔽2)11yescharacteristic
325C23×C61H(5,𝔽2)11yescharacteristic
326C23×C61H(5,𝔽2)11yescharacteristic
327C23×C61H(5,𝔽2)11yescharacteristic
328C23×C61H(5,𝔽2)11yescharacteristic
329C23×C61H(5,𝔽2)11yescharacteristic
330C23×C61H(5,𝔽2)11yescharacteristic
331C23×C61H(5,𝔽2)11yescharacteristic
332C23×C61H(5,𝔽2)11yescharacteristic
333C23×C612−1+411yescharacteristic
334C23×C612−1+411yescharacteristic
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—41no—
343C22×D61—41no—
344C22×D61—41no—
345C22×D61—41no—
346C22×D61—41no—
347C22×D61—41no—
348C22×D61—41no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—41no—
353C22×D61—41no—
354C22×D61—41no—
355C22×D61—41no—
356C22×D61—41no—
357C22×D61—41no—
358C22×D61—41no—
359C22×D61—41no—
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—
370C2×C4×C61—22no—
371C2×C4×C61—22no—
372C2×C4×C61—22no—
373C2×C4×C61—22no—
374C2×C4×C61—22no—
375C2×C4×C61—22no—
376C2×C4×C61—22no—
377C2×C4×C61—22no—
378C2×C4×C61—22no—
379C2×C4×C61—22no—
380C2×C4×C61—22no—
381C2×C4×C61—22no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
394C2×C4×C61—41no—
395C2×C4×C61—41no—
396C2×C4×C61—41no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61—41no—
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—
412C22⋊D61—416no—
413C2×Dic61—22no—
414C2×Dic61—22no—
415C2×Dic61—22no—
416C2×Dic61—22no—
417C2×Dic61—22no—
418C2×Dic61—22no—
419C2×Dic61—22no—
420C2×Dic61—22no—
421C2×Dic61—22no—
422C2×Dic61—41no—
423C2×Dic61—41no—
424C2×Dic61—41no—
425C2×Dic61—41no—
426C2×Dic61—41no—
427C2×Dic61—41no—
428C2×Dic61—41no—
429C2×Dic61—41no—
430C2×Dic61—41no—
431C2×Dic61—41no—
432C2×Dic61—41no—
433C2×Dic61—41no—
434C2×Dic61—41no—
435C2×Dic61—41no—
436C2×Dic61—41no—
437C2×Dic61—41no—
438C2×Dic61—41no—
439C2×Dic61—41no—
440C2×Dic61—41no—
441C2×Dic61—41no—
442C2×Dic61—41no—
443C2×Dic61—41no—
444C2×Dic61—41no—
445C2×Dic61—41no—
446C2×Dic61—41no—
447C2×Dic61—41no—
448C2×Dic61—41no—
449C2×Dic61—41no—
450C2×Dic61—41no—
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—
462#14645—611nomaximal, Sylow
463C22×C61—42no—
464C22×C61—42no—
465C22×C61—42no—
466C22×C61—42no—
467C22×C61—42no—
468C22×C61—42no—
469C22×C61—42no—
470C22×C61—81no—
471C22×C61—81no—
472C22×C61—81no—
473C22×C61—81no—
474C22×C61—81no—
475C22×C61—81no—
476C22×C61—81no—
477C22×C61—81no—
478C22×C61C4×#4111yescharacteristic
479C22×C61#51811yescharacteristic
480C22×C61#51811yescharacteristic
481C22×C61#51811yescharacteristic
482C22×C61#51811yescharacteristic
483C22×C61#52011yescharacteristic
484C22×C61#52011yescharacteristic
485C22×C61#53811yescharacteristic
486C22×C61#53811yescharacteristic
487C22×C61#53811yescharacteristic
488C22×C61#53811yescharacteristic
489C22×C61#53811yescharacteristic
490C22×C61#53911yescharacteristic
491C22×C61#54011yescharacteristic
492C22×C61#54011yescharacteristic
493C22×C61#54011yescharacteristic
494C22×C61#54211yescharacteristic
495C22×C61#54211yescharacteristic
496C22×C61#54211yescharacteristic
497C22×C61#56011yescharacteristic
498C22×C61#56011yescharacteristic
499C22×C61#56011yescharacteristic
500C22×C61#56011yescharacteristic
501C22×C61#56011yescharacteristic
502C22×C61#56011yescharacteristic
503C22×C61#56011yescharacteristic
504C22×C61#56011yescharacteristic
505C22×C61H(3,𝔽4)11yescharacteristic
506C22×C61#56211yescharacteristic
507C22×C61#56211yescharacteristic
508C22×C61#56211yescharacteristic
509C22×C61#56211yescharacteristic
510C22×C61#56211yescharacteristic
511C22×C61#56211yescharacteristic
512C22×C61#56311yescharacteristic
513C2×D61—42no—
514C2×D61—42no—
515C2×D61—42no—
516C2×D61—42no—
517C2×D61—42no—
518C2×D61—42no—
519C2×D61—42no—
520C2×D61—81no—
521C2×D61—81no—
522C2×D61—81no—
523C2×D61—81no—
524C2×D61—81no—
525C2×D61—81no—
526C2×D61—81no—
527C2×D61—81no—
528C4×C61—42no—
529C4×C61—42no—
530C4×C61—42no—
531C4×C61—42no—
532C4×C61—81no—
533C4×C61—81no—
534Dic61—42no—
535Dic61—42no—
536Dic61—42no—
537Dic61—81no—
538Dic61—81no—
539Dic61—81no—
540Dic61—81no—
541C2×#394—611no—
542#1445—611no—
543#1443—611no—
544#1441—611no—
545#1440—611no—
546#1440—611no—
547#1439—611no—
548#1439—611no—
549#1439—611no—
550#1439—611no—
551#1438—611no—
552#1438—611no—
553#1437—611no—
554#1437D6111yescharacteristic, complemented
555#1436—611no—
556C2×C61—82no—
557C2×C61#233311yescharacteristic
558C2×C61#233511yescharacteristic
559C2×C61#233711yescharacteristic
560C2×C61#237511yescharacteristic
561C2×C61#237611yescharacteristic
562C2×C61#237711yescharacteristic
563C2×C61#237711yescharacteristic
564C2×C61#282511yescharacteristic
565C2×C61#282611yescharacteristic
566C2×C61#282811yescharacteristic
567C2×C61#282911yescharacteristic
568C2×C61#282911yescharacteristic
569C2×C61#282911yescharacteristic
570C2×C61#283211yescharacteristic
571C2×C61#283711yescharacteristic
572D61—82no—
573C23×D4—611no—
574C22×C4⋊C4—611no—
575C22×C4⋊C4—611no—
576C22×C4⋊C4—611no—
577C22×C22⋊C4—611no—
578C22×C22⋊C4—611no—
579C22×C22⋊C4—611no—
580C22×C22⋊C4—611no—
581C22×C22⋊C4—611no—
582C22×C22⋊C4—611no—
583C22×C22⋊C4—611no—
584C22×C22⋊C4—611no—
585C22×C22⋊C4—611no—
586C22×C22⋊C4C2×D6111yescharacteristic
587C22×C22⋊C4C2×D6111yescharacteristic
588C22×C22⋊C4C2×D6111yescharacteristic
589C22×C42C2×D6111yescharacteristic
590#394—618no—
591C2×#95—611no—
592C2×#95—611no—
593C2×#95—611no—
594C2×#95—611no—
595C2×#95—611no—
596C2×#95—611no—
597C2×#95—611no—
598C2×#95—611no—
599C2×#95—611no—
600C2×#95—611no—
601C2×#95—611no—
602C2×#95—611no—
603C2×#95—611no—
604C2×#95—611no—
605C2×#95—611no—
606C2×#95C2×D6111yescharacteristic
607C2×#95C2×D6111yescharacteristic
608C2×#95C2×D6111yescharacteristic
609C61#1464511yescharacteristic, complemented, Sylow
610C25—611no—
611C25C22×D6111yescharacteristic
612C22×D4—614no—
613C22×D4—2441no—
614C22×D4—2441no—
615C22×D4—2441no—
616C22×D4—2441no—
617C22×D4—2441no—
618C22×D4—2441no—
619C23×C4—611no—
620C23×C4—611no—
621C23×C4—611no—
622C23×C4—611no—
623C23×C4—611no—
624C23×C4—611no—
625C23×C4—611no—
626C23×C4C22×D6111yescharacteristic
627C23×C4C22×D6111yescharacteristic
628C23×C4C22×D6111yescharacteristic
629C23×C4C22×D6111yescharacteristic
630C23×C4C22×D6111yescharacteristic
631C23×C4C22×D6111yescharacteristic
632C2×C4⋊C4—614no—
633C2×C4⋊C4—1222no—
634C2×C4⋊C4—2441no—
635C2×C4⋊C4—2441no—
636C2×C4⋊C4—2441no—
637C2×C4⋊C4—2441no—
638C2×C4⋊C4—2441no—
639C2×C4⋊C4—2441no—
640C2×C4⋊C4—2441no—
641C2×C22⋊C4—22no—
642C2×C22⋊C4—22no—
643C2×C22⋊C4—41no—
644C2×C22⋊C4—41no—
645C2×C22⋊C4—41no—
646C2×C22⋊C4—41no—
647C2×C22⋊C4—41no—
648C2×C22⋊C4—41no—
649C2×C22⋊C4—614no—
650C2×C22⋊C4—614no—
651C2×C22⋊C4—614no—
652C2×C22⋊C4—1222no—
653C2×C22⋊C4—1222no—
654C2×C22⋊C4—2441no—
655C2×C22⋊C4—2441no—
656C2×C22⋊C4—2441no—
657C2×C22⋊C4—2441no—
658C2×C22⋊C4—2441no—
659C2×C22⋊C4—2441no—
660C2×C22⋊C4—2441no—
661C2×C22⋊C4—2441no—
662C2×C22⋊C4—2441no—
663C2×C22⋊C4—2441no—
664C2×C22⋊C4—2441no—
665C2×C22⋊C4—2441no—
666C2×C22⋊C4—2441no—
667C2×C22⋊C4—2441no—
668C2×C22⋊C4—2441no—
669C2×C22⋊C4—2441no—
670C2×C22⋊C4—2441no—
671C2×C22⋊C4—2441no—
672C2×C22⋊C4—2441no—
673C2×C22⋊C4—2441no—
674C2×C22⋊C4—2441no—
675C2×C22⋊C4—2441no—
676C2×C22⋊C4C4×D6114yes—
677C2×C42—41no—
678C2×C42—41no—
679C2×C42—41no—
680#95—41no—
681#95—41no—
682#95—41no—
683#95—614no—
684#95—1222no—
685#95—2441no—
686#95—2441no—
687#95—2441no—
688#95—2441no—
689#95—2441no—
690#95—2441no—
691#95—2441no—
692#95—2441no—
693#95—2441no—
694#95—2441no—
695#95—2441no—
696#95—2441no—
697#95—2441no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24—21no—
705C24—21no—
706C24—21no—
707C24—21no—
708C24—21no—
709C24—21no—
710C24—21no—
711C24—21no—
712C24—612no—
713C24—1221no—
714C24—1221no—
715C24—1221no—
716C24—1221no—
717C24—1221no—
718C24—1221no—
719C24—1221no—
720C24—1221no—
721C24—1221no—
722C24—1221no—
723C24—1221no—
724C24—1221no—
725C24—1221no—
726C24—1221no—
727C24C2×C4×D6112yes—
728C24C23×D6111yescharacteristic
729C2×D4—2444no—
730C2×D4—2444no—
731C2×D4—2444no—
732C2×D4—2444no—
733C2×D4—2444no—
734C2×D4—2444no—
735C2×D4—2444no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—612no—
775C22×C4—612no—
776C22×C4—612no—
777C22×C4—1221no—
778C22×C4—1221no—
779C22×C4—1221no—
780C22×C4—1221no—
781C22×C4—1221no—
782C22×C4—1221no—
783C22×C4—1221no—
784C22×C4—1221no—
785C22×C4—1221no—
786C22×C4—1221no—
787C22×C4—1221no—
788C22×C4—1221no—
789C22×C4—1221no—
790C22×C4—1221no—
791C22×C4—1221no—
792C22×C4—1221no—
793C22×C4—1221no—
794C22×C4—1221no—
795C22×C4—1221no—
796C22×C4—1221no—
797C22×C4—1221no—
798C22×C4—1221no—
799C22×C4—1221no—
800C22×C4—1221no—
801C22×C4—1221no—
802C22×C4—1221no—
803C22×C4—1221no—
804C22×C4—1221no—
805C22×C4—1221no—
806C22×C4—1221no—
807C22×C4—1221no—
808C22×C4—1221no—
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×C4C2×C4×D6112yes—
824C22×C4C2×C4×D6112yes—
825C22×C4#1175822212yes—
826C22×C4#1175822212yes—
827C4⋊C4—2444no—
828C4⋊C4—2444no—
829C4⋊C4—2444no—
830C22⋊C4—44no—
831C22⋊C4—44no—
832C22⋊C4—44no—
833C22⋊C4—2444no—
834C22⋊C4—2444no—
835C22⋊C4—2444no—
836C22⋊C4—2444no—
837C22⋊C4—2444no—
838C22⋊C4—2444no—
839C22⋊C4—2444no—
840C22⋊C4—2444no—
841C22⋊C4—2444no—
842C42—44no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—1222no—
879C23—1222no—
880C23—1222no—
881C23—1222no—
882C23—1222no—
883C23—1222no—
884C23—1222no—
885C23—2441no—
886C23—2441no—
887C23—2441no—
888C23—2441no—
889C23—2441no—
890C23—2441no—
891C23—2441no—
892C23—2441no—
893C23—2441no—
894C23—2441no—
895C23—2441no—
896C23—2441no—
897C23—2441no—
898C23—2441no—
899C23—2441no—
900C23—2441no—
901C23—2441no—
902C23—2441no—
903C23—2441no—
904C23—2441no—
905C23—2441no—
906C23—2441no—
907C23—2441no—
908C23—2441no—
909C23—2441no—
910C23—2441no—
911C23—2441no—
912C23—2441no—
913C23C22×C4×D6111yescharacteristic
914C23C2×#1175822211yescharacteristic
915C23C2×#1175822211yescharacteristic
916C23#1451982211yescharacteristic
917C23#1451982211yescharacteristic
918C23#1451982211yescharacteristic
919C23#1451982211yescharacteristic
920C23#1451982211yescharacteristic
921C23#1451982211yescharacteristic
922C23#1451982311yescharacteristic
923C23#1451982311yescharacteristic
924C23#1451982311yescharacteristic
925C23#1451982311yescharacteristic
926C23#1451982411yescharacteristic
927C23#1451982411yescharacteristic
928D4—24416no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—1222no—
972C2×C4—1222no—
973C2×C4—1222no—
974C2×C4—1222no—
975C2×C4—1222no—
976C2×C4—1222no—
977C2×C4—1222no—
978C2×C4—1222no—
979C2×C4—1222no—
980C2×C4—2441no—
981C2×C4—2441no—
982C2×C4—2441no—
983C2×C4—2441no—
984C2×C4—2441no—
985C2×C4—2441no—
986C2×C4—2441no—
987C2×C4—2441no—
988C2×C4—2441no—
989C2×C4—2441no—
990C2×C4—2441no—
991C2×C4—2441no—
992C2×C4—2441no—
993C2×C4—2441no—
994C2×C4—2441no—
995C2×C4—2441no—
996C2×C4—2441no—
997C2×C4—2441no—
998C2×C4—2441no—
999C2×C4—2441no—
1000C2×C4—2441no—
1001C2×C4—2441no—
1002C2×C4—2441no—
1003C2×C4—2441no—
1004C2×C4—2441no—
1005C2×C4—2441no—
1006C2×C4—2441no—
1007C2×C4—2441no—
1008C2×C4—2441no—
1009C2×C4—2441no—
1010C2×C4—2441no—
1011C2×C4—2441no—
1012C2×C4—2441no—
1013C2×C4—2441no—
1014C2×C4—2441no—
1015C2×C4—2441no—
1016C2×C4—2441no—
1017C2×C4—2441no—
1018C2×C4—2441no—
1019C2×C4—2441no—
1020C22—42no—
1021C22—42no—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—81no—
1031C22—81no—
1032C22—81no—
1033C22—81no—
1034C22—81no—
1035C22—4881no—
1036C22—4881no—
1037C22—4881no—
1038C22—4881no—
1039C22—4881no—
1040C22—4881no—
1041C22—4881no—
1042C22—4881no—
1043C22—2442no—
1044C22—2442no—
1045C22—2442no—
1046C22—2442no—
1047C22—2442no—
1048C22—2442no—
1049C22—2442no—
1050C22C4×#1175822211yescharacteristic
1051C22#1684023411yescharacteristic
1052C22#1684023411yescharacteristic
1053C22#1684023411yescharacteristic
1054C22#1684023511yescharacteristic
1055C22#1684024111yescharacteristic
1056C22#1684024211yescharacteristic
1057C22#1684034511yescharacteristic
1058C22#1684034511yescharacteristic
1059C22#1684034511yescharacteristic
1060C22#1684035011yescharacteristic
1061C22#1684035011yescharacteristic
1062C22#1684035411yescharacteristic
1063C22#1684036311yescharacteristic
1064C22#1684036311yescharacteristic
1065C22#1684036711yescharacteristic
1066C22#1684037711yescharacteristic
1067C22#1684037711yescharacteristic
1068C22#1684038311yescharacteristic
1069C22#1684049911yescharacteristic
1070C22#1684050011yescharacteristic
1071C22#1684050011yescharacteristic
1072C22#1684050011yescharacteristic
1073C22#1684050011yescharacteristic
1074C22#1684050111yescharacteristic
1075C22#1684050211yescharacteristic
1076C22#1684050311yescharacteristic
1077C22#1684050411yescharacteristic
1078C22#1684050611yescharacteristic
1079C22#1684050611yescharacteristic
1080C22#1684050711yescharacteristic
1081C22#1684050711yescharacteristic
1082C22#1684050911yescharacteristic
1083C22#1684050911yescharacteristic
1084C22#1684051411yescharacteristic
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—42no—
1089C4—81no—
1090C4—81no—
1091C4—4881no—
1092C4—4881no—
1093C4—4881no—
1094C4—4881no—
1095C4—2442no—
1096C4—2442no—
1097C4—2442no—
1098C2—82no—
1099C2—4882no—
1100C2#2144857911yescharacteristic
1101C2#2144860911yescharacteristic
1102C2#2144862711yescharacteristic
1103C2#2144895611yescharacteristic
1104C2#2144896111yescharacteristic
1105C2#2144897211yescharacteristic
1106C2#2144897711yescharacteristic
1107C2#2145390511yescharacteristic
1108C2#2145391411yescharacteristic
1109C2#2145393611yescharacteristic
1110C2#2145394511yescharacteristic
1111C2#2145394711yescharacteristic
1112C2#2145394711yescharacteristic
1113C2#2145398411yescharacteristic
1114C2#2145403111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1437C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenter#1437D61
hypocenterC61#14645
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. #21444085C2semidirect
3. #21444080C2semidirect
4. #21444073C2semidirect
5. #21444067C2semidirect
6. #21444066C2semidirect
7. #21444065C2semidirect
8. #21444064C2semidirect
9. #21444063C2semidirect
10. #21444062C2semidirect
13. #21444057C2semidirect
14. #21444052C2semidirect
15. C61×#1437C2semidirect
29. #16839677C4semidirect
554. #1437D61semidirect
609. C61#14645semidirect

Maximal subgroups

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

subgroupindex
C2×#168396772
#214440852
#214440802
#214440732
#214440672
#214440662
#214440652
#214440642
#214440632
#214440622
#214440582
#214440572
#214440522
C61×#14372
#1464561