Finite Group Databasebeta

← #29603491

Subgroups — #29603491

Order 15616.

2358 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519763C211yesmaximal, characteristic
2C22×#14519742C211yesmaximal, characteristic, complemented
3C2×#16839666C211yesmaximal, characteristic, complemented
4C2×#16839662C211yesmaximal, characteristic
5C2×#16839662C211yesmaximal, characteristic
6#21444063C211yesmaximal, characteristic, complemented
7#21444062C211yesmaximal, characteristic, complemented
8#21444061C211yesmaximal, characteristic, complemented
9#21444056C211yesmaximal, characteristic, complemented
10#21444056C211yesmaximal, characteristic, complemented
11#21444055C211yesmaximal, characteristic, complemented
12#21444055C211yesmaximal, characteristic, complemented
13#21444047C211yesmaximal, characteristic, complemented
14#95×Dic61C211yesmaximal, characteristic, complemented
15C61×#1439C211yesmaximal, characteristic, complemented
16C23×Dic122C2211yescharacteristic
17C23×C22⋊D61C2211yescharacteristic
18C2×#14519763—24no—
19C2×#14519763—24no—
20C2×#14519763C418yescomplemented
21C2×#14519742—24no—
22C2×#14519742—24no—
23C2×#14519742—24no—
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37C22×C4×Dic61C2211yescharacteristic
38C22×C4×Dic61C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic
40C22×C4×Dic61C2211yescharacteristic
41#16839666—24no—
42#16839662—24no—
43#16839662—24no—
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C22×C4⋊C4×C61C2211yescharacteristic
54C22×C22⋊C4×C61C2211yescharacteristic
55C22×C22⋊C4×C61C2211yescharacteristic
56C22×C22⋊C4×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C2×#95×C61C2211yescharacteristic
59C2×#95×C61C2211yescharacteristic
60C24×D61C2311yescharacteristic
61C22×Dic122—22no—
62C22×Dic122—22no—
63C22×Dic122—22no—
64C22×Dic122—22no—
65C22×Dic122C2×C414yes—
66C22×Dic122D414yes—
67C22×Dic122D414yes—
68C22×C22⋊D61—22no—
69C22×C22⋊D61—22no—
70C22×C22⋊D61—22no—
71C22×C22⋊D61—22no—
72C22×C22⋊D61—22no—
73C22×C22⋊D61—22no—
74C22×C22⋊D61C2×C414yes—
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82#14519763—232no—
83#14519742—232no—
84C2×#11758196—22no—
85C2×#11758196—22no—
86C2×#11758196—22no—
87C2×#11758196—22no—
88C2×#11758196—22no—
89C2×#11758196—22no—
90C2×#11758196—22no—
91C2×#11758196—22no—
92C2×#11758196D414yes—
93C2×C22⋊Dic61—22no—
94C2×C22⋊Dic61—22no—
95C2×C22⋊Dic61—22no—
96C2×C22⋊Dic61—22no—
97C2×C22⋊Dic61—22no—
98C2×C22⋊Dic61—22no—
99C2×C22⋊Dic61—22no—
100C2×C22⋊Dic61—41no—
101C2×C22⋊Dic61C2×C414yes—
102C2×#11758198—22no—
103C2×#11758198—22no—
104C2×#11758198—22no—
105C2×#11758198—22no—
106C2×#11758198—22no—
107C2×#11758198—22no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×#11758198—22no—
111C2×#11758198—22no—
112C2×#11758198—22no—
113C2×#11758198—22no—
114C2×#11758198—41no—
115C2×#11758198—41no—
116C2×#11758198—41no—
117C2×#11758198—41no—
118C2×#11758198C2×C414yes—
119C2×#11758198C2×C414yes—
120C2×C4×Dic61—22no—
121C2×C4×Dic61—22no—
122C2×C4×Dic61—22no—
123C2×C4×Dic61—22no—
124C2×C4×Dic61—22no—
125C2×C4×Dic61—22no—
126C2×C4×Dic61—22no—
127C2×C4×Dic61—22no—
128C2×C4×Dic61—22no—
129C2×C4×Dic61—22no—
130C2×C4×Dic61—22no—
131C2×C4×Dic61—22no—
132C2×C4×Dic61—22no—
133C2×C4×Dic61C2×C414yes—
134C2×C4×Dic61D414yes—
135#14519684—22no—
136#14519684—22no—
137#14519684—22no—
138#14519684—22no—
139#14519684—22no—
140#14519684—22no—
141#14519684—41no—
142#14519684—41no—
143#14519684—41no—
144C25×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149C23×C4×C61C2311yescharacteristic
150C23×C4×C61C2311yescharacteristic
151C2×C4⋊C4×C61—22no—
152C2×C4⋊C4×C61—22no—
153C2×C4⋊C4×C61—22no—
154C2×C22⋊C4×C61—22no—
155C2×C22⋊C4×C61—22no—
156C2×C22⋊C4×C61—22no—
157C2×C22⋊C4×C61—22no—
158C2×C22⋊C4×C61—22no—
159C2×C22⋊C4×C61—41no—
160C2×C22⋊C4×C61—41no—
161C2×C22⋊C4×C61—41no—
162C2×C22⋊C4×C61C2×C414yes—
163#95×C61—22no—
164#95×C61—22no—
165#95×C61—41no—
166C24×C61—21no—
167C24×C61—21no—
168C24×C61—21no—
169C24×C61—21no—
170C24×C61—21no—
171C24×C61—21no—
172C24×C61—21no—
173C24×C61—21no—
174C24×C61—21no—
175C24×C61—21no—
176C24×C61—21no—
177C24×C61—21no—
178C24×C61—21no—
179C24×C61—21no—
180C24×C61C22×C412yes—
181C24×C61C2411yescharacteristic
182C23×D61—21no—
183C23×D61—21no—
184C23×D61—21no—
185C23×D61—21no—
186C23×D61—21no—
187C23×D61—21no—
188C23×D61—21no—
189C23×D61—21no—
190C23×D61—21no—
191C23×D61—21no—
192C23×D61—21no—
193C23×D61—21no—
194C23×D61—21no—
195C23×D61—21no—
196C23×D61C22×C412yes—
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×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61C22×C412yes—
233C22×C4×C61C22×C412yes—
234C22×C4×C61C2×D412yes—
235C22×C4×C61C2×D412yes—
236C22×C4×C61C2×D412yes—
237C22×C4×C61C2×D412yes—
238C22×C4×C61#4112yes—
239C2×C22⋊D61—28no—
240C2×C22⋊D61—28no—
241C2×C22⋊D61—28no—
242C2×C22⋊D61—44no—
243C2×C22⋊D61—44no—
244C2×C22⋊D61—44no—
245C2×C22⋊D61—44no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—21no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255C22×Dic61—21no—
256C22×Dic61—21no—
257C22×Dic61—21no—
258C22×Dic61—21no—
259C22×Dic61—21no—
260C22×Dic61—21no—
261C22×Dic61—21no—
262C22×Dic61—21no—
263C22×Dic61—21no—
264C22×Dic61—21no—
265C22×Dic61—21no—
266C22×Dic61—21no—
267C22×Dic61—21no—
268C22×Dic61—21no—
269C22×Dic61—21no—
270C22×Dic61—21no—
271C22×Dic61—21no—
272C22×Dic61—21no—
273C22×Dic61—21no—
274C22×Dic61—21no—
275C22×Dic61—21no—
276C22×Dic61—21no—
277C22×Dic61—21no—
278C22×Dic61—21no—
279C22×Dic61C22×C412yes—
280C22×Dic61C22×C412yes—
281C22×Dic61C22×C412yes—
282C22×Dic61C2×D412yes—
283C22×Dic61C2×D412yes—
284C22×Dic61C2×D412yes—
285C22×Dic61C2×D412yes—
286C22×Dic61C2×D412yes—
287C22×Dic61C2×D412yes—
288C22×Dic61C2×D412yes—
289C22×Dic61C2×D412yes—
290C22×Dic61#4112yes—
291C22×Dic61#4112yes—
292C22×Dic61#4112yes—
293C22×Dic61#4112yes—
294C22×Dic61#4112yes—
295C2×Dic122—28no—
296C2×Dic122—28no—
297C2×Dic122—28no—
298C2×Dic122—28no—
299C2×Dic122—28no—
300C2×Dic122—28no—
301C2×Dic122C22⋊C4116yescomplemented
302C4⋊C4×C61—28no—
303C22⋊C4×C61—28no—
304C22⋊C4×C61—44no—
305C22⋊C4×C61—44no—
306C22⋊Dic61—28no—
307C22⋊Dic61—44no—
308C22⋊Dic61—44no—
309#11758198—28no—
310#11758198—28no—
311#11758198—44no—
312#11758198—44no—
313#11758198—44no—
314#11758198—44no—
315#11758196—28no—
316#11758196—28no—
317#11758196—44no—
318C4×Dic61—28no—
319C4×Dic61—28no—
320C4×Dic61—28no—
321C4×Dic61—28no—
322C4×Dic61—44no—
323C23×C61—22no—
324C23×C61—22no—
325C23×C61—22no—
326C23×C61—22no—
327C23×C61—22no—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—41no—
331C23×C61—41no—
332C23×C61—41no—
333C23×C61—41no—
334C23×C61—41no—
335C23×C61—41no—
336C23×C61—41no—
337C23×C61—41no—
338C23×C61—41no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—41no—
348C23×C61—41no—
349C23×C61—41no—
350C23×C61—41no—
351C23×C61—41no—
352C23×C61—41no—
353C23×C61—41no—
354C23×C61—41no—
355C23×C61—41no—
356C23×C61—41no—
357C23×C61—41no—
358C23×C61C23×C411yescharacteristic
359C23×C61C22×D411yescharacteristic
360C23×C61C22×D411yescharacteristic
361C23×C61C22×D411yescharacteristic
362C23×C61C22×D411yescharacteristic
363C23×C61C2×#4111yescharacteristic
364C23×C61C2×#4111yescharacteristic
365C23×C61C2×#4111yescharacteristic
366C23×C61C2×#4111yescharacteristic
367C23×C61C2×#4111yescharacteristic
368C23×C61C2×#4111yescharacteristic
369C23×C61H(5,𝔽2)11yescharacteristic
370C23×C61H(5,𝔽2)11yescharacteristic
371C23×C612−1+411yescharacteristic
372C23×C612−1+411yescharacteristic
373C22×D61—22no—
374C22×D61—22no—
375C22×D61—22no—
376C22×D61—22no—
377C22×D61—22no—
378C22×D61—22no—
379C22×D61—22no—
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—41no—
393C22×D61—41no—
394C22×D61—41no—
395C22×D61—41no—
396C22×D61—41no—
397C22×D61—41no—
398C22×D61—41no—
399C22×D61—41no—
400C22×D61—41no—
401C22×D61—41no—
402C22×D61—41no—
403C22×D61—41no—
404C22×D61—41no—
405C22×D61—41no—
406C22×D61—41no—
407C22×D61—41no—
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—22no—
419C2×C4×C61—22no—
420C2×C4×C61—22no—
421C2×C4×C61—22no—
422C2×C4×C61—22no—
423C2×C4×C61—22no—
424C2×C4×C61—22no—
425C2×C4×C61—22no—
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×C4×C61—41no—
444C2×C4×C61—41no—
445C2×C4×C61—41no—
446C2×C4×C61—41no—
447C2×C4×C61—41no—
448C2×C4×C61—41no—
449C2×C4×C61C2×C22⋊C414yes—
450C22⋊D61—416no—
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—22no—
462C2×Dic61—22no—
463C2×Dic61—22no—
464C2×Dic61—22no—
465C2×Dic61—22no—
466C2×Dic61—22no—
467C2×Dic61—22no—
468C2×Dic61—22no—
469C2×Dic61—22no—
470C2×Dic61—22no—
471C2×Dic61—22no—
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—
485C2×Dic61—41no—
486C2×Dic61—41no—
487C2×Dic61—41no—
488C2×Dic61—41no—
489C2×Dic61—41no—
490C2×Dic61—41no—
491C2×Dic61C2×C22⋊C414yes—
492C2×Dic61C2×C22⋊C414yes—
493C2×Dic61C4×D414yes—
494C2×Dic61C4×D414yes—
495C2×Dic61#12014yes—
496C2×Dic61#12114yes—
497C2×Dic61#12114yes—
498C2×Dic61#12314yes—
499C2×Dic61#12414yescomplemented
500Dic122—232no—
501#14026—611nomaximal, Sylow
502C22×C61—42no—
503C22×C61—42no—
504C22×C61—42no—
505C22×C61—42no—
506C22×C61—42no—
507C22×C61—42no—
508C22×C61—42no—
509C22×C61—81no—
510C22×C61—81no—
511C22×C61—81no—
512C22×C61—81no—
513C22×C61—81no—
514C22×C61—81no—
515C22×C61—81no—
516C22×C61—81no—
517C22×C61C22×C22⋊C411yescharacteristic
518C22×C61C2×C4×D411yescharacteristic
519C22×C61C2×C4×D411yescharacteristic
520C22×C61C4×#4111yescharacteristic
521C22×C61C4×#4111yescharacteristic
522C22×C61#52011yescharacteristic
523C22×C61#52011yescharacteristic
524C22×C61C2×#12011yescharacteristic
525C22×C61C2×#12111yescharacteristic
526C22×C61C2×#12111yescharacteristic
527C22×C61C2×#12311yescharacteristic
528C22×C61C2×#12411yescharacteristic
529C22×C61#52911yescharacteristic
530C22×C61#52911yescharacteristic
531C22×C61#53211yescharacteristic
532C22×C61#53511yescharacteristic
533C22×C61#53611yescharacteristic
534C22×C61#54211yescharacteristic
535C22×C61#54211yescharacteristic
536C22×C61#54611yescharacteristic
537C22×C61#54611yescharacteristic
538C22×C61#54811yescharacteristic
539C22×C61#54811yescharacteristic
540C22×C61#54811yescharacteristic
541C22×C61#54811yescharacteristic
542C22×C61#54811yescharacteristic
543C22×C61#54811yescharacteristic
544C22×C61#55011yescharacteristic
545C22×C61#55011yescharacteristic
546C22×C61#55011yescharacteristic
547C22×C61#55011yescharacteristic
548C22×C61#55611yescharacteristic
549C22×C61#55611yescharacteristic
550C22×C61#55911yescharacteristic
551C22×C61#55911yescharacteristic
552C2×D61—42no—
553C2×D61—42no—
554C2×D61—42no—
555C2×D61—42no—
556C2×D61—42no—
557C2×D61—42no—
558C2×D61—42no—
559C2×D61—81no—
560C2×D61—81no—
561C2×D61—81no—
562C2×D61—81no—
563C2×D61—81no—
564C2×D61—81no—
565C2×D61—81no—
566C2×D61—81no—
567C4×C61—24no—
568C4×C61—42no—
569C4×C61—42no—
570C4×C61—42no—
571C4×C61—42no—
572C4×C61—81no—
573Dic61—24no—
574Dic61—24no—
575Dic61—42no—
576Dic61—42no—
577Dic61—42no—
578Dic61—81no—
579Dic61#38618yes—
580C22×#124—611no—
581C22×C4×Q8—611no—
582C2×#391—611no—
583C2×#390—611no—
584C2×#390—611no—
585#1439—611no—
586#1439—611no—
587#1439—611no—
588#1439D6111yescharacteristic, complemented
589#1437—611no—
590#1437—611no—
591#1437—611no—
592#1437—611no—
593C4⋊#95—611no—
594C4×#95—611no—
595C2×C61—82no—
596C2×C61C2×#38611yescharacteristic
597C2×C61C4×#12411yescharacteristic
598C2×C61#232611yescharacteristic
599C2×C61#234111yescharacteristic
600C2×C61#234111yescharacteristic
601C2×C61#236711yescharacteristic
602C2×C61#236711yescharacteristic
603C2×C61#242611yescharacteristic
604C2×C61#242611yescharacteristic
605C2×C61#243111yescharacteristic
606C2×C61#243611yescharacteristic
607C2×C61#244811yescharacteristic
608C2×C61#244811yescharacteristic
609C2×C61#254511yescharacteristic
610C2×C61#254811yescharacteristic
611D61—82no—
612C23×Q8—611no—
613C23×D4—611no—
614C2×#124—618no—
615C2×#124—1224no—
616C2×#124—1224no—
617C2×C4×Q8—1224no—
618C2×C4×Q8—1224no—
619C2×C4×Q8—1224no—
620C22×C4⋊C4—611no—
621C22×C4⋊C4—611no—
622C22×C4⋊C4—611no—
623C22×C4⋊C4C2×D6111yescharacteristic
624C22×C22⋊C4—611no—
625C22×C22⋊C4—611no—
626C22×C22⋊C4—611no—
627C22×C22⋊C4—611no—
628C22×C22⋊C4—611no—
629C22×C22⋊C4—611no—
630C22×C22⋊C4—611no—
631C22×C22⋊C4—611no—
632C22×C22⋊C4—611no—
633C22×C22⋊C4C2×D6111yescharacteristic
634C22×C22⋊C4C2×D6111yescharacteristic
635C22×C22⋊C4C2×D6111yescharacteristic
636C22×C42—611no—
637C22×C42—611no—
638C22×C42—611no—
639C22×C42—611no—
640C22×C42—611no—
641#391—1224no—
642#390—1224no—
643#390—1224no—
644C2×#95—611no—
645C2×#95—611no—
646C2×#95—611no—
647C2×#95—611no—
648C2×#95—611no—
649C2×#95—611no—
650C2×#95—611no—
651C2×#95—611no—
652C2×#95—611no—
653C2×#95C2×D6111yescharacteristic
654C2×#95C2×D6111yescharacteristic
655C2×#95C2×D6111yescharacteristic
656C61#1402611yescharacteristic, complemented, Sylow
657C25—611no—
658C25C22×D6111yescharacteristic
659C22×Q8—614no—
660C22×Q8—614no—
661C22×Q8—614no—
662C22×Q8—1222no—
663C22×Q8—1222no—
664C22×Q8—1222no—
665C22×Q8—1222no—
666C22×D4—614no—
667C22×D4—1222no—
668C22×D4—1222no—
669C22×D4—1222no—
670C22×D4—1222no—
671C22×D4—1222no—
672C22×D4—1222no—
673C23×C4—611no—
674C23×C4—611no—
675C23×C4—611no—
676C23×C4—611no—
677C23×C4—611no—
678C23×C4—611no—
679C23×C4—611no—
680C23×C4C22×D6111yescharacteristic
681C23×C4C22×D6111yescharacteristic
682C23×C4C22×D6111yescharacteristic
683C23×C4C22×D6111yescharacteristic
684C23×C4C22×D6111yescharacteristic
685C23×C4C22×D6111yescharacteristic
686#124—12232no—
687C4×Q8—12232no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—614no—
692C2×C4⋊C4—1222no—
693C2×C4⋊C4—1222no—
694C2×C4⋊C4—1222no—
695C2×C4⋊C4—1222no—
696C2×C4⋊C4—1222no—
697C2×C4⋊C4—1222no—
698C2×C4⋊C4—1222no—
699C2×C4⋊C4—1222no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—41no—
706C2×C22⋊C4—41no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4—614no—
709C2×C22⋊C4—614no—
710C2×C22⋊C4—614no—
711C2×C22⋊C4—1222no—
712C2×C22⋊C4—1222no—
713C2×C22⋊C4—1222no—
714C2×C22⋊C4—1222no—
715C2×C22⋊C4—1222no—
716C2×C22⋊C4—1222no—
717C2×C22⋊C4—1222no—
718C2×C22⋊C4—1222no—
719C2×C22⋊C4—1222no—
720C2×C22⋊C4—1222no—
721C2×C22⋊C4—1222no—
722C2×C22⋊C4—1222no—
723C2×C22⋊C4—1222no—
724C2×C22⋊C4—1222no—
725C2×C22⋊C4—1222no—
726C2×C22⋊C4—1222no—
727C2×C22⋊C4—1222no—
728C2×C22⋊C4—1222no—
729C2×C22⋊C4—1222no—
730C2×C22⋊C4—2441no—
731C2×C22⋊C4—2441no—
732C2×C22⋊C4—2441no—
733C2×C22⋊C4—2441no—
734C2×C22⋊C4—2441no—
735C2×C22⋊C4C4×D6114yes—
736C2×C42—614no—
737C2×C42—614no—
738C2×C42—1222no—
739C2×C42—1222no—
740C2×C42—1222no—
741C2×C42—1222no—
742C2×C42—1222no—
743C2×C42—1222no—
744C2×C42—1222no—
745C2×C42—1222no—
746C2×C42—1222no—
747C2×C42—1222no—
748C2×C42—1222no—
749C2×C42—1222no—
750C2×C42—1222no—
751#95—22no—
752#95—22no—
753#95—41no—
754#95—1222no—
755#95—1222no—
756#95—1222no—
757#95—1222no—
758#95—1222no—
759#95—1222no—
760#95—2441no—
761#95—2441no—
762#95—2441no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—612no—
778C24—1221no—
779C24—1221no—
780C24—1221no—
781C24—1221no—
782C24—1221no—
783C24—1221no—
784C24—1221no—
785C24—1221no—
786C24—1221no—
787C24—1221no—
788C24—1221no—
789C24—1221no—
790C24—1221no—
791C24—1221no—
792C24C2×C4×D6112yes—
793C24C23×D6111yescharacteristic
794C2×Q8—6116no—
795C2×Q8—1228no—
796C2×Q8—1228no—
797C2×Q8—1228no—
798C2×Q8—1228no—
799C2×Q8—1228no—
800C2×Q8—1228no—
801C2×D4—1228no—
802C2×D4—1228no—
803C2×D4—1228no—
804C2×D4—2444no—
805C2×D4—2444no—
806C2×D4—2444no—
807C2×D4—2444no—
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—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—612no—
844C22×C4—612no—
845C22×C4—612no—
846C22×C4—612no—
847C22×C4—612no—
848C22×C4—612no—
849C22×C4—612no—
850C22×C4—612no—
851C22×C4—612no—
852C22×C4—612no—
853C22×C4—612no—
854C22×C4—612no—
855C22×C4—612no—
856C22×C4—612no—
857C22×C4—612no—
858C22×C4—612no—
859C22×C4—1221no—
860C22×C4—1221no—
861C22×C4—1221no—
862C22×C4—1221no—
863C22×C4—1221no—
864C22×C4—1221no—
865C22×C4—1221no—
866C22×C4—1221no—
867C22×C4—1221no—
868C22×C4—1221no—
869C22×C4—1221no—
870C22×C4—1221no—
871C22×C4—1221no—
872C22×C4—1221no—
873C22×C4—1221no—
874C22×C4—1221no—
875C22×C4—1221no—
876C22×C4—1221no—
877C22×C4—1221no—
878C22×C4—1221no—
879C22×C4—1221no—
880C22×C4—1221no—
881C22×C4—1221no—
882C22×C4—1221no—
883C22×C4—1221no—
884C22×C4—1221no—
885C22×C4—1221no—
886C22×C4—1221no—
887C22×C4—1221no—
888C22×C4—1221no—
889C22×C4—1221no—
890C22×C4—1221no—
891C22×C4—1221no—
892C22×C4C2×C4×D6112yes—
893C22×C4C2×C4×D6112yes—
894C22×C4D4×D6112yes—
895C22×C4D4×D6112yes—
896C22×C4D4×D6112yes—
897C22×C4D4×D6112yes—
898C22×C4#1175822412yes—
899C4⋊C4—28no—
900C4⋊C4—1228no—
901C4⋊C4—1228no—
902C4⋊C4—2444no—
903C22⋊C4—28no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—1228no—
907C22⋊C4—1228no—
908C22⋊C4—1228no—
909C22⋊C4—2444no—
910C22⋊C4—2444no—
911C22⋊C4—2444no—
912C22⋊C4—2444no—
913C22⋊C4—2444no—
914C22⋊C4—2444no—
915C42—1228no—
916C42—1228no—
917C42—1228no—
918C42—1228no—
919C42—2444no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—1222no—
956C23—1222no—
957C23—1222no—
958C23—1222no—
959C23—1222no—
960C23—1222no—
961C23—1222no—
962C23—2441no—
963C23—2441no—
964C23—2441no—
965C23—2441no—
966C23—2441no—
967C23—2441no—
968C23—2441no—
969C23—2441no—
970C23—2441no—
971C23—2441no—
972C23—2441no—
973C23—2441no—
974C23—2441no—
975C23—2441no—
976C23—2441no—
977C23—2441no—
978C23—2441no—
979C23—2441no—
980C23—2441no—
981C23—2441no—
982C23—2441no—
983C23—2441no—
984C23—2441no—
985C23—2441no—
986C23—2441no—
987C23—2441no—
988C23—2441no—
989C23—2441no—
990C23C22×C4×D6111yescharacteristic
991C23C2×D4×D6111yescharacteristic
992C23C2×D4×D6111yescharacteristic
993C23C2×D4×D6111yescharacteristic
994C23C2×D4×D6111yescharacteristic
995C23#41×D6111yescharacteristic
996C23#41×D6111yescharacteristic
997C23#41×D6111yescharacteristic
998C23#41×D6111yescharacteristic
999C23#41×D6111yescharacteristic
1000C23C2×#1175822411yescharacteristic
1001C23#1451982211yescharacteristic
1002C23#1451982211yescharacteristic
1003C23#1451982411yescharacteristic
1004C23#1451982511yescharacteristic
1005Q8—12232no—
1006D4—24416no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—614no—
1049C2×C4—614no—
1050C2×C4—614no—
1051C2×C4—614no—
1052C2×C4—614no—
1053C2×C4—614no—
1054C2×C4—614no—
1055C2×C4—614no—
1056C2×C4—614no—
1057C2×C4—1222no—
1058C2×C4—1222no—
1059C2×C4—1222no—
1060C2×C4—1222no—
1061C2×C4—1222no—
1062C2×C4—1222no—
1063C2×C4—1222no—
1064C2×C4—1222no—
1065C2×C4—1222no—
1066C2×C4—1222no—
1067C2×C4—1222no—
1068C2×C4—1222no—
1069C2×C4—1222no—
1070C2×C4—1222no—
1071C2×C4—1222no—
1072C2×C4—1222no—
1073C2×C4—1222no—
1074C2×C4—1222no—
1075C2×C4—1222no—
1076C2×C4—1222no—
1077C2×C4—1222no—
1078C2×C4—2441no—
1079C2×C4—2441no—
1080C2×C4—2441no—
1081C2×C4—2441no—
1082C2×C4—2441no—
1083C2×C4—2441no—
1084C2×C4—2441no—
1085C2×C4—2441no—
1086C2×C4—2441no—
1087C2×C4—2441no—
1088C2×C4—2441no—
1089C2×C4—2441no—
1090C2×C4—2441no—
1091C2×C4—2441no—
1092C2×C4—2441no—
1093C2×C4—2441no—
1094C2×C4—2441no—
1095C2×C4—2441no—
1096C2×C4—2441no—
1097C2×C4C22⋊C4×D6114yes—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22—81no—
1113C22—4881no—
1114C22—4881no—
1115C22—4881no—
1116C22—4881no—
1117C22—4881no—
1118C22—4881no—
1119C22—4881no—
1120C22—4881no—
1121C22—2442no—
1122C22—2442no—
1123C22—2442no—
1124C22—2442no—
1125C22—2442no—
1126C22—2442no—
1127C22—2442no—
1128C22C2×C22⋊C4×D6111yescharacteristic
1129C22C4×D4×D6111yescharacteristic
1130C22C4×D4×D6111yescharacteristic
1131C22C4×#1175822411yescharacteristic
1132C22#1684023011yescharacteristic
1133C22#1684024111yescharacteristic
1134C22#1684024311yescharacteristic
1135C22#120×D6111yescharacteristic
1136C22#121×D6111yescharacteristic
1137C22#121×D6111yescharacteristic
1138C22#123×D6111yescharacteristic
1139C22#124×D6111yescharacteristic
1140C22#1684028911yescharacteristic
1141C22#1684029511yescharacteristic
1142C22#1684030711yescharacteristic
1143C22#1684032711yescharacteristic
1144C22#1684033511yescharacteristic
1145C22#1684038011yescharacteristic
1146C22#1684038211yescharacteristic
1147C22#1684039911yescharacteristic
1148C22#1684040111yescharacteristic
1149C22#1684041811yescharacteristic
1150C22#1684042011yescharacteristic
1151C22#1684042011yescharacteristic
1152C22#1684042211yescharacteristic
1153C22#1684042211yescharacteristic
1154C22#1684042211yescharacteristic
1155C22#1684043011yescharacteristic
1156C22#1684043011yescharacteristic
1157C22#1684043011yescharacteristic
1158C22#1684043211yescharacteristic
1159C22#1684047911yescharacteristic
1160C22#1684048311yescharacteristic
1161C22#1684049611yescharacteristic
1162C22#1684049611yescharacteristic
1163C4—24no—
1164C4—42no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—81no—
1169C4—618no—
1170C4—1224no—
1171C4—1224no—
1172C4—4881no—
1173C4—2442no—
1174C4—2442no—
1175C4—2442no—
1176C2—82no—
1177C2—4882no—
1178C2#386×D6111yescharacteristic
1179C2#2144836011yescharacteristic
1180C2#2144852511yescharacteristic
1181C2#2144865611yescharacteristic
1182C2#2144865811yescharacteristic
1183C2#2144888511yescharacteristic
1184C2#2144888711yescharacteristic
1185C2#2144937811yescharacteristic
1186C2#2144938011yescharacteristic
1187C2#2144943311yescharacteristic
1188C2#2144947211yescharacteristic
1189C2#2144961011yescharacteristic
1190C2#2144961211yescharacteristic
1191C2#2145079411yescharacteristic
1192C2#2145081711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1439C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenter#1439D61
hypocenterC61#14026
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C22×#14519742C2semidirect
3. C2×#16839666C2semidirect
6. #21444063C2semidirect
7. #21444062C2semidirect
8. #21444061C2semidirect
9. #21444056C2semidirect
10. #21444056C2semidirect
11. #21444055C2semidirect
12. #21444055C2semidirect
13. #21444047C2semidirect
14. #95×Dic61C2semidirect
15. C61×#1439C2semidirect
20. C2×#14519763C4semidirect
301. C2×Dic122C22⋊C4semidirect
499. C2×Dic61#124semidirect
588. #1439D61semidirect
656. C61#14026semidirect

Maximal subgroups

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

subgroupindex
C22×#145197632
C22×#145197422
C2×#168396662
C2×#168396622
#214440632
#214440622
#214440612
#214440562
#214440552
#214440472
#95×Dic612
C61×#14392
#1402661