Finite Group Databasebeta

← #29602874

Subgroups — #29602874

Order 15616.

2690 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519737C211yesmaximal, characteristic
2C2×#16839638C211yesmaximal, characteristic
3C2×#16839638C211yesmaximal, characteristic
4C2×#16839637C211yesmaximal, characteristic, complemented
5C2×#16839636C211yesmaximal, characteristic, complemented
6C2×#16839619C211yesmaximal, characteristic, complemented
7C2×#95×D61C211yesmaximal, characteristic, complemented
8#21444083C211yesmaximal, characteristic, complemented
9#21444077C211yesmaximal, characteristic, complemented
10#21444062C211yesmaximal, characteristic, complemented
11#21444053C211yesmaximal, characteristic, complemented
12#21444051C211yesmaximal, characteristic, complemented
13#21444041C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C24×Dic61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C2×#14519737—24no—
22C2×#14519737—24no—
23C2×#14519737—24no—
24C22×C4⋊Dic61C2211yescharacteristic
25C22×C4⋊Dic61C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34#16839638—24no—
35#16839638C418yescomplemented
36#16839637—24no—
37#16839636—24no—
38#16839619—24no—
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52#95×D61—24no—
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×C22⋊D61—22no—
62C22×C22⋊D61—22no—
63C22×C22⋊D61—22no—
64C22×C22⋊D61—22no—
65C22×C22⋊D61C2×C414yes—
66C22×C22⋊D61D414yes—
67C22×C22⋊D61Q814yes—
68C23×Dic61—22no—
69C23×Dic61—22no—
70C23×Dic61—22no—
71C23×Dic61—22no—
72C23×Dic61—22no—
73C23×Dic61—41no—
74C23×Dic61—41no—
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C22×C4×D61—22no—
83C22×C4×D61—22no—
84C22×C4×D61—22no—
85C22×C4×D61—22no—
86C22×C4×D61—22no—
87C22×C4×D61—22no—
88C22×C4×D61—22no—
89C22×C4×D61—22no—
90C22×C4×D61—22no—
91C22×C4×D61—22no—
92C22×C4×D61—22no—
93C22×C4×D61—22no—
94C22×C4×D61—22no—
95C22×C4×D61—41no—
96C22×C4×D61—41no—
97C22×C4×D61—41no—
98C22×C4×D61—41no—
99C22×C4×D61—41no—
100C22×C4×D61—41no—
101C22×C4×D61C2×C414yescomplemented
102C22×C4×D61D414yes—
103#14519737—232no—
104C2×C4⋊Dic61—22no—
105C2×C4⋊Dic61—22no—
106C2×C4⋊Dic61—22no—
107C2×C4⋊Dic61—22no—
108C2×C4⋊Dic61—22no—
109C2×C4⋊Dic61—41no—
110C2×#11758196—22no—
111C2×#11758196—22no—
112C2×#11758196—22no—
113C2×#11758196—22no—
114C2×#11758196—41no—
115C2×#11758196—41no—
116C2×C22⋊Dic61—22no—
117C2×C22⋊Dic61—22no—
118C2×C22⋊Dic61—41no—
119C2×C22⋊Dic61—41no—
120C2×C22⋊Dic61—41no—
121C2×C22⋊Dic61C2×C414yescomplemented
122C2×#11758198—22no—
123C2×#11758198—22no—
124C2×#11758198—22no—
125C2×#11758198—22no—
126C2×#11758198—22no—
127C2×#11758198—22no—
128C2×#11758198—22no—
129C2×#11758198C2×C414yescomplemented
130C2×#11758198D414yes—
131C2×C4×Dic61—22no—
132C2×C4×Dic61—22no—
133C2×C4×Dic61—22no—
134#14519684—22no—
135#14519684—22no—
136#14519684—22no—
137#14519684—22no—
138#14519684—22no—
139#14519684—22no—
140#14519684—22no—
141#14519684—22no—
142#14519684—41no—
143#14519684—41no—
144#14519684C2×C414yescomplemented
145#14519684C2×C414yescomplemented
146#14519684D414yescomplemented
147C25×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149C23×C4×C61C2311yescharacteristic
150C23×C4×C61C2311yescharacteristic
151C23×C4×C61C2311yescharacteristic
152C23×C4×C61C2311yescharacteristic
153C23×C4×C61C2311yescharacteristic
154C2×C4⋊C4×C61—22no—
155C2×C4⋊C4×C61—22no—
156C2×C4⋊C4×C61—41no—
157C2×C22⋊C4×C61—22no—
158C2×C22⋊C4×C61—22no—
159C2×C22⋊C4×C61—22no—
160C2×C22⋊C4×C61—22no—
161C2×C22⋊C4×C61—22no—
162C2×C22⋊C4×C61—22no—
163C2×C22⋊C4×C61—22no—
164C2×C22⋊C4×C61—41no—
165C2×C22⋊C4×C61C2×C414yescomplemented
166#95×C61—22no—
167#95×C61—22no—
168#95×C61—22no—
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×C61—21no—
181C24×C61C22×C412yes—
182C24×C61C2×D412yes—
183C24×C61C2×Q812yes—
184C24×C61C2411yescharacteristic
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×D61C22×C412yes—
194C23×D61C2×D412yes—
195C23×D61C2×D412yes—
196C23×D61C2×D412yes—
197C23×D61C2×Q812yes—
198C23×D61#4112yes—
199C23×D61#4112yes—
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×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61C22×C412yes—
236C22×C4×C61C22×C412yes—
237C22×C4×C61C2×D412yes—
238C22×C4×C61C2×D412yes—
239C22×C4×C61C2×D412yes—
240C22×C4×C61#4112yes—
241C22×C4×C61#4112yes—
242C2×C22⋊D61—28no—
243C2×C22⋊D61—28no—
244C2×C22⋊D61—28no—
245C2×C22⋊D61—28no—
246C2×C22⋊D61—28no—
247C2×C22⋊D61—28no—
248C2×C22⋊D61C4⋊C4116yescomplemented
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—28no—
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×Dic61—21no—
280C22×Dic61—21no—
281C22×Dic61—21no—
282C22×Dic61—21no—
283C22×Dic61—21no—
284C22×Dic61—21no—
285C22×Dic61—21no—
286C22×Dic61—21no—
287C22×Dic61—21no—
288C22×Dic61—21no—
289C22×Dic61—44no—
290C22×Dic61—44no—
291C22×Dic61—44no—
292C22×Dic61—44no—
293C22×Dic61—44no—
294C22×Dic61—44no—
295C22×Dic61C22×C412yes—
296C22×Dic61C22×C412yes—
297C22×Dic61C22×C412yes—
298C22×Dic61C2×D412yes—
299C22×Dic61C2×D412yes—
300C22×Dic61C2×D412yes—
301C22×Dic61C2×D412yes—
302C22×Dic61C2×D412yes—
303C22×Dic61C2×Q812yes—
304C22×Dic61#4112yes—
305C2×C4×D61—28no—
306C2×C4×D61—28no—
307C2×C4×D61—28no—
308C2×C4×D61—28no—
309C2×C4×D61—28no—
310C2×C4×D61—44no—
311C2×C4×D61—44no—
312C2×C4×D61—44no—
313C2×C4×D61—44no—
314C2×C4×D61—44no—
315C2×C4×D61—44no—
316C2×C4×D61—44no—
317C2×C4×D61—44no—
318C2×C4×D61—44no—
319C2×C4×D61—44no—
320C2×C4×D61—44no—
321C2×C4×D61—44no—
322C2×C4×D61—44no—
323C2×C4×D61—44no—
324C2×C4×D61—44no—
325C2×C4×D61—44no—
326C4⋊C4×C61—44no—
327C22⋊C4×C61—28no—
328C22⋊C4×C61—28no—
329C22⋊C4×C61—44no—
330C22⋊Dic61—44no—
331C22⋊Dic61—44no—
332#11758198—28no—
333#11758198—28no—
334#11758198—44no—
335C4⋊Dic61—44no—
336C4⋊Dic61—44no—
337#11758196—28no—
338#11758196—44no—
339C4×Dic61—28no—
340C23×C61—22no—
341C23×C61—22no—
342C23×C61—22no—
343C23×C61—22no—
344C23×C61—22no—
345C23×C61—22no—
346C23×C61—22no—
347C23×C61—22no—
348C23×C61—22no—
349C23×C61—22no—
350C23×C61—22no—
351C23×C61—22no—
352C23×C61—22no—
353C23×C61—22no—
354C23×C61—22no—
355C23×C61—22no—
356C23×C61—22no—
357C23×C61—22no—
358C23×C61—41no—
359C23×C61—41no—
360C23×C61—41no—
361C23×C61—41no—
362C23×C61—41no—
363C23×C61—41no—
364C23×C61—41no—
365C23×C61—41no—
366C23×C61—41no—
367C23×C61—41no—
368C23×C61—41no—
369C23×C61—41no—
370C23×C61—41no—
371C23×C61—41no—
372C23×C61—41no—
373C23×C61—41no—
374C23×C61C2×C4⋊C414yes—
375C23×C61C23×C411yescharacteristic
376C23×C61C22×D411yescharacteristic
377C23×C61C22×D411yescharacteristic
378C23×C61C22×D411yescharacteristic
379C23×C61C22×D411yescharacteristic
380C23×C61C22×Q811yescharacteristic
381C23×C61C2×#4111yescharacteristic
382C23×C61C2×#4111yescharacteristic
383C23×C61C2×#4111yescharacteristic
384C23×C61C2×#4111yescharacteristic
385C23×C61C2×#4111yescharacteristic
386C23×C61H(5,𝔽2)11yescharacteristic
387C23×C61H(5,𝔽2)11yescharacteristic
388C23×C61H(5,𝔽2)11yescharacteristic
389C23×C612−1+411yescharacteristic
390C22×D61—22no—
391C22×D61—22no—
392C22×D61—22no—
393C22×D61—22no—
394C22×D61—22no—
395C22×D61—22no—
396C22×D61—22no—
397C22×D61—22no—
398C22×D61—22no—
399C22×D61—22no—
400C22×D61—22no—
401C22×D61—22no—
402C22×D61—22no—
403C22×D61—22no—
404C22×D61—22no—
405C22×D61—22no—
406C22×D61—22no—
407C22×D61—22no—
408C22×D61—22no—
409C22×D61—22no—
410C22×D61—22no—
411C22×D61—22no—
412C22×D61—22no—
413C22×D61—22no—
414C22×D61—22no—
415C22×D61—22no—
416C22×D61—22no—
417C22×D61—22no—
418C22×D61C2×C4⋊C414yes—
419C22×D61C4×D414yes—
420C22×D61C4×D414yes—
421C22×D61#12014yes—
422C22×D61C22⋊Q814yes—
423C22×D61C22⋊Q814yes—
424C22×D61#12314yes—
425C2×C4×C61—22no—
426C2×C4×C61—22no—
427C2×C4×C61—22no—
428C2×C4×C61—22no—
429C2×C4×C61—22no—
430C2×C4×C61—22no—
431C2×C4×C61—22no—
432C2×C4×C61—22no—
433C2×C4×C61—22no—
434C2×C4×C61—22no—
435C2×C4×C61—22no—
436C2×C4×C61—22no—
437C2×C4×C61—22no—
438C2×C4×C61—22no—
439C2×C4×C61—22no—
440C2×C4×C61—22no—
441C2×C4×C61—22no—
442C2×C4×C61—22no—
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×C61—41no—
450C2×C4×C61—41no—
451C2×C4×C61—41no—
452C2×C4×C61—41no—
453C2×C4×C61—41no—
454C2×C4×C61—41no—
455C2×C4×C61—41no—
456C2×C4×C61—41no—
457C2×C4×C61—41no—
458C2×C4×C61—41no—
459C2×C4×C61—41no—
460C2×C4×C61—41no—
461C2×C4×C61—41no—
462C2×C4×C61—41no—
463C2×C4×C61—41no—
464C2×C4×C61—41no—
465C2×C4×C61—41no—
466C2×C4×C61C4×D414yescomplemented
467C22⋊D61—232no—
468C2×Dic61—22no—
469C2×Dic61—22no—
470C2×Dic61—22no—
471C2×Dic61—22no—
472C2×Dic61—22no—
473C2×Dic61—22no—
474C2×Dic61—22no—
475C2×Dic61—22no—
476C2×Dic61—22no—
477C2×Dic61—22no—
478C2×Dic61—22no—
479C2×Dic61—22no—
480C2×Dic61—22no—
481C2×Dic61—22no—
482C2×Dic61—22no—
483C2×Dic61—22no—
484C2×Dic61—22no—
485C2×Dic61—22no—
486C2×Dic61—22no—
487C2×Dic61—22no—
488C2×Dic61—22no—
489C2×Dic61—22no—
490C2×Dic61—22no—
491C2×Dic61—22no—
492C2×Dic61—416no—
493C2×Dic61—41no—
494C2×Dic61—41no—
495C2×Dic61—41no—
496C2×Dic61—41no—
497C2×Dic61—41no—
498C2×Dic61—41no—
499C2×Dic61—41no—
500C2×Dic61—41no—
501C2×Dic61—41no—
502C2×Dic61—41no—
503C2×Dic61—41no—
504C2×Dic61—41no—
505C2×Dic61—41no—
506C2×Dic61—41no—
507C2×Dic61—41no—
508C2×Dic61—41no—
509C2×Dic61—41no—
510C2×Dic61—41no—
511C2×Dic61—41no—
512C2×Dic61—41no—
513C2×Dic61—41no—
514C2×Dic61—41no—
515C2×Dic61—41no—
516C2×Dic61C2×C4⋊C414yes—
517C2×Dic61#12114yes—
518C4×D61—416no—
519C4×D61—416no—
520C4×D61—416no—
521#13975—611nomaximal, Sylow
522C22×C61—24no—
523C22×C61—24no—
524C22×C61—24no—
525C22×C61—42no—
526C22×C61—42no—
527C22×C61—42no—
528C22×C61—42no—
529C22×C61—42no—
530C22×C61—42no—
531C22×C61—42no—
532C22×C61—42no—
533C22×C61—42no—
534C22×C61—42no—
535C22×C61—42no—
536C22×C61—42no—
537C22×C61C22×C4⋊C411yescharacteristic
538C22×C61C2×C4×D411yescharacteristic
539C22×C61C2×C4×D411yescharacteristic
540C22×C61C2×C4×D411yescharacteristic
541C22×C61C4×#4111yescharacteristic
542C22×C61#51811yescharacteristic
543C22×C61#52011yescharacteristic
544C22×C61C2×#12011yescharacteristic
545C22×C61C2×#12111yescharacteristic
546C22×C61C2×C22⋊Q811yescharacteristic
547C22×C61C2×C22⋊Q811yescharacteristic
548C22×C61C2×#12311yescharacteristic
549C22×C61#52511yescharacteristic
550C22×C61#52911yescharacteristic
551C22×C61#53211yescharacteristic
552C22×C61#53411yescharacteristic
553C22×C61#53711yescharacteristic
554C22×C61#53811yescharacteristic
555C22×C61#53911yescharacteristic
556C22×C61D4211yescharacteristic
557C22×C61D4211yescharacteristic
558C22×C61#54611yescharacteristic
559C22×C61#54611yescharacteristic
560C22×C61#54611yescharacteristic
561C22×C61#54611yescharacteristic
562C22×C61#54611yescharacteristic
563C22×C61#54711yescharacteristic
564C22×C61#54711yescharacteristic
565C22×C61D4×Q811yescharacteristic
566C22×C61#55111yescharacteristic
567C22×C61#55111yescharacteristic
568C22×C61#55211yescharacteristic
569C22×C61#55411yescharacteristic
570C22×C61#55411yescharacteristic
571C22×C61#55411yescharacteristic
572C2×D61—24no—
573C2×D61—24no—
574C2×D61—24no—
575C2×D61—24no—
576C2×D61—24no—
577C2×D61—24no—
578C2×D61—24no—
579C2×D61—24no—
580C2×D61—24no—
581C2×D61—24no—
582C2×D61—24no—
583C2×D61—24no—
584C2×D61—24no—
585C2×D61—24no—
586C2×D61#38518yescomplemented
587C4×C61—24no—
588C4×C61—42no—
589C4×C61—42no—
590C4×C61—42no—
591C4×C61—42no—
592C4×C61—81no—
593Dic61—24no—
594Dic61—24no—
595Dic61—42no—
596Dic61—42no—
597Dic61—42no—
598Dic61—42no—
599Dic61—81no—
600C22×C4×D4—611no—
601C2×#386—611no—
602C2×#386—611no—
603C2×#385—611no—
604C2×#385—611no—
605C2×#380—611no—
606C22×#95—611no—
607#1444—611no—
608#1442—611no—
609#1439—611no—
610#1439D6111yescharacteristic, complemented
611#1436—611no—
612#1436—611no—
613C22⋊#95—611no—
614C22⋊#95—611no—
615C2×C61—44no—
616C2×C61C2×#38511yescharacteristic
617C2×C61C4×#12111yescharacteristic
618C2×C61#232511yescharacteristic
619C2×C61D4×C4⋊C411yescharacteristic
620C2×C61#234911yescharacteristic
621C2×C61#235811yescharacteristic
622C2×C61#235911yescharacteristic
623C2×C61#241011yescharacteristic
624C2×C61#241711yescharacteristic
625C2×C61#241811yescharacteristic
626C2×C61#241911yescharacteristic
627C2×C61#243011yescharacteristic
628C2×C61#244911yescharacteristic
629C2×C61#245011yescharacteristic
630C2×C61#256411yescharacteristic
631D61—28no—
632C23×D4—611no—
633C24×C4—611no—
634C24×C4—611no—
635C24×C4—611no—
636C24×C4—611no—
637C2×C4×D4—1224no—
638C2×C4×D4—1224no—
639C2×C4×D4—1224no—
640C22×C4⋊C4—611no—
641C22×C4⋊C4—611no—
642C22×C4⋊C4—611no—
643C22×C4⋊C4—611no—
644C22×C4⋊C4C2×D6111yescharacteristic
645C22×C22⋊C4—611no—
646C22×C22⋊C4—611no—
647C22×C22⋊C4—611no—
648C22×C22⋊C4—611no—
649C22×C22⋊C4—611no—
650C22×C22⋊C4C2×D6111yescharacteristic
651C22×C22⋊C4C2×D6111yescharacteristic
652C22×C22⋊C4C2×D6111yescharacteristic
653C22×C42—611no—
654#386—618no—
655#386—1224no—
656#385—1224no—
657#385—1224no—
658#380—1224no—
659C2×#95—611no—
660C2×#95—611no—
661C2×#95—611no—
662C2×#95—611no—
663C2×#95—611no—
664C2×#95—611no—
665C2×#95—611no—
666C2×#95—611no—
667C2×#95—611no—
668C2×#95—611no—
669C2×#95—611no—
670C2×#95—611no—
671C2×#95—611no—
672C2×#95—1224no—
673C2×#95C2×D6111yescharacteristic
674C2×#95C2×D6111yescharacteristic
675C2×#95C2×D6111yescharacteristic
676C61#1397511yescharacteristic, complemented, Sylow
677C25—611no—
678C25C22×D6111yescharacteristic
679C22×D4—614no—
680C22×D4—614no—
681C22×D4—614no—
682C22×D4—1222no—
683C22×D4—1222no—
684C22×D4—1222no—
685C22×D4—1222no—
686C23×C4—611no—
687C23×C4—611no—
688C23×C4—611no—
689C23×C4—611no—
690C23×C4—611no—
691C23×C4—611no—
692C23×C4—614no—
693C23×C4—614no—
694C23×C4—611no—
695C23×C4—1222no—
696C23×C4—1222no—
697C23×C4—1222no—
698C23×C4—1222no—
699C23×C4—1222no—
700C23×C4—1222no—
701C23×C4—1222no—
702C23×C4—1222no—
703C23×C4—1222no—
704C23×C4—1222no—
705C23×C4—1222no—
706C23×C4—1222no—
707C23×C4—1222no—
708C23×C4—1222no—
709C23×C4—1222no—
710C23×C4—1222no—
711C23×C4—1222no—
712C23×C4—1222no—
713C23×C4—2441no—
714C23×C4—2441no—
715C23×C4—2441no—
716C23×C4—2441no—
717C23×C4—2441no—
718C23×C4—2441no—
719C23×C4—2441no—
720C23×C4—2441no—
721C23×C4C22×D6111yescharacteristic
722C23×C4C22×D6111yescharacteristic
723C23×C4C22×D6111yescharacteristic
724C23×C4C22×D6111yescharacteristic
725C23×C4C22×D6111yescharacteristic
726C23×C4C22×D6111yescharacteristic
727C4×D4—12232no—
728C2×C4⋊C4—22no—
729C2×C4⋊C4—22no—
730C2×C4⋊C4—41no—
731C2×C4⋊C4—1222no—
732C2×C4⋊C4—1222no—
733C2×C4⋊C4—1222no—
734C2×C4⋊C4—1222no—
735C2×C4⋊C4—1222no—
736C2×C4⋊C4—1222no—
737C2×C4⋊C4—1222no—
738C2×C4⋊C4—1222no—
739C2×C4⋊C4—1222no—
740C2×C4⋊C4—2441no—
741C2×C4⋊C4—2441no—
742C2×C4⋊C4—2441no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—22no—
748C2×C22⋊C4—22no—
749C2×C22⋊C4—22no—
750C2×C22⋊C4—41no—
751C2×C22⋊C4—614no—
752C2×C22⋊C4—614no—
753C2×C22⋊C4—614no—
754C2×C22⋊C4—1222no—
755C2×C22⋊C4—1222no—
756C2×C22⋊C4—1222no—
757C2×C22⋊C4—1222no—
758C2×C22⋊C4—1222no—
759C2×C22⋊C4—1222no—
760C2×C22⋊C4—1222no—
761C2×C22⋊C4—1222no—
762C2×C22⋊C4—1222no—
763C2×C22⋊C4—2441no—
764C2×C22⋊C4—2441no—
765C2×C22⋊C4—2441no—
766C2×C22⋊C4C4×D6114yescomplemented
767C2×C42—1222no—
768C2×C42—1222no—
769C2×C42—1222no—
770#95—22no—
771#95—22no—
772#95—22no—
773#95—614no—
774#95—614no—
775#95—614no—
776#95—1222no—
777#95—1222no—
778#95—1222no—
779#95—1222no—
780#95—1222no—
781#95—1222no—
782#95—1222no—
783#95—1222no—
784#95—2441no—
785#95—2441no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—612no—
799C24—612no—
800C24—612no—
801C24—612no—
802C24—612no—
803C24—612no—
804C24—612no—
805C24—1221no—
806C24—1221no—
807C24—1221no—
808C24—1221no—
809C24—1221no—
810C24—1221no—
811C24—1221no—
812C24—1221no—
813C24C2×C4×D6112yes—
814C24D4×D6112yes—
815C24Q8×D6112yes—
816C24C23×D6111yescharacteristic
817C2×D4—6116no—
818C2×D4—1228no—
819C2×D4—1228no—
820C2×D4—1228no—
821C2×D4—1228no—
822C2×D4—1228no—
823C2×D4—1228no—
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—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—612no—
860C22×C4—612no—
861C22×C4—612no—
862C22×C4—612no—
863C22×C4—612no—
864C22×C4—612no—
865C22×C4—612no—
866C22×C4—612no—
867C22×C4—612no—
868C22×C4—612no—
869C22×C4—1228no—
870C22×C4—1228no—
871C22×C4—1228no—
872C22×C4—1228no—
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—1228no—
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×C4—1221no—
893C22×C4—1221no—
894C22×C4—1221no—
895C22×C4—1221no—
896C22×C4—1221no—
897C22×C4—1221no—
898C22×C4—1221no—
899C22×C4—1221no—
900C22×C4—1221no—
901C22×C4—1221no—
902C22×C4—1221no—
903C22×C4—1221no—
904C22×C4—1221no—
905C22×C4—1221no—
906C22×C4—1228no—
907C22×C4—1221no—
908C22×C4—1221no—
909C22×C4—1221no—
910C22×C4—1221no—
911C22×C4—1221no—
912C22×C4—1221no—
913C22×C4—1221no—
914C22×C4—2444no—
915C22×C4—2444no—
916C22×C4—2444no—
917C22×C4—2444no—
918C22×C4—2444no—
919C22×C4—2444no—
920C22×C4—2444no—
921C22×C4—2444no—
922C22×C4—2444no—
923C22×C4—2444no—
924C22×C4—2444no—
925C22×C4—2444no—
926C22×C4—2444no—
927C22×C4—2444no—
928C22×C4—2444no—
929C22×C4—2444no—
930C22×C4—2444no—
931C22×C4—2444no—
932C22×C4—2444no—
933C22×C4—2444no—
934C22×C4—2444no—
935C22×C4—2444no—
936C22×C4C2×C4×D6112yes—
937C22×C4C2×C4×D6112yes—
938C22×C4D4×D6112yes—
939C22×C4D4×D6112yes—
940C22×C4D4×D6112yes—
941C22×C4#1175822412yes—
942C22×C4#1175822412yes—
943C4⋊C4—44no—
944C4⋊C4—1228no—
945C4⋊C4—2444no—
946C4⋊C4—2444no—
947C4⋊C4—2444no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—44no—
951C22⋊C4—1228no—
952C22⋊C4—1228no—
953C22⋊C4—2444no—
954C22⋊C4—2444no—
955C22⋊C4—2444no—
956C42—1228no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—614no—
992C23—614no—
993C23—614no—
994C23—614no—
995C23—614no—
996C23—614no—
997C23—614no—
998C23—1222no—
999C23—1222no—
1000C23—1222no—
1001C23—1222no—
1002C23—1222no—
1003C23—1222no—
1004C23—1222no—
1005C23—1222no—
1006C23—1222no—
1007C23—1222no—
1008C23—1222no—
1009C23—1222no—
1010C23—1222no—
1011C23—1222no—
1012C23—1222no—
1013C23—1222no—
1014C23—1222no—
1015C23—1222no—
1016C23—1222no—
1017C23—1222no—
1018C23—1222no—
1019C23—1222no—
1020C23—1222no—
1021C23—1222no—
1022C23—1222no—
1023C23—1222no—
1024C23—1222no—
1025C23—1222no—
1026C23C4⋊C4×D6114yes—
1027C23C22×C4×D6111yescharacteristic
1028C23C2×D4×D6111yescharacteristic
1029C23C2×D4×D6111yescharacteristic
1030C23C2×D4×D6111yescharacteristic
1031C23C2×D4×D6111yescharacteristic
1032C23C2×Q8×D6111yescharacteristic
1033C23#41×D6111yescharacteristic
1034C23#41×D6111yescharacteristic
1035C23#41×D6111yescharacteristic
1036C23C2×#1175822411yescharacteristic
1037C23C2×#1175822411yescharacteristic
1038C23#1451982211yescharacteristic
1039C23#1451982311yescharacteristic
1040C23#1451982311yescharacteristic
1041C23#1451982411yescharacteristic
1042D4—12232no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—614no—
1085C2×C4—614no—
1086C2×C4—1222no—
1087C2×C4—1222no—
1088C2×C4—1222no—
1089C2×C4—1222no—
1090C2×C4—1222no—
1091C2×C4—1222no—
1092C2×C4—1222no—
1093C2×C4—1222no—
1094C2×C4—1222no—
1095C2×C4—1222no—
1096C2×C4—1222no—
1097C2×C4—1222no—
1098C2×C4—1222no—
1099C2×C4—1222no—
1100C2×C4—1222no—
1101C2×C4—1222no—
1102C2×C4—1222no—
1103C2×C4—1222no—
1104C2×C4—1222no—
1105C2×C4—1222no—
1106C2×C4—1222no—
1107C2×C4—1222no—
1108C2×C4—1222no—
1109C2×C4—1222no—
1110C2×C4—24416no—
1111C2×C4—24416no—
1112C2×C4—24416no—
1113C2×C4—24416no—
1114C2×C4—2441no—
1115C2×C4—2441no—
1116C2×C4—2441no—
1117C2×C4—2441no—
1118C2×C4—2441no—
1119C2×C4—2441no—
1120C2×C4—2441no—
1121C2×C4—2441no—
1122C2×C4—2441no—
1123C2×C4—2441no—
1124C2×C4—2441no—
1125C2×C4—2441no—
1126C2×C4—2441no—
1127C2×C4—2441no—
1128C2×C4—2441no—
1129C2×C4—2441no—
1130C2×C4—2441no—
1131C2×C4—2441no—
1132C2×C4—2441no—
1133C2×C4—2441no—
1134C2×C4—2441no—
1135C2×C4—2441no—
1136C2×C4—2441no—
1137C2×C4#1451973714yescomplemented
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—42no—
1148C22—42no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—618no—
1154C22—1224no—
1155C22—1224no—
1156C22—1224no—
1157C22—1224no—
1158C22—1224no—
1159C22—1224no—
1160C22—1224no—
1161C22—1224no—
1162C22—1224no—
1163C22—1224no—
1164C22—1224no—
1165C22—1224no—
1166C22—1224no—
1167C22—1224no—
1168C22C2×C4⋊C4×D6111yescharacteristic
1169C22C4×D4×D6111yescharacteristic
1170C22C4×D4×D6111yescharacteristic
1171C22C2×#1451973711yescharacteristic
1172C22C4×#1175822411yescharacteristic
1173C22#1684023411yescharacteristic
1174C22#1684024211yescharacteristic
1175C22#120×D6111yescharacteristic
1176C22#121×D6111yescharacteristic
1177C22C22⋊Q8×D6111yescharacteristic
1178C22C22⋊Q8×D6111yescharacteristic
1179C22#123×D6111yescharacteristic
1180C22#1684027211yescharacteristic
1181C22#1684029111yescharacteristic
1182C22#1684031011yescharacteristic
1183C22#1684032311yescharacteristic
1184C22#1684034111yescharacteristic
1185C22#1684034611yescharacteristic
1186C22#1684035311yescharacteristic
1187C22#1684039611yescharacteristic
1188C22#1684039611yescharacteristic
1189C22#1684039911yescharacteristic
1190C22#1684039911yescharacteristic
1191C22#1684040111yescharacteristic
1192C22#1684040411yescharacteristic
1193C22#1684040511yescharacteristic
1194C22#1684041211yescharacteristic
1195C22#1684041211yescharacteristic
1196C22#1684042511yescharacteristic
1197C22#1684043511yescharacteristic
1198C22#1684043511yescharacteristic
1199C22#1684044811yescharacteristic
1200C22#1684046611yescharacteristic
1201C22#1684047011yescharacteristic
1202C22#1684047011yescharacteristic
1203C4—24no—
1204C4—42no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—81no—
1209C4—1224no—
1210C4—1224no—
1211C4—4881no—
1212C4—2442no—
1213C4—2442no—
1214C4—2442no—
1215C4—2442no—
1216C2—44no—
1217C2—1228no—
1218C2#385×D6111yescharacteristic
1219C2#2144833511yescharacteristic
1220C2#2144852311yescharacteristic
1221C2#2144871511yescharacteristic
1222C2#2144872511yescharacteristic
1223C2#2144879911yescharacteristic
1224C2#2144881011yescharacteristic
1225C2#2144918811yescharacteristic
1226C2#2144926311yescharacteristic
1227C2#2144927611yescharacteristic
1228C2#2144928911yescharacteristic
1229C2#2144942211yescharacteristic
1230C2#2144962911yescharacteristic
1231C2#2144963611yescharacteristic
1232C2#2145099411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1439C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenter#1439D61
hypocenterC61#13975
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
4. C2×#16839637C2semidirect
5. C2×#16839636C2semidirect
6. C2×#16839619C2semidirect
7. C2×#95×D61C2semidirect
8. #21444083C2semidirect
9. #21444077C2semidirect
10. #21444062C2semidirect
11. #21444053C2semidirect
12. #21444051C2semidirect
13. #21444041C2semidirect
14. #21444040C2semidirect
15. C61×#1439C2semidirect
35. #16839638C4semidirect
101. C22×C4×D61C2×C4semidirect
121. C2×C22⋊Dic61C2×C4semidirect
129. C2×#11758198C2×C4semidirect
144. #14519684C2×C4semidirect
145. #14519684C2×C4semidirect
146. #14519684D4semidirect
165. C2×C22⋊C4×C61C2×C4semidirect
248. C2×C22⋊D61C4⋊C4semidirect
466. C2×C4×C61C4×D4semidirect
586. C2×D61#385semidirect
610. #1439D61semidirect
676. C61#13975semidirect
766. C2×C22⋊C4C4×D61semidirect
1137. C2×C4#14519737semidirect

Maximal subgroups

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

subgroupindex
C22×#145197372
C2×#168396382
C2×#168396372
C2×#168396362
C2×#168396192
C2×#95×D612
#214440832
#214440772
#214440622
#214440532
#214440512
#214440412
#214440402
C61×#14392
#1397561