Finite Group Databasebeta

← #29601973

Subgroups — #29601973

Order 15616.

4046 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11758198C211yesmaximal, characteristic
2C22×C22⋊C4×D61C211yesmaximal, characteristic
3C2×#16839635C211yesmaximal, characteristic, complemented
4C2×#16839634C211yesmaximal, characteristic, complemented
5C2×#16839621C212yesmaximal, complemented
6C2×#16839617C211yesmaximal, characteristic
7#21444063C212yesmaximal, complemented
8#21444063C212yesmaximal, complemented
9#21444041C211yesmaximal, characteristic, complemented
10#21444040C212yesmaximal, complemented
11C61×C22⋊#95C211yesmaximal, characteristic, complemented
12C25×D61C2211yescharacteristic
13C24×Dic61C2211yescharacteristic
14C23×C4×D61C2212yes—
15C22×#11758196C2212yescomplemented
16C22×#11758196C2212yescomplemented
17C22×C22⋊Dic61C2211yescharacteristic
18C22×C22⋊Dic61C2211yescharacteristic
19C22×#11758198—28no—
20C22×#11758198—24no—
21C22×#11758198C2212yes—
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2212yes—
25C22×#11758198C2212yes—
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C2×C22⋊C4×D61—24no—
29C2×C22⋊C4×D61—24no—
30C2×C22⋊C4×D61C418yescomplemented
31#16839635—24no—
32#16839634—24no—
33#16839621—28no—
34#16839617—24no—
35C2×#14519684C2212yescomplemented
36C2×#14519684C2212yescomplemented
37C2×#14519684C2212yescomplemented
38C2×#14519684C2212yescomplemented
39C24×C4×C61C2211yescharacteristic
40C22×C22⋊C4×C61C2211yescharacteristic
41C22×C22⋊C4×C61C2211yescharacteristic
42C2×#95×C61C2212yescomplemented
43C2×#95×C61C2212yescomplemented
44C24×D61—22no—
45C24×D61—22no—
46C24×D61—22no—
47C24×D61—22no—
48C24×D61—24no—
49C24×D61—24no—
50C24×D61—42no—
51C24×D61—42no—
52C24×D61C2×C414yes—
53C24×D61D414yes—
54C24×D61Q814yes—
55C24×D61C2311yescharacteristic
56C24×D61C2311yescharacteristic
57C23×Dic61—22no—
58C23×Dic61—24no—
59C23×Dic61—22no—
60C23×Dic61—22no—
61C23×Dic61—42no—
62C23×Dic61C2311yescharacteristic
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2312yes—
65C23×Dic61C2312yes—
66C22×C4×D61—24no—
67C22×C4×D61—24no—
68C22×C4×D61—24no—
69C22×C4×D61—24no—
70C22×C4×D61—42no—
71C22×C4×D61—42no—
72C22×C4×D61C2×C418yescomplemented
73C2×#11758196—24no—
74C2×#11758196—24no—
75C2×#11758196—24no—
76C2×#11758196—24no—
77C2×#11758196—42no—
78C2×#11758196—42no—
79C2×C22⋊Dic61—22no—
80C2×C22⋊Dic61—22no—
81C2×C22⋊Dic61—22no—
82C2×C22⋊Dic61C2×C414yes—
83C2×C22⋊Dic61D414yes—
84C2×C22⋊Dic61D414yes—
85C2×#11758198—232no—
86C2×#11758198—24no—
87C2×#11758198—24no—
88C2×#11758198—24no—
89C2×#11758198—24no—
90C2×#11758198—24no—
91C2×#11758198—24no—
92C2×#11758198—24no—
93C2×#11758198—22no—
94C2×#11758198—22no—
95C2×#11758198—22no—
96C2×#11758198—22no—
97C2×#11758198—24no—
98C2×#11758198—24no—
99C2×#11758198—42no—
100C2×#11758198—42no—
101C2×#11758198C2×C418yescomplemented
102C2×#11758198D418yes—
103C22⋊C4×D61—232no—
104#14519684—24no—
105#14519684—24no—
106#14519684—24no—
107#14519684—42no—
108C25×C61C2311yescharacteristic
109C23×C4×C61—22no—
110C23×C4×C61—24no—
111C23×C4×C61—22no—
112C23×C4×C61—22no—
113C23×C4×C61—42no—
114C23×C4×C61C2311yescharacteristic
115C23×C4×C61C2311yescharacteristic
116C23×C4×C61C2312yes—
117C23×C4×C61C2312yes—
118C2×C22⋊C4×C61—22no—
119C2×C22⋊C4×C61—22no—
120C2×C22⋊C4×C61—22no—
121C2×C22⋊C4×C61—22no—
122C2×C22⋊C4×C61—22no—
123C2×C22⋊C4×C61C2×C414yes—
124#95×C61—24no—
125#95×C61—42no—
126C24×C61—22no—
127C24×C61—22no—
128C24×C61—22no—
129C24×C61—22no—
130C24×C61C22×C412yes—
131C24×C61C2×D412yes—
132C24×C61C2×D412yes—
133C24×C61C2×D412yes—
134C24×C61C2×Q812yes—
135C24×C61#4112yes—
136C24×C61#4112yes—
137C24×C61C2411yescharacteristic
138C23×D61—21no—
139C23×D61—21no—
140C23×D61—21no—
141C23×D61—21no—
142C23×D61—22no—
143C23×D61—22no—
144C23×D61—28no—
145C23×D61—28no—
146C23×D61—28no—
147C23×D61—28no—
148C23×D61—28no—
149C23×D61—28no—
150C23×D61—21no—
151C23×D61—21no—
152C23×D61—22no—
153C23×D61—21no—
154C23×D61—21no—
155C23×D61—22no—
156C23×D61—22no—
157C23×D61—22no—
158C23×D61—216no—
159C23×D61—28no—
160C23×D61—216no—
161C23×D61—28no—
162C23×D61—48no—
163C23×D61—44no—
164C23×D61—44no—
165C23×D61—48no—
166C23×D61—48no—
167C23×D61—48no—
168C23×D61—48no—
169C23×D61—48no—
170C23×D61—48no—
171C23×D61—48no—
172C23×D61—48no—
173C23×D61—48no—
174C23×D61C4⋊C4116yescomplemented
175C23×D61C22×C412yes—
176C23×D61C22×C412yes—
177C23×D61C2×D412yes—
178C23×D61C2×D412yes—
179C23×D61C2×D414yes—
180C23×D61C2×Q812yes—
181C23×D61C2×Q812yes—
182C23×D61#4114yes—
183C22×C4×C61—28no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61—22no—
193C22×C4×C61—22no—
194C22×C4×C61—22no—
195C22×C4×C61—22no—
196C22×C4×C61—22no—
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—22no—
204C22×C4×C61—22no—
205C22×C4×C61—22no—
206C22×C4×C61—48no—
207C22×C4×C61—48no—
208C22×C4×C61—44no—
209C22×C4×C61—44no—
210C22×C4×C61C22×C414yes—
211C22×C4×C61C2×D414yes—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—28no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—22no—
220C22×Dic61—22no—
221C22×Dic61—22no—
222C22×Dic61—22no—
223C22×Dic61—21no—
224C22×Dic61—22no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—22no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—22no—
232C22×Dic61—22no—
233C22×Dic61—48no—
234C22×Dic61—48no—
235C22×Dic61—44no—
236C22×Dic61—44no—
237C22×Dic61C22×C414yes—
238C22×Dic61C2×D414yes—
239C22×Dic61C2×D414yes—
240C22×Dic61C2×D414yes—
241C2×C4×D61—216no—
242C2×C4×D61—216no—
243C2×C4×D61—48no—
244C2×C4×D61—48no—
245C2×C4×D61—48no—
246C2×C4×D61—48no—
247C2×C4×D61—48no—
248C22⋊C4×C61—28no—
249C22⋊C4×C61—44no—
250C22⋊Dic61—44no—
251C22⋊Dic61C22⋊C4116yescomplemented
252#11758198—216no—
253#11758198—216no—
254#11758198—216no—
255#11758198—44no—
256#11758198—44no—
257#11758198—44no—
258#11758198—44no—
259#11758196—48no—
260#11758196—48no—
261C23×C61—24no—
262C23×C61—24no—
263C23×C61—22no—
264C23×C61—24no—
265C23×C61—22no—
266C23×C61—22no—
267C23×C61—22no—
268C23×C61—24no—
269C23×C61—24no—
270C23×C61—24no—
271C23×C61—24no—
272C23×C61—24no—
273C23×C61—24no—
274C23×C61—24no—
275C23×C61—24no—
276C23×C61—24no—
277C23×C61C2×C22⋊C414yes—
278C23×C61C2×C4⋊C414yes—
279C23×C61#11714yes—
280C23×C61#12114yes—
281C23×C61#12114yes—
282C23×C61C22⋊Q814yes—
283C23×C61C22⋊Q814yes—
284C23×C61C23×C411yescharacteristic
285C23×C61C22×D411yescharacteristic
286C23×C61C22×D411yescharacteristic
287C23×C61C22×D411yescharacteristic
288C23×C61C22×D412yes—
289C23×C61C22×Q811yescharacteristic
290C23×C61C2×#4111yescharacteristic
291C23×C61C2×#4111yescharacteristic
292C23×C61C2×#4112yes—
293C23×C61H(5,𝔽2)12yes—
294C23×C61H(5,𝔽2)12yes—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—24no—
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—22no—
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—24no—
305C22×D61—24no—
306C22×D61—24no—
307C22×D61—24no—
308C22×D61—24no—
309C22×D61—24no—
310C22×D61—24no—
311C22×D61—24no—
312C22×D61—24no—
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—24no—
316C22×D61—24no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—24no—
323C22×D61—22no—
324C22×D61—22no—
325C22×D61—22no—
326C22×D61—24no—
327C22×D61—232no—
328C22×D61—232no—
329C22×D61—416no—
330C22×D61—432no—
331C22×D61—432no—
332C22×D61—416no—
333C22×D61—416no—
334C22×D61—416no—
335C22×D61—416no—
336C22×D61—432no—
337C22×D61—432no—
338C22×D61—42no—
339C22×D61—42no—
340C22×D61—42no—
341C22×D61—42no—
342C22×D61—42no—
343C22×D61—42no—
344C22×D61—42no—
345C22×D61—42no—
346C22×D61C2×C4⋊C414yes—
347C22×D61C2×C4⋊C414yes—
348C22×D61C4×D418yes—
349C22×D61#12014yes—
350C22×D61C22⋊Q818yes—
351C22×D61#12314yes—
352C2×C4×C61—24no—
353C2×C4×C61—24no—
354C2×C4×C61—24no—
355C2×C4×C61—24no—
356C2×C4×C61—24no—
357C2×C4×C61—24no—
358C2×C4×C61—416no—
359C2×C4×C61—42no—
360C2×C4×C61—42no—
361C2×C4×C61—42no—
362C2×C4×C61—42no—
363C2×C4×C61—42no—
364C2×C4×C61—42no—
365C2×C4×C61—42no—
366C2×C4×C61—42no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—42no—
374C2×C4×C61—42no—
375C2×C4×C61—42no—
376C2×C4×C61—42no—
377C2×Dic61—24no—
378C2×Dic61—24no—
379C2×Dic61—24no—
380C2×Dic61—24no—
381C2×Dic61—24no—
382C2×Dic61—24no—
383C2×Dic61—24no—
384C2×Dic61—24no—
385C2×Dic61—24no—
386C2×Dic61—416no—
387C2×Dic61—42no—
388C2×Dic61—42no—
389C2×Dic61—42no—
390C2×Dic61—42no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—42no—
398C2×Dic61—42no—
399C2×Dic61—42no—
400C2×Dic61—42no—
401C2×Dic61C2×C22⋊C418yescomplemented
402C4×D61—432no—
403#13877—611nomaximal, Sylow
404C22×C61—24no—
405C22×C61—28no—
406C22×C61—28no—
407C22×C61—24no—
408C22×C61—24no—
409C22×C61—24no—
410C22×C61—24no—
411C22×C61—28no—
412C22×C61—28no—
413C22×C61—24no—
414C22×C61#38018yescomplemented
415C22×C61C22×C22⋊C411yescharacteristic
416C22×C61C22×C4⋊C411yescharacteristic
417C22×C61C2×#11711yescharacteristic
418C22×C61C2×C4×D412yes—
419C22×C61#51812yes—
420C22×C61C2×#12011yescharacteristic
421C22×C61C2×#12111yescharacteristic
422C22×C61C2×#12111yescharacteristic
423C22×C61C2×C22⋊Q812yes—
424C22×C61C2×C22⋊Q811yescharacteristic
425C22×C61C2×C22⋊Q811yescharacteristic
426C22×C61C2×#12311yescharacteristic
427C22×C61#53411yescharacteristic
428C22×C61#53411yescharacteristic
429C22×C61#54312yes—
430C22×C61D4212yes—
431C22×C61D4212yes—
432C22×C61#54612yes—
433C22×C61#54612yes—
434C22×C61#54612yes—
435C22×C61#54612yes—
436C22×C61#55112yes—
437C22×C61#55112yes—
438C2×D61—24no—
439C2×D61—28no—
440C2×D61—28no—
441C2×D61—24no—
442C2×D61—24no—
443C2×D61—24no—
444C2×D61—24no—
445C2×D61—28no—
446C2×D61—28no—
447C2×D61—24no—
448C2×D61—24no—
449C2×D61—24no—
450C2×D61—24no—
451C2×D61—464no—
452C2×D61—44no—
453C2×D61—44no—
454C2×D61—42no—
455C2×D61—42no—
456C2×D61—42no—
457C2×D61—42no—
458C2×D61—44no—
459C2×D61—44no—
460C2×D61#38518yescomplemented
461C4×C61—44no—
462C4×C61—44no—
463C4×C61—81no—
464C4×C61—81no—
465Dic61—28no—
466Dic61—44no—
467Dic61—81no—
468Dic61—81no—
469C23×C22⋊C4—611no—
470C23×C22⋊C4—611no—
471C2×#385—611no—
472C2×#385—611no—
473C2×#380—612no—
474C2×#379—611no—
475#1439—612no—
476#1439—612no—
477C22⋊#95—612no—
478C22⋊#95—611no—
479C22⋊#95D6111yescharacteristic, complemented
480C2×C61—28no—
481C2×C61C2×#38011yescharacteristic
482C2×C61C2×#38511yescharacteristic
483C2×C61#231511yescharacteristic
484C2×C61D4×C22⋊C412yes—
485C2×C61#234212yes—
486C2×C61#241011yescharacteristic
487C2×C61#241011yescharacteristic
488C2×C61#241211yescharacteristic
489C2×C61#241211yescharacteristic
490C2×C61#243712yes—
491C2×C61#243712yes—
492D61—28no—
493D61—44no—
494C26—611no—
495C24×C4—612no—
496C24×C4—611no—
497C24×C4C2×D6111yescharacteristic
498C22×C4⋊C4—612no—
499C22×C4⋊C4—612no—
500C22×C22⋊C4—611no—
501C22×C22⋊C4—612no—
502C22×C22⋊C4—612no—
503C22×C22⋊C4—618no—
504C22×C22⋊C4—611no—
505C22×C22⋊C4—612no—
506C22×C22⋊C4—611no—
507C22×C22⋊C4—611no—
508C22×C22⋊C4—611no—
509C22×C22⋊C4—611no—
510C22×C22⋊C4—1224no—
511C22×C22⋊C4—1224no—
512C22×C22⋊C4—1228no—
513C22×C22⋊C4—1224no—
514C22×C22⋊C4C2×D6111yescharacteristic
515C22×C22⋊C4C2×D6111yescharacteristic
516#385—1224no—
517#385—1224no—
518#380—1228no—
519#379—1224no—
520C2×#95—612no—
521C2×#95—612no—
522C2×#95—612no—
523C2×#95—612no—
524C2×#95C2×D6112yescomplemented
525C2×#95C2×D6112yescomplemented
526C61#1387711yescharacteristic, complemented, Sylow
527C25—611no—
528C25—611no—
529C25—614no—
530C25—614no—
531C25—614no—
532C25—1224no—
533C25—1224no—
534C25—1222no—
535C25—1222no—
536C25—1222no—
537C25—1222no—
538C25—2442no—
539C25—2442no—
540C25C22×D6111yescharacteristic
541C23×C4—22no—
542C23×C4—24no—
543C23×C4—22no—
544C23×C4—22no—
545C23×C4—42no—
546C23×C4—612no—
547C23×C4—612no—
548C23×C4—618no—
549C23×C4—611no—
550C23×C4—611no—
551C23×C4—1224no—
552C23×C4—1224no—
553C23×C4—1224no—
554C23×C4—1224no—
555C23×C4—1224no—
556C23×C4—1222no—
557C23×C4—1222no—
558C23×C4—1222no—
559C23×C4—2442no—
560C23×C4—2442no—
561C23×C4—2442no—
562C23×C4C22×D6111yescharacteristic
563C23×C4C22×D6111yescharacteristic
564C23×C4C22×D6112yes—
565C23×C4C22×D6112yes—
566C2×C4⋊C4—1224no—
567C2×C4⋊C4—1224no—
568C2×C4⋊C4—1224no—
569C2×C4⋊C4—1224no—
570C2×C4⋊C4—2442no—
571C2×C4⋊C4—2442no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—614no—
578C2×C22⋊C4—614no—
579C2×C22⋊C4—614no—
580C2×C22⋊C4—618no—
581C2×C22⋊C4—618no—
582C2×C22⋊C4—12232no—
583C2×C22⋊C4—1224no—
584C2×C22⋊C4—1224no—
585C2×C22⋊C4—1224no—
586C2×C22⋊C4—1224no—
587C2×C22⋊C4—1224no—
588C2×C22⋊C4—1224no—
589C2×C22⋊C4—12232no—
590C2×C22⋊C4—1224no—
591C2×C22⋊C4—1222no—
592C2×C22⋊C4—1222no—
593C2×C22⋊C4—1222no—
594C2×C22⋊C4—1222no—
595C2×C22⋊C4—1224no—
596C2×C22⋊C4—1224no—
597C2×C22⋊C4—1222no—
598C2×C22⋊C4—1222no—
599C2×C22⋊C4—1222no—
600C2×C22⋊C4—2442no—
601C2×C22⋊C4—2442no—
602C2×C22⋊C4C4×D6114yes—
603#95—24no—
604#95—42no—
605#95—1224no—
606#95—1224no—
607#95—1224no—
608#95—2442no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—612no—
614C24—614no—
615C24—612no—
616C24—612no—
617C24—614no—
618C24—612no—
619C24—612no—
620C24—612no—
621C24—6116no—
622C24—1228no—
623C24—12216no—
624C24—12216no—
625C24—1228no—
626C24—1221no—
627C24—1221no—
628C24—1221no—
629C24—1221no—
630C24—1222no—
631C24—1222no—
632C24—1221no—
633C24—1221no—
634C24—1222no—
635C24—1222no—
636C24—1221no—
637C24—1221no—
638C24—1222no—
639C24—1222no—
640C24—1228no—
641C24—1228no—
642C24—1228no—
643C24—1228no—
644C24—1228no—
645C24—1228no—
646C24—2448no—
647C24—2444no—
648C24—2444no—
649C24—2448no—
650C24—2448no—
651C24—2448no—
652C24—2448no—
653C24—2448no—
654C24—2448no—
655C24—2448no—
656C24—2448no—
657C24—2448no—
658C24C2×C4×D6112yes—
659C24#1175822212yes—
660C24#1175822212yes—
661C24D4×D6112yes—
662C24D4×D6112yes—
663C24D4×D6112yes—
664C24Q8×D6112yes—
665C24C23×D6111yescharacteristic
666C22×C4—28no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—22no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—48no—
690C22×C4—48no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4—614no—
694C22×C4—614no—
695C22×C4—614no—
696C22×C4—614no—
697C22×C4—12216no—
698C22×C4—12216no—
699C22×C4—1222no—
700C22×C4—1222no—
701C22×C4—1222no—
702C22×C4—1222no—
703C22×C4—1228no—
704C22×C4—1222no—
705C22×C4—1222no—
706C22×C4—1222no—
707C22×C4—1222no—
708C22×C4—1222no—
709C22×C4—1222no—
710C22×C4—1221no—
711C22×C4—1222no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1222no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1222no—
719C22×C4—1222no—
720C22×C4—2448no—
721C22×C4—2448no—
722C22×C4—2448no—
723C22×C4—2448no—
724C22×C4—2448no—
725C22×C4—2448no—
726C22×C4—2448no—
727C22×C4—2444no—
728C22×C4—2444no—
729C22×C4C2×C4×D6114yes—
730C22×C4D4×D6114yes—
731C4⋊C4—2448no—
732C4⋊C4—2448no—
733C22⋊C4—28no—
734C22⋊C4—44no—
735C22⋊C4—6116no—
736C22⋊C4—12216no—
737C22⋊C4—12216no—
738C22⋊C4—12216no—
739C22⋊C4—2444no—
740C22⋊C4—2444no—
741C22⋊C4—2444no—
742C22⋊C4—2444no—
743C22⋊C4—2444no—
744C23—24no—
745C23—24no—
746C23—22no—
747C23—24no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—24no—
759C23—24no—
760C23—614no—
761C23—618no—
762C23—614no—
763C23—618no—
764C23—614no—
765C23—614no—
766C23—12232no—
767C23—1222no—
768C23—1222no—
769C23—1224no—
770C23—1222no—
771C23—1222no—
772C23—1222no—
773C23—1222no—
774C23—1222no—
775C23—1222no—
776C23—1224no—
777C23—1224no—
778C23—1224no—
779C23—1224no—
780C23—1224no—
781C23—1224no—
782C23—1224no—
783C23—1224no—
784C23—1224no—
785C23—1222no—
786C23—1222no—
787C23—1224no—
788C23—1224no—
789C23—1222no—
790C23—1222no—
791C23—1222no—
792C23—1224no—
793C23—1222no—
794C23—1222no—
795C23—1222no—
796C23—1222no—
797C23—1222no—
798C23—1224no—
799C23—12232no—
800C23—24416no—
801C23—24416no—
802C23—24416no—
803C23—24432no—
804C23—24432no—
805C23—24432no—
806C23—24432no—
807C23—24416no—
808C23—24416no—
809C23—2442no—
810C23—2442no—
811C23—2442no—
812C23—2442no—
813C23—2442no—
814C23—2442no—
815C23—2442no—
816C23—2442no—
817C23C22⋊C4×D6114yes—
818C23C4⋊C4×D6114yes—
819C23#1451973414yes—
820C23#1451975014yes—
821C23#1451975014yes—
822C23#1451975514yes—
823C23#1451975514yes—
824C23C22×C4×D6111yescharacteristic
825C23C2×D4×D6111yescharacteristic
826C23C2×D4×D6111yescharacteristic
827C23C2×D4×D6111yescharacteristic
828C23C2×D4×D6112yes—
829C23C2×Q8×D6111yescharacteristic
830C23#41×D6112yes—
831C23C2×#1175822211yescharacteristic
832C23C2×#1175822211yescharacteristic
833C23#1451982212yes—
834C23#1451982312yes—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—416no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—618no—
861C2×C4—1224no—
862C2×C4—1224no—
863C2×C4—1224no—
864C2×C4—1224no—
865C2×C4—1224no—
866C2×C4—1224no—
867C2×C4—1224no—
868C2×C4—1224no—
869C2×C4—1224no—
870C2×C4—24432no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2442no—
878C2×C4—2442no—
879C2×C4—2442no—
880C2×C4—2442no—
881C2×C4—24416no—
882C2×C4—2442no—
883C2×C4—2442no—
884C2×C4—2442no—
885C2×C4—2442no—
886C22—24no—
887C22—24no—
888C22—28no—
889C22—28no—
890C22—24no—
891C22—28no—
892C22—28no—
893C22—24no—
894C22—24no—
895C22—24no—
896C22—618no—
897C22—1224no—
898C22—1224no—
899C22—1228no—
900C22—1228no—
901C22—1228no—
902C22—1228no—
903C22—1224no—
904C22—1224no—
905C22—1224no—
906C22—1224no—
907C22—1224no—
908C22—1224no—
909C22—1224no—
910C22—24464no—
911C22—2442no—
912C22—2442no—
913C22—2444no—
914C22—2444no—
915C22—2444no—
916C22—2444no—
917C22—2442no—
918C22—2442no—
919C22#1683962118yescomplemented
920C22C2×C22⋊C4×D6111yescharacteristic
921C22C2×C4⋊C4×D6111yescharacteristic
922C22C2×#1451973411yescharacteristic
923C22C4×D4×D6112yes—
924C22#1684023412yes—
925C22#120×D6111yescharacteristic
926C22C2×#1451975011yescharacteristic
927C22C2×#1451975011yescharacteristic
928C22C22⋊Q8×D6112yes—
929C22C2×#1451975511yescharacteristic
930C22C2×#1451975511yescharacteristic
931C22#123×D6111yescharacteristic
932C22#1684032211yescharacteristic
933C22#1684032311yescharacteristic
934C22#1684038712yes—
935C22#1684039412yes—
936C22#1684039612yes—
937C22#1684040112yes—
938C22#1684040212yes—
939C22#1684040412yes—
940C22#1684040812yes—
941C22#1684043612yes—
942C22#1684044112yes—
943C4—44no—
944C4—44no—
945C4—81no—
946C4—81no—
947C4—1228no—
948C4—4881no—
949C4—4881no—
950C4—2444no—
951C2—28no—
952C2—1228no—
953C2—2444no—
954C2C2×#1683962111yescharacteristic
955C2#385×D6111yescharacteristic
956C2#2144843011yescharacteristic
957C2#2144863712yes—
958C2#2144866212yes—
959C2#2144919511yescharacteristic
960C2#2144919611yescharacteristic
961C2#2144921711yescharacteristic
962C2#2144921811yescharacteristic
963C2#2144948412yes—
964C2#2144948712yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C22⋊#95C2
socle, cosocleC24×C61C24
prime radicalC25×D61C22
hypercenterC22⋊#95D61
hypocenterC61#13877
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#16839635C2semidirect
4. C2×#16839634C2semidirect
5. C2×#16839621C2semidirect
7. #21444063C2semidirect
8. #21444063C2semidirect
9. #21444041C2semidirect
10. #21444040C2semidirect
11. C61×C22⋊#95C2semidirect
15. C22×#11758196C22semidirect
16. C22×#11758196C22semidirect
30. C2×C22⋊C4×D61C4semidirect
35. C2×#14519684C22semidirect
36. C2×#14519684C22semidirect
37. C2×#14519684C22semidirect
38. C2×#14519684C22semidirect
42. C2×#95×C61C22semidirect
43. C2×#95×C61C22semidirect
72. C22×C4×D61C2×C4semidirect
101. C2×#11758198C2×C4semidirect
174. C23×D61C4⋊C4semidirect
251. C22⋊Dic61C22⋊C4semidirect
401. C2×Dic61C2×C22⋊C4semidirect
414. C22×C61#380semidirect
460. C2×D61#385semidirect
479. C22⋊#95D61semidirect
524. C2×#95C2×D61semidirect
525. C2×#95C2×D61semidirect
526. C61#13877semidirect
919. C22#16839621semidirect

Maximal subgroups

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

subgroupindex
C23×#117581982
C22×C22⋊C4×D612
C2×#168396352
C2×#168396342
C2×#168396212
C2×#168396172
#214440632
#214440412
#214440402
C61×C22⋊#952
#1387761