Finite Group Databasebeta

← #29601971

Subgroups — #29601971

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×#16839637C211yesmaximal, characteristic, complemented
4C2×#16839619C212yesmaximal, complemented
5C2×#16839617C211yesmaximal, characteristic
6#21444065C212yesmaximal, complemented
7#21444061C212yesmaximal, complemented
8#21444042C211yesmaximal, characteristic, complemented
9#21444041C211yesmaximal, characteristic, complemented
10#21444040C212yesmaximal, complemented
11C2×C61×#385C211yesmaximal, characteristic, complemented
12C25×D61C2211yescharacteristic
13C24×Dic61C2211yescharacteristic
14C23×C4×D61C2212yes—
15C22×C4⋊Dic61C2212yescomplemented
16C22×C22⋊Dic61C2211yescharacteristic
17C22×C22⋊Dic61C2211yescharacteristic
18C22×#11758198—28no—
19C22×#11758198—24no—
20C22×#11758198C2212yes—
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2212yes—
24C22×#11758198C2212yes—
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C2×C22⋊C4×D61—24no—
28C2×C22⋊C4×D61—24no—
29C2×C22⋊C4×D61C418yescomplemented
30#16839637—24no—
31#16839619—28no—
32#16839617—24no—
33C2×#14519684C2212yescomplemented
34C2×#14519684C2212yescomplemented
35C2×#14519684C2212yescomplemented
36C2×#14519684C2212yescomplemented
37C2×#14519684C2212yescomplemented
38C24×C4×C61C2211yescharacteristic
39C22×C4⋊C4×C61C2212yescomplemented
40C22×C22⋊C4×C61C2211yescharacteristic
41C22×C22⋊C4×C61C2211yescharacteristic
42C61×#385—24no—
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×C4⋊Dic61—24no—
74C2×C4⋊Dic61—24no—
75C2×C4⋊Dic61—42no—
76C2×C22⋊Dic61—22no—
77C2×C22⋊Dic61—22no—
78C2×C22⋊Dic61—22no—
79C2×C22⋊Dic61—22no—
80C2×C22⋊Dic61—22no—
81C2×C22⋊Dic61C2×C414yes—
82C2×#11758198—232no—
83C2×#11758198—24no—
84C2×#11758198—24no—
85C2×#11758198—24no—
86C2×#11758198—24no—
87C2×#11758198—24no—
88C2×#11758198—24no—
89C2×#11758198—24no—
90C2×#11758198—22no—
91C2×#11758198—22no—
92C2×#11758198—22no—
93C2×#11758198—22no—
94C2×#11758198—24no—
95C2×#11758198—24no—
96C2×#11758198—42no—
97C2×#11758198—42no—
98C2×#11758198C2×C418yescomplemented
99C2×#11758198D418yes—
100C22⋊C4×D61—232no—
101#14519684—24no—
102#14519684—24no—
103#14519684—24no—
104#14519684—42no—
105#14519684—42no—
106C25×C61C2311yescharacteristic
107C23×C4×C61—22no—
108C23×C4×C61—24no—
109C23×C4×C61—22no—
110C23×C4×C61—22no—
111C23×C4×C61—42no—
112C23×C4×C61C2311yescharacteristic
113C23×C4×C61C2311yescharacteristic
114C23×C4×C61C2312yes—
115C23×C4×C61C2312yes—
116C2×C4⋊C4×C61—24no—
117C2×C4⋊C4×C61—24no—
118C2×C4⋊C4×C61—42no—
119C2×C22⋊C4×C61—22no—
120C2×C22⋊C4×C61—22no—
121C2×C22⋊C4×C61—22no—
122C2×C22⋊C4×C61C2×C414yes—
123C2×C22⋊C4×C61D414yes—
124C2×C22⋊C4×C61D414yes—
125#95×C61—24no—
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—22no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—28no—
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—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—22no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—22no—
202C22×C4×C61—22no—
203C22×C4×C61—22no—
204C22×C4×C61—48no—
205C22×C4×C61—48no—
206C22×C4×C61—44no—
207C22×C4×C61—44no—
208C22×C4×C61C22×C414yes—
209C22×C4×C61C2×D414yes—
210C22×C4×C61C2×D414yes—
211C22×C4×C61C2×D414yes—
212C22×Dic61—28no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—22no—
220C22×Dic61—22no—
221C22×Dic61—22no—
222C22×Dic61—22no—
223C22×Dic61—22no—
224C22×Dic61—22no—
225C22×Dic61—21no—
226C22×Dic61—22no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—22no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—22no—
234C22×Dic61—22no—
235C22×Dic61—48no—
236C22×Dic61—48no—
237C22×Dic61—44no—
238C22×Dic61—44no—
239C22×Dic61C22×C414yes—
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—
248C4⋊C4×C61—48no—
249C22⋊C4×C61—44no—
250C22⋊C4×C61C22⋊C4116yescomplemented
251C22⋊Dic61—28no—
252C22⋊Dic61—44no—
253#11758198—216no—
254#11758198—216no—
255#11758198—216no—
256#11758198—44no—
257#11758198—44no—
258#11758198—44no—
259#11758198—44no—
260C4⋊Dic61—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—24no—
359C2×C4×C61—24no—
360C2×C4×C61—24no—
361C2×C4×C61—416no—
362C2×C4×C61—42no—
363C2×C4×C61—42no—
364C2×C4×C61—42no—
365C2×C4×C61—42no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—42no—
373C2×C4×C61—42no—
374C2×C4×C61—42no—
375C2×C4×C61—42no—
376C2×C4×C61C2×C22⋊C418yescomplemented
377C2×Dic61—24no—
378C2×Dic61—24no—
379C2×Dic61—24no—
380C2×Dic61—24no—
381C2×Dic61—24no—
382C2×Dic61—24no—
383C2×Dic61—416no—
384C2×Dic61—42no—
385C2×Dic61—42no—
386C2×Dic61—42no—
387C2×Dic61—42no—
388C2×Dic61—42no—
389C2×Dic61—42no—
390C2×Dic61—42no—
391C2×Dic61—42no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—42no—
399C2×Dic61—42no—
400C2×Dic61—42no—
401C2×Dic61—42no—
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—28no—
462C4×C61—44no—
463C4×C61—81no—
464C4×C61—81no—
465Dic61—44no—
466Dic61—44no—
467Dic61—81no—
468Dic61—81no—
469C23×C22⋊C4—611no—
470C23×C22⋊C4—611no—
471C2×#385—611no—
472C2×#385D6111yescharacteristic, complemented
473C2×#380—612no—
474C2×#379—611no—
475#1439—612no—
476#1439—612no—
477C22⋊#95—612no—
478C22⋊#95—611no—
479C22⋊#95—611no—
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⋊C4C2×D6112yescomplemented
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—1228no—
511C22×C22⋊C4—1224no—
512C22×C22⋊C4—1224no—
513C22×C22⋊C4—1224no—
514C22×C22⋊C4C2×D6111yescharacteristic
515C22×C22⋊C4C2×D6111yescharacteristic
516#385—24no—
517#385—1224no—
518#380—1228no—
519#379—1224no—
520C2×#95—612no—
521C2×#95—612no—
522C2×#95—612no—
523C2×#95—612no—
524C2×#95—612no—
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—1222no—
555C23×C4—1224no—
556C23×C4—1224no—
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—24no—
567C2×C4⋊C4—24no—
568C2×C4⋊C4—42no—
569C2×C4⋊C4—1224no—
570C2×C4⋊C4—1224no—
571C2×C4⋊C4—2442no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—614no—
576C2×C22⋊C4—618no—
577C2×C22⋊C4—618no—
578C2×C22⋊C4—1224no—
579C2×C22⋊C4—1224no—
580C2×C22⋊C4—1224no—
581C2×C22⋊C4—1224no—
582C2×C22⋊C4—12232no—
583C2×C22⋊C4—1222no—
584C2×C22⋊C4—1222no—
585C2×C22⋊C4—1224no—
586C2×C22⋊C4—1224no—
587C2×C22⋊C4—1224no—
588C2×C22⋊C4—12232no—
589C2×C22⋊C4—1222no—
590C2×C22⋊C4—1222no—
591C2×C22⋊C4—1222no—
592C2×C22⋊C4—1222no—
593C2×C22⋊C4—1224no—
594C2×C22⋊C4—1224no—
595C2×C22⋊C4—1222no—
596C2×C22⋊C4—1222no—
597C2×C22⋊C4—1222no—
598C2×C22⋊C4—2442no—
599C2×C22⋊C4—2442no—
600C2×C22⋊C4C4×D6114yes—
601C2×C22⋊C4D24414yes—
602C2×C22⋊C4C22⋊D6114yes—
603#95—24no—
604#95—1224no—
605#95—1224no—
606#95—1224no—
607#95—2442no—
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—1222no—
633C24—1221no—
634C24—1221no—
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—
659C24C2×D24412yes—
660C24D4×D6112yes—
661C24#1175822412yes—
662C24Q8×D6112yes—
663C24#1175822612yes—
664C24C2×C22⋊D6112yes—
665C24C23×D6111yescharacteristic
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—28no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—22no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—48no—
688C22×C4—48no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—614no—
692C22×C4—614no—
693C22×C4—12216no—
694C22×C4—1228no—
695C22×C4—1222no—
696C22×C4—1222no—
697C22×C4—1222no—
698C22×C4—1222no—
699C22×C4—1222no—
700C22×C4—1222no—
701C22×C4—1222no—
702C22×C4—1222no—
703C22×C4—1222no—
704C22×C4—1222no—
705C22×C4—1222no—
706C22×C4—1222no—
707C22×C4—12216no—
708C22×C4—1222no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1222no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1222no—
717C22×C4—1222no—
718C22×C4—2448no—
719C22×C4—2448no—
720C22×C4—2448no—
721C22×C4—2448no—
722C22×C4—2448no—
723C22×C4—2448no—
724C22×C4—2448no—
725C22×C4—2444no—
726C22×C4—2444no—
727C22×C4C2×C4×D6114yes—
728C22×C4C2×D24414yes—
729C22×C4D4×D6114yes—
730C22×C4C2×C22⋊D6114yes—
731C4⋊C4—48no—
732C4⋊C4—2448no—
733C22⋊C4—44no—
734C22⋊C4—12216no—
735C22⋊C4—12216no—
736C22⋊C4—1228no—
737C22⋊C4—12216no—
738C22⋊C4—2444no—
739C22⋊C4—2444no—
740C22⋊C4—2444no—
741C22⋊C4—2444no—
742C22⋊C4—2444no—
743C22⋊C4#11758198116yescomplemented
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—12232no—
799C23—1224no—
800C23—24416no—
801C23—24432no—
802C23—24432no—
803C23—24432no—
804C23—24432no—
805C23—24416no—
806C23—24416no—
807C23—24416no—
808C23—24416no—
809C23—2442no—
810C23—2442no—
811C23—2442no—
812C23—2442no—
813C23—2442no—
814C23—2442no—
815C23—2442no—
816C23—2442no—
817C23C2×#1175819814yes—
818C23C4⋊C4×D6114yes—
819C23#1451973514yes—
820C23#1451974814yes—
821C23#1451975214yes—
822C23#1451975314yes—
823C23#1451975714yes—
824C23C22×C4×D6111yescharacteristic
825C23C2×D4×D6111yescharacteristic
826C23C2×D4×D6112yes—
827C23C22×C22⋊D6111yescharacteristic
828C23C22×D24411yescharacteristic
829C23C2×Q8×D6111yescharacteristic
830C23#41×D6112yes—
831C23C2×#1175822411yescharacteristic
832C23C2×#1175822611yescharacteristic
833C23#1451982212yes—
834C23#1451982312yes—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—416no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—1224no—
860C2×C4—1224no—
861C2×C4—1224no—
862C2×C4—1224no—
863C2×C4—1224no—
864C2×C4—1224no—
865C2×C4—24432no—
866C2×C4—2441no—
867C2×C4—2441no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2442no—
873C2×C4—2442no—
874C2×C4—2442no—
875C2×C4—2442no—
876C2×C4—24416no—
877C2×C4—2442no—
878C2×C4—2442no—
879C2×C4—2442no—
880C2×C4—2442no—
881C2×C4—2442no—
882C2×C4—2442no—
883C2×C4—2442no—
884C2×C4—2442no—
885C2×C4C2×#1175819818yescomplemented
886C22—28no—
887C22—28no—
888C22—24no—
889C22—28no—
890C22—28no—
891C22—24no—
892C22—24no—
893C22—24no—
894C22—24no—
895C22—24no—
896C22—618no—
897C22—1228no—
898C22—1228no—
899C22—1228no—
900C22—1228no—
901C22—1224no—
902C22—1224no—
903C22—1224no—
904C22—1224no—
905C22—1224no—
906C22—1224no—
907C22—1224no—
908C22—1224no—
909C22—1224no—
910C22—24464no—
911C22—2444no—
912C22—2444no—
913C22—2444no—
914C22—2444no—
915C22—2442no—
916C22—2442no—
917C22—2442no—
918C22—2442no—
919C22#1683961918yescomplemented
920C22C22×#1175819811yescharacteristic
921C22C2×C4⋊C4×D6111yescharacteristic
922C22C2×#1451973511yescharacteristic
923C22C4×D4×D6112yes—
924C22#1684023412yes—
925C22#120×D6111yescharacteristic
926C22C2×#1451974811yescharacteristic
927C22C2×#1451975211yescharacteristic
928C22C22⋊Q8×D6112yes—
929C22C2×#1451975311yescharacteristic
930C22C2×#1451975711yescharacteristic
931C22#123×D6111yescharacteristic
932C22#1684032211yescharacteristic
933C22#1684032311yescharacteristic
934C22#1684038712yes—
935C22D4×C22⋊D6112yes—
936C22D4×D24412yes—
937C22#1684039912yes—
938C22#1684040012yes—
939C22#1684040312yes—
940C22#1684040712yes—
941C22#1684043512yes—
942C22#1684043912yes—
943C4—28no—
944C4—44no—
945C4—81no—
946C4—81no—
947C4—4881no—
948C4—4881no—
949C4—2444no—
950C4—2444no—
951C2—28no—
952C2—1228no—
953C2—2444no—
954C2C2×#1683961911yescharacteristic
955C2#385×D6111yescharacteristic
956C2#2144843011yescharacteristic
957C2D4×#1175819812yes—
958C2#2144866612yes—
959C2#2144918911yescharacteristic
960C2#2144919111yescharacteristic
961C2#2144921111yescharacteristic
962C2#2144921311yescharacteristic
963C2#2144948212yes—
964C2#2144948312yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#385C2
socle, cosocleC24×C61C24
prime radicalC25×D61C22
hypercenterC2×#385D61
hypocenterC61#13877
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. C2×#16839637C2semidirect
4. C2×#16839619C2semidirect
6. #21444065C2semidirect
7. #21444061C2semidirect
8. #21444042C2semidirect
9. #21444041C2semidirect
10. #21444040C2semidirect
11. C2×C61×#385C2semidirect
15. C22×C4⋊Dic61C22semidirect
29. C2×C22⋊C4×D61C4semidirect
33. C2×#14519684C22semidirect
34. C2×#14519684C22semidirect
35. C2×#14519684C22semidirect
36. C2×#14519684C22semidirect
37. C2×#14519684C22semidirect
39. C22×C4⋊C4×C61C22semidirect
43. C2×#95×C61C22semidirect
72. C22×C4×D61C2×C4semidirect
98. C2×#11758198C2×C4semidirect
174. C23×D61C4⋊C4semidirect
250. C22⋊C4×C61C22⋊C4semidirect
376. C2×C4×C61C2×C22⋊C4semidirect
414. C22×C61#380semidirect
460. C2×D61#385semidirect
472. C2×#385D61semidirect
499. C22×C4⋊C4C2×D61semidirect
525. C2×#95C2×D61semidirect
526. C61#13877semidirect
743. C22⋊C4#11758198semidirect
885. C2×C4C2×#11758198semidirect
919. C22#16839619semidirect

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×#168396372
C2×#168396192
C2×#168396172
#214440652
#214440612
#214440422
#214440412
#214440402
C2×C61×#3852
#1387761