Finite Group Databasebeta

← #29601972

Subgroups — #29601972

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×#16839636C212yesmaximal, complemented
4C2×#16839622C211yesmaximal, characteristic, complemented
5C2×#16839620C211yesmaximal, characteristic, complemented
6C2×#16839617C211yesmaximal, characteristic
7#21444065C212yesmaximal, complemented
8#21444063C212yesmaximal, complemented
9#21444041C211yesmaximal, characteristic, complemented
10#21444040C212yesmaximal, complemented
11C61×C22⋊#95C211yesmaximal, characteristic, complemented
12C25×D61C2211yescharacteristic
13C24×Dic61C2211yescharacteristic
14C23×C4×D61C2212yes—
15C22×C4⋊Dic61C2212yescomplemented
16C22×#11758196C2212yescomplemented
17C22×C22⋊Dic61C2211yescharacteristic
18C22×C22⋊Dic61C2211yescharacteristic
19C22×#11758198—28no—
20C22×#11758198C418yescomplemented
21C22×#11758198C2212yes—
22C22×#11758198C2212yes—
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2212yes—
27C22×#11758198C2211yescharacteristic
28C2×C22⋊C4×D61—24no—
29C2×C22⋊C4×D61—24no—
30C2×C22⋊C4×D61—24no—
31#16839636—28no—
32#16839622—24no—
33#16839620—24no—
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—22no—
59C23×Dic61—24no—
60C23×Dic61—42no—
61C23×Dic61C2×C414yescomplemented
62C23×Dic61C2312yes—
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2312yes—
65C23×Dic61C2311yescharacteristic
66C22×C4×D61—24no—
67C22×C4×D61—24no—
68C22×C4×D61—24no—
69C22×C4×D61—24no—
70C22×C4×D61—24no—
71C22×C4×D61—42no—
72C22×C4×D61—42no—
73C2×C4⋊Dic61—24no—
74C2×C4⋊Dic61—24no—
75C2×C4⋊Dic61—42no—
76C2×#11758196—24no—
77C2×#11758196—24no—
78C2×#11758196—42no—
79C2×C22⋊Dic61—22no—
80C2×C22⋊Dic61—22no—
81C2×C22⋊Dic61—22no—
82C2×C22⋊Dic61—22no—
83C2×C22⋊Dic61—22no—
84C2×C22⋊Dic61D414yes—
85C2×#11758198—24no—
86C2×#11758198—24no—
87C2×#11758198—24no—
88C2×#11758198—24no—
89C2×#11758198—24no—
90C2×#11758198—24no—
91C2×#11758198—232no—
92C2×#11758198—24no—
93C2×#11758198—24no—
94C2×#11758198—24no—
95C2×#11758198—24no—
96C2×#11758198—42no—
97C2×#11758198—42no—
98C2×#11758198C2×C414yes—
99C2×#11758198C2×C414yes—
100C2×#11758198C2×C414yescomplemented
101C2×#11758198C2×C414yescomplemented
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—22no—
111C23×C4×C61—24no—
112C23×C4×C61—42no—
113C23×C4×C61C2×C414yescomplemented
114C23×C4×C61C2312yes—
115C23×C4×C61C2311yescharacteristic
116C23×C4×C61C2312yes—
117C23×C4×C61C2311yescharacteristic
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×C61D414yes—
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—22no—
151C23×D61—21no—
152C23×D61—21no—
153C23×D61—22no—
154C23×D61—21no—
155C23×D61—21no—
156C23×D61—22no—
157C23×D61—22no—
158C23×D61—28no—
159C23×D61—28no—
160C23×D61—216no—
161C23×D61—216no—
162C23×D61—44no—
163C23×D61—44no—
164C23×D61—48no—
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×D414yes—
179C23×D61C2×D412yes—
180C23×D61C2×Q812yes—
181C23×D61C2×Q812yes—
182C23×D61#4114yes—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—22no—
186C22×C4×C61—28no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61—22no—
190C22×C4×C61—21no—
191C22×C4×C61—22no—
192C22×C4×C61—22no—
193C22×C4×C61—21no—
194C22×C4×C61—22no—
195C22×C4×C61—22no—
196C22×C4×C61—22no—
197C22×C4×C61—28no—
198C22×C4×C61—22no—
199C22×C4×C61—22no—
200C22×C4×C61—22no—
201C22×C4×C61—22no—
202C22×C4×C61—22no—
203C22×C4×C61—22no—
204C22×C4×C61—22no—
205C22×C4×C61—44no—
206C22×C4×C61—48no—
207C22×C4×C61—48no—
208C22×C4×C61C22×C412yes—
209C22×C4×C61C22×C412yes—
210C22×C4×C61C2×D414yes—
211C22×C4×C61C2×D414yes—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—22no—
215C22×Dic61—28no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—21no—
220C22×Dic61—22no—
221C22×Dic61—22no—
222C22×Dic61—21no—
223C22×Dic61—22no—
224C22×Dic61—22no—
225C22×Dic61—22no—
226C22×Dic61—28no—
227C22×Dic61—22no—
228C22×Dic61—22no—
229C22×Dic61—22no—
230C22×Dic61—22no—
231C22×Dic61—22no—
232C22×Dic61—22no—
233C22×Dic61—22no—
234C22×Dic61—44no—
235C22×Dic61—48no—
236C22×Dic61—48no—
237C22×Dic61C22×C412yes—
238C22×Dic61C22×C412yes—
239C22×Dic61C2×D414yes—
240C22×Dic61C2×D414yes—
241C2×C4×D61—216no—
242C2×C4×D61—48no—
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—28no—
251C22⋊Dic61—44no—
252#11758198—216no—
253#11758198—28no—
254#11758198—28no—
255#11758198—28no—
256#11758198—48no—
257#11758198—48no—
258#11758198C22⋊C4116yescomplemented
259C4⋊Dic61—48no—
260#11758196—48no—
261C23×C61—22no—
262C23×C61—22no—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61—24no—
266C23×C61—24no—
267C23×C61—24no—
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×C4⋊C414yes—
278C23×C61C4×D414yes—
279C23×C61C4×D414yes—
280C23×C61#12014yes—
281C23×C61C22⋊Q814yes—
282C23×C61C22⋊Q814yes—
283C23×C61#12314yes—
284C23×C61C23×C411yescharacteristic
285C23×C61C22×D412yes—
286C23×C61C22×D411yescharacteristic
287C23×C61C22×D411yescharacteristic
288C23×C61C22×D411yescharacteristic
289C23×C61C22×Q811yescharacteristic
290C23×C61C2×#4112yes—
291C23×C61C2×#4111yescharacteristic
292C23×C61C2×#4111yescharacteristic
293C23×C61H(5,𝔽2)12yes—
294C23×C61H(5,𝔽2)12yes—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—22no—
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—24no—
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—22no—
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—24no—
321C22×D61—24no—
322C22×D61—22no—
323C22×D61—22no—
324C22×D61—22no—
325C22×D61—24no—
326C22×D61—24no—
327C22×D61—232no—
328C22×D61—232no—
329C22×D61—416no—
330C22×D61—416no—
331C22×D61—416no—
332C22×D61—416no—
333C22×D61—416no—
334C22×D61—432no—
335C22×D61—432no—
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×C22⋊C414yes—
347C22×D61C2×C4⋊C414yes—
348C22×D61C2×C4⋊C414yes—
349C22×D61#11714yes—
350C22×D61#12118yes—
351C22×D61C22⋊Q818yes—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—24no—
355C2×C4×C61—24no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—24no—
360C2×C4×C61—24no—
361C2×C4×C61—24no—
362C2×C4×C61—416no—
363C2×C4×C61—42no—
364C2×C4×C61—42no—
365C2×C4×C61—42no—
366C2×C4×C61—42no—
367C2×C4×C61—42no—
368C2×C4×C61—42no—
369C2×C4×C61—42no—
370C2×C4×C61—42no—
371C2×C4×C61—42no—
372C2×C4×C61—42no—
373C2×C4×C61—42no—
374C2×C4×C61—42no—
375C2×C4×C61—42no—
376C2×C4×C61C2×C22⋊C414yescomplemented
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—24no—
380C2×Dic61—24no—
381C2×Dic61—22no—
382C2×Dic61—22no—
383C2×Dic61—22no—
384C2×Dic61—24no—
385C2×Dic61—24no—
386C2×Dic61—24no—
387C2×Dic61—416no—
388C2×Dic61—42no—
389C2×Dic61—42no—
390C2×Dic61—42no—
391C2×Dic61—42no—
392C2×Dic61—42no—
393C2×Dic61—42no—
394C2×Dic61—42no—
395C2×Dic61—42no—
396C2×Dic61—42no—
397C2×Dic61—42no—
398C2×Dic61—42no—
399C2×Dic61—42no—
400C2×Dic61—42no—
401C2×Dic61C2×C22⋊C414yescomplemented
402C4×D61—432no—
403#13877—611nomaximal, Sylow
404C22×C61—24no—
405C22×C61—24no—
406C22×C61—24no—
407C22×C61—24no—
408C22×C61—24no—
409C22×C61—28no—
410C22×C61—28no—
411C22×C61—28no—
412C22×C61—28no—
413C22×C61—24no—
414C22×C61#38518yescomplemented
415C22×C61C22×C22⋊C411yescharacteristic
416C22×C61C22×C4⋊C411yescharacteristic
417C22×C61C2×#11711yescharacteristic
418C22×C61C2×C4×D411yescharacteristic
419C22×C61C2×C4×D411yescharacteristic
420C22×C61#51811yescharacteristic
421C22×C61#51811yescharacteristic
422C22×C61C2×#12011yescharacteristic
423C22×C61C2×#12112yes—
424C22×C61C2×C22⋊Q812yes—
425C22×C61C2×C22⋊Q811yescharacteristic
426C22×C61C2×C22⋊Q811yescharacteristic
427C22×C61C2×#12311yescharacteristic
428C22×C61#53412yes—
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—24no—
440C2×D61—24no—
441C2×D61—24no—
442C2×D61—24no—
443C2×D61—28no—
444C2×D61—28no—
445C2×D61—28no—
446C2×D61—28no—
447C2×D61—24no—
448C2×D61—24no—
449C2×D61—24no—
450C2×D61—24no—
451C2×D61—464no—
452C2×D61—42no—
453C2×D61—42no—
454C2×D61—42no—
455C2×D61—42no—
456C2×D61—44no—
457C2×D61—44no—
458C2×D61—44no—
459C2×D61—44no—
460C2×D61#38018yescomplemented
461C4×C61—24no—
462C4×C61—42no—
463C4×C61—44no—
464C4×C61—82no—
465Dic61—24no—
466Dic61—42no—
467Dic61—44no—
468Dic61—82no—
469C23×C22⋊C4—611no—
470C23×C22⋊C4—611no—
471C2×#385—612no—
472C2×#380—611no—
473C2×#380—611no—
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⋊C411yescharacteristic
485C2×C61D4×C22⋊C411yescharacteristic
486C2×C61#234211yescharacteristic
487C2×C61#234211yescharacteristic
488C2×C61#241012yes—
489C2×C61#241212yes—
490C2×C61#243712yes—
491C2×C61#243712yes—
492D61—28no—
493D61—44no—
494C26—611no—
495C24×C4—611no—
496C24×C4—612no—
497C24×C4C2×D6111yescharacteristic
498C22×C4⋊C4—612no—
499C22×C4⋊C4—612no—
500C22×C22⋊C4—611no—
501C22×C22⋊C4—611no—
502C22×C22⋊C4—618no—
503C22×C22⋊C4—611no—
504C22×C22⋊C4—611no—
505C22×C22⋊C4—611no—
506C22×C22⋊C4—611no—
507C22×C22⋊C4—612no—
508C22×C22⋊C4—612no—
509C22×C22⋊C4—612no—
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—1228no—
517#380—1224no—
518#380—1224no—
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—22no—
543C23×C4—24no—
544C23×C4—42no—
545C23×C4—611no—
546C23×C4—612no—
547C23×C4—611no—
548C23×C4—614no—
549C23×C4—612no—
550C23×C4—1224no—
551C23×C4—1224no—
552C23×C4—1224no—
553C23×C4—1224no—
554C23×C4—1224no—
555C23×C4—1222no—
556C23×C4—1222no—
557C23×C4—1224no—
558C23×C4—2442no—
559C23×C4—2442no—
560C23×C4—2442no—
561C23×C4C4×D6114yescomplemented
562C23×C4C22×D6112yes—
563C23×C4C22×D6111yescharacteristic
564C23×C4C22×D6112yes—
565C23×C4C22×D6111yescharacteristic
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—618no—
579C2×C22⋊C4—614no—
580C2×C22⋊C4—614no—
581C2×C22⋊C4—614no—
582C2×C22⋊C4—614no—
583C2×C22⋊C4—12232no—
584C2×C22⋊C4—12232no—
585C2×C22⋊C4—1224no—
586C2×C22⋊C4—1224no—
587C2×C22⋊C4—1224no—
588C2×C22⋊C4—1224no—
589C2×C22⋊C4—1222no—
590C2×C22⋊C4—1222no—
591C2×C22⋊C4—1224no—
592C2×C22⋊C4—1224no—
593C2×C22⋊C4—1224no—
594C2×C22⋊C4—1224no—
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⋊C4D24414yes—
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—1228no—
624C24—12216no—
625C24—12216no—
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—2444no—
647C24—2444no—
648C24—2448no—
649C24—2448no—
650C24—2448no—
651C24—2448no—
652C24—2448no—
653C24—2448no—
654C24—2448no—
655C24—2448no—
656C24—2448no—
657C24—2448no—
658C24C2×C4×D6112yes—
659C24C2×D24412yes—
660C24#1175822212yes—
661C24D4×D6112yes—
662C24D4×D6112yes—
663C24#1175822412yes—
664C24Q8×D6112yes—
665C24C23×D6111yescharacteristic
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—21no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—21no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—28no—
680C22×C4—28no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—44no—
689C22×C4—48no—
690C22×C4—48no—
691C22×C4—612no—
692C22×C4—614no—
693C22×C4—612no—
694C22×C4—614no—
695C22×C4—12216no—
696C22×C4—1228no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1222no—
700C22×C4—1222no—
701C22×C4—1222no—
702C22×C4—1222no—
703C22×C4—1221no—
704C22×C4—1222no—
705C22×C4—1222no—
706C22×C4—1221no—
707C22×C4—1222no—
708C22×C4—1222no—
709C22×C4—1222no—
710C22×C4—1228no—
711C22×C4—1222no—
712C22×C4—1222no—
713C22×C4—1222no—
714C22×C4—1222no—
715C22×C4—1222no—
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—2444no—
725C22×C4—2448no—
726C22×C4—2448no—
727C22×C4C2×C4×D6112yes—
728C22×C4C2×C4×D6112yes—
729C22×C4C2×D24414yes—
730C22×C4D4×D6114yes—
731C4⋊C4—2448no—
732C4⋊C4—2448no—
733C22⋊C4—28no—
734C22⋊C4—44no—
735C22⋊C4—6116no—
736C22⋊C4—1228no—
737C22⋊C4—1228no—
738C22⋊C4—12216no—
739C22⋊C4—1228no—
740C22⋊C4—1228no—
741C22⋊C4—2448no—
742C22⋊C4—2448no—
743C22⋊C4—2444no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—24no—
759C23—24no—
760C23—614no—
761C23—614no—
762C23—614no—
763C23—618no—
764C23—618no—
765C23—614no—
766C23—12232no—
767C23—1222no—
768C23—1222no—
769C23—1222no—
770C23—1222no—
771C23—1222no—
772C23—1222no—
773C23—1222no—
774C23—1222no—
775C23—1224no—
776C23—1224no—
777C23—1224no—
778C23—1224no—
779C23—1224no—
780C23—1224no—
781C23—1224no—
782C23—1224no—
783C23—1224no—
784C23—1224no—
785C23—1222no—
786C23—1222no—
787C23—1222no—
788C23—1222no—
789C23—1222no—
790C23—1222no—
791C23—1222no—
792C23—1224no—
793C23—1224no—
794C23—1222no—
795C23—1222no—
796C23—1222no—
797C23—1224no—
798C23—1224no—
799C23—12232no—
800C23—24416no—
801C23—24432no—
802C23—24432no—
803C23—24416no—
804C23—24416no—
805C23—24416no—
806C23—24416no—
807C23—24432no—
808C23—24432no—
809C23—2442no—
810C23—2442no—
811C23—2442no—
812C23—2442no—
813C23—2442no—
814C23—2442no—
815C23—2442no—
816C23—2442no—
817C23C4⋊C4×D6114yes—
818C23#1451973714yes—
819C23C4×D24414yes—
820C23#1451974714yes—
821C23#1451975514yes—
822C23#1451975714yes—
823C23#1451975914yes—
824C23C22×C4×D6111yescharacteristic
825C23C2×D4×D6112yes—
826C23C2×D4×D6111yescharacteristic
827C23C2×D4×D6111yescharacteristic
828C23C22×D24411yescharacteristic
829C23C2×Q8×D6111yescharacteristic
830C23#41×D6112yes—
831C23C2×#1175822411yescharacteristic
832C23C2×#1175822211yescharacteristic
833C23#1451982212yes—
834C23#1451982312yes—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—416no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—614no—
860C2×C4—1222no—
861C2×C4—1222no—
862C2×C4—1224no—
863C2×C4—1224no—
864C2×C4—1222no—
865C2×C4—1222no—
866C2×C4—1222no—
867C2×C4—1224no—
868C2×C4—1224no—
869C2×C4—1224no—
870C2×C4—24432no—
871C2×C4—24416no—
872C2×C4—2442no—
873C2×C4—2442no—
874C2×C4—2442no—
875C2×C4—2442no—
876C2×C4—2442no—
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×C4C22⋊C4×D6114yescomplemented
886C22—28no—
887C22—28no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—24no—
892C22—28no—
893C22—24no—
894C22—24no—
895C22—28no—
896C22—618no—
897C22—1228no—
898C22—1228no—
899C22—1224no—
900C22—1224no—
901C22—1224no—
902C22—1224no—
903C22—1224no—
904C22—1228no—
905C22—1224no—
906C22—1228no—
907C22—1224no—
908C22—1224no—
909C22—1224no—
910C22—24464no—
911C22—2444no—
912C22—2444no—
913C22—2442no—
914C22—2442no—
915C22—2442no—
916C22—2442no—
917C22—2444no—
918C22—2444no—
919C22#1683963618yescomplemented
920C22C2×C22⋊C4×D6111yescharacteristic
921C22C2×C4⋊C4×D6111yescharacteristic
922C22#117×D6111yescharacteristic
923C22C2×#1451973711yescharacteristic
924C22C2×C4×D24411yescharacteristic
925C22#1684023511yescharacteristic
926C22#1684023611yescharacteristic
927C22C2×#1451974711yescharacteristic
928C22#121×D6112yes—
929C22C22⋊Q8×D6112yes—
930C22C2×#1451975511yescharacteristic
931C22C2×#1451975711yescharacteristic
932C22C2×#1451975911yescharacteristic
933C22#1684032012yes—
934C22#1684038712yes—
935C22#1684039412yes—
936C22D4×D24412yes—
937C22#1684039912yes—
938C22#1684040412yes—
939C22#1684040712yes—
940C22#1684040812yes—
941C22#1684043512yes—
942C22#1684044112yes—
943C4—24no—
944C4—42no—
945C4—44no—
946C4—82no—
947C4—1224no—
948C4—4882no—
949C4—2442no—
950C4—2444no—
951C2—28no—
952C2—1228no—
953C2—2444no—
954C2#380×D6111yescharacteristic
955C2C2×#1683963611yescharacteristic
956C2#2144843211yescharacteristic
957C2#2144863511yescharacteristic
958C2C22⋊C4×D24411yescharacteristic
959C2#2144866111yescharacteristic
960C2#2144867111yescharacteristic
961C2#2144919212yes—
962C2#2144921412yes—
963C2#2144948312yes—
964C2#2144948412yes—
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×#16839636C2semidirect
4. C2×#16839622C2semidirect
5. C2×#16839620C2semidirect
7. #21444065C2semidirect
8. #21444063C2semidirect
9. #21444041C2semidirect
10. #21444040C2semidirect
11. C61×C22⋊#95C2semidirect
15. C22×C4⋊Dic61C22semidirect
16. C22×#11758196C22semidirect
20. C22×#11758198C4semidirect
35. C2×#14519684C22semidirect
36. C2×#14519684C22semidirect
37. C2×#14519684C22semidirect
38. C2×#14519684C22semidirect
42. C2×#95×C61C22semidirect
43. C2×#95×C61C22semidirect
61. C23×Dic61C2×C4semidirect
100. C2×#11758198C2×C4semidirect
101. C2×#11758198C2×C4semidirect
113. C23×C4×C61C2×C4semidirect
174. C23×D61C4⋊C4semidirect
258. #11758198C22⋊C4semidirect
376. C2×C4×C61C2×C22⋊C4semidirect
401. C2×Dic61C2×C22⋊C4semidirect
414. C22×C61#385semidirect
460. C2×D61#380semidirect
479. C22⋊#95D61semidirect
524. C2×#95C2×D61semidirect
525. C2×#95C2×D61semidirect
526. C61#13877semidirect
561. C23×C4C4×D61semidirect
885. C2×C4C22⋊C4×D61semidirect
919. C22#16839636semidirect

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×#168396362
C2×#168396222
C2×#168396202
C2×#168396172
#214440652
#214440632
#214440412
#214440402
C61×C22⋊#952
#1387761