Finite Group Databasebeta

← #29601927

Subgroups — #29601927

Order 15616.

3526 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊Dic61C211yesmaximal, characteristic
2C2×#16839650C212yesmaximal, complemented
3C2×#16839620C211yesmaximal, characteristic, complemented
4C2×#16839618C211yesmaximal, characteristic
5C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
6#21444066C212yesmaximal, complemented
7#21444062C212yesmaximal, complemented
8#21444056C212yesmaximal, complemented
9#21444041C211yesmaximal, characteristic, complemented
10#21444041C211yesmaximal, characteristic, complemented
11C2×C61×#379C211yesmaximal, characteristic
12C24×Dic61C2211yescharacteristic
13C24×Dic61C2211yescharacteristic
14C22×#11758196C2212yescomplemented
15C22×C22⋊Dic61—28no—
16C22×C22⋊Dic61C418yescomplemented
17C22×C22⋊Dic61C2211yescharacteristic
18C22×C22⋊Dic61C2212yes—
19C22×C22⋊Dic61C2212yes—
20C22×C22⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×C22⋊Dic61C2211yescharacteristic
23C22×C22⋊Dic61C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C4×Dic61C2212yescomplemented
26#16839650—28no—
27#16839620—24no—
28#16839618—24no—
29C22⋊C4×Dic61—24no—
30C2×#14519684C2212yescomplemented
31C2×#14519684C2212yescomplemented
32C2×#14519684C2212yescomplemented
33C2×#14519684C2212yescomplemented
34C2×#14519684C2212yescomplemented
35C2×#14519684C2212yescomplemented
36C26×C61C2211yescharacteristic
37C22×C22⋊C4×C61C2211yescharacteristic
38C22×C22⋊C4×C61C2212yes—
39C22×C22⋊C4×C61C2212yes—
40C22×C22⋊C4×C61C2211yescharacteristic
41C61×#379—24no—
42C23×Dic61—22no—
43C23×Dic61—22no—
44C23×Dic61—22no—
45C23×Dic61—22no—
46C23×Dic61—24no—
47C23×Dic61—24no—
48C23×Dic61—42no—
49C23×Dic61—42no—
50C23×Dic61C2×C414yes—
51C23×Dic61C2×C414yes—
52C23×Dic61C2312yes—
53C23×Dic61C2311yescharacteristic
54C23×Dic61C2311yescharacteristic
55C23×Dic61C2312yes—
56C23×Dic61C2311yescharacteristic
57C23×Dic61C2311yescharacteristic
58C2×#11758196—24no—
59C2×#11758196—24no—
60C2×#11758196—42no—
61C2×C22⋊Dic61—24no—
62C2×C22⋊Dic61—22no—
63C2×C22⋊Dic61—22no—
64C2×C22⋊Dic61—24no—
65C2×C22⋊Dic61—24no—
66C2×C22⋊Dic61—232no—
67C2×C22⋊Dic61—22no—
68C2×C22⋊Dic61—24no—
69C2×C22⋊Dic61—22no—
70C2×C22⋊Dic61—24no—
71C2×C22⋊Dic61—22no—
72C2×C22⋊Dic61—24no—
73C2×C22⋊Dic61—24no—
74C2×C22⋊Dic61—42no—
75C2×C22⋊Dic61—42no—
76C2×C22⋊Dic61C2×C414yes—
77C2×C22⋊Dic61C2×C414yes—
78C2×C22⋊Dic61C2×C414yes—
79C2×C22⋊Dic61C2×C414yes—
80C2×C22⋊Dic61D414yes—
81C2×C22⋊Dic61D418yes—
82C2×C4×Dic61—24no—
83C2×C4×Dic61—24no—
84C2×C4×Dic61—42no—
85#14519684—24no—
86#14519684—24no—
87#14519684—24no—
88#14519684—24no—
89#14519684—42no—
90#14519684—42no—
91C25×C61—24no—
92C25×C61—24no—
93C25×C61—22no—
94C25×C61—22no—
95C25×C61—22no—
96C25×C61—22no—
97C25×C61—22no—
98C25×C61—22no—
99C25×C61—42no—
100C25×C61—42no—
101C25×C61C2×C414yes—
102C25×C61C2311yescharacteristic
103C25×C61C2311yescharacteristic
104C25×C61C2311yescharacteristic
105C23×C4×C61C2312yes—
106C23×C4×C61C2312yes—
107C2×C22⋊C4×C61—22no—
108C2×C22⋊C4×C61—22no—
109C2×C22⋊C4×C61—22no—
110C2×C22⋊C4×C61—22no—
111C2×C22⋊C4×C61—24no—
112C2×C22⋊C4×C61—24no—
113C2×C22⋊C4×C61—22no—
114C2×C22⋊C4×C61—24no—
115C2×C22⋊C4×C61—24no—
116C2×C22⋊C4×C61—42no—
117C2×C22⋊C4×C61—42no—
118C2×C22⋊C4×C61D414yes—
119C24×C61—22no—
120C24×C61—22no—
121C24×C61—22no—
122C24×C61—22no—
123C24×C61—216no—
124C24×C61—216no—
125C24×C61—28no—
126C24×C61—28no—
127C24×C61—28no—
128C24×C61—21no—
129C24×C61—21no—
130C24×C61—22no—
131C24×C61—21no—
132C24×C61—21no—
133C24×C61—21no—
134C24×C61—21no—
135C24×C61—22no—
136C24×C61—21no—
137C24×C61—21no—
138C24×C61—21no—
139C24×C61—21no—
140C24×C61—21no—
141C24×C61—21no—
142C24×C61—22no—
143C24×C61—22no—
144C24×C61—22no—
145C24×C61—22no—
146C24×C61—28no—
147C24×C61—28no—
148C24×C61—44no—
149C24×C61—44no—
150C24×C61—48no—
151C24×C61—48no—
152C24×C61—48no—
153C24×C61—48no—
154C24×C61—48no—
155C24×C61—48no—
156C24×C61—48no—
157C24×C61—48no—
158C24×C61—48no—
159C24×C61—48no—
160C24×C61—44no—
161C24×C61—44no—
162C24×C61—44no—
163C24×C61—44no—
164C24×C61C22×C412yes—
165C24×C61C22×C412yes—
166C24×C61C22×C412yes—
167C24×C61C2×D414yes—
168C24×C61C2×D412yes—
169C24×C61C2×D412yes—
170C24×C61#4114yes—
171C24×C61#4112yes—
172C24×C61#4112yes—
173C24×C61#4112yes—
174C24×C61#4112yes—
175C24×C61C2411yescharacteristic
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61C2×D414yes—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—28no—
197C22×Dic61—28no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—28no—
213C22×Dic61—28no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—22no—
220C22×Dic61—22no—
221C22×Dic61—44no—
222C22×Dic61—44no—
223C22×Dic61—48no—
224C22×Dic61—48no—
225C22×Dic61—48no—
226C22×Dic61—48no—
227C22×Dic61C22×C412yes—
228C22×Dic61C22×C412yes—
229C22×Dic61C22×C412yes—
230C22×Dic61C22×C412yes—
231C22×Dic61C2×D414yes—
232C22×Dic61C2×D414yes—
233C22×Dic61C2×D414yes—
234C22⋊C4×C61—28no—
235C22⋊C4×C61—48no—
236C22⋊C4×C61—48no—
237C22⋊C4×C61—44no—
238C22⋊Dic61—28no—
239C22⋊Dic61—28no—
240C22⋊Dic61—28no—
241C22⋊Dic61—28no—
242C22⋊Dic61—48no—
243C22⋊Dic61—48no—
244C22⋊Dic61—44no—
245C22⋊Dic61C22⋊C4116yescomplemented
246#11758196—48no—
247C4×Dic61—48no—
248C23×C61—22no—
249C23×C61—22no—
250C23×C61—22no—
251C23×C61—22no—
252C23×C61—24no—
253C23×C61—24no—
254C23×C61—24no—
255C23×C61—24no—
256C23×C61—24no—
257C23×C61—24no—
258C23×C61—24no—
259C23×C61—24no—
260C23×C61—24no—
261C23×C61—24no—
262C23×C61—24no—
263C23×C61—24no—
264C23×C61—232no—
265C23×C61—22no—
266C23×C61—22no—
267C23×C61—22no—
268C23×C61—22no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61—24no—
278C23×C61—24no—
279C23×C61—24no—
280C23×C61—24no—
281C23×C61—24no—
282C23×C61—24no—
283C23×C61—24no—
284C23×C61—24no—
285C23×C61—24no—
286C23×C61—24no—
287C23×C61—24no—
288C23×C61—24no—
289C23×C61—416no—
290C23×C61—416no—
291C23×C61—416no—
292C23×C61—416no—
293C23×C61—416no—
294C23×C61—432no—
295C23×C61—432no—
296C23×C61—432no—
297C23×C61—432no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—42no—
307C23×C61—42no—
308C23×C61—42no—
309C23×C61—42no—
310C23×C61—42no—
311C23×C61—42no—
312C23×C61—42no—
313C23×C61—42no—
314C23×C61—42no—
315C23×C61—42no—
316C23×C61—42no—
317C23×C61—42no—
318C23×C61—416no—
319C23×C61C2×C22⋊C414yes—
320C23×C61#11714yes—
321C23×C61#11714yes—
322C23×C61C4×D414yes—
323C23×C61C4×D414yes—
324C23×C61#12114yes—
325C23×C61#12314yes—
326C23×C61#12414yes—
327C23×C61#12614yes—
328C23×C61C23×C411yescharacteristic
329C23×C61C22×D412yes—
330C23×C61C22×D411yescharacteristic
331C23×C61C22×D411yescharacteristic
332C23×C61C2×#4111yescharacteristic
333C23×C61C2×#4111yescharacteristic
334C23×C61C2×#4112yes—
335C23×C61C2×#4111yescharacteristic
336C23×C61C2×#4111yescharacteristic
337C23×C61H(5,𝔽2)12yes—
338C23×C61H(5,𝔽2)12yes—
339C2×C4×C61—24no—
340C2×C4×C61—24no—
341C2×C4×C61—24no—
342C2×C4×C61—42no—
343C2×C4×C61—42no—
344C2×C4×C61—42no—
345C2×C4×C61—42no—
346C2×C4×C61—42no—
347C2×C4×C61—42no—
348C2×C4×C61—42no—
349C2×C4×C61—42no—
350C2×C4×C61—42no—
351C2×C4×C61—42no—
352C2×C4×C61—42no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—24no—
358C2×Dic61—24no—
359C2×Dic61—24no—
360C2×Dic61—24no—
361C2×Dic61—22no—
362C2×Dic61—22no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—24no—
368C2×Dic61—24no—
369C2×Dic61—24no—
370C2×Dic61—416no—
371C2×Dic61—416no—
372C2×Dic61—42no—
373C2×Dic61—42no—
374C2×Dic61—42no—
375C2×Dic61—42no—
376C2×Dic61—42no—
377C2×Dic61—42no—
378C2×Dic61—42no—
379C2×Dic61—42no—
380C2×Dic61—42no—
381C2×Dic61—42no—
382C2×Dic61—42no—
383C2×Dic61—42no—
384C2×Dic61—42no—
385C2×Dic61—42no—
386C2×Dic61—42no—
387C2×Dic61C2×C22⋊C414yes—
388C2×Dic61C2×C22⋊C414yes—
389#13873—611nomaximal, Sylow
390C22×C61—24no—
391C22×C61—24no—
392C22×C61—24no—
393C22×C61—24no—
394C22×C61—24no—
395C22×C61—28no—
396C22×C61—28no—
397C22×C61—28no—
398C22×C61—28no—
399C22×C61—24no—
400C22×C61—24no—
401C22×C61—24no—
402C22×C61—24no—
403C22×C61—24no—
404C22×C61—24no—
405C22×C61—24no—
406C22×C61—464no—
407C22×C61—42no—
408C22×C61—42no—
409C22×C61—42no—
410C22×C61—42no—
411C22×C61—42no—
412C22×C61—42no—
413C22×C61—44no—
414C22×C61—44no—
415C22×C61—44no—
416C22×C61—44no—
417C22×C61—44no—
418C22×C61—44no—
419C22×C61—44no—
420C22×C61—44no—
421C22×C61—42no—
422C22×C61—42no—
423C22×C61#38818yescomplemented
424C22×C61C22×C22⋊C411yescharacteristic
425C22×C61C2×#11711yescharacteristic
426C22×C61C2×#11711yescharacteristic
427C22×C61C2×C4×D411yescharacteristic
428C22×C61C2×C4×D411yescharacteristic
429C22×C61#51811yescharacteristic
430C22×C61#51811yescharacteristic
431C22×C61C2×#12111yescharacteristic
432C22×C61C2×#12311yescharacteristic
433C22×C61#52512yes—
434C22×C61#52512yes—
435C22×C61C2×#12411yescharacteristic
436C22×C61C2×#12611yescharacteristic
437C22×C61#53812yes—
438C22×C61#53812yes—
439C22×C61D4212yes—
440C22×C61D4212yes—
441C22×C61#54612yes—
442C22×C61#54612yes—
443C22×C61#54612yes—
444C22×C61#54612yes—
445C22×C61#55112yes—
446C22×C61#55112yes—
447C4×C61—44no—
448C4×C61—82no—
449Dic61—24no—
450Dic61—24no—
451Dic61—42no—
452Dic61—42no—
453Dic61—44no—
454Dic61—82no—
455C23×C22⋊C4—611no—
456C2×#388—612no—
457C2×#380—611no—
458C2×#379—611no—
459C2×#379D6111yescharacteristic
460C2×C4×C22⋊C4—611no—
461#1440—612no—
462#1439—612no—
463#1437—612no—
464C22⋊#95—611no—
465C22⋊#95—611no—
466C2×C61—28no—
467C2×C61—44no—
468C2×C61—44no—
469C2×C61#228011yescharacteristic
470C2×C61C2×#38811yescharacteristic
471C2×C61#231211yescharacteristic
472C2×C61D4×C22⋊C411yescharacteristic
473C2×C61D4×C22⋊C411yescharacteristic
474C2×C61#234211yescharacteristic
475C2×C61#234211yescharacteristic
476C2×C61#241812yes—
477C2×C61#242412yes—
478C2×C61#247212yes—
479C2×C61#248012yes—
480C26C2×D6111yescharacteristic
481C24×C4—611no—
482C24×C4—611no—
483C22×C4⋊C4—612no—
484C22×C22⋊C4—611no—
485C22×C22⋊C4—618no—
486C22×C22⋊C4—611no—
487C22×C22⋊C4—611no—
488C22×C22⋊C4—611no—
489C22×C22⋊C4—611no—
490C22×C22⋊C4—611no—
491C22×C22⋊C4—612no—
492C22×C22⋊C4—612no—
493C22×C22⋊C4—1228no—
494C22×C22⋊C4C2×D6111yescharacteristic
495C22×C22⋊C4C2×D6112yes—
496C22×C22⋊C4C2×D6112yes—
497C22×C22⋊C4C2×D6111yescharacteristic
498C22×C42—612no—
499#388—1228no—
500#380—1224no—
501#379—24no—
502#379—1224no—
503C4×C22⋊C4—1224no—
504C2×#95—612no—
505C2×#95—612no—
506C2×#95—612no—
507C2×#95—612no—
508C2×#95—612no—
509C2×#95—612no—
510C61#1387311yescharacteristic, complemented, Sylow
511C25—24no—
512C25—24no—
513C25—22no—
514C25—22no—
515C25—22no—
516C25—22no—
517C25—22no—
518C25—22no—
519C25—42no—
520C25—42no—
521C25C4×D6114yes—
522C25C22×D6111yescharacteristic
523C25C22×D6111yescharacteristic
524C25C22×D6111yescharacteristic
525C23×C4—611no—
526C23×C4—611no—
527C23×C4—612no—
528C23×C4—611no—
529C23×C4—611no—
530C23×C4—614no—
531C23×C4—614no—
532C23×C4—612no—
533C23×C4—1224no—
534C23×C4—1224no—
535C23×C4—1222no—
536C23×C4—1222no—
537C23×C4—1222no—
538C23×C4—1222no—
539C23×C4—2442no—
540C23×C4—2442no—
541C23×C4C22×D6112yes—
542C23×C4C22×D6112yes—
543C2×C4⋊C4—1224no—
544C2×C4⋊C4—1224no—
545C2×C4⋊C4—2442no—
546C2×C22⋊C4—22no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—614no—
558C2×C22⋊C4—618no—
559C2×C22⋊C4—614no—
560C2×C22⋊C4—614no—
561C2×C22⋊C4—614no—
562C2×C22⋊C4—614no—
563C2×C22⋊C4—12232no—
564C2×C22⋊C4—1224no—
565C2×C22⋊C4—1224no—
566C2×C22⋊C4—1224no—
567C2×C22⋊C4—1222no—
568C2×C22⋊C4—1222no—
569C2×C22⋊C4—1224no—
570C2×C22⋊C4—1224no—
571C2×C22⋊C4—1222no—
572C2×C22⋊C4—1222no—
573C2×C22⋊C4—1224no—
574C2×C22⋊C4—1224no—
575C2×C22⋊C4—1222no—
576C2×C22⋊C4—2442no—
577C2×C22⋊C4—2442no—
578C2×C22⋊C4C22⋊D6114yes—
579C2×C42—1224no—
580C2×C42—1224no—
581C2×C42—2442no—
582#95—1224no—
583#95—1224no—
584#95—1224no—
585#95—1224no—
586#95—2442no—
587#95—2442no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—216no—
593C24—216no—
594C24—22no—
595C24—21no—
596C24—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—22no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—28no—
613C24—28no—
614C24—28no—
615C24—28no—
616C24—28no—
617C24—44no—
618C24—44no—
619C24—48no—
620C24—48no—
621C24—48no—
622C24—48no—
623C24—48no—
624C24—48no—
625C24—48no—
626C24—48no—
627C24—48no—
628C24—48no—
629C24—44no—
630C24—44no—
631C24—44no—
632C24—44no—
633C24C2×C4×D6112yes—
634C24C2×C4×D6112yes—
635C24C2×C4×D6112yes—
636C24#1175822212yes—
637C24D4×D6114yes—
638C24D4×D6112yes—
639C24#1175822414yes—
640C24#1175822412yes—
641C24#1175822412yes—
642C24#1175822412yes—
643C24C2×C22⋊D6112yes—
644C24C23×D6111yescharacteristic
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—612no—
659C22×C4—612no—
660C22×C4—614no—
661C22×C4—614no—
662C22×C4—612no—
663C22×C4—612no—
664C22×C4—614no—
665C22×C4—1228no—
666C22×C4—1228no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1222no—
672C22×C4—1222no—
673C22×C4—1221no—
674C22×C4—1222no—
675C22×C4—1222no—
676C22×C4—1222no—
677C22×C4—1221no—
678C22×C4—1222no—
679C22×C4—1222no—
680C22×C4—1222no—
681C22×C4—1221no—
682C22×C4—1221no—
683C22×C4—1222no—
684C22×C4—1222no—
685C22×C4—1222no—
686C22×C4—1222no—
687C22×C4—1228no—
688C22×C4—1228no—
689C22×C4—1222no—
690C22×C4—1222no—
691C22×C4—1222no—
692C22×C4—1222no—
693C22×C4—1222no—
694C22×C4—1222no—
695C22×C4—1222no—
696C22×C4—2444no—
697C22×C4—2444no—
698C22×C4—2448no—
699C22×C4—2448no—
700C22×C4—2448no—
701C22×C4—2448no—
702C22×C4C2×C22⋊D6114yes—
703C4⋊C4—2448no—
704C22⋊C4—28no—
705C22⋊C4—48no—
706C22⋊C4—48no—
707C22⋊C4—44no—
708C22⋊C4—6116no—
709C22⋊C4—1228no—
710C22⋊C4—1228no—
711C22⋊C4—1228no—
712C22⋊C4—1228no—
713C22⋊C4—2448no—
714C22⋊C4—2448no—
715C22⋊C4—2444no—
716C42—2448no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—232no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—416no—
759C23—416no—
760C23—416no—
761C23—416no—
762C23—432no—
763C23—432no—
764C23—432no—
765C23—432no—
766C23—416no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—416no—
786C23—42no—
787C23—42no—
788C23C22⋊C4×D6114yes—
789C23#1451973314yes—
790C23#1451973314yes—
791C23#1451973714yes—
792C23C4×C22⋊D6114yes—
793C23#1451974814yes—
794C23#1451975814yes—
795C23#1451976314yes—
796C23#1451977014yes—
797C23C22×C4×D6111yescharacteristic
798C23C2×D4×D6112yes—
799C23C2×D4×D6111yescharacteristic
800C23C22×C22⋊D6111yescharacteristic
801C23C2×#1175822411yescharacteristic
802C23C2×#1175822411yescharacteristic
803C23C2×#1175822412yes—
804C23C2×#1175822411yescharacteristic
805C23C2×#1175822211yescharacteristic
806C23#1451982212yes—
807C23#1451982212yes—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—614no—
823C2×C4—614no—
824C2×C4—1222no—
825C2×C4—1222no—
826C2×C4—1222no—
827C2×C4—1222no—
828C2×C4—1224no—
829C2×C4—1224no—
830C2×C4—1224no—
831C2×C4—1224no—
832C2×C4—1222no—
833C2×C4—1222no—
834C2×C4—1222no—
835C2×C4—1222no—
836C2×C4—1222no—
837C2×C4—1222no—
838C2×C4—1224no—
839C2×C4—1224no—
840C2×C4—1224no—
841C2×C4—24416no—
842C2×C4—24416no—
843C2×C4—2442no—
844C2×C4—2442no—
845C2×C4—2442no—
846C2×C4—2442no—
847C2×C4—2442no—
848C2×C4—2442no—
849C2×C4—2442no—
850C2×C4—2442no—
851C2×C4—2442no—
852C2×C4—2442no—
853C2×C4—2442no—
854C2×C4—2442no—
855C2×C4—2442no—
856C2×C4—2442no—
857C2×C4—2442no—
858C22—24no—
859C22—28no—
860C22—28no—
861C22—28no—
862C22—24no—
863C22—24no—
864C22—28no—
865C22—24no—
866C22—24no—
867C22—24no—
868C22—24no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—24no—
874C22—464no—
875C22—42no—
876C22—42no—
877C22—44no—
878C22—44no—
879C22—44no—
880C22—44no—
881C22—44no—
882C22—44no—
883C22—42no—
884C22—42no—
885C22—44no—
886C22—44no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22#1683965018yescomplemented
892C22C2×C22⋊C4×D6111yescharacteristic
893C22C2×#1451973311yescharacteristic
894C22C2×#1451973311yescharacteristic
895C22C2×#1451973711yescharacteristic
896C22C2×C4×C22⋊D6111yescharacteristic
897C22#1684023511yescharacteristic
898C22#1684023511yescharacteristic
899C22C2×#1451974811yescharacteristic
900C22C2×#1451975811yescharacteristic
901C22#1684026812yes—
902C22#1684026812yes—
903C22C2×#1451976311yescharacteristic
904C22C2×#1451977011yescharacteristic
905C22#1684034712yes—
906C22#1684034712yes—
907C22#1684039412yes—
908C22D4×C22⋊D6112yes—
909C22#1684039912yes—
910C22#1684039912yes—
911C22#1684040212yes—
912C22#1684040612yes—
913C22#1684043812yes—
914C22#1684044312yes—
915C4—44no—
916C4—82no—
917C4—1224no—
918C4—1224no—
919C4—4882no—
920C4—2444no—
921C4—2442no—
922C4—2442no—
923C2—28no—
924C2—44no—
925C2—44no—
926C2#2144819711yescharacteristic
927C2C2×#1683965011yescharacteristic
928C2#2144841511yescharacteristic
929C2#2144863511yescharacteristic
930C2C22⋊C4×C22⋊D6111yescharacteristic
931C2#2144866411yescharacteristic
932C2#2144867011yescharacteristic
933C2#2144927712yes—
934C2#2144935112yes—
935C2#2144994212yes—
936C2#2145006412yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#379C2
socle, cosocleC24×C61C24
prime radicalC26×C61C22
hypercenterC2×#379D61
hypocenterC61#13873
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
2. C2×#16839650C2semidirect
3. C2×#16839620C2semidirect
5. C2×C22⋊C4×Dic61C2semidirect
6. #21444066C2semidirect
7. #21444062C2semidirect
8. #21444056C2semidirect
9. #21444041C2semidirect
10. #21444041C2semidirect
14. C22×#11758196C22semidirect
16. C22×C22⋊Dic61C4semidirect
25. C22×C4×Dic61C22semidirect
30. C2×#14519684C22semidirect
31. C2×#14519684C22semidirect
32. C2×#14519684C22semidirect
33. C2×#14519684C22semidirect
34. C2×#14519684C22semidirect
35. C2×#14519684C22semidirect
245. C22⋊Dic61C22⋊C4semidirect
423. C22×C61#388semidirect
510. C61#13873semidirect
891. C22#16839650semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊Dic612
C2×#168396502
C2×#168396202
C2×#168396182
C2×C22⋊C4×Dic612
#214440662
#214440622
#214440562
#214440412
C2×C61×#3792
#1387361