Finite Group Databasebeta

← #29601931

Subgroups — #29601931

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
1C2×#16839655C212yesmaximal, complemented
2C2×#16839622C211yesmaximal, characteristic, complemented
3C2×#16839618C211yesmaximal, characteristic
4C2×#16839618C211yesmaximal, characteristic
5C2×C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
6#21444068C212yesmaximal, complemented
7#21444064C212yesmaximal, complemented
8#21444056C212yesmaximal, complemented
9#21444042C211yesmaximal, characteristic, complemented
10#21444042C211yesmaximal, characteristic, complemented
11C23×C22⋊C4×C61C211yesmaximal, characteristic
12C22×C4⋊Dic61C2212yescomplemented
13C22×C22⋊Dic61C2211yescharacteristic
14C22×C22⋊Dic61C2211yescharacteristic
15C22×C22⋊Dic61C2212yes—
16C22×C22⋊Dic61C2212yes—
17C22×C22⋊Dic61C2212yes—
18C22×C22⋊Dic61C2212yes—
19C22×C22⋊Dic61C2211yescharacteristic
20C22×C22⋊Dic61C2211yescharacteristic
21C22×C4×Dic61C2212yescomplemented
22#16839655—28no—
23#16839622—24no—
24#16839618—24no—
25#16839618—24no—
26C4×C22⋊Dic61—24no—
27C2×#14519684C2212yescomplemented
28C2×#14519684C2212yescomplemented
29C2×#14519684C2212yescomplemented
30C2×#14519684C2212yescomplemented
31C2×#14519684C2212yescomplemented
32C2×#14519684C2212yescomplemented
33C26×C61C2211yescharacteristic
34C24×C4×C61C2211yescharacteristic
35C24×C4×C61C2211yescharacteristic
36C22×C22⋊C4×C61—28no—
37C22×C22⋊C4×C61C418yescomplemented
38C22×C22⋊C4×C61C2211yescharacteristic
39C22×C22⋊C4×C61C2211yescharacteristic
40C22×C22⋊C4×C61C2211yescharacteristic
41C22×C22⋊C4×C61C2211yescharacteristic
42C23×Dic61C2312yes—
43C23×Dic61C2312yes—
44C23×Dic61C2312yes—
45C23×Dic61C2312yes—
46C2×C4⋊Dic61—24no—
47C2×C4⋊Dic61—24no—
48C2×C4⋊Dic61—42no—
49C2×C22⋊Dic61—22no—
50C2×C22⋊Dic61—22no—
51C2×C22⋊Dic61—22no—
52C2×C22⋊Dic61—22no—
53C2×C22⋊Dic61—22no—
54C2×C22⋊Dic61—22no—
55C2×C22⋊Dic61—22no—
56C2×C22⋊Dic61—24no—
57C2×C22⋊Dic61—24no—
58C2×C22⋊Dic61—24no—
59C2×C22⋊Dic61—24no—
60C2×C22⋊Dic61—22no—
61C2×C22⋊Dic61—22no—
62C2×C22⋊Dic61—22no—
63C2×C22⋊Dic61—24no—
64C2×C22⋊Dic61—24no—
65C2×C22⋊Dic61—24no—
66C2×C22⋊Dic61—24no—
67C2×C22⋊Dic61—42no—
68C2×C22⋊Dic61—42no—
69C2×C22⋊Dic61—42no—
70C2×C22⋊Dic61—42no—
71C2×C22⋊Dic61D414yes—
72C2×C22⋊Dic61D414yes—
73C2×C4×Dic61—24no—
74C2×C4×Dic61—24no—
75C2×C4×Dic61—42no—
76#14519684—24no—
77#14519684—24no—
78#14519684—24no—
79#14519684—24no—
80#14519684—42no—
81#14519684—42no—
82C25×C61—24no—
83C25×C61—24no—
84C25×C61—22no—
85C25×C61—22no—
86C25×C61—22no—
87C25×C61—22no—
88C25×C61—22no—
89C25×C61—22no—
90C25×C61—42no—
91C25×C61—42no—
92C25×C61C2×C414yes—
93C25×C61C2311yescharacteristic
94C25×C61C2311yescharacteristic
95C25×C61C2311yescharacteristic
96C23×C4×C61—22no—
97C23×C4×C61—22no—
98C23×C4×C61—22no—
99C23×C4×C61—22no—
100C23×C4×C61—24no—
101C23×C4×C61—24no—
102C23×C4×C61—42no—
103C23×C4×C61—42no—
104C23×C4×C61C2×C414yes—
105C23×C4×C61C2×C414yes—
106C23×C4×C61C2311yescharacteristic
107C23×C4×C61C2311yescharacteristic
108C23×C4×C61C2311yescharacteristic
109C23×C4×C61C2311yescharacteristic
110C2×C22⋊C4×C61—24no—
111C2×C22⋊C4×C61—24no—
112C2×C22⋊C4×C61—24no—
113C2×C22⋊C4×C61—232no—
114C2×C22⋊C4×C61C2×C414yes—
115C2×C22⋊C4×C61C2×C414yes—
116C2×C22⋊C4×C61C2×C414yes—
117C2×C22⋊C4×C61C2×C414yes—
118C2×C22⋊C4×C61D418yes—
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—22no—
129C24×C61—21no—
130C24×C61—21no—
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—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61—28no—
183C22×C4×C61—28no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61—28no—
193C22×C4×C61—28no—
194C22×C4×C61—44no—
195C22×C4×C61—44no—
196C22×C4×C61—48no—
197C22×C4×C61—48no—
198C22×C4×C61—48no—
199C22×C4×C61—48no—
200C22×C4×C61C22×C412yes—
201C22×C4×C61C22×C412yes—
202C22×C4×C61C22×C412yes—
203C22×C4×C61C22×C412yes—
204C22×C4×C61C2×D414yes—
205C22×C4×C61C2×D414yes—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—22no—
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—22no—
226C22×Dic61—22no—
227C22×Dic61—22no—
228C22×Dic61—22no—
229C22×Dic61—22no—
230C22×Dic61—22no—
231C22×Dic61—22no—
232C22×Dic61C2×D414yes—
233C22×Dic61C2×D414yes—
234C22⋊C4×C61—28no—
235C22⋊C4×C61—28no—
236C22⋊C4×C61—28no—
237C22⋊C4×C61C22⋊C4116yescomplemented
238C22⋊Dic61—28no—
239C22⋊Dic61—28no—
240C22⋊Dic61—48no—
241C22⋊Dic61—48no—
242C22⋊Dic61—48no—
243C22⋊Dic61—48no—
244C22⋊Dic61—44no—
245C22⋊Dic61—44no—
246C4⋊Dic61—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—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—24no—
344C2×C4×C61—24no—
345C2×C4×C61—24no—
346C2×C4×C61—24no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—416no—
354C2×C4×C61—416no—
355C2×C4×C61—42no—
356C2×C4×C61—42no—
357C2×C4×C61—42no—
358C2×C4×C61—42no—
359C2×C4×C61C2×C22⋊C414yes—
360C2×C4×C61C2×C22⋊C414yes—
361C2×Dic61—24no—
362C2×Dic61—24no—
363C2×Dic61—24no—
364C2×Dic61—24no—
365C2×Dic61—24no—
366C2×Dic61—24no—
367C2×Dic61—42no—
368C2×Dic61—42no—
369C2×Dic61—42no—
370C2×Dic61—42no—
371C2×Dic61—42no—
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×Dic61—42no—
388C2×Dic61—42no—
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—24no—
448C4×C61—24no—
449C4×C61—42no—
450C4×C61—42no—
451Dic61—44no—
452Dic61—44no—
453Dic61—82no—
454Dic61—82no—
455C23×C22⋊C4D6111yescharacteristic
456C2×#388—612no—
457C2×#380—611no—
458C2×#379—611no—
459C2×#379—611no—
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×C4C2×D6111yescharacteristic
482C24×C4C2×D6111yescharacteristic
483C22×C4⋊C4—612no—
484C22×C22⋊C4—28no—
485C22×C22⋊C4—611no—
486C22×C22⋊C4—611no—
487C22×C22⋊C4—611no—
488C22×C22⋊C4—611no—
489C22×C22⋊C4—612no—
490C22×C22⋊C4—612no—
491C22×C22⋊C4—612no—
492C22×C22⋊C4—612no—
493C22×C22⋊C4Dic6118yescomplemented
494C22×C22⋊C4C2×D6111yescharacteristic
495C22×C22⋊C4C2×D6111yescharacteristic
496C22×C22⋊C4C2×D6111yescharacteristic
497C22×C22⋊C4C2×D6111yescharacteristic
498C22×C42—612no—
499#388—1228no—
500#380—1224no—
501#379—1224no—
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—22no—
513C25—22no—
514C25—24no—
515C25—22no—
516C25—22no—
517C25—22no—
518C25—22no—
519C25—42no—
520C25—42no—
521C25C2×Dic6114yes—
522C25C22×D6111yescharacteristic
523C25C22×D6111yescharacteristic
524C25C22×D6111yescharacteristic
525C23×C4—22no—
526C23×C4—22no—
527C23×C4—22no—
528C23×C4—22no—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—42no—
532C23×C4—42no—
533C23×C4—612no—
534C23×C4—612no—
535C23×C4—612no—
536C23×C4—612no—
537C23×C4C2×Dic6114yes—
538C23×C4C2×Dic6114yes—
539C23×C4C22×D6111yescharacteristic
540C23×C4C22×D6111yescharacteristic
541C23×C4C22×D6111yescharacteristic
542C23×C4C22×D6111yescharacteristic
543C2×C4⋊C4—1224no—
544C2×C4⋊C4—1224no—
545C2×C4⋊C4—2442no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—232no—
550C2×C22⋊C4—614no—
551C2×C22⋊C4—614no—
552C2×C22⋊C4—1222no—
553C2×C22⋊C4—1222no—
554C2×C22⋊C4—1222no—
555C2×C22⋊C4—1222no—
556C2×C22⋊C4—1224no—
557C2×C22⋊C4—1224no—
558C2×C22⋊C4—1224no—
559C2×C22⋊C4—1224no—
560C2×C22⋊C4—1224no—
561C2×C22⋊C4—1224no—
562C2×C22⋊C4—1222no—
563C2×C22⋊C4—1222no—
564C2×C22⋊C4—1222no—
565C2×C22⋊C4—1222no—
566C2×C22⋊C4—1222no—
567C2×C22⋊C4—1222no—
568C2×C22⋊C4—1224no—
569C2×C22⋊C4—1224no—
570C2×C22⋊C4—2442no—
571C2×C22⋊C4—2442no—
572C2×C22⋊C4—2442no—
573C2×C22⋊C4—2442no—
574C2×C22⋊C4C2×Dic6114yes—
575C2×C22⋊C4C2×Dic6114yes—
576C2×C22⋊C4C2×Dic6114yes—
577C2×C22⋊C4C2×Dic6114yes—
578C2×C22⋊C4C22⋊D6118yes—
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—21no—
595C24—21no—
596C24—21no—
597C24—21no—
598C24—22no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—22no—
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—
633C24#1175822214yes—
634C24#1175822212yes—
635C24#1175822212yes—
636C24D4×D6112yes—
637C24D4×D6112yes—
638C24#1175822412yes—
639C24#1175822412yes—
640C24C22×Dic6112yes—
641C24C22×Dic6112yes—
642C24C22×Dic6112yes—
643C24C2×C22⋊D6114yes—
644C24C23×D6111yescharacteristic
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—28no—
660C22×C4—28no—
661C22×C4—28no—
662C22×C4—28no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—48no—
666C22×C4—48no—
667C22×C4—48no—
668C22×C4—48no—
669C22×C4—614no—
670C22×C4—614no—
671C22×C4—1222no—
672C22×C4—1222no—
673C22×C4—1222no—
674C22×C4—1222no—
675C22×C4—1222no—
676C22×C4—1222no—
677C22×C4—1222no—
678C22×C4—1222no—
679C22×C4—1222no—
680C22×C4—1222no—
681C22×C4—1222no—
682C22×C4—1222no—
683C22×C4—1222no—
684C22×C4—1222no—
685C22×C4—1222no—
686C22×C4—1222no—
687C22×C4—1222no—
688C22×C4—1222no—
689C22×C4—1222no—
690C22×C4—1222no—
691C22×C4—1222no—
692C22×C4—1222no—
693C22×C4—1222no—
694C22×C4—1222no—
695C22×C4—1222no—
696C22×C4—1222no—
697C22×C4C22×Dic6112yes—
698C22×C4C22×Dic6112yes—
699C22×C4C22×Dic6112yes—
700C22×C4C22×Dic6112yes—
701C22×C4C2×C22⋊D6114yes—
702C22×C4C2×C22⋊D6114yes—
703C4⋊C4—2448no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—1228no—
708C22⋊C4—1228no—
709C22⋊C4—2448no—
710C22⋊C4—2448no—
711C22⋊C4—2448no—
712C22⋊C4—2448no—
713C22⋊C4—2444no—
714C22⋊C4—2444no—
715C22⋊C4C22⋊Dic61116yescomplemented
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—
788C23C2×C22⋊Dic6114yes—
789C23#1451973614yes—
790C23#1451973614yes—
791C23D4×Dic6114yes—
792C23D4×Dic6114yes—
793C23#1451975014yes—
794C23#1451975914yes—
795C23#1451976314yes—
796C23#1451977014yes—
797C23C23×Dic6111yescharacteristic
798C23C2×D4×D6111yescharacteristic
799C23C2×D4×D6111yescharacteristic
800C23C22×C22⋊D6112yes—
801C23C2×#1175822411yescharacteristic
802C23C2×#1175822411yescharacteristic
803C23C2×#1175822211yescharacteristic
804C23C2×#1175822211yescharacteristic
805C23C2×#1175822212yes—
806C23#1451982212yes—
807C23#1451982212yes—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—416no—
823C2×C4—416no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—1224no—
829C2×C4—1224no—
830C2×C4—1224no—
831C2×C4—1224no—
832C2×C4—1224no—
833C2×C4—1224no—
834C2×C4—2442no—
835C2×C4—2442no—
836C2×C4—2442no—
837C2×C4—2442no—
838C2×C4—2442no—
839C2×C4—2442no—
840C2×C4—2442no—
841C2×C4—2442no—
842C2×C4—2442no—
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×C4C2×C22⋊Dic6114yes—
857C2×C4C2×C22⋊Dic6114yes—
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#1683965518yescomplemented
892C22C22×C22⋊Dic6111yescharacteristic
893C22C2×#1451973611yescharacteristic
894C22C2×#1451973611yescharacteristic
895C22C2×D4×Dic6111yescharacteristic
896C22C2×D4×Dic6111yescharacteristic
897C22#1684023711yescharacteristic
898C22#1684023711yescharacteristic
899C22C2×#1451975011yescharacteristic
900C22C2×#1451975911yescharacteristic
901C22#1684027312yes—
902C22#1684027312yes—
903C22C2×#1451976311yescharacteristic
904C22C2×#1451977011yescharacteristic
905C22#1684035012yes—
906C22#1684035012yes—
907C22D4×C22⋊D6112yes—
908C22D4×C22⋊D6112yes—
909C22#1684040212yes—
910C22#1684040212yes—
911C22#1684040612yes—
912C22#1684040612yes—
913C22#1684043812yes—
914C22#1684043812yes—
915C4—24no—
916C4—24no—
917C4—42no—
918C4—42no—
919C4—4882no—
920C4—4882no—
921C4—2444no—
922C4—2444no—
923C2—28no—
924C2—44no—
925C2—44no—
926C2#2144820211yescharacteristic
927C2C2×#1683965511yescharacteristic
928C2#2144841711yescharacteristic
929C2D4×C22⋊Dic6111yescharacteristic
930C2D4×C22⋊Dic6111yescharacteristic
931C2#2144866811yescharacteristic
932C2#2144866811yescharacteristic
933C2#2144928112yes—
934C2#2144935512yes—
935C2#2144993912yes—
936C2#2145005912yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC23×C22⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC26×C61C22
hypercenterC23×C22⋊C4D61
hypocenterC61#13873
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16839655C2semidirect
2. C2×#16839622C2semidirect
5. C2×C4×C22⋊Dic61C2semidirect
6. #21444068C2semidirect
7. #21444064C2semidirect
8. #21444056C2semidirect
9. #21444042C2semidirect
10. #21444042C2semidirect
12. C22×C4⋊Dic61C22semidirect
21. C22×C4×Dic61C22semidirect
27. C2×#14519684C22semidirect
28. C2×#14519684C22semidirect
29. C2×#14519684C22semidirect
30. C2×#14519684C22semidirect
31. C2×#14519684C22semidirect
32. C2×#14519684C22semidirect
37. C22×C22⋊C4×C61C4semidirect
237. C22⋊C4×C61C22⋊C4semidirect
423. C22×C61#388semidirect
493. C22×C22⋊C4Dic61semidirect
510. C61#13873semidirect
715. C22⋊C4C22⋊Dic61semidirect
891. C22#16839655semidirect

Maximal subgroups

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

subgroupindex
C2×#168396552
C2×#168396222
C2×#168396182
C2×C4×C22⋊Dic612
#214440682
#214440642
#214440562
#214440422
C23×C22⋊C4×C612
#1387361