Finite Group Databasebeta

← #29601925

Subgroups — #29601925

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×#11758198C211yesmaximal, characteristic
2C2×#16839653C212yesmaximal, complemented
3C2×#16839620C211yesmaximal, characteristic, complemented
4C2×#16839617C211yesmaximal, characteristic
5C2×#16839617C211yesmaximal, characteristic
6#21444067C212yesmaximal, complemented
7#21444063C212yesmaximal, complemented
8#21444057C212yesmaximal, complemented
9#21444042C211yesmaximal, characteristic, complemented
10#21444041C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
12C25×D61C2211yescharacteristic
13C24×Dic61C2211yescharacteristic
14C22×#11758196C2212yescomplemented
15C22×C22⋊Dic61C2211yescharacteristic
16C22×C22⋊Dic61C2211yescharacteristic
17C22×#11758198—28no—
18C22×#11758198C418yescomplemented
19C22×#11758198C2212yes—
20C22×#11758198C2212yes—
21C22×#11758198C2212yes—
22C22×#11758198C2212yes—
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27#16839653—28no—
28#16839620—24no—
29#16839617—24no—
30#16839617—24no—
31C2×#14519684C2212yescomplemented
32C2×#14519684C2212yescomplemented
33C2×#14519684C2212yescomplemented
34C2×#14519684C2212yescomplemented
35C2×#14519684C2212yescomplemented
36C24×C4×C61C2211yescharacteristic
37C22×C22⋊C4×C61C2211yescharacteristic
38C22×C22⋊C4×C61C2211yescharacteristic
39C22×C42×C61C2212yescomplemented
40C4×C22⋊C4×C61—24no—
41C2×#95×C61C2212yescomplemented
42C24×D61—22no—
43C24×D61—22no—
44C24×D61—24no—
45C24×D61—24no—
46C24×D61—22no—
47C24×D61—22no—
48C24×D61—22no—
49C24×D61—22no—
50C24×D61—42no—
51C24×D61—42no—
52C24×D61C2×C414yes—
53C24×D61C2311yescharacteristic
54C24×D61C2311yescharacteristic
55C23×Dic61—22no—
56C23×Dic61—22no—
57C23×Dic61—24no—
58C23×Dic61—42no—
59C23×Dic61C2×C414yes—
60C23×Dic61C2312yes—
61C23×Dic61C2312yes—
62C23×Dic61C2311yescharacteristic
63C23×Dic61C2311yescharacteristic
64C2×#11758196—24no—
65C2×#11758196—24no—
66C2×#11758196—42no—
67C2×C22⋊Dic61—22no—
68C2×C22⋊Dic61—22no—
69C2×C22⋊Dic61—22no—
70C2×C22⋊Dic61—22no—
71C2×C22⋊Dic61—22no—
72C2×C22⋊Dic61—22no—
73C2×#11758198—24no—
74C2×#11758198—24no—
75C2×#11758198—24no—
76C2×#11758198—232no—
77C2×#11758198—24no—
78C2×#11758198—24no—
79C2×#11758198—24no—
80C2×#11758198—24no—
81C2×#11758198—24no—
82C2×#11758198—24no—
83C2×#11758198—24no—
84C2×#11758198—24no—
85C2×#11758198—42no—
86C2×#11758198—42no—
87C2×#11758198—42no—
88C2×#11758198—42no—
89C2×#11758198C2×C414yes—
90C2×#11758198C2×C414yes—
91C2×#11758198C2×C414yes—
92C2×#11758198C2×C414yes—
93C2×#11758198D418yes—
94#14519684—24no—
95#14519684—24no—
96#14519684—24no—
97#14519684—42no—
98#14519684—42no—
99C25×C61C2311yescharacteristic
100C23×C4×C61—22no—
101C23×C4×C61—22no—
102C23×C4×C61—24no—
103C23×C4×C61—42no—
104C23×C4×C61C2×C414yes—
105C23×C4×C61C2311yescharacteristic
106C23×C4×C61C2312yes—
107C23×C4×C61C2312yes—
108C23×C4×C61C2311yescharacteristic
109C2×C22⋊C4×C61—22no—
110C2×C22⋊C4×C61—22no—
111C2×C22⋊C4×C61—22no—
112C2×C22⋊C4×C61—22no—
113C2×C22⋊C4×C61D414yes—
114C2×C22⋊C4×C61D414yes—
115C2×C42×C61—24no—
116C2×C42×C61—24no—
117C2×C42×C61—42no—
118#95×C61—24no—
119C24×C61—22no—
120C24×C61—22no—
121C24×C61—22no—
122C24×C61—22no—
123C24×C61C22×C412yes—
124C24×C61C2×D412yes—
125C24×C61C2×D412yes—
126C24×C61#4112yes—
127C24×C61#4112yes—
128C24×C61#4112yes—
129C24×C61#4112yes—
130C24×C61C2411yescharacteristic
131C23×D61—216no—
132C23×D61—216no—
133C23×D61—28no—
134C23×D61—22no—
135C23×D61—21no—
136C23×D61—21no—
137C23×D61—21no—
138C23×D61—21no—
139C23×D61—21no—
140C23×D61—21no—
141C23×D61—22no—
142C23×D61—21no—
143C23×D61—21no—
144C23×D61—21no—
145C23×D61—21no—
146C23×D61—21no—
147C23×D61—21no—
148C23×D61—22no—
149C23×D61—22no—
150C23×D61—22no—
151C23×D61—22no—
152C23×D61—28no—
153C23×D61—28no—
154C23×D61—28no—
155C23×D61—28no—
156C23×D61—44no—
157C23×D61—44no—
158C23×D61—48no—
159C23×D61—48no—
160C23×D61—48no—
161C23×D61—48no—
162C23×D61—48no—
163C23×D61—48no—
164C23×D61—48no—
165C23×D61—48no—
166C23×D61—48no—
167C23×D61—48no—
168C23×D61—44no—
169C23×D61—44no—
170C23×D61—44no—
171C23×D61—44no—
172C23×D61C22×C412yes—
173C23×D61C22×C412yes—
174C23×D61C2×D414yes—
175C23×D61#4114yes—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—22no—
179C22×C4×C61—28no—
180C22×C4×C61—21no—
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—21no—
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—28no—
197C22×C4×C61—44no—
198C22×C4×C61—48no—
199C22×C4×C61—48no—
200C22×C4×C61C22×C412yes—
201C22×C4×C61C22×C412yes—
202C22×C4×C61C2×D414yes—
203C22×C4×C61C2×D414yes—
204C22×C4×C61C2×D414yes—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—22no—
208C22×Dic61—28no—
209C22×Dic61—21no—
210C22×Dic61—22no—
211C22×Dic61—21no—
212C22×Dic61—22no—
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—22no—
222C22×Dic61—22no—
223C22×Dic61—22no—
224C22×Dic61—22no—
225C22×Dic61—22no—
226C22×Dic61—22no—
227C22×Dic61—22no—
228C22×Dic61—44no—
229C22×Dic61—48no—
230C22×Dic61—48no—
231C22×Dic61C22×C412yes—
232C22×Dic61C22×C412yes—
233C22×Dic61C2×D414yes—
234C22⋊C4×C61—28no—
235C22⋊C4×C61—28no—
236C42×C61—48no—
237C22⋊Dic61—44no—
238C22⋊Dic61—44no—
239#11758198—28no—
240#11758198—28no—
241#11758198—28no—
242#11758198—48no—
243#11758198—48no—
244#11758198—48no—
245#11758198—48no—
246#11758198C22⋊C4116yescomplemented
247#11758196—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#11714yes—
265C23×C61C4×D414yes—
266C23×C61C4×D414yes—
267C23×C61#12114yes—
268C23×C61#12314yes—
269C23×C61#12414yes—
270C23×C61#12614yes—
271C23×C61C23×C411yescharacteristic
272C23×C61C22×D412yes—
273C23×C61C22×D411yescharacteristic
274C23×C61C22×D411yescharacteristic
275C23×C61C2×#4111yescharacteristic
276C23×C61C2×#4111yescharacteristic
277C23×C61C2×#4112yes—
278C23×C61C2×#4111yescharacteristic
279C23×C61C2×#4111yescharacteristic
280C23×C61H(5,𝔽2)12yes—
281C23×C61H(5,𝔽2)12yes—
282C22×D61—232no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—22no—
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—24no—
296C22×D61—24no—
297C22×D61—24no—
298C22×D61—24no—
299C22×D61—24no—
300C22×D61—24no—
301C22×D61—24no—
302C22×D61—24no—
303C22×D61—24no—
304C22×D61—24no—
305C22×D61—24no—
306C22×D61—24no—
307C22×D61—416no—
308C22×D61—416no—
309C22×D61—416no—
310C22×D61—416no—
311C22×D61—416no—
312C22×D61—432no—
313C22×D61—432no—
314C22×D61—432no—
315C22×D61—432no—
316C22×D61—41no—
317C22×D61—41no—
318C22×D61—41no—
319C22×D61—41no—
320C22×D61—41no—
321C22×D61—41no—
322C22×D61—41no—
323C22×D61—41no—
324C22×D61—42no—
325C22×D61—42no—
326C22×D61—42no—
327C22×D61—42no—
328C22×D61—42no—
329C22×D61—42no—
330C22×D61—42no—
331C22×D61—42no—
332C22×D61—42no—
333C22×D61—42no—
334C22×D61—42no—
335C22×D61—42no—
336C22×D61—416no—
337C22×D61C2×C22⋊C414yes—
338C22×D61#11714yes—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—24no—
342C2×C4×C61—24no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—24no—
347C2×C4×C61—24no—
348C2×C4×C61—24no—
349C2×C4×C61—24no—
350C2×C4×C61—24no—
351C2×C4×C61—24no—
352C2×C4×C61—416no—
353C2×C4×C61—42no—
354C2×C4×C61—42no—
355C2×C4×C61—42no—
356C2×C4×C61—42no—
357C2×C4×C61—42no—
358C2×C4×C61—42no—
359C2×C4×C61—42no—
360C2×C4×C61—42no—
361C2×C4×C61—42no—
362C2×C4×C61—42no—
363C2×C4×C61C2×C22⋊C414yes—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—24no—
367C2×Dic61—24no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—22no—
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×Dic61—42no—
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#38818yescomplemented
401C22×C61C22×C22⋊C411yescharacteristic
402C22×C61C2×#11711yescharacteristic
403C22×C61C2×#11711yescharacteristic
404C22×C61C2×C4×D411yescharacteristic
405C22×C61C2×C4×D411yescharacteristic
406C22×C61#51811yescharacteristic
407C22×C61#51811yescharacteristic
408C22×C61C2×#12111yescharacteristic
409C22×C61C2×#12311yescharacteristic
410C22×C61#52512yes—
411C22×C61#52512yes—
412C22×C61C2×#12411yescharacteristic
413C22×C61C2×#12611yescharacteristic
414C22×C61#53812yes—
415C22×C61#53812yes—
416C22×C61D4212yes—
417C22×C61D4212yes—
418C22×C61#54612yes—
419C22×C61#54612yes—
420C22×C61#54612yes—
421C22×C61#54612yes—
422C22×C61#55112yes—
423C22×C61#55112yes—
424C2×D61—24no—
425C2×D61—24no—
426C2×D61—24no—
427C2×D61—24no—
428C2×D61—24no—
429C2×D61—24no—
430C2×D61—464no—
431C2×D61—42no—
432C2×D61—42no—
433C2×D61—42no—
434C2×D61—42no—
435C2×D61—42no—
436C2×D61—42no—
437C2×D61—44no—
438C2×D61—44no—
439C2×D61—44no—
440C2×D61—44no—
441C2×D61—44no—
442C2×D61—44no—
443C2×D61—44no—
444C2×D61—44no—
445C2×D61—42no—
446C2×D61—42no—
447C4×C61—24no—
448C4×C61—42no—
449C4×C61—44no—
450C4×C61—44no—
451Dic61—24no—
452Dic61—42no—
453Dic61—82no—
454Dic61—82no—
455C23×C22⋊C4—611no—
456C2×#388—612no—
457C2×#380—611no—
458C2×#379—611no—
459C2×#379—611no—
460C2×C4×C22⋊C4D6111yescharacteristic, complemented
461#1440—612no—
462#1439—612no—
463#1437—612no—
464C22⋊#95—611no—
465C22⋊#95—611no—
466C2×C61—28no—
467C2×C61#228011yescharacteristic
468C2×C61C2×#38811yescharacteristic
469C2×C61#231211yescharacteristic
470C2×C61D4×C22⋊C411yescharacteristic
471C2×C61D4×C22⋊C411yescharacteristic
472C2×C61#234211yescharacteristic
473C2×C61#234211yescharacteristic
474C2×C61#241812yes—
475C2×C61#242412yes—
476C2×C61#247212yes—
477C2×C61#248012yes—
478D61—44no—
479D61—44no—
480C26—611no—
481C24×C4—611no—
482C24×C4C2×D6111yescharacteristic
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—612no—
494C22×C22⋊C4—612no—
495C22×C22⋊C4—1228no—
496C22×C22⋊C4C2×D6111yescharacteristic
497C22×C22⋊C4C2×D6111yescharacteristic
498C22×C42C2×D6112yescomplemented
499#388—1228no—
500#380—1224no—
501#379—1224no—
502#379—1224no—
503C4×C22⋊C4—24no—
504C2×#95—612no—
505C2×#95—612no—
506C2×#95—612no—
507C2×#95—612no—
508C2×#95—612no—
509C2×#95C2×D6112yescomplemented
510C61#1387311yescharacteristic, complemented, Sylow
511C25—611no—
512C25—611no—
513C25—614no—
514C25—1224no—
515C25—1224no—
516C25—1222no—
517C25—1222no—
518C25—1222no—
519C25—1222no—
520C25—1222no—
521C25—1222no—
522C25—2442no—
523C25—2442no—
524C25C22×D6111yescharacteristic
525C23×C4—22no—
526C23×C4—22no—
527C23×C4—24no—
528C23×C4—42no—
529C23×C4—611no—
530C23×C4—611no—
531C23×C4—614no—
532C23×C4—612no—
533C23×C4—612no—
534C23×C4—1224no—
535C23×C4—1222no—
536C23×C4—1222no—
537C23×C4—2442no—
538C23×C4C4×D6114yes—
539C23×C4C22×D6111yescharacteristic
540C23×C4C22×D6112yes—
541C23×C4C22×D6112yes—
542C23×C4C22×D6111yescharacteristic
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—22no—
550C2×C22⋊C4—614no—
551C2×C22⋊C4—618no—
552C2×C22⋊C4—614no—
553C2×C22⋊C4—614no—
554C2×C22⋊C4—614no—
555C2×C22⋊C4—12232no—
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—1224no—
563C2×C22⋊C4—1222no—
564C2×C22⋊C4—1222no—
565C2×C22⋊C4—1222no—
566C2×C22⋊C4—1222no—
567C2×C22⋊C4—1222no—
568C2×C22⋊C4—1222no—
569C2×C22⋊C4—1224no—
570C2×C22⋊C4—1224no—
571C2×C22⋊C4—1224no—
572C2×C22⋊C4—1224no—
573C2×C22⋊C4—2442no—
574C2×C22⋊C4—2442no—
575C2×C22⋊C4—2442no—
576C2×C22⋊C4—2442no—
577C2×C22⋊C4D24414yes—
578C2×C22⋊C4C22⋊D6114yes—
579C2×C42—24no—
580C2×C42—24no—
581C2×C42—42no—
582#95—24no—
583#95—1224no—
584#95—1224no—
585#95—1224no—
586#95—2442no—
587#95—2442no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—612no—
593C24—612no—
594C24—614no—
595C24—614no—
596C24—1228no—
597C24—1228no—
598C24—12216no—
599C24—12216no—
600C24—1222no—
601C24—1221no—
602C24—1221no—
603C24—1221no—
604C24—1221no—
605C24—1222no—
606C24—1221no—
607C24—1221no—
608C24—1221no—
609C24—1221no—
610C24—1221no—
611C24—1221no—
612C24—1221no—
613C24—1221no—
614C24—1222no—
615C24—1222no—
616C24—1222no—
617C24—1222no—
618C24—1228no—
619C24—1228no—
620C24—1228no—
621C24—2444no—
622C24—2444no—
623C24—2448no—
624C24—2448no—
625C24—2448no—
626C24—2448no—
627C24—2448no—
628C24—2448no—
629C24—2448no—
630C24—2448no—
631C24—2448no—
632C24—2448no—
633C24—2444no—
634C24—2444no—
635C24—2444no—
636C24—2444no—
637C24C2×C4×D6112yes—
638C24C2×D24412yes—
639C24#1175822212yes—
640C24#1175822212yes—
641C24#1175822212yes—
642C24#1175822212yes—
643C24C2×C22⋊D6112yes—
644C24C23×D6111yescharacteristic
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—21no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—21no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—28no—
665C22×C4—28no—
666C22×C4—44no—
667C22×C4—48no—
668C22×C4—48no—
669C22×C4—612no—
670C22×C4—614no—
671C22×C4—612no—
672C22×C4—1228no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—1222no—
676C22×C4—1222no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1222no—
680C22×C4—1228no—
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—2444no—
696C22×C4—2448no—
697C22×C4—2448no—
698C22×C4C2×C4×D6112yes—
699C22×C4C2×C4×D6112yes—
700C22×C4C2×D24414yes—
701C22×C4D4×D6114yes—
702C22×C4C2×C22⋊D6114yes—
703C4⋊C4—2448no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—6116no—
707C22⋊C4—1228no—
708C22⋊C4—1228no—
709C22⋊C4—1228no—
710C22⋊C4—2448no—
711C22⋊C4—2448no—
712C22⋊C4—2448no—
713C22⋊C4—2448no—
714C22⋊C4—2444no—
715C22⋊C4—2444no—
716C42—48no—
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—614no—
734C23—614no—
735C23—12232no—
736C23—1222no—
737C23—1222no—
738C23—1222no—
739C23—1222no—
740C23—1222no—
741C23—1222no—
742C23—1222no—
743C23—1222no—
744C23—1222no—
745C23—1222no—
746C23—1222no—
747C23—1222no—
748C23—1224no—
749C23—1224no—
750C23—1224no—
751C23—1224no—
752C23—1224no—
753C23—1224no—
754C23—1224no—
755C23—1224no—
756C23—1224no—
757C23—1224no—
758C23—1224no—
759C23—1224no—
760C23—24416no—
761C23—24416no—
762C23—24416no—
763C23—24416no—
764C23—24432no—
765C23—24432no—
766C23—24432no—
767C23—24432no—
768C23—24416no—
769C23—2441no—
770C23—2441no—
771C23—2441no—
772C23—2441no—
773C23—2441no—
774C23—2441no—
775C23—2441no—
776C23—2441no—
777C23—2442no—
778C23—2442no—
779C23—2442no—
780C23—2442no—
781C23—2442no—
782C23—2442no—
783C23—2442no—
784C23—2442no—
785C23—2442no—
786C23—2442no—
787C23—24416no—
788C23—2442no—
789C23—2442no—
790C23#1451973414yes—
791C23C4×C22⋊D6114yes—
792C23C4×D24414yes—
793C23#1451975114yes—
794C23#1451976014yes—
795C23#1451976514yes—
796C23#1451977114yes—
797C23C22×C4×D6111yescharacteristic
798C23C2×D4×D6112yes—
799C23C22×C22⋊D6111yescharacteristic
800C23C22×D24411yescharacteristic
801C23#41×D6112yes—
802C23C2×#1175822211yescharacteristic
803C23C2×#1175822211yescharacteristic
804C23C2×#1175822211yescharacteristic
805C23C2×#1175822211yescharacteristic
806C23#1451982212yes—
807C23#1451982312yes—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—416no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—614no—
833C2×C4—1222no—
834C2×C4—1222no—
835C2×C4—1224no—
836C2×C4—1224no—
837C2×C4—1222no—
838C2×C4—1222no—
839C2×C4—1222no—
840C2×C4—24416no—
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×C4—2442no—
857C2×C4C22⋊C4×D6114yes—
858C22—24no—
859C22—28no—
860C22—28no—
861C22—28no—
862C22—24no—
863C22—24no—
864C22—28no—
865C22—24no—
866C22—24no—
867C22—24no—
868C22—1224no—
869C22—1224no—
870C22—1224no—
871C22—1224no—
872C22—1224no—
873C22—1224no—
874C22—24464no—
875C22—2442no—
876C22—2442no—
877C22—2444no—
878C22—2444no—
879C22—2444no—
880C22—2444no—
881C22—2444no—
882C22—2444no—
883C22—2442no—
884C22—2442no—
885C22—2444no—
886C22—2444no—
887C22—2442no—
888C22—2442no—
889C22—2442no—
890C22—2442no—
891C22#1683965318yescomplemented
892C22C2×C22⋊C4×D6111yescharacteristic
893C22#117×D6111yescharacteristic
894C22C2×#1451973411yescharacteristic
895C22C2×C4×C22⋊D6111yescharacteristic
896C22C2×C4×D24411yescharacteristic
897C22#1684023511yescharacteristic
898C22#1684023611yescharacteristic
899C22C2×#1451975111yescharacteristic
900C22C2×#1451976011yescharacteristic
901C22#1684027112yes—
902C22#1684027112yes—
903C22C2×#1451976511yescharacteristic
904C22C2×#1451977111yescharacteristic
905C22#1684034512yes—
906C22#1684034512yes—
907C22D4×C22⋊D6112yes—
908C22D4×D24412yes—
909C22#1684040012yes—
910C22#1684040212yes—
911C22#1684040712yes—
912C22#1684040812yes—
913C22#1684043612yes—
914C22#1684044112yes—
915C4—24no—
916C4—44no—
917C4—44no—
918C4—42no—
919C4—1224no—
920C4—4882no—
921C4—4882no—
922C4—2442no—
923C2—28no—
924C2—2444no—
925C2—2444no—
926C2#2144820011yescharacteristic
927C2C2×#1683965311yescharacteristic
928C2#2144841411yescharacteristic
929C2C22⋊C4×C22⋊D6111yescharacteristic
930C2C22⋊C4×D24411yescharacteristic
931C2#2144866911yescharacteristic
932C2#2144867111yescharacteristic
933C2#2144927512yes—
934C2#2144934912yes—
935C2#2144994512yes—
936C2#2145006512yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C4×C22⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC25×D61C22
hypercenterC2×C4×C22⋊C4D61
hypocenterC61#13873
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16839653C2semidirect
3. C2×#16839620C2semidirect
6. #21444067C2semidirect
7. #21444063C2semidirect
8. #21444057C2semidirect
9. #21444042C2semidirect
10. #21444041C2semidirect
11. C2×C4×C22⋊C4×C61C2semidirect
14. C22×#11758196C22semidirect
18. C22×#11758198C4semidirect
31. C2×#14519684C22semidirect
32. C2×#14519684C22semidirect
33. C2×#14519684C22semidirect
34. C2×#14519684C22semidirect
35. C2×#14519684C22semidirect
39. C22×C42×C61C22semidirect
41. C2×#95×C61C22semidirect
246. #11758198C22⋊C4semidirect
400. C22×C61#388semidirect
460. C2×C4×C22⋊C4D61semidirect
498. C22×C42C2×D61semidirect
509. C2×#95C2×D61semidirect
510. C61#13873semidirect
891. C22#16839653semidirect

Maximal subgroups

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

subgroupindex
C23×#117581982
C2×#168396532
C2×#168396202
C2×#168396172
#214440672
#214440632
#214440572
#214440422
#214440412
C2×C4×C22⋊C4×C612
#1387361