Finite Group Databasebeta

← #29601693

Subgroups — #29601693

Order 15616.

2702 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D244C211yesmaximal, characteristic
2C22×#14519734C211yesmaximal, characteristic, complemented
3C2×C4×#11758198C211yesmaximal, characteristic, complemented
4C2×C4×#11758198C211yesmaximal, characteristic, complemented
5C2×C4×#11758198C211yesmaximal, characteristic, complemented
6#21444071C212yesmaximal, complemented
7#21444067C212yesmaximal, complemented
8#21444063C212yesmaximal, complemented
9#21444059C212yesmaximal
10C4×#14519684C211yesmaximal, characteristic, complemented
11C4×#95×C61C211yesmaximal, characteristic, complemented
12C23×D244C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C23×C4×D61C2211yescharacteristic
15C2×C4×D244—24no—
16C2×C4×D244—24no—
17C2×C4×D244C418yescomplemented
18C2×#14519734—24no—
19C2×#14519734—24no—
20C2×#14519734—24no—
21C22×C4⋊Dic61C2211yescharacteristic
22C22×#11758196C2212yes—
23C22×#11758198C2212yes—
24C22×#11758198C2212yes—
25C22×#11758198C2212yes—
26C22×#11758198C2212yes—
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×C4×Dic61C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31C4×#11758198—24no—
32C4×#11758198—24no—
33C4×#11758198—24no—
34C2×#14519684C2212yes—
35C2×#14519684C2212yes—
36C2×#14519684C2212yes—
37C2×#14519684C2212yes—
38C2×#14519684C2212yes—
39C22×C42×C61C2211yescharacteristic
40C22×C42×C61C2211yescharacteristic
41C22×C42×C61C2211yescharacteristic
42C2×#95×C61C2212yes—
43C2×#95×C61C2212yes—
44C24×D61C2311yescharacteristic
45C24×D61C2311yescharacteristic
46C22×D244—22no—
47C22×D244—22no—
48C22×D244—24no—
49C22×D244—24no—
50C22×D244C2×C414yes—
51C23×Dic61C2311yescharacteristic
52C23×Dic61C2312yes—
53C23×Dic61C2312yes—
54C23×Dic61C2311yescharacteristic
55C22×C4×D61—22no—
56C22×C4×D61—22no—
57C22×C4×D61—22no—
58C22×C4×D61—22no—
59C22×C4×D61—22no—
60C22×C4×D61—22no—
61C22×C4×D61—22no—
62C22×C4×D61—22no—
63C22×C4×D61—22no—
64C22×C4×D61—22no—
65C22×C4×D61C2×C414yes—
66C22×C4×D61C2×C414yes—
67C22×C4×D61D414yes—
68C22×C4×D61D414yes—
69C4×D244—232no—
70#14519734—232no—
71C2×C4⋊Dic61—22no—
72C2×C4⋊Dic61—22no—
73C2×C4⋊Dic61C2×C414yes—
74C2×#11758196—24no—
75C2×#11758196—24no—
76C2×#11758196—24no—
77C2×#11758198—24no—
78C2×#11758198—22no—
79C2×#11758198—22no—
80C2×#11758198—24no—
81C2×#11758198—24no—
82C2×#11758198—24no—
83C2×#11758198—24no—
84C2×#11758198—24no—
85C2×#11758198—24no—
86C2×#11758198—24no—
87C2×#11758198—24no—
88C2×#11758198—22no—
89C2×#11758198—22no—
90C2×#11758198—24no—
91C2×#11758198—24no—
92C2×#11758198—24no—
93C2×#11758198C2×C414yes—
94C2×#11758198C2×C414yes—
95C2×C4×Dic61—22no—
96C2×C4×Dic61—22no—
97C2×C4×Dic61—22no—
98C2×C4×Dic61—22no—
99C2×C4×Dic61—22no—
100C2×C4×Dic61D414yescomplemented
101#14519684—24no—
102#14519684—24no—
103#14519684—24no—
104#14519684—24no—
105#14519684—24no—
106C23×C4×C61C2311yescharacteristic
107C23×C4×C61C2312yes—
108C23×C4×C61C2312yes—
109C23×C4×C61C2311yescharacteristic
110C23×C4×C61C2311yescharacteristic
111C2×C42×C61—22no—
112C2×C42×C61—22no—
113C2×C42×C61—22no—
114C2×C42×C61—22no—
115C2×C42×C61—22no—
116C2×C42×C61—22no—
117C2×C42×C61—22no—
118C2×C42×C61C2×C414yes—
119C2×C42×C61D414yescomplemented
120#95×C61—24no—
121#95×C61—24no—
122C24×C61C2411yescharacteristic
123C23×D61—21no—
124C23×D61—21no—
125C23×D61—21no—
126C23×D61—21no—
127C23×D61—21no—
128C23×D61—21no—
129C23×D61—21no—
130C23×D61—21no—
131C23×D61—21no—
132C23×D61—21no—
133C23×D61—22no—
134C23×D61—22no—
135C23×D61—22no—
136C23×D61—22no—
137C23×D61—22no—
138C23×D61—22no—
139C23×D61—22no—
140C23×D61C22×C412yes—
141C23×D61C22×C412yes—
142C23×D61C2×D412yes—
143C23×D61C2×D412yes—
144C23×D61#4114yes—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—22no—
161C22×C4×C61—22no—
162C22×C4×C61—22no—
163C22×C4×C61—22no—
164C22×C4×C61C22×C412yes—
165C22×C4×C61C22×C412yes—
166C22×C4×C61C22×C412yes—
167C22×C4×C61C2×D414yes—
168C22×C4×C61C2×D412yes—
169C22×C4×C61C2×D412yes—
170C22×C4×C61C2×D412yes—
171C22×C4×C61C2×D412yes—
172C22×C4×C61#4114yes—
173C22×C4×C61#4114yes—
174C22×C4×C61#4112yes—
175C22×C4×C61#4112yes—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61C22×C412yes—
199C22×Dic61C22×C412yes—
200C22×Dic61C2×D414yes—
201C22×Dic61C2×D412yes—
202C22×Dic61C2×D412yes—
203C22×Dic61#4114yes—
204C2×D244—216no—
205C2×D244—216no—
206C2×D244—28no—
207C2×D244—28no—
208C2×D244—28no—
209C2×C4×D61—28no—
210C2×C4×D61—28no—
211C2×C4×D61—28no—
212C2×C4×D61—28no—
213C2×C4×D61—28no—
214C2×C4×D61—28no—
215C2×C4×D61—28no—
216C2×C4×D61—28no—
217C2×C4×D61—28no—
218C2×C4×D61—44no—
219C2×C4×D61—44no—
220C2×C4×D61—44no—
221C2×C4×D61—44no—
222C2×C4×D61C22⋊C4116yescomplemented
223C42×C61—28no—
224C42×C61—28no—
225C42×C61—44no—
226#11758198—216no—
227#11758198—216no—
228#11758198—216no—
229#11758198—216no—
230#11758198—28no—
231#11758198—28no—
232C4⋊Dic61—28no—
233#11758196—216no—
234C4×Dic61—28no—
235C4×Dic61—44no—
236C23×C61C23×C411yescharacteristic
237C23×C61C22×D411yescharacteristic
238C23×C61C22×D411yescharacteristic
239C23×C61C22×D411yescharacteristic
240C23×C61C22×D411yescharacteristic
241C23×C61C2×#4112yes—
242C23×C61C2×#4112yes—
243C23×C61C2×#4111yescharacteristic
244C23×C61C2×#4111yescharacteristic
245C23×C61C2×#4112yes—
246C23×C61C2×#4112yes—
247C22×D61—22no—
248C22×D61—22no—
249C22×D61—22no—
250C22×D61—22no—
251C22×D61—22no—
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—22no—
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—22no—
263C22×D61—24no—
264C22×D61—24no—
265C22×D61—24no—
266C22×D61—24no—
267C22×D61—24no—
268C22×D61—24no—
269C22×D61—24no—
270C22×D61—24no—
271C22×D61—24no—
272C22×D61—24no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—42no—
278C22×D61—42no—
279C22×D61—42no—
280C22×D61—42no—
281C22×D61—42no—
282C22×D61—42no—
283C22×D61—42no—
284C22×D61—42no—
285C22×D61—42no—
286C22×D61—42no—
287C22×D61—42no—
288C22×D61—42no—
289C22×D61—42no—
290C22×D61—42no—
291C22×D61C2×C22⋊C414yes—
292C22×D61#11714yescomplemented
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—24no—
296C2×C4×C61—24no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—24no—
301C2×C4×C61—24no—
302C2×C4×C61—24no—
303C2×C4×C61—24no—
304C2×C4×C61—24no—
305C2×C4×C61—24no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61—42no—
310C2×C4×C61—42no—
311C2×C4×C61—42no—
312C2×C4×C61—42no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61C2×C22⋊C414yes—
317C2×C4×C61#11714yescomplemented
318C2×C4×C61C4×D414yes—
319C2×C4×C61C4×D414yes—
320C2×C4×C61#12014yes—
321C2×C4×C61#12114yes—
322C2×C4×C61#12114yes—
323C2×C4×C61#12314yes—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—24no—
334C2×Dic61—24no—
335C2×Dic61—24no—
336C2×Dic61—24no—
337C2×Dic61—24no—
338C2×Dic61—24no—
339C2×Dic61—41no—
340C2×Dic61—42no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—42no—
345C2×Dic61—42no—
346C2×Dic61—42no—
347C2×Dic61—42no—
348C2×Dic61—42no—
349C2×Dic61—42no—
350C2×Dic61—42no—
351C2×Dic61C2×C22⋊C414yes—
352D244—232no—
353C4×D61—232no—
354C4×D61—416no—
355#13839—611nomaximal, Sylow
356C22×C61C22×C22⋊C411yescharacteristic
357C22×C61C2×#11711yescharacteristic
358C22×C61C2×#11711yescharacteristic
359C22×C61C2×C4×D411yescharacteristic
360C22×C61C2×C4×D411yescharacteristic
361C22×C61C4×#4111yescharacteristic
362C22×C61C4×#4111yescharacteristic
363C22×C61C2×#12011yescharacteristic
364C22×C61C2×#12111yescharacteristic
365C22×C61C2×#12111yescharacteristic
366C22×C61C2×#12311yescharacteristic
367C22×C61#52512yes—
368C22×C61#52512yes—
369C22×C61#52512yes—
370C22×C61#52512yes—
371C22×C61#52512yes—
372C22×C61#52912yes—
373C22×C61#52912yes—
374C22×C61#52912yes—
375C22×C61#52912yes—
376C22×C61#53212yes—
377C22×C61#53212yes—
378C22×C61#53212yes—
379C2×D61—24no—
380C2×D61—24no—
381C2×D61—24no—
382C2×D61—24no—
383C2×D61—24no—
384C2×D61—24no—
385C2×D61—44no—
386C2×D61—44no—
387C2×D61—44no—
388C2×D61—44no—
389C2×D61—44no—
390C2×D61—44no—
391C2×D61—44no—
392C2×D61—44no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—42no—
397C2×D61—42no—
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—42no—
401C4×C61—24no—
402C4×C61—44no—
403C4×C61—44no—
404C4×C61—42no—
405C4×C61#38618yes—
406Dic61—24no—
407Dic61—44no—
408Dic61—44no—
409Dic61—42no—
410C22×C4×D4—611no—
411C22×#117—611no—
412C2×C4×C22⋊C4—611no—
413C2×C4×C22⋊C4—611no—
414C2×C4×C22⋊C4—611no—
415#1441—612no—
416#1440—612no—
417#1439—612no—
418#1438—612no—
419C4×#95—611no—
420C4×#95D6111yescharacteristic, complemented
421C2×C61#228011yescharacteristic
422C2×C61C2×#38611yescharacteristic
423C2×C61#229011yescharacteristic
424C2×C61#229011yescharacteristic
425C2×C61#229311yescharacteristic
426C2×C61#229311yescharacteristic
427C2×C61#229711yescharacteristic
428C2×C61#238812yes—
429C2×C61#239212yes—
430C2×C61#239212yes—
431C2×C61#239512yes—
432D61—44no—
433D61—44no—
434C23×D4—611no—
435C24×C4—611no—
436C24×C4—611no—
437C2×C4×D4—618no—
438C2×C4×D4—1224no—
439C2×C4×D4—1224no—
440C2×#117—1224no—
441C2×#117—1224no—
442C2×#117—1224no—
443C22×C4⋊C4—611no—
444C22×C4⋊C4—612no—
445C22×C22⋊C4—611no—
446C22×C22⋊C4—611no—
447C22×C22⋊C4—612no—
448C22×C22⋊C4—612no—
449C22×C22⋊C4—612no—
450C22×C22⋊C4—612no—
451C22×C42—611no—
452C22×C42—611no—
453C22×C42C2×D6111yescharacteristic
454C22×C42C2×D6111yescharacteristic
455C22×C42C2×D6111yescharacteristic
456C4×C22⋊C4—1224no—
457C4×C22⋊C4—1224no—
458C4×C22⋊C4—1224no—
459C2×#95—612no—
460C2×#95—612no—
461C2×#95—612no—
462C2×#95—612no—
463C2×#95—612no—
464C2×#95C2×D6112yes—
465C2×#95C2×D6112yes—
466C61#1383911yescharacteristic, complemented, Sylow
467C25—611no—
468C25—611no—
469C22×D4—614no—
470C22×D4—1222no—
471C22×D4—1222no—
472C22×D4—1224no—
473C22×D4—1224no—
474C23×C4—611no—
475C23×C4—614no—
476C23×C4—614no—
477C23×C4—614no—
478C23×C4—612no—
479C23×C4—612no—
480C23×C4—611no—
481C23×C4—614no—
482C23×C4—1222no—
483C23×C4—1222no—
484C23×C4—1222no—
485C23×C4—1222no—
486C23×C4—1222no—
487C23×C4—1222no—
488C23×C4—1222no—
489C23×C4—1222no—
490C23×C4—1222no—
491C23×C4—1222no—
492C23×C4C22×D6111yescharacteristic
493C23×C4C22×D6112yes—
494C23×C4C22×D6112yes—
495C23×C4C22×D6111yescharacteristic
496C23×C4C22×D6111yescharacteristic
497C4×D4—12232no—
498#117—12232no—
499C2×C4⋊C4—614no—
500C2×C4⋊C4—1224no—
501C2×C4⋊C4—1224no—
502C2×C4⋊C4—1222no—
503C2×C4⋊C4—1222no—
504C2×C4⋊C4—1224no—
505C2×C22⋊C4—614no—
506C2×C22⋊C4—614no—
507C2×C22⋊C4—1224no—
508C2×C22⋊C4—1222no—
509C2×C22⋊C4—1222no—
510C2×C22⋊C4—1224no—
511C2×C22⋊C4—1224no—
512C2×C22⋊C4—1224no—
513C2×C22⋊C4—1224no—
514C2×C22⋊C4—1222no—
515C2×C22⋊C4—1222no—
516C2×C22⋊C4—1224no—
517C2×C22⋊C4—1224no—
518C2×C22⋊C4—1224no—
519C2×C22⋊C4—1224no—
520C2×C22⋊C4—1224no—
521C2×C22⋊C4—1224no—
522C2×C22⋊C4—1224no—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—22no—
529C2×C42—22no—
530C2×C42—614no—
531C2×C42—1222no—
532C2×C42—1222no—
533C2×C42—1222no—
534C2×C42—1222no—
535C2×C42—1222no—
536C2×C42C4×D6114yes—
537C2×C42D24414yescomplemented
538#95—24no—
539#95—24no—
540#95—1224no—
541#95—1224no—
542#95—1224no—
543#95—1224no—
544#95—1224no—
545C24—612no—
546C24—612no—
547C24—612no—
548C24—612no—
549C24—614no—
550C24—1221no—
551C24—1221no—
552C24—1221no—
553C24—1221no—
554C24—1221no—
555C24—1221no—
556C24—1222no—
557C24—1222no—
558C24—1222no—
559C24—1222no—
560C24—1222no—
561C24—1221no—
562C24—1221no—
563C24—1222no—
564C24—1222no—
565C24—1221no—
566C24—1221no—
567C24C23×D6111yescharacteristic
568C2×D4—1228no—
569C2×D4—1228no—
570C2×D4—12216no—
571C2×D4—12216no—
572C2×D4—1228no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—612no—
593C22×C4—612no—
594C22×C4—612no—
595C22×C4—6116no—
596C22×C4—612no—
597C22×C4—614no—
598C22×C4—614no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—1228no—
604C22×C4—1228no—
605C22×C4—1228no—
606C22×C4—1228no—
607C22×C4—1228no—
608C22×C4—1228no—
609C22×C4—1221no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4—1222no—
622C22×C4—1222no—
623C22×C4—1222no—
624C22×C4—1221no—
625C22×C4—1222no—
626C22×C4—1221no—
627C22×C4—1228no—
628C22×C4—1228no—
629C22×C4—1228no—
630C22×C4—2444no—
631C22×C4—2444no—
632C22×C4—2444no—
633C22×C4—2444no—
634C22×C4C2×C4×D6112yes—
635C22×C4C2×C4×D6112yes—
636C22×C4C2×C4×D6112yes—
637C22×C4C2×D24414yes—
638C22×C4C2×D24412yes—
639C22×C4#1175822214yes—
640C22×C4#1175822214yes—
641C22×C4#1175822212yes—
642C22×C4D4×D6112yes—
643C22×C4D4×D6112yes—
644C22×C4D4×D6112yes—
645C22×C4#1175822612yes—
646C4⋊C4—1228no—
647C4⋊C4—12216no—
648C22⋊C4—1228no—
649C22⋊C4—1228no—
650C22⋊C4—12216no—
651C22⋊C4—12216no—
652C22⋊C4—12216no—
653C22⋊C4—12216no—
654C42—28no—
655C42—28no—
656C42—44no—
657C42—1228no—
658C42—2444no—
659C23—614no—
660C23—614no—
661C23—1222no—
662C23—1222no—
663C23—1222no—
664C23—1222no—
665C23—1222no—
666C23—1222no—
667C23—1222no—
668C23—1222no—
669C23—1222no—
670C23—1222no—
671C23—1222no—
672C23—1222no—
673C23—1222no—
674C23—1222no—
675C23—1222no—
676C23—1222no—
677C23—1224no—
678C23—1224no—
679C23—1224no—
680C23—1224no—
681C23—1224no—
682C23—1224no—
683C23—1224no—
684C23—1224no—
685C23—1224no—
686C23—1224no—
687C23—2441no—
688C23—2441no—
689C23—2441no—
690C23—2441no—
691C23—2442no—
692C23—2442no—
693C23—2442no—
694C23—2442no—
695C23—2442no—
696C23—2442no—
697C23—2442no—
698C23—2442no—
699C23—2442no—
700C23—2442no—
701C23—2442no—
702C23—2442no—
703C23—2442no—
704C23—2442no—
705C23C22×C4×D6111yescharacteristic
706C23C2×D4×D6111yescharacteristic
707C23C2×D4×D6111yescharacteristic
708C23C2×D4×D6111yescharacteristic
709C23C22×D24411yescharacteristic
710C23#41×D6112yes—
711C23#41×D6112yes—
712C23C2×#1175822212yes—
713C23C2×#1175822211yescharacteristic
714C23C2×#1175822212yes—
715C23C2×#1175822611yescharacteristic
716D4—12232no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—614no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—12232no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1224no—
752C2×C4—1224no—
753C2×C4—1224no—
754C2×C4—1224no—
755C2×C4—1224no—
756C2×C4—1224no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2442no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2442no—
763C2×C4—2442no—
764C2×C4—2442no—
765C2×C4—2442no—
766C2×C4—2442no—
767C2×C4—2442no—
768C2×C4—2442no—
769C2×C4—24416no—
770C2×C4C22⋊C4×D6114yes—
771C2×C4#1451973414yescomplemented
772C2×C4#1451973914yes—
773C2×C4C4×D24414yes—
774C2×C4#1451974714yes—
775C2×C4#1451975014yes—
776C2×C4#1451975214yes—
777C2×C4#1451976214yes—
778C22—1224no—
779C22—1224no—
780C22—1224no—
781C22—1224no—
782C22—1224no—
783C22—1224no—
784C22—2442no—
785C22—2442no—
786C22—2442no—
787C22—2444no—
788C22—2444no—
789C22—2442no—
790C22—2442no—
791C22—2442no—
792C22—2442no—
793C22—2444no—
794C22—2444no—
795C22—2444no—
796C22—2444no—
797C22—2442no—
798C22—2444no—
799C22—2444no—
800C22C2×C22⋊C4×D6111yescharacteristic
801C22#117×D6111yescharacteristic
802C22C2×#1451973411yescharacteristic
803C22C2×#1451973911yescharacteristic
804C22C2×C4×D24411yescharacteristic
805C22#1684023011yescharacteristic
806C22C4×#1175822211yescharacteristic
807C22C2×#1451974711yescharacteristic
808C22C2×#1451975011yescharacteristic
809C22C2×#1451975211yescharacteristic
810C22C2×#1451976211yescharacteristic
811C22#1684027112yes—
812C22#1684027112yes—
813C22#1684027112yes—
814C22#1684027112yes—
815C22#1684027412yes—
816C22#1684029012yes—
817C22#1684029612yes—
818C22#1684029912yes—
819C22#1684029912yes—
820C22#1684030912yes—
821C22#1684030912yes—
822C22#1684031212yes—
823C4—24no—
824C4—44no—
825C4—44no—
826C4—42no—
827C4—1224no—
828C4—2442no—
829C4—2444no—
830C4—2444no—
831C4#1683964018yes—
832C2—2444no—
833C2—2444no—
834C2#2144820011yescharacteristic
835C2C2×#1683964011yescharacteristic
836C2#2144826011yescharacteristic
837C2#2144826311yescharacteristic
838C2#2144828011yescharacteristic
839C2#2144828311yescharacteristic
840C2#2144830511yescharacteristic
841C2#2144903512yes—
842C2#2144905912yes—
843C2#2144906312yes—
844C2#2144908212yes—
subgroupG/H
centerC23×C4C22×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC4×#95×C61C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenterC4×#95D61
hypocenterC61#13839
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C22×#14519734C2semidirect
3. C2×C4×#11758198C2semidirect
4. C2×C4×#11758198C2semidirect
5. C2×C4×#11758198C2semidirect
6. #21444071C2semidirect
7. #21444067C2semidirect
8. #21444063C2semidirect
10. C4×#14519684C2semidirect
11. C4×#95×C61C2semidirect
17. C2×C4×D244C4semidirect
100. C2×C4×Dic61D4semidirect
119. C2×C42×C61D4semidirect
222. C2×C4×D61C22⋊C4semidirect
292. C22×D61#117semidirect
317. C2×C4×C61#117semidirect
420. C4×#95D61semidirect
466. C61#13839semidirect
537. C2×C42D244semidirect
771. C2×C4#14519734semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D2442
C22×#145197342
C2×C4×#117581982
#214440712
#214440672
#214440632
#214440592
C4×#145196842
C4×#95×C612
#1383961