Finite Group Databasebeta

← #29602347

Subgroups — #29602347

Order 15616.

2314 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519739C211yesmaximal, characteristic
2C2×#16839664C211yesmaximal, characteristic
3C2×#16839663C211yesmaximal, characteristic
4C2×#16839624C212yesmaximal, complemented
5#21444067C212yesmaximal, complemented
6#21444067C212yesmaximal, complemented
7#21444048C211yesmaximal, characteristic, complemented
8#21444048C211yesmaximal, characteristic, complemented
9#21444040C212yesmaximal, complemented
10C4×#14519684C211yesmaximal, characteristic, complemented
11C61×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×D244C2211yescharacteristic
13C23×C4×D61C2212yes—
14C2×#14519739—24no—
15C2×#14519739—24no—
16C2×#14519739C418yescomplemented
17C22×C4⋊Dic61C2211yescharacteristic
18C22×#11758198C2212yes—
19C22×#11758198C2212yes—
20C22×#11758198C2212yes—
21C22×#11758198C2212yes—
22C22×#11758198C2212yes—
23C22×C4×Dic61C2211yescharacteristic
24C22×C4×Dic61C2211yescharacteristic
25#16839664—24no—
26#16839663—24no—
27#16839624—28no—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2211yescharacteristic
31C2×#14519684C2211yescharacteristic
32C2×#14519684C2211yescharacteristic
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C2×#14519684C2211yescharacteristic
36C22×C4⋊C4×C61C2211yescharacteristic
37C22×C4⋊C4×C61C2211yescharacteristic
38C22×C42×C61C2211yescharacteristic
39C2×#95×C61C2212yes—
40C2×#95×C61C2212yes—
41C24×D61C2312yes—
42C22×D244—22no—
43C22×D244—22no—
44C22×D244—22no—
45C22×D244—22no—
46C22×D244C2×C414yes—
47C22×D244D414yes—
48C22×D244D414yes—
49C23×Dic61C2312yes—
50C23×Dic61C2311yescharacteristic
51C23×Dic61C2311yescharacteristic
52C23×Dic61C2311yescharacteristic
53C23×Dic61C2311yescharacteristic
54C22×C4×D61—24no—
55C22×C4×D61—24no—
56C22×C4×D61—24no—
57C22×C4×D61—24no—
58C22×C4×D61—42no—
59C22×C4×D61—42no—
60C22×C4×D61C2×C418yes—
61#14519739—232no—
62C2×C4⋊Dic61—22no—
63C2×C4⋊Dic61—22no—
64C2×C4⋊Dic61—22no—
65C2×#11758198—24no—
66C2×#11758198—24no—
67C2×#11758198—24no—
68C2×#11758198—24no—
69C2×#11758198—24no—
70C2×#11758198—24no—
71C2×#11758198—24no—
72C2×#11758198—24no—
73C2×#11758198—24no—
74C2×#11758198—24no—
75C2×#11758198—42no—
76C2×#11758198—42no—
77C2×#11758198—42no—
78C2×#11758198—42no—
79C2×#11758198C2×C418yes—
80C2×C4×Dic61—22no—
81C2×C4×Dic61—22no—
82C2×C4×Dic61—22no—
83C2×C4×Dic61—22no—
84C2×C4×Dic61—22no—
85C2×C4×Dic61C2×C414yes—
86#14519684—22no—
87#14519684—24no—
88#14519684—24no—
89#14519684—22no—
90#14519684—22no—
91#14519684—42no—
92#14519684—42no—
93#14519684D414yescomplemented
94C23×C4×C61C2312yes—
95C23×C4×C61C2312yes—
96C23×C4×C61C2311yescharacteristic
97C23×C4×C61C2311yescharacteristic
98C23×C4×C61C2311yescharacteristic
99C2×C4⋊C4×C61—22no—
100C2×C4⋊C4×C61—22no—
101C2×C4⋊C4×C61—22no—
102C2×C4⋊C4×C61—22no—
103C2×C4⋊C4×C61—22no—
104C2×C4⋊C4×C61C2×C414yes—
105C2×C42×C61—22no—
106C2×C42×C61—22no—
107C2×C42×C61—22no—
108#95×C61—24no—
109#95×C61—42no—
110C24×C61C2411yescharacteristic
111C23×D61—22no—
112C23×D61—22no—
113C23×D61—22no—
114C23×D61—22no—
115C23×D61—22no—
116C23×D61—22no—
117C23×D61—22no—
118C23×D61—22no—
119C23×D61—22no—
120C23×D61—22no—
121C23×D61—22no—
122C23×D61—22no—
123C23×D61C22×C414yes—
124C23×D61C2×D414yes—
125C23×D61C2×D414yes—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—22no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61C22×C414yes—
152C22×C4×C61C22×C412yes—
153C22×C4×C61C2×D412yes—
154C22×C4×C61C2×D412yes—
155C22×C4×C61C2×D412yes—
156C22×C4×C61#4112yes—
157C22×C4×C61#4112yes—
158C22×C4×C61#4112yes—
159C22×C4×C61#4112yes—
160C22×C4×C61#4112yes—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61C22×C412yes—
191C22×Dic61C22×C412yes—
192C22×Dic61C2×D412yes—
193C22×Dic61C2×D412yes—
194C22×Dic61#4112yes—
195C22×Dic61#4112yes—
196C2×D244—28no—
197C2×D244—28no—
198C2×D244—28no—
199C2×D244—28no—
200C2×D244—28no—
201C2×D244—28no—
202C2×D244C22⋊C4116yes—
203C2×C4×D61—216no—
204C2×C4×D61—216no—
205C2×C4×D61—48no—
206C2×C4×D61—48no—
207C2×C4×D61—48no—
208C2×C4×D61—48no—
209C2×C4×D61—48no—
210C4⋊C4×C61—28no—
211C4⋊C4×C61—44no—
212C42×C61—44no—
213#11758198—216no—
214#11758198—48no—
215#11758198—48no—
216#11758198—48no—
217#11758198—48no—
218C4⋊Dic61—44no—
219C4×Dic61—28no—
220C4×Dic61—44no—
221C23×C61C23×C411yescharacteristic
222C23×C61C22×D411yescharacteristic
223C23×C61C22×D411yescharacteristic
224C23×C61C22×D411yescharacteristic
225C23×C61C2×#4111yescharacteristic
226C23×C61C2×#4111yescharacteristic
227C23×C61C2×#4111yescharacteristic
228C23×C61C2×#4111yescharacteristic
229C23×C61C2×#4111yescharacteristic
230C23×C61C2×#4111yescharacteristic
231C23×C61C2×#4111yescharacteristic
232C23×C61H(5,𝔽2)11yescharacteristic
233C23×C61H(5,𝔽2)11yescharacteristic
234C23×C61H(5,𝔽2)11yescharacteristic
235C23×C612−1+411yescharacteristic
236C22×D61—24no—
237C22×D61—24no—
238C22×D61—24no—
239C22×D61—24no—
240C22×D61—24no—
241C22×D61—24no—
242C22×D61—24no—
243C22×D61—24no—
244C22×D61—24no—
245C22×D61—24no—
246C22×D61—24no—
247C22×D61—24no—
248C22×D61—24no—
249C22×D61—24no—
250C22×D61—24no—
251C22×D61—24no—
252C22×D61—24no—
253C22×D61—24no—
254C22×D61—42no—
255C22×D61—42no—
256C22×D61—42no—
257C22×D61—42no—
258C22×D61—42no—
259C22×D61—42no—
260C22×D61—42no—
261C22×D61—42no—
262C22×D61—42no—
263C22×D61—42no—
264C22×D61—42no—
265C22×D61—42no—
266C22×D61—42no—
267C22×D61—42no—
268C22×D61—42no—
269C22×D61—42no—
270C22×D61C2×C22⋊C418yes—
271C2×C4×C61—24no—
272C2×C4×C61—24no—
273C2×C4×C61—24no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—42no—
285C2×C4×C61—42no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61—42no—
295C2×C4×C61—42no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61—42no—
299C2×C4×C61C2×C22⋊C414yes—
300C2×C4×C61#11714yes—
301C2×C4×C61#11714yes—
302C2×C4×C61#12314yes—
303C2×C4×C61#12314yes—
304C2×C4×C61#12314yes—
305C2×C4×C61#12314yes—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340C2×Dic61C4×D414yes—
341D244—232no—
342C4×D61—432no—
343#13916—611nomaximal, Sylow
344C22×C61C22×C22⋊C411yescharacteristic
345C22×C61C2×#11711yescharacteristic
346C22×C61C2×#11711yescharacteristic
347C22×C61C2×C4×D411yescharacteristic
348C22×C61C4×#4111yescharacteristic
349C22×C61#51811yescharacteristic
350C22×C61#52011yescharacteristic
351C22×C61C2×#12311yescharacteristic
352C22×C61C2×#12311yescharacteristic
353C22×C61C2×#12311yescharacteristic
354C22×C61C2×#12311yescharacteristic
355C22×C61#52911yescharacteristic
356C22×C61#52911yescharacteristic
357C22×C61#53211yescharacteristic
358C22×C61#53211yescharacteristic
359C22×C61#54011yescharacteristic
360C22×C61#54011yescharacteristic
361C22×C61#54211yescharacteristic
362C22×C61#54211yescharacteristic
363C22×C61D4211yescharacteristic
364C22×C61D4211yescharacteristic
365C22×C61#54611yescharacteristic
366C22×C61#54611yescharacteristic
367C22×C61#54611yescharacteristic
368C22×C61#54611yescharacteristic
369C22×C61#54711yescharacteristic
370C22×C61#54711yescharacteristic
371C22×C61#54711yescharacteristic
372C22×C61#55011yescharacteristic
373C22×C61#55311yescharacteristic
374C22×C61#55311yescharacteristic
375C22×C61#55511yescharacteristic
376C22×C61#55611yescharacteristic
377C22×C61#55911yescharacteristic
378C22×C61#55911yescharacteristic
379C2×D61—28no—
380C2×D61—28no—
381C2×D61—28no—
382C2×D61—44no—
383C2×D61—44no—
384C2×D61—44no—
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—44no—
394C4×C61—44no—
395C4×C61—42no—
396C4×C61—42no—
397C4×C61—82no—
398C4×C61#38118yescomplemented
399Dic61—24no—
400Dic61—42no—
401Dic61—42no—
402Dic61—42no—
403Dic61—82no—
404C22×C4×D4—611no—
405C2×#390—611no—
406C2×#390—611no—
407C2×#381—612no—
408#1440—612no—
409#1440—612no—
410C4⋊#95—611no—
411C4⋊#95—611no—
412C4⋊#95D6111yescharacteristic, complemented
413C22⋊#95—612no—
414C4×#95—611no—
415C2×C61C2×#38111yescharacteristic
416C2×C61#229311yescharacteristic
417C2×C61#231911yescharacteristic
418C2×C61D4×C22⋊C411yescharacteristic
419C2×C61#233911yescharacteristic
420C2×C61#235411yescharacteristic
421C2×C61#235711yescharacteristic
422C2×C61#242011yescharacteristic
423C2×C61#242011yescharacteristic
424C2×C61#242211yescharacteristic
425C2×C61#242211yescharacteristic
426C2×C61#244511yescharacteristic
427C2×C61#244511yescharacteristic
428C2×C61#244711yescharacteristic
429C2×C61#244711yescharacteristic
430D61—48no—
431C23×D4—611no—
432C24×C4—612no—
433C2×C4×D4—618no—
434C2×C4×D4—1224no—
435C2×C4×D4—1224no—
436C22×C4⋊C4—611no—
437C22×C4⋊C4C2×D6111yescharacteristic
438C22×C4⋊C4C2×D6111yescharacteristic
439C22×C22⋊C4—612no—
440C22×C22⋊C4—612no—
441C22×C22⋊C4—612no—
442C22×C22⋊C4—612no—
443C22×C22⋊C4—612no—
444C22×C42—611no—
445C22×C42—611no—
446C22×C42C2×D6111yescharacteristic
447#390—1224no—
448#390—1224no—
449#381—1228no—
450C2×#95—611no—
451C2×#95—611no—
452C2×#95—611no—
453C2×#95—611no—
454C2×#95—612no—
455C2×#95—612no—
456C2×#95—612no—
457C2×#95—612no—
458C2×#95C2×D6112yes—
459C2×#95C2×D6112yes—
460C61#1391611yescharacteristic, complemented, Sylow
461C25—612no—
462C22×D4—614no—
463C22×D4—614no—
464C22×D4—614no—
465C22×D4—1222no—
466C22×D4—1222no—
467C22×D4—1222no—
468C22×D4—1222no—
469C23×C4—611no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—611no—
473C23×C4—618no—
474C23×C4—612no—
475C23×C4—1224no—
476C23×C4—1224no—
477C23×C4—1224no—
478C23×C4—1224no—
479C23×C4—2442no—
480C23×C4—2442no—
481C23×C4C22×D6112yes—
482C23×C4C22×D6112yes—
483C23×C4C22×D6111yescharacteristic
484C23×C4C22×D6111yescharacteristic
485C23×C4C22×D6111yescharacteristic
486C4×D4—12232no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—1222no—
493C2×C4⋊C4—1222no—
494C2×C4⋊C4—1222no—
495C2×C4⋊C4C4×D6114yes—
496C2×C22⋊C4—618no—
497C2×C22⋊C4—1224no—
498C2×C22⋊C4—1224no—
499C2×C22⋊C4—1224no—
500C2×C22⋊C4—1224no—
501C2×C22⋊C4—1224no—
502C2×C22⋊C4—1224no—
503C2×C22⋊C4—1224no—
504C2×C22⋊C4—1224no—
505C2×C22⋊C4—1224no—
506C2×C22⋊C4—1224no—
507C2×C22⋊C4—2442no—
508C2×C22⋊C4—2442no—
509C2×C22⋊C4—2442no—
510C2×C22⋊C4—2442no—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—22no—
514C2×C42—614no—
515C2×C42—1222no—
516C2×C42—1222no—
517C2×C42—1222no—
518C2×C42—1222no—
519C2×C42—1222no—
520#95—24no—
521#95—42no—
522#95—614no—
523#95—1224no—
524#95—1224no—
525#95—1222no—
526#95—1222no—
527#95—1222no—
528#95—2442no—
529#95—2442no—
530C24—614no—
531C24—614no—
532C24—614no—
533C24—1222no—
534C24—1222no—
535C24—1222no—
536C24—1222no—
537C24—1222no—
538C24—1222no—
539C24—1222no—
540C24—1222no—
541C24—1222no—
542C24—1222no—
543C24—1222no—
544C24—1222no—
545C24C23×D6111yescharacteristic
546C2×D4—6116no—
547C2×D4—1228no—
548C2×D4—1228no—
549C2×D4—1228no—
550C2×D4—1228no—
551C2×D4—1228no—
552C2×D4—1228no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—612no—
579C22×C4—612no—
580C22×C4—612no—
581C22×C4—612no—
582C22×C4—612no—
583C22×C4—612no—
584C22×C4—12216no—
585C22×C4—12216no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—2448no—
616C22×C4—2448no—
617C22×C4—2448no—
618C22×C4—2448no—
619C22×C4—2448no—
620C22×C4C2×C4×D6114yes—
621C22×C4C2×C4×D6112yes—
622C22×C4#1175822212yes—
623C22×C4#1175822212yes—
624C22×C4D4×D6112yes—
625C22×C4D4×D6112yes—
626C22×C4D4×D6112yes—
627C22×C4#1175822412yes—
628C22×C4#1175822612yes—
629C22×C4#1175822612yes—
630C4⋊C4—28no—
631C4⋊C4—44no—
632C4⋊C4—2444no—
633C22⋊C4—12216no—
634C22⋊C4—2448no—
635C22⋊C4—2448no—
636C22⋊C4—2448no—
637C22⋊C4—2448no—
638C42—44no—
639C42—1228no—
640C42—2444no—
641C23—618no—
642C23—1224no—
643C23—1224no—
644C23—1224no—
645C23—1224no—
646C23—1224no—
647C23—1224no—
648C23—1224no—
649C23—1224no—
650C23—1224no—
651C23—1224no—
652C23—1224no—
653C23—1224no—
654C23—1224no—
655C23—1224no—
656C23—1224no—
657C23—1224no—
658C23—1224no—
659C23—1224no—
660C23—2442no—
661C23—2442no—
662C23—2442no—
663C23—2442no—
664C23—2442no—
665C23—2442no—
666C23—2442no—
667C23—2442no—
668C23—2442no—
669C23—2442no—
670C23—2442no—
671C23—2442no—
672C23—2442no—
673C23—2442no—
674C23—2442no—
675C23—2442no—
676C23C22×C4×D6111yescharacteristic
677C23C2×D4×D6111yescharacteristic
678C23C2×D4×D6111yescharacteristic
679C23C2×D4×D6111yescharacteristic
680C23#41×D6111yescharacteristic
681C23#41×D6111yescharacteristic
682C23C2×#1175822411yescharacteristic
683C23C2×#1175822211yescharacteristic
684C23C2×#1175822211yescharacteristic
685C23C2×#1175822611yescharacteristic
686C23C2×#1175822611yescharacteristic
687C23#1451982211yescharacteristic
688C23#1451982311yescharacteristic
689C23#1451982311yescharacteristic
690C23#1451982511yescharacteristic
691D4—12232no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—614no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—24432no—
737C2×C4—2442no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4—2442no—
741C2×C4—2442no—
742C2×C4—2442no—
743C2×C4—2442no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4C22⋊C4×D6114yes—
757C2×C4#1451973414yes—
758C2×C4#1451973514yes—
759C2×C4#1451975914yes—
760C2×C4#1451975914yes—
761C2×C4#1451976214yes—
762C2×C4#1451976214yes—
763C22—1228no—
764C22—1228no—
765C22—1228no—
766C22—2444no—
767C22—2444no—
768C22—2444no—
769C22—2444no—
770C22—2444no—
771C22—2444no—
772C22—2444no—
773C22—2444no—
774C22—2444no—
775C22—2444no—
776C22—2444no—
777C22—2444no—
778C22C2×C22⋊C4×D6111yescharacteristic
779C22C2×#1451973411yescharacteristic
780C22C2×#1451973511yescharacteristic
781C22C4×D4×D6111yescharacteristic
782C22C4×#1175822611yescharacteristic
783C22#1684023411yescharacteristic
784C22#1684024411yescharacteristic
785C22C2×#1451975911yescharacteristic
786C22C2×#1451975911yescharacteristic
787C22C2×#1451976211yescharacteristic
788C22C2×#1451976211yescharacteristic
789C22#1684029711yescharacteristic
790C22#1684029811yescharacteristic
791C22#1684030711yescharacteristic
792C22#1684031311yescharacteristic
793C22#1684036511yescharacteristic
794C22#1684036811yescharacteristic
795C22#1684038511yescharacteristic
796C22#1684038611yescharacteristic
797C22#1684039611yescharacteristic
798C22#1684039711yescharacteristic
799C22#1684040311yescharacteristic
800C22#1684040511yescharacteristic
801C22#1684040511yescharacteristic
802C22#1684040911yescharacteristic
803C22#1684041311yescharacteristic
804C22#1684041411yescharacteristic
805C22#1684041511yescharacteristic
806C22#1684043311yescharacteristic
807C22#1684045611yescharacteristic
808C22#1684046011yescharacteristic
809C22#1684047511yescharacteristic
810C22#1684048411yescharacteristic
811C22#1684049511yescharacteristic
812C22#1684049711yescharacteristic
813C4—42no—
814C4—42no—
815C4—44no—
816C4—82no—
817C4—1224no—
818C4—4882no—
819C4—2442no—
820C4—2442no—
821C4—2442no—
822C4#1683962418yescomplemented
823C2—2448no—
824C2C2×#1683962411yescharacteristic
825C2#2144827711yescharacteristic
826C2#2144845811yescharacteristic
827C2#2144864011yescharacteristic
828C2#2144864811yescharacteristic
829C2#2144876411yescharacteristic
830C2#2144878811yescharacteristic
831C2#2144931311yescharacteristic
832C2#2144931411yescharacteristic
833C2#2144933511yescharacteristic
834C2#2144933611yescharacteristic
835C2#2144958611yescharacteristic
836C2#2144958711yescharacteristic
837C2#2144960811yescharacteristic
838C2#2144960911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C4⋊#95C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenterC4⋊#95D61
hypocenterC61#13916
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#16839624C2semidirect
5. #21444067C2semidirect
6. #21444067C2semidirect
7. #21444048C2semidirect
8. #21444048C2semidirect
9. #21444040C2semidirect
10. C4×#14519684C2semidirect
11. C61×C4⋊#95C2semidirect
16. C2×#14519739C4semidirect
93. #14519684D4semidirect
398. C4×C61#381semidirect
412. C4⋊#95D61semidirect
460. C61#13916semidirect
822. C4#16839624semidirect

Maximal subgroups

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

subgroupindex
C22×#145197392
C2×#168396642
C2×#168396632
C2×#168396242
#214440672
#214440482
#214440402
C4×#145196842
C61×C4⋊#952
#1391661