Finite Group Databasebeta

← #29601798

Subgroups — #29601798

Order 15616.

3502 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519739C211yesmaximal, characteristic, complemented
2C22×#14519737C212yesmaximal, complemented
3C2×#16839671C211yesmaximal, characteristic
4C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
5C2×#16839609C212yesmaximal, complemented
6#21444082C211yesmaximal, characteristic, complemented
7#21444063C212yesmaximal, complemented
8#21444059C211yesmaximal, characteristic, complemented
9#21444058C212yesmaximal, complemented
10#95×Dic61C211yesmaximal, characteristic, complemented
11C61×#1439C211yesmaximal, characteristic, complemented
12C23×D244C2211yescharacteristic
13C23×C22⋊D61C2212yes—
14C24×Dic61C2211yescharacteristic
15C23×C4×D61C2212yes—
16C2×#14519739—24no—
17C2×#14519739—28no—
18C2×#14519737—28no—
19C2×#14519737—28no—
20C2×#14519737—28no—
21C22×#11758196C2212yes—
22C22×C22⋊Dic61C2211yescharacteristic
23C22×#11758198C2212yes—
24C22×#11758198C2212yes—
25C22×#11758198C2212yes—
26C22×#11758198C2212yes—
27C22×C4×Dic61C2211yescharacteristic
28C22×C4×Dic61C2212yes—
29C22×C4×Dic61C2211yescharacteristic
30#16839671C418yescomplemented
31C22⋊C4×Dic61—24no—
32#16839609—28no—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2211yescharacteristic
38C22×C4⋊C4×C61C2211yescharacteristic
39C22×C22⋊C4×C61C2212yes—
40C22×C22⋊C4×C61C2211yescharacteristic
41C2×#95×C61C2211yescharacteristic
42C2×#95×C61C2212yes—
43C24×D61C2312yes—
44C22×D244—24no—
45C22×D244—24no—
46C22×D244—22no—
47C22×D244—22no—
48C22×D244C2×C414yescomplemented
49C22×C22⋊D61—24no—
50C22×C22⋊D61—24no—
51C22×C22⋊D61—24no—
52C22×C22⋊D61—24no—
53C22×C22⋊D61—24no—
54C22×C22⋊D61—24no—
55C22×C22⋊D61C2×C418yescomplemented
56C23×Dic61—24no—
57C23×Dic61—24no—
58C23×Dic61—22no—
59C23×Dic61—22no—
60C23×Dic61D414yescomplemented
61C23×Dic61C2311yescharacteristic
62C23×Dic61C2311yescharacteristic
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2312yes—
65C23×Dic61C2311yescharacteristic
66C22×C4×D61—24no—
67C22×C4×D61—24no—
68C22×C4×D61—24no—
69C22×C4×D61—24no—
70C22×C4×D61—24no—
71C22×C4×D61—24no—
72C22×C4×D61D418yescomplemented
73#14519739—232no—
74#14519737—264no—
75C2×#11758196—24no—
76C2×#11758196—24no—
77C2×#11758196—24no—
78C2×C22⋊Dic61—22no—
79C2×C22⋊Dic61—22no—
80C2×C22⋊Dic61—22no—
81C2×#11758198—24no—
82C2×#11758198—24no—
83C2×#11758198—24no—
84C2×#11758198—24no—
85C2×#11758198—24no—
86C2×#11758198—24no—
87C2×#11758198—24no—
88C2×#11758198—24no—
89C2×#11758198—24no—
90C2×#11758198—24no—
91C2×#11758198—24no—
92C2×#11758198C2×C418yescomplemented
93C2×C4×Dic61—24no—
94C2×C4×Dic61—24no—
95C2×C4×Dic61—24no—
96C2×C4×Dic61—24no—
97C2×C4×Dic61—22no—
98C2×C4×Dic61D418yescomplemented
99C2×C4×Dic61D414yescomplemented
100#14519684—22no—
101#14519684—24no—
102#14519684—22no—
103#14519684—24no—
104#14519684C2×C414yescomplemented
105C25×C61C2311yescharacteristic
106C23×C4×C61C2311yescharacteristic
107C23×C4×C61C2312yes—
108C23×C4×C61C2312yes—
109C23×C4×C61C2311yescharacteristic
110C2×C4⋊C4×C61—24no—
111C2×C4⋊C4×C61—22no—
112C2×C22⋊C4×C61—24no—
113C2×C22⋊C4×C61—24no—
114C2×C22⋊C4×C61—24no—
115C2×C22⋊C4×C61—22no—
116C2×C22⋊C4×C61—22no—
117C2×C22⋊C4×C61C2×C414yescomplemented
118#95×C61—24no—
119#95×C61—22no—
120C24×C61—22no—
121C24×C61—22no—
122C24×C61—21no—
123C24×C61—21no—
124C24×C61—22no—
125C24×C61—22no—
126C24×C61—21no—
127C24×C61—21no—
128C24×C61C22×C412yes—
129C24×C61C2×D412yes—
130C24×C61#4112yes—
131C24×C61C2411yescharacteristic
132C23×D61—22no—
133C23×D61—22no—
134C23×D61—22no—
135C23×D61—22no—
136C23×D61—22no—
137C23×D61—22no—
138C23×D61—22no—
139C23×D61—22no—
140C23×D61—22no—
141C23×D61—22no—
142C23×D61—22no—
143C23×D61—22no—
144C23×D61C22×C414yes—
145C23×D61C2×D414yes—
146C23×D61#4114yes—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—21no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—21no—
161C22×C4×C61—22no—
162C22×C4×C61—22no—
163C22×C4×C61—22no—
164C22×C4×C61—22no—
165C22×C4×C61C22×C412yes—
166C22×C4×C61C22×C412yes—
167C22×C4×C61C2×D414yes—
168C22×C4×C61C2×D414yes—
169C22×C4×C61C2×D412yes—
170C22×C4×C61#4112yes—
171C2×C22⋊D61—216no—
172C2×C22⋊D61—216no—
173C2×C22⋊D61—216no—
174C2×C22⋊D61—216no—
175C2×C22⋊D61—216no—
176C2×C22⋊D61—216no—
177C2×C22⋊D61—216no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—21no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—21no—
187C22×Dic61—22no—
188C22×Dic61—21no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—216no—
195C22×Dic61—28no—
196C22×Dic61—44no—
197C22×Dic61—48no—
198C22×Dic61—44no—
199C22×Dic61C22×C414yes—
200C22×Dic61C2×D412yes—
201C22×Dic61C2×D412yes—
202C22×Dic61C2×D414yes—
203C22×Dic61C2×D412yes—
204C22×Dic61C2×D414yes—
205C22×Dic61C2×D412yes—
206C22×Dic61C2×D414yes—
207C22×Dic61#4112yes—
208C22×Dic61#4114yes—
209C22×Dic61#4112yes—
210C2×D244—28no—
211C2×D244—216no—
212C2×D244—28no—
213C2×D244—216no—
214C2×D244—28no—
215C2×C4×D61—216no—
216C2×C4×D61—216no—
217C2×C4×D61—216no—
218C2×C4×D61—48no—
219C2×C4×D61—48no—
220C2×C4×D61—48no—
221C2×C4×D61—48no—
222C4⋊C4×C61—28no—
223C22⋊C4×C61—216no—
224C22⋊C4×C61—28no—
225C22⋊Dic61—28no—
226#11758198—216no—
227#11758198—216no—
228#11758198—216no—
229#11758198—216no—
230#11758196—216no—
231C4×Dic61—216no—
232C4×Dic61—28no—
233C4×Dic61—44no—
234C23×C61—22no—
235C23×C61—24no—
236C23×C61—24no—
237C23×C61—22no—
238C23×C61—24no—
239C23×C61—22no—
240C23×C61—22no—
241C23×C61—24no—
242C23×C61—24no—
243C23×C61—24no—
244C23×C61—22no—
245C23×C61—22no—
246C23×C61—41no—
247C23×C61—42no—
248C23×C61—42no—
249C23×C61—42no—
250C23×C61—41no—
251C23×C61—42no—
252C23×C61—41no—
253C23×C61—42no—
254C23×C61—41no—
255C23×C61—42no—
256C23×C61C4×D414yescomplemented
257C23×C61C23×C411yescharacteristic
258C23×C61C22×D412yes—
259C23×C61C22×D411yescharacteristic
260C23×C61C22×D412yes—
261C23×C61C22×D411yescharacteristic
262C23×C61C2×#4112yes—
263C23×C61C2×#4111yescharacteristic
264C23×C61C2×#4112yes—
265C23×C61C2×#4111yescharacteristic
266C23×C61C2×#4111yescharacteristic
267C23×C61C2×#4111yescharacteristic
268C22×D61—24no—
269C22×D61—24no—
270C22×D61—24no—
271C22×D61—24no—
272C22×D61—24no—
273C22×D61—24no—
274C22×D61—24no—
275C22×D61—24no—
276C22×D61—24no—
277C22×D61—24no—
278C22×D61—24no—
279C22×D61—24no—
280C22×D61—24no—
281C22×D61—24no—
282C22×D61—24no—
283C22×D61—24no—
284C22×D61—24no—
285C22×D61—24no—
286C22×D61—42no—
287C22×D61—42no—
288C22×D61—42no—
289C22×D61—42no—
290C22×D61—42no—
291C22×D61—42no—
292C22×D61—42no—
293C22×D61—42no—
294C22×D61—42no—
295C22×D61—42no—
296C22×D61—42no—
297C22×D61—42no—
298C22×D61—42no—
299C22×D61—42no—
300C22×D61—42no—
301C22×D61—42no—
302C22×D61C4×D418yescomplemented
303C2×C4×C61—24no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—24no—
307C2×C4×C61—24no—
308C2×C4×C61—22no—
309C2×C4×C61—24no—
310C2×C4×C61—24no—
311C2×C4×C61—24no—
312C2×C4×C61—24no—
313C2×C4×C61—24no—
314C2×C4×C61—24no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
318C2×C4×C61—42no—
319C2×C4×C61—42no—
320C2×C4×C61—41no—
321C2×C4×C61—42no—
322C2×C4×C61—42no—
323C2×C4×C61—41no—
324C2×C4×C61—42no—
325C2×C4×C61—42no—
326C2×C4×C61C4×D414yescomplemented
327C22⋊D61—264no—
328C2×Dic61—24no—
329C2×Dic61—24no—
330C2×Dic61—24no—
331C2×Dic61—24no—
332C2×Dic61—24no—
333C2×Dic61—24no—
334C2×Dic61—22no—
335C2×Dic61—24no—
336C2×Dic61—22no—
337C2×Dic61—24no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—41no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61—41no—
345C2×Dic61—42no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—42no—
349C2×Dic61—416no—
350C2×Dic61C4×D418yescomplemented
351C2×Dic61#12014yes—
352C2×Dic61#12018yes—
353C2×Dic61#12118yes—
354C2×Dic61#12114yes—
355C2×Dic61#12714yes—
356D244—232no—
357C4×D61—432no—
358C4×#392—611nomaximal, Sylow
359C22×C61—28no—
360C22×C61—24no—
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—44no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—44no—
367C22×C61—42no—
368C22×C61—42no—
369C22×C61—44no—
370C22×C61C2×C4×D412yes—
371C22×C61C2×C4×D412yes—
372C22×C61C2×C4×D411yescharacteristic
373C22×C61C2×C4×D411yescharacteristic
374C22×C61C4×#4111yescharacteristic
375C22×C61C2×#12012yes—
376C22×C61C2×#12011yescharacteristic
377C22×C61C2×#12111yescharacteristic
378C22×C61C2×#12112yes—
379C22×C61#52512yes—
380C22×C61#52512yes—
381C22×C61#52511yescharacteristic
382C22×C61#52512yes—
383C22×C61#52512yes—
384C22×C61#52511yescharacteristic
385C22×C61#52512yes—
386C22×C61#52912yes—
387C22×C61#52911yescharacteristic
388C22×C61C2×#12711yescharacteristic
389C22×C61#53212yes—
390C22×C61#53211yescharacteristic
391C22×C61#53211yescharacteristic
392C22×C61#53212yes—
393C2×D61—28no—
394C2×D61—28no—
395C2×D61—28no—
396C2×D61—44no—
397C2×D61—44no—
398C2×D61—44no—
399C2×D61—44no—
400C2×D61—44no—
401C2×D61—44no—
402C2×D61—44no—
403C2×D61—44no—
404C2×D61—44no—
405C2×D61—44no—
406C2×D61—44no—
407C2×D61—44no—
408C4×C61—24no—
409C4×C61—42no—
410C4×C61—44no—
411C4×C61—44no—
412Dic61—28no—
413Dic61—42no—
414Dic61—42no—
415Dic61—42no—
416Dic61#39218yescomplemented
417C22×C4×D4—611no—
418C22×C4×D4—612no—
419C2×#392—611no—
420C2×C4×C22⋊C4—612no—
421C2×C4×C22⋊C4—611no—
422#1444—611no—
423#1439—612no—
424#1439D6111yescharacteristic, complemented
425#1438—611no—
426#1438—612no—
427C4×#95—611no—
428C2×C61—44no—
429C2×C61C4×#12012yes—
430C2×C61C4×#12011yescharacteristic
431C2×C61C4×#12111yescharacteristic
432C2×C61C4×#12112yes—
433C2×C61C4×#12711yescharacteristic
434C2×C61C2×#39211yescharacteristic
435C2×C61#238812yes—
436C2×C61#238811yescharacteristic
437C2×C61#239211yescharacteristic
438C2×C61#239212yes—
439C2×C61#239711yescharacteristic
440D61—48no—
441C23×D4—612no—
442C23×D4—611no—
443C24×C4—611no—
444C24×C4—612no—
445C2×C4×D4—1228no—
446C2×C4×D4—1224no—
447C2×C4×D4—1228no—
448C2×C4×D4—1228no—
449C2×C4×D4—1228no—
450C22×C4⋊C4—612no—
451C22×C4⋊C4C2×D6111yescharacteristic
452C22×C22⋊C4—612no—
453C22×C22⋊C4—611no—
454C22×C22⋊C4—612no—
455C22×C22⋊C4—612no—
456C22×C22⋊C4—612no—
457C22×C22⋊C4C2×D6112yes—
458C22×C22⋊C4C2×D6111yescharacteristic
459C22×C42—612no—
460C22×C42—611no—
461C22×C42—611no—
462#392—618no—
463C4×C22⋊C4—1228no—
464C4×C22⋊C4—1224no—
465C2×#95—611no—
466C2×#95—612no—
467C2×#95—612no—
468C2×#95—611no—
469C2×#95—611no—
470C2×#95C2×D6111yescharacteristic
471C2×#95C2×D6112yes—
472C61C4×#39211yescharacteristic, complemented, Sylow
473C25—612no—
474C25C22×D6111yescharacteristic
475C22×D4—618no—
476C22×D4—614no—
477C22×D4—1224no—
478C22×D4—1224no—
479C22×D4—1224no—
480C22×D4—1224no—
481C22×D4—1224no—
482C22×D4—1224no—
483C22×D4—1224no—
484C22×D4—1224no—
485C22×D4—1222no—
486C22×D4—1222no—
487C23×C4—611no—
488C23×C4—612no—
489C23×C4—614no—
490C23×C4—611no—
491C23×C4—611no—
492C23×C4—611no—
493C23×C4—618no—
494C23×C4—1224no—
495C23×C4—1224no—
496C23×C4—1224no—
497C23×C4—1224no—
498C23×C4—1224no—
499C23×C4—1224no—
500C23×C4—1224no—
501C23×C4—1224no—
502C23×C4—1222no—
503C23×C4—1222no—
504C23×C4C22×D6111yescharacteristic
505C23×C4C22×D6112yes—
506C23×C4C22×D6112yes—
507C23×C4C22×D6111yescharacteristic
508C4×D4—12264no—
509C4×D4—12232no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—1224no—
513C2×C4⋊C4—1224no—
514C2×C4⋊C4—1224no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—618no—
521C2×C22⋊C4—1224no—
522C2×C22⋊C4—1224no—
523C2×C22⋊C4—1224no—
524C2×C22⋊C4—1224no—
525C2×C22⋊C4—1224no—
526C2×C22⋊C4—1224no—
527C2×C22⋊C4—1224no—
528C2×C22⋊C4—1224no—
529C2×C22⋊C4—1222no—
530C2×C22⋊C4—1222no—
531C2×C22⋊C4—1222no—
532C2×C22⋊C4—1224no—
533C2×C22⋊C4—1224no—
534C2×C22⋊C4—1224no—
535C2×C22⋊C4C4×D6114yescomplemented
536C2×C42—618no—
537C2×C42—614no—
538C2×C42—1224no—
539C2×C42—1224no—
540C2×C42—1224no—
541C2×C42—1224no—
542C2×C42—1222no—
543#95—24no—
544#95—22no—
545#95—614no—
546#95—1224no—
547#95—1222no—
548#95—1224no—
549#95—1222no—
550C24—21no—
551C24—22no—
552C24—22no—
553C24—21no—
554C24—21no—
555C24—22no—
556C24—22no—
557C24—21no—
558C24—614no—
559C24—614no—
560C24—614no—
561C24—1222no—
562C24—1222no—
563C24—1222no—
564C24—1222no—
565C24—1222no—
566C24—1222no—
567C24—1222no—
568C24—1222no—
569C24—1222no—
570C24—1222no—
571C24—1222no—
572C24—1222no—
573C24C2×C4×D6112yes—
574C24D4×D6112yes—
575C24#1175822612yes—
576C24C23×D6111yescharacteristic
577C2×D4—12216no—
578C2×D4—1228no—
579C2×D4—1228no—
580C2×D4—12216no—
581C2×D4—12216no—
582C2×D4—12216no—
583C2×D4—12216no—
584C2×D4—12216no—
585C2×D4—12216no—
586C2×D4—12216no—
587C2×D4—12216no—
588C2×D4—1228no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—614no—
608C22×C4—612no—
609C22×C4—614no—
610C22×C4—612no—
611C22×C4—612no—
612C22×C4—614no—
613C22×C4—614no—
614C22×C4—614no—
615C22×C4—612no—
616C22×C4—612no—
617C22×C4—612no—
618C22×C4—12216no—
619C22×C4—12216no—
620C22×C4—12216no—
621C22×C4—12216no—
622C22×C4—1228no—
623C22×C4—1222no—
624C22×C4—1222no—
625C22×C4—1222no—
626C22×C4—1222no—
627C22×C4—1221no—
628C22×C4—1222no—
629C22×C4—1221no—
630C22×C4—1222no—
631C22×C4—1222no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—2448no—
640C22×C4—2448no—
641C22×C4—2448no—
642C22×C4—2448no—
643C22×C4—2444no—
644C22×C4—2448no—
645C22×C4—2444no—
646C22×C4C2×C4×D6112yes—
647C22×C4C2×C4×D6112yes—
648C22×C4D4×D6114yes—
649C22×C4D4×D6114yes—
650C22×C4D4×D6112yes—
651C22×C4#1175822412yes—
652C4⋊C4—28no—
653C4⋊C4—12216no—
654C22⋊C4—216no—
655C22⋊C4—28no—
656C22⋊C4—12216no—
657C22⋊C4—12216no—
658C22⋊C4—12216no—
659C22⋊C4—12216no—
660C22⋊C4—1228no—
661C42—1228no—
662C42—12216no—
663C42—2444no—
664C23—24no—
665C23—24no—
666C23—22no—
667C23—22no—
668C23—24no—
669C23—22no—
670C23—24no—
671C23—22no—
672C23—24no—
673C23—24no—
674C23—22no—
675C23—22no—
676C23—41no—
677C23—42no—
678C23—42no—
679C23—41no—
680C23—42no—
681C23—42no—
682C23—41no—
683C23—42no—
684C23—42no—
685C23—41no—
686C23—618no—
687C23—1224no—
688C23—1224no—
689C23—1224no—
690C23—1224no—
691C23—1224no—
692C23—1224no—
693C23—1224no—
694C23—1224no—
695C23—1224no—
696C23—1224no—
697C23—1224no—
698C23—1224no—
699C23—1224no—
700C23—1224no—
701C23—1224no—
702C23—1224no—
703C23—1224no—
704C23—1224no—
705C23—2442no—
706C23—2442no—
707C23—2442no—
708C23—2442no—
709C23—2442no—
710C23—2442no—
711C23—2442no—
712C23—2442no—
713C23—2442no—
714C23—2442no—
715C23—2442no—
716C23—2442no—
717C23—2442no—
718C23—2442no—
719C23—2442no—
720C23—2442no—
721C23#1451973914yescomplemented
722C23C22×C4×D6111yescharacteristic
723C23C2×D4×D6112yes—
724C23C2×D4×D6112yes—
725C23C2×D4×D6111yescharacteristic
726C23C2×D4×D6111yescharacteristic
727C23#41×D6112yes—
728C23#41×D6112yes—
729C23#41×D6111yescharacteristic
730C23#41×D6111yescharacteristic
731C23C2×#1175822411yescharacteristic
732C23C2×#1175822611yescharacteristic
733D4—12232no—
734D4—12264no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—618no—
759C2×C4—614no—
760C2×C4—614no—
761C2×C4—618no—
762C2×C4—614no—
763C2×C4—618no—
764C2×C4—1224no—
765C2×C4—1224no—
766C2×C4—1224no—
767C2×C4—1224no—
768C2×C4—1224no—
769C2×C4—1224no—
770C2×C4—1222no—
771C2×C4—1224no—
772C2×C4—1222no—
773C2×C4—1224no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—24432no—
778C2×C4—24416no—
779C2×C4—2441no—
780C2×C4—2442no—
781C2×C4—2441no—
782C2×C4—2442no—
783C2×C4—2442no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4—2442no—
787C2×C4#1451973714yescomplemented
788C22—28no—
789C22—24no—
790C22—42no—
791C22—44no—
792C22—42no—
793C22—42no—
794C22—44no—
795C22—42no—
796C22—44no—
797C22—42no—
798C22—42no—
799C22—1228no—
800C22—1228no—
801C22—1228no—
802C22—2444no—
803C22—2444no—
804C22—2444no—
805C22—2444no—
806C22—2444no—
807C22—2444no—
808C22—2444no—
809C22—2444no—
810C22—2444no—
811C22—2444no—
812C22—2444no—
813C22—2444no—
814C22C4×D4×D6112yes—
815C22C4×D4×D6112yes—
816C22C2×#1451973711yescharacteristic
817C22C2×#1451973911yescharacteristic
818C22#1684023011yescharacteristic
819C22#120×D6112yes—
820C22#120×D6111yescharacteristic
821C22#121×D6111yescharacteristic
822C22#121×D6112yes—
823C22#1684027012yes—
824C22#1684027012yes—
825C22#1684027011yescharacteristic
826C22#1684027212yes—
827C22#1684027512yes—
828C22#1684027511yescharacteristic
829C22#1684027512yes—
830C22#1684029512yes—
831C22#1684029811yescharacteristic
832C22#127×D6111yescharacteristic
833C22#1684030711yescharacteristic
834C22#1684030712yes—
835C22#1684031112yes—
836C22#1684031111yescharacteristic
837C4—24no—
838C4—44no—
839C4—44no—
840C4—42no—
841C4—618no—
842C4—1228no—
843C4—2442no—
844C4—2442no—
845C4—2442no—
846C2—44no—
847C2—2448no—
848C2#2144832012yes—
849C2#2144832411yescharacteristic
850C2#2144832511yescharacteristic
851C2#2144833112yes—
852C2#2144838311yescharacteristic
853C2#392×D6111yescharacteristic
854C2#2144903312yes—
855C2#2144903611yescharacteristic
856C2#2144905611yescharacteristic
857C2#2144906412yes—
858C2#2144909911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1439C2
socle, cosocleC24×C61C24
prime radicalC2×#16839671C2
hypercenter#1439D61
hypocenterC61C4×#392
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#14519739C2semidirect
2. C22×#14519737C2semidirect
4. C2×C22⋊C4×Dic61C2semidirect
5. C2×#16839609C2semidirect
6. #21444082C2semidirect
7. #21444063C2semidirect
8. #21444059C2semidirect
9. #21444058C2semidirect
10. #95×Dic61C2semidirect
11. C61×#1439C2semidirect
30. #16839671C4semidirect
48. C22×D244C2×C4semidirect
55. C22×C22⋊D61C2×C4semidirect
60. C23×Dic61D4semidirect
72. C22×C4×D61D4semidirect
92. C2×#11758198C2×C4semidirect
98. C2×C4×Dic61D4semidirect
99. C2×C4×Dic61D4semidirect
104. #14519684C2×C4semidirect
117. C2×C22⋊C4×C61C2×C4semidirect
256. C23×C61C4×D4semidirect
302. C22×D61C4×D4semidirect
326. C2×C4×C61C4×D4semidirect
350. C2×Dic61C4×D4semidirect
416. Dic61#392semidirect
424. #1439D61semidirect
472. C61C4×#392semidirect
535. C2×C22⋊C4C4×D61semidirect
721. C23#14519739semidirect
787. C2×C4#14519737semidirect

Maximal subgroups

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

subgroupindex
C22×#145197392
C22×#145197372
C2×#168396712
C2×C22⋊C4×Dic612
C2×#168396092
#214440822
#214440632
#214440592
#214440582
#95×Dic612
C61×#14392
C4×#39261