Finite Group Databasebeta

← #29602236

Subgroups — #29602236

Order 15616.

3526 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C4×D61C211yesmaximal, characteristic
2C2×#16839624C212yesmaximal, complemented
3C2×#16839621C211yesmaximal, characteristic, complemented
4C2×#16839617C212yesmaximal
5C2×C4×#11758198C211yesmaximal, characteristic, complemented
6#21444063C212yesmaximal, complemented
7#21444062C212yesmaximal, complemented
8#21444057C211yesmaximal, characteristic, complemented
9#21444056C211yesmaximal, characteristic, complemented
10#21444055C211yesmaximal, characteristic, complemented
11C61×#1437C211yesmaximal, characteristic, complemented
12C25×D61C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C23×C4×D61C2211yescharacteristic
15C22×#11758196C2212yescomplemented
16C22×C22⋊Dic61C2212yes—
17C22×C22⋊Dic61C2211yescharacteristic
18C22×#11758198C2212yes—
19C22×#11758198C2212yes—
20C22×#11758198C2212yes—
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2212yes—
24C2×C22⋊C4×D61—24no—
25C2×C22⋊C4×D61—24no—
26C2×C22⋊C4×D61C418yescomplemented
27C22×C4×Dic61C2211yescharacteristic, complemented
28#16839624—28no—
29#16839621—24no—
30#16839617—28no—
31C4×#11758198—24no—
32C2×#14519684C2212yescomplemented
33C2×#14519684C2212yescomplemented
34C2×#14519684C2212yescomplemented
35C2×#14519684C2212yescomplemented
36C2×#14519684C2211yescharacteristic, complemented
37C22×C22⋊C4×C61C2212yes—
38C22×C22⋊C4×C61C2211yescharacteristic
39C22×C42×C61C2211yescharacteristic, complemented
40C2×#95×C61C2212yescomplemented
41C2×#95×C61C2211yescharacteristic, complemented
42C24×D61—24no—
43C24×D61—22no—
44C24×D61—22no—
45C24×D61—24no—
46C24×D61—24no—
47C24×D61—24no—
48C24×D61—42no—
49C24×D61—42no—
50C24×D61C2×C414yes—
51C24×D61C2311yescharacteristic
52C24×D61C2311yescharacteristic
53C23×Dic61C2312yes—
54C23×Dic61C2311yescharacteristic
55C23×Dic61C2312yes—
56C23×Dic61C2311yescharacteristic
57C22×C4×D61—22no—
58C22×C4×D61—22no—
59C22×C4×D61—24no—
60C22×C4×D61—24no—
61C22×C4×D61—42no—
62C22×C4×D61—42no—
63C22×C4×D61C2×C414yes—
64C22×C4×D61C2×C414yes—
65C22×C4×D61D414yes—
66C22×C4×D61D414yes—
67C2×#11758196—24no—
68C2×#11758196—42no—
69C2×#11758196—42no—
70C2×C22⋊Dic61—22no—
71C2×C22⋊Dic61—22no—
72C2×C22⋊Dic61—24no—
73C2×C22⋊Dic61—24no—
74C2×C22⋊Dic61—42no—
75C2×C22⋊Dic61C2×C414yes—
76C2×#11758198—24no—
77C2×#11758198—24no—
78C2×#11758198—22no—
79C2×#11758198—22no—
80C2×#11758198—22no—
81C2×#11758198—22no—
82C2×#11758198—24no—
83C2×#11758198—24no—
84C2×#11758198—24no—
85C2×#11758198—24no—
86C2×#11758198—24no—
87C2×#11758198—24no—
88C2×#11758198—24no—
89C2×#11758198—42no—
90C2×#11758198—42no—
91C2×#11758198C2×C414yes—
92C2×#11758198C2×C414yes—
93C2×#11758198D418yes—
94C22⋊C4×D61—232no—
95C2×C4×Dic61—22no—
96C2×C4×Dic61—42no—
97#14519684—22no—
98#14519684—24no—
99#14519684—24no—
100#14519684—24no—
101#14519684—24no—
102C25×C61C2311yescharacteristic
103C23×C4×C61C2312yes—
104C23×C4×C61C2311yescharacteristic
105C23×C4×C61C2312yes—
106C23×C4×C61C2311yescharacteristic
107C2×C22⋊C4×C61—22no—
108C2×C22⋊C4×C61—22no—
109C2×C22⋊C4×C61—24no—
110C2×C22⋊C4×C61—24no—
111C2×C22⋊C4×C61—42no—
112C2×C22⋊C4×C61C2×C414yes—
113C2×C42×C61—22no—
114C2×C42×C61—42no—
115#95×C61—22no—
116#95×C61—24no—
117C24×C61—21no—
118C24×C61—21no—
119C24×C61—22no—
120C24×C61—22no—
121C24×C61—22no—
122C24×C61—22no—
123C24×C61—22no—
124C24×C61C22×C412yes—
125C24×C61#4114yes—
126C24×C61C2411yescharacteristic
127C23×D61—22no—
128C23×D61—22no—
129C23×D61—22no—
130C23×D61—22no—
131C23×D61—216no—
132C23×D61—216no—
133C23×D61—28no—
134C23×D61—21no—
135C23×D61—21no—
136C23×D61—22no—
137C23×D61—22no—
138C23×D61—22no—
139C23×D61—22no—
140C23×D61—22no—
141C23×D61—28no—
142C23×D61—28no—
143C23×D61—216no—
144C23×D61—48no—
145C23×D61—48no—
146C23×D61—48no—
147C23×D61—48no—
148C23×D61—48no—
149C23×D61—48no—
150C23×D61—48no—
151C23×D61—48no—
152C23×D61—48no—
153C23×D61—48no—
154C23×D61—44no—
155C23×D61—44no—
156C23×D61—48no—
157C23×D61—44no—
158C23×D61—44no—
159C23×D61C22×C412yes—
160C23×D61C22×C412yes—
161C23×D61C2×D412yes—
162C23×D61C2×D412yes—
163C23×D61C2×D414yes—
164C23×D61#4114yes—
165C23×D61#4114yes—
166C22×C4×C61—22no—
167C22×C4×C61—22no—
168C22×C4×C61—22no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—22no—
172C22×C4×C61—22no—
173C22×C4×C61—22no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61C22×C412yes—
186C22×C4×C61C22×C412yes—
187C22×C4×C61C2×D414yes—
188C22×C4×C61C2×D412yes—
189C22×C4×C61C2×D412yes—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—22no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—22no—
209C22×Dic61C22×C412yes—
210C22×Dic61C22×C412yes—
211C22×Dic61C2×D414yes—
212C22×Dic61C2×D412yes—
213C22×Dic61C2×D412yes—
214C2×C4×D61—28no—
215C2×C4×D61—216no—
216C2×C4×D61—48no—
217C2×C4×D61—48no—
218C2×C4×D61—44no—
219C2×C4×D61—44no—
220C2×C4×D61—48no—
221C2×C4×D61—44no—
222C2×C4×D61—44no—
223C2×C4×D61C22⋊C4116yescomplemented
224C22⋊C4×C61—28no—
225C22⋊C4×C61—48no—
226C42×C61—44no—
227C22⋊Dic61—28no—
228C22⋊Dic61—48no—
229#11758198—216no—
230#11758198—28no—
231#11758198—28no—
232#11758198—48no—
233#11758198—48no—
234#11758198—48no—
235#11758196—48no—
236C4×Dic61—44no—
237C23×C61—22no—
238C23×C61—22no—
239C23×C61—24no—
240C23×C61—24no—
241C23×C61—24no—
242C23×C61—24no—
243C23×C61—24no—
244C23×C61—24no—
245C23×C61—24no—
246C23×C61—24no—
247C23×C61—42no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—42no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—42no—
254C23×C61—42no—
255C23×C61—42no—
256C23×C61—42no—
257C23×C61#11714yes—
258C23×C61C23×C411yescharacteristic
259C23×C61C22×D411yescharacteristic
260C23×C61C22×D411yescharacteristic
261C23×C61C22×D412yes—
262C23×C61C2×#4112yes—
263C23×C61C2×#4112yes—
264C23×C61C2×#4112yes—
265C23×C61H(5,𝔽2)12yes—
266C23×C61H(5,𝔽2)12yes—
267C22×D61—22no—
268C22×D61—22no—
269C22×D61—24no—
270C22×D61—24no—
271C22×D61—24no—
272C22×D61—24no—
273C22×D61—22no—
274C22×D61—22no—
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—232no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—24no—
287C22×D61—24no—
288C22×D61—24no—
289C22×D61—24no—
290C22×D61—24no—
291C22×D61—24no—
292C22×D61—24no—
293C22×D61—24no—
294C22×D61—432no—
295C22×D61—432no—
296C22×D61—432no—
297C22×D61—416no—
298C22×D61—432no—
299C22×D61—432no—
300C22×D61—432no—
301C22×D61—42no—
302C22×D61—41no—
303C22×D61—41no—
304C22×D61—42no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—42no—
308C22×D61—42no—
309C22×D61—42no—
310C22×D61—42no—
311C22×D61—416no—
312C22×D61C2×C22⋊C414yes—
313C22×D61#11714yes—
314C22×D61C4×D418yes—
315C22×D61#12118yes—
316C22×D61#12414yes—
317C22×D61#12714yes—
318C2×C4×C61—24no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—24no—
322C2×C4×C61—22no—
323C2×C4×C61—24no—
324C2×C4×C61—24no—
325C2×C4×C61—24no—
326C2×C4×C61—24no—
327C2×C4×C61—42no—
328C2×C4×C61—42no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—42no—
332C2×C4×C61—42no—
333C2×C4×C61—42no—
334C2×C4×C61—42no—
335C2×C4×C61—42no—
336C2×C4×C61—42no—
337C2×C4×C61—42no—
338C2×C4×C61—42no—
339C2×C4×C61—42no—
340C2×C4×C61—42no—
341C2×C4×C61C2×C22⋊C414yes—
342C2×Dic61—24no—
343C2×Dic61—24no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—24no—
348C2×Dic61—24no—
349C2×Dic61—24no—
350C2×Dic61—24no—
351C2×Dic61—42no—
352C2×Dic61—42no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—42no—
356C2×Dic61—42no—
357C2×Dic61—42no—
358C2×Dic61—42no—
359C2×Dic61—42no—
360C2×Dic61—42no—
361C2×Dic61—42no—
362C2×Dic61—42no—
363C2×Dic61—42no—
364C2×Dic61—42no—
365C2×Dic61C2×C22⋊C414yes—
366C4×D61—416no—
367C4×D61—416no—
368#13903—611nomaximal, Sylow
369C22×C61—28no—
370C22×C61—24no—
371C22×C61—44no—
372C22×C61—42no—
373C22×C61—44no—
374C22×C61—44no—
375C22×C61—44no—
376C22×C61—44no—
377C22×C61—42no—
378C22×C61C22×C22⋊C411yescharacteristic
379C22×C61C2×#11711yescharacteristic
380C22×C61C2×#11711yescharacteristic
381C22×C61C2×C4×D412yes—
382C22×C61#51812yes—
383C22×C61C2×#12112yes—
384C22×C61#52512yes—
385C22×C61#52512yes—
386C22×C61C2×#12411yescharacteristic
387C22×C61C2×#12711yescharacteristic
388C22×C61#53412yes—
389C22×C61#53411yescharacteristic
390C22×C61#53411yescharacteristic
391C22×C61#54612yes—
392C22×C61#54612yes—
393C22×C61#54612yes—
394C22×C61#54612yes—
395C22×C61#55112yes—
396C22×C61#55112yes—
397C22×C61#55112yes—
398C22×C61#55112yes—
399C2×D61—28no—
400C2×D61—24no—
401C2×D61—28no—
402C2×D61—28no—
403C2×D61—28no—
404C2×D61—28no—
405C2×D61—24no—
406C2×D61—28no—
407C2×D61—28no—
408C2×D61—24no—
409C2×D61—464no—
410C2×D61—44no—
411C2×D61—42no—
412C2×D61—44no—
413C2×D61—44no—
414C2×D61—44no—
415C2×D61—44no—
416C2×D61—42no—
417C2×D61#39018yes—
418C4×C61—24no—
419C4×C61—44no—
420C4×C61—42no—
421C4×C61—82no—
422Dic61—24no—
423Dic61—44no—
424Dic61—42no—
425Dic61—82no—
426C23×C22⋊C4—611no—
427C2×#381—612no—
428C2×#380—611no—
429C2×#379—612no—
430C2×C4×C22⋊C4—611no—
431#1439—612no—
432#1439—612no—
433#1437—611no—
434#1437—611no—
435#1437—611no—
436#1437D6111yescharacteristic, complemented
437C2×C61—44no—
438C2×C61#228011yescharacteristic
439C2×C61C2×#39011yescharacteristic
440C2×C61#230811yescharacteristic
441C2×C61#234212yes—
442C2×C61#234212yes—
443C2×C61#253412yes—
444C2×C61#253412yes—
445C2×C61#253912yes—
446C2×C61#256112yes—
447D61—28no—
448D61—44no—
449C26—611no—
450C24×C4—611no—
451C24×C4—611no—
452C22×C4⋊C4—612no—
453C22×C22⋊C4—611no—
454C22×C22⋊C4—611no—
455C22×C22⋊C4—611no—
456C22×C22⋊C4—612no—
457C22×C22⋊C4—618no—
458C22×C22⋊C4—612no—
459C22×C22⋊C4—612no—
460C22×C22⋊C4—612no—
461C22×C22⋊C4—612no—
462C22×C22⋊C4—1224no—
463C22×C22⋊C4—1224no—
464C22×C22⋊C4C2×D6112yes—
465C22×C22⋊C4C2×D6111yescharacteristic
466C22×C42—611no—
467C22×C42C2×D6111yescharacteristic, complemented
468#381—1228no—
469#380—1224no—
470#379—1228no—
471C4×C22⋊C4—1224no—
472C2×#95—611no—
473C2×#95—612no—
474C2×#95—612no—
475C2×#95—612no—
476C2×#95—612no—
477C2×#95C2×D6111yescharacteristic, complemented
478C2×#95C2×D6112yescomplemented
479C61#1390311yescharacteristic, complemented, Sylow
480C25—611no—
481C25—611no—
482C25—614no—
483C25—1222no—
484C25—1222no—
485C25—1224no—
486C25—1224no—
487C25—1224no—
488C25—1224no—
489C25—2442no—
490C25—2442no—
491C25C22×D6111yescharacteristic
492C23×C4—611no—
493C23×C4—614no—
494C23×C4—614no—
495C23×C4—614no—
496C23×C4—612no—
497C23×C4—611no—
498C23×C4—614no—
499C23×C4—612no—
500C23×C4—1222no—
501C23×C4—1222no—
502C23×C4—1224no—
503C23×C4—1224no—
504C23×C4—2442no—
505C23×C4—2442no—
506C23×C4C22×D6112yes—
507C23×C4C22×D6111yescharacteristic
508C23×C4C22×D6112yes—
509C23×C4C22×D6111yescharacteristic
510C2×C4⋊C4—1224no—
511C2×C4⋊C4—2442no—
512C2×C4⋊C4—2442no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—614no—
519C2×C22⋊C4—614no—
520C2×C22⋊C4—614no—
521C2×C22⋊C4—618no—
522C2×C22⋊C4—12232no—
523C2×C22⋊C4—1222no—
524C2×C22⋊C4—1222no—
525C2×C22⋊C4—1224no—
526C2×C22⋊C4—1224no—
527C2×C22⋊C4—1222no—
528C2×C22⋊C4—1222no—
529C2×C22⋊C4—1222no—
530C2×C22⋊C4—1222no—
531C2×C22⋊C4—1224no—
532C2×C22⋊C4—1224no—
533C2×C22⋊C4—1224no—
534C2×C22⋊C4—1224no—
535C2×C22⋊C4—1224no—
536C2×C22⋊C4—1224no—
537C2×C22⋊C4—1224no—
538C2×C22⋊C4—1224no—
539C2×C22⋊C4—1224no—
540C2×C22⋊C4—2442no—
541C2×C22⋊C4—2442no—
542C2×C22⋊C4—2442no—
543C2×C22⋊C4C4×D6114yes—
544C2×C42—22no—
545C2×C42—42no—
546C2×C42—1222no—
547C2×C42—2442no—
548#95—22no—
549#95—24no—
550#95—1224no—
551#95—1224no—
552#95—1224no—
553#95—1222no—
554#95—1224no—
555C24—21no—
556C24—21no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—612no—
563C24—614no—
564C24—612no—
565C24—612no—
566C24—614no—
567C24—612no—
568C24—614no—
569C24—1228no—
570C24—1228no—
571C24—12216no—
572C24—12216no—
573C24—12216no—
574C24—1222no—
575C24—1222no—
576C24—1222no—
577C24—1222no—
578C24—1221no—
579C24—1221no—
580C24—1222no—
581C24—1222no—
582C24—1222no—
583C24—1222no—
584C24—1222no—
585C24—1228no—
586C24—2448no—
587C24—2448no—
588C24—2448no—
589C24—2448no—
590C24—2448no—
591C24—2448no—
592C24—2444no—
593C24—2444no—
594C24—2448no—
595C24—2448no—
596C24—2448no—
597C24—2448no—
598C24—2448no—
599C24—2444no—
600C24—2444no—
601C24C2×C4×D6112yes—
602C24#1175822214yes—
603C24C23×D6111yescharacteristic
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—612no—
624C22×C4—612no—
625C22×C4—612no—
626C22×C4—6116no—
627C22×C4—612no—
628C22×C4—614no—
629C22×C4—1228no—
630C22×C4—12216no—
631C22×C4—1222no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—1222no—
638C22×C4—1222no—
639C22×C4—1222no—
640C22×C4—1222no—
641C22×C4—1222no—
642C22×C4—1222no—
643C22×C4—1222no—
644C22×C4—1222no—
645C22×C4—1222no—
646C22×C4—1222no—
647C22×C4—1222no—
648C22×C4—1222no—
649C22×C4—1222no—
650C22×C4—2448no—
651C22×C4—2448no—
652C22×C4—2444no—
653C22×C4—2444no—
654C22×C4—2448no—
655C22×C4—2444no—
656C22×C4—2444no—
657C22×C4C2×C4×D6112yes—
658C22×C4C2×C4×D6112yes—
659C22×C4D4×D6114yes—
660C22×C4D4×D6112yes—
661C22×C4D4×D6112yes—
662C4⋊C4—2448no—
663C22⋊C4—28no—
664C22⋊C4—48no—
665C22⋊C4—1228no—
666C22⋊C4—12216no—
667C22⋊C4—1228no—
668C22⋊C4—1228no—
669C22⋊C4—2448no—
670C22⋊C4—2448no—
671C22⋊C4—2448no—
672C22⋊C4—2448no—
673C42—44no—
674C42—2444no—
675C23—22no—
676C23—22no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—42no—
686C23—41no—
687C23—41no—
688C23—42no—
689C23—41no—
690C23—41no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—614no—
696C23—618no—
697C23—618no—
698C23—614no—
699C23—614no—
700C23—614no—
701C23—12232no—
702C23—1222no—
703C23—1222no—
704C23—1224no—
705C23—1224no—
706C23—1224no—
707C23—1224no—
708C23—1222no—
709C23—1222no—
710C23—1224no—
711C23—1224no—
712C23—1224no—
713C23—1224no—
714C23—1224no—
715C23—1224no—
716C23—1224no—
717C23—1224no—
718C23—1222no—
719C23—1222no—
720C23—1224no—
721C23—1224no—
722C23—1224no—
723C23—1224no—
724C23—1224no—
725C23—1224no—
726C23—1224no—
727C23—1224no—
728C23—24432no—
729C23—24416no—
730C23—24432no—
731C23—24416no—
732C23—24432no—
733C23—24432no—
734C23—24432no—
735C23—24432no—
736C23—2442no—
737C23—2441no—
738C23—2441no—
739C23—2442no—
740C23—2441no—
741C23—2441no—
742C23—2442no—
743C23—2442no—
744C23—2442no—
745C23—2442no—
746C23#1451973414yes—
747C23C22×C4×D6111yescharacteristic
748C23C2×D4×D6111yescharacteristic
749C23C2×D4×D6111yescharacteristic
750C23C2×D4×D6112yes—
751C23#41×D6112yes—
752C23#41×D6112yes—
753C23C2×#1175822212yes—
754C23#1451982212yes—
755C23#1451982312yes—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—614no—
780C2×C4—1224no—
781C2×C4—1224no—
782C2×C4—1222no—
783C2×C4—1222no—
784C2×C4—1222no—
785C2×C4—1224no—
786C2×C4—1224no—
787C2×C4—1224no—
788C2×C4—1224no—
789C2×C4—24416no—
790C2×C4—24416no—
791C2×C4—2442no—
792C2×C4—2442no—
793C2×C4—2442no—
794C2×C4—2442no—
795C2×C4—2442no—
796C2×C4—2442no—
797C2×C4—2442no—
798C2×C4—2442no—
799C2×C4—2442no—
800C2×C4—2441no—
801C2×C4—2441no—
802C2×C4—2442no—
803C2×C4—2442no—
804C2×C4—2442no—
805C2×C4C22⋊C4×D6114yes—
806C22—24no—
807C22—28no—
808C22—42no—
809C22—42no—
810C22—44no—
811C22—44no—
812C22—44no—
813C22—44no—
814C22—44no—
815C22—618no—
816C22—1224no—
817C22—1224no—
818C22—1228no—
819C22—1228no—
820C22—1228no—
821C22—1228no—
822C22—1228no—
823C22—1228no—
824C22—1224no—
825C22—1228no—
826C22—24464no—
827C22—2442no—
828C22—2442no—
829C22—2444no—
830C22—2444no—
831C22—2444no—
832C22—2444no—
833C22—2444no—
834C22C2×C22⋊C4×D6111yescharacteristic
835C22#117×D6111yescharacteristic
836C22C2×#1451973411yescharacteristic
837C22C4×D4×D6112yes—
838C22#1684023412yes—
839C22#121×D6112yes—
840C22#1684027112yes—
841C22#1684027112yes—
842C22#124×D6111yescharacteristic
843C22#127×D6111yescharacteristic
844C22#1684032012yes—
845C22#1684032211yescharacteristic
846C22#1684032311yescharacteristic
847C22#1684040112yes—
848C22#1684040212yes—
849C22#1684040512yes—
850C22#1684040812yes—
851C22#1684043612yes—
852C22#1684043712yes—
853C22#1684044012yes—
854C22#1684044112yes—
855C4—24no—
856C4—42no—
857C4—44no—
858C4—82no—
859C4—1224no—
860C4—4882no—
861C4—2442no—
862C4—2444no—
863C2—44no—
864C2—1228no—
865C2—2444no—
866C2#2144820011yescharacteristic
867C2#390×D6111yescharacteristic
868C2#2144839311yescharacteristic
869C2#2144866212yes—
870C2#2144866712yes—
871C2#2145070712yes—
872C2#2145071312yes—
873C2#2145074812yes—
874C2#2145097512yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1437C2
socle, cosocleC24×C61C24
prime radicalC25×D61C22
hypercenter#1437D61
hypocenterC61#13903
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C2×#16839624C2semidirect
3. C2×#16839621C2semidirect
5. C2×C4×#11758198C2semidirect
6. #21444063C2semidirect
7. #21444062C2semidirect
8. #21444057C2semidirect
9. #21444056C2semidirect
10. #21444055C2semidirect
11. C61×#1437C2semidirect
15. C22×#11758196C22semidirect
26. C2×C22⋊C4×D61C4semidirect
27. C22×C4×Dic61C22semidirect
32. C2×#14519684C22semidirect
33. C2×#14519684C22semidirect
34. C2×#14519684C22semidirect
35. C2×#14519684C22semidirect
36. C2×#14519684C22semidirect
39. C22×C42×C61C22semidirect
40. C2×#95×C61C22semidirect
41. C2×#95×C61C22semidirect
223. C2×C4×D61C22⋊C4semidirect
436. #1437D61semidirect
467. C22×C42C2×D61semidirect
477. C2×#95C2×D61semidirect
478. C2×#95C2×D61semidirect
479. C61#13903semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C4×D612
C2×#168396242
C2×#168396212
C2×#168396172
C2×C4×#117581982
#214440632
#214440622
#214440572
#214440562
#214440552
C61×#14372
#1390361