Finite Group Databasebeta

← #29611403

Subgroups — #29611403

Order 15616.

3654 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519754C211yesmaximal, characteristic, complemented
2C23×C22⋊Dic61C211yesmaximal, characteristic
3C2×#16839674C212yesmaximal, complemented
4C2×#16839618C211yesmaximal, characteristic
5#21444064C212yesmaximal, complemented
6#21444062C212yesmaximal, complemented
7#21444062C212yesmaximal, complemented
8#21444041C211yesmaximal, characteristic, complemented
9#21444041C211yesmaximal, characteristic, complemented
10#21444041C211yesmaximal, characteristic, complemented
11C2×C61×#379C211yesmaximal, characteristic
12C23×Dic122C2211yescharacteristic, complemented
13C24×Dic61C2211yescharacteristic
14C24×Dic61C2211yescharacteristic
15C2×#14519754—24no—
16C2×#14519754—24no—
17C2×#14519754—24no—
18C22×C4⋊Dic61C2211yescharacteristic, complemented
19C22×#11758196C2211yescharacteristic, complemented
20C22×#11758196C2211yescharacteristic, complemented
21C22×C22⋊Dic61—28no—
22C22×C22⋊Dic61—24no—
23C22×C22⋊Dic61C2212yes—
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2212yes—
26C22×C22⋊Dic61C2212yes—
27C22×C22⋊Dic61C2212yes—
28C22×C22⋊Dic61C2211yescharacteristic
29#16839674—28no—
30#16839618—24no—
31C2×#14519684C2212yescomplemented
32C2×#14519684C2212yescomplemented
33C2×#14519684C2212yescomplemented
34C2×#14519684C2212yescomplemented
35C2×#14519684C2212yescomplemented
36C2×#14519684C2212yescomplemented
37C26×C61C2211yescharacteristic
38C22×C22⋊C4×C61C2211yescharacteristic
39C22×C22⋊C4×C61C2212yes—
40C22×C22⋊C4×C61C2212yes—
41C22×C22⋊C4×C61C2211yescharacteristic
42C61×#379—24no—
43C22×Dic122—22no—
44C22×Dic122—22no—
45C22×Dic122—22no—
46C22×Dic122—24no—
47C22×Dic122—42no—
48C23×Dic61—22no—
49C23×Dic61—22no—
50C23×Dic61—22no—
51C23×Dic61—24no—
52C23×Dic61—24no—
53C23×Dic61—22no—
54C23×Dic61—22no—
55C23×Dic61—42no—
56C23×Dic61—42no—
57C23×Dic61D414yes—
58C23×Dic61C2312yes—
59C23×Dic61C2311yescharacteristic
60C23×Dic61C2311yescharacteristic
61C23×Dic61C2311yescharacteristic
62C23×Dic61C2312yes—
63C23×Dic61C2311yescharacteristic
64#14519754—232no—
65C2×C4⋊Dic61—22no—
66C2×C4⋊Dic61—22no—
67C2×C4⋊Dic61—22no—
68C2×#11758196—22no—
69C2×#11758196—22no—
70C2×#11758196—22no—
71C2×#11758196—22no—
72C2×#11758196—22no—
73C2×#11758196—22no—
74C2×C22⋊Dic61—232no—
75C2×C22⋊Dic61—24no—
76C2×C22⋊Dic61—22no—
77C2×C22⋊Dic61—22no—
78C2×C22⋊Dic61—24no—
79C2×C22⋊Dic61—24no—
80C2×C22⋊Dic61—24no—
81C2×C22⋊Dic61—24no—
82C2×C22⋊Dic61—22no—
83C2×C22⋊Dic61—24no—
84C2×C22⋊Dic61—22no—
85C2×C22⋊Dic61—24no—
86C2×C22⋊Dic61—22no—
87C2×C22⋊Dic61—24no—
88C2×C22⋊Dic61—24no—
89C2×C22⋊Dic61—42no—
90C2×C22⋊Dic61—42no—
91C2×C22⋊Dic61D418yes—
92C2×C22⋊Dic61D414yes—
93#14519684—24no—
94#14519684—24no—
95#14519684—24no—
96#14519684—42no—
97#14519684—42no—
98#14519684—42no—
99C25×C61—24no—
100C25×C61—22no—
101C25×C61—24no—
102C25×C61—22no—
103C25×C61—22no—
104C25×C61—22no—
105C25×C61—22no—
106C25×C61—22no—
107C25×C61—42no—
108C25×C61—42no—
109C25×C61Q814yescomplemented
110C25×C61C2312yes—
111C25×C61C2311yescharacteristic
112C23×C4×C61C2312yes—
113C23×C4×C61C2311yescharacteristic
114C23×C4×C61C2311yescharacteristic
115C2×C22⋊C4×C61—22no—
116C2×C22⋊C4×C61—22no—
117C2×C22⋊C4×C61—22no—
118C2×C22⋊C4×C61—24no—
119C2×C22⋊C4×C61—24no—
120C2×C22⋊C4×C61—22no—
121C2×C22⋊C4×C61—22no—
122C2×C22⋊C4×C61—24no—
123C2×C22⋊C4×C61—24no—
124C2×C22⋊C4×C61—42no—
125C2×C22⋊C4×C61—42no—
126C2×C22⋊C4×C61D414yes—
127C24×C61—22no—
128C24×C61—22no—
129C24×C61—22no—
130C24×C61—22no—
131C24×C61—28no—
132C24×C61—216no—
133C24×C61—28no—
134C24×C61—28no—
135C24×C61—216no—
136C24×C61—22no—
137C24×C61—22no—
138C24×C61—22no—
139C24×C61—22no—
140C24×C61—22no—
141C24×C61—22no—
142C24×C61—22no—
143C24×C61—22no—
144C24×C61—22no—
145C24×C61—22no—
146C24×C61—22no—
147C24×C61—22no—
148C24×C61—28no—
149C24×C61—28no—
150C24×C61—48no—
151C24×C61—48no—
152C24×C61—48no—
153C24×C61—48no—
154C24×C61—48no—
155C24×C61—48no—
156C24×C61—48no—
157C24×C61—48no—
158C24×C61—48no—
159C24×C61—44no—
160C24×C61—44no—
161C24×C61—48no—
162C24×C61—44no—
163C24×C61—44no—
164C24×C61—44no—
165C24×C61—44no—
166C24×C61C2×D414yes—
167C24×C61C2×D412yes—
168C24×C61C2×D412yes—
169C24×C61C2×D412yes—
170C24×C61C2×Q814yes—
171C24×C61C2×Q812yes—
172C24×C61#4114yes—
173C24×C61#4112yes—
174C24×C61#4112yes—
175C24×C61#4112yes—
176C24×C61C2411yescharacteristic
177C22×C4×C61—22no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
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—22no—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61C2×D412yes—
193C22×C4×C61C2×D412yes—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—22no—
197C22×Dic61—28no—
198C22×Dic61—28no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—22no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61—28no—
218C22×Dic61—22no—
219C22×Dic61—22no—
220C22×Dic61—22no—
221C22×Dic61—22no—
222C22×Dic61—22no—
223C22×Dic61—22no—
224C22×Dic61—22no—
225C22×Dic61—44no—
226C22×Dic61—48no—
227C22×Dic61—48no—
228C22×Dic61—48no—
229C22×Dic61—48no—
230C22×Dic61—44no—
231C22×Dic61—44no—
232C22×Dic61C2×D414yes—
233C22×Dic61C2×D412yes—
234C22×Dic61C2×D412yes—
235C22×Dic61C2×D412yes—
236C22×Dic61C2×D414yes—
237C22×Dic61C2×D412yes—
238C2×Dic122—28no—
239C2×Dic122—48no—
240C2×Dic122—48no—
241C2×Dic122—44no—
242C2×Dic122—44no—
243C22⋊C4×C61—28no—
244C22⋊C4×C61—48no—
245C22⋊C4×C61—48no—
246C22⋊C4×C61—44no—
247C22⋊Dic61—216no—
248C22⋊Dic61—28no—
249C22⋊Dic61—216no—
250C22⋊Dic61—48no—
251C22⋊Dic61—48no—
252C22⋊Dic61—44no—
253C4⋊Dic61—28no—
254#11758196—28no—
255#11758196—28no—
256C23×C61—22no—
257C23×C61—24no—
258C23×C61—22no—
259C23×C61—24no—
260C23×C61—22no—
261C23×C61—22no—
262C23×C61—24no—
263C23×C61—24no—
264C23×C61—24no—
265C23×C61—24no—
266C23×C61—24no—
267C23×C61—24no—
268C23×C61—24no—
269C23×C61—24no—
270C23×C61—24no—
271C23×C61—24no—
272C23×C61—232no—
273C23×C61—24no—
274C23×C61—24no—
275C23×C61—24no—
276C23×C61—24no—
277C23×C61—24no—
278C23×C61—24no—
279C23×C61—24no—
280C23×C61—24no—
281C23×C61—24no—
282C23×C61—24no—
283C23×C61—24no—
284C23×C61—24no—
285C23×C61—24no—
286C23×C61—24no—
287C23×C61—24no—
288C23×C61—24no—
289C23×C61—24no—
290C23×C61—24no—
291C23×C61—432no—
292C23×C61—432no—
293C23×C61—416no—
294C23×C61—416no—
295C23×C61—416no—
296C23×C61—416no—
297C23×C61—416no—
298C23×C61—432no—
299C23×C61—432no—
300C23×C61—42no—
301C23×C61—42no—
302C23×C61—42no—
303C23×C61—42no—
304C23×C61—42no—
305C23×C61—42no—
306C23×C61—42no—
307C23×C61—42no—
308C23×C61—42no—
309C23×C61—42no—
310C23×C61—42no—
311C23×C61—42no—
312C23×C61—42no—
313C23×C61—42no—
314C23×C61—42no—
315C23×C61—42no—
316C23×C61—416no—
317C23×C61#12014yes—
318C23×C61C22⋊Q814yes—
319C23×C61C22⋊Q814yes—
320C23×C61C22⋊Q814yes—
321C23×C61C22⋊Q818yescomplemented
322C23×C61#12414yes—
323C23×C61#12414yes—
324C23×C61#12414yes—
325C23×C61C22×D411yescharacteristic
326C23×C61C22×D412yes—
327C23×C61C22×D411yescharacteristic
328C23×C61C22×D411yescharacteristic
329C23×C61C22×Q811yescharacteristic
330C23×C61C2×#4111yescharacteristic
331C23×C61C2×#4112yes—
332C23×C61C2×#4111yescharacteristic
333C23×C61C2×#4111yescharacteristic
334C23×C61H(5,𝔽2)12yes—
335C23×C61H(5,𝔽2)12yes—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—24no—
339C2×C4×C61—24no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—42no—
345C2×C4×C61—42no—
346C2×C4×C61—42no—
347C2×C4×C61—42no—
348C2×C4×C61—42no—
349C2×C4×C61—42no—
350C2×C4×C61—42no—
351C2×C4×C61—42no—
352C2×C4×C61—42no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—24no—
356C2×Dic61—24no—
357C2×Dic61—22no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—24no—
362C2×Dic61—22no—
363C2×Dic61—24no—
364C2×Dic61—24no—
365C2×Dic61—24no—
366C2×Dic61—24no—
367C2×Dic61—416no—
368C2×Dic61—416no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—42no—
372C2×Dic61—41no—
373C2×Dic61—41no—
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×Dic61#12014yes—
389Dic122—416no—
390#14717—611nomaximal, Sylow
391C22×C61—24no—
392C22×C61—24no—
393C22×C61—24no—
394C22×C61—24no—
395C22×C61—24no—
396C22×C61—24no—
397C22×C61—28no—
398C22×C61—28no—
399C22×C61—28no—
400C22×C61—28no—
401C22×C61—28no—
402C22×C61—28no—
403C22×C61—28no—
404C22×C61—464no—
405C22×C61—44no—
406C22×C61—44no—
407C22×C61—44no—
408C22×C61—44no—
409C22×C61—44no—
410C22×C61—44no—
411C22×C61—44no—
412C22×C61—44no—
413C22×C61—44no—
414C22×C61—44no—
415C22×C61—44no—
416C22×C61—44no—
417C22×C61#39318yescomplemented
418C22×C61C2×#12011yescharacteristic
419C22×C61C2×#12011yescharacteristic
420C22×C61C2×C22⋊Q811yescharacteristic
421C22×C61C2×C22⋊Q812yes—
422C22×C61C2×C22⋊Q811yescharacteristic
423C22×C61C2×C22⋊Q811yescharacteristic
424C22×C61#52511yescharacteristic
425C22×C61#52512yes—
426C22×C61C2×#12411yescharacteristic
427C22×C61C2×#12411yescharacteristic
428C22×C61C2×#12411yescharacteristic
429C22×C61#53411yescharacteristic
430C22×C61#53511yescharacteristic
431C22×C61#53812yes—
432C22×C61#54312yes—
433C22×C61D4212yes—
434C22×C61D4212yes—
435C22×C61#54612yes—
436C22×C61#54612yes—
437C22×C61#54612yes—
438C22×C61#54612yes—
439C22×C61#55112yes—
440C22×C61#55112yes—
441C4×C61—42no—
442C4×C61—42no—
443C4×C61—82no—
444Dic61—24no—
445Dic61—42no—
446Dic61—42no—
447Dic61—42no—
448Dic61—44no—
449Dic61—82no—
450C22×C22⋊Q8—611no—
451C23×C22⋊C4—611no—
452C2×#393—612no—
453C2×#379—611no—
454C2×#379D6111yescharacteristic
455#1439—612no—
456#1439—612no—
457#1439—612no—
458C22⋊#95—611no—
459C22⋊#95—611no—
460C22⋊#95—611no—
461C2×C61—28no—
462C2×C61—48no—
463C2×C61C2×#39311yescharacteristic
464C2×C61#240311yescharacteristic
465C2×C61#240411yescharacteristic
466C2×C61#243511yescharacteristic
467C2×C61#243712yes—
468C2×C61#243712yes—
469C2×C61#247212yes—
470C2×C61#247212yes—
471C2×C61#256111yescharacteristic
472C2×C61#262611yescharacteristic
473C2×C61#284811yescharacteristic
474C26C2×D6111yescharacteristic
475C23×Q8—611no—
476C24×C4—611no—
477C24×C4—611no—
478C2×C22⋊Q8—1224no—
479C2×C22⋊Q8—1224no—
480C2×C22⋊Q8—1224no—
481C22×C4⋊C4—611no—
482C22×C4⋊C4—611no—
483C22×C4⋊C4—611no—
484C22×C22⋊C4—612no—
485C22×C22⋊C4—611no—
486C22×C22⋊C4—612no—
487C22×C22⋊C4—611no—
488C22×C22⋊C4—612no—
489C22×C22⋊C4—612no—
490C22×C22⋊C4—1228no—
491C22×C22⋊C4—1224no—
492C22×C22⋊C4C2×D6111yescharacteristic
493C22×C22⋊C4C2×D6112yes—
494C22×C22⋊C4C2×D6112yes—
495C22×C22⋊C4C2×D6111yescharacteristic
496#393—1228no—
497#379—24no—
498#379—1224no—
499C2×#95—612no—
500C2×#95—612no—
501C2×#95—612no—
502C2×#95—612no—
503C2×#95—612no—
504C2×#95—612no—
505C61#1471711yescharacteristic, complemented, Sylow
506C25—24no—
507C25—22no—
508C25—24no—
509C25—22no—
510C25—22no—
511C25—22no—
512C25—22no—
513C25—22no—
514C25—42no—
515C25—42no—
516C25Dic12214yescomplemented
517C25C22×D6112yes—
518C25C22×D6111yescharacteristic
519C22×Q8—1222no—
520C22×Q8—1222no—
521C22×Q8—1224no—
522C22×Q8—1222no—
523C22×Q8—2442no—
524C23×C4—611no—
525C23×C4—611no—
526C23×C4—611no—
527C23×C4—611no—
528C23×C4—612no—
529C23×C4—614no—
530C23×C4—612no—
531C23×C4—1224no—
532C23×C4—1224no—
533C23×C4—1222no—
534C23×C4—1222no—
535C23×C4—1222no—
536C23×C4—1222no—
537C23×C4—1222no—
538C23×C4—2442no—
539C23×C4—2442no—
540C23×C4C22×D6112yes—
541C23×C4C22×D6111yescharacteristic
542C23×C4C22×D6111yescharacteristic
543C22⋊Q8—12232no—
544C2×C4⋊C4—1222no—
545C2×C4⋊C4—1222no—
546C2×C4⋊C4—1222no—
547C2×C4⋊C4—1222no—
548C2×C4⋊C4—1222no—
549C2×C4⋊C4—1222no—
550C2×C4⋊C4—1222no—
551C2×C4⋊C4—1222no—
552C2×C4⋊C4—1222no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—24no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—618no—
565C2×C22⋊C4—614no—
566C2×C22⋊C4—1224no—
567C2×C22⋊C4—1224no—
568C2×C22⋊C4—1224no—
569C2×C22⋊C4—1224no—
570C2×C22⋊C4—12232no—
571C2×C22⋊C4—1224no—
572C2×C22⋊C4—1222no—
573C2×C22⋊C4—1222no—
574C2×C22⋊C4—1224no—
575C2×C22⋊C4—1224no—
576C2×C22⋊C4—1222no—
577C2×C22⋊C4—1222no—
578C2×C22⋊C4—1224no—
579C2×C22⋊C4—1224no—
580C2×C22⋊C4—1222no—
581C2×C22⋊C4—2442no—
582C2×C22⋊C4—2442no—
583C2×C22⋊C4C22⋊D6114yes—
584#95—1224no—
585#95—1224no—
586#95—1224no—
587#95—2442no—
588#95—2442no—
589#95—2442no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—28no—
595C24—28no—
596C24—216no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—28no—
610C24—216no—
611C24—28no—
612C24—28no—
613C24—48no—
614C24—48no—
615C24—48no—
616C24—48no—
617C24—48no—
618C24—48no—
619C24—48no—
620C24—48no—
621C24—48no—
622C24—44no—
623C24—44no—
624C24—48no—
625C24—44no—
626C24—44no—
627C24—44no—
628C24—44no—
629C24C2×Dic12214yes—
630C24C2×Dic12212yes—
631C24#1175822212yes—
632C24D4×D6114yes—
633C24D4×D6112yes—
634C24D4×D6112yes—
635C24#1175822414yes—
636C24#1175822412yes—
637C24#1175822412yes—
638C24C2×C22⋊D6112yes—
639C24C23×D6111yescharacteristic
640C2×Q8—1228no—
641C2×Q8—2448no—
642C2×Q8—2444no—
643C2×Q8—2448no—
644C2×Q8—2444no—
645C22×C4—22no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—614no—
661C22×C4—612no—
662C22×C4—614no—
663C22×C4—612no—
664C22×C4—612no—
665C22×C4—612no—
666C22×C4—1228no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1222no—
670C22×C4—1228no—
671C22×C4—1222no—
672C22×C4—1222no—
673C22×C4—1222no—
674C22×C4—1222no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
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—1228no—
690C22×C4—1222no—
691C22×C4—1222no—
692C22×C4—1222no—
693C22×C4—1222no—
694C22×C4—1222no—
695C22×C4—1222no—
696C22×C4—1222no—
697C22×C4—2444no—
698C22×C4—2448no—
699C22×C4—2448no—
700C22×C4—2448no—
701C22×C4—2448no—
702C22×C4—2444no—
703C22×C4—2444no—
704C22×C4C2×C22⋊D6112yes—
705C22×C4C2×C22⋊D6112yes—
706C4⋊C4—1228no—
707C4⋊C4—1228no—
708C4⋊C4—1228no—
709C22⋊C4—28no—
710C22⋊C4—48no—
711C22⋊C4—48no—
712C22⋊C4—44no—
713C22⋊C4—12216no—
714C22⋊C4—12216no—
715C22⋊C4—1228no—
716C22⋊C4—2448no—
717C22⋊C4—2448no—
718C22⋊C4—2444no—
719C23—22no—
720C23—24no—
721C23—22no—
722C23—24no—
723C23—22no—
724C23—22no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—24no—
735C23—232no—
736C23—24no—
737C23—24no—
738C23—24no—
739C23—24no—
740C23—24no—
741C23—24no—
742C23—24no—
743C23—24no—
744C23—24no—
745C23—24no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—432no—
755C23—432no—
756C23—416no—
757C23—416no—
758C23—416no—
759C23—432no—
760C23—432no—
761C23—416no—
762C23—416no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—416no—
779C23—42no—
780C23#1451974514yes—
781C23#1451975414yes—
782C23#1451975414yes—
783C23#1451975418yescomplemented
784C23#1451975614yes—
785C23#1451976314yes—
786C23#1451976314yes—
787C23#1451976414yes—
788C23C2×D4×D6111yescharacteristic
789C23C2×D4×D6112yes—
790C23C2×D4×D6111yescharacteristic
791C23C22×C22⋊D6111yescharacteristic
792C23C22×Dic12211yescharacteristic
793C23C2×#1175822411yescharacteristic
794C23C2×#1175822412yes—
795C23C2×#1175822411yescharacteristic
796C23C2×#1175822211yescharacteristic
797C23#1451982212yes—
798C23#1451982212yes—
799Q8—24416no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—614no—
818C2×C4—1222no—
819C2×C4—1222no—
820C2×C4—1224no—
821C2×C4—1224no—
822C2×C4—1222no—
823C2×C4—1224no—
824C2×C4—1222no—
825C2×C4—1222no—
826C2×C4—1222no—
827C2×C4—1222no—
828C2×C4—1224no—
829C2×C4—1224no—
830C2×C4—1224no—
831C2×C4—1224no—
832C2×C4—24416no—
833C2×C4—2442no—
834C2×C4—2442no—
835C2×C4—2442no—
836C2×C4—2442no—
837C2×C4—2442no—
838C2×C4—2442no—
839C2×C4—2442no—
840C2×C4—24416no—
841C2×C4—2441no—
842C2×C4—2441no—
843C2×C4—2442no—
844C2×C4—2441no—
845C2×C4—2441no—
846C2×C4—2442no—
847C2×C4—2442no—
848C2×C4—2442no—
849C2×C4—2442no—
850C2×C4—2442no—
851C2×C4—2442no—
852C2×C4—2442no—
853C22—28no—
854C22—28no—
855C22—24no—
856C22—24no—
857C22—24no—
858C22—24no—
859C22—28no—
860C22—28no—
861C22—24no—
862C22—24no—
863C22—28no—
864C22—28no—
865C22—28no—
866C22—464no—
867C22—44no—
868C22—44no—
869C22—44no—
870C22—44no—
871C22—44no—
872C22—44no—
873C22—44no—
874C22—44no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—44no—
879C22#1683967418yescomplemented
880C22#120×D6111yescharacteristic
881C22C2×#1451974511yescharacteristic
882C22C2×#1451975412yes—
883C22C2×#1451975411yescharacteristic
884C22C2×#1451975411yescharacteristic
885C22C2×#1451975611yescharacteristic
886C22#1684026811yescharacteristic
887C22#1684026812yes—
888C22C2×#1451976311yescharacteristic
889C22C2×#1451976311yescharacteristic
890C22C2×#1451976411yescharacteristic
891C22#1684032211yescharacteristic
892C22#1684032711yescharacteristic
893C22#1684034712yes—
894C22#1684038812yes—
895C22#1684039412yes—
896C22D4×C22⋊D6112yes—
897C22#1684039912yes—
898C22#1684039912yes—
899C22#1684040212yes—
900C22#1684040612yes—
901C22#1684043812yes—
902C22#1684044312yes—
903C4—42no—
904C4—42no—
905C4—82no—
906C4—1224no—
907C4—4882no—
908C4—2442no—
909C4—2442no—
910C4—2442no—
911C4—2444no—
912C2—28no—
913C2—48no—
914C2C2×#1683967411yescharacteristic
915C2#2144913011yescharacteristic
916C2#2144913511yescharacteristic
917C2#2144946811yescharacteristic
918C2#2144948012yes—
919C2#2144948512yes—
920C2#2144994212yes—
921C2#2144994412yes—
922C2#2145097411yescharacteristic
923C2#2145162811yescharacteristic
924C2#2145410411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutator, socle, cosocleC24×C61C24
FittingC2×C61×#379C2
prime radicalC26×C61C22
hypercenterC2×#379D61
hypocenterC61#14717
LCSG ▷ C24×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
1. C22×#14519754C2semidirect
3. C2×#16839674C2semidirect
5. #21444064C2semidirect
6. #21444062C2semidirect
7. #21444062C2semidirect
8. #21444041C2semidirect
9. #21444041C2semidirect
10. #21444041C2semidirect
12. C23×Dic122C22semidirect
18. C22×C4⋊Dic61C22semidirect
19. C22×#11758196C22semidirect
20. C22×#11758196C22semidirect
31. C2×#14519684C22semidirect
32. C2×#14519684C22semidirect
33. C2×#14519684C22semidirect
34. C2×#14519684C22semidirect
35. C2×#14519684C22semidirect
36. C2×#14519684C22semidirect
109. C25×C61Q8semidirect
321. C23×C61C22⋊Q8semidirect
417. C22×C61#393semidirect
505. C61#14717semidirect
516. C25Dic122semidirect
783. C23#14519754semidirect
879. C22#16839674semidirect

Maximal subgroups

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

subgroupindex
C22×#145197542
C23×C22⋊Dic612
C2×#168396742
C2×#168396182
#214440642
#214440622
#214440412
C2×C61×#3792
#1471761