Finite Group Databasebeta

← #29685740

Subgroups — #29685740

Order 15616.

1560 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840237C211yesmaximal, characteristic
2C2×#16839913C211yesmaximal, characteristic
3C2×#16839859C211yesmaximal, characteristic, complemented
4C2×#16839853C211yesmaximal, characteristic, complemented
5#21448497C211yesmaximal, characteristic, complemented
6#21446151C211yesmaximal, characteristic, complemented
7#21446151C211yesmaximal, characteristic, complemented
8#21446129C211yesmaximal, characteristic, complemented
9#21446078C211yesmaximal, characteristic, complemented
10#21446064C211yesmaximal, characteristic, complemented
11#21446016C211yesmaximal, characteristic, complemented
12#21445646C211yesmaximal, characteristic, complemented
13#102×Dic61C211yesmaximal, characteristic, complemented
14#21445587C211yesmaximal, characteristic, complemented
15C61×#1786C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C2×#14519756C2211yescharacteristic
19#16840237—24no—
20#16840237—24no—
21C2×#14519742C2211yescharacteristic, complemented
22C2×D4×Dic61—21no—
23C2×D4×Dic61—21no—
24C2×D4×Dic61C2211yescharacteristic
25C2×D4×Dic61C2211yescharacteristic
26C2×D4×Dic61C2211yescharacteristic
27C2×D4×Dic61C2211yescharacteristic
28C2×#14519736C2211yescharacteristic
29C2×#14519736C2211yescharacteristic
30C22×C22⋊Dic61—21no—
31C22×C22⋊Dic61—21no—
32#16839913C418yescomplemented
33#16839859—24no—
34#16839853—24no—
35C2×#14519710C2211yescharacteristic, complemented
36C2×#14519708C2211yescharacteristic, complemented
37C2×#14519702C2211yescharacteristic, complemented
38C2×#14519702C2211yescharacteristic, complemented
39C2×#14519698C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×#14519687C2211yescharacteristic, complemented
43C2×C8×Dic61C2211yescharacteristic, complemented
44#16839667C2211yescharacteristic, complemented
45#16839659—21no—
46#16839658C2211yescharacteristic, complemented
47#16839656—21no—
48#16839650—21no—
49#16839649—21no—
50C4⋊C4×Dic61C2211yescharacteristic, complemented
51#16839525C2211yescharacteristic, complemented
52#16839525C2211yescharacteristic, complemented
53#16839524C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839516C2211yescharacteristic, complemented
56#16839516C2211yescharacteristic, complemented
57C23×D4×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic
63C61×#380C2211yescharacteristic
64C22×Dic122C2311yescharacteristic
65C23×Dic61—21no—
66C23×Dic61—21no—
67C23×Dic61—21no—
68C23×Dic61—21no—
69C2×#11758200—22no—
70C2×#11758200—22no—
71C2×#11758200—22no—
72C2×#11758200—22no—
73C2×#11758200C2×C414yescomplemented
74C2×#11758200C2×C414yescomplemented
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77#14519756—22no—
78#14519756C2×C414yescomplemented
79#14519742—22no—
80#14519742—22no—
81D4×Dic61—28no—
82D4×Dic61—28no—
83D4×Dic61—22no—
84D4×Dic61—22no—
85D4×Dic61—22no—
86D4×Dic61—22no—
87D4×Dic61—22no—
88D4×Dic61—22no—
89D4×Dic61D414yes—
90D4×Dic61D414yes—
91#14519736—22no—
92#14519736—22no—
93#14519736—22no—
94#14519736—22no—
95C2×C4⋊Dic61D411yescharacteristic
96C2×C4⋊Dic61D411yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×C22⋊Dic61—28no—
104C2×C22⋊Dic61—28no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61—21no—
107C2×C22⋊Dic61—21no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61D411yescharacteristic
112C2×C22⋊Dic61D411yescharacteristic
113C2×C4×Dic61—21no—
114C2×C4×Dic61—21no—
115C2×C4×Dic61—21no—
116C2×C4×Dic61C2311yescharacteristic
117C2×C4×Dic61C2311yescharacteristic
118#14519710—22no—
119#14519708—22no—
120#14519702—22no—
121#14519702—22no—
122#14519698C2×C414yescomplemented
123#14519698C2×C414yescomplemented
124C22⋊#92418C2×C414yescomplemented
125#14519687—22no—
126C8×Dic61—22no—
127#14519684—21no—
128#14519684—21no—
129#14519684—21no—
130#14519684—21no—
131C25×C61—21no—
132C22×D4×C61—22no—
133C22×D4×C61—22no—
134C22×D4×C61—22no—
135C22×D4×C61—22no—
136C22×D4×C61—21no—
137C22×D4×C61—22no—
138C22×D4×C61C2×C414yes—
139C22×D4×C61C2311yescharacteristic
140C22×D4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C22×C8×C61C2311yescharacteristic
143C22×C8×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61—21no—
147#102×C61—22no—
148#102×C61—22no—
149#102×C61—22no—
150#102×C61—22no—
151C22⋊C8×C61—22no—
152#95×C61—21no—
153C24×C61—24no—
154C24×C61—24no—
155C24×C61—21no—
156C24×C61—21no—
157C24×C61—24no—
158C24×C61—81no—
159C24×C61—81no—
160C24×C61—81no—
161C24×C61—81no—
162C24×C61C2×D411yescharacteristic
163C2×D4×C61—24no—
164C2×D4×C61—28no—
165C2×D4×C61—28no—
166C2×D4×C61—24no—
167C2×D4×C61—28no—
168C2×D4×C61—28no—
169C2×D4×C61—24no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61C22×C412yes—
177C2×D4×C61C22×C412yes—
178C2×D4×C61C2×D412yes—
179C2×D4×C61C2×D412yes—
180C2×D4×C61#4112yes—
181C2×D4×C61#4112yes—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61C22×C412yes—
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61#4112yes—
191C22×C4×C61C2411yescharacteristic
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—24no—
197C22×Dic61—24no—
198C22×Dic61—24no—
199C22×Dic61—24no—
200C22×Dic61—81no—
201C22×Dic61—81no—
202C22×Dic61—81no—
203C22×Dic61—81no—
204C22×Dic61—81no—
205C22×Dic61—81no—
206C22×Dic61—81no—
207C22×Dic61—81no—
208C22×Dic61C2×D411yescharacteristic
209C22×Dic61C2×D411yescharacteristic
210C22×Dic61C2×D411yescharacteristic
211C22×Dic61C2×D411yescharacteristic
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122—21no—
215C2×Dic122—21no—
216C2×Dic122—21no—
217C2×Dic122C22×C412yes—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C2×C8×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C22⋊C4×C61—81no—
229C22⋊Dic61—24no—
230C22⋊Dic61—24no—
231C22⋊Dic61—24no—
232C22⋊Dic61—24no—
233C22⋊Dic61—22no—
234C22⋊Dic61—22no—
235C22⋊Dic61—24no—
236C22⋊Dic61—24no—
237#11758200—28no—
238#11758200—28no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242C4⋊Dic61—22no—
243C4⋊Dic61—22no—
244C4⋊Dic61C22×C412yes—
245C4⋊Dic61C2×D412yes—
246C4⋊Dic61C2×D412yes—
247#11758196—24no—
248#11758196—42no—
249#11758196—81no—
250C4×Dic61—24no—
251C4×Dic61—21no—
252C4×Dic61—21no—
253C4×Dic61—42no—
254C4×Dic61—81no—
255C4×Dic61C2×D412yes—
256C4×Dic61C2×D412yes—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418C22×C412yes—
262C2×#92418C22×C412yes—
263C23×C61—216no—
264C23×C61—22no—
265C23×C61—22no—
266C23×C61—21no—
267C23×C61—22no—
268C23×C61—22no—
269C23×C61—21no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—84no—
285C23×C61—84no—
286C23×C61—84no—
287C23×C61—84no—
288C23×C61—84no—
289C23×C61—84no—
290C23×C61C4×D412yes—
291C23×C61C22×D411yescharacteristic
292D4×C61—216no—
293D4×C61—22no—
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—22no—
297D4×C61—22no—
298D4×C61—22no—
299D4×C61C4×D414yes—
300D4×C61C4×D414yes—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61C4×D412yes—
314C2×C4×C61C23×C411yescharacteristic
315C2×C4×C61C22×D411yescharacteristic
316C2×C4×C61C22×D411yescharacteristic
317C2×C4×C61C2×#4111yescharacteristic
318C2×C4×C61C2×#4111yescharacteristic
319C2×C4×C61C2×#4111yescharacteristic
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—21no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—84no—
343C2×Dic61—84no—
344C2×Dic61—84no—
345C2×Dic61—84no—
346C2×Dic61#12012yes—
347C2×Dic61#12012yes—
348Dic122—22no—
349Dic122—22no—
350Dic122—41no—
351Dic122—41no—
352C8×C61—41no—
353C8×C61—41no—
354#92418—22no—
355#92418—22no—
356#21459—611nomaximal, Sylow
357C22×C61—22no—
358C22×C61—22no—
359C22×C61—22no—
360C22×C61—24no—
361C22×C61—24no—
362C22×C61—41no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—41no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—42no—
369C22×C61—42no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61—42no—
374C22×C61—41no—
375C22×C61—42no—
376C22×C61—42no—
377C22×C61—41no—
378C22×C61—816no—
379C22×C61C2×C4×D411yescharacteristic
380C22×C61C2×#12011yescharacteristic
381C22×C61#52511yescharacteristic
382C22×C61#57611yescharacteristic
383C22×C61#57711yescharacteristic
384C22×C61#57711yescharacteristic
385C22×C61#57711yescharacteristic
386C4×C61—22no—
387C4×C61—81no—
388C4×C61—81no—
389C4×C61C2×C4×D411yescharacteristic
390C4×C61C2×C4×D411yescharacteristic
391C4×C61#52511yescharacteristic
392C4×C61#52511yescharacteristic
393Dic61—22no—
394Dic61—22no—
395Dic61—42no—
396Dic61—41no—
397Dic61—42no—
398Dic61—41no—
399Dic61—42no—
400Dic61—42no—
401C2×#518—611no—
402C2×#450—611no—
403C2×#440—611no—
404C2×C4×SD16—611no—
405#2323—611no—
406#1877—611no—
407#1877—611no—
408#1873—611no—
409#1864—611no—
410#1862—611no—
411#1854—611no—
412#1786D6111yescharacteristic
413#1762—611no—
414C4×#102—611no—
415#1750—611no—
416C2×C61—42no—
417C2×C61—44no—
418C2×C61—44no—
419C2×C61C4×#12011yescharacteristic
420C2×C61#294611yescharacteristic
421C2×C61#294911yescharacteristic
422C2×C61#300911yescharacteristic
423C2×C61#301211yescharacteristic
424C2×C61#311811yescharacteristic
425C2×C61#312311yescharacteristic
426C23×D4C2×D6111yescharacteristic
427C22×SD16—611no—
428C22×SD16—611no—
429C2×C22⋊Q8—611no—
430#518—1224no—
431#518—1224no—
432C2×C4×Q8—611no—
433C2×C4×D4—611no—
434C2×C4×D4—611no—
435C2×C4×D4—611no—
436C2×C4×D4—611no—
437C2×C4×D4—1221no—
438C2×C4×D4—1221no—
439C2×#117—611no—
440C2×#117—611no—
441C22×C22⋊C4—1221no—
442C22×C22⋊C4—1221no—
443#450—618no—
444#440—1224no—
445C4×SD16—1224no—
446C2×#107—611no—
447C2×#106—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#102—611no—
451C2×#102—611no—
452C2×#102C2×D6111yescharacteristic
453C2×#102C2×D6111yescharacteristic
454C2×#102C2×D6111yescharacteristic
455C2×#102C2×D6111yescharacteristic
456C2×C22⋊C8—611no—
457C2×C22⋊C8C2×D6111yescharacteristic
458C2×#97—611no—
459C2×C4×C8—611no—
460#391—611no—
461#389—611no—
462#389—1221no—
463#388—1221no—
464#388—1221no—
465#387—1221no—
466#380C2×D6111yescharacteristic
467C4×C4⋊C4—611no—
468#340—611no—
469#340—611no—
470#340—611no—
471#340—611no—
472#336—611no—
473#336—611no—
474C61#2145911yescharacteristic, complemented, Sylow
475C25—21no—
476C22×Q8—611no—
477C22×D4—22no—
478C22×D4—22no—
479C22×D4—22no—
480C22×D4—22no—
481C22×D4—21no—
482C22×D4—22no—
483C22×D4C4×D6114yes—
484C22×D4C22×D6111yescharacteristic
485C22×D4C22×D6111yescharacteristic
486C23×C4—1221no—
487C23×C4—1221no—
488C23×C4—1221no—
489C23×C4—1221no—
490C23×C4C22×D6111yescharacteristic
491C2×SD16—614no—
492C2×SD16—614no—
493C2×SD16—1222no—
494C2×SD16—1222no—
495C2×SD16—1222no—
496C2×SD16—1222no—
497C22×C8—611no—
498C22×C8—611no—
499C22×C8C22×D6111yescharacteristic
500C22×C8C22×D6111yescharacteristic
501C22⋊Q8—614no—
502C22⋊Q8—1222no—
503C4×Q8—1222no—
504C4×Q8—1222no—
505C4×D4—614no—
506C4×D4—614no—
507C4×D4—1222no—
508C4×D4—1222no—
509C4×D4—1222no—
510C4×D4—1222no—
511C4×D4—1228no—
512C4×D4—1228no—
513C4×D4—1222no—
514C4×D4—1222no—
515#117—1222no—
516#117—1222no—
517#117—1222no—
518#117—1222no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4C22×D6111yescharacteristic
528C2×C4⋊C4C22×D6111yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—611no—
531C2×C22⋊C4—611no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1228no—
537C2×C22⋊C4—1228no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C42—611no—
541C2×C42—611no—
542C2×C42—1221no—
543C2×C42—1221no—
544C2×C42—1221no—
545#107—1222no—
546#106—1222no—
547#103—1222no—
548#103—1222no—
549#102—22no—
550#102—22no—
551#102—22no—
552#102—22no—
553#102—614no—
554#102—614no—
555C22⋊C8—22no—
556C22⋊C8—614no—
557#97—1222no—
558C4×C8—1222no—
559#95—21no—
560#95—1221no—
561#95—1221no—
562#95—1221no—
563#95—1221no—
564C24—24no—
565C24—24no—
566C24—21no—
567C24—21no—
568C24—24no—
569C24—81no—
570C24—81no—
571C24—81no—
572C24—81no—
573C24D4×D6111yescharacteristic
574C2×Q8—612no—
575C2×Q8—1221no—
576C2×Q8—1221no—
577C2×Q8—1221no—
578C2×Q8—1221no—
579C2×Q8—1221no—
580C2×D4—24no—
581C2×D4—24no—
582C2×D4—28no—
583C2×D4—28no—
584C2×D4—28no—
585C2×D4—28no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—24no—
593C2×D4C2×C4×D6112yes—
594C2×D4C2×C4×D6112yes—
595C2×D4D4×D6112yes—
596C2×D4D4×D6112yes—
597C2×D4#1175822412yes—
598C2×D4#1175822412yes—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—1224no—
610C22×C4—1224no—
611C22×C4—1224no—
612C22×C4—1224no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—4881no—
618C22×C4—4881no—
619C22×C4—4881no—
620C22×C4—4881no—
621C22×C4—4881no—
622C22×C4—4881no—
623C22×C4—4881no—
624C22×C4—4881no—
625C22×C4C2×C4×D6112yes—
626C22×C4D4×D6111yescharacteristic
627C22×C4#1175822412yes—
628C22×C4C23×D6111yescharacteristic
629SD16—1228no—
630SD16—1228no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—612no—
638C2×C8—612no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—1221no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—612no—
648C4⋊C4—612no—
649C4⋊C4—612no—
650C4⋊C4—1222no—
651C4⋊C4—1222no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1224no—
656C4⋊C4—4881no—
657C4⋊C4—2442no—
658C22⋊C4—81no—
659C22⋊C4—1222no—
660C22⋊C4—1222no—
661C22⋊C4—1224no—
662C22⋊C4—1224no—
663C22⋊C4—1224no—
664C22⋊C4—1224no—
665C22⋊C4—1224no—
666C22⋊C4—1224no—
667C42—612no—
668C42—612no—
669C42—1224no—
670C42—1221no—
671C42—1221no—
672C42—4881no—
673C42—2442no—
674C23—216no—
675C23—22no—
676C23—22no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—22no—
682C23—22no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—84no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23#1451973712yes—
702C23C2×D4×D6111yescharacteristic
703Q8—1222no—
704Q8—1222no—
705Q8—2441no—
706Q8—2441no—
707D4—216no—
708D4—22no—
709D4—22no—
710D4—22no—
711D4—22no—
712D4—22no—
713D4—22no—
714D4#1451973714yes—
715D4#1451973714yes—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—612no—
729C2×C4—612no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—1221no—
733C2×C4—1221no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1221no—
739C2×C4—1221no—
740C2×C4—1221no—
741C2×C4—1221no—
742C2×C4—1221no—
743C2×C4—1221no—
744C2×C4—4884no—
745C2×C4—4884no—
746C2×C4—4884no—
747C2×C4—4884no—
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×C4#1451973712yes—
757C2×C4C22×C4×D6111yescharacteristic
758C2×C4C2×D4×D6111yescharacteristic
759C2×C4C2×D4×D6111yescharacteristic
760C2×C4C2×#1175822411yescharacteristic
761C2×C4C2×#1175822411yescharacteristic
762C2×C4C2×#1175822411yescharacteristic
763C8—41no—
764C8—41no—
765C8—1222no—
766C8—1222no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—24no—
771C22—24no—
772C22—42no—
773C22—42no—
774C22—41no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—42no—
782C22—41no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—41no—
788C22—816no—
789C22C2×#1451973711yescharacteristic
790C22#120×D6111yescharacteristic
791C22#1684026811yescharacteristic
792C22#1684056311yescharacteristic
793C22#1684056811yescharacteristic
794C22#1684057211yescharacteristic
795C22#1684057211yescharacteristic
796C4—22no—
797C4—81no—
798C4—81no—
799C4—1222no—
800C4—1222no—
801C4—2441no—
802C4—2442no—
803C4—2442no—
804C4—2442no—
805C4—2441no—
806C4—2442no—
807C4C2×#1451973711yescharacteristic
808C4C2×#1451973711yescharacteristic
809C4#1684026811yescharacteristic
810C4#1684026811yescharacteristic
811C2—42no—
812C2—44no—
813C2—44no—
814C2#2144831811yescharacteristic
815C2#2145464511yescharacteristic
816C2#2145468111yescharacteristic
817C2#2145509111yescharacteristic
818C2#2145511811yescharacteristic
819C2#2145599611yescharacteristic
820C2#2145606511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1786C2
socleC23×C61C22×D4
prime radicalC23×D4×C61C22
cosocleC22×C4×C61C24
hypercenter#1786D61
hypocenterC61#21459
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
3. C2×#16839859C2semidirect
4. C2×#16839853C2semidirect
5. #21448497C2semidirect
6. #21446151C2semidirect
7. #21446151C2semidirect
8. #21446129C2semidirect
9. #21446078C2semidirect
10. #21446064C2semidirect
11. #21446016C2semidirect
12. #21445646C2semidirect
13. #102×Dic61C2semidirect
14. #21445587C2semidirect
21. C2×#14519742C22semidirect
32. #16839913C4semidirect
35. C2×#14519710C22semidirect
36. C2×#14519708C22semidirect
37. C2×#14519702C22semidirect
38. C2×#14519702C22semidirect
42. C2×#14519687C22semidirect
43. C2×C8×Dic61C22semidirect
44. #16839667C22semidirect
46. #16839658C22semidirect
50. C4⋊C4×Dic61C22semidirect
51. #16839525C22semidirect
52. #16839525C22semidirect
53. #16839524C22semidirect
54. #16839524C22semidirect
55. #16839516C22semidirect
56. #16839516C22semidirect
73. C2×#11758200C2×C4semidirect
74. C2×#11758200C2×C4semidirect
78. #14519756C2×C4semidirect
122. #14519698C2×C4semidirect
123. #14519698C2×C4semidirect
124. C22⋊#92418C2×C4semidirect
474. C61#21459semidirect

Maximal subgroups

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

subgroupindex
C2×#168402372
C2×#168399132
C2×#168398592
C2×#168398532
#214484972
#214461512
#214461292
#214460782
#214460642
#214460162
#214456462
#102×Dic612
#214455872
C61×#17862
#2145961