Finite Group Databasebeta

← #29695559

Subgroups — #29695559

Order 15616.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840396C211yesmaximal, characteristic
2C2×#16839833C211yesmaximal, characteristic, complemented
3C2×#16839765C211yesmaximal, characteristic, complemented
4C22×#14519699C211yesmaximal, characteristic, complemented
5#21448750C211yesmaximal, characteristic, complemented
6#21446744C211yesmaximal, characteristic, complemented
7#21446641C211yesmaximal, characteristic, complemented
8#21446256C211yesmaximal, characteristic, complemented
9#21446140C211yesmaximal, characteristic, complemented
10#21446137C211yesmaximal, characteristic, complemented
11#21445828C211yesmaximal, characteristic, complemented
12#21445749C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445643C211yesmaximal, characteristic, complemented
15C61×#1893C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×D4×D61—21no—
18C22×D4×D61C2211yescharacteristic
19C22×#11758189C2211yescharacteristic, complemented
20#16840396—24no—
21#16840396C418yescomplemented
22C2×#14519773C2211yescharacteristic
23C2×#14519752C2211yescharacteristic
24C2×#14519750—21no—
25C2×#14519747—21no—
26C2×#14519745—21no—
27C2×#14519739C2211yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×#14519735C2211yescharacteristic, complemented
30C22×C4⋊Dic61C2211yescharacteristic, complemented
31#16839833—24no—
32C2×#14519706C2211yescharacteristic, complemented
33#16839765—24no—
34C2×#14519699—24no—
35C2×#14519699C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37C2×#14519699C2211yescharacteristic, complemented
38C2×#14519699C2211yescharacteristic, complemented
39C2×#14519698C2211yescharacteristic, complemented
40C2×#14519698C2211yescharacteristic, complemented
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic, complemented
44C2×#14519697C2211yescharacteristic, complemented
45C2×C22⋊#92418C2211yescharacteristic, complemented
46C2×#14519689C2211yescharacteristic, complemented
47C2×#14519687C2211yescharacteristic, complemented
48#16839654—21no—
49#16839649—21no—
50#16839639—21no—
51#16839627C2211yescharacteristic, complemented
52#16839619C2211yescharacteristic, complemented
53C4⋊C4×Dic61C2211yescharacteristic, complemented
54C22⋊C4×Dic61—21no—
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C23×C8×C61C2211yescharacteristic, complemented
58C2×#121×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic, complemented
60C2×#102×C61C2211yescharacteristic, complemented
61C61×#380C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#340C2211yescharacteristic, complemented
64C24×D61—21no—
65C24×D61—21no—
66C22×D244—22no—
67C22×D244—22no—
68C22×D244—21no—
69C22×D244—21no—
70C22×D244—22no—
71C22×D244—41no—
72C22×D244—41no—
73C22×D244C2×C414yes—
74C22×D244C2311yescharacteristic
75C22×D244C2311yescharacteristic
76C22×C22⋊D61—21no—
77C22×C22⋊D61—21no—
78C22×C22⋊D61—21no—
79C22×C22⋊D61D411yescharacteristic
80C2×D4×D61—28no—
81C2×D4×D61—22no—
82C2×D4×D61—22no—
83C2×D4×D61—22no—
84C2×D4×D61—41no—
85C2×D4×D61—41no—
86C2×D4×D61—44no—
87C2×D4×D61—44no—
88C2×D4×D61C2×C414yescomplemented
89C23×Dic61—21no—
90C22×C4×D61—21no—
91C22×C4×D61C2311yescharacteristic
92C2×#11758189—22no—
93C2×#11758189—22no—
94C2×#11758189—41no—
95C22×#92418C2311yescharacteristic
96C22×#92418C2311yescharacteristic
97#14519773—22no—
98#14519773C2×C414yescomplemented
99#14519752—22no—
100#14519752C2×C414yescomplemented
101#14519750—28no—
102#14519747—28no—
103#14519745—28no—
104#14519739—22no—
105#14519739C2×C414yescomplemented
106C4×C22⋊D61C2×C414yes—
107C4×C22⋊D61D414yes—
108#14519735—22no—
109#14519735—41no—
110C2×C4⋊Dic61—22no—
111C2×C4⋊Dic61—21no—
112C2×C4⋊Dic61—41no—
113C2×C4⋊Dic61C2311yescharacteristic
114C2×C4⋊Dic61C2311yescharacteristic
115C2×#11758196D411yescharacteristic
116C2×C22⋊Dic61D411yescharacteristic
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×#11758198D411yescharacteristic
122C2×C4×Dic61—21no—
123C2×C4×Dic61—21no—
124C2×C4×Dic61C2311yescharacteristic
125#14519706—22no—
126#14519699—22no—
127#14519699—22no—
128#14519699—22no—
129#14519699D414yescomplemented
130#14519698—22no—
131#14519698—41no—
132#14519697—22no—
133#14519697—22no—
134#14519697—41no—
135#14519697—41no—
136C22⋊#92418—22no—
137#14519689—22no—
138#14519687—22no—
139#14519684—21no—
140#14519684—21no—
141#14519684—21no—
142#14519684—21no—
143C22×D4×C61—21no—
144C22×D4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C22×C8×C61—22no—
147C22×C8×C61—22no—
148C22×C8×C61—41no—
149C22×C8×C61C2311yescharacteristic
150C22×C8×C61C2311yescharacteristic
151#121×C61—22no—
152#121×C61C2×C414yes—
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C4⋊C4×C61C2311yescharacteristic
156C2×C22⋊C4×C61—21no—
157C2×C22⋊C4×C61—21no—
158#102×C61—22no—
159#102×C61—41no—
160#95×C61—21no—
161C24×C61—21no—
162C24×C61C2×D411yescharacteristic
163C23×D61—21no—
164C23×D61—21no—
165C23×D61—24no—
166C23×D61—24no—
167C23×D61—42no—
168C23×D61—42no—
169C23×D61—42no—
170C23×D61—42no—
171C23×D61—42no—
172C23×D61—42no—
173C23×D61—42no—
174C23×D61—42no—
175C23×D61—81no—
176C23×D61—81no—
177C23×D61—81no—
178C23×D61—81no—
179C23×D61C2×D411yescharacteristic
180C2×D4×C61—24no—
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—42no—
187C2×D4×C61—42no—
188C2×D4×C61C22×C412yes—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61C22×C412yes—
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D412yes—
199C22×C4×C61C2411yescharacteristic
200C2×C22⋊D61—22no—
201C2×C22⋊D61—22no—
202C2×C22⋊D61—24no—
203C2×C22⋊D61—24no—
204C2×C22⋊D61—24no—
205C2×C22⋊D61—42no—
206C2×C22⋊D61—42no—
207C2×C22⋊D61—42no—
208C2×C22⋊D61—42no—
209C2×C22⋊D61—81no—
210C2×C22⋊D61—81no—
211C2×C22⋊D61C22⋊C414yes—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—42no—
215C22×Dic61—42no—
216C22×Dic61—81no—
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220D4×D61—28no—
221D4×D61—44no—
222D4×D61—44no—
223D4×D61—44no—
224D4×D61—432no—
225C2×D244—21no—
226C2×D244—21no—
227C2×D244—21no—
228C2×D244—21no—
229C2×D244—21no—
230C2×D244—21no—
231C2×D244—21no—
232C2×D244—28no—
233C2×D244—24no—
234C2×D244—24no—
235C2×D244—21no—
236C2×D244—44no—
237C2×D244—44no—
238C2×D244—44no—
239C2×D244—42no—
240C2×D244—42no—
241C2×D244—42no—
242C2×D244—42no—
243C2×D244C22×C412yes—
244C2×D244C22×C412yes—
245C2×D244C2×D412yes—
246C2×D244#4112yes—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—24no—
252C2×C4×D61—42no—
253C2×C4×D61—42no—
254C2×C4×D61C22×C412yes—
255C2×C4×D61C2×D412yes—
256C2×C8×C61—21no—
257C2×C8×C61—21no—
258C2×C8×C61—21no—
259C2×C8×C61—21no—
260C2×C8×C61—21no—
261C2×C8×C61—44no—
262C2×C8×C61C2×D412yescomplemented
263C4⋊C4×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61C22×C412yes—
269C22⋊C4×C61—24no—
270C22⋊C4×C61—42no—
271C22⋊Dic61C22⋊C414yes—
272#11758198—24no—
273#11758198—24no—
274#11758198—42no—
275#11758198—81no—
276#11758198C22⋊C414yes—
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4⋊Dic61—42no—
281C4⋊Dic61C2×D412yescomplemented
282#11758196C22⋊C414yes—
283C4×Dic61—42no—
284C4×Dic61—81no—
285C4×Dic61C22×C412yes—
286C4×Dic61C2×D412yes—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—21no—
293#11758189—44no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—22no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61C2×C22⋊C412yes—
306C23×C61AGL(1,ℤ/8)12yes—
307C23×C61AGL(1,ℤ/8)12yes—
308C23×C61C22×D411yescharacteristic
309C22×D61—22no—
310C22×D61—21no—
311C22×D61—22no—
312C22×D61—21no—
313C22×D61—22no—
314C22×D61—21no—
315C22×D61—21no—
316C22×D61—21no—
317C22×D61—21no—
318C22×D61—22no—
319C22×D61—48no—
320C22×D61—48no—
321C22×D61—48no—
322C22×D61—41no—
323C22×D61—41no—
324C22×D61—41no—
325C22×D61—41no—
326C22×D61—41no—
327C22×D61—41no—
328C22×D61—41no—
329C22×D61—41no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61—48no—
333C22×D61—84no—
334C22×D61—84no—
335C22×D61—84no—
336C22×D61—84no—
337C22×D61—84no—
338C22×D61—84no—
339C22×D61—84no—
340C22×D61—84no—
341C22×D61—84no—
342C22×D61—84no—
343C22×D61C2×C22⋊C412yes—
344D4×C61—22no—
345D4×C61—22no—
346D4×C61—48no—
347D4×C61—41no—
348D4×C61—41no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61C2×C22⋊C412yes—
365C2×C4×C61C23×C411yescharacteristic
366C2×C4×C61C22×D411yescharacteristic
367C2×C4×C61C22×D411yescharacteristic
368C2×C4×C61C2×#4111yescharacteristic
369C2×C4×C61H(5,𝔽2)11yescharacteristic
370C2×C4×C61H(5,𝔽2)11yescharacteristic
371C22⋊D61—28no—
372C22⋊D61—48no—
373C22⋊D61—48no—
374C22⋊D61—84no—
375C2×Dic61—21no—
376C2×Dic61—21no—
377C2×Dic61—21no—
378C2×Dic61—21no—
379C2×Dic61—21no—
380C2×Dic61—21no—
381C2×Dic61—22no—
382C2×Dic61—41no—
383C2×Dic61—41no—
384C2×Dic61—41no—
385C2×Dic61—41no—
386C2×Dic61—41no—
387C2×Dic61—84no—
388C2×Dic61C2×C22⋊C412yes—
389C2×Dic61C2×C22⋊C412yes—
390C2×Dic61C2×C22⋊C412yes—
391D244—22no—
392D244—22no—
393D244—22no—
394D244—22no—
395D244—22no—
396D244—48no—
397D244—48no—
398D244—41no—
399D244—41no—
400D244C4×D414yes—
401C4×D61—22no—
402C4×D61—22no—
403C4×D61—22no—
404C4×D61—22no—
405C4×D61—48no—
406C8×C61—22no—
407C8×C61—41no—
408#92418—41no—
409#92418—41no—
410#22423—611nomaximal, Sylow
411C22×C61—22no—
412C22×C61—22no—
413C22×C61—22no—
414C22×C61—22no—
415C22×C61—22no—
416C22×C61—22no—
417C22×C61—42no—
418C22×C61—42no—
419C22×C61—42no—
420C22×C61—81no—
421C22×C61—81no—
422C22×C61—81no—
423C22×C61—81no—
424C22×C61#41814yescomplemented
425C22×C61C22×C22⋊C411yescharacteristic
426C22×C61D4211yescharacteristic
427C22×C61#54611yescharacteristic
428C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
429C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
430C22×C61#57611yescharacteristic
431C22×C61#57711yescharacteristic
432C2×D61—22no—
433C2×D61—24no—
434C2×D61—22no—
435C2×D61—22no—
436C2×D61—42no—
437C2×D61—42no—
438C2×D61—41no—
439C2×D61—42no—
440C2×D61—41no—
441C2×D61—42no—
442C2×D61—41no—
443C2×D61—42no—
444C2×D61—41no—
445C2×D61—42no—
446C2×D61—42no—
447C2×D61—42no—
448C2×D61—42no—
449C2×D61—816no—
450C2×D61—816no—
451C2×D61—81no—
452C2×D61—81no—
453C2×D61—81no—
454C2×D61—81no—
455C4×C61—22no—
456C4×C61—42no—
457C4×C61—81no—
458C4×C61—81no—
459C4×C61C2×C4×D411yescharacteristic
460C4×C61#51811yescharacteristic
461C4×C61D4211yescharacteristic
462C4×C61#54611yescharacteristic
463Dic61—22no—
464Dic61—22no—
465Dic61—22no—
466Dic61—42no—
467Dic61—81no—
468C2×D42—611no—
469C2×#435—611no—
470C2×#418—611no—
471C22×#102—611no—
472#2352—611no—
473#1982—611no—
474#1961—611no—
475#1895—611no—
476#1893D6111yescharacteristic, complemented
477#1875—611no—
478#1874—611no—
479#1804—611no—
480#1786—611no—
481#1786—611no—
482#1762—611no—
483C2×C61—24no—
484C2×C61—82no—
485C2×C61D4×C22⋊C411yescharacteristic
486C2×C61C2×#41811yescharacteristic
487C2×C61#289711yescharacteristic
488C2×C61#326411yescharacteristic
489C2×C61#326511yescharacteristic
490C2×C61#331011yescharacteristic
491C2×C61#331811yescharacteristic
492D61—42no—
493D61—44no—
494D61—82no—
495C23×D4—611no—
496C23×D4—611no—
497C23×D4—1221no—
498C22×M16—611no—
499C23×C8C2×D6111yescharacteristic, complemented
500D42—618no—
501D42—1224no—
502C2×#127—611no—
503C2×#121—611no—
504C2×#121—1221no—
505C2×#121C2×D6111yescharacteristic
506C2×#120—1221no—
507C2×#120—1221no—
508C2×C4×D4—611no—
509C2×C4×D4—611no—
510C2×#117—611no—
511C22×C4⋊C4—611no—
512#435—1224no—
513C2×C4⋊C8—611no—
514#418—1224no—
515C2×#102—611no—
516C2×#102—611no—
517C2×#102—611no—
518C2×#102—611no—
519C2×#102—611no—
520C2×#102—611no—
521C2×#102—611no—
522C2×#102—611no—
523C2×#102—611no—
524C2×#102—611no—
525C2×#102—1224no—
526C2×#102C2×D6111yescharacteristic, complemented
527C2×#102C2×D6111yescharacteristic, complemented
528C2×C22⋊C8—611no—
529C2×C22⋊C8—611no—
530C2×#97—611no—
531#388—1221no—
532#387—1221no—
533#386—1221no—
534#382—611no—
535#380—611no—
536#380C2×D6111yescharacteristic, complemented
537C4×C4⋊C4—611no—
538C4×C22⋊C4—1221no—
539#340—611no—
540#340—611no—
541#340C2×D6111yescharacteristic, complemented
542#340C2×D6111yescharacteristic, complemented
543C61#2242311yescharacteristic, complemented, Sylow
544C25—1221no—
545C25—1221no—
546C22×D4—21no—
547C22×D4—611no—
548C22×D4—614no—
549C22×D4—614no—
550C22×D4—611no—
551C22×D4—611no—
552C22×D4—1222no—
553C22×D4—1222no—
554C22×D4—1221no—
555C22×D4—1222no—
556C22×D4—1221no—
557C22×D4—1221no—
558C22×D4—1221no—
559C22×D4—1222no—
560C22×D4—1222no—
561C22×D4—1228no—
562C22×D4—1221no—
563C22×D4—1222no—
564C22×D4—2441no—
565C22×D4—2441no—
566C22×D4—2441no—
567C22×D4—2441no—
568C22×D4—2444no—
569C22×D4—2444no—
570C22×D4C22×D6111yescharacteristic
571C23×C4—611no—
572C23×C4—1221no—
573C23×C4—1221no—
574C23×C4C22×D6111yescharacteristic
575C2×M16—1222no—
576C2×M16—1222no—
577C2×M16—2441no—
578C22×C8—22no—
579C22×C8—22no—
580C22×C8—41no—
581C22×C8—611no—
582C22×C8—611no—
583C22×C8C22×D6111yescharacteristic
584C22×C8C22×D6111yescharacteristic
585#127—614no—
586#127—1222no—
587#121—22no—
588#121—614no—
589#121—1228no—
590#121—1222no—
591#121C4×D6114yes—
592#120—1228no—
593#120—1228no—
594C4×D4—614no—
595C4×D4—614no—
596C4×D4—614no—
597C4×D4—1222no—
598#117—1222no—
599#117—2441no—
600C2×C4⋊C4—611no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—611no—
603C2×C4⋊C4—1222no—
604C2×C4⋊C4—1221no—
605C2×C4⋊C4—2441no—
606C2×C4⋊C4C22×D6111yescharacteristic
607C2×C4⋊C4C22×D6111yescharacteristic
608C2×C4⋊C4C22×D6111yescharacteristic
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—611no—
612C2×C22⋊C4—611no—
613C2×C22⋊C4—1221no—
614C2×C22⋊C4—1221no—
615C2×C22⋊C4—1221no—
616C2×C22⋊C4—1221no—
617C2×C42—611no—
618C2×C42—1221no—
619C2×C42—1221no—
620C4⋊C8—1222no—
621#102—22no—
622#102—41no—
623#102—614no—
624#102—1222no—
625#102—1222no—
626#102—1222no—
627#102—1222no—
628#102—1222no—
629#102—1222no—
630#102—2441no—
631#102—2441no—
632#102—2441no—
633C22⋊C8—1222no—
634C22⋊C8—1222no—
635#97—1222no—
636#95—21no—
637#95—1221no—
638#95—1221no—
639#95—1221no—
640#95—1221no—
641C24—21no—
642C24—611no—
643C24—1224no—
644C24—1221no—
645C24—1224no—
646C24—1221no—
647C24—4881no—
648C24—4881no—
649C24—4881no—
650C24—4881no—
651C24—2442no—
652C24—2442no—
653C24—2442no—
654C24—2442no—
655C24—2442no—
656C24—2442no—
657C24—2442no—
658C24—2442no—
659C24D4×D6111yescharacteristic
660C2×D4—24no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—614no—
669C2×D4—612no—
670C2×D4—612no—
671C2×D4—612no—
672C2×D4—612no—
673C2×D4—1228no—
674C2×D4—1224no—
675C2×D4—1224no—
676C2×D4—1224no—
677C2×D4—1224no—
678C2×D4—1228no—
679C2×D4—1222no—
680C2×D4—1222no—
681C2×D4—1221no—
682C2×D4—1221no—
683C2×D4—1221no—
684C2×D4—1221no—
685C2×D4—1221no—
686C2×D4—1221no—
687C2×D4—1221no—
688C2×D4—1221no—
689C2×D4—1224no—
690C2×D4—4881no—
691C2×D4—4881no—
692C2×D4—2444no—
693C2×D4—2444no—
694C2×D4—2444no—
695C2×D4—2442no—
696C2×D4—2442no—
697C2×D4—2442no—
698C2×D4—2442no—
699C2×D4—2444no—
700C2×D4—2444no—
701C2×D4—2444no—
702C2×D4—2442no—
703C2×D4—2442no—
704C2×D4—2442no—
705C2×D4—2442no—
706C2×D4—24432no—
707C2×D4C2×C4×D6112yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—611no—
716C22×C4—611no—
717C22×C4—611no—
718C22×C4—612no—
719C22×C4—612no—
720C22×C4—1224no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—4881no—
728C22×C4—2442no—
729C22×C4—2442no—
730C22×C4—2442no—
731C22×C4—2442no—
732C22×C4C2×C4×D6112yes—
733C22×C4D4×D6112yes—
734C22×C4D4×D6111yescharacteristic
735C22×C4C23×D6111yescharacteristic
736M16—2444no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—44no—
743C2×C8—1221no—
744C2×C8—1221no—
745C2×C8—1221no—
746C2×C8—1221no—
747C2×C8—1221no—
748C2×C8—1221no—
749C2×C8D4×D6112yescomplemented
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—614no—
756C4⋊C4—612no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—2442no—
761C4⋊C4C2×C4×D6112yes—
762C22⋊C4—24no—
763C22⋊C4—42no—
764C22⋊C4—614no—
765C22⋊C4—614no—
766C22⋊C4—1224no—
767C22⋊C4—1224no—
768C22⋊C4—4881no—
769C22⋊C4—2442no—
770C42—612no—
771C42—612no—
772C42—4881no—
773C42—2442no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—22no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—612no—
786C23—1222no—
787C23—1221no—
788C23—1221no—
789C23—1221no—
790C23—1221no—
791C23—1221no—
792C23—1222no—
793C23—1221no—
794C23—1222no—
795C23—1222no—
796C23—4884no—
797C23—4884no—
798C23—4884no—
799C23—4884no—
800C23—4884no—
801C23—4884no—
802C23—4884no—
803C23—4884no—
804C23—4884no—
805C23—4884no—
806C23—2448no—
807C23—2448no—
808C23—2448no—
809C23—2448no—
810C23—2441no—
811C23—2441no—
812C23—2441no—
813C23—2441no—
814C23—2441no—
815C23—2441no—
816C23—2441no—
817C23—2441no—
818C23—2441no—
819C23—2441no—
820C23C22⋊C4×D6112yes—
821C23#1451980112yes—
822C23#1451980412yes—
823C23C2×D4×D6111yescharacteristic
824D4—22no—
825D4—22no—
826D4—48no—
827D4—41no—
828D4—41no—
829D4—614no—
830D4—1228no—
831D4—1222no—
832D4—1222no—
833D4—1222no—
834D4—1222no—
835D4—1222no—
836D4—4884no—
837D4—2448no—
838D4—2448no—
839D4—2448no—
840D4—2448no—
841D4—2441no—
842D4—2441no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—612no—
859C2×C4—612no—
860C2×C4—612no—
861C2×C4—1221no—
862C2×C4—1221no—
863C2×C4—1221no—
864C2×C4—1221no—
865C2×C4—1221no—
866C2×C4—1221no—
867C2×C4—1222no—
868C2×C4—1222no—
869C2×C4—1222no—
870C2×C4—1222no—
871C2×C4—1222no—
872C2×C4—4884no—
873C2×C4—2448no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4—2441no—
879C2×C4C22⋊C4×D6112yes—
880C2×C4C22×C4×D6111yescharacteristic
881C2×C4C2×D4×D6111yescharacteristic
882C2×C4C2×D4×D6111yescharacteristic
883C2×C4#41×D6111yescharacteristic
884C2×C4#1451982211yescharacteristic
885C2×C4#1451982311yescharacteristic
886C8—22no—
887C8—41no—
888C8—2441no—
889C8—2441no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—81no—
900C22—81no—
901C22—81no—
902C22—81no—
903C22—1222no—
904C22—1222no—
905C22—1224no—
906C22—1222no—
907C22—48816no—
908C22—48816no—
909C22—4881no—
910C22—4881no—
911C22—4881no—
912C22—4881no—
913C22—2442no—
914C22—2442no—
915C22—2442no—
916C22—2442no—
917C22—2441no—
918C22—2442no—
919C22—2441no—
920C22—2442no—
921C22—2441no—
922C22—2442no—
923C22—2441no—
924C22—2442no—
925C22—2442no—
926C22#1683976514yescomplemented
927C22C2×C22⋊C4×D6111yescharacteristic
928C22#1684039611yescharacteristic
929C22#1684040111yescharacteristic
930C22C2×#1451980111yescharacteristic
931C22C2×#1451980411yescharacteristic
932C22#1684056411yescharacteristic
933C22#1684056911yescharacteristic
934C4—22no—
935C4—42no—
936C4—81no—
937C4—81no—
938C4—1222no—
939C4—1222no—
940C4—1222no—
941C4—4881no—
942C4—2442no—
943C4C4×D4×D6111yescharacteristic
944C4#1684023411yescharacteristic
945C4#1684039411yescharacteristic
946C4#1684040411yescharacteristic
947C2—24no—
948C2—82no—
949C2—4882no—
950C2—2442no—
951C2—2444no—
952C2#2144863711yescharacteristic
953C2C2×#1683976511yescharacteristic
954C2#2145434111yescharacteristic
955C2#2145729611yescharacteristic
956C2#2145731111yescharacteristic
957C2#2145784611yescharacteristic
958C2#2145796611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1893C2
socleC23×C61C22×D4
prime radicalC2×#16840396C2
cosocleC22×C4×C61C24
hypercenter#1893D61
hypocenterC61#22423
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
2. C2×#16839833C2semidirect
3. C2×#16839765C2semidirect
4. C22×#14519699C2semidirect
5. #21448750C2semidirect
6. #21446744C2semidirect
7. #21446641C2semidirect
8. #21446256C2semidirect
9. #21446140C2semidirect
10. #21446137C2semidirect
11. #21445828C2semidirect
12. #21445749C2semidirect
13. #21445748C2semidirect
14. #21445643C2semidirect
15. C61×#1893C2semidirect
19. C22×#11758189C22semidirect
21. #16840396C4semidirect
29. C2×#14519735C22semidirect
30. C22×C4⋊Dic61C22semidirect
32. C2×#14519706C22semidirect
37. C2×#14519699C22semidirect
38. C2×#14519699C22semidirect
39. C2×#14519698C22semidirect
40. C2×#14519698C22semidirect
43. C2×#14519697C22semidirect
44. C2×#14519697C22semidirect
45. C2×C22⋊#92418C22semidirect
46. C2×#14519689C22semidirect
47. C2×#14519687C22semidirect
51. #16839627C22semidirect
52. #16839619C22semidirect
53. C4⋊C4×Dic61C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
57. C23×C8×C61C22semidirect
59. C2×#102×C61C22semidirect
60. C2×#102×C61C22semidirect
61. C61×#380C22semidirect
62. C61×#340C22semidirect
63. C61×#340C22semidirect
88. C2×D4×D61C2×C4semidirect
98. #14519773C2×C4semidirect
100. #14519752C2×C4semidirect
105. #14519739C2×C4semidirect
129. #14519699D4semidirect
262. C2×C8×C61C2×D4semidirect
281. C4⋊Dic61C2×D4semidirect
424. C22×C61#418semidirect
476. #1893D61semidirect
499. C23×C8C2×D61semidirect
526. C2×#102C2×D61semidirect
527. C2×#102C2×D61semidirect
536. #380C2×D61semidirect
541. #340C2×D61semidirect
542. #340C2×D61semidirect
543. C61#22423semidirect
749. C2×C8D4×D61semidirect
926. C22#16839765semidirect

Maximal subgroups

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

subgroupindex
C2×#168403962
C2×#168398332
C2×#168397652
C22×#145196992
#214487502
#214467442
#214466412
#214462562
#214461402
#214461372
#214458282
#214457492
#214457482
#214456432
C61×#18932
#2242361