Finite Group Databasebeta

← #28609160

Subgroups — #28609160

Order 15104.

1330 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837514C211yesmaximal, characteristic, complemented
2C2×#16837407C211yesmaximal, characteristic, complemented
3#21427138C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic59C211yesmaximal, characteristic, complemented
5#21424963C211yesmaximal, characteristic, complemented
6#21424795C211yesmaximal, characteristic, complemented
7#21424725C211yesmaximal, characteristic, complemented
8#21424535C211yesmaximal, characteristic, complemented
9#21424446C211yesmaximal, characteristic, complemented
10#21424446C211yesmaximal, characteristic, complemented
11#21424345C211yesmaximal, characteristic, complemented
12#21424297C211yesmaximal, characteristic, complemented
13#102×Dic59C211yesmaximal, characteristic, complemented
14#21423882C211yesmaximal, characteristic, complemented
15C2×C59×#447C211yesmaximal, characteristic
16C22×#11745664C2211yescharacteristic
17C2×D4×Dic59C2211yescharacteristic
18C2×D4×Dic59C2211yescharacteristic
19C2×D4×Dic59C2211yescharacteristic, complemented
20C2×#14273686C2211yescharacteristic
21C22×C22⋊Dic59—21no—
22#16837514—24no—
23C2×#14273661C2211yescharacteristic, complemented
24C2×#14273659C2211yescharacteristic, complemented
25#16837407—24no—
26C2×#14273648C2211yescharacteristic
27C2×#14273648C2211yescharacteristic
28C2×#14273648C2211yescharacteristic
29C2×#14273648C2211yescharacteristic
30C2×#14273648C2211yescharacteristic, complemented
31C2×#14273648C2211yescharacteristic, complemented
32C2×#14273637C2211yescharacteristic, complemented
33C2×C8×Dic59C2211yescharacteristic, complemented
34#16837305—21no—
35#16837305C2211yescharacteristic
36#16837305C2211yescharacteristic
37#16837305C2211yescharacteristic, complemented
38#16837301C2211yescharacteristic, complemented
39#16837295—21no—
40#16837282—21no—
41#16837282—21no—
42#16837282—21no—
43#16837262C2211yescharacteristic
44#16837258—21no—
45C4⋊C4×Dic59C2211yescharacteristic, complemented
46C22⋊C4×Dic59—21no—
47C4×C22⋊Dic59C2211yescharacteristic
48#16837165C2211yescharacteristic, complemented
49#16837165C2211yescharacteristic, complemented
50#16837164C2211yescharacteristic, complemented
51#16837164C2211yescharacteristic, complemented
52#16837156C2211yescharacteristic, complemented
53#16837156C2211yescharacteristic, complemented
54C23×D4×C59C2211yescharacteristic
55C22×D8×C59C2211yescharacteristic
56C22×D8×C59C2211yescharacteristic
57C2×#121×C59C2211yescharacteristic
58C59×#447C418yescomplemented
59C2×#102×C59C2211yescharacteristic
60C2×#102×C59C2211yescharacteristic
61C2×C22⋊C8×C59C2211yescharacteristic
62C23×Dic59—21no—
63C23×Dic59—21no—
64C23×Dic59—21no—
65C2×#11745664—22no—
66C2×#11745664—22no—
67C2×#11745664—41no—
68C22×C59⋊C8C2311yescharacteristic
69C22×C59⋊C8C2311yescharacteristic
70D4×Dic59—22no—
71D4×Dic59—22no—
72D4×Dic59—22no—
73D4×Dic59—41no—
74D4×Dic59—41no—
75D4×Dic59—41no—
76#14273686—22no—
77#14273686—41no—
78C2×C4⋊Dic59—21no—
79C2×C4⋊Dic59C2311yescharacteristic
80C2×C4⋊Dic59C2311yescharacteristic
81C2×C4⋊Dic59C2311yescharacteristic
82C2×C4⋊Dic59C2311yescharacteristic
83C2×C22⋊Dic59—21no—
84C2×C22⋊Dic59—21no—
85C2×C22⋊Dic59—21no—
86C2×C22⋊Dic59—21no—
87C2×C22⋊Dic59—21no—
88C2×C22⋊Dic59—21no—
89C2×C22⋊Dic59—21no—
90C2×C22⋊Dic59—21no—
91C2×C22⋊Dic59—21no—
92C2×C22⋊Dic59—21no—
93C2×C22⋊Dic59—21no—
94C2×C22⋊Dic59—44no—
95C2×C22⋊Dic59D411yescharacteristic
96C2×C22⋊Dic59D411yescharacteristic
97C2×C4×Dic59—21no—
98C2×C4×Dic59—21no—
99C2×C4×Dic59C2311yescharacteristic
100C2×C4×Dic59C2311yescharacteristic
101#14273661—41no—
102#14273659—22no—
103#14273648—22no—
104#14273648—22no—
105#14273648—22no—
106#14273648—22no—
107#14273648—41no—
108#14273648D414yescomplemented
109#14273637—22no—
110C8×Dic59—41no—
111C59⋊#95—21no—
112C59⋊#95—21no—
113C59⋊#95—21no—
114C59⋊#95D411yescharacteristic
115C59⋊#95D411yescharacteristic
116C25×C59—21no—
117C22×D4×C59—22no—
118C22×D4×C59—22no—
119C22×D4×C59—21no—
120C22×D4×C59—21no—
121C22×D4×C59—22no—
122C22×D4×C59—41no—
123C22×D4×C59—41no—
124C22×D4×C59C2×C414yescomplemented
125C22×D4×C59C2311yescharacteristic
126C22×D4×C59C2311yescharacteristic
127C22×D4×C59C2311yescharacteristic
128C23×C4×C59C2311yescharacteristic
129C2×D8×C59—22no—
130C2×D8×C59—22no—
131C2×D8×C59—41no—
132C2×D8×C59—41no—
133C2×D8×C59C2×C414yes—
134C2×D8×C59C2×C414yescomplemented
135C22×C8×C59C2311yescharacteristic
136C22×C8×C59C2311yescharacteristic
137#121×C59—22no—
138#121×C59C2×C414yescomplemented
139C2×C4⋊C4×C59C2311yescharacteristic
140C2×C22⋊C4×C59—21no—
141#102×C59C2×C414yescomplemented
142#102×C59C2×C414yescomplemented
143C22⋊C8×C59C2×C414yescomplemented
144C24×C59—21no—
145C24×C59—21no—
146C24×C59—21no—
147C24×C59—24no—
148C24×C59—42no—
149C24×C59—42no—
150C24×C59—42no—
151C24×C59—42no—
152C24×C59—81no—
153C24×C59—81no—
154C24×C59C2×D411yescharacteristic
155C2×D4×C59—28no—
156C2×D4×C59—24no—
157C2×D4×C59—24no—
158C2×D4×C59—21no—
159C2×D4×C59—21no—
160C2×D4×C59—21no—
161C2×D4×C59—21no—
162C2×D4×C59—21no—
163C2×D4×C59—21no—
164C2×D4×C59—21no—
165C2×D4×C59—21no—
166C2×D4×C59—21no—
167C2×D4×C59—21no—
168C2×D4×C59—21no—
169C2×D4×C59—21no—
170C2×D4×C59—21no—
171C2×D4×C59—44no—
172C2×D4×C59—44no—
173C2×D4×C59—44no—
174C2×D4×C59—42no—
175C2×D4×C59—42no—
176C2×D4×C59—81no—
177C2×D4×C59—81no—
178C2×D4×C59C22×C412yes—
179C2×D4×C59C22×C412yes—
180C2×D4×C59C22×C412yes—
181C2×D4×C59C2×D412yes—
182C2×D4×C59#4112yes—
183C22×C4×C59—21no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59C22×C412yes—
189C22×C4×C59C2×D411yescharacteristic
190C22×C4×C59#4112yes—
191C22×C4×C59C2411yescharacteristic
192C22×Dic59—21no—
193C22×Dic59—21no—
194C22×Dic59—21no—
195C22×Dic59—21no—
196C22×Dic59—42no—
197C22×Dic59—42no—
198C22×Dic59—42no—
199C22×Dic59—42no—
200C22×Dic59—42no—
201C22×Dic59—42no—
202C22×Dic59—81no—
203C22×Dic59—81no—
204C22×Dic59—81no—
205C22×Dic59C2×D411yescharacteristic
206C22×Dic59C2×D411yescharacteristic
207C22×Dic59C2×D411yescharacteristic
208C22×Dic59C2×D411yescharacteristic
209D8×C59—28no—
210D8×C59—44no—
211C2×C8×C59—21no—
212C2×C8×C59—21no—
213C2×C8×C59—21no—
214C2×C8×C59—21no—
215C2×C8×C59C22×C412yes—
216C2×C8×C59C22×C412yes—
217C4⋊C4×C59—21no—
218C4⋊C4×C59C22×C412yes—
219C22⋊C4×C59—24no—
220C22⋊Dic59—22no—
221C22⋊Dic59—41no—
222C22⋊Dic59—42no—
223C22⋊Dic59—42no—
224C22⋊Dic59—42no—
225C22⋊Dic59—42no—
226C22⋊Dic59—42no—
227C22⋊Dic59—42no—
228C22⋊Dic59—42no—
229C22⋊Dic59—42no—
230C22⋊Dic59—81no—
231C22⋊Dic59—81no—
232C22⋊Dic59—81no—
233C4⋊Dic59—21no—
234C4⋊Dic59—21no—
235C4⋊Dic59—21no—
236C4⋊Dic59—21no—
237C4⋊Dic59—21no—
238C4⋊Dic59—21no—
239C4⋊Dic59—21no—
240C4⋊Dic59—81no—
241C4⋊Dic59C2×D412yes—
242C4×Dic59—21no—
243C4×Dic59—21no—
244C4×Dic59—21no—
245C4×Dic59—21no—
246C4×Dic59—42no—
247C4×Dic59—81no—
248#11745664—44no—
249C2×C59⋊C8—21no—
250C2×C59⋊C8—21no—
251C2×C59⋊C8—21no—
252C2×C59⋊C8—21no—
253C2×C59⋊C8—21no—
254C2×C59⋊C8C2×D412yes—
255C23×C59—22no—
256C23×C59—21no—
257C23×C59—22no—
258C23×C59—22no—
259C23×C59—21no—
260C23×C59—21no—
261C23×C59—21no—
262C23×C59—21no—
263C23×C59—21no—
264C23×C59—22no—
265C23×C59—22no—
266C23×C59—48no—
267C23×C59—48no—
268C23×C59—41no—
269C23×C59—41no—
270C23×C59—41no—
271C23×C59—41no—
272C23×C59—41no—
273C23×C59—41no—
274C23×C59—41no—
275C23×C59—41no—
276C23×C59—41no—
277C23×C59—41no—
278C23×C59—41no—
279C23×C59—41no—
280C23×C59—41no—
281C23×C59—41no—
282C23×C59—41no—
283C23×C59—41no—
284C23×C59—84no—
285C23×C59—84no—
286C23×C59—84no—
287C23×C59—84no—
288C23×C59—84no—
289C23×C59C4×D412yes—
290C23×C59C22×D411yescharacteristic
291D4×C59—22no—
292D4×C59—22no—
293D4×C59—22no—
294D4×C59—22no—
295D4×C59—22no—
296D4×C59—22no—
297D4×C59—22no—
298D4×C59—48no—
299D4×C59—41no—
300D4×C59—41no—
301D4×C59—41no—
302D4×C59—41no—
303D4×C59—84no—
304D4×C59C4×D414yes—
305C2×C4×C59—21no—
306C2×C4×C59—21no—
307C2×C4×C59—22no—
308C2×C4×C59—22no—
309C2×C4×C59—22no—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59—41no—
313C2×C4×C59—41no—
314C2×C4×C59C4×D412yes—
315C2×C4×C59C23×C411yescharacteristic
316C2×C4×C59C22×D411yescharacteristic
317C2×C4×C59C2×#4111yescharacteristic
318C2×C4×C59C2×#4111yescharacteristic
319C2×C4×C59H(5,𝔽2)11yescharacteristic
320C2×C4×C59H(5,𝔽2)11yescharacteristic
321C2×Dic59—21no—
322C2×Dic59—21no—
323C2×Dic59—21no—
324C2×Dic59—21no—
325C2×Dic59—22no—
326C2×Dic59—21no—
327C2×Dic59—21no—
328C2×Dic59—21no—
329C2×Dic59—21no—
330C2×Dic59—21no—
331C2×Dic59—21no—
332C2×Dic59—21no—
333C2×Dic59—41no—
334C2×Dic59—41no—
335C2×Dic59—41no—
336C2×Dic59—41no—
337C2×Dic59—41no—
338C2×Dic59—41no—
339C2×Dic59—41no—
340C2×Dic59—41no—
341C2×Dic59—41no—
342C2×Dic59—41no—
343C2×Dic59—41no—
344C2×Dic59—84no—
345C2×Dic59—84no—
346C2×Dic59—84no—
347C2×Dic59AGL(1,ℤ/8)12yes—
348C8×C59—22no—
349C8×C59—22no—
350C59⋊C8—22no—
351C59⋊C8—41no—
352#22868—591nomaximal, Sylow
353C22×C59—22no—
354C22×C59—24no—
355C22×C59—22no—
356C22×C59—22no—
357C22×C59—42no—
358C22×C59—42no—
359C22×C59—41no—
360C22×C59—42no—
361C22×C59—42no—
362C22×C59—41no—
363C22×C59—42no—
364C22×C59—41no—
365C22×C59—41no—
366C22×C59—42no—
367C22×C59—42no—
368C22×C59—42no—
369C22×C59—42no—
370C22×C59—42no—
371C22×C59—42no—
372C22×C59—42no—
373C22×C59—816no—
374C22×C59—81no—
375C22×C59—81no—
376C22×C59—81no—
377C22×C59—81no—
378C22×C59—81no—
379C22×C59—81no—
380C22×C59—81no—
381C22×C59—81no—
382C22×C59C2×C4×D411yescharacteristic
383C22×C59D4211yescharacteristic
384C22×C59#54611yescharacteristic
385C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
386C22×C59#57511yescharacteristic
387C22×C59#57611yescharacteristic
388C22×C59#57611yescharacteristic
389C4×C59—22no—
390C4×C59—42no—
391C4×C59C2×C4×D411yescharacteristic
392C4×C59#51811yescharacteristic
393C4×C59#54611yescharacteristic
394C4×C59#55111yescharacteristic
395Dic59—22no—
396Dic59—41no—
397Dic59—42no—
398Dic59—41no—
399Dic59—41no—
400Dic59—81no—
401Dic59—81no—
402Dic59—81no—
403C2×#447D5911yescharacteristic
404C2×#442—591no—
405C2×#418—591no—
406#2363—591no—
407D4×C22⋊C4—591no—
408#1970—591no—
409#1936—591no—
410#1926—591no—
411#1895—591no—
412#1879—591no—
413#1879—591no—
414#1862—591no—
415#1854—591no—
416C4×#102—591no—
417#1753—591no—
418C2×C59—42no—
419C2×C59—44no—
420C2×C59—82no—
421C2×C59—82no—
422C2×C59#235811yescharacteristic
423C2×C59C4×AGL(1,ℤ/8)11yescharacteristic
424C2×C59#294811yescharacteristic
425C2×C59#327311yescharacteristic
426C2×C59#327411yescharacteristic
427C2×C59#331811yescharacteristic
428C2×C59#331911yescharacteristic
429C23×D4C2×D5911yescharacteristic
430C22×D8C2×D5911yescharacteristic
431C22×D8C2×D5911yescharacteristic
432C22×M16—591no—
433C2×#121C2×D5911yescharacteristic
434C2×C4×D4—591no—
435C2×C4×D4—591no—
436C2×C4×D4—591no—
437C2×#117—591no—
438C22×C22⋊C4—1181no—
439#447Dic5918yescomplemented
440#442—1184no—
441C2×#107—591no—
442C2×#106—591no—
443#418—1184no—
444C2×#102—591no—
445C2×#102—591no—
446C2×#102—591no—
447C2×#102—591no—
448C2×#102—591no—
449C2×#102—591no—
450C2×#102C2×D5911yescharacteristic
451C2×#102C2×D5911yescharacteristic
452C2×C22⋊C8C2×D5911yescharacteristic
453C2×#97—591no—
454C2×C4×C8—591no—
455#390—591no—
456#390—591no—
457#390—591no—
458#390—1181no—
459#389—591no—
460#388—1181no—
461#386—1181no—
462#386—1181no—
463#386—1181no—
464#380—591no—
465#379—1181no—
466C4×C4⋊C4—591no—
467C4×C22⋊C4—591no—
468C4×C22⋊C4—1181no—
469#340—591no—
470#340—591no—
471#340—591no—
472#340—591no—
473#336—591no—
474#336—591no—
475C59#2286811yescharacteristic, complemented, Sylow
476C25—21no—
477C22×D4—22no—
478C22×D4—22no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—22no—
482C22×D4—41no—
483C22×D4—41no—
484C22×D4C2×Dic5914yescomplemented
485C22×D4C22×D5911yescharacteristic
486C22×D4C22×D5911yescharacteristic
487C22×D4C22×D5911yescharacteristic
488C23×C4—1181no—
489C23×C4—1181no—
490C23×C4—1181no—
491C23×C4C22×D5911yescharacteristic
492C2×D8—22no—
493C2×D8—22no—
494C2×D8—41no—
495C2×D8—41no—
496C2×D8C2×Dic5914yes—
497C2×D8C2×Dic5914yescomplemented
498C2×M16—1182no—
499C2×M16—1182no—
500C2×M16—2361no—
501C22×C8—591no—
502C22×C8—591no—
503C22×C8C22×D5911yescharacteristic
504C22×C8C22×D5911yescharacteristic
505#121—22no—
506#121C2×Dic5914yescomplemented
507C4×D4—1182no—
508C4×D4—1182no—
509C4×D4—1182no—
510C4×D4—2361no—
511C4×D4—2361no—
512C4×D4—2361no—
513#117—1182no—
514#117—2361no—
515C2×C4⋊C4—591no—
516C2×C4⋊C4—591no—
517C2×C4⋊C4—591no—
518C2×C4⋊C4—591no—
519C2×C4⋊C4—1181no—
520C2×C4⋊C4C22×D5911yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—591no—
523C2×C22⋊C4—591no—
524C2×C22⋊C4—1181no—
525C2×C22⋊C4—1181no—
526C2×C22⋊C4—1181no—
527C2×C22⋊C4—1181no—
528C2×C22⋊C4—1181no—
529C2×C22⋊C4—1181no—
530C2×C22⋊C4—1181no—
531C2×C22⋊C4—1181no—
532C2×C22⋊C4—1181no—
533C2×C22⋊C4—1181no—
534C2×C22⋊C4—1181no—
535C2×C22⋊C4—2364no—
536C2×C42—591no—
537C2×C42—591no—
538C2×C42—1181no—
539C2×C42—1181no—
540#107—2361no—
541#106—1182no—
542#102—594no—
543#102—1182no—
544#102—1182no—
545#102—1182no—
546#102—1182no—
547#102—2361no—
548#102C2×Dic5914yescomplemented
549#102C2×Dic5914yescomplemented
550C22⋊C8C2×Dic5914yescomplemented
551#97—1182no—
552C4×C8—2361no—
553#95—591no—
554#95—591no—
555#95—1181no—
556#95—1181no—
557#95—1181no—
558C24—21no—
559C24—21no—
560C24—21no—
561C24—24no—
562C24—42no—
563C24—42no—
564C24—42no—
565C24—42no—
566C24—81no—
567C24—81no—
568C24D4×D5911yescharacteristic
569C2×D4—28no—
570C2×D4—24no—
571C2×D4—24no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—44no—
586C2×D4—44no—
587C2×D4—44no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4D4×D5912yes—
593C2×D4#1174568712yes—
594C2×D4C22×Dic5912yes—
595C2×D4C22×Dic5912yes—
596C2×D4C22×Dic5912yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—591no—
603C22×C4—591no—
604C22×C4—591no—
605C22×C4—591no—
606C22×C4—1181no—
607C22×C4—1181no—
608C22×C4—1181no—
609C22×C4—1181no—
610C22×C4—4721no—
611C22×C4—4721no—
612C22×C4—4721no—
613C22×C4—2362no—
614C22×C4—2362no—
615C22×C4—2362no—
616C22×C4—2362no—
617C22×C4—2362no—
618C22×C4—2362no—
619C22×C4D4×D5911yescharacteristic
620C22×C4#1174568712yes—
621C22×C4C22×Dic5912yes—
622C22×C4C23×D5911yescharacteristic
623D8—28no—
624D8—44no—
625M16—2364no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—592no—
631C2×C8—1181no—
632C2×C8—1181no—
633C2×C8—1181no—
634C2×C8—1181no—
635C2×C8—1181no—
636C2×C8C22×Dic5912yes—
637C2×C8C22×Dic5912yes—
638C4⋊C4—21no—
639C4⋊C4—592no—
640C4⋊C4—1181no—
641C4⋊C4—1181no—
642C4⋊C4—1181no—
643C4⋊C4—1181no—
644C4⋊C4—1181no—
645C4⋊C4—1181no—
646C4⋊C4—1181no—
647C4⋊C4—4721no—
648C4⋊C4C22×Dic5912yes—
649C22⋊C4—24no—
650C22⋊C4—1182no—
651C22⋊C4—4721no—
652C22⋊C4—4721no—
653C22⋊C4—4721no—
654C22⋊C4—2362no—
655C22⋊C4—2362no—
656C22⋊C4—2361no—
657C22⋊C4—2362no—
658C22⋊C4—2362no—
659C22⋊C4—2362no—
660C22⋊C4—2362no—
661C22⋊C4—2362no—
662C22⋊C4—2362no—
663C42—1181no—
664C42—1181no—
665C42—1181no—
666C42—1181no—
667C42—4721no—
668C42—2362no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—22no—
675C23—22no—
676C23—21no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—48no—
681C23—48no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—84no—
702C23—84no—
703C23D4×Dic5912yes—
704C23C2×D4×D5911yescharacteristic
705D4—22no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—84no—
718D4D4×Dic5914yes—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—592no—
729C2×C4—1181no—
730C2×C4—1181no—
731C2×C4—1181no—
732C2×C4—1181no—
733C2×C4—1181no—
734C2×C4—1181no—
735C2×C4—1181no—
736C2×C4—1181no—
737C2×C4—1181no—
738C2×C4—1181no—
739C2×C4—1182no—
740C2×C4—1181no—
741C2×C4—4724no—
742C2×C4—4724no—
743C2×C4—4724no—
744C2×C4—2361no—
745C2×C4—2361no—
746C2×C4—2361no—
747C2×C4—2361no—
748C2×C4—2361no—
749C2×C4—2361no—
750C2×C4—2361no—
751C2×C4—2361no—
752C2×C4—2361no—
753C2×C4—2361no—
754C2×C4—2361no—
755C2×C4D4×Dic5912yes—
756C2×C4C23×Dic5911yescharacteristic
757C2×C4C2×D4×D5911yescharacteristic
758C2×C4C2×#1174568711yescharacteristic
759C2×C4C2×#1174568711yescharacteristic
760C2×C4#1427377211yescharacteristic
761C2×C4#1427377211yescharacteristic
762C8—22no—
763C8—22no—
764C8—1182no—
765C8—2361no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—24no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—816no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22C2×D4×Dic5911yescharacteristic
796C22#1683803411yescharacteristic
797C22#1683803911yescharacteristic
798C22AGL(1,ℤ/8)×D5911yescharacteristic
799C22#1683819811yescharacteristic
800C22#1683820311yescharacteristic
801C22#1683820311yescharacteristic
802C4—22no—
803C4—42no—
804C4—1182no—
805C4—4721no—
806C4—4721no—
807C4—4721no—
808C4—2361no—
809C4—2362no—
810C4—2361no—
811C4—2361no—
812C4C2×D4×Dic5911yescharacteristic
813C4#1683787711yescharacteristic
814C4#1683803911yescharacteristic
815C4#1683808311yescharacteristic
816C2—42no—
817C2—44no—
818C2—82no—
819C2—82no—
820C2#2142708011yescharacteristic
821C2AGL(1,ℤ/8)×Dic5911yescharacteristic
822C2#2143294811yescharacteristic
823C2#2143570711yescharacteristic
824C2#2143571411yescharacteristic
825C2#2143623011yescharacteristic
826C2#2143624511yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
Fitting, prime radicalC2×C59×#447C2
socleC23×C59C22×D4
cosocleC22×C4×C59C24
hypercenterC2×#447D59
hypocenterC59#22868
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C2×#16837514C2semidirect
2. C2×#16837407C2semidirect
3. #21427138C2semidirect
4. D4×C22⋊Dic59C2semidirect
5. #21424963C2semidirect
6. #21424795C2semidirect
7. #21424725C2semidirect
8. #21424535C2semidirect
9. #21424446C2semidirect
10. #21424446C2semidirect
11. #21424345C2semidirect
12. #21424297C2semidirect
13. #102×Dic59C2semidirect
14. #21423882C2semidirect
19. C2×D4×Dic59C22semidirect
23. C2×#14273661C22semidirect
24. C2×#14273659C22semidirect
30. C2×#14273648C22semidirect
31. C2×#14273648C22semidirect
32. C2×#14273637C22semidirect
33. C2×C8×Dic59C22semidirect
37. #16837305C22semidirect
38. #16837301C22semidirect
45. C4⋊C4×Dic59C22semidirect
48. #16837165C22semidirect
49. #16837165C22semidirect
50. #16837164C22semidirect
51. #16837164C22semidirect
52. #16837156C22semidirect
53. #16837156C22semidirect
58. C59×#447C4semidirect
108. #14273648D4semidirect
124. C22×D4×C59C2×C4semidirect
134. C2×D8×C59C2×C4semidirect
138. #121×C59C2×C4semidirect
141. #102×C59C2×C4semidirect
142. #102×C59C2×C4semidirect
143. C22⋊C8×C59C2×C4semidirect
439. #447Dic59semidirect
475. C59#22868semidirect
484. C22×D4C2×Dic59semidirect
497. C2×D8C2×Dic59semidirect
506. #121C2×Dic59semidirect
548. #102C2×Dic59semidirect
549. #102C2×Dic59semidirect
550. C22⋊C8C2×Dic59semidirect

Maximal subgroups

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

subgroupindex
C2×#168375142
C2×#168374072
#214271382
D4×C22⋊Dic592
#214249632
#214247952
#214247252
#214245352
#214244462
#214243452
#214242972
#102×Dic592
#214238822
C2×C59×#4472
#2286859