Finite Group Databasebeta

← #28609152

Subgroups — #28609152

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×#16837536C211yesmaximal, characteristic
2C2×#16837512C211yesmaximal, characteristic, complemented
3C2×#16837407C211yesmaximal, characteristic, complemented
4#21427132C211yesmaximal, characteristic, complemented
5#21424961C211yesmaximal, characteristic, complemented
6#21424796C211yesmaximal, characteristic, complemented
7#21424720C211yesmaximal, characteristic, complemented
8#21424532C211yesmaximal, characteristic, complemented
9#21424447C211yesmaximal, characteristic, complemented
10#21424444C211yesmaximal, characteristic, complemented
11#21424343C211yesmaximal, characteristic, complemented
12#21424293C211yesmaximal, characteristic, complemented
13C4×#14273648C211yesmaximal, characteristic, complemented
14#21423880C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C59C211yesmaximal, characteristic, complemented
16C22×#11745669C2211yescharacteristic
17C22×#11745669C2211yescharacteristic
18C22×#11745664C2211yescharacteristic
19C2×#14273701C2211yescharacteristic
20C2×C4×D236C2211yescharacteristic, complemented
21C2×#14273686C2211yescharacteristic
22#16837536C418yescomplemented
23#16837512—24no—
24C2×#14273660C2211yescharacteristic, complemented
25C2×#14273658C2211yescharacteristic, complemented
26#16837407—24no—
27C2×#14273648C2211yescharacteristic
28C2×#14273648C2211yescharacteristic
29C2×#14273648C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×#14273648C2211yescharacteristic
32C2×#14273648C2211yescharacteristic
33C2×#14273647C2211yescharacteristic, complemented
34C2×#14273647C2211yescharacteristic, complemented
35C2×C22⋊(C59⋊C8)C2211yescharacteristic
36C2×#14273638C2211yescharacteristic, complemented
37C2×C4×C59⋊C8C2211yescharacteristic, complemented
38#16837304C2211yescharacteristic, complemented
39#16837302—21no—
40#16837300C2211yescharacteristic, complemented
41#16837291—21no—
42#16837278—21no—
43C4×C4⋊Dic59C2211yescharacteristic, complemented
44#16837249—21no—
45#16837164C2211yescharacteristic, complemented
46#16837164C2211yescharacteristic, complemented
47#16837164C2211yescharacteristic, complemented
48#16837164C2211yescharacteristic, complemented
49#16837157C2211yescharacteristic, complemented
50#16837157C2211yescharacteristic, complemented
51C23×D4×C59C2211yescharacteristic
52C2×C4×D4×C59C2211yescharacteristic
53C2×C4×D4×C59C2211yescharacteristic
54C22×C22⋊C4×C59—21no—
55C59×#390C2211yescharacteristic
56C59×#390C2211yescharacteristic
57C59×#386—21no—
58C59×#386—21no—
59C59×#380C2211yescharacteristic
60C59×#379—21no—
61C4×C22⋊C4×C59C2211yescharacteristic
62C22×D236C2311yescharacteristic
63C22×C22⋊D59—21no—
64C22×C4×D59—21no—
65C2×#11745669—22no—
66C2×#11745669—22no—
67C2×#11745669—41no—
68C2×#11745669—41no—
69C2×#11745669C2×C414yes—
70C2×#11745669C2×C414yescomplemented
71C2×#11745664—22no—
72C2×#11745664—22no—
73C2×#11745664—41no—
74C22×C59⋊C8C2311yescharacteristic
75C22×C59⋊C8C2311yescharacteristic
76C22×C59⋊C8C2311yescharacteristic
77C22×C59⋊C8C2311yescharacteristic
78#14273701—22no—
79#14273701C2×C414yescomplemented
80C4×D236—22no—
81C4×D236—41no—
82#14273686—22no—
83#14273686—41no—
84C2×C4⋊Dic59C2311yescharacteristic
85C2×C4⋊Dic59C2311yescharacteristic
86C2×C4⋊Dic59C2311yescharacteristic
87C2×Dic59⋊C4—21no—
88C2×C22⋊Dic59—21no—
89C2×(C2×D59)⋊C4—21no—
90C2×(C2×D59)⋊C4—21no—
91C2×(C2×D59)⋊C4—21no—
92C2×(C2×D59)⋊C4—21no—
93C2×C4×Dic59—21no—
94C2×C4×Dic59—21no—
95#14273660—41no—
96#14273658—22no—
97#14273648—22no—
98#14273648—22no—
99#14273648—22no—
100#14273648C2×C414yescomplemented
101#14273648C2×C414yescomplemented
102#14273648D414yescomplemented
103#14273647—22no—
104#14273647—41no—
105C22⋊(C59⋊C8)C2×C414yescomplemented
106#14273638—22no—
107C4×C59⋊C8—41no—
108C59⋊#95—21no—
109C59⋊#95—21no—
110C25×C59—21no—
111C22×D4×C59—22no—
112C22×D4×C59—22no—
113C22×D4×C59—21no—
114C22×D4×C59—22no—
115C22×D4×C59—41no—
116C22×D4×C59—41no—
117C22×D4×C59C2×C414yescomplemented
118C22×D4×C59C2311yescharacteristic
119C22×D4×C59C2311yescharacteristic
120C23×C4×C59—21no—
121C23×C4×C59—21no—
122C23×C4×C59C2311yescharacteristic
123C4×D4×C59—22no—
124C4×D4×C59—22no—
125C4×D4×C59—41no—
126C4×D4×C59—41no—
127C2×C4⋊C4×C59C2311yescharacteristic
128C2×C4⋊C4×C59C2311yescharacteristic
129C2×C22⋊C4×C59—21no—
130C2×C22⋊C4×C59—21no—
131C2×C22⋊C4×C59—21no—
132C2×C22⋊C4×C59—21no—
133C2×C22⋊C4×C59—21no—
134C2×C22⋊C4×C59—21no—
135C2×C22⋊C4×C59—21no—
136C2×C22⋊C4×C59—44no—
137C2×C22⋊C4×C59D411yescharacteristic
138C2×C22⋊C4×C59D411yescharacteristic
139C2×C42×C59C2311yescharacteristic
140C2×C42×C59C2311yescharacteristic
141#95×C59—21no—
142#95×C59D411yescharacteristic
143#95×C59D411yescharacteristic
144C24×C59—21no—
145C24×C59—21no—
146C24×C59—24no—
147C24×C59—42no—
148C24×C59—42no—
149C24×C59—42no—
150C24×C59—42no—
151C24×C59—81no—
152C24×C59—81no—
153C24×C59C2×D411yescharacteristic
154C23×D59—21no—
155C2×D4×C59—28no—
156C2×D4×C59—24no—
157C2×D4×C59—21no—
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—44no—
166C2×D4×C59—44no—
167C2×D4×C59—44no—
168C2×D4×C59—42no—
169C2×D4×C59—42no—
170C2×D4×C59C22×C412yes—
171C2×D4×C59C22×C412yes—
172C2×D4×C59C2×D412yes—
173C2×D4×C59#4112yes—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—21no—
178C22×C4×C59—21no—
179C22×C4×C59—21no—
180C22×C4×C59—42no—
181C22×C4×C59—42no—
182C22×C4×C59—42no—
183C22×C4×C59—42no—
184C22×C4×C59—81no—
185C22×C4×C59—81no—
186C22×C4×C59C22×C412yes—
187C22×C4×C59C2×D411yescharacteristic
188C22×C4×C59C2×D411yescharacteristic
189C22×C4×C59C2×D411yescharacteristic
190C22×C4×C59C2×D411yescharacteristic
191C22×C4×C59C2×D411yescharacteristic
192C22×C4×C59#4112yes—
193C22×C4×C59C2411yescharacteristic
194C2×C22⋊D59—24no—
195C2×C22⋊D59—81no—
196C2×C22⋊D59—81no—
197C22×Dic59—21no—
198C22×Dic59—21no—
199C22×Dic59—21no—
200C2×D236—21no—
201C2×D236—21no—
202C2×D236—21no—
203C2×D236—21no—
204C2×D236—21no—
205C2×D236C22×C412yes—
206C2×C4×D59—42no—
207C2×C4×D59—42no—
208C2×C4×D59—81no—
209C4⋊C4×C59—21no—
210C4⋊C4×C59—21no—
211C4⋊C4×C59—21no—
212C4⋊C4×C59—21no—
213C22⋊C4×C59—22no—
214C22⋊C4×C59—41no—
215C22⋊C4×C59—42no—
216C22⋊C4×C59—42no—
217C22⋊C4×C59—42no—
218C22⋊C4×C59—42no—
219C22⋊C4×C59—42no—
220C22⋊C4×C59—81no—
221C22⋊C4×C59—81no—
222C42×C59—21no—
223C42×C59—21no—
224C42×C59—21no—
225C42×C59—21no—
226C22⋊Dic59—42no—
227#11745669—28no—
228#11745669—44no—
229(C2×D59)⋊C4—24no—
230(C2×D59)⋊C4—42no—
231(C2×D59)⋊C4—42no—
232(C2×D59)⋊C4—81no—
233C4⋊Dic59—21no—
234C4⋊Dic59—21no—
235C4⋊Dic59—21no—
236C4⋊Dic59—21no—
237C4⋊Dic59C22×C412yes—
238C4⋊Dic59C2×D412yes—
239Dic59⋊C4—81no—
240C4×Dic59—42no—
241C4×Dic59—81no—
242#11745664—44no—
243C2×C59⋊C8—21no—
244C2×C59⋊C8—21no—
245C2×C59⋊C8—21no—
246C2×C59⋊C8—21no—
247C2×C59⋊C8—21no—
248C2×C59⋊C8—21no—
249C2×C59⋊C8—21no—
250C2×C59⋊C8—21no—
251C2×C59⋊C8—21no—
252C2×C59⋊C8C22×C412yes—
253C2×C59⋊C8C22×C412yes—
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—48no—
266C23×C59—48no—
267C23×C59—41no—
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—84no—
278C23×C59—84no—
279C23×C59—84no—
280C23×C59—84no—
281C23×C59—84no—
282C23×C59C4×D412yes—
283C23×C59C22×D411yescharacteristic
284C22×D59—22no—
285C22×D59—41no—
286C22×D59—41no—
287C22×D59—41no—
288C22×D59—41no—
289C22×D59—41no—
290C22×D59—41no—
291D4×C59—22no—
292D4×C59—22no—
293D4×C59—22no—
294D4×C59—22no—
295D4×C59—22no—
296D4×C59—48no—
297D4×C59—41no—
298D4×C59—41no—
299D4×C59C4×D414yes—
300C2×C4×C59—21no—
301C2×C4×C59—21no—
302C2×C4×C59—21no—
303C2×C4×C59—21no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—22no—
307C2×C4×C59—22no—
308C2×C4×C59—21no—
309C2×C4×C59—21no—
310C2×C4×C59—21no—
311C2×C4×C59—21no—
312C2×C4×C59—21no—
313C2×C4×C59—21no—
314C2×C4×C59—21no—
315C2×C4×C59—21no—
316C2×C4×C59—21no—
317C2×C4×C59—41no—
318C2×C4×C59—41no—
319C2×C4×C59—41no—
320C2×C4×C59—41no—
321C2×C4×C59—41no—
322C2×C4×C59—41no—
323C2×C4×C59—84no—
324C2×C4×C59—84no—
325C2×C4×C59C4×D412yes—
326C2×C4×C59AGL(1,ℤ/8)12yes—
327C2×C4×C59C23×C411yescharacteristic
328C2×C4×C59C22×D411yescharacteristic
329C2×C4×C59C2×#4111yescharacteristic
330C2×C4×C59C2×#4111yescharacteristic
331C2×C4×C59H(5,𝔽2)11yescharacteristic
332C2×C4×C59H(5,𝔽2)11yescharacteristic
333C22⋊D59—84no—
334C2×Dic59—22no—
335C2×Dic59—22no—
336C2×Dic59—41no—
337C2×Dic59—41no—
338C2×Dic59—41no—
339C2×Dic59—41no—
340C2×Dic59—41no—
341C2×Dic59—41no—
342C2×Dic59—41no—
343D236—22no—
344D236—22no—
345D236—41no—
346D236—41no—
347C4×D59—84no—
348C59⋊C8—22no—
349C59⋊C8—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—816no—
371C22×C59—81no—
372C22×C59—81no—
373C22×C59—81no—
374C22×C59—81no—
375C22×C59C2×C4×D411yescharacteristic
376C22×C59D4211yescharacteristic
377C22×C59#54611yescharacteristic
378C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
379C22×C59#57511yescharacteristic
380C22×C59#57611yescharacteristic
381C22×C59#57611yescharacteristic
382C2×D59—42no—
383C2×D59—42no—
384C2×D59—42no—
385C2×D59—81no—
386C2×D59—81no—
387C2×D59—81no—
388C2×D59—81no—
389C4×C59—22no—
390C4×C59—22no—
391C4×C59—41no—
392C4×C59—41no—
393C4×C59—41no—
394C4×C59—81no—
395C4×C59—81no—
396C4×C59C2×C4×D411yescharacteristic
397C4×C59#51811yescharacteristic
398C4×C59#54611yescharacteristic
399C4×C59#55111yescharacteristic
400Dic59—42no—
401Dic59—42no—
402Dic59—81no—
403C2×#447—591no—
404C2×#442—591no—
405C2×#418—591no—
406#2363—591no—
407D4×C22⋊C4D5911yescharacteristic, complemented
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#235811yescharacteristic
422C2×C59C4×AGL(1,ℤ/8)11yescharacteristic
423C2×C59#294811yescharacteristic
424C2×C59#327311yescharacteristic
425C2×C59#327411yescharacteristic
426C2×C59#331811yescharacteristic
427C2×C59#331911yescharacteristic
428D59—82no—
429C23×D4C2×D5911yescharacteristic
430C22×D8—591no—
431C22×D8—591no—
432C22×M16—591no—
433C2×#121—591no—
434C2×C4×D4—591no—
435C2×C4×D4C2×D5911yescharacteristic
436C2×C4×D4C2×D5911yescharacteristic
437C2×#117—591no—
438C22×C22⋊C4—21no—
439#447—598no—
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×#102—591no—
451C2×#102—591no—
452C2×C22⋊C8—591no—
453C2×#97—591no—
454C2×C4×C8—591no—
455#390—591no—
456#390—1181no—
457#390C2×D5911yescharacteristic
458#390C2×D5911yescharacteristic
459#389—591no—
460#388—1181no—
461#386—21no—
462#386—21no—
463#386—1181no—
464#380C2×D5911yescharacteristic
465#379—21no—
466C4×C4⋊C4—591no—
467C4×C22⋊C4—1181no—
468C4×C22⋊C4C2×D5911yescharacteristic
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—22no—
480C22×D4—21no—
481C22×D4—41no—
482C22×D4—41no—
483C22×D4—591no—
484C22×D4—1181no—
485C22×D4C4×D5914yescomplemented
486C22×D4C22×D5911yescharacteristic
487C22×D4C22×D5911yescharacteristic
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—1181no—
491C23×C4C22×D5911yescharacteristic
492C2×D8—594no—
493C2×D8—594no—
494C2×D8—1182no—
495C2×D8—1182no—
496C2×D8—2361no—
497C2×D8—2361no—
498C2×M16—1182no—
499C2×M16—1182no—
500C2×M16—2361no—
501C22×C8—591no—
502C22×C8—591no—
503C22×C8—591no—
504C22×C8—591no—
505#121—594no—
506#121—1182no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—41no—
510C4×D4—41no—
511C4×D4—1182no—
512C4×D4—2361no—
513#117—1182no—
514#117—2361no—
515C2×C4⋊C4—591no—
516C2×C4⋊C4—591no—
517C2×C4⋊C4—591no—
518C2×C4⋊C4—1181no—
519C2×C4⋊C4C22×D5911yescharacteristic
520C2×C4⋊C4C22×D5911yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—44no—
529C2×C22⋊C4—1181no—
530C2×C22⋊C4—1181no—
531C2×C22⋊C4—1181no—
532C2×C22⋊C4—1181no—
533C2×C22⋊C4—1181no—
534C2×C22⋊C4C22⋊D5911yescharacteristic
535C2×C22⋊C4C22⋊D5911yescharacteristic
536C2×C42—1181no—
537C2×C42—1181no—
538C2×C42C22×D5911yescharacteristic
539C2×C42C22×D5911yescharacteristic
540#107—2361no—
541#106—1182no—
542#102—594no—
543#102—594no—
544#102—594no—
545#102—1182no—
546#102—1182no—
547#102—1182no—
548#102—1182no—
549#102—2361no—
550C22⋊C8—594no—
551#97—1182no—
552C4×C8—2361no—
553#95—21no—
554#95—1181no—
555#95—1181no—
556#95C22⋊D5911yescharacteristic
557#95C22⋊D5911yescharacteristic
558C24—21no—
559C24—21no—
560C24—24no—
561C24—42no—
562C24—42no—
563C24—42no—
564C24—42no—
565C24—81no—
566C24—81no—
567C24—1181no—
568C24C2×C22⋊D5911yescharacteristic
569C2×D4—28no—
570C2×D4—24no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—44no—
580C2×D4—44no—
581C2×D4—44no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—592no—
585C2×D4—1184no—
586C2×D4—1181no—
587C2×D4—1181no—
588C2×D4—1181no—
589C2×D4—1181no—
590C2×D4—1181no—
591C2×D4—4721no—
592C2×D4—4721no—
593C2×D4C2×C4×D5912yes—
594C2×D4C2×C4×D5912yes—
595C2×D4D4×D5912yes—
596C2×D4#1174568712yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4—1181no—
610C22×C4—1181no—
611C22×C4—1181no—
612C22×C4—4721no—
613C22×C4—2362no—
614C22×C4—2362no—
615C22×C4C2×C4×D5912yes—
616C22×C4#1174568512yes—
617C22×C4C2×C22⋊D5911yescharacteristic
618C22×C4C2×C22⋊D5911yescharacteristic
619C22×C4C2×C22⋊D5911yescharacteristic
620C22×C4C2×C22⋊D5911yescharacteristic
621C22×C4C2×C22⋊D5911yescharacteristic
622C22×C4C23×D5911yescharacteristic
623D8—1188no—
624D8—2364no—
625M16—2364no—
626C2×C8—592no—
627C2×C8—592no—
628C2×C8—592no—
629C2×C8—1181no—
630C2×C8—1181no—
631C2×C8—1181no—
632C2×C8—1181no—
633C2×C8—1181no—
634C2×C8—1181no—
635C2×C8—1181no—
636C2×C8—1181no—
637C2×C8—1181no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—592no—
643C4⋊C4—592no—
644C4⋊C4—1181no—
645C4⋊C4—1181no—
646C4⋊C4—1181no—
647C4⋊C4—1181no—
648C4⋊C4—4721no—
649C22⋊C4—22no—
650C22⋊C4—41no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—81no—
657C22⋊C4—81no—
658C22⋊C4—1184no—
659C22⋊C4—4721no—
660C22⋊C4—2362no—
661C22⋊C4—2362no—
662C22⋊C4—2362no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—4721no—
668C42—2362no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—22no—
674C23—21no—
675C23—22no—
676C23—21no—
677C23—22no—
678C23—22no—
679C23—48no—
680C23—48no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—84no—
692C23—84no—
693C23—84no—
694C23—84no—
695C23—84no—
696C23—1182no—
697C23—2361no—
698C23—2361no—
699C23—2361no—
700C23—2361no—
701C23—2361no—
702C23—2361no—
703C23C4×C22⋊D5912yes—
704C23C22×C22⋊D5911yescharacteristic
705D4—22no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—48no—
711D4—41no—
712D4—41no—
713D4—1182no—
714D4—1182no—
715D4—4724no—
716D4—2361no—
717D4—2361no—
718D4(C22⋊D59)⋊C414yes—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4—1182no—
745C2×C4—1182no—
746C2×C4—4724no—
747C2×C4—2361no—
748C2×C4—2361no—
749C2×C4—2361no—
750C2×C4—2361no—
751C2×C4—2361no—
752C2×C4—2361no—
753C2×C4—2361no—
754C2×C4C4×C22⋊D5912yes—
755C2×C4#1427375312yes—
756C2×C4C22×C4×D5911yescharacteristic
757C2×C4C2×D4×D5911yescharacteristic
758C2×C4C2×#1174568711yescharacteristic
759C2×C4C2×#1174568511yescharacteristic
760C2×C4#1427377211yescharacteristic
761C2×C4#1427377211yescharacteristic
762C8—1182no—
763C8—1182no—
764C8—1182no—
765C8—2361no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—24no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—816no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—4721no—
789C22—4721no—
790C22—4721no—
791C22—4721no—
792C22—2362no—
793C22—2362no—
794C22—2362no—
795C22C2×C4×C22⋊D5911yescharacteristic
796C22D4×C22⋊D5911yescharacteristic
797C22#1683804611yescharacteristic
798C22C2×#1427375311yescharacteristic
799C22#1683820011yescharacteristic
800C22#1683820511yescharacteristic
801C22#1683820511yescharacteristic
802C4—22no—
803C4—22no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—81no—
808C4—81no—
809C4—4721no—
810C4—2362no—
811C4—2362no—
812C4C2×(C22⋊D59)⋊C411yescharacteristic
813C4#1683787511yescharacteristic
814C4#1683804211yescharacteristic
815C4#1683807811yescharacteristic
816C2—42no—
817C2—44no—
818C2—82no—
819C2—4722no—
820C2#2142707511yescharacteristic
821C2C4×#1427375311yescharacteristic
822C2#2143294611yescharacteristic
823C2#2143570311yescharacteristic
824C2#2143571211yescharacteristic
825C2#2143623711yescharacteristic
826C2#2143625211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingD4×C22⋊C4×C59C2
socleC23×C59C22×D4
prime radicalC2×#16837536C2
cosocleC22×C4×C59C24
hypercenterD4×C22⋊C4D59
hypocenterC59#22868
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16837512C2semidirect
3. C2×#16837407C2semidirect
4. #21427132C2semidirect
5. #21424961C2semidirect
6. #21424796C2semidirect
7. #21424720C2semidirect
8. #21424532C2semidirect
9. #21424447C2semidirect
10. #21424444C2semidirect
11. #21424343C2semidirect
12. #21424293C2semidirect
13. C4×#14273648C2semidirect
14. #21423880C2semidirect
15. D4×C22⋊C4×C59C2semidirect
20. C2×C4×D236C22semidirect
22. #16837536C4semidirect
24. C2×#14273660C22semidirect
25. C2×#14273658C22semidirect
33. C2×#14273647C22semidirect
34. C2×#14273647C22semidirect
36. C2×#14273638C22semidirect
37. C2×C4×C59⋊C8C22semidirect
38. #16837304C22semidirect
40. #16837300C22semidirect
43. C4×C4⋊Dic59C22semidirect
45. #16837164C22semidirect
46. #16837164C22semidirect
47. #16837164C22semidirect
48. #16837164C22semidirect
49. #16837157C22semidirect
50. #16837157C22semidirect
70. C2×#11745669C2×C4semidirect
79. #14273701C2×C4semidirect
100. #14273648C2×C4semidirect
101. #14273648C2×C4semidirect
102. #14273648D4semidirect
105. C22⋊(C59⋊C8)C2×C4semidirect
117. C22×D4×C59C2×C4semidirect
407. D4×C22⋊C4D59semidirect
475. C59#22868semidirect
485. C22×D4C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168375362
C2×#168375122
C2×#168374072
#214271322
#214249612
#214247962
#214247202
#214245322
#214244472
#214244442
#214243432
#214242932
C4×#142736482
#214238802
D4×C22⋊C4×C592
#2286859