Finite Group Databasebeta

← #28599790

Subgroups — #28599790

Order 15104.

1156 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837477C211yesmaximal, characteristic, complemented
2C2×#16837365C211yesmaximal, characteristic, complemented
3C4×#14273697C211yesmaximal, characteristic
4#21424893C211yesmaximal, characteristic, complemented
5#21424889C211yesmaximal, characteristic, complemented
6#21424707C211yesmaximal, characteristic, complemented
7#21424701C211yesmaximal, characteristic, complemented
8#21424701C211yesmaximal, characteristic, complemented
9#21424700C211yesmaximal, characteristic, complemented
10#21424393C211yesmaximal, characteristic, complemented
11#21424392C211yesmaximal, characteristic, complemented
12#21424392C211yesmaximal, characteristic, complemented
13#21424005C211yesmaximal, characteristic, complemented
14#21423880C211yesmaximal, characteristic, complemented
15C59×#1851C211yesmaximal, characteristic, complemented
16C23×C4×D59C2211yescharacteristic
17C22×#11745664C2211yescharacteristic
18C22×#11745659C2211yescharacteristic, complemented
19C2×#14273697C411yescharacteristic
20C2×C4×D236C2211yescharacteristic
21C2×C4×D236C2211yescharacteristic
22C2×C4×C22⋊D59C2211yescharacteristic
23#16837477—24no—
24C2×Dic59⋊C8C2211yescharacteristic, complemented
25#16837365—24no—
26C2×C22⋊(C59⋊C8)C2211yescharacteristic
27C2×(C2×D59)⋊C8C2211yescharacteristic
28C2×(C2×D59)⋊C8C2211yescharacteristic
29C2×(C2×D59)⋊C8C2211yescharacteristic
30C2×(C2×D59)⋊C8C2211yescharacteristic
31C2×(C2×D59)⋊C8C2211yescharacteristic
32C2×(C2×D59)⋊C8C2211yescharacteristic
33C2×(C2×D59)⋊C8C2211yescharacteristic
34C2×(C2×D59)⋊C8C2211yescharacteristic
35C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
36C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
37C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
38C2×#14273638C2211yescharacteristic, complemented
39C2×C4×C59⋊C8C2211yescharacteristic, complemented
40C2×C8×Dic59C2211yescharacteristic, complemented
41#16837280C411yescharacteristic
42#16837280C411yescharacteristic
43#16837279C411yescharacteristic
44#16837277C411yescharacteristic
45#16837276C411yescharacteristic
46#16837276C411yescharacteristic
47#16837257C411yescharacteristic
48C4×(C2×D59)⋊C4C2211yescharacteristic
49C4×(C2×D59)⋊C4C2211yescharacteristic
50#16837157C2211yescharacteristic, complemented
51#16837157C2211yescharacteristic, complemented
52#16837156C2211yescharacteristic, complemented
53#16837156C2211yescharacteristic, complemented
54C22×M16×C59C2211yescharacteristic
55C2×C4⋊C8×C59C2211yescharacteristic, complemented
56C2×C4⋊C8×C59C2211yescharacteristic, complemented
57C2×C22⋊C8×C59C2211yescharacteristic
58C4×C22⋊C4×C59C2211yescharacteristic
59C59×#336C2211yescharacteristic, complemented
60C59×#336C2211yescharacteristic, complemented
61C24×D59C2×C411yescharacteristic
62C22×D236C2×C411yescharacteristic
63C22×D236C2×C411yescharacteristic
64C22×C22⋊D59C2×C411yescharacteristic
65C23×Dic59C2×C411yescharacteristic
66C22×C4×D59—22no—
67C22×C4×D59—22no—
68C22×C4×D59—41no—
69C22×C4×D59—41no—
70C22×C4×D59—41no—
71C22×C4×D59—41no—
72C22×C4×D59C2×C411yescharacteristic
73C22×C4×D59C2×C411yescharacteristic
74C22×C4×D59C2311yescharacteristic
75C22×C4×D59C2311yescharacteristic
76C22×C4×D59C2311yescharacteristic
77C2×#11745664—41no—
78C2×#11745664—41no—
79C2×#11745664D414yescomplemented
80C2×#11745659—22no—
81C2×#11745659—41no—
82C2×#11745659—41no—
83C22×C59⋊C8C2311yescharacteristic
84C22×C59⋊C8C2311yescharacteristic
85C22×C59⋊C8C2311yescharacteristic
86C22×C59⋊C8C2311yescharacteristic
87#14273697—24no—
88C4×D236—41no—
89C4×D236—41no—
90C4×D236—41no—
91C4×D236—41no—
92C4×C22⋊D59—22no—
93C4×C22⋊D59—22no—
94C2×C4⋊Dic59C2×C411yescharacteristic
95C2×C4⋊Dic59C2×C411yescharacteristic
96C2×Dic59⋊C4C2×C411yescharacteristic
97C2×C22⋊Dic59C2×C411yescharacteristic
98C2×(C2×D59)⋊C4C2×C411yescharacteristic
99C2×(C2×D59)⋊C4C2×C411yescharacteristic
100C2×(C2×D59)⋊C4C2×C411yescharacteristic
101C2×(C2×D59)⋊C4C2×C411yescharacteristic
102C2×(C2×D59)⋊C4C2×C411yescharacteristic
103C2×(C2×D59)⋊C4C2×C411yescharacteristic
104C2×(C2×D59)⋊C4C2×C411yescharacteristic
105C2×(C2×D59)⋊C4C2×C411yescharacteristic
106C2×(C2×D59)⋊C4C2×C411yescharacteristic
107C2×C4×Dic59C2311yescharacteristic
108Dic59⋊C8—22no—
109C22⋊(C59⋊C8)—22no—
110(C2×D59)⋊C8—22no—
111(C2×D59)⋊C8—22no—
112(C2×D59)⋊C8—22no—
113(C2×D59)⋊C8—22no—
114(C2×D59)⋊C8—22no—
115(C2×D59)⋊C8—41no—
116(C2×D59)⋊C8—41no—
117(C2×D59)⋊C8—41no—
118(C2×D59)⋊C8—41no—
119(C2×D59)⋊C8—41no—
120(C2×D59)⋊C8—41no—
121#14273638—41no—
122C4×C59⋊C8—41no—
123C8×Dic59—22no—
124C59⋊#95C2×C411yescharacteristic
125C59⋊#95C2×C411yescharacteristic
126C59⋊#95C2×C411yescharacteristic
127C59⋊#95C2×C411yescharacteristic
128C23×C4×C59C2311yescharacteristic
129C2×M16×C59—22no—
130C2×M16×C59—41no—
131C2×M16×C59—41no—
132C22×C8×C59C2311yescharacteristic
133C22×C8×C59C2311yescharacteristic
134C22×C8×C59C2311yescharacteristic
135C22×C8×C59C2311yescharacteristic
136C2×C22⋊C4×C59C2×C411yescharacteristic
137C2×C22⋊C4×C59C2×C411yescharacteristic
138C2×C42×C59C2311yescharacteristic
139C2×C42×C59C2311yescharacteristic
140C4⋊C8×C59—41no—
141C4⋊C8×C59—41no—
142C22⋊C8×C59—22no—
143#95×C59C2×C411yescharacteristic
144#95×C59C2×C411yescharacteristic
145C24×C59C22×C411yescharacteristic
146C23×D59—22no—
147C23×D59—22no—
148C23×D59—22no—
149C23×D59—41no—
150C23×D59—41no—
151C23×D59—41no—
152C23×D59—41no—
153C23×D59C22×C411yescharacteristic
154C23×D59C22×C411yescharacteristic
155C23×D59C22×C411yescharacteristic
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—21no—
159C22×C4×C59—21no—
160C22×C4×C59C22×C411yescharacteristic
161C22×C4×C59C22×C411yescharacteristic
162C22×C4×C59C22×C411yescharacteristic
163C22×C4×C59C22×C411yescharacteristic
164C22×C4×C59C22×C411yescharacteristic
165C22×C4×C59C2×D412yes—
166C22×C4×C59#4112yes—
167C22×C4×C59C2411yescharacteristic
168C2×C22⋊D59—22no—
169C2×C22⋊D59—22no—
170C2×C22⋊D59—41no—
171C22×Dic59—22no—
172C22×Dic59—41no—
173C22×Dic59—41no—
174C22×Dic59C22×C411yescharacteristic
175C22×Dic59C22×C411yescharacteristic
176C22×Dic59C22×C411yescharacteristic
177C22×Dic59C22×C411yescharacteristic
178C22×Dic59C22×C411yescharacteristic
179C2×D236—22no—
180C2×D236—22no—
181C2×D236—22no—
182C2×D236—41no—
183C2×D236—41no—
184C2×D236—41no—
185C2×C4×D59—22no—
186C2×C4×D59—22no—
187C2×C4×D59—21no—
188C2×C4×D59—21no—
189C2×C4×D59—21no—
190C2×C4×D59—21no—
191C2×C4×D59—21no—
192C2×C4×D59—21no—
193C2×C4×D59—21no—
194C2×C4×D59—21no—
195C2×C4×D59—21no—
196C2×C4×D59—21no—
197C2×C4×D59—21no—
198C2×C4×D59—21no—
199C2×C4×D59—21no—
200C2×C4×D59—21no—
201C2×C4×D59—21no—
202C2×C4×D59—21no—
203C2×C4×D59—21no—
204C2×C4×D59—21no—
205C2×C4×D59—41no—
206C2×C4×D59—41no—
207C2×C4×D59—41no—
208C2×C4×D59—41no—
209C2×C4×D59—44no—
210C2×C4×D59—44no—
211C2×C4×D59—44no—
212C2×C4×D59—44no—
213M16×C59—44no—
214C2×C8×C59—21no—
215C2×C8×C59—21no—
216C2×C8×C59—21no—
217C2×C8×C59—21no—
218C2×C8×C59—21no—
219C2×C8×C59—21no—
220C2×C8×C59—21no—
221C2×C8×C59—21no—
222C2×C8×C59—21no—
223C2×C8×C59—21no—
224C2×C8×C59—21no—
225C2×C8×C59—21no—
226C22⋊C4×C59—22no—
227C22⋊C4×C59—41no—
228C42×C59—21no—
229C42×C59—21no—
230C42×C59—21no—
231C42×C59—21no—
232C22⋊Dic59—22no—
233(C2×D59)⋊C4—22no—
234(C2×D59)⋊C4—22no—
235(C2×D59)⋊C4—22no—
236(C2×D59)⋊C4—41no—
237(C2×D59)⋊C4—41no—
238(C2×D59)⋊C4—41no—
239(C2×D59)⋊C4—41no—
240(C2×D59)⋊C4—41no—
241(C2×D59)⋊C4M1614yescomplemented
242C4⋊Dic59—41no—
243C4⋊Dic59—41no—
244Dic59⋊C4—22no—
245C4×Dic59—21no—
246C4×Dic59—21no—
247#11745664—44no—
248C2×C59⋊C8—21no—
249C2×C59⋊C8—21no—
250C2×C59⋊C8—21no—
251C2×C59⋊C8—21no—
252C2×C59⋊C8—21no—
253C2×C59⋊C8—21no—
254C2×C59⋊C8—21no—
255C2×C59⋊C8—21no—
256C2×C59⋊C8—21no—
257C2×C59⋊C8—21no—
258C2×C59⋊C8C2×D412yes—
259C2×C59⋊C8C2×D412yes—
260#11745659—44no—
261C23×C59—21no—
262C23×C59—21no—
263C23×C59—21no—
264C23×C59—21no—
265C23×C59—21no—
266C23×C59—21no—
267C23×C59C4×D412yes—
268C23×C59C23×C411yescharacteristic
269C22×D59—21no—
270C22×D59—21no—
271C22×D59—21no—
272C22×D59—21no—
273C22×D59—21no—
274C22×D59—21no—
275C22×D59—21no—
276C22×D59—21no—
277C22×D59—21no—
278C22×D59—21no—
279C22×D59—21no—
280C22×D59—21no—
281C22×D59—21no—
282C22×D59—21no—
283C22×D59—21no—
284C22×D59—21no—
285C22×D59—21no—
286C22×D59—21no—
287C22×D59—21no—
288C22×D59—44no—
289C22×D59—44no—
290C22×D59—44no—
291C22×D59—44no—
292C22×D59—44no—
293C22×D59—44no—
294C22×D59—44no—
295C22×D59C2×M1612yes—
296C22×D59#13112yes—
297C2×C4×C59—21no—
298C2×C4×C59—21no—
299C2×C4×C59—21no—
300C2×C4×C59—21no—
301C2×C4×C59—22no—
302C2×C4×C59—22no—
303C2×C4×C59—22no—
304C2×C4×C59—22no—
305C2×C4×C59—21no—
306C2×C4×C59—21no—
307C2×C4×C59—21no—
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×C59C4×D412yes—
315C2×C4×C59C2×M1612yes—
316C2×C4×C59C22×D411yescharacteristic
317C2×C4×C59C2×#4111yescharacteristic
318C2×C4×C59H(5,𝔽2)11yescharacteristic
319C2×C4×C59H(5,𝔽2)11yescharacteristic
320C2×C4×C59H(5,𝔽2)11yescharacteristic
321C2×C4×C59H(5,𝔽2)11yescharacteristic
322C22⋊D59—44no—
323C2×Dic59—21no—
324C2×Dic59—21no—
325C2×Dic59—21no—
326C2×Dic59—21no—
327C2×Dic59—21no—
328C2×Dic59—21no—
329C2×Dic59—21no—
330C2×Dic59—21no—
331C2×Dic59—21no—
332C2×Dic59—21no—
333C2×Dic59—21no—
334C2×Dic59—21no—
335C2×Dic59—21no—
336C2×Dic59—21no—
337C2×Dic59—44no—
338C2×Dic59C2×M1612yes—
339D236—44no—
340D236—44no—
341C4×D59—44no—
342C4×D59—44no—
343C4×D59—41no—
344C4×D59—41no—
345C4×D59—41no—
346C4×D59—41no—
347C4×D59—41no—
348C4×D59—41no—
349C4×D59—41no—
350C4×D59—41no—
351C4×D59—41no—
352C4×D59—41no—
353C4×D59—41no—
354C4×D59—41no—
355C8×C59—41no—
356C8×C59—41no—
357C8×C59—41no—
358C8×C59—41no—
359C59⋊C8—22no—
360C59⋊C8—22no—
361C59⋊C8—41no—
362C59⋊C8—41no—
363#22038—591nomaximal, Sylow
364C22×C59—22no—
365C22×C59—22no—
366C22×C59—22no—
367C22×C59—41no—
368C22×C59—41no—
369C22×C59—41no—
370C22×C59—41no—
371C22×C59C2×C4×D411yescharacteristic
372C22×C59#51811yescharacteristic
373C22×C59#51811yescharacteristic
374C22×C59C22×M1611yescharacteristic
375C22×C59C2×#13111yescharacteristic
376C22×C59#56811yescharacteristic
377C22×C59#56811yescharacteristic
378C2×D59—22no—
379C2×D59—22no—
380C2×D59—22no—
381C2×D59—22no—
382C2×D59—22no—
383C2×D59—22no—
384C2×D59—416no—
385C2×D59—41no—
386C2×D59—41no—
387C2×D59—41no—
388C2×D59—41no—
389C2×D59—41no—
390C2×D59—41no—
391C2×D59—41no—
392C2×D59—41no—
393C2×D59—41no—
394C2×D59—41no—
395C2×D59—41no—
396C2×D59—41no—
397C2×D59—41no—
398C2×D59—41no—
399C2×D59—41no—
400C4×C59—22no—
401C4×C59—22no—
402C4×C59—41no—
403C4×C59—41no—
404C4×C59—41no—
405C4×C59#53411yescharacteristic
406C4×C59#53511yescharacteristic
407C4×C59#53811yescharacteristic
408C4×C59#53811yescharacteristic
409Dic59—22no—
410Dic59—41no—
411Dic59—41no—
412Dic59—41no—
413Dic59—41no—
414C2×#436—591no—
415C2×#407—591no—
416C4×#120—591no—
417#1955—591no—
418#1954—591no—
419#1924—591no—
420#1923—591no—
421#1923—591no—
422#1923—591no—
423#1870—591no—
424#1870—591no—
425#1870—591no—
426#1851D5911yescharacteristic, complemented
427#1779—591no—
428#1753—591no—
429C2×C59—42no—
430C2×C59#232111yescharacteristic
431C2×C59#293311yescharacteristic
432C2×C59D4×M1611yescharacteristic
433C2×C59#297411yescharacteristic
434C2×C59#297511yescharacteristic
435C2×C59#297611yescharacteristic
436C2×C59#297811yescharacteristic
437D59—42no—
438D59—42no—
439D59—81no—
440C24×C4—591no—
441C22×M16—591no—
442C22×M16—591no—
443C22×M16C2×D5911yescharacteristic
444C2×#120—591no—
445C2×C4×D4—591no—
446C2×C4×D4—591no—
447C2×C4×D4—591no—
448#436—1184no—
449C2×C4⋊C8—591no—
450C2×C4⋊C8C2×D5911yescharacteristic, complemented
451C2×C4⋊C8C2×D5911yescharacteristic, complemented
452#407—1184no—
453C2×C22⋊C8—591no—
454C2×C22⋊C8—591no—
455C2×C22⋊C8—591no—
456C2×C22⋊C8—591no—
457C2×C22⋊C8—591no—
458C2×C22⋊C8—591no—
459C2×C22⋊C8—591no—
460C2×C22⋊C8—591no—
461C2×C22⋊C8—591no—
462C2×C22⋊C8—591no—
463C2×C22⋊C8—591no—
464C2×C22⋊C8—591no—
465C2×C22⋊C8C2×D5911yescharacteristic
466C2×#97—591no—
467C2×C4×C8—591no—
468C2×C4×C8—591no—
469#386—591no—
470#386—591no—
471#386—591no—
472#385—591no—
473#385—591no—
474#385—591no—
475#379—591no—
476C4×C22⋊C4—591no—
477C4×C22⋊C4—591no—
478C4×C22⋊C4C2×D5911yescharacteristic
479#336—591no—
480#336—591no—
481#336—591no—
482#336—591no—
483#336C2×D5911yescharacteristic, complemented
484#336C2×D5911yescharacteristic, complemented
485C59#2203811yescharacteristic, complemented, Sylow
486C25—591no—
487C22×D4—591no—
488C22×D4—591no—
489C22×D4—591no—
490C23×C4—591no—
491C23×C4—591no—
492C23×C4—591no—
493C23×C4—591no—
494C23×C4—591no—
495C23×C4—591no—
496C23×C4—1182no—
497C23×C4—1182no—
498C23×C4—2361no—
499C23×C4—2361no—
500C23×C4—2361no—
501C23×C4—2361no—
502C23×C4C22×D5911yescharacteristic
503C2×M16—22no—
504C2×M16—41no—
505C2×M16—41no—
506C2×M16—594no—
507C2×M16—1182no—
508C2×M16—2361no—
509C2×M16—2361no—
510C2×M16—2361no—
511C2×M16—2361no—
512C22×C8—591no—
513C22×C8—591no—
514C22×C8—591no—
515C22×C8—591no—
516C22×C8C22×D5911yescharacteristic
517C22×C8C22×D5911yescharacteristic
518C22×C8C22×D5911yescharacteristic
519C22×C8C22×D5911yescharacteristic
520#120—1184no—
521C4×D4—1182no—
522C4×D4—1182no—
523C4×D4—2361no—
524C4×D4—2361no—
525C4×D4—2361no—
526C4×D4—2361no—
527C2×C4⋊C4—591no—
528C2×C4⋊C4—591no—
529C2×C4⋊C4—591no—
530C2×C22⋊C4—591no—
531C2×C22⋊C4—591no—
532C2×C22⋊C4—591no—
533C2×C22⋊C4—591no—
534C2×C22⋊C4—591no—
535C2×C22⋊C4—591no—
536C2×C22⋊C4—591no—
537C2×C22⋊C4—591no—
538C2×C22⋊C4—591no—
539C2×C22⋊C4—591no—
540C2×C22⋊C4C4×D5911yescharacteristic
541C2×C22⋊C4C4×D5911yescharacteristic
542C2×C42—591no—
543C2×C42C22×D5911yescharacteristic
544C2×C42C22×D5911yescharacteristic
545C4⋊C8—41no—
546C4⋊C8—41no—
547C4⋊C8—1182no—
548C22⋊C8—22no—
549C22⋊C8—1182no—
550C22⋊C8—1182no—
551C22⋊C8—1182no—
552C22⋊C8—1182no—
553C22⋊C8—1182no—
554C22⋊C8—1182no—
555C22⋊C8—2361no—
556C22⋊C8—2361no—
557C22⋊C8—2361no—
558C22⋊C8—2361no—
559C22⋊C8—2361no—
560C22⋊C8—2361no—
561#97—2361no—
562C4×C8—1182no—
563C4×C8—2361no—
564#95—591no—
565#95—591no—
566#95—591no—
567#95—591no—
568#95C4×D5911yescharacteristic
569#95C4×D5911yescharacteristic
570C24—591no—
571C24—591no—
572C24—591no—
573C24—1182no—
574C24—1182no—
575C24—1182no—
576C24—2361no—
577C24—2361no—
578C24—2361no—
579C24—2361no—
580C24C2×C4×D5911yescharacteristic
581C2×D4—1182no—
582C2×D4—1182no—
583C2×D4—1182no—
584C2×D4—1182no—
585C2×D4—1182no—
586C2×D4—2361no—
587C2×D4—2361no—
588C2×D4—2361no—
589C2×D4—2361no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—591no—
595C22×C4—591no—
596C22×C4—591no—
597C22×C4—591no—
598C22×C4—591no—
599C22×C4—1182no—
600C22×C4—1182no—
601C22×C4—1182no—
602C22×C4—1181no—
603C22×C4—1181no—
604C22×C4—1181no—
605C22×C4—1181no—
606C22×C4—1181no—
607C22×C4—1181no—
608C22×C4—1181no—
609C22×C4—1181no—
610C22×C4—1181no—
611C22×C4—1181no—
612C22×C4—1181no—
613C22×C4—1181no—
614C22×C4—1181no—
615C22×C4—1181no—
616C22×C4—1181no—
617C22×C4—1181no—
618C22×C4—1181no—
619C22×C4—1181no—
620C22×C4—2361no—
621C22×C4—2361no—
622C22×C4—2361no—
623C22×C4—2361no—
624C22×C4—2364no—
625C22×C4—2364no—
626C22×C4—2364no—
627C22×C4—2364no—
628C22×C4—2361no—
629C22×C4—2361no—
630C22×C4C2×C4×D5911yescharacteristic
631C22×C4C2×C4×D5911yescharacteristic
632C22×C4C2×C4×D5911yescharacteristic
633C22×C4C2×C4×D5911yescharacteristic
634C22×C4C2×C4×D5911yescharacteristic
635C22×C4D4×D5912yes—
636C22×C4#1174568912yes—
637C22×C4C23×D5911yescharacteristic
638M16—44no—
639M16—2364no—
640M16—2364no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—592no—
654C2×C8—592no—
655C2×C8—1181no—
656C2×C8—1181no—
657C2×C8—1181no—
658C2×C8—1181no—
659C2×C8—1181no—
660C2×C8—1181no—
661C2×C8—1181no—
662C2×C8—1181no—
663C2×C8—1181no—
664C2×C8—1181no—
665C4⋊C4—1182no—
666C4⋊C4—2361no—
667C4⋊C4—2361no—
668C22⋊C4—22no—
669C22⋊C4—41no—
670C22⋊C4—594no—
671C22⋊C4—1182no—
672C22⋊C4—1182no—
673C22⋊C4—1182no—
674C22⋊C4—1182no—
675C22⋊C4—2361no—
676C22⋊C4—2361no—
677C22⋊C4—2361no—
678C22⋊C4—2361no—
679C22⋊C4—2361no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—1181no—
685C42—1181no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—592no—
693C23—592no—
694C23—1181no—
695C23—1181no—
696C23—1181no—
697C23—1181no—
698C23—1181no—
699C23—1181no—
700C23—1181no—
701C23—1181no—
702C23—1181no—
703C23—1181no—
704C23—1181no—
705C23—1181no—
706C23—1181no—
707C23—1181no—
708C23—1181no—
709C23—1181no—
710C23—1181no—
711C23—1181no—
712C23—1181no—
713C23—2364no—
714C23—2364no—
715C23—2364no—
716C23—2364no—
717C23—2364no—
718C23—2364no—
719C23—2364no—
720C23#1427368912yes—
721C23C22×C4×D5911yescharacteristic
722D4—2364no—
723D4—2364no—
724D4—2364no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—592no—
743C2×C4—1181no—
744C2×C4—1181no—
745C2×C4—1181no—
746C2×C4—1181no—
747C2×C4—1181no—
748C2×C4—1181no—
749C2×C4—1181no—
750C2×C4—1181no—
751C2×C4—1181no—
752C2×C4—1181no—
753C2×C4—1181no—
754C2×C4—1181no—
755C2×C4—1181no—
756C2×C4—1181no—
757C2×C4—2364no—
758C2×C4—2364no—
759C2×C4—2364no—
760C2×C4—2361no—
761C2×C4—2361no—
762C2×C4—2361no—
763C2×C4—2361no—
764C2×C4—2361no—
765C2×C4—2361no—
766C2×C4—2361no—
767C2×C4—2361no—
768C2×C4—2361no—
769C2×C4—2361no—
770C2×C4—2361no—
771C2×C4—2361no—
772C2×C4#1427368912yes—
773C2×C4M16×D5912yes—
774C2×C4C2×D4×D5911yescharacteristic
775C2×C4C2×#1174568911yescharacteristic
776C2×C4#1427377211yescharacteristic
777C2×C4#1427377211yescharacteristic
778C2×C4#1427377311yescharacteristic
779C2×C4#1427377311yescharacteristic
780C8—41no—
781C8—41no—
782C8—41no—
783C8—41no—
784C8—1182no—
785C8—1182no—
786C8—2361no—
787C8—2361no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—1182no—
796C22—1182no—
797C22—1182no—
798C22—1182no—
799C22—1182no—
800C22—1182no—
801C22—23616no—
802C22—2361no—
803C22—2361no—
804C22—2361no—
805C22—2361no—
806C22—2361no—
807C22—2361no—
808C22—2361no—
809C22—2361no—
810C22—2361no—
811C22—2361no—
812C22—2361no—
813C22—2361no—
814C22—2361no—
815C22—2361no—
816C22—2361no—
817C22C2×#1427368911yescharacteristic
818C22#1683787411yescharacteristic
819C22#1683787411yescharacteristic
820C22C2×M16×D5911yescharacteristic
821C22#131×D5911yescharacteristic
822C22#1683816711yescharacteristic
823C22#1683816811yescharacteristic
824C4—22no—
825C4—22no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—1182no—
830C4—2361no—
831C4—2361no—
832C4—2361no—
833C4—2361no—
834C4#1683796311yescharacteristic
835C4#1683796711yescharacteristic
836C4#1683799211yescharacteristic
837C4#1683799211yescharacteristic
838C2—42no—
839C2—4721no—
840C2—2362no—
841C2—2362no—
842C2#2142675311yescharacteristic
843C2#2143282011yescharacteristic
844C2#2143283111yescharacteristic
845C2#2143312611yescharacteristic
846C2#2143313411yescharacteristic
847C2#2143314311yescharacteristic
848C2#2143315311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D59
commutator, socleC23×C59C23×C4
FittingC59×#1851C2
prime radicalC2×#14273697C4
cosocleC22×C4×C59C24
hypercenter#1851D59
hypocenterC59#22038
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
1. C2×#16837477C2semidirect
2. C2×#16837365C2semidirect
4. #21424893C2semidirect
5. #21424889C2semidirect
6. #21424707C2semidirect
7. #21424701C2semidirect
8. #21424701C2semidirect
9. #21424700C2semidirect
10. #21424393C2semidirect
11. #21424392C2semidirect
12. #21424392C2semidirect
13. #21424005C2semidirect
14. #21423880C2semidirect
15. C59×#1851C2semidirect
18. C22×#11745659C22semidirect
24. C2×Dic59⋊C8C22semidirect
35. C2×(C2×D59)⋊C8C22semidirect
36. C2×(C2×D59)⋊C8C22semidirect
37. C2×(C2×D59)⋊C8C22semidirect
38. C2×#14273638C22semidirect
39. C2×C4×C59⋊C8C22semidirect
40. C2×C8×Dic59C22semidirect
50. #16837157C22semidirect
51. #16837157C22semidirect
52. #16837156C22semidirect
53. #16837156C22semidirect
55. C2×C4⋊C8×C59C22semidirect
56. C2×C4⋊C8×C59C22semidirect
59. C59×#336C22semidirect
60. C59×#336C22semidirect
79. C2×#11745664D4semidirect
241. (C2×D59)⋊C4M16semidirect
426. #1851D59semidirect
450. C2×C4⋊C8C2×D59semidirect
451. C2×C4⋊C8C2×D59semidirect
483. #336C2×D59semidirect
484. #336C2×D59semidirect
485. C59#22038semidirect

Maximal subgroups

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

subgroupindex
C2×#168374772
C2×#168373652
C4×#142736972
#214248932
#214248892
#214247072
#214247012
#214247002
#214243932
#214243922
#214240052
#214238802
C59×#18512
#2203859