Finite Group Databasebeta

← #28594776

Subgroups — #28594776

Order 15104.

1096 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837478C211yesmaximal, characteristic, complemented
2C2×#16837475C211yesmaximal, characteristic, complemented
3C2×#16837471C211yesmaximal, characteristic, complemented
4C4×#14273701C211yesmaximal, characteristic
5#21424894C211yesmaximal, characteristic, complemented
6#21424819C211yesmaximal, characteristic, complemented
7#21424702C211yesmaximal, characteristic, complemented
8#21424702C211yesmaximal, characteristic, complemented
9#21424393C211yesmaximal, characteristic, complemented
10#21424393C211yesmaximal, characteristic, complemented
11#21424076C211yesmaximal, characteristic, complemented
12#21423968C211yesmaximal, characteristic, complemented
13#21423879C211yesmaximal, characteristic, complemented
14C8×(C2×D59)⋊C4C211yesmaximal, characteristic, complemented
15C2×C4×M16×C59C211yesmaximal, characteristic, complemented
16C22×#11745659C2211yescharacteristic
17C22×C8×D59C2211yescharacteristic
18C2×#14273701C411yescharacteristic
19C2×C4×D236C2211yescharacteristic
20C2×C4×C22⋊D59C2211yescharacteristic
21C2×C4×C22⋊D59C2211yescharacteristic
22#16837478—24no—
23#16837475—24no—
24#16837471—24no—
25C2×C4⋊(C59⋊C8)C2211yescharacteristic
26C2×C4⋊(C59⋊C8)C2211yescharacteristic
27C2×Dic59⋊C8C2211yescharacteristic
28C2×Dic59⋊C8C2211yescharacteristic
29C2×C22⋊(C59⋊C8)C2211yescharacteristic
30C2×C22⋊(C59⋊C8)C2211yescharacteristic
31C2×(C2×D59)⋊C8C2211yescharacteristic
32C2×(C2×D59)⋊C8C2211yescharacteristic
33C2×(C2×D59)⋊C8C2211yescharacteristic
34C2×(C2×D59)⋊C8C2211yescharacteristic
35C2×(C2×D59)⋊C8C2211yescharacteristic
36C2×(C2×D59)⋊C8C2211yescharacteristic
37C2×#14273637C2211yescharacteristic
38C2×C8×Dic59C2211yescharacteristic
39#16837304C411yescharacteristic
40#16837300C411yescharacteristic
41#16837293C411yescharacteristic
42#16837293C411yescharacteristic
43#16837281C411yescharacteristic
44#16837281C411yescharacteristic
45#16837262C411yescharacteristic
46C4×C4⋊Dic59C2211yescharacteristic
47C4×(C2×D59)⋊C4C2211yescharacteristic
48C4×(C2×D59)⋊C4C2211yescharacteristic
49#16837157C2211yescharacteristic
50#16837157C2211yescharacteristic
51#16837156C2211yescharacteristic
52#16837156C2211yescharacteristic
53#16837156C2211yescharacteristic
54#16837156C2211yescharacteristic
55C22×M16×C59C2211yescharacteristic
56C22×M16×C59C2211yescharacteristic
57C22×C42×C59C2211yescharacteristic
58C4×M16×C59—24no—
59C2×#97×C59C2211yescharacteristic
60C2×#97×C59C2211yescharacteristic
61C2×C4×C8×C59C2211yescharacteristic
62C2×C4×C8×C59C2211yescharacteristic
63C22×D236C2×C411yescharacteristic
64C22×C22⋊D59C2×C411yescharacteristic
65C22×C22⋊D59C2×C411yescharacteristic
66C22×C4×D59C2311yescharacteristic
67C22×C4×D59C2311yescharacteristic
68C2×#11745659—22no—
69C2×#11745659—22no—
70C2×#11745659—22no—
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74C22×C59⋊C8C2311yescharacteristic
75C2×C8×D59—22no—
76C2×C8×D59—22no—
77C2×C8×D59—22no—
78#14273701—24no—
79C4×D236—22no—
80C4×D236—22no—
81C4×C22⋊D59—22no—
82C4×C22⋊D59—22no—
83C4×C22⋊D59—22no—
84C4×C22⋊D59—22no—
85C2×C4⋊Dic59C2×C411yescharacteristic
86C2×C4⋊Dic59C2×C411yescharacteristic
87C2×C4⋊Dic59C2×C411yescharacteristic
88C2×Dic59⋊C4C2×C411yescharacteristic
89C2×Dic59⋊C4C2×C411yescharacteristic
90C2×C22⋊Dic59C2×C411yescharacteristic
91C2×C22⋊Dic59C2×C411yescharacteristic
92C2×(C2×D59)⋊C4C2×C411yescharacteristic
93C2×(C2×D59)⋊C4C2×C411yescharacteristic
94C2×(C2×D59)⋊C4C2×C411yescharacteristic
95C2×(C2×D59)⋊C4C2×C411yescharacteristic
96C2×(C2×D59)⋊C4C2×C411yescharacteristic
97C2×(C2×D59)⋊C4C2×C411yescharacteristic
98C2×(C2×D59)⋊C4C2×C411yescharacteristic
99C2×(C2×D59)⋊C4C2×C411yescharacteristic
100C2×C4×Dic59C2311yescharacteristic
101C2×C4×Dic59C2311yescharacteristic
102C4⋊(C59⋊C8)—22no—
103C4⋊(C59⋊C8)—22no—
104Dic59⋊C8—22no—
105Dic59⋊C8—22no—
106C22⋊(C59⋊C8)—22no—
107C22⋊(C59⋊C8)—22no—
108(C2×D59)⋊C8—22no—
109(C2×D59)⋊C8—22no—
110(C2×D59)⋊C8—22no—
111(C2×D59)⋊C8—22no—
112(C2×D59)⋊C8—22no—
113(C2×D59)⋊C8—22no—
114#14273637—22no—
115C8×Dic59—22no—
116C59⋊#95C2×C411yescharacteristic
117C59⋊#95C2×C411yescharacteristic
118C59⋊#95C2×C411yescharacteristic
119C59⋊#95C2×C411yescharacteristic
120C59⋊#95C2×C411yescharacteristic
121C59⋊#95C2×C411yescharacteristic
122C23×C4×C59C2×C411yescharacteristic
123C23×C4×C59C2×C411yescharacteristic
124C23×C4×C59C2311yescharacteristic
125C2×M16×C59—22no—
126C2×M16×C59—22no—
127C2×M16×C59—22no—
128C2×M16×C59—22no—
129C2×M16×C59—22no—
130C2×M16×C59D414yescomplemented
131C22×C8×C59C2311yescharacteristic
132C22×C8×C59C2311yescharacteristic
133C22×C8×C59C2311yescharacteristic
134C22×C8×C59C2311yescharacteristic
135C2×C42×C59—22no—
136C2×C42×C59—22no—
137C2×C42×C59C2×C411yescharacteristic
138C2×C42×C59C2×C411yescharacteristic
139C2×C42×C59C2311yescharacteristic
140C2×C42×C59C2311yescharacteristic
141#97×C59—22no—
142#97×C59D414yescomplemented
143C4×C8×C59—22no—
144C4×C8×C59—22no—
145C24×C59C22×C411yescharacteristic
146C23×D59C22×C411yescharacteristic
147C23×D59C22×C411yescharacteristic
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—22no—
153C22×C4×C59—22no—
154C22×C4×C59—22no—
155C22×C4×C59—22no—
156C22×C4×C59—41no—
157C22×C4×C59—41no—
158C22×C4×C59C22×C411yescharacteristic
159C22×C4×C59C22×C411yescharacteristic
160C22×C4×C59C22×C411yescharacteristic
161C22×C4×C59C22×C411yescharacteristic
162C22×C4×C59C22×C411yescharacteristic
163C22×C4×C59C2×D412yes—
164C22×C4×C59#4112yes—
165C22×C4×C59C2411yescharacteristic
166C2×C22⋊D59—22no—
167C2×C22⋊D59—22no—
168C2×C22⋊D59—22no—
169C2×C22⋊D59—22no—
170C2×C22⋊D59—41no—
171C2×C22⋊D59—41no—
172C22×Dic59C22×C411yescharacteristic
173C22×Dic59C22×C411yescharacteristic
174C22×Dic59C22×C411yescharacteristic
175C22×Dic59C22×C411yescharacteristic
176C22×Dic59C22×C411yescharacteristic
177C22×Dic59C22×C411yescharacteristic
178C2×D236—22no—
179C2×D236—22no—
180C2×D236—41no—
181C2×C4×D59—21no—
182C2×C4×D59—21no—
183C2×C4×D59—21no—
184C2×C4×D59—21no—
185C2×C4×D59—21no—
186C2×C4×D59—21no—
187C2×C4×D59—21no—
188C2×C4×D59—21no—
189C2×C4×D59—21no—
190C2×C4×D59—21no—
191C2×C4×D59—21no—
192C2×C4×D59—21no—
193M16×C59—28no—
194M16×C59—28no—
195C2×C8×C59—21no—
196C2×C8×C59—21no—
197C2×C8×C59—21no—
198C2×C8×C59—21no—
199C2×C8×C59—21no—
200C2×C8×C59—21no—
201C2×C8×C59C2×D412yes—
202C2×C8×C59C2×D412yes—
203C2×C8×C59C2×D412yes—
204C2×C8×C59C2×D412yes—
205C2×C8×C59#4112yes—
206C2×C8×C59#4112yes—
207C42×C59—22no—
208C42×C59—22no—
209C42×C59—21no—
210C42×C59—21no—
211C42×C59C2×D412yes—
212C42×C59#4112yes—
213C22⋊Dic59—22no—
214C22⋊Dic59—22no—
215(C2×D59)⋊C4—22no—
216(C2×D59)⋊C4—22no—
217(C2×D59)⋊C4—22no—
218(C2×D59)⋊C4—22no—
219(C2×D59)⋊C4—22no—
220(C2×D59)⋊C4—22no—
221(C2×D59)⋊C4—22no—
222(C2×D59)⋊C4M1614yescomplemented
223C4⋊Dic59—22no—
224C4⋊Dic59—22no—
225C4⋊Dic59—41no—
226Dic59⋊C4—22no—
227Dic59⋊C4—22no—
228C4×Dic59—21no—
229C4×Dic59—21no—
230C4×Dic59—21no—
231C4×Dic59—21no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8—21no—
236C2×C59⋊C8—21no—
237C2×C59⋊C8—21no—
238C2×C59⋊C8—21no—
239C2×C59⋊C8—21no—
240C2×C59⋊C8—21no—
241C2×C59⋊C8—21no—
242C2×C59⋊C8—21no—
243C2×C59⋊C8—21no—
244#11745659—44no—
245C8×D59—44no—
246C23×C59—21no—
247C23×C59—21no—
248C23×C59—21no—
249C23×C59—21no—
250C23×C59—21no—
251C23×C59—21no—
252C23×C59C4×D412yes—
253C23×C59C23×C411yescharacteristic
254C22×D59—21no—
255C22×D59—21no—
256C22×D59—21no—
257C22×D59—21no—
258C22×D59—21no—
259C22×D59—21no—
260C22×D59—21no—
261C22×D59—21no—
262C22×D59—21no—
263C22×D59—21no—
264C22×D59—21no—
265C22×D59—21no—
266C22×D59—21no—
267C22×D59C2×M1612yes—
268C2×C4×C59—21no—
269C2×C4×C59—21no—
270C2×C4×C59—21no—
271C2×C4×C59—21no—
272C2×C4×C59—21no—
273C2×C4×C59—21no—
274C2×C4×C59—21no—
275C2×C4×C59—21no—
276C2×C4×C59—21no—
277C2×C4×C59—21no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—44no—
283C2×C4×C59—44no—
284C2×C4×C59C4×D412yes—
285C2×C4×C59C4×D412yes—
286C2×C4×C59C4×D412yes—
287C2×C4×C59C2×M1612yes—
288C2×C4×C59#13112yes—
289C2×C4×C59C22×D411yescharacteristic
290C2×C4×C59C22×D411yescharacteristic
291C2×C4×C59C2×#4111yescharacteristic
292C2×C4×C59C2×#4111yescharacteristic
293C2×C4×C59C2×#4111yescharacteristic
294C2×C4×C59C2×#4111yescharacteristic
295C22⋊D59—44no—
296C22⋊D59—44no—
297C2×Dic59—21no—
298C2×Dic59—21no—
299C2×Dic59—21no—
300C2×Dic59—21no—
301C2×Dic59—21no—
302C2×Dic59—21no—
303C2×Dic59—21no—
304C2×Dic59—21no—
305C2×Dic59—21no—
306C2×Dic59—21no—
307C2×Dic59—21no—
308C2×Dic59—21no—
309C2×Dic59—21no—
310C2×Dic59—21no—
311C2×Dic59—21no—
312C2×Dic59—21no—
313C2×Dic59—21no—
314C2×Dic59C2×M1612yes—
315D236—44no—
316C4×D59—41no—
317C4×D59—41no—
318C4×D59—41no—
319C4×D59—41no—
320C4×D59—41no—
321C4×D59—41no—
322C4×D59—41no—
323C4×D59—41no—
324C8×C59—22no—
325C8×C59—22no—
326C8×C59—22no—
327C8×C59#12114yescomplemented
328C59⋊C8—41no—
329C59⋊C8—41no—
330C59⋊C8—41no—
331C59⋊C8—41no—
332#21490—591nomaximal, Sylow
333C22×C59—22no—
334C22×C59—22no—
335C22×C59—22no—
336C22×C59—41no—
337C22×C59—41no—
338C22×C59—41no—
339C22×C59—41no—
340C22×C59C2×C4×D411yescharacteristic
341C22×C59C2×C4×D411yescharacteristic
342C22×C59C4×#4111yescharacteristic
343C22×C59C22×M1611yescharacteristic
344C22×C59C2×#13111yescharacteristic
345C22×C59#56811yescharacteristic
346C22×C59#56811yescharacteristic
347C2×D59—22no—
348C2×D59—22no—
349C2×D59—22no—
350C2×D59—41no—
351C2×D59—41no—
352C2×D59—41no—
353C2×D59—41no—
354C2×D59—41no—
355C2×D59—41no—
356C2×D59—41no—
357C2×D59—41no—
358C2×D59—41no—
359C2×D59—41no—
360C2×D59—41no—
361C4×C59—22no—
362C4×C59—22no—
363C4×C59—22no—
364C4×C59—22no—
365C4×C59—22no—
366C4×C59C2×#12111yescharacteristic
367C4×C59#52511yescharacteristic
368C4×C59#52911yescharacteristic
369C4×C59#53211yescharacteristic
370Dic59—22no—
371Dic59—41no—
372Dic59—41no—
373Dic59—41no—
374Dic59—41no—
375Dic59—41no—
376C2×#436—591no—
377C2×#435—591no—
378C2×#435—591no—
379C2×C4×M16D5911yescharacteristic, complemented
380C4×#121—591no—
381#1955—591no—
382#1940—591no—
383#1923—591no—
384#1923—591no—
385#1870—591no—
386#1870—591no—
387#1797—591no—
388#1771—591no—
389#1753—591no—
390C8×C22⋊C4—591no—
391C2×C59—42no—
392C2×C59C4×#12111yescharacteristic
393C2×C59#293311yescharacteristic
394C2×C59D4×M1611yescharacteristic
395C2×C59D4×M1611yescharacteristic
396C2×C59#293511yescharacteristic
397C2×C59#296511yescharacteristic
398C2×C59#296711yescharacteristic
399D59—42no—
400D59—81no—
401C22×M16—591no—
402C22×M16C2×D5911yescharacteristic
403C22×M16C2×D5911yescharacteristic
404C23×C8—591no—
405C2×#121—591no—
406C2×C4×D4—591no—
407C2×C4×D4—591no—
408C2×C4×D4—591no—
409C22×C42C2×D5911yescharacteristic
410#436—1184no—
411#435—1184no—
412#435—1184no—
413C2×C4⋊C8—591no—
414C2×C4⋊C8—591no—
415C2×C4⋊C8—591no—
416C2×C4⋊C8—591no—
417C2×C22⋊C8—591no—
418C2×C22⋊C8—591no—
419C2×C22⋊C8—591no—
420C2×C22⋊C8—591no—
421C2×C22⋊C8—591no—
422C2×C22⋊C8—591no—
423C2×C22⋊C8—591no—
424C2×C22⋊C8—591no—
425C4×M16—24no—
426C2×#97—591no—
427C2×#97C2×D5911yescharacteristic
428C2×#97C2×D5911yescharacteristic
429C2×C4×C8—591no—
430C2×C4×C8C2×D5911yescharacteristic
431C2×C4×C8C2×D5911yescharacteristic
432#390—591no—
433#389—591no—
434#388—591no—
435#388—591no—
436#386—591no—
437#386—591no—
438#380—591no—
439C4×C4⋊C4—591no—
440C4×C22⋊C4—591no—
441C4×C22⋊C4—591no—
442#336—591no—
443#336—591no—
444#336—591no—
445#336—591no—
446#336—591no—
447#336—591no—
448C59#2149011yescharacteristic, complemented, Sylow
449C22×D4—591no—
450C22×D4—591no—
451C22×D4—591no—
452C23×C4—591no—
453C23×C4—591no—
454C23×C4C4×D5911yescharacteristic
455C23×C4C4×D5911yescharacteristic
456C23×C4C22×D5911yescharacteristic
457C2×M16—22no—
458C2×M16—22no—
459C2×M16—22no—
460C2×M16—22no—
461C2×M16—22no—
462C2×M16—1182no—
463C2×M16—1182no—
464C2×M16—1182no—
465C2×M16D23614yescomplemented
466C22×C8—591no—
467C22×C8—591no—
468C22×C8—591no—
469C22×C8—591no—
470C22×C8—1182no—
471C22×C8—1182no—
472C22×C8—1182no—
473C22×C8C22×D5911yescharacteristic
474C22×C8C22×D5911yescharacteristic
475C22×C8C22×D5911yescharacteristic
476C22×C8C22×D5911yescharacteristic
477#121—1184no—
478C4×D4—1182no—
479C4×D4—1182no—
480C4×D4—1182no—
481C4×D4—1182no—
482C4×D4—1182no—
483C4×D4—1182no—
484C2×C4⋊C4—591no—
485C2×C4⋊C4—591no—
486C2×C4⋊C4—591no—
487C2×C4⋊C4—591no—
488C2×C4⋊C4—591no—
489C2×C22⋊C4—591no—
490C2×C22⋊C4—591no—
491C2×C22⋊C4—591no—
492C2×C22⋊C4—591no—
493C2×C22⋊C4—591no—
494C2×C22⋊C4—591no—
495C2×C22⋊C4—591no—
496C2×C22⋊C4—591no—
497C2×C22⋊C4—591no—
498C2×C22⋊C4—591no—
499C2×C42—22no—
500C2×C42—22no—
501C2×C42—591no—
502C2×C42—591no—
503C2×C42C4×D5911yescharacteristic
504C2×C42C4×D5911yescharacteristic
505C2×C42C22×D5911yescharacteristic
506C2×C42C22×D5911yescharacteristic
507C4⋊C8—1182no—
508C4⋊C8—1182no—
509C4⋊C8—1182no—
510C4⋊C8—1182no—
511C22⋊C8—1182no—
512C22⋊C8—1182no—
513C22⋊C8—1182no—
514C22⋊C8—1182no—
515C22⋊C8—1182no—
516C22⋊C8—1182no—
517C22⋊C8—1182no—
518C22⋊C8—1182no—
519#97—22no—
520#97—1182no—
521#97C22⋊D5914yescomplemented
522C4×C8—22no—
523C4×C8—22no—
524C4×C8—1182no—
525#95—591no—
526#95—591no—
527#95—591no—
528#95—591no—
529#95—591no—
530#95—591no—
531C24—591no—
532C24—591no—
533C24C2×C4×D5911yescharacteristic
534C2×D4—1182no—
535C2×D4—1182no—
536C2×D4—1182no—
537C2×D4—1182no—
538C2×D4—1182no—
539C2×D4—1182no—
540C2×D4—2361no—
541C2×D4—2361no—
542C2×D4—2361no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—591no—
554C22×C4—591no—
555C22×C4—591no—
556C22×C4—591no—
557C22×C4—591no—
558C22×C4—591no—
559C22×C4—1181no—
560C22×C4—1181no—
561C22×C4—1181no—
562C22×C4—1181no—
563C22×C4—1181no—
564C22×C4—1181no—
565C22×C4—1181no—
566C22×C4—1181no—
567C22×C4—1181no—
568C22×C4—1181no—
569C22×C4—1181no—
570C22×C4—1181no—
571C22×C4C2×C4×D5911yescharacteristic
572C22×C4C2×C4×D5911yescharacteristic
573C22×C4C2×C4×D5911yescharacteristic
574C22×C4C2×C4×D5911yescharacteristic
575C22×C4C2×C4×D5911yescharacteristic
576C22×C4C2×D23612yes—
577C22×C4#1174568512yes—
578C22×C4C23×D5911yescharacteristic
579M16—28no—
580M16—28no—
581M16—2364no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—1181no—
589C2×C8—1181no—
590C2×C8—1181no—
591C2×C8—1181no—
592C2×C8—1181no—
593C2×C8—1181no—
594C2×C8—1181no—
595C2×C8—1181no—
596C2×C8—1181no—
597C2×C8—1181no—
598C2×C8—1181no—
599C2×C8—1181no—
600C2×C8—2364no—
601C2×C8C2×D23612yes—
602C2×C8C2×D23612yes—
603C2×C8#1174568512yes—
604C2×C8#1174568512yes—
605C2×C8C2×C22⋊D5912yes—
606C2×C8C2×C22⋊D5912yes—
607C4⋊C4—1182no—
608C4⋊C4—1182no—
609C4⋊C4—1182no—
610C4⋊C4—1182no—
611C4⋊C4—2361no—
612C22⋊C4—594no—
613C22⋊C4—1182no—
614C22⋊C4—1182no—
615C22⋊C4—1182no—
616C22⋊C4—1182no—
617C22⋊C4—1182no—
618C22⋊C4—1182no—
619C22⋊C4—1182no—
620C22⋊C4—1182no—
621C22⋊C4—1182no—
622C42—22no—
623C42—22no—
624C42—21no—
625C42—21no—
626C42—1181no—
627C42—1181no—
628C42—1181no—
629C42—1181no—
630C42#1174568512yes—
631C42C2×C22⋊D5912yes—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—592no—
639C23—1181no—
640C23—1181no—
641C23—1181no—
642C23—1181no—
643C23—1181no—
644C23—1181no—
645C23—1181no—
646C23—1181no—
647C23—1181no—
648C23—1181no—
649C23—1181no—
650C23—1181no—
651C23—1181no—
652C23C4×D23612yes—
653C23C22×C4×D5911yescharacteristic
654D4—2364no—
655D4—2364no—
656D4—2364no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—592no—
674C2×C4—1181no—
675C2×C4—1181no—
676C2×C4—1181no—
677C2×C4—1181no—
678C2×C4—1181no—
679C2×C4—1181no—
680C2×C4—1181no—
681C2×C4—1181no—
682C2×C4—1181no—
683C2×C4—1181no—
684C2×C4—1181no—
685C2×C4—1181no—
686C2×C4—1181no—
687C2×C4—1181no—
688C2×C4—1181no—
689C2×C4—1181no—
690C2×C4—1181no—
691C2×C4—2361no—
692C2×C4—2361no—
693C2×C4—2361no—
694C2×C4—2361no—
695C2×C4—2361no—
696C2×C4—2361no—
697C2×C4—2361no—
698C2×C4—2361no—
699C2×C4C4×C22⋊D5912yes—
700C2×C4C4×C22⋊D5912yes—
701C2×C4C4×D23612yes—
702C2×C4M16×D5912yes—
703C2×C4#1427373512yes—
704C2×C4C22×C22⋊D5911yescharacteristic
705C2×C4C22×D23611yescharacteristic
706C2×C4C2×#1174568511yescharacteristic
707C2×C4C2×#1174568511yescharacteristic
708C2×C4C2×#1174568511yescharacteristic
709C2×C4C2×#1174568511yescharacteristic
710C8—22no—
711C8—22no—
712C8—22no—
713C8—2361no—
714C8—2361no—
715C8—2361no—
716C8—2361no—
717C8#1427370114yescomplemented
718C22—22no—
719C22—22no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—1182no—
726C22—1182no—
727C22—1182no—
728C22—2361no—
729C22—2361no—
730C22—2361no—
731C22—2361no—
732C22—2361no—
733C22—2361no—
734C22—2361no—
735C22—2361no—
736C22—2361no—
737C22—2361no—
738C22—2361no—
739C22C2×C4×C22⋊D5911yescharacteristic
740C22C2×C4×D23611yescharacteristic
741C22C4×#1174568511yescharacteristic
742C22C2×M16×D5911yescharacteristic
743C22C2×#1427373511yescharacteristic
744C22#1683816811yescharacteristic
745C22#1683816811yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—1182no—
752C4—2361no—
753C4—2361no—
754C4—2361no—
755C4—2361no—
756C4—2361no—
757C4C2×#1427370111yescharacteristic
758C4#1683791311yescharacteristic
759C4#1683793611yescharacteristic
760C4#1683795211yescharacteristic
761C2—42no—
762C2—4721no—
763C2—2362no—
764C2C4×#1427370111yescharacteristic
765C2#2143282111yescharacteristic
766C2M16×C22⋊D5911yescharacteristic
767C2M16×D23611yescharacteristic
768C2#2143284211yescharacteristic
769C2#2143305811yescharacteristic
770C2#2143308111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D59
commutator, socleC23×C59C23×C4
FittingC2×C4×M16×C59C2
prime radicalC2×#14273701C4
cosocleC22×C4×C59C24
hypercenterC2×C4×M16D59
hypocenterC59#21490
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×C4×M16

Complements

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

NH ≅ G/Ntype
1. C2×#16837478C2semidirect
2. C2×#16837475C2semidirect
3. C2×#16837471C2semidirect
5. #21424894C2semidirect
6. #21424819C2semidirect
7. #21424702C2semidirect
8. #21424702C2semidirect
9. #21424393C2semidirect
10. #21424393C2semidirect
11. #21424076C2semidirect
12. #21423968C2semidirect
13. #21423879C2semidirect
14. C8×(C2×D59)⋊C4C2semidirect
15. C2×C4×M16×C59C2semidirect
130. C2×M16×C59D4semidirect
142. #97×C59D4semidirect
222. (C2×D59)⋊C4M16semidirect
327. C8×C59#121semidirect
379. C2×C4×M16D59semidirect
448. C59#21490semidirect
465. C2×M16D236semidirect
521. #97C22⋊D59semidirect
717. C8#14273701semidirect

Maximal subgroups

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

subgroupindex
C2×#168374782
C2×#168374752
C2×#168374712
C4×#142737012
#214248942
#214248192
#214247022
#214243932
#214240762
#214239682
#214238792
C8×(C2×D59)⋊C42
C2×C4×M16×C592
#2149059