Finite Group Databasebeta

← #28626325

Subgroups — #28626325

Order 15104.

1508 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837633C211yesmaximal, characteristic, complemented
2C2×#16837541C211yesmaximal, characteristic, complemented
3C2×#16837541C211yesmaximal, characteristic, complemented
4C22×#14273651C211yesmaximal, characteristic, complemented
5#21427536C211yesmaximal, characteristic
6#21425339C211yesmaximal, characteristic, complemented
7#21425289C211yesmaximal, characteristic, complemented
8#21425179C211yesmaximal, characteristic, complemented
9#21425097C211yesmaximal, characteristic, complemented
10#21424451C211yesmaximal, characteristic, complemented
11#21424404C211yesmaximal, characteristic, complemented
12#21424389C211yesmaximal, characteristic, complemented
13#21424364C211yesmaximal, characteristic, complemented
14#21424031C211yesmaximal, characteristic, complemented
15C2×D4×Q8×C59C211yesmaximal, characteristic, complemented
16C22×#11745671C2211yescharacteristic
17C22×#11745671C2211yescharacteristic
18C22×#11745671C2211yescharacteristic
19C23×C59⋊C8C2211yescharacteristic
20C2×#14273701C2211yescharacteristic
21C2×#14273701C2211yescharacteristic
22C2×#14273699—21no—
23C22×C4⋊Dic59C2211yescharacteristic
24#16837633—24no—
25#16837541—24no—
26#16837541—24no—
27C2×#14273658C2211yescharacteristic
28C2×#14273651—24no—
29C2×#14273651C2211yescharacteristic
30C2×#14273651C2211yescharacteristic
31C2×#14273651C2211yescharacteristic
32C2×#14273651C2211yescharacteristic
33C2×#14273651C2211yescharacteristic
34C2×#14273651C2211yescharacteristic
35C2×#14273651C2211yescharacteristic
36C2×#14273651C2211yescharacteristic
37C2×#14273651C2211yescharacteristic
38C2×#14273647C2211yescharacteristic
39C2×C22⋊(C59⋊C8)C2211yescharacteristic
40C2×C22⋊(C59⋊C8)C2211yescharacteristic
41C2×C22⋊(C59⋊C8)C2211yescharacteristic
42#16837324—21no—
43#16837318—21no—
44#16837304C2211yescharacteristic
45#16837300C2211yescharacteristic
46#16837279—21no—
47#16837262C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837157C2211yescharacteristic
51#16837157C2211yescharacteristic
52C23×Q8×C59C2211yescharacteristic
53C23×Q8×C59C2211yescharacteristic
54D4×Q8×C59—24no—
55D4×Q8×C59—24no—
56C2×C4⋊Q8×C59—21no—
57C2×C4⋊Q8×C59C2211yescharacteristic
58C2×C22⋊Q8×C59—21no—
59C2×C22⋊Q8×C59—21no—
60C2×C22⋊Q8×C59C2211yescharacteristic
61C2×C22⋊Q8×C59C2211yescharacteristic
62C2×C4×Q8×C59C2211yescharacteristic
63C2×C4×D4×C59—21no—
64C2×C4×D4×C59C2211yescharacteristic
65C22×D236C2311yescharacteristic
66C22×C22⋊D59—21no—
67C22×C22⋊D59—21no—
68C23×Dic59—21no—
69C2×#11745671—22no—
70C2×#11745671—22no—
71C2×#11745671—22no—
72C2×#11745671—22no—
73C2×#11745671—22no—
74C2×#11745671—22no—
75C2×#11745671—41no—
76C2×#11745671—41no—
77C2×#11745671—41no—
78C22×C59⋊C8—22no—
79C22×C59⋊C8—22no—
80C22×C59⋊C8—41no—
81C22×C59⋊C8C2311yescharacteristic
82C22×C59⋊C8C2311yescharacteristic
83C22×C59⋊C8C2311yescharacteristic
84C22×C59⋊C8C2311yescharacteristic
85#14273701—22no—
86#14273701—22no—
87#14273701—22no—
88#14273701—41no—
89#14273699—44no—
90C2×C4⋊Dic59—22no—
91C2×C4⋊Dic59—21no—
92C2×C4⋊Dic59—41no—
93C2×C4⋊Dic59C2311yescharacteristic
94C2×C4⋊Dic59C2311yescharacteristic
95C2×C4⋊Dic59C2311yescharacteristic
96C2×Dic59⋊C4—21no—
97C2×C22⋊Dic59—21no—
98C2×(C2×D59)⋊C4—21no—
99C2×(C2×D59)⋊C4—21no—
100C2×(C2×D59)⋊C4—21no—
101C2×(C2×D59)⋊C4—21no—
102#14273658—22no—
103#14273651—22no—
104#14273651—22no—
105#14273651—22no—
106#14273651—22no—
107#14273651—22no—
108#14273651—22no—
109#14273651—22no—
110#14273651—41no—
111#14273651D414yescomplemented
112#14273647—22no—
113C22⋊(C59⋊C8)—22no—
114C22⋊(C59⋊C8)—22no—
115C22⋊(C59⋊C8)—41no—
116C59⋊#95—21no—
117C59⋊#95—21no—
118C22×Q8×C59—22no—
119C22×Q8×C59—22no—
120C22×Q8×C59—21no—
121C22×Q8×C59—21no—
122C22×Q8×C59—22no—
123C22×Q8×C59—22no—
124C22×Q8×C59—22no—
125C22×Q8×C59—22no—
126C22×Q8×C59—22no—
127C22×Q8×C59—41no—
128C22×Q8×C59—41no—
129C22×Q8×C59—41no—
130C22×Q8×C59—41no—
131C22×Q8×C59D414yescomplemented
132C22×Q8×C59C2311yescharacteristic
133C22×Q8×C59C2311yescharacteristic
134C22×Q8×C59C2311yescharacteristic
135C22×D4×C59D411yescharacteristic
136C23×C4×C59—21no—
137C23×C4×C59—21no—
138C23×C4×C59C2311yescharacteristic
139C23×C4×C59C2311yescharacteristic
140C4⋊Q8×C59—28no—
141C4⋊Q8×C59—22no—
142C4⋊Q8×C59—22no—
143C22⋊Q8×C59—28no—
144C22⋊Q8×C59—28no—
145C22⋊Q8×C59—22no—
146C22⋊Q8×C59—22no—
147C22⋊Q8×C59—22no—
148C22⋊Q8×C59D414yescomplemented
149C4×Q8×C59—22no—
150C4×Q8×C59—22no—
151C4×D4×C59—28no—
152C4×D4×C59—22no—
153C4×D4×C59—22no—
154C2×C4⋊C4×C59—21no—
155C2×C4⋊C4×C59—21no—
156C2×C4⋊C4×C59—21no—
157C2×C4⋊C4×C59—21no—
158C2×C4⋊C4×C59—21no—
159C2×C4⋊C4×C59D411yescharacteristic
160C2×C4⋊C4×C59C2311yescharacteristic
161C2×C22⋊C4×C59—21no—
162C2×C22⋊C4×C59—21no—
163C2×C22⋊C4×C59D411yescharacteristic
164C2×C22⋊C4×C59D411yescharacteristic
165C2×C42×C59—21no—
166C2×C42×C59C2311yescharacteristic
167C24×C59C2×D411yescharacteristic
168C24×C59C2×D411yescharacteristic
169C23×D59—21no—
170C2×Q8×C59—24no—
171C2×Q8×C59—24no—
172C2×Q8×C59—21no—
173C2×Q8×C59—21no—
174C2×Q8×C59—21no—
175C2×Q8×C59—21no—
176C2×Q8×C59—21no—
177C2×Q8×C59—28no—
178C2×Q8×C59—21no—
179C2×Q8×C59—21no—
180C2×Q8×C59—21no—
181C2×Q8×C59—21no—
182C2×Q8×C59—21no—
183C2×Q8×C59—21no—
184C2×Q8×C59—21no—
185C2×Q8×C59—21no—
186C2×Q8×C59—42no—
187C2×Q8×C59—42no—
188C2×Q8×C59—42no—
189C2×Q8×C59—42no—
190C2×Q8×C59—44no—
191C2×Q8×C59—44no—
192C2×Q8×C59—44no—
193C2×Q8×C59—44no—
194C2×Q8×C59—44no—
195C2×Q8×C59—44no—
196C2×Q8×C59—44no—
197C2×Q8×C59C2×D412yes—
198C2×Q8×C59C2×D412yes—
199C2×Q8×C59C2×D412yes—
200C2×Q8×C59C2×D412yes—
201C2×Q8×C59#4112yes—
202C2×D4×C59—22no—
203C2×D4×C59—22no—
204C2×D4×C59SD1614yescomplemented
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59—24no—
211C22×C4×C59—24no—
212C22×C4×C59—21no—
213C22×C4×C59—21no—
214C22×C4×C59—21no—
215C22×C4×C59—21no—
216C22×C4×C59—21no—
217C22×C4×C59—21no—
218C22×C4×C59—21no—
219C22×C4×C59—21no—
220C22×C4×C59—21no—
221C22×C4×C59—42no—
222C22×C4×C59—42no—
223C22×C4×C59—42no—
224C22×C4×C59—42no—
225C22×C4×C59C2×D411yescharacteristic
226C22×C4×C59C2×D411yescharacteristic
227C22×C4×C59C2×D411yescharacteristic
228C22×C4×C59C2×D412yes—
229C22×C4×C59C2×D412yes—
230C22×C4×C59C2×D411yescharacteristic
231C22×C4×C59C2411yescharacteristic
232C2×C22⋊D59—42no—
233C2×C22⋊D59—42no—
234C2×C22⋊D59—42no—
235C2×C22⋊D59—42no—
236C2×C22⋊D59—42no—
237C2×C22⋊D59—81no—
238C22×Dic59—21no—
239C22×Dic59—21no—
240C22×Dic59—21no—
241C22×Dic59—42no—
242C22×Dic59—42no—
243C22×Dic59—81no—
244C2×D236—21no—
245C2×D236—21no—
246C2×D236—21no—
247C2×D236—21no—
248C2×D236—21no—
249C2×D236—21no—
250C4⋊C4×C59—24no—
251C4⋊C4×C59—24no—
252C4⋊C4×C59—24no—
253C4⋊C4×C59—24no—
254C4⋊C4×C59—24no—
255C4⋊C4×C59—22no—
256C4⋊C4×C59—21no—
257C4⋊C4×C59C2×D412yes—
258C22⋊C4×C59—24no—
259C22⋊C4×C59—24no—
260C22⋊C4×C59—22no—
261C22⋊C4×C59—22no—
262C42×C59—24no—
263C42×C59—21no—
264C42×C59—21no—
265C22⋊Dic59—42no—
266#11745671—44no—
267#11745671—44no—
268#11745671—44no—
269(C2×D59)⋊C4—42no—
270(C2×D59)⋊C4—42no—
271(C2×D59)⋊C4—42no—
272(C2×D59)⋊C4—81no—
273C4⋊Dic59—21no—
274C4⋊Dic59—21no—
275C4⋊Dic59—21no—
276C4⋊Dic59—21no—
277C4⋊Dic59—21no—
278C4⋊Dic59—42no—
279C4⋊Dic59C2×D412yes—
280Dic59⋊C4—42no—
281C2×C59⋊C8—21no—
282C2×C59⋊C8—21no—
283C2×C59⋊C8—21no—
284C2×C59⋊C8—21no—
285C2×C59⋊C8—21no—
286C2×C59⋊C8—21no—
287C2×C59⋊C8—21no—
288C2×C59⋊C8—21no—
289C2×C59⋊C8—21no—
290C2×C59⋊C8—21no—
291C2×C59⋊C8—21no—
292C2×C59⋊C8—44no—
293C2×C59⋊C8C2×D412yes—
294C23×C59—21no—
295C23×C59—21no—
296C23×C59—21no—
297C23×C59—21no—
298C23×C59—21no—
299C23×C59—21no—
300C23×C59—21no—
301C23×C59—21no—
302C23×C59—21no—
303C23×C59—21no—
304C23×C59#12012yes—
305C23×C59C2×SD1612yes—
306C23×C59C2×SD1612yes—
307C23×C59#13712yes—
308C23×C59C22×D411yescharacteristic
309C22×D59—41no—
310C22×D59—41no—
311C22×D59—41no—
312C22×D59—41no—
313C22×D59—41no—
314C22×D59—41no—
315C22×D59—41no—
316Q8×C59—22no—
317Q8×C59—22no—
318Q8×C59—22no—
319Q8×C59—22no—
320Q8×C59—22no—
321Q8×C59—22no—
322Q8×C59—22no—
323Q8×C59—48no—
324Q8×C59—48no—
325Q8×C59—41no—
326Q8×C59—41no—
327Q8×C59—41no—
328Q8×C59—41no—
329Q8×C59#12114yescomplemented
330D4×C59—28no—
331C2×C4×C59—21no—
332C2×C4×C59—22no—
333C2×C4×C59—21no—
334C2×C4×C59—22no—
335C2×C4×C59—21no—
336C2×C4×C59—22no—
337C2×C4×C59—21no—
338C2×C4×C59—22no—
339C2×C4×C59—22no—
340C2×C4×C59—22no—
341C2×C4×C59—22no—
342C2×C4×C59—21no—
343C2×C4×C59—22no—
344C2×C4×C59—22no—
345C2×C4×C59—22no—
346C2×C4×C59—21no—
347C2×C4×C59—21no—
348C2×C4×C59—21no—
349C2×C4×C59—21no—
350C2×C4×C59—21no—
351C2×C4×C59—48no—
352C2×C4×C59—48no—
353C2×C4×C59—41no—
354C2×C4×C59—41no—
355C2×C4×C59—41no—
356C2×C4×C59—41no—
357C2×C4×C59—41no—
358C2×C4×C59—41no—
359C2×C4×C59—41no—
360C2×C4×C59—41no—
361C2×C4×C59—41no—
362C2×C4×C59—41no—
363C2×C4×C59#12012yes—
364C2×C4×C59C2×SD1612yes—
365C2×C4×C59C22×D411yescharacteristic
366C2×C4×C59C22×D411yescharacteristic
367C2×C4×C59C22×D411yescharacteristic
368C2×C4×C59C2×#4111yescharacteristic
369C2×C4×C59H(5,𝔽2)11yescharacteristic
370C2×C4×C59H(5,𝔽2)11yescharacteristic
371C22⋊D59—84no—
372C22⋊D59—84no—
373C2×Dic59—22no—
374C2×Dic59—41no—
375C2×Dic59—41no—
376C2×Dic59—41no—
377C2×Dic59—41no—
378C2×Dic59—41no—
379C2×Dic59—41no—
380C2×Dic59—41no—
381C2×Dic59—41no—
382C2×Dic59—84no—
383D236—41no—
384D236—41no—
385D236—41no—
386D236—41no—
387C59⋊C8—22no—
388C59⋊C8—41no—
389C59⋊C8—41no—
390C59⋊C8—41no—
391#24429—591nomaximal, Sylow
392C22×C59—22no—
393C22×C59—22no—
394C22×C59—22no—
395C22×C59—22no—
396C22×C59—22no—
397C22×C59—22no—
398C22×C59—22no—
399C22×C59—22no—
400C22×C59—22no—
401C22×C59—41no—
402C22×C59—41no—
403C22×C59—41no—
404C22×C59—41no—
405C22×C59#44814yescomplemented
406C22×C59C2×#12011yescharacteristic
407C22×C59D4211yescharacteristic
408C22×C59#54611yescharacteristic
409C22×C59C22×SD1611yescharacteristic
410C22×C59C2×#13711yescharacteristic
411C22×C59#57711yescharacteristic
412C22×C59#57811yescharacteristic
413C2×D59—81no—
414C2×D59—81no—
415C2×D59—81no—
416C2×D59—81no—
417C2×D59—81no—
418C2×D59—81no—
419C2×D59—81no—
420C4×C59—22no—
421C4×C59—24no—
422C4×C59—22no—
423C4×C59—41no—
424C4×C59—42no—
425C4×C59—42no—
426C4×C59—41no—
427C4×C59—42no—
428C4×C59C2×#12111yescharacteristic
429C4×C59#53411yescharacteristic
430C4×C59D4211yescharacteristic
431C4×C59#54611yescharacteristic
432Dic59—42no—
433Dic59—81no—
434Dic59—81no—
435C2×D4×Q8D5911yescharacteristic, complemented
436C2×#465—591no—
437C2×#448—591no—
438C2×#448—591no—
439C22×#103—591no—
440#2416—591no—
441#2043—591no—
442#2035—591no—
443#2013—591no—
444#2000—591no—
445#1880—591no—
446#1872—591no—
447#1869—591no—
448#1865—591no—
449#1787—591no—
450C2×C59—24no—
451C2×C59—42no—
452C2×C59#241011yescharacteristic
453C2×C59C2×#44811yescharacteristic
454C2×C59#301311yescharacteristic
455C2×C59#327011yescharacteristic
456C2×C59D4×SD1611yescharacteristic
457C2×C59#329811yescharacteristic
458C2×C59#332011yescharacteristic
459D59—161no—
460C23×Q8C2×D5911yescharacteristic
461C23×Q8C2×D5911yescharacteristic
462C22×SD16—591no—
463C22×SD16—591no—
464C22×SD16—591no—
465C23×C8—591no—
466D4×Q8—24no—
467D4×Q8—24no—
468C2×C4⋊Q8—21no—
469C2×C4⋊Q8C2×D5911yescharacteristic
470C2×C22⋊Q8—21no—
471C2×C22⋊Q8—21no—
472C2×C22⋊Q8C2×D5911yescharacteristic
473C2×C22⋊Q8C2×D5911yescharacteristic
474C2×#121—591no—
475C2×#121—591no—
476C2×#121—1181no—
477C2×C4×Q8C2×D5911yescharacteristic
478C2×C4×D4—21no—
479C2×C4×D4C2×D5911yescharacteristic
480C22×C4⋊C4—591no—
481#465—1184no—
482#448—1184no—
483#448—1184no—
484C2×#106—591no—
485C2×#103—591no—
486C2×#103—591no—
487C2×#103—591no—
488C2×#103—591no—
489C2×#103—591no—
490C2×#103—591no—
491C2×#103—591no—
492C2×#103—591no—
493C2×#103—591no—
494C2×#103—1184no—
495C2×#102—591no—
496C2×C22⋊C8—591no—
497C2×C22⋊C8—591no—
498C2×C22⋊C8—591no—
499#396—1181no—
500#394—1181no—
501#390—591no—
502#389—591no—
503#386—1181no—
504#380—591no—
505#340—591no—
506#340—591no—
507#336—591no—
508#336—591no—
509C59#2442911yescharacteristic, complemented, Sylow
510C22×Q8—22no—
511C22×Q8—22no—
512C22×Q8—21no—
513C22×Q8—21no—
514C22×Q8—22no—
515C22×Q8—22no—
516C22×Q8—22no—
517C22×Q8—22no—
518C22×Q8—22no—
519C22×Q8—41no—
520C22×Q8—41no—
521C22×Q8—41no—
522C22×Q8—41no—
523C22×Q8C22⋊D5914yescomplemented
524C22×Q8C22×D5911yescharacteristic
525C22×Q8C22×D5911yescharacteristic
526C22×Q8C22×D5911yescharacteristic
527C22×D4—591no—
528C22×D4—1181no—
529C22×D4—1181no—
530C22×D4C22⋊D5911yescharacteristic
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—1181no—
534C23×C4C22×D5911yescharacteristic
535C23×C4C22×D5911yescharacteristic
536C2×SD16—1182no—
537C2×SD16—1182no—
538C2×SD16—1182no—
539C2×SD16—1182no—
540C2×SD16—1182no—
541C2×SD16—1182no—
542C2×SD16—2361no—
543C2×SD16—2361no—
544C2×SD16—2361no—
545C22×C8—591no—
546C22×C8—591no—
547C22×C8—591no—
548C22×C8—591no—
549C22×C8—1182no—
550C22×C8—1182no—
551C22×C8—2361no—
552C4⋊Q8—28no—
553C4⋊Q8—22no—
554C4⋊Q8—22no—
555C22⋊Q8—28no—
556C22⋊Q8—28no—
557C22⋊Q8—22no—
558C22⋊Q8—22no—
559C22⋊Q8—22no—
560C22⋊Q8C22⋊D5914yescomplemented
561#121—1182no—
562#121—1182no—
563#121—1182no—
564#121—2361no—
565#121—2364no—
566C4×Q8—22no—
567C4×Q8—22no—
568C4×D4—28no—
569C4×D4—22no—
570C4×D4—22no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—591no—
577C2×C4⋊C4—591no—
578C2×C4⋊C4—591no—
579C2×C4⋊C4—1182no—
580C2×C4⋊C4—1181no—
581C2×C4⋊C4—1181no—
582C2×C4⋊C4—2361no—
583C2×C4⋊C4C22⋊D5911yescharacteristic
584C2×C4⋊C4C22×D5911yescharacteristic
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—1181no—
588C2×C22⋊C4—1181no—
589C2×C22⋊C4—1181no—
590C2×C22⋊C4—1181no—
591C2×C22⋊C4—1181no—
592C2×C22⋊C4C22⋊D5911yescharacteristic
593C2×C22⋊C4C22⋊D5911yescharacteristic
594C2×C42—21no—
595C2×C42C22×D5911yescharacteristic
596#106—1182no—
597#103—594no—
598#103—1182no—
599#103—1182no—
600#103—1182no—
601#103—1182no—
602#103—1182no—
603#103—1182no—
604#103—1182no—
605#103—2361no—
606#102—1182no—
607C22⋊C8—1182no—
608C22⋊C8—1182no—
609C22⋊C8—2361no—
610#95—1181no—
611#95—1181no—
612C24—1181no—
613C24C2×C22⋊D5911yescharacteristic
614C24C2×C22⋊D5911yescharacteristic
615C2×Q8—24no—
616C2×Q8—24no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—28no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—42no—
632C2×Q8—42no—
633C2×Q8—42no—
634C2×Q8—42no—
635C2×Q8—44no—
636C2×Q8—44no—
637C2×Q8—44no—
638C2×Q8—44no—
639C2×Q8—44no—
640C2×Q8—44no—
641C2×Q8—44no—
642C2×Q8D4×D5912yes—
643C2×Q8#1174568712yes—
644C2×Q8C2×C22⋊D5912yes—
645C2×Q8C2×C22⋊D5912yes—
646C2×Q8C2×C22⋊D5912yes—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—1181no—
650C2×D4—1181no—
651C2×D4—1181no—
652C2×D4—1181no—
653C2×D4—1181no—
654C2×D4—1181no—
655C2×D4—4721no—
656C2×D4—2362no—
657C2×D4—2362no—
658C2×D4—2362no—
659C2×D4—2362no—
660C2×D4—2362no—
661C2×D4#1174567114yescomplemented
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—24no—
668C22×C4—24no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—1181no—
683C22×C4—1181no—
684C22×C4—1181no—
685C22×C4—4721no—
686C22×C4—2362no—
687C22×C4—2362no—
688C22×C4C2×C22⋊D5911yescharacteristic
689C22×C4C2×C22⋊D5911yescharacteristic
690C22×C4C2×C22⋊D5911yescharacteristic
691C22×C4C2×C22⋊D5912yes—
692C22×C4C2×C22⋊D5912yes—
693C22×C4C2×C22⋊D5911yescharacteristic
694C22×C4C23×D5911yescharacteristic
695SD16—2364no—
696SD16—2364no—
697SD16—2364no—
698C2×C8—592no—
699C2×C8—1181no—
700C2×C8—1181no—
701C2×C8—1181no—
702C2×C8—1181no—
703C2×C8—1181no—
704C2×C8—1181no—
705C2×C8—1181no—
706C2×C8—1181no—
707C2×C8—1181no—
708C2×C8—1181no—
709C2×C8—1181no—
710C2×C8—2364no—
711C4⋊C4—24no—
712C4⋊C4—24no—
713C4⋊C4—24no—
714C4⋊C4—24no—
715C4⋊C4—24no—
716C4⋊C4—22no—
717C4⋊C4—21no—
718C4⋊C4—592no—
719C4⋊C4—1181no—
720C4⋊C4—1181no—
721C4⋊C4—1181no—
722C4⋊C4—1181no—
723C4⋊C4—1181no—
724C4⋊C4—2362no—
725C4⋊C4—2362no—
726C4⋊C4C2×C22⋊D5912yes—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—4721no—
732C22⋊C4—2362no—
733C22⋊C4—2362no—
734C22⋊C4—2362no—
735C22⋊C4—2362no—
736C42—24no—
737C42—21no—
738C42—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—2361no—
750C23—2361no—
751C23—2361no—
752C23—2361no—
753C23—2361no—
754C23—2361no—
755C23—2361no—
756C23#1427369612yes—
757C23C2×#1174567112yes—
758C23C2×#1174567112yes—
759C23#1427375812yes—
760C23C22×C22⋊D5911yescharacteristic
761Q8—22no—
762Q8—22no—
763Q8—22no—
764Q8—22no—
765Q8—22no—
766Q8—22no—
767Q8—22no—
768Q8—48no—
769Q8—48no—
770Q8—41no—
771Q8—41no—
772Q8—41no—
773Q8—41no—
774Q8#1427369914yescomplemented
775D4—28no—
776D4—4724no—
777D4—4724no—
778D4—2361no—
779D4—2361no—
780D4—2361no—
781D4—2361no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—48no—
803C2×C4—48no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—1182no—
815C2×C4—4724no—
816C2×C4—2361no—
817C2×C4—2361no—
818C2×C4—2361no—
819C2×C4—2361no—
820C2×C4—2361no—
821C2×C4—2361no—
822C2×C4—2361no—
823C2×C4—2361no—
824C2×C4#1427369612yes—
825C2×C4C2×#1174567112yes—
826C2×C4C2×D4×D5911yescharacteristic
827C2×C4C22×C22⋊D5911yescharacteristic
828C2×C4C22×C22⋊D5911yescharacteristic
829C2×C4C2×#1174568711yescharacteristic
830C2×C4#1427377211yescharacteristic
831C2×C4#1427377211yescharacteristic
832C8—1182no—
833C8—2361no—
834C8—2361no—
835C8—2361no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—4721no—
850C22—4721no—
851C22—4721no—
852C22—4721no—
853C22—4721no—
854C22—4721no—
855C22—4721no—
856C22#1683754114yescomplemented
857C22C2×#1427369611yescharacteristic
858C22D4×C22⋊D5911yescharacteristic
859C22#1683804611yescharacteristic
860C22C22×#1174567111yescharacteristic
861C22C2×#1427375811yescharacteristic
862C22#1683821011yescharacteristic
863C22#1683821711yescharacteristic
864C4—22no—
865C4—24no—
866C4—22no—
867C4—41no—
868C4—42no—
869C4—42no—
870C4—41no—
871C4—42no—
872C4—4721no—
873C4—4721no—
874C4—2362no—
875C4C2×#1427369911yescharacteristic
876C4#1683796111yescharacteristic
877C4D4×C22⋊D5911yescharacteristic
878C4#1683804611yescharacteristic
879C2—24no—
880C2—42no—
881C2—9441no—
882C2#2142747011yescharacteristic
883C2C2×#1683754111yescharacteristic
884C2#2143341111yescharacteristic
885C2#2143566711yescharacteristic
886C2D4×#1174567111yescharacteristic
887C2#2143596111yescharacteristic
888C2#2143626711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×D4×Q8×C59C2
socleC23×C59C22×D4
prime radical#21427536C2
hypercenterC2×D4×Q8D59
hypocenterC59#24429
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#16837633C2semidirect
2. C2×#16837541C2semidirect
3. C2×#16837541C2semidirect
4. C22×#14273651C2semidirect
6. #21425339C2semidirect
7. #21425289C2semidirect
8. #21425179C2semidirect
9. #21425097C2semidirect
10. #21424451C2semidirect
11. #21424404C2semidirect
12. #21424389C2semidirect
13. #21424364C2semidirect
14. #21424031C2semidirect
15. C2×D4×Q8×C59C2semidirect
111. #14273651D4semidirect
131. C22×Q8×C59D4semidirect
148. C22⋊Q8×C59D4semidirect
204. C2×D4×C59SD16semidirect
329. Q8×C59#121semidirect
405. C22×C59#448semidirect
435. C2×D4×Q8D59semidirect
509. C59#24429semidirect
523. C22×Q8C22⋊D59semidirect
560. C22⋊Q8C22⋊D59semidirect
661. C2×D4#11745671semidirect
774. Q8#14273699semidirect
856. C22#16837541semidirect

Maximal subgroups

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

subgroupindex
C2×#168376332
C2×#168375412
C22×#142736512
#214275362
#214253392
#214252892
#214251792
#214250972
#214244512
#214244042
#214243892
#214243642
#214240312
C2×D4×Q8×C592
#2442959