Finite Group Databasebeta

← #28626445

Subgroups — #28626445

Order 15104.

1438 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×#16837641C211yesmaximal, characteristic, complemented
2C2×#16837558C211yesmaximal, characteristic, complemented
3C2×#16837558C211yesmaximal, characteristic, complemented
4C22×#14273651C211yesmaximal, characteristic, complemented
5#21427547C211yesmaximal, characteristic
6#21425339C211yesmaximal, characteristic, complemented
7#21425296C211yesmaximal, characteristic, complemented
8#21425196C211yesmaximal, characteristic, complemented
9#21425104C211yesmaximal, characteristic, complemented
10#21424437C211yesmaximal, characteristic, complemented
11#21424404C211yesmaximal, characteristic, complemented
12#21424389C211yesmaximal, characteristic
13#21424350C211yesmaximal, characteristic, complemented
14#21424031C211yesmaximal, characteristic, complemented
15C2×D4×Q8×C59C211yesmaximal, characteristic
16C22×#11745672C2211yescharacteristic
17C22×#11745672C2211yescharacteristic
18C22×#11745672C2211yescharacteristic
19C23×C59⋊C8C2211yescharacteristic
20C2×#14273706C2211yescharacteristic
21C2×#14273706C2211yescharacteristic
22C22×C4⋊Dic59C2211yescharacteristic
23#16837641—24no—
24#16837558—24no—
25#16837558—24no—
26C2×#14273660C2211yescharacteristic
27C2×#14273651—24no—
28C2×#14273651C2211yescharacteristic
29C2×#14273651C2211yescharacteristic
30C2×#14273651C2211yescharacteristic
31C2×#14273651C2211yescharacteristic
32C2×#14273651C2211yescharacteristic
33C2×#14273651C2211yescharacteristic
34C2×#14273651C2211yescharacteristic
35C2×#14273651C2211yescharacteristic
36C2×#14273651C2211yescharacteristic
37C2×#14273650C2211yescharacteristic
38C2×C22⋊(C59⋊C8)C2211yescharacteristic
39C2×C22⋊(C59⋊C8)C2211yescharacteristic
40C2×C22⋊(C59⋊C8)C2211yescharacteristic
41#16837335—21no—
42#16837325—21no—
43#16837308C2211yescharacteristic
44#16837300C2211yescharacteristic
45#16837282—21no—
46#16837262C2211yescharacteristic
47#16837260—21no—
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×Dic118C2311yescharacteristic
66C23×Dic59—21no—
67C2×#11745672—22no—
68C2×#11745672—22no—
69C2×#11745672—22no—
70C2×#11745672—22no—
71C2×#11745672—22no—
72C2×#11745672—22no—
73C2×#11745672—41no—
74C2×#11745672—41no—
75C2×#11745672—41no—
76C22×C59⋊C8—22no—
77C22×C59⋊C8—22no—
78C22×C59⋊C8—41no—
79C22×C59⋊C8C2311yescharacteristic
80C22×C59⋊C8C2311yescharacteristic
81C22×C59⋊C8C2311yescharacteristic
82C22×C59⋊C8C2311yescharacteristic
83#14273706—22no—
84#14273706—22no—
85#14273706—22no—
86#14273706—41no—
87C2×C4⋊Dic59—22no—
88C2×C4⋊Dic59—21no—
89C2×C4⋊Dic59—41no—
90C2×C4⋊Dic59C2311yescharacteristic
91C2×C4⋊Dic59C2311yescharacteristic
92C2×C4⋊Dic59C2311yescharacteristic
93C2×Dic59⋊C4—21no—
94C2×Dic59⋊C4—21no—
95C2×Dic59⋊C4—21no—
96C2×C22⋊Dic59—21no—
97C2×C22⋊Dic59—21no—
98C2×C22⋊Dic59—21no—
99#14273660—22no—
100#14273651—22no—
101#14273651—22no—
102#14273651—22no—
103#14273651—22no—
104#14273651—22no—
105#14273651—22no—
106#14273651—22no—
107#14273651—41no—
108#14273651D414yescomplemented
109#14273650—22no—
110C22⋊(C59⋊C8)—22no—
111C22⋊(C59⋊C8)—22no—
112C22⋊(C59⋊C8)—41no—
113C59⋊#95—21no—
114C59⋊#95—21no—
115C59⋊#95—21no—
116C59⋊#95—21no—
117C22×Q8×C59—22no—
118C22×Q8×C59—22no—
119C22×Q8×C59—21no—
120C22×Q8×C59—21no—
121C22×Q8×C59—22no—
122C22×Q8×C59—22no—
123C22×Q8×C59—22no—
124C22×Q8×C59—22no—
125C22×Q8×C59—22no—
126C22×Q8×C59—41no—
127C22×Q8×C59—41no—
128C22×Q8×C59—41no—
129C22×Q8×C59—41no—
130C22×Q8×C59D414yes—
131C22×Q8×C59C2311yescharacteristic
132C22×Q8×C59C2311yescharacteristic
133C22×Q8×C59C2311yescharacteristic
134C22×D4×C59D411yescharacteristic
135C23×C4×C59—21no—
136C23×C4×C59—21no—
137C23×C4×C59C2311yescharacteristic
138C23×C4×C59C2311yescharacteristic
139C4⋊Q8×C59—28no—
140C4⋊Q8×C59—22no—
141C4⋊Q8×C59—22no—
142C22⋊Q8×C59—28no—
143C22⋊Q8×C59—28no—
144C22⋊Q8×C59—22no—
145C22⋊Q8×C59—22no—
146C22⋊Q8×C59—22no—
147C22⋊Q8×C59D414yes—
148C4×Q8×C59—22no—
149C4×Q8×C59—22no—
150C4×D4×C59—28no—
151C4×D4×C59—22no—
152C4×D4×C59—22no—
153C2×C4⋊C4×C59—21no—
154C2×C4⋊C4×C59—21no—
155C2×C4⋊C4×C59—21no—
156C2×C4⋊C4×C59—21no—
157C2×C4⋊C4×C59—21no—
158C2×C4⋊C4×C59D411yescharacteristic
159C2×C4⋊C4×C59C2311yescharacteristic
160C2×C22⋊C4×C59—21no—
161C2×C22⋊C4×C59—21no—
162C2×C22⋊C4×C59D411yescharacteristic
163C2×C22⋊C4×C59D411yescharacteristic
164C2×C42×C59—21no—
165C2×C42×C59C2311yescharacteristic
166C24×C59C2×D411yescharacteristic
167C24×C59C2×D411yescharacteristic
168C2×Q8×C59—24no—
169C2×Q8×C59—24no—
170C2×Q8×C59—21no—
171C2×Q8×C59—21no—
172C2×Q8×C59—21no—
173C2×Q8×C59—21no—
174C2×Q8×C59—21no—
175C2×Q8×C59—28no—
176C2×Q8×C59—21no—
177C2×Q8×C59—21no—
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—42no—
185C2×Q8×C59—42no—
186C2×Q8×C59—42no—
187C2×Q8×C59—42no—
188C2×Q8×C59—44no—
189C2×Q8×C59—44no—
190C2×Q8×C59—44no—
191C2×Q8×C59—44no—
192C2×Q8×C59—44no—
193C2×Q8×C59—44no—
194C2×Q8×C59—44no—
195C2×Q8×C59C2×D412yes—
196C2×Q8×C59C2×D412yes—
197C2×Q8×C59C2×D412yes—
198C2×Q8×C59C2×D412yes—
199C2×Q8×C59#4112yes—
200C2×D4×C59—22no—
201C2×D4×C59—22no—
202C2×D4×C59Q1614yescomplemented
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59—24no—
209C22×C4×C59—24no—
210C22×C4×C59—21no—
211C22×C4×C59—21no—
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—42no—
220C22×C4×C59—42no—
221C22×C4×C59—42no—
222C22×C4×C59—42no—
223C22×C4×C59C2×D411yescharacteristic
224C22×C4×C59C2×D411yescharacteristic
225C22×C4×C59C2×D411yescharacteristic
226C22×C4×C59C2×D412yes—
227C22×C4×C59C2×D412yes—
228C22×C4×C59C2×D411yescharacteristic
229C22×C4×C59C2411yescharacteristic
230C22×Dic59—21no—
231C22×Dic59—21no—
232C22×Dic59—21no—
233C22×Dic59—21no—
234C22×Dic59—42no—
235C22×Dic59—42no—
236C22×Dic59—81no—
237C2×Dic118—21no—
238C2×Dic118—21no—
239C2×Dic118—21no—
240C2×Dic118—21no—
241C2×Dic118—21no—
242C2×Dic118—21no—
243C4⋊C4×C59—24no—
244C4⋊C4×C59—24no—
245C4⋊C4×C59—24no—
246C4⋊C4×C59—24no—
247C4⋊C4×C59—24no—
248C4⋊C4×C59—22no—
249C4⋊C4×C59—21no—
250C4⋊C4×C59C2×D412yes—
251C22⋊C4×C59—24no—
252C22⋊C4×C59—24no—
253C22⋊C4×C59—22no—
254C22⋊C4×C59—22no—
255C42×C59—24no—
256C42×C59—21no—
257C42×C59—21no—
258C22⋊Dic59—42no—
259C22⋊Dic59—42no—
260C22⋊Dic59—81no—
261#11745672—44no—
262#11745672—44no—
263#11745672—44no—
264C4⋊Dic59—21no—
265C4⋊Dic59—21no—
266C4⋊Dic59—21no—
267C4⋊Dic59—21no—
268C4⋊Dic59—21no—
269C4⋊Dic59—42no—
270C4⋊Dic59C2×D412yes—
271Dic59⋊C4—42no—
272Dic59⋊C4—42no—
273Dic59⋊C4—81no—
274C2×C59⋊C8—21no—
275C2×C59⋊C8—21no—
276C2×C59⋊C8—21no—
277C2×C59⋊C8—21no—
278C2×C59⋊C8—21no—
279C2×C59⋊C8—21no—
280C2×C59⋊C8—21no—
281C2×C59⋊C8—21no—
282C2×C59⋊C8—21no—
283C2×C59⋊C8—21no—
284C2×C59⋊C8—21no—
285C2×C59⋊C8—44no—
286C2×C59⋊C8C2×D412yes—
287C23×C59—21no—
288C23×C59—21no—
289C23×C59—21no—
290C23×C59—21no—
291C23×C59—21no—
292C23×C59—21no—
293C23×C59—21no—
294C23×C59—21no—
295C23×C59—21no—
296C23×C59—21no—
297C23×C59#12012yes—
298C23×C59C2×Q1612yes—
299C23×C59C2×Q1612yes—
300C23×C59#13712yes—
301C23×C59C22×D411yescharacteristic
302Q8×C59—22no—
303Q8×C59—22no—
304Q8×C59—22no—
305Q8×C59—22no—
306Q8×C59—22no—
307Q8×C59—22no—
308Q8×C59—22no—
309Q8×C59—48no—
310Q8×C59—48no—
311Q8×C59—41no—
312Q8×C59—41no—
313Q8×C59—41no—
314Q8×C59—41no—
315Q8×C59#12114yes—
316D4×C59—28no—
317C2×C4×C59—21no—
318C2×C4×C59—22no—
319C2×C4×C59—21no—
320C2×C4×C59—22no—
321C2×C4×C59—21no—
322C2×C4×C59—22no—
323C2×C4×C59—21no—
324C2×C4×C59—22no—
325C2×C4×C59—22no—
326C2×C4×C59—22no—
327C2×C4×C59—22no—
328C2×C4×C59—21no—
329C2×C4×C59—22no—
330C2×C4×C59—22no—
331C2×C4×C59—22no—
332C2×C4×C59—21no—
333C2×C4×C59—21no—
334C2×C4×C59—21no—
335C2×C4×C59—21no—
336C2×C4×C59—21no—
337C2×C4×C59—48no—
338C2×C4×C59—48no—
339C2×C4×C59—41no—
340C2×C4×C59—41no—
341C2×C4×C59—41no—
342C2×C4×C59—41no—
343C2×C4×C59—41no—
344C2×C4×C59—41no—
345C2×C4×C59—41no—
346C2×C4×C59—41no—
347C2×C4×C59—41no—
348C2×C4×C59—41no—
349C2×C4×C59#12012yes—
350C2×C4×C59C2×Q1612yes—
351C2×C4×C59C22×D411yescharacteristic
352C2×C4×C59C22×D411yescharacteristic
353C2×C4×C59C22×D411yescharacteristic
354C2×C4×C59C2×#4111yescharacteristic
355C2×C4×C59H(5,𝔽2)11yescharacteristic
356C2×C4×C59H(5,𝔽2)11yescharacteristic
357C2×Dic59—22no—
358C2×Dic59—41no—
359C2×Dic59—41no—
360C2×Dic59—41no—
361C2×Dic59—41no—
362C2×Dic59—41no—
363C2×Dic59—41no—
364C2×Dic59—41no—
365C2×Dic59—41no—
366C2×Dic59—41no—
367C2×Dic59—41no—
368C2×Dic59—41no—
369C2×Dic59—84no—
370Dic118—41no—
371Dic118—41no—
372Dic118—41no—
373Dic118—41no—
374C59⋊C8—22no—
375C59⋊C8—41no—
376C59⋊C8—41no—
377C59⋊C8—41no—
378#24437—591nomaximal, Sylow
379C22×C59—22no—
380C22×C59—22no—
381C22×C59—22no—
382C22×C59—22no—
383C22×C59—22no—
384C22×C59—22no—
385C22×C59—22no—
386C22×C59—22no—
387C22×C59—22no—
388C22×C59—41no—
389C22×C59—41no—
390C22×C59—41no—
391C22×C59—41no—
392C22×C59#45114yescomplemented
393C22×C59C2×#12011yescharacteristic
394C22×C59D4211yescharacteristic
395C22×C59#54611yescharacteristic
396C22×C59C22×Q1611yescharacteristic
397C22×C59C2×#13711yescharacteristic
398C22×C59#57711yescharacteristic
399C22×C59#57811yescharacteristic
400C4×C59—22no—
401C4×C59—24no—
402C4×C59—22no—
403C4×C59—41no—
404C4×C59—42no—
405C4×C59—42no—
406C4×C59—41no—
407C4×C59—42no—
408C4×C59C2×#12111yescharacteristic
409C4×C59#53411yescharacteristic
410C4×C59D4211yescharacteristic
411C4×C59#54611yescharacteristic
412Dic59—42no—
413Dic59—81no—
414Dic59—81no—
415Dic59—81no—
416C2×D4×Q8D5911yescharacteristic
417C2×#467—591no—
418C2×#451—591no—
419C2×#451—591no—
420C22×#103—591no—
421#2417—591no—
422#2043—591no—
423#2036—591no—
424#2016—591no—
425#2001—591no—
426#1878—591no—
427#1872—591no—
428#1869—591no—
429#1863—591no—
430#1787—591no—
431C2×C59—24no—
432C2×C59—42no—
433C2×C59#241011yescharacteristic
434C2×C59C2×#45111yescharacteristic
435C2×C59#301311yescharacteristic
436C2×C59#326611yescharacteristic
437C2×C59D4×Q1611yescharacteristic
438C2×C59#329911yescharacteristic
439C2×C59#331211yescharacteristic
440C23×Q8C2×D5911yescharacteristic
441C23×Q8C2×D5911yescharacteristic
442C22×Q16—591no—
443C22×Q16—591no—
444C22×Q16—591no—
445C23×C8—591no—
446D4×Q8—24no—
447D4×Q8—24no—
448C2×C4⋊Q8—21no—
449C2×C4⋊Q8C2×D5911yescharacteristic
450C2×C22⋊Q8—21no—
451C2×C22⋊Q8—21no—
452C2×C22⋊Q8—591no—
453C2×C22⋊Q8—591no—
454C2×C22⋊Q8C2×D5911yescharacteristic
455C2×C22⋊Q8C2×D5911yescharacteristic
456C2×C4×Q8C2×D5911yescharacteristic
457C2×C4×D4—21no—
458C2×C4×D4C2×D5911yescharacteristic
459C22×C4⋊C4—591no—
460#467—1184no—
461#451—1184no—
462#451—1184no—
463C2×#107—591no—
464C2×#103—591no—
465C2×#103—591no—
466C2×#103—591no—
467C2×#103—591no—
468C2×#103—591no—
469C2×#103—591no—
470C2×#103—591no—
471C2×#103—591no—
472C2×#103—591no—
473C2×#103—591no—
474C2×#103—1184no—
475C2×C22⋊C8—591no—
476C2×C22⋊C8—591no—
477C2×C22⋊C8—591no—
478#398—1181no—
479#396—1181no—
480#391—591no—
481#389—591no—
482#386—1181no—
483#380—591no—
484#380—1181no—
485#340—591no—
486#340—591no—
487#336—591no—
488#336—591no—
489C59#2443711yescharacteristic, complemented, Sylow
490C22×Q8—22no—
491C22×Q8—22no—
492C22×Q8—21no—
493C22×Q8—21no—
494C22×Q8—22no—
495C22×Q8—22no—
496C22×Q8—22no—
497C22×Q8—22no—
498C22×Q8—22no—
499C22×Q8—41no—
500C22×Q8—41no—
501C22×Q8—41no—
502C22×Q8—41no—
503C22×Q8—591no—
504C22×Q8C22⋊D5914yes—
505C22×Q8C22×D5911yescharacteristic
506C22×Q8C22×D5911yescharacteristic
507C22×Q8C22×D5911yescharacteristic
508C22×D4C22⋊D5911yescharacteristic
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—1181no—
512C23×C4C22×D5911yescharacteristic
513C23×C4C22×D5911yescharacteristic
514C2×Q16—1182no—
515C2×Q16—1182no—
516C2×Q16—1182no—
517C2×Q16—1182no—
518C2×Q16—1182no—
519C2×Q16—1182no—
520C2×Q16—2361no—
521C2×Q16—2361no—
522C2×Q16—2361no—
523C22×C8—591no—
524C22×C8—591no—
525C22×C8—591no—
526C22×C8—591no—
527C22×C8—1182no—
528C22×C8—1182no—
529C22×C8—2361no—
530C4⋊Q8—28no—
531C4⋊Q8—22no—
532C4⋊Q8—22no—
533C22⋊Q8—28no—
534C22⋊Q8—28no—
535C22⋊Q8—22no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8—1182no—
539C22⋊Q8—1182no—
540C22⋊Q8—1182no—
541C22⋊Q8—2361no—
542C22⋊Q8C22⋊D5914yes—
543C4×Q8—22no—
544C4×Q8—22no—
545C4×D4—28no—
546C4×D4—22no—
547C4×D4—22no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—591no—
554C2×C4⋊C4—591no—
555C2×C4⋊C4—591no—
556C2×C4⋊C4—1182no—
557C2×C4⋊C4—1181no—
558C2×C4⋊C4—1181no—
559C2×C4⋊C4—1181no—
560C2×C4⋊C4—1181no—
561C2×C4⋊C4—2361no—
562C2×C4⋊C4C22⋊D5911yescharacteristic
563C2×C4⋊C4C22×D5911yescharacteristic
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—1181no—
567C2×C22⋊C4—1181no—
568C2×C22⋊C4—1181no—
569C2×C22⋊C4C22⋊D5911yescharacteristic
570C2×C22⋊C4C22⋊D5911yescharacteristic
571C2×C42—21no—
572C2×C42C22×D5911yescharacteristic
573#107—1182no—
574#103—594no—
575#103—1182no—
576#103—1182no—
577#103—1182no—
578#103—1182no—
579#103—1182no—
580#103—1182no—
581#103—1182no—
582#103—1182no—
583#103—2361no—
584C22⋊C8—1182no—
585C22⋊C8—1182no—
586C22⋊C8—2361no—
587#95—1181no—
588#95—1181no—
589#95—1181no—
590#95—1181no—
591C24C2×C22⋊D5911yescharacteristic
592C24C2×C22⋊D5911yescharacteristic
593C2×Q8—24no—
594C2×Q8—24no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—28no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—42no—
610C2×Q8—42no—
611C2×Q8—42no—
612C2×Q8—42no—
613C2×Q8—44no—
614C2×Q8—44no—
615C2×Q8—44no—
616C2×Q8—44no—
617C2×Q8—44no—
618C2×Q8—44no—
619C2×Q8—44no—
620C2×Q8—1181no—
621C2×Q8—1181no—
622C2×Q8—1181no—
623C2×Q8—1181no—
624C2×Q8—1181no—
625C2×Q8—1181no—
626C2×Q8D4×D5912yes—
627C2×Q8#1174568712yes—
628C2×Q8C2×C22⋊D5912yes—
629C2×Q8C2×C22⋊D5912yes—
630C2×Q8C2×C22⋊D5912yes—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4#1174567214yescomplemented
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—24no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—1181no—
655C22×C4—1181no—
656C22×C4—1181no—
657C22×C4—1181no—
658C22×C4—4721no—
659C22×C4—2362no—
660C22×C4—2362no—
661C22×C4C2×C22⋊D5911yescharacteristic
662C22×C4C2×C22⋊D5911yescharacteristic
663C22×C4C2×C22⋊D5911yescharacteristic
664C22×C4C2×C22⋊D5912yes—
665C22×C4C2×C22⋊D5912yes—
666C22×C4C2×C22⋊D5911yescharacteristic
667C22×C4C23×D5911yescharacteristic
668Q16—2364no—
669Q16—2364no—
670Q16—2364no—
671C2×C8—592no—
672C2×C8—1181no—
673C2×C8—1181no—
674C2×C8—1181no—
675C2×C8—1181no—
676C2×C8—1181no—
677C2×C8—1181no—
678C2×C8—1181no—
679C2×C8—1181no—
680C2×C8—1181no—
681C2×C8—1181no—
682C2×C8—1181no—
683C2×C8—2364no—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—22no—
690C4⋊C4—21no—
691C4⋊C4—592no—
692C4⋊C4—1181no—
693C4⋊C4—1181no—
694C4⋊C4—1181no—
695C4⋊C4—1181no—
696C4⋊C4—1181no—
697C4⋊C4—4721no—
698C4⋊C4—2362no—
699C4⋊C4—2362no—
700C4⋊C4—2362no—
701C4⋊C4C2×C22⋊D5912yes—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—4721no—
707C22⋊C4—2362no—
708C22⋊C4—2362no—
709C42—24no—
710C42—21no—
711C42—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23#1427369612yes—
723C23C2×#1174567212yes—
724C23C2×#1174567212yes—
725C23#1427375812yes—
726C23C22×C22⋊D5911yescharacteristic
727Q8—22no—
728Q8—22no—
729Q8—22no—
730Q8—22no—
731Q8—22no—
732Q8—22no—
733Q8—22no—
734Q8—48no—
735Q8—48no—
736Q8—41no—
737Q8—41no—
738Q8—41no—
739Q8—41no—
740Q8—2361no—
741Q8—2361no—
742Q8—2361no—
743Q8—2361no—
744Q8#1427369914yes—
745D4—28no—
746C2×C4—21no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—48no—
767C2×C4—48no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—1182no—
779C2×C4—4724no—
780C2×C4—2361no—
781C2×C4—2361no—
782C2×C4—2361no—
783C2×C4—2361no—
784C2×C4—2361no—
785C2×C4—2361no—
786C2×C4—2361no—
787C2×C4—2361no—
788C2×C4—2361no—
789C2×C4—2361no—
790C2×C4—2361no—
791C2×C4#1427369612yes—
792C2×C4C2×#1174567212yes—
793C2×C4C2×D4×D5911yescharacteristic
794C2×C4C22×C22⋊D5911yescharacteristic
795C2×C4C22×C22⋊D5911yescharacteristic
796C2×C4C2×#1174568711yescharacteristic
797C2×C4#1427377211yescharacteristic
798C2×C4#1427377211yescharacteristic
799C8—1182no—
800C8—2361no—
801C8—2361no—
802C8—2361no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22#1683755814yescomplemented
817C22C2×#1427369611yescharacteristic
818C22D4×C22⋊D5911yescharacteristic
819C22#1683804611yescharacteristic
820C22C22×#1174567211yescharacteristic
821C22C2×#1427375811yescharacteristic
822C22#1683821011yescharacteristic
823C22#1683821711yescharacteristic
824C4—22no—
825C4—24no—
826C4—22no—
827C4—41no—
828C4—42no—
829C4—42no—
830C4—41no—
831C4—42no—
832C4—4721no—
833C4—4721no—
834C4—4721no—
835C4—2362no—
836C4C2×#1427369911yescharacteristic
837C4#1683796111yescharacteristic
838C4D4×C22⋊D5911yescharacteristic
839C4#1683804611yescharacteristic
840C2—24no—
841C2—42no—
842C2#2142747011yescharacteristic
843C2C2×#1683755811yescharacteristic
844C2#2143341111yescharacteristic
845C2#2143560711yescharacteristic
846C2D4×#1174567211yescharacteristic
847C2#2143597211yescharacteristic
848C2#2143614711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×D4×Q8×C59C2
socleC23×C59C22×D4
prime radicalC22×D4×C59D4
hypercenterC2×D4×Q8D59
hypocenterC59#24437
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×#16837641C2semidirect
2. C2×#16837558C2semidirect
3. C2×#16837558C2semidirect
4. C22×#14273651C2semidirect
6. #21425339C2semidirect
7. #21425296C2semidirect
8. #21425196C2semidirect
9. #21425104C2semidirect
10. #21424437C2semidirect
11. #21424404C2semidirect
13. #21424350C2semidirect
14. #21424031C2semidirect
108. #14273651D4semidirect
202. C2×D4×C59Q16semidirect
392. C22×C59#451semidirect
489. C59#24437semidirect
633. C2×D4#11745672semidirect
816. C22#16837558semidirect

Maximal subgroups

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

subgroupindex
C2×#168376412
C2×#168375582
C22×#142736512
#214275472
#214253392
#214252962
#214251962
#214251042
#214244372
#214244042
#214243892
#214243502
#214240312
C2×D4×Q8×C592
#2443759