Finite Group Databasebeta

← #28517865

Subgroups — #28517865

Order 15104.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273711C211yesmaximal, characteristic
2C2×#16837295C211yesmaximal, characteristic, complemented
3#21422365C211yesmaximal, characteristic, complemented
4#21422363C211yesmaximal, characteristic, complemented
5#21422342C211yesmaximal, characteristic, complemented
6#21422338C211yesmaximal, characteristic, complemented
7#21422335C211yesmaximal, characteristic
8#21422335C211yesmaximal, characteristic
9#21422334C211yesmaximal, characteristic, complemented
10#21422332C211yesmaximal, characteristic, complemented
11#21422326C211yesmaximal, characteristic, complemented
12#21422325C211yesmaximal, characteristic, complemented
13#21422318C211yesmaximal, characteristic, complemented
14#21422318C211yesmaximal, characteristic, complemented
15C2×C59×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D59C2211yescharacteristic
17C24×Dic59C2211yescharacteristic
18C2×#14273711—24no—
19C2×#14273711—24no—
20C2×#14273711C418yescomplemented
21C22×C4⋊Dic59C2211yescharacteristic
22C22×C4⋊Dic59C2211yescharacteristic
23C22×C4⋊Dic59C2211yescharacteristic
24C22×C22⋊Dic59C2211yescharacteristic
25C22×C22⋊Dic59C2211yescharacteristic
26C22×(C2×D59)⋊C4C2211yescharacteristic
27C22×(C2×D59)⋊C4C2211yescharacteristic
28C22×(C2×D59)⋊C4C2211yescharacteristic
29C22×(C2×D59)⋊C4C2211yescharacteristic
30C22×(C2×D59)⋊C4C2211yescharacteristic
31C22×(C2×D59)⋊C4C2211yescharacteristic
32C22×C4×Dic59C2211yescharacteristic
33#16837295—24no—
34C2×C59⋊#95C2211yescharacteristic
35C2×C59⋊#95C2211yescharacteristic
36C2×C59⋊#95C2211yescharacteristic
37C2×C59⋊#95C2211yescharacteristic
38C2×C59⋊#95C2211yescharacteristic
39C2×C59⋊#95C2211yescharacteristic
40C2×C59⋊#95C2211yescharacteristic
41C2×C59⋊#95C2211yescharacteristic
42C2×C59⋊#95C2211yescharacteristic
43C2×C59⋊#95C2211yescharacteristic
44C2×C59⋊#95C2211yescharacteristic
45C2×C59⋊#95C2211yescharacteristic
46C2×C59⋊#95C2211yescharacteristic
47C2×C59⋊#95C2211yescharacteristic
48C22×C4⋊C4×C59C2211yescharacteristic
49C22×C22⋊C4×C59C2211yescharacteristic
50C22×C22⋊C4×C59C2211yescharacteristic
51C22×C22⋊C4×C59C2211yescharacteristic
52C22×C42×C59C2211yescharacteristic
53C59×#388—24no—
54C2×#95×C59C2211yescharacteristic
55C2×#95×C59C2211yescharacteristic
56C24×D59C2311yescharacteristic
57C22×C22⋊D59—22no—
58C22×C22⋊D59—22no—
59C22×C22⋊D59—41no—
60C22×C22⋊D59—41no—
61C22×C22⋊D59—41no—
62C22×C22⋊D59—41no—
63C22×C22⋊D59C2×C414yes—
64C23×Dic59—22no—
65C23×Dic59—22no—
66C23×Dic59—41no—
67C23×Dic59—41no—
68C23×Dic59—41no—
69C23×Dic59—41no—
70C23×Dic59C2×C414yes—
71C23×Dic59C2311yescharacteristic
72C23×Dic59C2311yescharacteristic
73C23×Dic59C2311yescharacteristic
74C23×Dic59C2311yescharacteristic
75C23×Dic59C2311yescharacteristic
76C23×Dic59C2311yescharacteristic
77C23×Dic59C2311yescharacteristic
78#14273711—232no—
79C2×C4⋊Dic59—22no—
80C2×C4⋊Dic59—22no—
81C2×C4⋊Dic59—22no—
82C2×C4⋊Dic59—22no—
83C2×C4⋊Dic59—22no—
84C2×C4⋊Dic59—22no—
85C2×C4⋊Dic59—41no—
86C2×C4⋊Dic59C2×C414yes—
87C2×C4⋊Dic59C2×C414yes—
88C2×C22⋊Dic59—22no—
89C2×C22⋊Dic59—22no—
90C2×C22⋊Dic59—22no—
91C2×C22⋊Dic59—22no—
92C2×C22⋊Dic59—41no—
93C2×C22⋊Dic59—41no—
94C2×(C2×D59)⋊C4—22no—
95C2×(C2×D59)⋊C4—22no—
96C2×(C2×D59)⋊C4—22no—
97C2×(C2×D59)⋊C4—22no—
98C2×(C2×D59)⋊C4—22no—
99C2×(C2×D59)⋊C4—22no—
100C2×(C2×D59)⋊C4—22no—
101C2×(C2×D59)⋊C4—22no—
102C2×(C2×D59)⋊C4—41no—
103C2×(C2×D59)⋊C4—41no—
104C2×(C2×D59)⋊C4—41no—
105C2×(C2×D59)⋊C4—41no—
106C2×(C2×D59)⋊C4—41no—
107C2×(C2×D59)⋊C4—41no—
108C2×(C2×D59)⋊C4—41no—
109C2×(C2×D59)⋊C4—41no—
110C2×(C2×D59)⋊C4C2×C414yes—
111C2×(C2×D59)⋊C4C2×C414yes—
112C2×C4×Dic59—22no—
113C2×C4×Dic59—22no—
114C2×C4×Dic59—41no—
115C59⋊#95—22no—
116C59⋊#95—22no—
117C59⋊#95—41no—
118C59⋊#95—41no—
119C59⋊#95—41no—
120C59⋊#95—41no—
121C59⋊#95—41no—
122C59⋊#95—41no—
123C59⋊#95—41no—
124C59⋊#95—41no—
125C59⋊#95—41no—
126C59⋊#95—41no—
127C59⋊#95—41no—
128C59⋊#95—41no—
129C25×C59C2311yescharacteristic
130C23×C4×C59C2311yescharacteristic
131C23×C4×C59C2311yescharacteristic
132C23×C4×C59C2311yescharacteristic
133C23×C4×C59C2311yescharacteristic
134C23×C4×C59C2311yescharacteristic
135C23×C4×C59C2311yescharacteristic
136C2×C4⋊C4×C59—22no—
137C2×C4⋊C4×C59—22no—
138C2×C4⋊C4×C59—41no—
139C2×C22⋊C4×C59—22no—
140C2×C22⋊C4×C59—22no—
141C2×C22⋊C4×C59—22no—
142C2×C22⋊C4×C59—22no—
143C2×C22⋊C4×C59—41no—
144C2×C22⋊C4×C59—41no—
145C2×C22⋊C4×C59C2×C414yes—
146C2×C22⋊C4×C59D414yes—
147C2×C22⋊C4×C59D414yes—
148C2×C42×C59—22no—
149C2×C42×C59—22no—
150C2×C42×C59—41no—
151#95×C59—22no—
152#95×C59—22no—
153C24×C59—21no—
154C24×C59—21no—
155C24×C59—21no—
156C24×C59—21no—
157C24×C59—21no—
158C24×C59—21no—
159C24×C59—21no—
160C24×C59—21no—
161C24×C59—21no—
162C24×C59—21no—
163C24×C59—21no—
164C24×C59—21no—
165C24×C59C22×C412yes—
166C24×C59C2×D412yes—
167C24×C59C2×D412yes—
168C24×C59C2411yescharacteristic
169C23×D59—21no—
170C23×D59—21no—
171C23×D59—21no—
172C23×D59—21no—
173C23×D59—21no—
174C23×D59—21no—
175C23×D59—21no—
176C23×D59—21no—
177C23×D59—21no—
178C23×D59—21no—
179C23×D59—21no—
180C23×D59—21no—
181C23×D59—21no—
182C23×D59—21no—
183C23×D59C22×C412yes—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—21no—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
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×C59C22×C412yes—
219C22×C4×C59C22×C412yes—
220C22×C4×C59C2×D412yes—
221C22×C4×C59C2×D412yes—
222C22×C4×C59C2×D412yes—
223C22×C4×C59C2×D412yes—
224C22×C4×C59#4112yes—
225C22×C4×C59#4112yes—
226C2×C22⋊D59—28no—
227C2×C22⋊D59—44no—
228C2×C22⋊D59—44no—
229C2×C22⋊D59—44no—
230C2×C22⋊D59—44no—
231C2×C22⋊D59—44no—
232C2×C22⋊D59—44no—
233C22×Dic59—28no—
234C22×Dic59—21no—
235C22×Dic59—21no—
236C22×Dic59—21no—
237C22×Dic59—21no—
238C22×Dic59—21no—
239C22×Dic59—21no—
240C22×Dic59—21no—
241C22×Dic59—21no—
242C22×Dic59—21no—
243C22×Dic59—21no—
244C22×Dic59—21no—
245C22×Dic59—21no—
246C22×Dic59—21no—
247C22×Dic59—21no—
248C22×Dic59—21no—
249C22×Dic59—21no—
250C22×Dic59—21no—
251C22×Dic59—21no—
252C22×Dic59—21no—
253C22×Dic59—21no—
254C22×Dic59—21no—
255C22×Dic59—21no—
256C22×Dic59—21no—
257C22×Dic59—21no—
258C22×Dic59—21no—
259C22×Dic59—21no—
260C22×Dic59—21no—
261C22×Dic59—21no—
262C22×Dic59—21no—
263C22×Dic59—21no—
264C22×Dic59—21no—
265C22×Dic59—21no—
266C22×Dic59—21no—
267C22×Dic59—21no—
268C22×Dic59—21no—
269C22×Dic59—21no—
270C22×Dic59—21no—
271C22×Dic59—21no—
272C22×Dic59—21no—
273C22×Dic59—21no—
274C22×Dic59—21no—
275C22×Dic59—21no—
276C22×Dic59—21no—
277C22×Dic59—21no—
278C22×Dic59—44no—
279C22×Dic59—44no—
280C22×Dic59—44no—
281C22×Dic59—44no—
282C22×Dic59—44no—
283C22×Dic59—44no—
284C22×Dic59C22×C412yes—
285C22×Dic59C22×C412yes—
286C22×Dic59C22×C412yes—
287C22×Dic59#4112yes—
288C22×Dic59#4112yes—
289C4⋊C4×C59—44no—
290C22⋊C4×C59—44no—
291C22⋊C4×C59—44no—
292C22⋊C4×C59C22⋊C4116yescomplemented
293C42×C59—44no—
294C22⋊Dic59—44no—
295C22⋊Dic59—44no—
296(C2×D59)⋊C4—28no—
297(C2×D59)⋊C4—28no—
298(C2×D59)⋊C4—44no—
299(C2×D59)⋊C4—44no—
300(C2×D59)⋊C4—44no—
301(C2×D59)⋊C4—44no—
302C4⋊Dic59—28no—
303C4⋊Dic59—28no—
304C4⋊Dic59—44no—
305C4×Dic59—44no—
306C23×C59—22no—
307C23×C59—22no—
308C23×C59—22no—
309C23×C59—22no—
310C23×C59—22no—
311C23×C59—22no—
312C23×C59—22no—
313C23×C59—22no—
314C23×C59—22no—
315C23×C59—22no—
316C23×C59—22no—
317C23×C59—22no—
318C23×C59—22no—
319C23×C59—22no—
320C23×C59—22no—
321C23×C59—22no—
322C23×C59—22no—
323C23×C59—22no—
324C23×C59—41no—
325C23×C59—41no—
326C23×C59—41no—
327C23×C59—41no—
328C23×C59—41no—
329C23×C59—41no—
330C23×C59—41no—
331C23×C59—41no—
332C23×C59—41no—
333C23×C59—41no—
334C23×C59—41no—
335C23×C59—41no—
336C23×C59—41no—
337C23×C59—41no—
338C23×C59—41no—
339C23×C59—41no—
340C23×C59C2×C22⋊C414yes—
341C23×C59C23×C411yescharacteristic
342C23×C59C22×D411yescharacteristic
343C23×C59C22×D411yescharacteristic
344C23×C59C2×#4111yescharacteristic
345C23×C59C2×#4111yescharacteristic
346C23×C59C2×#4111yescharacteristic
347C23×C59C2×#4111yescharacteristic
348C23×C59H(5,𝔽2)11yescharacteristic
349C23×C59H(5,𝔽2)11yescharacteristic
350C23×C59H(5,𝔽2)11yescharacteristic
351C23×C59H(5,𝔽2)11yescharacteristic
352C23×C59H(5,𝔽2)11yescharacteristic
353C23×C59H(5,𝔽2)11yescharacteristic
354C23×C592−1+411yescharacteristic
355C23×C592−1+411yescharacteristic
356C22×D59—22no—
357C22×D59—22no—
358C22×D59—22no—
359C22×D59—22no—
360C22×D59—22no—
361C22×D59—22no—
362C22×D59—22no—
363C22×D59—41no—
364C22×D59—41no—
365C22×D59—41no—
366C22×D59—41no—
367C22×D59—41no—
368C22×D59—41no—
369C22×D59—41no—
370C22×D59—41no—
371C22×D59—41no—
372C22×D59—41no—
373C22×D59—41no—
374C22×D59—41no—
375C22×D59—41no—
376C22×D59—41no—
377C22×D59—41no—
378C22×D59—41no—
379C22×D59—41no—
380C22×D59—41no—
381C22×D59—41no—
382C22×D59—41no—
383C22×D59—41no—
384C22×D59—41no—
385C22×D59—41no—
386C22×D59—41no—
387C22×D59—41no—
388C22×D59—41no—
389C22×D59—41no—
390C22×D59—41no—
391C2×C4×C59—22no—
392C2×C4×C59—22no—
393C2×C4×C59—22no—
394C2×C4×C59—22no—
395C2×C4×C59—22no—
396C2×C4×C59—22no—
397C2×C4×C59—22no—
398C2×C4×C59—22no—
399C2×C4×C59—22no—
400C2×C4×C59—22no—
401C2×C4×C59—22no—
402C2×C4×C59—22no—
403C2×C4×C59—22no—
404C2×C4×C59—22no—
405C2×C4×C59—22no—
406C2×C4×C59—22no—
407C2×C4×C59—22no—
408C2×C4×C59—22no—
409C2×C4×C59—41no—
410C2×C4×C59—41no—
411C2×C4×C59—41no—
412C2×C4×C59—41no—
413C2×C4×C59—41no—
414C2×C4×C59—41no—
415C2×C4×C59—41no—
416C2×C4×C59—41no—
417C2×C4×C59—41no—
418C2×C4×C59—41no—
419C2×C4×C59—41no—
420C2×C4×C59—41no—
421C2×C4×C59—41no—
422C2×C4×C59—41no—
423C2×C4×C59—41no—
424C2×C4×C59—41no—
425C2×C4×C59—41no—
426C2×C4×C59—41no—
427C2×C4×C59—41no—
428C2×C4×C59—41no—
429C2×C4×C59—41no—
430C2×C4×C59—41no—
431C2×C4×C59C2×C22⋊C414yes—
432C2×C4×C59C2×C22⋊C414yes—
433C22⋊D59—416no—
434C2×Dic59—22no—
435C2×Dic59—22no—
436C2×Dic59—22no—
437C2×Dic59—22no—
438C2×Dic59—22no—
439C2×Dic59—22no—
440C2×Dic59—22no—
441C2×Dic59—22no—
442C2×Dic59—22no—
443C2×Dic59—22no—
444C2×Dic59—22no—
445C2×Dic59—22no—
446C2×Dic59—22no—
447C2×Dic59—22no—
448C2×Dic59—22no—
449C2×Dic59—416no—
450C2×Dic59—41no—
451C2×Dic59—41no—
452C2×Dic59—41no—
453C2×Dic59—41no—
454C2×Dic59—41no—
455C2×Dic59—41no—
456C2×Dic59—41no—
457C2×Dic59—41no—
458C2×Dic59—41no—
459C2×Dic59—41no—
460C2×Dic59—41no—
461C2×Dic59—41no—
462C2×Dic59—41no—
463C2×Dic59—41no—
464C2×Dic59—41no—
465C2×Dic59—41no—
466C2×Dic59—41no—
467C2×Dic59—41no—
468C2×Dic59—41no—
469C2×Dic59—41no—
470C2×Dic59—41no—
471C2×Dic59—41no—
472C2×Dic59—41no—
473C2×Dic59—41no—
474C2×Dic59—41no—
475C2×Dic59—41no—
476C2×Dic59—41no—
477C2×Dic59—41no—
478C2×Dic59—41no—
479C2×Dic59—41no—
480C2×Dic59—41no—
481C2×Dic59—41no—
482C2×Dic59—41no—
483C2×Dic59—41no—
484#14506—591nomaximal, Sylow
485C22×C59—24no—
486C22×C59—24no—
487C22×C59—24no—
488C22×C59—42no—
489C22×C59—42no—
490C22×C59—42no—
491C22×C59—42no—
492C22×C59—42no—
493C22×C59—42no—
494C22×C59—42no—
495C22×C59—42no—
496C22×C59—42no—
497C22×C59—42no—
498C22×C59—42no—
499C22×C59—42no—
500C22×C59C22×C22⋊C411yescharacteristic
501C22×C59C4×#4111yescharacteristic
502C22×C59C4×#4111yescharacteristic
503C22×C59#51811yescharacteristic
504C22×C59#51811yescharacteristic
505C22×C59#52011yescharacteristic
506C22×C59#52011yescharacteristic
507C22×C59#53511yescharacteristic
508C22×C59#53511yescharacteristic
509C22×C59#53511yescharacteristic
510C22×C59#53511yescharacteristic
511C22×C59#53811yescharacteristic
512C22×C59#53811yescharacteristic
513C22×C59#53911yescharacteristic
514C22×C59#53911yescharacteristic
515C22×C59#54011yescharacteristic
516C22×C59#54011yescharacteristic
517C22×C59#54211yescharacteristic
518C22×C59#54211yescharacteristic
519C22×C59#54611yescharacteristic
520C22×C59#54611yescharacteristic
521C22×C59#54611yescharacteristic
522C22×C59#54611yescharacteristic
523C22×C59#54711yescharacteristic
524C22×C59#54711yescharacteristic
525C22×C59#54711yescharacteristic
526C22×C59#54711yescharacteristic
527C22×C59#55111yescharacteristic
528C22×C59#55311yescharacteristic
529C22×C59#55311yescharacteristic
530C22×C59#55911yescharacteristic
531C22×C59#56011yescharacteristic
532C22×C59#56211yescharacteristic
533C22×C59#56211yescharacteristic
534C22×C59#56311yescharacteristic
535C2×D59—42no—
536C2×D59—42no—
537C2×D59—42no—
538C2×D59—42no—
539C2×D59—42no—
540C2×D59—42no—
541C2×D59—42no—
542C2×D59—81no—
543C2×D59—81no—
544C2×D59—81no—
545C2×D59—81no—
546C2×D59—81no—
547C2×D59—81no—
548C2×D59—81no—
549C2×D59—81no—
550C4×C59—24no—
551C4×C59—24no—
552C4×C59—42no—
553C4×C59—42no—
554C4×C59—81no—
555C4×C59—81no—
556Dic59—42no—
557Dic59—42no—
558Dic59—42no—
559Dic59—42no—
560Dic59—42no—
561Dic59—81no—
562Dic59—81no—
563C22×#123—591no—
564C2×#388—591no—
565C2×#388D5911yescharacteristic, complemented
566#1445—591no—
567#1445—591no—
568#1439—591no—
569#1439—591no—
570#1438—591no—
571#1438—591no—
572#1437—591no—
573#1437—591no—
574C4⋊#95—591no—
575C4⋊#95—591no—
576C22⋊#95—591no—
577C22⋊#95—591no—
578C2×C59—44no—
579C2×C59#230911yescharacteristic
580C2×C59#233511yescharacteristic
581C2×C59#233511yescharacteristic
582C2×C59#233911yescharacteristic
583C2×C59#233911yescharacteristic
584C2×C59#237411yescharacteristic
585C2×C59#237611yescharacteristic
586C2×C59#270311yescharacteristic
587C2×C59#270311yescharacteristic
588C2×C59#270611yescharacteristic
589C2×C59#270611yescharacteristic
590C2×C59#271011yescharacteristic
591C2×C59#271011yescharacteristic
592C2×C59#271811yescharacteristic
593C2×C59#271811yescharacteristic
594D59—82no—
595C23×D4—591no—
596C24×C4—591no—
597C2×#123—598no—
598C2×#123—1184no—
599C2×#123—1184no—
600C22×C4⋊C4—591no—
601C22×C4⋊C4—591no—
602C22×C4⋊C4—591no—
603C22×C4⋊C4C2×D5911yescharacteristic
604C22×C22⋊C4—591no—
605C22×C22⋊C4—591no—
606C22×C22⋊C4—591no—
607C22×C22⋊C4—591no—
608C22×C22⋊C4—591no—
609C22×C22⋊C4—591no—
610C22×C22⋊C4—591no—
611C22×C22⋊C4—591no—
612C22×C22⋊C4C2×D5911yescharacteristic
613C22×C22⋊C4C2×D5911yescharacteristic
614C22×C22⋊C4C2×D5911yescharacteristic
615C22×C42—591no—
616C22×C42C2×D5911yescharacteristic
617#388—24no—
618#388—1184no—
619C2×#95—591no—
620C2×#95—591no—
621C2×#95—591no—
622C2×#95—591no—
623C2×#95—591no—
624C2×#95—591no—
625C2×#95—591no—
626C2×#95—591no—
627C2×#95—591no—
628C2×#95—591no—
629C2×#95—591no—
630C2×#95—591no—
631C2×#95—591no—
632C2×#95—591no—
633C2×#95C2×D5911yescharacteristic
634C2×#95C2×D5911yescharacteristic
635C59#1450611yescharacteristic, complemented, Sylow
636C25—591no—
637C25C22×D5911yescharacteristic
638C22×D4—594no—
639C22×D4—1182no—
640C22×D4—1182no—
641C22×D4—2361no—
642C22×D4—2361no—
643C22×D4—2361no—
644C22×D4—2361no—
645C23×C4—591no—
646C23×C4—591no—
647C23×C4—591no—
648C23×C4—591no—
649C23×C4—591no—
650C23×C4—594no—
651C23×C4—591no—
652C23×C4—591no—
653C23×C4—1182no—
654C23×C4—1182no—
655C23×C4—2361no—
656C23×C4—2361no—
657C23×C4—2361no—
658C23×C4—2361no—
659C23×C4C22×D5911yescharacteristic
660C23×C4C22×D5911yescharacteristic
661C23×C4C22×D5911yescharacteristic
662C23×C4C22×D5911yescharacteristic
663C23×C4C22×D5911yescharacteristic
664C23×C4C22×D5911yescharacteristic
665#123—11832no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—594no—
670C2×C4⋊C4—594no—
671C2×C4⋊C4—1182no—
672C2×C4⋊C4—1182no—
673C2×C4⋊C4—1182no—
674C2×C4⋊C4—1182no—
675C2×C4⋊C4—1182no—
676C2×C4⋊C4—1182no—
677C2×C4⋊C4—2361no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—41no—
683C2×C22⋊C4—41no—
684C2×C22⋊C4—594no—
685C2×C22⋊C4—594no—
686C2×C22⋊C4—1182no—
687C2×C22⋊C4—1182no—
688C2×C22⋊C4—1182no—
689C2×C22⋊C4—1182no—
690C2×C22⋊C4—1182no—
691C2×C22⋊C4—1182no—
692C2×C22⋊C4—1182no—
693C2×C22⋊C4—1182no—
694C2×C22⋊C4—1182no—
695C2×C22⋊C4—1182no—
696C2×C22⋊C4—1182no—
697C2×C22⋊C4—1182no—
698C2×C22⋊C4—2361no—
699C2×C22⋊C4—2361no—
700C2×C22⋊C4—2361no—
701C2×C22⋊C4—2361no—
702C2×C22⋊C4—2361no—
703C2×C22⋊C4—2361no—
704C2×C22⋊C4—2361no—
705C2×C22⋊C4—2361no—
706C2×C22⋊C4—2361no—
707C2×C22⋊C4—2361no—
708C2×C22⋊C4C4×D5914yes—
709C2×C22⋊C4D23614yes—
710C2×C22⋊C4C22⋊D5914yes—
711C2×C42—22no—
712C2×C42—22no—
713C2×C42—41no—
714C2×C42—1182no—
715C2×C42—1182no—
716C2×C42—2361no—
717#95—22no—
718#95—22no—
719#95—1182no—
720#95—1182no—
721#95—2361no—
722#95—2361no—
723#95—2361no—
724#95—2361no—
725#95—2361no—
726#95—2361no—
727#95—2361no—
728#95—2361no—
729#95—2361no—
730#95—2361no—
731#95—2361no—
732#95—2361no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—592no—
746C24—1181no—
747C24—1181no—
748C24—1181no—
749C24—1181no—
750C24—1181no—
751C24—1181no—
752C24—1181no—
753C24—1181no—
754C24—1181no—
755C24—1181no—
756C24—1181no—
757C24—1181no—
758C24—1181no—
759C24—1181no—
760C24C2×C4×D5912yes—
761C24C2×D23612yes—
762C24C2×C22⋊D5912yes—
763C24C23×D5911yescharacteristic
764C2×D4—1188no—
765C2×D4—2364no—
766C2×D4—2364no—
767C2×D4—2364no—
768C2×D4—2364no—
769C2×D4—2364no—
770C2×D4—2364no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—592no—
806C22×C4—592no—
807C22×C4—592no—
808C22×C4—592no—
809C22×C4—592no—
810C22×C4—1188no—
811C22×C4—1181no—
812C22×C4—1181no—
813C22×C4—1181no—
814C22×C4—1181no—
815C22×C4—1181no—
816C22×C4—1181no—
817C22×C4—1181no—
818C22×C4—1181no—
819C22×C4—1181no—
820C22×C4—1181no—
821C22×C4—1181no—
822C22×C4—1181no—
823C22×C4—1181no—
824C22×C4—1181no—
825C22×C4—1181no—
826C22×C4—1181no—
827C22×C4—1181no—
828C22×C4—1181no—
829C22×C4—1181no—
830C22×C4—1181no—
831C22×C4—1181no—
832C22×C4—1181no—
833C22×C4—1181no—
834C22×C4—1181no—
835C22×C4—1181no—
836C22×C4—1181no—
837C22×C4—1181no—
838C22×C4—1181no—
839C22×C4—1181no—
840C22×C4—1181no—
841C22×C4—1181no—
842C22×C4—1181no—
843C22×C4—1181no—
844C22×C4—1181no—
845C22×C4—1181no—
846C22×C4—1181no—
847C22×C4—1181no—
848C22×C4—1181no—
849C22×C4—1181no—
850C22×C4—1181no—
851C22×C4—1181no—
852C22×C4—1181no—
853C22×C4—1181no—
854C22×C4—1181no—
855C22×C4—2364no—
856C22×C4—2364no—
857C22×C4—2364no—
858C22×C4—2364no—
859C22×C4—2364no—
860C22×C4—2364no—
861C22×C4C2×C4×D5912yes—
862C22×C4C2×C4×D5912yes—
863C22×C4C2×D23612yes—
864C22×C4C2×D23612yes—
865C22×C4#1174568712yes—
866C22×C4#1174568712yes—
867C22×C4C2×C22⋊D5912yes—
868C22×C4C2×C22⋊D5912yes—
869C4⋊C4—44no—
870C4⋊C4—1188no—
871C4⋊C4—1188no—
872C4⋊C4—2364no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—1188no—
876C22⋊C4—1188no—
877C22⋊C4—2364no—
878C22⋊C4—2364no—
879C22⋊C4—2364no—
880C22⋊C4—2364no—
881C22⋊C4—2364no—
882C22⋊C4—2364no—
883C22⋊C4(C2×D59)⋊C4116yescomplemented
884C42—44no—
885C42—2364no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—1182no—
921C23—1182no—
922C23—1182no—
923C23—1182no—
924C23—1182no—
925C23—1182no—
926C23—1182no—
927C23—2361no—
928C23—2361no—
929C23—2361no—
930C23—2361no—
931C23—2361no—
932C23—2361no—
933C23—2361no—
934C23—2361no—
935C23—2361no—
936C23—2361no—
937C23—2361no—
938C23—2361no—
939C23—2361no—
940C23—2361no—
941C23—2361no—
942C23—2361no—
943C23—2361no—
944C23—2361no—
945C23—2361no—
946C23—2361no—
947C23—2361no—
948C23—2361no—
949C23—2361no—
950C23—2361no—
951C23—2361no—
952C23—2361no—
953C23—2361no—
954C23—2361no—
955C23C2×(C2×D59)⋊C414yes—
956C23C22×C4×D5911yescharacteristic
957C23C22×C22⋊D5911yescharacteristic
958C23C22×D23611yescharacteristic
959C23#41×D5911yescharacteristic
960C23#41×D5911yescharacteristic
961C23C2×#1174568711yescharacteristic
962C23C2×#1174568711yescharacteristic
963C23#1427377211yescharacteristic
964C23#1427377211yescharacteristic
965C23#1427377311yescharacteristic
966C23#1427377311yescharacteristic
967C23#1427377311yescharacteristic
968C23#1427377311yescharacteristic
969C23#1427377411yescharacteristic
970C23#1427377411yescharacteristic
971D4—23616no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—1182no—
1013C2×C4—1182no—
1014C2×C4—1182no—
1015C2×C4—1182no—
1016C2×C4—1182no—
1017C2×C4—1182no—
1018C2×C4—1182no—
1019C2×C4—1182no—
1020C2×C4—1182no—
1021C2×C4—1182no—
1022C2×C4—1182no—
1023C2×C4—1182no—
1024C2×C4—1182no—
1025C2×C4—1182no—
1026C2×C4—1182no—
1027C2×C4—2361no—
1028C2×C4—2361no—
1029C2×C4—2361no—
1030C2×C4—2361no—
1031C2×C4—2361no—
1032C2×C4—2361no—
1033C2×C4—2361no—
1034C2×C4—2361no—
1035C2×C4—2361no—
1036C2×C4—2361no—
1037C2×C4—2361no—
1038C2×C4—2361no—
1039C2×C4—2361no—
1040C2×C4—2361no—
1041C2×C4—23616no—
1042C2×C4—2361no—
1043C2×C4—2361no—
1044C2×C4—2361no—
1045C2×C4—2361no—
1046C2×C4—2361no—
1047C2×C4—2361no—
1048C2×C4—2361no—
1049C2×C4—2361no—
1050C2×C4—2361no—
1051C2×C4—2361no—
1052C2×C4—2361no—
1053C2×C4—2361no—
1054C2×C4—2361no—
1055C2×C4—2361no—
1056C2×C4—2361no—
1057C2×C4—2361no—
1058C2×C4—2361no—
1059C2×C4—2361no—
1060C2×C4—2361no—
1061C2×C4—2361no—
1062C2×C4C2×(C2×D59)⋊C414yes—
1063C2×C4C2×(C2×D59)⋊C414yes—
1064C22—24no—
1065C22—24no—
1066C22—24no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—4721no—
1080C22—4721no—
1081C22—4721no—
1082C22—4721no—
1083C22—4721no—
1084C22—4721no—
1085C22—4721no—
1086C22—4721no—
1087C22—2362no—
1088C22—2362no—
1089C22—2362no—
1090C22—2362no—
1091C22—2362no—
1092C22—2362no—
1093C22—2362no—
1094C22C22×(C2×D59)⋊C411yescharacteristic
1095C22C4×#1174568711yescharacteristic
1096C22C4×#1174568711yescharacteristic
1097C22#1683787611yescharacteristic
1098C22#1683787611yescharacteristic
1099C22#1683788111yescharacteristic
1100C22#1683788111yescharacteristic
1101C22#1683796611yescharacteristic
1102C22#1683796611yescharacteristic
1103C22#1683797111yescharacteristic
1104C22#1683797111yescharacteristic
1105C22#1683798611yescharacteristic
1106C22#1683798911yescharacteristic
1107C22#1683799311yescharacteristic
1108C22#1683799611yescharacteristic
1109C22#1683800411yescharacteristic
1110C22#1683800511yescharacteristic
1111C22#1683801811yescharacteristic
1112C22#1683802111yescharacteristic
1113C22#1683804611yescharacteristic
1114C22#1683804611yescharacteristic
1115C22#1683804711yescharacteristic
1116C22#1683804711yescharacteristic
1117C22#1683805111yescharacteristic
1118C22#1683805111yescharacteristic
1119C22#1683805611yescharacteristic
1120C22#1683805611yescharacteristic
1121C22#1683807511yescharacteristic
1122C22#1683810311yescharacteristic
1123C22#1683810411yescharacteristic
1124C22#1683813411yescharacteristic
1125C22#1683814011yescharacteristic
1126C22#1683814611yescharacteristic
1127C22#1683814911yescharacteristic
1128C22#1683815411yescharacteristic
1129C4—24no—
1130C4—24no—
1131C4—42no—
1132C4—42no—
1133C4—81no—
1134C4—81no—
1135C4—4721no—
1136C4—4721no—
1137C4—2362no—
1138C4—2362no—
1139C4—2362no—
1140C4—2362no—
1141C4—2362no—
1142C2—44no—
1143C2—4722no—
1144C2#2142667611yescharacteristic
1145C2#2142687911yescharacteristic
1146C2#2142689111yescharacteristic
1147C2#2142692111yescharacteristic
1148C2#2142692111yescharacteristic
1149C2#2142722611yescharacteristic
1150C2#2142724211yescharacteristic
1151C2#2143073511yescharacteristic
1152C2#2143073711yescharacteristic
1153C2#2143078011yescharacteristic
1154C2#2143078211yescharacteristic
1155C2#2143083211yescharacteristic
1156C2#2143083611yescharacteristic
1157C2#2143094011yescharacteristic
1158C2#2143094411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC2×C59×#388C2
socle, cosocleC24×C59C24
prime radicalC23×C22⋊D59C22
hypercenterC2×#388D59
hypocenterC59#14506
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#16837295C2semidirect
3. #21422365C2semidirect
4. #21422363C2semidirect
5. #21422342C2semidirect
6. #21422338C2semidirect
9. #21422334C2semidirect
10. #21422332C2semidirect
11. #21422326C2semidirect
12. #21422325C2semidirect
13. #21422318C2semidirect
14. #21422318C2semidirect
15. C2×C59×#388C2semidirect
20. C2×#14273711C4semidirect
292. C22⋊C4×C59C22⋊C4semidirect
565. C2×#388D59semidirect
635. C59#14506semidirect
883. C22⋊C4(C2×D59)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#142737112
C2×#168372952
#214223652
#214223632
#214223422
#214223382
#214223352
#214223342
#214223322
#214223262
#214223252
#214223182
C2×C59×#3882
#1450659