Finite Group Databasebeta

← #28512390

Subgroups — #28512390

Order 15104.

2366 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D59C211yesmaximal, characteristic
2C2×#16837297C211yesmaximal, characteristic, complemented
3C2×#16837273C211yesmaximal, characteristic
4C2×#16837273C211yesmaximal, characteristic
5C2×#16837273C211yesmaximal, characteristic
6C2×C4×(C2×D59)⋊C4C211yesmaximal, characteristic
7#21422360C211yesmaximal, characteristic, complemented
8#21422359C211yesmaximal, characteristic, complemented
9#21422349C211yesmaximal, characteristic, complemented
10#21422347C211yesmaximal, characteristic, complemented
11#21422329C211yesmaximal, characteristic, complemented
12#21422328C211yesmaximal, characteristic, complemented
13(C2×D59)⋊#95C211yesmaximal, characteristic
14(C2×D59)⋊#95C211yesmaximal, characteristic
15C2×C59×#389C211yesmaximal, characteristic, complemented
16C23×C4×D59C2211yescharacteristic
17C23×C4×D59C2211yescharacteristic
18C23×C4×D59C2211yescharacteristic
19C22×C4⋊Dic59C2211yescharacteristic
20C22×Dic59⋊C4C2211yescharacteristic
21C22×Dic59⋊C4C2211yescharacteristic
22C22×Dic59⋊C4C2211yescharacteristic
23C22×Dic59⋊C4C2211yescharacteristic
24C22×Dic59⋊C4C2211yescharacteristic
25C2×C4⋊C4×D59—24no—
26C2×C4⋊C4×D59—24no—
27C2×C4⋊C4×D59—24no—
28C22×(C2×D59)⋊C4C2211yescharacteristic
29C22×(C2×D59)⋊C4C2211yescharacteristic
30C22×(C2×D59)⋊C4C2211yescharacteristic
31C22×(C2×D59)⋊C4C2211yescharacteristic
32C22×C4×Dic59C2211yescharacteristic
33#16837297—24no—
34#16837273—24no—
35#16837273—24no—
36#16837273C418yescomplemented
37C4×(C2×D59)⋊C4—24no—
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
48C2×C59⋊#95C2211yescharacteristic
49C2×C59⋊#95C2211yescharacteristic
50C2×C59⋊#95C2211yescharacteristic
51C2×C59⋊#95C2211yescharacteristic
52C22×C4⋊C4×C59C2211yescharacteristic
53C22×C4⋊C4×C59C2211yescharacteristic
54C22×C4⋊C4×C59C2211yescharacteristic
55C22×C4⋊C4×C59C2211yescharacteristic
56C22×C42×C59C2211yescharacteristic
57C59×#389—24no—
58C2×#95×C59C2211yescharacteristic
59C2×#95×C59C2211yescharacteristic
60C24×D59C2311yescharacteristic
61C23×Dic59C2311yescharacteristic
62C23×Dic59C2311yescharacteristic
63C23×Dic59C2311yescharacteristic
64C23×Dic59C2311yescharacteristic
65C23×Dic59C2311yescharacteristic
66C23×Dic59C2311yescharacteristic
67C23×Dic59C2311yescharacteristic
68C22×C4×D59—22no—
69C22×C4×D59—22no—
70C22×C4×D59—22no—
71C22×C4×D59—22no—
72C22×C4×D59—22no—
73C22×C4×D59—22no—
74C22×C4×D59—22no—
75C22×C4×D59—22no—
76C22×C4×D59—22no—
77C22×C4×D59—22no—
78C22×C4×D59—22no—
79C22×C4×D59—22no—
80C22×C4×D59—22no—
81C22×C4×D59—22no—
82C22×C4×D59—22no—
83C22×C4×D59—41no—
84C22×C4×D59—41no—
85C22×C4×D59—41no—
86C22×C4×D59—41no—
87C22×C4×D59C2×C414yes—
88C22×C4×D59D414yes—
89C2×C4⋊Dic59—22no—
90C2×C4⋊Dic59—22no—
91C2×C4⋊Dic59—22no—
92C2×Dic59⋊C4—22no—
93C2×Dic59⋊C4—22no—
94C2×Dic59⋊C4—22no—
95C2×Dic59⋊C4—22no—
96C2×Dic59⋊C4—22no—
97C2×Dic59⋊C4—22no—
98C2×Dic59⋊C4—22no—
99C2×Dic59⋊C4—22no—
100C2×Dic59⋊C4—22no—
101C2×Dic59⋊C4—22no—
102C2×Dic59⋊C4—41no—
103C2×Dic59⋊C4—41no—
104C2×Dic59⋊C4—41no—
105C2×Dic59⋊C4C2×C414yescomplemented
106C2×Dic59⋊C4D414yes—
107C4⋊C4×D59—232no—
108C2×(C2×D59)⋊C4—22no—
109C2×(C2×D59)⋊C4—22no—
110C2×(C2×D59)⋊C4—22no—
111C2×(C2×D59)⋊C4—22no—
112C2×(C2×D59)⋊C4—22no—
113C2×(C2×D59)⋊C4—22no—
114C2×(C2×D59)⋊C4—22no—
115C2×(C2×D59)⋊C4C2×C414yes—
116C2×(C2×D59)⋊C4C2×C414yes—
117C2×(C2×D59)⋊C4D414yes—
118C2×(C2×D59)⋊C4Q814yes—
119C2×(C2×D59)⋊C4Q814yes—
120C2×C4×Dic59—22no—
121C2×C4×Dic59—22no—
122C2×C4×Dic59—41no—
123C59⋊#95—22no—
124C59⋊#95—22no—
125C59⋊#95—22no—
126C59⋊#95—22no—
127C59⋊#95—22no—
128C59⋊#95—22no—
129C59⋊#95—22no—
130C59⋊#95—22no—
131C59⋊#95—22no—
132C59⋊#95—22no—
133C59⋊#95—41no—
134C59⋊#95—41no—
135C59⋊#95C2×C414yescomplemented
136C59⋊#95C2×C414yescomplemented
137C23×C4×C59C2311yescharacteristic
138C23×C4×C59C2311yescharacteristic
139C23×C4×C59C2311yescharacteristic
140C23×C4×C59C2311yescharacteristic
141C23×C4×C59C2311yescharacteristic
142C23×C4×C59C2311yescharacteristic
143C23×C4×C59C2311yescharacteristic
144C2×C4⋊C4×C59—22no—
145C2×C4⋊C4×C59—22no—
146C2×C4⋊C4×C59—22no—
147C2×C4⋊C4×C59—22no—
148C2×C4⋊C4×C59—22no—
149C2×C4⋊C4×C59—22no—
150C2×C4⋊C4×C59—22no—
151C2×C4⋊C4×C59—22no—
152C2×C4⋊C4×C59—22no—
153C2×C4⋊C4×C59—41no—
154C2×C4⋊C4×C59C2×C414yescomplemented
155C2×C4⋊C4×C59D414yes—
156C2×C42×C59—22no—
157C2×C42×C59—22no—
158C2×C42×C59—41no—
159#95×C59—22no—
160#95×C59—22no—
161C24×C59C2411yescharacteristic
162C23×D59—21no—
163C23×D59—21no—
164C23×D59—21no—
165C23×D59—21no—
166C23×D59—21no—
167C23×D59—21no—
168C23×D59—21no—
169C23×D59—21no—
170C23×D59C22×C412yes—
171C23×D59C2×D412yes—
172C23×D59C2×D412yes—
173C23×D59C2×Q812yes—
174C23×D59C2×Q812yes—
175C23×D59#4112yes—
176C23×D59#4112yes—
177C22×C4×C59—21no—
178C22×C4×C59—21no—
179C22×C4×C59—21no—
180C22×C4×C59—21no—
181C22×C4×C59—21no—
182C22×C4×C59—21no—
183C22×C4×C59—21no—
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×C59C22×C412yes—
215C22×C4×C59C22×C412yes—
216C22×C4×C59C22×C412yes—
217C22×C4×C59C2×D412yes—
218C22×C4×C59C2×D412yes—
219C22×C4×C59C2×D412yes—
220C22×C4×C59C2×D412yes—
221C22×C4×C59C2×D412yes—
222C22×C4×C59C2×D412yes—
223C22×C4×C59C2×Q812yes—
224C22×C4×C59C2×Q812yes—
225C22×C4×C59#4112yes—
226C22×Dic59—21no—
227C22×Dic59—21no—
228C22×Dic59—21no—
229C22×Dic59—21no—
230C22×Dic59—21no—
231C22×Dic59—21no—
232C22×Dic59—21no—
233C22×Dic59—21no—
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×Dic59C22×C412yes—
266C22×Dic59C22×C412yes—
267C22×Dic59C22×C412yes—
268C22×Dic59C2×D412yes—
269C22×Dic59C2×D412yes—
270C22×Dic59C2×D412yes—
271C22×Dic59C2×D412yes—
272C22×Dic59C2×Q812yes—
273C22×Dic59C2×Q812yes—
274C22×Dic59#4112yes—
275C2×C4×D59—28no—
276C2×C4×D59—28no—
277C2×C4×D59—28no—
278C2×C4×D59—28no—
279C2×C4×D59—28no—
280C2×C4×D59—28no—
281C2×C4×D59—28no—
282C2×C4×D59—28no—
283C2×C4×D59—28no—
284C2×C4×D59—28no—
285C2×C4×D59—44no—
286C2×C4×D59—44no—
287C2×C4×D59—44no—
288C2×C4×D59—44no—
289C2×C4×D59—44no—
290C2×C4×D59—44no—
291C2×C4×D59—44no—
292C2×C4×D59—44no—
293C2×C4×D59—44no—
294C2×C4×D59—44no—
295C2×C4×D59—44no—
296C4⋊C4×C59—28no—
297C4⋊C4×C59—28no—
298C4⋊C4×C59—44no—
299C4⋊C4×C59—44no—
300C42×C59—44no—
301(C2×D59)⋊C4—28no—
302(C2×D59)⋊C4—28no—
303(C2×D59)⋊C4—44no—
304(C2×D59)⋊C4C4⋊C4116yescomplemented
305C4⋊Dic59—28no—
306Dic59⋊C4—28no—
307Dic59⋊C4—28no—
308Dic59⋊C4—28no—
309Dic59⋊C4—44no—
310Dic59⋊C4—44no—
311C4×Dic59—44no—
312C23×C59C23×C411yescharacteristic
313C23×C59C22×D411yescharacteristic
314C23×C59C22×D411yescharacteristic
315C23×C59C22×D411yescharacteristic
316C23×C59C22×D411yescharacteristic
317C23×C59C22×Q811yescharacteristic
318C23×C59C22×Q811yescharacteristic
319C23×C59C2×#4111yescharacteristic
320C23×C59C2×#4111yescharacteristic
321C23×C59C2×#4111yescharacteristic
322C23×C59C2×#4111yescharacteristic
323C23×C59H(5,𝔽2)11yescharacteristic
324C23×C59H(5,𝔽2)11yescharacteristic
325C23×C592−1+411yescharacteristic
326C23×C592−1+411yescharacteristic
327C22×D59—22no—
328C22×D59—22no—
329C22×D59—22no—
330C22×D59—22no—
331C22×D59—22no—
332C22×D59—22no—
333C22×D59—22no—
334C22×D59—22no—
335C22×D59—22no—
336C22×D59—22no—
337C22×D59—22no—
338C22×D59—22no—
339C22×D59—22no—
340C22×D59—22no—
341C22×D59—22no—
342C22×D59—22no—
343C22×D59—22no—
344C22×D59—22no—
345C22×D59—22no—
346C22×D59—22no—
347C22×D59—22no—
348C22×D59—22no—
349C22×D59—22no—
350C22×D59—22no—
351C22×D59—22no—
352C22×D59—22no—
353C22×D59—22no—
354C22×D59—22no—
355C22×D59C2×C4⋊C414yes—
356C22×D59C4×D414yes—
357C22×D59C4×Q814yes—
358C22×D59#12114yes—
359C22×D59C22⋊Q814yes—
360C22×D59#12514yes—
361C22×D59C4⋊Q814yes—
362C2×C4×C59—22no—
363C2×C4×C59—22no—
364C2×C4×C59—22no—
365C2×C4×C59—22no—
366C2×C4×C59—22no—
367C2×C4×C59—22no—
368C2×C4×C59—22no—
369C2×C4×C59—22no—
370C2×C4×C59—22no—
371C2×C4×C59—22no—
372C2×C4×C59—22no—
373C2×C4×C59—22no—
374C2×C4×C59—22no—
375C2×C4×C59—22no—
376C2×C4×C59—22no—
377C2×C4×C59—22no—
378C2×C4×C59—22no—
379C2×C4×C59—22no—
380C2×C4×C59—22no—
381C2×C4×C59—22no—
382C2×C4×C59—22no—
383C2×C4×C59—22no—
384C2×C4×C59—22no—
385C2×C4×C59—22no—
386C2×C4×C59—22no—
387C2×C4×C59—22no—
388C2×C4×C59—22no—
389C2×C4×C59—41no—
390C2×C4×C59—41no—
391C2×C4×C59—41no—
392C2×C4×C59—41no—
393C2×C4×C59—41no—
394C2×C4×C59—41no—
395C2×C4×C59—41no—
396C2×C4×C59—41no—
397C2×C4×C59—41no—
398C2×C4×C59—41no—
399C2×C4×C59—41no—
400C2×C4×C59—41no—
401C2×C4×C59—41no—
402C2×C4×C59—41no—
403C2×C4×C59—41no—
404C2×C4×C59—41no—
405C2×C4×C59—41no—
406C2×C4×C59—41no—
407C2×C4×C59—41no—
408C2×C4×C59C2×C4⋊C414yescomplemented
409C2×C4×C59C4×D414yes—
410C2×C4×C59#12014yes—
411C2×Dic59—22no—
412C2×Dic59—22no—
413C2×Dic59—22no—
414C2×Dic59—22no—
415C2×Dic59—22no—
416C2×Dic59—22no—
417C2×Dic59—22no—
418C2×Dic59—22no—
419C2×Dic59—22no—
420C2×Dic59—22no—
421C2×Dic59—22no—
422C2×Dic59—22no—
423C2×Dic59—22no—
424C2×Dic59—22no—
425C2×Dic59—22no—
426C2×Dic59—22no—
427C2×Dic59—22no—
428C2×Dic59—22no—
429C2×Dic59—22no—
430C2×Dic59—22no—
431C2×Dic59—22no—
432C2×Dic59—22no—
433C2×Dic59—22no—
434C2×Dic59—22no—
435C2×Dic59—41no—
436C2×Dic59—41no—
437C2×Dic59—41no—
438C2×Dic59—41no—
439C2×Dic59—41no—
440C2×Dic59—41no—
441C2×Dic59—41no—
442C2×Dic59—41no—
443C2×Dic59—41no—
444C2×Dic59—41no—
445C2×Dic59—41no—
446C2×Dic59—41no—
447C2×Dic59—41no—
448C2×Dic59—41no—
449C2×Dic59—41no—
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×Dic59C2×C4⋊C414yescomplemented
459C2×Dic59C4×D414yes—
460C4×D59—232no—
461C4×D59—416no—
462C4×D59—416no—
463#14043—591nomaximal, Sylow
464C22×C59C22×C4⋊C411yescharacteristic
465C22×C59C2×C4×D411yescharacteristic
466C22×C59C2×C4×D411yescharacteristic
467C22×C59C2×C4×D411yescharacteristic
468C22×C59C2×C4×Q811yescharacteristic
469C22×C59#52011yescharacteristic
470C22×C59#52011yescharacteristic
471C22×C59C2×#12011yescharacteristic
472C22×C59C2×#12111yescharacteristic
473C22×C59C2×C22⋊Q811yescharacteristic
474C22×C59#52511yescharacteristic
475C22×C59#52511yescharacteristic
476C22×C59#52511yescharacteristic
477C22×C59C2×#12511yescharacteristic
478C22×C59C2×C4⋊Q811yescharacteristic
479C22×C59#53411yescharacteristic
480C22×C59#53611yescharacteristic
481C22×C59#53911yescharacteristic
482C22×C59#53911yescharacteristic
483C22×C59D4211yescharacteristic
484C22×C59D4211yescharacteristic
485C22×C59#54611yescharacteristic
486C22×C59#54611yescharacteristic
487C22×C59#54711yescharacteristic
488C22×C59#54711yescharacteristic
489C22×C59D4×Q811yescharacteristic
490C22×C59D4×Q811yescharacteristic
491C22×C59D4×Q811yescharacteristic
492C22×C59D4×Q811yescharacteristic
493C22×C59#55211yescharacteristic
494C22×C59#55211yescharacteristic
495C22×C59#55411yescharacteristic
496C22×C59#55411yescharacteristic
497C22×C59#55411yescharacteristic
498C22×C59#55411yescharacteristic
499C2×D59—24no—
500C2×D59—24no—
501C2×D59—24no—
502C2×D59—24no—
503C2×D59—24no—
504C2×D59—24no—
505C2×D59—24no—
506C2×D59—24no—
507C2×D59—24no—
508C2×D59—24no—
509C2×D59—24no—
510C2×D59—24no—
511C2×D59—24no—
512C2×D59—24no—
513C2×D59#38918yescomplemented
514C4×C59—24no—
515C4×C59—24no—
516C4×C59—24no—
517C4×C59—42no—
518C4×C59—42no—
519C4×C59—42no—
520C4×C59—81no—
521Dic59—24no—
522Dic59—24no—
523Dic59—42no—
524Dic59—42no—
525Dic59—42no—
526Dic59—42no—
527Dic59—81no—
528C23×C4⋊C4—591no—
529C2×#389—591no—
530C2×#389D5911yescharacteristic, complemented
531C2×#385—591no—
532C2×#385—591no—
533C2×#385—591no—
534C2×C4×C22⋊C4—591no—
535#1444—591no—
536#1444—591no—
537#1441—591no—
538#1441—591no—
539#1436—591no—
540#1436—591no—
541C22⋊#95—591no—
542C22⋊#95—591no—
543C2×C59C2×#38911yescharacteristic
544C2×C59C4×#12011yescharacteristic
545C2×C59#232211yescharacteristic
546C2×C59D4×C4⋊C411yescharacteristic
547C2×C59D4×C4⋊C411yescharacteristic
548C2×C59#236011yescharacteristic
549C2×C59#236011yescharacteristic
550C2×C59#241011yescharacteristic
551C2×C59#241311yescharacteristic
552C2×C59#243411yescharacteristic
553C2×C59#244911yescharacteristic
554C2×C59#244911yescharacteristic
555C2×C59#247311yescharacteristic
556C2×C59#247311yescharacteristic
557C2×C59#258311yescharacteristic
558D59—28no—
559C24×C4—591no—
560C24×C4—591no—
561C24×C4—591no—
562C22×C4⋊C4—591no—
563C22×C4⋊C4—591no—
564C22×C4⋊C4—591no—
565C22×C4⋊C4—591no—
566C22×C4⋊C4—591no—
567C22×C4⋊C4—591no—
568C22×C4⋊C4—1184no—
569C22×C4⋊C4—1184no—
570C22×C4⋊C4—1184no—
571C22×C4⋊C4C2×D5911yescharacteristic
572C22×C4⋊C4C2×D5911yescharacteristic
573C22×C4⋊C4C2×D5911yescharacteristic
574C22×C4⋊C4C2×D5911yescharacteristic
575C22×C22⋊C4—591no—
576C22×C22⋊C4—591no—
577C22×C22⋊C4—591no—
578C22×C22⋊C4—591no—
579C22×C42—591no—
580C22×C42C2×D5911yescharacteristic
581#389—24no—
582#389—1184no—
583#385—598no—
584#385—1184no—
585#385—1184no—
586C4×C22⋊C4—1184no—
587C2×#95—591no—
588C2×#95—591no—
589C2×#95—591no—
590C2×#95—591no—
591C2×#95—591no—
592C2×#95—591no—
593C2×#95—591no—
594C2×#95—591no—
595C2×#95—591no—
596C2×#95—591no—
597C2×#95—591no—
598C2×#95—591no—
599C2×#95—591no—
600C2×#95—591no—
601C2×#95C2×D5911yescharacteristic
602C2×#95C2×D5911yescharacteristic
603C59#1404311yescharacteristic, complemented, Sylow
604C25—591no—
605C23×C4—591no—
606C23×C4—591no—
607C23×C4—591no—
608C23×C4—591no—
609C23×C4—591no—
610C23×C4—591no—
611C23×C4—594no—
612C23×C4—594no—
613C23×C4—591no—
614C23×C4—1182no—
615C23×C4—1182no—
616C23×C4—1182no—
617C23×C4—1182no—
618C23×C4—1182no—
619C23×C4—1182no—
620C23×C4—1182no—
621C23×C4—1182no—
622C23×C4—1182no—
623C23×C4—1182no—
624C23×C4—1182no—
625C23×C4—1182no—
626C23×C4—1182no—
627C23×C4—1182no—
628C23×C4—1182no—
629C23×C4—2361no—
630C23×C4—2361no—
631C23×C4—2361no—
632C23×C4—2361no—
633C23×C4C22×D5911yescharacteristic
634C23×C4C22×D5911yescharacteristic
635C23×C4C22×D5911yescharacteristic
636C23×C4C22×D5911yescharacteristic
637C23×C4C22×D5911yescharacteristic
638C23×C4C22×D5911yescharacteristic
639C23×C4C22×D5911yescharacteristic
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—22no—
643C2×C4⋊C4—22no—
644C2×C4⋊C4—22no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—22no—
649C2×C4⋊C4—41no—
650C2×C4⋊C4—594no—
651C2×C4⋊C4—594no—
652C2×C4⋊C4—11832no—
653C2×C4⋊C4—1182no—
654C2×C4⋊C4—1182no—
655C2×C4⋊C4—1182no—
656C2×C4⋊C4—1182no—
657C2×C4⋊C4—1182no—
658C2×C4⋊C4—1182no—
659C2×C4⋊C4—1182no—
660C2×C4⋊C4—1182no—
661C2×C4⋊C4—1182no—
662C2×C4⋊C4—1182no—
663C2×C4⋊C4—1182no—
664C2×C4⋊C4—1182no—
665C2×C4⋊C4—1182no—
666C2×C4⋊C4—2361no—
667C2×C4⋊C4—2361no—
668C2×C4⋊C4—2361no—
669C2×C4⋊C4C4×D5914yescomplemented
670C2×C4⋊C4C22⋊D5914yes—
671C2×C22⋊C4—594no—
672C2×C22⋊C4—594no—
673C2×C22⋊C4—594no—
674C2×C22⋊C4—594no—
675C2×C22⋊C4—594no—
676C2×C22⋊C4—1182no—
677C2×C22⋊C4—1182no—
678C2×C22⋊C4—1182no—
679C2×C22⋊C4—1182no—
680C2×C22⋊C4—1182no—
681C2×C22⋊C4—1182no—
682C2×C22⋊C4—1182no—
683C2×C42—22no—
684C2×C42—22no—
685C2×C42—41no—
686C2×C42—1182no—
687C2×C42—1182no—
688C2×C42—2361no—
689#95—22no—
690#95—22no—
691#95—594no—
692#95—594no—
693#95—1182no—
694#95—1182no—
695#95—1182no—
696#95—1182no—
697#95—1182no—
698#95—1182no—
699#95—1182no—
700#95—1182no—
701#95—1182no—
702#95—1182no—
703#95—2361no—
704#95—2361no—
705C24—592no—
706C24—592no—
707C24—592no—
708C24—592no—
709C24—592no—
710C24—592no—
711C24—592no—
712C24—1181no—
713C24—1181no—
714C24—1181no—
715C24—1181no—
716C24—1181no—
717C24—1181no—
718C24—1181no—
719C24—1181no—
720C24C23×D5911yescharacteristic
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—592no—
759C22×C4—592no—
760C22×C4—592no—
761C22×C4—592no—
762C22×C4—592no—
763C22×C4—592no—
764C22×C4—592no—
765C22×C4—592no—
766C22×C4—592no—
767C22×C4—592no—
768C22×C4—1188no—
769C22×C4—1188no—
770C22×C4—1188no—
771C22×C4—1188no—
772C22×C4—1188no—
773C22×C4—1188no—
774C22×C4—1188no—
775C22×C4—1188no—
776C22×C4—1181no—
777C22×C4—1181no—
778C22×C4—1181no—
779C22×C4—1181no—
780C22×C4—1181no—
781C22×C4—1181no—
782C22×C4—1181no—
783C22×C4—1181no—
784C22×C4—1188no—
785C22×C4—1181no—
786C22×C4—1181no—
787C22×C4—1181no—
788C22×C4—1181no—
789C22×C4—1181no—
790C22×C4—1181no—
791C22×C4—1181no—
792C22×C4—1181no—
793C22×C4—1181no—
794C22×C4—1181no—
795C22×C4—1181no—
796C22×C4—1181no—
797C22×C4—1181no—
798C22×C4—1181no—
799C22×C4—1181no—
800C22×C4—1181no—
801C22×C4—1181no—
802C22×C4—1181no—
803C22×C4—1181no—
804C22×C4—1181no—
805C22×C4—1181no—
806C22×C4—1181no—
807C22×C4—1181no—
808C22×C4—1181no—
809C22×C4—1188no—
810C22×C4—1181no—
811C22×C4—1181no—
812C22×C4—1181no—
813C22×C4—1181no—
814C22×C4—1181no—
815C22×C4—1181no—
816C22×C4—1181no—
817C22×C4—2364no—
818C22×C4—2364no—
819C22×C4—2364no—
820C22×C4—2364no—
821C22×C4—2364no—
822C22×C4—2364no—
823C22×C4—2364no—
824C22×C4—2364no—
825C22×C4—2364no—
826C22×C4—2364no—
827C22×C4—2364no—
828C22×C4C2×C4×D5912yes—
829C22×C4C2×C4×D5912yes—
830C22×C4C2×C4×D5912yes—
831C22×C4#1174568512yes—
832C22×C4D4×D5912yes—
833C22×C4D4×D5912yes—
834C22×C4D4×D5912yes—
835C22×C4Q8×D5912yes—
836C22×C4Q8×D5912yes—
837C22×C4C2×C22⋊D5912yes—
838C22×C4C2×C22⋊D5912yes—
839C22×C4C2×C22⋊D5912yes—
840C4⋊C4—28no—
841C4⋊C4—28no—
842C4⋊C4—44no—
843C4⋊C4—44no—
844C4⋊C4—1188no—
845C4⋊C4—1188no—
846C4⋊C4—1188no—
847C4⋊C4—1188no—
848C4⋊C4—2364no—
849C4⋊C4—2364no—
850C22⋊C4—5916no—
851C22⋊C4—1188no—
852C22⋊C4—1188no—
853C22⋊C4—2364no—
854C42—44no—
855C42—2364no—
856C23—594no—
857C23—594no—
858C23—594no—
859C23—594no—
860C23—594no—
861C23—594no—
862C23—594no—
863C23—1182no—
864C23—1182no—
865C23—1182no—
866C23—1182no—
867C23—1182no—
868C23—1182no—
869C23—1182no—
870C23—1182no—
871C23—1182no—
872C23—1182no—
873C23—1182no—
874C23—1182no—
875C23—1182no—
876C23—1182no—
877C23—1182no—
878C23—1182no—
879C23—1182no—
880C23—1182no—
881C23—1182no—
882C23—1182no—
883C23—1182no—
884C23—1182no—
885C23—1182no—
886C23—1182no—
887C23—1182no—
888C23—1182no—
889C23—1182no—
890C23—1182no—
891C23C22×C4×D5911yescharacteristic
892C23C2×D4×D5911yescharacteristic
893C23C2×D4×D5911yescharacteristic
894C23C2×D4×D5911yescharacteristic
895C23C22×C22⋊D5911yescharacteristic
896C23C2×Q8×D5911yescharacteristic
897C23C2×Q8×D5911yescharacteristic
898C23#41×D5911yescharacteristic
899C23#41×D5911yescharacteristic
900C23#41×D5911yescharacteristic
901C23C2×#1174568511yescharacteristic
902C23#1427377211yescharacteristic
903C23#1427377311yescharacteristic
904C23#1427377511yescharacteristic
905C23#1427377511yescharacteristic
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—594no—
953C2×C4—594no—
954C2×C4—11832no—
955C2×C4—1182no—
956C2×C4—1182no—
957C2×C4—1182no—
958C2×C4—1182no—
959C2×C4—1182no—
960C2×C4—1182no—
961C2×C4—1182no—
962C2×C4—1182no—
963C2×C4—1182no—
964C2×C4—1182no—
965C2×C4—1182no—
966C2×C4—1182no—
967C2×C4—1182no—
968C2×C4—1182no—
969C2×C4—1182no—
970C2×C4—1182no—
971C2×C4—1182no—
972C2×C4—1182no—
973C2×C4—1182no—
974C2×C4—1182no—
975C2×C4—1182no—
976C2×C4—1182no—
977C2×C4—1182no—
978C2×C4—1182no—
979C2×C4—23616no—
980C2×C4—23616no—
981C2×C4—2361no—
982C2×C4—2361no—
983C2×C4—2361no—
984C2×C4—2361no—
985C2×C4—2361no—
986C2×C4—2361no—
987C2×C4—2361no—
988C2×C4—2361no—
989C2×C4—2361no—
990C2×C4—2361no—
991C2×C4—2361no—
992C2×C4—2361no—
993C2×C4—2361no—
994C2×C4—2361no—
995C2×C4—2361no—
996C2×C4—2361no—
997C2×C4—2361no—
998C2×C4—2361no—
999C2×C4—2361no—
1000C2×C4—2361no—
1001C2×C4—2361no—
1002C2×C4—2361no—
1003C2×C4—2361no—
1004C2×C4C4⋊C4×D5914yescomplemented
1005C2×C4C4×C22⋊D5914yes—
1006C2×C4#1427369514yes—
1007C22—598no—
1008C22—1184no—
1009C22—1184no—
1010C22—1184no—
1011C22—1184no—
1012C22—1184no—
1013C22—1184no—
1014C22—1184no—
1015C22—1184no—
1016C22—1184no—
1017C22—1184no—
1018C22—1184no—
1019C22—1184no—
1020C22—1184no—
1021C22—1184no—
1022C22C2×C4⋊C4×D5911yescharacteristic
1023C22C4×D4×D5911yescharacteristic
1024C22C4×D4×D5911yescharacteristic
1025C22C2×C4×C22⋊D5911yescharacteristic
1026C22C4×Q8×D5911yescharacteristic
1027C22#1683788311yescharacteristic
1028C22#1683788411yescharacteristic
1029C22C2×#1427369511yescharacteristic
1030C22#121×D5911yescharacteristic
1031C22C22⋊Q8×D5911yescharacteristic
1032C22#1683790911yescharacteristic
1033C22#1683791111yescharacteristic
1034C22#1683791111yescharacteristic
1035C22#125×D5911yescharacteristic
1036C22C4⋊Q8×D5911yescharacteristic
1037C22#1683796011yescharacteristic
1038C22#1683797711yescharacteristic
1039C22#1683799811yescharacteristic
1040C22#1683800011yescharacteristic
1041C22D4×C22⋊D5911yescharacteristic
1042C22#1683803611yescharacteristic
1043C22#1683804011yescharacteristic
1044C22#1683804111yescharacteristic
1045C22#1683805311yescharacteristic
1046C22#1683805411yescharacteristic
1047C22Q8×C22⋊D5911yescharacteristic
1048C22Q8×C22⋊D5911yescharacteristic
1049C22#1683806711yescharacteristic
1050C22#1683806711yescharacteristic
1051C22#1683808411yescharacteristic
1052C22#1683809311yescharacteristic
1053C22#1683810611yescharacteristic
1054C22#1683810711yescharacteristic
1055C22#1683810811yescharacteristic
1056C22#1683811211yescharacteristic
1057C4—24no—
1058C4—24no—
1059C4—24no—
1060C4—42no—
1061C4—42no—
1062C4—42no—
1063C4—81no—
1064C4—1184no—
1065C4—1184no—
1066C4—4721no—
1067C4—2362no—
1068C4—2362no—
1069C4—2362no—
1070C4—2362no—
1071C2—1188no—
1072C2#389×D5911yescharacteristic
1073C2C4×#1427369511yescharacteristic
1074C2#2142676011yescharacteristic
1075C2C4⋊C4×C22⋊D5911yescharacteristic
1076C2#2142699711yescharacteristic
1077C2#2142709711yescharacteristic
1078C2#2142709811yescharacteristic
1079C2#2142746711yescharacteristic
1080C2#2142750011yescharacteristic
1081C2#2142773711yescharacteristic
1082C2#2142790211yescharacteristic
1083C2#2142791211yescharacteristic
1084C2#2142823311yescharacteristic
1085C2#2142824311yescharacteristic
1086C2#2142947411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC2×C59×#389C2
socle, cosocleC24×C59C24
prime radicalC24×D59C23
hypercenterC2×#389D59
hypocenterC59#14043
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#16837297C2semidirect
7. #21422360C2semidirect
8. #21422359C2semidirect
9. #21422349C2semidirect
10. #21422347C2semidirect
11. #21422329C2semidirect
12. #21422328C2semidirect
15. C2×C59×#389C2semidirect
36. #16837273C4semidirect
105. C2×Dic59⋊C4C2×C4semidirect
135. C59⋊#95C2×C4semidirect
136. C59⋊#95C2×C4semidirect
154. C2×C4⋊C4×C59C2×C4semidirect
304. (C2×D59)⋊C4C4⋊C4semidirect
408. C2×C4×C59C2×C4⋊C4semidirect
458. C2×Dic59C2×C4⋊C4semidirect
513. C2×D59#389semidirect
530. C2×#389D59semidirect
603. C59#14043semidirect
669. C2×C4⋊C4C4×D59semidirect
1004. C2×C4C4⋊C4×D59semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D592
C2×#168372972
C2×#168372732
C2×C4×(C2×D59)⋊C42
#214223602
#214223592
#214223492
#214223472
#214223292
#214223282
(C2×D59)⋊#952
C2×C59×#3892
#1404359