Finite Group Databasebeta

← #28516615

Subgroups — #28516615

Order 15104.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837298C211yesmaximal, characteristic, complemented
2C2×#16837297C211yesmaximal, characteristic, complemented
3C2×#16837292C211yesmaximal, characteristic
4C2×#16837291C211yesmaximal, characteristic
5C2×#16837276C211yesmaximal, characteristic
6C2×#16837261C211yesmaximal, characteristic
7C2×#16837259C211yesmaximal, characteristic
8#21422359C211yesmaximal, characteristic, complemented
9#21422350C211yesmaximal, characteristic, complemented
10#21422348C211yesmaximal, characteristic, complemented
11#21422340C211yesmaximal, characteristic
12#21422338C211yesmaximal, characteristic
13#21422330C211yesmaximal, characteristic, complemented
14#21422327C211yesmaximal, characteristic, complemented
15C59×#1444C211yesmaximal, characteristic, complemented
16C23×C4×D59C2211yescharacteristic
17C22×C4⋊Dic59C2211yescharacteristic
18C22×C4⋊Dic59C2211yescharacteristic
19C22×Dic59⋊C4C2211yescharacteristic
20C22×Dic59⋊C4C2211yescharacteristic
21C22×Dic59⋊C4C2211yescharacteristic
22C22×Dic59⋊C4C2211yescharacteristic
23C22×Dic59⋊C4C2211yescharacteristic
24C22×(C2×D59)⋊C4C2211yescharacteristic
25C22×(C2×D59)⋊C4C2211yescharacteristic
26C22×(C2×D59)⋊C4C2211yescharacteristic
27C22×(C2×D59)⋊C4C2211yescharacteristic
28C22×(C2×D59)⋊C4C2211yescharacteristic
29C22×(C2×D59)⋊C4C2211yescharacteristic
30C22×C4×Dic59C2211yescharacteristic
31C22×C4×Dic59C2211yescharacteristic
32#16837298—24no—
33#16837297—24no—
34#16837292—24no—
35#16837291—24no—
36#16837276C418yescomplemented
37#16837261—24no—
38#16837259—24no—
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
51C22×C4⋊C4×C59C2211yescharacteristic
52C22×C4⋊C4×C59C2211yescharacteristic
53C22×C4⋊C4×C59C2211yescharacteristic
54C2×#95×C59C2211yescharacteristic
55C2×#95×C59C2211yescharacteristic
56C2×#95×C59C2211yescharacteristic
57C2×#95×C59C2211yescharacteristic
58C24×D59C2311yescharacteristic
59C23×Dic59C2311yescharacteristic
60C23×Dic59C2311yescharacteristic
61C23×Dic59C2311yescharacteristic
62C23×Dic59C2311yescharacteristic
63C23×Dic59C2311yescharacteristic
64C23×Dic59C2311yescharacteristic
65C23×Dic59C2311yescharacteristic
66C22×C4×D59—22no—
67C22×C4×D59—22no—
68C22×C4×D59—22no—
69C22×C4×D59—22no—
70C22×C4×D59—41no—
71C22×C4×D59—41no—
72C22×C4×D59C2×C414yes—
73C2×C4⋊Dic59—22no—
74C2×C4⋊Dic59—22no—
75C2×C4⋊Dic59—22no—
76C2×C4⋊Dic59—22no—
77C2×C4⋊Dic59—41no—
78C2×C4⋊Dic59C2×C414yes—
79C2×Dic59⋊C4—22no—
80C2×Dic59⋊C4—22no—
81C2×Dic59⋊C4—22no—
82C2×Dic59⋊C4—22no—
83C2×Dic59⋊C4—22no—
84C2×Dic59⋊C4—22no—
85C2×Dic59⋊C4—22no—
86C2×Dic59⋊C4—22no—
87C2×Dic59⋊C4—22no—
88C2×Dic59⋊C4—22no—
89C2×Dic59⋊C4—41no—
90C2×Dic59⋊C4—41no—
91C2×Dic59⋊C4—41no—
92C2×Dic59⋊C4—41no—
93C2×Dic59⋊C4C2×C414yes—
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)⋊C4C2×C414yes—
109C2×(C2×D59)⋊C4C2×C414yes—
110C2×(C2×D59)⋊C4D414yes—
111C2×(C2×D59)⋊C4Q814yes—
112C2×C4×Dic59—22no—
113C2×C4×Dic59—22no—
114C2×C4×Dic59—22no—
115C2×C4×Dic59—22no—
116C2×C4×Dic59—41no—
117C2×C4×Dic59—41no—
118C59⋊#95—22no—
119C59⋊#95—22no—
120C59⋊#95—22no—
121C59⋊#95—22no—
122C59⋊#95—22no—
123C59⋊#95—22no—
124C59⋊#95—41no—
125C59⋊#95—41no—
126C59⋊#95—41no—
127C59⋊#95C2×C414yes—
128C59⋊#95D414yes—
129C59⋊#95D414yes—
130C23×C4×C59C2311yescharacteristic
131C23×C4×C59C2311yescharacteristic
132C23×C4×C59C2311yescharacteristic
133C23×C4×C59C2311yescharacteristic
134C23×C4×C59C2311yescharacteristic
135C23×C4×C59C2311yescharacteristic
136C23×C4×C59C2311yescharacteristic
137C2×C4⋊C4×C59—22no—
138C2×C4⋊C4×C59—22no—
139C2×C4⋊C4×C59—22no—
140C2×C4⋊C4×C59—22no—
141C2×C4⋊C4×C59—41no—
142C2×C4⋊C4×C59—41no—
143C2×C4⋊C4×C59—41no—
144C2×C4⋊C4×C59—41no—
145C2×C4⋊C4×C59—41no—
146#95×C59—22no—
147#95×C59—22no—
148#95×C59—41no—
149#95×C59C2×C414yes—
150C24×C59C2411yescharacteristic
151C23×D59—21no—
152C23×D59—21no—
153C23×D59—21no—
154C23×D59—21no—
155C23×D59—21no—
156C23×D59—21no—
157C23×D59—21no—
158C23×D59—21no—
159C23×D59—21no—
160C23×D59—21no—
161C23×D59—21no—
162C23×D59—21no—
163C23×D59C22×C412yes—
164C23×D59C2×D412yes—
165C23×D59C2×Q812yes—
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—21no—
172C22×C4×C59—21no—
173C22×C4×C59—21no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—21no—
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×C59C22×C412yes—
208C22×C4×C59C22×C412yes—
209C22×C4×C59C22×C412yes—
210C22×C4×C59C2×D412yes—
211C22×C4×C59C2×D412yes—
212C22×C4×C59C2×D412yes—
213C22×C4×C59C2×Q812yes—
214C22×C4×C59#4112yes—
215C22×Dic59—21no—
216C22×Dic59—21no—
217C22×Dic59—21no—
218C22×Dic59—21no—
219C22×Dic59—21no—
220C22×Dic59—21no—
221C22×Dic59—21no—
222C22×Dic59—21no—
223C22×Dic59—21no—
224C22×Dic59—21no—
225C22×Dic59—21no—
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×Dic59C22×C412yes—
255C22×Dic59C22×C412yes—
256C22×Dic59C22×C412yes—
257C22×Dic59C2×D412yes—
258C22×Dic59C2×D412yes—
259C22×Dic59C2×D412yes—
260C22×Dic59C2×D412yes—
261C22×Dic59C2×D412yes—
262C22×Dic59C2×Q812yes—
263C22×Dic59#4112yes—
264C2×C4×D59—28no—
265C2×C4×D59—28no—
266C2×C4×D59—44no—
267C2×C4×D59—44no—
268C2×C4×D59—44no—
269C2×C4×D59—44no—
270C2×C4×D59—44no—
271C4⋊C4×C59—44no—
272C4⋊C4×C59—44no—
273C4⋊C4×C59—44no—
274(C2×D59)⋊C4—44no—
275(C2×D59)⋊C4—44no—
276(C2×D59)⋊C4—44no—
277(C2×D59)⋊C4—44no—
278(C2×D59)⋊C4—44no—
279(C2×D59)⋊C4C4⋊C4116yescomplemented
280C4⋊Dic59—28no—
281C4⋊Dic59—44no—
282Dic59⋊C4—28no—
283Dic59⋊C4—44no—
284Dic59⋊C4—44no—
285Dic59⋊C4—44no—
286Dic59⋊C4—44no—
287C4×Dic59—44no—
288C4×Dic59—44no—
289C23×C59C23×C411yescharacteristic
290C23×C59C22×D411yescharacteristic
291C23×C59C22×D411yescharacteristic
292C23×C59C22×D411yescharacteristic
293C23×C59C22×Q811yescharacteristic
294C23×C59C2×#4111yescharacteristic
295C23×C59C2×#4111yescharacteristic
296C23×C59H(5,𝔽2)11yescharacteristic
297C23×C59H(5,𝔽2)11yescharacteristic
298C23×C59H(5,𝔽2)11yescharacteristic
299C23×C59H(5,𝔽2)11yescharacteristic
300C23×C592−1+411yescharacteristic
301C23×C592−1+411yescharacteristic
302C23×C592−1+411yescharacteristic
303C23×C592−1+411yescharacteristic
304C22×D59—22no—
305C22×D59—22no—
306C22×D59—22no—
307C22×D59—22no—
308C22×D59—22no—
309C22×D59—22no—
310C22×D59—22no—
311C22×D59—22no—
312C22×D59—22no—
313C22×D59—22no—
314C22×D59—22no—
315C22×D59—22no—
316C22×D59—22no—
317C22×D59—22no—
318C22×D59—22no—
319C22×D59—22no—
320C22×D59—22no—
321C22×D59—22no—
322C22×D59—41no—
323C22×D59—41no—
324C22×D59—41no—
325C22×D59—41no—
326C22×D59—41no—
327C22×D59—41no—
328C22×D59—41no—
329C22×D59—41no—
330C22×D59—41no—
331C22×D59—41no—
332C22×D59—41no—
333C22×D59—41no—
334C22×D59—41no—
335C22×D59—41no—
336C22×D59—41no—
337C22×D59—41no—
338C22×D59C2×C4⋊C414yes—
339C2×C4×C59—22no—
340C2×C4×C59—22no—
341C2×C4×C59—22no—
342C2×C4×C59—22no—
343C2×C4×C59—22no—
344C2×C4×C59—22no—
345C2×C4×C59—22no—
346C2×C4×C59—22no—
347C2×C4×C59—22no—
348C2×C4×C59—22no—
349C2×C4×C59—22no—
350C2×C4×C59—22no—
351C2×C4×C59—22no—
352C2×C4×C59—22no—
353C2×C4×C59—22no—
354C2×C4×C59—22no—
355C2×C4×C59—22no—
356C2×C4×C59—22no—
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—41no—
364C2×C4×C59—41no—
365C2×C4×C59—41no—
366C2×C4×C59—41no—
367C2×C4×C59—41no—
368C2×C4×C59—41no—
369C2×C4×C59—41no—
370C2×C4×C59—41no—
371C2×C4×C59—41no—
372C2×C4×C59—41no—
373C2×C4×C59—41no—
374C2×C4×C59—41no—
375C2×C4×C59—41no—
376C2×C4×C59—41no—
377C2×C4×C59—41no—
378C2×C4×C59—41no—
379C2×C4×C59—41no—
380C2×C4×C59—41no—
381C2×C4×C59—41no—
382C2×C4×C59—41no—
383C2×C4×C59—41no—
384C2×C4×C59—41no—
385C2×C4×C59—41no—
386C2×C4×C59C2×C4⋊C414yes—
387C2×C4×C59C4×D414yes—
388C2×Dic59—22no—
389C2×Dic59—22no—
390C2×Dic59—22no—
391C2×Dic59—22no—
392C2×Dic59—22no—
393C2×Dic59—22no—
394C2×Dic59—22no—
395C2×Dic59—22no—
396C2×Dic59—22no—
397C2×Dic59—22no—
398C2×Dic59—22no—
399C2×Dic59—22no—
400C2×Dic59—22no—
401C2×Dic59—22no—
402C2×Dic59—22no—
403C2×Dic59—22no—
404C2×Dic59—22no—
405C2×Dic59—22no—
406C2×Dic59—22no—
407C2×Dic59—22no—
408C2×Dic59—22no—
409C2×Dic59—22no—
410C2×Dic59—22no—
411C2×Dic59—22no—
412C2×Dic59—41no—
413C2×Dic59—41no—
414C2×Dic59—41no—
415C2×Dic59—41no—
416C2×Dic59—41no—
417C2×Dic59—41no—
418C2×Dic59—41no—
419C2×Dic59—41no—
420C2×Dic59—41no—
421C2×Dic59—41no—
422C2×Dic59—41no—
423C2×Dic59—41no—
424C2×Dic59—41no—
425C2×Dic59—41no—
426C2×Dic59—41no—
427C2×Dic59—41no—
428C2×Dic59—41no—
429C2×Dic59—41no—
430C2×Dic59—41no—
431C2×Dic59—41no—
432C2×Dic59—41no—
433C2×Dic59—41no—
434C2×Dic59—41no—
435C2×Dic59C2×C4⋊C414yes—
436C2×Dic59C4×D414yes—
437C4×D59—416no—
438#14402—591nomaximal, Sylow
439C22×C59C22×C4⋊C411yescharacteristic
440C22×C59C2×C4×D411yescharacteristic
441C22×C59C2×C4×D411yescharacteristic
442C22×C59#51811yescharacteristic
443C22×C59#51911yescharacteristic
444C22×C59#52011yescharacteristic
445C22×C59#52011yescharacteristic
446C22×C59#53611yescharacteristic
447C22×C59#53611yescharacteristic
448C22×C59#53711yescharacteristic
449C22×C59#53711yescharacteristic
450C22×C59#53711yescharacteristic
451C22×C59#53711yescharacteristic
452C22×C59#54111yescharacteristic
453C22×C59#54111yescharacteristic
454C22×C59#54211yescharacteristic
455C22×C59#54211yescharacteristic
456C22×C59#54411yescharacteristic
457C22×C59#54411yescharacteristic
458C22×C59D4211yescharacteristic
459C22×C59D4211yescharacteristic
460C22×C59D4211yescharacteristic
461C22×C59#54611yescharacteristic
462C22×C59#54611yescharacteristic
463C22×C59#54711yescharacteristic
464C22×C59#54711yescharacteristic
465C22×C59D4×Q811yescharacteristic
466C22×C59D4×Q811yescharacteristic
467C22×C59#55111yescharacteristic
468C22×C59#55411yescharacteristic
469C22×C59#55411yescharacteristic
470C22×C59#56011yescharacteristic
471C22×C59#56211yescharacteristic
472C22×C59#56211yescharacteristic
473C22×C59#56311yescharacteristic
474C2×D59—24no—
475C2×D59—24no—
476C2×D59—24no—
477C2×D59—42no—
478C2×D59—42no—
479C2×D59—42no—
480C2×D59—42no—
481C2×D59—42no—
482C2×D59—42no—
483C2×D59—42no—
484C2×D59—42no—
485C2×D59—42no—
486C2×D59—42no—
487C2×D59—42no—
488C2×D59—42no—
489C4×C59—24no—
490C4×C59—24no—
491C4×C59—42no—
492C4×C59—42no—
493C4×C59—81no—
494C4×C59—81no—
495C4×C59—81no—
496Dic59—24no—
497Dic59—24no—
498Dic59—42no—
499Dic59—42no—
500Dic59—42no—
501Dic59—42no—
502Dic59—81no—
503C2×#389—591no—
504C2×#389—591no—
505C2×#388—591no—
506C2×#388—591no—
507C2×#385—591no—
508C2×#380—591no—
509C2×#380—591no—
510#1444—591no—
511#1444D5911yescharacteristic, complemented
512#1441—591no—
513#1441—591no—
514#1439—591no—
515#1439—591no—
516#1436—591no—
517#1436—591no—
518C2×C59#231611yescharacteristic
519C2×C59#232311yescharacteristic
520C2×C59#232311yescharacteristic
521C2×C59D4×C4⋊C411yescharacteristic
522C2×C59D4×C4⋊C411yescharacteristic
523C2×C59#235811yescharacteristic
524C2×C59#237611yescharacteristic
525C2×C59#267211yescharacteristic
526C2×C59#267211yescharacteristic
527C2×C59#267511yescharacteristic
528C2×C59#267711yescharacteristic
529C2×C59#270411yescharacteristic
530C2×C59#270411yescharacteristic
531C2×C59#272211yescharacteristic
532C2×C59#274211yescharacteristic
533D59—44no—
534C24×C4—591no—
535C22×C4⋊C4—591no—
536C22×C4⋊C4—591no—
537C22×C4⋊C4—591no—
538C22×C4⋊C4—591no—
539C22×C4⋊C4—591no—
540C22×C4⋊C4—591no—
541C22×C4⋊C4—591no—
542C22×C4⋊C4C2×D5911yescharacteristic
543C22×C4⋊C4C2×D5911yescharacteristic
544C22×C4⋊C4C2×D5911yescharacteristic
545C22×C22⋊C4—591no—
546C22×C22⋊C4—591no—
547C22×C22⋊C4—591no—
548C22×C22⋊C4—591no—
549C22×C22⋊C4—591no—
550C22×C22⋊C4—591no—
551C22×C42—591no—
552C22×C42—591no—
553#389—1184no—
554#389—1184no—
555#388—1184no—
556#388—1184no—
557#385—598no—
558#380—1184no—
559#380—1184no—
560C2×#95—591no—
561C2×#95—591no—
562C2×#95—591no—
563C2×#95—591no—
564C2×#95—591no—
565C2×#95—591no—
566C2×#95—591no—
567C2×#95—591no—
568C2×#95—591no—
569C2×#95—591no—
570C2×#95—591no—
571C2×#95—591no—
572C2×#95C2×D5911yescharacteristic
573C2×#95C2×D5911yescharacteristic
574C2×#95C2×D5911yescharacteristic
575C2×#95C2×D5911yescharacteristic
576C59#1440211yescharacteristic, complemented, Sylow
577C25—591no—
578C23×C4—591no—
579C23×C4—591no—
580C23×C4—591no—
581C23×C4—591no—
582C23×C4—591no—
583C23×C4—591no—
584C23×C4—594no—
585C23×C4—591no—
586C23×C4—1182no—
587C23×C4—1182no—
588C23×C4—1182no—
589C23×C4—1182no—
590C23×C4—2361no—
591C23×C4—2361no—
592C23×C4C22×D5911yescharacteristic
593C23×C4C22×D5911yescharacteristic
594C23×C4C22×D5911yescharacteristic
595C23×C4C22×D5911yescharacteristic
596C23×C4C22×D5911yescharacteristic
597C23×C4C22×D5911yescharacteristic
598C23×C4C22×D5911yescharacteristic
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—594no—
609C2×C4⋊C4—594no—
610C2×C4⋊C4—1182no—
611C2×C4⋊C4—1182no—
612C2×C4⋊C4—1182no—
613C2×C4⋊C4—1182no—
614C2×C4⋊C4—1182no—
615C2×C4⋊C4—1182no—
616C2×C4⋊C4—1182no—
617C2×C4⋊C4—1182no—
618C2×C4⋊C4—1182no—
619C2×C4⋊C4—1182no—
620C2×C4⋊C4—1182no—
621C2×C4⋊C4—1182no—
622C2×C4⋊C4—1182no—
623C2×C4⋊C4—1182no—
624C2×C4⋊C4—2361no—
625C2×C4⋊C4—2361no—
626C2×C4⋊C4—2361no—
627C2×C4⋊C4—2361no—
628C2×C4⋊C4—2361no—
629C2×C22⋊C4—594no—
630C2×C22⋊C4—594no—
631C2×C22⋊C4—594no—
632C2×C22⋊C4—594no—
633C2×C22⋊C4—1182no—
634C2×C22⋊C4—1182no—
635C2×C22⋊C4—1182no—
636C2×C22⋊C4—1182no—
637C2×C22⋊C4—1182no—
638C2×C22⋊C4—1182no—
639C2×C22⋊C4—1182no—
640C2×C22⋊C4—1182no—
641C2×C22⋊C4—2361no—
642C2×C22⋊C4—2361no—
643C2×C22⋊C4—2361no—
644C2×C22⋊C4—2361no—
645C2×C22⋊C4—2361no—
646C2×C22⋊C4—2361no—
647C2×C42—1182no—
648C2×C42—1182no—
649C2×C42—1182no—
650C2×C42—1182no—
651C2×C42—2361no—
652C2×C42—2361no—
653#95—22no—
654#95—22no—
655#95—41no—
656#95—594no—
657#95—594no—
658#95—594no—
659#95—1182no—
660#95—1182no—
661#95—1182no—
662#95—1182no—
663#95—1182no—
664#95—1182no—
665#95—2361no—
666#95—2361no—
667#95—2361no—
668#95C4×D5914yes—
669C24—592no—
670C24—592no—
671C24—592no—
672C24—1181no—
673C24—1181no—
674C24—1181no—
675C24—1181no—
676C24—1181no—
677C24—1181no—
678C24—1181no—
679C24—1181no—
680C24—1181no—
681C24—1181no—
682C24—1181no—
683C24—1181no—
684C24C23×D5911yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—592no—
727C22×C4—592no—
728C22×C4—592no—
729C22×C4—592no—
730C22×C4—592no—
731C22×C4—592no—
732C22×C4—592no—
733C22×C4—592no—
734C22×C4—592no—
735C22×C4—592no—
736C22×C4—1188no—
737C22×C4—1181no—
738C22×C4—1181no—
739C22×C4—1181no—
740C22×C4—1181no—
741C22×C4—1181no—
742C22×C4—1181no—
743C22×C4—1181no—
744C22×C4—1181no—
745C22×C4—1181no—
746C22×C4—1181no—
747C22×C4—1181no—
748C22×C4—1181no—
749C22×C4—1181no—
750C22×C4—1181no—
751C22×C4—1181no—
752C22×C4—1181no—
753C22×C4—1181no—
754C22×C4—1181no—
755C22×C4—1181no—
756C22×C4—1181no—
757C22×C4—1181no—
758C22×C4—1181no—
759C22×C4—1181no—
760C22×C4—1181no—
761C22×C4—1181no—
762C22×C4—1181no—
763C22×C4—1181no—
764C22×C4—1181no—
765C22×C4—1181no—
766C22×C4—1181no—
767C22×C4—1181no—
768C22×C4—1181no—
769C22×C4—1188no—
770C22×C4—1181no—
771C22×C4—1181no—
772C22×C4—1181no—
773C22×C4—1181no—
774C22×C4—1181no—
775C22×C4—1181no—
776C22×C4—1181no—
777C22×C4—2364no—
778C22×C4—2364no—
779C22×C4—2364no—
780C22×C4—2364no—
781C22×C4—2364no—
782C22×C4C2×C4×D5912yes—
783C22×C4C2×C4×D5912yes—
784C22×C4C2×C4×D5912yes—
785C22×C4D4×D5912yes—
786C22×C4D4×D5912yes—
787C22×C4D4×D5912yes—
788C22×C4Q8×D5912yes—
789C22×C4#1174568912yes—
790C4⋊C4—44no—
791C4⋊C4—44no—
792C4⋊C4—44no—
793C4⋊C4—1188no—
794C4⋊C4—1188no—
795C4⋊C4—2364no—
796C4⋊C4—2364no—
797C4⋊C4—2364no—
798C4⋊C4—2364no—
799C4⋊C4—2364no—
800C22⋊C4—5916no—
801C22⋊C4—2364no—
802C22⋊C4—2364no—
803C22⋊C4—2364no—
804C22⋊C4—2364no—
805C22⋊C4—2364no—
806C42—2364no—
807C42—2364no—
808C23—594no—
809C23—1182no—
810C23—1182no—
811C23—1182no—
812C23—1182no—
813C23—1182no—
814C23—1182no—
815C23—1182no—
816C23—1182no—
817C23—1182no—
818C23—1182no—
819C23—1182no—
820C23—1182no—
821C23—1182no—
822C23—1182no—
823C23—1182no—
824C23—1182no—
825C23—1182no—
826C23—1182no—
827C23—2361no—
828C23—2361no—
829C23—2361no—
830C23—2361no—
831C23—2361no—
832C23—2361no—
833C23—2361no—
834C23—2361no—
835C23—2361no—
836C23—2361no—
837C23—2361no—
838C23—2361no—
839C23—2361no—
840C23—2361no—
841C23—2361no—
842C23—2361no—
843C23C22×C4×D5911yescharacteristic
844C23C2×D4×D5911yescharacteristic
845C23C2×D4×D5911yescharacteristic
846C23C2×D4×D5911yescharacteristic
847C23C2×Q8×D5911yescharacteristic
848C23#41×D5911yescharacteristic
849C23C2×#1174568911yescharacteristic
850C23#1427377211yescharacteristic
851C23#1427377211yescharacteristic
852C23#1427377211yescharacteristic
853C23#1427377311yescharacteristic
854C23#1427377411yescharacteristic
855C23#1427377411yescharacteristic
856C23#1427377511yescharacteristic
857C23#1427377511yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—594no—
906C2×C4—594no—
907C2×C4—1182no—
908C2×C4—1182no—
909C2×C4—1182no—
910C2×C4—1182no—
911C2×C4—1182no—
912C2×C4—1182no—
913C2×C4—1182no—
914C2×C4—1182no—
915C2×C4—1182no—
916C2×C4—1182no—
917C2×C4—1182no—
918C2×C4—1182no—
919C2×C4—1182no—
920C2×C4—1182no—
921C2×C4—1182no—
922C2×C4—1182no—
923C2×C4—1182no—
924C2×C4—1182no—
925C2×C4—1182no—
926C2×C4—1182no—
927C2×C4—1182no—
928C2×C4—1182no—
929C2×C4—1182no—
930C2×C4—1182no—
931C2×C4—23616no—
932C2×C4—2361no—
933C2×C4—2361no—
934C2×C4—2361no—
935C2×C4—2361no—
936C2×C4—2361no—
937C2×C4—2361no—
938C2×C4—2361no—
939C2×C4—2361no—
940C2×C4—2361no—
941C2×C4—2361no—
942C2×C4—2361no—
943C2×C4—2361no—
944C2×C4—2361no—
945C2×C4—2361no—
946C2×C4—2361no—
947C2×C4—2361no—
948C2×C4—2361no—
949C2×C4—2361no—
950C2×C4—2361no—
951C2×C4—2361no—
952C2×C4—2361no—
953C2×C4—2361no—
954C2×C4—2361no—
955C2×C4C4⋊C4×D5914yes—
956C2×C4#1427368914yes—
957C22—1184no—
958C22—1184no—
959C22—1184no—
960C22—2362no—
961C22—2362no—
962C22—2362no—
963C22—2362no—
964C22—2362no—
965C22—2362no—
966C22—2362no—
967C22—2362no—
968C22—2362no—
969C22—2362no—
970C22—2362no—
971C22—2362no—
972C22C2×C4⋊C4×D5911yescharacteristic
973C22C4×D4×D5911yescharacteristic
974C22C2×#1427368911yescharacteristic
975C22#1683787411yescharacteristic
976C22#1683787811yescharacteristic
977C22#1683788111yescharacteristic
978C22#1683788311yescharacteristic
979C22#1683797511yescharacteristic
980C22#1683797711yescharacteristic
981C22#1683797911yescharacteristic
982C22#1683798111yescharacteristic
983C22#1683798111yescharacteristic
984C22#1683798211yescharacteristic
985C22#1683801111yescharacteristic
986C22#1683801511yescharacteristic
987C22#1683802211yescharacteristic
988C22#1683802611yescharacteristic
989C22#1683802911yescharacteristic
990C22#1683803211yescharacteristic
991C22#1683803411yescharacteristic
992C22#1683803411yescharacteristic
993C22#1683803711yescharacteristic
994C22#1683804311yescharacteristic
995C22#1683804411yescharacteristic
996C22#1683805011yescharacteristic
997C22#1683805511yescharacteristic
998C22#1683806511yescharacteristic
999C22#1683806711yescharacteristic
1000C22#1683807911yescharacteristic
1001C22#1683810611yescharacteristic
1002C22#1683811311yescharacteristic
1003C22#1683814111yescharacteristic
1004C22#1683814811yescharacteristic
1005C22#1683814911yescharacteristic
1006C22#1683815311yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—42no—
1010C4—42no—
1011C4—81no—
1012C4—81no—
1013C4—81no—
1014C4—1184no—
1015C4—1184no—
1016C4—4721no—
1017C4—2362no—
1018C4—2362no—
1019C4—2362no—
1020C4—2362no—
1021C2—2364no—
1022C2#2142671111yescharacteristic
1023C2#2142677311yescharacteristic
1024C2#2142677611yescharacteristic
1025C2#2142699411yescharacteristic
1026C2#2142699611yescharacteristic
1027C2#2142707211yescharacteristic
1028C2#2142724511yescharacteristic
1029C2#2143034611yescharacteristic
1030C2#2143035211yescharacteristic
1031C2#2143038811yescharacteristic
1032C2#2143041011yescharacteristic
1033C2#2143075311yescharacteristic
1034C2#2143075611yescharacteristic
1035C2#2143100511yescharacteristic
1036C2#2143122711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC59×#1444C2
socle, cosocleC24×C59C24
prime radicalC24×D59C23
hypercenter#1444D59
hypocenterC59#14402
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
1. C2×#16837298C2semidirect
2. C2×#16837297C2semidirect
8. #21422359C2semidirect
9. #21422350C2semidirect
10. #21422348C2semidirect
13. #21422330C2semidirect
14. #21422327C2semidirect
15. C59×#1444C2semidirect
36. #16837276C4semidirect
279. (C2×D59)⋊C4C4⋊C4semidirect
511. #1444D59semidirect
576. C59#14402semidirect

Maximal subgroups

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

subgroupindex
C2×#168372982
C2×#168372972
C2×#168372922
C2×#168372912
C2×#168372762
C2×#168372612
C2×#168372592
#214223592
#214223502
#214223482
#214223402
#214223382
#214223302
#214223272
C59×#14442
#1440259