Finite Group Databasebeta

← #28516617

Subgroups — #28516617

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×#16837300C211yesmaximal, characteristic, complemented
2C2×#16837298C211yesmaximal, characteristic, complemented
3C2×#16837295C211yesmaximal, characteristic
4C2×#16837277C211yesmaximal, characteristic
5C2×#16837260C211yesmaximal, characteristic
6C2×#16837260C211yesmaximal, characteristic
7#21422360C211yesmaximal, characteristic, complemented
8#21422359C211yesmaximal, characteristic, complemented
9#21422348C211yesmaximal, characteristic, complemented
10#21422348C211yesmaximal, characteristic, complemented
11#21422339C211yesmaximal, characteristic
12#21422339C211yesmaximal, characteristic
13#21422329C211yesmaximal, characteristic, complemented
14#21422327C211yesmaximal, characteristic, complemented
15C2×C59×#388C211yesmaximal, characteristic
16C24×Dic59C2211yescharacteristic
17C22×C4⋊Dic59C2211yescharacteristic
18C22×C4⋊Dic59C2211yescharacteristic
19C22×C4⋊Dic59C2211yescharacteristic
20C22×Dic59⋊C4C2211yescharacteristic
21C22×Dic59⋊C4C2211yescharacteristic
22C22×Dic59⋊C4C2211yescharacteristic
23C22×Dic59⋊C4C2211yescharacteristic
24C22×Dic59⋊C4C2211yescharacteristic
25C22×Dic59⋊C4C2211yescharacteristic
26C22×C22⋊Dic59C2211yescharacteristic
27C22×C22⋊Dic59C2211yescharacteristic
28C22×C22⋊Dic59C2211yescharacteristic
29C22×C4×Dic59C2211yescharacteristic
30#16837300—24no—
31#16837298—24no—
32#16837295—24no—
33#16837277C418yescomplemented
34#16837260—24no—
35#16837260—24no—
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
48C2×C59⋊#95C2211yescharacteristic
49C2×C59⋊#95C2211yescharacteristic
50C22×C4⋊C4×C59C2211yescharacteristic
51C22×C22⋊C4×C59C2211yescharacteristic
52C22×C22⋊C4×C59C2211yescharacteristic
53C22×C22⋊C4×C59C2211yescharacteristic
54C22×C42×C59C2211yescharacteristic
55C59×#388—24no—
56C2×#95×C59C2211yescharacteristic
57C2×#95×C59C2211yescharacteristic
58C23×Dic59—22no—
59C23×Dic59—22no—
60C23×Dic59—22no—
61C23×Dic59—22no—
62C23×Dic59—41no—
63C23×Dic59—41no—
64C23×Dic59C2×C414yes—
65C23×Dic59C2311yescharacteristic
66C23×Dic59C2311yescharacteristic
67C23×Dic59C2311yescharacteristic
68C23×Dic59C2311yescharacteristic
69C23×Dic59C2311yescharacteristic
70C23×Dic59C2311yescharacteristic
71C23×Dic59C2311yescharacteristic
72C23×Dic59C2311yescharacteristic
73C2×C4⋊Dic59—22no—
74C2×C4⋊Dic59—22no—
75C2×C4⋊Dic59—22no—
76C2×C4⋊Dic59—22no—
77C2×C4⋊Dic59—22no—
78C2×C4⋊Dic59—22no—
79C2×C4⋊Dic59—41no—
80C2×C4⋊Dic59C2×C414yes—
81C2×C4⋊Dic59C2×C414yes—
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—22no—
90C2×Dic59⋊C4—22no—
91C2×Dic59⋊C4—22no—
92C2×Dic59⋊C4—41no—
93C2×Dic59⋊C4—41no—
94C2×Dic59⋊C4—41no—
95C2×Dic59⋊C4—41no—
96C2×Dic59⋊C4—41no—
97C2×Dic59⋊C4—41no—
98C2×Dic59⋊C4—41no—
99C2×Dic59⋊C4—41no—
100C2×C22⋊Dic59—22no—
101C2×C22⋊Dic59—22no—
102C2×C22⋊Dic59—22no—
103C2×C22⋊Dic59—22no—
104C2×C22⋊Dic59—41no—
105C2×C22⋊Dic59—41no—
106C2×C22⋊Dic59—41no—
107C2×C22⋊Dic59—41no—
108C2×C22⋊Dic59C2×C414yes—
109C2×C4×Dic59—22no—
110C2×C4×Dic59—22no—
111C2×C4×Dic59—41no—
112C59⋊#95—22no—
113C59⋊#95—22no—
114C59⋊#95—22no—
115C59⋊#95—22no—
116C59⋊#95—22no—
117C59⋊#95—22no—
118C59⋊#95—41no—
119C59⋊#95—41no—
120C59⋊#95—41no—
121C59⋊#95—41no—
122C59⋊#95C2×C414yes—
123C59⋊#95C2×C414yes—
124C59⋊#95D414yes—
125C59⋊#95D414yes—
126C25×C59C2311yescharacteristic
127C23×C4×C59C2311yescharacteristic
128C23×C4×C59C2311yescharacteristic
129C23×C4×C59C2311yescharacteristic
130C23×C4×C59C2311yescharacteristic
131C23×C4×C59C2311yescharacteristic
132C23×C4×C59C2311yescharacteristic
133C2×C4⋊C4×C59—22no—
134C2×C4⋊C4×C59—22no—
135C2×C4⋊C4×C59—41no—
136C2×C22⋊C4×C59—22no—
137C2×C22⋊C4×C59—22no—
138C2×C22⋊C4×C59—22no—
139C2×C22⋊C4×C59—22no—
140C2×C22⋊C4×C59—41no—
141C2×C22⋊C4×C59—41no—
142C2×C22⋊C4×C59C2×C414yes—
143C2×C22⋊C4×C59D414yes—
144C2×C22⋊C4×C59Q814yes—
145C2×C42×C59—22no—
146C2×C42×C59—22no—
147C2×C42×C59—41no—
148#95×C59—22no—
149#95×C59—22no—
150C24×C59—21no—
151C24×C59—21no—
152C24×C59—21no—
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×C59C22×C412yes—
163C24×C59C2×D412yes—
164C24×C59C2×Q812yes—
165C24×C59C2411yescharacteristic
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×C59C22×C412yes—
201C22×C4×C59C22×C412yes—
202C22×C4×C59C2×D412yes—
203C22×C4×C59C2×D412yes—
204C22×C4×C59C2×D412yes—
205C22×C4×C59C2×D412yes—
206C22×C4×C59C2×Q812yes—
207C22×C4×C59C2×Q812yes—
208C22×Dic59—21no—
209C22×Dic59—21no—
210C22×Dic59—21no—
211C22×Dic59—21no—
212C22×Dic59—21no—
213C22×Dic59—21no—
214C22×Dic59—21no—
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—28no—
241C22×Dic59—28no—
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—44no—
257C22×Dic59—44no—
258C22×Dic59—44no—
259C22×Dic59—44no—
260C22×Dic59—44no—
261C22×Dic59C22×C412yes—
262C22×Dic59C22×C412yes—
263C22×Dic59C22×C412yes—
264C22×Dic59C22×C412yes—
265C22×Dic59C2×D412yes—
266C22×Dic59C2×D412yes—
267C22×Dic59C2×D412yes—
268C22×Dic59C2×D412yes—
269C22×Dic59#4112yes—
270C22×Dic59#4112yes—
271C4⋊C4×C59—44no—
272C22⋊C4×C59—44no—
273C22⋊C4×C59—44no—
274C22⋊C4×C59C4⋊C4116yescomplemented
275C42×C59—44no—
276C22⋊Dic59—44no—
277C22⋊Dic59—44no—
278C22⋊Dic59—44no—
279C4⋊Dic59—28no—
280C4⋊Dic59—28no—
281C4⋊Dic59—44no—
282Dic59⋊C4—44no—
283Dic59⋊C4—44no—
284Dic59⋊C4—44no—
285Dic59⋊C4—44no—
286Dic59⋊C4—44no—
287Dic59⋊C4—44no—
288C4×Dic59—44no—
289C23×C59—22no—
290C23×C59—22no—
291C23×C59—22no—
292C23×C59—22no—
293C23×C59—22no—
294C23×C59—22no—
295C23×C59—22no—
296C23×C59—22no—
297C23×C59—22no—
298C23×C59—22no—
299C23×C59—22no—
300C23×C59—22no—
301C23×C59—22no—
302C23×C59—22no—
303C23×C59—22no—
304C23×C59—22no—
305C23×C59—22no—
306C23×C59—22no—
307C23×C59—41no—
308C23×C59—41no—
309C23×C59—41no—
310C23×C59—41no—
311C23×C59—41no—
312C23×C59—41no—
313C23×C59—41no—
314C23×C59—41no—
315C23×C59—41no—
316C23×C59—41no—
317C23×C59—41no—
318C23×C59—41no—
319C23×C59—41no—
320C23×C59—41no—
321C23×C59—41no—
322C23×C59—41no—
323C23×C59C2×C4⋊C414yes—
324C23×C59C23×C411yescharacteristic
325C23×C59C22×D411yescharacteristic
326C23×C59C22×D411yescharacteristic
327C23×C59C22×D411yescharacteristic
328C23×C59C22×Q811yescharacteristic
329C23×C59C2×#4111yescharacteristic
330C23×C59C2×#4111yescharacteristic
331C23×C59H(5,𝔽2)11yescharacteristic
332C23×C59H(5,𝔽2)11yescharacteristic
333C23×C59H(5,𝔽2)11yescharacteristic
334C23×C59H(5,𝔽2)11yescharacteristic
335C23×C592−1+411yescharacteristic
336C23×C592−1+411yescharacteristic
337C23×C592−1+411yescharacteristic
338C23×C592−1+411yescharacteristic
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×C59C2×C4⋊C414yes—
380C2×C4×C59C2×C4⋊C414yes—
381C2×Dic59—22no—
382C2×Dic59—22no—
383C2×Dic59—22no—
384C2×Dic59—22no—
385C2×Dic59—22no—
386C2×Dic59—22no—
387C2×Dic59—22no—
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—416no—
406C2×Dic59—41no—
407C2×Dic59—41no—
408C2×Dic59—41no—
409C2×Dic59—41no—
410C2×Dic59—41no—
411C2×Dic59—41no—
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×Dic59—41no—
436C2×Dic59C4×D414yes—
437C2×Dic59C4×D414yes—
438#14402—591nomaximal, Sylow
439C22×C59—24no—
440C22×C59—24no—
441C22×C59—24no—
442C22×C59—42no—
443C22×C59—42no—
444C22×C59—42no—
445C22×C59—42no—
446C22×C59—42no—
447C22×C59—42no—
448C22×C59—42no—
449C22×C59—42no—
450C22×C59—42no—
451C22×C59—42no—
452C22×C59—42no—
453C22×C59—42no—
454C22×C59C22×C4⋊C411yescharacteristic
455C22×C59C2×C4×D411yescharacteristic
456C22×C59C2×C4×D411yescharacteristic
457C22×C59#51811yescharacteristic
458C22×C59#51911yescharacteristic
459C22×C59#52011yescharacteristic
460C22×C59#52011yescharacteristic
461C22×C59#53611yescharacteristic
462C22×C59#53611yescharacteristic
463C22×C59#53711yescharacteristic
464C22×C59#53711yescharacteristic
465C22×C59#53711yescharacteristic
466C22×C59#53711yescharacteristic
467C22×C59#54111yescharacteristic
468C22×C59#54111yescharacteristic
469C22×C59#54211yescharacteristic
470C22×C59#54211yescharacteristic
471C22×C59#54411yescharacteristic
472C22×C59#54411yescharacteristic
473C22×C59D4211yescharacteristic
474C22×C59D4211yescharacteristic
475C22×C59D4211yescharacteristic
476C22×C59#54611yescharacteristic
477C22×C59#54611yescharacteristic
478C22×C59#54711yescharacteristic
479C22×C59#54711yescharacteristic
480C22×C59D4×Q811yescharacteristic
481C22×C59D4×Q811yescharacteristic
482C22×C59#55111yescharacteristic
483C22×C59#55411yescharacteristic
484C22×C59#55411yescharacteristic
485C22×C59#56011yescharacteristic
486C22×C59#56211yescharacteristic
487C22×C59#56211yescharacteristic
488C22×C59#56311yescharacteristic
489C4×C59—24no—
490C4×C59—24no—
491C4×C59—42no—
492C4×C59—42no—
493C4×C59—81no—
494C4×C59—81no—
495Dic59—24no—
496Dic59—24no—
497Dic59—42no—
498Dic59—42no—
499Dic59—42no—
500Dic59—42no—
501Dic59—81no—
502Dic59—81no—
503C2×#389—591no—
504C2×#389—591no—
505C2×#388—591no—
506C2×#388D5911yescharacteristic
507C2×#385—591no—
508C2×#380—591no—
509C2×#380—591no—
510#1444—591no—
511#1444—591no—
512#1441—591no—
513#1441—591no—
514#1439—591no—
515#1439—591no—
516#1436—591no—
517#1436—591no—
518C2×C59—44no—
519C2×C59#231611yescharacteristic
520C2×C59#232311yescharacteristic
521C2×C59#232311yescharacteristic
522C2×C59D4×C4⋊C411yescharacteristic
523C2×C59D4×C4⋊C411yescharacteristic
524C2×C59#235811yescharacteristic
525C2×C59#237611yescharacteristic
526C2×C59#267211yescharacteristic
527C2×C59#267211yescharacteristic
528C2×C59#267511yescharacteristic
529C2×C59#267711yescharacteristic
530C2×C59#270411yescharacteristic
531C2×C59#270411yescharacteristic
532C2×C59#272211yescharacteristic
533C2×C59#274211yescharacteristic
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⋊C4—591no—
543C22×C4⋊C4—591no—
544C22×C4⋊C4C2×D5911yescharacteristic
545C22×C22⋊C4—591no—
546C22×C22⋊C4—591no—
547C22×C22⋊C4—591no—
548C22×C22⋊C4C2×D5911yescharacteristic
549C22×C22⋊C4C2×D5911yescharacteristic
550C22×C22⋊C4C2×D5911yescharacteristic
551C22×C42—591no—
552C22×C42C2×D5911yescharacteristic
553#389—1184no—
554#389—1184no—
555#388—24no—
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×#95—591no—
573C2×#95—591no—
574C2×#95C2×D5911yescharacteristic
575C2×#95C2×D5911yescharacteristic
576C59#1440211yescharacteristic, complemented, Sylow
577C25C22×D5911yescharacteristic
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—591no—
587C23×C4—1182no—
588C23×C4—1182no—
589C23×C4—1182no—
590C23×C4—1182no—
591C23×C4—2361no—
592C23×C4—2361no—
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—41no—
602C2×C4⋊C4—594no—
603C2×C4⋊C4—594no—
604C2×C4⋊C4—1182no—
605C2×C4⋊C4—1182no—
606C2×C4⋊C4—1182no—
607C2×C4⋊C4—1182no—
608C2×C4⋊C4—1182no—
609C2×C4⋊C4—1182no—
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—2361no—
621C2×C4⋊C4—2361no—
622C2×C4⋊C4—2361no—
623C2×C4⋊C4—2361no—
624C2×C4⋊C4—2361no—
625C2×C4⋊C4—2361no—
626C2×C4⋊C4—2361no—
627C2×C4⋊C4—2361no—
628C2×C4⋊C4—2361no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—41no—
634C2×C22⋊C4—41no—
635C2×C22⋊C4—594no—
636C2×C22⋊C4—1182no—
637C2×C22⋊C4—1182no—
638C2×C22⋊C4—1182no—
639C2×C22⋊C4—1182no—
640C2×C22⋊C4—2361no—
641C2×C22⋊C4—2361no—
642C2×C22⋊C4—2361no—
643C2×C22⋊C4—2361no—
644C2×C22⋊C4Dic11814yes—
645C2×C22⋊C4C4×D5914yes—
646C2×C22⋊C4C22⋊D5914yes—
647C2×C42—22no—
648C2×C42—22no—
649C2×C42—41no—
650C2×C42—1182no—
651C2×C42—1182no—
652C2×C42—2361no—
653#95—22no—
654#95—22no—
655#95—594no—
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#95—2361no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C2×Dic11812yes—
682C24C2×C4×D5912yes—
683C24C2×C22⋊D5912yes—
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—592no—
720C22×C4—592no—
721C22×C4—592no—
722C22×C4—592no—
723C22×C4—592no—
724C22×C4—592no—
725C22×C4—592no—
726C22×C4—592no—
727C22×C4—592no—
728C22×C4—592no—
729C22×C4—1188no—
730C22×C4—1188no—
731C22×C4—1181no—
732C22×C4—1181no—
733C22×C4—1181no—
734C22×C4—1181no—
735C22×C4—1181no—
736C22×C4—1181no—
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—1181no—
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×Dic11812yes—
783C22×C4C2×Dic11812yes—
784C22×C4C2×C4×D5912yes—
785C22×C4C2×C4×D5912yes—
786C22×C4D4×D5912yes—
787C22×C4D4×D5912yes—
788C22×C4C2×C22⋊D5912yes—
789C22×C4C2×C22⋊D5912yes—
790C4⋊C4—44no—
791C4⋊C4—1188no—
792C4⋊C4—1188no—
793C4⋊C4—2364no—
794C4⋊C4—2364no—
795C4⋊C4—2364no—
796C4⋊C4—2364no—
797C4⋊C4—2364no—
798C4⋊C4—2364no—
799C4⋊C4—2364no—
800C22⋊C4—44no—
801C22⋊C4—44no—
802C22⋊C4—2364no—
803C22⋊C4—2364no—
804C22⋊C4—2364no—
805C22⋊C4Dic59⋊C4116yescomplemented
806C42—44no—
807C42—2364no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C2×Dic59⋊C414yes—
843C23C22×C4×D5911yescharacteristic
844C23C2×D4×D5911yescharacteristic
845C23C2×D4×D5911yescharacteristic
846C23C22×C22⋊D5911yescharacteristic
847C23C22×Dic11811yescharacteristic
848C23#41×D5911yescharacteristic
849C23#41×D5911yescharacteristic
850C23#1427377211yescharacteristic
851C23#1427377211yescharacteristic
852C23#1427377311yescharacteristic
853C23#1427377311yescharacteristic
854C23#1427377411yescharacteristic
855C23#1427377411yescharacteristic
856C23#1427377411yescharacteristic
857C23#1427377411yescharacteristic
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—594no—
899C2×C4—594no—
900C2×C4—1182no—
901C2×C4—1182no—
902C2×C4—1182no—
903C2×C4—1182no—
904C2×C4—1182no—
905C2×C4—1182no—
906C2×C4—1182no—
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—23616no—
925C2×C4—2361no—
926C2×C4—2361no—
927C2×C4—2361no—
928C2×C4—2361no—
929C2×C4—2361no—
930C2×C4—2361no—
931C2×C4—2361no—
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×C4C2×Dic59⋊C414yes—
956C2×C4C2×Dic59⋊C414yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C22×Dic59⋊C411yescharacteristic
973C22C4×D4×D5911yescharacteristic
974C22C4×D4×D5911yescharacteristic
975C22#1683787611yescharacteristic
976C22#1683787911yescharacteristic
977C22#1683788111yescharacteristic
978C22#1683788111yescharacteristic
979C22#1683797211yescharacteristic
980C22#1683797411yescharacteristic
981C22#1683797911yescharacteristic
982C22#1683798011yescharacteristic
983C22#1683798011yescharacteristic
984C22#1683798111yescharacteristic
985C22#1683800911yescharacteristic
986C22#1683800911yescharacteristic
987C22#1683801611yescharacteristic
988C22#1683802011yescharacteristic
989C22#1683803011yescharacteristic
990C22#1683803011yescharacteristic
991C22D4×C22⋊D5911yescharacteristic
992C22D4×C22⋊D5911yescharacteristic
993C22#1683803611yescharacteristic
994C22#1683804411yescharacteristic
995C22#1683804511yescharacteristic
996C22#1683805111yescharacteristic
997C22#1683805111yescharacteristic
998C22D4×Dic11811yescharacteristic
999C22D4×Dic11811yescharacteristic
1000C22#1683807711yescharacteristic
1001C22#1683811111yescharacteristic
1002C22#1683811111yescharacteristic
1003C22#1683814011yescharacteristic
1004C22#1683814611yescharacteristic
1005C22#1683814911yescharacteristic
1006C22#1683815411yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—42no—
1010C4—42no—
1011C4—81no—
1012C4—81no—
1013C4—1184no—
1014C4—1184no—
1015C4—4721no—
1016C4—4721no—
1017C4—2362no—
1018C4—2362no—
1019C4—2362no—
1020C4—2362no—
1021C2—44no—
1022C2#2142671211yescharacteristic
1023C2#2142677111yescharacteristic
1024C2#2142677511yescharacteristic
1025C2D4×Dic59⋊C411yescharacteristic
1026C2D4×Dic59⋊C411yescharacteristic
1027C2#2142707411yescharacteristic
1028C2#2142724211yescharacteristic
1029C2#2143034211yescharacteristic
1030C2#2143034711yescharacteristic
1031C2#2143038611yescharacteristic
1032C2#2143040811yescharacteristic
1033C2#2143075111yescharacteristic
1034C2#2143075511yescharacteristic
1035C2#2143100011yescharacteristic
1036C2#2143122211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC2×C59×#388C2
socle, cosocleC24×C59C24
prime radicalC25×C59C23
hypercenterC2×#388D59
hypocenterC59#14402
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C2×#16837300C2semidirect
2. C2×#16837298C2semidirect
7. #21422360C2semidirect
8. #21422359C2semidirect
9. #21422348C2semidirect
10. #21422348C2semidirect
13. #21422329C2semidirect
14. #21422327C2semidirect
33. #16837277C4semidirect
274. C22⋊C4×C59C4⋊C4semidirect
576. C59#14402semidirect
805. C22⋊C4Dic59⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#168373002
C2×#168372982
C2×#168372952
C2×#168372772
C2×#168372602
#214223602
#214223592
#214223482
#214223392
#214223292
#214223272
C2×C59×#3882
#1440259