Finite Group Databasebeta

← #28517184

Subgroups — #28517184

Order 15104.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273703C211yesmaximal, characteristic
2C2×#16837287C211yesmaximal, characteristic, complemented
3C2×#16837285C211yesmaximal, characteristic, complemented
4#21422367C211yesmaximal, characteristic, complemented
5#21422362C211yesmaximal, characteristic, complemented
6#21422362C211yesmaximal, characteristic, complemented
7#21422340C211yesmaximal, characteristic
8#21422340C211yesmaximal, characteristic
9#21422332C211yesmaximal, characteristic
10#21422332C211yesmaximal, characteristic
11Dic59⋊#95C211yesmaximal, characteristic, complemented
12Dic59⋊#95C211yesmaximal, characteristic, complemented
13(C2×D59)⋊#95C211yesmaximal, characteristic
14(C2×D59)⋊#95C211yesmaximal, characteristic
15C59×#1446C211yesmaximal, characteristic, complemented
16C23×C4×D59C2211yescharacteristic
17C2×#14273703—24no—
18C2×#14273703—24no—
19C2×#14273703C418yescomplemented
20C22×C4⋊Dic59C2211yescharacteristic
21C22×Dic59⋊C4C2211yescharacteristic
22C22×Dic59⋊C4C2211yescharacteristic
23C22×Dic59⋊C4C2211yescharacteristic
24C22×Dic59⋊C4C2211yescharacteristic
25C22×(C2×D59)⋊C4C2211yescharacteristic
26C22×(C2×D59)⋊C4C2211yescharacteristic
27C22×(C2×D59)⋊C4C2211yescharacteristic
28C22×(C2×D59)⋊C4C2211yescharacteristic
29C22×(C2×D59)⋊C4C2211yescharacteristic
30C22×(C2×D59)⋊C4C2211yescharacteristic
31C22×C4×Dic59C2211yescharacteristic
32C22×C4×Dic59C2211yescharacteristic
33#16837287—24no—
34#16837285—24no—
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
48C2×C59⋊#95C2211yescharacteristic
49C23×Q8×C59C2211yescharacteristic
50C2×#95×C59C2211yescharacteristic
51C2×#95×C59C2211yescharacteristic
52C2×#95×C59C2211yescharacteristic
53C2×#95×C59C2211yescharacteristic
54C2×#95×C59C2211yescharacteristic
55C2×#95×C59C2211yescharacteristic
56C24×D59C2311yescharacteristic
57C23×Dic59C2311yescharacteristic
58C23×Dic59C2311yescharacteristic
59C23×Dic59C2311yescharacteristic
60C23×Dic59C2311yescharacteristic
61C23×Dic59C2311yescharacteristic
62C23×Dic59C2311yescharacteristic
63C23×Dic59C2311yescharacteristic
64C22×C4×D59—22no—
65C22×C4×D59—22no—
66C22×C4×D59—41no—
67C22×C4×D59—41no—
68C22×C4×D59—41no—
69C22×C4×D59—41no—
70C22×C4×D59C2×C414yes—
71#14273703—232no—
72C2×C4⋊Dic59C2×C414yes—
73C2×C4⋊Dic59D414yes—
74C2×C4⋊Dic59D414yes—
75C2×Dic59⋊C4—22no—
76C2×Dic59⋊C4—22no—
77C2×Dic59⋊C4—22no—
78C2×Dic59⋊C4—22no—
79C2×Dic59⋊C4—22no—
80C2×Dic59⋊C4—22no—
81C2×Dic59⋊C4—22no—
82C2×Dic59⋊C4—22no—
83C2×Dic59⋊C4—41no—
84C2×Dic59⋊C4—41no—
85C2×Dic59⋊C4C2×C414yes—
86C2×Dic59⋊C4C2×C414yes—
87C2×(C2×D59)⋊C4—22no—
88C2×(C2×D59)⋊C4—22no—
89C2×(C2×D59)⋊C4—22no—
90C2×(C2×D59)⋊C4—22no—
91C2×(C2×D59)⋊C4—22no—
92C2×(C2×D59)⋊C4—22no—
93C2×(C2×D59)⋊C4—22no—
94C2×(C2×D59)⋊C4—22no—
95C2×(C2×D59)⋊C4—22no—
96C2×(C2×D59)⋊C4—41no—
97C2×(C2×D59)⋊C4—41no—
98C2×(C2×D59)⋊C4—41no—
99C2×(C2×D59)⋊C4—41no—
100C2×(C2×D59)⋊C4—41no—
101C2×(C2×D59)⋊C4—41no—
102C2×(C2×D59)⋊C4C2×C414yes—
103C2×(C2×D59)⋊C4C2×C414yes—
104C2×(C2×D59)⋊C4Q814yescomplemented
105C2×C4×Dic59—22no—
106C2×C4×Dic59—22no—
107C2×C4×Dic59—22no—
108C2×C4×Dic59—22no—
109C2×C4×Dic59—41no—
110C2×C4×Dic59—41no—
111C59⋊#95—22no—
112C59⋊#95—22no—
113C59⋊#95—22no—
114C59⋊#95—22no—
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—
125C22×Q8×C59—22no—
126C22×Q8×C59—22no—
127C22×Q8×C59—41no—
128C22×Q8×C59—41no—
129C22×Q8×C59—41no—
130C22×Q8×C59—41no—
131C22×Q8×C59C2×C414yes—
132C23×C4×C59C2311yescharacteristic
133C23×C4×C59C2311yescharacteristic
134C23×C4×C59C2311yescharacteristic
135C23×C4×C59C2311yescharacteristic
136C23×C4×C59C2311yescharacteristic
137C23×C4×C59C2311yescharacteristic
138C23×C4×C59C2311yescharacteristic
139#95×C59—22no—
140#95×C59—22no—
141#95×C59—41no—
142#95×C59—41no—
143#95×C59—41no—
144#95×C59—41no—
145C24×C59C2411yescharacteristic
146C23×D59—21no—
147C23×D59—21no—
148C23×D59—21no—
149C23×D59—21no—
150C23×D59—21no—
151C23×D59—21no—
152C23×D59—21no—
153C23×D59—21no—
154C23×D59—21no—
155C23×D59—21no—
156C23×D59—21no—
157C23×D59—21no—
158C23×D59C22×C412yes—
159C23×D59C2×Q812yes—
160C23×D59#4112yes—
161C2×Q8×C59—28no—
162C2×Q8×C59—44no—
163C2×Q8×C59—44no—
164C2×Q8×C59—44no—
165C2×Q8×C59—44no—
166C2×Q8×C59—44no—
167C2×Q8×C59—44no—
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×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59C22×C412yes—
211C22×C4×C59C22×C412yes—
212C22×C4×C59C22×C412yes—
213C22×C4×C59C2×D412yes—
214C22×C4×C59C2×D412yes—
215C22×C4×C59C2×Q812yes—
216C22×C4×C59#4112yes—
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×Dic59—21no—
255C22×Dic59—21no—
256C22×Dic59—21no—
257C22×Dic59C22×C412yes—
258C22×Dic59C22×C412yes—
259C22×Dic59C22×C412yes—
260C22×Dic59C2×D412yes—
261C22×Dic59C2×D412yes—
262C22×Dic59C2×D412yes—
263C22×Dic59C2×D412yes—
264C22×Dic59C2×Q812yes—
265C22×Dic59#4112yes—
266C2×C4×D59—28no—
267C2×C4×D59—44no—
268C2×C4×D59—44no—
269C2×C4×D59—44no—
270C2×C4×D59—44no—
271C2×C4×D59—44no—
272C2×C4×D59—44no—
273(C2×D59)⋊C4—28no—
274(C2×D59)⋊C4—28no—
275(C2×D59)⋊C4—44no—
276(C2×D59)⋊C4—44no—
277(C2×D59)⋊C4—44no—
278(C2×D59)⋊C4—44no—
279C4⋊Dic59C22⋊C4116yescomplemented
280Dic59⋊C4—28no—
281Dic59⋊C4—28no—
282Dic59⋊C4—44no—
283Dic59⋊C4—44no—
284C4×Dic59—44no—
285C4×Dic59—44no—
286C23×C59C23×C411yescharacteristic
287C23×C59C22×D411yescharacteristic
288C23×C59C22×D411yescharacteristic
289C23×C59C22×Q811yescharacteristic
290C23×C59C2×#4111yescharacteristic
291C23×C59C2×#4111yescharacteristic
292C23×C59C2×#4111yescharacteristic
293C23×C59H(5,𝔽2)11yescharacteristic
294C23×C59H(5,𝔽2)11yescharacteristic
295C23×C59H(5,𝔽2)11yescharacteristic
296C23×C59H(5,𝔽2)11yescharacteristic
297C23×C59H(5,𝔽2)11yescharacteristic
298C23×C592−1+411yescharacteristic
299C23×C592−1+411yescharacteristic
300C23×C592−1+411yescharacteristic
301C22×D59—22no—
302C22×D59—22no—
303C22×D59—22no—
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—41no—
320C22×D59—41no—
321C22×D59—41no—
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×D59C4×Q814yes—
336Q8×C59—416no—
337C2×C4×C59—22no—
338C2×C4×C59—22no—
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—41no—
356C2×C4×C59—41no—
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×C59C2×C22⋊C414yes—
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—22no—
406C2×Dic59—22no—
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×Dic59C2×C22⋊C414yes—
434C2×Dic59C2×C22⋊C414yes—
435C4×D59—416no—
436#14448—591nomaximal, Sylow
437C22×C59C22×C22⋊C411yescharacteristic
438C22×C59C2×C4×Q811yescharacteristic
439C22×C59C4×#4111yescharacteristic
440C22×C59#51811yescharacteristic
441C22×C59#51811yescharacteristic
442C22×C59#51911yescharacteristic
443C22×C59#52011yescharacteristic
444C22×C59#53511yescharacteristic
445C22×C59#53511yescharacteristic
446C22×C59#53511yescharacteristic
447C22×C59#53511yescharacteristic
448C22×C59#53811yescharacteristic
449C22×C59#53911yescharacteristic
450C22×C59#53911yescharacteristic
451C22×C59#53911yescharacteristic
452C22×C59#54211yescharacteristic
453C22×C59#54211yescharacteristic
454C22×C59#54311yescharacteristic
455C22×C59#54411yescharacteristic
456C22×C59#54611yescharacteristic
457C22×C59#54611yescharacteristic
458C22×C59#54711yescharacteristic
459C22×C59#54711yescharacteristic
460C22×C59#54811yescharacteristic
461C22×C59#54811yescharacteristic
462C22×C59D4×Q811yescharacteristic
463C22×C59D4×Q811yescharacteristic
464C22×C59#55111yescharacteristic
465C22×C59#55111yescharacteristic
466C22×C59#55411yescharacteristic
467C22×C59#55411yescharacteristic
468C22×C59#56211yescharacteristic
469C22×C59#56211yescharacteristic
470C22×C59#56311yescharacteristic
471C22×C59#56311yescharacteristic
472C2×D59—24no—
473C2×D59—24no—
474C2×D59—24no—
475C2×D59—42no—
476C2×D59—42no—
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—
487C4×C59—24no—
488C4×C59—42no—
489C4×C59—42no—
490C4×C59—42no—
491C4×C59—42no—
492C4×C59—81no—
493C4×C59—81no—
494Dic59—24no—
495Dic59—24no—
496Dic59—42no—
497Dic59—42no—
498Dic59—42no—
499Dic59—81no—
500Dic59—81no—
501C22×C22⋊Q8—591no—
502C2×#387—591no—
503C2×#387—591no—
504#1446—591no—
505#1446D5911yescharacteristic, complemented
506#1445—591no—
507#1445—591no—
508#1439—591no—
509#1439—591no—
510#1437—591no—
511#1437—591no—
512C4⋊#95—591no—
513C4⋊#95—591no—
514C22⋊#95—591no—
515C22⋊#95—591no—
516C2×C59#230911yescharacteristic
517C2×C59#232911yescharacteristic
518C2×C59#233211yescharacteristic
519C2×C59#233911yescharacteristic
520C2×C59Q8×C22⋊C411yescharacteristic
521C2×C59#236811yescharacteristic
522C2×C59#237811yescharacteristic
523C2×C59#269211yescharacteristic
524C2×C59#269211yescharacteristic
525C2×C59#269611yescharacteristic
526C2×C59#269611yescharacteristic
527C2×C59#272011yescharacteristic
528C2×C59#272011yescharacteristic
529C2×C59#272311yescharacteristic
530C2×C59#272311yescharacteristic
531D59—44no—
532C23×Q8C2×D5911yescharacteristic
533C24×C4—591no—
534C2×C22⋊Q8—598no—
535C2×C22⋊Q8—1184no—
536C2×C22⋊Q8—1184no—
537C22×C4⋊C4—591no—
538C22×C4⋊C4—591no—
539C22×C4⋊C4—591no—
540C22×C4⋊C4—591no—
541C22×C4⋊C4—591no—
542C22×C22⋊C4—591no—
543C22×C22⋊C4—591no—
544C22×C22⋊C4—591no—
545C22×C22⋊C4—591no—
546C22×C22⋊C4—591no—
547C22×C22⋊C4—591no—
548C22×C42—591no—
549C22×C42—591no—
550#387—1184no—
551#387—1184no—
552C2×#95—591no—
553C2×#95—591no—
554C2×#95—591no—
555C2×#95—591no—
556C2×#95—591no—
557C2×#95—591no—
558C2×#95—591no—
559C2×#95—591no—
560C2×#95—591no—
561C2×#95—591no—
562C2×#95—591no—
563C2×#95—591no—
564C2×#95—591no—
565C2×#95—591no—
566C2×#95C2×D5911yescharacteristic
567C2×#95C2×D5911yescharacteristic
568C2×#95C2×D5911yescharacteristic
569C2×#95C2×D5911yescharacteristic
570C2×#95C2×D5911yescharacteristic
571C2×#95C2×D5911yescharacteristic
572C59#1444811yescharacteristic, complemented, Sylow
573C25—591no—
574C22×Q8—22no—
575C22×Q8—22no—
576C22×Q8—41no—
577C22×Q8—41no—
578C22×Q8—41no—
579C22×Q8—41no—
580C22×Q8C4×D5914yes—
581C23×C4—591no—
582C23×C4—591no—
583C23×C4—591no—
584C23×C4—591no—
585C23×C4—591no—
586C23×C4—594no—
587C23×C4—591no—
588C23×C4—591no—
589C23×C4—1182no—
590C23×C4—1182no—
591C23×C4—2361no—
592C23×C4—2361no—
593C23×C4—2361no—
594C23×C4—2361no—
595C23×C4C22×D5911yescharacteristic
596C23×C4C22×D5911yescharacteristic
597C23×C4C22×D5911yescharacteristic
598C23×C4C22×D5911yescharacteristic
599C23×C4C22×D5911yescharacteristic
600C23×C4C22×D5911yescharacteristic
601C23×C4C22×D5911yescharacteristic
602C22⋊Q8—11832no—
603C2×C4⋊C4—594no—
604C2×C4⋊C4—594no—
605C2×C4⋊C4—594no—
606C2×C4⋊C4—594no—
607C2×C4⋊C4—594no—
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—2361no—
617C2×C4⋊C4—2361no—
618C2×C22⋊C4—594no—
619C2×C22⋊C4—594no—
620C2×C22⋊C4—594no—
621C2×C22⋊C4—1182no—
622C2×C22⋊C4—1182no—
623C2×C22⋊C4—1182no—
624C2×C22⋊C4—1182no—
625C2×C22⋊C4—1182no—
626C2×C22⋊C4—1182no—
627C2×C22⋊C4—1182no—
628C2×C22⋊C4—1182no—
629C2×C22⋊C4—1182no—
630C2×C22⋊C4—2361no—
631C2×C22⋊C4—2361no—
632C2×C22⋊C4—2361no—
633C2×C22⋊C4—2361no—
634C2×C22⋊C4—2361no—
635C2×C22⋊C4—2361no—
636C2×C42—1182no—
637C2×C42—1182no—
638C2×C42—1182no—
639C2×C42—1182no—
640C2×C42—2361no—
641C2×C42—2361no—
642#95—22no—
643#95—22no—
644#95—41no—
645#95—41no—
646#95—41no—
647#95—41no—
648#95—1182no—
649#95—1182no—
650#95—1182no—
651#95—1182no—
652#95—1182no—
653#95—1182no—
654#95—2361no—
655#95—2361no—
656#95—2361no—
657#95—2361no—
658#95—2361no—
659#95—2361no—
660#95—2361no—
661#95—2361no—
662C24—592no—
663C24—592no—
664C24—592no—
665C24—1181no—
666C24—1181no—
667C24—1181no—
668C24—1181no—
669C24—1181no—
670C24—1181no—
671C24—1181no—
672C24—1181no—
673C24—1181no—
674C24—1181no—
675C24—1181no—
676C24—1181no—
677C24C23×D5911yescharacteristic
678C2×Q8—28no—
679C2×Q8—44no—
680C2×Q8—44no—
681C2×Q8—44no—
682C2×Q8—44no—
683C2×Q8—44no—
684C2×Q8—44no—
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—21no—
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—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—1188no—
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×C4—2364no—
783C22×C4C2×C4×D5912yes—
784C22×C4C2×C4×D5912yes—
785C22×C4C2×C4×D5912yes—
786C22×C4D4×D5912yes—
787C22×C4D4×D5912yes—
788C22×C4Q8×D5912yes—
789C22×C4#1174568912yes—
790C4⋊C4—5916no—
791C4⋊C4—1188no—
792C4⋊C4—1188no—
793C4⋊C4—2364no—
794C4⋊C4—2364no—
795C22⋊C4—1188no—
796C22⋊C4—1188no—
797C22⋊C4—2364no—
798C22⋊C4—2364no—
799C22⋊C4—2364no—
800C22⋊C4—2364no—
801C42—2364no—
802C42—2364no—
803C23—594no—
804C23—1182no—
805C23—1182no—
806C23—1182no—
807C23—1182no—
808C23—1182no—
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—2361no—
823C23—2361no—
824C23—2361no—
825C23—2361no—
826C23—2361no—
827C23—2361no—
828C23—2361no—
829C23—2361no—
830C23—2361no—
831C23—2361no—
832C23—2361no—
833C23—2361no—
834C23—2361no—
835C23—2361no—
836C23—2361no—
837C23—2361no—
838C23C22×C4×D5911yescharacteristic
839C23C2×D4×D5911yescharacteristic
840C23C2×D4×D5911yescharacteristic
841C23C2×Q8×D5911yescharacteristic
842C23#41×D5911yescharacteristic
843C23#41×D5911yescharacteristic
844C23C2×#1174568911yescharacteristic
845C23#1427377211yescharacteristic
846C23#1427377211yescharacteristic
847C23#1427377211yescharacteristic
848C23#1427377211yescharacteristic
849C23#1427377311yescharacteristic
850C23#1427377411yescharacteristic
851C23#1427377511yescharacteristic
852C23#1427377511yescharacteristic
853Q8—416no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
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—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
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—594no—
903C2×C4—594no—
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—1182no—
925C2×C4—23616no—
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×C4C22⋊C4×D5914yes—
953C22—1184no—
954C22—1184no—
955C22—1184no—
956C22—2362no—
957C22—2362no—
958C22—2362no—
959C22—2362no—
960C22—2362no—
961C22—2362no—
962C22—2362no—
963C22—2362no—
964C22—2362no—
965C22—2362no—
966C22—2362no—
967C22—2362no—
968C22C2×C22⋊C4×D5911yescharacteristic
969C22C4×Q8×D5911yescharacteristic
970C22C4×#1174568911yescharacteristic
971C22#1683787511yescharacteristic
972C22#1683787511yescharacteristic
973C22#1683787811yescharacteristic
974C22#1683788411yescharacteristic
975C22#1683796711yescharacteristic
976C22#1683796711yescharacteristic
977C22#1683796711yescharacteristic
978C22#1683796711yescharacteristic
979C22#1683798611yescharacteristic
980C22#1683799811yescharacteristic
981C22#1683799811yescharacteristic
982C22#1683800111yescharacteristic
983C22#1683801611yescharacteristic
984C22#1683802611yescharacteristic
985C22#1683802711yescharacteristic
986C22#1683802911yescharacteristic
987C22#1683804311yescharacteristic
988C22#1683804511yescharacteristic
989C22#1683805411yescharacteristic
990C22#1683805511yescharacteristic
991C22#1683806011yescharacteristic
992C22#1683806211yescharacteristic
993C22#1683806511yescharacteristic
994C22#1683806711yescharacteristic
995C22#1683807911yescharacteristic
996C22#1683808211yescharacteristic
997C22#1683810611yescharacteristic
998C22#1683811311yescharacteristic
999C22#1683814611yescharacteristic
1000C22#1683814811yescharacteristic
1001C22#1683815111yescharacteristic
1002C22#1683815311yescharacteristic
1003C4—24no—
1004C4—42no—
1005C4—42no—
1006C4—42no—
1007C4—42no—
1008C4—81no—
1009C4—81no—
1010C4—1184no—
1011C4—1184no—
1012C4—4721no—
1013C4—4721no—
1014C4—2362no—
1015C4—2362no—
1016C4—2362no—
1017C2—2364no—
1018C2#2142667711yescharacteristic
1019C2#2142682811yescharacteristic
1020C2#2142685111yescharacteristic
1021C2#2142692511yescharacteristic
1022C2#2142693011yescharacteristic
1023C2#2142717511yescharacteristic
1024C2#2142725711yescharacteristic
1025C2#2143059711yescharacteristic
1026C2#2143059911yescharacteristic
1027C2#2143065111yescharacteristic
1028C2#2143065311yescharacteristic
1029C2#2143098111yescharacteristic
1030C2#2143098311yescharacteristic
1031C2#2143102011yescharacteristic
1032C2#2143102211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC59×#1446C2
socle, cosocleC24×C59C24
prime radicalC24×D59C23
hypercenter#1446D59
hypocenterC59#14448
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
2. C2×#16837287C2semidirect
3. C2×#16837285C2semidirect
4. #21422367C2semidirect
5. #21422362C2semidirect
6. #21422362C2semidirect
11. Dic59⋊#95C2semidirect
12. Dic59⋊#95C2semidirect
15. C59×#1446C2semidirect
19. C2×#14273703C4semidirect
104. C2×(C2×D59)⋊C4Q8semidirect
279. C4⋊Dic59C22⋊C4semidirect
505. #1446D59semidirect
572. C59#14448semidirect

Maximal subgroups

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

subgroupindex
C22×#142737032
C2×#168372872
C2×#168372852
#214223672
#214223622
#214223402
#214223322
Dic59⋊#952
(C2×D59)⋊#952
C59×#14462
#1444859