Finite Group Databasebeta

← #28514366

Subgroups — #28514366

Order 15104.

1686 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837324C211yesmaximal, characteristic
2C2×#16837297C211yesmaximal, characteristic, complemented
3C2×#16837293C211yesmaximal, characteristic
4C2×#16837293C211yesmaximal, characteristic
5C2×#16837292C211yesmaximal, characteristic
6C2×C4×C4⋊Dic59C211yesmaximal, characteristic, complemented
7#21422349C211yesmaximal, characteristic, complemented
8#21422348C211yesmaximal, characteristic, complemented
9#21422342C211yesmaximal, characteristic
10#21422334C211yesmaximal, characteristic
11#21422332C211yesmaximal, characteristic
12#21422331C211yesmaximal, characteristic, complemented
13#21422329C211yesmaximal, characteristic, complemented
14#21422323C211yesmaximal, characteristic, complemented
15C2×C4×C4⋊C4×C59C211yesmaximal, characteristic, complemented
16C22×C4⋊Dic59C2211yescharacteristic
17C22×C4⋊Dic59C2211yescharacteristic
18C22×Dic59⋊C4C2211yescharacteristic
19C22×Dic59⋊C4C2211yescharacteristic
20C22×Dic59⋊C4C2211yescharacteristic
21C22×(C2×D59)⋊C4C2211yescharacteristic
22C22×(C2×D59)⋊C4C2211yescharacteristic
23C22×(C2×D59)⋊C4C2211yescharacteristic
24C22×(C2×D59)⋊C4C2211yescharacteristic
25C22×(C2×D59)⋊C4C2211yescharacteristic
26C22×(C2×D59)⋊C4C2211yescharacteristic
27C22×(C2×D59)⋊C4C2211yescharacteristic
28C22×C4×Dic59C2211yescharacteristic
29C22×C4×Dic59C2211yescharacteristic
30#16837324C418yescomplemented
31#16837297—24no—
32#16837293—24no—
33#16837293—24no—
34#16837292—24no—
35C4×C4⋊Dic59—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×C4⋊C4×C59C2211yescharacteristic
52C22×C42×C59C2211yescharacteristic
53C22×C42×C59C2211yescharacteristic
54C22×C42×C59C2211yescharacteristic
55C4×C4⋊C4×C59—24no—
56C2×#95×C59C2211yescharacteristic
57C2×#95×C59C2211yescharacteristic
58C24×D59C2311yescharacteristic
59C23×Dic59C2311yescharacteristic
60C23×Dic59C2311yescharacteristic
61C23×Dic59C2311yescharacteristic
62C23×Dic59C2311yescharacteristic
63C23×Dic59C2311yescharacteristic
64C23×Dic59C2311yescharacteristic
65C23×Dic59C2311yescharacteristic
66C2×C4⋊Dic59—22no—
67C2×C4⋊Dic59—22no—
68C2×C4⋊Dic59—22no—
69C2×C4⋊Dic59—22no—
70C2×C4⋊Dic59—22no—
71C2×C4⋊Dic59C2×C414yes—
72C2×Dic59⋊C4—22no—
73C2×Dic59⋊C4—22no—
74C2×Dic59⋊C4—22no—
75C2×Dic59⋊C4—22no—
76C2×Dic59⋊C4—22no—
77C2×Dic59⋊C4—22no—
78C2×Dic59⋊C4—22no—
79C2×Dic59⋊C4—41no—
80C2×Dic59⋊C4C2×C414yes—
81C2×(C2×D59)⋊C4—22no—
82C2×(C2×D59)⋊C4—22no—
83C2×(C2×D59)⋊C4—22no—
84C2×(C2×D59)⋊C4—22no—
85C2×(C2×D59)⋊C4—22no—
86C2×(C2×D59)⋊C4—22no—
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—22no—
97C2×(C2×D59)⋊C4—41no—
98C2×(C2×D59)⋊C4—41no—
99C2×(C2×D59)⋊C4C2×C414yes—
100C2×(C2×D59)⋊C4C2×C414yes—
101C2×(C2×D59)⋊C4C2×C414yes—
102C2×C4×Dic59—22no—
103C2×C4×Dic59—22no—
104C2×C4×Dic59—22no—
105C2×C4×Dic59—22no—
106C2×C4×Dic59—41no—
107C2×C4×Dic59—41no—
108C59⋊#95—22no—
109C59⋊#95—22no—
110C59⋊#95—22no—
111C59⋊#95—22no—
112C59⋊#95—22no—
113C59⋊#95—22no—
114C59⋊#95—22no—
115C59⋊#95—22no—
116C59⋊#95—22no—
117C59⋊#95—22no—
118C59⋊#95—22no—
119C59⋊#95—41no—
120C59⋊#95C2×C414yes—
121C59⋊#95D414yes—
122C23×C4×C59C2311yescharacteristic
123C23×C4×C59C2311yescharacteristic
124C23×C4×C59C2311yescharacteristic
125C23×C4×C59C2311yescharacteristic
126C23×C4×C59C2311yescharacteristic
127C23×C4×C59C2311yescharacteristic
128C23×C4×C59C2311yescharacteristic
129C2×C4⋊C4×C59—22no—
130C2×C4⋊C4×C59—22no—
131C2×C4⋊C4×C59—22no—
132C2×C4⋊C4×C59—22no—
133C2×C4⋊C4×C59C2×C414yes—
134C2×C4⋊C4×C59D414yes—
135C2×C42×C59—22no—
136C2×C42×C59—22no—
137C2×C42×C59—22no—
138C2×C42×C59—22no—
139C2×C42×C59—22no—
140C2×C42×C59—22no—
141C2×C42×C59—22no—
142C2×C42×C59—22no—
143C2×C42×C59D414yes—
144#95×C59—22no—
145#95×C59—22no—
146C24×C59C2411yescharacteristic
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×D59—21no—
159C23×D59—21no—
160C23×D59—21no—
161C23×D59C22×C412yes—
162C22×C4×C59—21no—
163C22×C4×C59—21no—
164C22×C4×C59—21no—
165C22×C4×C59—21no—
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×C59C22×C412yes—
197C22×C4×C59C22×C412yes—
198C22×C4×C59C22×C412yes—
199C22×C4×C59C2×D412yes—
200C22×C4×C59C2×D412yes—
201C22×C4×C59C2×D412yes—
202C22×C4×C59C2×D412yes—
203C22×C4×C59C2×D412yes—
204C22×C4×C59C2×D412yes—
205C22×C4×C59C2×D412yes—
206C22×C4×C59#4112yes—
207C22×C4×C59#4112yes—
208C22×C4×C59#4112yes—
209C22×C4×C59#4112yes—
210C22×C4×C59#4112yes—
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—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×Dic59C22×C412yes—
254C22×Dic59C22×C412yes—
255C22×Dic59C22×C412yes—
256C22×Dic59C2×D412yes—
257C22×Dic59C2×D412yes—
258C22×Dic59#4112yes—
259C22×Dic59#4112yes—
260C4⋊C4×C59—28no—
261C4⋊C4×C59—28no—
262C42×C59—28no—
263C42×C59—28no—
264C42×C59—44no—
265(C2×D59)⋊C4—28no—
266(C2×D59)⋊C4—28no—
267(C2×D59)⋊C4—28no—
268(C2×D59)⋊C4—44no—
269(C2×D59)⋊C4—44no—
270(C2×D59)⋊C4—44no—
271(C2×D59)⋊C4—44no—
272C4⋊Dic59—28no—
273C4⋊Dic59—28no—
274Dic59⋊C4—28no—
275Dic59⋊C4—44no—
276Dic59⋊C4—44no—
277C4×Dic59—44no—
278C4×Dic59—44no—
279C23×C59C23×C411yescharacteristic
280C23×C59C22×D411yescharacteristic
281C23×C59C22×D411yescharacteristic
282C23×C59C22×D411yescharacteristic
283C23×C59C2×#4111yescharacteristic
284C23×C59C2×#4111yescharacteristic
285C23×C59C2×#4111yescharacteristic
286C23×C59C2×#4111yescharacteristic
287C23×C59C2×#4111yescharacteristic
288C23×C59C2×#4111yescharacteristic
289C23×C59C2×#4111yescharacteristic
290C23×C59H(5,𝔽2)11yescharacteristic
291C23×C592−1+411yescharacteristic
292C23×C592−1+411yescharacteristic
293C23×C592−1+411yescharacteristic
294C22×D59—22no—
295C22×D59—22no—
296C22×D59—22no—
297C22×D59—22no—
298C22×D59—22no—
299C22×D59—22no—
300C22×D59—22no—
301C22×D59—41no—
302C22×D59—41no—
303C22×D59—41no—
304C22×D59—41no—
305C22×D59—41no—
306C22×D59—41no—
307C22×D59—41no—
308C22×D59—41no—
309C22×D59—41no—
310C22×D59—41no—
311C22×D59—41no—
312C22×D59—41no—
313C22×D59—41no—
314C22×D59—41no—
315C22×D59—41no—
316C22×D59—41no—
317C22×D59—41no—
318C22×D59—41no—
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—
329C2×C4×C59—22no—
330C2×C4×C59—22no—
331C2×C4×C59—22no—
332C2×C4×C59—22no—
333C2×C4×C59—22no—
334C2×C4×C59—22no—
335C2×C4×C59—22no—
336C2×C4×C59—22no—
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—22no—
356C2×C4×C59—22no—
357C2×C4×C59—22no—
358C2×C4×C59—22no—
359C2×C4×C59—22no—
360C2×C4×C59—22no—
361C2×C4×C59—22no—
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×C59C4×D414yes—
375C2×C4×C59C4×D414yes—
376C2×C4×C59#12114yes—
377C2×C4×C59#12114yes—
378C2×Dic59—22no—
379C2×Dic59—22no—
380C2×Dic59—22no—
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—41no—
397C2×Dic59—41no—
398C2×Dic59—41no—
399C2×Dic59—41no—
400C2×Dic59—41no—
401C2×Dic59—41no—
402C2×Dic59—41no—
403C2×Dic59—41no—
404C2×Dic59—41no—
405C2×Dic59—41no—
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×Dic59C4×D414yes—
427#14200—591nomaximal, Sylow
428C22×C59C2×C4×D411yescharacteristic
429C22×C59C2×C4×D411yescharacteristic
430C22×C59C2×C4×D411yescharacteristic
431C22×C59C4×#4111yescharacteristic
432C22×C59C4×#4111yescharacteristic
433C22×C59#51911yescharacteristic
434C22×C59#52011yescharacteristic
435C22×C59C2×#12111yescharacteristic
436C22×C59C2×#12111yescharacteristic
437C22×C59#52511yescharacteristic
438C22×C59#52511yescharacteristic
439C22×C59#52911yescharacteristic
440C22×C59#52911yescharacteristic
441C22×C59#53211yescharacteristic
442C22×C59#53211yescharacteristic
443C22×C59#53611yescharacteristic
444C22×C59#53711yescharacteristic
445C22×C59#54111yescharacteristic
446C22×C59#54211yescharacteristic
447C22×C59D4211yescharacteristic
448C22×C59#54711yescharacteristic
449C22×C59#54711yescharacteristic
450C22×C59#54711yescharacteristic
451C22×C59#54811yescharacteristic
452C22×C59#54811yescharacteristic
453C22×C59#54811yescharacteristic
454C22×C59#55111yescharacteristic
455C22×C59#55211yescharacteristic
456C22×C59#55211yescharacteristic
457C22×C59#55211yescharacteristic
458C22×C59#55311yescharacteristic
459C22×C59#55311yescharacteristic
460C22×C59#55611yescharacteristic
461C22×C59#55611yescharacteristic
462C22×C59#55611yescharacteristic
463C2×D59—42no—
464C2×D59—42no—
465C2×D59—42no—
466C2×D59—42no—
467C2×D59—42no—
468C2×D59—42no—
469C2×D59—42no—
470C2×D59—81no—
471C2×D59—81no—
472C2×D59—81no—
473C2×D59—81no—
474C2×D59—81no—
475C2×D59—81no—
476C2×D59—81no—
477C2×D59—81no—
478C4×C59—24no—
479C4×C59—24no—
480C4×C59—24no—
481C4×C59—24no—
482C4×C59—42no—
483C4×C59—42no—
484C4×C59—42no—
485Dic59—24no—
486Dic59—42no—
487Dic59—42no—
488Dic59—42no—
489Dic59—42no—
490Dic59—81no—
491Dic59—81no—
492C2×#396—591no—
493C2×#389—591no—
494C2×#388—591no—
495C2×#388—591no—
496C2×#388—591no—
497C2×C4×C4⋊C4—591no—
498C2×C4×C4⋊C4D5911yescharacteristic, complemented
499#1441—591no—
500#1441—591no—
501#1439—591no—
502#1437—591no—
503#1437—591no—
504#1436—591no—
505#1436—591no—
506#1434—591no—
507C2×C59C4×#12111yescharacteristic
508C2×C59C4×#12111yescharacteristic
509C2×C59#232311yescharacteristic
510C2×C59#236111yescharacteristic
511C2×C59#236211yescharacteristic
512C2×C59#236211yescharacteristic
513C2×C59#237311yescharacteristic
514C2×C59#241311yescharacteristic
515C2×C59#241611yescharacteristic
516C2×C59#246111yescharacteristic
517C2×C59#246911yescharacteristic
518C2×C59#251911yescharacteristic
519C2×C59#252511yescharacteristic
520C2×C59#254511yescharacteristic
521C2×C59#260111yescharacteristic
522D59—82no—
523C22×C4⋊C4—591no—
524C22×C4⋊C4—591no—
525C22×C4⋊C4—591no—
526C22×C4⋊C4—591no—
527C22×C4⋊C4—591no—
528C22×C4⋊C4C2×D5911yescharacteristic
529C22×C4⋊C4C2×D5911yescharacteristic
530C22×C22⋊C4—591no—
531C22×C22⋊C4—591no—
532C22×C22⋊C4—591no—
533C22×C22⋊C4—591no—
534C22×C22⋊C4—591no—
535C22×C22⋊C4—591no—
536C22×C22⋊C4—591no—
537C22×C42—591no—
538C22×C42—591no—
539C22×C42C2×D5911yescharacteristic
540C22×C42C2×D5911yescharacteristic
541C22×C42C2×D5911yescharacteristic
542#396—598no—
543#389—1184no—
544#388—1184no—
545#388—1184no—
546#388—1184no—
547C4×C4⋊C4—24no—
548C4×C4⋊C4—1184no—
549C2×#95—591no—
550C2×#95—591no—
551C2×#95—591no—
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×#95C2×D5911yescharacteristic
564C2×#95C2×D5911yescharacteristic
565C59#1420011yescharacteristic, complemented, Sylow
566C25—591no—
567C23×C4—591no—
568C23×C4—591no—
569C23×C4—591no—
570C23×C4—591no—
571C23×C4—591no—
572C23×C4—591no—
573C23×C4—591no—
574C23×C4C22×D5911yescharacteristic
575C23×C4C22×D5911yescharacteristic
576C23×C4C22×D5911yescharacteristic
577C23×C4C22×D5911yescharacteristic
578C23×C4C22×D5911yescharacteristic
579C23×C4C22×D5911yescharacteristic
580C23×C4C22×D5911yescharacteristic
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—594no—
586C2×C4⋊C4—594no—
587C2×C4⋊C4—1182no—
588C2×C4⋊C4—1182no—
589C2×C4⋊C4—1182no—
590C2×C4⋊C4—1182no—
591C2×C4⋊C4—1182no—
592C2×C4⋊C4—1182no—
593C2×C4⋊C4—1182no—
594C2×C4⋊C4—1182no—
595C2×C4⋊C4—1182no—
596C2×C4⋊C4—1182no—
597C2×C4⋊C4—1182no—
598C2×C4⋊C4—1182no—
599C2×C4⋊C4—2361no—
600C2×C4⋊C4C4×D5914yes—
601C2×C4⋊C4D23614yes—
602C2×C22⋊C4—594no—
603C2×C22⋊C4—594no—
604C2×C22⋊C4—594no—
605C2×C22⋊C4—1182no—
606C2×C22⋊C4—1182no—
607C2×C22⋊C4—1182no—
608C2×C22⋊C4—1182no—
609C2×C22⋊C4—1182no—
610C2×C22⋊C4—1182no—
611C2×C22⋊C4—1182no—
612C2×C22⋊C4—1182no—
613C2×C22⋊C4—1182no—
614C2×C22⋊C4—1182no—
615C2×C22⋊C4—1182no—
616C2×C22⋊C4—1182no—
617C2×C22⋊C4—1182no—
618C2×C22⋊C4—1182no—
619C2×C22⋊C4—1182no—
620C2×C22⋊C4—1182no—
621C2×C22⋊C4—2361no—
622C2×C22⋊C4—2361no—
623C2×C42—22no—
624C2×C42—22no—
625C2×C42—22no—
626C2×C42—22no—
627C2×C42—22no—
628C2×C42—22no—
629C2×C42—22no—
630C2×C42—22no—
631C2×C42—1182no—
632C2×C42—1182no—
633C2×C42—1182no—
634C2×C42—1182no—
635C2×C42—2361no—
636C2×C42—2361no—
637C2×C42C22⋊D5914yes—
638#95—22no—
639#95—22no—
640#95—594no—
641#95—594no—
642#95—1182no—
643#95—1182no—
644#95—1182no—
645#95—1182no—
646#95—1182no—
647#95—1182no—
648#95—1182no—
649#95—1182no—
650#95—1182no—
651#95—1182no—
652#95—1182no—
653#95—2361no—
654C24—592no—
655C24—1181no—
656C24—1181no—
657C24—1181no—
658C24—1181no—
659C24—1181no—
660C24—1181no—
661C24—1181no—
662C24—1181no—
663C24—1181no—
664C24—1181no—
665C24—1181no—
666C24—1181no—
667C24—1181no—
668C24—1181no—
669C24C23×D5911yescharacteristic
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
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—592no—
705C22×C4—592no—
706C22×C4—592no—
707C22×C4—592no—
708C22×C4—592no—
709C22×C4—592no—
710C22×C4—592no—
711C22×C4—1181no—
712C22×C4—1181no—
713C22×C4—1181no—
714C22×C4—1181no—
715C22×C4—1181no—
716C22×C4—1181no—
717C22×C4—1181no—
718C22×C4—1181no—
719C22×C4—1181no—
720C22×C4—1181no—
721C22×C4—1181no—
722C22×C4—1181no—
723C22×C4—1181no—
724C22×C4—1181no—
725C22×C4—1181no—
726C22×C4—1181no—
727C22×C4—1181no—
728C22×C4—1181no—
729C22×C4—1181no—
730C22×C4—1181no—
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×C4C2×C4×D5912yes—
754C22×C4C2×C4×D5912yes—
755C22×C4C2×C4×D5912yes—
756C22×C4C2×D23612yes—
757C22×C4C2×D23612yes—
758C22×C4C2×D23612yes—
759C22×C4#1174568512yes—
760C22×C4#1174568512yes—
761C22×C4#1174568512yes—
762C22×C4#1174568512yes—
763C22×C4D4×D5912yes—
764C22×C4#1174568712yes—
765C22×C4C2×C22⋊D5912yes—
766C22×C4C2×C22⋊D5912yes—
767C22×C4C2×C22⋊D5912yes—
768C4⋊C4—28no—
769C4⋊C4—28no—
770C4⋊C4—1188no—
771C4⋊C4—1188no—
772C4⋊C4—1188no—
773C4⋊C4—2364no—
774C4⋊C4—2364no—
775C22⋊C4—1188no—
776C22⋊C4—1188no—
777C22⋊C4—1188no—
778C22⋊C4—2364no—
779C22⋊C4—2364no—
780C22⋊C4—2364no—
781C22⋊C4—2364no—
782C42—28no—
783C42—28no—
784C42—44no—
785C42—2364no—
786C42—2364no—
787C23—1182no—
788C23—1182no—
789C23—1182no—
790C23—1182no—
791C23—1182no—
792C23—1182no—
793C23—1182no—
794C23—2361no—
795C23—2361no—
796C23—2361no—
797C23—2361no—
798C23—2361no—
799C23—2361no—
800C23—2361no—
801C23—2361no—
802C23—2361no—
803C23—2361no—
804C23—2361no—
805C23—2361no—
806C23—2361no—
807C23—2361no—
808C23—2361no—
809C23—2361no—
810C23—2361no—
811C23—2361no—
812C23—2361no—
813C23—2361no—
814C23—2361no—
815C23—2361no—
816C23—2361no—
817C23—2361no—
818C23—2361no—
819C23—2361no—
820C23—2361no—
821C23—2361no—
822C23C22×C4×D5911yescharacteristic
823C23C2×D4×D5911yescharacteristic
824C23C22×C22⋊D5911yescharacteristic
825C23C22×D23611yescharacteristic
826C23#41×D5911yescharacteristic
827C23#41×D5911yescharacteristic
828C23C2×#1174568711yescharacteristic
829C23C2×#1174568511yescharacteristic
830C23C2×#1174568511yescharacteristic
831C23C2×#1174568511yescharacteristic
832C23C2×#1174568511yescharacteristic
833C23#1427377311yescharacteristic
834C23#1427377411yescharacteristic
835C23#1427377511yescharacteristic
836C23#1427377511yescharacteristic
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
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—41no—
871C2×C4—41no—
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—594no—
883C2×C4—1182no—
884C2×C4—1182no—
885C2×C4—1182no—
886C2×C4—1182no—
887C2×C4—1182no—
888C2×C4—1182no—
889C2×C4—1182no—
890C2×C4—1182no—
891C2×C4—1182no—
892C2×C4—1182no—
893C2×C4—1182no—
894C2×C4—1182no—
895C2×C4—1182no—
896C2×C4—1182no—
897C2×C4—1182no—
898C2×C4—1182no—
899C2×C4—1182no—
900C2×C4—1182no—
901C2×C4—2361no—
902C2×C4—2361no—
903C2×C4—2361no—
904C2×C4—2361no—
905C2×C4—2361no—
906C2×C4—2361no—
907C2×C4—2361no—
908C2×C4—2361no—
909C2×C4—2361no—
910C2×C4—2361no—
911C2×C4—2361no—
912C2×C4—2361no—
913C2×C4—2361no—
914C2×C4—2361no—
915C2×C4—2361no—
916C2×C4—2361no—
917C2×C4—2361no—
918C2×C4—2361no—
919C2×C4—2361no—
920C2×C4—2361no—
921C2×C4—2361no—
922C2×C4—2361no—
923C2×C4—2361no—
924C2×C4—2361no—
925C2×C4—2361no—
926C2×C4—2361no—
927C2×C4—2361no—
928C2×C4—2361no—
929C2×C4—2361no—
930C2×C4—2361no—
931C2×C4C4×C22⋊D5914yes—
932C2×C4C4×D23614yes—
933C2×C4#1427369914yes—
934C2×C4#1427370114yes—
935C22—4721no—
936C22—4721no—
937C22—4721no—
938C22—4721no—
939C22—4721no—
940C22—4721no—
941C22—4721no—
942C22—4721no—
943C22—2362no—
944C22—2362no—
945C22—2362no—
946C22—2362no—
947C22—2362no—
948C22—2362no—
949C22—2362no—
950C22C4×D4×D5911yescharacteristic
951C22C2×C4×C22⋊D5911yescharacteristic
952C22C2×C4×D23611yescharacteristic
953C22C4×#1174568711yescharacteristic
954C22C4×#1174568511yescharacteristic
955C22#1683787811yescharacteristic
956C22#1683788411yescharacteristic
957C22C2×#1427369911yescharacteristic
958C22C2×#1427370111yescharacteristic
959C22#1683791111yescharacteristic
960C22#1683791311yescharacteristic
961C22#1683793211yescharacteristic
962C22#1683793611yescharacteristic
963C22#1683794811yescharacteristic
964C22#1683795211yescharacteristic
965C22#1683797611yescharacteristic
966C22#1683798011yescharacteristic
967C22#1683801011yescharacteristic
968C22#1683802411yescharacteristic
969C22D4×D23611yescharacteristic
970C22#1683805311yescharacteristic
971C22#1683805311yescharacteristic
972C22#1683805611yescharacteristic
973C22#1683806111yescharacteristic
974C22#1683806411yescharacteristic
975C22#1683806411yescharacteristic
976C22#1683807611yescharacteristic
977C22#1683808511yescharacteristic
978C22#1683808711yescharacteristic
979C22#1683808711yescharacteristic
980C22#1683809611yescharacteristic
981C22#1683809811yescharacteristic
982C22#1683812011yescharacteristic
983C22#1683812411yescharacteristic
984C22#1683812411yescharacteristic
985C4—24no—
986C4—24no—
987C4—24no—
988C4—24no—
989C4—42no—
990C4—42no—
991C4—42no—
992C4—1184no—
993C4—4721no—
994C4—4721no—
995C4—2362no—
996C4—2362no—
997C4—2362no—
998C4—2362no—
999C2—4722no—
1000C2C4×#1427369911yescharacteristic
1001C2C4×#1427370111yescharacteristic
1002C2#2142677211yescharacteristic
1003C2#2142711411yescharacteristic
1004C2#2142712411yescharacteristic
1005C2#2142712511yescharacteristic
1006C2#2142722111yescharacteristic
1007C2#2142750311yescharacteristic
1008C2#2142753611yescharacteristic
1009C2#2142806311yescharacteristic
1010C2#2142817711yescharacteristic
1011C2#2142876911yescharacteristic
1012C2#2142885311yescharacteristic
1013C2#2142907211yescharacteristic
1014C2#2142969311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC2×C4×C4⋊C4×C59C2
socle, cosocleC24×C59C24
prime radicalC24×D59C23
hypercenterC2×C4×C4⋊C4D59
hypocenterC59#14200
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16837297C2semidirect
6. C2×C4×C4⋊Dic59C2semidirect
7. #21422349C2semidirect
8. #21422348C2semidirect
12. #21422331C2semidirect
13. #21422329C2semidirect
14. #21422323C2semidirect
15. C2×C4×C4⋊C4×C59C2semidirect
30. #16837324C4semidirect
498. C2×C4×C4⋊C4D59semidirect
565. C59#14200semidirect

Maximal subgroups

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

subgroupindex
C2×#168373242
C2×#168372972
C2×#168372932
C2×#168372922
C2×C4×C4⋊Dic592
#214223492
#214223482
#214223422
#214223342
#214223322
#214223312
#214223292
#214223232
C2×C4×C4⋊C4×C592
#1420059