Finite Group Databasebeta

← #28518784

Subgroups — #28518784

Order 15104.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837314C211yesmaximal, characteristic
2C2×#16837308C211yesmaximal, characteristic, complemented
3C2×#16837306C211yesmaximal, characteristic, complemented
4C2×#16837277C211yesmaximal, characteristic
5C2×#16837274C211yesmaximal, characteristic
6#21422360C211yesmaximal, characteristic, complemented
7#21422360C211yesmaximal, characteristic, complemented
8#21422354C211yesmaximal, characteristic, complemented
9#21422352C211yesmaximal, characteristic, complemented
10#21422339C211yesmaximal, characteristic
11#21422333C211yesmaximal, characteristic
12#21422323C211yesmaximal, characteristic, complemented
13#21422322C211yesmaximal, characteristic, complemented
14#21422318C211yesmaximal, characteristic
15C59×#1437C211yesmaximal, characteristic
16C23×Dic118C2211yescharacteristic
17C24×Dic59C2211yescharacteristic
18C22×C4⋊Dic59C2211yescharacteristic
19C22×C4⋊Dic59C2211yescharacteristic
20C22×Dic59⋊C4C2211yescharacteristic
21C22×Dic59⋊C4C2211yescharacteristic
22C22×Dic59⋊C4C2211yescharacteristic
23C22×C22⋊Dic59C2211yescharacteristic
24C22×C22⋊Dic59C2211yescharacteristic
25C22×C22⋊Dic59C2211yescharacteristic
26C22×C4×Dic59C2211yescharacteristic
27#16837314C418yescomplemented
28#16837308—24no—
29#16837306—24no—
30#16837277—24no—
31#16837274—24no—
32C2×C59⋊#95C2211yescharacteristic
33C2×C59⋊#95C2211yescharacteristic
34C2×C59⋊#95C2211yescharacteristic
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
49C22×C22⋊C4×C59C2211yescharacteristic
50C22×C22⋊C4×C59C2211yescharacteristic
51C22×C22⋊C4×C59C2211yescharacteristic
52C22×C42×C59C2211yescharacteristic
53C2×#95×C59C2211yescharacteristic
54C2×#95×C59C2211yescharacteristic
55C2×#95×C59C2211yescharacteristic
56C22×Dic118—22no—
57C22×Dic118—22no—
58C22×Dic118—22no—
59C22×Dic118—22no—
60C22×Dic118—41no—
61C22×Dic118—41no—
62C22×Dic118C2×C414yescomplemented
63C23×Dic59—22no—
64C23×Dic59—22no—
65C23×Dic59—22no—
66C23×Dic59—41no—
67C23×Dic59—41no—
68C23×Dic59—41no—
69C23×Dic59—41no—
70C23×Dic59C2311yescharacteristic
71C23×Dic59C2311yescharacteristic
72C23×Dic59C2311yescharacteristic
73C23×Dic59C2311yescharacteristic
74C23×Dic59C2311yescharacteristic
75C23×Dic59C2311yescharacteristic
76C23×Dic59C2311yescharacteristic
77C23×Dic59C2311yescharacteristic
78C2×C4⋊Dic59—22no—
79C2×C4⋊Dic59—22no—
80C2×C4⋊Dic59—22no—
81C2×C4⋊Dic59—41no—
82C2×C4⋊Dic59—41no—
83C2×C4⋊Dic59—41no—
84C2×Dic59⋊C4—22no—
85C2×Dic59⋊C4—22no—
86C2×Dic59⋊C4—22no—
87C2×Dic59⋊C4—41no—
88C2×Dic59⋊C4—41no—
89C2×Dic59⋊C4—41no—
90C2×Dic59⋊C4—41no—
91C2×Dic59⋊C4—41no—
92C2×Dic59⋊C4—41no—
93C2×C22⋊Dic59—22no—
94C2×C22⋊Dic59—22no—
95C2×C22⋊Dic59—22no—
96C2×C22⋊Dic59—22no—
97C2×C22⋊Dic59—41no—
98C2×C22⋊Dic59—41no—
99C2×C22⋊Dic59—41no—
100C2×C22⋊Dic59C2×C414yes—
101C2×C22⋊Dic59C2×C414yes—
102C2×C4×Dic59—22no—
103C2×C4×Dic59—22no—
104C2×C4×Dic59—41no—
105C59⋊#95—22no—
106C59⋊#95—22no—
107C59⋊#95—22no—
108C59⋊#95—22no—
109C59⋊#95—22no—
110C59⋊#95—22no—
111C59⋊#95—22no—
112C59⋊#95—41no—
113C59⋊#95—41no—
114C59⋊#95—41no—
115C59⋊#95—41no—
116C59⋊#95—41no—
117C59⋊#95C2×C414yescomplemented
118C59⋊#95C2×C414yescomplemented
119C59⋊#95C2×C414yescomplemented
120C59⋊#95D414yes—
121C59⋊#95D414yes—
122C25×C59C2311yescharacteristic
123C23×C4×C59C2311yescharacteristic
124C23×C4×C59C2311yescharacteristic
125C23×C4×C59C2311yescharacteristic
126C23×C4×C59C2311yescharacteristic
127C23×C4×C59C2311yescharacteristic
128C23×C4×C59C2311yescharacteristic
129C2×C22⋊C4×C59—22no—
130C2×C22⋊C4×C59—22no—
131C2×C22⋊C4×C59—22no—
132C2×C22⋊C4×C59—22no—
133C2×C22⋊C4×C59—41no—
134C2×C22⋊C4×C59—41no—
135C2×C22⋊C4×C59—41no—
136C2×C22⋊C4×C59C2×C414yes—
137C2×C22⋊C4×C59Q814yescomplemented
138C2×C42×C59—22no—
139C2×C42×C59—22no—
140C2×C42×C59—41no—
141#95×C59—22no—
142#95×C59—41no—
143#95×C59—41no—
144C24×C59—21no—
145C24×C59—21no—
146C24×C59—21no—
147C24×C59—21no—
148C24×C59—21no—
149C24×C59—21no—
150C24×C59—21no—
151C24×C59—21no—
152C24×C59—21no—
153C24×C59—21no—
154C24×C59—21no—
155C24×C59—21no—
156C24×C59C22×C412yes—
157C24×C59C2×Q812yes—
158C24×C59#4112yes—
159C24×C59C2411yescharacteristic
160C22×C4×C59—21no—
161C22×C4×C59—21no—
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×C59C22×C412yes—
196C22×C4×C59C22×C412yes—
197C22×C4×C59C2×D412yes—
198C22×C4×C59C2×D412yes—
199C22×C4×C59C2×Q812yes—
200C22×C4×C59C2×Q812yes—
201C22×C4×C59#4112yes—
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C22×Dic59—21no—
207C22×Dic59—21no—
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—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—44no—
250C22×Dic59—44no—
251C22×Dic59—44no—
252C22×Dic59—44no—
253C22×Dic59—44no—
254C22×Dic59—44no—
255C22×Dic59—44no—
256C22×Dic59C22×C412yes—
257C22×Dic59C22×C412yes—
258C22×Dic59C22×C412yes—
259C22×Dic59C22×C412yes—
260C22×Dic59C2×D412yes—
261C22×Dic59C2×D412yes—
262C22×Dic59C2×D412yes—
263C22×Dic59C2×D412yes—
264C22×Dic59#4112yes—
265C2×Dic118—28no—
266C2×Dic118—28no—
267C2×Dic118—44no—
268C2×Dic118—44no—
269C2×Dic118—44no—
270C2×Dic118—44no—
271C2×Dic118—44no—
272C22⋊C4×C59—28no—
273C22⋊C4×C59—44no—
274C22⋊C4×C59—44no—
275C42×C59—44no—
276C22⋊Dic59—28no—
277C22⋊Dic59—44no—
278C22⋊Dic59—44no—
279C4⋊Dic59—44no—
280C4⋊Dic59—44no—
281Dic59⋊C4—44no—
282Dic59⋊C4—44no—
283Dic59⋊C4—44no—
284C4×Dic59—44no—
285C23×C59—22no—
286C23×C59—22no—
287C23×C59—22no—
288C23×C59—22no—
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—41no—
304C23×C59—41no—
305C23×C59—41no—
306C23×C59—41no—
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×C59C4×Q814yes—
320C23×C59C23×C411yescharacteristic
321C23×C59C22×D411yescharacteristic
322C23×C59C22×D411yescharacteristic
323C23×C59C22×Q811yescharacteristic
324C23×C59C2×#4111yescharacteristic
325C23×C59C2×#4111yescharacteristic
326C23×C59C2×#4111yescharacteristic
327C23×C59H(5,𝔽2)11yescharacteristic
328C23×C59H(5,𝔽2)11yescharacteristic
329C23×C59H(5,𝔽2)11yescharacteristic
330C23×C59H(5,𝔽2)11yescharacteristic
331C23×C59H(5,𝔽2)11yescharacteristic
332C23×C592−1+411yescharacteristic
333C23×C592−1+411yescharacteristic
334C23×C592−1+411yescharacteristic
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—41no—
354C2×C4×C59—41no—
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×C59C4×D414yes—
377C2×Dic59—22no—
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—22no—
397C2×Dic59—22no—
398C2×Dic59—22no—
399C2×Dic59—22no—
400C2×Dic59—22no—
401C2×Dic59—416no—
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×Dic59—41no—
427C2×Dic59—41no—
428C2×Dic59—41no—
429C2×Dic59—41no—
430C2×Dic59—41no—
431C2×Dic59—41no—
432C2×Dic59—41no—
433C2×Dic59C4×D414yes—
434Dic118—416no—
435#14575—591nomaximal, Sylow
436C22×C59—24no—
437C22×C59—24no—
438C22×C59—24no—
439C22×C59—42no—
440C22×C59—42no—
441C22×C59—42no—
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×C59C2×C4×D411yescharacteristic
452C22×C59C2×C4×D411yescharacteristic
453C22×C59C2×C4×Q811yescharacteristic
454C22×C59#51811yescharacteristic
455C22×C59#52011yescharacteristic
456C22×C59#52011yescharacteristic
457C22×C59#52011yescharacteristic
458C22×C59#53511yescharacteristic
459C22×C59#53511yescharacteristic
460C22×C59#53611yescharacteristic
461C22×C59#53611yescharacteristic
462C22×C59#53811yescharacteristic
463C22×C59#53911yescharacteristic
464C22×C59#54211yescharacteristic
465C22×C59#54211yescharacteristic
466C22×C59#54211yescharacteristic
467C22×C59#54211yescharacteristic
468C22×C59#54311yescharacteristic
469C22×C59#54411yescharacteristic
470C22×C59D4211yescharacteristic
471C22×C59#54611yescharacteristic
472C22×C59#54611yescharacteristic
473C22×C59#54611yescharacteristic
474C22×C59#54611yescharacteristic
475C22×C59D4×Q811yescharacteristic
476C22×C59D4×Q811yescharacteristic
477C22×C59#55111yescharacteristic
478C22×C59#55211yescharacteristic
479C22×C59#55211yescharacteristic
480C22×C59#55411yescharacteristic
481C22×C59#55411yescharacteristic
482C22×C59H(3,𝔽4)11yescharacteristic
483C22×C59#56211yescharacteristic
484C22×C59#56211yescharacteristic
485C22×C59#56311yescharacteristic
486C4×C59—24no—
487C4×C59—42no—
488C4×C59—42no—
489C4×C59—42no—
490C4×C59—42no—
491C4×C59—81no—
492Dic59—24no—
493Dic59—42no—
494Dic59—42no—
495Dic59—42no—
496Dic59—42no—
497Dic59—42no—
498Dic59—42no—
499Dic59—81no—
500C2×#393—591no—
501C2×#391—591no—
502C2×#391—591no—
503C2×#385—591no—
504C2×#385—591no—
505#1444—591no—
506#1444—591no—
507#1442—591no—
508#1442—591no—
509#1439—591no—
510#1437—591no—
511#1437D5911yescharacteristic
512#1434—591no—
513#1434—591no—
514C22⋊#95—591no—
515C2×C59—44no—
516C2×C59#232611yescharacteristic
517C2×C59#232611yescharacteristic
518C2×C59#232911yescharacteristic
519C2×C59#235811yescharacteristic
520C2×C59#236011yescharacteristic
521C2×C59#236011yescharacteristic
522C2×C59#237911yescharacteristic
523C2×C59#267011yescharacteristic
524C2×C59#267711yescharacteristic
525C2×C59#268711yescharacteristic
526C2×C59#268711yescharacteristic
527C2×C59#269211yescharacteristic
528C2×C59#269211yescharacteristic
529C2×C59#276311yescharacteristic
530C2×C59#276411yescharacteristic
531C23×Q8—591no—
532C24×C4—591no—
533C22×C4⋊C4—591no—
534C22×C4⋊C4—591no—
535C22×C4⋊C4—591no—
536C22×C4⋊C4—591no—
537C22×C4⋊C4—591no—
538C22×C22⋊C4—591no—
539C22×C22⋊C4—591no—
540C22×C22⋊C4—591no—
541C22×C22⋊C4C2×D5911yescharacteristic
542C22×C22⋊C4C2×D5911yescharacteristic
543C22×C22⋊C4C2×D5911yescharacteristic
544C22×C42—591no—
545C22×C42C2×D5911yescharacteristic
546#393—598no—
547#391—1184no—
548#391—1184no—
549#385—1184no—
550#385—1184no—
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×#95—591no—
564C2×#95—591no—
565C2×#95—591no—
566C2×#95—591no—
567C2×#95—591no—
568C2×#95C2×D5911yescharacteristic
569C2×#95C2×D5911yescharacteristic
570C2×#95C2×D5911yescharacteristic
571C59#1457511yescharacteristic, complemented, Sylow
572C25C22×D5911yescharacteristic
573C22×Q8—594no—
574C22×Q8—1182no—
575C22×Q8—1182no—
576C22×Q8—1182no—
577C22×Q8—1182no—
578C22×Q8—2361no—
579C22×Q8—2361no—
580C23×C4—591no—
581C23×C4—591no—
582C23×C4—591no—
583C23×C4—591no—
584C23×C4—591no—
585C23×C4—591no—
586C23×C4—591no—
587C23×C4—591no—
588C23×C4—1182no—
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
601C2×C4⋊C4—1182no—
602C2×C4⋊C4—1182no—
603C2×C4⋊C4—1182no—
604C2×C4⋊C4—1182no—
605C2×C4⋊C4—1182no—
606C2×C4⋊C4—1182no—
607C2×C4⋊C4—2361no—
608C2×C4⋊C4—2361no—
609C2×C4⋊C4—2361no—
610C2×C4⋊C4—2361no—
611C2×C4⋊C4—2361no—
612C2×C4⋊C4—2361no—
613C2×C4⋊C4—2361no—
614C2×C4⋊C4—2361no—
615C2×C4⋊C4—2361no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—41no—
621C2×C22⋊C4—41no—
622C2×C22⋊C4—41no—
623C2×C22⋊C4—594no—
624C2×C22⋊C4—594no—
625C2×C22⋊C4—1182no—
626C2×C22⋊C4—1182no—
627C2×C22⋊C4—1182no—
628C2×C22⋊C4—1182no—
629C2×C22⋊C4—2361no—
630C2×C22⋊C4—2361no—
631C2×C22⋊C4—2361no—
632C2×C22⋊C4Dic11814yescomplemented
633C2×C22⋊C4C4×D5914yes—
634C2×C42—22no—
635C2×C42—22no—
636C2×C42—41no—
637C2×C42—1182no—
638C2×C42—1182no—
639C2×C42—2361no—
640#95—22no—
641#95—41no—
642#95—41no—
643#95—594no—
644#95—594no—
645#95—594no—
646#95—594no—
647#95—594no—
648#95—1182no—
649#95—1182no—
650#95—1182no—
651#95—1182no—
652#95—1182no—
653#95—1182no—
654#95—1182no—
655#95—2361no—
656#95—2361no—
657#95—2361no—
658#95—2361no—
659#95—2361no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24C2×Dic11812yes—
673C24C2×C4×D5912yes—
674C24#1174568512yes—
675C24C23×D5911yescharacteristic
676C2×Q8—1188no—
677C2×Q8—1188no—
678C2×Q8—2364no—
679C2×Q8—2364no—
680C2×Q8—2364no—
681C2×Q8—2364no—
682C2×Q8—2364no—
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—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—592no—
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—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×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—2364no—
775C22×C4—2364no—
776C22×C4—2364no—
777C22×C4—2364no—
778C22×C4—2364no—
779C22×C4—2364no—
780C22×C4—2364no—
781C22×C4C2×Dic11812yes—
782C22×C4C2×Dic11812yes—
783C22×C4C2×C4×D5912yes—
784C22×C4C2×C4×D5912yes—
785C22×C4D4×D5912yes—
786C22×C4D4×D5912yes—
787C22×C4#1174568712yes—
788C4⋊C4—2364no—
789C4⋊C4—2364no—
790C4⋊C4—2364no—
791C4⋊C4—2364no—
792C4⋊C4—2364no—
793C22⋊C4—28no—
794C22⋊C4—44no—
795C22⋊C4—44no—
796C22⋊C4—1188no—
797C22⋊C4—2364no—
798C22⋊C4—2364no—
799C42—44no—
800C42—2364no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23C4×Dic11814yes—
836C23C22×C4×D5911yescharacteristic
837C23C2×D4×D5911yescharacteristic
838C23C2×D4×D5911yescharacteristic
839C23C22×Dic11811yescharacteristic
840C23#41×D5911yescharacteristic
841C23C2×#1174568711yescharacteristic
842C23C2×#1174568511yescharacteristic
843C23#1427377211yescharacteristic
844C23#1427377211yescharacteristic
845C23#1427377211yescharacteristic
846C23#1427377311yescharacteristic
847C23#1427377311yescharacteristic
848C23#1427377411yescharacteristic
849C23#1427377411yescharacteristic
850C23#1427377411yescharacteristic
851Q8—23616no—
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—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—594no—
894C2×C4—1182no—
895C2×C4—1182no—
896C2×C4—1182no—
897C2×C4—1182no—
898C2×C4—1182no—
899C2×C4—1182no—
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—2361no—
919C2×C4—2361no—
920C2×C4—2361no—
921C2×C4—2361no—
922C2×C4—2361no—
923C2×C4—2361no—
924C2×C4—2361no—
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(C22⋊D59)⋊C414yes—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22C4×D4×D5911yescharacteristic
967C22C2×(C22⋊D59)⋊C411yescharacteristic
968C22C2×C4×Dic11811yescharacteristic
969C22#1683787411yescharacteristic
970C22#1683788111yescharacteristic
971C22#1683788111yescharacteristic
972C22#1683788211yescharacteristic
973C22#1683796511yescharacteristic
974C22#1683796811yescharacteristic
975C22#1683797211yescharacteristic
976C22#1683797411yescharacteristic
977C22#1683798511yescharacteristic
978C22#1683799411yescharacteristic
979C22#1683801611yescharacteristic
980C22#1683801811yescharacteristic
981C22#1683801911yescharacteristic
982C22#1683801911yescharacteristic
983C22#1683802811yescharacteristic
984C22#1683803011yescharacteristic
985C22#1683803611yescharacteristic
986C22#1683803911yescharacteristic
987C22#1683804111yescharacteristic
988C22#1683804211yescharacteristic
989C22#1683804811yescharacteristic
990C22D4×Dic11811yescharacteristic
991C22D4×Dic11811yescharacteristic
992C22#1683807511yescharacteristic
993C22#1683808511yescharacteristic
994C22#1683809211yescharacteristic
995C22#1683810911yescharacteristic
996C22#1683811111yescharacteristic
997C22#1683814411yescharacteristic
998C22#1683814711yescharacteristic
999C22#1683814911yescharacteristic
1000C22#1683815411yescharacteristic
1001C4—24no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—81no—
1007C4—1184no—
1008C4—4721no—
1009C4—2362no—
1010C4—2362no—
1011C4—2362no—
1012C4—2362no—
1013C4—2362no—
1014C4—2362no—
1015C2—44no—
1016C2#2142680511yescharacteristic
1017C2#2142680611yescharacteristic
1018C2#2142682411yescharacteristic
1019C2#2142707611yescharacteristic
1020C2#2142709911yescharacteristic
1021C2#2142710211yescharacteristic
1022C2#2142726511yescharacteristic
1023C2#2143031911yescharacteristic
1024C2#2143040811yescharacteristic
1025C2#2143051411yescharacteristic
1026C2#2143052111yescharacteristic
1027C2#2143058911yescharacteristic
1028C2#2143059611yescharacteristic
1029C2#2143151211yescharacteristic
1030C2#2143152111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC59×#1437C2
socle, cosocleC24×C59C24
prime radicalC25×C59C23
hypercenter#1437D59
hypocenterC59#14575
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C2×#16837308C2semidirect
3. C2×#16837306C2semidirect
6. #21422360C2semidirect
7. #21422360C2semidirect
8. #21422354C2semidirect
9. #21422352C2semidirect
12. #21422323C2semidirect
13. #21422322C2semidirect
27. #16837314C4semidirect
62. C22×Dic118C2×C4semidirect
117. C59⋊#95C2×C4semidirect
118. C59⋊#95C2×C4semidirect
119. C59⋊#95C2×C4semidirect
137. C2×C22⋊C4×C59Q8semidirect
571. C59#14575semidirect
632. C2×C22⋊C4Dic118semidirect

Maximal subgroups

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

subgroupindex
C2×#168373142
C2×#168373082
C2×#168373062
C2×#168372772
C2×#168372742
#214223602
#214223542
#214223522
#214223392
#214223332
#214223232
#214223222
#214223182
C59×#14372
#1457559