Finite Group Databasebeta

← #28609182

Subgroups — #28609182

Order 15104.

1398 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837536C211yesmaximal, characteristic
2C2×C4×#11745669C211yesmaximal, characteristic, complemented
3C22×#14273648C211yesmaximal, characteristic, complemented
4#21427110C211yesmaximal, characteristic, complemented
5#21424961C211yesmaximal, characteristic, complemented
6#21424782C211yesmaximal, characteristic, complemented
7#21424713C211yesmaximal, characteristic, complemented
8#21424522C211yesmaximal, characteristic, complemented
9#21424447C211yesmaximal, characteristic, complemented
10#21424444C211yesmaximal, characteristic, complemented
11#21424343C211yesmaximal, characteristic, complemented
12#21424283C211yesmaximal, characteristic, complemented
13C4×#14273648C211yesmaximal, characteristic, complemented
14C22⋊C4×C59⋊C8C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C59C211yesmaximal, characteristic, complemented
16C22×#11745669C2211yescharacteristic
17C22×#11745669C2211yescharacteristic
18C23×C59⋊C8C2211yescharacteristic
19C2×#14273701C2211yescharacteristic
20C2×C4×D236C2211yescharacteristic, complemented
21C2×(C22⋊D59)⋊C4—21no—
22C22×C4⋊Dic59C2211yescharacteristic
23#16837536C418yescomplemented
24C4×#11745669—24no—
25C2×#14273660C2211yescharacteristic, complemented
26C2×#14273660C2211yescharacteristic, complemented
27C2×#14273648—24no—
28C2×#14273648C2211yescharacteristic
29C2×#14273648C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×#14273648C2211yescharacteristic
32C2×#14273648C2211yescharacteristic
33C2×#14273648C2211yescharacteristic
34C2×#14273647C2211yescharacteristic, complemented
35C2×#14273647C2211yescharacteristic, complemented
36C2×C22⋊(C59⋊C8)C2211yescharacteristic
37C2×C4×C59⋊C8C2211yescharacteristic, complemented
38C2×C4×C59⋊C8C2211yescharacteristic, complemented
39#16837304C2211yescharacteristic, complemented
40#16837300C2211yescharacteristic, complemented
41#16837294—21no—
42#16837279—21no—
43#16837276—21no—
44C4×C4⋊Dic59C2211yescharacteristic, complemented
45#16837164C2211yescharacteristic, complemented
46#16837164C2211yescharacteristic, complemented
47#16837164C2211yescharacteristic, complemented
48#16837164C2211yescharacteristic, complemented
49#16837157C2211yescharacteristic, complemented
50#16837157C2211yescharacteristic, complemented
51C23×D4×C59C2211yescharacteristic
52C2×C4×D4×C59C2211yescharacteristic
53C2×C4×D4×C59C2211yescharacteristic
54C22×C22⋊C4×C59—21no—
55C59×#390C2211yescharacteristic
56C59×#390C2211yescharacteristic
57C59×#386—21no—
58C59×#386—21no—
59C59×#380C2211yescharacteristic
60C59×#379—21no—
61C4×C22⋊C4×C59C2211yescharacteristic
62C22×D236C2311yescharacteristic
63C22×C22⋊D59—21no—
64C23×Dic59—21no—
65C22×C4×D59—21no—
66C2×#11745669—22no—
67C2×#11745669—22no—
68C2×#11745669—41no—
69C2×#11745669—41no—
70C2×#11745669C2×C414yescomplemented
71C2×#11745669C2×C414yescomplemented
72C22×C59⋊C8—22no—
73C22×C59⋊C8—22no—
74C22×C59⋊C8—41no—
75C22×C59⋊C8C2311yescharacteristic
76C22×C59⋊C8C2311yescharacteristic
77C22×C59⋊C8C2311yescharacteristic
78C22×C59⋊C8C2311yescharacteristic
79#14273701—22no—
80#14273701C2×C414yescomplemented
81C4×D236—22no—
82C4×D236—41no—
83(C22⋊D59)⋊C4—44no—
84C2×C4⋊Dic59—22no—
85C2×C4⋊Dic59—21no—
86C2×C4⋊Dic59—41no—
87C2×C4⋊Dic59C2311yescharacteristic
88C2×C4⋊Dic59C2311yescharacteristic
89C2×C4⋊Dic59C2311yescharacteristic
90C2×Dic59⋊C4—21no—
91C2×(C2×D59)⋊C4—21no—
92C2×(C2×D59)⋊C4—21no—
93C2×(C2×D59)⋊C4—21no—
94C2×(C2×D59)⋊C4—21no—
95C2×C4×Dic59—21no—
96#14273660—22no—
97#14273660—41no—
98#14273648—22no—
99#14273648—22no—
100#14273648—22no—
101#14273648C2×C414yescomplemented
102#14273648C2×C414yescomplemented
103#14273648D414yescomplemented
104#14273647—22no—
105#14273647—41no—
106C22⋊(C59⋊C8)C2×C414yescomplemented
107C4×C59⋊C8—22no—
108C4×C59⋊C8—41no—
109C59⋊#95—21no—
110C59⋊#95—21no—
111C25×C59—21no—
112C22×D4×C59—22no—
113C22×D4×C59—22no—
114C22×D4×C59—21no—
115C22×D4×C59—22no—
116C22×D4×C59—41no—
117C22×D4×C59—41no—
118C22×D4×C59C2×C414yescomplemented
119C22×D4×C59C2311yescharacteristic
120C22×D4×C59C2311yescharacteristic
121C23×C4×C59—21no—
122C23×C4×C59—21no—
123C23×C4×C59C2311yescharacteristic
124C4×D4×C59—22no—
125C4×D4×C59—22no—
126C4×D4×C59—41no—
127C4×D4×C59—41no—
128C2×C4⋊C4×C59C2311yescharacteristic
129C2×C4⋊C4×C59C2311yescharacteristic
130C2×C22⋊C4×C59—21no—
131C2×C22⋊C4×C59—21no—
132C2×C22⋊C4×C59—21no—
133C2×C22⋊C4×C59—21no—
134C2×C22⋊C4×C59—21no—
135C2×C22⋊C4×C59—21no—
136C2×C22⋊C4×C59—21no—
137C2×C22⋊C4×C59—44no—
138C2×C22⋊C4×C59D411yescharacteristic
139C2×C22⋊C4×C59D411yescharacteristic
140C2×C42×C59C2311yescharacteristic
141C2×C42×C59C2311yescharacteristic
142#95×C59—21no—
143#95×C59D411yescharacteristic
144#95×C59D411yescharacteristic
145C24×C59—21no—
146C24×C59—21no—
147C24×C59—24no—
148C24×C59—42no—
149C24×C59—42no—
150C24×C59—42no—
151C24×C59—42no—
152C24×C59—81no—
153C24×C59—81no—
154C24×C59C2×D411yescharacteristic
155C23×D59—21no—
156C2×D4×C59—28no—
157C2×D4×C59—24no—
158C2×D4×C59—21no—
159C2×D4×C59—21no—
160C2×D4×C59—21no—
161C2×D4×C59—21no—
162C2×D4×C59—21no—
163C2×D4×C59—21no—
164C2×D4×C59—21no—
165C2×D4×C59—21no—
166C2×D4×C59—44no—
167C2×D4×C59—44no—
168C2×D4×C59—44no—
169C2×D4×C59—42no—
170C2×D4×C59—42no—
171C2×D4×C59C22×C412yes—
172C2×D4×C59C22×C412yes—
173C2×D4×C59C2×D412yes—
174C2×D4×C59#4112yes—
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—42no—
182C22×C4×C59—42no—
183C22×C4×C59—42no—
184C22×C4×C59—42no—
185C22×C4×C59—81no—
186C22×C4×C59—81no—
187C22×C4×C59C22×C412yes—
188C22×C4×C59C2×D411yescharacteristic
189C22×C4×C59C2×D411yescharacteristic
190C22×C4×C59C2×D411yescharacteristic
191C22×C4×C59C2×D411yescharacteristic
192C22×C4×C59C2×D411yescharacteristic
193C22×C4×C59#4112yes—
194C22×C4×C59C2411yescharacteristic
195C2×C22⋊D59—24no—
196C2×C22⋊D59—42no—
197C2×C22⋊D59—42no—
198C22×Dic59—21no—
199C22×Dic59—21no—
200C22×Dic59—21no—
201C22×Dic59—42no—
202C22×Dic59—42no—
203C22×Dic59—81no—
204C2×D236—21no—
205C2×D236—21no—
206C2×D236—21no—
207C2×D236—21no—
208C2×D236—21no—
209C2×D236C22×C412yes—
210C2×C4×D59—42no—
211C2×C4×D59—42no—
212C2×C4×D59—81no—
213C4⋊C4×C59—21no—
214C4⋊C4×C59—21no—
215C4⋊C4×C59—21no—
216C4⋊C4×C59—21no—
217C22⋊C4×C59—22no—
218C22⋊C4×C59—42no—
219C22⋊C4×C59—42no—
220C22⋊C4×C59—42no—
221C22⋊C4×C59—42no—
222C22⋊C4×C59—42no—
223C22⋊C4×C59—81no—
224C22⋊C4×C59—81no—
225C22⋊C4×C59D814yescomplemented
226C42×C59—21no—
227C42×C59—21no—
228C42×C59—21no—
229C42×C59—21no—
230#11745669—28no—
231#11745669—44no—
232(C2×D59)⋊C4—24no—
233(C2×D59)⋊C4—42no—
234(C2×D59)⋊C4—42no—
235(C2×D59)⋊C4—81no—
236C4⋊Dic59—21no—
237C4⋊Dic59—21no—
238C4⋊Dic59—21no—
239C4⋊Dic59—21no—
240C4⋊Dic59—42no—
241C4⋊Dic59C22×C412yes—
242C4⋊Dic59C2×D412yes—
243Dic59⋊C4—42no—
244C4×Dic59—42no—
245C2×C59⋊C8—21no—
246C2×C59⋊C8—21no—
247C2×C59⋊C8—21no—
248C2×C59⋊C8—21no—
249C2×C59⋊C8—21no—
250C2×C59⋊C8—21no—
251C2×C59⋊C8—21no—
252C2×C59⋊C8—21no—
253C2×C59⋊C8—21no—
254C2×C59⋊C8—44no—
255C2×C59⋊C8C22×C412yes—
256C2×C59⋊C8C22×C412yes—
257C2×C59⋊C8C2×D412yes—
258C23×C59—21no—
259C23×C59—21no—
260C23×C59—21no—
261C23×C59—21no—
262C23×C59—22no—
263C23×C59—22no—
264C23×C59—22no—
265C23×C59—22no—
266C23×C59—48no—
267C23×C59—41no—
268C23×C59—41no—
269C23×C59—41no—
270C23×C59—41no—
271C23×C59—41no—
272C23×C59—41no—
273C23×C59—41no—
274C23×C59—41no—
275C23×C59—41no—
276C23×C59—41no—
277C23×C59—48no—
278C23×C59—84no—
279C23×C59—84no—
280C23×C59—84no—
281C23×C59—84no—
282C23×C59—84no—
283C23×C59C4×D412yes—
284C23×C59C2×D812yes—
285C23×C59#13512yes—
286C23×C59C22×D411yescharacteristic
287C22×D59—22no—
288C22×D59—41no—
289C22×D59—41no—
290C22×D59—41no—
291C22×D59—41no—
292C22×D59—41no—
293C22×D59—41no—
294D4×C59—22no—
295D4×C59—22no—
296D4×C59—22no—
297D4×C59—22no—
298D4×C59—22no—
299D4×C59—48no—
300D4×C59—41no—
301D4×C59—41no—
302D4×C59C4×D414yescomplemented
303C2×C4×C59—21no—
304C2×C4×C59—21no—
305C2×C4×C59—21no—
306C2×C4×C59—21no—
307C2×C4×C59—21no—
308C2×C4×C59—21no—
309C2×C4×C59—22no—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59—22no—
313C2×C4×C59—21no—
314C2×C4×C59—21no—
315C2×C4×C59—21no—
316C2×C4×C59—21no—
317C2×C4×C59—21no—
318C2×C4×C59—21no—
319C2×C4×C59—41no—
320C2×C4×C59—41no—
321C2×C4×C59—41no—
322C2×C4×C59—41no—
323C2×C4×C59—41no—
324C2×C4×C59—41no—
325C2×C4×C59—84no—
326C2×C4×C59—84no—
327C2×C4×C59C4×D412yes—
328C2×C4×C59C2×D812yes—
329C2×C4×C59C2×D812yes—
330C2×C4×C59C23×C411yescharacteristic
331C2×C4×C59C22×D411yescharacteristic
332C2×C4×C59C2×#4111yescharacteristic
333C2×C4×C59C2×#4111yescharacteristic
334C2×C4×C59H(5,𝔽2)11yescharacteristic
335C2×C4×C59H(5,𝔽2)11yescharacteristic
336C22⋊D59—48no—
337C2×Dic59—22no—
338C2×Dic59—22no—
339C2×Dic59—41no—
340C2×Dic59—41no—
341C2×Dic59—41no—
342C2×Dic59—41no—
343C2×Dic59—41no—
344C2×Dic59—41no—
345C2×Dic59—41no—
346C2×Dic59—84no—
347D236—22no—
348D236—22no—
349D236—41no—
350D236—41no—
351C4×D59—84no—
352C59⋊C8—22no—
353C59⋊C8—22no—
354C59⋊C8—22no—
355C59⋊C8—41no—
356#22870—591nomaximal, Sylow
357C22×C59—22no—
358C22×C59—22no—
359C22×C59—22no—
360C22×C59—22no—
361C22×C59—22no—
362C22×C59—22no—
363C22×C59—24no—
364C22×C59—42no—
365C22×C59—42no—
366C22×C59—42no—
367C22×C59—42no—
368C22×C59—42no—
369C22×C59—42no—
370C22×C59—42no—
371C22×C59—42no—
372C22×C59—42no—
373C22×C59—816no—
374C22×C59—81no—
375C22×C59—81no—
376C22×C59—81no—
377C22×C59—81no—
378C22×C59C4×D814yescomplemented
379C22×C59C2×C4×D411yescharacteristic
380C22×C59D4211yescharacteristic
381C22×C59#54611yescharacteristic
382C22×C59C22×D811yescharacteristic
383C22×C59C2×#13511yescharacteristic
384C22×C59#57611yescharacteristic
385C22×C59#57711yescharacteristic
386C2×D59—42no—
387C2×D59—42no—
388C2×D59—42no—
389C2×D59—81no—
390C2×D59—81no—
391C2×D59—81no—
392C2×D59—81no—
393C4×C59—22no—
394C4×C59—22no—
395C4×C59—22no—
396C4×C59—41no—
397C4×C59—41no—
398C4×C59—81no—
399C4×C59—81no—
400C4×C59C2×C4×D411yescharacteristic
401C4×C59#51811yescharacteristic
402C4×C59#54611yescharacteristic
403C4×C59#55111yescharacteristic
404Dic59—42no—
405Dic59—42no—
406Dic59—81no—
407C2×#447—591no—
408C2×C4×D8—591no—
409C22×#102—591no—
410#2361—591no—
411D4×C22⋊C4D5911yescharacteristic, complemented
412#1970—591no—
413#1934—591no—
414#1925—591no—
415#1893—591no—
416#1879—591no—
417#1879—591no—
418#1862—591no—
419#1852—591no—
420C4×#102—591no—
421C8×C22⋊C4—591no—
422C2×C59—24no—
423C2×C59—44no—
424C2×C59—82no—
425C2×C59#235811yescharacteristic
426C2×C59C2×C4×D811yescharacteristic
427C2×C59#294611yescharacteristic
428C2×C59D4×D811yescharacteristic
429C2×C59#328211yescharacteristic
430C2×C59#329411yescharacteristic
431C2×C59#329711yescharacteristic
432D59—82no—
433C23×D4C2×D5911yescharacteristic
434C22×D8—591no—
435C22×D8—591no—
436C23×C8—591no—
437C2×#121—591no—
438C2×C4×D4—591no—
439C2×C4×D4—1181no—
440C2×C4×D4C2×D5911yescharacteristic
441C2×C4×D4C2×D5911yescharacteristic
442C22×C4⋊C4—591no—
443C22×C22⋊C4—21no—
444#447—598no—
445C4×D8—1184no—
446C2×#107—591no—
447C2×#107—591no—
448C2×#102—591no—
449C2×#102—591no—
450C2×#102—591no—
451C2×#102—591no—
452C2×#102—591no—
453C2×#102—591no—
454C2×#102—591no—
455C2×#102—591no—
456C2×#102—1184no—
457C2×C22⋊C8—591no—
458C2×C4×C8—591no—
459C2×C4×C8—591no—
460#390—591no—
461#390C2×D5911yescharacteristic
462#390C2×D5911yescharacteristic
463#389—591no—
464#388—1181no—
465#386—21no—
466#386—21no—
467#386—1181no—
468#385—1181no—
469#380C2×D5911yescharacteristic
470#379—21no—
471C4×C4⋊C4—591no—
472C4×C22⋊C4C2×D5911yescharacteristic
473#340—591no—
474#340—591no—
475#340—591no—
476#340—591no—
477#336—591no—
478#336—591no—
479C59#2287011yescharacteristic, complemented, Sylow
480C25—21no—
481C22×D4—22no—
482C22×D4—22no—
483C22×D4—22no—
484C22×D4—21no—
485C22×D4—41no—
486C22×D4—41no—
487C22×D4—591no—
488C22×D4—1181no—
489C22×D4C4×D5914yescomplemented
490C22×D4C22×D5911yescharacteristic
491C22×D4C22×D5911yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—1181no—
495C23×C4—1181no—
496C23×C4C22×D5911yescharacteristic
497C2×D8—594no—
498C2×D8—594no—
499C2×D8—1182no—
500C2×D8—1182no—
501C2×D8—2361no—
502C2×D8—2361no—
503C22×C8—591no—
504C22×C8—591no—
505C22×C8—591no—
506C22×C8—591no—
507C22×C8—1182no—
508C22×C8—1182no—
509C22×C8—2361no—
510#121—594no—
511#121—1182no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—41no—
515C4×D4—41no—
516C4×D4—1182no—
517C4×D4—2361no—
518C4×D4—2364no—
519C2×C4⋊C4—591no—
520C2×C4⋊C4—591no—
521C2×C4⋊C4—591no—
522C2×C4⋊C4—1182no—
523C2×C4⋊C4—1181no—
524C2×C4⋊C4—1181no—
525C2×C4⋊C4—2361no—
526C2×C4⋊C4C22×D5911yescharacteristic
527C2×C4⋊C4C22×D5911yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—44no—
536C2×C22⋊C4—1181no—
537C2×C22⋊C4—1181no—
538C2×C22⋊C4—1181no—
539C2×C22⋊C4—1181no—
540C2×C22⋊C4C22⋊D5911yescharacteristic
541C2×C22⋊C4C22⋊D5911yescharacteristic
542C2×C42—1181no—
543C2×C42C22×D5911yescharacteristic
544C2×C42C22×D5911yescharacteristic
545#107—1182no—
546#107—2361no—
547#102—594no—
548#102—594no—
549#102—594no—
550#102—1182no—
551#102—1182no—
552#102—1182no—
553#102—1182no—
554#102—2361no—
555C22⋊C8—594no—
556C4×C8—1182no—
557C4×C8—2361no—
558#95—21no—
559#95—1181no—
560#95—1181no—
561#95C22⋊D5911yescharacteristic
562#95C22⋊D5911yescharacteristic
563C24—21no—
564C24—21no—
565C24—24no—
566C24—42no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—81no—
571C24—81no—
572C24—1181no—
573C24C2×C22⋊D5911yescharacteristic
574C2×D4—28no—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—44no—
585C2×D4—44no—
586C2×D4—44no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—592no—
590C2×D4—1184no—
591C2×D4—1181no—
592C2×D4—1181no—
593C2×D4—1181no—
594C2×D4—1181no—
595C2×D4—1181no—
596C2×D4—2362no—
597C2×D4—2362no—
598C2×D4C2×C4×D5912yes—
599C2×D4C2×C4×D5912yes—
600C2×D4D4×D5912yes—
601C2×D4#1174568712yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—1181no—
615C22×C4—1181no—
616C22×C4—1181no—
617C22×C4—4721no—
618C22×C4—4721no—
619C22×C4—2362no—
620C22×C4—2362no—
621C22×C4—2362no—
622C22×C4—2362no—
623C22×C4C2×C4×D5912yes—
624C22×C4#1174568512yes—
625C22×C4C2×C22⋊D5911yescharacteristic
626C22×C4C2×C22⋊D5911yescharacteristic
627C22×C4C2×C22⋊D5911yescharacteristic
628C22×C4C2×C22⋊D5911yescharacteristic
629C22×C4C2×C22⋊D5911yescharacteristic
630C22×C4C23×D5911yescharacteristic
631D8—1188no—
632D8—2364no—
633C2×C8—592no—
634C2×C8—592no—
635C2×C8—592no—
636C2×C8—1181no—
637C2×C8—1181no—
638C2×C8—1181no—
639C2×C8—1181no—
640C2×C8—1181no—
641C2×C8—1181no—
642C2×C8—1181no—
643C2×C8—1181no—
644C2×C8—1181no—
645C2×C8—2364no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—592no—
651C4⋊C4—592no—
652C4⋊C4—1181no—
653C4⋊C4—1181no—
654C4⋊C4—1181no—
655C4⋊C4—1181no—
656C4⋊C4—2362no—
657C4⋊C4—2362no—
658C22⋊C4—22no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—81no—
665C22⋊C4—81no—
666C22⋊C4—1184no—
667C22⋊C4—4721no—
668C22⋊C4—2362no—
669C22⋊C4—2362no—
670C22⋊C4#1174566914yescomplemented
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—2362no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—48no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—48no—
694C23—41no—
695C23—41no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—1182no—
702C23—2361no—
703C23—2361no—
704C23—2361no—
705C23—2361no—
706C23—2361no—
707C23—2361no—
708C23C4×C22⋊D5912yes—
709C23C2×#1174566912yes—
710C23#1427374712yes—
711C23C22×C22⋊D5911yescharacteristic
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—48no—
718D4—41no—
719D4—41no—
720D4—1182no—
721D4—1182no—
722D4—2368no—
723D4—2361no—
724D4—2361no—
725D4(C22⋊D59)⋊C414yescomplemented
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—84no—
749C2×C4—84no—
750C2×C4—1182no—
751C2×C4—1182no—
752C2×C4—4724no—
753C2×C4—4724no—
754C2×C4—2361no—
755C2×C4—2361no—
756C2×C4—2361no—
757C2×C4—2361no—
758C2×C4—2361no—
759C2×C4—2361no—
760C2×C4—2361no—
761C2×C4C4×C22⋊D5912yes—
762C2×C4C2×#1174566912yes—
763C2×C4C2×#1174566912yes—
764C2×C4C22×C4×D5911yescharacteristic
765C2×C4C2×D4×D5911yescharacteristic
766C2×C4C2×#1174568711yescharacteristic
767C2×C4C2×#1174568511yescharacteristic
768C2×C4#1427377211yescharacteristic
769C2×C4#1427377211yescharacteristic
770C8—1182no—
771C8—1182no—
772C8—1182no—
773C8—2361no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—24no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—816no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—4721no—
796C22—4721no—
797C22—4721no—
798C22—4721no—
799C22—2362no—
800C22—2362no—
801C22—2362no—
802C22C4×#1174566914yescomplemented
803C22C2×C4×C22⋊D5911yescharacteristic
804C22D4×C22⋊D5911yescharacteristic
805C22#1683804611yescharacteristic
806C22C22×#1174566911yescharacteristic
807C22C2×#1427374711yescharacteristic
808C22#1683820511yescharacteristic
809C22#1683821311yescharacteristic
810C4—22no—
811C4—22no—
812C4—22no—
813C4—41no—
814C4—41no—
815C4—81no—
816C4—81no—
817C4—4721no—
818C4—2362no—
819C4—2362no—
820C4C2×(C22⋊D59)⋊C411yescharacteristic
821C4#1683787511yescharacteristic
822C4#1683804211yescharacteristic
823C4#1683807811yescharacteristic
824C2—24no—
825C2—44no—
826C2—82no—
827C2—4722no—
828C2#2142707511yescharacteristic
829C2C2×C4×#1174566911yescharacteristic
830C2#2143292811yescharacteristic
831C2D4×#1174566911yescharacteristic
832C2#2143579911yescharacteristic
833C2#2143590911yescharacteristic
834C2#2143594611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingD4×C22⋊C4×C59C2
socleC23×C59C22×D4
prime radicalC2×#16837536C2
cosocleC22×C4×C59C24
hypercenterD4×C22⋊C4D59
hypocenterC59#22870
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11745669C2semidirect
3. C22×#14273648C2semidirect
4. #21427110C2semidirect
5. #21424961C2semidirect
6. #21424782C2semidirect
7. #21424713C2semidirect
8. #21424522C2semidirect
9. #21424447C2semidirect
10. #21424444C2semidirect
11. #21424343C2semidirect
12. #21424283C2semidirect
13. C4×#14273648C2semidirect
14. C22⋊C4×C59⋊C8C2semidirect
15. D4×C22⋊C4×C59C2semidirect
20. C2×C4×D236C22semidirect
23. #16837536C4semidirect
25. C2×#14273660C22semidirect
26. C2×#14273660C22semidirect
34. C2×#14273647C22semidirect
35. C2×#14273647C22semidirect
37. C2×C4×C59⋊C8C22semidirect
38. C2×C4×C59⋊C8C22semidirect
39. #16837304C22semidirect
40. #16837300C22semidirect
44. C4×C4⋊Dic59C22semidirect
45. #16837164C22semidirect
46. #16837164C22semidirect
47. #16837164C22semidirect
48. #16837164C22semidirect
49. #16837157C22semidirect
50. #16837157C22semidirect
70. C2×#11745669C2×C4semidirect
71. C2×#11745669C2×C4semidirect
80. #14273701C2×C4semidirect
101. #14273648C2×C4semidirect
102. #14273648C2×C4semidirect
103. #14273648D4semidirect
106. C22⋊(C59⋊C8)C2×C4semidirect
118. C22×D4×C59C2×C4semidirect
225. C22⋊C4×C59D8semidirect
302. D4×C59C4×D4semidirect
378. C22×C59C4×D8semidirect
411. D4×C22⋊C4D59semidirect
479. C59#22870semidirect
489. C22×D4C4×D59semidirect
670. C22⋊C4#11745669semidirect
725. D4(C22⋊D59)⋊C4semidirect
802. C22C4×#11745669semidirect

Maximal subgroups

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

subgroupindex
C2×#168375362
C2×C4×#117456692
C22×#142736482
#214271102
#214249612
#214247822
#214247132
#214245222
#214244472
#214244442
#214243432
#214242832
C4×#142736482
C22⋊C4×C59⋊C82
D4×C22⋊C4×C592
#2287059