Finite Group Databasebeta

← #28609187

Subgroups — #28609187

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×#16837535C211yesmaximal, characteristic
2C2×C4×#11745669C211yesmaximal, characteristic, complemented
3C22×#14273647C211yesmaximal, characteristic, complemented
4C22⋊C4×D236C211yesmaximal, characteristic, complemented
5#21424961C211yesmaximal, characteristic, complemented
6#21424778C211yesmaximal, characteristic, complemented
7#21424716C211yesmaximal, characteristic, complemented
8#21424525C211yesmaximal, characteristic, complemented
9#21424447C211yesmaximal, characteristic, complemented
10#21424444C211yesmaximal, characteristic, complemented
11#21424342C211yesmaximal, characteristic, complemented
12#21424284C211yesmaximal, characteristic, complemented
13C4×#14273647C211yesmaximal, characteristic, complemented
14C22⋊C4×C59⋊C8C211yesmaximal, characteristic, complemented
15C59×#2361C211yesmaximal, characteristic, complemented
16C23×D236C2211yescharacteristic
17C22×#11745669C2211yescharacteristic
18C22×#11745669C2211yescharacteristic
19C23×C59⋊C8C2211yescharacteristic
20C2×C4×D236C2211yescharacteristic
21C2×C4×D236C2211yescharacteristic
22C2×C22⋊C4×D59—21no—
23#16837535C418yescomplemented
24C4×#11745669—24no—
25C2×#14273660C2211yescharacteristic, complemented
26C2×#14273660C2211yescharacteristic, complemented
27C2×#14273648C2211yescharacteristic, complemented
28C2×#14273648C2211yescharacteristic, complemented
29C2×#14273647—24no—
30C2×#14273647C2211yescharacteristic
31C2×#14273647C2211yescharacteristic
32C2×#14273647C2211yescharacteristic
33C2×#14273647C2211yescharacteristic
34C2×#14273647C2211yescharacteristic
35C2×#14273647C2211yescharacteristic
36C2×C22⋊(C59⋊C8)C2211yescharacteristic
37C2×C4×C59⋊C8C2211yescharacteristic, complemented
38C2×C4×C59⋊C8C2211yescharacteristic, complemented
39#16837304C2211yescharacteristic
40#16837304C2211yescharacteristic
41#16837280—21no—
42#16837280—21no—
43#16837262C2211yescharacteristic
44#16837257—21no—
45#16837164C2211yescharacteristic, complemented
46#16837164C2211yescharacteristic, complemented
47#16837164C2211yescharacteristic, complemented
48#16837164C2211yescharacteristic, complemented
49#16837157C2211yescharacteristic, complemented
50#16837157C2211yescharacteristic, complemented
51C2×#121×C59C2211yescharacteristic
52C2×C4×D4×C59—21no—
53C2×C4×D4×C59C2211yescharacteristic, complemented
54C22×C4⋊C4×C59C2211yescharacteristic
55C59×#390C2211yescharacteristic, complemented
56C59×#389C2211yescharacteristic, complemented
57C59×#388—21no—
58C59×#386—21no—
59C59×#385—21no—
60C4×C4⋊C4×C59C2211yescharacteristic, complemented
61C4×C22⋊C4×C59C2211yescharacteristic
62C24×D59—21no—
63C22×D236—22no—
64C22×D236—22no—
65C22×D236—21no—
66C22×D236—22no—
67C22×D236—41no—
68C22×D236—41no—
69C22×D236C2×C414yescomplemented
70C22×D236C2311yescharacteristic
71C22×D236C2311yescharacteristic
72C22×C4×D59—21no—
73C22×C4×D59—21no—
74C2×#11745669—22no—
75C2×#11745669—22no—
76C2×#11745669—41no—
77C2×#11745669—41no—
78C2×#11745669C2×C414yescomplemented
79C2×#11745669C2×C414yescomplemented
80C22×C59⋊C8—22no—
81C22×C59⋊C8—22no—
82C22×C59⋊C8—41no—
83C22×C59⋊C8C2311yescharacteristic
84C22×C59⋊C8C2311yescharacteristic
85C22×C59⋊C8C2311yescharacteristic
86C22×C59⋊C8C2311yescharacteristic
87C4×D236—22no—
88C4×D236—22no—
89C4×D236—41no—
90C4×D236—41no—
91C2×C4⋊Dic59C2311yescharacteristic
92C2×C4⋊Dic59C2311yescharacteristic
93C2×C22⋊Dic59—21no—
94C2×(C2×D59)⋊C4—21no—
95C2×(C2×D59)⋊C4—21no—
96C2×(C2×D59)⋊C4—21no—
97C2×(C2×D59)⋊C4—21no—
98C2×(C2×D59)⋊C4—21no—
99C2×(C2×D59)⋊C4—21no—
100C22⋊C4×D59—44no—
101#14273660—22no—
102#14273660—41no—
103#14273648—22no—
104#14273648—41no—
105#14273647—22no—
106#14273647—22no—
107#14273647—22no—
108#14273647C2×C414yescomplemented
109#14273647C2×C414yescomplemented
110#14273647D414yescomplemented
111C22⋊(C59⋊C8)C2×C414yescomplemented
112C4×C59⋊C8—22no—
113C4×C59⋊C8—41no—
114C59⋊#95—21no—
115C22×D4×C59—21no—
116C22×D4×C59C2311yescharacteristic
117C23×C4×C59—21no—
118C23×C4×C59—21no—
119C23×C4×C59C2311yescharacteristic
120#121×C59—22no—
121#121×C59C2×C414yescomplemented
122C4×D4×C59—22no—
123C4×D4×C59—41no—
124C4×D4×C59—44no—
125C2×C4⋊C4×C59—22no—
126C2×C4⋊C4×C59—21no—
127C2×C4⋊C4×C59—21no—
128C2×C4⋊C4×C59—41no—
129C2×C4⋊C4×C59C2311yescharacteristic
130C2×C4⋊C4×C59C2311yescharacteristic
131C2×C4⋊C4×C59C2311yescharacteristic
132C2×C22⋊C4×C59—21no—
133C2×C22⋊C4×C59—21no—
134C2×C22⋊C4×C59—21no—
135C2×C22⋊C4×C59—21no—
136C2×C22⋊C4×C59D411yescharacteristic
137C2×C22⋊C4×C59D411yescharacteristic
138C2×C42×C59—21no—
139C2×C42×C59C2311yescharacteristic
140C2×C42×C59C2311yescharacteristic
141#95×C59—21no—
142#95×C59—21no—
143#95×C59D411yescharacteristic
144#95×C59D411yescharacteristic
145C24×C59—21no—
146C24×C59C2×D411yescharacteristic
147C23×D59—21no—
148C23×D59—21no—
149C23×D59—24no—
150C23×D59—42no—
151C23×D59—42no—
152C23×D59—42no—
153C23×D59—42no—
154C23×D59—81no—
155C23×D59—81no—
156C2×D4×C59—24no—
157C2×D4×C59—21no—
158C2×D4×C59—21no—
159C2×D4×C59—21no—
160C2×D4×C59—21no—
161C2×D4×C59—21no—
162C2×D4×C59—42no—
163C2×D4×C59—42no—
164C2×D4×C59C22×C412yes—
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—42no—
173C22×C4×C59—42no—
174C22×C4×C59—42no—
175C22×C4×C59—42no—
176C22×C4×C59—81no—
177C22×C4×C59—81no—
178C22×C4×C59C22×C412yes—
179C22×C4×C59C2×D411yescharacteristic
180C22×C4×C59C2×D411yescharacteristic
181C22×C4×C59C2×D411yescharacteristic
182C22×C4×C59C2×D411yescharacteristic
183C22×C4×C59C2×D411yescharacteristic
184C22×C4×C59#4112yes—
185C22×C4×C59C2411yescharacteristic
186C22×Dic59—21no—
187C22×Dic59—21no—
188C2×D236—21no—
189C2×D236—21no—
190C2×D236—21no—
191C2×D236—21no—
192C2×D236—21no—
193C2×D236—21no—
194C2×D236—21no—
195C2×D236—28no—
196C2×D236—24no—
197C2×D236—21no—
198C2×D236—44no—
199C2×D236—44no—
200C2×D236—44no—
201C2×D236—42no—
202C2×D236—42no—
203C2×D236C22×C412yes—
204C2×D236C22×C412yes—
205C2×D236C2×D412yes—
206C2×D236#4112yes—
207C2×C4×D59—42no—
208C2×C4×D59—42no—
209C2×C4×D59—42no—
210C2×C4×D59—42no—
211C2×C4×D59—81no—
212C2×C4×D59—81no—
213C4⋊C4×C59—21no—
214C4⋊C4×C59—21no—
215C4⋊C4×C59—21no—
216C4⋊C4×C59—21no—
217C4⋊C4×C59—42no—
218C4⋊C4×C59—42no—
219C4⋊C4×C59C22×C412yes—
220C4⋊C4×C59C2×D412yes—
221C22⋊C4×C59—22no—
222C22⋊C4×C59—24no—
223C22⋊C4×C59—42no—
224C22⋊C4×C59—42no—
225C22⋊C4×C59—81no—
226C22⋊C4×C59D814yescomplemented
227C42×C59—21no—
228C42×C59—21no—
229C42×C59—21no—
230C42×C59—21no—
231C42×C59—42no—
232C22⋊Dic59—42no—
233#11745669—28no—
234#11745669—44no—
235(C2×D59)⋊C4—42no—
236(C2×D59)⋊C4—42no—
237(C2×D59)⋊C4—42no—
238(C2×D59)⋊C4—42no—
239(C2×D59)⋊C4—81no—
240(C2×D59)⋊C4—81no—
241C4⋊Dic59—21no—
242C4⋊Dic59—21no—
243C4⋊Dic59—21no—
244C4⋊Dic59—21no—
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—41no—
264C23×C59—41no—
265C23×C59—41no—
266C23×C59—41no—
267C23×C59—41no—
268C23×C59—41no—
269C23×C59C4×D412yes—
270C23×C59C2×D812yes—
271C23×C59#13512yes—
272C23×C59C22×D411yescharacteristic
273C22×D59—22no—
274C22×D59—22no—
275C22×D59—22no—
276C22×D59—22no—
277C22×D59—48no—
278C22×D59—41no—
279C22×D59—41no—
280C22×D59—41no—
281C22×D59—41no—
282C22×D59—41no—
283C22×D59—41no—
284C22×D59—41no—
285C22×D59—41no—
286C22×D59—41no—
287C22×D59—41no—
288C22×D59—48no—
289C22×D59—84no—
290C22×D59—84no—
291C22×D59—84no—
292C22×D59—84no—
293C22×D59—84no—
294D4×C59—22no—
295D4×C59—22no—
296D4×C59—48no—
297D4×C59—41no—
298D4×C59—41no—
299C2×C4×C59—21no—
300C2×C4×C59—21no—
301C2×C4×C59—21no—
302C2×C4×C59—21no—
303C2×C4×C59—21no—
304C2×C4×C59—21no—
305C2×C4×C59—22no—
306C2×C4×C59—22no—
307C2×C4×C59—22no—
308C2×C4×C59—22no—
309C2×C4×C59—22no—
310C2×C4×C59—21no—
311C2×C4×C59—22no—
312C2×C4×C59—21no—
313C2×C4×C59—21no—
314C2×C4×C59—21no—
315C2×C4×C59—21no—
316C2×C4×C59—21no—
317C2×C4×C59—41no—
318C2×C4×C59—41no—
319C2×C4×C59—41no—
320C2×C4×C59—41no—
321C2×C4×C59—41no—
322C2×C4×C59—41no—
323C2×C4×C59—41no—
324C2×C4×C59—84no—
325C2×C4×C59—84no—
326C2×C4×C59C4×D412yes—
327C2×C4×C59C2×D812yes—
328C2×C4×C59C2×D812yes—
329C2×C4×C59C23×C411yescharacteristic
330C2×C4×C59C22×D411yescharacteristic
331C2×C4×C59C2×#4111yescharacteristic
332C2×C4×C59C2×#4111yescharacteristic
333C2×C4×C59H(5,𝔽2)11yescharacteristic
334C2×C4×C59H(5,𝔽2)11yescharacteristic
335C2×Dic59—41no—
336C2×Dic59—41no—
337C2×Dic59—41no—
338C2×Dic59—41no—
339C2×Dic59—41no—
340C2×Dic59—41no—
341D236—22no—
342D236—22no—
343D236—22no—
344D236—22no—
345D236—22no—
346D236—48no—
347D236—41no—
348D236—41no—
349D236C4×D414yescomplemented
350C4×D59—84no—
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—42no—
364C22×C59—42no—
365C22×C59—42no—
366C22×C59—81no—
367C22×C59—81no—
368C22×C59—81no—
369C22×C59—81no—
370C22×C59C4×D814yescomplemented
371C22×C59C2×C4×D411yescharacteristic
372C22×C59D4211yescharacteristic
373C22×C59#54611yescharacteristic
374C22×C59C22×D811yescharacteristic
375C22×C59C2×#13511yescharacteristic
376C22×C59#57611yescharacteristic
377C22×C59#57711yescharacteristic
378C2×D59—24no—
379C2×D59—42no—
380C2×D59—42no—
381C2×D59—42no—
382C2×D59—42no—
383C2×D59—42no—
384C2×D59—42no—
385C2×D59—42no—
386C2×D59—42no—
387C2×D59—42no—
388C2×D59—816no—
389C2×D59—81no—
390C2×D59—81no—
391C2×D59—81no—
392C2×D59—81no—
393C4×C59—22no—
394C4×C59—22no—
395C4×C59—22no—
396C4×C59—42no—
397C4×C59—42no—
398C4×C59—41no—
399C4×C59—41no—
400C4×C59—81no—
401C4×C59C2×C4×D411yescharacteristic
402C4×C59#51811yescharacteristic
403C4×C59#54611yescharacteristic
404C4×C59#55111yescharacteristic
405Dic59—81no—
406Dic59—81no—
407C2×#447—591no—
408C2×C4×D8—591no—
409C22×#102—591no—
410#2361D5911yescharacteristic, complemented
411D4×C22⋊C4—591no—
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—82no—
424C2×C59#235811yescharacteristic
425C2×C59C2×C4×D811yescharacteristic
426C2×C59#294611yescharacteristic
427C2×C59D4×D811yescharacteristic
428C2×C59#328211yescharacteristic
429C2×C59#329411yescharacteristic
430C2×C59#329711yescharacteristic
431D59—44no—
432D59—82no—
433C23×D4—591no—
434C22×D8—591no—
435C22×D8—591no—
436C23×C8—591no—
437C2×#121C2×D5911yescharacteristic
438C2×C4×D4—21no—
439C2×C4×D4—591no—
440C2×C4×D4—591no—
441C2×C4×D4C2×D5911yescharacteristic, complemented
442C22×C4⋊C4C2×D5911yescharacteristic
443C22×C22⋊C4—1181no—
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#390—591no—
462#390C2×D5911yescharacteristic, complemented
463#389C2×D5911yescharacteristic, complemented
464#388—21no—
465#386—21no—
466#386—1181no—
467#386—1181no—
468#385—21no—
469#380—591no—
470#379—1181no—
471C4×C4⋊C4C2×D5911yescharacteristic, complemented
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—1181no—
481C22×D4—21no—
482C22×D4—594no—
483C22×D4—591no—
484C22×D4—591no—
485C22×D4—1182no—
486C22×D4—1182no—
487C22×D4—1182no—
488C22×D4—1181no—
489C22×D4—2361no—
490C22×D4—2361no—
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—22no—
511#121C4×D5914yescomplemented
512C4×D4—22no—
513C4×D4—41no—
514C4×D4—44no—
515C4×D4—1182no—
516C4×D4—1182no—
517C4×D4—2361no—
518C4×D4—2361no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—41no—
523C2×C4⋊C4—591no—
524C2×C4⋊C4—591no—
525C2×C4⋊C4C22×D5911yescharacteristic
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—1181no—
533C2×C22⋊C4—1181no—
534C2×C22⋊C4—1181no—
535C2×C22⋊C4—1181no—
536C2×C22⋊C4—1181no—
537C2×C22⋊C4—1181no—
538C2×C22⋊C4—1181no—
539C2×C22⋊C4—2364no—
540C2×C22⋊C4C22⋊D5911yescharacteristic
541C2×C22⋊C4C22⋊D5911yescharacteristic
542C2×C42—21no—
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—21no—
560#95—1181no—
561#95C22⋊D5911yescharacteristic
562#95C22⋊D5911yescharacteristic
563C24—21no—
564C24—1181no—
565C24—1184no—
566C24—1181no—
567C24—4721no—
568C24—4721no—
569C24—2362no—
570C24—2362no—
571C24—2362no—
572C24—2362no—
573C24C2×C22⋊D5911yescharacteristic
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—592no—
583C2×D4—592no—
584C2×D4—592no—
585C2×D4—592no—
586C2×D4—1188no—
587C2×D4—1184no—
588C2×D4—1181no—
589C2×D4—1181no—
590C2×D4—1181no—
591C2×D4—1181no—
592C2×D4—1181no—
593C2×D4—1181no—
594C2×D4—1181no—
595C2×D4—1181no—
596C2×D4—2364no—
597C2×D4—2364no—
598C2×D4—2364no—
599C2×D4—2362no—
600C2×D4—2362no—
601C2×D4C2×C4×D5912yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—81no—
614C22×C4—81no—
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—42no—
651C4⋊C4—42no—
652C4⋊C4—1181no—
653C4⋊C4—1181no—
654C4⋊C4—1181no—
655C4⋊C4—1181no—
656C4⋊C4C2×C4×D5912yes—
657C4⋊C4D4×D5912yes—
658C22⋊C4—22no—
659C22⋊C4—24no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—81no—
663C22⋊C4—4721no—
664C22⋊C4—4721no—
665C22⋊C4—2362no—
666C22⋊C4—2362no—
667C22⋊C4—2362no—
668C22⋊C4—2362no—
669C22⋊C4—2362no—
670C22⋊C4#1174566914yescomplemented
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—42no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—1182no—
688C23—1182no—
689C23—1182no—
690C23—1182no—
691C23—4724no—
692C23—4724no—
693C23—4724no—
694C23—4724no—
695C23—4724no—
696C23—2368no—
697C23—2361no—
698C23—2361no—
699C23—2361no—
700C23—2361no—
701C23—2368no—
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—48no—
715D4—41no—
716D4—41no—
717D4—594no—
718D4—1182no—
719D4—1182no—
720D4—1182no—
721D4—1182no—
722D4—1182no—
723D4—2368no—
724D4—2361no—
725D4—2361no—
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—22no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—84no—
752C2×C4—84no—
753C2×C4—4724no—
754C2×C4—4724no—
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×C4#41×D5911yescharacteristic
767C2×C4C2×#1174568511yescharacteristic
768C2×C4#1427377211yescharacteristic
769C2×C4#1427377311yescharacteristic
770C8—1182no—
771C8—1182no—
772C8—1182no—
773C8—2361no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—1184no—
788C22—47216no—
789C22—4721no—
790C22—4721no—
791C22—4721no—
792C22—4721no—
793C22—2362no—
794C22—2362no—
795C22—2362no—
796C22—2362no—
797C22—2362no—
798C22—2362no—
799C22—2362no—
800C22—2362no—
801C22—2362no—
802C22C4×#1174566914yescomplemented
803C22C2×C4×C22⋊D5911yescharacteristic
804C22D4×C22⋊D5911yescharacteristic
805C22#1683804011yescharacteristic
806C22C22×#1174566911yescharacteristic
807C22C2×#1427374711yescharacteristic
808C22#1683820511yescharacteristic
809C22#1683821011yescharacteristic
810C4—22no—
811C4—22no—
812C4—22no—
813C4—42no—
814C4—41no—
815C4—42no—
816C4—41no—
817C4—81no—
818C4—4721no—
819C4—4721no—
820C4C4×D4×D5911yescharacteristic
821C4#1683787411yescharacteristic
822C4#1683804811yescharacteristic
823C4#1683808111yescharacteristic
824C2—24no—
825C2—82no—
826C2—4722no—
827C2—2364no—
828C2#2142707311yescharacteristic
829C2C2×C4×#1174566911yescharacteristic
830C2#2143292411yescharacteristic
831C2D4×#1174566911yescharacteristic
832C2#2143580411yescharacteristic
833C2#2143590311yescharacteristic
834C2#2143594011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2361C2
socleC23×C59C22×D4
prime radicalC2×#16837535C2
cosocleC22×C4×C59C24
hypercenter#2361D59
hypocenterC59#22870
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11745669C2semidirect
3. C22×#14273647C2semidirect
4. C22⋊C4×D236C2semidirect
5. #21424961C2semidirect
6. #21424778C2semidirect
7. #21424716C2semidirect
8. #21424525C2semidirect
9. #21424447C2semidirect
10. #21424444C2semidirect
11. #21424342C2semidirect
12. #21424284C2semidirect
13. C4×#14273647C2semidirect
14. C22⋊C4×C59⋊C8C2semidirect
15. C59×#2361C2semidirect
23. #16837535C4semidirect
25. C2×#14273660C22semidirect
26. C2×#14273660C22semidirect
27. C2×#14273648C22semidirect
28. C2×#14273648C22semidirect
37. C2×C4×C59⋊C8C22semidirect
38. C2×C4×C59⋊C8C22semidirect
45. #16837164C22semidirect
46. #16837164C22semidirect
47. #16837164C22semidirect
48. #16837164C22semidirect
49. #16837157C22semidirect
50. #16837157C22semidirect
53. C2×C4×D4×C59C22semidirect
55. C59×#390C22semidirect
56. C59×#389C22semidirect
60. C4×C4⋊C4×C59C22semidirect
69. C22×D236C2×C4semidirect
78. C2×#11745669C2×C4semidirect
79. C2×#11745669C2×C4semidirect
108. #14273647C2×C4semidirect
109. #14273647C2×C4semidirect
110. #14273647D4semidirect
111. C22⋊(C59⋊C8)C2×C4semidirect
121. #121×C59C2×C4semidirect
226. C22⋊C4×C59D8semidirect
349. D236C4×D4semidirect
370. C22×C59C4×D8semidirect
410. #2361D59semidirect
441. C2×C4×D4C2×D59semidirect
462. #390C2×D59semidirect
463. #389C2×D59semidirect
471. C4×C4⋊C4C2×D59semidirect
479. C59#22870semidirect
511. #121C4×D59semidirect
670. C22⋊C4#11745669semidirect
802. C22C4×#11745669semidirect

Maximal subgroups

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

subgroupindex
C2×#168375352
C2×C4×#117456692
C22×#142736472
C22⋊C4×D2362
#214249612
#214247782
#214247162
#214245252
#214244472
#214244442
#214243422
#214242842
C4×#142736472
C22⋊C4×C59⋊C82
C59×#23612
#2287059