Finite Group Databasebeta

← #28588271

Subgroups — #28588271

Order 15104.

1590 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D59C211yesmaximal, characteristic
2C2×#16837443C211yesmaximal, characteristic, complemented
3C2×#16837441C211yesmaximal, characteristic, complemented
4#21426478C211yesmaximal, characteristic
5#380×D59C211yesmaximal, characteristic
6#21424129C211yesmaximal, characteristic, complemented
7#21424127C211yesmaximal, characteristic, complemented
8#21424127C211yesmaximal, characteristic, complemented
9#21424124C211yesmaximal, characteristic, complemented
10#21424122C211yesmaximal, characteristic, complemented
11#21424120C211yesmaximal, characteristic, complemented
12#21424118C211yesmaximal, characteristic, complemented
13#21423814C211yesmaximal, characteristic, complemented
14#21423814C211yesmaximal, characteristic, complemented
15C59×#1809C211yesmaximal, characteristic, complemented
16C23×C4×D59C2211yescharacteristic
17C22×#11745664C2211yescharacteristic
18C22×#11745659C2211yescharacteristic
19C22×#11745659C2211yescharacteristic
20C2×M16×D59—24no—
21C2×M16×D59—24no—
22C2×M16×D59C418yescomplemented
23C22×C8×D59C2211yescharacteristic
24C22×C8×D59C2211yescharacteristic
25C2×#14273685C2211yescharacteristic
26C2×#14273685C2211yescharacteristic
27C2×C4⋊C4×D59C2211yescharacteristic
28C2×C4⋊C4×D59C2211yescharacteristic
29C2×C22⋊C4×D59—21no—
30#16837443—24no—
31#16837441—24no—
32C2×#14273661C2211yescharacteristic, complemented
33C2×#14273660C2211yescharacteristic, complemented
34C2×#14273660C2211yescharacteristic, complemented
35C2×#14273659C2211yescharacteristic, complemented
36C2×#14273658C2211yescharacteristic, complemented
37C2×#14273658C2211yescharacteristic, complemented
38#16837264—21no—
39#16837262C2211yescharacteristic
40#16837262C2211yescharacteristic
41#16837261—21no—
42#16837260—21no—
43#16837259C2211yescharacteristic
44#16837259C2211yescharacteristic
45#16837259C2211yescharacteristic
46#16837259C2211yescharacteristic
47#16837257—21no—
48C22⋊C4×Dic59—21no—
49#16837249—21no—
50#95×D59—21no—
51#16837165C2211yescharacteristic, complemented
52#16837165C2211yescharacteristic, complemented
53#16837164C2211yescharacteristic, complemented
54#16837164C2211yescharacteristic, complemented
55#16837164C2211yescharacteristic, complemented
56#16837164C2211yescharacteristic, complemented
57C22×M16×C59C2211yescharacteristic
58C2×#107×C59C2211yescharacteristic, complemented
59C2×#106×C59C2211yescharacteristic, complemented
60C59×#380C2211yescharacteristic
61C59×#380C2211yescharacteristic
62C59×#340C2211yescharacteristic, complemented
63C59×#340C2211yescharacteristic, complemented
64C24×D59D411yescharacteristic
65C23×Dic59D411yescharacteristic
66C22×C4×D59—22no—
67C22×C4×D59—22no—
68C22×C4×D59—22no—
69C22×C4×D59—22no—
70C22×C4×D59—21no—
71C22×C4×D59—21no—
72C22×C4×D59C2×C414yes—
73C22×C4×D59D411yescharacteristic
74C22×C4×D59D411yescharacteristic
75C22×C4×D59Q814yes—
76C22×C4×D59C2311yescharacteristic
77C22×C4×D59C2311yescharacteristic
78C2×#11745664—22no—
79C2×#11745664—22no—
80C2×#11745664C2×C414yescomplemented
81C2×#11745659—22no—
82C2×#11745659—22no—
83C2×#11745659C2×C414yes—
84C2×#11745659C2×C414yes—
85C2×#11745659D414yes—
86C2×#11745659D414yes—
87M16×D59—232no—
88C22×C59⋊C8C2311yescharacteristic
89C22×C59⋊C8C2311yescharacteristic
90C2×C8×D59—22no—
91C2×C8×D59—22no—
92C2×C8×D59—22no—
93C2×C8×D59—22no—
94C2×C8×D59C2×C414yescomplemented
95C2×C8×D59C2×C414yescomplemented
96#14273685—22no—
97#14273685—22no—
98#14273685—22no—
99#14273685—22no—
100C2×C4⋊Dic59C2311yescharacteristic
101C2×C4⋊Dic59C2311yescharacteristic
102C2×C4⋊Dic59C2311yescharacteristic
103C2×C4⋊Dic59C2311yescharacteristic
104C2×Dic59⋊C4—21no—
105C2×Dic59⋊C4—21no—
106C4⋊C4×D59—22no—
107C4⋊C4×D59—22no—
108C4⋊C4×D59—22no—
109C4⋊C4×D59—22no—
110C2×C22⋊Dic59—21no—
111C2×C22⋊Dic59—21no—
112C2×(C2×D59)⋊C4—21no—
113C2×(C2×D59)⋊C4—21no—
114C2×(C2×D59)⋊C4—21no—
115C2×(C2×D59)⋊C4—21no—
116C2×(C2×D59)⋊C4—21no—
117C2×(C2×D59)⋊C4—21no—
118C22⋊C4×D59—44no—
119C2×C4×Dic59—21no—
120C2×C4×Dic59—21no—
121#14273661—22no—
122#14273660—22no—
123#14273660—22no—
124#14273659—22no—
125#14273658—22no—
126#14273658—22no—
127C59⋊#95—21no—
128C59⋊#95—21no—
129C59⋊#95—21no—
130C59⋊#95—21no—
131C59⋊#95—21no—
132C59⋊#95—21no—
133C23×C4×C59C2311yescharacteristic
134C2×M16×C59—22no—
135C2×M16×C59—22no—
136C2×M16×C59C2×C414yescomplemented
137C22×C8×C59C2311yescharacteristic
138C22×C8×C59C2311yescharacteristic
139C2×C4⋊C4×C59C2311yescharacteristic
140C2×C4⋊C4×C59C2311yescharacteristic
141C2×C4⋊C4×C59C2311yescharacteristic
142C2×C4⋊C4×C59C2311yescharacteristic
143C2×C22⋊C4×C59—21no—
144C2×C22⋊C4×C59—21no—
145#107×C59—22no—
146#106×C59—22no—
147#95×C59—21no—
148#95×C59—21no—
149C24×C59C2×D411yescharacteristic
150C23×D59—22no—
151C23×D59—22no—
152C23×D59—22no—
153C23×D59—22no—
154C23×D59—41no—
155C23×D59—41no—
156C23×D59C4⋊C414yes—
157C23×D59C2×D411yescharacteristic
158C23×D59C2×D411yescharacteristic
159C22×C4×C59—21no—
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×C59C22×C412yes—
168C22×C4×C59C2×D411yescharacteristic
169C22×C4×C59C2×Q812yes—
170C22×C4×C59C2411yescharacteristic
171C22×Dic59—22no—
172C22×Dic59—22no—
173C22×Dic59—21no—
174C22×Dic59—21no—
175C22×Dic59—21no—
176C22×Dic59—21no—
177C22×Dic59C4⋊C414yes—
178C22×Dic59C2×D411yescharacteristic
179C22×Dic59C2×D411yescharacteristic
180C2×C4×D59—22no—
181C2×C4×D59—22no—
182C2×C4×D59—21no—
183C2×C4×D59—21no—
184C2×C4×D59—21no—
185C2×C4×D59—21no—
186C2×C4×D59—22no—
187C2×C4×D59—22no—
188C2×C4×D59—28no—
189C2×C4×D59—28no—
190C2×C4×D59—28no—
191C2×C4×D59—28no—
192C2×C4×D59—42no—
193C2×C4×D59—42no—
194C2×C4×D59—42no—
195C2×C4×D59—42no—
196C2×C4×D59—42no—
197C2×C4×D59—42no—
198C2×C4×D59C4⋊C414yes—
199C2×C4×D59C4⋊C414yes—
200C2×C4×D59C22×C412yes—
201C2×C4×D59C22×C412yes—
202C2×C4×D59C2×D412yes—
203C2×C4×D59C2×D412yes—
204C2×C4×D59C2×Q812yes—
205C2×C4×D59C2×Q812yes—
206C2×C4×D59#4112yes—
207C2×C4×D59#4112yes—
208M16×C59—28no—
209C2×C8×C59—21no—
210C2×C8×C59—21no—
211C2×C8×C59C22×C412yes—
212C2×C8×C59C22×C412yes—
213C2×C8×C59C2×D412yes—
214C2×C8×C59C2×D412yes—
215C4⋊C4×C59—21no—
216C4⋊C4×C59—21no—
217C4⋊C4×C59—21no—
218C4⋊C4×C59—21no—
219C4⋊C4×C59—21no—
220C4⋊C4×C59—21no—
221C4⋊C4×C59—21no—
222C4⋊C4×C59—21no—
223C22⋊C4×C59—42no—
224C22⋊C4×C59—42no—
225C22⋊Dic59—42no—
226C22⋊Dic59—42no—
227(C2×D59)⋊C4—42no—
228(C2×D59)⋊C4—42no—
229(C2×D59)⋊C4—42no—
230(C2×D59)⋊C4—42no—
231(C2×D59)⋊C4—42no—
232(C2×D59)⋊C4—42no—
233C4⋊Dic59—21no—
234C4⋊Dic59—21no—
235C4⋊Dic59—21no—
236C4⋊Dic59—21no—
237C4⋊Dic59—21no—
238C4⋊Dic59—21no—
239C4⋊Dic59—21no—
240C4⋊Dic59—21no—
241Dic59⋊C4—42no—
242Dic59⋊C4—42no—
243C4×Dic59—42no—
244C4×Dic59—42no—
245#11745664—28no—
246C2×C59⋊C8—21no—
247C2×C59⋊C8—21no—
248C2×C59⋊C8C22×C412yes—
249C2×C59⋊C8C22×C412yes—
250C2×C59⋊C8C2×D412yes—
251C2×C59⋊C8C2×D412yes—
252#11745659—28no—
253#11745659C22⋊C4116yescomplemented
254C8×D59—28no—
255C8×D59—28no—
256C23×C59—21no—
257C23×C59—21no—
258C23×C59—21no—
259C23×C59—21no—
260C23×C59—21no—
261C23×C59—21no—
262C23×C59C2×C4⋊C412yes—
263C23×C59C22×D411yescharacteristic
264C22×D59—21no—
265C22×D59—21no—
266C22×D59—21no—
267C22×D59—21no—
268C22×D59—21no—
269C22×D59—21no—
270C22×D59—21no—
271C22×D59—21no—
272C22×D59—28no—
273C22×D59—28no—
274C22×D59—44no—
275C22×D59—44no—
276C22×D59—44no—
277C22×D59—44no—
278C22×D59—44no—
279C22×D59C2×C4⋊C412yes—
280C22×D59C2×C4⋊C412yes—
281C22×D59#12112yes—
282C22×D59#12112yes—
283C22×D59AGL(1,ℤ/8)12yes—
284C22×D59#13712yes—
285C2×C4×C59—21no—
286C2×C4×C59—21no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—41no—
292C2×C4×C59—41no—
293C2×C4×C59—41no—
294C2×C4×C59—41no—
295C2×C4×C59—41no—
296C2×C4×C59—41no—
297C2×C4×C59—41no—
298C2×C4×C59—41no—
299C2×C4×C59—41no—
300C2×C4×C59—41no—
301C2×C4×C59—41no—
302C2×C4×C59—41no—
303C2×C4×C59C2×C4⋊C412yes—
304C2×C4×C59C23×C411yescharacteristic
305C2×C4×C59C22×D411yescharacteristic
306C2×C4×C59C22×D411yescharacteristic
307C2×C4×C59C22×Q811yescharacteristic
308C2×C4×C59C2×#4111yescharacteristic
309C2×C4×C59C2×#4111yescharacteristic
310C2×Dic59—21no—
311C2×Dic59—21no—
312C2×Dic59—28no—
313C2×Dic59—41no—
314C2×Dic59—41no—
315C2×Dic59—41no—
316C2×Dic59—41no—
317C2×Dic59—41no—
318C2×Dic59—41no—
319C2×Dic59—41no—
320C2×Dic59—41no—
321C2×Dic59—41no—
322C2×Dic59—41no—
323C2×Dic59—41no—
324C2×Dic59—41no—
325C2×Dic59C2×C4⋊C412yes—
326C2×Dic59C2×C4⋊C412yes—
327C2×Dic59#12112yes—
328C2×Dic59#12112yes—
329C4×D59—28no—
330C4×D59—22no—
331C4×D59—22no—
332C4×D59—22no—
333C4×D59—22no—
334C4×D59—28no—
335C4×D59—84no—
336C4×D59—84no—
337C4×D59C2×C22⋊C414yes—
338C4×D59#11714yes—
339C4×D59C22⋊Q814yes—
340C4×D59C22⋊Q814yes—
341C8×C59—22no—
342C8×C59C2×C22⋊C414yescomplemented
343C59⋊C8—22no—
344C59⋊C8C2×C22⋊C414yescomplemented
345#20661—591nomaximal, Sylow
346C22×C59—22no—
347C22×C59—22no—
348C22×C59—22no—
349C22×C59—41no—
350C22×C59—41no—
351C22×C59—41no—
352C22×C59—41no—
353C22×C59C22×C4⋊C411yescharacteristic
354C22×C59C2×#12111yescharacteristic
355C22×C59C2×#12111yescharacteristic
356C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
357C22×C59C2×#13711yescharacteristic
358C22×C59#57511yescharacteristic
359C22×C59#57511yescharacteristic
360C2×D59—22no—
361C2×D59—22no—
362C2×D59—22no—
363C2×D59—22no—
364C2×D59—22no—
365C2×D59—22no—
366C2×D59—22no—
367C2×D59—22no—
368C2×D59—22no—
369C2×D59—22no—
370C2×D59—22no—
371C2×D59—22no—
372C2×D59—416no—
373C2×D59#38014yes—
374C2×D59#42814yescomplemented
375C4×C59—22no—
376C4×C59—81no—
377C4×C59—81no—
378C4×C59—81no—
379C4×C59—81no—
380C4×C59C22×C22⋊C411yescharacteristic
381C4×C59C2×#11711yescharacteristic
382C4×C59C2×C22⋊Q811yescharacteristic
383C4×C59C2×C22⋊Q811yescharacteristic
384Dic59—22no—
385Dic59—81no—
386Dic59—81no—
387Dic59—81no—
388Dic59—81no—
389Dic59#38014yes—
390C23×M16—591no—
391C2×#428—591no—
392C2×#428—591no—
393#2280—591no—
394C2×#380—591no—
395#1809—591no—
396#1809—591no—
397#1809—591no—
398#1809D5911yescharacteristic, complemented
399#1808—591no—
400#1808—591no—
401#1807—591no—
402#1807—591no—
403#1736—591no—
404#1736—591no—
405C2×C59—42no—
406C2×C59C2×#38011yescharacteristic
407C2×C59C2×#42811yescharacteristic
408C2×C59#291111yescharacteristic
409C2×C59#305511yescharacteristic
410C2×C59#305511yescharacteristic
411C2×C59#305611yescharacteristic
412C2×C59#305611yescharacteristic
413D59—24no—
414D59—24no—
415C24×C4—591no—
416C22×M16—591no—
417C22×M16—598no—
418C22×M16—591no—
419C22×M16—591no—
420C22×M16—1184no—
421C22×M16—1184no—
422C22×M16C2×D5911yescharacteristic
423C23×C8—591no—
424C23×C8—591no—
425C2×#117—591no—
426C2×#117—591no—
427C22×C4⋊C4—591no—
428C22×C4⋊C4—591no—
429C22×C22⋊C4—1181no—
430#428—1184no—
431#428—1184no—
432C2×#107—591no—
433C2×#107—591no—
434C2×#107—591no—
435C2×#107C2×D5911yescharacteristic, complemented
436C2×#106—591no—
437C2×#106—591no—
438C2×#106—591no—
439C2×#106C2×D5911yescharacteristic, complemented
440#381—1181no—
441#380—591no—
442#380—591no—
443#380—591no—
444#380—591no—
445#380—591no—
446#380—591no—
447#380—1181no—
448#380—1181no—
449#380C2×D5911yescharacteristic
450#380C2×D5911yescharacteristic
451#379—1181no—
452C4×C22⋊C4—1181no—
453C4×C22⋊C4—1181no—
454C2×#95—1181no—
455#340—591no—
456#340—591no—
457#340—591no—
458#340—591no—
459#340—591no—
460#340—591no—
461#340C2×D5911yescharacteristic, complemented
462#340C2×D5911yescharacteristic, complemented
463C59#2066111yescharacteristic, complemented, Sylow
464C25—591no—
465C23×C4—591no—
466C23×C4—591no—
467C23×C4—594no—
468C23×C4—591no—
469C23×C4—591no—
470C23×C4—594no—
471C23×C4—591no—
472C23×C4—1182no—
473C23×C4—1182no—
474C23×C4—1182no—
475C23×C4—1182no—
476C23×C4—1181no—
477C23×C4—1181no—
478C23×C4C22×D5911yescharacteristic
479C2×M16—22no—
480C2×M16—22no—
481C2×M16—594no—
482C2×M16—594no—
483C2×M16—594no—
484C2×M16—594no—
485C2×M16—594no—
486C2×M16—1182no—
487C2×M16—1182no—
488C2×M16—1182no—
489C2×M16—1182no—
490C2×M16—11832no—
491C2×M16C4×D5914yescomplemented
492C22×C8—591no—
493C22×C8—591no—
494C22×C8—594no—
495C22×C8—594no—
496C22×C8—1182no—
497C22×C8—1182no—
498C22×C8—1182no—
499C22×C8—1182no—
500C22×C8C22×D5911yescharacteristic
501C22×C8C22×D5911yescharacteristic
502#117—1182no—
503#117—1182no—
504#117—1182no—
505#117—1182no—
506C2×C4⋊C4—591no—
507C2×C4⋊C4—591no—
508C2×C4⋊C4—591no—
509C2×C4⋊C4—591no—
510C2×C4⋊C4—1182no—
511C2×C4⋊C4—1182no—
512C2×C4⋊C4—1182no—
513C2×C4⋊C4—1182no—
514C2×C4⋊C4—1181no—
515C2×C4⋊C4—1181no—
516C2×C4⋊C4C22×D5911yescharacteristic
517C2×C4⋊C4C22×D5911yescharacteristic
518C2×C4⋊C4C22×D5911yescharacteristic
519C2×C4⋊C4C22×D5911yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—1181no—
523C2×C22⋊C4—1181no—
524C2×C22⋊C4—1181no—
525C2×C22⋊C4—1181no—
526C2×C22⋊C4—1181no—
527C2×C22⋊C4—1181no—
528C2×C22⋊C4—1181no—
529C2×C22⋊C4—1181no—
530C2×C22⋊C4—2364no—
531C2×C42—1181no—
532C2×C42—1181no—
533#107—22no—
534#107—1182no—
535#107—1182no—
536#107—1182no—
537#106—22no—
538#106—1182no—
539#106—1182no—
540#106—1182no—
541#95—21no—
542#95—21no—
543#95—1181no—
544#95—1181no—
545#95—1181no—
546#95—1181no—
547#95—1181no—
548#95—1181no—
549C24—591no—
550C24—591no—
551C24—594no—
552C24—1182no—
553C24—1182no—
554C24—1182no—
555C24—1182no—
556C24—2361no—
557C24—2361no—
558C24D4×D5911yescharacteristic
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—591no—
568C22×C4—592no—
569C22×C4—592no—
570C22×C4—592no—
571C22×C4—592no—
572C22×C4—592no—
573C22×C4—592no—
574C22×C4—594no—
575C22×C4—591no—
576C22×C4—594no—
577C22×C4—594no—
578C22×C4—592no—
579C22×C4—592no—
580C22×C4—1188no—
581C22×C4—1182no—
582C22×C4—1182no—
583C22×C4—1188no—
584C22×C4—1188no—
585C22×C4—1188no—
586C22×C4—1182no—
587C22×C4—1182no—
588C22×C4—1182no—
589C22×C4—1182no—
590C22×C4—1181no—
591C22×C4—1181no—
592C22×C4—1181no—
593C22×C4—1181no—
594C22×C4—1181no—
595C22×C4—1181no—
596C22×C4—1181no—
597C22×C4—1181no—
598C22×C4—2362no—
599C22×C4—2362no—
600C22×C4—2362no—
601C22×C4—2362no—
602C22×C4—2362no—
603C22×C4—2362no—
604C22×C4C2×C4×D5912yes—
605C22×C4D4×D5911yescharacteristic
606C22×C4Q8×D5912yes—
607C22×C4C23×D5911yescharacteristic
608M16—28no—
609M16—5916no—
610M16—1188no—
611M16—1188no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—592no—
615C2×C8—592no—
616C2×C8—592no—
617C2×C8—592no—
618C2×C8—1188no—
619C2×C8—1181no—
620C2×C8—1181no—
621C2×C8—1188no—
622C2×C8C2×C4×D5912yes—
623C2×C8C2×C4×D5912yes—
624C2×C8D4×D5912yes—
625C2×C8D4×D5912yes—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—1181no—
635C4⋊C4—1181no—
636C4⋊C4—1181no—
637C4⋊C4—1181no—
638C4⋊C4—1181no—
639C4⋊C4—1181no—
640C4⋊C4—1181no—
641C4⋊C4—1181no—
642C4⋊C4—2362no—
643C4⋊C4—2362no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—2362no—
647C22⋊C4—2362no—
648C22⋊C4—2362no—
649C22⋊C4—2362no—
650C22⋊C4—2362no—
651C22⋊C4—2362no—
652C22⋊C4—2362no—
653C22⋊C4—2362no—
654C42—2362no—
655C42—2362no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—592no—
663C23—592no—
664C23—592no—
665C23—592no—
666C23—592no—
667C23—592no—
668C23—1188no—
669C23—1188no—
670C23—1181no—
671C23—1181no—
672C23—1181no—
673C23—1181no—
674C23—1181no—
675C23—1181no—
676C23—1181no—
677C23—1181no—
678C23—2364no—
679C23—2364no—
680C23—2364no—
681C23—2364no—
682C23—2364no—
683C23C4⋊C4×D5912yes—
684C23C2×D4×D5911yescharacteristic
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—592no—
704C2×C4—592no—
705C2×C4—592no—
706C2×C4—594no—
707C2×C4—594no—
708C2×C4—594no—
709C2×C4—594no—
710C2×C4—592no—
711C2×C4—1188no—
712C2×C4—1188no—
713C2×C4—1188no—
714C2×C4—1181no—
715C2×C4—1181no—
716C2×C4—1182no—
717C2×C4—1182no—
718C2×C4—1182no—
719C2×C4—1182no—
720C2×C4—4724no—
721C2×C4—4724no—
722C2×C4—2361no—
723C2×C4—2361no—
724C2×C4—2361no—
725C2×C4—2361no—
726C2×C4—2361no—
727C2×C4—2361no—
728C2×C4—2361no—
729C2×C4—2361no—
730C2×C4—2361no—
731C2×C4—2361no—
732C2×C4—2361no—
733C2×C4—2361no—
734C2×C4C4⋊C4×D5912yes—
735C2×C4C22×C4×D5911yescharacteristic
736C2×C4C2×D4×D5911yescharacteristic
737C2×C4C2×D4×D5911yescharacteristic
738C2×C4C2×Q8×D5911yescharacteristic
739C2×C4#41×D5911yescharacteristic
740C2×C4#41×D5911yescharacteristic
741C8—22no—
742C8—594no—
743C8—1182no—
744C8C22⋊C4×D5914yescomplemented
745C22—22no—
746C22—22no—
747C22—22no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—594no—
753C22—594no—
754C22—1182no—
755C22—1182no—
756C22—1182no—
757C22—1182no—
758C22—1182no—
759C22—1182no—
760C22—1182no—
761C22—1182no—
762C22—1182no—
763C22—1182no—
764C22—1182no—
765C22—1182no—
766C22—23616no—
767C22C2×C4⋊C4×D5911yescharacteristic
768C22#121×D5911yescharacteristic
769C22#121×D5911yescharacteristic
770C22AGL(1,ℤ/8)×D5911yescharacteristic
771C22#137×D5911yescharacteristic
772C22#1683819811yescharacteristic
773C22#1683820111yescharacteristic
774C4—22no—
775C4—81no—
776C4—81no—
777C4—81no—
778C4—81no—
779C4—594no—
780C4—1182no—
781C4—4721no—
782C4—4721no—
783C4—4721no—
784C4—4721no—
785C4C2×C22⋊C4×D5911yescharacteristic
786C4#117×D5911yescharacteristic
787C4C22⋊Q8×D5911yescharacteristic
788C4C22⋊Q8×D5911yescharacteristic
789C2—42no—
790C2—1184no—
791C2—1184no—
792C2#380×D5911yescharacteristic
793C2#428×D5911yescharacteristic
794C2#2143268311yescharacteristic
795C2#2143371011yescharacteristic
796C2#2143371411yescharacteristic
797C2#2143372111yescharacteristic
798C2#2143372511yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1809C2
socleC23×C59C22×D4
prime radicalC24×D59D4
cosocleC22×C4×C59C24
hypercenter#1809D59
hypocenterC59#20661
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
2. C2×#16837443C2semidirect
3. C2×#16837441C2semidirect
6. #21424129C2semidirect
7. #21424127C2semidirect
8. #21424127C2semidirect
9. #21424124C2semidirect
10. #21424122C2semidirect
11. #21424120C2semidirect
12. #21424118C2semidirect
13. #21423814C2semidirect
14. #21423814C2semidirect
15. C59×#1809C2semidirect
22. C2×M16×D59C4semidirect
32. C2×#14273661C22semidirect
33. C2×#14273660C22semidirect
34. C2×#14273660C22semidirect
35. C2×#14273659C22semidirect
36. C2×#14273658C22semidirect
37. C2×#14273658C22semidirect
51. #16837165C22semidirect
52. #16837165C22semidirect
53. #16837164C22semidirect
54. #16837164C22semidirect
55. #16837164C22semidirect
56. #16837164C22semidirect
58. C2×#107×C59C22semidirect
59. C2×#106×C59C22semidirect
62. C59×#340C22semidirect
63. C59×#340C22semidirect
80. C2×#11745664C2×C4semidirect
94. C2×C8×D59C2×C4semidirect
95. C2×C8×D59C2×C4semidirect
136. C2×M16×C59C2×C4semidirect
253. #11745659C22⋊C4semidirect
342. C8×C59C2×C22⋊C4semidirect
344. C59⋊C8C2×C22⋊C4semidirect
374. C2×D59#428semidirect
398. #1809D59semidirect
435. C2×#107C2×D59semidirect
439. C2×#106C2×D59semidirect
461. #340C2×D59semidirect
462. #340C2×D59semidirect
463. C59#20661semidirect
491. C2×M16C4×D59semidirect
744. C8C22⋊C4×D59semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D592
C2×#168374432
C2×#168374412
#214264782
#380×D592
#214241292
#214241272
#214241242
#214241222
#214241202
#214241182
#214238142
C59×#18092
#2066159