Finite Group Databasebeta

← #28594498

Subgroups — #28594498

Order 15104.

1476 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837547C211yesmaximal, characteristic
2C2×#16837512C211yesmaximal, characteristic, complemented
3C2×C4×#11745671C211yesmaximal, characteristic, complemented
4#21426789C211yesmaximal, characteristic, complemented
5#21424451C211yesmaximal, characteristic, complemented
6#21424444C211yesmaximal, characteristic, complemented
7#21424413C211yesmaximal, characteristic, complemented
8#21424364C211yesmaximal, characteristic, complemented
9#21424357C211yesmaximal, characteristic, complemented
10#21424289C211yesmaximal, characteristic, complemented
11#21424036C211yesmaximal, characteristic, complemented
12#21423926C211yesmaximal, characteristic, complemented
13C4×#14273648C211yesmaximal, characteristic, complemented
14#21423862C211yesmaximal, characteristic, complemented
15C2×C59×#520C211yesmaximal, characteristic, complemented
16C22×#11745671C2211yescharacteristic
17C22×#11745669C2211yescharacteristic
18C2×#14273701C2211yescharacteristic
19C2×C4×D236C2211yescharacteristic
20#16837547C418yescomplemented
21#16837512—24no—
22C4×#11745671—24no—
23C2×#14273658C2211yescharacteristic
24C2×#14273658C2211yescharacteristic
25C2×#14273651C2211yescharacteristic
26C2×#14273651C2211yescharacteristic
27C2×#14273651C2211yescharacteristic
28C2×#14273648C2211yescharacteristic
29C2×#14273648C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×#14273647C2211yescharacteristic
32C2×#14273647C2211yescharacteristic
33C2×C22⋊(C59⋊C8)C2211yescharacteristic
34C2×C22⋊(C59⋊C8)C2211yescharacteristic
35C2×#14273638C2211yescharacteristic
36C2×C4×C59⋊C8C2211yescharacteristic
37#16837304C2211yescharacteristic
38#16837302—21no—
39#16837300C2211yescharacteristic
40#16837292—21no—
41#16837278—21no—
42#16837273—21no—
43#16837262C2211yescharacteristic
44C4×C4⋊Dic59C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837157C2211yescharacteristic
50#16837157C2211yescharacteristic
51C22×#41×C59C2211yescharacteristic
52C59×#520—24no—
53C59×#520—24no—
54C2×C4×Q8×C59C2211yescharacteristic
55C2×C4×Q8×C59C2211yescharacteristic
56C2×C4×D4×C59—21no—
57C2×C4×D4×C59—21no—
58C2×C4×D4×C59C2211yescharacteristic
59C2×C4×D4×C59C2211yescharacteristic
60C2×#117×C59—21no—
61C2×#117×C59C2211yescharacteristic
62C22×C4⋊C4×C59—21no—
63C22×C4⋊C4×C59C2211yescharacteristic
64C22×D236C2311yescharacteristic
65C22×C22⋊D59—21no—
66C22×C4×D59—21no—
67C2×#11745671—22no—
68C2×#11745671—22no—
69C2×#11745671C2×C414yescomplemented
70C2×#11745669—22no—
71C2×#11745669—22no—
72C2×#11745669C2×C414yescomplemented
73C22×C59⋊C8C2311yescharacteristic
74C22×C59⋊C8C2311yescharacteristic
75C22×C59⋊C8C2311yescharacteristic
76C22×C59⋊C8C2311yescharacteristic
77#14273701—22no—
78#14273701C2×C414yescomplemented
79C4×D236—22no—
80C4×D236—22no—
81C2×C4⋊Dic59C2311yescharacteristic
82C2×C4⋊Dic59C2311yescharacteristic
83C2×C4⋊Dic59C2311yescharacteristic
84C2×Dic59⋊C4—21no—
85C2×C22⋊Dic59—21no—
86C2×(C2×D59)⋊C4—21no—
87C2×(C2×D59)⋊C4—21no—
88C2×(C2×D59)⋊C4—21no—
89C2×(C2×D59)⋊C4—21no—
90C2×C4×Dic59—21no—
91#14273658—22no—
92#14273658—22no—
93#14273651—22no—
94#14273651—22no—
95#14273651C2×C414yescomplemented
96#14273648—22no—
97#14273648—22no—
98#14273648C2×C414yescomplemented
99#14273647—22no—
100#14273647—22no—
101C22⋊(C59⋊C8)—22no—
102C22⋊(C59⋊C8)C2×C414yescomplemented
103#14273638—22no—
104C4×C59⋊C8—22no—
105C59⋊#95—21no—
106C59⋊#95—21no—
107C59⋊#95—21no—
108C2×#41×C59—22no—
109C2×#41×C59—22no—
110C2×#41×C59—22no—
111C2×#41×C59—22no—
112C2×#41×C59—22no—
113C2×#41×C59C2×C414yescomplemented
114C22×Q8×C59C2311yescharacteristic
115C22×D4×C59—21no—
116C22×D4×C59C2311yescharacteristic
117C23×C4×C59—21no—
118C23×C4×C59—21no—
119C23×C4×C59—21no—
120C23×C4×C59—21no—
121C23×C4×C59C2311yescharacteristic
122C4×Q8×C59—22no—
123C4×Q8×C59—22no—
124C4×Q8×C59—22no—
125C4×Q8×C59D414yescomplemented
126C4×D4×C59—28no—
127C4×D4×C59—28no—
128C4×D4×C59—22no—
129C4×D4×C59—22no—
130C4×D4×C59—22no—
131C4×D4×C59D414yescomplemented
132#117×C59—28no—
133#117×C59—22no—
134#117×C59—22no—
135C2×C4⋊C4×C59—28no—
136C2×C4⋊C4×C59—21no—
137C2×C4⋊C4×C59—21no—
138C2×C4⋊C4×C59—21no—
139C2×C4⋊C4×C59—22no—
140C2×C4⋊C4×C59—22no—
141C2×C4⋊C4×C59D411yescharacteristic
142C2×C4⋊C4×C59D411yescharacteristic
143C2×C4⋊C4×C59C2311yescharacteristic
144C2×C4⋊C4×C59C2311yescharacteristic
145C2×C22⋊C4×C59—21no—
146C2×C22⋊C4×C59—21no—
147C2×C22⋊C4×C59D411yescharacteristic
148C2×C22⋊C4×C59D411yescharacteristic
149C2×C42×C59—21no—
150C2×C42×C59—21no—
151C2×C42×C59C2311yescharacteristic
152C2×C42×C59C2311yescharacteristic
153C24×C59—21no—
154C24×C59C2×D411yescharacteristic
155C23×D59—21no—
156#41×C59—28no—
157#41×C59—28no—
158#41×C59—28no—
159#41×C59—28no—
160C2×Q8×C59—21no—
161C2×Q8×C59—21no—
162C2×Q8×C59—21no—
163C2×Q8×C59C22×C412yes—
164C2×Q8×C59C2×D412yes—
165C2×Q8×C59#4112yes—
166C2×D4×C59—24no—
167C2×D4×C59—24no—
168C2×D4×C59—24no—
169C2×D4×C59—21no—
170C2×D4×C59—21no—
171C2×D4×C59—21no—
172C2×D4×C59C22×C412yes—
173C2×D4×C59C2×D412yes—
174C2×D4×C59#4112yes—
175C22×C4×C59—24no—
176C22×C4×C59—24no—
177C22×C4×C59—21no—
178C22×C4×C59—24no—
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—24no—
186C22×C4×C59—24no—
187C22×C4×C59—24no—
188C22×C4×C59—81no—
189C22×C4×C59—81no—
190C22×C4×C59—81no—
191C22×C4×C59—81no—
192C22×C4×C59—81no—
193C22×C4×C59—81no—
194C22×C4×C59C22×C412yes—
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59#4112yes—
201C22×C4×C59C2411yescharacteristic
202C2×C22⋊D59—24no—
203C2×C22⋊D59—81no—
204C2×C22⋊D59—81no—
205C22×Dic59—21no—
206C22×Dic59—21no—
207C22×Dic59—21no—
208C2×D236—21no—
209C2×D236—21no—
210C2×D236—21no—
211C2×D236—21no—
212C2×D236—21no—
213C2×D236C22×C412yes—
214C2×C4×D59—42no—
215C2×C4×D59—81no—
216C2×C4×D59—81no—
217C4⋊C4×C59—24no—
218C4⋊C4×C59—24no—
219C4⋊C4×C59—22no—
220C4⋊C4×C59—24no—
221C4⋊C4×C59—22no—
222C4⋊C4×C59—21no—
223C4⋊C4×C59—21no—
224C4⋊C4×C59C2×D412yes—
225C4⋊C4×C59C2×D412yes—
226C22⋊C4×C59—24no—
227C22⋊C4×C59—24no—
228C22⋊C4×C59—22no—
229C22⋊C4×C59—22no—
230C42×C59—24no—
231C42×C59—24no—
232C42×C59—21no—
233C42×C59—21no—
234C42×C59C2×D412yes—
235C42×C59C2×D412yes—
236C22⋊Dic59—81no—
237#11745671—28no—
238#11745669—28no—
239(C2×D59)⋊C4—24no—
240(C2×D59)⋊C4—42no—
241(C2×D59)⋊C4—81no—
242(C2×D59)⋊C4—81no—
243C4⋊Dic59—21no—
244C4⋊Dic59—21no—
245C4⋊Dic59—21no—
246C4⋊Dic59—21no—
247C4⋊Dic59—21no—
248C4⋊Dic59C22×C412yes—
249Dic59⋊C4—81no—
250C4×Dic59—81no—
251C2×C59⋊C8—21no—
252C2×C59⋊C8—21no—
253C2×C59⋊C8—21no—
254C2×C59⋊C8—21no—
255C2×C59⋊C8—21no—
256C2×C59⋊C8—21no—
257C2×C59⋊C8—21no—
258C2×C59⋊C8—21no—
259C2×C59⋊C8—21no—
260C2×C59⋊C8—21no—
261C2×C59⋊C8C22×C412yes—
262C2×C59⋊C8C22×C412yes—
263C23×C59—22no—
264C23×C59—21no—
265C23×C59—22no—
266C23×C59—21no—
267C23×C59—22no—
268C23×C59—21no—
269C23×C59—21no—
270C23×C59—21no—
271C23×C59—21no—
272C23×C59—41no—
273C23×C59—41no—
274C23×C59—41no—
275C23×C59—41no—
276C23×C59C4×D412yes—
277C23×C59C22×D411yescharacteristic
278C22×D59—22no—
279C22×D59—41no—
280C22×D59—41no—
281C22×D59—41no—
282C22×D59—41no—
283C22×D59—41no—
284C22×D59—41no—
285Q8×C59—22no—
286Q8×C59—22no—
287Q8×C59—22no—
288Q8×C59C4×D414yes—
289D4×C59—216no—
290D4×C59—22no—
291D4×C59—22no—
292D4×C59—22no—
293D4×C59C4×D414yes—
294C2×C4×C59—216no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—21no—
298C2×C4×C59—21no—
299C2×C4×C59—22no—
300C2×C4×C59—21no—
301C2×C4×C59—21no—
302C2×C4×C59—21no—
303C2×C4×C59—21no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—22no—
307C2×C4×C59—22no—
308C2×C4×C59—21no—
309C2×C4×C59—21no—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59—21no—
313C2×C4×C59—21no—
314C2×C4×C59—21no—
315C2×C4×C59—21no—
316C2×C4×C59—41no—
317C2×C4×C59—41no—
318C2×C4×C59—41no—
319C2×C4×C59—41no—
320C2×C4×C59—84no—
321C2×C4×C59—84no—
322C2×C4×C59—84no—
323C2×C4×C59C4×D412yes—
324C2×C4×C59#12012yes—
325C2×C4×C59#12012yes—
326C2×C4×C59C23×C411yescharacteristic
327C2×C4×C59C22×D411yescharacteristic
328C2×C4×C59C22×D411yescharacteristic
329C2×C4×C59C2×#4111yescharacteristic
330C2×C4×C59C2×#4111yescharacteristic
331C2×C4×C59C2×#4111yescharacteristic
332C22⋊D59—84no—
333C2×Dic59—22no—
334C2×Dic59—41no—
335C2×Dic59—41no—
336C2×Dic59—41no—
337C2×Dic59—41no—
338C2×Dic59—41no—
339C2×Dic59—41no—
340C2×Dic59—41no—
341C2×Dic59—41no—
342D236—22no—
343D236—22no—
344D236—41no—
345D236—41no—
346C4×D59—84no—
347C59⋊C8—22no—
348C59⋊C8—22no—
349C59⋊C8—41no—
350C59⋊C8—41no—
351#21464—591nomaximal, Sylow
352C22×C59—22no—
353C22×C59—22no—
354C22×C59—22no—
355C22×C59—24no—
356C22×C59—41no—
357C22×C59—42no—
358C22×C59—41no—
359C22×C59—42no—
360C22×C59—42no—
361C22×C59—42no—
362C22×C59—41no—
363C22×C59—42no—
364C22×C59—41no—
365C22×C59—42no—
366C22×C59C2×C4×D411yescharacteristic
367C22×C59C2×#12011yescharacteristic
368C22×C59#52511yescharacteristic
369C22×C59#57611yescharacteristic
370C22×C59#57711yescharacteristic
371C22×C59#57711yescharacteristic
372C22×C59#57711yescharacteristic
373C2×D59—42no—
374C2×D59—42no—
375C2×D59—42no—
376C2×D59—81no—
377C2×D59—81no—
378C2×D59—81no—
379C2×D59—81no—
380C4×C59—22no—
381C4×C59—22no—
382C4×C59—22no—
383C4×C59—24no—
384C4×C59—41no—
385C4×C59—41no—
386C4×C59—42no—
387C4×C59—42no—
388C4×C59C2×C4×D411yescharacteristic
389C4×C59C2×C4×D411yescharacteristic
390C4×C59#52511yescharacteristic
391C4×C59#52511yescharacteristic
392Dic59—42no—
393Dic59—81no—
394Dic59—81no—
395C2×#520D5911yescharacteristic, complemented
396C2×#449—591no—
397C2×#442—591no—
398C2×C4×SD16—591no—
399#2324—591no—
400#1880—591no—
401#1879—591no—
402#1874—591no—
403#1865—591no—
404#1864—591no—
405#1853—591no—
406#1788—591no—
407#1763—591no—
408C4×#102—591no—
409#1750—591no—
410C2×C59—42no—
411C2×C59—44no—
412C2×C59C4×#12011yescharacteristic
413C2×C59#294611yescharacteristic
414C2×C59#295211yescharacteristic
415C2×C59#301011yescharacteristic
416C2×C59#301211yescharacteristic
417C2×C59#311911yescharacteristic
418C2×C59#312511yescharacteristic
419D59—82no—
420C22×#41C2×D5911yescharacteristic
421C22×SD16—591no—
422C22×D8—591no—
423C2×#121—591no—
424#520—24no—
425#520—24no—
426C2×C4×Q8C2×D5911yescharacteristic
427C2×C4×Q8C2×D5911yescharacteristic
428C2×C4×D4—21no—
429C2×C4×D4—21no—
430C2×C4×D4—591no—
431C2×C4×D4C2×D5911yescharacteristic
432C2×C4×D4C2×D5911yescharacteristic
433C2×#117—21no—
434C2×#117C2×D5911yescharacteristic
435C22×C4⋊C4—21no—
436C22×C4⋊C4C2×D5911yescharacteristic
437#449—598no—
438#442—1184no—
439C4×SD16—1184no—
440C2×#106—591no—
441C2×#106—591no—
442C2×#103—591no—
443C2×#103—591no—
444C2×#103—591no—
445C2×#102—591no—
446C2×#102—591no—
447C2×#102—591no—
448C2×#102—591no—
449C2×#102—591no—
450C2×C22⋊C8—591no—
451C2×C22⋊C8—591no—
452C2×#97—591no—
453C2×C4×C8—591no—
454#390—591no—
455#390—1181no—
456#389—591no—
457#388—1181no—
458#386—1181no—
459#385—1181no—
460#380—591no—
461C4×C4⋊C4—591no—
462#340—591no—
463#340—591no—
464#340—591no—
465#340—591no—
466#336—591no—
467#336—591no—
468C59#2146411yescharacteristic, complemented, Sylow
469C2×#41—22no—
470C2×#41—22no—
471C2×#41—22no—
472C2×#41—22no—
473C2×#41—22no—
474C2×#41C4×D5914yescomplemented
475C22×Q8C22×D5911yescharacteristic
476C22×D4—21no—
477C22×D4—591no—
478C22×D4—1181no—
479C22×D4C22×D5911yescharacteristic
480C23×C4—21no—
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4—1181no—
485C23×C4C22×D5911yescharacteristic
486C2×SD16—594no—
487C2×SD16—1182no—
488C2×SD16—1182no—
489C2×D8—594no—
490C2×D8—1182no—
491C2×D8—1182no—
492C22×C8—591no—
493C22×C8—591no—
494C22×C8—591no—
495C22×C8—591no—
496#121—594no—
497#121—1182no—
498C4×Q8—22no—
499C4×Q8—22no—
500C4×Q8—22no—
501C4×Q8C22⋊D5914yescomplemented
502C4×D4—28no—
503C4×D4—28no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—1182no—
508C4×D4—1182no—
509C4×D4C22⋊D5914yescomplemented
510#117—28no—
511#117—22no—
512#117—22no—
513C2×C4⋊C4—28no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—591no—
520C2×C4⋊C4—591no—
521C2×C4⋊C4—591no—
522C2×C4⋊C4—1181no—
523C2×C4⋊C4C22⋊D5911yescharacteristic
524C2×C4⋊C4C22⋊D5911yescharacteristic
525C2×C4⋊C4C22×D5911yescharacteristic
526C2×C4⋊C4C22×D5911yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—1181no—
530C2×C22⋊C4—1181no—
531C2×C22⋊C4—1181no—
532C2×C22⋊C4—1181no—
533C2×C22⋊C4—1181no—
534C2×C22⋊C4C22⋊D5911yescharacteristic
535C2×C22⋊C4C22⋊D5911yescharacteristic
536C2×C42—21no—
537C2×C42—21no—
538C2×C42—1181no—
539C2×C42C22×D5911yescharacteristic
540C2×C42C22×D5911yescharacteristic
541#106—1182no—
542#106—1182no—
543#103—594no—
544#103—1182no—
545#103—1182no—
546#102—594no—
547#102—1182no—
548#102—1182no—
549#102—1182no—
550#102—1182no—
551C22⋊C8—594no—
552C22⋊C8—1182no—
553#97—1182no—
554C4×C8—1182no—
555#95—1181no—
556#95—1181no—
557#95—1181no—
558C24—21no—
559C24—1181no—
560C24C2×C22⋊D5911yescharacteristic
561#41—28no—
562#41—28no—
563#41—28no—
564#41—28no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8C2×C4×D5912yes—
569C2×Q8#1174568512yes—
570C2×Q8C2×C22⋊D5912yes—
571C2×D4—24no—
572C2×D4—24no—
573C2×D4—24no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—592no—
578C2×D4—1184no—
579C2×D4—1181no—
580C2×D4—1181no—
581C2×D4—1181no—
582C2×D4—1181no—
583C2×D4—1181no—
584C2×D4—4721no—
585C2×D4—4721no—
586C2×D4C2×C4×D5912yes—
587C2×D4#1174568512yes—
588C2×D4C2×C22⋊D5912yes—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—21no—
592C22×C4—24no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—81no—
603C22×C4—81no—
604C22×C4—81no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4—1181no—
609C22×C4—1181no—
610C22×C4—1181no—
611C22×C4—4721no—
612C22×C4—4721no—
613C22×C4—2362no—
614C22×C4C2×C4×D5912yes—
615C22×C4#1174568512yes—
616C22×C4C2×C22⋊D5911yescharacteristic
617C22×C4C2×C22⋊D5911yescharacteristic
618C22×C4C2×C22⋊D5911yescharacteristic
619C22×C4C2×C22⋊D5911yescharacteristic
620C22×C4C2×C22⋊D5911yescharacteristic
621C22×C4C23×D5911yescharacteristic
622SD16—1188no—
623D8—1188no—
624C2×C8—592no—
625C2×C8—592no—
626C2×C8—1181no—
627C2×C8—1181no—
628C2×C8—1181no—
629C2×C8—1181no—
630C2×C8—1181no—
631C2×C8—1181no—
632C2×C8—1181no—
633C2×C8—1181no—
634C2×C8—1181no—
635C2×C8—1181no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—22no—
639C4⋊C4—24no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—592no—
644C4⋊C4—1181no—
645C4⋊C4—1181no—
646C4⋊C4—1181no—
647C4⋊C4—1181no—
648C4⋊C4—1181no—
649C4⋊C4—4721no—
650C4⋊C4C2×C22⋊D5912yes—
651C4⋊C4C2×C22⋊D5912yes—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—1184no—
657C22⋊C4—4721no—
658C22⋊C4—4721no—
659C22⋊C4—4721no—
660C22⋊C4—2362no—
661C42—24no—
662C42—24no—
663C42—21no—
664C42—21no—
665C42—4721no—
666C42C2×C22⋊D5912yes—
667C42C2×C22⋊D5912yes—
668C23—21no—
669C23—22no—
670C23—21no—
671C23—22no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—22no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—1182no—
682C23—2361no—
683C23—2361no—
684C23—2361no—
685C23—2361no—
686C23—2361no—
687C23—2361no—
688C23C4×C22⋊D5912yes—
689C23C22×C22⋊D5911yescharacteristic
690Q8—22no—
691Q8—22no—
692Q8—22no—
693Q8C4×C22⋊D5914yes—
694D4—216no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—1182no—
699D4—1182no—
700D4—4724no—
701D4—2361no—
702D4—2361no—
703D4C4×C22⋊D5914yes—
704C2×C4—216no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—84no—
731C2×C4—84no—
732C2×C4—84no—
733C2×C4—1182no—
734C2×C4—4724no—
735C2×C4—2361no—
736C2×C4—2361no—
737C2×C4—2361no—
738C2×C4—2361no—
739C2×C4—2361no—
740C2×C4—2361no—
741C2×C4—2361no—
742C2×C4—2361no—
743C2×C4C4×C22⋊D5912yes—
744C2×C4#1427369612yes—
745C2×C4#1427369612yes—
746C2×C4C22×C4×D5911yescharacteristic
747C2×C4C22×C22⋊D5911yescharacteristic
748C2×C4C22×C22⋊D5911yescharacteristic
749C2×C4C2×#1174568511yescharacteristic
750C2×C4C2×#1174568511yescharacteristic
751C2×C4C2×#1174568511yescharacteristic
752C8—1182no—
753C8—1182no—
754C8—2361no—
755C8—2361no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—24no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—41no—
769C22—42no—
770C22—4721no—
771C22—4721no—
772C22—4721no—
773C22—4721no—
774C22—2362no—
775C22—2362no—
776C22—2362no—
777C22C2×C4×C22⋊D5911yescharacteristic
778C22C2×#1427369611yescharacteristic
779C22#1683791311yescharacteristic
780C22#1683820511yescharacteristic
781C22#1683821011yescharacteristic
782C22#1683821011yescharacteristic
783C22#1683821311yescharacteristic
784C4—22no—
785C4—22no—
786C4—22no—
787C4—24no—
788C4—41no—
789C4—41no—
790C4—42no—
791C4—42no—
792C4—4721no—
793C4—4721no—
794C4—2362no—
795C4C2×C4×C22⋊D5911yescharacteristic
796C4C2×C4×C22⋊D5911yescharacteristic
797C4#1683791311yescharacteristic
798C4#1683791311yescharacteristic
799C2—42no—
800C2—44no—
801C2—4722no—
802C2C4×#1427369611yescharacteristic
803C2#2143292411yescharacteristic
804C2#2143297711yescharacteristic
805C2#2143338211yescharacteristic
806C2#2143340011yescharacteristic
807C2#2143429511yescharacteristic
808C2#2143437311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C59×#520C2
socleC23×C59C22×D4
prime radicalC2×#16837547C2
cosocleC22×C4×C59C24
hypercenterC2×#520D59
hypocenterC59#21464
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
2. C2×#16837512C2semidirect
3. C2×C4×#11745671C2semidirect
4. #21426789C2semidirect
5. #21424451C2semidirect
6. #21424444C2semidirect
7. #21424413C2semidirect
8. #21424364C2semidirect
9. #21424357C2semidirect
10. #21424289C2semidirect
11. #21424036C2semidirect
12. #21423926C2semidirect
13. C4×#14273648C2semidirect
14. #21423862C2semidirect
15. C2×C59×#520C2semidirect
20. #16837547C4semidirect
69. C2×#11745671C2×C4semidirect
72. C2×#11745669C2×C4semidirect
78. #14273701C2×C4semidirect
95. #14273651C2×C4semidirect
98. #14273648C2×C4semidirect
102. C22⋊(C59⋊C8)C2×C4semidirect
113. C2×#41×C59C2×C4semidirect
125. C4×Q8×C59D4semidirect
131. C4×D4×C59D4semidirect
395. C2×#520D59semidirect
468. C59#21464semidirect
474. C2×#41C4×D59semidirect
501. C4×Q8C22⋊D59semidirect
509. C4×D4C22⋊D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168375472
C2×#168375122
C2×C4×#117456712
#214267892
#214244512
#214244442
#214244132
#214243642
#214243572
#214242892
#214240362
#214239262
C4×#142736482
#214238622
C2×C59×#5202
#2146459