Finite Group Databasebeta

← #28645770

Subgroups — #28645770

Order 15104.

1162 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837700C211yesmaximal, characteristic, complemented
2#21427814C211yesmaximal, characteristic, complemented
3D4×C22⋊Dic59C211yesmaximal, characteristic
4#21425615C211yesmaximal, characteristic, complemented
5#21425482C211yesmaximal, characteristic, complemented
6#21425466C211yesmaximal, characteristic, complemented
7#21425240C211yesmaximal, characteristic, complemented
8#21424355C211yesmaximal, characteristic, complemented
9#21424345C211yesmaximal, characteristic, complemented
10#21424289C211yesmaximal, characteristic, complemented
11#21424274C211yesmaximal, characteristic, complemented
12#21424125C211yesmaximal, characteristic, complemented
13#21424104C211yesmaximal, characteristic, complemented
14#21424027C211yesmaximal, characteristic
15C22×#102×C59C211yesmaximal, characteristic
16C2×#14273718C2211yescharacteristic, complemented
17C2×D4×Dic59C2211yescharacteristic
18C2×D4×Dic59C2211yescharacteristic
19C22×C22⋊Dic59—21no—
20#16837700—24no—
21C2×#14273661C2211yescharacteristic, complemented
22C2×#14273661C2211yescharacteristic, complemented
23C2×#14273658C2211yescharacteristic, complemented
24C2×#14273658C2211yescharacteristic, complemented
25C2×Dic59⋊C8C2211yescharacteristic, complemented
26C2×Dic59⋊C8C2211yescharacteristic, complemented
27C2×#14273648C2211yescharacteristic
28C2×#14273648C2211yescharacteristic
29C2×#14273648C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×C22⋊(C59⋊C8)C2211yescharacteristic
32#16837341—21no—
33#16837335—21no—
34#16837305C2211yescharacteristic
35#16837305C2211yescharacteristic
36#16837301C2211yescharacteristic, complemented
37#16837298C2211yescharacteristic, complemented
38#16837282—21no—
39#16837282—21no—
40#16837275—21no—
41#16837267C2211yescharacteristic, complemented
42#16837262—21no—
43#16837262C2211yescharacteristic
44#16837262C2211yescharacteristic
45#16837258—21no—
46C4×C22⋊Dic59C2211yescharacteristic
47#16837165C2211yescharacteristic, complemented
48#16837165C2211yescharacteristic, complemented
49#16837164C2211yescharacteristic, complemented
50#16837164C2211yescharacteristic, complemented
51#16837156C2211yescharacteristic, complemented
52#16837156C2211yescharacteristic, complemented
53C23×D4×C59C2211yescharacteristic
54C23×C8×C59C2211yescharacteristic
55C22×C4⋊C4×C59C2211yescharacteristic
56C2×#102×C59—24no—
57C2×#102×C59C2211yescharacteristic
58C2×#102×C59C2211yescharacteristic
59C2×#102×C59C2211yescharacteristic
60C2×#102×C59C2211yescharacteristic
61C23×Dic59—21no—
62C23×Dic59—21no—
63C22×C59⋊C8C2311yescharacteristic
64C22×C59⋊C8C2311yescharacteristic
65#14273718—22no—
66#14273718—41no—
67D4×Dic59—22no—
68D4×Dic59—22no—
69D4×Dic59—41no—
70D4×Dic59—41no—
71C2×C4⋊Dic59—21no—
72C2×C4⋊Dic59—21no—
73C2×C4⋊Dic59C2311yescharacteristic
74C2×C4⋊Dic59C2311yescharacteristic
75C2×C4⋊Dic59C2311yescharacteristic
76C2×C4⋊Dic59C2311yescharacteristic
77C2×Dic59⋊C4—21no—
78C2×Dic59⋊C4—21no—
79C2×C22⋊Dic59—21no—
80C2×C22⋊Dic59—21no—
81C2×C22⋊Dic59—21no—
82C2×C22⋊Dic59—21no—
83C2×C22⋊Dic59—21no—
84C2×C22⋊Dic59—21no—
85C2×C22⋊Dic59—21no—
86C2×C22⋊Dic59—21no—
87C2×C22⋊Dic59—44no—
88C2×C22⋊Dic59D411yescharacteristic
89C2×C22⋊Dic59D411yescharacteristic
90C2×C4×Dic59C2311yescharacteristic
91C2×C4×Dic59C2311yescharacteristic
92#14273661—22no—
93#14273661—41no—
94#14273658—22no—
95#14273658—41no—
96Dic59⋊C8—22no—
97Dic59⋊C8—41no—
98#14273648—22no—
99#14273648—22no—
100#14273648—41no—
101#14273648—41no—
102C22⋊(C59⋊C8)—22no—
103C59⋊#95—21no—
104C59⋊#95—21no—
105C59⋊#95—21no—
106C59⋊#95—21no—
107C59⋊#95—21no—
108C59⋊#95—21no—
109C59⋊#95D411yescharacteristic
110C59⋊#95D411yescharacteristic
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×C59Q814yes—
119C22×D4×C59C2311yescharacteristic
120C22×D4×C59C2311yescharacteristic
121C23×C4×C59—21no—
122C23×C4×C59C2311yescharacteristic
123C22×C8×C59—22no—
124C22×C8×C59—22no—
125C22×C8×C59—41no—
126C22×C8×C59C2311yescharacteristic
127C22×C8×C59C2311yescharacteristic
128C2×C4⋊C4×C59—22no—
129C2×C4⋊C4×C59—21no—
130C2×C4⋊C4×C59—41no—
131C2×C4⋊C4×C59C2311yescharacteristic
132C2×C4⋊C4×C59C2311yescharacteristic
133#102×C59—22no—
134#102×C59—22no—
135#102×C59—22no—
136#102×C59D414yes—
137C24×C59—21no—
138C24×C59—21no—
139C24×C59—24no—
140C24×C59—42no—
141C24×C59—42no—
142C24×C59—42no—
143C24×C59—42no—
144C24×C59—81no—
145C24×C59—81no—
146C24×C59C2×D411yescharacteristic
147C2×D4×C59—28no—
148C2×D4×C59—24no—
149C2×D4×C59—21no—
150C2×D4×C59—21no—
151C2×D4×C59—21no—
152C2×D4×C59—21no—
153C2×D4×C59—21no—
154C2×D4×C59—21no—
155C2×D4×C59—21no—
156C2×D4×C59—21no—
157C2×D4×C59—44no—
158C2×D4×C59—44no—
159C2×D4×C59—44no—
160C2×D4×C59—42no—
161C2×D4×C59—42no—
162C2×D4×C59C2×D412yes—
163C2×D4×C59C2×Q812yes—
164C2×D4×C59C2×Q812yes—
165C2×D4×C59#4112yes—
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—81no—
175C22×C4×C59C2×D411yescharacteristic
176C22×C4×C59C2×Q812yes—
177C22×C4×C59#4112yes—
178C22×C4×C59C2411yescharacteristic
179C22×Dic59—21no—
180C22×Dic59—21no—
181C22×Dic59—21no—
182C22×Dic59—21no—
183C22×Dic59—42no—
184C22×Dic59—42no—
185C22×Dic59—42no—
186C22×Dic59—42no—
187C22×Dic59—81no—
188C22×Dic59—81no—
189C22×Dic59C2×D411yescharacteristic
190C22×Dic59C2×D411yescharacteristic
191C22×Dic59C2×D411yescharacteristic
192C22×Dic59C2×D411yescharacteristic
193C2×C8×C59—21no—
194C2×C8×C59—21no—
195C2×C8×C59—21no—
196C2×C8×C59—21no—
197C2×C8×C59—21no—
198C2×C8×C59—44no—
199C2×C8×C59C2×D412yes—
200C4⋊C4×C59—21no—
201C4⋊C4×C59—21no—
202C4⋊C4×C59—21no—
203C4⋊C4×C59—42no—
204C4⋊C4×C59C2×D412yes—
205C22⋊Dic59—22no—
206C22⋊Dic59—22no—
207C22⋊Dic59—42no—
208C22⋊Dic59—42no—
209C22⋊Dic59—42no—
210C22⋊Dic59—42no—
211C22⋊Dic59—42no—
212C22⋊Dic59—42no—
213C22⋊Dic59—81no—
214C22⋊Dic59—81no—
215C4⋊Dic59—21no—
216C4⋊Dic59—21no—
217C4⋊Dic59—21no—
218C4⋊Dic59—21no—
219C4⋊Dic59—21no—
220C4⋊Dic59—21no—
221C4⋊Dic59—21no—
222C4⋊Dic59—21no—
223C4⋊Dic59—42no—
224C4⋊Dic59—81no—
225Dic59⋊C4—42no—
226Dic59⋊C4—81no—
227C4×Dic59—21no—
228C4×Dic59—21no—
229C4×Dic59—21no—
230C4×Dic59—21no—
231C2×C59⋊C8—21no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8—21no—
236C2×C59⋊C8—21no—
237C23×C59—21no—
238C23×C59—21no—
239C23×C59—21no—
240C23×C59—21no—
241C23×C59—22no—
242C23×C59—22no—
243C23×C59—22no—
244C23×C59—22no—
245C23×C59—48no—
246C23×C59—41no—
247C23×C59—41no—
248C23×C59—41no—
249C23×C59—41no—
250C23×C59—41no—
251C23×C59—41no—
252C23×C59—41no—
253C23×C59—41no—
254C23×C59—41no—
255C23×C59—41no—
256C23×C59—48no—
257C23×C59—84no—
258C23×C59—84no—
259C23×C59—84no—
260C23×C59—84no—
261C23×C59—84no—
262C23×C59C22⋊Q812yes—
263C23×C59#13512yes—
264C23×C59AGL(1,ℤ/8)12yes—
265C23×C59C22×D411yescharacteristic
266D4×C59—22no—
267D4×C59—22no—
268D4×C59—22no—
269D4×C59—22no—
270D4×C59—22no—
271D4×C59—48no—
272D4×C59—41no—
273D4×C59—41no—
274D4×C59C22⋊Q814yes—
275C2×C4×C59—21no—
276C2×C4×C59—21no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—41no—
283C2×C4×C59—41no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59—41no—
287C2×C4×C59—84no—
288C2×C4×C59C22⋊Q812yes—
289C2×C4×C59C22×D411yescharacteristic
290C2×C4×C59C22×Q811yescharacteristic
291C2×C4×C59C2×#4111yescharacteristic
292C2×C4×C59C2×#4111yescharacteristic
293C2×C4×C59H(5,𝔽2)11yescharacteristic
294C2×C4×C59H(5,𝔽2)11yescharacteristic
295C2×Dic59—21no—
296C2×Dic59—21no—
297C2×Dic59—21no—
298C2×Dic59—21no—
299C2×Dic59—21no—
300C2×Dic59—21no—
301C2×Dic59—21no—
302C2×Dic59—21no—
303C2×Dic59—21no—
304C2×Dic59—21no—
305C2×Dic59—21no—
306C2×Dic59—21no—
307C2×Dic59—41no—
308C2×Dic59—41no—
309C2×Dic59—41no—
310C2×Dic59—41no—
311C2×Dic59—41no—
312C2×Dic59—41no—
313C2×Dic59—41no—
314C2×Dic59—41no—
315C2×Dic59—41no—
316C2×Dic59—41no—
317C2×Dic59—41no—
318C2×Dic59—41no—
319C2×Dic59—84no—
320C2×Dic59—84no—
321C8×C59—22no—
322C8×C59—41no—
323C59⋊C8—41no—
324C59⋊C8—41no—
325#25952—591nomaximal, Sylow
326C22×C59—22no—
327C22×C59—22no—
328C22×C59—22no—
329C22×C59—22no—
330C22×C59—22no—
331C22×C59—22no—
332C22×C59—24no—
333C22×C59—42no—
334C22×C59—42no—
335C22×C59—42no—
336C22×C59—42no—
337C22×C59—42no—
338C22×C59—42no—
339C22×C59—42no—
340C22×C59—42no—
341C22×C59—42no—
342C22×C59—816no—
343C22×C59—81no—
344C22×C59—81no—
345C22×C59—81no—
346C22×C59—81no—
347C22×C59#47814yescomplemented
348C22×C59C2×C22⋊Q811yescharacteristic
349C22×C59D4211yescharacteristic
350C22×C59#54611yescharacteristic
351C22×C59C2×#13511yescharacteristic
352C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
353C22×C59#57611yescharacteristic
354C22×C59#57711yescharacteristic
355C4×C59—22no—
356C4×C59—42no—
357C4×C59—81no—
358C4×C59C2×C22⋊Q811yescharacteristic
359C4×C59#54311yescharacteristic
360C4×C59#54611yescharacteristic
361C4×C59#55111yescharacteristic
362Dic59—41no—
363Dic59—41no—
364Dic59—41no—
365Dic59—41no—
366Dic59—81no—
367Dic59—81no—
368Dic59—81no—
369Dic59—81no—
370C2×#478—591no—
371C22×#102D5911yescharacteristic
372#2442—591no—
373D4×C22⋊C4—591no—
374#2092—591no—
375#2067—591no—
376#2065—591no—
377#2025—591no—
378#1864—591no—
379#1862—591no—
380#1853—591no—
381#1850—591no—
382#1808—591no—
383#1804—591no—
384#1786—591no—
385C2×C59—24no—
386C2×C59—44no—
387C2×C59—82no—
388C2×C59#243711yescharacteristic
389C2×C59C2×#47811yescharacteristic
390C2×C59#308111yescharacteristic
391C2×C59#326511yescharacteristic
392C2×C59#328011yescharacteristic
393C2×C59#329611yescharacteristic
394C2×C59#331811yescharacteristic
395C23×D4C2×D5911yescharacteristic
396C23×C8C2×D5911yescharacteristic
397C2×#125—591no—
398C2×C4×D4—591no—
399C2×C4×D4—591no—
400C22×C4⋊C4C2×D5911yescharacteristic
401C22×C22⋊C4—1181no—
402#478—1184no—
403C2×#107—591no—
404C2×#107—591no—
405C2×#106—591no—
406C2×#106—591no—
407C2×C4⋊C8—591no—
408C2×C4⋊C8—591no—
409C2×#102—24no—
410C2×#102—591no—
411C2×#102—591no—
412C2×#102—591no—
413C2×#102—591no—
414C2×#102C2×D5911yescharacteristic
415C2×#102C2×D5911yescharacteristic
416C2×#102C2×D5911yescharacteristic
417C2×#102C2×D5911yescharacteristic
418C2×C22⋊C8—591no—
419#400—1181no—
420#398—1181no—
421#390—591no—
422#390—591no—
423#389—591no—
424#389—591no—
425#386—1181no—
426#386—1181no—
427#385—1181no—
428#382—591no—
429#380—591no—
430#380—591no—
431#380—1181no—
432#379—1181no—
433C4×C22⋊C4—591no—
434#340—591no—
435#340—591no—
436#340—591no—
437#340—591no—
438#336—591no—
439#336—591no—
440C59#2595211yescharacteristic, complemented, Sylow
441C25—21no—
442C22×D4—22no—
443C22×D4—22no—
444C22×D4—21no—
445C22×D4—22no—
446C22×D4—41no—
447C22×D4—41no—
448C22×D4Dic11814yes—
449C22×D4C22×D5911yescharacteristic
450C22×D4C22×D5911yescharacteristic
451C23×C4—21no—
452C23×C4—1181no—
453C23×C4—1181no—
454C23×C4C22×D5911yescharacteristic
455C22×C8—22no—
456C22×C8—22no—
457C22×C8—41no—
458C22×C8—591no—
459C22×C8—591no—
460C22×C8C22×D5911yescharacteristic
461C22×C8C22×D5911yescharacteristic
462#125—1182no—
463#125—2361no—
464C4×D4—1182no—
465C4×D4—1182no—
466C4×D4—2361no—
467C4×D4—2361no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—41no—
471C2×C4⋊C4—591no—
472C2×C4⋊C4—591no—
473C2×C4⋊C4—591no—
474C2×C4⋊C4—591no—
475C2×C4⋊C4—1181no—
476C2×C4⋊C4—1181no—
477C2×C4⋊C4—1181no—
478C2×C4⋊C4—1181no—
479C2×C4⋊C4C22×D5911yescharacteristic
480C2×C4⋊C4C22×D5911yescharacteristic
481C2×C22⋊C4—591no—
482C2×C22⋊C4—591no—
483C2×C22⋊C4—1181no—
484C2×C22⋊C4—1181no—
485C2×C22⋊C4—1181no—
486C2×C22⋊C4—1181no—
487C2×C22⋊C4—1181no—
488C2×C22⋊C4—1181no—
489C2×C22⋊C4—1181no—
490C2×C22⋊C4—1181no—
491C2×C22⋊C4—2364no—
492C2×C42—591no—
493C2×C42—591no—
494#107—1182no—
495#107—2361no—
496#106—1182no—
497#106—2361no—
498C4⋊C8—1182no—
499C4⋊C8—2361no—
500#102—22no—
501#102—22no—
502#102—22no—
503#102—1182no—
504#102—1182no—
505#102—2361no—
506#102—2361no—
507#102C22⋊D5914yes—
508C22⋊C8—1182no—
509#95—591no—
510#95—591no—
511#95—1181no—
512#95—1181no—
513#95—1181no—
514#95—1181no—
515#95—1181no—
516#95—1181no—
517C24—21no—
518C24—21no—
519C24—24no—
520C24—42no—
521C24—42no—
522C24—42no—
523C24—42no—
524C24—81no—
525C24—81no—
526C24D4×D5911yescharacteristic
527C2×D4—28no—
528C2×D4—24no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—44no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4C2×Dic11812yes—
543C2×D4C2×Dic11812yes—
544C2×D4#1174568512yes—
545C2×D4C2×C22⋊D5912yes—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—81no—
555C22×C4—591no—
556C22×C4—591no—
557C22×C4—591no—
558C22×C4—591no—
559C22×C4—1181no—
560C22×C4—1181no—
561C22×C4—1181no—
562C22×C4—1181no—
563C22×C4—4721no—
564C22×C4—4721no—
565C22×C4—2362no—
566C22×C4—2362no—
567C22×C4—2362no—
568C22×C4—2362no—
569C22×C4C2×Dic11812yes—
570C22×C4D4×D5911yescharacteristic
571C22×C4#1174568712yes—
572C22×C4C23×D5911yescharacteristic
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—44no—
579C2×C8—1181no—
580C2×C8—1181no—
581C2×C8—1181no—
582C2×C8—1181no—
583C2×C8—1181no—
584C2×C8—1181no—
585C2×C8C2×C22⋊D5912yes—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—42no—
590C4⋊C4—1181no—
591C4⋊C4—1181no—
592C4⋊C4—1181no—
593C4⋊C4—1181no—
594C4⋊C4—1181no—
595C4⋊C4—1181no—
596C4⋊C4—1181no—
597C4⋊C4—1181no—
598C4⋊C4—4721no—
599C4⋊C4—4721no—
600C4⋊C4—2362no—
601C4⋊C4—2362no—
602C4⋊C4C2×C22⋊D5912yes—
603C22⋊C4—1182no—
604C22⋊C4—1182no—
605C22⋊C4—4721no—
606C22⋊C4—4721no—
607C22⋊C4—2362no—
608C22⋊C4—2362no—
609C22⋊C4—2362no—
610C22⋊C4—2362no—
611C22⋊C4—2362no—
612C22⋊C4—2362no—
613C42—1181no—
614C42—1181no—
615C42—1181no—
616C42—1181no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—48no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—48no—
635C23—41no—
636C23—41no—
637C23—84no—
638C23—84no—
639C23—84no—
640C23—84no—
641C23—84no—
642C23#1427370412yes—
643C23#1427374612yes—
644C23#1427375412yes—
645C23C2×D4×D5911yescharacteristic
646D4—22no—
647D4—22no—
648D4—22no—
649D4—22no—
650D4—22no—
651D4—48no—
652D4—41no—
653D4—41no—
654D4#1427370614yes—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—84no—
668C2×C4—1181no—
669C2×C4—1181no—
670C2×C4—1181no—
671C2×C4—1181no—
672C2×C4—1181no—
673C2×C4—1181no—
674C2×C4—1181no—
675C2×C4—1181no—
676C2×C4—1181no—
677C2×C4—1181no—
678C2×C4—1181no—
679C2×C4—1181no—
680C2×C4—4724no—
681C2×C4—4724no—
682C2×C4—2361no—
683C2×C4—2361no—
684C2×C4—2361no—
685C2×C4—2361no—
686C2×C4—2361no—
687C2×C4—2361no—
688C2×C4—2361no—
689C2×C4—2361no—
690C2×C4—2361no—
691C2×C4—2361no—
692C2×C4—2361no—
693C2×C4—2361no—
694C2×C4#1427370412yes—
695C2×C4C22×C22⋊D5911yescharacteristic
696C2×C4C22×Dic11811yescharacteristic
697C2×C4C2×#1174568711yescharacteristic
698C2×C4C2×#1174568511yescharacteristic
699C2×C4#1427377211yescharacteristic
700C2×C4#1427377211yescharacteristic
701C8—22no—
702C8—41no—
703C8—2361no—
704C8—2361no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—24no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—816no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22#1683770014yescomplemented
727C22C2×#1427370411yescharacteristic
728C22D4×C22⋊D5911yescharacteristic
729C22#1683804211yescharacteristic
730C22C2×#1427374611yescharacteristic
731C22C2×#1427375411yescharacteristic
732C22#1683820311yescharacteristic
733C22#1683820811yescharacteristic
734C4—22no—
735C4—42no—
736C4—81no—
737C4—4721no—
738C4—4721no—
739C4—4721no—
740C4—4721no—
741C4—2361no—
742C4—2361no—
743C4—2361no—
744C4—2361no—
745C4C2×#1427370611yescharacteristic
746C4#1683802811yescharacteristic
747C4#1683804611yescharacteristic
748C4#1683807811yescharacteristic
749C2—24no—
750C2—44no—
751C2—82no—
752C2#2142775711yescharacteristic
753C2C2×#1683770011yescharacteristic
754C2#2143392311yescharacteristic
755C2#2143559111yescharacteristic
756C2#2143578111yescharacteristic
757C2#2143592711yescharacteristic
758C2#2143623311yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC22×#102×C59C2
socleC23×C59C22×D4
prime radicalC23×D4×C59C22
hypercenterC22×#102D59
hypocenterC59#25952
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
1. C2×#16837700C2semidirect
2. #21427814C2semidirect
4. #21425615C2semidirect
5. #21425482C2semidirect
6. #21425466C2semidirect
7. #21425240C2semidirect
8. #21424355C2semidirect
9. #21424345C2semidirect
10. #21424289C2semidirect
11. #21424274C2semidirect
12. #21424125C2semidirect
13. #21424104C2semidirect
16. C2×#14273718C22semidirect
21. C2×#14273661C22semidirect
22. C2×#14273661C22semidirect
23. C2×#14273658C22semidirect
24. C2×#14273658C22semidirect
25. C2×Dic59⋊C8C22semidirect
26. C2×Dic59⋊C8C22semidirect
36. #16837301C22semidirect
37. #16837298C22semidirect
41. #16837267C22semidirect
47. #16837165C22semidirect
48. #16837165C22semidirect
49. #16837164C22semidirect
50. #16837164C22semidirect
51. #16837156C22semidirect
52. #16837156C22semidirect
347. C22×C59#478semidirect
440. C59#25952semidirect
726. C22#16837700semidirect

Maximal subgroups

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

subgroupindex
C2×#168377002
#214278142
D4×C22⋊Dic592
#214256152
#214254822
#214254662
#214252402
#214243552
#214243452
#214242892
#214242742
#214241252
#214241042
#214240272
C22×#102×C592
#2595259