Finite Group Databasebeta

← #28609145

Subgroups — #28609145

Order 15104.

1106 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837509C211yesmaximal, characteristic, complemented
2C2×#16837403C211yesmaximal, characteristic
3#21427105C211yesmaximal, characteristic, complemented
4#21426937C211yesmaximal, characteristic
5#21424952C211yesmaximal, characteristic, complemented
6#21424795C211yesmaximal, characteristic, complemented
7#21424725C211yesmaximal, characteristic, complemented
8#21424530C211yesmaximal, characteristic, complemented
9#21424453C211yesmaximal, characteristic, complemented
10#21424439C211yesmaximal, characteristic, complemented
11#21424366C211yesmaximal, characteristic, complemented
12#21424291C211yesmaximal, characteristic, complemented
13#103×Dic59C211yesmaximal, characteristic, complemented
14#21423882C211yesmaximal, characteristic, complemented
15C2×C59×#452C211yesmaximal, characteristic
16C22×#11745664C2211yescharacteristic
17C2×Q8×Dic59C2211yescharacteristic
18C2×Q8×Dic59C2211yescharacteristic
19C2×Q8×Dic59C2211yescharacteristic
20C22×C4⋊Dic59C2211yescharacteristic
21#16837509—24no—
22C2×#14273659C2211yescharacteristic
23C2×#14273659C2211yescharacteristic
24#16837403—24no—
25C2×#14273651C2211yescharacteristic
26C2×#14273651C2211yescharacteristic
27C2×#14273651C2211yescharacteristic
28C2×#14273651C2211yescharacteristic
29C2×#14273648C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×#14273637C2211yescharacteristic
32C2×C8×Dic59C2211yescharacteristic
33#16837309C2211yescharacteristic
34#16837305—21no—
35#16837305—21no—
36#16837305C2211yescharacteristic
37#16837305C2211yescharacteristic
38#16837301—21no—
39#16837301C2211yescharacteristic
40#16837288—21no—
41#16837277—21no—
42#16837262—21no—
43#16837262C2211yescharacteristic
44C4⋊C4×Dic59C2211yescharacteristic
45C22⋊C4×Dic59—21no—
46C4×C22⋊Dic59—21no—
47C4×C22⋊Dic59C2211yescharacteristic
48#16837165C2211yescharacteristic
49#16837165C2211yescharacteristic
50#16837164C2211yescharacteristic
51#16837164C2211yescharacteristic
52#16837156C2211yescharacteristic
53#16837156C2211yescharacteristic
54C22×#41×C59C2211yescharacteristic
55C22×Q16×C59C2211yescharacteristic
56C22×SD16×C59C2211yescharacteristic
57C2×C22⋊Q8×C59C2211yescharacteristic
58C59×#452C418yescomplemented
59C2×#103×C59C2211yescharacteristic
60C2×#102×C59C2211yescharacteristic
61C2×C22⋊C8×C59C2211yescharacteristic
62C23×Dic59—21no—
63C2×#11745664—22no—
64C2×#11745664—22no—
65C2×#11745664—41no—
66C22×C59⋊C8C2311yescharacteristic
67C22×C59⋊C8C2311yescharacteristic
68Q8×Dic59—22no—
69Q8×Dic59—22no—
70Q8×Dic59—22no—
71Q8×Dic59—41no—
72Q8×Dic59—41no—
73Q8×Dic59—41no—
74C2×C4⋊Dic59—22no—
75C2×C4⋊Dic59—21no—
76C2×C4⋊Dic59—21no—
77C2×C4⋊Dic59—21no—
78C2×C4⋊Dic59—21no—
79C2×C4⋊Dic59—21no—
80C2×C4⋊Dic59—41no—
81C2×C4⋊Dic59C2311yescharacteristic
82C2×C4⋊Dic59C2311yescharacteristic
83C2×C4⋊Dic59C2311yescharacteristic
84C2×C4⋊Dic59C2311yescharacteristic
85C2×C22⋊Dic59—21no—
86C2×C22⋊Dic59—21no—
87C2×C22⋊Dic59—21no—
88C2×C22⋊Dic59—21no—
89C2×C22⋊Dic59—21no—
90C2×C22⋊Dic59D411yescharacteristic
91C2×C22⋊Dic59D411yescharacteristic
92C2×C4×Dic59—21no—
93C2×C4×Dic59—21no—
94C2×C4×Dic59—21no—
95C2×C4×Dic59—21no—
96C2×C4×Dic59C2311yescharacteristic
97C2×C4×Dic59C2311yescharacteristic
98#14273659—22no—
99#14273659—41no—
100#14273651—22no—
101#14273651—22no—
102#14273651—41no—
103#14273651D414yes—
104#14273648—22no—
105#14273648—22no—
106#14273637—22no—
107C8×Dic59—41no—
108C59⋊#95—21no—
109C59⋊#95—21no—
110C59⋊#95—21no—
111C59⋊#95—21no—
112C59⋊#95—21no—
113C59⋊#95D411yescharacteristic
114C59⋊#95D411yescharacteristic
115C2×#41×C59—22no—
116C2×#41×C59—22no—
117C2×#41×C59—22no—
118C2×#41×C59—41no—
119C2×#41×C59—41no—
120C2×#41×C59C2×C414yes—
121C22×Q8×C59C2311yescharacteristic
122C22×Q8×C59C2311yescharacteristic
123C22×D4×C59—21no—
124C22×D4×C59C2311yescharacteristic
125C23×C4×C59—21no—
126C23×C4×C59C2311yescharacteristic
127C2×Q16×C59—22no—
128C2×Q16×C59—22no—
129C2×Q16×C59C2×C414yescomplemented
130C2×SD16×C59—41no—
131C2×SD16×C59—41no—
132C2×SD16×C59C2×C414yescomplemented
133C22×C8×C59C2311yescharacteristic
134C22×C8×C59C2311yescharacteristic
135C22⋊Q8×C59—22no—
136C22⋊Q8×C59C2×C414yes—
137C2×C4⋊C4×C59—21no—
138C2×C4⋊C4×C59C2311yescharacteristic
139C2×C22⋊C4×C59—21no—
140#103×C59C2×C414yescomplemented
141#102×C59C2×C414yescomplemented
142C22⋊C8×C59C2×C414yes—
143C24×C59—21no—
144C24×C59C2×D411yescharacteristic
145#41×C59—28no—
146#41×C59—44no—
147#41×C59—44no—
148#41×C59—44no—
149C2×Q8×C59—21no—
150C2×Q8×C59—21no—
151C2×Q8×C59—21no—
152C2×Q8×C59—21no—
153C2×Q8×C59—21no—
154C2×Q8×C59—21no—
155C2×Q8×C59—21no—
156C2×Q8×C59—21no—
157C2×Q8×C59C22×C412yes—
158C2×Q8×C59C22×C412yes—
159C2×Q8×C59C2×D412yes—
160C2×Q8×C59#4112yes—
161C2×D4×C59—24no—
162C2×D4×C59—21no—
163C2×D4×C59—21no—
164C2×D4×C59—21no—
165C2×D4×C59—21no—
166C2×D4×C59—21no—
167C2×D4×C59—42no—
168C2×D4×C59—42no—
169C2×D4×C59C22×C412yes—
170C22×C4×C59—21no—
171C22×C4×C59—21no—
172C22×C4×C59—21no—
173C22×C4×C59—21no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—24no—
178C22×C4×C59—42no—
179C22×C4×C59—42no—
180C22×C4×C59C22×C412yes—
181C22×C4×C59C2×D411yescharacteristic
182C22×C4×C59#4112yes—
183C22×C4×C59C2411yescharacteristic
184C22×Dic59—21no—
185C22×Dic59—21no—
186C22×Dic59—21no—
187C22×Dic59—21no—
188C22×Dic59—42no—
189C22×Dic59—42no—
190C22×Dic59—81no—
191C22×Dic59C2×D411yescharacteristic
192C22×Dic59C2×D411yescharacteristic
193C22×Dic59C2×D411yescharacteristic
194C22×Dic59C2×D411yescharacteristic
195Q16×C59—28no—
196SD16×C59—44no—
197C2×C8×C59—21no—
198C2×C8×C59—21no—
199C2×C8×C59—21no—
200C2×C8×C59—21no—
201C2×C8×C59C22×C412yes—
202C2×C8×C59C22×C412yes—
203C4⋊C4×C59—24no—
204C4⋊C4×C59—21no—
205C4⋊C4×C59C22×C412yes—
206C22⋊C4×C59—24no—
207C22⋊Dic59—22no—
208C22⋊Dic59—41no—
209C22⋊Dic59—42no—
210C22⋊Dic59—42no—
211C22⋊Dic59—81no—
212C22⋊Dic59—81no—
213C22⋊Dic59—81no—
214C4⋊Dic59—21no—
215C4⋊Dic59—21no—
216C4⋊Dic59—21no—
217C4⋊Dic59—21no—
218C4⋊Dic59—21no—
219C4⋊Dic59—21no—
220C4⋊Dic59—21no—
221C4⋊Dic59—42no—
222C4⋊Dic59—42no—
223C4⋊Dic59—42no—
224C4⋊Dic59—42no—
225C4⋊Dic59—81no—
226C4⋊Dic59C2×D412yes—
227C4×Dic59—21no—
228C4×Dic59—21no—
229C4×Dic59—21no—
230C4×Dic59—21no—
231C4×Dic59—42no—
232C4×Dic59—42no—
233C4×Dic59—42no—
234C4×Dic59—81no—
235#11745664—44no—
236C2×C59⋊C8—21no—
237C2×C59⋊C8—21no—
238C2×C59⋊C8—21no—
239C2×C59⋊C8—21no—
240C2×C59⋊C8—21no—
241C2×C59⋊C8C2×D412yes—
242C23×C59—21no—
243C23×C59—21no—
244C23×C59—21no—
245C23×C59—21no—
246C23×C59—21no—
247C23×C59—21no—
248C23×C59—22no—
249C23×C59—41no—
250C23×C59—41no—
251C23×C59—41no—
252C23×C59—41no—
253C23×C59—41no—
254C23×C59—41no—
255C23×C59C4×D412yes—
256C23×C59C22×D411yescharacteristic
257Q8×C59—22no—
258Q8×C59—22no—
259Q8×C59—22no—
260Q8×C59—22no—
261Q8×C59—22no—
262Q8×C59—41no—
263Q8×C59—41no—
264Q8×C59C4×D414yes—
265D4×C59—22no—
266D4×C59—22no—
267D4×C59—48no—
268D4×C59—41no—
269D4×C59—41no—
270C2×C4×C59—22no—
271C2×C4×C59—22no—
272C2×C4×C59—21no—
273C2×C4×C59—22no—
274C2×C4×C59—21no—
275C2×C4×C59—22no—
276C2×C4×C59—22no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—48no—
282C2×C4×C59—41no—
283C2×C4×C59—41no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59C4×D412yes—
287C2×C4×C59C23×C411yescharacteristic
288C2×C4×C59C22×D411yescharacteristic
289C2×C4×C59C2×#4111yescharacteristic
290C2×C4×C59C2×#4111yescharacteristic
291C2×C4×C59H(5,𝔽2)11yescharacteristic
292C2×C4×C59H(5,𝔽2)11yescharacteristic
293C2×Dic59—21no—
294C2×Dic59—21no—
295C2×Dic59—21no—
296C2×Dic59—21no—
297C2×Dic59—22no—
298C2×Dic59—21no—
299C2×Dic59—21no—
300C2×Dic59—21no—
301C2×Dic59—21no—
302C2×Dic59—21no—
303C2×Dic59—21no—
304C2×Dic59—21no—
305C2×Dic59—41no—
306C2×Dic59—41no—
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—84no—
317C2×Dic59#13712yes—
318C8×C59—22no—
319C8×C59—22no—
320C59⋊C8—22no—
321C59⋊C8—41no—
322#22867—591nomaximal, Sylow
323C22×C59—22no—
324C22×C59—22no—
325C22×C59—22no—
326C22×C59—41no—
327C22×C59—41no—
328C22×C59—41no—
329C22×C59—41no—
330C22×C59—42no—
331C22×C59—42no—
332C22×C59—42no—
333C22×C59—81no—
334C22×C59—81no—
335C22×C59—81no—
336C22×C59—81no—
337C22×C59C2×C4×D411yescharacteristic
338C22×C59D4211yescharacteristic
339C22×C59#54611yescharacteristic
340C22×C59C2×#13711yescharacteristic
341C22×C59#57511yescharacteristic
342C22×C59#57711yescharacteristic
343C22×C59#57711yescharacteristic
344C4×C59—22no—
345C4×C59—24no—
346C4×C59—42no—
347C4×C59—42no—
348C4×C59C2×C4×D411yescharacteristic
349C4×C59#51811yescharacteristic
350C4×C59#54611yescharacteristic
351C4×C59#55111yescharacteristic
352Dic59—22no—
353Dic59—41no—
354Dic59—42no—
355Dic59—41no—
356Dic59—41no—
357Dic59—81no—
358Dic59—81no—
359Dic59—81no—
360C2×#452D5911yescharacteristic
361C2×#441—591no—
362C2×#417—591no—
363#2360—591no—
364#2341—591no—
365#1968—591no—
366#1936—591no—
367#1926—591no—
368#1894—591no—
369#1880—591no—
370#1878—591no—
371#1865—591no—
372#1853—591no—
373C4×#103—591no—
374#1753—591no—
375C2×C59—42no—
376C2×C59—82no—
377C2×C59#235811yescharacteristic
378C2×C59C4×#13711yescharacteristic
379C2×C59#295211yescharacteristic
380C2×C59#327511yescharacteristic
381C2×C59#327811yescharacteristic
382C2×C59#331611yescharacteristic
383C2×C59#331711yescharacteristic
384C22×#41C2×D5911yescharacteristic
385C22×Q16C2×D5911yescharacteristic
386C22×SD16C2×D5911yescharacteristic
387C22×M16—591no—
388C2×C22⋊Q8C2×D5911yescharacteristic
389C2×C4×Q8—591no—
390C2×C4×Q8—591no—
391C2×C4×Q8—591no—
392C22×C4⋊C4—591no—
393#452Dic5918yescomplemented
394#441—1184no—
395C2×#106—591no—
396C2×#106—591no—
397#417—1184no—
398C2×#103—591no—
399C2×#103—591no—
400C2×#103—591no—
401C2×#103—591no—
402C2×#103C2×D5911yescharacteristic
403C2×#102—591no—
404C2×#102—591no—
405C2×#102C2×D5911yescharacteristic
406C2×C22⋊C8C2×D5911yescharacteristic
407C2×#97—591no—
408C2×C4×C8—591no—
409#391—591no—
410#390—591no—
411#390—591no—
412#390—1181no—
413#390—1181no—
414#389—591no—
415#389—1181no—
416#387—1181no—
417#385—1181no—
418#380—591no—
419#380—1181no—
420C4×C4⋊C4—591no—
421C4×C22⋊C4—591no—
422C4×C22⋊C4—1181no—
423C4×C22⋊C4—1181no—
424#340—591no—
425#340—591no—
426#340—591no—
427#340—591no—
428#336—591no—
429#336—591no—
430C59#2286711yescharacteristic, complemented, Sylow
431C2×#41—22no—
432C2×#41—22no—
433C2×#41—22no—
434C2×#41—41no—
435C2×#41—41no—
436C2×#41C2×Dic5914yes—
437C22×Q8C22×D5911yescharacteristic
438C22×Q8C22×D5911yescharacteristic
439C22×D4—21no—
440C22×D4C22×D5911yescharacteristic
441C23×C4—21no—
442C23×C4—1181no—
443C23×C4C22×D5911yescharacteristic
444C2×Q16—22no—
445C2×Q16—22no—
446C2×Q16C2×Dic5914yescomplemented
447C2×SD16—41no—
448C2×SD16—41no—
449C2×SD16C2×Dic5914yescomplemented
450C2×M16—1182no—
451C2×M16—1182no—
452C2×M16—2361no—
453C22×C8—591no—
454C22×C8—591no—
455C22×C8C22×D5911yescharacteristic
456C22×C8C22×D5911yescharacteristic
457C22⋊Q8—22no—
458C22⋊Q8C2×Dic5914yes—
459C4×Q8—1182no—
460C4×Q8—1182no—
461C4×Q8—1182no—
462C4×Q8—2361no—
463C4×Q8—2361no—
464C4×Q8—2361no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—591no—
467C2×C4⋊C4—591no—
468C2×C4⋊C4—591no—
469C2×C4⋊C4—591no—
470C2×C4⋊C4—1182no—
471C2×C4⋊C4—1181no—
472C2×C4⋊C4—1181no—
473C2×C4⋊C4—1181no—
474C2×C4⋊C4—1181no—
475C2×C4⋊C4—1181no—
476C2×C4⋊C4—2361no—
477C2×C4⋊C4C22×D5911yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—591no—
480C2×C22⋊C4—591no—
481C2×C22⋊C4—1181no—
482C2×C22⋊C4—1181no—
483C2×C22⋊C4—1181no—
484C2×C22⋊C4—1181no—
485C2×C22⋊C4—1181no—
486C2×C42—591no—
487C2×C42—591no—
488C2×C42—1181no—
489C2×C42—1181no—
490C2×C42—1181no—
491C2×C42—1181no—
492#106—1182no—
493#106—2361no—
494#103—594no—
495#103—1182no—
496#103—1182no—
497#103—2361no—
498#103C2×Dic5914yescomplemented
499#102—1182no—
500#102—1182no—
501#102C2×Dic5914yescomplemented
502C22⋊C8C2×Dic5914yes—
503#97—1182no—
504C4×C8—2361no—
505#95—591no—
506#95—591no—
507#95—1181no—
508#95—1181no—
509#95—1181no—
510#95—1181no—
511#95—1181no—
512C24—21no—
513C24D4×D5911yescharacteristic
514#41—28no—
515#41—44no—
516#41—44no—
517#41—44no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8D4×D5912yes—
527C2×Q8#1174568712yes—
528C2×Q8C22×Dic5912yes—
529C2×Q8C22×Dic5912yes—
530C2×D4—24no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4C22×Dic5912yes—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—24no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—591no—
550C22×C4—591no—
551C22×C4—591no—
552C22×C4—591no—
553C22×C4—1181no—
554C22×C4—1181no—
555C22×C4—1181no—
556C22×C4—1181no—
557C22×C4—4721no—
558C22×C4—2362no—
559C22×C4—2362no—
560C22×C4D4×D5911yescharacteristic
561C22×C4#1174568712yes—
562C22×C4C22×Dic5912yes—
563C22×C4C23×D5911yescharacteristic
564Q16—28no—
565SD16—44no—
566M16—2364no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—592no—
572C2×C8—1181no—
573C2×C8—1181no—
574C2×C8—1181no—
575C2×C8—1181no—
576C2×C8—1181no—
577C2×C8C22×Dic5912yes—
578C2×C8C22×Dic5912yes—
579C4⋊C4—24no—
580C4⋊C4—21no—
581C4⋊C4—592no—
582C4⋊C4—1181no—
583C4⋊C4—1181no—
584C4⋊C4—1181no—
585C4⋊C4—1181no—
586C4⋊C4—1181no—
587C4⋊C4—1181no—
588C4⋊C4—1181no—
589C4⋊C4—4721no—
590C4⋊C4—2362no—
591C4⋊C4—2362no—
592C4⋊C4—2362no—
593C4⋊C4—2362no—
594C4⋊C4C22×Dic5912yes—
595C22⋊C4—24no—
596C22⋊C4—1182no—
597C22⋊C4—4721no—
598C22⋊C4—4721no—
599C22⋊C4—4721no—
600C22⋊C4—2362no—
601C22⋊C4—2361no—
602C22⋊C4—2362no—
603C42—1181no—
604C42—1181no—
605C42—1181no—
606C42—1181no—
607C42—4721no—
608C42—2362no—
609C42—2362no—
610C42—2362no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23D4×Dic5912yes—
625C23C2×D4×D5911yescharacteristic
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—41no—
632Q8—41no—
633Q8D4×Dic5914yes—
634D4—22no—
635D4—22no—
636D4—48no—
637D4—41no—
638D4—41no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—48no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—592no—
656C2×C4—1181no—
657C2×C4—1181no—
658C2×C4—1181no—
659C2×C4—1181no—
660C2×C4—1181no—
661C2×C4—1181no—
662C2×C4—1181no—
663C2×C4—1181no—
664C2×C4—1181no—
665C2×C4—1181no—
666C2×C4—1182no—
667C2×C4—1181no—
668C2×C4—4724no—
669C2×C4—2361no—
670C2×C4—2361no—
671C2×C4—2361no—
672C2×C4—2361no—
673C2×C4—2361no—
674C2×C4—2361no—
675C2×C4—2361no—
676C2×C4—2361no—
677C2×C4—2361no—
678C2×C4—2361no—
679C2×C4—2361no—
680C2×C4D4×Dic5912yes—
681C2×C4C23×Dic5911yescharacteristic
682C2×C4C2×D4×D5911yescharacteristic
683C2×C4C2×#1174568711yescharacteristic
684C2×C4C2×#1174568711yescharacteristic
685C2×C4#1427377211yescharacteristic
686C2×C4#1427377211yescharacteristic
687C8—22no—
688C8—22no—
689C8—1182no—
690C8—2361no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22C2×D4×Dic5911yescharacteristic
706C22#1683803411yescharacteristic
707C22#1683803911yescharacteristic
708C22#137×D5911yescharacteristic
709C22#1683820111yescharacteristic
710C22#1683820911yescharacteristic
711C22#1683820911yescharacteristic
712C4—22no—
713C4—24no—
714C4—42no—
715C4—42no—
716C4—1182no—
717C4—4721no—
718C4—4721no—
719C4—4721no—
720C4—2361no—
721C4—2361no—
722C4—2362no—
723C4—2361no—
724C4C2×D4×Dic5911yescharacteristic
725C4#1683787711yescharacteristic
726C4#1683803911yescharacteristic
727C4#1683808311yescharacteristic
728C2—42no—
729C2—82no—
730C2#2142708011yescharacteristic
731C2#137×Dic5911yescharacteristic
732C2#2143298011yescharacteristic
733C2#2143572011yescharacteristic
734C2#2143575511yescharacteristic
735C2#2143620011yescharacteristic
736C2#2143621511yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C59×#452C2
socleC23×C59C22×D4
prime radicalC22×#41×C59C22
cosocleC22×C4×C59C24
hypercenterC2×#452D59
hypocenterC59#22867
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#16837509C2semidirect
3. #21427105C2semidirect
5. #21424952C2semidirect
6. #21424795C2semidirect
7. #21424725C2semidirect
8. #21424530C2semidirect
9. #21424453C2semidirect
10. #21424439C2semidirect
11. #21424366C2semidirect
12. #21424291C2semidirect
13. #103×Dic59C2semidirect
14. #21423882C2semidirect
58. C59×#452C4semidirect
129. C2×Q16×C59C2×C4semidirect
132. C2×SD16×C59C2×C4semidirect
140. #103×C59C2×C4semidirect
141. #102×C59C2×C4semidirect
393. #452Dic59semidirect
430. C59#22867semidirect
446. C2×Q16C2×Dic59semidirect
449. C2×SD16C2×Dic59semidirect
498. #103C2×Dic59semidirect
501. #102C2×Dic59semidirect

Maximal subgroups

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

subgroupindex
C2×#168375092
C2×#168374032
#214271052
#214269372
#214249522
#214247952
#214247252
#214245302
#214244532
#214244392
#214243662
#214242912
#103×Dic592
#214238822
C2×C59×#4522
#2286759