Finite Group Databasebeta

← #28609107

Subgroups — #28609107

Order 15104.

1114 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837541C211yesmaximal, characteristic
2C2×#16837500C211yesmaximal, characteristic, complemented
3C2×#16837411C211yesmaximal, characteristic, complemented
4#21427132C211yesmaximal, characteristic
5#21424953C211yesmaximal, characteristic, complemented
6#21424789C211yesmaximal, characteristic, complemented
7#21424734C211yesmaximal, characteristic, complemented
8#21424532C211yesmaximal, characteristic
9#21424451C211yesmaximal, characteristic, complemented
10#21424433C211yesmaximal, characteristic, complemented
11#21424364C211yesmaximal, characteristic, complemented
12#21424293C211yesmaximal, characteristic, complemented
13C4×#14273651C211yesmaximal, characteristic, complemented
14#21423880C211yesmaximal, characteristic, complemented
15Q8×C22⋊C4×C59C211yesmaximal, characteristic, complemented
16C22×#11745671C2211yescharacteristic
17C22×#11745671C2211yescharacteristic
18C22×#11745664C2211yescharacteristic
19C2×#14273701C2211yescharacteristic
20C2×C4×D236C2211yescharacteristic
21C2×#14273686C2211yescharacteristic
22#16837541C418yescomplemented
23#16837500—24no—
24C2×#14273660C2211yescharacteristic
25C2×#14273658C2211yescharacteristic
26#16837411—24no—
27C2×#14273651C2211yescharacteristic
28C2×#14273651C2211yescharacteristic
29C2×#14273651C2211yescharacteristic
30C2×#14273651C2211yescharacteristic
31C2×#14273651C2211yescharacteristic
32C2×#14273651C2211yescharacteristic
33C2×#14273647C2211yescharacteristic
34C2×#14273647C2211yescharacteristic
35C2×C22⋊(C59⋊C8)C2211yescharacteristic
36C2×#14273638C2211yescharacteristic
37C2×C4×C59⋊C8C2211yescharacteristic
38#16837304C2211yescharacteristic
39#16837302—21no—
40#16837300C2211yescharacteristic
41#16837291—21no—
42#16837278—21no—
43C4×C4⋊Dic59C2211yescharacteristic
44#16837249—21no—
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837157C2211yescharacteristic
50#16837157C2211yescharacteristic
51C23×Q8×C59C2211yescharacteristic
52C2×C4×Q8×C59C2211yescharacteristic
53C2×C4×Q8×C59C2211yescharacteristic
54C59×#391—21no—
55C59×#391—21no—
56C59×#391C2211yescharacteristic
57C59×#391C2211yescharacteristic
58C59×#380—21no—
59C59×#380C2211yescharacteristic
60C4×C22⋊C4×C59—21no—
61C4×C22⋊C4×C59C2211yescharacteristic
62C22×D236C2311yescharacteristic
63C22×C22⋊D59—21no—
64C22×C4×D59—21no—
65C2×#11745671—22no—
66C2×#11745671—22no—
67C2×#11745671—41no—
68C2×#11745671—41no—
69C2×#11745671C2×C414yes—
70C2×#11745671C2×C414yes—
71C2×#11745664—22no—
72C2×#11745664—22no—
73C2×#11745664—41no—
74C22×C59⋊C8C2311yescharacteristic
75C22×C59⋊C8C2311yescharacteristic
76C22×C59⋊C8C2311yescharacteristic
77C22×C59⋊C8C2311yescharacteristic
78#14273701—22no—
79#14273701C2×C414yes—
80C4×D236—22no—
81C4×D236—41no—
82#14273686—22no—
83#14273686—41no—
84C2×C4⋊Dic59C2311yescharacteristic
85C2×C4⋊Dic59C2311yescharacteristic
86C2×C4⋊Dic59C2311yescharacteristic
87C2×Dic59⋊C4—21no—
88C2×C22⋊Dic59—21no—
89C2×(C2×D59)⋊C4—21no—
90C2×(C2×D59)⋊C4—21no—
91C2×(C2×D59)⋊C4—21no—
92C2×(C2×D59)⋊C4—21no—
93C2×C4×Dic59—21no—
94C2×C4×Dic59—21no—
95#14273660—22no—
96#14273658—41no—
97#14273651—22no—
98#14273651—22no—
99#14273651—22no—
100#14273651C2×C414yescomplemented
101#14273651C2×C414yescomplemented
102#14273651D414yescomplemented
103#14273647—22no—
104#14273647—41no—
105C22⋊(C59⋊C8)C2×C414yescomplemented
106#14273638—22no—
107C4×C59⋊C8—41no—
108C59⋊#95—21no—
109C59⋊#95—21no—
110C22×Q8×C59—21no—
111C22×Q8×C59—22no—
112C22×Q8×C59—22no—
113C22×Q8×C59—22no—
114C22×Q8×C59—41no—
115C22×Q8×C59—41no—
116C22×Q8×C59C2×C414yescomplemented
117C22×Q8×C59C2311yescharacteristic
118C22×Q8×C59C2311yescharacteristic
119C23×C4×C59—21no—
120C23×C4×C59C2311yescharacteristic
121C4×Q8×C59—22no—
122C4×Q8×C59—22no—
123C4×Q8×C59—41no—
124C4×Q8×C59—41no—
125C2×C4⋊C4×C59—21no—
126C2×C4⋊C4×C59—21no—
127C2×C4⋊C4×C59C2311yescharacteristic
128C2×C4⋊C4×C59C2311yescharacteristic
129C2×C22⋊C4×C59—21no—
130C2×C22⋊C4×C59D411yescharacteristic
131C2×C22⋊C4×C59D411yescharacteristic
132C2×C42×C59—21no—
133C2×C42×C59—21no—
134C2×C42×C59C2311yescharacteristic
135C2×C42×C59C2311yescharacteristic
136#95×C59—21no—
137#95×C59—21no—
138#95×C59—21no—
139#95×C59—21no—
140#95×C59—21no—
141#95×C59D411yescharacteristic
142#95×C59D411yescharacteristic
143C24×C59C2×D411yescharacteristic
144C23×D59—21no—
145C2×Q8×C59—24no—
146C2×Q8×C59—21no—
147C2×Q8×C59—21no—
148C2×Q8×C59—21no—
149C2×Q8×C59—21no—
150C2×Q8×C59—28no—
151C2×Q8×C59—21no—
152C2×Q8×C59—21no—
153C2×Q8×C59—21no—
154C2×Q8×C59—21no—
155C2×Q8×C59—42no—
156C2×Q8×C59—42no—
157C2×Q8×C59—44no—
158C2×Q8×C59—44no—
159C2×Q8×C59—44no—
160C2×Q8×C59C22×C412yes—
161C2×Q8×C59C22×C412yes—
162C2×Q8×C59C2×D412yes—
163C2×Q8×C59#4112yes—
164C22×C4×C59—21no—
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—24no—
170C22×C4×C59—21no—
171C22×C4×C59—21no—
172C22×C4×C59—21no—
173C22×C4×C59—42no—
174C22×C4×C59—42no—
175C22×C4×C59C22×C412yes—
176C22×C4×C59C2×D411yescharacteristic
177C22×C4×C59C2×D411yescharacteristic
178C22×C4×C59C2×D411yescharacteristic
179C22×C4×C59C2×D411yescharacteristic
180C22×C4×C59C2×D411yescharacteristic
181C22×C4×C59#4112yes—
182C22×C4×C59C2411yescharacteristic
183C2×C22⋊D59—24no—
184C2×C22⋊D59—81no—
185C2×C22⋊D59—81no—
186C22×Dic59—21no—
187C22×Dic59—21no—
188C22×Dic59—21no—
189C2×D236—21no—
190C2×D236—21no—
191C2×D236—21no—
192C2×D236—21no—
193C2×D236—21no—
194C2×D236C22×C412yes—
195C2×C4×D59—42no—
196C2×C4×D59—42no—
197C2×C4×D59—81no—
198C4⋊C4×C59—21no—
199C4⋊C4×C59—21no—
200C4⋊C4×C59—21no—
201C4⋊C4×C59—21no—
202C4⋊C4×C59—42no—
203C4⋊C4×C59—42no—
204C22⋊C4×C59—22no—
205C22⋊C4×C59—41no—
206C22⋊C4×C59—42no—
207C42×C59—21no—
208C42×C59—21no—
209C42×C59—21no—
210C42×C59—21no—
211C42×C59—42no—
212C42×C59—42no—
213C22⋊Dic59—42no—
214#11745671—28no—
215#11745671—44no—
216(C2×D59)⋊C4—24no—
217(C2×D59)⋊C4—42no—
218(C2×D59)⋊C4—42no—
219(C2×D59)⋊C4—81no—
220C4⋊Dic59—21no—
221C4⋊Dic59—21no—
222C4⋊Dic59—21no—
223C4⋊Dic59—21no—
224C4⋊Dic59C22×C412yes—
225C4⋊Dic59C2×D412yes—
226Dic59⋊C4—81no—
227C4×Dic59—42no—
228C4×Dic59—81no—
229#11745664—44no—
230C2×C59⋊C8—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—
237C2×C59⋊C8—21no—
238C2×C59⋊C8—21no—
239C2×C59⋊C8C22×C412yes—
240C2×C59⋊C8C22×C412yes—
241C2×C59⋊C8C2×D412yes—
242C23×C59—21no—
243C23×C59—21no—
244C23×C59—21no—
245C23×C59—21no—
246C23×C59—21no—
247C23×C59—21no—
248C23×C59C4×D412yes—
249C23×C59C22×D411yescharacteristic
250C22×D59—22no—
251C22×D59—41no—
252C22×D59—41no—
253C22×D59—41no—
254C22×D59—41no—
255C22×D59—41no—
256C22×D59—41no—
257Q8×C59—22no—
258Q8×C59—22no—
259Q8×C59—22no—
260Q8×C59—22no—
261Q8×C59—22no—
262Q8×C59—48no—
263Q8×C59—41no—
264Q8×C59—41no—
265Q8×C59C4×D414yes—
266C2×C4×C59—22no—
267C2×C4×C59—21no—
268C2×C4×C59—22no—
269C2×C4×C59—21no—
270C2×C4×C59—22no—
271C2×C4×C59—21no—
272C2×C4×C59—21no—
273C2×C4×C59—22no—
274C2×C4×C59—22no—
275C2×C4×C59—22no—
276C2×C4×C59—22no—
277C2×C4×C59—22no—
278C2×C4×C59—21no—
279C2×C4×C59—21no—
280C2×C4×C59—21no—
281C2×C4×C59—21no—
282C2×C4×C59—21no—
283C2×C4×C59—21no—
284C2×C4×C59—21no—
285C2×C4×C59—21no—
286C2×C4×C59—21no—
287C2×C4×C59—48no—
288C2×C4×C59—41no—
289C2×C4×C59—41no—
290C2×C4×C59—41no—
291C2×C4×C59—41no—
292C2×C4×C59—41no—
293C2×C4×C59—41no—
294C2×C4×C59—41no—
295C2×C4×C59—41no—
296C2×C4×C59C4×D412yes—
297C2×C4×C59#13712yes—
298C2×C4×C59C23×C411yescharacteristic
299C2×C4×C59C22×D411yescharacteristic
300C2×C4×C59C2×#4111yescharacteristic
301C2×C4×C59C2×#4111yescharacteristic
302C2×C4×C59H(5,𝔽2)11yescharacteristic
303C2×C4×C59H(5,𝔽2)11yescharacteristic
304C22⋊D59—84no—
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—41no—
308C2×Dic59—41no—
309C2×Dic59—41no—
310C2×Dic59—41no—
311C2×Dic59—41no—
312C2×Dic59—41no—
313C2×Dic59—41no—
314D236—22no—
315D236—22no—
316D236—41no—
317D236—41no—
318C4×D59—84no—
319C59⋊C8—22no—
320C59⋊C8—22no—
321C59⋊C8—22no—
322C59⋊C8—41no—
323#22865—591nomaximal, Sylow
324C22×C59—22no—
325C22×C59—22no—
326C22×C59—22no—
327C22×C59—41no—
328C22×C59—41no—
329C22×C59—41no—
330C22×C59—41no—
331C22×C59C2×C4×D411yescharacteristic
332C22×C59D4211yescharacteristic
333C22×C59#54611yescharacteristic
334C22×C59C2×#13711yescharacteristic
335C22×C59#57511yescharacteristic
336C22×C59#57711yescharacteristic
337C22×C59#57711yescharacteristic
338C2×D59—42no—
339C2×D59—42no—
340C2×D59—42no—
341C2×D59—81no—
342C2×D59—81no—
343C2×D59—81no—
344C2×D59—81no—
345C4×C59—22no—
346C4×C59—24no—
347C4×C59—22no—
348C4×C59—42no—
349C4×C59—41no—
350C4×C59—41no—
351C4×C59—41no—
352C4×C59—81no—
353C4×C59—81no—
354C4×C59C2×C4×D411yescharacteristic
355C4×C59#51811yescharacteristic
356C4×C59#54611yescharacteristic
357C4×C59#55111yescharacteristic
358Dic59—42no—
359Dic59—42no—
360Dic59—81no—
361C2×#448—591no—
362C2×#440—591no—
363C2×#419—591no—
364#2363—591no—
365Q8×C22⋊C4D5911yescharacteristic, complemented
366#1968—591no—
367#1935—591no—
368#1928—591no—
369#1895—591no—
370#1880—591no—
371#1877—591no—
372#1865—591no—
373#1854—591no—
374C4×#103—591no—
375#1753—591no—
376C2×C59—42no—
377C2×C59#235811yescharacteristic
378C2×C59C4×#13711yescharacteristic
379C2×C59#294911yescharacteristic
380C2×C59#327511yescharacteristic
381C2×C59#327811yescharacteristic
382C2×C59#332011yescharacteristic
383C2×C59#332111yescharacteristic
384D59—82no—
385C23×Q8C2×D5911yescharacteristic
386C22×SD16—591no—
387C22×SD16—591no—
388C22×M16—591no—
389C2×#121—591no—
390C2×C4×Q8C2×D5911yescharacteristic
391C2×C4×Q8C2×D5911yescharacteristic
392C2×C4×D4—591no—
393C2×#117—591no—
394#448—598no—
395#440—1184no—
396C2×#107—591no—
397C2×#106—591no—
398#419—1184no—
399C2×#103—591no—
400C2×#103—591no—
401C2×#103—591no—
402C2×#103—591no—
403C2×#103—591no—
404C2×#103—591no—
405C2×#102—591no—
406C2×#102—591no—
407C2×C22⋊C8—591no—
408C2×#97—591no—
409C2×C4×C8—591no—
410#391—21no—
411#391—21no—
412#391C2×D5911yescharacteristic
413#391C2×D5911yescharacteristic
414#390—591no—
415#390—1181no—
416#389—591no—
417#388—1181no—
418#386—1181no—
419#380—21no—
420#380C2×D5911yescharacteristic
421C4×C4⋊C4—591no—
422C4×C22⋊C4—21no—
423C4×C22⋊C4—1181no—
424C4×C22⋊C4C2×D5911yescharacteristic
425#340—591no—
426#340—591no—
427#340—591no—
428#340—591no—
429#336—591no—
430#336—591no—
431C59#2286511yescharacteristic, complemented, Sylow
432C22×Q8—22no—
433C22×Q8—21no—
434C22×Q8—22no—
435C22×Q8—22no—
436C22×Q8—41no—
437C22×Q8—41no—
438C22×Q8C4×D5914yescomplemented
439C22×Q8C22×D5911yescharacteristic
440C22×Q8C22×D5911yescharacteristic
441C22×D4—591no—
442C22×D4—1181no—
443C23×C4—21no—
444C23×C4—1181no—
445C23×C4C22×D5911yescharacteristic
446C2×SD16—594no—
447C2×SD16—594no—
448C2×SD16—1182no—
449C2×SD16—1182no—
450C2×SD16—2361no—
451C2×SD16—2361no—
452C2×M16—1182no—
453C2×M16—1182no—
454C2×M16—2361no—
455C22×C8—591no—
456C22×C8—591no—
457C22×C8—591no—
458C22×C8—591no—
459#121—594no—
460#121—1182no—
461C4×Q8—22no—
462C4×Q8—22no—
463C4×Q8—41no—
464C4×Q8—41no—
465C4×D4—1182no—
466C4×D4—2361no—
467#117—1182no—
468#117—2361no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—591no—
472C2×C4⋊C4—591no—
473C2×C4⋊C4—591no—
474C2×C4⋊C4—1181no—
475C2×C4⋊C4C22×D5911yescharacteristic
476C2×C4⋊C4C22×D5911yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—1181no—
479C2×C22⋊C4—1181no—
480C2×C22⋊C4—1181no—
481C2×C22⋊C4—1181no—
482C2×C22⋊C4—1181no—
483C2×C22⋊C4C22⋊D5911yescharacteristic
484C2×C22⋊C4C22⋊D5911yescharacteristic
485C2×C42—21no—
486C2×C42—21no—
487C2×C42—1181no—
488C2×C42—1181no—
489C2×C42C22×D5911yescharacteristic
490C2×C42C22×D5911yescharacteristic
491#107—1182no—
492#106—2361no—
493#103—594no—
494#103—594no—
495#103—594no—
496#103—1182no—
497#103—1182no—
498#103—1182no—
499#102—1182no—
500#102—2361no—
501C22⋊C8—594no—
502#97—1182no—
503C4×C8—2361no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—1181no—
510#95—1181no—
511#95C22⋊D5911yescharacteristic
512#95C22⋊D5911yescharacteristic
513C24—1181no—
514C24C2×C22⋊D5911yescharacteristic
515C2×Q8—24no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—28no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—42no—
526C2×Q8—42no—
527C2×Q8—44no—
528C2×Q8—44no—
529C2×Q8—44no—
530C2×Q8C2×C4×D5912yes—
531C2×Q8C2×C4×D5912yes—
532C2×Q8D4×D5912yes—
533C2×Q8#1174568712yes—
534C2×D4—592no—
535C2×D4—1184no—
536C2×D4—1181no—
537C2×D4—1181no—
538C2×D4—1181no—
539C2×D4—1181no—
540C2×D4—1181no—
541C2×D4—4721no—
542C2×D4—4721no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—24no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—1181no—
555C22×C4—1181no—
556C22×C4—1181no—
557C22×C4—4721no—
558C22×C4—2362no—
559C22×C4—2362no—
560C22×C4C2×C4×D5912yes—
561C22×C4#1174568512yes—
562C22×C4C2×C22⋊D5911yescharacteristic
563C22×C4C2×C22⋊D5911yescharacteristic
564C22×C4C2×C22⋊D5911yescharacteristic
565C22×C4C2×C22⋊D5911yescharacteristic
566C22×C4C2×C22⋊D5911yescharacteristic
567C22×C4C23×D5911yescharacteristic
568SD16—1188no—
569SD16—2364no—
570M16—2364no—
571C2×C8—592no—
572C2×C8—592no—
573C2×C8—592no—
574C2×C8—1181no—
575C2×C8—1181no—
576C2×C8—1181no—
577C2×C8—1181no—
578C2×C8—1181no—
579C2×C8—1181no—
580C2×C8—1181no—
581C2×C8—1181no—
582C2×C8—1181no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—592no—
590C4⋊C4—592no—
591C4⋊C4—1181no—
592C4⋊C4—1181no—
593C4⋊C4—1181no—
594C4⋊C4—1181no—
595C4⋊C4—4721no—
596C22⋊C4—22no—
597C22⋊C4—41no—
598C22⋊C4—42no—
599C22⋊C4—1184no—
600C22⋊C4—4721no—
601C22⋊C4—2362no—
602C22⋊C4—2362no—
603C22⋊C4—2362no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—21no—
608C42—42no—
609C42—42no—
610C42—4721no—
611C42—2362no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—1182no—
619C23—2361no—
620C23—2361no—
621C23—2361no—
622C23—2361no—
623C23—2361no—
624C23—2361no—
625C23C4×C22⋊D5912yes—
626C23C22×C22⋊D5911yescharacteristic
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—22no—
632Q8—48no—
633Q8—41no—
634Q8—41no—
635Q8(C22⋊D59)⋊C414yes—
636D4—1182no—
637D4—1182no—
638D4—4724no—
639D4—2361no—
640D4—2361no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—48no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—1182no—
672C2×C4—1182no—
673C2×C4—4724no—
674C2×C4—2361no—
675C2×C4—2361no—
676C2×C4—2361no—
677C2×C4—2361no—
678C2×C4—2361no—
679C2×C4—2361no—
680C2×C4—2361no—
681C2×C4C4×C22⋊D5912yes—
682C2×C4#1427375812yes—
683C2×C4C22×C4×D5911yescharacteristic
684C2×C4C2×D4×D5911yescharacteristic
685C2×C4C2×#1174568711yescharacteristic
686C2×C4C2×#1174568511yescharacteristic
687C2×C4#1427377211yescharacteristic
688C2×C4#1427377211yescharacteristic
689C8—1182no—
690C8—1182no—
691C8—1182no—
692C8—2361no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—4721no—
701C22—4721no—
702C22—4721no—
703C22—4721no—
704C22—2362no—
705C22—2362no—
706C22—2362no—
707C22C2×C4×C22⋊D5911yescharacteristic
708C22D4×C22⋊D5911yescharacteristic
709C22#1683804611yescharacteristic
710C22C2×#1427375811yescharacteristic
711C22#1683820011yescharacteristic
712C22#1683821011yescharacteristic
713C22#1683821011yescharacteristic
714C4—22no—
715C4—22no—
716C4—24no—
717C4—41no—
718C4—41no—
719C4—41no—
720C4—42no—
721C4—81no—
722C4—81no—
723C4—4721no—
724C4—2362no—
725C4—2362no—
726C4C2×(C22⋊D59)⋊C411yescharacteristic
727C4#1683787511yescharacteristic
728C4#1683804211yescharacteristic
729C4#1683807811yescharacteristic
730C2—42no—
731C2—4722no—
732C2#2142707511yescharacteristic
733C2C4×#1427375811yescharacteristic
734C2#2143295511yescharacteristic
735C2#2143572811yescharacteristic
736C2#2143575811yescharacteristic
737C2#2143626711yescharacteristic
738C2#2143628211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingQ8×C22⋊C4×C59C2
socleC23×C59C22×D4
prime radicalC2×#14273701C22
cosocleC22×C4×C59C24
hypercenterQ8×C22⋊C4D59
hypocenterC59#22865
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16837500C2semidirect
3. C2×#16837411C2semidirect
5. #21424953C2semidirect
6. #21424789C2semidirect
7. #21424734C2semidirect
9. #21424451C2semidirect
10. #21424433C2semidirect
11. #21424364C2semidirect
12. #21424293C2semidirect
13. C4×#14273651C2semidirect
14. #21423880C2semidirect
15. Q8×C22⋊C4×C59C2semidirect
22. #16837541C4semidirect
100. #14273651C2×C4semidirect
101. #14273651C2×C4semidirect
102. #14273651D4semidirect
105. C22⋊(C59⋊C8)C2×C4semidirect
116. C22×Q8×C59C2×C4semidirect
365. Q8×C22⋊C4D59semidirect
431. C59#22865semidirect
438. C22×Q8C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168375412
C2×#168375002
C2×#168374112
#214271322
#214249532
#214247892
#214247342
#214245322
#214244512
#214244332
#214243642
#214242932
C4×#142736512
#214238802
Q8×C22⋊C4×C592
#2286559