Finite Group Databasebeta

← #28611502

Subgroups — #28611502

Order 15104.

1082 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×#16837653C211yesmaximal, characteristic
2C2×#16837512C211yesmaximal, characteristic, complemented
3C2×#16837442C211yesmaximal, characteristic, complemented
4#21427132C211yesmaximal, characteristic, complemented
5#21424961C211yesmaximal, characteristic, complemented
6#21424836C211yesmaximal, characteristic, complemented
7#21424720C211yesmaximal, characteristic, complemented
8#21424716C211yesmaximal, characteristic, complemented
9#21424419C211yesmaximal, characteristic, complemented
10#21424413C211yesmaximal, characteristic, complemented
11#21424356C211yesmaximal, characteristic, complemented
12#21424343C211yesmaximal, characteristic, complemented
13C4×#14273658C211yesmaximal, characteristic, complemented
14#21423880C211yesmaximal, characteristic, complemented
15C59×#2361C211yesmaximal, characteristic, complemented
16C22×#11745669C2211yescharacteristic
17C22×#11745664C2211yescharacteristic
18C2×#14273701C2211yescharacteristic
19C2×C4×D236C2211yescharacteristic
20C2×#14273686C2211yescharacteristic
21#16837653C418yescomplemented
22#16837512—24no—
23#16837442—24no—
24C2×#14273660C2211yescharacteristic
25C2×#14273660C2211yescharacteristic
26C2×#14273658C2211yescharacteristic
27C2×#14273658C2211yescharacteristic
28C2×#14273658C2211yescharacteristic
29C2×#14273648C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×#14273648C2211yescharacteristic
32C2×#14273647C2211yescharacteristic
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
51C2×#121×C59C2211yescharacteristic
52C2×C4×D4×C59—21no—
53C2×C4×D4×C59C2211yescharacteristic
54C22×C4⋊C4×C59C2211yescharacteristic
55C59×#390C2211yescharacteristic
56C59×#389C2211yescharacteristic
57C59×#388—21no—
58C59×#386—21no—
59C59×#385—21no—
60C4×C4⋊C4×C59C2211yescharacteristic
61C4×C22⋊C4×C59C2211yescharacteristic
62C22×D236C2311yescharacteristic
63C22×C22⋊D59—21no—
64C22×C4×D59—21no—
65C2×#11745669—22no—
66C2×#11745669—22no—
67C2×#11745669C2×C414yescomplemented
68C2×#11745664—22no—
69C2×#11745664—22no—
70C2×#11745664C2×C414yescomplemented
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74C22×C59⋊C8C2311yescharacteristic
75#14273701—22no—
76#14273701C2×C414yescomplemented
77C4×D236—22no—
78C4×D236—41no—
79#14273686—22no—
80#14273686—41no—
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—
91C2×C4×Dic59—21no—
92#14273660—22no—
93#14273660—22no—
94#14273658—22no—
95#14273658C2×C414yescomplemented
96#14273658D414yescomplemented
97#14273648—22no—
98#14273648—41no—
99#14273648C2×C414yescomplemented
100#14273647—22no—
101#14273647—41no—
102#14273647C2×C414yescomplemented
103C22⋊(C59⋊C8)—22no—
104#14273638—22no—
105C4×C59⋊C8—22no—
106C59⋊#95—21no—
107C59⋊#95—21no—
108C22×D4×C59—21no—
109C22×D4×C59C2311yescharacteristic
110C23×C4×C59—21no—
111C23×C4×C59—21no—
112C23×C4×C59C2311yescharacteristic
113#121×C59—22no—
114#121×C59C2×C414yescomplemented
115C4×D4×C59—22no—
116C4×D4×C59—41no—
117C4×D4×C59—44no—
118C2×C4⋊C4×C59—22no—
119C2×C4⋊C4×C59—21no—
120C2×C4⋊C4×C59—21no—
121C2×C4⋊C4×C59—41no—
122C2×C4⋊C4×C59C2311yescharacteristic
123C2×C4⋊C4×C59C2311yescharacteristic
124C2×C4⋊C4×C59C2311yescharacteristic
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59—21no—
127C2×C22⋊C4×C59—21no—
128C2×C22⋊C4×C59—21no—
129C2×C22⋊C4×C59D411yescharacteristic
130C2×C22⋊C4×C59D411yescharacteristic
131C2×C42×C59—21no—
132C2×C42×C59C2311yescharacteristic
133C2×C42×C59C2311yescharacteristic
134#95×C59—21no—
135#95×C59—21no—
136#95×C59D411yescharacteristic
137#95×C59D411yescharacteristic
138C24×C59—21no—
139C24×C59C2×D411yescharacteristic
140C23×D59—21no—
141C2×D4×C59—24no—
142C2×D4×C59—21no—
143C2×D4×C59—21no—
144C2×D4×C59—21no—
145C2×D4×C59—21no—
146C2×D4×C59—21no—
147C2×D4×C59—42no—
148C2×D4×C59—42no—
149C2×D4×C59C22×C412yes—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—42no—
158C22×C4×C59—42no—
159C22×C4×C59—42no—
160C22×C4×C59—42no—
161C22×C4×C59—81no—
162C22×C4×C59—81no—
163C22×C4×C59C22×C412yes—
164C22×C4×C59C2×D411yescharacteristic
165C22×C4×C59C2×D411yescharacteristic
166C22×C4×C59C2×D411yescharacteristic
167C22×C4×C59C2×D411yescharacteristic
168C22×C4×C59C2×D411yescharacteristic
169C22×C4×C59#4112yes—
170C22×C4×C59C2411yescharacteristic
171C2×C22⋊D59—24no—
172C2×C22⋊D59—81no—
173C2×C22⋊D59—81no—
174C22×Dic59—21no—
175C22×Dic59—21no—
176C22×Dic59—21no—
177C2×D236—21no—
178C2×D236—21no—
179C2×D236—21no—
180C2×D236—21no—
181C2×D236—21no—
182C2×D236C22×C412yes—
183C2×C4×D59—42no—
184C2×C4×D59—42no—
185C2×C4×D59—81no—
186C4⋊C4×C59—21no—
187C4⋊C4×C59—21no—
188C4⋊C4×C59—21no—
189C4⋊C4×C59—21no—
190C4⋊C4×C59—42no—
191C4⋊C4×C59—42no—
192C4⋊C4×C59C22×C412yes—
193C4⋊C4×C59C2×D412yes—
194C22⋊C4×C59—24no—
195C22⋊C4×C59—22no—
196C22⋊C4×C59—41no—
197C22⋊C4×C59—42no—
198C22⋊C4×C59—42no—
199C22⋊C4×C59—81no—
200C42×C59—21no—
201C42×C59—21no—
202C42×C59—21no—
203C42×C59—21no—
204C42×C59—42no—
205C22⋊Dic59—42no—
206#11745669—28no—
207(C2×D59)⋊C4—24no—
208(C2×D59)⋊C4—42no—
209(C2×D59)⋊C4—42no—
210(C2×D59)⋊C4—81no—
211C4⋊Dic59—21no—
212C4⋊Dic59—21no—
213C4⋊Dic59—21no—
214C4⋊Dic59—21no—
215C4⋊Dic59C22×C412yes—
216C4⋊Dic59C2×D412yes—
217Dic59⋊C4—81no—
218C4×Dic59—42no—
219C4×Dic59—81no—
220#11745664—28no—
221C2×C59⋊C8—21no—
222C2×C59⋊C8—21no—
223C2×C59⋊C8—21no—
224C2×C59⋊C8—21no—
225C2×C59⋊C8—21no—
226C2×C59⋊C8—21no—
227C2×C59⋊C8—21no—
228C2×C59⋊C8—21no—
229C2×C59⋊C8C22×C412yes—
230C2×C59⋊C8C22×C412yes—
231C2×C59⋊C8C2×D412yes—
232C2×C59⋊C8#4112yes—
233C23×C59—21no—
234C23×C59—21no—
235C23×C59—21no—
236C23×C59—21no—
237C23×C59—21no—
238C23×C59—21no—
239C23×C59—22no—
240C23×C59—41no—
241C23×C59—41no—
242C23×C59—41no—
243C23×C59—41no—
244C23×C59—41no—
245C23×C59—41no—
246C23×C59C4×D412yes—
247C23×C59C22×D411yescharacteristic
248C22×D59—22no—
249C22×D59—41no—
250C22×D59—41no—
251C22×D59—41no—
252C22×D59—41no—
253C22×D59—41no—
254C22×D59—41no—
255D4×C59—22no—
256D4×C59—22no—
257D4×C59—48no—
258D4×C59—41no—
259D4×C59—41no—
260C2×C4×C59—21no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—21no—
264C2×C4×C59—22no—
265C2×C4×C59—22no—
266C2×C4×C59—22no—
267C2×C4×C59—22no—
268C2×C4×C59—22no—
269C2×C4×C59—21no—
270C2×C4×C59—21no—
271C2×C4×C59—22no—
272C2×C4×C59—21no—
273C2×C4×C59—21no—
274C2×C4×C59—21no—
275C2×C4×C59—21no—
276C2×C4×C59—21no—
277C2×C4×C59—21no—
278C2×C4×C59—21no—
279C2×C4×C59—41no—
280C2×C4×C59—41no—
281C2×C4×C59—41no—
282C2×C4×C59—41no—
283C2×C4×C59—41no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59—84no—
287C2×C4×C59—84no—
288C2×C4×C59C4×D412yes—
289C2×C4×C59AGL(1,ℤ/8)12yes—
290C2×C4×C59C23×C411yescharacteristic
291C2×C4×C59C22×D411yescharacteristic
292C2×C4×C59C2×#4111yescharacteristic
293C2×C4×C59C2×#4111yescharacteristic
294C2×C4×C59H(5,𝔽2)11yescharacteristic
295C2×C4×C592−1+411yescharacteristic
296C22⋊D59—84no—
297C2×Dic59—22no—
298C2×Dic59—22no—
299C2×Dic59—41no—
300C2×Dic59—41no—
301C2×Dic59—41no—
302C2×Dic59—41no—
303C2×Dic59—41no—
304C2×Dic59—41no—
305C2×Dic59—41no—
306D236—22no—
307D236—22no—
308D236—41no—
309D236—41no—
310C4×D59—84no—
311C59⋊C8—22no—
312C59⋊C8—41no—
313C59⋊C8—41no—
314C59⋊C8C4×D414yescomplemented
315#23039—591nomaximal, Sylow
316C22×C59—22no—
317C22×C59—22no—
318C22×C59—22no—
319C22×C59—41no—
320C22×C59—41no—
321C22×C59—41no—
322C22×C59—41no—
323C22×C59—42no—
324C22×C59—42no—
325C22×C59—42no—
326C22×C59—81no—
327C22×C59—81no—
328C22×C59—81no—
329C22×C59—81no—
330C22×C59C2×C4×D411yescharacteristic
331C22×C59D4211yescharacteristic
332C22×C59#54711yescharacteristic
333C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
334C22×C59#57511yescharacteristic
335C22×C59#57611yescharacteristic
336C22×C59#57711yescharacteristic
337C2×D59—42no—
338C2×D59—42no—
339C2×D59—42no—
340C2×D59—81no—
341C2×D59—81no—
342C2×D59—81no—
343C2×D59—81no—
344C4×C59—22no—
345C4×C59—22no—
346C4×C59—41no—
347C4×C59—42no—
348C4×C59—41no—
349C4×C59—42no—
350C4×C59—41no—
351C4×C59—81no—
352C4×C59C2×C4×D411yescharacteristic
353C4×C59#52011yescharacteristic
354C4×C59#54811yescharacteristic
355C4×C59#55311yescharacteristic
356Dic59—42no—
357Dic59—42no—
358Dic59—81no—
359C2×#469—591no—
360C2×#442—591no—
361C2×#428—591no—
362#2363—591no—
363#2361D5911yescharacteristic, complemented
364#1970—591no—
365#1944—591no—
366#1926—591no—
367#1925—591no—
368#1875—591no—
369#1874—591no—
370#1864—591no—
371#1862—591no—
372C4×#106—591no—
373#1753—591no—
374C2×C59—42no—
375C2×C59—82no—
376C2×C59#236111yescharacteristic
377C2×C59C4×AGL(1,ℤ/8)11yescharacteristic
378C2×C59#294611yescharacteristic
379C2×C59#327411yescharacteristic
380C2×C59#327511yescharacteristic
381C2×C59#334511yescharacteristic
382C2×C59#334711yescharacteristic
383D59—82no—
384C22×D8—591no—
385C22×M16—591no—
386C2×#121—591no—
387C2×#121C2×D5911yescharacteristic
388C2×C4×D4—21no—
389C2×C4×D4—591no—
390C2×C4×D4C2×D5911yescharacteristic
391C2×#117—591no—
392C22×C4⋊C4C2×D5911yescharacteristic
393#469—598no—
394#442—1184no—
395#428—1184no—
396C2×#107—591no—
397C2×#107—591no—
398C2×#106—591no—
399C2×#106—591no—
400C2×#106—591no—
401C2×#102—591no—
402C2×#102—591no—
403C2×#102—591no—
404C2×#102—591no—
405C2×#102—591no—
406C2×#102—591no—
407C2×C22⋊C8—591no—
408C2×#97—591no—
409C2×C4×C8—591no—
410#390—591no—
411#390—1181no—
412#390C2×D5911yescharacteristic
413#389—591no—
414#389C2×D5911yescharacteristic
415#388—21no—
416#388—1181no—
417#386—21no—
418#386—1181no—
419#385—21no—
420C4×C4⋊C4—591no—
421C4×C4⋊C4C2×D5911yescharacteristic
422C4×C22⋊C4—1181no—
423C4×C22⋊C4C2×D5911yescharacteristic
424#340—591no—
425#340—591no—
426#340—591no—
427#340—591no—
428#336—591no—
429#336—591no—
430C59#2303911yescharacteristic, complemented, Sylow
431C22×D4—21no—
432C22×D4—591no—
433C22×D4—1181no—
434C22×D4C22×D5911yescharacteristic
435C23×C4—21no—
436C23×C4—21no—
437C23×C4—1181no—
438C23×C4C22×D5911yescharacteristic
439C2×D8—594no—
440C2×D8—1182no—
441C2×D8—1182no—
442C2×M16—594no—
443C2×M16—1182no—
444C2×M16—1182no—
445C22×C8—591no—
446C22×C8—591no—
447C22×C8—591no—
448C22×C8—591no—
449#121—22no—
450#121—594no—
451#121—1182no—
452#121C4×D5914yescomplemented
453C4×D4—22no—
454C4×D4—41no—
455C4×D4—44no—
456C4×D4—1182no—
457C4×D4—2361no—
458#117—1182no—
459#117—2361no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—41no—
464C2×C4⋊C4—591no—
465C2×C4⋊C4—591no—
466C2×C4⋊C4—591no—
467C2×C4⋊C4—1181no—
468C2×C4⋊C4C22×D5911yescharacteristic
469C2×C4⋊C4C22×D5911yescharacteristic
470C2×C4⋊C4C22×D5911yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—1181no—
476C2×C22⋊C4—1181no—
477C2×C22⋊C4—1181no—
478C2×C22⋊C4—1181no—
479C2×C22⋊C4—1181no—
480C2×C22⋊C4C22⋊D5911yescharacteristic
481C2×C22⋊C4C22⋊D5911yescharacteristic
482C2×C42—21no—
483C2×C42—1181no—
484C2×C42—1181no—
485C2×C42C22×D5911yescharacteristic
486C2×C42C22×D5911yescharacteristic
487#107—1182no—
488#107—1182no—
489#106—594no—
490#106—594no—
491#106—1182no—
492#102—594no—
493#102—594no—
494#102—1182no—
495#102—1182no—
496#102—2361no—
497#102—2361no—
498C22⋊C8—1182no—
499#97—1182no—
500C4×C8—1182no—
501#95—21no—
502#95—21no—
503#95—1181no—
504#95—1181no—
505#95C22⋊D5911yescharacteristic
506#95C22⋊D5911yescharacteristic
507C24—21no—
508C24—1181no—
509C24C2×C22⋊D5911yescharacteristic
510C2×D4—24no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—592no—
519C2×D4—1184no—
520C2×D4—1181no—
521C2×D4—1181no—
522C2×D4—1181no—
523C2×D4—1181no—
524C2×D4—1181no—
525C2×D4—4721no—
526C2×D4—4721no—
527C2×D4C2×C4×D5912yes—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—81no—
540C22×C4—81no—
541C22×C4—1181no—
542C22×C4—1181no—
543C22×C4—1181no—
544C22×C4—4721no—
545C22×C4—2362no—
546C22×C4—2362no—
547C22×C4C2×C4×D5912yes—
548C22×C4#1174568512yes—
549C22×C4C2×C22⋊D5911yescharacteristic
550C22×C4C2×C22⋊D5911yescharacteristic
551C22×C4C2×C22⋊D5911yescharacteristic
552C22×C4C2×C22⋊D5911yescharacteristic
553C22×C4C2×C22⋊D5911yescharacteristic
554C22×C4C23×D5911yescharacteristic
555D8—1188no—
556M16—1188no—
557C2×C8—592no—
558C2×C8—592no—
559C2×C8—592no—
560C2×C8—592no—
561C2×C8—1181no—
562C2×C8—1181no—
563C2×C8—1181no—
564C2×C8—1181no—
565C2×C8—1181no—
566C2×C8—1181no—
567C2×C8—1181no—
568C2×C8—1181no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—592no—
576C4⋊C4—592no—
577C4⋊C4—1181no—
578C4⋊C4—1181no—
579C4⋊C4—1181no—
580C4⋊C4—1181no—
581C4⋊C4—4721no—
582C4⋊C4C2×C4×D5912yes—
583C4⋊C4D4×D5912yes—
584C22⋊C4—24no—
585C22⋊C4—22no—
586C22⋊C4—41no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—81no—
590C22⋊C4—1184no—
591C22⋊C4—4721no—
592C22⋊C4—2362no—
593C22⋊C4—2362no—
594C22⋊C4—2362no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—42no—
600C42—4721no—
601C42—2362no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—22no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—1182no—
616C23—2361no—
617C23—2361no—
618C23—2361no—
619C23—2361no—
620C23—2361no—
621C23—2361no—
622C23C4×C22⋊D5912yes—
623C23C22×C22⋊D5911yescharacteristic
624D4—22no—
625D4—22no—
626D4—48no—
627D4—41no—
628D4—41no—
629D4—1182no—
630D4—1182no—
631D4—4724no—
632D4—2361no—
633D4—2361no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—84no—
661C2×C4—84no—
662C2×C4—1182no—
663C2×C4—1182no—
664C2×C4—4724no—
665C2×C4—2361no—
666C2×C4—2361no—
667C2×C4—2361no—
668C2×C4—2361no—
669C2×C4—2361no—
670C2×C4—2361no—
671C2×C4—2361no—
672C2×C4C4×C22⋊D5912yes—
673C2×C4#1427375312yes—
674C2×C4C22×C4×D5911yescharacteristic
675C2×C4C2×D4×D5911yescharacteristic
676C2×C4#41×D5911yescharacteristic
677C2×C4C2×#1174568511yescharacteristic
678C2×C4#1427377211yescharacteristic
679C2×C4#1427377411yescharacteristic
680C8—594no—
681C8—1182no—
682C8—2361no—
683C8—2361no—
684C22—22no—
685C22—22no—
686C22—22no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22—81no—
698C22—4721no—
699C22—4721no—
700C22—4721no—
701C22—4721no—
702C22—2362no—
703C22—2362no—
704C22—2362no—
705C22C2×C4×C22⋊D5911yescharacteristic
706C22D4×C22⋊D5911yescharacteristic
707C22#1683805111yescharacteristic
708C22C2×#1427375311yescharacteristic
709C22#1683820011yescharacteristic
710C22#1683820511yescharacteristic
711C22#1683821011yescharacteristic
712C4—22no—
713C4—22no—
714C4—41no—
715C4—42no—
716C4—42no—
717C4—41no—
718C4—41no—
719C4—81no—
720C4—4721no—
721C4—2362no—
722C4—2362no—
723C4C4×D4×D5911yescharacteristic
724C4#1683788111yescharacteristic
725C4#1683806111yescharacteristic
726C4#1683810111yescharacteristic
727C2—42no—
728C2—82no—
729C2—4722no—
730C2#2142711311yescharacteristic
731C2C4×#1427375311yescharacteristic
732C2#2143292411yescharacteristic
733C2#2143571211yescharacteristic
734C2#2143572811yescharacteristic
735C2#2143656611yescharacteristic
736C2#2143659011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2361C2
socleC23×C59C22×D4
prime radicalC2×#16837653C2
cosocleC22×C4×C59C24
hypercenter#2361D59
hypocenterC59#23039
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
2. C2×#16837512C2semidirect
3. C2×#16837442C2semidirect
4. #21427132C2semidirect
5. #21424961C2semidirect
6. #21424836C2semidirect
7. #21424720C2semidirect
8. #21424716C2semidirect
9. #21424419C2semidirect
10. #21424413C2semidirect
11. #21424356C2semidirect
12. #21424343C2semidirect
13. C4×#14273658C2semidirect
14. #21423880C2semidirect
15. C59×#2361C2semidirect
21. #16837653C4semidirect
67. C2×#11745669C2×C4semidirect
70. C2×#11745664C2×C4semidirect
76. #14273701C2×C4semidirect
95. #14273658C2×C4semidirect
96. #14273658D4semidirect
99. #14273648C2×C4semidirect
102. #14273647C2×C4semidirect
114. #121×C59C2×C4semidirect
314. C59⋊C8C4×D4semidirect
363. #2361D59semidirect
430. C59#23039semidirect
452. #121C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168376532
C2×#168375122
C2×#168374422
#214271322
#214249612
#214248362
#214247202
#214247162
#214244192
#214244132
#214243562
#214243432
C4×#142736582
#214238802
C59×#23612
#2303959