Finite Group Databasebeta

← #28636838

Subgroups — #28636838

Order 15104.

1024 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837715C211yesmaximal, characteristic, complemented
2C2×#16837636C211yesmaximal, characteristic
3#21427110C211yesmaximal, characteristic, complemented
4#21425568C211yesmaximal, characteristic, complemented
5#21425500C211yesmaximal, characteristic, complemented
6#21425484C211yesmaximal, characteristic, complemented
7#21425406C211yesmaximal, characteristic, complemented
8#21424852C211yesmaximal, characteristic, complemented
9#21424713C211yesmaximal, characteristic, complemented
10#21424447C211yesmaximal, characteristic, complemented
11#21424414C211yesmaximal, characteristic, complemented
12#21424276C211yesmaximal, characteristic, complemented
13#21424093C211yesmaximal, characteristic, complemented
14C2×#16837164C211yesmaximal, characteristic, complemented
15C59×#2501C211yesmaximal, characteristic, complemented
16C22×#11745669C2211yescharacteristic
17C23×C59⋊C8C2211yescharacteristic
18C2×#14273701C2211yescharacteristic
19C2×C4×D236C2211yescharacteristic
20C2×(C22⋊D59)⋊C4—21no—
21C22×C4⋊Dic59C2211yescharacteristic
22#16837715—24no—
23#16837636—24no—
24C2×#14273660C2211yescharacteristic
25C2×#14273660C2211yescharacteristic
26C2×#14273660C2211yescharacteristic
27C2×C4⋊(C59⋊C8)C2211yescharacteristic
28C2×C4⋊(C59⋊C8)C2211yescharacteristic
29C2×#14273648C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×#14273648C2211yescharacteristic
32C2×#14273647C2211yescharacteristic
33C2×#14273647C2211yescharacteristic
34C2×#14273647C2211yescharacteristic
35C2×C22⋊(C59⋊C8)C2211yescharacteristic
36#16837304C2211yescharacteristic
37#16837300C2211yescharacteristic
38#16837294—21no—
39#16837279—21no—
40#16837276—21no—
41C4×C4⋊Dic59C2211yescharacteristic
42#16837164C2211yescharacteristic
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837157C2211yescharacteristic
49#16837157C2211yescharacteristic
50C2×#123×C59—21no—
51C2×#123×C59—21no—
52C2×#121×C59C2211yescharacteristic
53C22×C4⋊C4×C59C2211yescharacteristic
54C59×#399—21no—
55C59×#399—21no—
56C59×#390C2211yescharacteristic
57C59×#390C2211yescharacteristic
58C59×#384C2211yescharacteristic
59C59×#384C2211yescharacteristic
60C4×C22⋊C4×C59C2211yescharacteristic
61C22×D236C2311yescharacteristic
62C22×C22⋊D59—21no—
63C23×Dic59—21no—
64C22×C4×D59—21no—
65C2×#11745669—22no—
66C2×#11745669—22no—
67C2×#11745669—41no—
68C22×C59⋊C8—22no—
69C22×C59⋊C8—22no—
70C22×C59⋊C8—41no—
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74C22×C59⋊C8C2311yescharacteristic
75#14273701—22no—
76#14273701D414yes—
77C4×D236—22no—
78C4×D236—41no—
79(C22⋊D59)⋊C4—44no—
80C2×C4⋊Dic59—22no—
81C2×C4⋊Dic59—21no—
82C2×C4⋊Dic59—41no—
83C2×C4⋊Dic59C2311yescharacteristic
84C2×C4⋊Dic59C2311yescharacteristic
85C2×C4⋊Dic59C2311yescharacteristic
86C2×Dic59⋊C4—21no—
87C2×(C2×D59)⋊C4—21no—
88C2×(C2×D59)⋊C4—21no—
89C2×(C2×D59)⋊C4—21no—
90C2×(C2×D59)⋊C4—21no—
91C2×C4×Dic59—21no—
92#14273660—22no—
93#14273660—22no—
94#14273660—22no—
95C4⋊(C59⋊C8)—22no—
96C4⋊(C59⋊C8)—41no—
97#14273648—22no—
98#14273648—22no—
99#14273648—41no—
100#14273647—22no—
101#14273647—22no—
102#14273647—22no—
103C22⋊(C59⋊C8)—22no—
104C59⋊#95—21no—
105C59⋊#95—21no—
106C22×D4×C59—21no—
107C22×D4×C59C2311yescharacteristic
108C23×C4×C59—21no—
109C23×C4×C59C2311yescharacteristic
110#123×C59—44no—
111#123×C59—44no—
112#121×C59—22no—
113#121×C59—22no—
114C2×C4⋊C4×C59—22no—
115C2×C4⋊C4×C59—22no—
116C2×C4⋊C4×C59—21no—
117C2×C4⋊C4×C59—21no—
118C2×C4⋊C4×C59—21no—
119C2×C4⋊C4×C59—21no—
120C2×C4⋊C4×C59—21no—
121C2×C4⋊C4×C59C2311yescharacteristic
122C2×C4⋊C4×C59C2311yescharacteristic
123C2×C4⋊C4×C59C2311yescharacteristic
124C2×C22⋊C4×C59—21no—
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×C59C2311yescharacteristic
132C2×C42×C59C2311yescharacteristic
133#95×C59D411yescharacteristic
134#95×C59D411yescharacteristic
135C24×C59—21no—
136C24×C59C2×D411yescharacteristic
137C23×D59—21no—
138C2×D4×C59—21no—
139C2×D4×C59—21no—
140C2×D4×C59—21no—
141C2×D4×C59—21no—
142C2×D4×C59—21no—
143C2×D4×C59—21no—
144C2×D4×C59—42no—
145C2×D4×C59—42no—
146C2×D4×C59—42no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—42no—
155C22×C4×C59—42no—
156C22×C4×C59—42no—
157C22×C4×C59C2×D411yescharacteristic
158C22×C4×C59C2×D411yescharacteristic
159C22×C4×C59C2×D411yescharacteristic
160C22×C4×C59C2×D412yes—
161C22×C4×C59C2×D411yescharacteristic
162C22×C4×C59C2×D411yescharacteristic
163C22×C4×C59#4112yes—
164C22×C4×C59C2411yescharacteristic
165C2×C22⋊D59—24no—
166C2×C22⋊D59—42no—
167C2×C22⋊D59—42no—
168C22×Dic59—21no—
169C22×Dic59—21no—
170C22×Dic59—21no—
171C22×Dic59—42no—
172C22×Dic59—42no—
173C22×Dic59—81no—
174C2×D236—21no—
175C2×D236—21no—
176C2×D236—21no—
177C2×D236—21no—
178C2×D236—21no—
179C2×D236C2×D412yes—
180C2×C4×D59—42no—
181C2×C4×D59—42no—
182C2×C4×D59—81no—
183C4⋊C4×C59—21no—
184C4⋊C4×C59—21no—
185C4⋊C4×C59—21no—
186C4⋊C4×C59—21no—
187C4⋊C4×C59—21no—
188C4⋊C4×C59—21no—
189C4⋊C4×C59—42no—
190C4⋊C4×C59—42no—
191C4⋊C4×C59—42no—
192C4⋊C4×C59—42no—
193C4⋊C4×C59—42no—
194C22⋊C4×C59—22no—
195C22⋊C4×C59—42no—
196C22⋊C4×C59—42no—
197C22⋊C4×C59—42no—
198C22⋊C4×C59—42no—
199C22⋊C4×C59—42no—
200C22⋊C4×C59D814yescomplemented
201C42×C59—21no—
202C42×C59—21no—
203C42×C59—21no—
204C42×C59—21no—
205#11745669—44no—
206(C2×D59)⋊C4—24no—
207(C2×D59)⋊C4—42no—
208(C2×D59)⋊C4—42no—
209(C2×D59)⋊C4—81no—
210C4⋊Dic59—21no—
211C4⋊Dic59—21no—
212C4⋊Dic59—21no—
213C4⋊Dic59—21no—
214C4⋊Dic59—42no—
215C4⋊Dic59C2×D412yes—
216C4⋊Dic59#4112yes—
217Dic59⋊C4—42no—
218C4×Dic59—42no—
219C2×C59⋊C8—21no—
220C2×C59⋊C8—21no—
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⋊C8—21no—
230C2×C59⋊C8—44no—
231C2×C59⋊C8#4112yes—
232C23×C59—21no—
233C23×C59—21no—
234C23×C59—21no—
235C23×C59—21no—
236C23×C59—41no—
237C23×C59—41no—
238C23×C59—41no—
239C23×C59—41no—
240C23×C59—41no—
241C23×C59—41no—
242C23×C59—41no—
243C23×C59#12112yes—
244C23×C59C2×D812yes—
245C23×C59AGL(1,ℤ/8)12yes—
246C23×C59C22×D411yescharacteristic
247C22×D59—22no—
248C22×D59—41no—
249C22×D59—41no—
250C22×D59—41no—
251C22×D59—41no—
252C22×D59—41no—
253C22×D59—41no—
254D4×C59—41no—
255D4×C59—41no—
256D4×C59—41no—
257D4×C59—41no—
258D4×C59—84no—
259C2×C4×C59—21no—
260C2×C4×C59—21no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—21no—
264C2×C4×C59—21no—
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—21no—
272C2×C4×C59—21no—
273C2×C4×C59—21no—
274C2×C4×C59—21no—
275C2×C4×C59—41no—
276C2×C4×C59—41no—
277C2×C4×C59—41no—
278C2×C4×C59—41no—
279C2×C4×C59—41no—
280C2×C4×C59—41no—
281C2×C4×C59—41no—
282C2×C4×C59—41no—
283C2×C4×C59—41no—
284C2×C4×C59—84no—
285C2×C4×C59#12112yes—
286C2×C4×C59C2×D812yes—
287C2×C4×C59C2×D812yes—
288C2×C4×C59C22×D411yescharacteristic
289C2×C4×C59C2×#4111yescharacteristic
290C2×C4×C59C2×#4111yescharacteristic
291C2×C4×C59C2×#4111yescharacteristic
292C2×C4×C59H(5,𝔽2)11yescharacteristic
293C2×C4×C592−1+411yescharacteristic
294C22⋊D59—48no—
295C2×Dic59—22no—
296C2×Dic59—22no—
297C2×Dic59—41no—
298C2×Dic59—41no—
299C2×Dic59—41no—
300C2×Dic59—41no—
301C2×Dic59—41no—
302C2×Dic59—41no—
303C2×Dic59—41no—
304C2×Dic59—84no—
305D236—22no—
306D236—22no—
307D236—41no—
308D236—41no—
309C4×D59—84no—
310C59⋊C8—22no—
311C59⋊C8—41no—
312C59⋊C8—41no—
313C59⋊C8—41no—
314#25200—591nomaximal, Sylow
315C22×C59—22no—
316C22×C59—22no—
317C22×C59—22no—
318C22×C59—22no—
319C22×C59—22no—
320C22×C59—22no—
321C22×C59—81no—
322C22×C59—81no—
323C22×C59—81no—
324C22×C59—81no—
325C22×C59—81no—
326C22×C59—81no—
327C22×C59—81no—
328C22×C59#45914yes—
329C22×C59C2×#12111yescharacteristic
330C22×C59#54611yescharacteristic
331C22×C59#54711yescharacteristic
332C22×C59C22×D811yescharacteristic
333C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
334C22×C59#57711yescharacteristic
335C22×C59#57811yescharacteristic
336C2×D59—42no—
337C2×D59—42no—
338C2×D59—42no—
339C2×D59—81no—
340C2×D59—81no—
341C2×D59—81no—
342C2×D59—81no—
343C4×C59—22no—
344C4×C59—22no—
345C4×C59—22no—
346C4×C59—41no—
347C4×C59—41no—
348C4×C59—81no—
349C4×C59—81no—
350C4×C59—81no—
351C4×C59#52911yescharacteristic
352C4×C59#53911yescharacteristic
353C4×C59#54611yescharacteristic
354C4×C59#54711yescharacteristic
355Dic59—42no—
356Dic59—42no—
357Dic59—81no—
358C2×#480—591no—
359C2×#466—591no—
360#2501D5911yescharacteristic, complemented
361#2361—591no—
362#2083—591no—
363#2071—591no—
364#2067—591no—
365#2054—591no—
366#1947—591no—
367#1925—591no—
368#1879—591no—
369#1874—591no—
370#1850—591no—
371#1802—591no—
372C2×#340—591no—
373C2×C59—24no—
374C2×C59—161no—
375C2×C59#242511yescharacteristic
376C2×C59C2×#45911yescharacteristic
377C2×C59#304611yescharacteristic
378C2×C59#329411yescharacteristic
379C2×C59#330811yescharacteristic
380C2×C59#333411yescharacteristic
381C2×C59#334511yescharacteristic
382D59—82no—
383C22×D8—591no—
384C23×C8—591no—
385C2×#123—21no—
386C2×#123—21no—
387C2×#121—591no—
388C2×#121C2×D5911yescharacteristic
389C2×C4×D4—591no—
390C2×C4×D4—1181no—
391C22×C4⋊C4—591no—
392C22×C4⋊C4C2×D5911yescharacteristic
393#480—1184no—
394#466—1184no—
395C2×#107—591no—
396C2×#107—591no—
397C2×#107—591no—
398C2×C4⋊C8—591no—
399C2×C4⋊C8—591no—
400C2×#102—591no—
401C2×#102—591no—
402C2×#102—591no—
403C2×#102—591no—
404C2×#102—591no—
405C2×#102—591no—
406C2×C22⋊C8—591no—
407#399—21no—
408#399—21no—
409#390—591no—
410#390C2×D5911yescharacteristic
411#390C2×D5911yescharacteristic
412#389—591no—
413#388—1181no—
414#386—1181no—
415#385—1181no—
416#384C2×D5911yescharacteristic
417#384C2×D5911yescharacteristic
418C4×C4⋊C4—591no—
419C4×C22⋊C4C2×D5911yescharacteristic
420#340—591no—
421#340—591no—
422#340—591no—
423#340—591no—
424#340—591no—
425#340—591no—
426#336—591no—
427#336—591no—
428C59#2520011yescharacteristic, complemented, Sylow
429C22×D4—21no—
430C22×D4—591no—
431C22×D4—1181no—
432C22×D4C22×D5911yescharacteristic
433C23×C4—21no—
434C23×C4—1181no—
435C23×C4—1181no—
436C23×C4C22×D5911yescharacteristic
437C2×D8—1182no—
438C2×D8—1182no—
439C2×D8—2361no—
440C22×C8—591no—
441C22×C8—591no—
442C22×C8—591no—
443C22×C8—591no—
444C22×C8—1182no—
445C22×C8—1182no—
446C22×C8—2361no—
447#123—44no—
448#123—44no—
449#121—22no—
450#121—22no—
451#121—594no—
452#121—1182no—
453C4×D4—1182no—
454C4×D4—2361no—
455C4×D4—2364no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—591no—
464C2×C4⋊C4—591no—
465C2×C4⋊C4—591no—
466C2×C4⋊C4—1182no—
467C2×C4⋊C4—1181no—
468C2×C4⋊C4—1181no—
469C2×C4⋊C4—2361no—
470C2×C4⋊C4C22×D5911yescharacteristic
471C2×C4⋊C4C22×D5911yescharacteristic
472C2×C4⋊C4C22×D5911yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—1181no—
479C2×C22⋊C4—1181no—
480C2×C22⋊C4—1181no—
481C2×C22⋊C4—1181no—
482C2×C22⋊C4C22⋊D5911yescharacteristic
483C2×C22⋊C4C22⋊D5911yescharacteristic
484C2×C42—1181no—
485C2×C42C22×D5911yescharacteristic
486C2×C42C22×D5911yescharacteristic
487#107—1182no—
488#107—1182no—
489#107—1182no—
490C4⋊C8—1182no—
491C4⋊C8—2361no—
492#102—1182no—
493#102—1182no—
494#102—1182no—
495#102—1182no—
496#102—1182no—
497#102—2361no—
498C22⋊C8—1182no—
499#95—1181no—
500#95—1181no—
501#95C22⋊D5911yescharacteristic
502#95C22⋊D5911yescharacteristic
503C24—21no—
504C24—1181no—
505C24C2×C22⋊D5911yescharacteristic
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—592no—
516C2×D4—1184no—
517C2×D4—1181no—
518C2×D4—1181no—
519C2×D4—1181no—
520C2×D4—1181no—
521C2×D4—1181no—
522C2×D4—2362no—
523C2×D4—2362no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—1181no—
535C22×C4—1181no—
536C22×C4—1181no—
537C22×C4—4721no—
538C22×C4—4721no—
539C22×C4—2362no—
540C22×C4—2362no—
541C22×C4—2362no—
542C22×C4—2362no—
543C22×C4D4×D5912yes—
544C22×C4#1174568712yes—
545C22×C4C2×C22⋊D5911yescharacteristic
546C22×C4C2×C22⋊D5911yescharacteristic
547C22×C4C2×C22⋊D5911yescharacteristic
548C22×C4C2×C22⋊D5911yescharacteristic
549C22×C4C2×C22⋊D5911yescharacteristic
550C22×C4C23×D5911yescharacteristic
551D8—2364no—
552C2×C8—592no—
553C2×C8—1181no—
554C2×C8—1181no—
555C2×C8—1181no—
556C2×C8—1181no—
557C2×C8—1181no—
558C2×C8—1181no—
559C2×C8—1181no—
560C2×C8—1181no—
561C2×C8—1181no—
562C2×C8—1181no—
563C2×C8—1181no—
564C2×C8—2364no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—592no—
577C4⋊C4—592no—
578C4⋊C4—1181no—
579C4⋊C4—1181no—
580C4⋊C4—1181no—
581C4⋊C4—1181no—
582C4⋊C4—2362no—
583C4⋊C4—2362no—
584C22⋊C4—22no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—1184no—
591C22⋊C4—4721no—
592C22⋊C4—2362no—
593C22⋊C4—2362no—
594C22⋊C4#1174566914yescomplemented
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—2362no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—1182no—
612C23—2361no—
613C23—2361no—
614C23—2361no—
615C23—2361no—
616C23—2361no—
617C23—2361no—
618C23#1427369812yes—
619C23C2×#1174566912yes—
620C23#1427375312yes—
621C23C22×C22⋊D5911yescharacteristic
622D4—41no—
623D4—41no—
624D4—41no—
625D4—41no—
626D4—84no—
627D4—1182no—
628D4—1182no—
629D4—2368no—
630D4—2361no—
631D4—2361no—
632C2×C4—21no—
633C2×C4—21no—
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—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—84no—
658C2×C4—1182no—
659C2×C4—1182no—
660C2×C4—4724no—
661C2×C4—4724no—
662C2×C4—2361no—
663C2×C4—2361no—
664C2×C4—2361no—
665C2×C4—2361no—
666C2×C4—2361no—
667C2×C4—2361no—
668C2×C4—2361no—
669C2×C4#1427369812yes—
670C2×C4C2×#1174566912yes—
671C2×C4C2×#1174566912yes—
672C2×C4C2×D4×D5911yescharacteristic
673C2×C4#41×D5911yescharacteristic
674C2×C4#41×D5911yescharacteristic
675C2×C4C2×#1174568711yescharacteristic
676C2×C4#1427377311yescharacteristic
677C2×C4#1427377411yescharacteristic
678C8—1182no—
679C8—2361no—
680C8—2361no—
681C8—2361no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22—4721no—
696C22—4721no—
697C22—4721no—
698C22—4721no—
699C22—2362no—
700C22—2362no—
701C22—2362no—
702C22#1683759414yes—
703C22C2×#1427369811yescharacteristic
704C22#1683804011yescharacteristic
705C22#1683805111yescharacteristic
706C22C22×#1174566911yescharacteristic
707C22C2×#1427375311yescharacteristic
708C22#1683821011yescharacteristic
709C22#1683821711yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—41no—
714C4—41no—
715C4—81no—
716C4—81no—
717C4—81no—
718C4—4721no—
719C4—2362no—
720C4—2362no—
721C4#1683792911yescharacteristic
722C4#1683799611yescharacteristic
723C4#1683804411yescharacteristic
724C4#1683805011yescharacteristic
725C2—24no—
726C2—161no—
727C2—4722no—
728C2#2142764311yescharacteristic
729C2C2×#1683759411yescharacteristic
730C2#2143364211yescharacteristic
731C2#2143590311yescharacteristic
732C2#2143608111yescharacteristic
733C2#2143643911yescharacteristic
734C2#2143656611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2501C2
socleC23×C59C22×D4
prime radicalC2×#16837636C2
hypercenter#2501D59
hypocenterC59#25200
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2501

Complements

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

NH ≅ G/Ntype
1. C2×#16837715C2semidirect
3. #21427110C2semidirect
4. #21425568C2semidirect
5. #21425500C2semidirect
6. #21425484C2semidirect
7. #21425406C2semidirect
8. #21424852C2semidirect
9. #21424713C2semidirect
10. #21424447C2semidirect
11. #21424414C2semidirect
12. #21424276C2semidirect
13. #21424093C2semidirect
14. C2×#16837164C2semidirect
15. C59×#2501C2semidirect
200. C22⋊C4×C59D8semidirect
360. #2501D59semidirect
428. C59#25200semidirect
594. C22⋊C4#11745669semidirect

Maximal subgroups

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

subgroupindex
C2×#168377152
C2×#168376362
#214271102
#214255682
#214255002
#214254842
#214254062
#214248522
#214247132
#214244472
#214244142
#214242762
#214240932
C2×#168371642
C59×#25012
#2520059