Finite Group Databasebeta

← #28634246

Subgroups — #28634246

Order 15104.

948 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837720C211yesmaximal, characteristic, complemented
2C2×#16837715C211yesmaximal, characteristic, complemented
3#21428997C211yesmaximal, characteristic
4#21425532C211yesmaximal, characteristic, complemented
5#21425527C211yesmaximal, characteristic, complemented
6#21425285C211yesmaximal, characteristic, complemented
7#21425278C211yesmaximal, characteristic, complemented
8#21424895C211yesmaximal, characteristic, complemented
9#21424864C211yesmaximal, characteristic, complemented
10#21424289C211yesmaximal, characteristic, complemented
11#21424284C211yesmaximal, characteristic, complemented
12#21424262C211yesmaximal, characteristic, complemented
13#21424093C211yesmaximal, characteristic, complemented
14#21423924C211yesmaximal, characteristic, complemented
15D4×C4⋊C4×C59C211yesmaximal, characteristic, complemented
16C2×#14273701C2211yescharacteristic
17C2×#14273701C2211yescharacteristic
18C2×C4×D236C2211yescharacteristic
19#16837720—24no—
20#16837715—24no—
21C2×#14273660C2211yescharacteristic
22C2×#14273660C2211yescharacteristic
23C2×#14273660C2211yescharacteristic
24C2×#14273658C2211yescharacteristic
25C2×#14273658C2211yescharacteristic
26C2×#14273658C2211yescharacteristic
27C2×C4⋊(C59⋊C8)C2211yescharacteristic
28C2×#14273647C2211yescharacteristic
29C2×#14273647C2211yescharacteristic
30C2×#14273647C2211yescharacteristic
31C2×#14273647C2211yescharacteristic
32C2×C22⋊(C59⋊C8)C2211yescharacteristic
33C2×C22⋊(C59⋊C8)C2211yescharacteristic
34C2×C22⋊(C59⋊C8)C2211yescharacteristic
35C2×C22⋊(C59⋊C8)C2211yescharacteristic
36C2×#14273638C2211yescharacteristic
37#16837328—21no—
38#16837310—21no—
39#16837278—21no—
40#16837278—21no—
41#16837268C2211yescharacteristic
42#16837262C2211yescharacteristic
43#16837262C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50C2×C4×D4×C59—21no—
51C2×C4×D4×C59C2211yescharacteristic
52C22×C4⋊C4×C59C2211yescharacteristic
53C22×C4⋊C4×C59C2211yescharacteristic
54C59×#389—21no—
55C59×#385—21no—
56C59×#385—21no—
57C59×#384C2211yescharacteristic
58C59×#380C2211yescharacteristic
59C59×#380C2211yescharacteristic
60C4×C4⋊C4×C59C2211yescharacteristic
61C22×D236C2311yescharacteristic
62C22×C22⋊D59—21no—
63C22×C22⋊D59—21no—
64C22×C4×D59—21no—
65C22×C59⋊C8C2311yescharacteristic
66C22×C59⋊C8C2311yescharacteristic
67C22×C59⋊C8C2311yescharacteristic
68C22×C59⋊C8C2311yescharacteristic
69#14273701—22no—
70#14273701—22no—
71#14273701—41no—
72#14273701—41no—
73C4×D236—22no—
74C4×D236—22no—
75C2×C4⋊Dic59C2311yescharacteristic
76C2×C4⋊Dic59C2311yescharacteristic
77C2×C4⋊Dic59C2311yescharacteristic
78C2×C22⋊Dic59—21no—
79C2×C22⋊Dic59—21no—
80C2×(C2×D59)⋊C4—21no—
81C2×(C2×D59)⋊C4—21no—
82C2×(C2×D59)⋊C4—21no—
83#14273660—22no—
84#14273660—22no—
85#14273660—41no—
86#14273658—22no—
87#14273658—22no—
88#14273658—41no—
89C4⋊(C59⋊C8)—22no—
90#14273647—22no—
91#14273647—22no—
92#14273647—22no—
93#14273647D414yescomplemented
94C22⋊(C59⋊C8)—22no—
95C22⋊(C59⋊C8)—22no—
96C22⋊(C59⋊C8)—22no—
97C22⋊(C59⋊C8)—22no—
98#14273638—22no—
99C59⋊#95—21no—
100C59⋊#95—21no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C22×D4×C59D411yescharacteristic
104C23×C4×C59—21no—
105C23×C4×C59—21no—
106C23×C4×C59C2311yescharacteristic
107C23×C4×C59C2311yescharacteristic
108C4×D4×C59—22no—
109C4×D4×C59—22no—
110C4×D4×C59—44no—
111C2×C4⋊C4×C59—22no—
112C2×C4⋊C4×C59—22no—
113C2×C4⋊C4×C59—21no—
114C2×C4⋊C4×C59—21no—
115C2×C4⋊C4×C59—21no—
116C2×C4⋊C4×C59—21no—
117C2×C4⋊C4×C59—41no—
118C2×C4⋊C4×C59—41no—
119C2×C4⋊C4×C59D411yescharacteristic
120C2×C4⋊C4×C59C2311yescharacteristic
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×C59D411yescharacteristic
127C2×C22⋊C4×C59D411yescharacteristic
128C2×C42×C59—21no—
129C2×C42×C59C2311yescharacteristic
130#95×C59—21no—
131#95×C59—21no—
132#95×C59—21no—
133C24×C59C2×D411yescharacteristic
134C24×C59C2×D411yescharacteristic
135C23×D59—21no—
136C2×D4×C59—22no—
137C2×D4×C59—22no—
138C2×D4×C59—22no—
139C22×C4×C59—21no—
140C22×C4×C59—21no—
141C22×C4×C59—21no—
142C22×C4×C59—21no—
143C22×C4×C59—21no—
144C22×C4×C59—21no—
145C22×C4×C59—21no—
146C22×C4×C59—21no—
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—21no—
155C22×C4×C59—42no—
156C22×C4×C59—42no—
157C22×C4×C59—42no—
158C22×C4×C59—42no—
159C22×C4×C59—81no—
160C22×C4×C59—81no—
161C22×C4×C59C2×D411yescharacteristic
162C22×C4×C59C2×D411yescharacteristic
163C22×C4×C59C2×D411yescharacteristic
164C22×C4×C59C2×D411yescharacteristic
165C22×C4×C59C2411yescharacteristic
166C2×C22⋊D59—42no—
167C2×C22⋊D59—42no—
168C2×C22⋊D59—42no—
169C2×C22⋊D59—42no—
170C2×C22⋊D59—81no—
171C2×C22⋊D59—81no—
172C22×Dic59—21no—
173C22×Dic59—21no—
174C22×Dic59—21no—
175C2×D236—21no—
176C2×D236—21no—
177C2×D236—21no—
178C2×D236—21no—
179C2×D236—21no—
180C2×D236C2×D412yes—
181C2×C4×D59—42no—
182C2×C4×D59—81no—
183C2×C4×D59—81no—
184C4⋊C4×C59—22no—
185C4⋊C4×C59—21no—
186C4⋊C4×C59—21no—
187C4⋊C4×C59—21no—
188C4⋊C4×C59—21no—
189C4⋊C4×C59—21no—
190C4⋊C4×C59—21no—
191C4⋊C4×C59—21no—
192C4⋊C4×C59—42no—
193C4⋊C4×C59—42no—
194C4⋊C4×C59—42no—
195C4⋊C4×C59—81no—
196C4⋊C4×C59C2×D412yes—
197C22⋊C4×C59—22no—
198C22⋊C4×C59—22no—
199C22⋊C4×C59—42no—
200C22⋊C4×C59—42no—
201C42×C59—42no—
202C42×C59#4112yes—
203C42×C59#4112yes—
204C22⋊Dic59—81no—
205C22⋊Dic59—81no—
206(C2×D59)⋊C4—42no—
207(C2×D59)⋊C4—42no—
208(C2×D59)⋊C4—42no—
209C4⋊Dic59—21no—
210C4⋊Dic59—21no—
211C4⋊Dic59—21no—
212C4⋊Dic59—21no—
213C4⋊Dic59—21no—
214C4⋊Dic59—21no—
215C2×C59⋊C8—21no—
216C2×C59⋊C8—21no—
217C2×C59⋊C8—21no—
218C2×C59⋊C8—21no—
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⋊C8C2×D412yes—
226C2×C59⋊C8#4112yes—
227C23×C59—21no—
228C23×C59—21no—
229C23×C59—21no—
230C23×C59—21no—
231C23×C59—21no—
232C23×C59—21no—
233C23×C59—21no—
234C23×C59—21no—
235C23×C59—21no—
236C23×C59—21no—
237C23×C59—21no—
238C23×C59—21no—
239C23×C59AGL(1,ℤ/8)12yes—
240C23×C59#13712yes—
241C23×C59C22×D411yescharacteristic
242C22×D59—22no—
243C22×D59—41no—
244C22×D59—41no—
245C22×D59—41no—
246C22×D59—41no—
247C22×D59—41no—
248C22×D59—41no—
249D4×C59—28no—
250C2×C4×C59—21no—
251C2×C4×C59—21no—
252C2×C4×C59—21no—
253C2×C4×C59—21no—
254C2×C4×C59—21no—
255C2×C4×C59—21no—
256C2×C4×C59—21no—
257C2×C4×C59—21no—
258C2×C4×C59—22no—
259C2×C4×C59—21no—
260C2×C4×C59—21no—
261C2×C4×C59—41no—
262C2×C4×C59—41no—
263C2×C4×C59—41no—
264C2×C4×C59—41no—
265C2×C4×C59—41no—
266C2×C4×C59—41no—
267C2×C4×C59—41no—
268C2×C4×C59—41no—
269C2×C4×C59—41no—
270C2×C4×C59—41no—
271C2×C4×C59—41no—
272C2×C4×C59—41no—
273C2×C4×C59—41no—
274C2×C4×C59—41no—
275C2×C4×C59—41no—
276C2×C4×C59—41no—
277C2×C4×C59—41no—
278C2×C4×C59—41no—
279C2×C4×C59—41no—
280C2×C4×C59—84no—
281C2×C4×C59—84no—
282C2×C4×C59#12312yes—
283C2×C4×C59#12312yes—
284C2×C4×C59C22×D411yescharacteristic
285C2×C4×C59C2×#4111yescharacteristic
286C2×C4×C59C2×#4111yescharacteristic
287C2×C4×C59C2×#4111yescharacteristic
288C2×C4×C59H(5,𝔽2)11yescharacteristic
289C2×C4×C592−1+411yescharacteristic
290C22⋊D59—84no—
291C22⋊D59—84no—
292C2×Dic59—41no—
293C2×Dic59—41no—
294C2×Dic59—41no—
295C2×Dic59—41no—
296C2×Dic59—41no—
297C2×Dic59—41no—
298C2×Dic59—41no—
299C2×Dic59—41no—
300C2×Dic59—41no—
301D236—22no—
302D236—22no—
303D236—41no—
304D236—41no—
305C4×D59—84no—
306C59⋊C8—22no—
307C59⋊C8—22no—
308C59⋊C8—41no—
309C59⋊C8—41no—
310#25022—591nomaximal, Sylow
311C22×C59—22no—
312C22×C59—22no—
313C22×C59—22no—
314C22×C59—22no—
315C22×C59—22no—
316C22×C59—22no—
317C22×C59—41no—
318C22×C59—41no—
319C22×C59—41no—
320C22×C59—41no—
321C22×C59—41no—
322C22×C59—41no—
323C22×C59—41no—
324C22×C59—41no—
325C22×C59C2×#12311yescharacteristic
326C22×C59D4211yescharacteristic
327C22×C59#54711yescharacteristic
328C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
329C22×C59C2×#13711yescharacteristic
330C22×C59#57611yescharacteristic
331C22×C59#57711yescharacteristic
332C2×D59—42no—
333C2×D59—42no—
334C2×D59—42no—
335C2×D59—81no—
336C2×D59—81no—
337C2×D59—81no—
338C2×D59—81no—
339C4×C59—22no—
340C4×C59—22no—
341C4×C59—41no—
342C4×C59—41no—
343C4×C59—42no—
344C4×C59—81no—
345C4×C59—81no—
346C4×C59—81no—
347C4×C59#53211yescharacteristic
348C4×C59#54211yescharacteristic
349C4×C59#54711yescharacteristic
350C4×C59#55311yescharacteristic
351Dic59—81no—
352Dic59—81no—
353Dic59—81no—
354C2×#481—591no—
355C2×#480—591no—
356#2535—591no—
357D4×C4⋊C4D5911yescharacteristic, complemented
358#2077—591no—
359#2076—591no—
360#2034—591no—
361#2033—591no—
362#1955—591no—
363#1949—591no—
364#1853—591no—
365#1852—591no—
366#1847—591no—
367#1802—591no—
368#1762—591no—
369C2×C59—42no—
370C2×C59—42no—
371C2×C59#242211yescharacteristic
372C2×C59#309211yescharacteristic
373C2×C59#309611yescharacteristic
374C2×C59#326411yescharacteristic
375C2×C59#326611yescharacteristic
376C2×C59#334511yescharacteristic
377C2×C59#334611yescharacteristic
378D59—82no—
379C2×#121—591no—
380C2×#121—591no—
381C2×C4×D4—21no—
382C2×C4×D4—591no—
383C2×C4×D4C2×D5911yescharacteristic
384C22×C4⋊C4C2×D5911yescharacteristic
385C22×C4⋊C4C2×D5911yescharacteristic
386#481—1184no—
387#480—1184no—
388C2×#107—591no—
389C2×#107—591no—
390C2×#107—591no—
391C2×#106—591no—
392C2×#106—591no—
393C2×#106—591no—
394C2×C4⋊C8—591no—
395C2×#102—591no—
396C2×#102—591no—
397C2×#102—591no—
398C2×#102—591no—
399C2×C22⋊C8—591no—
400C2×C22⋊C8—591no—
401C2×C22⋊C8—591no—
402C2×C22⋊C8—591no—
403C2×#97—591no—
404#397—1181no—
405#392—1181no—
406#389—21no—
407#386—1181no—
408#386—1181no—
409#385—21no—
410#385—21no—
411#384C2×D5911yescharacteristic
412#382—591no—
413#380—591no—
414#380—591no—
415#380C2×D5911yescharacteristic
416#380C2×D5911yescharacteristic
417C4×C4⋊C4C2×D5911yescharacteristic
418#340—591no—
419#340—591no—
420#340—591no—
421#340—591no—
422#340—591no—
423#340—591no—
424C59#2502211yescharacteristic, complemented, Sylow
425C22×D4—591no—
426C22×D4—1181no—
427C22×D4—1181no—
428C22×D4C22⋊D5911yescharacteristic
429C23×C4—21no—
430C23×C4—21no—
431C23×C4—1181no—
432C23×C4C22×D5911yescharacteristic
433C23×C4C22×D5911yescharacteristic
434C22×C8—591no—
435C22×C8—591no—
436C22×C8—591no—
437C22×C8—591no—
438#121—1182no—
439#121—1182no—
440#121—2361no—
441#121—2361no—
442C4×D4—22no—
443C4×D4—22no—
444C4×D4—44no—
445C4×D4—1182no—
446C4×D4—1182no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—41no—
454C2×C4⋊C4—41no—
455C2×C4⋊C4—591no—
456C2×C4⋊C4—591no—
457C2×C4⋊C4—591no—
458C2×C4⋊C4C22⋊D5911yescharacteristic
459C2×C4⋊C4C22×D5911yescharacteristic
460C2×C4⋊C4C22×D5911yescharacteristic
461C2×C4⋊C4C22×D5911yescharacteristic
462C2×C4⋊C4C22×D5911yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—1181no—
466C2×C22⋊C4—1181no—
467C2×C22⋊C4—1181no—
468C2×C22⋊C4—1181no—
469C2×C22⋊C4—1181no—
470C2×C22⋊C4C22⋊D5911yescharacteristic
471C2×C22⋊C4C22⋊D5911yescharacteristic
472C2×C42—21no—
473C2×C42C22×D5911yescharacteristic
474#107—1182no—
475#107—1182no—
476#107—2361no—
477#106—1182no—
478#106—1182no—
479#106—2361no—
480C4⋊C8—1182no—
481#102—594no—
482#102—1182no—
483#102—1182no—
484#102—1182no—
485C22⋊C8—1182no—
486C22⋊C8—1182no—
487C22⋊C8—1182no—
488C22⋊C8—1182no—
489#97—1182no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—1181no—
494#95—1181no—
495#95—1181no—
496#95—1181no—
497C24—1181no—
498C24C2×C22⋊D5911yescharacteristic
499C24C2×C22⋊D5911yescharacteristic
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—592no—
504C2×D4—1181no—
505C2×D4—1181no—
506C2×D4—1181no—
507C2×D4—1181no—
508C2×D4—1181no—
509C2×D4—4721no—
510C2×D4—4721no—
511C2×D4—2362no—
512C2×D4—2362no—
513C2×D4—2362no—
514C2×D4—2362no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
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—42no—
535C22×C4—81no—
536C22×C4—81no—
537C22×C4—1181no—
538C22×C4—1181no—
539C22×C4—1181no—
540C22×C4—4721no—
541C22×C4—4721no—
542C22×C4—2362no—
543C22×C4C2×C22⋊D5911yescharacteristic
544C22×C4C2×C22⋊D5911yescharacteristic
545C22×C4C2×C22⋊D5911yescharacteristic
546C22×C4C2×C22⋊D5911yescharacteristic
547C22×C4C23×D5911yescharacteristic
548C2×C8—592no—
549C2×C8—592no—
550C2×C8—1181no—
551C2×C8—1181no—
552C2×C8—1181no—
553C2×C8—1181no—
554C2×C8—1181no—
555C2×C8—1181no—
556C2×C8—1181no—
557C2×C8—1181no—
558C2×C8—1181no—
559C2×C8—1181no—
560C4⋊C4—22no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—81no—
572C4⋊C4—1181no—
573C4⋊C4—1181no—
574C4⋊C4—1181no—
575C4⋊C4—1181no—
576C4⋊C4—1181no—
577C4⋊C4—1181no—
578C4⋊C4D4×D5912yes—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—4721no—
584C22⋊C4—4721no—
585C22⋊C4—2362no—
586C22⋊C4—2362no—
587C22⋊C4—2362no—
588C42—42no—
589C42#1174568512yes—
590C42#1174568512yes—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—1182no—
604C23—2361no—
605C23—2361no—
606C23—2361no—
607C23—2361no—
608C23—2361no—
609C23—2361no—
610C23#1427375312yes—
611C23#1427375812yes—
612C23C22×C22⋊D5911yescharacteristic
613D4—28no—
614D4—1182no—
615D4—1182no—
616D4—4724no—
617D4—4724no—
618D4—2361no—
619D4—2361no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—84no—
651C2×C4—84no—
652C2×C4—4724no—
653C2×C4—2361no—
654C2×C4—2361no—
655C2×C4—2361no—
656C2×C4—2361no—
657C2×C4—2361no—
658C2×C4—2361no—
659C2×C4—2361no—
660C2×C4—2361no—
661C2×C4—2361no—
662C2×C4#1427371012yes—
663C2×C4#1427371012yes—
664C2×C4C2×D4×D5911yescharacteristic
665C2×C4#41×D5911yescharacteristic
666C2×C4C2×#1174568511yescharacteristic
667C2×C4C2×#1174568511yescharacteristic
668C2×C4#1427377211yescharacteristic
669C2×C4#1427377411yescharacteristic
670C8—1182no—
671C8—1182no—
672C8—2361no—
673C8—2361no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—4721no—
689C22—4721no—
690C22—4721no—
691C22—4721no—
692C22—2362no—
693C22—2362no—
694C22—2362no—
695C22C2×#1427371011yescharacteristic
696C22D4×C22⋊D5911yescharacteristic
697C22#1683805111yescharacteristic
698C22C2×#1427375311yescharacteristic
699C22C2×#1427375811yescharacteristic
700C22#1683820511yescharacteristic
701C22#1683821011yescharacteristic
702C4—22no—
703C4—22no—
704C4—41no—
705C4—41no—
706C4—42no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4—4721no—
711C4—4721no—
712C4—4721no—
713C4#1683794911yescharacteristic
714C4#1683801711yescharacteristic
715C4#1683805711yescharacteristic
716C4#1683810211yescharacteristic
717C2—42no—
718C2—42no—
719C2—4722no—
720C2#2142760411yescharacteristic
721C2#2143401911yescharacteristic
722C2#2143405411yescharacteristic
723C2#2143557211yescharacteristic
724C2#2143560711yescharacteristic
725C2#2143656611yescharacteristic
726C2#2143657511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingD4×C4⋊C4×C59C2
socleC23×C59C22×D4
prime radical#21428997C2
hypercenterD4×C4⋊C4D59
hypocenterC59#25022
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16837720C2semidirect
2. C2×#16837715C2semidirect
4. #21425532C2semidirect
5. #21425527C2semidirect
6. #21425285C2semidirect
7. #21425278C2semidirect
8. #21424895C2semidirect
9. #21424864C2semidirect
10. #21424289C2semidirect
11. #21424284C2semidirect
12. #21424262C2semidirect
13. #21424093C2semidirect
14. #21423924C2semidirect
15. D4×C4⋊C4×C59C2semidirect
93. #14273647D4semidirect
357. D4×C4⋊C4D59semidirect
424. C59#25022semidirect

Maximal subgroups

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

subgroupindex
C2×#168377202
C2×#168377152
#214289972
#214255322
#214255272
#214252852
#214252782
#214248952
#214248642
#214242892
#214242842
#214242622
#214240932
#214239242
D4×C4⋊C4×C592
#2502259