Finite Group Databasebeta

← #28634248

Subgroups — #28634248

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×#16837718C211yesmaximal, characteristic, complemented
2C2×#16837713C211yesmaximal, characteristic, complemented
3D4×C4⋊Dic59C211yesmaximal, characteristic, complemented
4#21425533C211yesmaximal, characteristic, complemented
5#21425527C211yesmaximal, characteristic, complemented
6#21425282C211yesmaximal, characteristic, complemented
7#21425275C211yesmaximal, characteristic, complemented
8#21424895C211yesmaximal, characteristic, complemented
9#21424862C211yesmaximal, characteristic, complemented
10#21424288C211yesmaximal, characteristic, complemented
11#21424283C211yesmaximal, characteristic, complemented
12#21424265C211yesmaximal, characteristic, complemented
13#21424096C211yesmaximal, characteristic, complemented
14#21423921C211yesmaximal, characteristic, complemented
15C59×#2535C211yesmaximal, characteristic
16C2×D4×Dic59—21no—
17C22×C4⋊Dic59C2211yescharacteristic
18C22×C4⋊Dic59C2211yescharacteristic
19#16837718—24no—
20#16837713—24no—
21C2×#14273660C2211yescharacteristic
22C2×#14273660C2211yescharacteristic
23C2×#14273660C2211yescharacteristic
24C2×#14273658C2211yescharacteristic
25C2×#14273658C2211yescharacteristic
26C2×#14273658C2211yescharacteristic
27C2×C4⋊(C59⋊C8)C2211yescharacteristic
28C2×#14273648C2211yescharacteristic
29C2×#14273648C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×#14273648C2211yescharacteristic
32C2×C22⋊(C59⋊C8)C2211yescharacteristic
33C2×C22⋊(C59⋊C8)C2211yescharacteristic
34C2×C22⋊(C59⋊C8)C2211yescharacteristic
35C2×C22⋊(C59⋊C8)C2211yescharacteristic
36C2×#14273638C2211yescharacteristic
37#16837301—21no—
38#16837277—21no—
39#16837277—21no—
40#16837272C2211yescharacteristic
41#16837262C2211yescharacteristic
42#16837262C2211yescharacteristic
43C4×C4⋊Dic59C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50C2×#121×C59C2211yescharacteristic
51C2×#121×C59C2211yescharacteristic
52C2×C4×D4×C59C2211yescharacteristic
53C2×C4×D4×C59C2211yescharacteristic
54C59×#397—21no—
55C59×#392—21no—
56C59×#386—21no—
57C59×#386—21no—
58C59×#382C2211yescharacteristic
59C59×#380C2211yescharacteristic
60C59×#380C2211yescharacteristic
61C23×Dic59—21no—
62C23×Dic59—21no—
63C22×C59⋊C8C2311yescharacteristic
64C22×C59⋊C8C2311yescharacteristic
65C22×C59⋊C8C2311yescharacteristic
66C22×C59⋊C8C2311yescharacteristic
67D4×Dic59—44no—
68C2×C4⋊Dic59—22no—
69C2×C4⋊Dic59—22no—
70C2×C4⋊Dic59—21no—
71C2×C4⋊Dic59—21no—
72C2×C4⋊Dic59—21no—
73C2×C4⋊Dic59—21no—
74C2×C4⋊Dic59—41no—
75C2×C4⋊Dic59—41no—
76C2×C4⋊Dic59C2311yescharacteristic
77C2×C4⋊Dic59C2311yescharacteristic
78C2×C4⋊Dic59C2311yescharacteristic
79C2×C4⋊Dic59C2311yescharacteristic
80C2×C22⋊Dic59—21no—
81C2×C22⋊Dic59—21no—
82C2×C4×Dic59—21no—
83#14273660—22no—
84#14273660—22no—
85#14273660—41no—
86#14273658—22no—
87#14273658—22no—
88#14273658—41no—
89C4⋊(C59⋊C8)—22no—
90#14273648—22no—
91#14273648—22no—
92#14273648—22no—
93#14273648D414yescomplemented
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—
102C22×D4×C59—21no—
103C22×D4×C59—21no—
104C22×D4×C59D411yescharacteristic
105C22×D4×C59C2311yescharacteristic
106C23×C4×C59—21no—
107C23×C4×C59C2311yescharacteristic
108C23×C4×C59C2311yescharacteristic
109#121×C59—22no—
110#121×C59—22no—
111#121×C59—41no—
112#121×C59—41no—
113C4×D4×C59—22no—
114C4×D4×C59—22no—
115C4×D4×C59—22no—
116C4×D4×C59—22no—
117C2×C4⋊C4×C59D411yescharacteristic
118C2×C4⋊C4×C59C2311yescharacteristic
119C2×C4⋊C4×C59C2311yescharacteristic
120C2×C4⋊C4×C59C2311yescharacteristic
121C2×C22⋊C4×C59—21no—
122C2×C22⋊C4×C59—21no—
123C2×C22⋊C4×C59—21no—
124C2×C22⋊C4×C59—21no—
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59D411yescharacteristic
127C2×C22⋊C4×C59D411yescharacteristic
128C2×C42×C59C2311yescharacteristic
129#95×C59—21no—
130#95×C59—21no—
131#95×C59—21no—
132#95×C59—21no—
133C24×C59—21no—
134C24×C59C2×D411yescharacteristic
135C24×C59C2×D411yescharacteristic
136C2×D4×C59—22no—
137C2×D4×C59—22no—
138C2×D4×C59—22no—
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—
147C2×D4×C59—42no—
148C2×D4×C59—81no—
149C2×D4×C59—81no—
150C2×D4×C59C2×D412yes—
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—21no—
158C22×C4×C59—21no—
159C22×C4×C59—21no—
160C22×C4×C59—21no—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59—21no—
164C22×C4×C59—21no—
165C22×C4×C59—21no—
166C22×C4×C59—42no—
167C22×C4×C59—81no—
168C22×C4×C59—81no—
169C22×C4×C59C2×D411yescharacteristic
170C22×C4×C59C2×D411yescharacteristic
171C22×C4×C59C2×D411yescharacteristic
172C22×C4×C59C2×D411yescharacteristic
173C22×C4×C59C2411yescharacteristic
174C22×Dic59—21no—
175C22×Dic59—21no—
176C22×Dic59—21no—
177C22×Dic59—21no—
178C22×Dic59—42no—
179C22×Dic59—42no—
180C22×Dic59—42no—
181C22×Dic59—42no—
182C22×Dic59—81no—
183C22×Dic59—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—
191C22⋊C4×C59—22no—
192C22⋊C4×C59—22no—
193C22⋊C4×C59—42no—
194C22⋊C4×C59—42no—
195C22⋊C4×C59—42no—
196C22⋊C4×C59—81no—
197C22⋊C4×C59—81no—
198C42×C59#4112yes—
199C42×C59#4112yes—
200C22⋊Dic59—42no—
201C22⋊Dic59—42no—
202C4⋊Dic59—21no—
203C4⋊Dic59—21no—
204C4⋊Dic59—21no—
205C4⋊Dic59—21no—
206C4⋊Dic59—21no—
207C4⋊Dic59—21no—
208C4⋊Dic59—21no—
209C4⋊Dic59—42no—
210C4⋊Dic59—42no—
211C4⋊Dic59—42no—
212C4⋊Dic59—81no—
213C4⋊Dic59C2×D412yes—
214C4×Dic59—42no—
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×C59—22no—
240C23×C59—41no—
241C23×C59—41no—
242C23×C59—41no—
243C23×C59—41no—
244C23×C59—41no—
245C23×C59—41no—
246C23×C59AGL(1,ℤ/8)12yes—
247C23×C59#13712yes—
248C23×C59C22×D411yescharacteristic
249D4×C59—28no—
250D4×C59—22no—
251D4×C59—22no—
252D4×C59—41no—
253D4×C59—41no—
254D4×C59—84no—
255D4×C59—84no—
256C2×C4×C59—21no—
257C2×C4×C59—21no—
258C2×C4×C59—21no—
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—21no—
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—41no—
281C2×C4×C59—41no—
282C2×C4×C59—41no—
283C2×C4×C59—84no—
284C2×C4×C59#12312yes—
285C2×C4×C59#12312yes—
286C2×C4×C59C22×D411yescharacteristic
287C2×C4×C59C2×#4111yescharacteristic
288C2×C4×C59C2×#4111yescharacteristic
289C2×C4×C59C2×#4111yescharacteristic
290C2×C4×C59H(5,𝔽2)11yescharacteristic
291C2×C4×C592−1+411yescharacteristic
292C2×Dic59—22no—
293C2×Dic59—41no—
294C2×Dic59—41no—
295C2×Dic59—41no—
296C2×Dic59—41no—
297C2×Dic59—41no—
298C2×Dic59—41no—
299C2×Dic59—41no—
300C2×Dic59—41no—
301C2×Dic59—41no—
302C2×Dic59—41no—
303C2×Dic59—41no—
304C2×Dic59—84no—
305C2×Dic59—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×C59—42no—
326C22×C59—42no—
327C22×C59—42no—
328C22×C59—81no—
329C22×C59—81no—
330C22×C59—81no—
331C22×C59—81no—
332C22×C59C2×#12311yescharacteristic
333C22×C59D4211yescharacteristic
334C22×C59#54711yescharacteristic
335C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
336C22×C59C2×#13711yescharacteristic
337C22×C59#57611yescharacteristic
338C22×C59#57711yescharacteristic
339C4×C59—22no—
340C4×C59—22no—
341C4×C59—41no—
342C4×C59—41no—
343C4×C59—81no—
344C4×C59—81no—
345C4×C59—81no—
346C4×C59#53211yescharacteristic
347C4×C59#54211yescharacteristic
348C4×C59#54711yescharacteristic
349C4×C59#55311yescharacteristic
350Dic59—42no—
351Dic59—81no—
352Dic59—81no—
353Dic59—81no—
354C2×#481—591no—
355C2×#480—591no—
356#2535D5911yescharacteristic
357D4×C4⋊C4—591no—
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—82no—
372C2×C59#242211yescharacteristic
373C2×C59#309211yescharacteristic
374C2×C59#309611yescharacteristic
375C2×C59#326411yescharacteristic
376C2×C59#326611yescharacteristic
377C2×C59#334511yescharacteristic
378C2×C59#334611yescharacteristic
379C2×#121C2×D5911yescharacteristic
380C2×#121C2×D5911yescharacteristic
381C2×C4×D4—1181no—
382C2×C4×D4C2×D5911yescharacteristic
383C2×C4×D4C2×D5911yescharacteristic
384C22×C4⋊C4—591no—
385C22×C4⋊C4—591no—
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—21no—
405#392—21no—
406#389—1181no—
407#386—21no—
408#386—21no—
409#385—1181no—
410#385—1181no—
411#384—591no—
412#382C2×D5911yescharacteristic
413#380—591no—
414#380—591no—
415#380C2×D5911yescharacteristic
416#380C2×D5911yescharacteristic
417C4×C4⋊C4—591no—
418#340—591no—
419#340—591no—
420#340—591no—
421#340—591no—
422#340—591no—
423#340—591no—
424C59#2502211yescharacteristic, complemented, Sylow
425C22×D4—21no—
426C22×D4—21no—
427C22×D4C22⋊D5911yescharacteristic
428C22×D4C22×D5911yescharacteristic
429C23×C4—21no—
430C23×C4—1181no—
431C23×C4—1181no—
432C23×C4C22×D5911yescharacteristic
433C23×C4C22×D5911yescharacteristic
434C22×C8—591no—
435C22×C8—591no—
436C22×C8—591no—
437C22×C8—591no—
438#121—22no—
439#121—22no—
440#121—41no—
441#121—41no—
442C4×D4—22no—
443C4×D4—22no—
444C4×D4—22no—
445C4×D4—22no—
446C4×D4—2364no—
447C2×C4⋊C4—591no—
448C2×C4⋊C4—591no—
449C2×C4⋊C4—591no—
450C2×C4⋊C4—591no—
451C2×C4⋊C4—1182no—
452C2×C4⋊C4—1182no—
453C2×C4⋊C4—1181no—
454C2×C4⋊C4—1181no—
455C2×C4⋊C4—1181no—
456C2×C4⋊C4—1181no—
457C2×C4⋊C4—2361no—
458C2×C4⋊C4—2361no—
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—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—1181no—
469C2×C22⋊C4—1181no—
470C2×C22⋊C4C22⋊D5911yescharacteristic
471C2×C22⋊C4C22⋊D5911yescharacteristic
472C2×C42—1181no—
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—21no—
494#95—1181no—
495#95—1181no—
496#95—1181no—
497C24—21no—
498C24C2×C22⋊D5911yescharacteristic
499C24C2×C22⋊D5911yescharacteristic
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—81no—
513C2×D4—81no—
514C2×D4D4×D5912yes—
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—42no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4—1181no—
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×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—592no—
568C4⋊C4—1181no—
569C4⋊C4—1181no—
570C4⋊C4—1181no—
571C4⋊C4—1181no—
572C4⋊C4—1181no—
573C4⋊C4—1181no—
574C4⋊C4—1181no—
575C4⋊C4—4721no—
576C4⋊C4—2362no—
577C4⋊C4—2362no—
578C4⋊C4—2362no—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—81no—
585C22⋊C4—81no—
586C22⋊C4—2362no—
587C22⋊C4—2362no—
588C42—2362no—
589C42#1174568712yes—
590C42#1174568712yes—
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—22no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23#1427375212yes—
611C23#1427375712yes—
612C23C22×C22⋊D5911yescharacteristic
613D4—28no—
614D4—22no—
615D4—22no—
616D4—41no—
617D4—41no—
618D4—84no—
619D4—84no—
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—21no—
629C2×C4—21no—
630C2×C4—41no—
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—84no—
648C2×C4—1182no—
649C2×C4—4724no—
650C2×C4—4724no—
651C2×C4—2361no—
652C2×C4—2361no—
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#1427370812yes—
663C2×C4#1427370812yes—
664C2×C4C2×D4×D5911yescharacteristic
665C2×C4#41×D5911yescharacteristic
666C2×C4C2×#1174568711yescharacteristic
667C2×C4C2×#1174568711yescharacteristic
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—42no—
689C22—42no—
690C22—42no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22C2×#1427370811yescharacteristic
696C22D4×C22⋊D5911yescharacteristic
697C22#1683805111yescharacteristic
698C22C2×#1427375211yescharacteristic
699C22C2×#1427375711yescharacteristic
700C22#1683820511yescharacteristic
701C22#1683821311yescharacteristic
702C4—22no—
703C4—22no—
704C4—41no—
705C4—41no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—4721no—
710C4—4721no—
711C4—4721no—
712C4—2362no—
713C4#1683794711yescharacteristic
714C4#1683801911yescharacteristic
715C4#1683805211yescharacteristic
716C4#1683809911yescharacteristic
717C2—42no—
718C2—42no—
719C2—82no—
720C2#2142760611yescharacteristic
721C2#2143401611yescharacteristic
722C2#2143404811yescharacteristic
723C2#2143557711yescharacteristic
724C2#2143560211yescharacteristic
725C2#2143656011yescharacteristic
726C2#2143658111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
Fitting, prime radicalC59×#2535C2
socleC23×C59C22×D4
hypercenter#2535D59
hypocenterC59#25022
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. C2×#16837718C2semidirect
2. C2×#16837713C2semidirect
3. D4×C4⋊Dic59C2semidirect
4. #21425533C2semidirect
5. #21425527C2semidirect
6. #21425282C2semidirect
7. #21425275C2semidirect
8. #21424895C2semidirect
9. #21424862C2semidirect
10. #21424288C2semidirect
11. #21424283C2semidirect
12. #21424265C2semidirect
13. #21424096C2semidirect
14. #21423921C2semidirect
93. #14273648D4semidirect
424. C59#25022semidirect

Maximal subgroups

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

subgroupindex
C2×#168377182
C2×#168377132
D4×C4⋊Dic592
#214255332
#214255272
#214252822
#214252752
#214248952
#214248622
#214242882
#214242832
#214242652
#214240962
#214239212
C59×#25352
#2502259