Finite Group Databasebeta

← #28615027

Subgroups — #28615027

Order 15104.

776 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21427340C211yesmaximal, characteristic
2#21424893C211yesmaximal, characteristic, complemented
3#21424892C211yesmaximal, characteristic, complemented
4#21424711C211yesmaximal, characteristic, complemented
5#21424708C211yesmaximal, characteristic, complemented
6#21424658C211yesmaximal, characteristic, complemented
7#21424657C211yesmaximal, characteristic, complemented
8#21424392C211yesmaximal, characteristic, complemented
9#21424390C211yesmaximal, characteristic, complemented
10#21424388C211yesmaximal, characteristic, complemented
11#21424388C211yesmaximal, characteristic, complemented
12#21424280C211yesmaximal, characteristic, complemented
13#21424166C211yesmaximal, characteristic, complemented
14#21424077C211yesmaximal, characteristic, complemented
15C59×#1850C211yesmaximal, characteristic, complemented
16C22×#11745659C2211yescharacteristic
17C2×C4×D236C2211yescharacteristic
18C2×C4×C22⋊D59C2211yescharacteristic
19C2×C4×C22⋊D59C2211yescharacteristic
20C2×#14273684C2211yescharacteristic
21C2×C4⋊(C59⋊C8)C2211yescharacteristic
22C2×Dic59⋊C8C2211yescharacteristic
23C2×C22⋊(C59⋊C8)C2211yescharacteristic
24C2×C22⋊(C59⋊C8)C2211yescharacteristic
25C2×(C2×D59)⋊C8C2211yescharacteristic
26C2×(C2×D59)⋊C8C2211yescharacteristic
27C2×(C2×D59)⋊C8C2211yescharacteristic
28C2×(C2×D59)⋊C8C2211yescharacteristic
29C2×(C2×D59)⋊C8C2211yescharacteristic
30C2×(C2×D59)⋊C8C2211yescharacteristic
31C2×(C2×D59)⋊C8C2211yescharacteristic
32C2×#14273638C2211yescharacteristic
33C2×#14273637C2211yescharacteristic
34#16837336C411yescharacteristic
35#16837331C411yescharacteristic
36#16837326C411yescharacteristic
37#16837325C411yescharacteristic
38#16837320C411yescharacteristic
39#16837317C411yescharacteristic
40#16837317C411yescharacteristic
41#16837311C411yescharacteristic
42C4×Dic59⋊C4C2211yescharacteristic
43C4×(C2×D59)⋊C4C2211yescharacteristic
44#16837157C2211yescharacteristic
45#16837157C2211yescharacteristic
46#16837156C2211yescharacteristic
47#16837156C2211yescharacteristic
48#16837156C2211yescharacteristic
49#16837156C2211yescharacteristic
50#16837156C2211yescharacteristic
51#16837156C2211yescharacteristic
52C23×C8×C59C2211yescharacteristic
53C2×C4⋊C8×C59C2211yescharacteristic
54C2×C4⋊C8×C59C2211yescharacteristic
55C2×C22⋊C8×C59C2211yescharacteristic
56C4×C22⋊C4×C59C2211yescharacteristic
57C59×#336C2211yescharacteristic
58C59×#336C2211yescharacteristic
59C22×D236C2×C411yescharacteristic
60C22×C22⋊D59C2×C411yescharacteristic
61C22×C22⋊D59C2×C411yescharacteristic
62C22×C4×D59C2311yescharacteristic
63C22×C4×D59C2311yescharacteristic
64C2×#11745659—41no—
65C2×#11745659—41no—
66C2×#11745659—41no—
67C22×C59⋊C8C2311yescharacteristic
68C22×C59⋊C8C2311yescharacteristic
69C22×C59⋊C8C2311yescharacteristic
70C22×C59⋊C8C2311yescharacteristic
71C4×D236—41no—
72C4×D236—41no—
73C4×C22⋊D59—41no—
74C4×C22⋊D59—41no—
75C4×C22⋊D59—41no—
76C4×C22⋊D59—41no—
77#14273684—41no—
78#14273684—41no—
79C2×C4⋊Dic59C2×C411yescharacteristic
80C2×Dic59⋊C4C2×C411yescharacteristic
81C2×Dic59⋊C4C2×C411yescharacteristic
82C2×Dic59⋊C4C2×C411yescharacteristic
83C2×Dic59⋊C4C2×C411yescharacteristic
84C2×Dic59⋊C4C2×C411yescharacteristic
85C2×Dic59⋊C4C2×C411yescharacteristic
86C2×C22⋊Dic59C2×C411yescharacteristic
87C2×C22⋊Dic59C2×C411yescharacteristic
88C2×(C2×D59)⋊C4C2×C411yescharacteristic
89C2×(C2×D59)⋊C4C2×C411yescharacteristic
90C2×(C2×D59)⋊C4C2×C411yescharacteristic
91C2×(C2×D59)⋊C4C2×C411yescharacteristic
92C2×(C2×D59)⋊C4C2×C411yescharacteristic
93C2×(C2×D59)⋊C4C2×C411yescharacteristic
94C2×(C2×D59)⋊C4C2×C411yescharacteristic
95C2×(C2×D59)⋊C4C2×C411yescharacteristic
96C2×C4×Dic59C2311yescharacteristic
97C2×C4×Dic59C2311yescharacteristic
98C4⋊(C59⋊C8)—41no—
99Dic59⋊C8—41no—
100C22⋊(C59⋊C8)—41no—
101C22⋊(C59⋊C8)—41no—
102(C2×D59)⋊C8—41no—
103(C2×D59)⋊C8—41no—
104(C2×D59)⋊C8—41no—
105(C2×D59)⋊C8—41no—
106(C2×D59)⋊C8—41no—
107(C2×D59)⋊C8—41no—
108(C2×D59)⋊C8—41no—
109#14273638—41no—
110#14273637—41no—
111C59⋊#95C2×C411yescharacteristic
112C59⋊#95C2×C411yescharacteristic
113C59⋊#95C2×C411yescharacteristic
114C59⋊#95C2×C411yescharacteristic
115C23×C4×C59C2311yescharacteristic
116C22×C8×C59—41no—
117C22×C8×C59—41no—
118C22×C8×C59—41no—
119C22×C8×C59C2311yescharacteristic
120C22×C8×C59C2311yescharacteristic
121C22×C8×C59C2311yescharacteristic
122C22×C8×C59C2311yescharacteristic
123C2×C22⋊C4×C59C2×C411yescharacteristic
124C2×C22⋊C4×C59C2×C411yescharacteristic
125C2×C42×C59C2311yescharacteristic
126C2×C42×C59C2311yescharacteristic
127C4⋊C8×C59—41no—
128C4⋊C8×C59—41no—
129C22⋊C8×C59—41no—
130#95×C59C2×C411yescharacteristic
131#95×C59C2×C411yescharacteristic
132C24×C59C22×C411yescharacteristic
133C23×D59C22×C411yescharacteristic
134C23×D59C22×C411yescharacteristic
135C22×C4×C59—21no—
136C22×C4×C59—21no—
137C22×C4×C59—21no—
138C22×C4×C59—21no—
139C22×C4×C59—21no—
140C22×C4×C59—21no—
141C22×C4×C59C22×C411yescharacteristic
142C22×C4×C59C22×C411yescharacteristic
143C22×C4×C59C22×C411yescharacteristic
144C22×C4×C59C22×C411yescharacteristic
145C22×C4×C59C22×C411yescharacteristic
146C22×C4×C59C2411yescharacteristic
147C2×C22⋊D59—22no—
148C2×C22⋊D59—22no—
149C2×C22⋊D59—41no—
150C2×C22⋊D59—41no—
151C2×C22⋊D59—41no—
152C2×C22⋊D59—41no—
153C22×Dic59C22×C411yescharacteristic
154C22×Dic59C22×C411yescharacteristic
155C22×Dic59C22×C411yescharacteristic
156C22×Dic59C22×C411yescharacteristic
157C22×Dic59C22×C411yescharacteristic
158C22×Dic59C22×C411yescharacteristic
159C2×D236—41no—
160C2×D236—41no—
161C2×D236—41no—
162C2×C4×D59—21no—
163C2×C4×D59—21no—
164C2×C4×D59—21no—
165C2×C4×D59—21no—
166C2×C4×D59—21no—
167C2×C4×D59—21no—
168C2×C4×D59—21no—
169C2×C4×D59—21no—
170C2×C4×D59—21no—
171C2×C4×D59—21no—
172C2×C4×D59—21no—
173C2×C4×D59—21no—
174C2×C8×C59—21no—
175C2×C8×C59—21no—
176C2×C8×C59—21no—
177C2×C8×C59—21no—
178C2×C8×C59—21no—
179C2×C8×C59—21no—
180C2×C8×C59—21no—
181C2×C8×C59—21no—
182C2×C8×C59—21no—
183C2×C8×C59—21no—
184C2×C8×C59—21no—
185C2×C8×C59—21no—
186C2×C8×C59—44no—
187C22⋊C4×C59—22no—
188C22⋊C4×C59—41no—
189C42×C59—21no—
190C42×C59—21no—
191C42×C59—21no—
192C42×C59—21no—
193C22⋊Dic59—41no—
194C22⋊Dic59—41no—
195(C2×D59)⋊C4—41no—
196(C2×D59)⋊C4—41no—
197(C2×D59)⋊C4—41no—
198(C2×D59)⋊C4—41no—
199(C2×D59)⋊C4—41no—
200(C2×D59)⋊C4—41no—
201(C2×D59)⋊C4—41no—
202(C2×D59)⋊C4—41no—
203C4⋊Dic59—41no—
204Dic59⋊C4—41no—
205Dic59⋊C4—41no—
206Dic59⋊C4—41no—
207Dic59⋊C4—41no—
208Dic59⋊C4—41no—
209Dic59⋊C4—41no—
210C4×Dic59—21no—
211C4×Dic59—21no—
212C4×Dic59—21no—
213C4×Dic59—21no—
214C2×C59⋊C8—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⋊C8—21no—
226#11745659—44no—
227C23×C59—21no—
228C23×C59—21no—
229C23×C59—21no—
230C23×C59—21no—
231C23×C59—21no—
232C23×C59—21no—
233C23×C59#13112yes—
234C23×C59C23×C411yescharacteristic
235C22×D59—21no—
236C22×D59—21no—
237C22×D59—21no—
238C22×D59—21no—
239C22×D59—21no—
240C22×D59—21no—
241C22×D59—21no—
242C22×D59—21no—
243C22×D59—21no—
244C22×D59—21no—
245C22×D59—21no—
246C22×D59—21no—
247C22×D59—21no—
248C22×D59—21no—
249C2×C4×C59—21no—
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—21no—
259C2×C4×C59—21no—
260C2×C4×C59—21no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—21no—
264C2×C4×C59—41no—
265C2×C4×C59—41no—
266C2×C4×C59—41no—
267C2×C4×C59—41no—
268C2×C4×C59H(5,𝔽2)11yescharacteristic
269C2×C4×C59H(5,𝔽2)11yescharacteristic
270C2×C4×C59H(5,𝔽2)11yescharacteristic
271C2×C4×C59H(5,𝔽2)11yescharacteristic
272C2×C4×C59H(5,𝔽2)11yescharacteristic
273C2×C4×C592−1+411yescharacteristic
274C22⋊D59—44no—
275C22⋊D59—44no—
276C2×Dic59—21no—
277C2×Dic59—21no—
278C2×Dic59—21no—
279C2×Dic59—21no—
280C2×Dic59—21no—
281C2×Dic59—21no—
282C2×Dic59—21no—
283C2×Dic59—21no—
284C2×Dic59—21no—
285C2×Dic59—21no—
286C2×Dic59—21no—
287C2×Dic59—21no—
288C2×Dic59—21no—
289C2×Dic59—21no—
290C2×Dic59—21no—
291C2×Dic59—21no—
292C2×Dic59—21no—
293C2×Dic59—21no—
294D236—44no—
295C4×D59—41no—
296C4×D59—41no—
297C4×D59—41no—
298C4×D59—41no—
299C4×D59—41no—
300C4×D59—41no—
301C4×D59—41no—
302C4×D59—41no—
303C8×C59—41no—
304C8×C59—41no—
305C8×C59—41no—
306C8×C59—41no—
307C59⋊C8—41no—
308C59⋊C8—41no—
309C59⋊C8—41no—
310C59⋊C8—41no—
311#23335—591nomaximal, Sylow
312C22×C59—22no—
313C22×C59—22no—
314C22×C59—22no—
315C22×C59—41no—
316C22×C59—41no—
317C22×C59—41no—
318C22×C59—41no—
319C22×C59#51811yescharacteristic
320C22×C59#51811yescharacteristic
321C22×C59#52011yescharacteristic
322C22×C59C2×#13111yescharacteristic
323C22×C59#56811yescharacteristic
324C22×C59#56811yescharacteristic
325C22×C59#56811yescharacteristic
326C2×D59—41no—
327C2×D59—41no—
328C2×D59—41no—
329C2×D59—41no—
330C2×D59—41no—
331C2×D59—41no—
332C2×D59—41no—
333C2×D59—41no—
334C2×D59—41no—
335C2×D59—41no—
336C2×D59—41no—
337C2×D59—41no—
338C2×D59—41no—
339C2×D59—41no—
340C4×C59—41no—
341C4×C59—41no—
342C4×C59—41no—
343C4×C59—41no—
344C4×C59—41no—
345C4×C59#56011yescharacteristic
346C4×C59#56011yescharacteristic
347C4×C59#56211yescharacteristic
348C4×C59#56211yescharacteristic
349Dic59—41no—
350Dic59—41no—
351Dic59—41no—
352Dic59—41no—
353Dic59—41no—
354Dic59—41no—
355#2392—591no—
356#1955—591no—
357#1955—591no—
358#1924—591no—
359#1924—591no—
360#1917—591no—
361#1917—591no—
362#1870—591no—
363#1870—591no—
364#1869—591no—
365#1869—591no—
366#1851—591no—
367#1850D5911yescharacteristic, complemented
368#1818—591no—
369#1798—591no—
370C2×C59—42no—
371C2×C59#237711yescharacteristic
372C2×C59#297611yescharacteristic
373C2×C59#297611yescharacteristic
374C2×C59#297811yescharacteristic
375C2×C59#298011yescharacteristic
376C2×C59#299211yescharacteristic
377C2×C59#299511yescharacteristic
378D59—81no—
379D59—81no—
380C22×M16—591no—
381C23×C8C2×D5911yescharacteristic
382C2×C4×D4—591no—
383C2×C4×D4—591no—
384C2×C4×D4—591no—
385C2×#117—591no—
386C2×C4⋊C8—591no—
387C2×C4⋊C8—591no—
388C2×C4⋊C8C2×D5911yescharacteristic
389C2×C4⋊C8C2×D5911yescharacteristic
390C2×C22⋊C8—591no—
391C2×C22⋊C8—591no—
392C2×C22⋊C8—591no—
393C2×C22⋊C8—591no—
394C2×C22⋊C8—591no—
395C2×C22⋊C8—591no—
396C2×C22⋊C8—591no—
397C2×C22⋊C8—591no—
398C2×C22⋊C8—591no—
399C2×C22⋊C8C2×D5911yescharacteristic
400C2×#97—591no—
401C2×#97—591no—
402#398—591no—
403#397—591no—
404#396—591no—
405#396—591no—
406#394—591no—
407#394—591no—
408#394—591no—
409#392—591no—
410C4×C4⋊C4—591no—
411C4×C22⋊C4—591no—
412C4×C22⋊C4C2×D5911yescharacteristic
413#336—591no—
414#336—591no—
415#336—591no—
416#336—591no—
417#336—591no—
418#336—591no—
419#336—591no—
420#336—591no—
421#336C2×D5911yescharacteristic
422#336C2×D5911yescharacteristic
423C59#2333511yescharacteristic, complemented, Sylow
424C22×D4—591no—
425C22×D4—591no—
426C22×D4—591no—
427C23×C4—591no—
428C23×C4—591no—
429C23×C4C22×D5911yescharacteristic
430C2×M16—2361no—
431C2×M16—2361no—
432C2×M16—2361no—
433C22×C8—41no—
434C22×C8—41no—
435C22×C8—41no—
436C22×C8—591no—
437C22×C8—591no—
438C22×C8—591no—
439C22×C8—591no—
440C22×C8C22×D5911yescharacteristic
441C22×C8C22×D5911yescharacteristic
442C22×C8C22×D5911yescharacteristic
443C22×C8C22×D5911yescharacteristic
444C4×D4—2361no—
445C4×D4—2361no—
446C4×D4—2361no—
447C4×D4—2361no—
448C4×D4—2361no—
449C4×D4—2361no—
450#117—2361no—
451#117—2361no—
452C2×C4⋊C4—591no—
453C2×C4⋊C4—591no—
454C2×C4⋊C4—591no—
455C2×C4⋊C4—591no—
456C2×C4⋊C4—591no—
457C2×C4⋊C4—591no—
458C2×C4⋊C4—591no—
459C2×C22⋊C4—591no—
460C2×C22⋊C4—591no—
461C2×C22⋊C4—591no—
462C2×C22⋊C4—591no—
463C2×C22⋊C4—591no—
464C2×C22⋊C4—591no—
465C2×C22⋊C4—591no—
466C2×C22⋊C4—591no—
467C2×C22⋊C4—591no—
468C2×C22⋊C4—591no—
469C2×C22⋊C4C4×D5911yescharacteristic
470C2×C22⋊C4C4×D5911yescharacteristic
471C2×C42—591no—
472C2×C42—591no—
473C2×C42C22×D5911yescharacteristic
474C2×C42C22×D5911yescharacteristic
475C4⋊C8—41no—
476C4⋊C8—41no—
477C4⋊C8—2361no—
478C4⋊C8—2361no—
479C22⋊C8—41no—
480C22⋊C8—2361no—
481C22⋊C8—2361no—
482C22⋊C8—2361no—
483C22⋊C8—2361no—
484C22⋊C8—2361no—
485C22⋊C8—2361no—
486C22⋊C8—2361no—
487C22⋊C8—2361no—
488C22⋊C8—2361no—
489#97—2361no—
490#97—2361no—
491#95—591no—
492#95—591no—
493#95—591no—
494#95—591no—
495#95C4×D5911yescharacteristic
496#95C4×D5911yescharacteristic
497C24—591no—
498C24—591no—
499C24C2×C4×D5911yescharacteristic
500C2×D4—1182no—
501C2×D4—1182no—
502C2×D4—2361no—
503C2×D4—2361no—
504C2×D4—2361no—
505C2×D4—2361no—
506C2×D4—2361no—
507C2×D4—2361no—
508C2×D4—2361no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—591no—
516C22×C4—591no—
517C22×C4—591no—
518C22×C4—591no—
519C22×C4—591no—
520C22×C4—591no—
521C22×C4—1181no—
522C22×C4—1181no—
523C22×C4—1181no—
524C22×C4—1181no—
525C22×C4—1181no—
526C22×C4—1181no—
527C22×C4—1181no—
528C22×C4—1181no—
529C22×C4—1181no—
530C22×C4—1181no—
531C22×C4—1181no—
532C22×C4—1181no—
533C22×C4C2×C4×D5911yescharacteristic
534C22×C4C2×C4×D5911yescharacteristic
535C22×C4C2×C4×D5911yescharacteristic
536C22×C4C2×C4×D5911yescharacteristic
537C22×C4C2×C4×D5911yescharacteristic
538C22×C4C23×D5911yescharacteristic
539M16—2364no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—44no—
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—1181no—
565C4⋊C4—2361no—
566C4⋊C4—2361no—
567C4⋊C4—2361no—
568C4⋊C4—2361no—
569C4⋊C4—2361no—
570C4⋊C4—2361no—
571C4⋊C4—2361no—
572C22⋊C4—22no—
573C22⋊C4—41no—
574C22⋊C4—2361no—
575C22⋊C4—2361no—
576C22⋊C4—2361no—
577C22⋊C4—2361no—
578C22⋊C4—2361no—
579C22⋊C4—2361no—
580C22⋊C4—2361no—
581C22⋊C4—2361no—
582C22⋊C4—2361no—
583C22⋊C4—2361no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—1181no—
589C42—1181no—
590C42—1181no—
591C42—1181no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—1181no—
599C23—1181no—
600C23—1181no—
601C23—1181no—
602C23—1181no—
603C23—1181no—
604C23—1181no—
605C23—1181no—
606C23—1181no—
607C23—1181no—
608C23—1181no—
609C23—1181no—
610C23—1181no—
611C23—1181no—
612C23#1427373312yes—
613C23C22×C4×D5911yescharacteristic
614D4—2364no—
615D4—2364no—
616D4—2364no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
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—21no—
631C2×C4—21no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—1181no—
637C2×C4—1181no—
638C2×C4—1181no—
639C2×C4—1181no—
640C2×C4—1181no—
641C2×C4—1181no—
642C2×C4—1181no—
643C2×C4—1181no—
644C2×C4—1181no—
645C2×C4—1181no—
646C2×C4—1181no—
647C2×C4—1181no—
648C2×C4—1181no—
649C2×C4—1181no—
650C2×C4—1181no—
651C2×C4—1181no—
652C2×C4—1181no—
653C2×C4—1181no—
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#1427377211yescharacteristic
663C2×C4#1427377211yescharacteristic
664C2×C4#1427377211yescharacteristic
665C2×C4#1427377311yescharacteristic
666C2×C4#1427377311yescharacteristic
667C2×C4#1427377511yescharacteristic
668C8—41no—
669C8—41no—
670C8—41no—
671C8—41no—
672C8—2361no—
673C8—2361no—
674C8—2361no—
675C8—2361no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—2361no—
684C22—2361no—
685C22—2361no—
686C22—2361no—
687C22—2361no—
688C22—2361no—
689C22—2361no—
690C22—2361no—
691C22—2361no—
692C22—2361no—
693C22—2361no—
694C22—2361no—
695C22—2361no—
696C22—2361no—
697C22#1683787411yescharacteristic
698C22#1683787411yescharacteristic
699C22#1683788311yescharacteristic
700C22C2×#1427373311yescharacteristic
701C22#1683816711yescharacteristic
702C22#1683816711yescharacteristic
703C22#1683816811yescharacteristic
704C4—41no—
705C4—41no—
706C4—41no—
707C4—41no—
708C4—41no—
709C4—2361no—
710C4—2361no—
711C4—2361no—
712C4—2361no—
713C4—2361no—
714C4—2361no—
715C4#1683814111yescharacteristic
716C4#1683814211yescharacteristic
717C4#1683814811yescharacteristic
718C4#1683814811yescharacteristic
719C2—42no—
720C2—4721no—
721C2—4721no—
722C2#2142725211yescharacteristic
723C2#2143313811yescharacteristic
724C2#2143313811yescharacteristic
725C2#2143315511yescharacteristic
726C2#2143316411yescharacteristic
727C2#2143323211yescharacteristic
728C2#2143326411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D59
commutator, socleC23×C59C23×C4
FittingC59×#1850C2
prime radical#16837311C4
cosocleC22×C4×C59C24
hypercenter#1850D59
hypocenterC59#23335
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
2. #21424893C2semidirect
3. #21424892C2semidirect
4. #21424711C2semidirect
5. #21424708C2semidirect
6. #21424658C2semidirect
7. #21424657C2semidirect
8. #21424392C2semidirect
9. #21424390C2semidirect
10. #21424388C2semidirect
11. #21424388C2semidirect
12. #21424280C2semidirect
13. #21424166C2semidirect
14. #21424077C2semidirect
15. C59×#1850C2semidirect
367. #1850D59semidirect
423. C59#23335semidirect

Maximal subgroups

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

subgroupindex
#214273402
#214248932
#214248922
#214247112
#214247082
#214246582
#214246572
#214243922
#214243902
#214243882
#214242802
#214241662
#214240772
C59×#18502
#2333559