Finite Group Databasebeta

← #28610899

Subgroups — #28610899

Order 15104.

998 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837473C211yesmaximal, characteristic, complemented
2C2×#16837472C211yesmaximal, characteristic, complemented
3C2×#16837471C211yesmaximal, characteristic, complemented
4#21427332C211yesmaximal, characteristic
5#21424889C211yesmaximal, characteristic, complemented
6#21424817C211yesmaximal, characteristic, complemented
7#21424708C211yesmaximal, characteristic, complemented
8#21424708C211yesmaximal, characteristic, complemented
9#21424393C211yesmaximal, characteristic, complemented
10#21424388C211yesmaximal, characteristic, complemented
11#21424277C211yesmaximal, characteristic, complemented
12#21424272C211yesmaximal, characteristic, complemented
13#21423966C211yesmaximal, characteristic, complemented
14#21423862C211yesmaximal, characteristic, complemented
15C2×C59×#424C211yesmaximal, characteristic, complemented
16C22×#11745659C2211yescharacteristic
17C22×C8×D59C2211yescharacteristic
18C2×C4×D236C2211yescharacteristic
19C2×C4×C22⋊D59C2211yescharacteristic
20C2×C4×C22⋊D59C2211yescharacteristic
21#16837473—24no—
22#16837472—24no—
23#16837471—24no—
24C2×Dic59⋊C8C2211yescharacteristic
25C2×Dic59⋊C8C2211yescharacteristic
26C2×C22⋊(C59⋊C8)C2211yescharacteristic
27C2×C22⋊(C59⋊C8)C2211yescharacteristic
28C2×(C2×D59)⋊C8C2211yescharacteristic
29C2×(C2×D59)⋊C8C2211yescharacteristic
30C2×(C2×D59)⋊C8C2211yescharacteristic
31C2×(C2×D59)⋊C8C2211yescharacteristic
32C2×(C2×D59)⋊C8C2211yescharacteristic
33C2×(C2×D59)⋊C8C2211yescharacteristic
34C2×#14273638C2211yescharacteristic
35C2×#14273637C2211yescharacteristic
36C2×#14273637C2211yescharacteristic
37C2×C4×C59⋊C8C2211yescharacteristic
38#16837332C411yescharacteristic
39#16837327C411yescharacteristic
40#16837324C411yescharacteristic
41#16837324C411yescharacteristic
42#16837319C411yescharacteristic
43#16837318C411yescharacteristic
44#16837318C411yescharacteristic
45#16837311C411yescharacteristic
46C4×C4⋊Dic59C2211yescharacteristic
47C4×(C2×D59)⋊C4C2211yescharacteristic
48C4×(C2×D59)⋊C4C2211yescharacteristic
49#16837157C2211yescharacteristic
50#16837157C2211yescharacteristic
51#16837156C2211yescharacteristic
52#16837156C2211yescharacteristic
53#16837156C2211yescharacteristic
54#16837156C2211yescharacteristic
55C22×M16×C59C2211yescharacteristic
56C23×C8×C59C2211yescharacteristic
57C2×#117×C59C2211yescharacteristic
58C59×#424—24no—
59C2×C4⋊C8×C59C2211yescharacteristic
60C2×C4⋊C8×C59C2211yescharacteristic
61C2×C4⋊C8×C59C2211yescharacteristic
62C2×C4⋊C8×C59C2211yescharacteristic
63C22×D236C2×C411yescharacteristic
64C22×C22⋊D59C2×C411yescharacteristic
65C22×C22⋊D59C2×C411yescharacteristic
66C22×C4×D59C2311yescharacteristic
67C22×C4×D59C2311yescharacteristic
68C2×#11745659—22no—
69C2×#11745659—22no—
70C2×#11745659—41no—
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74C22×C59⋊C8C2311yescharacteristic
75C2×C8×D59—22no—
76C2×C8×D59—22no—
77C2×C8×D59—41no—
78C4×D236—22no—
79C4×D236—22no—
80C4×C22⋊D59—22no—
81C4×C22⋊D59—22no—
82C4×C22⋊D59—22no—
83C4×C22⋊D59—22no—
84C2×C4⋊Dic59C2×C411yescharacteristic
85C2×C4⋊Dic59C2×C411yescharacteristic
86C2×C4⋊Dic59C2×C411yescharacteristic
87C2×Dic59⋊C4C2×C411yescharacteristic
88C2×Dic59⋊C4C2×C411yescharacteristic
89C2×C22⋊Dic59C2×C411yescharacteristic
90C2×C22⋊Dic59C2×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×(C2×D59)⋊C4C2×C411yescharacteristic
97C2×(C2×D59)⋊C4C2×C411yescharacteristic
98C2×(C2×D59)⋊C4C2×C411yescharacteristic
99C2×C4×Dic59C2311yescharacteristic
100C2×C4×Dic59C2311yescharacteristic
101Dic59⋊C8—22no—
102Dic59⋊C8—22no—
103C22⋊(C59⋊C8)—22no—
104C22⋊(C59⋊C8)D414yescomplemented
105(C2×D59)⋊C8—22no—
106(C2×D59)⋊C8—22no—
107(C2×D59)⋊C8—22no—
108(C2×D59)⋊C8—22no—
109(C2×D59)⋊C8—41no—
110(C2×D59)⋊C8—41no—
111#14273638—22no—
112#14273637—22no—
113#14273637—22no—
114C4×C59⋊C8—22no—
115C59⋊#95C2×C411yescharacteristic
116C59⋊#95C2×C411yescharacteristic
117C59⋊#95C2×C411yescharacteristic
118C59⋊#95C2×C411yescharacteristic
119C59⋊#95C2×C411yescharacteristic
120C59⋊#95C2×C411yescharacteristic
121C23×C4×C59C2311yescharacteristic
122C2×M16×C59—22no—
123C2×M16×C59—22no—
124C2×M16×C59—41no—
125C22×C8×C59—22no—
126C22×C8×C59—22no—
127C22×C8×C59—41no—
128C22×C8×C59C2311yescharacteristic
129C22×C8×C59C2311yescharacteristic
130C22×C8×C59C2311yescharacteristic
131C22×C8×C59C2311yescharacteristic
132#117×C59—22no—
133#117×C59—22no—
134C2×C4⋊C4×C59C2×C411yescharacteristic
135C2×C4⋊C4×C59C2×C411yescharacteristic
136C2×C22⋊C4×C59C2×C411yescharacteristic
137C2×C22⋊C4×C59C2×C411yescharacteristic
138C2×C42×C59C2311yescharacteristic
139C2×C42×C59C2311yescharacteristic
140C4⋊C8×C59—22no—
141C4⋊C8×C59—22no—
142C4⋊C8×C59—22no—
143C4⋊C8×C59D414yescomplemented
144C24×C59C22×C411yescharacteristic
145C23×D59C22×C411yescharacteristic
146C23×D59C22×C411yescharacteristic
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
151C22×C4×C59C22×C411yescharacteristic
152C22×C4×C59C22×C411yescharacteristic
153C22×C4×C59C22×C411yescharacteristic
154C22×C4×C59C22×C411yescharacteristic
155C22×C4×C59C22×C411yescharacteristic
156C22×C4×C59C2×D412yes—
157C22×C4×C59#4112yes—
158C22×C4×C59C2411yescharacteristic
159C2×C22⋊D59—22no—
160C2×C22⋊D59—22no—
161C2×C22⋊D59—22no—
162C2×C22⋊D59—41no—
163C2×C22⋊D59—41no—
164C2×C22⋊D59—41no—
165C22×Dic59C22×C411yescharacteristic
166C22×Dic59C22×C411yescharacteristic
167C22×Dic59C22×C411yescharacteristic
168C22×Dic59C22×C411yescharacteristic
169C22×Dic59C22×C411yescharacteristic
170C22×Dic59C22×C411yescharacteristic
171C2×D236—22no—
172C2×D236—22no—
173C2×D236—41no—
174C2×C4×D59—21no—
175C2×C4×D59—21no—
176C2×C4×D59—21no—
177C2×C4×D59—21no—
178C2×C4×D59—21no—
179C2×C4×D59—21no—
180C2×C4×D59—21no—
181C2×C4×D59—21no—
182C2×C4×D59—21no—
183C2×C4×D59—21no—
184C2×C4×D59—21no—
185C2×C4×D59—21no—
186M16×C59—44no—
187C2×C8×C59—21no—
188C2×C8×C59—21no—
189C2×C8×C59—21no—
190C2×C8×C59—21no—
191C2×C8×C59—21no—
192C2×C8×C59—21no—
193C2×C8×C59—21no—
194C2×C8×C59—21no—
195C2×C8×C59—21no—
196C2×C8×C59—21no—
197C2×C8×C59—44no—
198C2×C8×C59C2×D412yes—
199C2×C8×C59C2×D412yes—
200C4⋊C4×C59—22no—
201C4⋊C4×C59—22no—
202C22⋊C4×C59—22no—
203C22⋊C4×C59—22no—
204C42×C59—21no—
205C42×C59—21no—
206C42×C59C2×D412yes—
207C42×C59#4112yes—
208C22⋊Dic59—22no—
209C22⋊Dic59—22no—
210(C2×D59)⋊C4—22no—
211(C2×D59)⋊C4—22no—
212(C2×D59)⋊C4—22no—
213(C2×D59)⋊C4—22no—
214(C2×D59)⋊C4—22no—
215(C2×D59)⋊C4—41no—
216(C2×D59)⋊C4—41no—
217(C2×D59)⋊C4—41no—
218C4⋊Dic59—22no—
219C4⋊Dic59—41no—
220C4⋊Dic59—41no—
221Dic59⋊C4—22no—
222Dic59⋊C4—22no—
223C4×Dic59—21no—
224C4×Dic59—21no—
225C4×Dic59—21no—
226C4×Dic59—21no—
227C2×C59⋊C8—21no—
228C2×C59⋊C8—21no—
229C2×C59⋊C8—21no—
230C2×C59⋊C8—21no—
231C2×C59⋊C8—21no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8—21no—
236C2×C59⋊C8—21no—
237C2×C59⋊C8C2×D412yes—
238C2×C59⋊C8C2×D412yes—
239#11745659—44no—
240C8×D59—44no—
241C23×C59—21no—
242C23×C59—21no—
243C23×C59—21no—
244C23×C59—21no—
245C23×C59—21no—
246C23×C59—21no—
247C23×C59C4×D412yes—
248C23×C59C23×C411yescharacteristic
249C22×D59—21no—
250C22×D59—21no—
251C22×D59—21no—
252C22×D59—21no—
253C22×D59—21no—
254C22×D59—21no—
255C22×D59—21no—
256C22×D59—21no—
257C22×D59—21no—
258C22×D59—21no—
259C22×D59—21no—
260C22×D59—21no—
261C22×D59—21no—
262C22×D59#13112yes—
263C2×C4×C59—21no—
264C2×C4×C59—21no—
265C2×C4×C59—21no—
266C2×C4×C59—21no—
267C2×C4×C59—21no—
268C2×C4×C59—21no—
269C2×C4×C59—22no—
270C2×C4×C59—22no—
271C2×C4×C59—22no—
272C2×C4×C59—22no—
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×C59C4×D412yes—
280C2×C4×C59C4×D412yes—
281C2×C4×C59C4×D412yes—
282C2×C4×C59C22×D411yescharacteristic
283C2×C4×C59C22×D411yescharacteristic
284C2×C4×C59C2×#4111yescharacteristic
285C2×C4×C59C2×#4111yescharacteristic
286C2×C4×C59H(5,𝔽2)11yescharacteristic
287C2×C4×C592−1+411yescharacteristic
288C22⋊D59—44no—
289C22⋊D59—44no—
290C2×Dic59—21no—
291C2×Dic59—21no—
292C2×Dic59—21no—
293C2×Dic59—21no—
294C2×Dic59—21no—
295C2×Dic59—21no—
296C2×Dic59—21no—
297C2×Dic59—21no—
298C2×Dic59—21no—
299C2×Dic59—21no—
300C2×Dic59—21no—
301C2×Dic59—21no—
302C2×Dic59—21no—
303C2×Dic59—21no—
304C2×Dic59—21no—
305C2×Dic59—21no—
306C2×Dic59—21no—
307C2×Dic59—21no—
308D236—44no—
309C4×D59—41no—
310C4×D59—41no—
311C4×D59—41no—
312C4×D59—41no—
313C4×D59—41no—
314C4×D59—41no—
315C4×D59—41no—
316C4×D59—41no—
317C8×C59—22no—
318C8×C59—22no—
319C8×C59—41no—
320C8×C59—41no—
321C59⋊C8—22no—
322C59⋊C8—22no—
323C59⋊C8—41no—
324C59⋊C8—41no—
325#22993—591nomaximal, Sylow
326C22×C59—22no—
327C22×C59—22no—
328C22×C59—22no—
329C22×C59—41no—
330C22×C59—41no—
331C22×C59—41no—
332C22×C59—41no—
333C22×C59C2×C4×D411yescharacteristic
334C22×C59C2×C4×D411yescharacteristic
335C22×C59#52011yescharacteristic
336C22×C59C2×#13111yescharacteristic
337C22×C59#56811yescharacteristic
338C22×C59#56811yescharacteristic
339C22×C59#56811yescharacteristic
340C2×D59—22no—
341C2×D59—22no—
342C2×D59—22no—
343C2×D59—41no—
344C2×D59—41no—
345C2×D59—41no—
346C2×D59—41no—
347C2×D59—41no—
348C2×D59—41no—
349C2×D59—41no—
350C2×D59—41no—
351C2×D59—41no—
352C2×D59—41no—
353C2×D59—41no—
354C4×C59—22no—
355C4×C59—22no—
356C4×C59—22no—
357C4×C59—41no—
358C4×C59—41no—
359C4×C59D4211yescharacteristic
360C4×C59#54711yescharacteristic
361C4×C59#54811yescharacteristic
362C4×C59#55311yescharacteristic
363Dic59—41no—
364Dic59—41no—
365Dic59—41no—
366Dic59—41no—
367Dic59—41no—
368Dic59—41no—
369C2×#435—591no—
370C2×#435—591no—
371C2×#435—591no—
372C2×#424D5911yescharacteristic, complemented
373#2392—591no—
374#1954—591no—
375#1940—591no—
376#1924—591no—
377#1924—591no—
378#1870—591no—
379#1869—591no—
380#1851—591no—
381#1850—591no—
382#1770—591no—
383#1750—591no—
384C2×C59—42no—
385C2×C59#236111yescharacteristic
386C2×C59#293011yescharacteristic
387C2×C59#293211yescharacteristic
388C2×C59#293311yescharacteristic
389C2×C59#293311yescharacteristic
390C2×C59#299211yescharacteristic
391C2×C59#299511yescharacteristic
392D59—42no—
393D59—81no—
394C22×M16—591no—
395C22×M16C2×D5911yescharacteristic
396C23×C8—591no—
397C23×C8C2×D5911yescharacteristic
398C2×C4×D4—591no—
399C2×C4×D4—591no—
400C2×C4×D4—591no—
401C2×#117C2×D5911yescharacteristic
402#435—1184no—
403#435—1184no—
404#435—1184no—
405#424—24no—
406C2×C4⋊C8—591no—
407C2×C4⋊C8—591no—
408C2×C4⋊C8C2×D5911yescharacteristic
409C2×C4⋊C8C2×D5911yescharacteristic
410C2×C4⋊C8C2×D5911yescharacteristic
411C2×C4⋊C8C2×D5911yescharacteristic
412C2×C22⋊C8—591no—
413C2×C22⋊C8—591no—
414C2×C22⋊C8—591no—
415C2×C22⋊C8—591no—
416C2×C22⋊C8—591no—
417C2×C22⋊C8—591no—
418C2×C22⋊C8—591no—
419C2×C22⋊C8—591no—
420C2×#97—591no—
421C2×#97—591no—
422C2×#97—591no—
423C2×C4×C8—591no—
424#398—591no—
425#397—591no—
426#396—591no—
427#396—591no—
428#394—591no—
429#394—591no—
430#394—591no—
431#392—591no—
432C4×C4⋊C4—591no—
433C4×C22⋊C4—591no—
434C4×C22⋊C4—591no—
435#336—591no—
436#336—591no—
437#336—591no—
438#336—591no—
439#336—591no—
440#336—591no—
441C59#2299311yescharacteristic, complemented, Sylow
442C22×D4—591no—
443C22×D4—591no—
444C22×D4—591no—
445C23×C4—591no—
446C23×C4—591no—
447C23×C4C22×D5911yescharacteristic
448C2×M16—22no—
449C2×M16—22no—
450C2×M16—41no—
451C2×M16—1182no—
452C2×M16—1182no—
453C2×M16—2361no—
454C22×C8—22no—
455C22×C8—22no—
456C22×C8—41no—
457C22×C8—591no—
458C22×C8—591no—
459C22×C8—591no—
460C22×C8—591no—
461C22×C8—1182no—
462C22×C8—1182no—
463C22×C8—2361no—
464C22×C8C22×D5911yescharacteristic
465C22×C8C22×D5911yescharacteristic
466C22×C8C22×D5911yescharacteristic
467C22×C8C22×D5911yescharacteristic
468C4×D4—1182no—
469C4×D4—1182no—
470C4×D4—1182no—
471C4×D4—1182no—
472C4×D4—1182no—
473C4×D4—1182no—
474#117—22no—
475#117—22no—
476C2×C4⋊C4—591no—
477C2×C4⋊C4—591no—
478C2×C4⋊C4—591no—
479C2×C4⋊C4—591no—
480C2×C4⋊C4—591no—
481C2×C4⋊C4C4×D5911yescharacteristic
482C2×C4⋊C4C4×D5911yescharacteristic
483C2×C22⋊C4—591no—
484C2×C22⋊C4—591no—
485C2×C22⋊C4—591no—
486C2×C22⋊C4—591no—
487C2×C22⋊C4—591no—
488C2×C22⋊C4—591no—
489C2×C22⋊C4—591no—
490C2×C22⋊C4—591no—
491C2×C22⋊C4—591no—
492C2×C22⋊C4—591no—
493C2×C22⋊C4C4×D5911yescharacteristic
494C2×C22⋊C4C4×D5911yescharacteristic
495C2×C42—591no—
496C2×C42—591no—
497C2×C42C22×D5911yescharacteristic
498C2×C42C22×D5911yescharacteristic
499C4⋊C8—22no—
500C4⋊C8—22no—
501C4⋊C8—22no—
502C4⋊C8—1182no—
503C4⋊C8—1182no—
504C4⋊C8C22⋊D5914yescomplemented
505C22⋊C8—594no—
506C22⋊C8—1182no—
507C22⋊C8—1182no—
508C22⋊C8—1182no—
509C22⋊C8—1182no—
510C22⋊C8—1182no—
511C22⋊C8—2361no—
512C22⋊C8—2361no—
513#97—1182no—
514#97—1182no—
515#97—1182no—
516C4×C8—1182no—
517#95—591no—
518#95—591no—
519#95—591no—
520#95—591no—
521#95—591no—
522#95—591no—
523C24—591no—
524C24—591no—
525C24C2×C4×D5911yescharacteristic
526C2×D4—1182no—
527C2×D4—1182no—
528C2×D4—1182no—
529C2×D4—1182no—
530C2×D4—1182no—
531C2×D4—2361no—
532C2×D4—2361no—
533C2×D4—2361no—
534C2×D4—2361no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—591no—
540C22×C4—591no—
541C22×C4—591no—
542C22×C4—591no—
543C22×C4—591no—
544C22×C4—591no—
545C22×C4—1181no—
546C22×C4—1181no—
547C22×C4—1181no—
548C22×C4—1181no—
549C22×C4—1181no—
550C22×C4—1181no—
551C22×C4—1181no—
552C22×C4—1181no—
553C22×C4—1181no—
554C22×C4—1181no—
555C22×C4—1181no—
556C22×C4—1181no—
557C22×C4C2×C4×D5911yescharacteristic
558C22×C4C2×C4×D5911yescharacteristic
559C22×C4C2×C4×D5911yescharacteristic
560C22×C4C2×C4×D5911yescharacteristic
561C22×C4C2×C4×D5911yescharacteristic
562C22×C4D4×D5912yes—
563C22×C4#1174568912yes—
564C22×C4C23×D5911yescharacteristic
565M16—44no—
566M16—2364no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—44no—
578C2×C8—592no—
579C2×C8—592no—
580C2×C8—1181no—
581C2×C8—1181no—
582C2×C8—1181no—
583C2×C8—1181no—
584C2×C8—1181no—
585C2×C8—1181no—
586C2×C8—1181no—
587C2×C8—1181no—
588C2×C8—1181no—
589C2×C8—1181no—
590C2×C8—2364no—
591C2×C8C2×C22⋊D5912yes—
592C2×C8C2×C22⋊D5912yes—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—1182no—
596C4⋊C4—1182no—
597C4⋊C4—1182no—
598C4⋊C4—2361no—
599C4⋊C4—2361no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—1182no—
603C22⋊C4—1182no—
604C22⋊C4—1182no—
605C22⋊C4—1182no—
606C22⋊C4—1182no—
607C22⋊C4—1182no—
608C22⋊C4—1182no—
609C22⋊C4—2361no—
610C22⋊C4—2361no—
611C22⋊C4—2361no—
612C42—21no—
613C42—21no—
614C42—1181no—
615C42—1181no—
616C42—1181no—
617C42—1181no—
618C42#1174568512yes—
619C42C2×C22⋊D5912yes—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—592no—
627C23—1181no—
628C23—1181no—
629C23—1181no—
630C23—1181no—
631C23—1181no—
632C23—1181no—
633C23—1181no—
634C23—1181no—
635C23—1181no—
636C23—1181no—
637C23—1181no—
638C23—1181no—
639C23—1181no—
640C23#1427368912yes—
641C23C22×C4×D5911yescharacteristic
642D4—2364no—
643D4—2364no—
644D4—2364no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—1181no—
662C2×C4—1181no—
663C2×C4—1181no—
664C2×C4—1181no—
665C2×C4—1181no—
666C2×C4—1181no—
667C2×C4—1181no—
668C2×C4—1181no—
669C2×C4—1181no—
670C2×C4—1181no—
671C2×C4—1181no—
672C2×C4—1181no—
673C2×C4—1181no—
674C2×C4—1181no—
675C2×C4—1181no—
676C2×C4—1181no—
677C2×C4—1181no—
678C2×C4—1181no—
679C2×C4—2361no—
680C2×C4—2361no—
681C2×C4—2361no—
682C2×C4—2361no—
683C2×C4—2361no—
684C2×C4—2361no—
685C2×C4—2361no—
686C2×C4—2361no—
687C2×C4C4×C22⋊D5912yes—
688C2×C4C4×C22⋊D5912yes—
689C2×C4#1427368912yes—
690C2×C4C2×D4×D5911yescharacteristic
691C2×C4C22×C22⋊D5911yescharacteristic
692C2×C4C2×#1174568511yescharacteristic
693C2×C4C2×#1174568911yescharacteristic
694C2×C4#1427377211yescharacteristic
695C2×C4#1427377511yescharacteristic
696C8—22no—
697C8—22no—
698C8—41no—
699C8—41no—
700C8—1182no—
701C8—1182no—
702C8—2361no—
703C8—2361no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—1182no—
712C22—1182no—
713C22—1182no—
714C22—2361no—
715C22—2361no—
716C22—2361no—
717C22—2361no—
718C22—2361no—
719C22—2361no—
720C22—2361no—
721C22—2361no—
722C22—2361no—
723C22—2361no—
724C22—2361no—
725C22C2×C4×C22⋊D5911yescharacteristic
726C22C2×#1427368911yescharacteristic
727C22#1683788311yescharacteristic
728C22#131×D5911yescharacteristic
729C22#1683816711yescharacteristic
730C22#1683816711yescharacteristic
731C22#1683816711yescharacteristic
732C4—22no—
733C4—22no—
734C4—22no—
735C4—41no—
736C4—41no—
737C4—2361no—
738C4—2361no—
739C4—2361no—
740C4—2361no—
741C4—2361no—
742C4—2361no—
743C4D4×C22⋊D5911yescharacteristic
744C4#1683805311yescharacteristic
745C4#1683806311yescharacteristic
746C4#1683810011yescharacteristic
747C2—42no—
748C2—4721no—
749C2—2362no—
750C2#2142711211yescharacteristic
751C2#2143279811yescharacteristic
752C2#2143281211yescharacteristic
753C2#2143281811yescharacteristic
754C2#2143282011yescharacteristic
755C2#2143323311yescharacteristic
756C2#2143326411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D59
commutator, socleC23×C59C23×C4
FittingC2×C59×#424C2
prime radical#16837311C4
cosocleC22×C4×C59C24
hypercenterC2×#424D59
hypocenterC59#22993
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
1. C2×#16837473C2semidirect
2. C2×#16837472C2semidirect
3. C2×#16837471C2semidirect
5. #21424889C2semidirect
6. #21424817C2semidirect
7. #21424708C2semidirect
8. #21424708C2semidirect
9. #21424393C2semidirect
10. #21424388C2semidirect
11. #21424277C2semidirect
12. #21424272C2semidirect
13. #21423966C2semidirect
14. #21423862C2semidirect
15. C2×C59×#424C2semidirect
104. C22⋊(C59⋊C8)D4semidirect
143. C4⋊C8×C59D4semidirect
372. C2×#424D59semidirect
441. C59#22993semidirect
504. C4⋊C8C22⋊D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168374732
C2×#168374722
C2×#168374712
#214273322
#214248892
#214248172
#214247082
#214243932
#214243882
#214242772
#214242722
#214239662
#214238622
C2×C59×#4242
#2299359