Finite Group Databasebeta

← C2×#21429404 #28759142

Subgroups — C2×#21429404 #28759142

Order 15104.

2550 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21429404C2116yesmaximal, direct product factor
2C2×C59⋊#401C211yesmaximal, characteristic, complemented
3C2×#16837327C211yesmaximal, characteristic, complemented
4C2×#16837325C211yesmaximal, characteristic, complemented
5C2×#16837316C211yesmaximal, characteristic
6C2×#16837290C211yesmaximal, characteristic, complemented
7C2×#16837290C211yesmaximal, characteristic, complemented
8C2×#16837289C211yesmaximal, characteristic, complemented
9C2×#16837284C211yesmaximal, characteristic, complemented
10C2×#16837282C211yesmaximal, characteristic
11C2×#16837274C211yesmaximal, characteristic, complemented
12C2×#16837266C211yesmaximal, characteristic, complemented
13C2×#16837265C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic59C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic59C211yesmaximal, characteristic, complemented
16C2×C59×#386C211yesmaximal, characteristic
17C24×Dic59C2211yescharacteristic
18C22×C4⋊Dic59C2211yescharacteristic
19C22×Dic59⋊C4C2211yescharacteristic
20C22×Dic59⋊C4C2211yescharacteristic
21C22×Dic59⋊C4C2211yescharacteristic
22C22×Dic59⋊C4C2211yescharacteristic
23C22×C22⋊Dic59C2211yescharacteristic
24C22×C22⋊Dic59C2211yescharacteristic
25C22×C22⋊Dic59C2211yescharacteristic
26C22×C22⋊Dic59C2211yescharacteristic
27C22×C22⋊Dic59C2211yescharacteristic
28C22×C22⋊Dic59C2211yescharacteristic
29C22×C22⋊Dic59C2211yescharacteristic
30C22×C4×Dic59C2211yescharacteristic
31C22×C4×Dic59C2211yescharacteristic
32C22×C4×Dic59C2211yescharacteristic
33C59⋊#401C2218yescomplemented
34#16837327C2218yescomplemented
35#16837325C2218yescomplemented
36#16837316C2218yes—
37#16837290C2218yescomplemented
38#16837290C2218yescomplemented
39#16837289C2218yescomplemented
40#16837284C2218yescomplemented
41#16837282C2218yes—
42#16837274C2218yescomplemented
43#16837266C2218yescomplemented
44#16837265C2218yescomplemented
45C22⋊C4×Dic59C2218yescomplemented
46C4×C22⋊Dic59C2218yescomplemented
47C2×C59⋊#95C2211yescharacteristic
48C2×C59⋊#95C2211yescharacteristic
49C2×C59⋊#95C2211yescharacteristic
50C2×C59⋊#95C2211yescharacteristic
51C2×C59⋊#95C2211yescharacteristic
52C2×C59⋊#95C2211yescharacteristic
53C2×C59⋊#95C2211yescharacteristic
54C2×C59⋊#95C2211yescharacteristic
55C2×C59⋊#95C2211yescharacteristic
56C2×C59⋊#95C2211yescharacteristic
57C2×C59⋊#95C2211yescharacteristic
58C2×C59⋊#95C2211yescharacteristic
59C23×D4×C59C2211yescharacteristic
60C24×C4×C59C2211yescharacteristic
61C22×C22⋊C4×C59C2211yescharacteristic
62C22×C22⋊C4×C59C2211yescharacteristic
63C22×C22⋊C4×C59C2211yescharacteristic
64C59×#386C2218yes—
65C2×#95×C59C2211yescharacteristic
66C2×#95×C59C2211yescharacteristic
67C23×Dic59—24no—
68C23×Dic59—42no—
69C23×Dic59—42no—
70C23×Dic59C2311yescharacteristic
71C23×Dic59C2311yescharacteristic
72C23×Dic59C2311yescharacteristic
73C23×Dic59C2311yescharacteristic
74C23×Dic59C2311yescharacteristic
75C23×Dic59C2311yescharacteristic
76C23×Dic59C2311yescharacteristic
77C23×Dic59C2311yescharacteristic
78C23×Dic59C2314yes—
79C2×C4⋊Dic59—42no—
80C2×C4⋊Dic59C2314yes—
81C2×Dic59⋊C4—24no—
82C2×Dic59⋊C4—24no—
83C2×Dic59⋊C4—42no—
84C2×Dic59⋊C4—42no—
85C2×Dic59⋊C4C2314yes—
86C2×Dic59⋊C4C2314yes—
87C2×Dic59⋊C4C2314yes—
88C2×Dic59⋊C4C2314yes—
89C2×C22⋊Dic59—24no—
90C2×C22⋊Dic59—24no—
91C2×C22⋊Dic59—24no—
92C2×C22⋊Dic59—24no—
93C2×C22⋊Dic59—24no—
94C2×C22⋊Dic59—24no—
95C2×C22⋊Dic59—42no—
96C2×C22⋊Dic59C2314yes—
97C2×C22⋊Dic59C2314yes—
98C2×C22⋊Dic59C2314yes—
99C2×C22⋊Dic59C2314yes—
100C2×C22⋊Dic59C2314yes—
101C2×C22⋊Dic59C2314yes—
102C2×C22⋊Dic59C2314yes—
103C2×C4×Dic59—24no—
104C2×C4×Dic59—42no—
105C2×C4×Dic59—42no—
106C2×C4×Dic59C2314yes—
107C2×C4×Dic59C2314yes—
108C2×C4×Dic59C2314yes—
109C59⋊#95C2314yes—
110C59⋊#95C2314yes—
111C59⋊#95C2314yes—
112C59⋊#95C2314yes—
113C59⋊#95C2314yes—
114C59⋊#95C2314yes—
115C59⋊#95C2314yes—
116C59⋊#95C2314yes—
117C59⋊#95C2314yes—
118C59⋊#95C2314yes—
119C59⋊#95C2314yes—
120C59⋊#95C2314yes—
121C25×C59C2311yescharacteristic
122C25×C59C2311yescharacteristic
123C22×D4×C59—24no—
124C22×D4×C59—24no—
125C22×D4×C59—42no—
126C22×D4×C59C2314yes—
127C23×C4×C59—24no—
128C23×C4×C59—24no—
129C23×C4×C59—42no—
130C23×C4×C59C2311yescharacteristic
131C23×C4×C59C2311yescharacteristic
132C23×C4×C59C2311yescharacteristic
133C23×C4×C59C2311yescharacteristic
134C23×C4×C59C2314yes—
135C23×C4×C59C2311yescharacteristic
136C2×C22⋊C4×C59—24no—
137C2×C22⋊C4×C59—42no—
138C2×C22⋊C4×C59—42no—
139C2×C22⋊C4×C59C2314yes—
140C2×C22⋊C4×C59C2314yes—
141C2×C22⋊C4×C59C2314yes—
142#95×C59C2314yes—
143#95×C59C2314yes—
144C24×C59—22no—
145C24×C59—22no—
146C24×C59—22no—
147C24×C59—22no—
148C24×C59—22no—
149C24×C59—22no—
150C24×C59—22no—
151C24×C59—22no—
152C24×C59—22no—
153C24×C59—22no—
154C24×C59—22no—
155C24×C59—22no—
156C24×C59#4114yes—
157C24×C59#4114yes—
158C24×C59C2412yes—
159C24×C59C2412yes—
160C24×C59C2411yescharacteristic
161C2×D4×C59—28no—
162C2×D4×C59—28no—
163C2×D4×C59—44no—
164C2×D4×C59—416no—
165C22×C4×C59—22no—
166C22×C4×C59—22no—
167C22×C4×C59—22no—
168C22×C4×C59—28no—
169C22×C4×C59—22no—
170C22×C4×C59—22no—
171C22×C4×C59—22no—
172C22×C4×C59—22no—
173C22×C4×C59—22no—
174C22×C4×C59—22no—
175C22×C4×C59—22no—
176C22×C4×C59—22no—
177C22×C4×C59—22no—
178C22×C4×C59—22no—
179C22×C4×C59—22no—
180C22×C4×C59—28no—
181C22×C4×C59—44no—
182C22×C4×C59—416no—
183C22×C4×C59#4114yes—
184C22×C4×C59C2412yes—
185C22×C4×C59C2412yes—
186C22×C4×C59C2412yes—
187C22×C4×C59C2412yes—
188C22×C4×C59C2412yes—
189C22×Dic59—22no—
190C22×Dic59—22no—
191C22×Dic59—22no—
192C22×Dic59—22no—
193C22×Dic59—22no—
194C22×Dic59—22no—
195C22×Dic59—22no—
196C22×Dic59—22no—
197C22×Dic59—22no—
198C22×Dic59—22no—
199C22×Dic59—22no—
200C22×Dic59—22no—
201C22×Dic59—22no—
202C22×Dic59—22no—
203C22×Dic59—22no—
204C22×Dic59—22no—
205C22×Dic59—22no—
206C22×Dic59—22no—
207C22×Dic59—22no—
208C22×Dic59—22no—
209C22×Dic59—22no—
210C22×Dic59—22no—
211C22×Dic59—28no—
212C22×Dic59—44no—
213C22×Dic59—44no—
214C22×Dic59—416no—
215C22×Dic59#4114yes—
216C22×Dic59#4114yes—
217C22×Dic59C2412yes—
218C22×Dic59C2412yes—
219C22×Dic59C2412yes—
220C22×Dic59C2412yes—
221C22×Dic59C2412yes—
222C22×Dic59C2412yes—
223C22×Dic59C2412yes—
224C22×Dic59C2412yes—
225C22⋊C4×C59—28no—
226C22⋊C4×C59—44no—
227C22⋊C4×C59—44no—
228C22⋊Dic59—28no—
229C22⋊Dic59—28no—
230C22⋊Dic59—28no—
231C22⋊Dic59—28no—
232C22⋊Dic59—28no—
233C22⋊Dic59—28no—
234C22⋊Dic59—44no—
235C4⋊Dic59—44no—
236Dic59⋊C4—28no—
237Dic59⋊C4—28no—
238Dic59⋊C4—44no—
239Dic59⋊C4—44no—
240C4×Dic59—28no—
241C4×Dic59—44no—
242C4×Dic59—44no—
243C23×C59—28no—
244C23×C59—28no—
245C23×C59—28no—
246C23×C59—28no—
247C23×C59—28no—
248C23×C59—28no—
249C23×C59—22no—
250C23×C59—22no—
251C23×C59—22no—
252C23×C59—22no—
253C23×C59—22no—
254C23×C59—22no—
255C23×C59—22no—
256C23×C59—22no—
257C23×C59—22no—
258C23×C59—22no—
259C23×C59—22no—
260C23×C59—22no—
261C23×C59—44no—
262C23×C59—44no—
263C23×C59—44no—
264C23×C59—44no—
265C23×C59—44no—
266C23×C59—44no—
267C23×C59—44no—
268C23×C59—44no—
269C23×C59C2×#4112yes—
270C23×C59C2×#4112yes—
271C23×C59C2×#4114yes—
272C23×C59C2×#4112yes—
273C23×C59C2×#4112yes—
274C23×C59C2×#4114yes—
275C23×C59C2×#4112yes—
276C23×C59H(5,𝔽2)12yes—
277C23×C59H(5,𝔽2)12yes—
278C23×C59C2511yescharacteristic
279D4×C59—416no—
280C2×C4×C59—28no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—416no—
296C2×C4×C59—44no—
297C2×C4×C59—44no—
298C2×C4×C59—44no—
299C2×C4×C59—44no—
300C2×C4×C59C2×#4114yes—
301C2×Dic59—28no—
302C2×Dic59—28no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—22no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—22no—
318C2×Dic59—22no—
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—22no—
323C2×Dic59—22no—
324C2×Dic59—22no—
325C2×Dic59—416no—
326C2×Dic59—44no—
327C2×Dic59—44no—
328C2×Dic59—44no—
329C2×Dic59—44no—
330C2×Dic59—44no—
331C2×Dic59—44no—
332C2×Dic59C2×#4114yes—
333C2×Dic59C2×#4114yes—
334C2×#2576—591nomaximal, Sylow
335C22×C59—24no—
336C22×C59—24no—
337C22×C59—24no—
338C22×C59—24no—
339C22×C59—24no—
340C22×C59—24no—
341C22×C59—416no—
342C22×C59—416no—
343C22×C59—42no—
344C22×C59—42no—
345C22×C59—42no—
346C22×C59—42no—
347C22×C59—42no—
348C22×C59—42no—
349C22×C59—42no—
350C22×C59—42no—
351C22×C59#52914yes—
352C22×C59#52914yes—
353C22×C59#53814yes—
354C22×C59#55114yes—
355C22×C59#55114yes—
356C22×C59#55314yes—
357C22×C59#55314yes—
358C22×C59C22×#4111yescharacteristic
359C22×C59C22×#4111yescharacteristic
360C22×C59C22×#4111yescharacteristic
361C22×C59C22×#4111yescharacteristic
362C22×C59C22×#4111yescharacteristic
363C22×C59C2×H(5,𝔽2)11yescharacteristic
364C22×C59C2×H(5,𝔽2)11yescharacteristic
365C4×C59—24no—
366C4×C59—42no—
367C4×C59—42no—
368C4×C59—42no—
369C4×C59—42no—
370Dic59—24no—
371Dic59—24no—
372Dic59—42no—
373Dic59—42no—
374Dic59—42no—
375Dic59—42no—
376Dic59—42no—
377Dic59—42no—
378#2576—5916no—
379C2×#401—591no—
380C2×#397—591no—
381C2×#396—591no—
382C2×#394—591no—
383C2×#388—591no—
384C2×#388—591no—
385C2×#387—591no—
386C2×#387—591no—
387C2×#386—591no—
388C2×#386D5911yescharacteristic
389C2×#385—591no—
390C2×#382—591no—
391C2×#381—591no—
392C2×C4×C22⋊C4—591no—
393C2×C4×C22⋊C4—591no—
394C2×C59—44no—
395C2×C59—44no—
396C2×C59#257618yescomplemented
397C2×C59C2×#52911yescharacteristic
398C2×C59C2×#52911yescharacteristic
399C2×C59C2×#53811yescharacteristic
400C2×C59C2×#55111yescharacteristic
401C2×C59C2×#55111yescharacteristic
402C2×C59C2×#55311yescharacteristic
403C2×C59C2×#55311yescharacteristic
404C23×D4C2×D5911yescharacteristic
405C24×C4—591no—
406C24×C4C2×D5911yescharacteristic
407C22×C4⋊C4—591no—
408C22×C4⋊C4—591no—
409C22×C4⋊C4—591no—
410C22×C4⋊C4—591no—
411C22×C4⋊C4—591no—
412C22×C22⋊C4—591no—
413C22×C22⋊C4—591no—
414C22×C22⋊C4—591no—
415C22×C22⋊C4—591no—
416C22×C22⋊C4—591no—
417C22×C22⋊C4—591no—
418C22×C22⋊C4—591no—
419C22×C22⋊C4C2×D5911yescharacteristic
420C22×C22⋊C4C2×D5911yescharacteristic
421C22×C22⋊C4C2×D5911yescharacteristic
422C22×C42—591no—
423C22×C42—591no—
424C22×C42—591no—
425#401—598no—
426#397—598no—
427#396—598no—
428#394—598no—
429#388—598no—
430#388—598no—
431#387—598no—
432#387—598no—
433#386—598no—
434#386C2×D5918yes—
435#385—598no—
436#382—598no—
437#381—598no—
438C4×C22⋊C4—598no—
439C4×C22⋊C4—598no—
440C2×#95—591no—
441C2×#95—591no—
442C2×#95—591no—
443C2×#95—591no—
444C2×#95—591no—
445C2×#95—591no—
446C2×#95—591no—
447C2×#95—591no—
448C2×#95—591no—
449C2×#95—591no—
450C2×#95—591no—
451C2×#95—591no—
452C2×#95C2×D5911yescharacteristic
453C2×#95C2×D5911yescharacteristic
454C59C2×#257611yescharacteristic, complemented, Sylow
455C25C22×D5911yescharacteristic
456C25C22×D5911yescharacteristic
457C22×D4—24no—
458C22×D4—24no—
459C22×D4—42no—
460C22×D4C22×D5914yes—
461C23×C4—24no—
462C23×C4—24no—
463C23×C4—42no—
464C23×C4—591no—
465C23×C4—591no—
466C23×C4—591no—
467C23×C4—591no—
468C23×C4—591no—
469C23×C4—591no—
470C23×C4—591no—
471C23×C4—591no—
472C23×C4—594no—
473C23×C4—1184no—
474C23×C4—2362no—
475C23×C4—2362no—
476C23×C4C22×D5911yescharacteristic
477C23×C4C22×D5911yescharacteristic
478C23×C4C22×D5911yescharacteristic
479C23×C4C22×D5911yescharacteristic
480C23×C4C22×D5914yes—
481C23×C4C22×D5911yescharacteristic
482C2×C4⋊C4—594no—
483C2×C4⋊C4—594no—
484C2×C4⋊C4—594no—
485C2×C4⋊C4—594no—
486C2×C4⋊C4—594no—
487C2×C4⋊C4—1184no—
488C2×C4⋊C4—1184no—
489C2×C4⋊C4—2362no—
490C2×C4⋊C4—2362no—
491C2×C4⋊C4—2362no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—594no—
496C2×C22⋊C4—594no—
497C2×C22⋊C4—594no—
498C2×C22⋊C4—594no—
499C2×C22⋊C4—594no—
500C2×C22⋊C4—594no—
501C2×C22⋊C4—594no—
502C2×C22⋊C4—1184no—
503C2×C22⋊C4—1184no—
504C2×C22⋊C4—1184no—
505C2×C22⋊C4—1184no—
506C2×C22⋊C4—1184no—
507C2×C22⋊C4—1184no—
508C2×C22⋊C4—2362no—
509C2×C22⋊C4C22×D5914yes—
510C2×C22⋊C4C22×D5914yes—
511C2×C22⋊C4C22×D5914yes—
512C2×C42—594no—
513C2×C42—594no—
514C2×C42—594no—
515C2×C42—1184no—
516C2×C42—2362no—
517C2×C42—2362no—
518#95—594no—
519#95—594no—
520#95—594no—
521#95—594no—
522#95—594no—
523#95—594no—
524#95—594no—
525#95—594no—
526#95—594no—
527#95—594no—
528#95—594no—
529#95—594no—
530#95C22×D5914yes—
531#95C22×D5914yes—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24#1174568514yes—
545C24#1174568714yes—
546C24C23×D5912yes—
547C24C23×D5912yes—
548C24C23×D5911yescharacteristic
549C2×D4—28no—
550C2×D4—28no—
551C2×D4—44no—
552C2×D4—416no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—28no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—28no—
569C22×C4—44no—
570C22×C4—416no—
571C22×C4—594no—
572C22×C4—594no—
573C22×C4—592no—
574C22×C4—592no—
575C22×C4—592no—
576C22×C4—592no—
577C22×C4—592no—
578C22×C4—592no—
579C22×C4—592no—
580C22×C4—592no—
581C22×C4—1188no—
582C22×C4—1182no—
583C22×C4—1182no—
584C22×C4—1182no—
585C22×C4—1182no—
586C22×C4—1182no—
587C22×C4—1182no—
588C22×C4—1182no—
589C22×C4—1182no—
590C22×C4—1182no—
591C22×C4—1182no—
592C22×C4—1182no—
593C22×C4—1182no—
594C22×C4—1182no—
595C22×C4—1182no—
596C22×C4—1182no—
597C22×C4—1182no—
598C22×C4—1182no—
599C22×C4—1182no—
600C22×C4—1182no—
601C22×C4—1182no—
602C22×C4—1182no—
603C22×C4—1182no—
604C22×C4—2364no—
605C22×C4—2364no—
606C22×C4—23616no—
607C22×C4#1174568714yes—
608C22×C4C23×D5912yes—
609C22×C4C23×D5912yes—
610C22×C4C23×D5912yes—
611C22×C4C23×D5912yes—
612C22×C4C23×D5912yes—
613C4⋊C4—1188no—
614C4⋊C4—1188no—
615C4⋊C4—2364no—
616C4⋊C4—2364no—
617C4⋊C4—2364no—
618C22⋊C4—28no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—1188no—
622C22⋊C4—1188no—
623C22⋊C4—1188no—
624C22⋊C4—1188no—
625C22⋊C4—1188no—
626C22⋊C4—1188no—
627C22⋊C4—2364no—
628C42—1188no—
629C42—2364no—
630C42—2364no—
631C23—28no—
632C23—28no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—28no—
646C23—28no—
647C23—28no—
648C23—28no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23#41×D5912yes—
658C23#41×D5912yes—
659C23C2×#1174568714yes—
660C23C2×#1174568712yes—
661C23C2×#1174568712yes—
662C23C2×#1174568514yes—
663C23C2×#1174568512yes—
664C23#1427377212yes—
665C23#1427377212yes—
666C23C24×D5911yescharacteristic
667D4—416no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—28no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—416no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—594no—
689C2×C4—594no—
690C2×C4—1182no—
691C2×C4—1182no—
692C2×C4—1182no—
693C2×C4—1182no—
694C2×C4—1188no—
695C2×C4—1188no—
696C2×C4—1182no—
697C2×C4—1182no—
698C2×C4—1182no—
699C2×C4—1182no—
700C2×C4—1182no—
701C2×C4—1182no—
702C2×C4—1182no—
703C2×C4—1182no—
704C2×C4—1182no—
705C2×C4—1182no—
706C2×C4—1182no—
707C2×C4—1182no—
708C2×C4—1182no—
709C2×C4—1182no—
710C2×C4—1182no—
711C2×C4—1182no—
712C2×C4—1182no—
713C2×C4—1182no—
714C2×C4—23616no—
715C2×C4—2364no—
716C2×C4—2364no—
717C2×C4—2364no—
718C2×C4—2364no—
719C2×C4—2364no—
720C2×C4—2364no—
721C2×C4C2×#1174568714yes—
722C22—24no—
723C22—24no—
724C22—24no—
725C22—24no—
726C22—24no—
727C22—24no—
728C22—416no—
729C22—416no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22#1683792914yes—
739C22#1683793214yes—
740C22#1683798414yes—
741C22#1683807814yes—
742C22#1683808314yes—
743C22#1683809914yes—
744C22#1683810114yes—
745C22C2×#41×D5911yescharacteristic
746C22C2×#41×D5911yescharacteristic
747C22C22×#1174568711yescharacteristic
748C22C22×#1174568711yescharacteristic
749C22C22×#1174568511yescharacteristic
750C22C2×#1427377211yescharacteristic
751C22C2×#1427377211yescharacteristic
752C4—24no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—1184no—
758C4—1184no—
759C4—2362no—
760C4—2362no—
761C4—2362no—
762C4—2362no—
763C4—2362no—
764C4—2362no—
765C2—44no—
766C2—44no—
767C2#2142940418yesdirect product factor
768C2C2×#1683792911yescharacteristic
769C2C2×#1683793211yescharacteristic
770C2C2×#1683798411yescharacteristic
771C2C2×#1683807811yescharacteristic
772C2C2×#1683808311yescharacteristic
773C2C2×#1683809911yescharacteristic
774C2C2×#1683810111yescharacteristic
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#386C2
socleC24×C59C24
prime radicalC23×D4×C59C22
hypercenterC2×#386D59
hypocenterC59C2×#2576
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. #21429404C2direct (N × H)
2. C2×C59⋊#401C2semidirect
3. C2×#16837327C2semidirect
4. C2×#16837325C2semidirect
6. C2×#16837290C2semidirect
7. C2×#16837290C2semidirect
8. C2×#16837289C2semidirect
9. C2×#16837284C2semidirect
11. C2×#16837274C2semidirect
12. C2×#16837266C2semidirect
13. C2×#16837265C2semidirect
14. C2×C22⋊C4×Dic59C2semidirect
15. C2×C4×C22⋊Dic59C2semidirect
33. C59⋊#401C22semidirect
34. #16837327C22semidirect
35. #16837325C22semidirect
37. #16837290C22semidirect
38. #16837290C22semidirect
39. #16837289C22semidirect
40. #16837284C22semidirect
42. #16837274C22semidirect
43. #16837266C22semidirect
44. #16837265C22semidirect
45. C22⋊C4×Dic59C22semidirect
46. C4×C22⋊Dic59C22semidirect
396. C2×C59#2576semidirect
454. C59C2×#2576semidirect
767. C2#21429404direct (N × H)

Maximal subgroups

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

subgroupindex
#214294042
C2×C59⋊#4012
C2×#168373272
C2×#168373252
C2×#168373162
C2×#168372902
C2×#168372892
C2×#168372842
C2×#168372822
C2×#168372742
C2×#168372662
C2×#168372652
C2×C22⋊C4×Dic592
C2×C4×C22⋊Dic592
C2×C59×#3862
C2×#257659