Finite Group Databasebeta

← C2×#342×D59 #28586115

Subgroups — C2×#342×D59 #28586115

Order 15104.

4334 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C4×D59C212yesmaximal
2C22×C22⋊C4×D59C211yesmaximal, characteristic
3C2×#16837169C211yesmaximal, characteristic, complemented
4C2×#16837168C212yesmaximal, complemented
5#342×D59C218yesmaximal, direct product factor
6C2×C59×#342C211yesmaximal, characteristic, complemented
7C25×D59C2211yescharacteristic
8C23×C4×D59—22no—
9C23×C4×D59C412yescomplemented
10C22×C22⋊Dic59C2211yescharacteristic
11C22×C22⋊Dic59C2212yes—
12C22×(C2×D59)⋊C4—22no—
13C22×(C2×D59)⋊C4C412yescomplemented
14C2×C22⋊C4×D59—24no—
15C2×C22⋊C4×D59—22no—
16C2×C22⋊C4×D59—24no—
17C2×C22⋊C4×D59—22no—
18C2×C22⋊C4×D59—28no—
19C2×C22⋊C4×D59C414yescomplemented
20C2×C22⋊C4×D59C4116yescomplemented
21C2×C22⋊C4×D59C2214yes—
22C2×C22⋊C4×D59C2218yes—
23#16837169C2214yescomplemented
24#16837168C2218yescomplemented
25C22×C22⋊C4×C59C2211yescharacteristic
26C22×C22⋊C4×C59C2212yes—
27C59×#342C2214yescomplemented
28C24×D59—48no—
29C24×D59C2×C411yescharacteristic
30C24×D59C2×C418yes—
31C24×D59C2×C412yes—
32C24×D59C2×C411yescharacteristic
33C24×D59D412yes—
34C24×D59D414yes—
35C24×D59D414yes—
36C24×D59D412yes—
37C24×D59Q814yes—
38C24×D59C2312yes—
39C23×Dic59—22no—
40C23×Dic59C2×C412yescomplemented
41C22×C4×D59—216no—
42C22×C4×D59—24no—
43C22×C4×D59—22no—
44C22×C4×D59—22no—
45C22×C4×D59—28no—
46C22×C4×D59—416no—
47C22×C4×D59—48no—
48C22×C4×D59C2×C418yescomplemented
49C2×C22⋊Dic59—22no—
50C2×C22⋊Dic59—22no—
51C2×C22⋊Dic59—22no—
52C2×C22⋊Dic59—24no—
53C2×C22⋊Dic59C2×C412yescomplemented
54C2×C22⋊Dic59C2×C418yescomplemented
55C2×C22⋊Dic59C2312yes—
56C2×C22⋊Dic59C2314yes—
57C2×(C2×D59)⋊C4—24no—
58C2×(C2×D59)⋊C4—24no—
59C2×(C2×D59)⋊C4—216no—
60C2×(C2×D59)⋊C4—28no—
61C2×(C2×D59)⋊C4C2×C418yescomplemented
62C22⋊C4×D59—28no—
63C22⋊C4×D59—28no—
64C22⋊C4×D59—232no—
65C22⋊C4×D59—28no—
66C22⋊C4×D59—28no—
67C22⋊C4×D59—216no—
68C22⋊C4×D59C2×C4132yescomplemented
69C25×C59C2311yescharacteristic
70C23×C4×C59—22no—
71C23×C4×C59C2×C412yescomplemented
72C2×C22⋊C4×C59—22no—
73C2×C22⋊C4×C59—22no—
74C2×C22⋊C4×C59—22no—
75C2×C22⋊C4×C59—24no—
76C2×C22⋊C4×C59C2×C412yescomplemented
77C2×C22⋊C4×C59C2×C418yescomplemented
78C2×C22⋊C4×C59C2312yes—
79C2×C22⋊C4×C59C2314yes—
80C24×C59—44no—
81C24×C59C22×C411yescharacteristic
82C24×C59C22×C414yes—
83C24×C59C22×C411yescharacteristic
84C24×C59C2×D412yes—
85C24×C59C2×D412yes—
86C24×C59C2×D412yes—
87C24×C59C2×Q812yes—
88C24×C59C2411yescharacteristic
89C23×D59—28no—
90C23×D59—216no—
91C23×D59—432no—
92C23×D59—48no—
93C23×D59—416no—
94C23×D59—416no—
95C23×D59—416no—
96C23×D59—48no—
97C23×D59—44no—
98C23×D59—48no—
99C23×D59C4214yes—
100C23×D59C4218yes—
101C23×D59C4214yes—
102C23×D59C22⋊C414yes—
103C23×D59C22⋊C412yes—
104C23×D59C22⋊C411yescharacteristic
105C23×D59C22⋊C418yes—
106C23×D59C22⋊C412yes—
107C23×D59C22⋊C4116yes—
108C23×D59C22⋊C414yes—
109C23×D59C22⋊C418yes—
110C23×D59C22⋊C412yes—
111C23×D59C22⋊C411yescharacteristic
112C23×D59C4⋊C414yes—
113C23×D59C4⋊C418yes—
114C23×D59C4⋊C4116yes—
115C23×D59C4⋊C418yes—
116C23×D59C4⋊C418yes—
117C23×D59C4⋊C414yes—
118C23×D59C22×C412yes—
119C23×D59C22×C418yes—
120C23×D59C22×C412yes—
121C23×D59C2×D414yes—
122C23×D59C2×D414yes—
123C23×D59C2×D414yes—
124C23×D59C2×Q814yes—
125C22×C4×C59—22no—
126C22×C4×C59—22no—
127C22×C4×C59—28no—
128C22×C4×C59—24no—
129C22×C4×C59—48no—
130C22×C4×C59—44no—
131C22×C4×C59C22×C414yescomplemented
132C22×Dic59—22no—
133C22×Dic59—22no—
134C22×Dic59—28no—
135C22×Dic59—24no—
136C22×Dic59—48no—
137C22×Dic59—44no—
138C22×Dic59C22×C414yescomplemented
139C2×C4×D59—28no—
140C2×C4×D59—28no—
141C2×C4×D59—232no—
142C2×C4×D59—464no—
143C2×C4×D59—432no—
144C2×C4×D59—48no—
145C2×C4×D59—416no—
146C2×C4×D59—48no—
147C2×C4×D59—416no—
148C22⋊C4×C59—24no—
149C22⋊C4×C59—28no—
150C22⋊C4×C59—24no—
151C22⋊C4×C59—24no—
152C22⋊C4×C59C22×C418yescomplemented
153C22⋊Dic59—24no—
154C22⋊Dic59—28no—
155C22⋊Dic59—24no—
156C22⋊Dic59—24no—
157C22⋊Dic59C22×C418yescomplemented
158(C2×D59)⋊C4—216no—
159(C2×D59)⋊C4—232no—
160C23×C59—24no—
161C23×C59—28no—
162C23×C59—42no—
163C23×C59—48no—
164C23×C59—44no—
165C23×C59—44no—
166C23×C59—44no—
167C23×C59—42no—
168C23×C59C2×C4212yes—
169C23×C59C2×C4212yes—
170C23×C59C2×C22⋊C412yes—
171C23×C59C2×C22⋊C411yescharacteristic
172C23×C59C2×C22⋊C414yes—
173C23×C59C2×C22⋊C414yes—
174C23×C59C2×C22⋊C411yescharacteristic
175C23×C59C2×C4⋊C412yes—
176C23×C59C2×C4⋊C414yes—
177C23×C59C2×C4⋊C412yes—
178C23×C59C2×C4⋊C414yes—
179C23×C59C23×C411yescharacteristic
180C23×C59C23×C412yes—
181C23×C59C22×D412yes—
182C23×C59C22×D411yescharacteristic
183C23×C59C22×Q811yescharacteristic
184C22×D59—24no—
185C22×D59—28no—
186C22×D59—232no—
187C22×D59—216no—
188C22×D59—216no—
189C22×D59—232no—
190C22×D59—28no—
191C22×D59—28no—
192C22×D59—216no—
193C22×D59—216no—
194C22×D59—416no—
195C22×D59—432no—
196C22×D59—416no—
197C22×D59—432no—
198C22×D59—416no—
199C22×D59—48no—
200C22×D59—48no—
201C22×D59—48no—
202C22×D59—48no—
203C22×D59—44no—
204C22×D59—416no—
205C22×D59—416no—
206C22×D59—48no—
207C22×D59—44no—
208C22×D59—48no—
209C22×D59#9514yes—
210C22×D59#9518yes—
211C22×D59#9518yes—
212C22×D59#95116yes—
213C22×D59#95116yes—
214C22×D59#9518yes—
215C22×D59#9514yes—
216C22×D59#9918yes—
217C22×D59C2×C4214yes—
218C22×D59C2×C4214yes—
219C22×D59C2×C22⋊C414yes—
220C22×D59C2×C22⋊C412yes—
221C22×D59C2×C22⋊C418yes—
222C22×D59C2×C22⋊C418yes—
223C22×D59C2×C22⋊C412yes—
224C22×D59C2×C4⋊C414yes—
225C22×D59C2×C4⋊C418yes—
226C22×D59C2×C4⋊C418yes—
227C22×D59C2×C4⋊C414yes—
228C2×C4×C59—24no—
229C2×C4×C59—28no—
230C2×C4×C59—48no—
231C2×C4×C59—416no—
232C2×C4×C59—44no—
233C2×C4×C59—44no—
234C2×C4×C59—44no—
235C2×Dic59—24no—
236C2×Dic59—28no—
237C2×Dic59—48no—
238C2×Dic59—416no—
239C2×Dic59—44no—
240C2×Dic59—44no—
241C2×Dic59—44no—
242C4×D59—464no—
243C4×D59—416no—
244C4×D59—416no—
245C22×#342—591nomaximal, Sylow
246C22×C59—22no—
247C22×C59—22no—
248C22×C59—24no—
249C22×C59—24no—
250C22×C59—28no—
251C22×C59—24no—
252C22×C59—24no—
253C22×C59—28no—
254C22×C59—42no—
255C22×C59—44no—
256C22×C59—42no—
257C22×C59—44no—
258C22×C59—42no—
259C22×C59—41no—
260C22×C59—41no—
261C22×C59C2×#9512yes—
262C22×C59C2×#9514yes—
263C22×C59C2×#9512yes—
264C22×C59C2×#9914yes—
265C22×C59C22×C4211yescharacteristic
266C22×C59C22×C22⋊C412yes—
267C22×C59C22×C22⋊C411yescharacteristic
268C22×C59C22×C4⋊C411yescharacteristic
269C22×C59C22×C4⋊C412yes—
270C2×D59—24no—
271C2×D59—28no—
272C2×D59—28no—
273C2×D59—216no—
274C2×D59—216no—
275C2×D59—232no—
276C2×D59—216no—
277C2×D59—28no—
278C2×D59—28no—
279C2×D59—216no—
280C2×D59—416no—
281C2×D59—48no—
282C2×D59—44no—
283C2×D59—48no—
284C2×D59—48no—
285C2×D59—44no—
286C2×D59#342116yesdirect product factor
287C2×D59C2×#9514yes—
288C2×D59C2×#9518yes—
289C2×D59C2×#9514yes—
290C2×D59C2×#9918yes—
291C4×C59—48no—
292C4×C59—44no—
293Dic59—48no—
294Dic59—44no—
295C23×C22⋊C4—592no—
296C23×C22⋊C4—591no—
297C2×#342—598no—
298C2×#342—592no—
299C2×#342—591no—
300C2×#342D5911yescharacteristic, direct product factor
301C2×C59—22no—
302C2×C59—21no—
303C2×C59—22no—
304C2×C59—22no—
305C2×C59—24no—
306C2×C59—21no—
307C2×C59C2×#34214yescomplemented
308C2×C59C22×#9511yescharacteristic
309C2×C59C22×#9912yes—
310D59—24no—
311D59—28no—
312D59C2×#34218yesdirect product factor
313C26—591no—
314C24×C4—592no—
315C24×C4—1182no—
316C22×C22⋊C4—592no—
317C22×C22⋊C4—5916no—
318C22×C22⋊C4—598no—
319C22×C22⋊C4—591no—
320C22×C22⋊C4—592no—
321C22×C22⋊C4—594no—
322C22×C22⋊C4—594no—
323C22×C22⋊C4—1184no—
324C22×C22⋊C4—1188no—
325C22×C22⋊C4—1182no—
326C22×C22⋊C4—1184no—
327C22×C22⋊C4—1182no—
328C22×C22⋊C4—1182no—
329C22×C22⋊C4C2×D5911yescharacteristic
330C22×C22⋊C4C2×D5912yes—
331#342—598no—
332#342—594no—
333#342C2×D5914yesdirect product factor
334C59C22×#34211yescharacteristic, complemented, Sylow
335C25—591no—
336C25—592no—
337C25—598no—
338C25—592no—
339C25—591no—
340C25—594no—
341C25—594no—
342C25—592no—
343C25—594no—
344C25—592no—
345C25—2368no—
346C25C22×D5911yescharacteristic
347C23×C4—22no—
348C23×C4—592no—
349C23×C4—598no—
350C23×C4—11816no—
351C23×C4—1188no—
352C23×C4—1184no—
353C23×C4—1182no—
354C23×C4—1182no—
355C23×C4—1182no—
356C23×C4—23616no—
357C23×C4—2368no—
358C23×C4C4×D5912yescomplemented
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—598no—
364C2×C22⋊C4—594no—
365C2×C22⋊C4—5932no—
366C2×C22⋊C4—592no—
367C2×C22⋊C4—592no—
368C2×C22⋊C4—598no—
369C2×C22⋊C4—11832no—
370C2×C22⋊C4—1188no—
371C2×C22⋊C4—1188no—
372C2×C22⋊C4—11816no—
373C2×C22⋊C4—1188no—
374C2×C22⋊C4—1188no—
375C2×C22⋊C4—1184no—
376C2×C22⋊C4—11816no—
377C2×C22⋊C4—1184no—
378C2×C22⋊C4—1188no—
379C2×C22⋊C4—1182no—
380C2×C22⋊C4—1184no—
381C2×C22⋊C4—1182no—
382C2×C22⋊C4—1182no—
383C2×C22⋊C4C4×D5912yescomplemented
384C2×C22⋊C4C4×D5918yescomplemented
385C2×C22⋊C4C22×D5912yes—
386C2×C22⋊C4C22×D5914yes—
387C24—44no—
388C24—591no—
389C24—594no—
390C24—594no—
391C24—598no—
392C24—592no—
393C24—592no—
394C24—591no—
395C24—594no—
396C24—598no—
397C24—592no—
398C24—594no—
399C24—598no—
400C24—594no—
401C24—5916no—
402C24—598no—
403C24—592no—
404C24—594no—
405C24—5916no—
406C24—598no—
407C24—598no—
408C24—594no—
409C24—598no—
410C24—592no—
411C24—594no—
412C24—594no—
413C24—594no—
414C24—1188no—
415C24—11816no—
416C24—2364no—
417C24—2368no—
418C24—23632no—
419C24—2368no—
420C24—23616no—
421C24—23616no—
422C24—23616no—
423C24—2368no—
424C24C2×C4×D5911yescharacteristic
425C24C2×C4×D5914yes—
426C24C2×C4×D5911yescharacteristic
427C24D4×D5912yes—
428C24D4×D5912yes—
429C24D4×D5912yes—
430C24Q8×D5912yes—
431C24C23×D5911yescharacteristic
432C22×C4—22no—
433C22×C4—28no—
434C22×C4—22no—
435C22×C4—24no—
436C22×C4—48no—
437C22×C4—44no—
438C22×C4—594no—
439C22×C4—11832no—
440C22×C4—1188no—
441C22×C4—1188no—
442C22×C4—1188no—
443C22×C4—1182no—
444C22×C4—1182no—
445C22×C4—1184no—
446C22×C4—2368no—
447C22×C4—23616no—
448C22×C4—23664no—
449C22×C4—23632no—
450C22×C4—2368no—
451C22×C4—23616no—
452C22×C4—2368no—
453C22×C4—2364no—
454C22×C4C2×C4×D5914yescomplemented
455C22⋊C4—24no—
456C22⋊C4—28no—
457C22⋊C4—24no—
458C22⋊C4—24no—
459C22⋊C4—598no—
460C22⋊C4—11816no—
461C22⋊C4—11832no—
462C22⋊C4—1188no—
463C22⋊C4—1184no—
464C22⋊C4—1184no—
465C22⋊C4—1184no—
466C22⋊C4C2×C4×D5918yescomplemented
467C23—24no—
468C23—28no—
469C23—48no—
470C23—42no—
471C23—44no—
472C23—44no—
473C23—44no—
474C23—42no—
475C23—594no—
476C23—592no—
477C23—598no—
478C23—598no—
479C23—5916no—
480C23—594no—
481C23—598no—
482C23—594no—
483C23—594no—
484C23—598no—
485C23—592no—
486C23—594no—
487C23—598no—
488C23—5916no—
489C23—598no—
490C23—594no—
491C23—598no—
492C23—598no—
493C23—594no—
494C23—11832no—
495C23—1188no—
496C23—1188no—
497C23—11816no—
498C23—11816no—
499C23—11816no—
500C23—11832no—
501C23—11816no—
502C23—1184no—
503C23—1188no—
504C23—23616no—
505C23—2368no—
506C23—2368no—
507C23—23616no—
508C23—2364no—
509C23—2364no—
510C23—2368no—
511C23—2368no—
512C23—23616no—
513C23—23632no—
514C23—23616no—
515C23—23632no—
516C23—23616no—
517C23—2368no—
518C23—2368no—
519C23C42×D5912yes—
520C23C42×D5912yes—
521C23C22⋊C4×D5912yes—
522C23C22⋊C4×D5914yes—
523C23C22⋊C4×D5911yescharacteristic
524C23C22⋊C4×D5914yes—
525C23C22⋊C4×D5911yescharacteristic
526C23C4⋊C4×D5912yes—
527C23C4⋊C4×D5914yes—
528C23C4⋊C4×D5914yes—
529C23C4⋊C4×D5912yes—
530C23C22×C4×D5911yescharacteristic
531C23C22×C4×D5912yes—
532C23C2×D4×D5912yes—
533C23C2×D4×D5911yescharacteristic
534C23C2×Q8×D5911yescharacteristic
535C2×C4—24no—
536C2×C4—28no—
537C2×C4—416no—
538C2×C4—48no—
539C2×C4—44no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—1188no—
543C2×C4—1184no—
544C2×C4—23616no—
545C2×C4—23664no—
546C2×C4—23616no—
547C2×C4—23616no—
548C2×C4—2368no—
549C2×C4—2364no—
550C2×C4—2364no—
551C2×C4—2364no—
552C22—28no—
553C22—24no—
554C22—24no—
555C22—28no—
556C22—22no—
557C22—22no—
558C22—24no—
559C22—24no—
560C22—42no—
561C22—44no—
562C22—42no—
563C22—44no—
564C22—42no—
565C22—41no—
566C22—41no—
567C22—5916no—
568C22—598no—
569C22—594no—
570C22—594no—
571C22—598no—
572C22—11816no—
573C22—11832no—
574C22—11816no—
575C22—1188no—
576C22—1188no—
577C22—11816no—
578C22—11816no—
579C22—1188no—
580C22—1184no—
581C22—1188no—
582C22—2368no—
583C22—23616no—
584C22—2368no—
585C22—2364no—
586C22—2364no—
587C22—2368no—
588C22#95×D5912yes—
589C22#95×D5914yes—
590C22#95×D5912yes—
591C22#99×D5914yes—
592C22C2×C42×D5911yescharacteristic
593C22C2×C22⋊C4×D5912yes—
594C22C2×C22⋊C4×D5911yescharacteristic
595C22C2×C4⋊C4×D5911yescharacteristic
596C22C2×C4⋊C4×D5912yes—
597C4—48no—
598C4—44no—
599C4—2368no—
600C4—2364no—
601C2—22no—
602C2—24no—
603C2—22no—
604C2—21no—
605C2—21no—
606C2—22no—
607C2—598no—
608C2—1188no—
609C2—1184no—
610C2#342×D5914yesdirect product factor
611C2C2×#95×D5911yescharacteristic
612C2C2×#99×D5912yes—
subgroupG/H
centerC23C22⋊C4×D59
commutatorC22×C59C22×C42
FrattiniC24C23×D59
FittingC2×C59×#342C2
socleC23×C59C2×C22⋊C4
prime radicalC25×D59C22
cosocleC24×C59C24
hypercenterC2×#342D59
hypocenterC59C22×#342
LCSG ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
3. C2×#16837169C2semidirect
4. C2×#16837168C2semidirect
5. #342×D59C2direct (N × H)
6. C2×C59×#342C2semidirect
9. C23×C4×D59C4semidirect
13. C22×(C2×D59)⋊C4C4semidirect
19. C2×C22⋊C4×D59C4semidirect
20. C2×C22⋊C4×D59C4semidirect
23. #16837169C22semidirect
24. #16837168C22semidirect
27. C59×#342C22semidirect
40. C23×Dic59C2×C4semidirect
48. C22×C4×D59C2×C4semidirect
53. C2×C22⋊Dic59C2×C4semidirect
54. C2×C22⋊Dic59C2×C4semidirect
61. C2×(C2×D59)⋊C4C2×C4semidirect
68. C22⋊C4×D59C2×C4semidirect
71. C23×C4×C59C2×C4semidirect
76. C2×C22⋊C4×C59C2×C4semidirect
77. C2×C22⋊C4×C59C2×C4semidirect
131. C22×C4×C59C22×C4semidirect
138. C22×Dic59C22×C4semidirect
152. C22⋊C4×C59C22×C4semidirect
157. C22⋊Dic59C22×C4semidirect
286. C2×D59#342direct (N × H)
300. C2×#342D59direct (N × H)
307. C2×C59C2×#342semidirect
312. D59C2×#342direct (N × H)
333. #342C2×D59direct (N × H)
334. C59C22×#342semidirect
358. C23×C4C4×D59semidirect
383. C2×C22⋊C4C4×D59semidirect
384. C2×C22⋊C4C4×D59semidirect
454. C22×C4C2×C4×D59semidirect
466. C22⋊C4C2×C4×D59semidirect
610. C2#342×D59direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C22⋊C4×D592
C2×#168371692
C2×#168371682
#342×D592
C2×C59×#3422
C22×#34259