Finite Group Databasebeta

← #28606869

Subgroups — #28606869

Order 15104.

1042 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837473C211yesmaximal, characteristic
2C2×#16837443C211yesmaximal, characteristic, complemented
3#21427021C211yesmaximal, characteristic
4C4⋊C4×C22⋊D59C211yesmaximal, characteristic
5#21424861C211yesmaximal, characteristic, complemented
6#21424851C211yesmaximal, characteristic, complemented
7#21424292C211yesmaximal, characteristic, complemented
8#21424289C211yesmaximal, characteristic, complemented
9#21424284C211yesmaximal, characteristic, complemented
10#21424282C211yesmaximal, characteristic, complemented
11#21424263C211yesmaximal, characteristic, complemented
12#21424130C211yesmaximal, characteristic, complemented
13#21424121C211yesmaximal, characteristic, complemented
14#21423995C211yesmaximal, characteristic, complemented
15C22×#107×C59C211yesmaximal, characteristic, complemented
16C22×#11745659C2211yescharacteristic
17C2×C4×C22⋊D59—21no—
18C2×C4×C22⋊D59C2211yescharacteristic
19C2×#14273685C2211yescharacteristic
20C2×C4⋊C4×D59C2211yescharacteristic
21#16837473C418yescomplemented
22#16837443—24no—
23C2×#14273660C2211yescharacteristic
24C2×#14273660C2211yescharacteristic
25C2×#14273659C2211yescharacteristic
26C2×#14273659C2211yescharacteristic
27C2×#14273658C2211yescharacteristic
28C2×#14273658C2211yescharacteristic
29C2×Dic59⋊C8C2211yescharacteristic
30C2×C22⋊(C59⋊C8)C2211yescharacteristic
31C2×(C2×D59)⋊C8C2211yescharacteristic
32C2×#14273637C2211yescharacteristic
33#16837297—21no—
34#16837292—21no—
35#16837283—21no—
36#16837281—21no—
37#16837275—21no—
38#16837273—21no—
39#16837271C2211yescharacteristic
40#16837267C2211yescharacteristic
41#16837262C2211yescharacteristic
42#16837262C2211yescharacteristic
43#16837259C2211yescharacteristic
44#16837259C2211yescharacteristic
45C4⋊C4×Dic59C2211yescharacteristic
46C4⋊C4×Dic59C2211yescharacteristic
47C4×C22⋊Dic59—21no—
48#16837165C2211yescharacteristic
49#16837165C2211yescharacteristic
50#16837164C2211yescharacteristic
51#16837164C2211yescharacteristic
52#16837164C2211yescharacteristic
53#16837164C2211yescharacteristic
54C23×C8×C59C2211yescharacteristic
55C22×C4⋊C4×C59C2211yescharacteristic
56C22×C4⋊C4×C59C2211yescharacteristic
57C2×#107×C59—24no—
58C2×#107×C59C2211yescharacteristic
59C2×#107×C59C2211yescharacteristic
60C2×#107×C59C2211yescharacteristic
61C2×#107×C59C2211yescharacteristic
62C22×C22⋊D59D411yescharacteristic
63C22×C4×D59—21no—
64C22×C4×D59C2311yescharacteristic
65C2×#11745659—22no—
66C2×#11745659—22no—
67C2×#11745659C2×C414yescomplemented
68C22×C59⋊C8C2311yescharacteristic
69C22×C59⋊C8C2311yescharacteristic
70C4×C22⋊D59—44no—
71C4×C22⋊D59C2×C414yes—
72C4×C22⋊D59Q814yes—
73#14273685—22no—
74#14273685—41no—
75C2×C4⋊Dic59C2311yescharacteristic
76C2×C4⋊Dic59C2311yescharacteristic
77C2×C4⋊Dic59C2311yescharacteristic
78C2×C4⋊Dic59C2311yescharacteristic
79C2×Dic59⋊C4—21no—
80C2×Dic59⋊C4—21no—
81C2×Dic59⋊C4—21no—
82C2×Dic59⋊C4D411yescharacteristic
83C4⋊C4×D59—22no—
84C4⋊C4×D59—41no—
85C2×C22⋊Dic59—21no—
86C2×C22⋊Dic59—21no—
87C2×C22⋊Dic59D411yescharacteristic
88C2×(C2×D59)⋊C4—21no—
89C2×(C2×D59)⋊C4—21no—
90C2×(C2×D59)⋊C4—21no—
91C2×(C2×D59)⋊C4D411yescharacteristic
92C2×C4×Dic59—21no—
93C2×C4×Dic59—21no—
94C2×C4×Dic59—21no—
95C2×C4×Dic59C2311yescharacteristic
96#14273660—22no—
97#14273660—41no—
98#14273659—22no—
99#14273659—22no—
100#14273658—22no—
101#14273658—41no—
102Dic59⋊C8C2×C414yescomplemented
103C22⋊(C59⋊C8)C2×C414yescomplemented
104(C2×D59)⋊C8C2×C414yescomplemented
105#14273637C2×C414yescomplemented
106C59⋊#95—21no—
107C59⋊#95—21no—
108C59⋊#95—21no—
109C59⋊#95—21no—
110C59⋊#95—21no—
111C59⋊#95—21no—
112C59⋊#95—21no—
113C59⋊#95—21no—
114C23×C4×C59—21no—
115C23×C4×C59—21no—
116C23×C4×C59C2311yescharacteristic
117C22×C8×C59—22no—
118C22×C8×C59—22no—
119C22×C8×C59C2×C414yescomplemented
120C22×C8×C59C2311yescharacteristic
121C22×C8×C59C2311yescharacteristic
122C2×C4⋊C4×C59—22no—
123C2×C4⋊C4×C59—22no—
124C2×C4⋊C4×C59—21no—
125C2×C4⋊C4×C59—21no—
126C2×C4⋊C4×C59—41no—
127C2×C4⋊C4×C59—41no—
128C2×C4⋊C4×C59C2311yescharacteristic
129C2×C4⋊C4×C59C2311yescharacteristic
130C2×C4⋊C4×C59C2311yescharacteristic
131C2×C4⋊C4×C59C2311yescharacteristic
132#107×C59—22no—
133#107×C59—22no—
134#107×C59—22no—
135#107×C59D414yescomplemented
136C24×C59C2×D411yescharacteristic
137C23×D59C2×D411yescharacteristic
138C22×C4×C59—21no—
139C22×C4×C59—21no—
140C22×C4×C59—21no—
141C22×C4×C59—21no—
142C22×C4×C59—21no—
143C22×C4×C59—21no—
144C22×C4×C59—21no—
145C22×C4×C59—21no—
146C22×C4×C59—42no—
147C22×C4×C59—42no—
148C22×C4×C59—42no—
149C22×C4×C59—42no—
150C22×C4×C59—81no—
151C22×C4×C59—81no—
152C22×C4×C59C22×C412yes—
153C22×C4×C59C2×D411yescharacteristic
154C22×C4×C59C2×Q812yes—
155C22×C4×C59C2411yescharacteristic
156C2×C22⋊D59—22no—
157C2×C22⋊D59—22no—
158C2×C22⋊D59C4⋊C414yes—
159C22×Dic59—21no—
160C22×Dic59—21no—
161C22×Dic59—21no—
162C22×Dic59—21no—
163C22×Dic59C2×D411yescharacteristic
164C22×Dic59C2×D411yescharacteristic
165C22×Dic59C2×D411yescharacteristic
166C2×C4×D59—21no—
167C2×C4×D59—21no—
168C2×C4×D59—21no—
169C2×C4×D59—21no—
170C2×C4×D59—42no—
171C2×C4×D59—42no—
172C2×C4×D59—81no—
173C2×C4×D59C22×C412yes—
174C2×C4×D59C2×Q812yes—
175C2×C8×C59—21no—
176C2×C8×C59—21no—
177C2×C8×C59—28no—
178C2×C8×C59C22×C412yes—
179C2×C8×C59C22×C412yes—
180C2×C8×C59C2×D412yes—
181C2×C8×C59#4112yes—
182C4⋊C4×C59—21no—
183C4⋊C4×C59—21no—
184C4⋊C4×C59—21no—
185C4⋊C4×C59—21no—
186C4⋊C4×C59—21no—
187C4⋊C4×C59—21no—
188C4⋊C4×C59—42no—
189C4⋊C4×C59—42no—
190C4⋊C4×C59C2×D412yes—
191C4⋊C4×C59C2×D412yes—
192C22⋊Dic59—42no—
193C22⋊Dic59—42no—
194C22⋊Dic59C4⋊C414yes—
195(C2×D59)⋊C4—42no—
196(C2×D59)⋊C4—42no—
197(C2×D59)⋊C4—81no—
198(C2×D59)⋊C4C4⋊C414yes—
199C4⋊Dic59—21no—
200C4⋊Dic59—21no—
201C4⋊Dic59—21no—
202C4⋊Dic59—21no—
203C4⋊Dic59—21no—
204C4⋊Dic59—21no—
205C4⋊Dic59—21no—
206C4⋊Dic59—21no—
207Dic59⋊C4—42no—
208Dic59⋊C4—42no—
209Dic59⋊C4—81no—
210Dic59⋊C4C4⋊C414yes—
211C4×Dic59—42no—
212C4×Dic59—42no—
213C4×Dic59—81no—
214C4×Dic59C22×C412yes—
215C4×Dic59C2×Q812yes—
216C2×C59⋊C8—21no—
217C2×C59⋊C8—21no—
218C2×C59⋊C8—21no—
219C2×C59⋊C8—21no—
220C2×C59⋊C8C22×C412yes—
221C2×C59⋊C8C22×C412yes—
222#11745659—28no—
223C23×C59—21no—
224C23×C59—21no—
225C23×C59—21no—
226C23×C59—21no—
227C23×C59C2×C4⋊C412yes—
228C23×C59AGL(1,ℤ/8)12yes—
229C23×C59#13712yes—
230C23×C59C22×D411yescharacteristic
231C22×D59—21no—
232C22×D59—21no—
233C22×D59—21no—
234C22×D59—21no—
235C22×D59—21no—
236C22×D59—21no—
237C22×D59C2×C4⋊C412yes—
238C2×C4×C59—21no—
239C2×C4×C59—21no—
240C2×C4×C59—22no—
241C2×C4×C59—22no—
242C2×C4×C59—22no—
243C2×C4×C59—22no—
244C2×C4×C59—22no—
245C2×C4×C59—22no—
246C2×C4×C59—41no—
247C2×C4×C59—41no—
248C2×C4×C59—41no—
249C2×C4×C59—41no—
250C2×C4×C59—41no—
251C2×C4×C59—41no—
252C2×C4×C59—41no—
253C2×C4×C59—41no—
254C2×C4×C59—41no—
255C2×C4×C59—41no—
256C2×C4×C59—84no—
257C2×C4×C59—84no—
258C2×C4×C59C2×C4⋊C412yes—
259C2×C4×C59C23×C411yescharacteristic
260C2×C4×C59C22×D411yescharacteristic
261C2×C4×C59C22×Q811yescharacteristic
262C2×C4×C59C2×#4111yescharacteristic
263C2×C4×C59H(5,𝔽2)11yescharacteristic
264C2×C4×C592−1+411yescharacteristic
265C22⋊D59—28no—
266C2×Dic59—21no—
267C2×Dic59—21no—
268C2×Dic59—21no—
269C2×Dic59—21no—
270C2×Dic59—21no—
271C2×Dic59—21no—
272C2×Dic59—41no—
273C2×Dic59—41no—
274C2×Dic59—41no—
275C2×Dic59—41no—
276C2×Dic59—41no—
277C2×Dic59—41no—
278C2×Dic59—41no—
279C2×Dic59—41no—
280C2×Dic59—41no—
281C2×Dic59—41no—
282C2×Dic59—41no—
283C2×Dic59—41no—
284C2×Dic59C2×C4⋊C412yes—
285C2×Dic59C2×C4⋊C412yes—
286C2×Dic59C2×C4⋊C412yes—
287C4×D59—22no—
288C4×D59—22no—
289C4×D59—22no—
290C4×D59—22no—
291C4×D59—84no—
292C8×C59—22no—
293C8×C59C4×D414yescomplemented
294C59⋊C8—22no—
295C59⋊C8—22no—
296#22661—591nomaximal, Sylow
297C22×C59—22no—
298C22×C59—22no—
299C22×C59—22no—
300C22×C59—22no—
301C22×C59—22no—
302C22×C59—22no—
303C22×C59#42814yescomplemented
304C22×C59C22×C4⋊C411yescharacteristic
305C22×C59D4211yescharacteristic
306C22×C59#54711yescharacteristic
307C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
308C22×C59C2×#13711yescharacteristic
309C22×C59#57611yescharacteristic
310C22×C59#57811yescharacteristic
311C2×D59—22no—
312C2×D59—22no—
313C2×D59—22no—
314C2×D59—41no—
315C2×D59—41no—
316C2×D59—41no—
317C2×D59—41no—
318C4×C59—22no—
319C4×C59—42no—
320C4×C59—42no—
321C4×C59—81no—
322C4×C59—81no—
323C4×C59C2×C4×D411yescharacteristic
324C4×C59#52011yescharacteristic
325C4×C59D4×Q811yescharacteristic
326C4×C59#55411yescharacteristic
327Dic59—22no—
328Dic59—22no—
329Dic59—22no—
330Dic59—81no—
331Dic59—81no—
332Dic59—81no—
333Dic59—81no—
334C2×#435—591no—
335C2×#428—591no—
336C22×#107D5911yescharacteristic, complemented
337#2352—591no—
338D4×C4⋊C4—591no—
339#1949—591no—
340#1947—591no—
341#1854—591no—
342#1853—591no—
343#1852—591no—
344#1852—591no—
345#1847—591no—
346#1809—591no—
347#1807—591no—
348#1776—591no—
349C2×C59—24no—
350C2×C59D4×C4⋊C411yescharacteristic
351C2×C59C2×#42811yescharacteristic
352C2×C59#291311yescharacteristic
353C2×C59#326411yescharacteristic
354C2×C59#327011yescharacteristic
355C2×C59#334311yescharacteristic
356C2×C59#334611yescharacteristic
357D59—42no—
358C22×M16—591no—
359C23×C8C2×D5911yescharacteristic
360C2×C4×D4—591no—
361C2×C4×D4—1181no—
362C2×#117—591no—
363C22×C4⋊C4—591no—
364C22×C4⋊C4C2×D5911yescharacteristic
365C22×C4⋊C4C2×D5911yescharacteristic
366#435—598no—
367#428—1184no—
368C2×#107—24no—
369C2×#107—591no—
370C2×#107—591no—
371C2×#107C2×D5911yescharacteristic
372C2×#107C2×D5911yescharacteristic
373C2×#107C2×D5911yescharacteristic
374C2×#107C2×D5911yescharacteristic
375C2×#106—591no—
376C2×#106—591no—
377C2×#106—591no—
378C2×#106—591no—
379C2×C4⋊C8—591no—
380C2×C22⋊C8—591no—
381C2×C22⋊C8—591no—
382C2×#97—591no—
383#389—1181no—
384#388—1181no—
385#387—1181no—
386#386—1181no—
387#385—1181no—
388#385—1181no—
389#384—591no—
390#382—591no—
391#380—591no—
392#380—591no—
393#380—591no—
394#380—591no—
395C4×C4⋊C4—591no—
396C4×C4⋊C4—591no—
397C4×C22⋊C4—1181no—
398#340—591no—
399#340—591no—
400#340—591no—
401#340—591no—
402#340—591no—
403#340—591no—
404C59#2266111yescharacteristic, complemented, Sylow
405C22×D4—591no—
406C23×C4—21no—
407C23×C4—21no—
408C23×C4—591no—
409C23×C4—1181no—
410C23×C4C22×D5911yescharacteristic
411C2×M16—594no—
412C2×M16—1182no—
413C2×M16—1182no—
414C22×C8—22no—
415C22×C8—22no—
416C22×C8—591no—
417C22×C8—591no—
418C22×C8C4×D5914yescomplemented
419C22×C8C22×D5911yescharacteristic
420C22×C8C22×D5911yescharacteristic
421C4×D4—594no—
422C4×D4—594no—
423C4×D4—2364no—
424#117—1182no—
425#117—2361no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—41no—
431C2×C4⋊C4—41no—
432C2×C4⋊C4—591no—
433C2×C4⋊C4—591no—
434C2×C4⋊C4—591no—
435C2×C4⋊C4—591no—
436C2×C4⋊C4—591no—
437C2×C4⋊C4—1182no—
438C2×C4⋊C4—1181no—
439C2×C4⋊C4—1181no—
440C2×C4⋊C4—1181no—
441C2×C4⋊C4—2361no—
442C2×C4⋊C4C22×D5911yescharacteristic
443C2×C4⋊C4C22×D5911yescharacteristic
444C2×C4⋊C4C22×D5911yescharacteristic
445C2×C4⋊C4C22×D5911yescharacteristic
446C2×C22⋊C4—591no—
447C2×C22⋊C4—591no—
448C2×C22⋊C4—1181no—
449C2×C22⋊C4—1181no—
450C2×C22⋊C4—1181no—
451C2×C22⋊C4—1181no—
452C2×C22⋊C4—1181no—
453C2×C42—591no—
454C2×C42—1181no—
455C2×C42—1181no—
456C2×C42—1181no—
457#107—22no—
458#107—22no—
459#107—22no—
460#107—1182no—
461#107—2361no—
462#107C22⋊D5914yescomplemented
463#106—1182no—
464#106—1182no—
465#106—1182no—
466#106—2361no—
467C4⋊C8—594no—
468C22⋊C8—594no—
469C22⋊C8—594no—
470#97—594no—
471#95—1181no—
472#95—1181no—
473#95—1181no—
474#95—1181no—
475#95—1181no—
476#95—1181no—
477#95—1181no—
478#95—1181no—
479C24—591no—
480C24D4×D5911yescharacteristic
481C2×D4—594no—
482C2×D4—1182no—
483C2×D4—1182no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—81no—
497C22×C4—81no—
498C22×C4—591no—
499C22×C4—591no—
500C22×C4—591no—
501C22×C4—592no—
502C22×C4—592no—
503C22×C4—1181no—
504C22×C4—1181no—
505C22×C4—1181no—
506C22×C4—1181no—
507C22×C4—1181no—
508C22×C4—1181no—
509C22×C4—1181no—
510C22×C4—1181no—
511C22×C4—4721no—
512C22×C4—2362no—
513C22×C4—2362no—
514C22×C4C2×C4×D5912yes—
515C22×C4D4×D5911yescharacteristic
516C22×C4Q8×D5912yes—
517C22×C4C23×D5911yescharacteristic
518M16—1188no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—28no—
522C2×C8—592no—
523C2×C8—592no—
524C2×C8—1181no—
525C2×C8—1181no—
526C2×C8—1181no—
527C2×C8—1181no—
528C2×C8C2×C4×D5912yes—
529C2×C8C2×C4×D5912yes—
530C2×C8#1174568512yes—
531C2×C8C2×C22⋊D5912yes—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—594no—
541C4⋊C4—1181no—
542C4⋊C4—1181no—
543C4⋊C4—1181no—
544C4⋊C4—1181no—
545C4⋊C4—1181no—
546C4⋊C4—1181no—
547C4⋊C4—1181no—
548C4⋊C4—1181no—
549C4⋊C4—4721no—
550C4⋊C4—2362no—
551C4⋊C4—2362no—
552C4⋊C4C2×C22⋊D5912yes—
553C4⋊C4C2×C22⋊D5912yes—
554C22⋊C4—594no—
555C22⋊C4—594no—
556C22⋊C4—4721no—
557C22⋊C4—2362no—
558C22⋊C4—2362no—
559C22⋊C4—2362no—
560C22⋊C4—2362no—
561C42—592no—
562C42—592no—
563C42—4721no—
564C42—2362no—
565C42—2362no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—592no—
571C23—1181no—
572C23—1181no—
573C23—1181no—
574C23—1181no—
575C23—1181no—
576C23—1181no—
577C23C4⋊C4×D5912yes—
578C23#1427375112yes—
579C23#1427375912yes—
580C23C2×D4×D5911yescharacteristic
581D4—1188no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—84no—
601C2×C4—84no—
602C2×C4—592no—
603C2×C4—592no—
604C2×C4—592no—
605C2×C4—1181no—
606C2×C4—1181no—
607C2×C4—1181no—
608C2×C4—1181no—
609C2×C4—1181no—
610C2×C4—1181no—
611C2×C4—1182no—
612C2×C4—1182no—
613C2×C4—1182no—
614C2×C4—1182no—
615C2×C4—4724no—
616C2×C4—2361no—
617C2×C4—2361no—
618C2×C4—2361no—
619C2×C4—2361no—
620C2×C4—2361no—
621C2×C4—2361no—
622C2×C4—2361no—
623C2×C4—2361no—
624C2×C4—2361no—
625C2×C4—2361no—
626C2×C4—2361no—
627C2×C4—2361no—
628C2×C4C4⋊C4×D5912yes—
629C2×C4C22×C4×D5911yescharacteristic
630C2×C4C22×C22⋊D5911yescharacteristic
631C2×C4C2×Q8×D5911yescharacteristic
632C2×C4C2×#1174568511yescharacteristic
633C2×C4#1427377211yescharacteristic
634C2×C4#1427377511yescharacteristic
635C8—22no—
636C8—1182no—
637C8—1182no—
638C8C4×C22⋊D5914yescomplemented
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—1182no—
646C22—1182no—
647C22—1182no—
648C22—2361no—
649C22—2361no—
650C22—2361no—
651C22—2361no—
652C22#1683744314yescomplemented
653C22C2×C4⋊C4×D5911yescharacteristic
654C22D4×C22⋊D5911yescharacteristic
655C22#1683805311yescharacteristic
656C22C2×#1427375111yescharacteristic
657C22C2×#1427375911yescharacteristic
658C22#1683820311yescharacteristic
659C22#1683821511yescharacteristic
660C4—22no—
661C4—42no—
662C4—42no—
663C4—81no—
664C4—81no—
665C4—1182no—
666C4—1182no—
667C4—1182no—
668C4—4721no—
669C4—4721no—
670C4—4721no—
671C4—4721no—
672C4C2×C4×C22⋊D5911yescharacteristic
673C4#1683788311yescharacteristic
674C4Q8×C22⋊D5911yescharacteristic
675C4#1683810711yescharacteristic
676C2—24no—
677C2—2362no—
678C2C4⋊C4×C22⋊D5911yescharacteristic
679C2C2×#1683744311yescharacteristic
680C2#2143269211yescharacteristic
681C2#2143557611yescharacteristic
682C2#2143566611yescharacteristic
683C2#2143653211yescharacteristic
684C2#2143657711yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC22×#107×C59C2
socleC23×C59C22×D4
prime radicalC22×C22⋊D59D4
cosocleC22×C4×C59C24
hypercenterC22×#107D59
hypocenterC59#22661
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
2. C2×#16837443C2semidirect
5. #21424861C2semidirect
6. #21424851C2semidirect
7. #21424292C2semidirect
8. #21424289C2semidirect
9. #21424284C2semidirect
10. #21424282C2semidirect
11. #21424263C2semidirect
12. #21424130C2semidirect
13. #21424121C2semidirect
14. #21423995C2semidirect
15. C22×#107×C59C2semidirect
21. #16837473C4semidirect
67. C2×#11745659C2×C4semidirect
102. Dic59⋊C8C2×C4semidirect
103. C22⋊(C59⋊C8)C2×C4semidirect
104. (C2×D59)⋊C8C2×C4semidirect
105. #14273637C2×C4semidirect
119. C22×C8×C59C2×C4semidirect
135. #107×C59D4semidirect
293. C8×C59C4×D4semidirect
303. C22×C59#428semidirect
336. C22×#107D59semidirect
404. C59#22661semidirect
418. C22×C8C4×D59semidirect
462. #107C22⋊D59semidirect
638. C8C4×C22⋊D59semidirect
652. C22#16837443semidirect

Maximal subgroups

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

subgroupindex
C2×#168374732
C2×#168374432
#214270212
C4⋊C4×C22⋊D592
#214248612
#214248512
#214242922
#214242892
#214242842
#214242822
#214242632
#214241302
#214241212
#214239952
C22×#107×C592
#2266159