Finite Group Databasebeta

← #28600049

Subgroups — #28600049

Order 15104.

968 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21426780C211yesmaximal, characteristic, complemented
2#21426688C211yesmaximal, characteristic
3#21424979C211yesmaximal, characteristic, complemented
4#21424958C211yesmaximal, characteristic, complemented
5#21424788C211yesmaximal, characteristic, complemented
6#21424781C211yesmaximal, characteristic, complemented
7#21424739C211yesmaximal, characteristic, complemented
8#21424718C211yesmaximal, characteristic, complemented
9#21424453C211yesmaximal, characteristic, complemented
10#21424439C211yesmaximal, characteristic, complemented
11#21424404C211yesmaximal, characteristic, complemented
12#21424286C211yesmaximal, characteristic, complemented
13#21424036C211yesmaximal, characteristic
14#21423864C211yesmaximal, characteristic, complemented
15C2×C59×#452C211yesmaximal, characteristic
16C2×Q8×Dic59C2211yescharacteristic
17C2×#14273686C2211yescharacteristic
18C22×C4⋊Dic59C2211yescharacteristic
19C2×#14273661C2211yescharacteristic
20C2×#14273661C2211yescharacteristic
21C2×#14273651C2211yescharacteristic
22C2×#14273651C2211yescharacteristic
23C2×#14273651C2211yescharacteristic
24C2×#14273651C2211yescharacteristic
25C2×#14273648C2211yescharacteristic
26C2×#14273648C2211yescharacteristic
27C2×C22⋊(C59⋊C8)C2211yescharacteristic
28C2×#14273637C2211yescharacteristic
29C2×C8×Dic59C2211yescharacteristic
30#16837309C2211yescharacteristic
31#16837309C2211yescharacteristic
32#16837309C2211yescharacteristic
33#16837305C2211yescharacteristic
34#16837305C2211yescharacteristic
35#16837301—21no—
36#16837301C2211yescharacteristic
37#16837295—21no—
38#16837295—21no—
39#16837288—21no—
40#16837282—21no—
41#16837282—21no—
42#16837262—21no—
43#16837262—21no—
44#16837262C2211yescharacteristic
45C4⋊C4×Dic59C2211yescharacteristic
46#16837165C2211yescharacteristic
47#16837165C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837156C2211yescharacteristic
51#16837156C2211yescharacteristic
52C22×#41×C59C2211yescharacteristic
53C22×Q16×C59C2211yescharacteristic
54C22×SD16×C59C2211yescharacteristic
55C2×C22⋊Q8×C59C2211yescharacteristic
56C59×#452C418yescomplemented
57C2×#103×C59C2211yescharacteristic
58C2×#102×C59C2211yescharacteristic
59C2×C22⋊C8×C59C2211yescharacteristic
60C23×Dic59—21no—
61C22×C59⋊C8C2311yescharacteristic
62C22×C59⋊C8C2311yescharacteristic
63Q8×Dic59—41no—
64Q8×Dic59—41no—
65#14273686—41no—
66#14273686—41no—
67C2×C4⋊Dic59—21no—
68C2×C4⋊Dic59—21no—
69C2×C4⋊Dic59—21no—
70C2×C4⋊Dic59—41no—
71C2×C4⋊Dic59—41no—
72C2×C4⋊Dic59D411yescharacteristic
73C2×C4⋊Dic59D411yescharacteristic
74C2×C4⋊Dic59C2311yescharacteristic
75C2×C4⋊Dic59C2311yescharacteristic
76C2×C4⋊Dic59C2311yescharacteristic
77C2×C4⋊Dic59C2311yescharacteristic
78C2×C22⋊Dic59—21no—
79C2×C22⋊Dic59—21no—
80C2×C22⋊Dic59—21no—
81C2×C22⋊Dic59—21no—
82C2×C22⋊Dic59—21no—
83C2×C22⋊Dic59D411yescharacteristic
84C2×C22⋊Dic59D411yescharacteristic
85C2×C4×Dic59—21no—
86C2×C4×Dic59—21no—
87C2×C4×Dic59C2311yescharacteristic
88C2×C4×Dic59C2311yescharacteristic
89#14273661—41no—
90#14273661—41no—
91#14273651—41no—
92#14273651—41no—
93#14273651—41no—
94#14273651—41no—
95#14273648—41no—
96#14273648—41no—
97C22⋊(C59⋊C8)—22no—
98#14273637—41no—
99C8×Dic59—41no—
100C59⋊#95—21no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C59⋊#95—21no—
105C59⋊#95—21no—
106C59⋊#95—21no—
107C59⋊#95—21no—
108C59⋊#95—21no—
109C2×#41×C59—22no—
110C2×#41×C59—41no—
111C2×#41×C59—41no—
112C2×#41×C59—41no—
113C2×#41×C59—41no—
114C2×#41×C59C2×C414yes—
115C22×Q8×C59C2311yescharacteristic
116C22×Q8×C59C2311yescharacteristic
117C22×D4×C59—21no—
118C22×D4×C59C2311yescharacteristic
119C23×C4×C59—21no—
120C23×C4×C59C2311yescharacteristic
121C2×Q16×C59—41no—
122C2×Q16×C59—41no—
123C2×Q16×C59C2×C414yescomplemented
124C2×SD16×C59—41no—
125C2×SD16×C59—41no—
126C2×SD16×C59C2×C414yescomplemented
127C22×C8×C59C2311yescharacteristic
128C22×C8×C59C2311yescharacteristic
129C22⋊Q8×C59—22no—
130C22⋊Q8×C59C2×C414yes—
131C2×C4⋊C4×C59—21no—
132C2×C4⋊C4×C59C2311yescharacteristic
133C2×C22⋊C4×C59—21no—
134#103×C59C2×C414yescomplemented
135#102×C59C2×C414yescomplemented
136C22⋊C8×C59C2×C414yes—
137C24×C59—21no—
138C24×C59C2×D411yescharacteristic
139#41×C59—44no—
140#41×C59—44no—
141#41×C59—44no—
142#41×C59—44no—
143C2×Q8×C59—21no—
144C2×Q8×C59—21no—
145C2×Q8×C59—21no—
146C2×Q8×C59—21no—
147C2×Q8×C59—21no—
148C2×Q8×C59—21no—
149C2×Q8×C59—21no—
150C2×Q8×C59—21no—
151C2×Q8×C59—21no—
152C2×Q8×C59—21no—
153C2×Q8×C59C22×C412yes—
154C2×Q8×C59C22×C412yes—
155C2×D4×C59—24no—
156C2×D4×C59—21no—
157C2×D4×C59—21no—
158C2×D4×C59—21no—
159C2×D4×C59—21no—
160C2×D4×C59—21no—
161C2×D4×C59—42no—
162C2×D4×C59—42no—
163C2×D4×C59C22×C412yes—
164C22×C4×C59—21no—
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—24no—
172C22×C4×C59—42no—
173C22×C4×C59—42no—
174C22×C4×C59C22×C412yes—
175C22×C4×C59C2×D411yescharacteristic
176C22×C4×C59#4112yes—
177C22×C4×C59C2411yescharacteristic
178C22×Dic59—21no—
179C22×Dic59—21no—
180C22×Dic59—21no—
181C22×Dic59—21no—
182C22×Dic59—42no—
183C22×Dic59—81no—
184C22×Dic59—81no—
185C22×Dic59C2×D411yescharacteristic
186C22×Dic59C2×D411yescharacteristic
187C22×Dic59C2×D411yescharacteristic
188C22×Dic59C2×D411yescharacteristic
189Q16×C59—44no—
190SD16×C59—44no—
191C2×C8×C59—21no—
192C2×C8×C59—21no—
193C2×C8×C59—21no—
194C2×C8×C59—21no—
195C2×C8×C59C22×C412yes—
196C2×C8×C59C22×C412yes—
197C4⋊C4×C59—24no—
198C4⋊C4×C59—21no—
199C4⋊C4×C59C22×C412yes—
200C22⋊C4×C59—24no—
201C22⋊Dic59—41no—
202C22⋊Dic59—41no—
203C22⋊Dic59—81no—
204C22⋊Dic59—81no—
205C22⋊Dic59—81no—
206C22⋊Dic59—81no—
207C22⋊Dic59—81no—
208C4⋊Dic59—21no—
209C4⋊Dic59—21no—
210C4⋊Dic59—21no—
211C4⋊Dic59—21no—
212C4⋊Dic59—21no—
213C4⋊Dic59—21no—
214C4⋊Dic59—21no—
215C4⋊Dic59—21no—
216C4⋊Dic59—41no—
217C4⋊Dic59—41no—
218C4⋊Dic59—42no—
219C4⋊Dic59—42no—
220C4⋊Dic59—81no—
221C4×Dic59—21no—
222C4×Dic59—21no—
223C4×Dic59—21no—
224C4×Dic59—21no—
225C4×Dic59—42no—
226C4×Dic59—81no—
227C2×C59⋊C8—21no—
228C2×C59⋊C8—21no—
229C2×C59⋊C8—21no—
230C2×C59⋊C8—21no—
231C2×C59⋊C8—21no—
232C2×C59⋊C8—21no—
233C23×C59—21no—
234C23×C59—21no—
235C23×C59—21no—
236C23×C59—21no—
237C23×C59—21no—
238C23×C59—21no—
239C23×C59—22no—
240C23×C59—41no—
241C23×C59—41no—
242C23×C59—41no—
243C23×C59—41no—
244C23×C59—41no—
245C23×C59—41no—
246C23×C59C4×D412yes—
247C23×C59C22×D411yescharacteristic
248Q8×C59—22no—
249Q8×C59—22no—
250Q8×C59—22no—
251Q8×C59—22no—
252Q8×C59—41no—
253Q8×C59—41no—
254Q8×C59—41no—
255Q8×C59—41no—
256D4×C59—22no—
257D4×C59—22no—
258D4×C59—48no—
259D4×C59—41no—
260D4×C59—41no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—22no—
264C2×C4×C59—22no—
265C2×C4×C59—22no—
266C2×C4×C59—22no—
267C2×C4×C59—22no—
268C2×C4×C59—22no—
269C2×C4×C59—22no—
270C2×C4×C59—48no—
271C2×C4×C59—41no—
272C2×C4×C59—41no—
273C2×C4×C59—41no—
274C2×C4×C59—41no—
275C2×C4×C59—41no—
276C2×C4×C59—41no—
277C2×C4×C59C4×D412yes—
278C2×C4×C59C23×C411yescharacteristic
279C2×C4×C59C2×#4111yescharacteristic
280C2×C4×C59H(5,𝔽2)11yescharacteristic
281C2×C4×C59H(5,𝔽2)11yescharacteristic
282C2×C4×C59H(5,𝔽2)11yescharacteristic
283C2×C4×C59H(5,𝔽2)11yescharacteristic
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—
294C2×Dic59—21no—
295C2×Dic59—21no—
296C2×Dic59—41no—
297C2×Dic59—41no—
298C2×Dic59—41no—
299C2×Dic59—41no—
300C2×Dic59—41no—
301C2×Dic59—41no—
302C2×Dic59—41no—
303C2×Dic59—41no—
304C2×Dic59—41no—
305C2×Dic59—41no—
306C2×Dic59—41no—
307C2×Dic59—41no—
308C2×Dic59—84no—
309C8×C59—22no—
310C8×C59—22no—
311C59⋊C8—41no—
312C59⋊C8—41no—
313#22057—591nomaximal, Sylow
314C22×C59—22no—
315C22×C59—22no—
316C22×C59—22no—
317C22×C59—41no—
318C22×C59—41no—
319C22×C59—41no—
320C22×C59—41no—
321C22×C59—42no—
322C22×C59—42no—
323C22×C59—42no—
324C22×C59—81no—
325C22×C59—81no—
326C22×C59—81no—
327C22×C59—81no—
328C22×C59C2×C4×D411yescharacteristic
329C22×C59#53411yescharacteristic
330C22×C59#53511yescharacteristic
331C22×C59#57611yescharacteristic
332C22×C59#57711yescharacteristic
333C22×C59#57811yescharacteristic
334C22×C59#57811yescharacteristic
335C4×C59—22no—
336C4×C59—42no—
337C4×C59—42no—
338C4×C59—42no—
339C4×C59#51811yescharacteristic
340C4×C59#51811yescharacteristic
341C4×C59#53811yescharacteristic
342C4×C59#53811yescharacteristic
343Dic59—41no—
344Dic59—41no—
345Dic59—41no—
346Dic59—41no—
347Dic59—81no—
348Dic59—81no—
349Dic59—81no—
350Dic59—81no—
351C2×#452D5911yescharacteristic
352#2323—591no—
353#2311—591no—
354#1973—591no—
355#1969—591no—
356#1935—591no—
357#1934—591no—
358#1928—591no—
359#1925—591no—
360#1880—591no—
361#1878—591no—
362#1872—591no—
363#1852—591no—
364#1788—591no—
365#1750—591no—
366C2×C59—42no—
367C2×C59—82no—
368C2×C59#232111yescharacteristic
369C2×C59#294711yescharacteristic
370C2×C59#295111yescharacteristic
371C2×C59#320111yescharacteristic
372C2×C59#320311yescharacteristic
373C2×C59#322311yescharacteristic
374C2×C59#322411yescharacteristic
375C22×#41C2×D5911yescharacteristic
376C22×Q16C2×D5911yescharacteristic
377C22×SD16C2×D5911yescharacteristic
378C2×C22⋊Q8C2×D5911yescharacteristic
379C2×C4×Q8—591no—
380C2×#117—591no—
381C22×C4⋊C4—591no—
382#452Dic5918yescomplemented
383C2×#107—591no—
384C2×#107—591no—
385C2×#103—591no—
386C2×#103—591no—
387C2×#103—591no—
388C2×#103—591no—
389C2×#103C2×D5911yescharacteristic
390C2×#102—591no—
391C2×#102—591no—
392C2×#102C2×D5911yescharacteristic
393C2×C22⋊C8—591no—
394C2×C22⋊C8C2×D5911yescharacteristic
395C2×#97—591no—
396C2×C4×C8—591no—
397#391—591no—
398#391—591no—
399#391—591no—
400#390—591no—
401#390—591no—
402#389—591no—
403#389—1181no—
404#388—1181no—
405#388—1181no—
406#387—1181no—
407#386—1181no—
408#386—1181no—
409#380—591no—
410#380—1181no—
411#380—1181no—
412C4×C4⋊C4—591no—
413#340—591no—
414#340—591no—
415#340—591no—
416#340—591no—
417#336—591no—
418#336—591no—
419C59#2205711yescharacteristic, complemented, Sylow
420C2×#41—22no—
421C2×#41—41no—
422C2×#41—41no—
423C2×#41—41no—
424C2×#41—41no—
425C2×#41C2×Dic5914yes—
426C22×Q8C22×D5911yescharacteristic
427C22×Q8C22×D5911yescharacteristic
428C22×D4—21no—
429C22×D4C22×D5911yescharacteristic
430C23×C4—21no—
431C23×C4—1181no—
432C23×C4C22×D5911yescharacteristic
433C2×Q16—41no—
434C2×Q16—41no—
435C2×Q16C2×Dic5914yescomplemented
436C2×SD16—41no—
437C2×SD16—41no—
438C2×SD16C2×Dic5914yescomplemented
439C22×C8—591no—
440C22×C8—591no—
441C22×C8C22×D5911yescharacteristic
442C22×C8C22×D5911yescharacteristic
443C22⋊Q8—22no—
444C22⋊Q8C2×Dic5914yes—
445C4×Q8—2361no—
446C4×Q8—2361no—
447#117—2361no—
448#117—2361no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—591no—
451C2×C4⋊C4—591no—
452C2×C4⋊C4—591no—
453C2×C4⋊C4—591no—
454C2×C4⋊C4—591no—
455C2×C4⋊C4—591no—
456C2×C4⋊C4—1181no—
457C2×C4⋊C4—1181no—
458C2×C4⋊C4—1181no—
459C2×C4⋊C4—2361no—
460C2×C4⋊C4—2361no—
461C2×C4⋊C4C22×D5911yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—591no—
464C2×C22⋊C4—591no—
465C2×C22⋊C4—1181no—
466C2×C22⋊C4—1181no—
467C2×C22⋊C4—1181no—
468C2×C22⋊C4—1181no—
469C2×C22⋊C4—1181no—
470C2×C42—591no—
471C2×C42—591no—
472C2×C42—1181no—
473C2×C42—1181no—
474#107—2361no—
475#107—2361no—
476#103—2361no—
477#103—2361no—
478#103—2361no—
479#103—2361no—
480#103C2×Dic5914yescomplemented
481#102—2361no—
482#102—2361no—
483#102C2×Dic5914yescomplemented
484C22⋊C8—1182no—
485C22⋊C8C2×Dic5914yes—
486#97—2361no—
487C4×C8—2361no—
488#95—1181no—
489#95—1181no—
490#95—1181no—
491#95—1181no—
492#95—1181no—
493#95—1181no—
494#95—1181no—
495#95—1181no—
496#95—1181no—
497C24—21no—
498C24D4×D5911yescharacteristic
499#41—44no—
500#41—44no—
501#41—44no—
502#41—44no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8C22×Dic5912yes—
514C2×Q8C22×Dic5912yes—
515C2×D4—24no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4C22×Dic5912yes—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—24no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—591no—
535C22×C4—591no—
536C22×C4—591no—
537C22×C4—591no—
538C22×C4—1181no—
539C22×C4—1181no—
540C22×C4—1181no—
541C22×C4—1181no—
542C22×C4—4721no—
543C22×C4—4721no—
544C22×C4—2362no—
545C22×C4D4×D5911yescharacteristic
546C22×C4#1174568712yes—
547C22×C4C22×Dic5912yes—
548C22×C4C23×D5911yescharacteristic
549Q16—44no—
550SD16—44no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—1181no—
556C2×C8—1181no—
557C2×C8—1181no—
558C2×C8—1181no—
559C2×C8—1181no—
560C2×C8—1181no—
561C2×C8C22×Dic5912yes—
562C2×C8C22×Dic5912yes—
563C4⋊C4—24no—
564C4⋊C4—21no—
565C4⋊C4—1181no—
566C4⋊C4—1181no—
567C4⋊C4—1181no—
568C4⋊C4—1181no—
569C4⋊C4—1181no—
570C4⋊C4—1181no—
571C4⋊C4—1181no—
572C4⋊C4—1181no—
573C4⋊C4—4721no—
574C4⋊C4—2361no—
575C4⋊C4—2361no—
576C4⋊C4—2362no—
577C4⋊C4—2362no—
578C4⋊C4C22×Dic5912yes—
579C22⋊C4—24no—
580C22⋊C4—4721no—
581C22⋊C4—4721no—
582C22⋊C4—4721no—
583C22⋊C4—4721no—
584C22⋊C4—4721no—
585C22⋊C4—2361no—
586C22⋊C4—2361no—
587C42—1181no—
588C42—1181no—
589C42—1181no—
590C42—1181no—
591C42—4721no—
592C42—2362no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—22no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23D4×Dic5912yes—
607C23C2×D4×D5911yescharacteristic
608Q8—22no—
609Q8—22no—
610Q8—22no—
611Q8—22no—
612Q8—41no—
613Q8—41no—
614Q8—41no—
615Q8—41no—
616D4—22no—
617D4—22no—
618D4—48no—
619D4—41no—
620D4—41no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—48no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
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—4724no—
650C2×C4—2361no—
651C2×C4—2361no—
652C2×C4—2361no—
653C2×C4—2361no—
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×C4D4×Dic5912yes—
663C2×C4C23×Dic5911yescharacteristic
664C2×C4C2×#1174568711yescharacteristic
665C2×C4#1427377211yescharacteristic
666C2×C4#1427377211yescharacteristic
667C2×C4#1427377211yescharacteristic
668C2×C4#1427377211yescharacteristic
669C8—22no—
670C8—22no—
671C8—2361no—
672C8—2361no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22C2×D4×Dic5911yescharacteristic
688C22#1683796211yescharacteristic
689C22#1683796711yescharacteristic
690C22#1683820411yescharacteristic
691C22#1683821111yescharacteristic
692C22#1683821611yescharacteristic
693C22#1683821811yescharacteristic
694C4—22no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—4721no—
699C4—4721no—
700C4—4721no—
701C4—4721no—
702C4—2361no—
703C4—2361no—
704C4—2361no—
705C4—2361no—
706C4#1683787711yescharacteristic
707C4#1683787711yescharacteristic
708C4#1683798711yescharacteristic
709C4#1683798711yescharacteristic
710C2—42no—
711C2—82no—
712C2#2142675711yescharacteristic
713C2#2143294011yescharacteristic
714C2#2143297211yescharacteristic
715C2#2143497711yescharacteristic
716C2#2143499711yescharacteristic
717C2#2143517711yescharacteristic
718C2#2143519611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C59×#452C2
socleC23×C59C22×D4
prime radicalC22×#41×C59C22
cosocleC22×C4×C59C24
hypercenterC2×#452D59
hypocenterC59#22057
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. #21426780C2semidirect
3. #21424979C2semidirect
4. #21424958C2semidirect
5. #21424788C2semidirect
6. #21424781C2semidirect
7. #21424739C2semidirect
8. #21424718C2semidirect
9. #21424453C2semidirect
10. #21424439C2semidirect
11. #21424404C2semidirect
12. #21424286C2semidirect
14. #21423864C2semidirect
56. C59×#452C4semidirect
123. C2×Q16×C59C2×C4semidirect
126. C2×SD16×C59C2×C4semidirect
134. #103×C59C2×C4semidirect
135. #102×C59C2×C4semidirect
382. #452Dic59semidirect
419. C59#22057semidirect
435. C2×Q16C2×Dic59semidirect
438. C2×SD16C2×Dic59semidirect
480. #103C2×Dic59semidirect
483. #102C2×Dic59semidirect

Maximal subgroups

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

subgroupindex
#214267802
#214266882
#214249792
#214249582
#214247882
#214247812
#214247392
#214247182
#214244532
#214244392
#214244042
#214242862
#214240362
#214238642
C2×C59×#4522
#2205759