Finite Group Databasebeta

← #28611141

Subgroups — #28611141

Order 15104.

1058 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837503C211yesmaximal, characteristic, complemented
2C2×D8×Dic59C211yesmaximal, characteristic
3#21427171C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic59C211yesmaximal, characteristic, complemented
5#21424913C211yesmaximal, characteristic, complemented
6#21424855C211yesmaximal, characteristic, complemented
7#21424795C211yesmaximal, characteristic, complemented
8#21424774C211yesmaximal, characteristic, complemented
9#21424446C211yesmaximal, characteristic
10#21424432C211yesmaximal, characteristic, complemented
11#21424352C211yesmaximal, characteristic, complemented
12#21424345C211yesmaximal, characteristic, complemented
13#21423973C211yesmaximal, characteristic, complemented
14#21423921C211yesmaximal, characteristic, complemented
15C2×C59×#463C211yesmaximal, characteristic
16C2×Q8×Dic59C2211yescharacteristic
17C2×D4×Dic59C2211yescharacteristic
18C2×D4×Dic59C2211yescharacteristic
19C2×D4×Dic59C2211yescharacteristic
20C22×C4⋊Dic59—21no—
21#16837503—24no—
22D8×Dic59—24no—
23C2×#14273661C2211yescharacteristic
24C2×#14273661C2211yescharacteristic
25C2×#14273651C2211yescharacteristic
26C2×#14273651C2211yescharacteristic
27C2×#14273648C2211yescharacteristic
28C2×#14273648C2211yescharacteristic
29C2×#14273648C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×#14273638C2211yescharacteristic
32C2×#14273637C2211yescharacteristic
33C2×C8×Dic59C2211yescharacteristic
34#16837309C2211yescharacteristic
35#16837305C2211yescharacteristic
36#16837301C2211yescharacteristic
37#16837301C2211yescharacteristic
38#16837295—21no—
39#16837295—21no—
40#16837277—21no—
41#16837277—21no—
42#16837277—21no—
43#16837272C2211yescharacteristic
44#16837262—21no—
45C4×C4⋊Dic59C2211yescharacteristic
46C4×C4⋊Dic59C2211yescharacteristic
47C22⋊C4×Dic59—21no—
48#16837165C2211yescharacteristic
49#16837165C2211yescharacteristic
50#16837164C2211yescharacteristic
51#16837164C2211yescharacteristic
52#16837156C2211yescharacteristic
53#16837156C2211yescharacteristic
54C22×SD16×C59C2211yescharacteristic
55C22×D8×C59C2211yescharacteristic
56C2×#124×C59C2211yescharacteristic
57C2×C4×D4×C59C2211yescharacteristic
58C59×#463C418yescomplemented
59C2×C4⋊C8×C59C2211yescharacteristic
60C2×#103×C59C2211yescharacteristic
61C2×#102×C59C2211yescharacteristic
62C23×Dic59—21no—
63C23×Dic59—21no—
64C23×Dic59—21no—
65C22×C59⋊C8C2311yescharacteristic
66C22×C59⋊C8C2311yescharacteristic
67Q8×Dic59—22no—
68Q8×Dic59—41no—
69D4×Dic59—22no—
70D4×Dic59—22no—
71D4×Dic59—22no—
72D4×Dic59—41no—
73D4×Dic59—41no—
74D4×Dic59—41no—
75C2×C4⋊Dic59—21no—
76C2×C4⋊Dic59—21no—
77C2×C4⋊Dic59—21no—
78C2×C4⋊Dic59—21no—
79C2×C4⋊Dic59—21no—
80C2×C4⋊Dic59—44no—
81C2×C4⋊Dic59D411yescharacteristic
82C2×C4⋊Dic59D411yescharacteristic
83C2×C4⋊Dic59C2311yescharacteristic
84C2×C4⋊Dic59C2311yescharacteristic
85C2×C4⋊Dic59C2311yescharacteristic
86C2×C4⋊Dic59C2311yescharacteristic
87C2×C22⋊Dic59—21no—
88C2×C22⋊Dic59—21no—
89C2×C22⋊Dic59—21no—
90C2×C22⋊Dic59—21no—
91C2×C22⋊Dic59—21no—
92C2×C4×Dic59—21no—
93C2×C4×Dic59—21no—
94C2×C4×Dic59C2311yescharacteristic
95C2×C4×Dic59C2311yescharacteristic
96#14273661—22no—
97#14273661—22no—
98#14273651—22no—
99#14273651—41no—
100#14273648—22no—
101#14273648—22no—
102#14273648—41no—
103#14273648D414yes—
104#14273638—22no—
105#14273637—22no—
106C8×Dic59—22no—
107C59⋊#95—21no—
108C59⋊#95—21no—
109C59⋊#95—21no—
110C59⋊#95—21no—
111C59⋊#95—21no—
112C59⋊#95D411yescharacteristic
113C59⋊#95D411yescharacteristic
114C22×Q8×C59C2311yescharacteristic
115C22×D4×C59C2311yescharacteristic
116C22×D4×C59C2311yescharacteristic
117C23×C4×C59—21no—
118C2×SD16×C59—22no—
119C2×SD16×C59—22no—
120C2×SD16×C59C2×C414yescomplemented
121C2×D8×C59—22no—
122C2×D8×C59—22no—
123C2×D8×C59C2×C414yes—
124C22×C8×C59C2311yescharacteristic
125C22×C8×C59C2311yescharacteristic
126#124×C59—22no—
127#124×C59C2×C414yescomplemented
128C4×D4×C59—22no—
129C4×D4×C59C2×C414yescomplemented
130C2×C4⋊C4×C59C2311yescharacteristic
131C2×C22⋊C4×C59—21no—
132C2×C22⋊C4×C59—21no—
133C2×C22⋊C4×C59—21no—
134C2×C42×C59C2311yescharacteristic
135C4⋊C8×C59C2×C414yescomplemented
136#103×C59C2×C414yescomplemented
137#102×C59C2×C414yescomplemented
138C24×C59—21no—
139C24×C59—21no—
140C2×Q8×C59—21no—
141C2×Q8×C59—21no—
142C2×Q8×C59—21no—
143C2×Q8×C59—21no—
144C2×Q8×C59—21no—
145C2×Q8×C59C22×C412yes—
146C2×D4×C59—21no—
147C2×D4×C59—21no—
148C2×D4×C59—21no—
149C2×D4×C59—21no—
150C2×D4×C59—21no—
151C2×D4×C59—21no—
152C2×D4×C59—21no—
153C2×D4×C59—21no—
154C2×D4×C59C22×C412yes—
155C2×D4×C59C22×C412yes—
156C2×D4×C59C2×D412yes—
157C2×D4×C59#4112yes—
158C22×C4×C59—21no—
159C22×C4×C59—21no—
160C22×C4×C59—24no—
161C22×C4×C59—42no—
162C22×C4×C59—42no—
163C22×C4×C59C2×D411yescharacteristic
164C22×C4×C59C2×D411yescharacteristic
165C22×C4×C59C2411yescharacteristic
166C22×Dic59—21no—
167C22×Dic59—21no—
168C22×Dic59—21no—
169C22×Dic59—21no—
170C22×Dic59—42no—
171C22×Dic59—42no—
172C22×Dic59—42no—
173C22×Dic59—42no—
174C22×Dic59—42no—
175C22×Dic59—42no—
176C22×Dic59—81no—
177C22×Dic59—81no—
178C22×Dic59—81no—
179C22×Dic59C2×D411yescharacteristic
180C22×Dic59C2×D411yescharacteristic
181C22×Dic59C2×D411yescharacteristic
182C22×Dic59C2×D411yescharacteristic
183SD16×C59—28no—
184D8×C59—28no—
185C2×C8×C59—21no—
186C2×C8×C59—21no—
187C2×C8×C59—21no—
188C2×C8×C59—21no—
189C2×C8×C59C22×C412yes—
190C2×C8×C59C22×C412yes—
191C4⋊C4×C59—21no—
192C4⋊C4×C59C22×C412yes—
193C22⋊C4×C59—24no—
194C22⋊C4×C59—24no—
195C22⋊C4×C59—24no—
196C42×C59C22×C412yes—
197C42×C59#4112yes—
198C22⋊Dic59—42no—
199C22⋊Dic59—42no—
200C22⋊Dic59—42no—
201C22⋊Dic59—42no—
202C22⋊Dic59—81no—
203C4⋊Dic59—21no—
204C4⋊Dic59—22no—
205C4⋊Dic59—21no—
206C4⋊Dic59—21no—
207C4⋊Dic59—21no—
208C4⋊Dic59—21no—
209C4⋊Dic59—21no—
210C4⋊Dic59—21no—
211C4⋊Dic59—41no—
212C4⋊Dic59—42no—
213C4⋊Dic59—42no—
214C4⋊Dic59—42no—
215C4⋊Dic59—42no—
216C4⋊Dic59—81no—
217C4⋊Dic59C2×D412yes—
218C4×Dic59—21no—
219C4×Dic59—21no—
220C4×Dic59—21no—
221C4×Dic59—21no—
222C4×Dic59—42no—
223C4×Dic59—81no—
224C2×C59⋊C8—21no—
225C2×C59⋊C8—21no—
226C2×C59⋊C8—21no—
227C2×C59⋊C8—21no—
228C2×C59⋊C8—21no—
229C2×C59⋊C8C2×D412yes—
230C23×C59—22no—
231C23×C59—22no—
232C23×C59—22no—
233C23×C59—22no—
234C23×C59—41no—
235C23×C59—41no—
236C23×C59—41no—
237C23×C59—41no—
238C23×C59—41no—
239C23×C59—41no—
240C23×C59—41no—
241C23×C59—41no—
242C23×C59—41no—
243C23×C59—41no—
244C23×C59C22×D411yescharacteristic
245Q8×C59—22no—
246Q8×C59—22no—
247Q8×C59—41no—
248Q8×C59—41no—
249D4×C59—22no—
250D4×C59—22no—
251D4×C59—22no—
252D4×C59—22no—
253D4×C59—22no—
254D4×C59—41no—
255D4×C59—41no—
256D4×C59C4×D414yes—
257C2×C4×C59—21no—
258C2×C4×C59—21no—
259C2×C4×C59—21no—
260C2×C4×C59—21no—
261C2×C4×C59—22no—
262C2×C4×C59—22no—
263C2×C4×C59—48no—
264C2×C4×C59—41no—
265C2×C4×C59—41no—
266C2×C4×C59—41no—
267C2×C4×C59—41no—
268C2×C4×C59C4×D412yes—
269C2×C4×C59C4×D412yes—
270C2×C4×C59C23×C411yescharacteristic
271C2×C4×C59C22×D411yescharacteristic
272C2×C4×C59C2×#4111yescharacteristic
273C2×C4×C59C2×#4111yescharacteristic
274C2×C4×C59H(5,𝔽2)11yescharacteristic
275C2×C4×C592−1+411yescharacteristic
276C2×Dic59—21no—
277C2×Dic59—21no—
278C2×Dic59—21no—
279C2×Dic59—21no—
280C2×Dic59—21no—
281C2×Dic59—22no—
282C2×Dic59—21no—
283C2×Dic59—21no—
284C2×Dic59—21no—
285C2×Dic59—21no—
286C2×Dic59—21no—
287C2×Dic59—21no—
288C2×Dic59—41no—
289C2×Dic59—41no—
290C2×Dic59—41no—
291C2×Dic59—41no—
292C2×Dic59—41no—
293C2×Dic59—41no—
294C2×Dic59—41no—
295C2×Dic59—41no—
296C2×Dic59—41no—
297C2×Dic59—41no—
298C2×Dic59—41no—
299C2×Dic59—84no—
300C2×Dic59—84no—
301C2×Dic59—84no—
302C2×Dic59AGL(1,ℤ/8)12yes—
303C8×C59—22no—
304C8×C59—22no—
305C59⋊C8—22no—
306C59⋊C8—41no—
307#23011—591nomaximal, Sylow
308C22×C59—24no—
309C22×C59—42no—
310C22×C59—42no—
311C22×C59—42no—
312C22×C59—42no—
313C22×C59—42no—
314C22×C59—42no—
315C22×C59—42no—
316C22×C59—42no—
317C22×C59—42no—
318C22×C59—81no—
319C22×C59—81no—
320C22×C59—81no—
321C22×C59—81no—
322C22×C59C2×C4×D411yescharacteristic
323C22×C59D4211yescharacteristic
324C22×C59#54811yescharacteristic
325C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
326C22×C59#57511yescharacteristic
327C22×C59#57611yescharacteristic
328C22×C59#57811yescharacteristic
329C4×C59—22no—
330C4×C59—22no—
331C4×C59—42no—
332C4×C59—42no—
333C4×C59C2×C4×D411yescharacteristic
334C4×C59#52011yescharacteristic
335C4×C59#54711yescharacteristic
336C4×C59#55311yescharacteristic
337Dic59—22no—
338Dic59—41no—
339Dic59—42no—
340Dic59—41no—
341Dic59—41no—
342Dic59—81no—
343Dic59—81no—
344Dic59—81no—
345C2×#463D5911yescharacteristic
346C2×#440—591no—
347C2×C4×D8—591no—
348#2367—591no—
349D4×C4⋊C4—591no—
350#1959—591no—
351#1947—591no—
352#1936—591no—
353#1933—591no—
354#1879—591no—
355#1877—591no—
356#1863—591no—
357#1862—591no—
358#1771—591no—
359#1762—591no—
360C2×C59—44no—
361C2×C59—82no—
362C2×C59#236111yescharacteristic
363C2×C59C4×AGL(1,ℤ/8)11yescharacteristic
364C2×C59#295111yescharacteristic
365C2×C59#326411yescharacteristic
366C2×C59#326911yescharacteristic
367C2×C59#336711yescharacteristic
368C2×C59#337011yescharacteristic
369C22×SD16C2×D5911yescharacteristic
370C22×D8C2×D5911yescharacteristic
371C2×#124C2×D5911yescharacteristic
372C2×C4×Q8—591no—
373C2×C4×D4—591no—
374C2×C4×D4—591no—
375C2×C4×D4—591no—
376C2×C4×D4C2×D5911yescharacteristic
377C22×C4⋊C4—1181no—
378#463Dic5918yescomplemented
379#440—1184no—
380C4×D8—1184no—
381C2×#107—591no—
382C2×#107—591no—
383C2×C4⋊C8C2×D5911yescharacteristic
384C2×#103—591no—
385C2×#103—591no—
386C2×#103C2×D5911yescharacteristic
387C2×#102—591no—
388C2×#102—591no—
389C2×#102—591no—
390C2×#102—591no—
391C2×#102C2×D5911yescharacteristic
392C2×#97—591no—
393C2×#97—591no—
394C2×C4×C8—591no—
395#391—591no—
396#390—591no—
397#389—591no—
398#389—591no—
399#388—1181no—
400#388—1181no—
401#385—1181no—
402#385—1181no—
403#385—1181no—
404#384—591no—
405#380—1181no—
406C4×C4⋊C4—591no—
407C4×C4⋊C4—591no—
408C4×C22⋊C4—1181no—
409#340—591no—
410#340—591no—
411#340—591no—
412#340—591no—
413#336—591no—
414#336—591no—
415C59#2301111yescharacteristic, complemented, Sylow
416C22×Q8C22×D5911yescharacteristic
417C22×D4C22×D5911yescharacteristic
418C22×D4C22×D5911yescharacteristic
419C23×C4—21no—
420C23×C4—1181no—
421C23×C4—1181no—
422C23×C4—1181no—
423C2×SD16—22no—
424C2×SD16—22no—
425C2×SD16C2×Dic5914yescomplemented
426C2×D8—22no—
427C2×D8—22no—
428C2×D8C2×Dic5914yes—
429C22×C8—591no—
430C22×C8—591no—
431C22×C8C22×D5911yescharacteristic
432C22×C8C22×D5911yescharacteristic
433#124—22no—
434#124C2×Dic5914yescomplemented
435C4×Q8—1182no—
436C4×Q8—2361no—
437C4×D4—22no—
438C4×D4—1182no—
439C4×D4—1182no—
440C4×D4—1182no—
441C4×D4—2361no—
442C4×D4—2361no—
443C4×D4—2361no—
444C4×D4C2×Dic5914yescomplemented
445C2×C4⋊C4—591no—
446C2×C4⋊C4—591no—
447C2×C4⋊C4—591no—
448C2×C4⋊C4—591no—
449C2×C4⋊C4—591no—
450C2×C4⋊C4—591no—
451C2×C4⋊C4—1181no—
452C2×C4⋊C4—1181no—
453C2×C4⋊C4—1181no—
454C2×C4⋊C4—1181no—
455C2×C4⋊C4—1181no—
456C2×C4⋊C4—2364no—
457C2×C4⋊C4C22×D5911yescharacteristic
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—1181no—
462C2×C22⋊C4—1181no—
463C2×C22⋊C4—1181no—
464C2×C22⋊C4—1181no—
465C2×C22⋊C4—1181no—
466C2×C42—591no—
467C2×C42—591no—
468C2×C42—1181no—
469C2×C42—1181no—
470C2×C42C22×D5911yescharacteristic
471#107—1182no—
472#107—1182no—
473C4⋊C8C2×Dic5914yescomplemented
474#103—1182no—
475#103—2361no—
476#103C2×Dic5914yescomplemented
477#102—594no—
478#102—1182no—
479#102—1182no—
480#102—2361no—
481#102C2×Dic5914yescomplemented
482#97—1182no—
483#97—1182no—
484C4×C8—1182no—
485#95—591no—
486#95—591no—
487#95—1181no—
488#95—1181no—
489#95—1181no—
490#95—1181no—
491#95—1181no—
492C24—21no—
493C24—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8C22×Dic5912yes—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4D4×D5912yes—
509C2×D4#1174568712yes—
510C2×D4C22×Dic5912yes—
511C2×D4C22×Dic5912yes—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—24no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—591no—
518C22×C4—591no—
519C22×C4—591no—
520C22×C4—591no—
521C22×C4—1181no—
522C22×C4—1181no—
523C22×C4—1181no—
524C22×C4—1181no—
525C22×C4—4721no—
526C22×C4—4721no—
527C22×C4—4721no—
528C22×C4—2362no—
529C22×C4—2362no—
530C22×C4—2362no—
531C22×C4—2362no—
532C22×C4—2362no—
533C22×C4—2362no—
534C22×C4D4×D5911yescharacteristic
535C22×C4D4×D5911yescharacteristic
536C22×C4C23×D5911yescharacteristic
537SD16—28no—
538D8—28no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—592no—
544C2×C8—1181no—
545C2×C8—1181no—
546C2×C8—1181no—
547C2×C8—1181no—
548C2×C8—1181no—
549C2×C8C22×Dic5912yes—
550C2×C8C22×Dic5912yes—
551C4⋊C4—21no—
552C4⋊C4—592no—
553C4⋊C4—1182no—
554C4⋊C4—1181no—
555C4⋊C4—1181no—
556C4⋊C4—1181no—
557C4⋊C4—1181no—
558C4⋊C4—1181no—
559C4⋊C4—1181no—
560C4⋊C4—1181no—
561C4⋊C4—4721no—
562C4⋊C4—2361no—
563C4⋊C4—2362no—
564C4⋊C4—2362no—
565C4⋊C4—2362no—
566C4⋊C4—2362no—
567C4⋊C4C22×Dic5912yes—
568C22⋊C4—24no—
569C22⋊C4—24no—
570C22⋊C4—24no—
571C22⋊C4—4721no—
572C22⋊C4—2362no—
573C22⋊C4—2362no—
574C22⋊C4—2362no—
575C22⋊C4—2362no—
576C42—1181no—
577C42—1181no—
578C42—1181no—
579C42—1181no—
580C42—4721no—
581C42—2362no—
582C42#1174568712yes—
583C42C22×Dic5912yes—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23C2×D4×D5911yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—41no—
602Q8—41no—
603D4—22no—
604D4—22no—
605D4—22no—
606D4—22no—
607D4—22no—
608D4—41no—
609D4—41no—
610D4D4×Dic5914yes—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—48no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—592no—
623C2×C4—1181no—
624C2×C4—1181no—
625C2×C4—1181no—
626C2×C4—1181no—
627C2×C4—1181no—
628C2×C4—1181no—
629C2×C4—1181no—
630C2×C4—1181no—
631C2×C4—1181no—
632C2×C4—1181no—
633C2×C4—1181no—
634C2×C4—1182no—
635C2×C4—4724no—
636C2×C4—4724no—
637C2×C4—4724no—
638C2×C4—2361no—
639C2×C4—2361no—
640C2×C4—2361no—
641C2×C4—2361no—
642C2×C4—2361no—
643C2×C4—2361no—
644C2×C4—2361no—
645C2×C4—2361no—
646C2×C4—2361no—
647C2×C4—2361no—
648C2×C4—2361no—
649C2×C4D4×Dic5912yes—
650C2×C4D4×Dic5912yes—
651C2×C4C23×Dic5911yescharacteristic
652C2×C4C2×D4×D5911yescharacteristic
653C2×C4C2×#1174568711yescharacteristic
654C2×C4C2×#1174568711yescharacteristic
655C2×C4#1427377311yescharacteristic
656C2×C4#1427377411yescharacteristic
657C8—22no—
658C8—22no—
659C8—1182no—
660C8—2361no—
661C22—24no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22C2×D4×Dic5911yescharacteristic
676C22#1683803611yescharacteristic
677C22#1683805811yescharacteristic
678C22AGL(1,ℤ/8)×D5911yescharacteristic
679C22#1683819811yescharacteristic
680C22#1683820411yescharacteristic
681C22#1683821611yescharacteristic
682C4—22no—
683C4—22no—
684C4—42no—
685C4—42no—
686C4—1182no—
687C4—4721no—
688C4—4721no—
689C4—4721no—
690C4—2361no—
691C4—2361no—
692C4—2361no—
693C4—2362no—
694C4C2×D4×Dic5911yescharacteristic
695C4#1683788511yescharacteristic
696C4#1683805211yescharacteristic
697C4#1683810411yescharacteristic
698C2—44no—
699C2—82no—
700C2#2142711611yescharacteristic
701C2AGL(1,ℤ/8)×Dic5911yescharacteristic
702C2#2143297211yescharacteristic
703C2#2143558211yescharacteristic
704C2#2143565711yescharacteristic
705C2#2143680911yescharacteristic
706C2#2143684611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C59×#463C2
socleC23×C59C22×D4
prime radicalC22×D8×C59C22
cosocleC22×C4×C59C24
hypercenterC2×#463D59
hypocenterC59#23011
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#16837503C2semidirect
3. #21427171C2semidirect
4. D4×C4⋊Dic59C2semidirect
5. #21424913C2semidirect
6. #21424855C2semidirect
7. #21424795C2semidirect
8. #21424774C2semidirect
10. #21424432C2semidirect
11. #21424352C2semidirect
12. #21424345C2semidirect
13. #21423973C2semidirect
14. #21423921C2semidirect
58. C59×#463C4semidirect
120. C2×SD16×C59C2×C4semidirect
127. #124×C59C2×C4semidirect
129. C4×D4×C59C2×C4semidirect
135. C4⋊C8×C59C2×C4semidirect
136. #103×C59C2×C4semidirect
137. #102×C59C2×C4semidirect
378. #463Dic59semidirect
415. C59#23011semidirect
425. C2×SD16C2×Dic59semidirect
434. #124C2×Dic59semidirect
444. C4×D4C2×Dic59semidirect
473. C4⋊C8C2×Dic59semidirect
476. #103C2×Dic59semidirect
481. #102C2×Dic59semidirect

Maximal subgroups

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

subgroupindex
C2×#168375032
C2×D8×Dic592
#214271712
D4×C4⋊Dic592
#214249132
#214248552
#214247952
#214247742
#214244462
#214244322
#214243522
#214243452
#214239732
#214239212
C2×C59×#4632
#2301159