Finite Group Databasebeta

← #30564902

Subgroups — #30564902

Order 15616.

2094 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459658C211yesmaximal, characteristic
2C2×D4×Dic122C211yesmaximal, characteristic, complemented
3#21457992C214yesmaximal, complemented
4#21457872C214yesmaximal, complemented
5#21457394C214yesmaximal, complemented
6#21457334C214yesmaximal, complemented
7#21456848C212yesmaximal, complemented
8#21456651C212yesmaximal, complemented
9#21456594C211yesmaximal, characteristic, complemented
10#21456577C211yesmaximal, characteristic, complemented
11#21455992C212yesmaximal, complemented
12#21455056C212yesmaximal, complemented
13C2×#16839920C211yesmaximal, characteristic, complemented
14C2×#16839903C211yesmaximal, characteristic, complemented
15C61×#2973C211yesmaximal, characteristic, complemented
16C23×Dic122C2211yescharacteristic
17C23×Dic122C2211yescharacteristic, complemented
18C2×#14519810C2214yescomplemented
19C22×Dic244C2212yescomplemented
20C22×#11758190C2212yescomplemented
21#16840461—22no—
22#16840458C2212yes—
23#16840452C2212yes—
24#16840441—22no—
25D4×Dic122—22no—
26D4×Dic122—22no—
27D4×Dic122C2214yes—
28D4×Dic122C2214yescomplemented
29#16840421C2212yes—
30#16840408C2212yes—
31#16840359—21no—
32#16840350—21no—
33#16840321—21no—
34C2×#14519777C2211yescharacteristic, complemented
35C2×#14519776—21no—
36#16840296C2212yes—
37#16840273C2212yes—
38C2×#14519756C2211yescharacteristic
39C2×#14519756C2211yescharacteristic
40C2×#14519756C2211yescharacteristic, complemented
41C2×#14519754—21no—
42C2×#14519754—21no—
43C2×#14519751C2211yescharacteristic
44#16840235—21no—
45C2×C4×Dic122C2211yescharacteristic, complemented
46C2×D4×Dic61—21no—
47#16840156C2214yescomplemented
48#16840131C2214yescomplemented
49#16840104C2214yescomplemented
50#16840098C2212yescomplemented
51#16840098C2212yescomplemented
52#16840093C2212yescomplemented
53#16840081C2212yes—
54#16840070C2214yescomplemented
55#16840020C2214yescomplemented
56#16840008C2214yescomplemented
57#16840003C2214yescomplemented
58#16839991C2214yescomplemented
59#16839985C2214yescomplemented
60#16839973C2214yescomplemented
61#16839968C2214yescomplemented
62#16839926C2214yescomplemented
63#16839920C2212yescomplemented
64#16839920C2212yescomplemented
65#16839920C2214yescomplemented
66#16839920C2212yescomplemented
67#16839920C2214yescomplemented
68#16839920C2212yescomplemented
69#16839915C2212yescomplemented
70#16839903C2212yes—
71#16839903C2212yes—
72#16839903C2212yes—
73#16839903C2214yescomplemented
74#16839903C2214yescomplemented
75#16839870C2214yescomplemented
76#16839864C2214yescomplemented
77#16839772C2214yescomplemented
78C2×#14519702C2212yescomplemented
79C2×#14519702C2212yescomplemented
80C2×C4×D4×C61C2211yescharacteristic
81C61×#435C2214yes—
82C61×#435C2214yescomplemented
83C61×#432C2212yescomplemented
84C61×#407C2212yescomplemented
85C2×C22⋊C8×C61C2211yescharacteristic
86C2×C22⋊C8×C61C2211yescharacteristic
87C2×#11758222C2312yes—
88C22×Dic122—21no—
89C22×Dic122—21no—
90C22×Dic122—21no—
91C22×Dic122—21no—
92C22×Dic122—22no—
93C22×Dic122—44no—
94C22×Dic122—44no—
95C22×Dic122C2311yescharacteristic
96C22×Dic122C2312yes—
97C22×Dic122C2312yes—
98C22×Dic122C2314yes—
99C22×Dic122C2311yescharacteristic
100C22×Dic122C2311yescharacteristic
101C22×Dic122C2311yescharacteristic
102C22×D244C2311yescharacteristic
103C22×C22⋊D61—21no—
104C23×Dic61—21no—
105C23×Dic61—21no—
106#14519810—48no—
107C2×Dic244—44no—
108C2×Dic244C2314yes—
109C2×Dic244C2314yes—
110C2×Dic244C2314yes—
111C2×#11758190—44no—
112C2×#11758190C2314yes—
113C2×#11758190C2314yes—
114C2×#11758190C2314yes—
115#14519777—22no—
116#14519777C2314yes—
117#14519776—24no—
118#14519776—24no—
119#14519772—22no—
120#14519771—22no—
121#14519770—22no—
122#14519769C2312yes—
123#14519767—22no—
124#14519765C2312yes—
125#14519763—22no—
126#14519762—22no—
127#14519760—22no—
128#14519760—22no—
129#14519759—22no—
130#14519758—22no—
131#14519756—21no—
132#14519756—21no—
133#14519756—21no—
134#14519756—21no—
135#14519756—22no—
136#14519756C2312yes—
137#14519756C2312yes—
138#14519756C2312yes—
139#14519756C2312yes—
140#14519756C2312yes—
141#14519756C2314yes—
142#14519755—22no—
143#14519754—24no—
144#14519754—24no—
145#14519754—24no—
146#14519754—24no—
147#14519751—21no—
148#14519751—21no—
149#14519751C2312yes—
150#14519751C2312yes—
151#14519751C2312yes—
152#14519750—22no—
153#14519749—22no—
154#14519749—22no—
155#14519746—22no—
156#14519745—22no—
157C4×Dic122—22no—
158C4×Dic122C2312yes—
159C4×Dic122C2314yes—
160C4×D244C2312yes—
161D4×Dic61—24no—
162D4×Dic61—24no—
163C4×C22⋊D61—22no—
164C4×C22⋊D61—22no—
165C4×C22⋊D61—22no—
166#14519737—22no—
167#14519737—22no—
168#14519736C2312yes—
169#14519734—22no—
170#14519733—22no—
171C2×C4⋊Dic61—21no—
172C2×C4⋊Dic61—21no—
173C2×C4⋊Dic61C2311yescharacteristic
174C2×C4⋊Dic61C2311yescharacteristic
175C2×C4⋊Dic61C2311yescharacteristic
176C2×#11758196—21no—
177C2×#11758196—21no—
178C2×#11758196—21no—
179C2×#11758196—21no—
180C2×C22⋊Dic61—21no—
181C2×C22⋊Dic61—21no—
182C2×C22⋊Dic61—21no—
183C2×#11758198—21no—
184C22⋊C4×D61—22no—
185C2×C4×Dic61—21no—
186#14519711C2314yes—
187#14519709C2314yes—
188#14519702C2314yes—
189#14519702C2314yes—
190#14519702C2314yes—
191#14519702C2314yes—
192#14519702C2314yes—
193#14519702C2314yes—
194#14519702C2314yes—
195#14519699C2314yes—
196C22×D4×C61D411yescharacteristic
197C23×C4×C61C2311yescharacteristic
198C23×C4×C61C2311yescharacteristic
199C2×M16×C61C2314yes—
200C22×C8×C61C2312yes—
201C22×C8×C61C2312yes—
202C4×D4×C61D412yes—
203C4×D4×C61D412yes—
204C4×D4×C61C2312yes—
205C4×D4×C61C2312yes—
206C2×C4⋊C4×C61D411yescharacteristic
207C2×C22⋊C4×C61D411yescharacteristic
208C2×C22⋊C4×C61D411yescharacteristic
209C2×C42×C61C2311yescharacteristic
210C4⋊C8×C61C2314yes—
211C22⋊C8×C61C2312yes—
212C22⋊C8×C61C2312yes—
213C22⋊C8×C61C2312yes—
214C22⋊C8×C61C2312yes—
215C22⋊C8×C61C2314yes—
216#97×C61C2314yes—
217C24×C61C2×D411yescharacteristic
218C24×C61C2×D411yescharacteristic
219C23×D61—21no—
220C2×D4×C61—24no—
221C2×D4×C61C2×D412yes—
222C2×D4×C61C2×D412yes—
223C22×C4×C61—42no—
224C22×C4×C61—42no—
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D412yes—
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2411yescharacteristic
233C22×C4×C61C2411yescharacteristic
234C22×C4×C61C2411yescharacteristic
235C22×C4×C61C2412yes—
236C2×C22⋊D61—22no—
237C2×C22⋊D61—22no—
238C2×C22⋊D61—22no—
239C2×C22⋊D61—22no—
240C2×C22⋊D61—44no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—24no—
245C22×Dic61—22no—
246C22×Dic61—22no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—44no—
252C22×Dic61—44no—
253#11758222—44no—
254C2×D244—21no—
255C2×D244—42no—
256C2×D244C2412yes—
257C2×C4×D61—22no—
258C2×C4×D61—22no—
259C2×Dic122—21no—
260C2×Dic122—24no—
261C2×Dic122—28no—
262C2×Dic122—24no—
263C2×Dic122—24no—
264C2×Dic122—24no—
265C2×Dic122—22no—
266C2×Dic122—22no—
267C2×Dic122—21no—
268C2×Dic122—21no—
269C2×Dic122—21no—
270C2×Dic122—42no—
271C2×Dic122—44no—
272C2×Dic122—42no—
273C2×Dic122—42no—
274C2×Dic122—42no—
275C2×Dic122—42no—
276C2×Dic122—44no—
277C2×Dic122—44no—
278C2×Dic122—48no—
279C2×Dic122—44no—
280C2×Dic122—44no—
281C2×Dic122C2412yes—
282C2×Dic122C2412yes—
283C2×Dic122C2412yes—
284C2×Dic122C2412yes—
285M16×C61—44no—
286C2×C8×C61—42no—
287C2×C8×C61—42no—
288C2×C8×C61C2414yes—
289C2×C8×C61C2414yes—
290C4⋊C4×C61C2×D412yes—
291C4⋊C4×C61C2×D412yes—
292C22⋊C4×C61C2×D412yes—
293C22⋊C4×C61C2×D412yes—
294C22⋊C4×C61C2×D412yes—
295C22⋊C4×C61C2×D412yes—
296C42×C61C2×D412yes—
297C42×C61C2412yes—
298C22⋊Dic61—22no—
299C22⋊Dic61—22no—
300C22⋊Dic61—24no—
301C22⋊Dic61—22no—
302C22⋊Dic61—22no—
303C22⋊Dic61—22no—
304C22⋊Dic61—22no—
305#11758198—22no—
306#11758198—22no—
307#11758198—22no—
308#11758198—22no—
309#11758198—22no—
310#11758198—22no—
311C4⋊Dic61—24no—
312C4⋊Dic61—24no—
313C4⋊Dic61—21no—
314C4⋊Dic61—21no—
315C4⋊Dic61—21no—
316C4⋊Dic61C2412yes—
317C4⋊Dic61C2412yes—
318C4⋊Dic61C2412yes—
319#11758196—22no—
320#11758196—24no—
321#11758196—22no—
322#11758196—24no—
323#11758196—22no—
324#11758196—22no—
325#11758196—22no—
326#11758196—22no—
327#11758196—22no—
328#11758196—22no—
329C4×Dic61—24no—
330C4×Dic61—22no—
331C4×Dic61—22no—
332Dic244—28no—
333Dic244—44no—
334Dic244—44no—
335#11758190—28no—
336#11758190—44no—
337#11758190—44no—
338C23×C61—22no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61#13714yescomplemented
344C23×C61C22×D412yes—
345C23×C61C22×D411yescharacteristic
346C23×C61C22×D411yescharacteristic
347C23×C61C22×D411yescharacteristic
348C22×D61—22no—
349C22×D61—42no—
350C22×D61—81no—
351C22×D61—81no—
352D4×C61—24no—
353D4×C61—24no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—24no—
358C2×C4×C61—22no—
359C2×C4×C61—41no—
360C2×C4×C61—42no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61C22×D412yes—
366C2×C4×C61C22×D412yes—
367C2×C4×C61C22×D412yes—
368C2×C4×C61C22×D411yescharacteristic
369C2×C4×C61C22×D411yescharacteristic
370C2×C4×C61C22×D411yescharacteristic
371C2×C4×C61C2511yescharacteristic
372C22⋊D61—44no—
373C22⋊D61—44no—
374C22⋊D61—82no—
375C22⋊D61—82no—
376C2×Dic61—24no—
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—22no—
380C2×Dic61—22no—
381C2×Dic61—22no—
382C2×Dic61—22no—
383C2×Dic61—22no—
384C2×Dic61—44no—
385C2×Dic61—44no—
386C2×Dic61—48no—
387C2×Dic61—42no—
388C2×Dic61—42no—
389C2×Dic61—42no—
390C2×Dic61—42no—
391C2×Dic61—81no—
392C2×Dic61—81no—
393D244—24no—
394D244—81no—
395C4×D61—82no—
396C4×D61—82no—
397Dic122—24no—
398Dic122—22no—
399Dic122—22no—
400Dic122—24no—
401Dic122—24no—
402Dic122—22no—
403Dic122—44no—
404Dic122—48no—
405Dic122—44no—
406Dic122—42no—
407Dic122—42no—
408Dic122—81no—
409Dic122H(5,𝔽2)14yes—
410C8×C61—24no—
411C8×C61—24no—
412#61574—611nomaximal, Sylow
413C22×C61—21no—
414C22×C61—21no—
415C22×C61—21no—
416C22×C61—21no—
417C22×C61—21no—
418C22×C61—21no—
419C22×C61—22no—
420C22×C61—22no—
421C22×C61—22no—
422C22×C61—44no—
423C22×C61—44no—
424C22×C61C2×#13712yes—
425C22×C61C2×#13712yes—
426C22×C61C2×#13712yes—
427C22×C61C23×D411yescharacteristic
428C2×D61—42no—
429C2×D61—42no—
430C2×D61—42no—
431C2×D61—162no—
432C4×C61—22no—
433C4×C61—21no—
434C4×C61—21no—
435C4×C61—22no—
436C4×C61—21no—
437C4×C61—22no—
438C4×C61C2×H(5,𝔽2)12yes—
439Dic61—24no—
440Dic61—42no—
441Dic61—42no—
442Dic61—42no—
443Dic61—42no—
444Dic61—42no—
445Dic61—42no—
446#3505—611no—
447C2×D4×Q8—611no—
448#3320—614no—
449#3312—614no—
450#3270—614no—
451#3266—614no—
452#3218—612no—
453#3196—612no—
454#3189—611no—
455#3187—611no—
456#3117—612no—
457#3004—612no—
458C2×#451—611no—
459C2×#448—611no—
460#2973D6111yescharacteristic, complemented
461C2×C61—22no—
462C2×C61—22no—
463C2×C61—22no—
464C2×C61—42no—
465C2×C61#348411yescharacteristic
466C2×C61C22×#13711yescharacteristic
467C2×C61#358611yescharacteristic
468D61—82no—
469C23×Q8—611no—
470C23×Q8—611no—
471C2×#137—614no—
472C22×Q16—612no—
473C22×SD16—612no—
474#553—612no—
475#553—1222no—
476#552—612no—
477#551—1222no—
478D4×Q8—614no—
479D4×Q8—614no—
480D4×Q8—1222no—
481D4×Q8—1222no—
482#548—612no—
483#546—612no—
484#539—1221no—
485#538—1221no—
486#534—1221no—
487C2×C4⋊Q8—611no—
488C2×C4⋊Q8—1221no—
489#529—612no—
490#525—612no—
491C2×C22⋊Q8—611no—
492C2×C22⋊Q8—611no—
493C2×C22⋊Q8—611no—
494C2×C22⋊Q8—1221no—
495C2×C22⋊Q8—1221no—
496C2×#121—611no—
497#518—1221no—
498C2×C4×Q8—611no—
499C2×C4×D4—1221no—
500C2×C4×D4C2×D6111yescharacteristic
501#497—614no—
502#491—614no—
503#485—614no—
504#484—612no—
505#484—612no—
506#483—612no—
507#481—612no—
508#479—614no—
509#470—614no—
510#468—614no—
511#467—614no—
512#465—614no—
513#464—614no—
514#462—614no—
515#461—614no—
516#452—614no—
517#451—612no—
518#451—612no—
519#451—612no—
520#451—612no—
521#451—614no—
522#451—614no—
523#450—612no—
524#448—612no—
525#448—612no—
526#448—612no—
527#448—614no—
528#448—614no—
529#441—614no—
530#440—614no—
531#435C2×D6114yes—
532#435C2×D6114yescomplemented
533#432C2×D6112yescomplemented
534#419—614no—
535C2×#103—612no—
536C2×#103—612no—
537#407C2×D6112yescomplemented
538C2×C22⋊C8C2×D6111yescharacteristic
539C2×C22⋊C8C2×D6111yescharacteristic
540C61#6157411yescharacteristic, complemented, Sylow
541C2×#41—612no—
542C22×Q8—611no—
543C22×Q8—612no—
544C22×Q8—612no—
545C22×Q8—614no—
546C22×Q8—611no—
547C22×Q8—611no—
548C22×Q8—611no—
549C22×Q8—1221no—
550C22×Q8—1221no—
551C22×Q8—1221no—
552C22×Q8—1221no—
553C22×Q8—1222no—
554C22×Q8—2444no—
555C22×Q8—2444no—
556C22×D4—611no—
557C22×D4—1221no—
558C22×D4D24411yescharacteristic
559C23×C4—1221no—
560C23×C4—1221no—
561C23×C4C22×D6111yescharacteristic
562C23×C4C22×D6111yescharacteristic
563#137—2448no—
564C2×Q16—614no—
565C2×Q16—614no—
566C2×Q16—614no—
567C2×Q16—2444no—
568C2×SD16—614no—
569C2×SD16—614no—
570C2×SD16—614no—
571C2×SD16—2444no—
572C2×M16C22×D6114yes—
573C22×C8C22×D6112yes—
574C22×C8C22×D6112yes—
575C4⋊Q8—614no—
576C4⋊Q8—1224no—
577C4⋊Q8—1224no—
578C4⋊Q8—1222no—
579#126—1222no—
580#126—1222no—
581#126—1222no—
582#125—612no—
583#125—1222no—
584#124—612no—
585#124—1222no—
586#123—1222no—
587#123—1222no—
588#123—1222no—
589#123—1222no—
590#123—1222no—
591C22⋊Q8—612no—
592C22⋊Q8—612no—
593C22⋊Q8—612no—
594C22⋊Q8—612no—
595C22⋊Q8—614no—
596C22⋊Q8—612no—
597C22⋊Q8—1221no—
598C22⋊Q8—1221no—
599C22⋊Q8—1221no—
600C22⋊Q8—1222no—
601C22⋊Q8—1221no—
602C22⋊Q8—1222no—
603C22⋊Q8—1224no—
604C22⋊Q8—1224no—
605C22⋊Q8—1224no—
606C22⋊Q8—1224no—
607#121—612no—
608#121—612no—
609#121—612no—
610#121—1222no—
611#121—1222no—
612#121—1221no—
613#121—1221no—
614#121—1222no—
615#120—1222no—
616#120—1222no—
617C4×Q8—614no—
618C4×Q8—612no—
619C4×Q8—1222no—
620C4×D4—612no—
621C4×D4—1224no—
622C4×D4—1224no—
623C4×D4—1222no—
624C4×D4—1222no—
625C4×D4—1222no—
626C4×D4—1222no—
627C4×D4—1222no—
628C4×D4D24412yes—
629C4×D4D24412yes—
630C4×D4C22×D6112yes—
631C4×D4C22×D6112yes—
632#117—612no—
633#117—1222no—
634#117—1222no—
635C2×C4⋊C4—611no—
636C2×C4⋊C4—611no—
637C2×C4⋊C4—611no—
638C2×C4⋊C4—1221no—
639C2×C4⋊C4—1221no—
640C2×C4⋊C4—1221no—
641C2×C4⋊C4—1221no—
642C2×C4⋊C4—1221no—
643C2×C4⋊C4—1221no—
644C2×C4⋊C4D24411yescharacteristic
645C2×C22⋊C4—1221no—
646C2×C22⋊C4—1221no—
647C2×C22⋊C4—1221no—
648C2×C22⋊C4—1221no—
649C2×C22⋊C4—1222no—
650C2×C22⋊C4D24411yescharacteristic
651C2×C22⋊C4D24411yescharacteristic
652C2×C42—1221no—
653C2×C42C22×D6111yescharacteristic
654#107—614no—
655#106—614no—
656C4⋊C8C22×D6114yes—
657#103—614no—
658#103—614no—
659#103—614no—
660#103—614no—
661#103—614no—
662#103—614no—
663#103—614no—
664#102—614no—
665C22⋊C8C22×D6112yes—
666C22⋊C8C22×D6112yes—
667C22⋊C8C22×D6112yes—
668C22⋊C8C22×D6112yes—
669C22⋊C8C22×D6114yes—
670#97C22×D6114yes—
671C24—1221no—
672C24C2×D24411yescharacteristic
673C24C2×D24411yescharacteristic
674#41—2444no—
675C2×Q8—612no—
676C2×Q8—612no—
677C2×Q8—612no—
678C2×Q8—612no—
679C2×Q8—1224no—
680C2×Q8—1224no—
681C2×Q8—1224no—
682C2×Q8—1228no—
683C2×Q8—1221no—
684C2×Q8—1221no—
685C2×Q8—1224no—
686C2×Q8—1222no—
687C2×Q8—1222no—
688C2×Q8—1221no—
689C2×Q8—1221no—
690C2×Q8—2442no—
691C2×Q8—2442no—
692C2×Q8—2442no—
693C2×Q8—2444no—
694C2×Q8—2442no—
695C2×Q8—2442no—
696C2×Q8—2444no—
697C2×Q8—2444no—
698C2×Q8—2448no—
699C2×Q8—2444no—
700C2×Q8—2444no—
701C2×D4—24no—
702C2×D4—612no—
703C2×D4—1222no—
704C2×D4—1222no—
705C2×D4—1222no—
706C2×D4—1222no—
707C2×D4—1221no—
708C2×D4—2442no—
709C2×D4—2444no—
710C2×D4C2×D24412yes—
711C2×D4C2×D24412yes—
712C22×C4—42no—
713C22×C4—42no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1224no—
722C22×C4—1222no—
723C22×C4—1222no—
724C22×C4—1222no—
725C22×C4—1222no—
726C22×C4—2444no—
727C22×C4—2444no—
728C22×C4C2×D24411yescharacteristic
729C22×C4C2×D24411yescharacteristic
730C22×C4C2×D24411yescharacteristic
731C22×C4C2×D24411yescharacteristic
732C22×C4C2×D24411yescharacteristic
733C22×C4C2×D24411yescharacteristic
734C22×C4C2×D24412yes—
735C22×C4C23×D6111yescharacteristic
736C22×C4C23×D6111yescharacteristic
737C22×C4C23×D6111yescharacteristic
738C22×C4C23×D6112yes—
739Q16—1228no—
740Q16—2444no—
741Q16—2444no—
742SD16—1228no—
743SD16—2444no—
744SD16—2444no—
745M16—44no—
746C2×C8—42no—
747C2×C8—42no—
748C2×C8C23×D6114yes—
749C2×C8C23×D6114yes—
750C4⋊C4—612no—
751C4⋊C4—612no—
752C4⋊C4—612no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—1222no—
757C4⋊C4—1224no—
758C4⋊C4—1222no—
759C4⋊C4—1224no—
760C4⋊C4—1222no—
761C4⋊C4—1222no—
762C4⋊C4—1224no—
763C4⋊C4—1224no—
764C4⋊C4—1222no—
765C4⋊C4—1222no—
766C4⋊C4—1222no—
767C4⋊C4—1222no—
768C4⋊C4C2×D24412yes—
769C4⋊C4C2×D24412yes—
770C22⋊C4—1222no—
771C22⋊C4—1222no—
772C22⋊C4—1224no—
773C22⋊C4—1222no—
774C22⋊C4—1222no—
775C22⋊C4—1222no—
776C22⋊C4—1222no—
777C22⋊C4—1222no—
778C22⋊C4—1222no—
779C22⋊C4—1222no—
780C22⋊C4—1222no—
781C22⋊C4—1222no—
782C22⋊C4—1222no—
783C22⋊C4C2×D24412yes—
784C22⋊C4C2×D24412yes—
785C22⋊C4C2×D24412yes—
786C22⋊C4C2×D24412yes—
787C42—1224no—
788C42—1222no—
789C42—1222no—
790C42C2×D24412yes—
791C42C23×D6112yes—
792C23—22no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—1222no—
798C23—4881no—
799C23—4881no—
800C23—2442no—
801C23#1451981014yescomplemented
802C23C22×D24412yes—
803C23C22×D24411yescharacteristic
804C23C22×D24411yescharacteristic
805C23C22×D24411yescharacteristic
806Q8—614no—
807Q8—1224no—
808Q8—1222no—
809Q8—1222no—
810Q8—1224no—
811Q8—1224no—
812Q8—1222no—
813Q8—4881no—
814Q8—2448no—
815Q8—2444no—
816Q8—2444no—
817Q8—2442no—
818Q8—2442no—
819D4—24no—
820D4—24no—
821D4—1224no—
822D4—4881no—
823D4—4882no—
824D4—4882no—
825D4—2444no—
826D4—2444no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—24no—
831C2×C4—22no—
832C2×C4—42no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—1224no—
839C2×C4—1222no—
840C2×C4—1222no—
841C2×C4—1222no—
842C2×C4—1222no—
843C2×C4—1222no—
844C2×C4—1222no—
845C2×C4—1222no—
846C2×C4—4882no—
847C2×C4—4882no—
848C2×C4—4881no—
849C2×C4—4881no—
850C2×C4—2444no—
851C2×C4—2444no—
852C2×C4—2448no—
853C2×C4—2442no—
854C2×C4—2442no—
855C2×C4—2442no—
856C2×C4—2442no—
857C2×C4C22×D24412yes—
858C2×C4C22×D24412yes—
859C2×C4C22×D24412yes—
860C2×C4C22×D24411yescharacteristic
861C2×C4C22×D24411yescharacteristic
862C2×C4C22×D24411yescharacteristic
863C2×C4C24×D6111yescharacteristic
864C8—24no—
865C8—24no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—44no—
876C22—44no—
877C22—9762no—
878C22—2442no—
879C22—2442no—
880C22—2442no—
881C22C2×#1451981012yes—
882C22C2×#1451981012yes—
883C22C2×#1451981012yes—
884C22C23×D24411yescharacteristic
885C4—22no—
886C4—22no—
887C4—21no—
888C4—22no—
889C4—21no—
890C4—21no—
891C4—1224no—
892C4—2442no—
893C4—2442no—
894C4—2442no—
895C4—2442no—
896C4—2442no—
897C4—2442no—
898C4H(5,𝔽2)×D6112yes—
899C2—22no—
900C2—22no—
901C2—22no—
902C2—42no—
903C2—4882no—
904C2#2145945511yescharacteristic
905C2C22×#1451981011yescharacteristic
906C2#2146060711yescharacteristic
subgroupG/H
centerC22C23×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#2973C2
socleC22×C61C23×D4
prime radical#21459658C2
hypercenter#2973D61
hypocenterC61#61574
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic122C2semidirect
3. #21457992C2semidirect
4. #21457872C2semidirect
5. #21457394C2semidirect
6. #21457334C2semidirect
7. #21456848C2semidirect
8. #21456651C2semidirect
9. #21456594C2semidirect
10. #21456577C2semidirect
11. #21455992C2semidirect
12. #21455056C2semidirect
13. C2×#16839920C2semidirect
14. C2×#16839903C2semidirect
15. C61×#2973C2semidirect
17. C23×Dic122C22semidirect
18. C2×#14519810C22semidirect
19. C22×Dic244C22semidirect
20. C22×#11758190C22semidirect
28. D4×Dic122C22semidirect
34. C2×#14519777C22semidirect
40. C2×#14519756C22semidirect
45. C2×C4×Dic122C22semidirect
47. #16840156C22semidirect
48. #16840131C22semidirect
49. #16840104C22semidirect
50. #16840098C22semidirect
51. #16840098C22semidirect
52. #16840093C22semidirect
54. #16840070C22semidirect
55. #16840020C22semidirect
56. #16840008C22semidirect
57. #16840003C22semidirect
58. #16839991C22semidirect
59. #16839985C22semidirect
60. #16839973C22semidirect
61. #16839968C22semidirect
62. #16839926C22semidirect
63. #16839920C22semidirect
64. #16839920C22semidirect
65. #16839920C22semidirect
66. #16839920C22semidirect
67. #16839920C22semidirect
68. #16839920C22semidirect
69. #16839915C22semidirect
73. #16839903C22semidirect
74. #16839903C22semidirect
75. #16839870C22semidirect
76. #16839864C22semidirect
77. #16839772C22semidirect
78. C2×#14519702C22semidirect
79. C2×#14519702C22semidirect
82. C61×#435C22semidirect
83. C61×#432C22semidirect
84. C61×#407C22semidirect
343. C23×C61#137semidirect
460. #2973D61semidirect
532. #435C2×D61semidirect
533. #432C2×D61semidirect
537. #407C2×D61semidirect
540. C61#61574semidirect
801. C23#14519810semidirect

Maximal subgroups

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

subgroupindex
#214596582
C2×D4×Dic1222
#214579922
#214578722
#214573942
#214573342
#214568482
#214566512
#214565942
#214565772
#214559922
#214550562
C2×#168399202
C2×#168399032
C61×#29732
#6157461