Finite Group Databasebeta

← #29851736

Subgroups — #29851736

Order 15616.

2014 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451481C211yesmaximal, characteristic, complemented
2#21451426C212yesmaximal, complemented
3#21451407C211yesmaximal, characteristic, complemented
4#21451353C212yesmaximal, complemented
5#21451276C212yesmaximal, complemented
6#21451106C212yesmaximal, complemented
7#21450924C212yesmaximal, complemented
8#21449756C212yesmaximal, complemented
9#21449701C211yesmaximal, characteristic, complemented
10#21449104C212yesmaximal, complemented
11#21449099C211yesmaximal, characteristic
12#21449081C211yesmaximal, characteristic, complemented
13#21448358C212yesmaximal, complemented
14#21448340C212yesmaximal, complemented
15#21448338C211yesmaximal, characteristic, complemented
16#21448292C212yesmaximal, complemented
17#21448257C212yesmaximal, complemented
18C4×#14519737C212yesmaximal, complemented
19C61×#2517C211yesmaximal, characteristic, complemented
20C2×#14519765C2212yes—
21C2×#14519762C2212yes—
22C2×#14519761C2211yescharacteristic
23C2×#14519742C2212yes—
24C2×#14519739C2212yes—
25C2×#14519739C2211yescharacteristic
26C2×C4×C22⋊D61C2212yes—
27C2×#14519737C2212yes—
28C2×#14519737C2212yes—
29C2×#14519737C2211yescharacteristic
30C2×#14519735C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32C2×C42×D61C2212yes—
33#16839703C2212yes—
34#16839703C2212yes—
35#16839702C2211yescharacteristic
36#16839698C2211yescharacteristic
37#16839697C2212yes—
38#16839697C2211yescharacteristic
39#16839693C2211yescharacteristic
40#16839691C2212yes—
41#16839688C2212yes—
42#16839677C2212yes—
43#16839677C2212yes—
44#16839677C2212yes—
45#16839675C2212yes—
46#16839674C2212yes—
47#16839672C2211yescharacteristic
48#16839671C2212yes—
49#16839671C2211yescharacteristic
50#16839667C2212yes—
51#16839666C2212yes—
52#16839666C2212yes—
53#16839663C2212yes—
54#16839659C2212yes—
55#16839657C2212yes—
56#16839654C2212yes—
57#16839653C2212yes—
58#16839653C2212yes—
59#16839652C2212yes—
60#16839651C2212yes—
61#16839651C2212yes—
62#16839651C2212yes—
63#16839651C2212yes—
64#16839651C2212yes—
65#16839648C2212yes—
66#16839648C2212yes—
67#16839646C2212yes—
68#16839645C2212yes—
69#16839644C2212yes—
70#16839643C2212yes—
71#16839641C2211yescharacteristic
72#16839640C2212yes—
73#16839640C2212yes—
74#16839640C2212yes—
75#16839636C2212yes—
76#16839636C2212yes—
77#16839633C2212yes—
78#16839624C2212yes—
79#16839623C2211yescharacteristic
80C4⋊C4×Dic61C2212yes—
81C4×#11758196C2212yes—
82#16839613C2212yes—
83#16839613C2212yes—
84#16839613C2212yes—
85C22⋊C4×Dic61C2212yes—
86C22⋊C4×Dic61C2211yescharacteristic
87C22⋊C4×Dic61C2212yes—
88C4×#11758198C2212yes—
89#16839609C2212yes—
90#16839609C2212yes—
91#16839609C2212yes—
92#16839609C2211yescharacteristic
93#16839609C2212yes—
94#16839609C2212yes—
95#16839607C2212yes—
96#16839607C2211yescharacteristic
97C42×Dic61C2212yes—
98C61×#399C2211yescharacteristic
99C61×#397C2211yescharacteristic
100C61×#397C2212yes—
101C61×#387C2212yes—
102C61×#387C2212yes—
103C61×#387C2212yes—
104C61×#385C2211yescharacteristic
105C61×#382C2212yes—
106C4×C22⋊C4×C61C2212yes—
107C22×Dic122C2312yes—
108C22×D244C2311yescharacteristic
109C22×D244C2312yes—
110C22×C22⋊D61C2312yes—
111C22×C22⋊D61C2311yescharacteristic
112C23×Dic61C2311yescharacteristic
113C23×Dic61C2311yescharacteristic
114C22×C4×D61C2312yes—
115C22×C4×D61C2311yescharacteristic
116C22×C4×D61C2312yes—
117C22×C4×D61C2312yes—
118#14519765—28no—
119#14519762—28no—
120#14519761—24no—
121#14519742—28no—
122#14519739—28no—
123#14519739—42no—
124C4×C22⋊D61—28no—
125#14519737—28no—
126#14519737—28no—
127#14519737—42no—
128#14519735—42no—
129C2×C4⋊Dic61C2312yes—
130C2×C4⋊Dic61C2311yescharacteristic
131C2×#11758196C2312yes—
132C2×#11758196C2312yes—
133C2×#11758196C2312yes—
134C2×#11758196C2312yes—
135C2×#11758196C2312yes—
136C2×#11758196C2312yes—
137C2×#11758196C2311yescharacteristic
138C2×#11758196C2312yes—
139C2×C22⋊Dic61C2312yes—
140C2×C22⋊Dic61C2311yescharacteristic
141C2×#11758198C2312yes—
142C2×#11758198C2312yes—
143C2×#11758198C2312yes—
144C2×#11758198C2312yes—
145C2×#11758198C2312yes—
146C2×#11758198C2312yes—
147C2×#11758198C2312yes—
148C2×#11758198C2312yes—
149C2×#11758198C2312yes—
150C2×#11758198C2312yes—
151C2×#11758198C2311yescharacteristic
152C2×#11758198C2312yes—
153C2×#11758198C2312yes—
154C2×#11758198C2312yes—
155C2×#11758198C2312yes—
156C2×C4×Dic61—42no—
157C2×C4×Dic61C2312yes—
158C2×C4×Dic61C2312yes—
159C2×C4×Dic61C2311yescharacteristic
160C2×C4×Dic61C2312yes—
161C2×C4×Dic61C2312yes—
162C2×C4×Dic61C2312yes—
163C2×C4×Dic61C2312yes—
164C2×C4×Dic61C2312yes—
165C2×C4×Dic61C2312yes—
166C2×C4×Dic61C2312yes—
167C2×C4×Dic61C2312yes—
168C42×D61—44no—
169#14519684C2312yes—
170#14519684C2312yes—
171#14519684C2312yes—
172#14519684C2312yes—
173#14519684C2311yescharacteristic
174#14519684C2311yescharacteristic
175#14519684C2312yes—
176#14519684C2312yes—
177#14519684C2312yes—
178#14519684C2312yes—
179#14519684C2312yes—
180#14519684C2312yes—
181#14519684C2312yes—
182#14519684C2312yes—
183#14519684C2312yes—
184#14519684C2312yes—
185#14519684C2312yes—
186C23×C4×C61C2311yescharacteristic
187C2×C4⋊C4×C61C2312yes—
188C2×C4⋊C4×C61C2312yes—
189C2×C4⋊C4×C61C2312yes—
190C2×C4⋊C4×C61C2311yescharacteristic
191C2×C4⋊C4×C61C2311yescharacteristic
192C2×C22⋊C4×C61C2312yes—
193C2×C22⋊C4×C61C2312yes—
194C2×C22⋊C4×C61C2311yescharacteristic
195C2×C22⋊C4×C61C2311yescharacteristic
196C2×C42×C61C2312yes—
197C2×C42×C61C2312yes—
198#95×C61C2312yes—
199#95×C61C2311yescharacteristic
200#95×C61C2312yes—
201#95×C61C2312yes—
202#95×C61C2312yes—
203#95×C61C2312yes—
204#95×C61C2312yes—
205#95×C61C2312yes—
206#95×C61C2311yescharacteristic
207C24×C61C2411yescharacteristic
208C23×D61C2411yescharacteristic
209C23×D61C2412yes—
210C22×C4×C61—24no—
211C22×C4×C61—41no—
212C22×C4×C61C2412yes—
213C22×C4×C61C2412yes—
214C22×C4×C61C2411yescharacteristic
215C22×C4×C61C2411yescharacteristic
216C22×C4×C61C2412yes—
217C22×C4×C61C2412yes—
218C22×C4×C61C2412yes—
219C22×C4×C61C2412yes—
220C2×C22⋊D61—24no—
221C2×C22⋊D61—24no—
222C2×C22⋊D61—22no—
223C2×C22⋊D61—24no—
224C2×C22⋊D61—41no—
225C2×C22⋊D61—41no—
226C22×Dic61—24no—
227C22×Dic61—22no—
228C22×Dic61—41no—
229C22×Dic61—41no—
230C22×Dic61#4114yes—
231C22×Dic61C2412yes—
232C22×Dic61C2411yescharacteristic
233C22×Dic61C2411yescharacteristic
234C22×Dic61C2412yes—
235C22×Dic61C2412yes—
236C22×Dic61C2412yes—
237C22×Dic61C2412yes—
238C22×Dic61C2411yescharacteristic
239C2×D244—24no—
240C2×D244—24no—
241C2×D244—24no—
242C2×D244—42no—
243C2×D244—41no—
244C2×C4×D61—24no—
245C2×C4×D61—24no—
246C2×C4×D61—24no—
247C2×C4×D61—24no—
248C2×C4×D61—24no—
249C2×C4×D61—24no—
250C2×C4×D61—24no—
251C2×C4×D61—22no—
252C2×C4×D61—42no—
253C2×C4×D61—42no—
254C2×C4×D61—42no—
255C2×Dic122—24no—
256C2×Dic122—24no—
257C2×Dic122—42no—
258C4⋊C4×C61—24no—
259C4⋊C4×C61—24no—
260C4⋊C4×C61—24no—
261C4⋊C4×C61—41no—
262C4⋊C4×C61—41no—
263C22⋊C4×C61—24no—
264C22⋊C4×C61—22no—
265C22⋊C4×C61—24no—
266C22⋊C4×C61—41no—
267C42×C61—24no—
268C42×C61—42no—
269C22⋊Dic61—24no—
270C22⋊Dic61—41no—
271#11758198—24no—
272#11758198—24no—
273#11758198—24no—
274#11758198—24no—
275#11758198—24no—
276#11758198—24no—
277#11758198—24no—
278#11758198—24no—
279#11758198—24no—
280#11758198—24no—
281#11758198—42no—
282#11758198—42no—
283#11758198—41no—
284#11758198—42no—
285#11758198#4118yes—
286C4⋊Dic61—24no—
287C4⋊Dic61—41no—
288#11758196—24no—
289#11758196—24no—
290#11758196—24no—
291#11758196—24no—
292#11758196—24no—
293#11758196—24no—
294#11758196—42no—
295#11758196—41no—
296C4×Dic61—24no—
297C4×Dic61—24no—
298C4×Dic61—24no—
299C4×Dic61—24no—
300C4×Dic61—24no—
301C4×Dic61—24no—
302C4×Dic61—22no—
303C4×Dic61—42no—
304C4×Dic61—42no—
305C4×Dic61—42no—
306C4×Dic61#4118yes—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—21no—
310C23×C61—21no—
311C23×C61C2×#4112yes—
312C23×C61C2511yescharacteristic
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—21no—
321C22×D61—22no—
322C22×D61—21no—
323C22×D61—21no—
324C22×D61C2×#4114yes—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—21no—
342C2×C4×C61—22no—
343C2×C4×C61—21no—
344C2×C4×C61—22no—
345C2×C4×C61—44no—
346C2×C4×C61C2×#4114yes—
347C2×C4×C61C2×#4114yes—
348C22⋊D61—216no—
349C22⋊D61—44no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—22no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—21no—
361C2×Dic61—22no—
362C2×Dic61—22no—
363C2×Dic61—21no—
364C2×Dic61—21no—
365C2×Dic61—21no—
366C2×Dic61—22no—
367C2×Dic61—44no—
368C2×Dic61—44no—
369C2×Dic61C2×#4114yes—
370C2×Dic61C2×#4114yes—
371C2×Dic61C2×#4114yes—
372C2×Dic61C2×#4114yes—
373C2×Dic61H(5,𝔽2)12yes—
374D244—48no—
375D244—44no—
376C4×D61—48no—
377C4×D61—48no—
378C4×D61—48no—
379C4×D61—44no—
380Dic122—48no—
381#34921—611nomaximal, Sylow
382C22×C61—24no—
383C22×C61—22no—
384C22×C61—42no—
385C22×C61—41no—
386C22×C61—41no—
387C22×C61C22×#4111yescharacteristic
388C22×C61C22×#4112yes—
389C22×C61C22×#4112yes—
390C22×C61C2×H(5,𝔽2)11yescharacteristic
391C22×C61#58511yescharacteristic
392C2×D61—24no—
393C2×D61—24no—
394C2×D61—24no—
395C2×D61—42no—
396C2×D61—42no—
397C2×D61—42no—
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—41no—
401C2×D61—42no—
402C2×D61—41no—
403C2×D61—41no—
404C4×C61—24no—
405C4×C61—24no—
406C4×C61—42no—
407C4×C61—42no—
408C4×C61—42no—
409C4×C61—42no—
410C4×C61—41no—
411C4×C61—41no—
412Dic61—24no—
413Dic61—24no—
414Dic61—24no—
415Dic61—41no—
416Dic61—42no—
417Dic61—41no—
418Dic61—42no—
419Dic61#55914yes—
420#2607—611no—
421#2602—612no—
422#2600—611no—
423#2596—612no—
424#2589—612no—
425#2575—612no—
426#2557—612no—
427#2517D6111yescharacteristic, complemented
428#2459—612no—
429#2455—611no—
430#2398—612no—
431#2397—611no—
432#2395—611no—
433C4×#124—612no—
434C4×#123—612no—
435C4×#123—611no—
436#2295—612no—
437#2290—612no—
438C42×D4—612no—
439C2×C61—42no—
440C2×C61#344412yes—
441C2×C61#345911yescharacteristic
442C2×C61#347512yes—
443C2×C61C2×#55911yescharacteristic
444C2×C61#348111yescharacteristic
445D61—44no—
446D61—81no—
447C2×#124—612no—
448C2×#123—612no—
449C2×#123—611no—
450C2×C4×Q8—612no—
451C2×C4×D4—612no—
452C2×C4×D4—612no—
453C2×C4×D4—611no—
454C2×C4×D4—612no—
455C2×C4×D4—612no—
456C2×C4×D4—611no—
457C2×#117—611no—
458C22×C42—611no—
459C22×C42—612no—
460#400—611no—
461#400—612no—
462#400—612no—
463#399—612no—
464#399—611no—
465#399—611no—
466#399C2×D6111yescharacteristic
467#398—611no—
468#397—612no—
469#397—612no—
470#397C2×D6111yescharacteristic
471#397C2×D6112yes—
472#394—612no—
473#394—612no—
474#394—612no—
475#393—612no—
476#393—612no—
477#392—611no—
478#392—612no—
479#392—611no—
480#391—612no—
481#391—612no—
482#391—612no—
483#390—612no—
484#389—612no—
485#389—612no—
486#388—612no—
487#388—612no—
488#388—612no—
489#388—612no—
490#388—612no—
491#388—612no—
492#388—612no—
493#388—612no—
494#388—612no—
495#387—612no—
496#387—612no—
497#387—612no—
498#387—612no—
499#387—612no—
500#387—612no—
501#387C2×D6112yes—
502#387C2×D6112yes—
503#387C2×D6112yes—
504#386—611no—
505#386—612no—
506#386—612no—
507#386—612no—
508#385—612no—
509#385—612no—
510#385—612no—
511#385C2×D6111yescharacteristic
512#382C2×D6112yes—
513#381—611no—
514#381—612no—
515C4×C4⋊C4—612no—
516C4×C4⋊C4—612no—
517C4×C4⋊C4—612no—
518C4×C4⋊C4—612no—
519C4×C4⋊C4—612no—
520C4×C22⋊C4—612no—
521C4×C22⋊C4—612no—
522C4×C22⋊C4—611no—
523C4×C22⋊C4—612no—
524C4×C22⋊C4—612no—
525C4×C22⋊C4—611no—
526C4×C22⋊C4—612no—
527C4×C22⋊C4—612no—
528C4×C22⋊C4—612no—
529C4×C22⋊C4—612no—
530C4×C22⋊C4C2×D6112yes—
531#376—611no—
532#376—612no—
533C43—612no—
534C61#3492111yescharacteristic, complemented, Sylow
535C22×Q8—612no—
536C22×D4—612no—
537C22×D4—611no—
538C22×D4—611no—
539C22×D4—612no—
540C23×C4—611no—
541C23×C4—611no—
542C23×C4—611no—
543C23×C4—612no—
544C23×C4—612no—
545C23×C4—612no—
546C23×C4C22×D6111yescharacteristic
547#124—1228no—
548#123—1224no—
549#123—1228no—
550C4×Q8—1228no—
551C4×D4—1228no—
552C4×D4—1228no—
553C4×D4—1228no—
554C4×D4—1228no—
555C4×D4—2442no—
556C4×D4—2442no—
557#117—2442no—
558C2×C4⋊C4—612no—
559C2×C4⋊C4—612no—
560C2×C4⋊C4—612no—
561C2×C4⋊C4—612no—
562C2×C4⋊C4—612no—
563C2×C4⋊C4—612no—
564C2×C4⋊C4—612no—
565C2×C4⋊C4—611no—
566C2×C4⋊C4—611no—
567C2×C4⋊C4—612no—
568C2×C4⋊C4C22×D6112yes—
569C2×C4⋊C4C22×D6112yes—
570C2×C4⋊C4C22×D6112yes—
571C2×C4⋊C4C22×D6111yescharacteristic
572C2×C4⋊C4C22×D6111yescharacteristic
573C2×C22⋊C4—612no—
574C2×C22⋊C4—612no—
575C2×C22⋊C4—612no—
576C2×C22⋊C4—612no—
577C2×C22⋊C4—612no—
578C2×C22⋊C4—612no—
579C2×C22⋊C4—612no—
580C2×C22⋊C4—612no—
581C2×C22⋊C4—612no—
582C2×C22⋊C4—612no—
583C2×C22⋊C4—612no—
584C2×C22⋊C4—612no—
585C2×C22⋊C4—611no—
586C2×C22⋊C4—612no—
587C2×C22⋊C4—612no—
588C2×C22⋊C4—611no—
589C2×C22⋊C4—612no—
590C2×C22⋊C4C22×D6112yes—
591C2×C22⋊C4C22×D6112yes—
592C2×C22⋊C4C22×D6111yescharacteristic
593C2×C22⋊C4C22×D6111yescharacteristic
594C2×C42—612no—
595C2×C42—612no—
596C2×C42—611no—
597C2×C42—612no—
598C2×C42—612no—
599C2×C42—612no—
600C2×C42—612no—
601C2×C42—612no—
602C2×C42—612no—
603C2×C42—612no—
604C2×C42—612no—
605C2×C42—2444no—
606C2×C42—2442no—
607C2×C42C22×D6112yes—
608C2×C42C22×D6112yes—
609#95—612no—
610#95—612no—
611#95—612no—
612#95—611no—
613#95—612no—
614#95—612no—
615#95—612no—
616#95—612no—
617#95—612no—
618#95—612no—
619#95—612no—
620#95—612no—
621#95—612no—
622#95—611no—
623#95—612no—
624#95—612no—
625#95—612no—
626#95C22×D6112yes—
627#95C22×D6111yescharacteristic
628#95C22×D6112yes—
629#95C22×D6112yes—
630#95C22×D6111yescharacteristic
631#95C22×D6112yes—
632#95C22×D6112yes—
633#95C22×D6112yes—
634#95C22×D6112yes—
635C24—612no—
636C24—611no—
637C24C23×D6111yescharacteristic
638C2×Q8—1224no—
639C2×Q8—1224no—
640C2×Q8—2442no—
641C2×D4—1224no—
642C2×D4—1224no—
643C2×D4—1224no—
644C2×D4—1224no—
645C2×D4—1224no—
646C2×D4—1222no—
647C2×D4—1224no—
648C2×D4—2441no—
649C2×D4—2442no—
650C2×D4—2441no—
651C2×D4—2441no—
652C22×C4—24no—
653C22×C4—41no—
654C22×C4—611no—
655C22×C4—612no—
656C22×C4—612no—
657C22×C4—612no—
658C22×C4—614no—
659C22×C4—612no—
660C22×C4—612no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—1224no—
664C22×C4—1222no—
665C22×C4—1224no—
666C22×C4—1224no—
667C22×C4—1224no—
668C22×C4—1224no—
669C22×C4—1224no—
670C22×C4—1222no—
671C22×C4—1224no—
672C22×C4—1224no—
673C22×C4—2442no—
674C22×C4—2442no—
675C22×C4—2442no—
676C22×C4—2441no—
677C22×C4—2441no—
678C22×C4C23×D6112yes—
679C22×C4C23×D6111yescharacteristic
680C22×C4C23×D6111yescharacteristic
681C22×C4C23×D6112yes—
682C22×C4C23×D6112yes—
683C22×C4C23×D6112yes—
684C22×C4C23×D6112yes—
685C22×C4C23×D6112yes—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—41no—
690C4⋊C4—41no—
691C4⋊C4—1224no—
692C4⋊C4—1224no—
693C4⋊C4—1224no—
694C4⋊C4—1224no—
695C4⋊C4—1224no—
696C4⋊C4—1224no—
697C4⋊C4—1224no—
698C4⋊C4—2442no—
699C4⋊C4—2441no—
700C4⋊C4—2441no—
701C22⋊C4—24no—
702C22⋊C4—22no—
703C22⋊C4—24no—
704C22⋊C4—41no—
705C22⋊C4—618no—
706C22⋊C4—1224no—
707C22⋊C4—1224no—
708C22⋊C4—1224no—
709C22⋊C4—1224no—
710C22⋊C4—1224no—
711C22⋊C4—1224no—
712C22⋊C4—1224no—
713C22⋊C4—1224no—
714C22⋊C4—1224no—
715C22⋊C4—1224no—
716C22⋊C4—1224no—
717C22⋊C4—2442no—
718C22⋊C4—2442no—
719C22⋊C4—2441no—
720C22⋊C4—2442no—
721C22⋊C4—2441no—
722C42—24no—
723C42—42no—
724C42—618no—
725C42—1224no—
726C42—1224no—
727C42—1224no—
728C42—1224no—
729C42—1222no—
730C42—1224no—
731C42—1224no—
732C42—2442no—
733C42—2442no—
734C42—2442no—
735C23—22no—
736C23—22no—
737C23—21no—
738C23—21no—
739C23—614no—
740C23—1222no—
741C23—1222no—
742C23—1222no—
743C23—1222no—
744C23—1222no—
745C23—1222no—
746C23—1221no—
747C23—1222no—
748C23—1222no—
749C23—1221no—
750C23—1221no—
751C23#41×D6112yes—
752C23C24×D6111yescharacteristic
753Q8—2448no—
754D4—12216no—
755D4—2448no—
756D4—2444no—
757D4—2444no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—44no—
779C2×C4—614no—
780C2×C4—612no—
781C2×C4—614no—
782C2×C4—614no—
783C2×C4—614no—
784C2×C4—1222no—
785C2×C4—1222no—
786C2×C4—1222no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—1222no—
790C2×C4—1222no—
791C2×C4—1222no—
792C2×C4—1222no—
793C2×C4—1222no—
794C2×C4—1222no—
795C2×C4—1221no—
796C2×C4—1222no—
797C2×C4—1221no—
798C2×C4—1221no—
799C2×C4—1222no—
800C2×C4—1221no—
801C2×C4—2448no—
802C2×C4—2444no—
803C2×C4—2448no—
804C2×C4—2448no—
805C2×C4—2444no—
806C2×C4—2444no—
807C2×C4#41×D6114yes—
808C2×C4#41×D6114yes—
809C22—22no—
810C22—24no—
811C22—42no—
812C22—41no—
813C22—41no—
814C22—1224no—
815C22—1224no—
816C22—1224no—
817C22—2441no—
818C22—2442no—
819C22—2442no—
820C22—2441no—
821C22—2441no—
822C22—2442no—
823C22—2442no—
824C22—2442no—
825C22—2442no—
826C22C2×#41×D6111yescharacteristic
827C22C2×#41×D6112yes—
828C22C2×#41×D6112yes—
829C22H(5,𝔽2)×D6111yescharacteristic
830C22#1684059911yescharacteristic
831C4—24no—
832C4—24no—
833C4—42no—
834C4—42no—
835C4—42no—
836C4—42no—
837C4—41no—
838C4—41no—
839C4—614no—
840C4—1224no—
841C4—1224no—
842C4—1224no—
843C4—2441no—
844C4—2442no—
845C4—2441no—
846C4—2442no—
847C2—42no—
848C2—4881no—
849C2—2444no—
850C2#2145911312yes—
851C2#2145922711yescharacteristic
852C2#2145938412yes—
853C2#559×D6111yescharacteristic
854C2#2145942211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, cosocleC23×C61C25
FittingC61×#2517C2
prime radical#21449099C2
hypercenter#2517D61
hypocenterC61#34921
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2517

Complements

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

NH ≅ G/Ntype
1. #21451481C2semidirect
2. #21451426C2semidirect
3. #21451407C2semidirect
4. #21451353C2semidirect
5. #21451276C2semidirect
6. #21451106C2semidirect
7. #21450924C2semidirect
8. #21449756C2semidirect
9. #21449701C2semidirect
10. #21449104C2semidirect
12. #21449081C2semidirect
13. #21448358C2semidirect
14. #21448340C2semidirect
15. #21448338C2semidirect
16. #21448292C2semidirect
17. #21448257C2semidirect
18. C4×#14519737C2semidirect
19. C61×#2517C2semidirect
427. #2517D61semidirect
534. C61#34921semidirect

Maximal subgroups

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

subgroupindex
#214514812
#214514262
#214514072
#214513532
#214512762
#214511062
#214509242
#214497562
#214497012
#214491042
#214490992
#214490812
#214483582
#214483402
#214483382
#214482922
#214482572
C4×#145197372
C61×#25172
#3492161