Finite Group Databasebeta

← #30543371

Subgroups — #30543371

Order 15616.

1854 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21453805C211yesmaximal, characteristic, complemented
2#21452849C211yesmaximal, characteristic, complemented
3#21452781C212yesmaximal, complemented
4#21451516C212yesmaximal, complemented
5#21451310C212yesmaximal, complemented
6#21450908C212yesmaximal, complemented
7#21450900C212yesmaximal, complemented
8#21450057C212yesmaximal, complemented
9#21450050C212yesmaximal, complemented
10#21449982C212yesmaximal, complemented
11#21449975C212yesmaximal, complemented
12#21449446C211yesmaximal, characteristic
13#21449444C211yesmaximal, characteristic
14#21448944C212yesmaximal, complemented
15#21448935C212yesmaximal, complemented
16#21448907C211yesmaximal, characteristic, complemented
17#21448308C211yesmaximal, characteristic
18#21448299C212yesmaximal, complemented
19C61×#2369C211yesmaximal, characteristic, complemented
20C22×#11758226C2211yescharacteristic
21C2×#14519775C2211yescharacteristic
22C2×#14519772C2212yes—
23C2×#14519771C2212yes—
24C2×#14519767C2212yes—
25C2×#14519766C2211yescharacteristic
26C2×#14519765C2211yescharacteristic
27C2×#14519757C2211yescharacteristic
28C2×#14519753C2211yescharacteristic
29C2×#14519735C2211yescharacteristic
30C2×#14519734C2212yes—
31C2×#14519734C2212yes—
32C2×C42×D61C2211yescharacteristic
33#16839704C2212yes—
34#16839697C2212yes—
35#16839697C2212yes—
36#16839697C2212yes—
37#16839696C2212yes—
38#16839695C2212yes—
39#16839695C2212yes—
40#16839691C2212yes—
41#16839686C2212yes—
42#16839684C2212yes—
43#16839682C2212yes—
44#16839681C2212yes—
45#16839680C2212yes—
46#16839680C2212yes—
47#16839679C2212yes—
48#16839679C2212yes—
49#16839669C2211yescharacteristic
50#16839669C2211yescharacteristic
51#16839666C2212yes—
52#16839664C2211yescharacteristic
53#16839664C2211yescharacteristic
54#16839663C2211yescharacteristic
55#16839663C2211yescharacteristic
56#16839659C2212yes—
57#16839659C2212yes—
58#16839659C2212yes—
59#16839657C2212yes—
60#16839657C2212yes—
61#16839657C2212yes—
62#16839653C2212yes—
63#16839653C2212yes—
64#16839653C2212yes—
65#16839653C2212yes—
66#16839653C2212yes—
67#16839653C2212yes—
68#16839652C2212yes—
69#16839652C2212yes—
70#16839652C2212yes—
71#16839651C2212yes—
72#16839651C2212yes—
73#16839651C2212yes—
74#16839648C2212yes—
75#16839646C2212yes—
76#16839646C2212yes—
77#16839645C2212yes—
78#16839644C2212yes—
79#16839643C2212yes—
80#16839640C2212yes—
81#16839640C2212yes—
82#16839636C2212yes—
83#16839636C2212yes—
84#16839636C2212yes—
85#16839633C2212yes—
86#16839633C2212yes—
87#16839633C2212yes—
88C4×#11758196C2212yes—
89C4×#11758196C2212yes—
90C4×C4⋊Dic61C2212yes—
91#16839613C2212yes—
92#16839613C2212yes—
93C4×#11758198C2211yescharacteristic
94C4×#11758198C2211yescharacteristic
95#16839609C2212yes—
96#16839609C2212yes—
97#16839608C2212yes—
98C2×C4⋊Q8×C61C2211yescharacteristic
99C61×#391C2211yescharacteristic
100C61×#391C2212yes—
101C61×#391C2211yescharacteristic
102C61×#389C2212yes—
103C61×#389C2212yes—
104C4×C4⋊C4×C61C2212yes—
105C4×C4⋊C4×C61C2212yes—
106C4×C4⋊C4×C61C2212yes—
107C2×#11758226—24no—
108C2×#11758226—42no—
109C2×#11758226—42no—
110C22×Dic122C2311yescharacteristic
111C22×D244C2311yescharacteristic
112C22×D244C2311yescharacteristic
113C22×D244C2311yescharacteristic
114C22×C4×D61C2312yes—
115C22×C4×D61C2311yescharacteristic
116C22×C4×D61C2311yescharacteristic
117C22×C4×D61C2311yescharacteristic
118#14519775—24no—
119#14519772—28no—
120#14519771—28no—
121#14519767—44no—
122#14519766—42no—
123#14519765—42no—
124#14519757—42no—
125#14519753—42no—
126#14519735—42no—
127#14519734—28no—
128#14519734—44no—
129C2×C4⋊Dic61C2312yes—
130C2×C4⋊Dic61C2312yes—
131C2×C4⋊Dic61C2311yescharacteristic
132C2×C4⋊Dic61C2311yescharacteristic
133C2×#11758196C2312yes—
134C2×#11758196C2312yes—
135C2×#11758196C2312yes—
136C2×#11758196C2312yes—
137C2×#11758196C2312yes—
138C2×#11758196C2312yes—
139C2×#11758196C2312yes—
140C2×#11758196C2312yes—
141C2×#11758196C2312yes—
142C2×#11758196C2312yes—
143C2×#11758196C2312yes—
144C2×#11758196C2312yes—
145C2×#11758196C2312yes—
146C2×#11758198C2312yes—
147C2×#11758198C2312yes—
148C2×#11758198C2312yes—
149C2×#11758198C2312yes—
150C2×#11758198C2312yes—
151C2×#11758198C2312yes—
152C2×#11758198C2312yes—
153C2×#11758198C2312yes—
154C2×#11758198C2312yes—
155C2×#11758198C2312yes—
156C2×#11758198C2312yes—
157C2×#11758198C2312yes—
158C2×#11758198C2312yes—
159C2×#11758198C2312yes—
160C2×#11758198C2312yes—
161C2×#11758198C2312yes—
162C2×#11758198C2312yes—
163C2×C4×Dic61C2312yes—
164C2×C4×Dic61C2312yes—
165C2×C4×Dic61C2312yes—
166C2×C4×Dic61C2311yescharacteristic
167C2×C4×Dic61C2312yes—
168C2×C4×Dic61C2311yescharacteristic
169C2×C4×Dic61C2312yes—
170C2×C4×Dic61C2311yescharacteristic
171C42×D61—42no—
172#14519684C2312yes—
173#14519684C2312yes—
174#14519684C2312yes—
175#14519684C2312yes—
176#14519684C2312yes—
177#14519684C2312yes—
178#14519684C2312yes—
179#14519684C2312yes—
180#14519684C2312yes—
181#14519684C2312yes—
182#14519684C2312yes—
183#14519684C2312yes—
184#14519684C2312yes—
185#14519684C2312yes—
186#14519684C2312yes—
187#14519684C2312yes—
188C22×Q8×C61C2311yescharacteristic
189C22×Q8×C61C2311yescharacteristic
190C4⋊Q8×C61—24no—
191C2×C4⋊C4×C61C2312yes—
192C2×C4⋊C4×C61C2312yes—
193C2×C4⋊C4×C61C2312yes—
194C2×C4⋊C4×C61C2312yes—
195C2×C4⋊C4×C61C2312yes—
196C2×C4⋊C4×C61C2311yescharacteristic
197C2×C4⋊C4×C61C2311yescharacteristic
198C2×C42×C61C2311yescharacteristic
199C2×C42×C61C2312yes—
200C2×C42×C61C2312yes—
201C2×C42×C61C2311yescharacteristic
202C2×C42×C61C2312yes—
203C2×C42×C61C2311yescharacteristic
204#95×C61C2312yes—
205#95×C61C2312yes—
206#95×C61C2312yes—
207#95×C61C2312yes—
208#95×C61C2312yes—
209#95×C61C2312yes—
210C23×D61C2411yescharacteristic
211C23×D61C2411yescharacteristic
212C23×D61C2411yescharacteristic
213C2×Q8×C61—22no—
214C2×Q8×C61—41no—
215C2×Q8×C61—41no—
216C2×Q8×C61—41no—
217C2×Q8×C61—41no—
218C2×Q8×C61#4114yes—
219C22×C4×C61C2412yes—
220C22×C4×C61C2412yes—
221C22×C4×C61C2412yes—
222C22×C4×C61C2412yes—
223C22×C4×C61C2411yescharacteristic
224C22×C4×C61C2411yescharacteristic
225C22×C4×C61C2411yescharacteristic
226C22×C4×C61C2412yes—
227C22×C4×C61C2412yes—
228C22×Dic61C2412yes—
229C22×Dic61C2412yes—
230C22×Dic61C2412yes—
231C22×Dic61C2412yes—
232C22×Dic61C2412yes—
233C22×Dic61C2412yes—
234C22×Dic61C2411yescharacteristic
235#11758226—416no—
236C2×D244—22no—
237C2×D244—22no—
238C2×D244—22no—
239C2×D244—22no—
240C2×D244—22no—
241C2×D244—41no—
242C2×D244—41no—
243C2×D244—41no—
244C2×D244—41no—
245C2×C4×D61—22no—
246C2×C4×D61—24no—
247C2×C4×D61—22no—
248C2×C4×D61—24no—
249C2×C4×D61—24no—
250C2×C4×D61—22no—
251C2×C4×D61—22no—
252C2×C4×D61—22no—
253C2×C4×D61—22no—
254C2×C4×D61—22no—
255C2×C4×D61—41no—
256C2×C4×D61—41no—
257C2×Dic122—22no—
258C2×Dic122—41no—
259C2×Dic122—41no—
260C4⋊C4×C61—24no—
261C4⋊C4×C61—24no—
262C4⋊C4×C61—24no—
263C4⋊C4×C61—24no—
264C4⋊C4×C61—41no—
265C4⋊C4×C61—41no—
266C4⋊C4×C61—42no—
267C42×C61—22no—
268C42×C61—24no—
269C42×C61—24no—
270C42×C61—41no—
271C42×C61—42no—
272C42×C61—41no—
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—24no—
282#11758198—24no—
283#11758198—24no—
284#11758198—24no—
285#11758198—42no—
286#11758198—42no—
287#11758198—42no—
288#11758198—42no—
289#11758198—42no—
290C4⋊Dic61—24no—
291C4⋊Dic61—24no—
292C4⋊Dic61—41no—
293C4⋊Dic61—41no—
294#11758196—24no—
295#11758196—24no—
296#11758196—24no—
297#11758196—24no—
298#11758196—24no—
299#11758196—24no—
300#11758196—24no—
301#11758196—42no—
302#11758196—42no—
303#11758196—42no—
304#11758196—42no—
305#11758196—42no—
306#11758196#4118yescomplemented
307C4×Dic61—22no—
308C4×Dic61—24no—
309C4×Dic61—24no—
310C4×Dic61—24no—
311C4×Dic61—41no—
312C4×Dic61—42no—
313C4×Dic61—42no—
314C4×Dic61—41no—
315C23×C61C2511yescharacteristic
316C22×D61—22no—
317C22×D61—21no—
318C22×D61—21no—
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—21no—
323C22×D61—21no—
324C22×D61—21no—
325C22×D61—21no—
326C22×D61—21no—
327C22×D61—21no—
328C22×D61—22no—
329C22×D61—22no—
330C22×D61H(5,𝔽2)12yes—
331Q8×C61—44no—
332Q8×C61—82no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61C2×#4114yes—
356C2×C4×C61C2×#4112yes—
357C2×C4×C61C2×#4112yes—
358C2×C4×C61C2×#4112yes—
359C2×C4×C612−1+414yes—
360C2×Dic61—22no—
361C2×Dic61—21no—
362C2×Dic61—22no—
363C2×Dic61—21no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—22no—
372C2×Dic61—22no—
373C2×Dic61—22no—
374C2×Dic61—22no—
375C2×Dic61—22no—
376C2×Dic61—22no—
377C2×Dic61—22no—
378C2×Dic61C2×#4114yes—
379C2×Dic61C2×#4114yes—
380C2×Dic61H(5,𝔽2)12yes—
381D244—44no—
382D244—44no—
383D244—44no—
384C4×D61—216no—
385C4×D61—28no—
386C4×D61—44no—
387C4×D61—44no—
388Dic122—82no—
389#60047—611nomaximal, Sylow
390C22×C61C22×#4112yes—
391C22×C61C22×#4111yescharacteristic
392C22×C61C2×H(5,𝔽2)11yescharacteristic
393C22×C61C2×H(5,𝔽2)11yescharacteristic
394C22×C61C2×2−1+412yes—
395C2×D61—22no—
396C2×D61—24no—
397C2×D61—42no—
398C2×D61—41no—
399C2×D61—41no—
400C2×D61—42no—
401C2×D61—42no—
402C2×D61—41no—
403C2×D61—41no—
404C2×D61—41no—
405C2×D61—41no—
406C2×D61—42no—
407C2×D61—42no—
408C2×D61—41no—
409C2×D61—41no—
410C4×C61—24no—
411C4×C61—22no—
412C4×C61—22no—
413C4×C61—22no—
414C4×C61—24no—
415C4×C61—42no—
416C4×C61—42no—
417C4×C61—42no—
418C4×C61—42no—
419Dic61—24no—
420Dic61—22no—
421Dic61—24no—
422Dic61—42no—
423Dic61—42no—
424Dic61—42no—
425Dic61—42no—
426#2809—611no—
427#2734—611no—
428#2727—612no—
429#2611—612no—
430#2593—612no—
431#2556—612no—
432#2556—612no—
433#2479—612no—
434#2479—612no—
435#2474—612no—
436#2474—612no—
437#2432—611no—
438#2432—611no—
439#2373—612no—
440#2373—612no—
441#2369—611no—
442#2369D6111yescharacteristic, complemented
443#2297—611no—
444#2296—612no—
445C2×C61#348212yes—
446C2×C61#348311yescharacteristic
447C2×C61#349011yescharacteristic
448C2×C61#349212yes—
449C2×C61#355011yescharacteristic
450D61—42no—
451D61—81no—
452D61—81no—
453C22×#41—611no—
454C2×C4⋊Q8—611no—
455C2×C4⋊Q8C2×D6111yescharacteristic
456C2×#126—612no—
457C2×#126—612no—
458C2×#125—612no—
459C2×#124—611no—
460C2×#124—611no—
461C2×C22⋊Q8—611no—
462C2×C22⋊Q8—611no—
463C2×#117—611no—
464C2×#117—612no—
465C2×#117—612no—
466C22×C42—611no—
467#400—612no—
468#399—612no—
469#399—612no—
470#399—612no—
471#398—612no—
472#398—612no—
473#398—612no—
474#397—612no—
475#396—612no—
476#396—612no—
477#395—612no—
478#395—612no—
479#394—612no—
480#394—612no—
481#394—612no—
482#394—612no—
483#391—611no—
484#391—611no—
485#391—612no—
486#391C2×D6111yescharacteristic
487#391C2×D6111yescharacteristic
488#391C2×D6112yes—
489#390—611no—
490#390—611no—
491#390—611no—
492#390—611no—
493#389—612no—
494#389—612no—
495#389—612no—
496#389—612no—
497#389—612no—
498#389—612no—
499#389C2×D6112yes—
500#389C2×D6112yes—
501#388—612no—
502#388—612no—
503#388—612no—
504#388—612no—
505#388—612no—
506#388—612no—
507#388—612no—
508#388—612no—
509#388—612no—
510#388—612no—
511#388—612no—
512#388—612no—
513#387—612no—
514#387—612no—
515#387—612no—
516#387—612no—
517#387—612no—
518#387—612no—
519#386—612no—
520#386—612no—
521#385—612no—
522#385—612no—
523#385—612no—
524#385—612no—
525#385—612no—
526#385—612no—
527C4×C4⋊C4—612no—
528C4×C4⋊C4—612no—
529C4×C4⋊C4—612no—
530C4×C4⋊C4—612no—
531C4×C4⋊C4—612no—
532C4×C4⋊C4C2×D6112yes—
533C4×C4⋊C4C2×D6112yes—
534C4×C4⋊C4C2×D6112yes—
535C4×C22⋊C4—611no—
536C4×C22⋊C4—611no—
537C4×C22⋊C4—612no—
538C4×C22⋊C4—612no—
539#376—612no—
540C61#6004711yescharacteristic, complemented, Sylow
541C2×#41—1224no—
542C2×#41—2442no—
543C2×#41—2442no—
544C22×Q8—611no—
545C22×Q8C22×D6111yescharacteristic
546C22×Q8C22×D6111yescharacteristic
547C22×D4—611no—
548C22×D4—611no—
549C22×D4—611no—
550C23×C4—612no—
551C23×C4—611no—
552C23×C4—611no—
553C23×C4—611no—
554C4⋊Q8—24no—
555C4⋊Q8—1224no—
556#126—1228no—
557#126—1228no—
558#125—2444no—
559#124—2442no—
560#124—2442no—
561C22⋊Q8—2442no—
562C22⋊Q8—2442no—
563#117—1228no—
564#117—2444no—
565#117—2442no—
566C2×C4⋊C4—612no—
567C2×C4⋊C4—612no—
568C2×C4⋊C4—612no—
569C2×C4⋊C4—612no—
570C2×C4⋊C4—612no—
571C2×C4⋊C4—612no—
572C2×C4⋊C4—612no—
573C2×C4⋊C4—612no—
574C2×C4⋊C4—612no—
575C2×C4⋊C4—612no—
576C2×C4⋊C4—612no—
577C2×C4⋊C4—612no—
578C2×C4⋊C4—611no—
579C2×C4⋊C4—611no—
580C2×C4⋊C4—612no—
581C2×C4⋊C4—612no—
582C2×C4⋊C4—612no—
583C2×C4⋊C4C22×D6112yes—
584C2×C4⋊C4C22×D6112yes—
585C2×C4⋊C4C22×D6112yes—
586C2×C4⋊C4C22×D6112yes—
587C2×C4⋊C4C22×D6111yescharacteristic
588C2×C4⋊C4C22×D6111yescharacteristic
589C2×C4⋊C4C22×D6112yes—
590C2×C22⋊C4—612no—
591C2×C22⋊C4—612no—
592C2×C22⋊C4—612no—
593C2×C22⋊C4—612no—
594C2×C22⋊C4—612no—
595C2×C22⋊C4—612no—
596C2×C22⋊C4—612no—
597C2×C22⋊C4—612no—
598C2×C22⋊C4—612no—
599C2×C22⋊C4—612no—
600C2×C22⋊C4—612no—
601C2×C22⋊C4—612no—
602C2×C22⋊C4—612no—
603C2×C22⋊C4—612no—
604C2×C22⋊C4—612no—
605C2×C22⋊C4—612no—
606C2×C22⋊C4—612no—
607C2×C42—612no—
608C2×C42—612no—
609C2×C42—612no—
610C2×C42—611no—
611C2×C42—612no—
612C2×C42—611no—
613C2×C42—612no—
614C2×C42—611no—
615C2×C42—2442no—
616C2×C42C22×D6112yes—
617C2×C42C22×D6112yes—
618C2×C42C22×D6111yescharacteristic
619C2×C42C22×D6112yes—
620C2×C42C22×D6111yescharacteristic
621C2×C42C22×D6111yescharacteristic
622#95—612no—
623#95—612no—
624#95—612no—
625#95—612no—
626#95—612no—
627#95—612no—
628#95—612no—
629#95—612no—
630#95—612no—
631#95—612no—
632#95—612no—
633#95—612no—
634#95—612no—
635#95—612no—
636#95—612no—
637#95—612no—
638#95C22×D6112yes—
639#95C22×D6112yes—
640#95C22×D6112yes—
641#95C22×D6112yes—
642#95C22×D6112yes—
643#95C22×D6112yes—
644C24—611no—
645C24—611no—
646C24—611no—
647#41—24416no—
648C2×Q8—22no—
649C2×Q8—41no—
650C2×Q8—41no—
651C2×Q8—41no—
652C2×Q8—41no—
653C2×Q8—1222no—
654C2×Q8—2441no—
655C2×Q8—2441no—
656C2×Q8#1175822214yes—
657C2×D4—1222no—
658C2×D4—1222no—
659C2×D4—1222no—
660C2×D4—1222no—
661C2×D4—1222no—
662C2×D4—2441no—
663C2×D4—2441no—
664C2×D4—2441no—
665C2×D4—2441no—
666C22×C4—611no—
667C22×C4—612no—
668C22×C4—612no—
669C22×C4—612no—
670C22×C4—612no—
671C22×C4—612no—
672C22×C4—612no—
673C22×C4—1224no—
674C22×C4—1222no—
675C22×C4—1222no—
676C22×C4—1222no—
677C22×C4—1224no—
678C22×C4—1222no—
679C22×C4—1222no—
680C22×C4—1224no—
681C22×C4—1222no—
682C22×C4—1222no—
683C22×C4—2441no—
684C22×C4—2441no—
685C22×C4C23×D6112yes—
686C22×C4C23×D6112yes—
687C22×C4C23×D6112yes—
688C22×C4C23×D6112yes—
689C22×C4C23×D6112yes—
690C22×C4C23×D6111yescharacteristic
691C22×C4C23×D6111yescharacteristic
692C22×C4C23×D6111yescharacteristic
693C22×C4C23×D6112yes—
694C4⋊C4—24no—
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—41no—
699C4⋊C4—41no—
700C4⋊C4—42no—
701C4⋊C4—618no—
702C4⋊C4—1224no—
703C4⋊C4—1224no—
704C4⋊C4—1224no—
705C4⋊C4—1224no—
706C4⋊C4—1224no—
707C4⋊C4—1224no—
708C4⋊C4—1224no—
709C4⋊C4—1224no—
710C4⋊C4—1224no—
711C4⋊C4—2442no—
712C4⋊C4—2442no—
713C4⋊C4—2442no—
714C4⋊C4—2442no—
715C4⋊C4—2442no—
716C4⋊C4—2441no—
717C4⋊C4—2441no—
718C22⋊C4—1224no—
719C22⋊C4—1224no—
720C22⋊C4—1224no—
721C22⋊C4—1224no—
722C22⋊C4—1224no—
723C22⋊C4—1224no—
724C22⋊C4—1224no—
725C22⋊C4—1224no—
726C22⋊C4—1224no—
727C22⋊C4—1224no—
728C22⋊C4—1224no—
729C22⋊C4—1224no—
730C22⋊C4—2442no—
731C22⋊C4—2442no—
732C22⋊C4—2442no—
733C22⋊C4—2442no—
734C22⋊C4—2442no—
735C42—24no—
736C42—24no—
737C42—22no—
738C42—41no—
739C42—42no—
740C42—41no—
741C42—1224no—
742C42—1224no—
743C42—1224no—
744C42—1222no—
745C42—2442no—
746C42—2441no—
747C42—2442no—
748C42—2441no—
749C23—612no—
750C23—1222no—
751C23—1221no—
752C23—1221no—
753C23—1222no—
754C23—1222no—
755C23—1222no—
756C23—1221no—
757C23—1221no—
758C23—1221no—
759C23—1221no—
760C23—1221no—
761C23—1221no—
762C23—1222no—
763C23—1222no—
764C23C24×D6111yescharacteristic
765Q8—44no—
766Q8—82no—
767Q8—4882no—
768D4—2444no—
769D4—2444no—
770D4—2444no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—614no—
794C2×C4—614no—
795C2×C4—612no—
796C2×C4—12216no—
797C2×C4—1228no—
798C2×C4—1222no—
799C2×C4—1221no—
800C2×C4—1222no—
801C2×C4—1221no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—1222no—
809C2×C4—1222no—
810C2×C4—1222no—
811C2×C4—1222no—
812C2×C4—1222no—
813C2×C4—1222no—
814C2×C4—1222no—
815C2×C4—1222no—
816C2×C4—2444no—
817C2×C4—2444no—
818C2×C4#41×D6114yes—
819C2×C4C2×#1175822212yes—
820C2×C4C2×#1175822212yes—
821C2×C4C2×#1175822212yes—
822C2×C4#1451982514yes—
823C22—1222no—
824C22—1224no—
825C22—2441no—
826C22—2441no—
827C22—2441no—
828C22—2441no—
829C22—2442no—
830C22—2442no—
831C22—2442no—
832C22—2442no—
833C22—2441no—
834C22—2441no—
835C22—2441no—
836C22—2442no—
837C22—2441no—
838C22C2×#41×D6112yes—
839C22C22×#1175822211yescharacteristic
840C22H(5,𝔽2)×D6111yescharacteristic
841C22H(5,𝔽2)×D6111yescharacteristic
842C22C2×#1451982512yes—
843C4—22no—
844C4—22no—
845C4—22no—
846C4—24no—
847C4—24no—
848C4—42no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—1222no—
853C4—1224no—
854C4—1224no—
855C4—2442no—
856C4—2442no—
857C4—2442no—
858C4—2442no—
859C2—4881no—
860C2—4881no—
861C2—2442no—
862C2#2145943612yes—
863C2#2145944411yescharacteristic
864C2#2145950411yescharacteristic
865C2#2145952712yes—
866C2#2146022511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, cosocleC23×C61C25
FittingC61×#2369C2
prime radicalC22×#11758226C22
hypercenter#2369D61
hypocenterC61#60047
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2369

Complements

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

NH ≅ G/Ntype
1. #21453805C2semidirect
2. #21452849C2semidirect
3. #21452781C2semidirect
4. #21451516C2semidirect
5. #21451310C2semidirect
6. #21450908C2semidirect
7. #21450900C2semidirect
8. #21450057C2semidirect
9. #21450050C2semidirect
10. #21449982C2semidirect
11. #21449975C2semidirect
14. #21448944C2semidirect
15. #21448935C2semidirect
16. #21448907C2semidirect
18. #21448299C2semidirect
19. C61×#2369C2semidirect
306. #11758196#41semidirect
442. #2369D61semidirect
540. C61#60047semidirect

Maximal subgroups

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

subgroupindex
#214538052
#214528492
#214527812
#214515162
#214513102
#214509082
#214509002
#214500572
#214500502
#214499822
#214499752
#214494462
#214494442
#214489442
#214489352
#214489072
#214483082
#214482992
C61×#23692
#6004761