Finite Group Databasebeta

← #29843298

Subgroups — #29843298

Order 15616.

2118 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840297C211yesmaximal, characteristic
2#21449010C212yesmaximal, complemented
3#21449009C212yesmaximal, complemented
4#21448816C212yesmaximal, complemented
5#21448804C212yesmaximal, complemented
6#21448758C212yesmaximal, complemented
7#21448728C212yesmaximal, complemented
8#21448708C212yesmaximal, complemented
9#21448678C212yesmaximal, complemented
10#21448632C211yesmaximal, characteristic, complemented
11#21448629C211yesmaximal, characteristic, complemented
12#21448625C211yesmaximal, characteristic, complemented
13#21448548C212yesmaximal, complemented
14#21448518C212yesmaximal
15#21448468C212yesmaximal, complemented
16#21448451C212yesmaximal, complemented
17#21448223C211yesmaximal, characteristic, complemented
18#383×D61C211yesmaximal, characteristic, complemented
19C61×#2336C211yesmaximal, characteristic, complemented
20#16840297C4116yescomplemented
21C2×#14519772C2212yes—
22C2×#14519765C2211yescharacteristic
23C2×#14519762C2212yes—
24C2×#14519757C2211yescharacteristic
25C2×#14519752C2211yescharacteristic
26C2×#14519742C2211yescharacteristic
27C2×C4×D244C2212yes—
28C2×#14519739C2212yes—
29C2×#14519739C2211yescharacteristic
30C2×#14519739C2212yes—
31C2×#14519735C2212yes—
32C2×#14519734C2211yescharacteristic
33C2×#14519734C2211yescharacteristic
34C2×C42×D61C2211yescharacteristic
35#16839666C2212yes—
36#16839666C2212yes—
37#16839661C2212yes—
38#16839660C2212yes—
39#16839659C2212yes—
40#16839658C2212yes—
41#16839657C2212yes—
42#16839654C2212yes—
43#16839653C2212yes—
44#16839653C2212yes—
45#16839653C2212yes—
46#16839652C2212yes—
47#16839651C2212yes—
48#16839651C2212yes—
49#16839651C2212yes—
50#16839648C2212yes—
51#16839648C2212yes—
52#16839648C2212yes—
53#16839648C2212yes—
54#16839647C2212yes—
55#16839646C2212yes—
56#16839645C2212yes—
57#16839644C2212yes—
58#16839640C2212yes—
59#16839640C2212yes—
60#16839640C2212yes—
61#16839640C2212yes—
62#16839636C2212yes—
63#16839636C2212yes—
64#16839636C2212yes—
65#16839636C2212yes—
66#16839633C2212yes—
67#16839633C2212yes—
68#16839633C2212yes—
69#16839633C2212yes—
70#16839631C2212yes—
71#16839630C2211yescharacteristic
72#16839629C2212yes—
73#16839629C2212yes—
74#16839629C2212yes—
75#16839629C2211yescharacteristic
76#16839629C2211yescharacteristic
77#16839627C2212yes—
78#16839626C2212yes—
79#16839624C2212yes—
80#16839621C2212yes—
81#16839619C2212yes—
82#16839619C2212yes—
83C4⋊C4×Dic61C2212yes—
84C4×#11758196C2211yescharacteristic
85C4×#11758196C2212yes—
86C4×#11758196C2211yescharacteristic
87C4×C4⋊Dic61C2211yescharacteristic
88C4×#11758198C2212yes—
89C4×#11758198C2212yes—
90C4×#11758198C2212yes—
91#16839609C2212yes—
92#16839609C2212yes—
93#16839607C2212yes—
94#95×D61C2212yes—
95#95×D61C2211yescharacteristic
96#95×D61C2211yescharacteristic
97#95×D61C2212yes—
98#95×D61C2212yes—
99C2×#125×C61C2211yescharacteristic
100C61×#389C2212yes—
101C61×#387C2212yes—
102C61×#387C2212yes—
103C61×#387C2212yes—
104C61×#387C2212yes—
105C61×#383C2211yescharacteristic
106C4×C4⋊C4×C61C2212yes—
107C4×C4⋊C4×C61C2211yescharacteristic
108C22×Dic122C2311yescharacteristic
109C22×D244C2312yes—
110C22×D244C2311yescharacteristic
111C22×C4×D61C2311yescharacteristic
112C22×C4×D61C2312yes—
113C22×C4×D61C2312yes—
114C22×C4×D61C2312yes—
115C22×C4×D61C2312yes—
116C22×C4×D61C2311yescharacteristic
117C22×C4×D61C2311yescharacteristic
118C22×C4×D61C2312yes—
119#14519772C2×C4116yescomplemented
120#14519765C2×C418yescomplemented
121#14519762C2×C4116yescomplemented
122#14519757C2×C418yescomplemented
123#14519752C2×C418yes—
124#14519742C2×C418yescomplemented
125C4×D244—44no—
126#14519739—44no—
127#14519739C2×C418yescomplemented
128#14519739C2×C4116yescomplemented
129#14519735C2×C4116yescomplemented
130#14519734—42no—
131#14519734—42no—
132C2×C4⋊Dic61C2312yes—
133C2×C4⋊Dic61C2312yes—
134C2×C4⋊Dic61C2312yes—
135C2×C4⋊Dic61C2312yes—
136C2×#11758196C2312yes—
137C2×#11758196C2312yes—
138C2×#11758196C2312yes—
139C2×#11758196C2312yes—
140C2×#11758196C2312yes—
141C2×#11758196C2312yes—
142C2×#11758196C2312yes—
143C2×#11758198C2312yes—
144C2×#11758198C2312yes—
145C2×#11758198C2312yes—
146C2×#11758198C2312yes—
147C2×#11758198C2312yes—
148C2×#11758198C2312yes—
149C2×#11758198C2312yes—
150C2×#11758198C2312yes—
151C2×#11758198C2312yes—
152C2×#11758198C2312yes—
153C2×#11758198C2312yes—
154C2×#11758198C2312yes—
155C2×#11758198C2312yes—
156C2×C4×Dic61C2311yescharacteristic
157C2×C4×Dic61C2311yescharacteristic
158C2×C4×Dic61C2312yes—
159C2×C4×Dic61C2312yes—
160C2×C4×Dic61C2312yes—
161C2×C4×Dic61C2312yes—
162C2×C4×Dic61C2311yescharacteristic
163C2×C4×Dic61C2311yescharacteristic
164C2×C4×Dic61C2311yescharacteristic
165C2×C4×Dic61C2312yes—
166C42×D61C2×C418yescomplemented
167#14519684C2312yes—
168#14519684C2312yes—
169#14519684C2312yes—
170#14519684C2312yes—
171#14519684C2312yes—
172#14519684C2312yes—
173#14519684C2312yes—
174#14519684C2312yes—
175#14519684C2311yescharacteristic
176#14519684C2312yes—
177#14519684C2311yescharacteristic
178#14519684C2312yes—
179#14519684C2312yes—
180#14519684C2312yes—
181#14519684C2312yes—
182#14519684C2312yes—
183#14519684C2312yes—
184#14519684C2312yes—
185#14519684C2312yes—
186#14519684C2312yes—
187#14519684C2312yes—
188#125×C61C2×C418yescomplemented
189C2×C4⋊C4×C61C2312yes—
190C2×C4⋊C4×C61C2312yes—
191C2×C4⋊C4×C61C2312yes—
192C2×C4⋊C4×C61C2312yes—
193C2×C4⋊C4×C61C2311yescharacteristic
194C2×C4⋊C4×C61C2312yes—
195C2×C4⋊C4×C61C2311yescharacteristic
196C2×C42×C61C2311yescharacteristic
197C2×C42×C61C2311yescharacteristic
198C2×C42×C61C2312yes—
199C2×C42×C61C2312yes—
200C2×C42×C61C2311yescharacteristic
201#95×C61C2312yes—
202#95×C61C2312yes—
203#95×C61C2312yes—
204#95×C61C2312yes—
205#95×C61C2311yescharacteristic
206#95×C61C2311yescharacteristic
207#95×C61C2312yes—
208#95×C61C2312yes—
209#95×C61C2312yes—
210C23×D61C2412yes—
211C23×D61C2411yescharacteristic
212C22×C4×C61C2412yes—
213C22×C4×C61C2412yes—
214C22×C4×C61C2412yes—
215C22×C4×C61C2412yes—
216C22×C4×C61C2411yescharacteristic
217C22×C4×C61C2411yescharacteristic
218C22×C4×C61C2412yes—
219C22×C4×C61C2411yescharacteristic
220C22×C4×C61C2412yes—
221C22×Dic61C2412yes—
222C22×Dic61C2412yes—
223C22×Dic61C2412yes—
224C22×Dic61C2412yes—
225C22×Dic61C2411yescharacteristic
226C22×Dic61C2411yescharacteristic
227C22×Dic61C2411yescharacteristic
228C22×Dic61C2412yes—
229C2×D244—24no—
230C2×D244—24no—
231C2×D244—42no—
232C2×D244C22×C418yes—
233C2×D244C22×C414yes—
234C2×C4×D61—22no—
235C2×C4×D61—22no—
236C2×C4×D61—24no—
237C2×C4×D61—24no—
238C2×C4×D61—42no—
239C2×C4×D61—42no—
240C2×C4×D61—42no—
241C2×C4×D61—42no—
242C2×C4×D61—42no—
243C2×C4×D61—42no—
244C2×C4×D61—42no—
245C2×C4×D61—42no—
246C2×C4×D61—42no—
247C2×C4×D61—42no—
248C2×C4×D61—42no—
249C2×C4×D61—42no—
250C2×C4×D61—42no—
251C2×C4×D61—42no—
252C2×C4×D61C22×C414yes—
253C2×C4×D61C22×C414yes—
254C2×C4×D61C22×C414yes—
255C2×C4×D61C22×C418yes—
256C2×Dic122—42no—
257C2×Dic122C22×C414yes—
258C4⋊C4×C61—42no—
259C4⋊C4×C61—42no—
260C4⋊C4×C61—42no—
261C4⋊C4×C61C22×C418yes—
262C4⋊C4×C61C22×C414yes—
263C4⋊C4×C61C22×C418yes—
264C4⋊C4×C61C22×C414yes—
265C42×C61—42no—
266C42×C61—41no—
267C42×C61—41no—
268C42×C61—42no—
269C42×C61C22×C414yes—
270#11758198—24no—
271#11758198—24no—
272#11758198—42no—
273#11758198—42no—
274#11758198—42no—
275#11758198—42no—
276#11758198—42no—
277#11758198—42no—
278#11758198C22×C418yes—
279#11758198C22×C418yes—
280#11758198C22×C418yes—
281#11758198C22×C418yes—
282#11758198C22×C418yes—
283C4⋊Dic61—42no—
284C4⋊Dic61—42no—
285C4⋊Dic61—42no—
286C4⋊Dic61C22×C418yes—
287#11758196—42no—
288#11758196—42no—
289#11758196—42no—
290#11758196—42no—
291#11758196—42no—
292#11758196—42no—
293#11758196C22×C418yes—
294C4×Dic61—42no—
295C4×Dic61—42no—
296C4×Dic61—42no—
297C4×Dic61—41no—
298C4×Dic61—41no—
299C4×Dic61—42no—
300C4×Dic61C22×C414yes—
301C4×Dic61C22×C414yes—
302C4×Dic61C22×C414yes—
303C4×Dic61C22×C418yes—
304C23×C61C2511yescharacteristic
305C22×D61—22no—
306C22×D61—22no—
307C22×D61—22no—
308C22×D61—22no—
309C22×D61—22no—
310C22×D61—22no—
311C22×D61—22no—
312C22×D61—22no—
313C22×D61C23×C414yes—
314C22×D61C23×C412yes—
315C22×D61H(5,𝔽2)12yes—
316C22×D612−1+412yes—
317C2×C4×C61—21no—
318C2×C4×C61—22no—
319C2×C4×C61—21no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
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×C61C23×C414yes—
338C2×C4×C61C23×C412yes—
339C2×C4×C61C23×C412yes—
340C2×C4×C61C23×C412yes—
341C2×C4×C61C23×C414yes—
342C2×Dic61—21no—
343C2×Dic61—21no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
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×Dic61C23×C412yes—
361C2×Dic61C23×C412yes—
362C2×Dic61C23×C412yes—
363C2×Dic61C23×C414yes—
364D244—216no—
365D244—44no—
366C4×D61—28no—
367C4×D61—44no—
368C4×D61—48no—
369C4×D61—44no—
370C4×D61—84no—
371C4×D61—84no—
372C4×D61—84no—
373C4×D61—84no—
374Dic122—44no—
375#34401—611nomaximal, Sylow
376C22×C61C24×C411yescharacteristic
377C22×C61C2×H(5,𝔽2)11yescharacteristic
378C22×C61C2×2−1+411yescharacteristic
379C22×C61#58512yes—
380C22×C61#58512yes—
381C2×D61—22no—
382C2×D61—22no—
383C2×D61—24no—
384C2×D61—24no—
385C2×D61—24no—
386C2×D61—24no—
387C2×D61—24no—
388C2×D61—42no—
389C2×D61—42no—
390C2×D61—42no—
391C2×D61—42no—
392C2×D61#52014yes—
393C4×C61—22no—
394C4×C61—24no—
395C4×C61—22no—
396C4×C61—24no—
397C4×C61—22no—
398C4×C61—42no—
399C4×C61—42no—
400C4×C61—42no—
401C4×C61—42no—
402Dic61—22no—
403Dic61—24no—
404Dic61—22no—
405Dic61—22no—
406Dic61—42no—
407Dic61—42no—
408Dic61—42no—
409Dic61—42no—
410C2×#529—611no—
411#2383—612no—
412#2383—612no—
413#2359—612no—
414#2359—612no—
415#2353—612no—
416#2349—612no—
417#2347—612no—
418#2343—612no—
419#2337—611no—
420#2337—611no—
421#2336—611no—
422#2336D6111yescharacteristic, complemented
423#2329—612no—
424#2325—612no—
425#2320—612no—
426#2318—612no—
427#2285—611no—
428C2×#383—611no—
429C2×C61C2×#52011yescharacteristic
430C2×C61#342811yescharacteristic
431C2×C61#342811yescharacteristic
432C2×C61#356012yes—
433C2×C61#356412yes—
434D61—24no—
435D61—44no—
436#529—6116no—
437C2×#126—612no—
438C2×#125C2×D6111yescharacteristic
439C2×#124—611no—
440C2×#123—612no—
441C2×C22⋊Q8—611no—
442C2×#121—611no—
443C2×C4×Q8—611no—
444C2×C4×D4—611no—
445C2×C4×D4—612no—
446C2×C4×D4—612no—
447C2×C4×D4—612no—
448C2×#117—612no—
449C2×#117—611no—
450C2×#117—611no—
451C22×C42—611no—
452#391—612no—
453#391—612no—
454#389—612no—
455#389—612no—
456#389—612no—
457#389—612no—
458#389—612no—
459#389C2×D6112yes—
460#388—612no—
461#388—612no—
462#388—612no—
463#388—612no—
464#388—612no—
465#388—612no—
466#388—612no—
467#388—612no—
468#387—612no—
469#387—612no—
470#387—612no—
471#387—612no—
472#387—612no—
473#387—612no—
474#387—612no—
475#387—612no—
476#387C2×D6112yes—
477#387C2×D6112yes—
478#387C2×D6112yes—
479#387C2×D6112yes—
480#386—612no—
481#386—612no—
482#386—612no—
483#386—612no—
484#385—612no—
485#385—612no—
486#385—612no—
487#385—612no—
488#385—612no—
489#385—612no—
490#385—612no—
491#385—612no—
492#384—612no—
493#383—611no—
494#383—612no—
495#383—612no—
496#383—612no—
497#383—611no—
498#383—611no—
499#383C2×D6111yescharacteristic
500#382—612no—
501#382—612no—
502#381—612no—
503#380—612no—
504#380—612no—
505#380—612no—
506C4×C4⋊C4—612no—
507C4×C4⋊C4—612no—
508C4×C4⋊C4—611no—
509C4×C4⋊C4—611no—
510C4×C4⋊C4—611no—
511C4×C4⋊C4C2×D6111yescharacteristic
512C4×C4⋊C4C2×D6112yes—
513C4×C22⋊C4—612no—
514C4×C22⋊C4—612no—
515C4×C22⋊C4—612no—
516C4×C22⋊C4—612no—
517C4×C22⋊C4—612no—
518#376—612no—
519C2×#95—612no—
520C2×#95—612no—
521C2×#95—611no—
522C2×#95—611no—
523C2×#95—612no—
524C61#3440111yescharacteristic, complemented, Sylow
525C22×Q8—611no—
526C22×D4—612no—
527C22×D4—611no—
528C23×C4—611no—
529C23×C4—612no—
530C23×C4—611no—
531C23×C4—611no—
532C23×C4—612no—
533C23×C4—612no—
534C23×C4—612no—
535C23×C4—612no—
536#126—6116no—
537#125C4×D6118yescomplemented
538#124—618no—
539#123—6116no—
540C22⋊Q8—618no—
541#121—618no—
542C4×Q8—618no—
543C4×D4—618no—
544C4×D4—6116no—
545C4×D4—2444no—
546C4×D4—2444no—
547#117—6116no—
548#117—2442no—
549#117—2442no—
550C2×C4⋊C4—612no—
551C2×C4⋊C4—612no—
552C2×C4⋊C4—612no—
553C2×C4⋊C4—612no—
554C2×C4⋊C4—612no—
555C2×C4⋊C4—612no—
556C2×C4⋊C4—612no—
557C2×C4⋊C4—612no—
558C2×C4⋊C4—612no—
559C2×C4⋊C4—612no—
560C2×C4⋊C4—612no—
561C2×C4⋊C4C22×D6112yes—
562C2×C4⋊C4C22×D6112yes—
563C2×C4⋊C4C22×D6112yes—
564C2×C4⋊C4C22×D6112yes—
565C2×C4⋊C4C22×D6111yescharacteristic
566C2×C4⋊C4C22×D6112yes—
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C22⋊C4—612no—
569C2×C22⋊C4—612no—
570C2×C22⋊C4—612no—
571C2×C22⋊C4—612no—
572C2×C22⋊C4—612no—
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×C42—611no—
582C2×C42—612no—
583C2×C42—611no—
584C2×C42—611no—
585C2×C42—618no—
586C2×C42—611no—
587C2×C42—611no—
588C2×C42—612no—
589C2×C42—612no—
590C2×C42—612no—
591C2×C42—612no—
592C2×C42C22×D6111yescharacteristic
593C2×C42C22×D6111yescharacteristic
594C2×C42C22×D6112yes—
595C2×C42C22×D6112yes—
596C2×C42C22×D6111yescharacteristic
597#95—612no—
598#95—612no—
599#95—612no—
600#95—612no—
601#95—611no—
602#95—612no—
603#95—612no—
604#95—612no—
605#95—612no—
606#95—612no—
607#95—611no—
608#95—612no—
609#95—612no—
610#95—612no—
611#95—612no—
612#95—612no—
613#95—612no—
614#95—612no—
615#95—612no—
616#95—612no—
617#95—612no—
618#95C22×D6112yes—
619#95C22×D6111yescharacteristic
620#95C22×D6112yes—
621#95C22×D6111yescharacteristic
622#95C22×D6112yes—
623#95C22×D6112yes—
624#95C22×D6112yes—
625#95C22×D6112yes—
626#95C22×D6112yes—
627C24—611no—
628C24—612no—
629C2×Q8—614no—
630C2×Q8—2442no—
631C2×D4—618no—
632C2×D4—614no—
633C2×D4—1224no—
634C2×D4—1224no—
635C2×D4—2442no—
636C22×C4—611no—
637C22×C4—612no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—614no—
641C22×C4—614no—
642C22×C4—614no—
643C22×C4—618no—
644C22×C4—612no—
645C22×C4—612no—
646C22×C4—612no—
647C22×C4—612no—
648C22×C4—1222no—
649C22×C4—1222no—
650C22×C4—1224no—
651C22×C4—1224no—
652C22×C4—2442no—
653C22×C4—2442no—
654C22×C4—2442no—
655C22×C4—2442no—
656C22×C4—2442no—
657C22×C4—2442no—
658C22×C4—2442no—
659C22×C4—2442no—
660C22×C4—2442no—
661C22×C4—2442no—
662C22×C4—2442no—
663C22×C4—2442no—
664C22×C4—2442no—
665C22×C4—2442no—
666C22×C4C23×D6112yes—
667C22×C4C23×D6112yes—
668C22×C4C23×D6112yes—
669C22×C4C23×D6112yes—
670C22×C4C23×D6111yescharacteristic
671C22×C4C23×D6111yescharacteristic
672C22×C4C23×D6112yes—
673C22×C4C23×D6112yes—
674C22×C4C23×D6111yescharacteristic
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—618no—
679C4⋊C4—618no—
680C4⋊C4—2442no—
681C4⋊C4—2442no—
682C4⋊C4—2442no—
683C4⋊C4—2442no—
684C4⋊C4—2442no—
685C4⋊C4—2442no—
686C4⋊C4—2442no—
687C4⋊C4—2442no—
688C4⋊C4—2442no—
689C4⋊C4C2×C4×D6118yes—
690C4⋊C4C2×C4×D6114yes—
691C4⋊C4C2×C4×D6118yes—
692C4⋊C4C2×C4×D6114yes—
693C22⋊C4—618no—
694C22⋊C4—618no—
695C22⋊C4—618no—
696C22⋊C4—618no—
697C22⋊C4—618no—
698C22⋊C4—1224no—
699C22⋊C4—1224no—
700C22⋊C4—2442no—
701C22⋊C4—2442no—
702C22⋊C4—2442no—
703C22⋊C4—2442no—
704C22⋊C4—2442no—
705C22⋊C4—2442no—
706C42—41no—
707C42—41no—
708C42—42no—
709C42—42no—
710C42—614no—
711C42—614no—
712C42—614no—
713C42—618no—
714C42—2442no—
715C42—2442no—
716C42—2442no—
717C42—2441no—
718C42—2441no—
719C42—2442no—
720C42C2×C4×D6114yes—
721C23—612no—
722C23—612no—
723C23—612no—
724C23—614no—
725C23—1222no—
726C23—1222no—
727C23—1222no—
728C23—1222no—
729C23—1222no—
730C23—1222no—
731C23—1222no—
732C23—1222no—
733C23C24×D6111yescharacteristic
734Q8—2444no—
735D4—12216no—
736D4—2444no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—612no—
758C2×C4—612no—
759C2×C4—612no—
760C2×C4—614no—
761C2×C4—1228no—
762C2×C4—1221no—
763C2×C4—1221no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—4884no—
781C2×C4—4884no—
782C2×C4—4884no—
783C2×C4—4884no—
784C2×C4—2444no—
785C2×C4—2448no—
786C2×C4—2444no—
787C2×C4C22×C4×D6112yes—
788C2×C4C22×C4×D6112yes—
789C2×C4C22×C4×D6112yes—
790C2×C4C22×C4×D6114yes—
791C2×C4C22×C4×D6114yes—
792C22—614no—
793C22—1222no—
794C22—1222no—
795C22—1224no—
796C22—1224no—
797C22—1224no—
798C22—1224no—
799C22—1224no—
800C22—2442no—
801C22—2442no—
802C22—2442no—
803C22—2442no—
804C22C23×C4×D6111yescharacteristic
805C22H(5,𝔽2)×D6111yescharacteristic
806C222−1+4×D6111yescharacteristic
807C22#1684059812yes—
808C22#1684059912yes—
809C4—22no—
810C4—24no—
811C4—24no—
812C4—22no—
813C4—22no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—42no—
818C4—1222no—
819C4—1222no—
820C4—1222no—
821C4—1224no—
822C4—2442no—
823C4—2442no—
824C4—2442no—
825C4—2442no—
826C2—1224no—
827C2—2444no—
828C2#520×D6111yescharacteristic
829C2#2145901811yescharacteristic
830C2#2145902111yescharacteristic
831C2#2146037212yes—
832C2#2146043212yes—
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingC61×#2336C2
socle, cosocleC23×C61C25
prime radicalC2×#14519752C22
hypercenter#2336D61
hypocenterC61#34401
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2336

Complements

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

NH ≅ G/Ntype
2. #21449010C2semidirect
3. #21449009C2semidirect
4. #21448816C2semidirect
5. #21448804C2semidirect
6. #21448758C2semidirect
7. #21448728C2semidirect
8. #21448708C2semidirect
9. #21448678C2semidirect
10. #21448632C2semidirect
11. #21448629C2semidirect
12. #21448625C2semidirect
13. #21448548C2semidirect
15. #21448468C2semidirect
16. #21448451C2semidirect
17. #21448223C2semidirect
18. #383×D61C2semidirect
19. C61×#2336C2semidirect
20. #16840297C4semidirect
119. #14519772C2×C4semidirect
120. #14519765C2×C4semidirect
121. #14519762C2×C4semidirect
122. #14519757C2×C4semidirect
124. #14519742C2×C4semidirect
127. #14519739C2×C4semidirect
128. #14519739C2×C4semidirect
129. #14519735C2×C4semidirect
166. C42×D61C2×C4semidirect
188. #125×C61C2×C4semidirect
422. #2336D61semidirect
524. C61#34401semidirect
537. #125C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402972
#214490102
#214490092
#214488162
#214488042
#214487582
#214487282
#214487082
#214486782
#214486322
#214486292
#214486252
#214485482
#214485182
#214484682
#214484512
#214482232
#383×D612
C61×#23362
#3440161