Finite Group Databasebeta

← #30616712

Subgroups — #30616712

Order 15616.

1218 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D61⋊M16C211yesmaximal, characteristic, complemented
2#21462268C211yesmaximal, characteristic, complemented
3#21462002C212yesmaximal, complemented
4#21461949C212yesmaximal, complemented
5#21461835C212yesmaximal
6#21461834C212yesmaximal, complemented
7C4×#14519840C212yesmaximal, complemented
8C4×#14519839C212yesmaximal, complemented
9#529×D61C211yesmaximal, characteristic
10C2×D61⋊M16C2212yes—
11C2×#14519856—21no—
12C2×#14519840C2214yes—
13C2×#14519839C2214yes—
14C4×#11758213—21no—
15C4×#11758213—21no—
16C4×#11758217—21no—
17C4×#11758217—21no—
18#16840721C2212yes—
19C4×D61⋊C8C2212yes—
20#16840708C2212yes—
21#16840706—21no—
22#16840704—21no—
23#16840704C2212yes—
24C4×C4⋊#6923—21no—
25C4×C4⋊#6923C2212yes—
26#16840635C2214yes—
27#16840635C2214yes—
28#16840299C411yescharacteristic, complemented
29#16840298C411yescharacteristic, complemented
30#16840297C411yescharacteristic, complemented
31#16840296C411yescharacteristic, complemented
32#16840295—21no—
33#16840294C411yescharacteristic, complemented
34#16840293C411yescharacteristic, complemented
35#16840292—21no—
36#16840291C411yescharacteristic, complemented
37#16840290—21no—
38#16840289—21no—
39#126×D61—21no—
40#125×D61C2211yescharacteristic
41#124×D61C2211yescharacteristic
42#123×D61—21no—
43C22⋊Q8×D61C2211yescharacteristic
44#121×D61C2211yescharacteristic
45C4×Q8×D61C2211yescharacteristic
46C4×D4×D61—21no—
47C4×D4×D61C2211yescharacteristic
48#117×D61—21no—
49C2×C42×D61C2211yescharacteristic
50C61×#529C411yescharacteristic, complemented
51C2×#11758213—22no—
52D61⋊M16—28no—
53C2×#11758217—22no—
54C2×D61⋊C8C2314yes—
55#14519856—44no—
56C2×C4⋊#6923—22no—
57C2×C4⋊#6923—22no—
58C2×C4⋊#6923C2314yes—
59C2×C22⋊#6923—22no—
60C2×C4×#6923—22no—
61#14519840—28no—
62#14519839—28no—
63#14519832—22no—
64#14519832—22no—
65C4×#92420—22no—
66C4×#92420—22no—
67(C2×#6923)⋊C4—22no—
68(C2×#6923)⋊C4—22no—
69C2×Q8×D61C2311yescharacteristic
70C2×D4×D61—21no—
71C2×D4×D61C2311yescharacteristic
72C22×C4×D61—21no—
73C22×C4×D61D411yescharacteristic
74C22×C4×D61D411yescharacteristic
75C22×C4×D61C2311yescharacteristic
76#14519772—21no—
77#14519772—21no—
78#14519772—21no—
79#14519771—21no—
80#14519770—21no—
81#14519770—21no—
82#14519770—21no—
83#14519769C2×C411yescharacteristic
84#14519768C2×C411yescharacteristic
85#14519768C2×C411yescharacteristic
86#14519767—21no—
87#14519767—21no—
88#14519766C2×C411yescharacteristic
89#14519765C2×C411yescharacteristic
90#14519764C2×C411yescharacteristic
91#14519763—21no—
92#14519763—21no—
93#14519762—21no—
94#14519762—21no—
95#14519761—21no—
96#14519760—21no—
97#14519759—21no—
98#14519759—21no—
99#14519758—21no—
100#14519757C2×C411yescharacteristic
101#14519756C2×C411yescharacteristic
102#14519755—21no—
103#14519754—21no—
104#14519753C2×C411yescharacteristic
105#14519752C2×C411yescharacteristic
106#14519751C2×C411yescharacteristic
107#14519750—21no—
108#14519749—21no—
109#14519748C2×C411yescharacteristic
110Q8×Dic61C2×C411yescharacteristic
111C4×Dic122—21no—
112C4×Dic122C2×C411yescharacteristic
113#14519742—21no—
114#14519742C2×C411yescharacteristic
115C4×D244—21no—
116C4×D244C2×C411yescharacteristic
117D4×Dic61—21no—
118D4×Dic61C2×C411yescharacteristic
119#14519739—21no—
120#14519739C2×C411yescharacteristic
121C4×C22⋊D61—21no—
122C4×C22⋊D61—21no—
123C4×C22⋊D61—21no—
124#14519737—21no—
125#14519737—21no—
126#14519737—21no—
127#14519736—21no—
128#14519735—21no—
129#14519735—21no—
130#14519734—21no—
131#14519734—21no—
132#14519733—21no—
133#14519733—21no—
134C4⋊C4×D61—21no—
135C4⋊C4×D61—21no—
136C4⋊C4×D61—21no—
137C4⋊C4×D61—21no—
138C4⋊C4×D61C2311yescharacteristic
139C4⋊C4×D61C2311yescharacteristic
140C22⋊C4×D61—21no—
141C22⋊C4×D61—21no—
142C22⋊C4×D61—21no—
143C22⋊C4×D61—21no—
144C22⋊C4×D61—21no—
145C2×C4×Dic61C2×C411yescharacteristic
146C2×C4×Dic61D411yescharacteristic
147C2×C4×Dic61D411yescharacteristic
148C42×D61—21no—
149C42×D61C2×C411yescharacteristic
150C42×D61C2×C411yescharacteristic
151C42×D61D411yescharacteristic
152C42×D61D411yescharacteristic
153C42×D61D411yescharacteristic
154C42×D61D411yescharacteristic
155C42×D61C2311yescharacteristic
156C42×D61C2311yescharacteristic
157#126×C61—21no—
158#125×C61C2×C411yescharacteristic
159#124×C61C2×C411yescharacteristic
160#123×C61—21no—
161C22⋊Q8×C61C2×C411yescharacteristic
162#121×C61C2×C411yescharacteristic
163C4×Q8×C61C2×C411yescharacteristic
164C4×D4×C61—21no—
165C4×D4×C61C2×C411yescharacteristic
166#117×C61—21no—
167C2×C42×C61C2×C411yescharacteristic
168C23×D61—21no—
169C23×D61C2×D411yescharacteristic
170C22×#6923—24no—
171C2×Q8×C61C22×C411yescharacteristic
172C2×D4×C61—21no—
173C2×D4×C61C22×C411yescharacteristic
174C22×C4×C61—21no—
175C22×C4×C61C22⋊C411yescharacteristic
176C22×C4×C61C22⋊C411yescharacteristic
177C22×C4×C61C22×C411yescharacteristic
178C2×C22⋊D61—21no—
179C2×C22⋊D61—21no—
180C2×C22⋊D61—21no—
181C22×Dic61—21no—
182C22×Dic61C22⋊C411yescharacteristic
183C22×Dic61C22⋊C411yescharacteristic
184C22×Dic61C2×D411yescharacteristic
185Q8×D61—24no—
186D4×D61—24no—
187D4×D61—44no—
188C2×D244—21no—
189C2×D244C22×C411yescharacteristic
190C2×C4×D61—22no—
191C2×C4×D61—22no—
192C2×C4×D61—24no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—42no—
199C2×C4×D61—42no—
200C2×C4×D61—42no—
201C2×C4×D61C22⋊C411yescharacteristic
202C2×C4×D61C22⋊C411yescharacteristic
203C2×C4×D61C22⋊C411yescharacteristic
204C2×C4×D61C22⋊C411yescharacteristic
205C2×C4×D61C22×C411yescharacteristic
206C2×C4×D61C2×D411yescharacteristic
207C2×C4×D61C2×D411yescharacteristic
208C2×C4×D61C2×D411yescharacteristic
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61C2×D411yescharacteristic
211C2×C4×D61C2×D411yescharacteristic
212C2×C4×D61C2411yescharacteristic
213C2×Dic122—21no—
214C2×Dic122C22×C411yescharacteristic
215C22⋊#6923—44no—
216#11758217—28no—
217C2×#92420—24no—
218C4⋊#6923—24no—
219C4⋊#6923—24no—
220C4⋊#6923—44no—
221C4⋊#6923—44no—
222C4×#6923—44no—
223#11758213—28no—
224D61⋊C8—24no—
225D61⋊C8#4118yes—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61C22×C411yescharacteristic
231C4⋊C4×C61C22×C411yescharacteristic
232C22⋊C4×C61—21no—
233C22⋊C4×C61—21no—
234C22⋊C4×C61—21no—
235C22⋊C4×C61—21no—
236C22⋊C4×C61—21no—
237C42×C61—21no—
238C42×C61C22⋊C411yescharacteristic
239C42×C61C22⋊C411yescharacteristic
240C42×C61C22×C411yescharacteristic
241C42×C61C22×C411yescharacteristic
242C22⋊Dic61—21no—
243C22⋊Dic61—21no—
244C22⋊Dic61—21no—
245C22⋊Dic61—21no—
246C22⋊Dic61—21no—
247#11758198—21no—
248#11758198—21no—
249#11758198—21no—
250#11758198—21no—
251#11758198—21no—
252#11758198—21no—
253#11758198—21no—
254#11758198—21no—
255#11758198—21no—
256#11758198—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61C22×C411yescharacteristic
262C4⋊Dic61C22×C411yescharacteristic
263#11758196—21no—
264#11758196—21no—
265#11758196—21no—
266#11758196—21no—
267#11758196—21no—
268#11758196—21no—
269#11758196—21no—
270#11758196—21no—
271#11758196—21no—
272#11758196—21no—
273C4×Dic61—21no—
274C4×Dic61—21no—
275C4×Dic61—21no—
276C4×Dic61C22⋊C411yescharacteristic
277C4×Dic61C22⋊C411yescharacteristic
278C4×Dic61C22⋊C411yescharacteristic
279C4×Dic61C22⋊C411yescharacteristic
280C4×Dic61C22⋊C411yescharacteristic
281C4×Dic61C22⋊C411yescharacteristic
282C4×Dic61C22×C411yescharacteristic
283C4×Dic61C22×C411yescharacteristic
284C4×Dic61C2×D411yescharacteristic
285C4×Dic61C2×D411yescharacteristic
286C4×Dic61C2×D411yescharacteristic
287C4×Dic61C2×D411yescharacteristic
288C23×C61—21no—
289C23×C61C2×C22⋊C411yescharacteristic
290C22×D61—22no—
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—22no—
294C22×D61—21no—
295C22×D61—42no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61—42no—
299C22×D61C2×C22⋊C411yescharacteristic
300C22×D61C22×D411yescharacteristic
301C2×#6923—44no—
302C2×#6923—44no—
303C2×#6923—44no—
304Q8×C61—22no—
305D4×C61—22no—
306D4×C61—42no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—41no—
313C2×C4×C61—42no—
314C2×C4×C61C2×C22⋊C411yescharacteristic
315C2×C4×C61C2×C22⋊C411yescharacteristic
316C2×C4×C61C2×C22⋊C411yescharacteristic
317C2×C4×C61C2×C22⋊C411yescharacteristic
318C2×C4×C61C2×C22⋊C411yescharacteristic
319C2×C4×C61C23×C411yescharacteristic
320C22⋊D61—42no—
321C22⋊D61—42no—
322C22⋊D61—42no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—41no—
329C2×Dic61—42no—
330C2×Dic61C2×C22⋊C411yescharacteristic
331C2×Dic61C2×C22⋊C411yescharacteristic
332C2×Dic61C2×C22⋊C411yescharacteristic
333C2×Dic61C2×C22⋊C411yescharacteristic
334C2×Dic61C2×C22⋊C411yescharacteristic
335C2×Dic61C22×D411yescharacteristic
336D244—22no—
337D244—42no—
338C4×D61—22no—
339C4×D61—21no—
340C4×D61—21no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—41no—
348C4×D61—41no—
349C4×D61—42no—
350C4×D61—41no—
351C4×D61—41no—
352C4×D61—42no—
353C4×D61—42no—
354C4×D61—42no—
355C4×D61AGL(1,ℤ/8)12yes—
356C4×D61#13712yes—
357C4×D61C2×#4114yes—
358Dic122—22no—
359Dic122—42no—
360#92420—28no—
361#21403—611nomaximal, Sylow
362C22×C61—21no—
363C22×C61—21no—
364C22×C61—21no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61C22×C22⋊C411yescharacteristic
369C2×D61—21no—
370C2×D61—21no—
371C2×D61—21no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—41no—
375C2×D61—41no—
376C2×D61—41no—
377C2×D61—82no—
378C2×D61—82no—
379C2×D61#53212yes—
380C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
381C2×D61C2×#13711yescharacteristic
382C2×D61#57512yes—
383#6923—84no—
384C4×C61—21no—
385C4×C61—21no—
386C4×C61—21no—
387C4×C61—21no—
388C4×C61—41no—
389C4×C61—41no—
390C4×C61—41no—
391C4×C61#41712yes—
392C4×C61C4×#4112yes—
393Dic61—21no—
394Dic61—21no—
395Dic61—21no—
396Dic61—21no—
397Dic61—41no—
398Dic61—41no—
399Dic61—41no—
400Dic61#41712yes—
401Dic61#52512yes—
402C2×#529—611no—
403C2×C4×M16—611no—
404#2285—611no—
405#1992—612no—
406#1959—612no—
407#1895—612no—
408#1894—612no—
409C4×#103—612no—
410C4×#102—612no—
411C2×C61—41no—
412C2×C61—81no—
413C2×C61#229711yescharacteristic
414C2×C61C2×#41711yescharacteristic
415C2×C61#289611yescharacteristic
416D61—41no—
417D61—81no—
418D61#317112yes—
419D61#317212yes—
420C22×M16—612no—
421#529—611no—
422#529—611no—
423#529—611no—
424#529—611no—
425#529—611no—
426#529—611no—
427#529—611no—
428#529—1221no—
429#529—1221no—
430#529—1221no—
431#529—1221no—
432#529#692311yescharacteristic, complemented
433C2×#126—1221no—
434C2×#125—611no—
435C2×#124—611no—
436C2×#123—1221no—
437C2×C22⋊Q8—611no—
438C2×#121—611no—
439C2×C4×Q8—611no—
440C2×C4×D4—611no—
441C2×C4×D4—1221no—
442C2×#117—1221no—
443C2×#117—1221no—
444C22×C42—611no—
445C2×#103—614no—
446C2×#102—614no—
447C4×M16—1221no—
448C4×M16—1221no—
449C4×M16—1221no—
450C4×M16—1221no—
451C2×#97—612no—
452C2×C4×C8—612no—
453#384—612no—
454#382—1221no—
455#380—612no—
456#380—1221no—
457C4×C4⋊C4—612no—
458C4×C4⋊C4—1221no—
459#340—614no—
460#340—614no—
461C61#2140311yescharacteristic, complemented, Sylow
462C22×Q8—611no—
463C22×D4—611no—
464C22×D4—1221no—
465C23×C4—611no—
466C23×C4—611no—
467C23×C4—611no—
468C23×C4—1221no—
469C2×M16—1228no—
470C2×M16—1222no—
471C2×M16—1222no—
472C22×C8—614no—
473#126—21no—
474#126—1221no—
475#126—1221no—
476#126—1221no—
477#126—1221no—
478#126—1221no—
479#126—1221no—
480#126—1221no—
481#125—611no—
482#125—611no—
483#125—611no—
484#125—1221no—
485#125—1221no—
486#125C2×#692311yescharacteristic
487#124—611no—
488#124—611no—
489#124—611no—
490#124—1221no—
491#124—1221no—
492#124C2×#692311yescharacteristic
493#123—21no—
494#123—1221no—
495#123—1221no—
496#123—1221no—
497#123—1221no—
498#123—1221no—
499#123—1221no—
500#123—1221no—
501C22⋊Q8—611no—
502C22⋊Q8—611no—
503C22⋊Q8—611no—
504C22⋊Q8—1221no—
505C22⋊Q8—1221no—
506C22⋊Q8C2×#692311yescharacteristic
507#121—611no—
508#121—611no—
509#121—611no—
510#121—1221no—
511#121—1221no—
512#121C2×#692311yescharacteristic
513C4×Q8—611no—
514C4×Q8—611no—
515C4×Q8—611no—
516C4×Q8—1221no—
517C4×Q8—1221no—
518C4×Q8C2×#692311yescharacteristic
519C4×D4—21no—
520C4×D4—611no—
521C4×D4—611no—
522C4×D4—611no—
523C4×D4—1221no—
524C4×D4—1221no—
525C4×D4—1221no—
526C4×D4—1221no—
527C4×D4—1221no—
528C4×D4—1221no—
529C4×D4—1221no—
530C4×D4—1221no—
531C4×D4—1221no—
532C4×D4C2×#692311yescharacteristic
533#117—21no—
534#117—1221no—
535#117—1221no—
536#117—1221no—
537#117—1221no—
538#117—1221no—
539#117—1221no—
540#117—1221no—
541#117—2444no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—611no—
544C2×C4⋊C4—614no—
545C2×C4⋊C4—1221no—
546C2×C4⋊C4—1221no—
547C2×C4⋊C4—1221no—
548C2×C4⋊C4—1221no—
549C2×C4⋊C4—1222no—
550C2×C4⋊C4—1222no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C22⋊C4—1222no—
557C2×C42—611no—
558C2×C42—611no—
559C2×C42—611no—
560C2×C42—611no—
561C2×C42—611no—
562C2×C42—611no—
563C2×C42—611no—
564C2×C42—611no—
565C2×C42—611no—
566C2×C42—611no—
567C2×C42—611no—
568C2×C42—1221no—
569C2×C42—1222no—
570C2×C42C2×#692311yescharacteristic
571#103—1228no—
572#102—1228no—
573#97—1222no—
574#97—1222no—
575C4×C8—1222no—
576C4×C8—1222no—
577#95—1222no—
578#95—1222no—
579C24—611no—
580C24—1221no—
581C2×Q8—611no—
582C2×Q8—1221no—
583C2×Q8—1224no—
584C2×Q8C22×#692311yescharacteristic
585C2×D4—21no—
586C2×D4—611no—
587C2×D4—1221no—
588C2×D4—1224no—
589C2×D4—1221no—
590C2×D4—1221no—
591C2×D4—1221no—
592C2×D4—2444no—
593C2×D4C22×#692311yescharacteristic
594C22×C4—21no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—1222no—
611C22×C4—1224no—
612C22×C4—1222no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1224no—
620C22×C4—2442no—
621C22×C4—2442no—
622C22×C4—2442no—
623C22×C4C22⋊#692311yescharacteristic
624C22×C4C22⋊#692311yescharacteristic
625C22×C4C22×#692311yescharacteristic
626M16—1228no—
627M16—1228no—
628C2×C8—618no—
629C2×C8—1224no—
630C2×C8—1224no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—611no—
636C4⋊C4—611no—
637C4⋊C4—1221no—
638C4⋊C4—1221no—
639C4⋊C4—1221no—
640C4⋊C4—1221no—
641C4⋊C4—1221no—
642C4⋊C4—1221no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—1221no—
647C4⋊C4—1224no—
648C4⋊C4—1224no—
649C4⋊C4—1221no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—2444no—
654C4⋊C4—2444no—
655C4⋊C4C22×#692311yescharacteristic
656C4⋊C4C22×#692311yescharacteristic
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—1221no—
663C22⋊C4—1221no—
664C22⋊C4—1221no—
665C22⋊C4—1221no—
666C22⋊C4—1221no—
667C22⋊C4—1221no—
668C22⋊C4—1221no—
669C22⋊C4—1221no—
670C22⋊C4—1221no—
671C22⋊C4—1221no—
672C22⋊C4—1221no—
673C22⋊C4—1221no—
674C22⋊C4—1221no—
675C22⋊C4—1221no—
676C22⋊C4—1221no—
677C22⋊C4—2444no—
678C42—21no—
679C42—611no—
680C42—611no—
681C42—611no—
682C42—611no—
683C42—611no—
684C42—611no—
685C42—611no—
686C42—611no—
687C42—611no—
688C42—611no—
689C42—611no—
690C42—611no—
691C42—1221no—
692C42—1221no—
693C42—1221no—
694C42—2444no—
695C42C22⋊#692311yescharacteristic
696C42C22⋊#692311yescharacteristic
697C42C22×#692311yescharacteristic
698C42C22×#692311yescharacteristic
699C23—21no—
700C23—611no—
701C23—611no—
702C23—1221no—
703C23—1222no—
704C23—1221no—
705C23—1222no—
706C23—1221no—
707C23—2441no—
708C23—2441no—
709C23—2442no—
710C23—2442no—
711C23C2×C22⋊#692311yescharacteristic
712Q8—22no—
713Q8—1222no—
714Q8—2442no—
715D4—22no—
716D4—42no—
717D4—1222no—
718D4—2442no—
719D4—2442no—
720D4—2442no—
721D4—2442no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—611no—
730C2×C4—611no—
731C2×C4—612no—
732C2×C4—612no—
733C2×C4—614no—
734C2×C4—611no—
735C2×C4—611no—
736C2×C4—611no—
737C2×C4—611no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1221no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1221no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1221no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2442no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2442no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4—2441no—
761C2×C4—2444no—
762C2×C4—2444no—
763C2×C4—2444no—
764C2×C4—2442no—
765C2×C4C2×C22⋊#692311yescharacteristic
766C2×C4C2×C22⋊#692311yescharacteristic
767C2×C4C2×C22⋊#692311yescharacteristic
768C2×C4C2×C22⋊#692311yescharacteristic
769C2×C4C2×C22⋊#692311yescharacteristic
770C2×C4C23×#692311yescharacteristic
771C8—1228no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—612no—
779C22—611no—
780C22—611no—
781C22—612no—
782C22—1221no—
783C22—1221no—
784C22—1221no—
785C22—4882no—
786C22—4882no—
787C22—2442no—
788C22—2442no—
789C22—2441no—
790C22—2441no—
791C22—2441no—
792C22C22×C22⋊#692311yescharacteristic
793C4—21no—
794C4—21no—
795C4—21no—
796C4—21no—
797C4—41no—
798C4—41no—
799C4—41no—
800C4—612no—
801C4—612no—
802C4—1221no—
803C4—1221no—
804C4—1221no—
805C4—1221no—
806C4—4884no—
807C4—2441no—
808C4—2441no—
809C4—2441no—
810C4#1684075312yes—
811C4#41×#692312yes—
812C2—41no—
813C2—81no—
814C2—612no—
815C2—612no—
816C2—4881no—
817C2—2441no—
818C2#2146228011yescharacteristic
819C2C2×#1684075311yescharacteristic
820C2#2146243911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#529C4
socleC22×C61C22×C22⋊C4
prime radical#121×D61C22
cosocleC2×C4×D61C24
hypercenter#529#6923
hypocenterC61#21403
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C4×D61⋊M16C2semidirect
2. #21462268C2semidirect
3. #21462002C2semidirect
4. #21461949C2semidirect
6. #21461834C2semidirect
7. C4×#14519840C2semidirect
8. C4×#14519839C2semidirect
28. #16840299C4semidirect
29. #16840298C4semidirect
30. #16840297C4semidirect
31. #16840296C4semidirect
33. #16840294C4semidirect
34. #16840293C4semidirect
36. #16840291C4semidirect
50. C61×#529C4semidirect
432. #529#6923semidirect
461. C61#21403semidirect

Maximal subgroups

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

subgroupindex
C4×D61⋊M162
#214622682
#214620022
#214619492
#214618352
#214618342
C4×#145198402
C4×#145198392
#529×D612
#2140361