Finite Group Databasebeta

← #29685696

Subgroups — #29685696

Order 15616.

1552 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758224C211yesmaximal, characteristic, complemented
2C2×#16839904C211yesmaximal, characteristic
3C2×#16839862C211yesmaximal, characteristic, complemented
4C4×#14519748C211yesmaximal, characteristic, complemented
5#21446171C211yesmaximal, characteristic, complemented
6#21446169C211yesmaximal, characteristic, complemented
7#21446138C211yesmaximal, characteristic, complemented
8#21446084C211yesmaximal, characteristic, complemented
9#21446064C211yesmaximal, characteristic, complemented
10#21446017C211yesmaximal, characteristic, complemented
11#21445756C211yesmaximal, characteristic, complemented
12#21445650C211yesmaximal, characteristic, complemented
13#21445644C211yesmaximal, characteristic, complemented
14#21445582C211yesmaximal, characteristic, complemented
15C2×C61×#442C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C2×#14519748C2211yescharacteristic
19C4×#11758224—24no—
20C4×#11758224—24no—
21C2×C4×Dic122C2211yescharacteristic
22C2×#14519742C2211yescharacteristic
23C2×D4×Dic61C2211yescharacteristic
24C2×C4×C22⋊D61—21no—
25C2×C4×C22⋊D61—21no—
26C2×#14519737—21no—
27C2×#14519735C2211yescharacteristic
28C2×#14519733—21no—
29C22×C4×Dic61—21no—
30C2×C42×D61C2211yescharacteristic
31#16839904C418yescomplemented
32#16839862—24no—
33C2×#14519710C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519702C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41C2×#14519689C2211yescharacteristic
42C2×#14519688C2211yescharacteristic
43#16839665C2211yescharacteristic
44#16839658C2211yescharacteristic
45#16839650—21no—
46#16839638—21no—
47#16839619C2211yescharacteristic
48C4×C4⋊Dic61C2211yescharacteristic
49C4×C22⋊Dic61—21no—
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C22×D8×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C2×C4×D4×C61C2211yescharacteristic
59C61×#442—24no—
60C2×#106×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C2×#97×C61C2211yescharacteristic
64C2×#11758224—22no—
65C2×#11758224—22no—
66C2×#11758224—22no—
67C2×#11758224—22no—
68C2×#11758224—22no—
69C2×#11758224C2×C414yescomplemented
70C22×Dic122C2311yescharacteristic
71C22×C22⋊D61—21no—
72C22×C22⋊D61—21no—
73C23×Dic61—21no—
74C23×Dic61—21no—
75C22×C4×D61D411yescharacteristic
76C22×C4×D61D411yescharacteristic
77C22×C4×D61C2311yescharacteristic
78C2×#11758200—22no—
79C2×#11758200—22no—
80C2×#11758200C2×C414yescomplemented
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83#14519748—22no—
84#14519748C2×C414yescomplemented
85C4×Dic122—22no—
86C4×Dic122D414yescomplemented
87#14519742—22no—
88#14519742—22no—
89D4×Dic61—22no—
90D4×Dic61—22no—
91C4×C22⋊D61—28no—
92C4×C22⋊D61—44no—
93#14519737—28no—
94#14519735—22no—
95#14519735—22no—
96#14519733—28no—
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×C22⋊Dic61—21no—
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×C4×Dic61—28no—
110C2×C4×Dic61—21no—
111C2×C4×Dic61—21no—
112C2×C4×Dic61—21no—
113C2×C4×Dic61—21no—
114C2×C4×Dic61D411yescharacteristic
115C2×C4×Dic61D411yescharacteristic
116C2×C4×Dic61C2311yescharacteristic
117C42×D61—22no—
118C42×D61—22no—
119#14519710—22no—
120#14519702—22no—
121#14519702C2×C414yescomplemented
122#14519700—22no—
123#14519698—22no—
124#14519698—22no—
125#14519698C2×C414yescomplemented
126#14519689—22no—
127#14519689C2×C414yescomplemented
128#14519688—22no—
129#14519684—21no—
130#14519684—21no—
131#14519684—21no—
132C22×D4×C61C2311yescharacteristic
133C22×D4×C61C2311yescharacteristic
134C23×C4×C61—21no—
135C23×C4×C61—21no—
136C2×D8×C61—22no—
137C2×D8×C61—22no—
138C2×D8×C61C2×C414yescomplemented
139C22×C8×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141C4×D4×C61—22no—
142C4×D4×C61—22no—
143C4×D4×C61—22no—
144C4×D4×C61D414yescomplemented
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C22⋊C4×C61—21no—
148C2×C22⋊C4×C61—21no—
149C2×C42×C61C2311yescharacteristic
150#106×C61—22no—
151#102×C61—22no—
152#102×C61—22no—
153#97×C61—22no—
154C24×C61—21no—
155C24×C61—21no—
156C23×D61C2×D411yescharacteristic
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61C22×C412yes—
166C2×D4×C61C22×C412yes—
167C2×D4×C61C2×D412yes—
168C2×D4×C61#4112yes—
169C22×C4×C61—21no—
170C22×C4×C61—24no—
171C22×C4×C61—21no—
172C22×C4×C61—42no—
173C22×C4×C61—42no—
174C22×C4×C61—42no—
175C22×C4×C61—42no—
176C22×C4×C61—42no—
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2411yescharacteristic
180C2×C22⋊D61—24no—
181C2×C22⋊D61—24no—
182C2×C22⋊D61—24no—
183C2×C22⋊D61—24no—
184C2×C22⋊D61—42no—
185C2×C22⋊D61—42no—
186C22×Dic61—24no—
187C22×Dic61—24no—
188C22×Dic61—21no—
189C22×Dic61—24no—
190C22×Dic61—24no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—42no—
195C22×Dic61—42no—
196C22×Dic61C2×D411yescharacteristic
197C22×Dic61C2×D411yescharacteristic
198C22×Dic61C2×D411yescharacteristic
199#11758224—28no—
200#11758224—28no—
201#11758224—28no—
202#11758224—28no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—22no—
208C2×C4×D61—22no—
209C2×C4×D61—22no—
210C2×C4×D61—41no—
211C2×C4×D61—41no—
212C2×C4×D61—41no—
213C2×C4×D61C22×C412yes—
214C2×C4×D61#4112yes—
215C2×Dic122—21no—
216C2×Dic122—21no—
217C2×Dic122—21no—
218C2×Dic122C22×C412yes—
219C2×Dic122C2×D412yes—
220C2×Dic122#4112yes—
221D8×C61—28no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61—21no—
227C2×C8×C61C22×C412yes—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61C2×D412yes—
232C22⋊C4×C61—24no—
233C22⋊C4×C61—42no—
234C42×C61C2×D412yes—
235C42×C61C2×D412yes—
236C22⋊Dic61—24no—
237C22⋊Dic61—24no—
238C22⋊Dic61—42no—
239C22⋊Dic61—42no—
240#11758200—28no—
241#11758198—24no—
242#11758198—42no—
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61C22×C412yes—
248C4⋊Dic61C2×D412yes—
249#11758196—24no—
250#11758196—24no—
251#11758196—42no—
252C4×Dic61—24no—
253C4×Dic61—24no—
254C4×Dic61—22no—
255C4×Dic61—22no—
256C4×Dic61—24no—
257C4×Dic61—21no—
258C4×Dic61—21no—
259C4×Dic61—42no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418C22×C412yes—
266C23×C61—22no—
267C23×C61—22no—
268C23×C61—22no—
269C23×C61—22no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61C22×D411yescharacteristic
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61C4×D412yes—
288D4×C61—22no—
289D4×C61—22no—
290D4×C61—22no—
291D4×C61—22no—
292D4×C61—22no—
293D4×C61—41no—
294D4×C61—41no—
295D4×C61C4×D414yescomplemented
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—22no—
301C2×C4×C61—48no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—84no—
308C2×C4×C61#12012yes—
309C2×C4×C61#12012yes—
310C2×C4×C61C23×C411yescharacteristic
311C2×C4×C61C22×D411yescharacteristic
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C2×#4111yescharacteristic
314C2×C4×C61C2×#4111yescharacteristic
315C2×C4×C61C2×#4111yescharacteristic
316C22⋊D61—216no—
317C22⋊D61—48no—
318C2×Dic61—216no—
319C2×Dic61—22no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—22no—
327C2×Dic61—21no—
328C2×Dic61—22no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—48no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61C4×D412yes—
340C2×Dic61AGL(1,ℤ/8)12yes—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—44no—
346C4×D61—44no—
347Dic122—22no—
348Dic122—22no—
349Dic122—22no—
350Dic122C4×D414yescomplemented
351C8×C61—22no—
352C8×C61—41no—
353#92418—22no—
354#92418—41no—
355#21456—611nomaximal, Sylow
356C22×C61—24no—
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—81no—
367C22×C61—81no—
368C22×C61—81no—
369C22×C61—81no—
370C22×C61C2×C4×D411yescharacteristic
371C22×C61C2×#12011yescharacteristic
372C22×C61#52511yescharacteristic
373C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
374C22×C61#57511yescharacteristic
375C22×C61#57511yescharacteristic
376C22×C61#57511yescharacteristic
377C2×D61—22no—
378C2×D61—22no—
379C2×D61—22no—
380C2×D61—41no—
381C2×D61—41no—
382C2×D61—41no—
383C2×D61—41no—
384C4×C61—22no—
385C4×C61—22no—
386C4×C61—42no—
387C4×C61—81no—
388C4×C61C2×C4×D411yescharacteristic
389C4×C61C2×C4×D411yescharacteristic
390C4×C61#52511yescharacteristic
391C4×C61#52511yescharacteristic
392Dic61—22no—
393Dic61—24no—
394Dic61—22no—
395Dic61—42no—
396Dic61—41no—
397Dic61—42no—
398Dic61—81no—
399C2×C4×#41—611no—
400C2×#449—611no—
401C2×#442D6111yescharacteristic, complemented
402C2×#440—611no—
403C4×#121—611no—
404#1880—611no—
405#1879—611no—
406#1875—611no—
407#1865—611no—
408#1862—611no—
409#1854—611no—
410#1788—611no—
411#1763—611no—
412#1762—611no—
413#1749—611no—
414C2×C61—44no—
415C2×C61—82no—
416C2×C61C4×#12011yescharacteristic
417C2×C61#294311yescharacteristic
418C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
419C2×C61#300511yescharacteristic
420C2×C61#300611yescharacteristic
421C2×C61#311111yescharacteristic
422C2×C61#311511yescharacteristic
423D61—42no—
424C22×#41—611no—
425C22×SD16—611no—
426C22×D8C2×D6111yescharacteristic
427C2×#121—611no—
428C4×#41—1224no—
429C4×#41—1224no—
430C2×C4×Q8—611no—
431C2×C4×Q8—611no—
432C2×C4×D4—611no—
433C2×C4×D4—1221no—
434C2×C4×D4—1221no—
435C2×C4×D4—1221no—
436C2×C4×D4C2×D6111yescharacteristic
437C2×C4×D4C2×D6111yescharacteristic
438C2×#117—611no—
439C2×#117—1221no—
440C22×C42—611no—
441C22×C42—1221no—
442#449—618no—
443#442—24no—
444#440—1224no—
445C2×#107—611no—
446C2×#106C2×D6111yescharacteristic
447C2×#103—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#102—611no—
451C2×#102—611no—
452C2×#102—611no—
453C2×#102C2×D6111yescharacteristic
454C2×#102C2×D6111yescharacteristic
455C2×C22⋊C8—611no—
456C2×C22⋊C8—611no—
457C2×#97—611no—
458C2×#97C2×D6111yescharacteristic
459#390—611no—
460#389—611no—
461#388—1221no—
462#386—1221no—
463#380—611no—
464C4×C4⋊C4—611no—
465C4×C22⋊C4—1221no—
466#340—611no—
467#340—611no—
468#340—611no—
469#340—611no—
470#336—611no—
471#336—611no—
472C61#2145611yescharacteristic, complemented, Sylow
473C2×#41—614no—
474C2×#41—1222no—
475C2×#41—1222no—
476C2×#41—1222no—
477C2×#41—1222no—
478C2×#41—1222no—
479C22×Q8—611no—
480C22×D4—1221no—
481C22×D4—1221no—
482C22×D4C22×D6111yescharacteristic
483C22×D4C22×D6111yescharacteristic
484C23×C4—21no—
485C23×C4—21no—
486C23×C4—611no—
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—1221no—
490C23×C4—1221no—
491C2×SD16—614no—
492C2×SD16—1222no—
493C2×SD16—1222no—
494C2×D8—22no—
495C2×D8—22no—
496C2×D8C4×D6114yescomplemented
497C22×C8—611no—
498C22×C8—611no—
499C22×C8C22×D6111yescharacteristic
500C22×C8C22×D6111yescharacteristic
501#121—614no—
502#121—1222no—
503C4×Q8—614no—
504C4×Q8—1222no—
505C4×Q8—1222no—
506C4×Q8—1222no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—1228no—
511C4×D4—1222no—
512C4×D4—1228no—
513C4×D4—1222no—
514C4×D4—2444no—
515C4×D4C22⋊D6114yescomplemented
516#117—1228no—
517#117—1222no—
518#117—1222no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4C22×D6111yescharacteristic
526C2×C4⋊C4C22×D6111yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C42—611no—
536C2×C42—611no—
537C2×C42—611no—
538C2×C42—1221no—
539C2×C42—1221no—
540C2×C42—1228no—
541C2×C42—1221no—
542C2×C42—1222no—
543C2×C42—1222no—
544C2×C42—1221no—
545C2×C42C22×D6111yescharacteristic
546#107—1222no—
547#106—22no—
548#103—614no—
549#103—1222no—
550#103—1222no—
551#102—22no—
552#102—22no—
553#102—614no—
554#102—1222no—
555#102—1222no—
556C22⋊C8—614no—
557C22⋊C8—1222no—
558#97—22no—
559#97—1222no—
560#95—1221no—
561#95—1221no—
562#95—1221no—
563C24—21no—
564C24—21no—
565C24—611no—
566#41—1228no—
567#41—1228no—
568#41—1228no—
569#41—1228no—
570C2×Q8—612no—
571C2×Q8—612no—
572C2×Q8—612no—
573C2×Q8—1221no—
574C2×Q8—1221no—
575C2×Q8—1221no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—1224no—
585C2×D4—1224no—
586C2×D4—1224no—
587C2×D4—1224no—
588C2×D4—2442no—
589C2×D4—2442no—
590C2×D4C2×C4×D6112yes—
591C2×D4C2×C4×D6112yes—
592C2×D4#1175822212yes—
593C2×D4C2×C22⋊D6112yes—
594C22×C4—21no—
595C22×C4—24no—
596C22×C4—21no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—612no—
605C22×C4—612no—
606C22×C4—611no—
607C22×C4—1222no—
608C22×C4—1224no—
609C22×C4—1224no—
610C22×C4—1224no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1224no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4—1221no—
622C22×C4—2441no—
623C22×C4—2441no—
624C22×C4—2441no—
625C22×C4—2442no—
626C22×C4—2442no—
627C22×C4D4×D6111yescharacteristic
628C22×C4D4×D6111yescharacteristic
629C22×C4C23×D6111yescharacteristic
630SD16—1228no—
631D8—28no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—612no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8C2×C4×D6112yes—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—612no—
648C4⋊C4—612no—
649C4⋊C4—1224no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4—1224no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—2442no—
656C4⋊C4C2×C22⋊D6112yes—
657C22⋊C4—24no—
658C22⋊C4—42no—
659C22⋊C4—1224no—
660C22⋊C4—1224no—
661C22⋊C4—1224no—
662C22⋊C4—2442no—
663C22⋊C4—2442no—
664C22⋊C4—2442no—
665C42—1224no—
666C42—1224no—
667C42—1221no—
668C42—1221no—
669C42—1222no—
670C42—1222no—
671C42—1224no—
672C42—2442no—
673C42D4×D6112yes—
674C42C2×C22⋊D6112yes—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—612no—
690C23—1221no—
691C23—1221no—
692C23—1221no—
693C23—1221no—
694C23—1221no—
695C23—1221no—
696C23C2×D4×D6111yescharacteristic
697Q8—614no—
698Q8—1222no—
699Q8—1222no—
700Q8—1222no—
701D4—22no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—22no—
706D4—41no—
707D4—41no—
708D4—12216no—
709D4—2448no—
710D4C4×C22⋊D6114yescomplemented
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—48no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—84no—
723C2×C4—612no—
724C2×C4—612no—
725C2×C4—12216no—
726C2×C4—1222no—
727C2×C4—1221no—
728C2×C4—1221no—
729C2×C4—1222no—
730C2×C4—1221no—
731C2×C4—1222no—
732C2×C4—1221no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1221no—
740C2×C4—1221no—
741C2×C4—1221no—
742C2×C4—2444no—
743C2×C4—2444no—
744C2×C4—2448no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4#1451974512yes—
753C2×C4#1451974512yes—
754C2×C4C22×C4×D6111yescharacteristic
755C2×C4C2×D4×D6111yescharacteristic
756C2×C4C22×C22⋊D6111yescharacteristic
757C2×C4#41×D6111yescharacteristic
758C2×C4#41×D6111yescharacteristic
759C2×C4C2×#1175822211yescharacteristic
760C8—22no—
761C8—41no—
762C8—1222no—
763C8—2441no—
764C22—24no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—1222no—
779C22—1222no—
780C22—1222no—
781C22—2441no—
782C22—2441no—
783C22—2441no—
784C22—2441no—
785C22C4×D4×D6111yescharacteristic
786C22C2×#1451974511yescharacteristic
787C22#1684027111yescharacteristic
788C22AGL(1,ℤ/8)×D6111yescharacteristic
789C22#1684055811yescharacteristic
790C22#1684055811yescharacteristic
791C22#1684055811yescharacteristic
792C4—22no—
793C4—22no—
794C4—42no—
795C4—81no—
796C4—1222no—
797C4—1224no—
798C4—1222no—
799C4—4881no—
800C4—2442no—
801C4—2441no—
802C4—2442no—
803C4C4×D4×D6111yescharacteristic
804C4C2×C4×C22⋊D6111yescharacteristic
805C4#1684026911yescharacteristic
806C4#1684027111yescharacteristic
807C2—44no—
808C2—82no—
809C2—2442no—
810C2C4×#1451974511yescharacteristic
811C2#2145461611yescharacteristic
812C2#2145463011yescharacteristic
813C2#2145505811yescharacteristic
814C2#2145506711yescharacteristic
815C2#2145592411yescharacteristic
816C2#2145596611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#442C2
socleC23×C61C22×D4
prime radicalC2×#16839904C2
cosocleC22×C4×C61C24
hypercenterC2×#442D61
hypocenterC61#21456
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×C4×#11758224C2semidirect
3. C2×#16839862C2semidirect
4. C4×#14519748C2semidirect
5. #21446171C2semidirect
6. #21446169C2semidirect
7. #21446138C2semidirect
8. #21446084C2semidirect
9. #21446064C2semidirect
10. #21446017C2semidirect
11. #21445756C2semidirect
12. #21445650C2semidirect
13. #21445644C2semidirect
14. #21445582C2semidirect
15. C2×C61×#442C2semidirect
31. #16839904C4semidirect
69. C2×#11758224C2×C4semidirect
80. C2×#11758200C2×C4semidirect
84. #14519748C2×C4semidirect
86. C4×Dic122D4semidirect
121. #14519702C2×C4semidirect
125. #14519698C2×C4semidirect
127. #14519689C2×C4semidirect
138. C2×D8×C61C2×C4semidirect
144. C4×D4×C61D4semidirect
295. D4×C61C4×D4semidirect
350. Dic122C4×D4semidirect
401. C2×#442D61semidirect
472. C61#21456semidirect
496. C2×D8C4×D61semidirect
515. C4×D4C22⋊D61semidirect
710. D4C4×C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582242
C2×#168399042
C2×#168398622
C4×#145197482
#214461712
#214461692
#214461382
#214460842
#214460642
#214460172
#214457562
#214456502
#214456442
#214455822
C2×C61×#4422
#2145661