Finite Group Databasebeta

← #29685353

Subgroups — #29685353

Order 15616.

1678 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840272C211yesmaximal, characteristic
2#21448201C211yesmaximal, characteristic, complemented
3C4×C22⋊C4×D61C211yesmaximal, characteristic, complemented
4#21446804C211yesmaximal, characteristic, complemented
5#21446803C211yesmaximal, characteristic, complemented
6#21446656C211yesmaximal, characteristic, complemented
7#21446269C214yesmaximal, complemented
8#99×Dic61C214yesmaximal, complemented
9C61×#1964C211yesmaximal, characteristic, complemented
10C22×#11758224C411yescharacteristic, complemented
11C23×C4×D61C2211yescharacteristic
12#16840272—21no—
13#16840272—21no—
14#16840272—21no—
15#16840272—21no—
16#16840272—21no—
17#16840272—21no—
18#16840272—21no—
19#16840272—21no—
20C2×#14519759C412yescomplemented
21C2×#14519757C411yescharacteristic, complemented
22C2×#14519756C2211yescharacteristic
23C2×#14519748C411yescharacteristic, complemented
24C2×#14519745C2212yes—
25C2×D4×Dic61C2212yes—
26C2×#14519737C412yescomplemented
27C2×#14519735—21no—
28C2×#14519735C411yescharacteristic, complemented
29C2×C22⋊C4×D61C2212yes—
30C2×C42×D61—21no—
31C2×#14519692C2214yes—
32#16839624—21no—
33#16839622C2211yescharacteristic
34#16839619—21no—
35#16839617C2212yes—
36C22⋊C4×Dic61C2212yes—
37C22⋊C4×Dic61C2212yes—
38C4×#11758198—21no—
39C4×C22⋊Dic61C2211yescharacteristic
40#16839609—21no—
41#16839609—21no—
42#95×D61—21no—
43#16839528C2214yes—
44#16839528C2214yes—
45C2×#121×C61C2211yescharacteristic
46C2×#99×C61C2214yes—
47C61×#380C2211yescharacteristic
48C4×C22⋊C4×C61C2211yescharacteristic
49C24×D61C2311yescharacteristic
50C2×#11758224—21no—
51C2×#11758224—21no—
52C2×#11758224—21no—
53C2×#11758224—21no—
54C2×#11758224—44no—
55C22×Dic122C2×C411yescharacteristic, complemented
56C22×C22⋊D61C2×C412yes—
57C22×C22⋊D61C2×C412yes—
58C23×Dic61C2×C412yescomplemented
59C23×Dic61C2311yescharacteristic
60C22×C4×D61—22no—
61C22×C4×D61—44no—
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61C2×C411yescharacteristic
65C22×C4×D61C2×C411yescharacteristic
66C22×C4×D61D411yescharacteristic
67C22×C4×D61D411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61D411yescharacteristic
73C22×C4×D61D411yescharacteristic
74#14519759—22no—
75#14519759—22no—
76#14519759—22no—
77#14519759—22no—
78#14519757—21no—
79#14519757—21no—
80#14519757—21no—
81#14519757—21no—
82#14519756—21no—
83#14519756—21no—
84#14519756—21no—
85#14519756—21no—
86#14519748—21no—
87#14519748—21no—
88#14519748—21no—
89#14519748—21no—
90#14519745—22no—
91#14519745—22no—
92#14519745—22no—
93#14519745—22no—
94D4×Dic61—22no—
95D4×Dic61—22no—
96D4×Dic61—22no—
97D4×Dic61—22no—
98#14519737—22no—
99#14519737—22no—
100#14519737—22no—
101#14519737—22no—
102#14519735—21no—
103#14519735—21no—
104#14519735—21no—
105#14519735—21no—
106#14519735—44no—
107C2×C4⋊Dic61—21no—
108C2×C4⋊Dic61C2×C411yescharacteristic, complemented
109C2×C4⋊Dic61C2×C412yescomplemented
110C2×#11758196C2×C412yescomplemented
111C2×C22⋊Dic61C2×C412yescomplemented
112C2×C22⋊Dic61C2312yes—
113C2×C22⋊Dic61C2312yes—
114C2×C22⋊Dic61C2312yes—
115C2×#11758198—22no—
116C2×#11758198—22no—
117C2×#11758198—22no—
118C2×#11758198C2×C412yes—
119C2×#11758198C2×C412yes—
120C22⋊C4×D61—24no—
121C22⋊C4×D61—24no—
122C2×C4×Dic61—21no—
123C2×C4×Dic61—22no—
124C2×C4×Dic61—22no—
125C2×C4×Dic61C2×C412yescomplemented
126C42×D61—44no—
127#14519692—28no—
128#14519684—21no—
129#14519684—21no—
130#14519684—22no—
131#14519684—22no—
132C22×D4×C61C2×C411yescharacteristic, complemented
133C22×D4×C61C2312yes—
134C23×C4×C61C2311yescharacteristic
135#121×C61—21no—
136#121×C61—21no—
137#121×C61—21no—
138#121×C61—21no—
139C2×C4⋊C4×C61—21no—
140C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
141C2×C22⋊C4×C61C2×C412yescomplemented
142C2×C22⋊C4×C61C2312yes—
143C2×C22⋊C4×C61C2312yes—
144C2×C42×C61—21no—
145#99×C61—28no—
146#95×C61—21no—
147#95×C61—21no—
148C24×C61C22×C412yes—
149C24×C61C2411yescharacteristic
150C23×D61—22no—
151C23×D61—22no—
152C23×D61—42no—
153C23×D61—42no—
154C23×D61C22×C411yescharacteristic
155C23×D61C22×C411yescharacteristic
156C23×D61C2×D411yescharacteristic
157C23×D61C2×D411yescharacteristic
158C23×D61C2×D411yescharacteristic
159C23×D61C2×D411yescharacteristic
160C2×D4×C61—22no—
161C2×D4×C61—22no—
162C2×D4×C61—24no—
163C2×D4×C61—24no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—42no—
167C22×C4×C61—22no—
168C22×C4×C61—22no—
169C22×C4×C61—42no—
170C22×C4×C61C22×C412yes—
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C22×C411yescharacteristic
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C2×C22⋊D61—22no—
178C2×C22⋊D61—22no—
179C2×C22⋊D61—22no—
180C2×C22⋊D61—22no—
181C2×C22⋊D61—44no—
182C2×C22⋊D61—44no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—42no—
188C22×Dic61—44no—
189C22×Dic61C22×C411yescharacteristic
190C22×Dic61C22×C412yes—
191C22×Dic61C22×C412yes—
192C22×Dic61C22×C411yescharacteristic
193C22×Dic61C2×D411yescharacteristic
194C22×Dic61C2×D411yescharacteristic
195C22×Dic61C2×D411yescharacteristic
196C22×Dic61C2×D411yescharacteristic
197#11758224—44no—
198#11758224—44no—
199#11758224—44no—
200#11758224—44no—
201C2×C4×D61—24no—
202C2×C4×D61—24no—
203C2×C4×D61—24no—
204C2×C4×D61—28no—
205C2×C4×D61—42no—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×C4×D61—42no—
209C2×C4×D61—42no—
210C2×C4×D61—42no—
211C2×C4×D61—42no—
212C2×C4×D61—42no—
213C2×C4×D61—42no—
214C2×C4×D61—44no—
215C2×C4×D61—44no—
216C2×C4×D61C22⋊C411yescharacteristic
217C2×C4×D61C22⋊C411yescharacteristic
218C2×C4×D61C22⋊C411yescharacteristic
219C2×C4×D61C22⋊C411yescharacteristic
220C2×C4×D61C22⋊C411yescharacteristic
221C2×C4×D61C22⋊C411yescharacteristic
222C2×C4×D61C22⋊C411yescharacteristic
223C2×C4×D61C22⋊C411yescharacteristic
224C2×C4×D61C22⋊C411yescharacteristic
225C2×C4×D61C22⋊C411yescharacteristic
226C2×C4×D61C22⋊C411yescharacteristic
227C2×C4×D61C22⋊C411yescharacteristic
228C2×C4×D61C22⋊C411yescharacteristic
229C2×C4×D61C22⋊C411yescharacteristic
230C2×C4×D61C22⋊C411yescharacteristic
231C2×C4×D61C22⋊C411yescharacteristic
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—42no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—42no—
238C22⋊C4×C61—22no—
239C22⋊C4×C61—22no—
240C22⋊C4×C61—22no—
241C22⋊C4×C61—24no—
242C22⋊C4×C61#4114yescomplemented
243C42×C61—42no—
244C22⋊Dic61—22no—
245C22⋊Dic61—22no—
246C22⋊Dic61—22no—
247C22⋊Dic61—22no—
248C22⋊Dic61—22no—
249C22⋊Dic61—24no—
250C22⋊Dic61#4114yescomplemented
251#11758198—28no—
252#11758198—22no—
253#11758198—22no—
254#11758198—22no—
255#11758198—22no—
256#11758198—44no—
257#11758198—44no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—22no—
261C4⋊Dic61—22no—
262C4⋊Dic61—42no—
263#11758196—22no—
264#11758196—22no—
265C4×Dic61—22no—
266C4×Dic61—22no—
267C4×Dic61—44no—
268C4×Dic61—44no—
269C4×Dic61—42no—
270C23×C61—22no—
271C23×C61—24no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61—42no—
275C23×C61—42no—
276C23×C61C23×C411yescharacteristic
277C23×C61C22×D411yescharacteristic
278C23×C61C22×D411yescharacteristic
279C23×C61C2×#4112yes—
280C23×C61C2×#4112yes—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—22no—
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61—41no—
300C22×D61—41no—
301C22×D61—48no—
302C22×D61—48no—
303C22×D61C2×C22⋊C411yescharacteristic
304C22×D61C2×C22⋊C411yescharacteristic
305C22×D61C2×C22⋊C411yescharacteristic
306C22×D61C2×C22⋊C411yescharacteristic
307D4×C61—42no—
308D4×C61—44no—
309D4×C61—42no—
310D4×C61—42no—
311D4×C61—42no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—24no—
317C2×C4×C61—24no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—42no—
322C2×C4×C61—42no—
323C2×C4×C61—42no—
324C2×C4×C61—42no—
325C2×C4×C61—42no—
326C2×C4×C61C2×C22⋊C411yescharacteristic
327C2×C4×C61C2×C22⋊C411yescharacteristic
328C2×C4×C61C2×C22⋊C411yescharacteristic
329C2×C4×C61C2×C22⋊C411yescharacteristic
330C22⋊D61—44no—
331C22⋊D61—44no—
332C22⋊D61—44no—
333C22⋊D61—44no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—24no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—44no—
344C2×Dic61—42no—
345C2×Dic61—42no—
346C2×Dic61—44no—
347C2×Dic61—42no—
348C2×Dic61—42no—
349C2×Dic61—42no—
350C2×Dic61—42no—
351C2×Dic61—42no—
352C2×Dic61C2×C22⋊C411yescharacteristic
353C2×Dic61C2×C22⋊C411yescharacteristic
354C2×Dic61C2×C22⋊C411yescharacteristic
355C2×Dic61C2×C22⋊C411yescharacteristic
356C4×D61—22no—
357C4×D61—22no—
358C4×D61—22no—
359C4×D61—22no—
360C4×D61—22no—
361C4×D61—22no—
362C4×D61—22no—
363C4×D61—22no—
364C4×D61—22no—
365C4×D61—41no—
366C4×D61—41no—
367C4×D61—41no—
368C4×D61—41no—
369C4×D61—41no—
370C4×D61—41no—
371C4×D61—416no—
372C4×D61#9914yescomplemented
373Dic122—42no—
374Dic122—42no—
375#21420—611nomaximal, Sylow
376C22×C61—21no—
377C22×C61—21no—
378C22×C61—21no—
379C22×C61—21no—
380C22×C61—21no—
381C22×C61—21no—
382C22×C61—42no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—42no—
387C22×C61—84no—
388C22×C61C22×C22⋊C411yescharacteristic
389C22×C61C4×#4112yes—
390C22×C61#52512yes—
391C22×C61#53211yescharacteristic
392C22×C61#53211yescharacteristic
393C2×D61—28no—
394C2×D61—21no—
395C2×D61—21no—
396C2×D61—21no—
397C2×D61—21no—
398C2×D61—21no—
399C2×D61—21no—
400C2×D61—21no—
401C2×D61—21no—
402C2×D61—21no—
403C2×D61—21no—
404C2×D61—42no—
405C2×D61—42no—
406C2×D61—44no—
407C2×D61—42no—
408C2×D61—42no—
409C2×D61—44no—
410C2×D61—44no—
411C2×D61C2×#9912yes—
412C2×D61#41012yes—
413C4×C61—21no—
414C4×C61—21no—
415C4×C61—21no—
416C4×C61—44no—
417C4×C61—42no—
418C4×C61—82no—
419C4×C61C2×#9912yes—
420Dic61—21no—
421Dic61—21no—
422Dic61—21no—
423Dic61—44no—
424Dic61—42no—
425Dic61—42no—
426Dic61—82no—
427Dic61C2×#9912yes—
428C2×#525—611no—
429#2280—611no—
430C2×C4×C22⋊C4—611no—
431#1996—611no—
432#1996—611no—
433#1964—611no—
434#1964D6111yescharacteristic, complemented
435#1898—614no—
436C4×#99—614no—
437C2×C61—22no—
438C2×C61—21no—
439C2×C61—21no—
440C2×C61—22no—
441C2×C61—82no—
442C2×C61#229711yescharacteristic
443C2×C61C22×#9911yescharacteristic
444C2×C61C2×#41011yescharacteristic
445D61—22no—
446D61—22no—
447D61—41no—
448D61—41no—
449C22×#41—611no—
450C24×C4—611no—
451#525—1221no—
452#525—1221no—
453#525—1221no—
454#525—1221no—
455#525—1221no—
456#525—1221no—
457#525—1221no—
458#525—1221no—
459C2×#123—612no—
460C2×C22⋊Q8—611no—
461C2×C22⋊Q8—611no—
462C2×#121—611no—
463C2×#121C2×D6111yescharacteristic
464C2×#120—612no—
465C2×C4×D4—612no—
466C2×C4×D4—612no—
467C2×#117—611no—
468C2×#117—1221no—
469C22×C22⋊C4—612no—
470C22×C42—1221no—
471C2×#99—614no—
472C2×#99C2×D6114yes—
473#381—1221no—
474#380—611no—
475#380—1221no—
476#380C2×D6111yescharacteristic
477#379—612no—
478C4×C22⋊C4—611no—
479C4×C22⋊C4—612no—
480C4×C22⋊C4—612no—
481C4×C22⋊C4—1221no—
482C4×C22⋊C4—1221no—
483C4×C22⋊C4—1221no—
484C4×C22⋊C4C2×D6111yescharacteristic
485C2×#95—1221no—
486#342—614no—
487#342—614no—
488C61#2142011yescharacteristic, complemented, Sylow
489C25—611no—
490C2×#41—1221no—
491C2×#41—1221no—
492C2×#41—1221no—
493C2×#41—1221no—
494C2×#41—2444no—
495C22×Q8—611no—
496C22×D4—612no—
497C22×D4—612no—
498C22×D4C4×D6111yescharacteristic, complemented
499C22×D4C22×D6112yes—
500C23×C4—611no—
501C23×C4—611no—
502C23×C4—611no—
503C23×C4—611no—
504C23×C4—611no—
505C23×C4—611no—
506C23×C4—611no—
507C23×C4—611no—
508C23×C4—611no—
509C23×C4—611no—
510C23×C4—611no—
511C23×C4—611no—
512C23×C4—611no—
513C23×C4—612no—
514C23×C4—1222no—
515C23×C4—2444no—
516C23×C4C22×D6111yescharacteristic
517#123—1222no—
518#123—1222no—
519#123—1222no—
520#123—1222no—
521C22⋊Q8—1221no—
522C22⋊Q8—1221no—
523C22⋊Q8—1221no—
524C22⋊Q8—1221no—
525C22⋊Q8—1221no—
526C22⋊Q8—1221no—
527C22⋊Q8—1221no—
528C22⋊Q8—1221no—
529#121—21no—
530#121—21no—
531#121—21no—
532#121—21no—
533#121—1221no—
534#121—1221no—
535#121—1221no—
536#121—1221no—
537#120—1222no—
538#120—1222no—
539#120—1222no—
540#120—1222no—
541C4×D4—1222no—
542C4×D4—1222no—
543C4×D4—1222no—
544C4×D4—1222no—
545C4×D4—1222no—
546C4×D4—1222no—
547C4×D4—1222no—
548C4×D4—1222no—
549#117—1221no—
550#117—1221no—
551#117—1221no—
552#117—1221no—
553#117—2444no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—611no—
556C2×C4⋊C4—612no—
557C2×C4⋊C4—612no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4C4×D6111yescharacteristic, complemented
560C2×C22⋊C4—612no—
561C2×C22⋊C4—612no—
562C2×C22⋊C4—612no—
563C2×C22⋊C4—612no—
564C2×C22⋊C4—612no—
565C2×C22⋊C4—612no—
566C2×C22⋊C4—1224no—
567C2×C22⋊C4—1222no—
568C2×C22⋊C4—1224no—
569C2×C22⋊C4—1222no—
570C2×C22⋊C4—1222no—
571C2×C22⋊C4C4×D6112yescomplemented
572C2×C22⋊C4C22×D6112yes—
573C2×C22⋊C4C22×D6112yes—
574C2×C42—21no—
575C2×C42—612no—
576C2×C42—1222no—
577C2×C42—1222no—
578C2×C42—1221no—
579C2×C42—2444no—
580#99—28no—
581#99—1228no—
582#95—21no—
583#95—21no—
584#95—1222no—
585#95—1222no—
586#95—1221no—
587#95—1221no—
588C24—611no—
589C24—611no—
590C24—611no—
591C24—611no—
592C24—611no—
593C24—611no—
594C24—1222no—
595C24—1222no—
596C24—2442no—
597C24—2442no—
598C24C2×C4×D6112yes—
599C24C23×D6111yescharacteristic
600#41—2444no—
601#41—2444no—
602#41—2444no—
603#41—2444no—
604C2×Q8—1221no—
605C2×Q8—1221no—
606C2×Q8—2442no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—42no—
614C2×D4—1222no—
615C2×D4—1222no—
616C2×D4—1222no—
617C2×D4—1222no—
618C2×D4—2444no—
619C2×D4—2444no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—42no—
623C22×C4—611no—
624C22×C4—611no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—611no—
641C22×C4—611no—
642C22×C4—611no—
643C22×C4—611no—
644C22×C4—611no—
645C22×C4—612no—
646C22×C4—612no—
647C22×C4—1224no—
648C22×C4—1224no—
649C22×C4—1224no—
650C22×C4—1228no—
651C22×C4—1222no—
652C22×C4—1222no—
653C22×C4—1222no—
654C22×C4—1222no—
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—2444no—
665C22×C4—2444no—
666C22×C4—2442no—
667C22×C4—2444no—
668C22×C4C2×C4×D6112yes—
669C22×C4C2×C4×D6111yescharacteristic
670C22×C4C2×C4×D6111yescharacteristic
671C22×C4D4×D6111yescharacteristic
672C22×C4D4×D6111yescharacteristic
673C22×C4D4×D6111yescharacteristic
674C22×C4D4×D6111yescharacteristic
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—42no—
678C4⋊C4—1222no—
679C4⋊C4—1222no—
680C4⋊C4—1222no—
681C4⋊C4—1222no—
682C4⋊C4—1221no—
683C4⋊C4—1221no—
684C4⋊C4—2442no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—24no—
689C22⋊C4—614no—
690C22⋊C4—1222no—
691C22⋊C4—1222no—
692C22⋊C4—1222no—
693C22⋊C4—1222no—
694C22⋊C4—1228no—
695C22⋊C4—1222no—
696C22⋊C4—1222no—
697C22⋊C4—1222no—
698C22⋊C4—1222no—
699C22⋊C4—1222no—
700C22⋊C4—1224no—
701C22⋊C4—2444no—
702C22⋊C4—2444no—
703C22⋊C4#1175822414yescomplemented
704C42—42no—
705C42—1222no—
706C42—1222no—
707C42—2442no—
708C42—2444no—
709C42—2444no—
710C23—22no—
711C23—24no—
712C23—41no—
713C23—41no—
714C23—42no—
715C23—42no—
716C23—611no—
717C23—611no—
718C23—611no—
719C23—611no—
720C23—1222no—
721C23—1222no—
722C23—1222no—
723C23—1222no—
724C23—1222no—
725C23—1222no—
726C23—1222no—
727C23—1222no—
728C23—1222no—
729C23—1222no—
730C23—1221no—
731C23—1221no—
732C23—1221no—
733C23—1221no—
734C23—2441no—
735C23—2441no—
736C23—2441no—
737C23—2441no—
738C23—2441no—
739C23—2441no—
740C23—2448no—
741C23—2448no—
742C23C22×C4×D6111yescharacteristic
743C23C2×D4×D6111yescharacteristic
744C23C2×D4×D6111yescharacteristic
745C23#41×D6112yes—
746C23C2×#1175822412yes—
747Q8—2442no—
748Q8—2442no—
749D4—42no—
750D4—44no—
751D4—42no—
752D4—42no—
753D4—42no—
754D4—2444no—
755D4—2444no—
756D4—2444no—
757D4—2444no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—611no—
773C2×C4—614no—
774C2×C4—611no—
775C2×C4—611no—
776C2×C4—611no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—1222no—
782C2×C4—1222no—
783C2×C4—1222no—
784C2×C4—1222no—
785C2×C4—1222no—
786C2×C4—1222no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—1222no—
790C2×C4—1222no—
791C2×C4—1224no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—24416no—
799C2×C4—2444no—
800C2×C4—2441no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4—2444no—
804C2×C4—2442no—
805C2×C4—2442no—
806C2×C4—2442no—
807C2×C4—2442no—
808C2×C4—2442no—
809C2×C4—2442no—
810C2×C4—2442no—
811C2×C4C22⋊C4×D6111yescharacteristic
812C2×C4C22⋊C4×D6111yescharacteristic
813C2×C4C22⋊C4×D6111yescharacteristic
814C2×C4C22⋊C4×D6111yescharacteristic
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—84no—
827C22—612no—
828C22—612no—
829C22—1228no—
830C22—1221no—
831C22—1221no—
832C22—1221no—
833C22—1221no—
834C22—1221no—
835C22—1221no—
836C22—1221no—
837C22—1221no—
838C22—1221no—
839C22—1221no—
840C22—2442no—
841C22—2442no—
842C22—2442no—
843C22—2442no—
844C22—2444no—
845C22—2444no—
846C22—2444no—
847C22C2×C22⋊C4×D6111yescharacteristic
848C22C4×#1175822412yes—
849C22#1684027212yes—
850C22#1684031011yescharacteristic
851C22#1684031111yescharacteristic
852C4—21no—
853C4—21no—
854C4—21no—
855C4—44no—
856C4—42no—
857C4—82no—
858C4—612no—
859C4—1221no—
860C4—1221no—
861C4—1221no—
862C4—4882no—
863C4—2444no—
864C4—2442no—
865C4—2442no—
866C4#99×D6112yes—
867C2—22no—
868C2—21no—
869C2—21no—
870C2—22no—
871C2—82no—
872C2—1222no—
873C2—1222no—
874C2—2441no—
875C2—2441no—
876C2#2144830611yescharacteristic
877C2C2×#99×D6111yescharacteristic
878C2#410×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1964C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840272C2
cosocleC24×C61C24
hypercenter#1964D61
hypocenterC61#21420
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. #21448201C2semidirect
3. C4×C22⋊C4×D61C2semidirect
4. #21446804C2semidirect
5. #21446803C2semidirect
6. #21446656C2semidirect
7. #21446269C2semidirect
8. #99×Dic61C2semidirect
9. C61×#1964C2semidirect
10. C22×#11758224C4semidirect
20. C2×#14519759C4semidirect
21. C2×#14519757C4semidirect
23. C2×#14519748C4semidirect
26. C2×#14519737C4semidirect
28. C2×#14519735C4semidirect
55. C22×Dic122C2×C4semidirect
58. C23×Dic61C2×C4semidirect
108. C2×C4⋊Dic61C2×C4semidirect
109. C2×C4⋊Dic61C2×C4semidirect
110. C2×#11758196C2×C4semidirect
111. C2×C22⋊Dic61C2×C4semidirect
125. C2×C4×Dic61C2×C4semidirect
132. C22×D4×C61C2×C4semidirect
140. C2×C4⋊C4×C61C2×C4semidirect
141. C2×C22⋊C4×C61C2×C4semidirect
242. C22⋊C4×C61#41semidirect
250. C22⋊Dic61#41semidirect
372. C4×D61#99semidirect
434. #1964D61semidirect
488. C61#21420semidirect
498. C22×D4C4×D61semidirect
559. C2×C4⋊C4C4×D61semidirect
571. C2×C22⋊C4C4×D61semidirect
703. C22⋊C4#11758224semidirect

Maximal subgroups

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

subgroupindex
C2×#168402722
#214482012
C4×C22⋊C4×D612
#214468042
#214468032
#214466562
#214462692
#99×Dic612
C61×#19642
#2142061