Finite Group Databasebeta

← #29685355

Subgroups — #29685355

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×#16840275C211yesmaximal, characteristic
2#21448201C211yesmaximal, characteristic, complemented
3C4×C22⋊C4×D61C211yesmaximal, characteristic, complemented
4#21446805C211yesmaximal, characteristic, complemented
5#21446655C211yesmaximal, characteristic, complemented
6#21446654C211yesmaximal, characteristic, complemented
7#21446271C214yesmaximal, complemented
8#21445606C214yesmaximal, complemented
9C61×#1996C211yesmaximal, characteristic, complemented
10C22×#11758226C411yescharacteristic, complemented
11C23×C4×D61C2211yescharacteristic
12#16840275—21no—
13#16840275—21no—
14#16840275—21no—
15#16840275—21no—
16#16840275—21no—
17#16840275—21no—
18#16840275—21no—
19#16840275—21no—
20C2×#14519762C412yescomplemented
21C2×#14519753C411yescharacteristic, complemented
22C2×#14519752C411yescharacteristic, complemented
23C2×#14519751C2211yescharacteristic
24C2×#14519747C2212yes—
25C2×#14519739C412yescomplemented
26C2×#14519737C2212yes—
27C2×#14519735—21no—
28C2×#14519735C411yescharacteristic, complemented
29C2×C22⋊C4×D61C2212yes—
30C2×C42×D61—21no—
31C2×#14519691C2214yes—
32C2×#14519691C2214yes—
33#16839624—21no—
34#16839622C2211yescharacteristic
35#16839619—21no—
36#16839617C2212yes—
37C22⋊C4×Dic61C2212yes—
38C22⋊C4×Dic61C2212yes—
39C4×#11758198—21no—
40C4×C22⋊Dic61C2211yescharacteristic
41#16839609—21no—
42#16839609—21no—
43#95×D61—21no—
44#16839529C2214yes—
45C2×C22⋊Q8×C61C2211yescharacteristic
46C61×#380C2211yescharacteristic
47C4×C22⋊C4×C61C2211yescharacteristic
48C61×#342C2214yes—
49C24×D61C2311yescharacteristic
50C2×#11758226—21no—
51C2×#11758226—21no—
52C2×#11758226—21no—
53C2×#11758226—21no—
54C2×#11758226—44no—
55C22×D244C2×C412yes—
56C22×D244C2×C412yes—
57C22×D244C2×C411yescharacteristic, complemented
58C22×C22⋊D61C2312yes—
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×D61C2×C412yescomplemented
67C22×C4×D61D411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61D411yescharacteristic
73C22×C4×D61D411yescharacteristic
74C22×C4×D61D411yescharacteristic
75#14519762—22no—
76#14519762—22no—
77#14519762—22no—
78#14519762—22no—
79#14519753—21no—
80#14519753—21no—
81#14519753—21no—
82#14519753—21no—
83#14519752—21no—
84#14519752—21no—
85#14519752—21no—
86#14519752—21no—
87#14519751—21no—
88#14519751—21no—
89#14519751—21no—
90#14519751—21no—
91#14519747—22no—
92#14519747—22no—
93#14519747—22no—
94#14519747—22no—
95#14519739—22no—
96#14519739—22no—
97#14519739—22no—
98#14519739—22no—
99#14519737—22no—
100#14519737—22no—
101#14519737—22no—
102#14519737—22no—
103#14519735—21no—
104#14519735—21no—
105#14519735—21no—
106#14519735—21no—
107#14519735—44no—
108C2×C4⋊Dic61—21no—
109C2×C4⋊Dic61C2×C411yescharacteristic, complemented
110C2×#11758196C2×C412yescomplemented
111C2×C22⋊Dic61C2312yes—
112C2×C22⋊Dic61C2312yes—
113C2×#11758198—22no—
114C2×#11758198—22no—
115C2×#11758198—22no—
116C2×#11758198C2×C412yes—
117C2×#11758198C2×C412yes—
118C2×#11758198C2×C412yescomplemented
119C2×#11758198C2×C412yescomplemented
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#14519691—28no—
128#14519691—28no—
129#14519684—21no—
130#14519684—21no—
131#14519684—22no—
132#14519684—22no—
133C22×Q8×C61C2×C411yescharacteristic, complemented
134C23×C4×C61C2311yescharacteristic
135C22⋊Q8×C61—21no—
136C22⋊Q8×C61—21no—
137C22⋊Q8×C61—21no—
138C22⋊Q8×C61—21no—
139C2×C4⋊C4×C61—21no—
140C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
141C2×C4⋊C4×C61C2×C412yescomplemented
142C2×C22⋊C4×C61C2312yes—
143C2×C22⋊C4×C61C2312yes—
144C2×C22⋊C4×C61C2312yes—
145C2×C42×C61—21no—
146#95×C61—21no—
147#95×C61—21no—
148C24×C61C2411yescharacteristic
149C23×D61—22no—
150C23×D61—22no—
151C23×D61—42no—
152C23×D61—42no—
153C23×D61C22×C411yescharacteristic
154C23×D61C22×C411yescharacteristic
155C23×D61C22×C412yes—
156C23×D61C2×D411yescharacteristic
157C23×D61C2×D411yescharacteristic
158C23×D61C2×D411yescharacteristic
159C23×D61C2×D411yescharacteristic
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—42no—
163C22×C4×C61—22no—
164C22×C4×C61—22no—
165C22×C4×C61—42no—
166C22×C4×C61C22×C411yescharacteristic
167C22×C4×C61C22×C412yes—
168C22×C4×C61C22×C412yes—
169C22×C4×C61C22×C411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D411yescharacteristic
174C2×C22⋊D61—22no—
175C2×C22⋊D61—22no—
176C2×C22⋊D61—24no—
177C2×C22⋊D61—24no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—42no—
181C22×Dic61C22×C412yes—
182C22×Dic61C22×C411yescharacteristic
183C22×Dic61C22×C411yescharacteristic
184C22×Dic61C2×D411yescharacteristic
185C22×Dic61C2×D411yescharacteristic
186C22×Dic61C2×D411yescharacteristic
187C22×Dic61C2×D411yescharacteristic
188#11758226—44no—
189#11758226—44no—
190#11758226—44no—
191#11758226—44no—
192C2×D244—22no—
193C2×D244—22no—
194C2×D244—22no—
195C2×D244—22no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244—42no—
199C2×D244—44no—
200C2×D244—44no—
201C2×C4×D61—24no—
202C2×C4×D61—24no—
203C2×C4×D61—24no—
204C2×C4×D61—28no—
205C2×C4×D61—22no—
206C2×C4×D61—22no—
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—42no—
215C2×C4×D61—42no—
216C2×C4×D61—44no—
217C2×C4×D61—44no—
218C2×C4×D61—44no—
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×C4×D61C22⋊C411yescharacteristic
233C2×C4×D61C22⋊C411yescharacteristic
234C2×C4×D61C22⋊C411yescharacteristic
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—22no—
238C4⋊C4×C61—22no—
239C4⋊C4×C61—42no—
240C22⋊C4×C61—22no—
241C22⋊C4×C61—22no—
242C22⋊C4×C61—22no—
243C22⋊C4×C61—24no—
244C22⋊C4×C61#4114yescomplemented
245C42×C61—42no—
246C22⋊Dic61—22no—
247C22⋊Dic61—24no—
248C22⋊Dic61#4114yescomplemented
249#11758198—28no—
250#11758198—22no—
251#11758198—22no—
252#11758198—22no—
253#11758198—22no—
254#11758198—22no—
255#11758198—22no—
256#11758198—22no—
257#11758198—22no—
258#11758198—44no—
259#11758198—44no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
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—41no—
271C23×C61—41no—
272C23×C61C23×C411yescharacteristic
273C23×C61C22×D411yescharacteristic
274C23×C61C22×D411yescharacteristic
275C23×C61C2×#4112yes—
276C23×C61C2×#4112yes—
277C22×D61—22no—
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—24no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61—48no—
300C22×D61—48no—
301C22×D61—42no—
302C22×D61—42no—
303C22×D61C2×C22⋊C411yescharacteristic
304C22×D61C2×C22⋊C411yescharacteristic
305C22×D61C2×C22⋊C411yescharacteristic
306C22×D61C2×C22⋊C411yescharacteristic
307Q8×C61—42no—
308Q8×C61—42no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—24no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—42no—
319C2×C4×C61—42no—
320C2×C4×C61—42no—
321C2×C4×C61—42no—
322C2×C4×C61—42no—
323C2×C4×C61—42no—
324C2×C4×C61—42no—
325C2×C4×C61C2×C22⋊C411yescharacteristic
326C2×C4×C61C2×C22⋊C411yescharacteristic
327C2×C4×C61C2×C22⋊C411yescharacteristic
328C2×C4×C61C2×C22⋊C411yescharacteristic
329C22⋊D61—44no—
330C22⋊D61—42no—
331C22⋊D61—42no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—24no—
337C2×Dic61—24no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—42no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345C2×Dic61—42no—
346C2×Dic61C2×C22⋊C411yescharacteristic
347C2×Dic61C2×C22⋊C411yescharacteristic
348C2×Dic61C2×C22⋊C411yescharacteristic
349C2×Dic61C2×C22⋊C411yescharacteristic
350D244—42no—
351D244—44no—
352D244—44no—
353D244—44no—
354D244—44no—
355D244—42no—
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—44no—
372C4×D61—416no—
373C4×D61—44no—
374C4×D61#9914yescomplemented
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×C61C22×C22⋊C411yescharacteristic
385C22×C61C4×#4112yes—
386C22×C61#52512yes—
387C22×C61#53211yescharacteristic
388C22×C61#53211yescharacteristic
389C2×D61—28no—
390C2×D61—21no—
391C2×D61—21no—
392C2×D61—21no—
393C2×D61—21no—
394C2×D61—21no—
395C2×D61—21no—
396C2×D61—21no—
397C2×D61—21no—
398C2×D61—21no—
399C2×D61—21no—
400C2×D61—42no—
401C2×D61—42no—
402C2×D61—44no—
403C2×D61—42no—
404C2×D61—42no—
405C2×D61—44no—
406C2×D61—44no—
407C2×D61—42no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—84no—
411C2×D61C2×#9912yes—
412C2×D61#41012yes—
413C4×C61—21no—
414C4×C61—21no—
415C4×C61—21no—
416C4×C61—44no—
417C4×C61—42no—
418C4×C61—42no—
419C4×C61—82no—
420C4×C61C2×#9912yes—
421Dic61—21no—
422Dic61—21no—
423Dic61—21no—
424Dic61—44no—
425Dic61—42no—
426Dic61—82no—
427Dic61C2×#9912yes—
428C2×#525—611no—
429#2280—611no—
430C2×C4×C22⋊C4—611no—
431#1996—611no—
432#1996D6111yescharacteristic, complemented
433#1964—611no—
434#1964—611no—
435#1898—614no—
436C4×#99—614no—
437C2×C61—22no—
438C2×C61—21no—
439C2×C61—21no—
440C2×C61—22no—
441C2×C61#229711yescharacteristic
442C2×C61C22×#9911yescharacteristic
443C2×C61C2×#41011yescharacteristic
444D61—22no—
445D61—22no—
446D61—41no—
447D61—41no—
448D61—82no—
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⋊Q8C2×D6111yescharacteristic
462C2×#121—611no—
463C2×#121—611no—
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×#99—614no—
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#342C2×D6114yes—
488C61#2142011yescharacteristic, complemented, Sylow
489C25—611no—
490C2×#41—1221no—
491C2×#41—1221no—
492C2×#41—1221no—
493C2×#41—1221no—
494C2×#41—2444no—
495C22×Q8C4×D6111yescharacteristic, complemented
496C22×D4—612no—
497C22×D4—612no—
498C22×D4—612no—
499C22×D4—611no—
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—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524C22⋊Q8—21no—
525C22⋊Q8—1221no—
526C22⋊Q8—1221no—
527C22⋊Q8—1221no—
528C22⋊Q8—1221no—
529#121—1221no—
530#121—1221no—
531#121—1221no—
532#121—1221no—
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—1221no—
558C2×C4⋊C4C4×D6111yescharacteristic, complemented
559C2×C4⋊C4C4×D6112yescomplemented
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⋊C4C22×D6112yes—
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—1228no—
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—612no—
595C24—1222no—
596C24—1222no—
597C24—2442no—
598C24—2442no—
599C24C23×D6111yescharacteristic
600#41—2444no—
601#41—2444no—
602#41—2444no—
603#41—2444no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—42no—
607C2×D4—1222no—
608C2×D4—1222no—
609C2×D4—1222no—
610C2×D4—1222no—
611C2×D4—1222no—
612C2×D4—1222no—
613C2×D4—1224no—
614C2×D4—1224no—
615C2×D4—1221no—
616C2×D4—1221no—
617C2×D4—2442no—
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—1224no—
647C22×C4—1224no—
648C22×C4—1224no—
649C22×C4—1222no—
650C22×C4—1222no—
651C22×C4—1228no—
652C22×C4—1222no—
653C22×C4—1222no—
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—2444no—
664C22×C4—2444no—
665C22×C4—2444no—
666C22×C4—2442no—
667C22×C4C2×C4×D6111yescharacteristic
668C22×C4C2×C4×D6112yes—
669C22×C4C2×C4×D6112yes—
670C22×C4C2×C4×D6111yescharacteristic
671C22×C4D4×D6111yescharacteristic
672C22×C4D4×D6111yescharacteristic
673C22×C4D4×D6111yescharacteristic
674C22×C4D4×D6111yescharacteristic
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—42no—
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—1222no—
695C22⋊C4—1222no—
696C22⋊C4—1228no—
697C22⋊C4—1222no—
698C22⋊C4—1222no—
699C22⋊C4—1222no—
700C22⋊C4—1224no—
701C22⋊C4—2444no—
702C22⋊C4—2444no—
703C22⋊C4#1175822614yescomplemented
704C42—42no—
705C42—1222no—
706C42—1222no—
707C42—2442no—
708C42—2444no—
709C42—2444no—
710C23—41no—
711C23—41no—
712C23—611no—
713C23—611no—
714C23—611no—
715C23—611no—
716C23—1222no—
717C23—1222no—
718C23—1222no—
719C23—1222no—
720C23—1222no—
721C23—1222no—
722C23—1222no—
723C23—1222no—
724C23—1222no—
725C23—1222no—
726C23—1221no—
727C23—1221no—
728C23—1221no—
729C23—1221no—
730C23—1224no—
731C23—1222no—
732C23—2441no—
733C23—2441no—
734C23—2441no—
735C23—2441no—
736C23—2441no—
737C23—2441no—
738C23—2442no—
739C23—2442no—
740C23—2448no—
741C23—2448no—
742C23C22×C4×D6111yescharacteristic
743C23C2×D4×D6111yescharacteristic
744C23C2×D4×D6111yescharacteristic
745C23#41×D6112yes—
746C23C2×#1175822612yes—
747Q8—42no—
748Q8—42no—
749D4—2442no—
750D4—2444no—
751D4—2444no—
752D4—2444no—
753D4—2444no—
754D4—2444no—
755D4—2442no—
756D4—2442no—
757D4—2442no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
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—42no—
773C2×C4—42no—
774C2×C4—611no—
775C2×C4—614no—
776C2×C4—611no—
777C2×C4—611no—
778C2×C4—611no—
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—1222no—
792C2×C4—1224no—
793C2×C4—1224no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4—2444no—
801C2×C4—2444no—
802C2×C4—24416no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4—2441no—
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—612no—
824C22—612no—
825C22—1228no—
826C22—1221no—
827C22—1221no—
828C22—1221no—
829C22—1221no—
830C22—1221no—
831C22—1221no—
832C22—1221no—
833C22—1221no—
834C22—1221no—
835C22—1221no—
836C22—4884no—
837C22—2442no—
838C22—2442no—
839C22—2442no—
840C22—2442no—
841C22—2444no—
842C22—2444no—
843C22—2444no—
844C22—2442no—
845C22—2442no—
846C22—2442no—
847C22C2×C22⋊C4×D6111yescharacteristic
848C22C4×#1175822612yes—
849C22#1684027512yes—
850C22#1684031111yescharacteristic
851C22#1684031311yescharacteristic
852C4—21no—
853C4—21no—
854C4—21no—
855C4—44no—
856C4—42no—
857C4—42no—
858C4—82no—
859C4—612no—
860C4—1221no—
861C4—1221no—
862C4—1221no—
863C4—4882no—
864C4—2444no—
865C4—2442no—
866C4#99×D6112yes—
867C2—22no—
868C2—21no—
869C2—21no—
870C2—22no—
871C2—1222no—
872C2—1222no—
873C2—4882no—
874C2—2441no—
875C2—2441no—
876C2#2144830811yescharacteristic
877C2C2×#99×D6111yescharacteristic
878C2#410×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1996C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840275C2
cosocleC24×C61C24
hypercenter#1996D61
hypocenterC61#21420
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
2. #21448201C2semidirect
3. C4×C22⋊C4×D61C2semidirect
4. #21446805C2semidirect
5. #21446655C2semidirect
6. #21446654C2semidirect
7. #21446271C2semidirect
8. #21445606C2semidirect
9. C61×#1996C2semidirect
10. C22×#11758226C4semidirect
20. C2×#14519762C4semidirect
21. C2×#14519753C4semidirect
22. C2×#14519752C4semidirect
25. C2×#14519739C4semidirect
28. C2×#14519735C4semidirect
57. C22×D244C2×C4semidirect
66. C22×C4×D61C2×C4semidirect
109. C2×C4⋊Dic61C2×C4semidirect
110. C2×#11758196C2×C4semidirect
118. C2×#11758198C2×C4semidirect
119. C2×#11758198C2×C4semidirect
125. C2×C4×Dic61C2×C4semidirect
133. C22×Q8×C61C2×C4semidirect
140. C2×C4⋊C4×C61C2×C4semidirect
141. C2×C4⋊C4×C61C2×C4semidirect
244. C22⋊C4×C61#41semidirect
248. C22⋊Dic61#41semidirect
374. C4×D61#99semidirect
432. #1996D61semidirect
488. C61#21420semidirect
495. C22×Q8C4×D61semidirect
558. C2×C4⋊C4C4×D61semidirect
559. C2×C4⋊C4C4×D61semidirect
703. C22⋊C4#11758226semidirect

Maximal subgroups

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

subgroupindex
C2×#168402752
#214482012
C4×C22⋊C4×D612
#214468052
#214466552
#214466542
#214462712
#214456062
C61×#19962
#2142061