Finite Group Databasebeta

← #29679946

Subgroups — #29679946

Order 15616.

1866 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D61C211yesmaximal, characteristic
2#21448201C212yesmaximal, complemented
3#21445892C212yesmaximal, complemented
4#21445807C211yesmaximal, characteristic, complemented
5#21445804C212yesmaximal, complemented
6#21445732C212yesmaximal
7#99×Dic61C212yesmaximal, complemented
8#21445606C212yesmaximal, complemented
9C61×#1799C211yesmaximal, characteristic, complemented
10C22×D4×D61C2211yescharacteristic
11C23×C4×D61C411yescharacteristic, complemented
12C23×C4×D61C2211yescharacteristic
13C2×C4×D244C411yescharacteristic, complemented
14C2×D4×Dic61C2211yescharacteristic
15C2×#14519739C411yescharacteristic, complemented
16C2×C4×C22⋊D61C411yescharacteristic, complemented
17C2×C4×C22⋊D61C2211yescharacteristic
18C2×#14519737C411yescharacteristic, complemented
19C2×#14519737C2211yescharacteristic
20C4×D4×D61—22no—
21C4×D4×D61—22no—
22C4×D4×D61—22no—
23C4×D4×D61—22no—
24C2×#14519735—22no—
25C2×C4⋊C4×D61C411yescharacteristic, complemented
26C2×C22⋊C4×D61C411yescharacteristic, complemented
27C2×C22⋊C4×D61C2211yescharacteristic
28C2×C42×D61C411yescharacteristic, complemented
29C2×#14519692C2212yes—
30C2×#14519691C2214yes—
31#16839624—22no—
32#16839622C2212yescomplemented
33#16839619—22no—
34#16839617C2214yes—
35C22⋊C4×Dic61C2214yescomplemented
36#16839609—22no—
37#16839529C2212yescomplemented
38#16839528C2214yescomplemented
39C2×C4×D4×C61C2211yescharacteristic
40C2×#99×C61C2212yes—
41C61×#380C2212yescomplemented
42C61×#342C2212yescomplemented
43C24×D61C2×C411yescharacteristic
44C24×D61C2311yescharacteristic
45C22×D244C2×C411yescharacteristic
46C22×C22⋊D61C2×C411yescharacteristic
47C22×C22⋊D61C2311yescharacteristic
48C2×D4×D61—22no—
49C2×D4×D61—22no—
50C2×D4×D61—22no—
51C2×D4×D61—22no—
52C2×D4×D61—24no—
53C23×Dic61C2×C411yescharacteristic
54C23×Dic61C2311yescharacteristic
55C22×C4×D61—21no—
56C22×C4×D61—21no—
57C22×C4×D61—21no—
58C22×C4×D61—21no—
59C22×C4×D61—44no—
60C22×C4×D61—44no—
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61C2×C411yescharacteristic
65C22×C4×D61C2×C411yescharacteristic
66C22×C4×D61C2×C411yescharacteristic
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61C2×C411yescharacteristic
69C22×C4×D61C2×C411yescharacteristic
70C22×C4×D61D412yes—
71C22×C4×D61D412yes—
72C22×C4×D61D412yes—
73C22×C4×D61D412yes—
74C4×D244—22no—
75C4×D244—22no—
76D4×Dic61—22no—
77D4×Dic61—22no—
78#14519739—22no—
79#14519739—22no—
80C4×C22⋊D61—22no—
81C4×C22⋊D61—22no—
82C4×C22⋊D61—22no—
83C4×C22⋊D61—22no—
84#14519737—22no—
85#14519737—22no—
86#14519737—22no—
87#14519737—22no—
88#14519735—48no—
89C2×C4⋊Dic61—22no—
90C2×C4⋊Dic61C2×C411yescharacteristic
91C2×#11758196C2×C411yescharacteristic
92C2×#11758196C2×C411yescharacteristic
93C4⋊C4×D61—22no—
94C4⋊C4×D61—22no—
95C2×C22⋊Dic61C2×C411yescharacteristic
96C2×C22⋊Dic61C2314yes—
97C2×C22⋊Dic61C2311yescharacteristic
98C2×#11758198—24no—
99C2×#11758198—24no—
100C2×#11758198C2×C411yescharacteristic
101C2×#11758198C2×C411yescharacteristic
102C2×#11758198C2×C411yescharacteristic
103C2×#11758198C2×C411yescharacteristic
104C22⋊C4×D61—22no—
105C22⋊C4×D61—22no—
106C22⋊C4×D61—22no—
107C22⋊C4×D61—22no—
108C2×C4×Dic61—24no—
109C2×C4×Dic61C2×C411yescharacteristic
110C2×C4×Dic61C2×C411yescharacteristic
111C2×C4×Dic61C2×C411yescharacteristic
112C42×D61—21no—
113C42×D61—21no—
114C42×D61—21no—
115C42×D61—21no—
116#14519692—24no—
117#14519691—28no—
118#14519684—22no—
119#14519684—24no—
120C22×D4×C61C2311yescharacteristic
121C23×C4×C61C2×C411yescharacteristic
122C23×C4×C61C2311yescharacteristic
123C4×D4×C61—22no—
124C4×D4×C61—22no—
125C2×C4⋊C4×C61—22no—
126C2×C4⋊C4×C61C2×C411yescharacteristic
127C2×C22⋊C4×C61C2×C411yescharacteristic
128C2×C22⋊C4×C61C2314yes—
129C2×C22⋊C4×C61C2311yescharacteristic
130C2×C42×C61C2×C411yescharacteristic
131#99×C61—24no—
132#95×C61—22no—
133C24×C61C22×C411yescharacteristic
134C24×C61C2411yescharacteristic
135C23×D61—22no—
136C23×D61—22no—
137C23×D61—21no—
138C23×D61—21no—
139C23×D61—21no—
140C23×D61—21no—
141C23×D61—22no—
142C23×D61—42no—
143C23×D61—42no—
144C23×D61—42no—
145C23×D61—42no—
146C23×D61C22×C411yescharacteristic
147C23×D61C22×C411yescharacteristic
148C23×D61C22×C411yescharacteristic
149C23×D61C2×D412yes—
150C23×D61C2×D412yes—
151C2×D4×C61—22no—
152C2×D4×C61—22no—
153C2×D4×C61#4112yes—
154C2×D4×C61#4112yes—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—24no—
158C22×C4×C61—42no—
159C22×C4×C61—42no—
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C2×D412yes—
166C22×C4×C61C2×D412yes—
167C2×C22⋊D61—22no—
168C2×C22⋊D61—22no—
169C2×C22⋊D61—21no—
170C2×C22⋊D61—21no—
171C2×C22⋊D61—22no—
172C2×C22⋊D61—22no—
173C2×C22⋊D61#4114yes—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—24no—
177C22×Dic61—42no—
178C22×Dic61—42no—
179C22×Dic61C22×C411yescharacteristic
180C22×Dic61C22×C411yescharacteristic
181C22×Dic61C22×C411yescharacteristic
182C22×Dic61C22×C411yescharacteristic
183C22×Dic61C22×C411yescharacteristic
184C22×Dic61C2×D412yes—
185C22×Dic61C2×D412yes—
186D4×D61—28no—
187D4×D61—28no—
188D4×D61—28no—
189D4×D61—28no—
190C2×D244—22no—
191C2×D244—22no—
192C2×D244—22no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—22no—
196C2×C4×D61—22no—
197C2×C4×D61—24no—
198C2×C4×D61—28no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—42no—
208C2×C4×D61—44no—
209C2×C4×D61—42no—
210C2×C4×D61—44no—
211C2×C4×D61—42no—
212C2×C4×D61—44no—
213C2×C4×D61—44no—
214C2×C4×D61—44no—
215C2×C4×D61—44no—
216C2×C4×D61—44no—
217C2×C4×D61—42no—
218C2×C4×D61—42no—
219C2×C4×D61—42no—
220C2×C4×D61—42no—
221C2×C4×D61C22⋊C411yescharacteristic
222C2×C4×D61C22⋊C411yescharacteristic
223C2×C4×D61C22⋊C411yescharacteristic
224C2×C4×D61C22⋊C412yes—
225C2×C4×D61C22⋊C412yes—
226C2×C4×D61C22⋊C412yes—
227C2×C4×D61C22⋊C412yes—
228C2×C4×D61C22⋊C412yes—
229C2×C4×D61C22⋊C412yes—
230C2×C4×D61C22⋊C411yescharacteristic
231C4⋊C4×C61—22no—
232C4⋊C4×C61—44no—
233C22⋊C4×C61—22no—
234C22⋊C4×C61—22no—
235C22⋊C4×C61—24no—
236C22⋊C4×C61—24no—
237C42×C61—21no—
238C42×C61—21no—
239C22⋊Dic61—22no—
240C22⋊Dic61—22no—
241C22⋊Dic61—24no—
242C22⋊Dic61—24no—
243#11758198—22no—
244#11758198—22no—
245#11758198—22no—
246#11758198—22no—
247#11758198—48no—
248#11758198—48no—
249C4⋊Dic61—22no—
250C4⋊Dic61—44no—
251#11758196—22no—
252#11758196—22no—
253C4×Dic61—21no—
254C4×Dic61—21no—
255C4×Dic61—21no—
256C4×Dic61—21no—
257C4×Dic61—21no—
258C4×Dic61—21no—
259C4×Dic61—48no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61#11712yescomplemented
267C23×C61C23×C411yescharacteristic
268C23×C61C22×D412yes—
269C23×C61C2×#4112yes—
270C23×C61C2×#4111yescharacteristic
271C23×C61C2×#4111yescharacteristic
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—24no—
277C22×D61—24no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—24no—
287C22×D61—24no—
288C22×D61—41no—
289C22×D61—42no—
290C22×D61—41no—
291C22×D61—42no—
292C22×D61—42no—
293C22×D61—44no—
294C22×D61—48no—
295C22×D61—44no—
296C22×D61—48no—
297C22×D61—48no—
298C22×D61—42no—
299C22×D61—42no—
300C22×D61—42no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61C2×C22⋊C412yes—
304C22×D61C2×C22⋊C411yescharacteristic
305C22×D61C2×C22⋊C411yescharacteristic
306C22×D61#11712yescomplemented
307D4×C61—24no—
308D4×C61—24no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—24no—
312C2×C4×C61—22no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—41no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
318C2×C4×C61—42no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—44no—
322C2×C4×C61—44no—
323C2×C4×C61—44no—
324C2×C4×C61C2×C22⋊C411yescharacteristic
325C2×C4×C61C2×C22⋊C412yes—
326C2×C4×C61C2×C22⋊C411yescharacteristic
327C2×C4×C61#11712yescomplemented
328C22⋊D61—28no—
329C22⋊D61—24no—
330C22⋊D61—24no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—24no—
334C2×Dic61—22no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—41no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—44no—
344C2×Dic61—44no—
345C2×Dic61—44no—
346C2×Dic61C2×C22⋊C411yescharacteristic
347C2×Dic61C2×C22⋊C412yes—
348C2×Dic61C2×C22⋊C411yescharacteristic
349C2×Dic61#11712yescomplemented
350D244—28no—
351C4×D61—24no—
352C4×D61—24no—
353C4×D61—22no—
354C4×D61—24no—
355C4×D61—22no—
356C4×D61—24no—
357C4×D61—22no—
358C4×D61—24no—
359C4×D61—42no—
360C4×D61—42no—
361C4×D61—42no—
362C4×D61—42no—
363C4×D61—42no—
364C4×D61—42no—
365C4×D61—42no—
366C4×D61—42no—
367C4×D61—42no—
368C4×D61—42no—
369C4×D61—42no—
370C4×D61#9914yescomplemented
371#20722—611nomaximal, Sylow
372C22×C61—22no—
373C22×C61—21no—
374C22×C61—22no—
375C22×C61—21no—
376C22×C61—22no—
377C22×C61—42no—
378C22×C61—41no—
379C22×C61—41no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61—41no—
383C22×C61—41no—
384C22×C61C22×C22⋊C411yescharacteristic
385C22×C61C2×#11711yescharacteristic
386C22×C61C2×#11711yescharacteristic
387C22×C61#52512yes—
388C22×C61#52512yes—
389C2×D61—24no—
390C2×D61—24no—
391C2×D61—21no—
392C2×D61—21no—
393C2×D61—21no—
394C2×D61—21no—
395C2×D61—22no—
396C2×D61—22no—
397C2×D61—22no—
398C2×D61—22no—
399C2×D61—44no—
400C2×D61—44no—
401C2×D61—44no—
402C2×D61—44no—
403C2×D61—48no—
404C2×D61—48no—
405C2×D61—42no—
406C2×D61—42no—
407C2×D61—42no—
408C2×D61—41no—
409C2×D61—41no—
410C2×D61—42no—
411C2×D61C2×#9912yes—
412C2×D61#41012yes—
413C4×C61—21no—
414C4×C61—22no—
415C4×C61—22no—
416C4×C61—41no—
417C4×C61—41no—
418C4×C61—84no—
419C4×C61C2×#9912yes—
420Dic61—21no—
421Dic61—22no—
422Dic61—22no—
423Dic61—41no—
424Dic61—41no—
425Dic61—84no—
426Dic61C2×#9912yes—
427C22×C4×D4—611no—
428#2280—612no—
429#1819—612no—
430#1799—612no—
431#1799—611no—
432#1799D6111yescharacteristic, complemented
433#1781—612no—
434C4×#99—612no—
435C4×#99—612no—
436C2×C61—22no—
437C2×C61—22no—
438C2×C61—21no—
439C2×C61—21no—
440C2×C61—42no—
441C2×C61#228011yescharacteristic
442C2×C61C22×#9911yescharacteristic
443C2×C61C2×#41011yescharacteristic
444D61—22no—
445D61—22no—
446D61—42no—
447D61—42no—
448C23×D4—611no—
449C24×C4—611no—
450C24×C4—611no—
451C2×C4×D4—611no—
452C2×C4×D4—611no—
453C2×C4×D4—611no—
454C2×C4×D4—611no—
455C2×C4×D4—611no—
456C2×C4×D4—611no—
457C2×C4×D4—611no—
458C2×C4×D4—1222no—
459C2×C4×D4—1222no—
460C2×C4×D4—1222no—
461C2×C4×D4—1222no—
462C2×C4×D4C2×D6111yescharacteristic
463C2×#117—1222no—
464C22×C4⋊C4—611no—
465C22×C22⋊C4—611no—
466C22×C22⋊C4—611no—
467C22×C42—611no—
468C2×#99—612no—
469C2×#99—614no—
470C2×#99C2×D6112yes—
471#381—1222no—
472#380—612no—
473#380—1222no—
474#380C2×D6112yescomplemented
475#379—614no—
476C4×C22⋊C4—614no—
477C4×C22⋊C4—1222no—
478#342—614no—
479#342—612no—
480#342C2×D6112yescomplemented
481C61#2072211yescharacteristic, complemented, Sylow
482C25—611no—
483C25—611no—
484C22×D4—611no—
485C22×D4—611no—
486C22×D4—611no—
487C22×D4—1224no—
488C22×D4—1222no—
489C22×D4—1222no—
490C22×D4—1222no—
491C22×D4—1222no—
492C22×D4C22×D6111yescharacteristic
493C23×C4—611no—
494C23×C4—611no—
495C23×C4—612no—
496C23×C4—611no—
497C23×C4—611no—
498C23×C4—611no—
499C23×C4—612no—
500C23×C4—612no—
501C23×C4—612no—
502C23×C4—611no—
503C23×C4—611no—
504C23×C4—611no—
505C23×C4—611no—
506C23×C4—611no—
507C23×C4—611no—
508C23×C4—1221no—
509C23×C4—1221no—
510C23×C4—1221no—
511C23×C4—1221no—
512C23×C4—2444no—
513C23×C4—2444no—
514C23×C4C4×D6111yescharacteristic
515C23×C4C22×D6111yescharacteristic
516C4×D4—22no—
517C4×D4—22no—
518C4×D4—1222no—
519C4×D4—1222no—
520C4×D4—1222no—
521C4×D4—1222no—
522C4×D4—1222no—
523C4×D4—1222no—
524C4×D4—1222no—
525C4×D4—1222no—
526C4×D4—1222no—
527C4×D4—1222no—
528C4×D4—1222no—
529C4×D4—1222no—
530C4×D4—1222no—
531C4×D4—1222no—
532#117—2448no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—611no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—1222no—
538C2×C4⋊C4—1222no—
539C2×C4⋊C4—1222no—
540C2×C4⋊C4C4×D6111yescharacteristic
541C2×C22⋊C4—611no—
542C2×C22⋊C4—611no—
543C2×C22⋊C4—611no—
544C2×C22⋊C4—611no—
545C2×C22⋊C4—611no—
546C2×C22⋊C4—611no—
547C2×C22⋊C4—614no—
548C2×C22⋊C4—1222no—
549C2×C22⋊C4—1222no—
550C2×C22⋊C4—1222no—
551C2×C22⋊C4—1222no—
552C2×C22⋊C4—1224no—
553C2×C22⋊C4—1224no—
554C2×C22⋊C4C4×D6111yescharacteristic
555C2×C22⋊C4C22×D6114yes—
556C2×C22⋊C4C22×D6111yescharacteristic
557C2×C42—611no—
558C2×C42—611no—
559C2×C42—611no—
560C2×C42—1221no—
561C2×C42—1221no—
562C2×C42—1221no—
563C2×C42—1221no—
564C2×C42—1224no—
565C2×C42C4×D6111yescharacteristic
566#99—24no—
567#99—1228no—
568#99—1224no—
569#95—22no—
570#95—1224no—
571#95—1222no—
572C24—611no—
573C24—612no—
574C24—612no—
575C24—611no—
576C24—611no—
577C24—1221no—
578C24—1221no—
579C24—1222no—
580C24—1222no—
581C24—1221no—
582C24—1221no—
583C24—1222no—
584C24—2442no—
585C24—2442no—
586C24—2442no—
587C24—2442no—
588C24C2×C4×D6111yescharacteristic
589C24C23×D6111yescharacteristic
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—614no—
593C2×D4—1222no—
594C2×D4—1222no—
595C2×D4—1222no—
596C2×D4—1228no—
597C2×D4—1228no—
598C2×D4—1228no—
599C2×D4—1228no—
600C2×D4—1222no—
601C2×D4—1222no—
602C2×D4—1221no—
603C2×D4—1221no—
604C2×D4—1222no—
605C2×D4—1222no—
606C2×D4#1175822412yes—
607C2×D4#1175822612yes—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—24no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—612no—
617C22×C4—611no—
618C22×C4—612no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—612no—
623C22×C4—612no—
624C22×C4—612no—
625C22×C4—612no—
626C22×C4—612no—
627C22×C4—612no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—1228no—
631C22×C4—1224no—
632C22×C4—1222no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—1222no—
644C22×C4—1221no—
645C22×C4—1221no—
646C22×C4—1224no—
647C22×C4—2444no—
648C22×C4—2442no—
649C22×C4—2442no—
650C22×C4—2444no—
651C22×C4—2442no—
652C22×C4—2444no—
653C22×C4—2442no—
654C22×C4—2444no—
655C22×C4—2444no—
656C22×C4—2444no—
657C22×C4—2444no—
658C22×C4—2442no—
659C22×C4—2442no—
660C22×C4—2442no—
661C22×C4—2442no—
662C22×C4—2442no—
663C22×C4C2×C4×D6111yescharacteristic
664C22×C4C2×C4×D6111yescharacteristic
665C22×C4C2×C4×D6111yescharacteristic
666C22×C4C2×C4×D6111yescharacteristic
667C22×C4C2×C4×D6111yescharacteristic
668C22×C4D4×D6112yes—
669C22×C4D4×D6112yes—
670C4⋊C4—22no—
671C4⋊C4—44no—
672C4⋊C4—1222no—
673C4⋊C4—1222no—
674C4⋊C4—1222no—
675C4⋊C4—2444no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—24no—
679C22⋊C4—24no—
680C22⋊C4—1222no—
681C22⋊C4—1222no—
682C22⋊C4—1222no—
683C22⋊C4—1222no—
684C22⋊C4—1222no—
685C22⋊C4—1222no—
686C22⋊C4—1224no—
687C22⋊C4—1224no—
688C22⋊C4—2448no—
689C22⋊C4—2448no—
690C42—21no—
691C42—21no—
692C42—1221no—
693C42—1221no—
694C42—1221no—
695C42—1221no—
696C42—1221no—
697C42—1221no—
698C42—2448no—
699C23—21no—
700C23—21no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—611no—
706C23—611no—
707C23—612no—
708C23—612no—
709C23—1222no—
710C23—1222no—
711C23—1224no—
712C23—1224no—
713C23—1224no—
714C23—1224no—
715C23—1221no—
716C23—1221no—
717C23—1221no—
718C23—1221no—
719C23—1221no—
720C23—1221no—
721C23—1222no—
722C23—1222no—
723C23—1222no—
724C23—1222no—
725C23—2442no—
726C23—2441no—
727C23—2442no—
728C23—2441no—
729C23—2441no—
730C23—2441no—
731C23—2442no—
732C23—2442no—
733C23—2442no—
734C23—2448no—
735C23—2444no—
736C23—2444no—
737C23—2448no—
738C23—2448no—
739C23—2442no—
740C23#1451973512yescomplemented
741C23C22×C4×D6111yescharacteristic
742C23C2×D4×D6112yes—
743C23#41×D6112yes—
744C23C2×#1175822411yescharacteristic
745C23C2×#1175822611yescharacteristic
746D4—24no—
747D4—24no—
748D4—1228no—
749D4—1228no—
750D4—1224no—
751D4—1224no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—24no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—41no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—611no—
768C2×C4—614no—
769C2×C4—611no—
770C2×C4—612no—
771C2×C4—612no—
772C2×C4—1224no—
773C2×C4—1222no—
774C2×C4—1224no—
775C2×C4—1222no—
776C2×C4—1224no—
777C2×C4—1224no—
778C2×C4—1224no—
779C2×C4—1222no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1224no—
783C2×C4—1222no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—2442no—
787C2×C4—2442no—
788C2×C4—2442no—
789C2×C4—2442no—
790C2×C4—2442no—
791C2×C4—2442no—
792C2×C4—2442no—
793C2×C4—2442no—
794C2×C4—2442no—
795C2×C4—2442no—
796C2×C4—2442no—
797C2×C4—2441no—
798C2×C4—2442no—
799C2×C4—2442no—
800C2×C4—2444no—
801C2×C4—2444no—
802C2×C4—2444no—
803C2×C4—2442no—
804C2×C4—2441no—
805C2×C4—2441no—
806C2×C4C22⋊C4×D6111yescharacteristic
807C2×C4C22⋊C4×D6112yes—
808C2×C4C22⋊C4×D6111yescharacteristic
809C2×C4#1451973512yescomplemented
810C22—22no—
811C22—21no—
812C22—22no—
813C22—21no—
814C22—22no—
815C22—42no—
816C22—41no—
817C22—41no—
818C22—42no—
819C22—42no—
820C22—41no—
821C22—41no—
822C22—612no—
823C22—612no—
824C22—1224no—
825C22—1224no—
826C22—1221no—
827C22—1221no—
828C22—1221no—
829C22—1221no—
830C22—1222no—
831C22—1222no—
832C22—1222no—
833C22—1222no—
834C22—2444no—
835C22—2444no—
836C22—2444no—
837C22—2444no—
838C22—2442no—
839C22—2442no—
840C22—2442no—
841C22—2442no—
842C22—2448no—
843C22—2448no—
844C22—2441no—
845C22—2441no—
846C22C2×C22⋊C4×D6111yescharacteristic
847C22#117×D6111yescharacteristic
848C22C2×#1451973511yescharacteristic
849C22#1684027212yes—
850C22#1684027512yes—
851C4—22no—
852C4—21no—
853C4—22no—
854C4—41no—
855C4—41no—
856C4—84no—
857C4—612no—
858C4—1222no—
859C4—1222no—
860C4—1221no—
861C4—4884no—
862C4—2441no—
863C4—2441no—
864C4#99×D6112yes—
865C2—22no—
866C2—22no—
867C2—21no—
868C2—21no—
869C2—42no—
870C2—1222no—
871C2—1222no—
872C2—2442no—
873C2—2442no—
874C2#2144820111yescharacteristic
875C2C2×#99×D6111yescharacteristic
876C2#410×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1799C2
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×D61C22
cosocleC24×C61C24
hypercenter#1799D61
hypocenterC61#20722
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #21448201C2semidirect
3. #21445892C2semidirect
4. #21445807C2semidirect
5. #21445804C2semidirect
7. #99×Dic61C2semidirect
8. #21445606C2semidirect
9. C61×#1799C2semidirect
11. C23×C4×D61C4semidirect
13. C2×C4×D244C4semidirect
15. C2×#14519739C4semidirect
16. C2×C4×C22⋊D61C4semidirect
18. C2×#14519737C4semidirect
25. C2×C4⋊C4×D61C4semidirect
26. C2×C22⋊C4×D61C4semidirect
28. C2×C42×D61C4semidirect
32. #16839622C22semidirect
35. C22⋊C4×Dic61C22semidirect
37. #16839529C22semidirect
38. #16839528C22semidirect
41. C61×#380C22semidirect
42. C61×#342C22semidirect
266. C23×C61#117semidirect
306. C22×D61#117semidirect
327. C2×C4×C61#117semidirect
349. C2×Dic61#117semidirect
370. C4×D61#99semidirect
432. #1799D61semidirect
474. #380C2×D61semidirect
480. #342C2×D61semidirect
481. C61#20722semidirect
740. C23#14519735semidirect
809. C2×C4#14519735semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D612
#214482012
#214458922
#214458072
#214458042
#214457322
#99×Dic612
#214456062
C61×#17992
#2072261