Finite Group Databasebeta

← #29679945

Subgroups — #29679945

Order 15616.

1866 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D61C211yesmaximal, characteristic
2#21448200C212yesmaximal, complemented
3#21445892C212yesmaximal, complemented
4#21445806C212yesmaximal, complemented
5#21445805C212yesmaximal, complemented
6#21445732C212yesmaximal
7C4×#14519691C212yesmaximal, complemented
8C4×#14519692C211yesmaximal, characteristic, complemented
9C4×#99×C61C211yesmaximal, 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×#14519734—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#16839621—22no—
33#16839620C2214yescomplemented
34#16839617C2214yes—
35C4×#11758198—22no—
36C4×C22⋊Dic61C2212yescomplemented
37#16839529C2212yescomplemented
38#16839528C2214yescomplemented
39C2×C4×D4×C61C2211yescharacteristic
40C2×#99×C61C2212yes—
41C4×C22⋊C4×C61C2212yescomplemented
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—24no—
51C2×D4×D61—24no—
52C23×Dic61C2×C411yescharacteristic
53C23×Dic61C2311yescharacteristic
54C22×C4×D61—21no—
55C22×C4×D61—21no—
56C22×C4×D61—21no—
57C22×C4×D61—21no—
58C22×C4×D61—44no—
59C22×C4×D61—44no—
60C22×C4×D61C2×C411yescharacteristic
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×D61D412yes—
70C22×C4×D61D412yes—
71C22×C4×D61D412yes—
72C22×C4×D61D412yes—
73C4×D244—22no—
74C4×D244—22no—
75D4×Dic61—22no—
76D4×Dic61—22no—
77#14519739—22no—
78#14519739—22no—
79C4×C22⋊D61—22no—
80C4×C22⋊D61—22no—
81C4×C22⋊D61—22no—
82C4×C22⋊D61—22no—
83#14519737—22no—
84#14519737—22no—
85#14519737—22no—
86#14519737—22no—
87#14519734—48no—
88C2×C4⋊Dic61C2×C411yescharacteristic
89C2×#11758196—24no—
90C2×#11758196C2×C411yescharacteristic
91C2×#11758196C2×C411yescharacteristic
92C4⋊C4×D61—22no—
93C4⋊C4×D61—22no—
94C2×C22⋊Dic61C2×C411yescharacteristic
95C2×C22⋊Dic61C2314yes—
96C2×C22⋊Dic61C2311yescharacteristic
97C2×#11758198—24no—
98C2×#11758198—24no—
99C2×#11758198C2×C411yescharacteristic
100C2×#11758198C2×C411yescharacteristic
101C2×#11758198C2×C411yescharacteristic
102C2×#11758198C2×C411yescharacteristic
103C22⋊C4×D61—22no—
104C22⋊C4×D61—22no—
105C22⋊C4×D61—22no—
106C22⋊C4×D61—22no—
107C2×C4×Dic61—22no—
108C2×C4×Dic61C2×C411yescharacteristic
109C2×C4×Dic61C2×C411yescharacteristic
110C2×C4×Dic61C2×C411yescharacteristic
111C42×D61—21no—
112C42×D61—21no—
113C42×D61—21no—
114C42×D61—21no—
115#14519692—24no—
116#14519691—28no—
117#14519684—22no—
118#14519684—24no—
119C22×D4×C61C2311yescharacteristic
120C23×C4×C61C2×C411yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C4×D4×C61—22no—
123C4×D4×C61—22no—
124C2×C4⋊C4×C61C2×C411yescharacteristic
125C2×C22⋊C4×C61C2×C411yescharacteristic
126C2×C22⋊C4×C61C2314yes—
127C2×C22⋊C4×C61C2311yescharacteristic
128C2×C42×C61—22no—
129C2×C42×C61C2×C411yescharacteristic
130#99×C61—24no—
131#95×C61—22no—
132C24×C61C22×C411yescharacteristic
133C24×C61C2411yescharacteristic
134C23×D61—22no—
135C23×D61—22no—
136C23×D61—22no—
137C23×D61—21no—
138C23×D61—21no—
139C23×D61—22no—
140C23×D61—42no—
141C23×D61—42no—
142C23×D61—42no—
143C23×D61—42no—
144C23×D61C22×C411yescharacteristic
145C23×D61C22×C411yescharacteristic
146C23×D61C22×C411yescharacteristic
147C23×D61C2×D412yes—
148C23×D61C2×D412yes—
149C2×D4×C61—22no—
150C2×D4×C61—22no—
151C2×D4×C61#4114yes—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—24no—
155C22×C4×C61—42no—
156C22×C4×C61—42no—
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C2×D412yes—
163C22×C4×C61C2×D412yes—
164C2×C22⋊D61—22no—
165C2×C22⋊D61—22no—
166C2×C22⋊D61—22no—
167C2×C22⋊D61—22no—
168C2×C22⋊D61—22no—
169C2×C22⋊D61#4114yes—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—24no—
173C22×Dic61—42no—
174C22×Dic61—42no—
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C22×Dic61C22×C411yescharacteristic
180C22×Dic61C2×D412yes—
181C22×Dic61C2×D412yes—
182D4×D61—216no—
183D4×D61—216no—
184C2×D244—22no—
185C2×D244—22no—
186C2×D244—22no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—22no—
190C2×C4×D61—22no—
191C2×C4×D61—24no—
192C2×C4×D61—28no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—42no—
202C2×C4×D61—44no—
203C2×C4×D61—42no—
204C2×C4×D61—44no—
205C2×C4×D61—42no—
206C2×C4×D61—44no—
207C2×C4×D61—44no—
208C2×C4×D61—44no—
209C2×C4×D61—44no—
210C2×C4×D61—44no—
211C2×C4×D61—42no—
212C2×C4×D61—42no—
213C2×C4×D61—42no—
214C2×C4×D61—42no—
215C2×C4×D61C22⋊C411yescharacteristic
216C2×C4×D61C22⋊C411yescharacteristic
217C2×C4×D61C22⋊C411yescharacteristic
218C2×C4×D61C22⋊C412yes—
219C2×C4×D61C22⋊C412yes—
220C2×C4×D61C22⋊C412yes—
221C2×C4×D61C22⋊C412yes—
222C2×C4×D61C22⋊C412yes—
223C2×C4×D61C22⋊C412yes—
224C2×C4×D61C22⋊C411yescharacteristic
225C4⋊C4×C61—22no—
226C22⋊C4×C61—22no—
227C22⋊C4×C61—22no—
228C22⋊C4×C61—24no—
229C22⋊C4×C61—24no—
230C42×C61—21no—
231C42×C61—21no—
232C42×C61—44no—
233C22⋊Dic61—22no—
234C22⋊Dic61—22no—
235C22⋊Dic61—24no—
236C22⋊Dic61—24no—
237#11758198—22no—
238#11758198—22no—
239#11758198—22no—
240#11758198—22no—
241#11758198—48no—
242#11758198—48no—
243C4⋊Dic61—22no—
244#11758196—22no—
245#11758196—22no—
246#11758196—48no—
247C4×Dic61—21no—
248C4×Dic61—21no—
249C4×Dic61—21no—
250C4×Dic61—21no—
251C4×Dic61—21no—
252C4×Dic61—21no—
253C4×Dic61—44no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61#11712yescomplemented
261C23×C61C23×C411yescharacteristic
262C23×C61C22×D412yes—
263C23×C61C2×#4112yes—
264C23×C61C2×#4112yes—
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—22no—
268C22×D61—22no—
269C22×D61—24no—
270C22×D61—24no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—24no—
276C22×D61—24no—
277C22×D61—24no—
278C22×D61—24no—
279C22×D61—41no—
280C22×D61—42no—
281C22×D61—41no—
282C22×D61—42no—
283C22×D61—42no—
284C22×D61—48no—
285C22×D61—48no—
286C22×D61—48no—
287C22×D61—48no—
288C22×D61—42no—
289C22×D61—42no—
290C22×D61—42no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61C2×C22⋊C412yes—
294C22×D61C2×C22⋊C411yescharacteristic
295C22×D61C2×C22⋊C411yescharacteristic
296C22×D61#11712yescomplemented
297D4×C61—28no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—24no—
301C2×C4×C61—22no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—41no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—44no—
311C2×C4×C61—44no—
312C2×C4×C61—44no—
313C2×C4×C61C2×C22⋊C411yescharacteristic
314C2×C4×C61C2×C22⋊C412yes—
315C2×C4×C61C2×C22⋊C411yescharacteristic
316C2×C4×C61#11712yescomplemented
317C22⋊D61—28no—
318C22⋊D61—28no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—24no—
322C2×Dic61—22no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—41no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—44no—
332C2×Dic61—44no—
333C2×Dic61—44no—
334C2×Dic61C2×C22⋊C411yescharacteristic
335C2×Dic61C2×C22⋊C412yes—
336C2×Dic61C2×C22⋊C411yescharacteristic
337C2×Dic61#11712yescomplemented
338D244—28no—
339C4×D61—24no—
340C4×D61—24no—
341C4×D61—22no—
342C4×D61—24no—
343C4×D61—22no—
344C4×D61—24no—
345C4×D61—22no—
346C4×D61—24no—
347C4×D61—42no—
348C4×D61—42no—
349C4×D61—42no—
350C4×D61—42no—
351C4×D61—42no—
352C4×D61—42no—
353C4×D61—42no—
354C4×D61—42no—
355C4×D61—42no—
356C4×D61—42no—
357C4×D61—42no—
358C4×D61#9914yescomplemented
359#20722—611nomaximal, Sylow
360C22×C61—22no—
361C22×C61—21no—
362C22×C61—22no—
363C22×C61—21no—
364C22×C61—22no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—42no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61C22×C22⋊C411yescharacteristic
372C22×C61C2×#11711yescharacteristic
373C22×C61C2×#11711yescharacteristic
374C22×C61#52514yes—
375C2×D61—24no—
376C2×D61—24no—
377C2×D61—21no—
378C2×D61—21no—
379C2×D61—21no—
380C2×D61—21no—
381C2×D61—22no—
382C2×D61—22no—
383C2×D61—22no—
384C2×D61—22no—
385C2×D61—48no—
386C2×D61—48no—
387C2×D61—48no—
388C2×D61—48no—
389C2×D61—42no—
390C2×D61—42no—
391C2×D61—42no—
392C2×D61—41no—
393C2×D61—41no—
394C2×D61—42no—
395C2×D61C2×#9912yes—
396C2×D61#41012yes—
397C4×C61—21no—
398C4×C61—22no—
399C4×C61—22no—
400C4×C61—41no—
401C4×C61—41no—
402C4×C61—84no—
403C4×C61C2×#9912yes—
404Dic61—21no—
405Dic61—22no—
406Dic61—22no—
407Dic61—41no—
408Dic61—41no—
409Dic61—84no—
410Dic61C2×#9912yes—
411C22×C4×D4—611no—
412#2280—612no—
413#1819—612no—
414#1799—612no—
415#1799—612no—
416#1781—612no—
417C4×#99—612no—
418C4×#99—611no—
419C4×#99D6111yescharacteristic, complemented
420C2×C61—24no—
421C2×C61—21no—
422C2×C61—21no—
423C2×C61—42no—
424C2×C61#228011yescharacteristic
425C2×C61C22×#9911yescharacteristic
426C2×C61C2×#41011yescharacteristic
427D61—22no—
428D61—22no—
429D61—42no—
430D61—42no—
431C23×D4—611no—
432C24×C4—611no—
433C24×C4—611no—
434C2×C4×D4—611no—
435C2×C4×D4—611no—
436C2×C4×D4—611no—
437C2×C4×D4—611no—
438C2×C4×D4—611no—
439C2×C4×D4—611no—
440C2×C4×D4—611no—
441C2×C4×D4—1222no—
442C2×C4×D4—1222no—
443C2×C4×D4—1222no—
444C2×C4×D4—1222no—
445C2×C4×D4C2×D6111yescharacteristic
446C2×#117—1222no—
447C22×C4⋊C4—611no—
448C22×C22⋊C4—611no—
449C22×C22⋊C4—611no—
450C22×C42—611no—
451C2×#99—612no—
452C2×#99—614no—
453C2×#99C2×D6112yes—
454#381—1222no—
455#380—614no—
456#380—1222no—
457#379—614no—
458C4×C22⋊C4—612no—
459C4×C22⋊C4—1222no—
460C4×C22⋊C4C2×D6112yescomplemented
461#342—614no—
462#342—612no—
463#342C2×D6112yescomplemented
464C61#2072211yescharacteristic, complemented, Sylow
465C25—611no—
466C25—611no—
467C22×D4—611no—
468C22×D4—611no—
469C22×D4—611no—
470C22×D4—1224no—
471C22×D4—1222no—
472C22×D4—1222no—
473C22×D4—1224no—
474C22×D4C22×D6111yescharacteristic
475C23×C4—611no—
476C23×C4—611no—
477C23×C4—612no—
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—611no—
481C23×C4—612no—
482C23×C4—612no—
483C23×C4—612no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—611no—
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—1221no—
491C23×C4—1221no—
492C23×C4—1221no—
493C23×C4—1221no—
494C23×C4—2444no—
495C23×C4—2444no—
496C23×C4C4×D6111yescharacteristic
497C23×C4C22×D6111yescharacteristic
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—1222no—
501C4×D4—1222no—
502C4×D4—1222no—
503C4×D4—1222no—
504C4×D4—1222no—
505C4×D4—1222no—
506C4×D4—1222no—
507C4×D4—1222no—
508C4×D4—1222no—
509C4×D4—1222no—
510C4×D4—1222no—
511C4×D4—1222no—
512C4×D4—1222no—
513C4×D4—1222no—
514#117—2448no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—1222no—
519C2×C4⋊C4—1222no—
520C2×C4⋊C4—1224no—
521C2×C4⋊C4C4×D6111yescharacteristic
522C2×C22⋊C4—611no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4—611no—
525C2×C22⋊C4—611no—
526C2×C22⋊C4—611no—
527C2×C22⋊C4—611no—
528C2×C22⋊C4—614no—
529C2×C22⋊C4—1222no—
530C2×C22⋊C4—1222no—
531C2×C22⋊C4—1222no—
532C2×C22⋊C4—1222no—
533C2×C22⋊C4—1224no—
534C2×C22⋊C4—1224no—
535C2×C22⋊C4C4×D6111yescharacteristic
536C2×C22⋊C4C22×D6114yes—
537C2×C22⋊C4C22×D6111yescharacteristic
538C2×C42—22no—
539C2×C42—611no—
540C2×C42—611no—
541C2×C42—611no—
542C2×C42—1221no—
543C2×C42—1221no—
544C2×C42—1221no—
545C2×C42—1221no—
546C2×C42—1222no—
547C2×C42C4×D6111yescharacteristic
548#99—24no—
549#99—1228no—
550#99—1224no—
551#95—22no—
552#95—1224no—
553#95—1222no—
554C24—611no—
555C24—612no—
556C24—612no—
557C24—611no—
558C24—611no—
559C24—1221no—
560C24—1221no—
561C24—1222no—
562C24—1222no—
563C24—1222no—
564C24—1222no—
565C24—2442no—
566C24—2442no—
567C24—2442no—
568C24—2442no—
569C24C2×C4×D6111yescharacteristic
570C24C23×D6111yescharacteristic
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—614no—
574C2×D4—1222no—
575C2×D4—1222no—
576C2×D4—1222no—
577C2×D4—12216no—
578C2×D4—12216no—
579C2×D4—1222no—
580C2×D4—1222no—
581C2×D4—1222no—
582C2×D4—1222no—
583C2×D4—1222no—
584C2×D4#1175822214yes—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—24no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—611no—
593C22×C4—612no—
594C22×C4—611no—
595C22×C4—612no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—612no—
599C22×C4—612no—
600C22×C4—611no—
601C22×C4—612no—
602C22×C4—612no—
603C22×C4—612no—
604C22×C4—612no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—1228no—
608C22×C4—1224no—
609C22×C4—1222no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1222no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1224no—
624C22×C4—2444no—
625C22×C4—2442no—
626C22×C4—2442no—
627C22×C4—2444no—
628C22×C4—2442no—
629C22×C4—2444no—
630C22×C4—2442no—
631C22×C4—2444no—
632C22×C4—2444no—
633C22×C4—2444no—
634C22×C4—2444no—
635C22×C4—2442no—
636C22×C4—2442no—
637C22×C4—2442no—
638C22×C4—2442no—
639C22×C4—2442no—
640C22×C4C2×C4×D6111yescharacteristic
641C22×C4C2×C4×D6111yescharacteristic
642C22×C4C2×C4×D6111yescharacteristic
643C22×C4C2×C4×D6111yescharacteristic
644C22×C4C2×C4×D6111yescharacteristic
645C22×C4D4×D6112yes—
646C22×C4D4×D6112yes—
647C4⋊C4—22no—
648C4⋊C4—1222no—
649C4⋊C4—1222no—
650C4⋊C4—1222no—
651C4⋊C4—2448no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—1222no—
657C22⋊C4—1222no—
658C22⋊C4—1222no—
659C22⋊C4—1222no—
660C22⋊C4—1222no—
661C22⋊C4—1222no—
662C22⋊C4—1224no—
663C22⋊C4—1224no—
664C22⋊C4—2448no—
665C22⋊C4—2448no—
666C42—21no—
667C42—21no—
668C42—44no—
669C42—1221no—
670C42—1221no—
671C42—1221no—
672C42—1221no—
673C42—1221no—
674C42—1221no—
675C42—2444no—
676C23—21no—
677C23—21no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—611no—
683C23—611no—
684C23—612no—
685C23—612no—
686C23—1222no—
687C23—1222no—
688C23—1224no—
689C23—1224no—
690C23—1224no—
691C23—1224no—
692C23—1221no—
693C23—1221no—
694C23—1221no—
695C23—1221no—
696C23—1221no—
697C23—1221no—
698C23—1224no—
699C23—1224no—
700C23—2442no—
701C23—2441no—
702C23—2442no—
703C23—2441no—
704C23—2441no—
705C23—2441no—
706C23—2442no—
707C23—2442no—
708C23—2442no—
709C23—2448no—
710C23—2448no—
711C23—2448no—
712C23—2448no—
713C23—2442no—
714C23#1451973412yescomplemented
715C23C22×C4×D6111yescharacteristic
716C23C2×D4×D6112yes—
717C23#41×D6112yes—
718C23C2×#1175822212yes—
719D4—28no—
720D4—1228no—
721D4—1228no—
722D4—1228no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—611no—
739C2×C4—614no—
740C2×C4—611no—
741C2×C4—612no—
742C2×C4—612no—
743C2×C4—1224no—
744C2×C4—1222no—
745C2×C4—1224no—
746C2×C4—1222no—
747C2×C4—1224no—
748C2×C4—1224no—
749C2×C4—1224no—
750C2×C4—1222no—
751C2×C4—1221no—
752C2×C4—1221no—
753C2×C4—1224no—
754C2×C4—1222no—
755C2×C4—1221no—
756C2×C4—1221no—
757C2×C4—2442no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4—2442no—
762C2×C4—2442no—
763C2×C4—2442no—
764C2×C4—2442no—
765C2×C4—2442no—
766C2×C4—2442no—
767C2×C4—2442no—
768C2×C4—2441no—
769C2×C4—2442no—
770C2×C4—2442no—
771C2×C4—2444no—
772C2×C4—2444no—
773C2×C4—2444no—
774C2×C4—2442no—
775C2×C4—2441no—
776C2×C4—2441no—
777C2×C4C22⋊C4×D6111yescharacteristic
778C2×C4C22⋊C4×D6112yes—
779C2×C4C22⋊C4×D6111yescharacteristic
780C2×C4#1451973412yescomplemented
781C22—22no—
782C22—21no—
783C22—22no—
784C22—21no—
785C22—22no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—41no—
791C22—41no—
792C22—612no—
793C22—612no—
794C22—1224no—
795C22—1224no—
796C22—1221no—
797C22—1221no—
798C22—1221no—
799C22—1221no—
800C22—1222no—
801C22—1222no—
802C22—1222no—
803C22—1222no—
804C22—2448no—
805C22—2448no—
806C22—2442no—
807C22—2442no—
808C22—2442no—
809C22—2442no—
810C22—2448no—
811C22—2448no—
812C22—2441no—
813C22—2441no—
814C22C2×C22⋊C4×D6111yescharacteristic
815C22#117×D6111yescharacteristic
816C22C2×#1451973411yescharacteristic
817C22#1684027114yes—
818C4—22no—
819C4—21no—
820C4—22no—
821C4—41no—
822C4—41no—
823C4—84no—
824C4—612no—
825C4—1222no—
826C4—1222no—
827C4—1221no—
828C4—4884no—
829C4—2441no—
830C4—2441no—
831C4#99×D6112yes—
832C2—24no—
833C2—21no—
834C2—21no—
835C2—42no—
836C2—1222no—
837C2—1222no—
838C2—2442no—
839C2—2442no—
840C2#2144820011yescharacteristic
841C2C2×#99×D6111yescharacteristic
842C2#410×D6111yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC4×#99×C61C2
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×D61C22
cosocleC24×C61C24
hypercenterC4×#99D61
hypocenterC61#20722
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #21448200C2semidirect
3. #21445892C2semidirect
4. #21445806C2semidirect
5. #21445805C2semidirect
7. C4×#14519691C2semidirect
8. C4×#14519692C2semidirect
9. C4×#99×C61C2semidirect
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
33. #16839620C22semidirect
36. C4×C22⋊Dic61C22semidirect
37. #16839529C22semidirect
38. #16839528C22semidirect
41. C4×C22⋊C4×C61C22semidirect
42. C61×#342C22semidirect
260. C23×C61#117semidirect
296. C22×D61#117semidirect
316. C2×C4×C61#117semidirect
337. C2×Dic61#117semidirect
358. C4×D61#99semidirect
419. C4×#99D61semidirect
460. C4×C22⋊C4C2×D61semidirect
463. #342C2×D61semidirect
464. C61#20722semidirect
714. C23#14519734semidirect
780. C2×C4#14519734semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D612
#214482002
#214458922
#214458062
#214458052
#214457322
C4×#145196912
C4×#145196922
C4×#99×C612
#2072261