Finite Group Databasebeta

← #29681804

Subgroups — #29681804

Order 15616.

1994 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840270C211yesmaximal, characteristic
2C2×#117×D61C211yesmaximal, characteristic, complemented
3C2×#16839734C212yesmaximal, complemented
4#21448199C211yesmaximal, characteristic, complemented
5#21446278C211yesmaximal, characteristic, complemented
6#21446277C211yesmaximal, characteristic, complemented
7#21446275C211yesmaximal, characteristic, complemented
8#21446271C212yesmaximal, complemented
9#21446269C212yesmaximal, complemented
10#21445550C212yesmaximal, complemented
11C61×#1899C211yesmaximal, characteristic, complemented
12C22×#11758224C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14#16840270—21no—
15#16840270—21no—
16#16840270—21no—
17#16840270—21no—
18#16840270—22no—
19#16840270—22no—
20C2×#14519760C2211yescharacteristic
21C2×#14519755C412yescomplemented
22C2×#14519750C412yescomplemented
23C2×#14519747C2211yescharacteristic
24C2×#14519745C2211yescharacteristic
25C2×#14519739C412yescomplemented
26C2×#14519737C412yescomplemented
27C2×#14519736C2211yescharacteristic
28C2×#14519735—21no—
29C2×#14519734—21no—
30C2×#14519733C2212yes—
31C2×#14519733C2212yes—
32C2×#14519733C2211yescharacteristic
33#117×D61—28no—
34C2×C4⋊C4×D61—21no—
35C2×C22⋊C4×D61C2212yes—
36C2×C42×D61—21no—
37#16839734—28no—
38C2×#14519692C2212yes—
39C2×#14519691C2212yes—
40C2×#14519691C2212yes—
41#16839625C2211yescharacteristic
42#16839621—22no—
43#16839617C2212yes—
44#16839609—22no—
45#16839529C2212yes—
46#16839528C2212yes—
47#16839528C2212yes—
48C2×#123×C61C2211yescharacteristic
49C2×#117×C61C2211yescharacteristic
50C2×#99×C61C2212yes—
51C61×#381C2211yescharacteristic
52C61×#342C2212yes—
53C24×D61C2311yescharacteristic
54C2×#11758224—24no—
55C2×#11758224—21no—
56C2×#11758224—21no—
57C2×#11758224—21no—
58C2×#11758224—21no—
59C2×#11758224—24no—
60C22×Dic122C2×C411yescharacteristic, complemented
61C22×D244C2×C412yes—
62C22×C22⋊D61C2×C412yes—
63C22×C22⋊D61C2×C411yescharacteristic, complemented
64C22×C22⋊D61C2311yescharacteristic
65C23×Dic61C2×C411yescharacteristic, complemented
66C23×Dic61C2311yescharacteristic
67C22×C4×D61—24no—
68C22×C4×D61—24no—
69C22×C4×D61—22no—
70C22×C4×D61C2×C412yes—
71C22×C4×D61C2×C412yes—
72C22×C4×D61C2×C411yescharacteristic, complemented
73C22×C4×D61D411yescharacteristic
74C22×C4×D61D411yescharacteristic
75C22×C4×D61D411yescharacteristic
76C22×C4×D61D411yescharacteristic
77C22×C4×D61D412yes—
78C22×C4×D61D412yes—
79#14519760—22no—
80#14519760—21no—
81#14519760—21no—
82#14519755—22no—
83#14519755—22no—
84#14519755—22no—
85#14519755—22no—
86#14519750—22no—
87#14519750—22no—
88#14519750—22no—
89#14519750—22no—
90#14519747—21no—
91#14519747—22no—
92#14519747—21no—
93#14519745—21no—
94#14519745—22no—
95#14519745—21no—
96#14519739—22no—
97#14519739—22no—
98#14519739—22no—
99#14519739—22no—
100#14519737—22no—
101#14519737—22no—
102#14519737—22no—
103#14519737—22no—
104#14519736—24no—
105#14519735—28no—
106#14519734—28no—
107#14519733—24no—
108#14519733—21no—
109#14519733—21no—
110#14519733—21no—
111#14519733—21no—
112#14519733—24no—
113#14519733—24no—
114#14519733D418yescomplemented
115C2×C4⋊Dic61—21no—
116C2×#11758196—22no—
117C2×#11758196—22no—
118C2×#11758196C2×C412yescomplemented
119C2×#11758196C2×C412yescomplemented
120C4⋊C4×D61—28no—
121C2×C22⋊Dic61C2312yes—
122C2×C22⋊Dic61C2311yescharacteristic
123C2×C22⋊Dic61C2312yes—
124C2×#11758198—22no—
125C2×#11758198—24no—
126C2×#11758198C2×C412yes—
127C2×#11758198C2×C412yes—
128C2×#11758198C2×C412yescomplemented
129C22⋊C4×D61—24no—
130C22⋊C4×D61—24no—
131C2×C4×Dic61—21no—
132C2×C4×Dic61—22no—
133C2×C4×Dic61—22no—
134C2×C4×Dic61C2×C412yescomplemented
135C42×D61—28no—
136#14519692—24no—
137#14519691—24no—
138#14519691—24no—
139#14519684—22no—
140C22×D4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142#123×C61—22no—
143#123×C61—21no—
144#123×C61—21no—
145#117×C61—24no—
146C2×C4⋊C4×C61—21no—
147C2×C4⋊C4×C61C2×C412yescomplemented
148C2×C22⋊C4×C61C2×C412yescomplemented
149C2×C22⋊C4×C61C2312yes—
150C2×C22⋊C4×C61C2311yescharacteristic
151C2×C22⋊C4×C61C2312yes—
152C2×C42×C61—21no—
153#99×C61—24no—
154#95×C61—22no—
155C24×C61C22×C411yescharacteristic
156C24×C61C2411yescharacteristic
157C23×D61—22no—
158C23×D61—22no—
159C23×D61—44no—
160C23×D61C22×C412yes—
161C23×D61C22×C411yescharacteristic
162C23×D61C2×D411yescharacteristic
163C23×D61C2×D412yes—
164C23×D61C2×D411yescharacteristic
165C2×D4×C61—22no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—22no—
169C22×C4×C61—22no—
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—22no—
173C22×C4×C61C22×C411yescharacteristic
174C22×C4×C61C22×C412yes—
175C22×C4×C61C22×C412yes—
176C22×C4×C61C2×D412yes—
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C2×C22⋊D61—22no—
180C2×C22⋊D61—21no—
181C2×C22⋊D61—21no—
182C2×C22⋊D61—22no—
183C2×C22⋊D61—22no—
184C2×C22⋊D61—22no—
185C2×C22⋊D61—21no—
186C2×C22⋊D61—21no—
187C2×C22⋊D61—24no—
188C2×C22⋊D61—44no—
189C22×Dic61—22no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—24no—
193C22×Dic61—22no—
194C22×Dic61C22×C411yescharacteristic
195C22×Dic61C22×C412yes—
196C22×Dic61C22×C411yescharacteristic
197C22×Dic61C22×C411yescharacteristic
198C22×Dic61C2×D411yescharacteristic
199C22×Dic61C2×D411yescharacteristic
200C22×Dic61C2×D411yescharacteristic
201C22×Dic61C2×D411yescharacteristic
202C22×Dic61C2×D414yes—
203C22×Dic61#4114yes—
204#11758224—42no—
205#11758224—42no—
206#11758224—44no—
207#11758224—44no—
208#11758224—42no—
209#11758224—42no—
210C2×D244—22no—
211C2×D244—22no—
212C2×D244—44no—
213C2×C4×D61—28no—
214C2×C4×D61—28no—
215C2×C4×D61—22no—
216C2×C4×D61—22no—
217C2×C4×D61—22no—
218C2×C4×D61—22no—
219C2×C4×D61—28no—
220C2×C4×D61—28no—
221C2×C4×D61—22no—
222C2×C4×D61—22no—
223C2×C4×D61—22no—
224C2×C4×D61—22no—
225C2×C4×D61—28no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—24no—
229C2×C4×D61—48no—
230C2×C4×D61C22⋊C412yes—
231C2×C4×D61C22⋊C412yes—
232C2×C4×D61C22⋊C412yes—
233C2×C4×D61C22⋊C412yes—
234C2×C4×D61C22⋊C412yes—
235C2×C4×D61C22⋊C412yes—
236C2×C4×D61C22⋊C412yes—
237C2×C4×D61C22⋊C412yes—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—24no—
241C4⋊C4×C61—24no—
242C4⋊C4×C61—22no—
243C4⋊C4×C61—22no—
244C22⋊C4×C61—22no—
245C22⋊C4×C61—21no—
246C22⋊C4×C61—21no—
247C22⋊C4×C61—22no—
248C22⋊C4×C61—22no—
249C22⋊C4×C61—22no—
250C22⋊C4×C61—22no—
251C22⋊C4×C61C2×D414yes—
252C42×C61—24no—
253C22⋊Dic61—22no—
254C22⋊Dic61—21no—
255C22⋊Dic61—21no—
256C22⋊Dic61—22no—
257C22⋊Dic61—22no—
258C22⋊Dic61C2×D414yes—
259#11758198—28no—
260#11758198—22no—
261#11758198—22no—
262#11758198—22no—
263#11758198—22no—
264#11758198—22no—
265#11758198—22no—
266#11758198—48no—
267C4⋊Dic61—24no—
268#11758196—22no—
269#11758196—22no—
270#11758196—22no—
271#11758196—22no—
272#11758196—28no—
273#11758196—44no—
274C4×Dic61—24no—
275C4×Dic61—22no—
276C4×Dic61—22no—
277C4×Dic61—28no—
278C4×Dic61—44no—
279C23×C61—21no—
280C23×C61—22no—
281C23×C61—42no—
282C23×C61—42no—
283C23×C61C23×C411yescharacteristic
284C23×C61C22×D411yescharacteristic
285C23×C61C22×D411yescharacteristic
286C23×C61C22×D412yes—
287C23×C61C2×#4112yes—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—24no—
291C22×D61—24no—
292C22×D61—21no—
293C22×D61—24no—
294C22×D61—21no—
295C22×D61—24no—
296C22×D61—24no—
297C22×D61—21no—
298C22×D61—22no—
299C22×D61—42no—
300C22×D61—42no—
301C22×D61—42no—
302C22×D61—48no—
303C22×D61—48no—
304C22×D61—42no—
305C22×D61C2×C22⋊C412yes—
306C22×D61C2×C22⋊C412yes—
307D4×C61—41no—
308D4×C61—42no—
309D4×C61—41no—
310C2×C4×C61—24no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—24no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—22no—
317C2×C4×C61—21no—
318C2×C4×C61—22no—
319C2×C4×C61—24no—
320C2×C4×C61—44no—
321C2×C4×C61—42no—
322C2×C4×C61—44no—
323C2×C4×C61—42no—
324C2×C4×C61C2×C22⋊C412yes—
325C2×C4×C61C2×C22⋊C412yes—
326C22⋊D61—44no—
327C22⋊D61—41no—
328C22⋊D61—42no—
329C22⋊D61—41no—
330C22⋊D61—44no—
331C22⋊D61—42no—
332C22⋊D61—42no—
333C2×Dic61—22no—
334C2×Dic61—21no—
335C2×Dic61—22no—
336C2×Dic61—24no—
337C2×Dic61—44no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61—44no—
342C2×Dic61—42no—
343C2×Dic61C2×C22⋊C411yescharacteristic
344C2×Dic61C2×C22⋊C411yescharacteristic
345C2×Dic61C2×C22⋊C411yescharacteristic
346C2×Dic61C2×C22⋊C411yescharacteristic
347C2×Dic61C4×D414yes—
348C2×Dic61C4×D414yes—
349C2×Dic61#12012yes—
350C2×Dic61#12012yes—
351C2×Dic61#12114yes—
352C2×Dic61#12114yes—
353C2×Dic61#12312yes—
354C2×Dic61#12312yes—
355D244—44no—
356D244—44no—
357C4×D61—24no—
358C4×D61—24no—
359C4×D61—24no—
360C4×D61—24no—
361C4×D61—24no—
362C4×D61—24no—
363C4×D61—24no—
364C4×D61—24no—
365C4×D61—416no—
366C4×D61—42no—
367C4×D61—42no—
368Dic122—42no—
369Dic122—42no—
370#20983—611nomaximal, Sylow
371C22×C61—22no—
372C22×C61—22no—
373C22×C61—22no—
374C22×C61—42no—
375C22×C61—42no—
376C22×C61—42no—
377C22×C61—41no—
378C22×C61—82no—
379C22×C61C22×C22⋊C411yescharacteristic
380C22×C61C2×C4×D412yes—
381C22×C61C2×#12011yescharacteristic
382C22×C61C2×#12112yes—
383C22×C61C2×#12311yescharacteristic
384C2×D61—24no—
385C2×D61—24no—
386C2×D61—22no—
387C2×D61—22no—
388C2×D61—22no—
389C2×D61—22no—
390C2×D61—22no—
391C2×D61—48no—
392C2×D61—48no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—41no—
397C2×D61—82no—
398C2×D61#41014yescomplemented
399C4×C61—22no—
400C4×C61—22no—
401C4×C61—44no—
402C4×C61—42no—
403C4×C61—41no—
404C4×C61—82no—
405Dic61—44no—
406Dic61—42no—
407Dic61—41no—
408Dic61—82no—
409Dic61#38612yes—
410Dic61#38612yes—
411Dic61#38612yes—
412Dic61#38612yes—
413C2×#525—611no—
414C22×#117—611no—
415C2×#410—612no—
416#2280—611no—
417#1899—611no—
418#1899—611no—
419#1899—611no—
420#1899D6111yescharacteristic, complemented
421#1898—612no—
422#1898—612no—
423#1740—612no—
424C2×C61—21no—
425C2×C61—22no—
426C2×C61—21no—
427C2×C61—22no—
428C2×C61—81no—
429C2×C61C2×#38611yescharacteristic
430C2×C61C2×#41012yes—
431D61—24no—
432D61—42no—
433D61—81no—
434C22×#41—611no—
435C24×C4—611no—
436#525—1221no—
437#525—1221no—
438#525—1221no—
439#525—1222no—
440#525—1222no—
441#525—1221no—
442C2×#123—611no—
443C2×#123C2×D6111yescharacteristic
444C2×C22⋊Q8—612no—
445C2×#121—612no—
446C2×#120—611no—
447C2×#120—611no—
448C2×C4×D4—612no—
449C2×C4×D4—612no—
450C2×#117—611no—
451C2×#117—611no—
452C2×#117—612no—
453C2×#117—612no—
454C2×#117—1221no—
455C2×#117—1221no—
456C2×#117—1228no—
457C2×#117C2×D6111yescharacteristic
458C22×C4⋊C4—1221no—
459C22×C22⋊C4—612no—
460C22×C42—1221no—
461#410—1228no—
462C2×#99—612no—
463C2×#99—612no—
464C2×#99—612no—
465C2×#99C2×D6112yes—
466#381—611no—
467#381C2×D6111yescharacteristic
468#380—1222no—
469#379—612no—
470C4×C22⋊C4—1222no—
471#342—612no—
472#342—612no—
473#342—612no—
474#342C2×D6112yes—
475C61#2098311yescharacteristic, complemented, Sylow
476C25—611no—
477C2×#41—1221no—
478C2×#41—1221no—
479C2×#41—1221no—
480C2×#41—1221no—
481C2×#41—1224no—
482C2×#41—1224no—
483C22×Q8—611no—
484C22×D4—611no—
485C22×D4—611no—
486C22×D4—612no—
487C22×D4—612no—
488C22×D4C22×D6111yescharacteristic
489C23×C4—611no—
490C23×C4—612no—
491C23×C4—612no—
492C23×C4—611no—
493C23×C4—611no—
494C23×C4—611no—
495C23×C4—612no—
496C23×C4—612no—
497C23×C4—611no—
498C23×C4—611no—
499C23×C4—611no—
500C23×C4—1224no—
501C23×C4—1224no—
502C23×C4—1222no—
503C23×C4C22×D6111yescharacteristic
504#123—22no—
505#123—21no—
506#123—21no—
507#123—1222no—
508#123—1221no—
509#123—1221no—
510C22⋊Q8—1222no—
511C22⋊Q8—1222no—
512C22⋊Q8—1222no—
513C22⋊Q8—1222no—
514#121—1222no—
515#121—1222no—
516#121—1222no—
517#121—1222no—
518#120—1221no—
519#120—1222no—
520#120—1221no—
521#120—1221no—
522#120—1222no—
523#120—1221no—
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—24no—
533#117—618no—
534#117—1228no—
535#117—1224no—
536#117—1221no—
537#117—1221no—
538#117—1221no—
539#117—1221no—
540#117—1224no—
541#117—1228no—
542#117—1224no—
543#117—1224no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—612no—
546C2×C4⋊C4—612no—
547C2×C4⋊C4—1228no—
548C2×C4⋊C4—1222no—
549C2×C4⋊C4—1221no—
550C2×C4⋊C4—1222no—
551C2×C4⋊C4C4×D6112yescomplemented
552C2×C22⋊C4—612no—
553C2×C22⋊C4—611no—
554C2×C22⋊C4—612no—
555C2×C22⋊C4—612no—
556C2×C22⋊C4—612no—
557C2×C22⋊C4—612no—
558C2×C22⋊C4—1224no—
559C2×C22⋊C4—1222no—
560C2×C22⋊C4—1224no—
561C2×C22⋊C4—1224no—
562C2×C22⋊C4C4×D6112yescomplemented
563C2×C22⋊C4C22×D6112yes—
564C2×C22⋊C4C22×D6111yescharacteristic
565C2×C22⋊C4C22×D6112yes—
566C2×C42—21no—
567C2×C42—612no—
568C2×C42—1228no—
569C2×C42—1222no—
570C2×C42—1221no—
571C2×C42—1222no—
572#99—24no—
573#99—1224no—
574#99—1224no—
575#99—1224no—
576#95—22no—
577#95—1222no—
578C24—611no—
579C24—612no—
580C24—612no—
581C24—611no—
582C24—611no—
583C24—1222no—
584C24—1222no—
585C24—2444no—
586C24C2×C4×D6111yescharacteristic
587C24C23×D6111yescharacteristic
588#41—2442no—
589#41—2442no—
590#41—2444no—
591#41—2444no—
592#41—2442no—
593#41—2442no—
594C2×Q8—1221no—
595C2×Q8—1221no—
596C2×Q8—1224no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—22no—
601C2×D4—1222no—
602C2×D4—1222no—
603C2×D4—1221no—
604C2×D4—1221no—
605C2×D4—1224no—
606C2×D4—1222no—
607C2×D4—1222no—
608C2×D4—1222no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1222no—
612C2×D4—2444no—
613C2×D4—2444no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—611no—
624C22×C4—614no—
625C22×C4—614no—
626C22×C4—612no—
627C22×C4—612no—
628C22×C4—612no—
629C22×C4—612no—
630C22×C4—612no—
631C22×C4—612no—
632C22×C4—612no—
633C22×C4—612no—
634C22×C4—611no—
635C22×C4—612no—
636C22×C4—1222no—
637C22×C4—1222no—
638C22×C4—1222no—
639C22×C4—1222no—
640C22×C4—1228no—
641C22×C4—1228no—
642C22×C4—1228no—
643C22×C4—1228no—
644C22×C4—1222no—
645C22×C4—1222no—
646C22×C4—1222no—
647C22×C4—1222no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4—1224no—
651C22×C4—1228no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4—1224no—
655C22×C4—1222no—
656C22×C4—1222no—
657C22×C4—2448no—
658C22×C4C2×C4×D6111yescharacteristic
659C22×C4C2×C4×D6112yes—
660C22×C4C2×C4×D6112yes—
661C22×C4D4×D6112yes—
662C22×C4D4×D6111yescharacteristic
663C22×C4D4×D6111yescharacteristic
664C4⋊C4—24no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—1222no—
668C4⋊C4—1222no—
669C4⋊C4—1228no—
670C4⋊C4—1224no—
671C4⋊C4—1222no—
672C4⋊C4—1222no—
673C4⋊C4—2444no—
674C22⋊C4—22no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—614no—
682C22⋊C4—1222no—
683C22⋊C4—1222no—
684C22⋊C4—1222no—
685C22⋊C4—1222no—
686C22⋊C4—1228no—
687C22⋊C4—1222no—
688C22⋊C4—1221no—
689C22⋊C4—1221no—
690C22⋊C4—1222no—
691C22⋊C4—1222no—
692C22⋊C4—1222no—
693C22⋊C4—1222no—
694C22⋊C4—2448no—
695C22⋊C4D4×D6114yes—
696C42—24no—
697C42—1222no—
698C42—1222no—
699C42—1228no—
700C42—1224no—
701C42—2444no—
702C23—21no—
703C23—22no—
704C23—42no—
705C23—42no—
706C23—612no—
707C23—612no—
708C23—1224no—
709C23—1224no—
710C23—1224no—
711C23—1221no—
712C23—1221no—
713C23—1224no—
714C23—1221no—
715C23—1224no—
716C23—1221no—
717C23—1222no—
718C23—1221no—
719C23—2442no—
720C23—2442no—
721C23—2442no—
722C23—2442no—
723C23—2448no—
724C23—2448no—
725C23C22×C4×D6111yescharacteristic
726C23C2×D4×D6111yescharacteristic
727C23C2×D4×D6111yescharacteristic
728C23C2×D4×D6112yes—
729C23#41×D6112yes—
730Q8—2442no—
731Q8—2442no—
732D4—41no—
733D4—42no—
734D4—41no—
735D4—2444no—
736D4—2444no—
737D4—2442no—
738D4—2442no—
739D4—2444no—
740D4—2444no—
741D4—2441no—
742D4—2442no—
743D4—2441no—
744C2×C4—24no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—24no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—44no—
755C2×C4—42no—
756C2×C4—44no—
757C2×C4—42no—
758C2×C4—611no—
759C2×C4—611no—
760C2×C4—611no—
761C2×C4—611no—
762C2×C4—614no—
763C2×C4—614no—
764C2×C4—612no—
765C2×C4—612no—
766C2×C4—614no—
767C2×C4—614no—
768C2×C4—612no—
769C2×C4—612no—
770C2×C4—1224no—
771C2×C4—1224no—
772C2×C4—1224no—
773C2×C4—1224no—
774C2×C4—1224no—
775C2×C4—1224no—
776C2×C4—1224no—
777C2×C4—1224no—
778C2×C4—1222no—
779C2×C4—1221no—
780C2×C4—1222no—
781C2×C4—1224no—
782C2×C4—2442no—
783C2×C4—2442no—
784C2×C4—24416no—
785C2×C4—2442no—
786C2×C4—2442no—
787C2×C4—2444no—
788C2×C4—2442no—
789C2×C4—2444no—
790C2×C4—2442no—
791C2×C4C22⋊C4×D6112yes—
792C2×C4C22⋊C4×D6112yes—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—42no—
797C22—42no—
798C22—41no—
799C22—42no—
800C22—82no—
801C22—614no—
802C22—1224no—
803C22—1224no—
804C22—1222no—
805C22—1222no—
806C22—1222no—
807C22—1222no—
808C22—1222no—
809C22—4882no—
810C22—2448no—
811C22—2448no—
812C22—2442no—
813C22—2442no—
814C22—2441no—
815C22—2442no—
816C22C2×C22⋊C4×D6111yescharacteristic
817C22C4×D4×D6112yes—
818C22#120×D6111yescharacteristic
819C22#121×D6112yes—
820C22#123×D6111yescharacteristic
821C4—22no—
822C4—22no—
823C4—44no—
824C4—41no—
825C4—42no—
826C4—82no—
827C4—612no—
828C4—612no—
829C4—612no—
830C4—612no—
831C4—4882no—
832C4—2444no—
833C4—2441no—
834C4—2442no—
835C2—21no—
836C2—22no—
837C2—22no—
838C2—21no—
839C2—81no—
840C2—1224no—
841C2—4881no—
842C2—2442no—
843C2#386×D6111yescharacteristic
844C2#410×D6112yes—
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1899C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840270C2
cosocleC24×C61C24
hypercenter#1899D61
hypocenterC61#20983
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1899

Complements

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

NH ≅ G/Ntype
2. C2×#117×D61C2semidirect
3. C2×#16839734C2semidirect
4. #21448199C2semidirect
5. #21446278C2semidirect
6. #21446277C2semidirect
7. #21446275C2semidirect
8. #21446271C2semidirect
9. #21446269C2semidirect
10. #21445550C2semidirect
11. C61×#1899C2semidirect
21. C2×#14519755C4semidirect
22. C2×#14519750C4semidirect
25. C2×#14519739C4semidirect
26. C2×#14519737C4semidirect
60. C22×Dic122C2×C4semidirect
63. C22×C22⋊D61C2×C4semidirect
65. C23×Dic61C2×C4semidirect
72. C22×C4×D61C2×C4semidirect
114. #14519733D4semidirect
118. C2×#11758196C2×C4semidirect
119. C2×#11758196C2×C4semidirect
128. C2×#11758198C2×C4semidirect
134. C2×C4×Dic61C2×C4semidirect
147. C2×C4⋊C4×C61C2×C4semidirect
148. C2×C22⋊C4×C61C2×C4semidirect
398. C2×D61#410semidirect
420. #1899D61semidirect
475. C61#20983semidirect
551. C2×C4⋊C4C4×D61semidirect
562. C2×C22⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402702
C2×#117×D612
C2×#168397342
#214481992
#214462782
#214462772
#214462752
#214462712
#214462692
#214455502
C61×#18992
#2098361