Finite Group Databasebeta

← #29681809

Subgroups — #29681809

Order 15616.

2102 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840322C211yesmaximal, characteristic
2C2×#16840235C211yesmaximal, characteristic, complemented
3C2×#99×D61C212yesmaximal, complemented
4#21448395C211yesmaximal, characteristic, complemented
5#21446276C212yesmaximal, complemented
6#21446274C212yesmaximal, complemented
7#21446273C211yesmaximal, characteristic, complemented
8#21446272C211yesmaximal, characteristic, complemented
9#21446270C211yesmaximal, characteristic, complemented
10#342×D61C212yesmaximal, complemented
11C61×#1898C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C22×D4×D61C2211yescharacteristic
14#16840322—22no—
15#16840322—22no—
16#16840322—24no—
17C2×#14519761C2211yescharacteristic
18C2×#14519759C412yescomplemented
19C2×#14519758C2211yescharacteristic
20C2×#14519750C412yescomplemented
21C2×#14519748C412yescomplemented
22C2×#14519746C2211yescharacteristic
23C2×#14519745C412yescomplemented
24#16840235—28no—
25C2×C4×C22⋊D61—22no—
26C2×#14519737—22no—
27C2×#14519733C2212yescomplemented
28C22×C22⋊Dic61C2211yescharacteristic, complemented
29C2×C22⋊C4×D61C2212yes—
30C2×C22⋊C4×D61C2212yes—
31C2×C22⋊C4×D61C2211yescharacteristic
32C2×#14519692C2212yes—
33C2×#14519691C2212yes—
34C2×#14519691C2212yes—
35#99×D61—28no—
36#16839638—24no—
37#16839623C2212yescomplemented
38#16839618C2211yescharacteristic, complemented
39#16839529C2212yescomplemented
40#16839528C2212yescomplemented
41#16839528C2212yescomplemented
42C2×#120×C61C2211yescharacteristic
43C22×C22⋊C4×C61C2211yescharacteristic, complemented
44C2×#99×C61C2212yes—
45C61×#379C2211yescharacteristic, complemented
46C61×#342C2212yescomplemented
47C24×D61C2×C411yescharacteristic, complemented
48C24×D61C2311yescharacteristic
49C22×D244C2×C411yescharacteristic, complemented
50C22×C22⋊D61—24no—
51C22×C22⋊D61—24no—
52C22×C22⋊D61C2×C412yes—
53C22×C22⋊D61C2×C412yes—
54C22×C22⋊D61C2×C411yescharacteristic, complemented
55C22×C22⋊D61C2×C412yescomplemented
56C22×C22⋊D61D412yes—
57C22×C22⋊D61D412yes—
58C22×C22⋊D61D414yes—
59C22×C22⋊D61C2311yescharacteristic
60C2×D4×D61—24no—
61C2×D4×D61—22no—
62C2×D4×D61—22no—
63C2×D4×D61—24no—
64C23×Dic61—21no—
65C23×Dic61C2311yescharacteristic
66C22×C4×D61—22no—
67C22×C4×D61—22no—
68C22×C4×D61C2×C411yescharacteristic, complemented
69C22×C4×D61C2×C412yescomplemented
70#14519761—22no—
71#14519761—22no—
72#14519759—24no—
73#14519759—24no—
74#14519758—22no—
75#14519758—22no—
76#14519750—24no—
77#14519750—24no—
78#14519748—24no—
79#14519748—24no—
80#14519746—21no—
81#14519746—22no—
82#14519746—21no—
83#14519745—24no—
84#14519745—24no—
85C4×C22⋊D61—216no—
86#14519737—216no—
87#14519733—24no—
88#14519733—24no—
89C2×C4⋊Dic61C2×C412yescomplemented
90C2×#11758196—22no—
91C2×#11758196C2×C412yescomplemented
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—24no—
94C2×C22⋊Dic61—22no—
95C2×C22⋊Dic61C2×C412yescomplemented
96C2×C22⋊Dic61C2×C412yescomplemented
97C2×C22⋊Dic61C2312yes—
98C2×C22⋊Dic61C2311yescharacteristic
99C2×C22⋊Dic61C2312yes—
100C2×#11758198—22no—
101C2×#11758198—22no—
102C2×#11758198C2×C412yescomplemented
103C2×#11758198C2×C412yescomplemented
104C22⋊C4×D61—24no—
105C22⋊C4×D61—22no—
106C22⋊C4×D61—22no—
107C22⋊C4×D61—24no—
108C22⋊C4×D61—24no—
109C22⋊C4×D61D418yescomplemented
110C2×C4×Dic61—22no—
111#14519692—24no—
112#14519691—24no—
113#14519691—24no—
114#14519684—24no—
115C25×C61C2311yescharacteristic
116C22×D4×C61C2×C412yescomplemented
117C22×D4×C61C2311yescharacteristic
118C23×C4×C61—21no—
119#120×C61—21no—
120#120×C61—22no—
121#120×C61—21no—
122C2×C22⋊C4×C61—21no—
123C2×C22⋊C4×C61—24no—
124C2×C22⋊C4×C61—22no—
125C2×C22⋊C4×C61C2×C412yescomplemented
126C2×C22⋊C4×C61C2312yes—
127C2×C22⋊C4×C61C2311yescharacteristic
128C2×C22⋊C4×C61C2312yes—
129#99×C61—24no—
130C24×C61—22no—
131C24×C61—22no—
132C24×C61—82no—
133C24×C61C22×C411yescharacteristic
134C24×C61C22×C412yes—
135C24×C61C2×D411yescharacteristic
136C24×C61C2×D412yes—
137C24×C61C2×D411yescharacteristic
138C24×C61C2411yescharacteristic
139C23×D61—22no—
140C23×D61—24no—
141C23×D61—82no—
142C23×D61—82no—
143C23×D61C22×C411yescharacteristic
144C23×D61C22×C411yescharacteristic
145C23×D61C22×C411yescharacteristic
146C23×D61C2×D412yes—
147C23×D61C2×D412yes—
148C23×D61C2×D414yes—
149C23×D61#4114yes—
150C2×D4×C61—22no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—22no—
154C2×D4×C61—22no—
155C2×D4×C61—22no—
156C2×D4×C61—82no—
157C22×C4×C61—22no—
158C22×C4×C61—24no—
159C22×C4×C61—22no—
160C22×C4×C61—82no—
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C412yes—
163C2×C22⋊D61—28no—
164C2×C22⋊D61—28no—
165C2×C22⋊D61—24no—
166C2×C22⋊D61—24no—
167C2×C22⋊D61—28no—
168C2×C22⋊D61—28no—
169C2×C22⋊D61—24no—
170C2×C22⋊D61—24no—
171C2×C22⋊D61—22no—
172C2×C22⋊D61—21no—
173C2×C22⋊D61—21no—
174C2×C22⋊D61—22no—
175C2×C22⋊D61—22no—
176C2×C22⋊D61—24no—
177C2×C22⋊D61—22no—
178C2×C22⋊D61—22no—
179C2×C22⋊D61—82no—
180C2×C22⋊D61C22⋊C414yes—
181C2×C22⋊D61C22⋊C414yes—
182C2×C22⋊D61C22⋊C414yes—
183C2×C22⋊D61C22⋊C414yes—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—24no—
188C22×Dic61—22no—
189C22×Dic61—82no—
190C22×Dic61C22×C411yescharacteristic
191C22×Dic61C22×C412yes—
192C22×Dic61C22×C412yes—
193C22×Dic61C2×D412yes—
194C22×Dic61C2×D412yes—
195D4×D61—44no—
196D4×D61—44no—
197D4×D61—44no—
198D4×D61—44no—
199C2×D244—22no—
200C2×D244—24no—
201C2×C4×D61—22no—
202C2×C4×D61—24no—
203C2×C4×D61—24no—
204C2×C4×D61—28no—
205C2×C4×D61—44no—
206C2×C4×D61—84no—
207C2×C4×D61—84no—
208C2×C4×D61—82no—
209C22⋊C4×C61—24no—
210C22⋊C4×C61—22no—
211C22⋊C4×C61—22no—
212C22⋊C4×C61—22no—
213C22⋊C4×C61—21no—
214C22⋊C4×C61—21no—
215C22⋊C4×C61—22no—
216C22⋊C4×C61—22no—
217C22⋊C4×C61—82no—
218C22⋊C4×C61C2×D414yes—
219C22⋊Dic61—24no—
220C22⋊Dic61—22no—
221C22⋊Dic61—22no—
222C22⋊Dic61—22no—
223C22⋊Dic61—21no—
224C22⋊Dic61—21no—
225C22⋊Dic61—24no—
226C22⋊Dic61—22no—
227C22⋊Dic61—22no—
228C22⋊Dic61—82no—
229C22⋊Dic61C2×D414yes—
230#11758198—24no—
231#11758198—28no—
232#11758198—24no—
233#11758198—44no—
234C4⋊Dic61—24no—
235#11758196—28no—
236#11758196—24no—
237C4×Dic61—28no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—24no—
243C23×C61—24no—
244C23×C61—21no—
245C23×C61—22no—
246C23×C61—42no—
247C23×C61—42no—
248C23×C61—42no—
249C23×C61—42no—
250C23×C61—42no—
251C23×C61—42no—
252C23×C61—42no—
253C23×C61—42no—
254C23×C61—84no—
255C23×C61—84no—
256C23×C61C2×C22⋊C412yes—
257C23×C61C2×C22⋊C412yes—
258C23×C61C23×C411yescharacteristic
259C23×C61C22×D411yescharacteristic
260C23×C61C22×D411yescharacteristic
261C23×C61C22×D412yes—
262C23×C61C2×#4112yes—
263C22×D61—21no—
264C22×D61—22no—
265C22×D61—42no—
266C22×D61—44no—
267C22×D61—44no—
268C22×D61—42no—
269C22×D61—44no—
270C22×D61—42no—
271C22×D61—84no—
272C22×D61—84no—
273C22×D61—84no—
274C22×D61—88no—
275C22×D61C2×C22⋊C412yes—
276C22×D61C2×C22⋊C412yes—
277C22×D61C4×D414yes—
278C22×D61C4×D414yes—
279C22×D61#12014yes—
280C22×D61#12114yes—
281C22×D61#12114yes—
282C22×D61#12314yes—
283D4×C61—41no—
284D4×C61—42no—
285D4×C61—41no—
286D4×C61—82no—
287D4×C61—82no—
288C2×C4×C61—21no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—24no—
292C2×C4×C61—44no—
293C2×C4×C61—42no—
294C2×C4×C61—44no—
295C2×C4×C61—42no—
296C2×C4×C61—84no—
297C22⋊D61—28no—
298C22⋊D61—28no—
299C22⋊D61—28no—
300C22⋊D61—28no—
301C22⋊D61—41no—
302C22⋊D61—42no—
303C22⋊D61—41no—
304C22⋊D61—44no—
305C22⋊D61—82no—
306C22⋊D61—82no—
307C2×Dic61—24no—
308C2×Dic61—22no—
309C2×Dic61—24no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—21no—
313C2×Dic61—22no—
314C2×Dic61—24no—
315C2×Dic61—44no—
316C2×Dic61—42no—
317C2×Dic61—44no—
318C2×Dic61—42no—
319C2×Dic61—84no—
320C2×Dic61C2×C22⋊C414yes—
321D244—44no—
322C4×D61—44no—
323C4×D61—84no—
324C4×D61—88no—
325C4×D61—88no—
326#20984—611nomaximal, Sylow
327C22×C61—22no—
328C22×C61—22no—
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—42no—
337C22×C61—42no—
338C22×C61—42no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—42no—
342C22×C61—42no—
343C22×C61—41no—
344C22×C61—84no—
345C22×C61—84no—
346C22×C61—82no—
347C22×C61C22×C22⋊C411yescharacteristic
348C22×C61C2×C4×D412yes—
349C22×C61C2×#12011yescharacteristic
350C22×C61C2×#12112yes—
351C22×C61C2×#12311yescharacteristic
352C2×D61—24no—
353C2×D61—24no—
354C2×D61—44no—
355C2×D61—44no—
356C2×D61—44no—
357C2×D61—44no—
358C2×D61—44no—
359C2×D61—44no—
360C2×D61—42no—
361C2×D61—41no—
362C2×D61—88no—
363C2×D61—82no—
364C2×D61#38614yes—
365C2×D61#38614yes—
366C4×C61—44no—
367C4×C61—42no—
368C4×C61—41no—
369C4×C61—82no—
370Dic61—24no—
371Dic61—44no—
372Dic61—42no—
373Dic61—41no—
374Dic61—82no—
375C2×#534—611no—
376C2×#518—611no—
377C22×#99—612no—
378#2308—611no—
379#1899—612no—
380#1899—612no—
381#1898—611no—
382#1898—611no—
383#1898—611no—
384#1898D6111yescharacteristic, complemented
385C2×#342—612no—
386C2×C61—21no—
387C2×C61—22no—
388C2×C61—22no—
389C2×C61—21no—
390C2×C61—42no—
391C2×C61—42no—
392C2×C61—81no—
393C2×C61C2×#38611yescharacteristic
394C2×C61#288312yes—
395D61—24no—
396D61—24no—
397D61—81no—
398C23×D4—611no—
399C23×D4—611no—
400#534—1222no—
401#534—1222no—
402#534—1224no—
403C2×#123—611no—
404C2×#123—612no—
405C2×#123—611no—
406C2×#121—612no—
407C2×#121—612no—
408C2×#120—611no—
409C2×#120—612no—
410C2×#120C2×D6111yescharacteristic
411#518—1228no—
412C2×C4×D4—1222no—
413C2×C4×D4—1222no—
414C2×#117—612no—
415C22×C22⋊C4—612no—
416C22×C22⋊C4—611no—
417C22×C22⋊C4—611no—
418C22×C22⋊C4—612no—
419C22×C22⋊C4C2×D6111yescharacteristic, complemented
420C2×#99—612no—
421C2×#99—612no—
422C2×#99—612no—
423C2×#99—1228no—
424C2×#99C2×D6112yes—
425#386—1224no—
426#381—612no—
427#379—611no—
428#379C2×D6111yescharacteristic, complemented
429#342—612no—
430#342—612no—
431#342—612no—
432#342C2×D6112yescomplemented
433C61#2098411yescharacteristic, complemented, Sylow
434C25—611no—
435C25—611no—
436C25C22×D6111yescharacteristic
437C22×D4—612no—
438C22×D4—612no—
439C22×D4—612no—
440C22×D4—612no—
441C22×D4—614no—
442C22×D4—611no—
443C22×D4—611no—
444C22×D4—612no—
445C22×D4—611no—
446C22×D4—1222no—
447C22×D4—1222no—
448C22×D4—1224no—
449C22×D4—1224no—
450C22×D4—1224no—
451C22×D4—1224no—
452C22×D4C4×D6112yescomplemented
453C22×D4C22×D6111yescharacteristic
454C23×C4—21no—
455C23×C4—611no—
456C23×C4—611no—
457C23×C4—612no—
458C23×C4—1222no—
459C23×C4—1222no—
460C23×C4—1221no—
461#123—1222no—
462#123—1222no—
463#123—1224no—
464#123—1224no—
465#123—1222no—
466#123—1222no—
467#121—1224no—
468#121—1224no—
469#121—1224no—
470#121—1224no—
471#120—22no—
472#120—21no—
473#120—21no—
474#120—1224no—
475#120—1224no—
476#120—1222no—
477#120—1221no—
478#120—1221no—
479C4×D4—12216no—
480C4×D4—12216no—
481#117—1224no—
482#117—1224no—
483C2×C4⋊C4—612no—
484C2×C4⋊C4—612no—
485C2×C4⋊C4—1222no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—612no—
490C2×C22⋊C4—618no—
491C2×C22⋊C4—612no—
492C2×C22⋊C4—612no—
493C2×C22⋊C4—611no—
494C2×C22⋊C4—612no—
495C2×C22⋊C4—612no—
496C2×C22⋊C4—612no—
497C2×C22⋊C4—1224no—
498C2×C22⋊C4—1222no—
499C2×C22⋊C4—1222no—
500C2×C22⋊C4—1224no—
501C2×C22⋊C4—1224no—
502C2×C22⋊C4—1224no—
503C2×C22⋊C4—1222no—
504C2×C22⋊C4—1221no—
505C2×C22⋊C4—1222no—
506C2×C22⋊C4—1222no—
507C2×C22⋊C4C4×D6112yescomplemented
508C2×C22⋊C4C22×D6112yes—
509C2×C22⋊C4C22×D6111yescharacteristic
510C2×C22⋊C4C22×D6112yes—
511C2×C42—1222no—
512#99—24no—
513#99—1224no—
514#99—1224no—
515#99—1224no—
516#95—1224no—
517C24—22no—
518C24—22no—
519C24—82no—
520C24—614no—
521C24—614no—
522C24—611no—
523C24—611no—
524C24—612no—
525C24—612no—
526C24—611no—
527C24—1222no—
528C24—1224no—
529C24—4882no—
530C24—4882no—
531C24C2×C4×D6111yescharacteristic
532C24C2×C4×D6112yes—
533C24D4×D6112yes—
534C24D4×D6111yescharacteristic
535C24D4×D6111yescharacteristic
536C24C23×D6111yescharacteristic
537C2×D4—22no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—82no—
544C2×D4—614no—
545C2×D4—614no—
546C2×D4—614no—
547C2×D4—614no—
548C2×D4—1222no—
549C2×D4—1224no—
550C2×D4—1224no—
551C2×D4—1224no—
552C2×D4—1228no—
553C2×D4—1228no—
554C2×D4—1228no—
555C2×D4—1228no—
556C2×D4—1224no—
557C2×D4—1224no—
558C2×D4—1222no—
559C2×D4—1222no—
560C2×D4—1222no—
561C2×D4—1224no—
562C2×D4—1222no—
563C2×D4—1221no—
564C2×D4—1221no—
565C2×D4—1222no—
566C2×D4—4882no—
567C2×D4—2444no—
568C2×D4—2444no—
569C2×D4—2444no—
570C2×D4—2444no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—82no—
575C22×C4—612no—
576C22×C4—612no—
577C22×C4—612no—
578C22×C4—611no—
579C22×C4—612no—
580C22×C4—1228no—
581C22×C4—1224no—
582C22×C4—1222no—
583C22×C4—1224no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1224no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—4884no—
590C22×C4—4884no—
591C22×C4—4882no—
592C22×C4—4882no—
593C22×C4—2444no—
594C22×C4C2×C4×D6111yescharacteristic
595C22×C4C2×C4×D6112yes—
596C4⋊C4—1224no—
597C4⋊C4—1224no—
598C4⋊C4—1228no—
599C22⋊C4—24no—
600C22⋊C4—22no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—82no—
608C22⋊C4—614no—
609C22⋊C4—1224no—
610C22⋊C4—1228no—
611C22⋊C4—1224no—
612C22⋊C4—1224no—
613C22⋊C4—1224no—
614C22⋊C4—1222no—
615C22⋊C4—1221no—
616C22⋊C4—1221no—
617C22⋊C4—1222no—
618C22⋊C4—1222no—
619C22⋊C4—1222no—
620C22⋊C4—1222no—
621C22⋊C4—4882no—
622C22⋊C4—2444no—
623C22⋊C4D4×D6114yes—
624C42—1228no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—24no—
630C23—24no—
631C23—21no—
632C23—22no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—84no—
642C23—84no—
643C23—612no—
644C23—612no—
645C23—614no—
646C23—614no—
647C23—614no—
648C23—614no—
649C23—614no—
650C23—614no—
651C23—1222no—
652C23—1221no—
653C23—4884no—
654C23—4884no—
655C23—4884no—
656C23—4888no—
657C23—2444no—
658C23—2444no—
659C23—2442no—
660C23—2442no—
661C23—2442no—
662C23—2444no—
663C23C22⋊C4×D6112yes—
664C23C22⋊C4×D6112yes—
665C23C22×C4×D6111yescharacteristic
666C23C2×D4×D6111yescharacteristic
667C23C2×D4×D6111yescharacteristic
668C23C2×D4×D6112yes—
669C23#41×D6112yes—
670D4—41no—
671D4—42no—
672D4—41no—
673D4—82no—
674D4—82no—
675D4—1228no—
676D4—1228no—
677D4—1228no—
678D4—1228no—
679D4—4882no—
680D4—4882no—
681D4—2444no—
682D4—2444no—
683D4—2441no—
684D4—2442no—
685D4—2441no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—44no—
691C2×C4—42no—
692C2×C4—44no—
693C2×C4—42no—
694C2×C4—84no—
695C2×C4—614no—
696C2×C4—1224no—
697C2×C4—1222no—
698C2×C4—1224no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1221no—
702C2×C4—1222no—
703C2×C4—1224no—
704C2×C4—4884no—
705C2×C4—4888no—
706C2×C4—4888no—
707C2×C4—4884no—
708C2×C4—2444no—
709C2×C4—2444no—
710C2×C4—2442no—
711C2×C4—2444no—
712C2×C4—2442no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—41no—
729C22—42no—
730C22—84no—
731C22—84no—
732C22—82no—
733C22—614no—
734C22—614no—
735C22—1224no—
736C22—1224no—
737C22—4882no—
738C22—4888no—
739C22—2444no—
740C22—2444no—
741C22—2444no—
742C22—2444no—
743C22—2444no—
744C22—2444no—
745C22—2441no—
746C22—2442no—
747C22C2×C22⋊C4×D6111yescharacteristic
748C22C4×D4×D6112yes—
749C22#120×D6111yescharacteristic
750C22#121×D6112yes—
751C22#123×D6111yescharacteristic
752C4—44no—
753C4—41no—
754C4—42no—
755C4—82no—
756C4—1224no—
757C4—4882no—
758C4—2444no—
759C4—2441no—
760C4—2442no—
761C2—21no—
762C2—22no—
763C2—21no—
764C2—22no—
765C2—42no—
766C2—42no—
767C2—81no—
768C2—1224no—
769C2—1224no—
770C2—4881no—
771C2#386×D6111yescharacteristic
772C2#2145427712yes—
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1898C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840322C2
cosocleC24×C61C24
hypercenter#1898D61
hypocenterC61#20984
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C25 ◁ #1898

Complements

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

NH ≅ G/Ntype
2. C2×#16840235C2semidirect
3. C2×#99×D61C2semidirect
4. #21448395C2semidirect
5. #21446276C2semidirect
6. #21446274C2semidirect
7. #21446273C2semidirect
8. #21446272C2semidirect
9. #21446270C2semidirect
10. #342×D61C2semidirect
11. C61×#1898C2semidirect
18. C2×#14519759C4semidirect
20. C2×#14519750C4semidirect
21. C2×#14519748C4semidirect
23. C2×#14519745C4semidirect
27. C2×#14519733C22semidirect
28. C22×C22⋊Dic61C22semidirect
37. #16839623C22semidirect
38. #16839618C22semidirect
39. #16839529C22semidirect
40. #16839528C22semidirect
41. #16839528C22semidirect
43. C22×C22⋊C4×C61C22semidirect
45. C61×#379C22semidirect
46. C61×#342C22semidirect
47. C24×D61C2×C4semidirect
49. C22×D244C2×C4semidirect
54. C22×C22⋊D61C2×C4semidirect
55. C22×C22⋊D61C2×C4semidirect
68. C22×C4×D61C2×C4semidirect
69. C22×C4×D61C2×C4semidirect
89. C2×C4⋊Dic61C2×C4semidirect
91. C2×#11758196C2×C4semidirect
95. C2×C22⋊Dic61C2×C4semidirect
96. C2×C22⋊Dic61C2×C4semidirect
102. C2×#11758198C2×C4semidirect
103. C2×#11758198C2×C4semidirect
109. C22⋊C4×D61D4semidirect
116. C22×D4×C61C2×C4semidirect
125. C2×C22⋊C4×C61C2×C4semidirect
384. #1898D61semidirect
419. C22×C22⋊C4C2×D61semidirect
428. #379C2×D61semidirect
432. #342C2×D61semidirect
433. C61#20984semidirect
452. C22×D4C4×D61semidirect
507. 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×#168403222
C2×#168402352
C2×#99×D612
#214483952
#214462762
#214462742
#214462732
#214462722
#214462702
#342×D612
C61×#18982
#2098461