Finite Group Databasebeta

← #30611243

Subgroups — #30611243

Order 15616.

1274 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#432C211yesmaximal, characteristic, complemented
2#21462266C211yesmaximal, characteristic, complemented
3#21461256C212yesmaximal, complemented
4#21461255C212yesmaximal, complemented
5#21461238C214yesmaximal, complemented
6#21461209C214yesmaximal, complemented
7C2×#16840309C211yesmaximal, characteristic
8#16840785C2212yescomplemented
9#16840784C2212yescomplemented
10#16840783—21no—
11#16840782—21no—
12D61⋊(C4⋊C8)—21no—
13D61⋊(C22⋊C8)C2212yes—
14#16840721—21no—
15#16840707C2212yescomplemented
16#16840706—21no—
17#16840705—21no—
18#16840704C2212yes—
19C4×C4⋊#6923—21no—
20C4×C22⋊#6923—21no—
21#16840698C2212yescomplemented
22#16840614C2218yescomplemented
23#16840613C2218yescomplemented
24C22×#11758222—21no—
25#16840309—21no—
26#16840309—21no—
27#16840309—21no—
28#16840309—21no—
29#16840309C412yescomplemented
30#16840309C412yescomplemented
31#16840309C2212yes—
32#16840309C2212yes—
33C2×#14519776C411yescharacteristic, complemented
34C2×#14519773C411yescharacteristic, complemented
35C2×#14519763—21no—
36C2×#14519752C2211yescharacteristic
37C2×#14519750—21no—
38C2×#14519748C2211yescharacteristic
39C2×C4×D244C411yescharacteristic, complemented
40C2×C4×C22⋊D61—21no—
41C2×C42×D61C2211yescharacteristic
42C2×C4×D4×C61C411yescharacteristic, complemented
43C2×D61⋊C8—22no—
44C2×C4⋊#6923—22no—
45C2×C22⋊#6923—22no—
46C2×C4×#6923—22no—
47#14519844—22no—
48C4⋊#92420—22no—
49#14519834C2314yes—
50C22⋊#92420—22no—
51#14519832—22no—
52#14519832—22no—
53(C2×#6923)⋊C4—22no—
54(C2×#6923)⋊C4—22no—
55(C2×#6923)⋊C4—22no—
56(C2×#6923)⋊C4C2314yes—
57C2×#11758222—22no—
58C2×#11758222—22no—
59C2×#11758222—22no—
60C2×#11758222—22no—
61C2×#11758222—48no—
62C22×Dic122—21no—
63C22×D244—21no—
64C22×D244C2×C411yescharacteristic
65C22×C22⋊D61—21no—
66C22×C22⋊D61—21no—
67C22×C22⋊D61—21no—
68C22×C4×D61—21no—
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61C2311yescharacteristic
72#14519776—21no—
73#14519776—21no—
74#14519776C2×C412yes—
75#14519776C2×C412yes—
76#14519773—21no—
77#14519773—21no—
78#14519773C2×C412yes—
79#14519773C2×C412yes—
80#14519763—22no—
81#14519763—22no—
82#14519763—22no—
83#14519763—22no—
84#14519752—21no—
85#14519752—21no—
86#14519752C2×C412yes—
87#14519752C2312yes—
88#14519750—22no—
89#14519750—22no—
90#14519750—22no—
91#14519750—22no—
92#14519748—21no—
93#14519748—21no—
94#14519748C2×C412yes—
95#14519748C2312yes—
96C4×D244—21no—
97C4×D244—21no—
98C4×D244C2×C412yes—
99C4×D244C2×C412yes—
100C4×C22⋊D61—22no—
101C4×C22⋊D61—22no—
102C4×C22⋊D61—22no—
103C4×C22⋊D61—22no—
104C2×C4⋊Dic61C2×C411yescharacteristic
105C2×#11758196—21no—
106C2×C22⋊Dic61—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×C4×Dic61C2×C411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C42×D61C2×C411yescharacteristic
113C42×D61C2×C411yescharacteristic
114C42×D61D411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61C2311yescharacteristic
119C42×D61C2311yescharacteristic
120C22×D4×C61C2×C411yescharacteristic
121C23×C4×C61—21no—
122C4×D4×C61—21no—
123C4×D4×C61—21no—
124C4×D4×C61C2×C412yes—
125C4×D4×C61C2×C412yes—
126C2×C4⋊C4×C61C2×C411yescharacteristic
127C2×C22⋊C4×C61—21no—
128C2×C42×C61C2×C411yescharacteristic
129C24×C61—21no—
130C23×D61—21no—
131C23×D61C2×D411yescharacteristic
132C22×#6923—24no—
133C2×D4×C61—21no—
134C2×D4×C61—42no—
135C2×D4×C61C22×C412yes—
136C22×C4×C61—21no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—44no—
140C22×C4×C61C22⋊C411yescharacteristic
141C22×C4×C61C22⋊C411yescharacteristic
142C22×C4×C61C22×C411yescharacteristic
143C2×C22⋊D61—22no—
144C2×C22⋊D61—22no—
145C2×C22⋊D61—22no—
146C2×C22⋊D61—22no—
147C2×C22⋊D61—22no—
148C2×C22⋊D61—22no—
149C2×C22⋊D61—44no—
150C2×C22⋊D61—44no—
151C2×C22⋊D61—44no—
152C22×Dic61—21no—
153C22×Dic61C22⋊C411yescharacteristic
154C22×Dic61C22⋊C411yescharacteristic
155C22×Dic61C2×D411yescharacteristic
156#11758222—48no—
157#11758222—48no—
158#11758222—48no—
159#11758222—48no—
160C2×D244—22no—
161C2×D244—22no—
162C2×D244—21no—
163C2×D244—44no—
164C2×D244—42no—
165C2×D244C22×C412yes—
166C2×C4×D61—24no—
167C2×C4×D61—22no—
168C2×C4×D61—22no—
169C2×C4×D61—42no—
170C2×C4×D61—42no—
171C2×C4×D61—44no—
172C2×C4×D61C22⋊C411yescharacteristic
173C2×C4×D61C22⋊C411yescharacteristic
174C2×C4×D61C22⋊C411yescharacteristic
175C2×C4×D61C22⋊C411yescharacteristic
176C2×C4×D61C22×C411yescharacteristic
177C2×C4×D61C2×D411yescharacteristic
178C2×C4×D61C2×D411yescharacteristic
179C2×C4×D61C2×D411yescharacteristic
180C2×C4×D61C2×D411yescharacteristic
181C2×C4×D61C2×D411yescharacteristic
182C2×C4×D61C2×D411yescharacteristic
183C2×C4×D61C2411yescharacteristic
184C2×Dic122—22no—
185C2×Dic122—22no—
186C2×Dic122—44no—
187C22⋊#6923—44no—
188C2×#92420—24no—
189C4⋊#6923—44no—
190C4×#6923—44no—
191D61⋊C8—44no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61C22×C412yes—
194C22⋊C4×C61—22no—
195C22⋊C4×C61—22no—
196C42×C61C22⋊C411yescharacteristic
197C42×C61C22⋊C411yescharacteristic
198C42×C61C22×C411yescharacteristic
199C42×C61C22×C411yescharacteristic
200C22⋊Dic61—22no—
201C22⋊Dic61—22no—
202#11758198—22no—
203#11758198—22no—
204#11758198—22no—
205#11758198—22no—
206C4⋊Dic61—21no—
207C4⋊Dic61C22×C412yes—
208#11758196—22no—
209#11758196—22no—
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C22×C411yescharacteristic
217C4×Dic61C22×C411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C4×Dic61C2×D411yescharacteristic
221C4×Dic61C2×D411yescharacteristic
222C23×C61—22no—
223C23×C61—42no—
224C23×C61—42no—
225C23×C61—42no—
226C23×C61C2×C22⋊C411yescharacteristic
227C22×D61—22no—
228C22×D61—41no—
229C22×D61—41no—
230C22×D61—42no—
231C22×D61—42no—
232C22×D61—42no—
233C22×D61C2×C22⋊C411yescharacteristic
234C22×D61AGL(1,ℤ/8)14yes—
235C22×D61C22×D411yescharacteristic
236C2×#6923—44no—
237C2×#6923—44no—
238C2×#6923—44no—
239D4×C61—42no—
240D4×C61—42no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—22no—
244C2×C4×C61—41no—
245C2×C4×C61—44no—
246C2×C4×C61—44no—
247C2×C4×C61—42no—
248C2×C4×C61C2×C22⋊C411yescharacteristic
249C2×C4×C61C2×C22⋊C411yescharacteristic
250C2×C4×C61C2×C22⋊C411yescharacteristic
251C2×C4×C61C2×C22⋊C411yescharacteristic
252C2×C4×C61C2×C22⋊C411yescharacteristic
253C2×C4×C61C23×C411yescharacteristic
254C22⋊D61—44no—
255C22⋊D61—44no—
256C22⋊D61—44no—
257C22⋊D61—44no—
258C22⋊D61—44no—
259C22⋊D61—44no—
260C2×Dic61—22no—
261C2×Dic61—22no—
262C2×Dic61—22no—
263C2×Dic61—41no—
264C2×Dic61—42no—
265C2×Dic61C2×C22⋊C411yescharacteristic
266C2×Dic61C2×C22⋊C411yescharacteristic
267C2×Dic61C2×C22⋊C411yescharacteristic
268C2×Dic61C2×C22⋊C411yescharacteristic
269C2×Dic61C2×C22⋊C411yescharacteristic
270C2×Dic61C22×D411yescharacteristic
271D244—42no—
272D244—44no—
273D244—44no—
274D244—42no—
275C4×D61—22no—
276C4×D61—22no—
277C4×D61—22no—
278C4×D61—22no—
279C4×D61—22no—
280C4×D61—22no—
281C4×D61—22no—
282C4×D61—22no—
283C4×D61—41no—
284C4×D61—41no—
285C4×D61—41no—
286C4×D61—41no—
287C4×D61—44no—
288C4×D61—44no—
289Dic122—44no—
290Dic122—44no—
291#92420—44no—
292#17595—611nomaximal, Sylow
293C22×C61—21no—
294C22×C61—21no—
295C22×C61—42no—
296C22×C61—42no—
297C22×C61—42no—
298C22×C61—84no—
299C22×C61#41812yes—
300C22×C61C22×C22⋊C411yescharacteristic
301C2×D61—21no—
302C2×D61—21no—
303C2×D61—21no—
304C2×D61—21no—
305C2×D61—44no—
306C2×D61—42no—
307C2×D61—42no—
308C2×D61—42no—
309C2×D61—84no—
310C2×D61#41812yes—
311C2×D61C2×AGL(1,ℤ/8)12yes—
312#6923—84no—
313C4×C61—21no—
314C4×C61—21no—
315C4×C61—21no—
316C4×C61—21no—
317C4×C61—21no—
318C4×C61—42no—
319C4×C61#41012yes—
320Dic61—21no—
321Dic61—21no—
322Dic61—21no—
323Dic61—21no—
324Dic61—21no—
325Dic61—42no—
326Dic61#42112yes—
327C2×#532—611no—
328C2×#432—611no—
329#2283—611no—
330#1519—612no—
331#1519—612no—
332#1514—614no—
333#1505—614no—
334C2×C61—22no—
335C2×C61—82no—
336C2×C61C2×#41011yescharacteristic
337C2×C61C2×#41811yescharacteristic
338C2×C61C2×#42111yescharacteristic
339D61—22no—
340D61—22no—
341D61—82no—
342C22×#41—1221no—
343#532—612no—
344#532—612no—
345#532—612no—
346#532—612no—
347#532—1221no—
348#532—1221no—
349#532—1221no—
350#532—1221no—
351C2×C4⋊Q8—611no—
352C2×#127—611no—
353C2×#124—1221no—
354C2×#121—611no—
355C2×#121—611no—
356C2×#121—1221no—
357C2×C4×D4—611no—
358C2×C4×D4—1221no—
359C2×C4×D4#692311yescharacteristic, complemented
360C22×C42—611no—
361#432—612no—
362#432—612no—
363#432—1221no—
364#432—1221no—
365C2×C4⋊C8—1221no—
366C2×C22⋊C8—612no—
367C2×#97—1221no—
368#383—612no—
369#382—1221no—
370#381—1221no—
371#380—612no—
372C4×C4⋊C4—1221no—
373C4×C22⋊C4—1221no—
374#376—612no—
375#327—618no—
376#327—618no—
377C61#1759511yescharacteristic, complemented, Sylow
378C2×#41—1222no—
379C2×#41—1222no—
380C2×#41—1222no—
381C2×#41—1222no—
382C2×#41—2448no—
383C22×Q8—1221no—
384C22×D4—611no—
385C22×D4—1221no—
386C22×D4—1221no—
387C22×D4—1221no—
388C22×D4—1221no—
389C22×D4C2×#692311yescharacteristic
390C23×C4—21no—
391C23×C4—611no—
392C23×C4—611no—
393C23×C4—611no—
394C23×C4—1221no—
395C22×C8—1222no—
396C4⋊Q8—612no—
397C4⋊Q8—612no—
398C4⋊Q8—1221no—
399C4⋊Q8—1221no—
400#127—612no—
401#127—612no—
402#127—1221no—
403#127—1221no—
404#124—1222no—
405#124—1222no—
406#124—1222no—
407#124—1222no—
408#121—612no—
409#121—612no—
410#121—612no—
411#121—612no—
412#121—1222no—
413#121—1222no—
414#121—1222no—
415#121—1222no—
416#121—1221no—
417#121—1221no—
418#121—1221no—
419#121—1221no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—612no—
423C4×D4—612no—
424C4×D4—1222no—
425C4×D4—1222no—
426C4×D4—1222no—
427C4×D4—1222no—
428C4×D4—1221no—
429C4×D4—1221no—
430C4×D4C2×#692312yes—
431C4×D4C2×#692312yes—
432C2×C4⋊C4—611no—
433C2×C4⋊C4—1221no—
434C2×C4⋊C4—1222no—
435C2×C4⋊C4C2×#692311yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—1221no—
438C2×C22⋊C4—1221no—
439C2×C22⋊C4—1221no—
440C2×C22⋊C4—1222no—
441C2×C42—611no—
442C2×C42—611no—
443C2×C42—611no—
444C2×C42—611no—
445C2×C42—611no—
446C2×C42—611no—
447C2×C42—611no—
448C2×C42—611no—
449C2×C42—611no—
450C2×C42—611no—
451C2×C42—611no—
452C2×C42—1222no—
453C2×C42C2×#692311yescharacteristic
454C4⋊C8—1222no—
455C4⋊C8—1222no—
456C22⋊C8—614no—
457C22⋊C8—1222no—
458#97—1222no—
459#97—1222no—
460#95—614no—
461#95—1222no—
462#95—1222no—
463#95—1222no—
464C24—21no—
465C24—611no—
466C24—1221no—
467#41—2448no—
468#41—2448no—
469#41—2448no—
470#41—2448no—
471C2×Q8—1222no—
472C2×Q8—1222no—
473C2×Q8—2444no—
474C2×D4—21no—
475C2×D4—42no—
476C2×D4—612no—
477C2×D4—1222no—
478C2×D4—1222no—
479C2×D4—1222no—
480C2×D4—1222no—
481C2×D4—1222no—
482C2×D4—1222no—
483C2×D4—1222no—
484C2×D4—1222no—
485C2×D4—1221no—
486C2×D4—2442no—
487C2×D4—2444no—
488C2×D4—2444no—
489C2×D4—2444no—
490C2×D4—2444no—
491C2×D4C22×#692312yes—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—44no—
496C22×C4—611no—
497C22×C4—611no—
498C22×C4—611no—
499C22×C4—611no—
500C22×C4—611no—
501C22×C4—611no—
502C22×C4—611no—
503C22×C4—611no—
504C22×C4—611no—
505C22×C4—611no—
506C22×C4—611no—
507C22×C4—611no—
508C22×C4—611no—
509C22×C4—611no—
510C22×C4—611no—
511C22×C4—1224no—
512C22×C4—1221no—
513C22×C4—1222no—
514C22×C4—1222no—
515C22×C4—1224no—
516C22×C4—2442no—
517C22×C4—2444no—
518C22×C4—2442no—
519C22×C4C22⋊#692311yescharacteristic
520C22×C4C22⋊#692311yescharacteristic
521C22×C4C22×#692311yescharacteristic
522C2×C8—1224no—
523C2×C8—2444no—
524C4⋊C4—21no—
525C4⋊C4—612no—
526C4⋊C4—1222no—
527C4⋊C4—1222no—
528C4⋊C4—1221no—
529C4⋊C4—2444no—
530C4⋊C4C22×#692312yes—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—1222no—
534C22⋊C4—1222no—
535C22⋊C4—1222no—
536C22⋊C4—1222no—
537C22⋊C4—1222no—
538C22⋊C4—1222no—
539C22⋊C4—2444no—
540C42—611no—
541C42—611no—
542C42—611no—
543C42—611no—
544C42—611no—
545C42—611no—
546C42—611no—
547C42—611no—
548C42—611no—
549C42—611no—
550C42—611no—
551C42—611no—
552C42—2444no—
553C42C22⋊#692311yescharacteristic
554C42C22⋊#692311yescharacteristic
555C42C22×#692311yescharacteristic
556C42C22×#692311yescharacteristic
557C23—22no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—611no—
562C23—611no—
563C23—614no—
564C23—1222no—
565C23—2441no—
566C23—2441no—
567C23—2442no—
568C23—2442no—
569C23—2442no—
570C23C2×C22⋊#692311yescharacteristic
571Q8—2444no—
572Q8—2444no—
573D4—42no—
574D4—42no—
575D4—2442no—
576D4—2444no—
577D4—2444no—
578D4—2444no—
579D4—2444no—
580D4—2444no—
581D4—2444no—
582D4—2444no—
583D4—2444no—
584D4—2442no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—44no—
590C2×C4—44no—
591C2×C4—42no—
592C2×C4—611no—
593C2×C4—611no—
594C2×C4—611no—
595C2×C4—611no—
596C2×C4—611no—
597C2×C4—611no—
598C2×C4—1222no—
599C2×C4—1222no—
600C2×C4—1222no—
601C2×C4—1222no—
602C2×C4—1222no—
603C2×C4—1222no—
604C2×C4—1222no—
605C2×C4—1222no—
606C2×C4—1222no—
607C2×C4—1222no—
608C2×C4—1222no—
609C2×C4—2441no—
610C2×C4—2441no—
611C2×C4—2441no—
612C2×C4—2441no—
613C2×C4—2444no—
614C2×C4—2444no—
615C2×C4—2441no—
616C2×C4—2444no—
617C2×C4—2444no—
618C2×C4—2444no—
619C2×C4—2442no—
620C2×C4C2×C22⋊#692311yescharacteristic
621C2×C4C2×C22⋊#692311yescharacteristic
622C2×C4C2×C22⋊#692311yescharacteristic
623C2×C4C2×C22⋊#692311yescharacteristic
624C2×C4C2×C22⋊#692311yescharacteristic
625C2×C4C23×#692311yescharacteristic
626C8—2444no—
627C22—21no—
628C22—21no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—84no—
633C22—612no—
634C22—612no—
635C22—1221no—
636C22—1221no—
637C22—1221no—
638C22—1221no—
639C22—4884no—
640C22—2444no—
641C22—2442no—
642C22—2442no—
643C22—2442no—
644C22#1684075412yes—
645C22C22×C22⋊#692311yescharacteristic
646C4—21no—
647C4—21no—
648C4—21no—
649C4—21no—
650C4—21no—
651C4—42no—
652C4—612no—
653C4—1221no—
654C4—1221no—
655C4—1221no—
656C4—1221no—
657C4—1221no—
658C4—4884no—
659C4—2442no—
660C4#1684074112yes—
661C2—22no—
662C2—82no—
663C2—1222no—
664C2—1222no—
665C2—4882no—
666C2C2×#1684074111yescharacteristic
667C2C2×#1684075411yescharacteristic
668C2D61⋊#42111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4×D4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840309C2
cosocleC2×C4×D61C24
hypercenterC2×C4×D4#6923
hypocenterC61#17595
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. D61⋊#432C2semidirect
2. #21462266C2semidirect
3. #21461256C2semidirect
4. #21461255C2semidirect
5. #21461238C2semidirect
6. #21461209C2semidirect
8. #16840785C22semidirect
9. #16840784C22semidirect
15. #16840707C22semidirect
21. #16840698C22semidirect
22. #16840614C22semidirect
23. #16840613C22semidirect
29. #16840309C4semidirect
30. #16840309C4semidirect
33. C2×#14519776C4semidirect
34. C2×#14519773C4semidirect
39. C2×C4×D244C4semidirect
42. C2×C4×D4×C61C4semidirect
359. C2×C4×D4#6923semidirect
377. C61#17595semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4322
#214622662
#214612562
#214612552
#214612382
#214612092
C2×#168403092
#1759561