Finite Group Databasebeta

← #30610470

Subgroups — #30610470

Order 15616.

1292 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462498C211yesmaximal, characteristic, complemented
2D61⋊#423C211yesmaximal, characteristic, complemented
3#21461157C214yesmaximal, complemented
4#21461147C212yesmaximal, complemented
5#21461146C212yesmaximal, complemented
6#21461117C214yesmaximal, complemented
7C2×C4×#11758226C211yesmaximal, characteristic
8C2×D61⋊M16—21no—
9#16840785—21no—
10#16840782—21no—
11#16840780C2212yescomplemented
12#16840779C2212yes—
13#16840767—21no—
14#16840767—21no—
15#16840766C2212yescomplemented
16#16840765—21no—
17#16840765C2212yes—
18D61⋊(C4⋊C8)—21no—
19D61⋊(C4⋊C8)C2212yescomplemented
20#16840733—21no—
21C4×#11758213C2212yescomplemented
22Q8⋊#92420C2218yescomplemented
23#16840610C2218yescomplemented
24C22×#11758226C411yescharacteristic
25C4×#11758226—21no—
26C4×#11758226—21no—
27C4×#11758226—21no—
28C4×#11758226—21no—
29C4×#11758226C412yes—
30C4×#11758226C412yes—
31C4×#11758226C2212yes—
32C4×#11758226C2212yes—
33C2×Q8×Dic61C2211yescharacteristic
34C2×C4×D244—21no—
35C2×C4×D244C411yescharacteristic
36C2×#14519739—21no—
37C2×#14519739C2211yescharacteristic
38C2×#14519735—21no—
39C2×#14519735C411yescharacteristic
40C2×C42×D61—21no—
41C2×C42×D61C2211yescharacteristic
42C2×C4×Q8×C61C411yescharacteristic
43C2×#11758213—22no—
44C2×#11758213—22no—
45D61⋊M16—44no—
46C2×#11758217—22no—
47C2×D61⋊C8—22no—
48#14519844—22no—
49#14519844—22no—
50#14519844—22no—
51#14519844—22no—
52C4⋊#92420—22no—
53C4⋊#92420C2314yes—
54#14519834—22no—
55C22⋊#92420—22no—
56#14519832—22no—
57C4×#92420C2314yes—
58C2×#11758226—28no—
59C2×#11758226—21no—
60C2×#11758226—21no—
61C2×#11758226C2×C412yes—
62C2×#11758226C2×C412yes—
63C22×D244—21no—
64C22×D244C2×C411yescharacteristic
65C22×C4×D61—21no—
66C22×C4×D61—21no—
67C22×C4×D61—21no—
68C22×C4×D61C2×C411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71Q8×Dic61—21no—
72Q8×Dic61—21no—
73Q8×Dic61C2×C412yes—
74Q8×Dic61C2312yes—
75C4×D244—22no—
76C4×D244—22no—
77C4×D244—22no—
78C4×D244—22no—
79C4×D244—21no—
80C4×D244—21no—
81C4×D244C2×C412yes—
82C4×D244C2×C412yes—
83#14519739—22no—
84#14519739—22no—
85#14519739—22no—
86#14519739—22no—
87#14519739—21no—
88#14519739—21no—
89#14519739C2×C412yes—
90#14519739C2312yes—
91#14519735—21no—
92#14519735—21no—
93#14519735—22no—
94#14519735—22no—
95#14519735—22no—
96#14519735—22no—
97#14519735C2×C412yes—
98#14519735C2×C412yes—
99C2×C4⋊Dic61—21no—
100C2×C4⋊Dic61C2×C411yescharacteristic
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61D411yescharacteristic
107C2×C4×Dic61D411yescharacteristic
108C2×C4×Dic61C2311yescharacteristic
109C42×D61—22no—
110C42×D61—22no—
111C42×D61—22no—
112C42×D61—22no—
113C42×D61C2×C411yescharacteristic
114C42×D61C2×C411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61D411yescharacteristic
119C42×D61C2311yescharacteristic
120C42×D61C2311yescharacteristic
121C22×Q8×C61C2×C411yescharacteristic
122C4×Q8×C61—21no—
123C4×Q8×C61—21no—
124C4×Q8×C61C2×C412yes—
125C4×Q8×C61C2×C412yes—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61C2×C411yescharacteristic
128C2×C42×C61—21no—
129C2×C42×C61C2×C411yescharacteristic
130C23×D61—21no—
131C23×D61C22⋊C411yescharacteristic
132C2×Q8×C61—24no—
133C2×Q8×C61—21no—
134C2×Q8×C61C22×C412yes—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61C22⋊C411yescharacteristic
138C22×C4×C61C22⋊C411yescharacteristic
139C22×C4×C61C22×C411yescharacteristic
140C22×Dic61—21no—
141C22×Dic61C22⋊C411yescharacteristic
142C22×Dic61C2×D411yescharacteristic
143C22×Dic61C2×D411yescharacteristic
144#11758226—28no—
145#11758226—28no—
146#11758226—24no—
147#11758226—24no—
148#11758226—24no—
149#11758226M1618yescomplemented
150C2×D244—28no—
151C2×D244—22no—
152C2×D244—22no—
153C2×D244—21no—
154C2×D244—24no—
155C2×D244C22×C412yes—
156C2×C4×D61—28no—
157C2×C4×D61—22no—
158C2×C4×D61—22no—
159C2×C4×D61—22no—
160C2×C4×D61—22no—
161C2×C4×D61—24no—
162C2×C4×D61—22no—
163C2×C4×D61—22no—
164C2×C4×D61—22no—
165C2×C4×D61—22no—
166C2×C4×D61—42no—
167C2×C4×D61—44no—
168C2×C4×D61—42no—
169C2×C4×D61—42no—
170C2×C4×D61C22⋊C411yescharacteristic
171C2×C4×D61C22⋊C411yescharacteristic
172C2×C4×D61C22⋊C411yescharacteristic
173C2×C4×D61C22⋊C411yescharacteristic
174C2×C4×D61C22⋊C411yescharacteristic
175C2×C4×D61C22⋊C411yescharacteristic
176C2×C4×D61C22×C411yescharacteristic
177C2×C4×D61C22×C411yescharacteristic
178C2×C4×D61C2×D411yescharacteristic
179C2×C4×D61C2×D411yescharacteristic
180C2×C4×D61C2×D411yescharacteristic
181C2×C4×D61C2×D411yescharacteristic
182#11758217—44no—
183C2×#92420—24no—
184C2×#92420—24no—
185#11758213—44no—
186#11758213—44no—
187D61⋊C8—44no—
188C4⋊C4×C61—22no—
189C4⋊C4×C61—22no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61C22×C412yes—
192C42×C61—22no—
193C42×C61—22no—
194C42×C61C22⋊C411yescharacteristic
195C42×C61C22⋊C411yescharacteristic
196C42×C61C22×C411yescharacteristic
197C42×C61C22×C411yescharacteristic
198#11758198—22no—
199#11758198—22no—
200#11758198—22no—
201#11758198—22no—
202#11758198—22no—
203#11758198—22no—
204C4⋊Dic61—21no—
205C4⋊Dic61—22no—
206C4⋊Dic61—22no—
207C4⋊Dic61C22×C412yes—
208C4×Dic61—22no—
209C4×Dic61—22no—
210C4×Dic61—22no—
211C4×Dic61—22no—
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C22×C411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C4×Dic61C2×D411yescharacteristic
221C4×Dic61C2×D411yescharacteristic
222C4×Dic61C2×D411yescharacteristic
223C4×Dic61C2411yescharacteristic
224C23×C61C2×C22⋊C411yescharacteristic
225C22×D61—24no—
226C22×D61—22no—
227C22×D61—22no—
228C22×D61—22no—
229C22×D61—41no—
230C22×D61—42no—
231C22×D61—42no—
232C22×D61C2×C22⋊C411yescharacteristic
233C22×D61C2×C22⋊C411yescharacteristic
234Q8×C61—24no—
235Q8×C61—22no—
236Q8×C61C2×M1614yescomplemented
237C2×C4×C61—24no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—42no—
244C2×C4×C61C2×C22⋊C411yescharacteristic
245C2×C4×C61C2×C22⋊C411yescharacteristic
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61C2×C22⋊C411yescharacteristic
248C2×C4×C61C2×C22⋊C411yescharacteristic
249C2×C4×C61C23×C411yescharacteristic
250C2×Dic61—22no—
251C2×Dic61—22no—
252C2×Dic61—41no—
253C2×Dic61—42no—
254C2×Dic61C2×C22⋊C411yescharacteristic
255C2×Dic61C2×C22⋊C411yescharacteristic
256C2×Dic61C2×C22⋊C411yescharacteristic
257C2×Dic61C2×C22⋊C411yescharacteristic
258C2×Dic61AGL(1,ℤ/8)12yes—
259C2×Dic61#13712yes—
260C2×Dic61C22×D411yescharacteristic
261C2×Dic61C22×D411yescharacteristic
262D244—28no—
263D244—24no—
264D244—28no—
265D244—22no—
266D244C2×M1614yescomplemented
267C4×D61—28no—
268C4×D61—22no—
269C4×D61—22no—
270C4×D61—22no—
271C4×D61—22no—
272C4×D61—21no—
273C4×D61—21no—
274C4×D61—21no—
275C4×D61—21no—
276C4×D61—28no—
277C4×D61—22no—
278C4×D61—22no—
279C4×D61—22no—
280C4×D61—41no—
281C4×D61—41no—
282C4×D61—44no—
283C4×D61—44no—
284C4×D61—42no—
285C4×D61—42no—
286C4×D61—44no—
287C4×D61C2×M1614yes—
288#92420—44no—
289#92420—44no—
290#17451—611nomaximal, Sylow
291C22×C61—21no—
292C22×C61—21no—
293C22×C61#41712yes—
294C22×C61C22×C22⋊C411yescharacteristic
295C2×D61—21no—
296C2×D61—21no—
297C2×D61—21no—
298C2×D61—24no—
299C2×D61—21no—
300C2×D61—21no—
301C2×D61—44no—
302C2×D61—48no—
303C2×D61—42no—
304C2×D61—42no—
305C2×D61#40712yes—
306C4×C61—24no—
307C4×C61—21no—
308C4×C61—21no—
309C4×C61—21no—
310C4×C61—21no—
311C4×C61—42no—
312C4×C61#42112yes—
313C4×C61C22×M1612yes—
314Dic61—21no—
315Dic61—21no—
316Dic61—21no—
317Dic61—42no—
318Dic61#40712yes—
319Dic61#41712yes—
320Dic61C2×AGL(1,ℤ/8)11yescharacteristic
321Dic61C2×#13711yescharacteristic
322C2×C4×#41—611no—
323#2920—611no—
324C2×#423—611no—
325#1489—614no—
326#1487—612no—
327#1486—612no—
328#1477—614no—
329C2×C61—22no—
330C2×C61C2×#40711yescharacteristic
331C2×C61C2×#41711yescharacteristic
332C2×C61C2×#42111yescharacteristic
333D61—22no—
334D61—41no—
335D61—44no—
336C22×#41—611no—
337C22×M16—1221no—
338C4×#41—612no—
339C4×#41—612no—
340C4×#41—612no—
341C4×#41—612no—
342C4×#41—1221no—
343C4×#41—1221no—
344C4×#41—1221no—
345C4×#41—1221no—
346C2×C4×Q8—611no—
347C2×C4×Q8#692311yescharacteristic
348C2×C4×D4—611no—
349C2×C4×D4—611no—
350C2×C4×D4—1221no—
351C2×C4×D4—1221no—
352C2×#117—611no—
353C2×#117—1221no—
354C22×C42—611no—
355C22×C42—1221no—
356#432—1221no—
357#432—1221no—
358#431—612no—
359#431—612no—
360#423—612no—
361#423—612no—
362#423—1221no—
363#423—1221no—
364#423—1221no—
365C2×C4⋊C8—612no—
366C2×C4⋊C8—1221no—
367#407—1221no—
368C4×M16—612no—
369Q8⋊C8—618no—
370D4⋊C8—618no—
371C61#1745111yescharacteristic, complemented, Sylow
372C2×#41—612no—
373C2×#41—612no—
374C2×#41—1221no—
375C2×#41—1221no—
376C2×#41—1228no—
377C22×Q8C2×#692311yescharacteristic
378C22×D4—611no—
379C22×D4—1221no—
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—611no—
383C23×C4—1221no—
384C23×C4—1221no—
385C23×C4—1221no—
386C2×M16—1222no—
387C2×M16—1222no—
388C2×M16—1222no—
389C2×M16—2444no—
390C22×C8—1222no—
391C4×Q8—21no—
392C4×Q8—21no—
393C4×Q8—612no—
394C4×Q8—612no—
395C4×Q8—1221no—
396C4×Q8—1221no—
397C4×Q8C2×#692312yes—
398C4×Q8C2×#692312yes—
399C4×D4—612no—
400C4×D4—612no—
401C4×D4—612no—
402C4×D4—612no—
403C4×D4—1222no—
404C4×D4—1222no—
405C4×D4—1222no—
406C4×D4—1222no—
407C4×D4—1221no—
408C4×D4—1221no—
409C4×D4—1222no—
410C4×D4—1222no—
411C4×D4—1222no—
412C4×D4—1222no—
413C4×D4—1221no—
414C4×D4—1221no—
415#117—612no—
416#117—612no—
417#117—1222no—
418#117—1222no—
419#117—1222no—
420#117—1222no—
421#117—1221no—
422#117—1221no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—1221no—
426C2×C4⋊C4C2×#692311yescharacteristic
427C2×C22⋊C4—1221no—
428C2×C22⋊C4—1221no—
429C2×C22⋊C4—1221no—
430C2×C42—21no—
431C2×C42—611no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—611no—
441C2×C42—611no—
442C2×C42—1222no—
443C2×C42—1222no—
444C2×C42—1222no—
445C2×C42—1222no—
446C2×C42—1221no—
447C2×C42—1221no—
448C2×C42C2×#692311yescharacteristic
449C4⋊C8—614no—
450C4⋊C8—1222no—
451C4⋊C8—1222no—
452C4⋊C8—1222no—
453C4⋊C8—1222no—
454C4⋊C8—1222no—
455C22⋊C8—1222no—
456C22⋊C8—1222no—
457#97—1222no—
458C4×C8—614no—
459C24—611no—
460C24—1221no—
461#41—618no—
462#41—1224no—
463#41—1224no—
464#41—1228no—
465#41—1228no—
466#41—1224no—
467C2×Q8—24no—
468C2×Q8—21no—
469C2×Q8C22×#692312yes—
470C2×D4—612no—
471C2×D4—1224no—
472C2×D4—1222no—
473C2×D4—1222no—
474C2×D4—1228no—
475C2×D4—1221no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—611no—
490C22×C4—611no—
491C22×C4—611no—
492C22×C4—611no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4—1222no—
496C22×C4—1222no—
497C22×C4—1224no—
498C22×C4—1222no—
499C22×C4—1222no—
500C22×C4—1228no—
501C22×C4—1221no—
502C22×C4—1222no—
503C22×C4—1222no—
504C22×C4—2442no—
505C22×C4—2444no—
506C22×C4—2442no—
507C22×C4—2442no—
508C22×C4C22⋊#692311yescharacteristic
509C22×C4C22⋊#692311yescharacteristic
510C22×C4C22×#692311yescharacteristic
511M16—2444no—
512M16—2444no—
513M16—2444no—
514C2×C8—1224no—
515C2×C8—1224no—
516C2×C8—2444no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—21no—
520C4⋊C4—612no—
521C4⋊C4—1222no—
522C4⋊C4—1222no—
523C4⋊C4—1221no—
524C4⋊C4C22×#692312yes—
525C22⋊C4—1222no—
526C22⋊C4—1222no—
527C22⋊C4—1222no—
528C22⋊C4—1222no—
529C22⋊C4—1222no—
530C22⋊C4—1222no—
531C42—22no—
532C42—22no—
533C42—611no—
534C42—611no—
535C42—611no—
536C42—611no—
537C42—611no—
538C42—611no—
539C42—611no—
540C42—611no—
541C42—611no—
542C42—611no—
543C42—611no—
544C42—611no—
545C42—1222no—
546C42—1222no—
547C42—1222no—
548C42—1222no—
549C42C22⋊#692311yescharacteristic
550C42C22⋊#692311yescharacteristic
551C42C22×#692311yescharacteristic
552C42C22×#692311yescharacteristic
553C23—611no—
554C23—611no—
555C23—1222no—
556C23—1224no—
557C23—1222no—
558C23—1222no—
559C23—2441no—
560C23—2442no—
561C23—2442no—
562C23C2×C22⋊#692311yescharacteristic
563Q8—24no—
564Q8—22no—
565Q8D61⋊M1614yescomplemented
566D4—614no—
567D4—1228no—
568D4—1228no—
569D4—1224no—
570D4—1222no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—42no—
578C2×C4—612no—
579C2×C4—612no—
580C2×C4—611no—
581C2×C4—611no—
582C2×C4—611no—
583C2×C4—614no—
584C2×C4—611no—
585C2×C4—611no—
586C2×C4—611no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—1221no—
590C2×C4—1221no—
591C2×C4—1222no—
592C2×C4—1222no—
593C2×C4—1222no—
594C2×C4—1228no—
595C2×C4—1222no—
596C2×C4—1228no—
597C2×C4—1222no—
598C2×C4—1222no—
599C2×C4—1222no—
600C2×C4—1222no—
601C2×C4—1222no—
602C2×C4—2441no—
603C2×C4—2441no—
604C2×C4—2444no—
605C2×C4—2442no—
606C2×C4—2442no—
607C2×C4—2444no—
608C2×C4—2441no—
609C2×C4—2442no—
610C2×C4—2444no—
611C2×C4C2×C22⋊#692311yescharacteristic
612C2×C4C2×C22⋊#692311yescharacteristic
613C2×C4C2×C22⋊#692311yescharacteristic
614C2×C4C2×C22⋊#692311yescharacteristic
615C2×C4C2×C22⋊#692311yescharacteristic
616C2×C4C23×#692311yescharacteristic
617C8—2444no—
618C8—2444no—
619C22—21no—
620C22—21no—
621C22—612no—
622C22—1221no—
623C22—1221no—
624C22—1224no—
625C22—1221no—
626C22—1221no—
627C22—1221no—
628C22—2444no—
629C22—2448no—
630C22—2442no—
631C22—2442no—
632C22#1684075312yes—
633C22C22×C22⋊#692311yescharacteristic
634C4—24no—
635C4—21no—
636C4—21no—
637C4—21no—
638C4—21no—
639C4—42no—
640C4—612no—
641C4—611no—
642C4—611no—
643C4—612no—
644C4—1221no—
645C4—1221no—
646C4—1221no—
647C4—2442no—
648C4#1684076112yes—
649C4C2×D61⋊M1612yes—
650C2—22no—
651C2—1222no—
652C2—2441no—
653C2—2444no—
654C2D61⋊#40711yescharacteristic
655C2C2×#1684075311yescharacteristic
656C2C2×#1684076111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4×Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×#11758226C4
cosocleC4×Dic61C24
hypercenterC2×C4×Q8#6923
hypocenterC61#17451
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #21462498C2semidirect
2. D61⋊#423C2semidirect
3. #21461157C2semidirect
4. #21461147C2semidirect
5. #21461146C2semidirect
6. #21461117C2semidirect
11. #16840780C22semidirect
15. #16840766C22semidirect
19. D61⋊(C4⋊C8)C22semidirect
21. C4×#11758213C22semidirect
22. Q8⋊#92420C22semidirect
23. #16840610C22semidirect
149. #11758226M16semidirect
236. Q8×C61C2×M16semidirect
266. D244C2×M16semidirect
371. C61#17451semidirect
565. Q8D61⋊M16semidirect

Maximal subgroups

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

subgroupindex
#214624982
D61⋊#4232
#214611572
#214611472
#214611462
#214611172
C2×C4×#117582262
#1745161