Finite Group Databasebeta

← #30602409

Subgroups — #30602409

Order 15616.

1510 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D61⋊M16C211yesmaximal, characteristic
2#21462263C211yesmaximal, characteristic
3C2×#16840633C214yesmaximal, complemented
4C4×C22⋊C4×D61C211yesmaximal, characteristic
5C22×#11758213C412yescomplemented
6C2×D61⋊M16—28no—
7C2×D61⋊M16—21no—
8C2×D61⋊M16—21no—
9C2×D61⋊M16C412yescomplemented
10C2×D61⋊M16C2212yes—
11C22×#11758217—21no—
12C22×D61⋊C8—21no—
13C2×#14519856C2212yes—
14#16840705—21no—
15#16840704C412yescomplemented
16#16840704C412yescomplemented
17#16840703—21no—
18C4×C22⋊#6923—21no—
19C4×C22⋊#6923—21no—
20#16840633—28no—
21C23×C4×D61C2211yescharacteristic
22C2×C22⋊C4×D61—21no—
23C2×C42×D61C2212yes—
24C22⋊C4×Dic61—21no—
25C4×#11758198C412yescomplemented
26C4×C22⋊Dic61C411yescharacteristic, complemented
27#16839609—21no—
28#95×D61—21no—
29C4×C22⋊C4×C61C411yescharacteristic, complemented
30C2×#11758213—22no—
31C2×#11758213—28no—
32C2×#11758213C2×C414yes—
33D61⋊M16—28no—
34D61⋊M16—28no—
35D61⋊M16—24no—
36D61⋊M16—28no—
37D61⋊M16D418yes—
38C2×#11758217—28no—
39C2×#11758217—22no—
40C2×#11758217—22no—
41C2×D61⋊C8—28no—
42C2×D61⋊C8—22no—
43C2×D61⋊C8—22no—
44C22×#92420—22no—
45#14519856—24no—
46#14519856—24no—
47C2×C4⋊#6923C2×C414yes—
48C2×C22⋊#6923—22no—
49C2×C22⋊#6923—22no—
50C2×C22⋊#6923—22no—
51C2×C4×#6923—22no—
52(C2×#6923)⋊C4—22no—
53(C2×#6923)⋊C4—22no—
54C24×D61D411yescharacteristic
55C23×Dic61D411yescharacteristic
56C22×C4×D61—24no—
57C22×C4×D61—24no—
58C22×C4×D61—22no—
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×C4×D61D411yescharacteristic
67C22×C4×D61D411yescharacteristic
68C22×C4×D61Q811yescharacteristic
69C22×C4×D61Q811yescharacteristic
70C22×C4×D61C2311yescharacteristic
71C2×C22⋊Dic61—21no—
72C2×#11758198—22no—
73C22⋊C4×D61—28no—
74C2×C4×Dic61—22no—
75C2×C4×Dic61C2×C412yes—
76C42×D61—24no—
77C42×D61—24no—
78#14519684—21no—
79#14519684—22no—
80C23×C4×C61C2×C411yescharacteristic
81C2×C22⋊C4×C61—21no—
82C2×C42×C61C2×C412yes—
83#95×C61—21no—
84C24×C61C22⋊C411yescharacteristic
85C23×D61—24no—
86C23×D61—24no—
87C23×D61—42no—
88C23×D61C22⋊C411yescharacteristic
89C23×D61C22⋊C411yescharacteristic
90C23×D61C22⋊C411yescharacteristic
91C23×D61C4⋊C411yescharacteristic
92C23×D61C4⋊C411yescharacteristic
93C23×D61C2×D411yescharacteristic
94C22×#6923—24no—
95C22×C4×C61—24no—
96C22×C4×C61—22no—
97C22×C4×C61C4211yescharacteristic
98C22×C4×C61C4211yescharacteristic
99C22×C4×C61C22⋊C411yescharacteristic
100C22×C4×C61C4⋊C411yescharacteristic
101C22×C4×C61C4⋊C411yescharacteristic
102C22×C4×C61C22×C411yescharacteristic
103C22×Dic61—22no—
104C22×Dic61—22no—
105C22×Dic61—22no—
106C22×Dic61C22⋊C411yescharacteristic
107C22×Dic61C22⋊C411yescharacteristic
108C22×Dic61C22⋊C411yescharacteristic
109C22×Dic61C4⋊C411yescharacteristic
110C22×Dic61C4⋊C411yescharacteristic
111C22×Dic61C2×D411yescharacteristic
112C2×C4×D61—24no—
113C2×C4×D61—24no—
114C2×C4×D61—22no—
115C2×C4×D61—22no—
116C2×C4×D61—22no—
117C2×C4×D61—22no—
118C2×C4×D61—22no—
119C2×C4×D61—22no—
120C2×C4×D61—24no—
121C2×C4×D61—24no—
122C2×C4×D61—22no—
123C2×C4×D61—22no—
124C2×C4×D61—24no—
125C2×C4×D61—24no—
126C2×C4×D61—22no—
127C2×C4×D61—22no—
128C2×C4×D61—28no—
129C2×C4×D61—44no—
130C2×C4×D61—44no—
131C2×C4×D61C4211yescharacteristic
132C2×C4×D61C4211yescharacteristic
133C2×C4×D61C22⋊C411yescharacteristic
134C2×C4×D61C22⋊C411yescharacteristic
135C2×C4×D61C22⋊C411yescharacteristic
136C2×C4×D61C22⋊C411yescharacteristic
137C2×C4×D61C4⋊C411yescharacteristic
138C2×C4×D61C4⋊C411yescharacteristic
139C2×C4×D61C4⋊C411yescharacteristic
140C2×C4×D61C4⋊C411yescharacteristic
141C2×C4×D61C4⋊C411yescharacteristic
142C2×C4×D61C4⋊C411yescharacteristic
143C2×C4×D61C22×C411yescharacteristic
144C2×C4×D61C22×C411yescharacteristic
145C2×C4×D61C2×D414yes—
146C2×C4×D61C2×D411yescharacteristic
147C2×C4×D61C2×Q811yescharacteristic
148C2×C4×D61#4114yes—
149C22⋊#6923—44no—
150C22⋊#6923—44no—
151C22⋊#6923—44no—
152#11758217—28no—
153#11758217—28no—
154C2×#92420—28no—
155C2×#92420—24no—
156C4⋊#6923—28no—
157C4×#6923—42no—
158C4×#6923—42no—
159#11758213—28no—
160#11758213—24no—
161#11758213C22⋊C418yescomplemented
162D61⋊C8—28no—
163D61⋊C8—28no—
164C22⋊C4×C61—24no—
165C42×C61—24no—
166C22⋊Dic61—24no—
167#11758198—28no—
168C4×Dic61—24no—
169C4×Dic61—42no—
170C4×Dic61—42no—
171C23×C61—22no—
172C23×C61—22no—
173C23×C61—41no—
174C23×C61#9511yescharacteristic
175C23×C61#9511yescharacteristic
176C23×C61C2×C22⋊C411yescharacteristic
177C22×D61—22no—
178C22×D61—22no—
179C22×D61—22no—
180C22×D61—22no—
181C22×D61—22no—
182C22×D61—22no—
183C22×D61—22no—
184C22×D61—22no—
185C22×D61—22no—
186C22×D61—22no—
187C22×D61—22no—
188C22×D61—22no—
189C22×D61—22no—
190C22×D61—41no—
191C22×D61—41no—
192C22×D61—41no—
193C22×D61—416no—
194C22×D61#9511yescharacteristic
195C22×D61#9511yescharacteristic
196C22×D61#10414yes—
197C22×D61C2×C22⋊C411yescharacteristic
198C22×D61C2×C4⋊C411yescharacteristic
199C22×D61#12114yes—
200C2×#6923—44no—
201C2×#6923—44no—
202C2×#6923—44no—
203C2×C4×C61—22no—
204C2×C4×C61—22no—
205C2×C4×C61—22no—
206C2×C4×C61—22no—
207C2×C4×C61—22no—
208C2×C4×C61—24no—
209C2×C4×C61—42no—
210C2×C4×C61—42no—
211C2×C4×C61#9511yescharacteristic
212C2×C4×C61#9511yescharacteristic
213C2×C4×C61C2×C4211yescharacteristic
214C2×C4×C61C2×C4⋊C411yescharacteristic
215C2×C4×C61C4×D414yes—
216C2×Dic61—22no—
217C2×Dic61—21no—
218C2×Dic61—21no—
219C2×Dic61—21no—
220C2×Dic61—21no—
221C2×Dic61—22no—
222C2×Dic61—22no—
223C2×Dic61—24no—
224C2×Dic61—42no—
225C2×Dic61—42no—
226C2×Dic61#9511yescharacteristic
227C2×Dic61#9511yescharacteristic
228C2×Dic61C2×C22⋊C411yescharacteristic
229C2×Dic61C2×C4⋊C411yescharacteristic
230C2×Dic61#12012yes—
231C2×Dic61#12312yes—
232C4×D61—22no—
233C4×D61—22no—
234C4×D61—22no—
235C4×D61—22no—
236C4×D61—22no—
237C4×D61—22no—
238C4×D61—22no—
239C4×D61—22no—
240C4×D61—21no—
241C4×D61—21no—
242C4×D61—21no—
243C4×D61—21no—
244C4×D61—22no—
245C4×D61—22no—
246C4×D61—416no—
247C4×D61C2×C22⋊C412yes—
248C4×D61#11712yes—
249C4×D61C4×D414yes—
250C4×D61#12012yes—
251C4×D61C22⋊Q814yes—
252C4×D61#12312yes—
253#92420—28no—
254#10732—611nomaximal, Sylow
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—21no—
258C22×C61—21no—
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—44no—
263C22×C61#33912yescomplemented
264C22×C61C2×#9511yescharacteristic
265C22×C61#38612yes—
266C2×D61—21no—
267C2×D61—21no—
268C2×D61—21no—
269C2×D61—21no—
270C2×D61—28no—
271C2×D61—28no—
272C2×D61—21no—
273C2×D61—21no—
274C2×D61—21no—
275C2×D61—44no—
276C2×D61—44no—
277C2×D61—44no—
278C2×D61—44no—
279C2×D61#33912yescomplemented
280C2×D61#38012yes—
281C2×D61#38612yes—
282C2×D61C2×#10412yes—
283C2×D61#42112yes—
284#6923—84no—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—44no—
288C4×C61C4×C22⋊C412yes—
289C4×C61#38512yes—
290Dic61—21no—
291Dic61—21no—
292Dic61—44no—
293Dic61#37911yescharacteristic
294Dic61#38111yescharacteristic
295Dic61#38512yes—
296C23×M16—611no—
297#2280—611no—
298C2×C4×C22⋊C4—611no—
299C2×#339—614no—
300C2×C61—22no—
301C2×C61—22no—
302C2×C61—41no—
303C2×C61C22⋊#9511yescharacteristic
304C2×C61C2×#33911yescharacteristic
305C2×C61#173311yescharacteristic
306D61—22no—
307D61—22no—
308D61—41no—
309D61#187114yes—
310C24×C4—611no—
311C22×M16—612no—
312C22×M16—612no—
313C22×M16—612no—
314C22×M16—1228no—
315C22×M16—1221no—
316C22×M16—1221no—
317C22×M16—1221no—
318C23×C8—1221no—
319C2×#117—612no—
320C22×C22⋊C4—1221no—
321C22×C42—612no—
322#381—1221no—
323#380—612no—
324#380—612no—
325#379—1221no—
326C4×C22⋊C4—611no—
327C4×C22⋊C4—612no—
328C4×C22⋊C4—1221no—
329C4×C22⋊C4—1221no—
330C4×C22⋊C4—1221no—
331C4×C22⋊C4—1221no—
332C4×C22⋊C4#692311yescharacteristic, complemented
333C2×#95—1221no—
334#339—1228no—
335C61#1073211yescharacteristic, complemented, Sylow
336C25—611no—
337C23×C4—611no—
338C23×C4—611no—
339C23×C4—611no—
340C23×C4—611no—
341C23×C4—611no—
342C23×C4—611no—
343C23×C4—611no—
344C23×C4—611no—
345C23×C4—611no—
346C23×C4—611no—
347C23×C4—611no—
348C23×C4—611no—
349C23×C4—611no—
350C23×C4—1224no—
351C23×C4—1224no—
352C23×C4—1222no—
353C23×C4C2×#692311yescharacteristic
354C2×M16—614no—
355C2×M16—618no—
356C2×M16—1228no—
357C2×M16—1228no—
358C2×M16—1222no—
359C2×M16—1222no—
360C2×M16—1224no—
361C2×M16—1222no—
362C2×M16—1228no—
363C2×M16—1228no—
364C2×M16—1228no—
365C22×C8—1222no—
366C22×C8—1222no—
367C22×C8—1222no—
368C22×C8—1228no—
369#117—1224no—
370#117—1224no—
371C2×C4⋊C4—614no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—1228no—
374C2×C22⋊C4—1222no—
375C2×C22⋊C4—1221no—
376C2×C22⋊C4—1222no—
377C2×C22⋊C4—1222no—
378C2×C22⋊C4—1222no—
379C2×C42—612no—
380C2×C42—1224no—
381C2×C42—1224no—
382C2×C42—1222no—
383C2×C42—1222no—
384C2×C42C2×#692312yes—
385#95—21no—
386#95—1222no—
387#95—1222no—
388#95—1222no—
389#95—1221no—
390C24—611no—
391C24—611no—
392C24—611no—
393C24—611no—
394C24—611no—
395C24—611no—
396C24—1224no—
397C24—1224no—
398C24—2442no—
399C24C22⋊#692311yescharacteristic
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—611no—
403C22×C4—611no—
404C22×C4—611no—
405C22×C4—611no—
406C22×C4—611no—
407C22×C4—614no—
408C22×C4—614no—
409C22×C4—611no—
410C22×C4—611no—
411C22×C4—611no—
412C22×C4—611no—
413C22×C4—611no—
414C22×C4—611no—
415C22×C4—611no—
416C22×C4—611no—
417C22×C4—611no—
418C22×C4—611no—
419C22×C4—611no—
420C22×C4—611no—
421C22×C4—611no—
422C22×C4—611no—
423C22×C4—611no—
424C22×C4—611no—
425C22×C4—611no—
426C22×C4—1222no—
427C22×C4—1222no—
428C22×C4—1222no—
429C22×C4—1222no—
430C22×C4—1222no—
431C22×C4—1222no—
432C22×C4—1224no—
433C22×C4—1224no—
434C22×C4—1222no—
435C22×C4—1222no—
436C22×C4—1222no—
437C22×C4—1222no—
438C22×C4—1224no—
439C22×C4—1224no—
440C22×C4—1224no—
441C22×C4—1228no—
442C22×C4—1222no—
443C22×C4—1222no—
444C22×C4—1224no—
445C22×C4—1222no—
446C22×C4—1224no—
447C22×C4—2444no—
448C22×C4—2444no—
449C22×C4C4×#692311yescharacteristic
450C22×C4C4×#692311yescharacteristic
451C22×C4C4⋊#692311yescharacteristic
452C22×C4C4⋊#692311yescharacteristic
453C22×C4C22⋊#692311yescharacteristic
454C22×C4C22×#692311yescharacteristic
455M16—618no—
456M16—1224no—
457M16—1228no—
458M16—1228no—
459M16—1228no—
460C2×C8—1228no—
461C2×C8—1224no—
462C2×C8—1228no—
463C2×C8—1228no—
464C4⋊C4—1228no—
465C22⋊C4—24no—
466C22⋊C4—1228no—
467C22⋊C4—1224no—
468C22⋊C4—2444no—
469C22⋊C4—2444no—
470C22⋊C4—2444no—
471C42—24no—
472C42—1224no—
473C42—2442no—
474C42—2442no—
475C42—2442no—
476C42—2442no—
477C23—22no—
478C23—22no—
479C23—41no—
480C23—611no—
481C23—614no—
482C23—614no—
483C23—611no—
484C23—611no—
485C23—611no—
486C23—1222no—
487C23—1222no—
488C23—1222no—
489C23—1222no—
490C23—1222no—
491C23—1222no—
492C23—1222no—
493C23—1222no—
494C23—1222no—
495C23—1222no—
496C23—1222no—
497C23—1222no—
498C23—1222no—
499C23—2441no—
500C23—2441no—
501C23—2441no—
502C23—24416no—
503C23(C2×#6923)⋊C411yescharacteristic
504C23(C2×#6923)⋊C411yescharacteristic
505C23C2×C22⋊#692311yescharacteristic
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—612no—
515C2×C4—612no—
516C2×C4—611no—
517C2×C4—611no—
518C2×C4—612no—
519C2×C4—614no—
520C2×C4—612no—
521C2×C4—612no—
522C2×C4—612no—
523C2×C4—614no—
524C2×C4—611no—
525C2×C4—611no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1222no—
531C2×C4—1222no—
532C2×C4—1222no—
533C2×C4—1222no—
534C2×C4—1222no—
535C2×C4—1222no—
536C2×C4—1221no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1222no—
541C2×C4—1222no—
542C2×C4—1222no—
543C2×C4—1222no—
544C2×C4—1222no—
545C2×C4—1222no—
546C2×C4—1222no—
547C2×C4—1224no—
548C2×C4—24416no—
549C2×C4—2444no—
550C2×C4—2444no—
551C2×C4—2444no—
552C2×C4—2442no—
553C2×C4—2442no—
554C2×C4(C2×#6923)⋊C411yescharacteristic
555C2×C4(C2×#6923)⋊C411yescharacteristic
556C2×C4C2×C4×#692311yescharacteristic
557C2×C4C2×C4⋊#692311yescharacteristic
558C2×C4D4×#692314yes—
559C8—1228no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—44no—
568C22—612no—
569C22—612no—
570C22—612no—
571C22—612no—
572C22—612no—
573C22—1228no—
574C22—1228no—
575C22—1221no—
576C22—1221no—
577C22—1221no—
578C22—1221no—
579C22—1221no—
580C22—1221no—
581C22—1221no—
582C22—2444no—
583C22—2444no—
584C22—2444no—
585C22—2444no—
586C22#1684063312yescomplemented
587C22C2×(C2×#6923)⋊C411yescharacteristic
588C22#1684071012yes—
589C4—21no—
590C4—21no—
591C4—44no—
592C4—611no—
593C4—611no—
594C4—612no—
595C4—1221no—
596C4—1221no—
597C4—4884no—
598C4—2444no—
599C4C22⋊C4×#692312yes—
600C4#1684070912yes—
601C2—22no—
602C2—22no—
603C2—41no—
604C2—614no—
605C2—1222no—
606C2—1222no—
607C2—2441no—
608C2#2146099211yescharacteristic
609C2C2×#1684063311yescharacteristic
610C2#2146150011yescharacteristic
subgroupG/H
centerC2×C4C2×C4⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61C2×#95
prime radicalC24×D61D4
cosocleC22×C4×D61C23
hypercenterC4×C22⋊C4#6923
hypocenterC61#10732
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#16840633C2semidirect
5. C22×#11758213C4semidirect
9. C2×D61⋊M16C4semidirect
15. #16840704C4semidirect
16. #16840704C4semidirect
25. C4×#11758198C4semidirect
26. C4×C22⋊Dic61C4semidirect
29. C4×C22⋊C4×C61C4semidirect
161. #11758213C22⋊C4semidirect
263. C22×C61#339semidirect
279. C2×D61#339semidirect
332. C4×C22⋊C4#6923semidirect
335. C61#10732semidirect
586. C22#16840633semidirect

Maximal subgroups

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

subgroupindex
C22×D61⋊M162
#214622632
C2×#168406332
C4×C22⋊C4×D612
#1073261