Finite Group Databasebeta

← #30602362

Subgroups — #30602362

Order 15616.

1374 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D61⋊M16C211yesmaximal, characteristic
2#21462263C211yesmaximal, characteristic
3C2×#16840629C214yesmaximal, complemented
4#21448200C211yesmaximal, characteristic
5C22×#11758213—21no—
6C2×D61⋊M16—28no—
7C2×D61⋊M16—21no—
8C2×D61⋊M16—21no—
9C2×D61⋊M16C412yescomplemented
10C2×D61⋊M16C2212yes—
11C22×#11758217—21no—
12C22×D61⋊C8C412yescomplemented
13C2×#14519856C2212yes—
14#16840705—21no—
15#16840704—21no—
16#16840704—21no—
17#16840703—21no—
18C4×C22⋊#6923C412yescomplemented
19C4×C22⋊#6923C412yescomplemented
20#16840629—28no—
21C23×C4×D61C2211yescharacteristic
22C2×#14519734C2212yes—
23#16839624—21no—
24#16839621—21no—
25#16839620—21no—
26#16839617—21no—
27C4×#11758198C412yescomplemented
28C4×C22⋊Dic61C411yescharacteristic, complemented
29C4×C22⋊C4×C61C411yescharacteristic, complemented
30C2×#11758213—28no—
31C2×#11758213—22no—
32C2×#11758213—22no—
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—22no—
42C2×D61⋊C8—28no—
43C2×D61⋊C8C2×C414yes—
44C22×#92420—22no—
45#14519856—24no—
46#14519856—24no—
47C2×C4⋊#6923—22no—
48C2×C22⋊#6923—22no—
49C2×C22⋊#6923—22no—
50C2×C22⋊#6923—22no—
51C2×C4×#6923C2×C414yes—
52(C2×#6923)⋊C4—22no—
53(C2×#6923)⋊C4—22no—
54C24×D61D411yescharacteristic
55C23×Dic61D411yescharacteristic
56C22×C4×D61—24no—
57C22×C4×D61—24no—
58C22×C4×D61C2×C411yescharacteristic
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×C4×D61D411yescharacteristic
67C22×C4×D61Q811yescharacteristic
68C22×C4×D61Q811yescharacteristic
69C22×C4×D61C2311yescharacteristic
70#14519734—24no—
71#14519734—24no—
72C2×#11758196—22no—
73C2×C22⋊Dic61—21no—
74C2×#11758198—22no—
75C2×#11758198—22no—
76C2×C4×Dic61C2×C412yes—
77#14519684—21no—
78#14519684—22no—
79C23×C4×C61C2×C411yescharacteristic
80C2×C22⋊C4×C61—21no—
81C2×C42×C61C2×C412yes—
82#95×C61—21no—
83C24×C61C22⋊C411yescharacteristic
84C23×D61—24no—
85C23×D61—42no—
86C23×D61—42no—
87C23×D61C22⋊C411yescharacteristic
88C23×D61C22⋊C411yescharacteristic
89C23×D61C22⋊C411yescharacteristic
90C23×D61C4⋊C411yescharacteristic
91C23×D61C4⋊C411yescharacteristic
92C23×D61C2×D411yescharacteristic
93C22×#6923—24no—
94C22×C4×C61—24no—
95C22×C4×C61—22no—
96C22×C4×C61C4211yescharacteristic
97C22×C4×C61C4211yescharacteristic
98C22×C4×C61C22⋊C411yescharacteristic
99C22×C4×C61C4⋊C411yescharacteristic
100C22×C4×C61C4⋊C411yescharacteristic
101C22×C4×C61C22×C411yescharacteristic
102C22×Dic61—22no—
103C22×Dic61—22no—
104C22×Dic61—22no—
105C22×Dic61C22⋊C411yescharacteristic
106C22×Dic61C22⋊C411yescharacteristic
107C22×Dic61C22⋊C411yescharacteristic
108C22×Dic61C4⋊C411yescharacteristic
109C22×Dic61C4⋊C411yescharacteristic
110C22×Dic61C2×D411yescharacteristic
111C2×C4×D61—24no—
112C2×C4×D61—24no—
113C2×C4×D61—22no—
114C2×C4×D61—22no—
115C2×C4×D61—22no—
116C2×C4×D61—22no—
117C2×C4×D61—22no—
118C2×C4×D61—22no—
119C2×C4×D61—24no—
120C2×C4×D61—24no—
121C2×C4×D61—22no—
122C2×C4×D61—22no—
123C2×C4×D61—24no—
124C2×C4×D61—24no—
125C2×C4×D61—22no—
126C2×C4×D61—22no—
127C2×C4×D61C4211yescharacteristic
128C2×C4×D61C4211yescharacteristic
129C2×C4×D61C22⋊C411yescharacteristic
130C2×C4×D61C22⋊C411yescharacteristic
131C2×C4×D61C22⋊C411yescharacteristic
132C2×C4×D61C22⋊C411yescharacteristic
133C2×C4×D61C4⋊C411yescharacteristic
134C2×C4×D61C4⋊C411yescharacteristic
135C2×C4×D61C4⋊C411yescharacteristic
136C2×C4×D61C4⋊C411yescharacteristic
137C2×C4×D61C4⋊C411yescharacteristic
138C2×C4×D61C4⋊C411yescharacteristic
139C2×C4×D61C22×C411yescharacteristic
140C2×C4×D61C22×C411yescharacteristic
141C2×C4×D61C2×D414yes—
142C2×C4×D61C2×D411yescharacteristic
143C2×C4×D61C2×Q811yescharacteristic
144C2×C4×D61#4114yes—
145C22⋊#6923—44no—
146C22⋊#6923—44no—
147C22⋊#6923—44no—
148#11758217—28no—
149#11758217—28no—
150C2×#92420—28no—
151C2×#92420—24no—
152C4⋊#6923—42no—
153C4⋊#6923—42no—
154C4×#6923—28no—
155#11758213—28no—
156#11758213—28no—
157D61⋊C8—28no—
158D61⋊C8—24no—
159D61⋊C8C22⋊C418yescomplemented
160C22⋊C4×C61—42no—
161C42×C61—24no—
162C22⋊Dic61—42no—
163#11758198—44no—
164#11758198—44no—
165#11758196—42no—
166#11758196—42no—
167C4×Dic61—24no—
168C23×C61—22no—
169C23×C61—22no—
170C23×C61—41no—
171C23×C61#9511yescharacteristic
172C23×C61#9511yescharacteristic
173C23×C61C2×C22⋊C411yescharacteristic
174C22×D61—22no—
175C22×D61—22no—
176C22×D61—22no—
177C22×D61—22no—
178C22×D61—22no—
179C22×D61—22no—
180C22×D61—22no—
181C22×D61—22no—
182C22×D61—22no—
183C22×D61—22no—
184C22×D61—41no—
185C22×D61—41no—
186C22×D61—41no—
187C22×D61—41no—
188C22×D61—41no—
189C22×D61—41no—
190C22×D61—41no—
191C22×D61—416no—
192C22×D61#9511yescharacteristic
193C22×D61#9511yescharacteristic
194C22×D61C2×C22⋊C411yescharacteristic
195C22×D61C2×C4⋊C411yescharacteristic
196C22×D61#12114yes—
197C2×#6923—44no—
198C2×#6923—44no—
199C2×#6923—44no—
200C2×C4×C61—22no—
201C2×C4×C61—22no—
202C2×C4×C61—22no—
203C2×C4×C61—22no—
204C2×C4×C61—22no—
205C2×C4×C61—42no—
206C2×C4×C61—42no—
207C2×C4×C61—42no—
208C2×C4×C61#9511yescharacteristic
209C2×C4×C61#9511yescharacteristic
210C2×C4×C61C2×C4211yescharacteristic
211C2×C4×C61C2×C4⋊C411yescharacteristic
212C2×C4×C61C4×D414yes—
213C2×Dic61—22no—
214C2×Dic61—21no—
215C2×Dic61—21no—
216C2×Dic61—21no—
217C2×Dic61—21no—
218C2×Dic61—22no—
219C2×Dic61—22no—
220C2×Dic61—42no—
221C2×Dic61—42no—
222C2×Dic61—42no—
223C2×Dic61#9511yescharacteristic
224C2×Dic61#9511yescharacteristic
225C2×Dic61C2×C22⋊C411yescharacteristic
226C2×Dic61C2×C4⋊C411yescharacteristic
227C2×Dic61#12012yes—
228C2×Dic61#12312yes—
229C4×D61—22no—
230C4×D61—22no—
231C4×D61—22no—
232C4×D61—22no—
233C4×D61—22no—
234C4×D61—22no—
235C4×D61—22no—
236C4×D61—22no—
237C4×D61—21no—
238C4×D61—21no—
239C4×D61—21no—
240C4×D61—21no—
241C4×D61—22no—
242C4×D61—22no—
243C4×D61C2×C22⋊C412yes—
244C4×D61#11712yes—
245C4×D61C4×D414yes—
246C4×D61#12012yes—
247C4×D61C22⋊Q814yes—
248C4×D61#12312yes—
249#92420—28no—
250#10717—611nomaximal, Sylow
251C22×C61—21no—
252C22×C61—21no—
253C22×C61—21no—
254C22×C61—21no—
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—21no—
258C22×C61—44no—
259C22×C61H(3,ℤ/4)12yescomplemented
260C22×C61C2×#9511yescharacteristic
261C22×C61#38612yes—
262C2×D61—28no—
263C2×D61—21no—
264C2×D61—21no—
265C2×D61—21no—
266C2×D61—21no—
267C2×D61—21no—
268C2×D61—21no—
269C2×D61—21no—
270C2×D61—21no—
271C2×D61—21no—
272C2×D61—44no—
273C2×D61—44no—
274C2×D61—44no—
275C2×D61—44no—
276C2×D61—44no—
277C2×D61H(3,ℤ/4)12yescomplemented
278C2×D61#38012yes—
279C2×D61#38612yes—
280#6923—84no—
281C4×C61—21no—
282C4×C61—21no—
283C4×C61—82no—
284C4×C61C4×C22⋊C412yes—
285C4×C61#38512yes—
286Dic61—21no—
287Dic61—21no—
288Dic61—82no—
289Dic61#37911yescharacteristic
290Dic61#38111yescharacteristic
291Dic61#38512yes—
292C23×M16—611no—
293#2280—611no—
294#2280—611no—
295C2×H(3,ℤ/4)—614no—
296C2×C61—22no—
297C2×C61—22no—
298C2×C61—41no—
299C2×C61C22⋊#9511yescharacteristic
300C2×C61C2×H(3,ℤ/4)11yescharacteristic
301C2×C61C2×H(3,ℤ/4)11yescharacteristic
302D61—22no—
303D61—22no—
304D61—22no—
305D61—41no—
306C24×C4—611no—
307C22×M16—612no—
308C22×M16—612no—
309C22×M16—1228no—
310C22×M16—1221no—
311C22×M16—1221no—
312C22×M16—1221no—
313C22×M16—1221no—
314C23×C8—612no—
315C2×#117—612no—
316C2×#117—612no—
317#381—1221no—
318#381—1221no—
319#380—1221no—
320#380—1221no—
321#380—1221no—
322#380—1221no—
323#379—1221no—
324#379—1221no—
325C4×C22⋊C4—612no—
326C4×C22⋊C4—612no—
327C4×C22⋊C4—611no—
328C4×C22⋊C4—612no—
329C4×C22⋊C4#692311yescharacteristic, complemented
330H(3,ℤ/4)—1228no—
331C61#1071711yescharacteristic, complemented, Sylow
332C25—611no—
333C23×C4—611no—
334C23×C4—611no—
335C23×C4—611no—
336C23×C4—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—1224no—
347C23×C4—1224no—
348C23×C4C2×#692311yescharacteristic
349C2×M16—618no—
350C2×M16—1228no—
351C2×M16—1222no—
352C2×M16—1222no—
353C2×M16—1224no—
354C2×M16—1222no—
355C2×M16—1222no—
356C2×M16—1228no—
357C2×M16—1228no—
358C2×M16—1228no—
359C2×M16—1228no—
360C22×C8—614no—
361C22×C8—1228no—
362C22×C8—1222no—
363C22×C8—1222no—
364#117—1224no—
365#117—1224no—
366#117—1224no—
367#117—1224no—
368C2×C4⋊C4—1222no—
369C2×C4⋊C4—1222no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—1222no—
372C2×C22⋊C4—1222no—
373C2×C22⋊C4—1222no—
374C2×C22⋊C4—1222no—
375C2×C22⋊C4—1222no—
376C2×C22⋊C4—1221no—
377C2×C42—614no—
378C2×C42—612no—
379C2×C42C2×#692312yes—
380#95—21no—
381#95—1222no—
382#95—1222no—
383#95—1222no—
384#95—1221no—
385C24—611no—
386C24—611no—
387C24—611no—
388C24—611no—
389C24—611no—
390C24—611no—
391C24—1224no—
392C24—2442no—
393C24—2442no—
394C24C22⋊#692311yescharacteristic
395C22×C4—24no—
396C22×C4—22no—
397C22×C4—611no—
398C22×C4—611no—
399C22×C4—611no—
400C22×C4—611no—
401C22×C4—611no—
402C22×C4—614no—
403C22×C4—614no—
404C22×C4—611no—
405C22×C4—611no—
406C22×C4—611no—
407C22×C4—611no—
408C22×C4—611no—
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—1222no—
422C22×C4—1222no—
423C22×C4—1222no—
424C22×C4—1222no—
425C22×C4—1222no—
426C22×C4—1222no—
427C22×C4—1224no—
428C22×C4—1224no—
429C22×C4—1222no—
430C22×C4—1222no—
431C22×C4—1222no—
432C22×C4—1222no—
433C22×C4—1224no—
434C22×C4—1224no—
435C22×C4—1224no—
436C22×C4—1222no—
437C22×C4—1222no—
438C22×C4—1224no—
439C22×C4—1224no—
440C22×C4—1222no—
441C22×C4C4×#692311yescharacteristic
442C22×C4C4×#692311yescharacteristic
443C22×C4C4⋊#692311yescharacteristic
444C22×C4C4⋊#692311yescharacteristic
445C22×C4C22⋊#692311yescharacteristic
446C22×C4C22×#692311yescharacteristic
447M16—1228no—
448M16—1228no—
449M16—1228no—
450M16—1228no—
451C2×C8—618no—
452C2×C8—1224no—
453C2×C8—1224no—
454C2×C8—1228no—
455C2×C8—1228no—
456C4⋊C4—2442no—
457C4⋊C4—2442no—
458C4⋊C4—2442no—
459C4⋊C4—2442no—
460C22⋊C4—42no—
461C22⋊C4—2444no—
462C22⋊C4—2444no—
463C22⋊C4—2442no—
464C22⋊C4—2444no—
465C22⋊C4—2444no—
466C22⋊C4—2444no—
467C42—24no—
468C42—1228no—
469C42—1224no—
470C23—22no—
471C23—22no—
472C23—41no—
473C23—611no—
474C23—611no—
475C23—611no—
476C23—614no—
477C23—611no—
478C23—1222no—
479C23—1222no—
480C23—1222no—
481C23—1222no—
482C23—1222no—
483C23—1222no—
484C23—1222no—
485C23—1222no—
486C23—1222no—
487C23—1222no—
488C23—2441no—
489C23—2441no—
490C23—2441no—
491C23—2441no—
492C23—2441no—
493C23—2441no—
494C23—2441no—
495C23—24416no—
496C23(C2×#6923)⋊C411yescharacteristic
497C23(C2×#6923)⋊C411yescharacteristic
498C23C2×C22⋊#692311yescharacteristic
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—612no—
508C2×C4—612no—
509C2×C4—611no—
510C2×C4—611no—
511C2×C4—612no—
512C2×C4—614no—
513C2×C4—612no—
514C2×C4—612no—
515C2×C4—612no—
516C2×C4—614no—
517C2×C4—611no—
518C2×C4—611no—
519C2×C4—1221no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—1222no—
524C2×C4—1222no—
525C2×C4—1222no—
526C2×C4—1222no—
527C2×C4—1222no—
528C2×C4—1222no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—1222no—
534C2×C4—1222no—
535C2×C4—1222no—
536C2×C4—1222no—
537C2×C4—1222no—
538C2×C4—1222no—
539C2×C4—1222no—
540C2×C4—2442no—
541C2×C4—2442no—
542C2×C4—2444no—
543C2×C4—2444no—
544C2×C4—2444no—
545C2×C4—2442no—
546C2×C4(C2×#6923)⋊C411yescharacteristic
547C2×C4(C2×#6923)⋊C411yescharacteristic
548C2×C4C2×C4×#692311yescharacteristic
549C2×C4C2×C4⋊#692311yescharacteristic
550C2×C4D4×#692314yes—
551C8—1228no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—44no—
560C22—612no—
561C22—612no—
562C22—612no—
563C22—1228no—
564C22—1221no—
565C22—1221no—
566C22—1221no—
567C22—1221no—
568C22—1221no—
569C22—1221no—
570C22—1221no—
571C22—1221no—
572C22—1221no—
573C22—2444no—
574C22—2444no—
575C22—2444no—
576C22—2444no—
577C22—2444no—
578C22#1684062912yescomplemented
579C22C2×(C2×#6923)⋊C411yescharacteristic
580C22#1684071012yes—
581C4—21no—
582C4—21no—
583C4—82no—
584C4—611no—
585C4—611no—
586C4—612no—
587C4—1221no—
588C4—1221no—
589C4—4882no—
590C4—4884no—
591C4C22⋊C4×#692312yes—
592C4#1684070912yes—
593C2—22no—
594C2—22no—
595C2—41no—
596C2—1222no—
597C2—1222no—
598C2—1222no—
599C2—2441no—
600C2#2146099211yescharacteristic
601C2C2×#1684062911yescharacteristic
602C2#2146148911yescharacteristic
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#10717
LCSG ▷ C2×C4×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#16840629C2semidirect
9. C2×D61⋊M16C4semidirect
12. C22×D61⋊C8C4semidirect
18. C4×C22⋊#6923C4semidirect
19. C4×C22⋊#6923C4semidirect
27. C4×#11758198C4semidirect
28. C4×C22⋊Dic61C4semidirect
29. C4×C22⋊C4×C61C4semidirect
159. D61⋊C8C22⋊C4semidirect
259. C22×C61H(3,ℤ/4)semidirect
277. C2×D61H(3,ℤ/4)semidirect
329. C4×C22⋊C4#6923semidirect
331. C61#10717semidirect
578. C22#16840629semidirect

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×#168406292
#214482002
#1071761