Finite Group Databasebeta

← #30603274

Subgroups — #30603274

Order 15616.

1050 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊(C4⋊C8)C211yesmaximal, characteristic
2C22×#14519840C212yesmaximal
3C2×#16840635C212yesmaximal
4#21460997C211yesmaximal, characteristic
5#391×D61C211yesmaximal, characteristic
6C22×D61⋊C8C2212yes—
7C22×C4⋊#6923C2212yes—
8C2×#14519844—21no—
9D61⋊(C4⋊C8)—24no—
10C2×C4⋊#92420—21no—
11C2×#14519840—24no—
12C2×#14519840—24no—
13C2×#14519840—24no—
14C2×(C2×#6923)⋊C4—21no—
15C2×(C2×#6923)⋊C4—21no—
16#16840635—24no—
17C22×Q8×D61C2211yescharacteristic
18C2×C4⋊C4×D61C2211yescharacteristic
19C2×C42×D61C2211yescharacteristic
20#16839669C411yescharacteristic, complemented
21#16839668C411yescharacteristic, complemented
22#16839667C411yescharacteristic, complemented
23#16839666—21no—
24#16839666—21no—
25#95×D61—21no—
26#95×D61—21no—
27C61×#391C411yescharacteristic, complemented
28C23×#6923—22no—
29C2×D61⋊C8—22no—
30C2×D61⋊C8—22no—
31C2×D61⋊C8—22no—
32C2×D61⋊C8—22no—
33C2×D61⋊C8—22no—
34C2×D61⋊C8D414yes—
35C22×#92420—22no—
36C2×C4⋊#6923—22no—
37C2×C4⋊#6923—22no—
38C2×C4⋊#6923—22no—
39C2×C4⋊#6923—22no—
40C2×C4⋊#6923—22no—
41C2×C4⋊#6923D414yes—
42#14519844—24no—
43C4⋊#92420—24no—
44#14519840—216no—
45(C2×#6923)⋊C4—42no—
46(C2×#6923)⋊C4—42no—
47C22×Dic122—21no—
48C22×Dic122C2×C411yescharacteristic
49C2×Q8×D61—21no—
50C2×Q8×D61—21no—
51C2×Q8×D61—22no—
52C2×Q8×D61—22no—
53C2×Q8×D61—22no—
54C2×Q8×D61—22no—
55C2×Q8×D61D412yes—
56C2×Q8×D61Q812yes—
57C22×C4×D61—21no—
58C22×C4×D61—21no—
59C22×C4×D61D411yescharacteristic
60C22×C4×D61D411yescharacteristic
61C22×C4×D61C2311yescharacteristic
62C2×C4⋊Dic61C2×C411yescharacteristic
63C2×#11758196—21no—
64C4⋊C4×D61—22no—
65C4⋊C4×D61—22no—
66C2×C4×Dic61C2×C411yescharacteristic
67C2×C4×Dic61D411yescharacteristic
68C2×C4×Dic61D411yescharacteristic
69C42×D61—22no—
70C42×D61—22no—
71#14519684—21no—
72#14519684—21no—
73#14519684—21no—
74#14519684—21no—
75#14519684—21no—
76#14519684—21no—
77C22×Q8×C61C2×C411yescharacteristic
78C2×C4⋊C4×C61C2×C411yescharacteristic
79C2×C42×C61C2×C411yescharacteristic
80#95×C61—21no—
81#95×C61—21no—
82C23×D61C2×D411yescharacteristic
83C22×#6923—24no—
84C22×#6923—42no—
85C22×#6923—42no—
86C22×#6923—42no—
87C22×#6923—42no—
88C22×#6923—42no—
89C22×#6923—42no—
90C2×Q8×C61—21no—
91C2×Q8×C61—22no—
92C2×Q8×C61—22no—
93C2×Q8×C61C4⋊C412yes—
94C22×C4×C61—21no—
95C22×C4×C61—21no—
96C22×C4×C61C22⋊C411yescharacteristic
97C22×C4×C61C22⋊C411yescharacteristic
98C22×C4×C61C22×C411yescharacteristic
99C22×Dic61—21no—
100C22×Dic61—21no—
101C22×Dic61C22⋊C411yescharacteristic
102C22×Dic61C22⋊C411yescharacteristic
103C22×Dic61C2×D411yescharacteristic
104Q8×D61—24no—
105Q8×D61—24no—
106Q8×D61—24no—
107Q8×D61—24no—
108Q8×D61—42no—
109Q8×D61—42no—
110Q8×D61—42no—
111Q8×D61—42no—
112C2×C4×D61—22no—
113C2×C4×D61—22no—
114C2×C4×D61—22no—
115C2×C4×D61—22no—
116C2×C4×D61—22no—
117C2×C4×D61—21no—
118C2×C4×D61—22no—
119C2×C4×D61—21no—
120C2×C4×D61—42no—
121C2×C4×D61—42no—
122C2×C4×D61—42no—
123C2×C4×D61—42no—
124C2×C4×D61—41no—
125C2×C4×D61—41no—
126C2×C4×D61SD1612yes—
127C2×C4×D61Q1612yes—
128C2×C4×D61C2×D411yescharacteristic
129C2×C4×D61C2×D412yes—
130C2×C4×D61C2×D412yes—
131C2×C4×D61C2×Q811yescharacteristic
132C2×C4×D61#4111yescharacteristic
133C2×C4×D61#4112yes—
134C2×C4×D61#4112yes—
135C2×C4×D61#4111yescharacteristic
136C2×Dic122—22no—
137C2×Dic122—22no—
138C2×Dic122—21no—
139C2×Dic122—22no—
140C2×Dic122—22no—
141C2×Dic122—41no—
142C2×Dic122—41no—
143C2×Dic122—41no—
144C2×Dic122—41no—
145C2×Dic122C4⋊C412yes—
146C2×#92420—24no—
147C2×#92420—42no—
148C2×#92420—42no—
149C4⋊#6923—24no—
150C4⋊#6923—24no—
151C4⋊#6923—42no—
152C4⋊#6923—42no—
153D61⋊C8—24no—
154D61⋊C8—24no—
155D61⋊C8—42no—
156D61⋊C8—42no—
157C4⋊C4×C61—22no—
158C42×C61—22no—
159C4⋊Dic61—22no—
160#11758196—41no—
161#11758196—41no—
162C4×Dic61—22no—
163C4×Dic61—21no—
164C4×Dic61—21no—
165C4×Dic61—21no—
166C4×Dic61—21no—
167C23×C61C2×C22⋊C411yescharacteristic
168C22×D61#12111yescharacteristic
169C22×D61#12112yes—
170C22×D61#12112yes—
171C22×D61C22⋊Q811yescharacteristic
172C22×D61C2×SD1611yescharacteristic
173C22×D61C2×Q1611yescharacteristic
174C22×D61#13512yes—
175C22×D61AGL(1,ℤ/8)11yescharacteristic
176C22×D61#13712yes—
177C22×D61#13711yescharacteristic
178C2×#6923—44no—
179C2×#6923—44no—
180C2×#6923—44no—
181C2×#6923—82no—
182C2×#6923—82no—
183C2×#6923—82no—
184C2×#6923—82no—
185Q8×C61—24no—
186Q8×C61—42no—
187C2×C4×C61—21no—
188C2×C4×C61—21no—
189C2×C4×C61—22no—
190C2×C4×C61—21no—
191C2×C4×C61—21no—
192C2×C4×C61—21no—
193C2×C4×C61—41no—
194C2×C4×C61—41no—
195C2×C4×C61—41no—
196C2×C4×C61—41no—
197C2×C4×C61—41no—
198C2×C4×C61#10312yescomplemented
199C2×C4×C61C2×C4⋊C411yescharacteristic
200C2×C4×C61#11711yescharacteristic
201C2×C4×C61C4×D412yes—
202C2×C4×C61C4×D412yes—
203C2×Dic61—21no—
204C2×Dic61—21no—
205C2×Dic61—22no—
206C2×Dic61—21no—
207C2×Dic61—21no—
208C2×Dic61—21no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211C2×Dic61—41no—
212C2×Dic61—41no—
213C2×Dic61—41no—
214C2×Dic61#10312yescomplemented
215C2×Dic61#12011yescharacteristic
216C2×Dic61#12111yescharacteristic
217C2×Dic61C22⋊Q811yescharacteristic
218C2×Dic61#12311yescharacteristic
219C2×Dic61#12411yescharacteristic
220C2×Dic61#12711yescharacteristic
221C4×D61—24no—
222C4×D61—24no—
223C4×D61—44no—
224C4×D61—44no—
225C4×D61—42no—
226C4×D61—42no—
227C4×D61—82no—
228C4×D61—82no—
229C4×D61#12012yes—
230C4×D61#12112yes—
231C4×D61C22⋊Q812yes—
232C4×D61C22⋊Q812yes—
233C4×D61#12312yes—
234C4×D61#12312yes—
235C4×D61#12412yes—
236C4×D61#12612yes—
237Dic122—24no—
238Dic122—42no—
239Dic122—42no—
240Dic122—42no—
241Dic122—42no—
242Dic122—42no—
243#92420—44no—
244#11077—611nomaximal, Sylow
245C22×C61#38011yescharacteristic
246C22×C61#38611yescharacteristic
247C22×C61#39011yescharacteristic
248C22×C61C2×#10311yescharacteristic
249C22×C61#41611yescharacteristic
250C22×C61#41711yescharacteristic
251C22×C61#41911yescharacteristic
252C2×D61#39412yes—
253C2×D61#39612yes—
254C2×D61#46011yescharacteristic
255C2×D61#46112yes—
256C2×D61#46211yescharacteristic
257C2×D61#46212yes—
258C2×D61#46312yes—
259C2×D61#46412yes—
260C2×D61#46412yes—
261C2×D61#46512yes—
262C2×D61#46712yes—
263C2×D61#46812yes—
264C2×D61#47012yes—
265C2×D61#47511yescharacteristic
266C2×D61#47711yescharacteristic
267C2×D61#47912yes—
268#6923—84no—
269C4×C61—22no—
270C4×C61—41no—
271C4×C61—42no—
272C4×C61—81no—
273C4×C61#38512yes—
274C4×C61#38812yes—
275Dic61—22no—
276Dic61—41no—
277Dic61—42no—
278Dic61—81no—
279Dic61#39211yescharacteristic
280Dic61#39311yescharacteristic
281Dic61#39711yescharacteristic
282Dic61#39911yescharacteristic
283C22×C4⋊C8—611no—
284C22×#103—612no—
285C2×#391—611no—
286C2×#340—612no—
287C4⋊#95—611no—
288C2×C61#143911yescharacteristic
289C2×C61#180311yescharacteristic
290C2×C61#180511yescharacteristic
291C2×C61#189211yescharacteristic
292C2×C61#189411yescharacteristic
293C2×C61#198111yescharacteristic
294C2×C61#198311yescharacteristic
295D61#205512yes—
296D61#205612yes—
297D61#206612yes—
298D61#206812yes—
299C23×Q8—611no—
300C23×C8—612no—
301C22×C4⋊C4—612no—
302C22×C4⋊C4—611no—
303C22×C42—611no—
304C2×C4⋊C8—1221no—
305C2×C4⋊C8—1221no—
306C2×C4⋊C8—1224no—
307C2×#103—1224no—
308C2×#103—1224no—
309C2×#103—1224no—
310#391—611no—
311#391—611no—
312#391—611no—
313#391—1221no—
314#391—1221no—
315#391#692311yescharacteristic, complemented
316C2×#95—1221no—
317C2×#95—1221no—
318C2×#95—1221no—
319C2×#95—1221no—
320#340—1224no—
321C61#1107711yescharacteristic, complemented, Sylow
322C22×Q8—612no—
323C22×Q8—612no—
324C22×Q8—611no—
325C22×Q8—1221no—
326C22×Q8—1221no—
327C22×Q8—1221no—
328C22×Q8—1222no—
329C22×Q8—1222no—
330C22×Q8—1222no—
331C22×Q8—1222no—
332C22×Q8C2×#692311yescharacteristic
333C23×C4—611no—
334C23×C4—611no—
335C23×C4—611no—
336C23×C4—1221no—
337C23×C4—1221no—
338C23×C4—1222no—
339C22×C8—614no—
340C22×C8—1222no—
341C22×C8—1222no—
342C22×C8—1222no—
343C22×C8—1222no—
344C22×C8—1222no—
345C22×C8—1222no—
346C2×C4⋊C4—614no—
347C2×C4⋊C4—611no—
348C2×C4⋊C4—1222no—
349C2×C4⋊C4—1222no—
350C2×C4⋊C4—1222no—
351C2×C4⋊C4—1222no—
352C2×C4⋊C4—1222no—
353C2×C4⋊C4—1222no—
354C2×C4⋊C4—1221no—
355C2×C4⋊C4—1222no—
356C2×C4⋊C4C2×#692311yescharacteristic
357C2×C42—611no—
358C2×C42—611no—
359C2×C42—611no—
360C2×C42—1222no—
361C2×C42—1222no—
362C2×C42C2×#692311yescharacteristic
363C4⋊C8—1224no—
364C4⋊C8—1224no—
365#103—12216no—
366#95—21no—
367#95—21no—
368#95—1221no—
369#95—1221no—
370#95—1221no—
371#95—1221no—
372#95—1221no—
373#95—1221no—
374#95—2442no—
375#95—2442no—
376C24—611no—
377C2×Q8—21no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—612no—
381C2×Q8—1222no—
382C2×Q8—1222no—
383C2×Q8—1224no—
384C2×Q8—1224no—
385C2×Q8—1224no—
386C2×Q8—1224no—
387C2×Q8—1221no—
388C2×Q8—1222no—
389C2×Q8—1222no—
390C2×Q8—2441no—
391C2×Q8—2441no—
392C2×Q8—2441no—
393C2×Q8—2441no—
394C2×Q8—2442no—
395C2×Q8—2442no—
396C2×Q8—2442no—
397C2×Q8—2442no—
398C2×Q8C4⋊#692312yes—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—611no—
402C22×C4—611no—
403C22×C4—611no—
404C22×C4—611no—
405C22×C4—611no—
406C22×C4—612no—
407C22×C4—612no—
408C22×C4—612no—
409C22×C4—612no—
410C22×C4—611no—
411C22×C4—612no—
412C22×C4—612no—
413C22×C4—611no—
414C22×C4—1222no—
415C22×C4—1222no—
416C22×C4—1221no—
417C22×C4—1222no—
418C22×C4—1221no—
419C22×C4—1222no—
420C22×C4—1222no—
421C22×C4—1222no—
422C22×C4—1221no—
423C22×C4—1224no—
424C22×C4—1221no—
425C22×C4—2442no—
426C22×C4—2442no—
427C22×C4—2441no—
428C22×C4—2441no—
429C22×C4—2442no—
430C22×C4—2442no—
431C22×C4—2442no—
432C22×C4—2442no—
433C22×C4—2442no—
434C22×C4—2442no—
435C22×C4—2442no—
436C22×C4—2442no—
437C22×C4C22⋊#692311yescharacteristic
438C22×C4C22⋊#692311yescharacteristic
439C22×C4C22×#692311yescharacteristic
440C2×C8—1224no—
441C2×C8—1224no—
442C2×C8—1224no—
443C2×C8—2442no—
444C2×C8—2442no—
445C2×C8—2442no—
446C2×C8—2442no—
447C4⋊C4—22no—
448C4⋊C4—1224no—
449C4⋊C4—1224no—
450C4⋊C4—1222no—
451C4⋊C4—2441no—
452C4⋊C4—2441no—
453C4⋊C4—2442no—
454C4⋊C4—2442no—
455C42—22no—
456C42—1221no—
457C42—1221no—
458C42—1221no—
459C42—1221no—
460C42—1222no—
461C23—611no—
462C23—611no—
463C23—612no—
464C23—612no—
465C23—611no—
466C23—611no—
467C23—612no—
468C23—611no—
469C23—611no—
470C23—612no—
471C23C2×C22⋊#692311yescharacteristic
472Q8—24no—
473Q8—42no—
474Q8—1224no—
475Q8—2442no—
476Q8—2442no—
477Q8—2442no—
478Q8—2442no—
479Q8—2442no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—611no—
492C2×C4—611no—
493C2×C4—611no—
494C2×C4—611no—
495C2×C4—611no—
496C2×C4—611no—
497C2×C4—612no—
498C2×C4—612no—
499C2×C4—612no—
500C2×C4—612no—
501C2×C4—612no—
502C2×C4—612no—
503C2×C4—612no—
504C2×C4—612no—
505C2×C4—612no—
506C2×C4—1224no—
507C2×C4—1224no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—1222no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—4882no—
515C2×C4—4882no—
516C2×C4—4882no—
517C2×C4—4882no—
518C2×C4—4882no—
519C2×C4—4882no—
520C2×C4—2442no—
521C2×C4—2442no—
522C2×C4—2444no—
523C2×C4—2444no—
524C2×C4—2444no—
525C2×C4—2444no—
526C2×C4—2444no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4#1451984012yescomplemented
533C2×C4C2×C4⋊#692311yescharacteristic
534C2×C4#1451985611yescharacteristic
535C2×C4D4×#692312yes—
536C2×C4D4×#692312yes—
537C8—2444no—
538C22—612no—
539C22—612no—
540C22—612no—
541C22—612no—
542C22—612no—
543C22—612no—
544C22—611no—
545C22—611no—
546C22—611no—
547C22—611no—
548C22—612no—
549C22—612no—
550C22—612no—
551C22—612no—
552C22—612no—
553C22—612no—
554C22#1684070411yescharacteristic
555C22#1684071011yescharacteristic
556C22#1684071411yescharacteristic
557C22C2×#1451984011yescharacteristic
558C22#1684075211yescharacteristic
559C22#1684075311yescharacteristic
560C22#1684075511yescharacteristic
561C4—22no—
562C4—42no—
563C4—41no—
564C4—81no—
565C4—611no—
566C4—611no—
567C4—611no—
568C4—611no—
569C4—1222no—
570C4—4884no—
571C4—4881no—
572C4—2442no—
573C4—2441no—
574C4#1684070912yes—
575C4#1684071212yes—
576C2—612no—
577C2—612no—
578C2—612no—
579C2—612no—
580C2#2146100211yescharacteristic
581C2#2146168811yescharacteristic
582C2#2146169011yescharacteristic
583C2#2146183211yescharacteristic
584C2#2146183411yescharacteristic
585C2#2146198511yescharacteristic
586C2#2146198711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C2×D4
cosocleC22×C4×D61C23
hypercenter#391#6923
hypocenterC61#11077
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
20. #16839669C4semidirect
21. #16839668C4semidirect
22. #16839667C4semidirect
27. C61×#391C4semidirect
198. C2×C4×C61#103semidirect
214. C2×Dic61#103semidirect
315. #391#6923semidirect
321. C61#11077semidirect
532. C2×C4#14519840semidirect

Maximal subgroups

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

subgroupindex
C2×D61⋊(C4⋊C8)2
C22×#145198402
C2×#168406352
#214609972
#391×D612
#1107761