Finite Group Databasebeta

← #30597266

Subgroups — #30597266

Order 15616.

986 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#407C211yesmaximal, characteristic
2C2×#16840704C211yesmaximal, characteristic
3#21460719C214yesmaximal, complemented
4C2×#16839725C211yesmaximal, characteristic
5C2×D61⋊M16—21no—
6C22×C4⋊#6923—21no—
7C22×C22⋊#6923C412yes—
8#16840734—21no—
9#16840733—21no—
10#16840733C2212yes—
11#16840732C412yescomplemented
12D61⋊(C22⋊C8)—21no—
13D61⋊(C22⋊C8)C412yescomplemented
14#16840704—21no—
15#16840704—21no—
16#16840704C412yes—
17#16840704C2212yes—
18C2×(C2×#6923)⋊C4—21no—
19C23×C4×D61C2211yescharacteristic
20C22×#11758194C411yescharacteristic, complemented
21#16839725—21no—
22#16839725—21no—
23#16839725C412yescomplemented
24#16839725C2212yes—
25C2×#14519689—21no—
26C2×#14519689—21no—
27C22×M16×C61C411yescharacteristic, complemented
28C23×#6923—22no—
29C2×#11758213—22no—
30D61⋊M16—42no—
31D61⋊M16—42no—
32C2×#11758217—22no—
33C2×D61⋊C8—22no—
34C2×C4⋊#6923—22no—
35C2×C4⋊#6923—22no—
36C2×C4⋊#6923—42no—
37C2×C4⋊#6923—42no—
38C2×C22⋊#6923—22no—
39C2×C22⋊#6923—44no—
40C2×C22⋊#6923C2×C414yes—
41#14519834—22no—
42#14519834—22no—
43C22⋊#92420—22no—
44C22⋊#92420C2×C414yescomplemented
45(C2×#6923)⋊C4—22no—
46(C2×#6923)⋊C4—22no—
47C24×D61C2×C411yescharacteristic
48C23×Dic61C2×C411yescharacteristic
49C22×C4×D61—42no—
50C22×C4×D61—42no—
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D411yescharacteristic
57C22×C4×D61D411yescharacteristic
58C22×C4×D61D411yescharacteristic
59C22×C4×D61D411yescharacteristic
60C22×C4×D61Q811yescharacteristic
61C22×C4×D61Q811yescharacteristic
62C22×C4×D61C2311yescharacteristic
63C2×#11758194—21no—
64C2×#11758194—42no—
65C2×#11758194C2×C412yescomplemented
66C22×#92418—21no—
67#14519689—22no—
68#14519689—22no—
69#14519689—22no—
70#14519689—22no—
71C23×C4×C61C2×C411yescharacteristic
72C2×M16×C61—21no—
73C2×M16×C61—42no—
74C2×M16×C61C2×C412yescomplemented
75C22×C8×C61—21no—
76C24×C61C4211yescharacteristic
77C23×D61—22no—
78C23×D61—22no—
79C23×D61—42no—
80C23×D61—42no—
81C23×D61C4211yescharacteristic
82C23×D61C22⋊C411yescharacteristic
83C23×D61C22⋊C411yescharacteristic
84C23×D61C4⋊C411yescharacteristic
85C23×D61C4⋊C411yescharacteristic
86C23×D61C22×C411yescharacteristic
87C22×#6923—24no—
88C22×#6923—44no—
89C22×#6923—44no—
90C22×#6923—44no—
91C22×C4×C61—22no—
92C22×C4×C61—22no—
93C22×C4×C61C4211yescharacteristic
94C22×C4×C61C22⋊C411yescharacteristic
95C22×C4×C61C22⋊C411yescharacteristic
96C22×C4×C61C4⋊C411yescharacteristic
97C22×C4×C61C4⋊C411yescharacteristic
98C22×C4×C61C22×C411yescharacteristic
99C22×Dic61—42no—
100C22×Dic61C4211yescharacteristic
101C22×Dic61C22⋊C411yescharacteristic
102C22×Dic61C22⋊C411yescharacteristic
103C22×Dic61C4⋊C411yescharacteristic
104C22×Dic61C4⋊C411yescharacteristic
105C22×Dic61C22×C411yescharacteristic
106C2×C4×D61—22no—
107C2×C4×D61—22no—
108C2×C4×D61—22no—
109C2×C4×D61—22no—
110C2×C4×D61—42no—
111C2×C4×D61—42no—
112C2×C4×D61—41no—
113C2×C4×D61—41no—
114C2×C4×D61—42no—
115C2×C4×D61—41no—
116C2×C4×D61—41no—
117C2×C4×D61—41no—
118C2×C4×D61—41no—
119C2×C4×D61—42no—
120C2×C4×D61—41no—
121C2×C4×D61—41no—
122C2×C4×D61—42no—
123C2×C4×D61—42no—
124C2×C4×D61C22⋊C411yescharacteristic
125C2×C4×D61C22⋊C411yescharacteristic
126C2×C4×D61C22⋊C411yescharacteristic
127C2×C4×D61C22⋊C411yescharacteristic
128C2×C4×D61C22⋊C411yescharacteristic
129C2×C4×D61C22⋊C411yescharacteristic
130C2×C4×D61C4⋊C411yescharacteristic
131C2×C4×D61C4⋊C411yescharacteristic
132C2×C4×D61C4⋊C411yescharacteristic
133C2×C4×D61C4⋊C411yescharacteristic
134C2×C4×D61C4⋊C411yescharacteristic
135C2×C4×D61C4⋊C411yescharacteristic
136C2×C4×D61C2×D411yescharacteristic
137C2×C4×D61C2×D411yescharacteristic
138C2×C4×D61C2×D411yescharacteristic
139C2×C4×D61C2×Q811yescharacteristic
140C22⋊#6923—44no—
141C22⋊#6923—44no—
142#11758217—44no—
143C2×#92420—24no—
144C4⋊#6923—44no—
145C4⋊#6923—42no—
146C4⋊#6923—42no—
147#11758213—42no—
148#11758213—42no—
149D61⋊C8—44no—
150M16×C61—42no—
151M16×C61—42no—
152C2×C8×C61—22no—
153C2×C8×C61—42no—
154#11758194—42no—
155#11758194—42no—
156C2×#92418—22no—
157C2×#92418—42no—
158C23×C61—22no—
159C23×C61—22no—
160C23×C61—41no—
161C23×C61#9511yescharacteristic
162C23×C61#9511yescharacteristic
163C23×C61C2×C4211yescharacteristic
164C22×D61—22no—
165C22×D61—22no—
166C22×D61—21no—
167C22×D61—21no—
168C22×D61—22no—
169C22×D61—22no—
170C22×D61—22no—
171C22×D61—22no—
172C22×D61—22no—
173C22×D61—22no—
174C22×D61—21no—
175C22×D61—21no—
176C22×D61—41no—
177C22×D61—41no—
178C22×D61—41no—
179C22×D61—41no—
180C22×D61—41no—
181C22×D61—41no—
182C22×D61—41no—
183C22×D61—48no—
184C22×D61—48no—
185C22×D61#9511yescharacteristic
186C22×D61#9511yescharacteristic
187C22×D61#10012yes—
188C22×D61#10112yes—
189C22×D61C2×C22⋊C411yescharacteristic
190C22×D61C2×C4⋊C411yescharacteristic
191C2×#6923—44no—
192C2×#6923—44no—
193C2×#6923—44no—
194C2×#6923—88no—
195C2×C4×C61—22no—
196C2×C4×C61—22no—
197C2×C4×C61—22no—
198C2×C4×C61—21no—
199C2×C4×C61—21no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61#9511yescharacteristic
203C2×C4×C61#9511yescharacteristic
204C2×C4×C61#9912yes—
205C2×C4×C61#9912yes—
206C2×C4×C61C2×C22⋊C411yescharacteristic
207C2×C4×C61C2×C4⋊C411yescharacteristic
208C2×Dic61—22no—
209C2×Dic61—22no—
210C2×Dic61—41no—
211C2×Dic61—41no—
212C2×Dic61—41no—
213C2×Dic61—41no—
214C2×Dic61#9511yescharacteristic
215C2×Dic61#9511yescharacteristic
216C2×Dic61C2×C22⋊C411yescharacteristic
217C2×Dic61C2×C4⋊C411yescharacteristic
218C4×D61—22no—
219C4×D61—22no—
220C4×D61—22no—
221C4×D61—22no—
222C4×D61—21no—
223C4×D61—21no—
224C4×D61—21no—
225C4×D61—21no—
226C4×D61—21no—
227C4×D61—21no—
228C4×D61—21no—
229C4×D61—21no—
230C4×D61—41no—
231C4×D61—41no—
232C4×D61—41no—
233C4×D61—41no—
234C4×D61—41no—
235C4×D61—41no—
236C4×D61—41no—
237C4×D61—41no—
238#92420—44no—
239C8×C61—42no—
240#92418—42no—
241#8107—611nomaximal, Sylow
242C22×C61—21no—
243C22×C61—21no—
244C22×C61—21no—
245C22×C61—21no—
246C22×C61—21no—
247C22×C61—21no—
248C22×C61—21no—
249C22×C61—44no—
250C22×C61#34212yes—
251C22×C61#34312yes—
252C22×C61C2×#9511yescharacteristic
253C2×D61—24no—
254C2×D61—24no—
255C2×D61—21no—
256C2×D61—21no—
257C2×D61—21no—
258C2×D61—21no—
259C2×D61—21no—
260C2×D61—21no—
261C2×D61—21no—
262C2×D61—21no—
263C2×D61—21no—
264C2×D61—42no—
265C2×D61—42no—
266C2×D61—44no—
267C2×D61—44no—
268C2×D61—44no—
269C2×D61—42no—
270C2×D61—42no—
271C2×D61#34312yes—
272C2×D61#34412yes—
273C2×D61C2×#10011yescharacteristic
274C2×D61C2×#10111yescharacteristic
275#6923—84no—
276C4×C61—21no—
277C4×C61—21no—
278C4×C61#34212yes—
279C4×C61C2×#9911yescharacteristic
280C4×C61C2×#9911yescharacteristic
281Dic61—21no—
282Dic61—21no—
283Dic61—21no—
284Dic61—21no—
285C2×#407—611no—
286C2×#407—611no—
287C2×#380—611no—
288#1305—614no—
289C2×C61—22no—
290C2×C61—22no—
291C2×C61—41no—
292C2×C61C2×#34211yescharacteristic
293C2×C61C2×#34311yescharacteristic
294C2×C61C2×#34411yescharacteristic
295D61—21no—
296D61—22no—
297D61—21no—
298D61—22no—
299D61—41no—
300C24×C4—611no—
301C22×M16—611no—
302C22×M16—1221no—
303C22×M16#692311yescharacteristic, complemented
304C22×C4⋊C4—1221no—
305C22×C22⋊C4—612no—
306#407—612no—
307#407—612no—
308#407—612no—
309#407—612no—
310#407—1221no—
311#407—1221no—
312#407—1221no—
313#407—1221no—
314C2×C22⋊C8—612no—
315C2×C22⋊C8—1221no—
316C2×C22⋊C8—1221no—
317C2×C22⋊C8—1221no—
318#380—612no—
319#380—612no—
320#380—1221no—
321#380—1221no—
322C2×#95—1221no—
323C61#810711yescharacteristic, complemented, Sylow
324C25—611no—
325C23×C4—611no—
326C23×C4—611no—
327C23×C4—611no—
328C23×C4—611no—
329C23×C4—611no—
330C23×C4—611no—
331C23×C4—611no—
332C23×C4—611no—
333C23×C4—611no—
334C23×C4—611no—
335C23×C4—611no—
336C23×C4—611no—
337C23×C4—611no—
338C23×C4—1222no—
339C23×C4—2442no—
340C23×C4—2442no—
341C23×C4C2×#692311yescharacteristic
342C2×M16—21no—
343C2×M16—42no—
344C2×M16—612no—
345C2×M16—1222no—
346C2×M16—1222no—
347C2×M16—1221no—
348C2×M16—2442no—
349C2×M16—2442no—
350C2×M16—2442no—
351C2×M16C2×#692312yescomplemented
352C22×C8—21no—
353C22×C8—1222no—
354C22×C8—1221no—
355C2×C4⋊C4—1222no—
356C2×C4⋊C4—1222no—
357C2×C4⋊C4—2442no—
358C2×C4⋊C4—2442no—
359C2×C22⋊C4—614no—
360C2×C22⋊C4—1222no—
361C2×C22⋊C4—2444no—
362C22⋊C8—614no—
363C22⋊C8—1222no—
364C22⋊C8—1222no—
365C22⋊C8—1222no—
366C22⋊C8—1222no—
367C22⋊C8—1222no—
368C22⋊C8—1222no—
369C22⋊C8—1222no—
370#95—1222no—
371#95—1222no—
372C24—611no—
373C24—611no—
374C24—611no—
375C24—611no—
376C24—611no—
377C24—611no—
378C24—1222no—
379C24—1222no—
380C24—2442no—
381C24—2442no—
382C24C4×#692311yescharacteristic
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—611no—
386C22×C4—611no—
387C22×C4—611no—
388C22×C4—611no—
389C22×C4—611no—
390C22×C4—611no—
391C22×C4—611no—
392C22×C4—611no—
393C22×C4—611no—
394C22×C4—611no—
395C22×C4—611no—
396C22×C4—611no—
397C22×C4—611no—
398C22×C4—611no—
399C22×C4—611no—
400C22×C4—611no—
401C22×C4—611no—
402C22×C4—611no—
403C22×C4—611no—
404C22×C4—611no—
405C22×C4—611no—
406C22×C4—611no—
407C22×C4—1222no—
408C22×C4—1222no—
409C22×C4—1222no—
410C22×C4—1222no—
411C22×C4—1224no—
412C22×C4—2441no—
413C22×C4—2441no—
414C22×C4—2441no—
415C22×C4—2441no—
416C22×C4—2441no—
417C22×C4—2441no—
418C22×C4—2441no—
419C22×C4—2441no—
420C22×C4—2442no—
421C22×C4—2442no—
422C22×C4—2442no—
423C22×C4—2442no—
424C22×C4—2442no—
425C22×C4—2442no—
426C22×C4—2442no—
427C22×C4—2444no—
428C22×C4—2444no—
429C22×C4—2444no—
430C22×C4C4×#692311yescharacteristic
431C22×C4C4⋊#692311yescharacteristic
432C22×C4C4⋊#692311yescharacteristic
433C22×C4C22⋊#692311yescharacteristic
434C22×C4C22⋊#692311yescharacteristic
435C22×C4C22×#692311yescharacteristic
436M16—42no—
437M16—42no—
438M16—2442no—
439M16—2442no—
440M16—2444no—
441M16—2442no—
442M16—2442no—
443C2×C8—22no—
444C2×C8—42no—
445C2×C8—1224no—
446C2×C8—1222no—
447C2×C8—2442no—
448C2×C8—2444no—
449C4⋊C4—2442no—
450C4⋊C4—2442no—
451C4⋊C4—2444no—
452C22⋊C4—2444no—
453C22⋊C4—2444no—
454C23—22no—
455C23—22no—
456C23—41no—
457C23—611no—
458C23—611no—
459C23—611no—
460C23—612no—
461C23—612no—
462C23—611no—
463C23—1221no—
464C23—1222no—
465C23—1221no—
466C23—1221no—
467C23—1222no—
468C23—1222no—
469C23—1221no—
470C23—1222no—
471C23—1222no—
472C23—1222no—
473C23—1222no—
474C23—1222no—
475C23—2441no—
476C23—2441no—
477C23—2441no—
478C23—2441no—
479C23—2441no—
480C23—2441no—
481C23—2441no—
482C23—2448no—
483C23—2448no—
484C23(C2×#6923)⋊C411yescharacteristic
485C23(C2×#6923)⋊C411yescharacteristic
486C23C2×C4×#692311yescharacteristic
487C2×C4—22no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—611no—
495C2×C4—611no—
496C2×C4—611no—
497C2×C4—611no—
498C2×C4—1222no—
499C2×C4—1222no—
500C2×C4—1221no—
501C2×C4—1221no—
502C2×C4—1221no—
503C2×C4—1221no—
504C2×C4—1221no—
505C2×C4—1221no—
506C2×C4—1221no—
507C2×C4—1221no—
508C2×C4—1222no—
509C2×C4—1222no—
510C2×C4—1222no—
511C2×C4—1222no—
512C2×C4—4888no—
513C2×C4—2441no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4—2441no—
517C2×C4—2441no—
518C2×C4—2441no—
519C2×C4—2441no—
520C2×C4—2441no—
521C2×C4—2441no—
522C2×C4—2441no—
523C2×C4—2441no—
524C2×C4—2441no—
525C2×C4—2444no—
526C2×C4—2444no—
527C2×C4—2444no—
528C2×C4(C2×#6923)⋊C411yescharacteristic
529C2×C4(C2×#6923)⋊C411yescharacteristic
530C2×C4#1451983512yes—
531C2×C4#1451983612yes—
532C2×C4C2×C22⋊#692311yescharacteristic
533C2×C4C2×C4⋊#692311yescharacteristic
534C8—42no—
535C8—2444no—
536C8—2442no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—44no—
545C22—611no—
546C22—612no—
547C22—611no—
548C22—612no—
549C22—1224no—
550C22—1224no—
551C22—1221no—
552C22—1221no—
553C22—1221no—
554C22—1221no—
555C22—1221no—
556C22—1221no—
557C22—1221no—
558C22—1221no—
559C22—1221no—
560C22—2442no—
561C22—2442no—
562C22—2444no—
563C22—2444no—
564C22—2444no—
565C22—2442no—
566C22—2442no—
567C22#1684064012yes—
568C22#1684064112yes—
569C22C2×(C2×#6923)⋊C411yescharacteristic
570C4—21no—
571C4—21no—
572C4—1221no—
573C4—1221no—
574C4—1221no—
575C4—1221no—
576C4—4884no—
577C4#1684064012yes—
578C4C2×#1451983511yescharacteristic
579C4C2×#1451983611yescharacteristic
580C2—22no—
581C2—22no—
582C2—41no—
583C2—1221no—
584C2—1221no—
585C2—1222no—
586C2—1222no—
587C2—2441no—
588C2C2×#1684064011yescharacteristic
589C2C2×#1684064111yescharacteristic
590C2#2146153111yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC23×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC22×M16×C61C4
socleC22×C61C2×#95
prime radicalC24×D61C2×C4
cosocleC22×C4×D61C23
hypercenterC22×M16#6923
hypocenterC61#8107
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
3. #21460719C2semidirect
11. #16840732C4semidirect
13. D61⋊(C22⋊C8)C4semidirect
20. C22×#11758194C4semidirect
23. #16839725C4semidirect
27. C22×M16×C61C4semidirect
44. C22⋊#92420C2×C4semidirect
65. C2×#11758194C2×C4semidirect
74. C2×M16×C61C2×C4semidirect
303. C22×M16#6923semidirect
323. C61#8107semidirect
351. C2×M16C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4072
C2×#168407042
#214607192
C2×#168397252
#810761