Finite Group Databasebeta

← #30597276

Subgroups — #30597276

Order 15616.

914 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#407C211yesmaximal, characteristic
2#21462263C211yesmaximal, characteristic
3#21460721C214yesmaximal, complemented
4#407×D61C211yesmaximal, characteristic
5C2×D61⋊M16C412yescomplemented
6C2×#14519856—21no—
7#16840734C2212yes—
8#16840733—21no—
9#16840733—21no—
10#16840732C412yescomplemented
11D61⋊(C22⋊C8)—21no—
12D61⋊(C22⋊C8)—21no—
13#16840705—21no—
14#16840704—21no—
15#16840704C2212yes—
16#16840703C412yes—
17C4×C22⋊#6923—21no—
18C4×C22⋊#6923C412yes—
19C23×C4×D61C2211yescharacteristic
20C2×M16×D61—21no—
21#16839726C411yescharacteristic, complemented
22#16839725—21no—
23#16839724—21no—
24#16839724C2212yes—
25C22⋊C8×D61—21no—
26C22⋊C8×D61C412yescomplemented
27C61×#407C411yescharacteristic, complemented
28C2×#11758213—22no—
29D61⋊M16—44no—
30C2×#11758217C2×C414yes—
31C2×D61⋊C8—22no—
32#14519856—44no—
33C2×C4⋊#6923—22no—
34C2×C22⋊#6923—22no—
35C2×C22⋊#6923—22no—
36C2×C22⋊#6923C2×C414yes—
37C2×C4×#6923—22no—
38#14519834—22no—
39#14519834—22no—
40C22⋊#92420—22no—
41C22⋊#92420—22no—
42(C2×#6923)⋊C4—22no—
43(C2×#6923)⋊C4—22no—
44C24×D61C2×C411yescharacteristic
45C23×Dic61C2×C411yescharacteristic
46C22×C4×D61—44no—
47C22×C4×D61C2×C411yescharacteristic
48C22×C4×D61C2×C411yescharacteristic
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61D411yescharacteristic
51C22×C4×D61D411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61Q811yescharacteristic
57C22×C4×D61Q811yescharacteristic
58C22×C4×D61C2311yescharacteristic
59C2×#11758194—21no—
60C2×#11758189—22no—
61M16×D61—44no—
62C2×C8×D61—22no—
63C22⋊#92418—21no—
64C22⋊#92418C2×C412yes—
65#14519689—22no—
66#14519689—22no—
67C23×C4×C61C2×C411yescharacteristic
68C2×M16×C61—21no—
69C22⋊C8×C61—21no—
70C22⋊C8×C61C2×C412yes—
71C24×C61C4211yescharacteristic
72C23×D61—42no—
73C23×D61—42no—
74C23×D61—42no—
75C23×D61C4211yescharacteristic
76C23×D61C22⋊C411yescharacteristic
77C23×D61C22⋊C411yescharacteristic
78C23×D61C4⋊C411yescharacteristic
79C23×D61C4⋊C411yescharacteristic
80C23×D61C22×C411yescharacteristic
81C22×#6923—24no—
82C22×C4×C61—42no—
83C22×C4×C61C4211yescharacteristic
84C22×C4×C61C22⋊C411yescharacteristic
85C22×C4×C61C22⋊C411yescharacteristic
86C22×C4×C61C4⋊C411yescharacteristic
87C22×C4×C61C4⋊C411yescharacteristic
88C22×C4×C61C22×C411yescharacteristic
89C22×Dic61—42no—
90C22×Dic61C4211yescharacteristic
91C22×Dic61C22⋊C411yescharacteristic
92C22×Dic61C22⋊C411yescharacteristic
93C22×Dic61C4⋊C411yescharacteristic
94C22×Dic61C4⋊C411yescharacteristic
95C22×Dic61C22×C411yescharacteristic
96C2×C4×D61—24no—
97C2×C4×D61—24no—
98C2×C4×D61—24no—
99C2×C4×D61—42no—
100C2×C4×D61—42no—
101C2×C4×D61—42no—
102C2×C4×D61—42no—
103C2×C4×D61—42no—
104C2×C4×D61—42no—
105C2×C4×D61—42no—
106C2×C4×D61—42no—
107C2×C4×D61—42no—
108C2×C4×D61C22⋊C411yescharacteristic
109C2×C4×D61C22⋊C411yescharacteristic
110C2×C4×D61C22⋊C411yescharacteristic
111C2×C4×D61C22⋊C411yescharacteristic
112C2×C4×D61C22⋊C411yescharacteristic
113C2×C4×D61C22⋊C411yescharacteristic
114C2×C4×D61C4⋊C411yescharacteristic
115C2×C4×D61C4⋊C411yescharacteristic
116C2×C4×D61C4⋊C411yescharacteristic
117C2×C4×D61C4⋊C411yescharacteristic
118C2×C4×D61C4⋊C411yescharacteristic
119C2×C4×D61C4⋊C411yescharacteristic
120C2×C4×D61C2×D411yescharacteristic
121C2×C4×D61C2×D411yescharacteristic
122C2×C4×D61C2×D411yescharacteristic
123C2×C4×D61C2×Q811yescharacteristic
124C22⋊#6923—44no—
125C22⋊#6923—44no—
126C22⋊#6923—44no—
127#11758217—44no—
128C2×#92420—24no—
129C4⋊#6923—44no—
130C4×#6923—44no—
131#11758213—44no—
132D61⋊C8—44no—
133M16×C61—42no—
134C2×C8×C61—22no—
135#11758194—42no—
136C2×#92418—22no—
137#11758189—44no—
138C8×D61—44no—
139C23×C61—41no—
140C23×C61—41no—
141C23×C61—41no—
142C23×C61#9511yescharacteristic
143C23×C61#9511yescharacteristic
144C23×C61C2×C4211yescharacteristic
145C22×D61—22no—
146C22×D61—22no—
147C22×D61—22no—
148C22×D61—22no—
149C22×D61—22no—
150C22×D61—22no—
151C22×D61—22no—
152C22×D61—22no—
153C22×D61—22no—
154C22×D61—41no—
155C22×D61—41no—
156C22×D61—41no—
157C22×D61—41no—
158C22×D61—41no—
159C22×D61—41no—
160C22×D61—41no—
161C22×D61—41no—
162C22×D61—41no—
163C22×D61—416no—
164C22×D61#9511yescharacteristic
165C22×D61#9511yescharacteristic
166C22×D61C2×C22⋊C411yescharacteristic
167C22×D61C2×C4⋊C411yescharacteristic
168C2×#6923—44no—
169C2×#6923—44no—
170C2×#6923—44no—
171C2×C4×C61—22no—
172C2×C4×C61—22no—
173C2×C4×C61—22no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61#9511yescharacteristic
178C2×C4×C61#9511yescharacteristic
179C2×C4×C61C2×C22⋊C411yescharacteristic
180C2×C4×C61C2×C4⋊C411yescharacteristic
181C2×Dic61—22no—
182C2×Dic61—22no—
183C2×Dic61—22no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61#9511yescharacteristic
188C2×Dic61#9511yescharacteristic
189C2×Dic61C2×C22⋊C411yescharacteristic
190C2×Dic61C2×C4⋊C411yescharacteristic
191C4×D61—22no—
192C4×D61—22no—
193C4×D61—22no—
194C4×D61—22no—
195C4×D61—22no—
196C4×D61—22no—
197C4×D61—22no—
198C4×D61—22no—
199C4×D61—22no—
200C4×D61—41no—
201C4×D61—41no—
202C4×D61—41no—
203C4×D61—41no—
204C4×D61—41no—
205C4×D61—41no—
206C4×D61#9914yes—
207#92420—44no—
208C8×C61—42no—
209#92418—42no—
210#8108—611nomaximal, Sylow
211C22×C61—21no—
212C22×C61—21no—
213C22×C61—21no—
214C22×C61—21no—
215C22×C61—21no—
216C22×C61—21no—
217C22×C61—21no—
218C22×C61—21no—
219C22×C61—21no—
220C22×C61—44no—
221C22×C61C2×#9511yescharacteristic
222C2×D61—21no—
223C2×D61—21no—
224C2×D61—21no—
225C2×D61—21no—
226C2×D61—21no—
227C2×D61—21no—
228C2×D61—21no—
229C2×D61—21no—
230C2×D61—21no—
231C2×D61—44no—
232C2×D61—44no—
233C2×D61—44no—
234C2×D61—44no—
235C2×D61—44no—
236C2×D61—44no—
237C2×D61#34212yes—
238C2×D61#34412yes—
239C2×D61#41312yes—
240#6923—84no—
241C4×C61—21no—
242C4×C61—21no—
243C4×C61—21no—
244C4×C61#34212yes—
245Dic61—21no—
246Dic61—21no—
247Dic61—21no—
248Dic61C2×#9912yes—
249C2×#407—611no—
250C2×#407—611no—
251#2280—611no—
252#1305—614no—
253C2×C61—41no—
254C2×C61—41no—
255C2×C61—41no—
256C2×C61C2×#34211yescharacteristic
257C2×C61#174211yescharacteristic
258C2×C61C2×#34411yescharacteristic
259D61—22no—
260D61—22no—
261D61—22no—
262D61—41no—
263C24×C4—611no—
264C22×M16—612no—
265C22×M16—1221no—
266C2×#117—1221no—
267#407—611no—
268#407—612no—
269#407—612no—
270#407—612no—
271#407—1221no—
272#407—1221no—
273#407—1221no—
274#407—1221no—
275#407#692311yescharacteristic, complemented
276C2×C22⋊C8—612no—
277C2×C22⋊C8—1221no—
278C2×C22⋊C8—1221no—
279C2×C22⋊C8—1221no—
280#381—1221no—
281#380—612no—
282#380—1221no—
283#379—612no—
284C4×C22⋊C4—612no—
285C4×C22⋊C4—1221no—
286C61#810811yescharacteristic, complemented, Sylow
287C25—611no—
288C23×C4—611no—
289C23×C4—611no—
290C23×C4—611no—
291C23×C4—611no—
292C23×C4—611no—
293C23×C4—611no—
294C23×C4—611no—
295C23×C4—611no—
296C23×C4—611no—
297C23×C4—611no—
298C23×C4—611no—
299C23×C4—611no—
300C23×C4—611no—
301C23×C4—2444no—
302C23×C4C2×#692311yescharacteristic
303C2×M16—21no—
304C2×M16—614no—
305C2×M16—1222no—
306C2×M16—1222no—
307C2×M16—1221no—
308C2×M16—2444no—
309C2×M16—2444no—
310C22×C8—1222no—
311C22×C8—1222no—
312#117—2444no—
313C2×C4⋊C4—1222no—
314C2×C22⋊C4—614no—
315C2×C22⋊C4—1222no—
316C2×C22⋊C4—1222no—
317C2×C42—1222no—
318C22⋊C8—21no—
319C22⋊C8—612no—
320C22⋊C8—1222no—
321C22⋊C8—1222no—
322C22⋊C8—1222no—
323C22⋊C8—1222no—
324C22⋊C8—1222no—
325C22⋊C8—1222no—
326C22⋊C8—1221no—
327C22⋊C8C2×#692312yes—
328#95—1222no—
329#95—1222no—
330C24—611no—
331C24—611no—
332C24—611no—
333C24—611no—
334C24—611no—
335C24—611no—
336C24—2442no—
337C24—2442no—
338C24—2442no—
339C24C4×#692311yescharacteristic
340C22×C4—42no—
341C22×C4—611no—
342C22×C4—611no—
343C22×C4—611no—
344C22×C4—611no—
345C22×C4—611no—
346C22×C4—611no—
347C22×C4—611no—
348C22×C4—611no—
349C22×C4—611no—
350C22×C4—611no—
351C22×C4—611no—
352C22×C4—611no—
353C22×C4—611no—
354C22×C4—611no—
355C22×C4—611no—
356C22×C4—611no—
357C22×C4—611no—
358C22×C4—611no—
359C22×C4—611no—
360C22×C4—611no—
361C22×C4—611no—
362C22×C4—611no—
363C22×C4—1224no—
364C22×C4—1224no—
365C22×C4—1224no—
366C22×C4—1224no—
367C22×C4—2442no—
368C22×C4—2442no—
369C22×C4—2442no—
370C22×C4—2442no—
371C22×C4—2442no—
372C22×C4—2442no—
373C22×C4—2442no—
374C22×C4—2442no—
375C22×C4—2442no—
376C22×C4—2442no—
377C22×C4C4×#692311yescharacteristic
378C22×C4C4⋊#692311yescharacteristic
379C22×C4C4⋊#692311yescharacteristic
380C22×C4C22⋊#692311yescharacteristic
381C22×C4C22⋊#692311yescharacteristic
382C22×C4C22×#692311yescharacteristic
383M16—42no—
384M16—2444no—
385M16—2442no—
386M16—2444no—
387M16—2444no—
388C2×C8—22no—
389C2×C8—1224no—
390C2×C8—1222no—
391C2×C8—2444no—
392C2×C8—2444no—
393C4⋊C4—2444no—
394C22⋊C4—2444no—
395C22⋊C4—2444no—
396C22⋊C4—2444no—
397C42—2444no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—611no—
402C23—611no—
403C23—611no—
404C23—611no—
405C23—1222no—
406C23—1222no—
407C23—1222no—
408C23—1222no—
409C23—1222no—
410C23—1222no—
411C23—1222no—
412C23—1222no—
413C23—1222no—
414C23—2441no—
415C23—2441no—
416C23—2441no—
417C23—2441no—
418C23—2441no—
419C23—2441no—
420C23—2441no—
421C23—2441no—
422C23—2441no—
423C23—24416no—
424C23(C2×#6923)⋊C411yescharacteristic
425C23(C2×#6923)⋊C411yescharacteristic
426C23C2×C4×#692311yescharacteristic
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—611no—
434C2×C4—614no—
435C2×C4—611no—
436C2×C4—611no—
437C2×C4—611no—
438C2×C4—1222no—
439C2×C4—1222no—
440C2×C4—1222no—
441C2×C4—1222no—
442C2×C4—1222no—
443C2×C4—1222no—
444C2×C4—1222no—
445C2×C4—1222no—
446C2×C4—1222no—
447C2×C4—1222no—
448C2×C4—1222no—
449C2×C4—1222no—
450C2×C4—2441no—
451C2×C4—2441no—
452C2×C4—2441no—
453C2×C4—2441no—
454C2×C4—2441no—
455C2×C4—2441no—
456C2×C4—2441no—
457C2×C4—2441no—
458C2×C4—2441no—
459C2×C4—2444no—
460C2×C4—2444no—
461C2×C4—2444no—
462C2×C4(C2×#6923)⋊C411yescharacteristic
463C2×C4(C2×#6923)⋊C411yescharacteristic
464C2×C4C2×C22⋊#692311yescharacteristic
465C2×C4C2×C4⋊#692311yescharacteristic
466C8—42no—
467C8—2442no—
468C8—2444no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—44no—
479C22—612no—
480C22—612no—
481C22—612no—
482C22—1221no—
483C22—1221no—
484C22—1221no—
485C22—1221no—
486C22—1221no—
487C22—1221no—
488C22—1221no—
489C22—1221no—
490C22—1221no—
491C22—2444no—
492C22—2444no—
493C22—2444no—
494C22—2444no—
495C22—2444no—
496C22—2444no—
497C22C2×(C2×#6923)⋊C411yescharacteristic
498C4—21no—
499C4—21no—
500C4—21no—
501C4—612no—
502C4—1221no—
503C4—1221no—
504C4—1221no—
505C4—4884no—
506C4#1684063912yes—
507C2—41no—
508C2—41no—
509C2—41no—
510C2—1222no—
511C2—1222no—
512C2—1222no—
513C2—2441no—
514C2C2×#1684063911yescharacteristic
515C2#2146152311yescharacteristic
516C2#2146152911yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC23×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#407C4
socleC22×C61C2×#95
prime radicalC24×D61C2×C4
cosocleC22×C4×D61C23
hypercenter#407#6923
hypocenterC61#8108
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. #21460721C2semidirect
5. C2×D61⋊M16C4semidirect
10. #16840732C4semidirect
21. #16839726C4semidirect
26. C22⋊C8×D61C4semidirect
27. C61×#407C4semidirect
275. #407#6923semidirect
286. C61#8108semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4072
#214622632
#214607212
#407×D612
#810861