Finite Group Databasebeta

← #30597250

Subgroups — #30597250

Order 15616.

914 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#407C211yesmaximal, characteristic
2D61⋊#407C211yesmaximal, characteristic
3#21460720C214yesmaximal, complemented
4#21448200C211yesmaximal, characteristic
5C2×D61⋊M16—21no—
6C2×D61⋊M16C412yescomplemented
7#16840734—21no—
8#16840734C412yescomplemented
9#16840733—21no—
10#16840733—21no—
11#16840733—21no—
12#16840733C412yescomplemented
13#16840732C2212yes—
14#16840732C2212yes—
15D61⋊(C22⋊C8)—21no—
16D61⋊(C22⋊C8)—21no—
17D61⋊(C22⋊C8)—21no—
18D61⋊(C22⋊C8)C412yescomplemented
19C23×C4×D61C2211yescharacteristic
20C2×#14519734—21no—
21#16839624—21no—
22#16839621—21no—
23#16839620C2212yes—
24#16839617C412yes—
25C4×#11758198—21no—
26C4×C22⋊Dic61C411yescharacteristic
27C4×C22⋊C4×C61C411yescharacteristic
28C2×#11758213—22no—
29C2×#11758213—22no—
30D61⋊M16—44no—
31D61⋊M16—44no—
32C2×#11758217—22no—
33C2×#11758217C2×C414yes—
34C2×D61⋊C8—22no—
35C2×D61⋊C8—22no—
36#14519834—22no—
37#14519834—22no—
38#14519834—22no—
39#14519834—22no—
40C22⋊#92420—22no—
41C22⋊#92420—22no—
42C22⋊#92420—22no—
43C22⋊#92420C2×C414yes—
44C24×D61C2×C411yescharacteristic
45C23×Dic61C2311yescharacteristic
46C22×C4×D61—44no—
47C22×C4×D61C2×C411yescharacteristic
48C22×C4×D61C2×C411yescharacteristic
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61D411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D411yescharacteristic
57C22×C4×D61Q811yescharacteristic
58C22×C4×D61Q811yescharacteristic
59#14519734—44no—
60C2×#11758196—22no—
61C2×C22⋊Dic61C2×C412yes—
62C2×#11758198—22no—
63C2×#11758198—22no—
64C2×C4×Dic61—21no—
65#14519684—21no—
66#14519684—22no—
67C23×C4×C61C2×C411yescharacteristic
68C2×C22⋊C4×C61C2×C412yes—
69C2×C42×C61—21no—
70#95×C61—21no—
71C24×C61C22×C411yescharacteristic
72C23×D61—42no—
73C23×D61—42no—
74C23×D61—42no—
75C23×D61C4211yescharacteristic
76C23×D61C4211yescharacteristic
77C23×D61C22⋊C411yescharacteristic
78C23×D61C22⋊C411yescharacteristic
79C23×D61C4⋊C411yescharacteristic
80C23×D61C4⋊C411yescharacteristic
81C22×C4×C61—22no—
82C22×C4×C61—42no—
83C22×C4×C61C4211yescharacteristic
84C22×C4×C61C4211yescharacteristic
85C22×C4×C61C22⋊C411yescharacteristic
86C22×C4×C61C22⋊C411yescharacteristic
87C22×C4×C61C4⋊C411yescharacteristic
88C22×C4×C61C4⋊C411yescharacteristic
89C22×Dic61—22no—
90C22×Dic61—42no—
91C22×Dic61C22×C411yescharacteristic
92C22×Dic61C22×C411yescharacteristic
93C22×Dic61C2×D411yescharacteristic
94C22×Dic61C2×D411yescharacteristic
95C22×Dic61C2×D411yescharacteristic
96C22×Dic61C2×Q811yescharacteristic
97C2×C4×D61—24no—
98C2×C4×D61—24no—
99C2×C4×D61—24no—
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×D61—42no—
109C2×C4×D61C22⋊C411yescharacteristic
110C2×C4×D61C22⋊C411yescharacteristic
111C2×C4×D61C22⋊C411yescharacteristic
112C2×C4×D61C22⋊C411yescharacteristic
113C2×C4×D61C22⋊C411yescharacteristic
114C2×C4×D61C22⋊C411yescharacteristic
115C2×C4×D61C22⋊C411yescharacteristic
116C2×C4×D61C22⋊C411yescharacteristic
117C2×C4×D61C4⋊C411yescharacteristic
118C2×C4×D61C4⋊C411yescharacteristic
119C2×C4×D61C4⋊C411yescharacteristic
120C2×C4×D61C4⋊C411yescharacteristic
121C2×C4×D61C4⋊C411yescharacteristic
122C2×C4×D61C4⋊C411yescharacteristic
123C2×C4×D61C4⋊C411yescharacteristic
124C2×C4×D61C4⋊C411yescharacteristic
125#11758217—44no—
126#11758217—44no—
127C2×#92420—24no—
128C2×#92420—24no—
129#11758213—44no—
130#11758213—44no—
131D61⋊C8—44no—
132D61⋊C8—44no—
133C22⋊C4×C61—42no—
134C42×C61—42no—
135C22⋊Dic61—42no—
136#11758198—44no—
137#11758198—44no—
138#11758196—44no—
139C4×Dic61—42no—
140C23×C61—22no—
141C23×C61—41no—
142C23×C61—41no—
143C23×C61C2×C4211yescharacteristic
144C23×C61C2×C22⋊C411yescharacteristic
145C23×C61C2×C4⋊C411yescharacteristic
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—41no—
164C22×D61—416no—
165C22×D61#9511yescharacteristic
166C22×D61#9511yescharacteristic
167C22×D61#9511yescharacteristic
168C22×D61#9511yescharacteristic
169C2×C4×C61—22no—
170C2×C4×C61—22no—
171C2×C4×C61—22no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—42no—
176C2×C4×C61—42no—
177C2×C4×C61—42no—
178C2×C4×C61#9511yescharacteristic
179C2×C4×C61#9511yescharacteristic
180C2×C4×C61#9511yescharacteristic
181C2×C4×C61#9511yescharacteristic
182C2×Dic61—22no—
183C2×Dic61—22no—
184C2×Dic61—22no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—42no—
189C2×Dic61—42no—
190C2×Dic61—42no—
191C2×Dic61C2×C22⋊C411yescharacteristic
192C2×Dic61C2×C22⋊C411yescharacteristic
193C2×Dic61C2×C4⋊C411yescharacteristic
194C2×Dic61C2×C4⋊C411yescharacteristic
195C4×D61—22no—
196C4×D61—22no—
197C4×D61—22no—
198C4×D61—22no—
199C4×D61—22no—
200C4×D61—22no—
201C4×D61—22no—
202C4×D61—22no—
203C4×D61—22no—
204C4×D61—41no—
205C4×D61—41no—
206C4×D61—41no—
207C4×D61—41no—
208C4×D61—41no—
209C4×D61—41no—
210C4×D61#9914yes—
211#92420—44no—
212#92420—44no—
213#8104—611nomaximal, Sylow
214C22×C61—21no—
215C22×C61—21no—
216C22×C61—21no—
217C22×C61—21no—
218C22×C61—21no—
219C22×C61—21no—
220C22×C61—21no—
221C22×C61—21no—
222C22×C61—44no—
223C22×C61C2×#9511yescharacteristic
224C22×C61#41312yes—
225C2×D61—21no—
226C2×D61—21no—
227C2×D61—21no—
228C2×D61—21no—
229C2×D61—21no—
230C2×D61—21no—
231C2×D61—21no—
232C2×D61—21no—
233C2×D61—21no—
234C2×D61—21no—
235C2×D61—44no—
236C2×D61—44no—
237C2×D61—44no—
238C2×D61—44no—
239C2×D61—44no—
240C2×D61—44no—
241C2×D61#34212yes—
242C2×D61#34412yes—
243C4×C61—21no—
244C4×C61—21no—
245C4×C61—21no—
246C4×C61—82no—
247C4×C61#34212yes—
248Dic61—21no—
249Dic61—21no—
250Dic61—21no—
251Dic61—82no—
252Dic61C2×#9912yes—
253C2×#407—611no—
254C2×#407—611no—
255#2280—611no—
256#1305—614no—
257C2×C61—22no—
258C2×C61—41no—
259C2×C61—41no—
260C2×C61C2×#34211yescharacteristic
261C2×C61#174211yescharacteristic
262C2×C61C2×#34411yescharacteristic
263D61—22no—
264D61—22no—
265D61—41no—
266D61—41no—
267C24×C4—611no—
268C22×M16—612no—
269C22×M16—1221no—
270C2×#117—1221no—
271#407—612no—
272#407—612no—
273#407—612no—
274#407—612no—
275#407—1221no—
276#407—1221no—
277#407—1221no—
278#407—1221no—
279C2×C22⋊C8—612no—
280C2×C22⋊C8—1221no—
281C2×C22⋊C8—1221no—
282C2×C22⋊C8—1221no—
283#381—1221no—
284#380—612no—
285#380—1221no—
286#379—612no—
287C4×C22⋊C4—611no—
288C4×C22⋊C4—1221no—
289C4×C22⋊C4#692311yescharacteristic
290C61#810411yescharacteristic, complemented, Sylow
291C25—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—611no—
302C23×C4—611no—
303C23×C4—611no—
304C23×C4—611no—
305C23×C4—2444no—
306C23×C4C2×#692311yescharacteristic
307C2×M16—614no—
308C2×M16—1222no—
309C2×M16—1222no—
310C2×M16—1222no—
311C2×M16—2444no—
312C2×M16—2444no—
313C22×C8—1222no—
314C22×C8—1222no—
315#117—2444no—
316C2×C4⋊C4—1222no—
317C2×C22⋊C4—612no—
318C2×C22⋊C4—1222no—
319C2×C22⋊C4—1222no—
320C2×C22⋊C4C2×#692312yes—
321C2×C42—21no—
322C2×C42—1221no—
323C22⋊C8—614no—
324C22⋊C8—1222no—
325C22⋊C8—1222no—
326C22⋊C8—1222no—
327C22⋊C8—1222no—
328C22⋊C8—1222no—
329C22⋊C8—1222no—
330C22⋊C8—1222no—
331#95—21no—
332#95—1222no—
333#95—1221no—
334C24—611no—
335C24—611no—
336C24—611no—
337C24—611no—
338C24—611no—
339C24—611no—
340C24—2442no—
341C24—2442no—
342C24—2442no—
343C24C22×#692311yescharacteristic
344C22×C4—22no—
345C22×C4—42no—
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—611no—
364C22×C4—611no—
365C22×C4—611no—
366C22×C4—611no—
367C22×C4—611no—
368C22×C4—1224no—
369C22×C4—1224no—
370C22×C4—1224no—
371C22×C4—1222no—
372C22×C4—2442no—
373C22×C4—2442no—
374C22×C4—2442no—
375C22×C4—2442no—
376C22×C4—2442no—
377C22×C4—2442no—
378C22×C4—2442no—
379C22×C4—2442no—
380C22×C4—2442no—
381C22×C4—2442no—
382C22×C4C4×#692311yescharacteristic
383C22×C4C4×#692311yescharacteristic
384C22×C4C4⋊#692311yescharacteristic
385C22×C4C4⋊#692311yescharacteristic
386C22×C4C22⋊#692311yescharacteristic
387C22×C4C22⋊#692311yescharacteristic
388M16—2444no—
389M16—2444no—
390M16—2444no—
391M16—2444no—
392C2×C8—1224no—
393C2×C8—1224no—
394C2×C8—2444no—
395C2×C8—2444no—
396C4⋊C4—2444no—
397C22⋊C4—42no—
398C22⋊C4—2444no—
399C22⋊C4—2444no—
400C22⋊C4—2442no—
401C42—42no—
402C42—2442no—
403C23—22no—
404C23—41no—
405C23—41no—
406C23—611no—
407C23—611no—
408C23—611no—
409C23—611no—
410C23—1222no—
411C23—1222no—
412C23—1222no—
413C23—1222no—
414C23—1222no—
415C23—1222no—
416C23—1222no—
417C23—1222no—
418C23—2441no—
419C23—2441no—
420C23—2441no—
421C23—2441no—
422C23—2441no—
423C23—2441no—
424C23—2441no—
425C23—2441no—
426C23—2441no—
427C23—2441no—
428C23—24416no—
429C23C2×C4×#692311yescharacteristic
430C23C2×C22⋊#692311yescharacteristic
431C23C2×C4⋊#692311yescharacteristic
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—611no—
442C2×C4—614no—
443C2×C4—611no—
444C2×C4—611no—
445C2×C4—611no—
446C2×C4—1222no—
447C2×C4—1222no—
448C2×C4—1222no—
449C2×C4—1222no—
450C2×C4—1222no—
451C2×C4—1222no—
452C2×C4—1222no—
453C2×C4—1222no—
454C2×C4—1222no—
455C2×C4—1222no—
456C2×C4—1222no—
457C2×C4—1222no—
458C2×C4—2441no—
459C2×C4—2441no—
460C2×C4—2441no—
461C2×C4—2441no—
462C2×C4—2441no—
463C2×C4—2441no—
464C2×C4—2441no—
465C2×C4—2441no—
466C2×C4—2441no—
467C2×C4—2442no—
468C2×C4—2442no—
469C2×C4—2442no—
470C2×C4(C2×#6923)⋊C411yescharacteristic
471C2×C4(C2×#6923)⋊C411yescharacteristic
472C2×C4(C2×#6923)⋊C411yescharacteristic
473C2×C4(C2×#6923)⋊C411yescharacteristic
474C8—2444no—
475C8—2444no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—44no—
485C22—612no—
486C22—612no—
487C22—1221no—
488C22—1221no—
489C22—1221no—
490C22—1221no—
491C22—1221no—
492C22—1221no—
493C22—1221no—
494C22—1221no—
495C22—1221no—
496C22—1221no—
497C22—2444no—
498C22—2444no—
499C22—2444no—
500C22—2444no—
501C22—2444no—
502C22—2444no—
503C22C2×(C2×#6923)⋊C411yescharacteristic
504C22#1684074812yes—
505C4—21no—
506C4—21no—
507C4—21no—
508C4—82no—
509C4—612no—
510C4—1221no—
511C4—1221no—
512C4—1221no—
513C4—4882no—
514C4#1684063912yes—
515C2—22no—
516C2—41no—
517C2—41no—
518C2—1222no—
519C2—1222no—
520C2—2441no—
521C2—2441no—
522C2C2×#1684063911yescharacteristic
523C2#2146152411yescharacteristic
524C2#2146152711yescharacteristic
subgroupG/H
centerC2×C4(C2×#6923)⋊C4
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61C2×#95
prime radicalC24×D61C2×C4
cosocleC23×Dic61C23
hypercenterC4×C22⋊C4#6923
hypocenterC61#8104
LCSG ▷ C23×C61 ▷ C22×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. #21460720C2semidirect
6. C2×D61⋊M16C4semidirect
8. #16840734C4semidirect
12. #16840733C4semidirect
18. D61⋊(C22⋊C8)C4semidirect
290. C61#8104semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4072
#214607202
#214482002
#810461