Finite Group Databasebeta

← #30597269

Subgroups — #30597269

Order 15616.

986 conjugacy classes of subgroups.

The subgroup lattice has 554 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#380×D61C211yesmaximal, 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×C4⋊C4×D61—21no—
21C2×C22⋊C4×D61C412yes—
22#16839622C411yescharacteristic
23#16839621—21no—
24#16839620C2212yes—
25#16839619—21no—
26#95×D61—21no—
27C61×#380C411yescharacteristic
28C2×#11758213—22no—
29C2×#11758213—22no—
30D61⋊M16—44no—
31D61⋊M16—44no—
32C2×#11758217—22no—
33C2×#11758217C2×C414yescomplemented
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×C414yescomplemented
44C24×D61C2×C411yescharacteristic
45C23×Dic61C2311yescharacteristic
46C22×C4×D61—22no—
47C22×C4×D61—44no—
48C22×C4×D61C2×C411yescharacteristic
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D411yescharacteristic
57C22×C4×D61D411yescharacteristic
58C22×C4×D61Q811yescharacteristic
59C22×C4×D61Q811yescharacteristic
60C2×C4⋊Dic61—21no—
61C2×#11758196—22no—
62C4⋊C4×D61—44no—
63C2×C22⋊Dic61C2×C412yes—
64C2×#11758198—22no—
65C22⋊C4×D61—44no—
66#14519684—21no—
67#14519684—22no—
68C23×C4×C61C2×C411yescharacteristic
69C2×C4⋊C4×C61—21no—
70C2×C22⋊C4×C61C2×C412yes—
71#95×C61—21no—
72C24×C61C22×C411yescharacteristic
73C23×D61—22no—
74C23×D61—22no—
75C23×D61—42no—
76C23×D61—42no—
77C23×D61C4211yescharacteristic
78C23×D61C4211yescharacteristic
79C23×D61C22⋊C411yescharacteristic
80C23×D61C22⋊C411yescharacteristic
81C23×D61C4⋊C411yescharacteristic
82C23×D61C4⋊C411yescharacteristic
83C22×C4×C61—22no—
84C22×C4×C61—42no—
85C22×C4×C61C4211yescharacteristic
86C22×C4×C61C4211yescharacteristic
87C22×C4×C61C22⋊C411yescharacteristic
88C22×C4×C61C22⋊C411yescharacteristic
89C22×C4×C61C4⋊C411yescharacteristic
90C22×C4×C61C4⋊C411yescharacteristic
91C22×Dic61—22no—
92C22×Dic61—42no—
93C22×Dic61C22×C411yescharacteristic
94C22×Dic61C22×C411yescharacteristic
95C22×Dic61C2×D411yescharacteristic
96C22×Dic61C2×D411yescharacteristic
97C22×Dic61C2×D411yescharacteristic
98C22×Dic61C2×Q811yescharacteristic
99C2×C4×D61—24no—
100C2×C4×D61—24no—
101C2×C4×D61—24no—
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×D61—42no—
110C2×C4×D61—42no—
111C2×C4×D61—44no—
112C2×C4×D61—44no—
113C2×C4×D61—44no—
114C2×C4×D61C22⋊C411yescharacteristic
115C2×C4×D61C22⋊C411yescharacteristic
116C2×C4×D61C22⋊C411yescharacteristic
117C2×C4×D61C22⋊C411yescharacteristic
118C2×C4×D61C22⋊C411yescharacteristic
119C2×C4×D61C22⋊C411yescharacteristic
120C2×C4×D61C22⋊C411yescharacteristic
121C2×C4×D61C22⋊C411yescharacteristic
122C2×C4×D61C4⋊C411yescharacteristic
123C2×C4×D61C4⋊C411yescharacteristic
124C2×C4×D61C4⋊C411yescharacteristic
125C2×C4×D61C4⋊C411yescharacteristic
126C2×C4×D61C4⋊C411yescharacteristic
127C2×C4×D61C4⋊C411yescharacteristic
128C2×C4×D61C4⋊C411yescharacteristic
129C2×C4×D61C4⋊C411yescharacteristic
130#11758217—44no—
131#11758217—44no—
132C2×#92420—24no—
133C2×#92420—24no—
134#11758213—44no—
135#11758213—44no—
136D61⋊C8—44no—
137D61⋊C8—44no—
138C4⋊C4×C61—42no—
139C22⋊C4×C61—42no—
140C22⋊Dic61—42no—
141#11758198—44no—
142C4⋊Dic61—42no—
143#11758196—44no—
144C23×C61—21no—
145C23×C61—21no—
146C23×C61—41no—
147C23×C61—41no—
148C23×C61C2×C4211yescharacteristic
149C23×C61C2×C22⋊C411yescharacteristic
150C23×C61C2×C4⋊C411yescharacteristic
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—22no—
154C22×D61—22no—
155C22×D61—22no—
156C22×D61—22no—
157C22×D61—22no—
158C22×D61—22no—
159C22×D61—22no—
160C22×D61—22no—
161C22×D61—22no—
162C22×D61—22no—
163C22×D61—41no—
164C22×D61—41no—
165C22×D61—41no—
166C22×D61—41no—
167C22×D61—41no—
168C22×D61—41no—
169C22×D61—48no—
170C22×D61—48no—
171C22×D61#9511yescharacteristic
172C22×D61#9511yescharacteristic
173C22×D61#9511yescharacteristic
174C22×D61#9511yescharacteristic
175C22×D61#10012yes—
176C22×D61#10112yes—
177C2×C4×C61—22no—
178C2×C4×C61—22no—
179C2×C4×C61—22no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—42no—
184C2×C4×C61—42no—
185C2×C4×C61—42no—
186C2×C4×C61#9511yescharacteristic
187C2×C4×C61#9511yescharacteristic
188C2×C4×C61#9511yescharacteristic
189C2×C4×C61#9511yescharacteristic
190C2×Dic61—22no—
191C2×Dic61—22no—
192C2×Dic61—22no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—41no—
196C2×Dic61—42no—
197C2×Dic61—42no—
198C2×Dic61—42no—
199C2×Dic61C2×C22⋊C411yescharacteristic
200C2×Dic61C2×C22⋊C411yescharacteristic
201C2×Dic61C2×C4⋊C411yescharacteristic
202C2×Dic61C2×C4⋊C411yescharacteristic
203C4×D61—22no—
204C4×D61—22no—
205C4×D61—22no—
206C4×D61—22no—
207C4×D61—22no—
208C4×D61—22no—
209C4×D61—22no—
210C4×D61—22no—
211C4×D61—22no—
212C4×D61—41no—
213C4×D61—41no—
214C4×D61—41no—
215C4×D61—41no—
216C4×D61—41no—
217C4×D61—41no—
218C4×D61—88no—
219C4×D61#9914yes—
220#92420—44no—
221#92420—44no—
222#8107—611nomaximal, Sylow
223C22×C61—21no—
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—21no—
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—42no—
232C22×C61—42no—
233C22×C61C2×#9511yescharacteristic
234C22×C61C2×#10011yescharacteristic
235C22×C61C2×#10111yescharacteristic
236C2×D61—24no—
237C2×D61—24no—
238C2×D61—21no—
239C2×D61—21no—
240C2×D61—21no—
241C2×D61—21no—
242C2×D61—21no—
243C2×D61—21no—
244C2×D61—21no—
245C2×D61—21no—
246C2×D61—42no—
247C2×D61—42no—
248C2×D61—44no—
249C2×D61—44no—
250C2×D61—44no—
251C2×D61—44no—
252C2×D61#34212yes—
253C2×D61#34312yes—
254C2×D61#34312yes—
255C2×D61#34412yes—
256C4×C61—21no—
257C4×C61—21no—
258C4×C61—21no—
259C4×C61—82no—
260C4×C61#34212yes—
261Dic61—21no—
262Dic61—21no—
263Dic61—21no—
264Dic61—82no—
265Dic61C2×#9912yes—
266C2×#407—611no—
267C2×#407—611no—
268C2×#380—611no—
269#1305—614no—
270C2×C61—21no—
271C2×C61—21no—
272C2×C61—41no—
273C2×C61—41no—
274C2×C61C2×#34211yescharacteristic
275C2×C61C2×#34311yescharacteristic
276C2×C61C2×#34411yescharacteristic
277D61—22no—
278D61—22no—
279D61—22no—
280D61—22no—
281C24×C4—611no—
282C22×M16—612no—
283C22×M16—1221no—
284C22×C4⋊C4—1221no—
285C22×C22⋊C4—612no—
286#407—612no—
287#407—612no—
288#407—612no—
289#407—612no—
290#407—1221no—
291#407—1221no—
292#407—1221no—
293#407—1221no—
294C2×C22⋊C8—612no—
295C2×C22⋊C8—1221no—
296C2×C22⋊C8—1221no—
297C2×C22⋊C8—1221no—
298#380—611no—
299#380—612no—
300#380—1221no—
301#380—1221no—
302#380#692311yescharacteristic
303C2×#95—1221no—
304C61#810711yescharacteristic, complemented, Sylow
305C25—611no—
306C23×C4—611no—
307C23×C4—611no—
308C23×C4—611no—
309C23×C4—611no—
310C23×C4—611no—
311C23×C4—611no—
312C23×C4—611no—
313C23×C4—611no—
314C23×C4—611no—
315C23×C4—611no—
316C23×C4—611no—
317C23×C4—611no—
318C23×C4—611no—
319C23×C4—1222no—
320C23×C4—2444no—
321C23×C4C2×#692311yescharacteristic
322C2×M16—614no—
323C2×M16—1222no—
324C2×M16—1222no—
325C2×M16—1222no—
326C2×M16—2444no—
327C2×M16—2444no—
328C22×C8—1222no—
329C22×C8—1222no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—1222no—
332C2×C4⋊C4—1221no—
333C2×C4⋊C4—2444no—
334C2×C22⋊C4—612no—
335C2×C22⋊C4—1222no—
336C2×C22⋊C4—2444no—
337C2×C22⋊C4C2×#692312yes—
338C22⋊C8—614no—
339C22⋊C8—1222no—
340C22⋊C8—1222no—
341C22⋊C8—1222no—
342C22⋊C8—1222no—
343C22⋊C8—1222no—
344C22⋊C8—1222no—
345C22⋊C8—1222no—
346#95—21no—
347#95—1222no—
348#95—1221no—
349C24—611no—
350C24—611no—
351C24—611no—
352C24—611no—
353C24—611no—
354C24—611no—
355C24—1222no—
356C24—1222no—
357C24—2442no—
358C24—2442no—
359C24C22×#692311yescharacteristic
360C22×C4—22no—
361C22×C4—42no—
362C22×C4—611no—
363C22×C4—611no—
364C22×C4—611no—
365C22×C4—611no—
366C22×C4—611no—
367C22×C4—611no—
368C22×C4—611no—
369C22×C4—611no—
370C22×C4—611no—
371C22×C4—611no—
372C22×C4—611no—
373C22×C4—611no—
374C22×C4—611no—
375C22×C4—611no—
376C22×C4—611no—
377C22×C4—611no—
378C22×C4—611no—
379C22×C4—611no—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—611no—
383C22×C4—611no—
384C22×C4—1224no—
385C22×C4—1224no—
386C22×C4—1224no—
387C22×C4—1222no—
388C22×C4—2442no—
389C22×C4—2442no—
390C22×C4—2442no—
391C22×C4—2442no—
392C22×C4—2442no—
393C22×C4—2442no—
394C22×C4—2442no—
395C22×C4—2442no—
396C22×C4—2442no—
397C22×C4—2444no—
398C22×C4—2444no—
399C22×C4—2444no—
400C22×C4—2442no—
401C22×C4C4×#692311yescharacteristic
402C22×C4C4×#692311yescharacteristic
403C22×C4C4⋊#692311yescharacteristic
404C22×C4C4⋊#692311yescharacteristic
405C22×C4C22⋊#692311yescharacteristic
406C22×C4C22⋊#692311yescharacteristic
407M16—2444no—
408M16—2444no—
409M16—2444no—
410M16—2444no—
411C2×C8—1224no—
412C2×C8—1224no—
413C2×C8—2444no—
414C2×C8—2444no—
415C4⋊C4—42no—
416C4⋊C4—2442no—
417C4⋊C4—2444no—
418C22⋊C4—42no—
419C22⋊C4—2444no—
420C22⋊C4—2442no—
421C23—21no—
422C23—21no—
423C23—41no—
424C23—41no—
425C23—611no—
426C23—611no—
427C23—611no—
428C23—611no—
429C23—612no—
430C23—612no—
431C23—1222no—
432C23—1222no—
433C23—1222no—
434C23—1222no—
435C23—1222no—
436C23—1222no—
437C23—1222no—
438C23—1222no—
439C23—1222no—
440C23—1222no—
441C23—1221no—
442C23—1221no—
443C23—2441no—
444C23—2441no—
445C23—2441no—
446C23—2441no—
447C23—2441no—
448C23—2441no—
449C23—2448no—
450C23—2448no—
451C23C2×C4×#692311yescharacteristic
452C23C2×C22⋊#692311yescharacteristic
453C23C2×C4⋊#692311yescharacteristic
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—611no—
464C2×C4—614no—
465C2×C4—611no—
466C2×C4—611no—
467C2×C4—611no—
468C2×C4—1222no—
469C2×C4—1222no—
470C2×C4—1222no—
471C2×C4—1222no—
472C2×C4—1222no—
473C2×C4—1222no—
474C2×C4—1222no—
475C2×C4—1222no—
476C2×C4—1222no—
477C2×C4—1222no—
478C2×C4—1222no—
479C2×C4—1222no—
480C2×C4—4888no—
481C2×C4—2441no—
482C2×C4—2441no—
483C2×C4—2441no—
484C2×C4—2441no—
485C2×C4—2441no—
486C2×C4—2441no—
487C2×C4—2441no—
488C2×C4—2441no—
489C2×C4—2441no—
490C2×C4—2442no—
491C2×C4—2442no—
492C2×C4—2442no—
493C2×C4(C2×#6923)⋊C411yescharacteristic
494C2×C4(C2×#6923)⋊C411yescharacteristic
495C2×C4(C2×#6923)⋊C411yescharacteristic
496C2×C4(C2×#6923)⋊C411yescharacteristic
497C8—2444no—
498C8—2444no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—42no—
508C22—42no—
509C22—612no—
510C22—612no—
511C22—612no—
512C22—612no—
513C22—1224no—
514C22—1224no—
515C22—1221no—
516C22—1221no—
517C22—1221no—
518C22—1221no—
519C22—1221no—
520C22—1221no—
521C22—1221no—
522C22—1221no—
523C22—2442no—
524C22—2442no—
525C22—2444no—
526C22—2444no—
527C22—2444no—
528C22—2444no—
529C22C2×(C2×#6923)⋊C411yescharacteristic
530C22D61⋊#10011yescharacteristic
531C22D61⋊#10111yescharacteristic
532C4—21no—
533C4—21no—
534C4—21no—
535C4—82no—
536C4—612no—
537C4—1221no—
538C4—1221no—
539C4—1221no—
540C4—4882no—
541C4#1684063912yes—
542C2—21no—
543C2—21no—
544C2—41no—
545C2—41no—
546C2—1222no—
547C2—1222no—
548C2—1222no—
549C2—1222no—
550C2C2×#1684063911yescharacteristic
551C2#2146152211yescharacteristic
552C2#2146152711yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC61×#380C4
socleC22×C61C2×#95
prime radicalC24×D61C2×C4
cosocleC23×Dic61C23
hypercenter#380#6923
hypocenterC61#8107
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

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
33. C2×#11758217C2×C4semidirect
43. C22⋊#92420C2×C4semidirect
304. C61#8107semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4072
#214607202
#380×D612
#810761