Finite Group Databasebeta

← #30596945

Subgroups — #30596945

Order 15616.

954 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#407C211yesmaximal, characteristic
2#21462263C211yesmaximal, characteristic
3#21460700C214yesmaximal, complemented
4#21448201C211yesmaximal, characteristic
5C2×D61⋊M16C412yescomplemented
6C2×#14519856—21no—
7#16840734—21no—
8#16840733C412yescomplemented
9#16840733C2212yes—
10#16840732—21no—
11D61⋊(C22⋊C8)—21no—
12D61⋊(C22⋊C8)—21no—
13#16840705C412yescomplemented
14#16840704—21no—
15#16840704C412yescomplemented
16#16840703—21no—
17C4×C22⋊#6923—21no—
18C4×C22⋊#6923C2212yes—
19C23×C4×D61C2211yescharacteristic
20C2×#14519735—21no—
21#16839624C412yescomplemented
22#16839622C411yescharacteristic, complemented
23#16839619—21no—
24#16839617—21no—
25C22⋊C4×Dic61—21no—
26#16839609C2212yes—
27C61×#380C411yescharacteristic, complemented
28C2×#11758213C2×C414yes—
29D61⋊M16—44no—
30C2×#11758217—22no—
31C2×D61⋊C8—22no—
32#14519856—44no—
33C2×C4⋊#6923—22no—
34C2×C22⋊#6923—22no—
35C2×C22⋊#6923—22no—
36C2×C22⋊#6923—22no—
37C2×C4×#6923—22no—
38#14519834—22no—
39#14519834—22no—
40C22⋊#92420—22no—
41C22⋊#92420—22no—
42(C2×#6923)⋊C4—22no—
43(C2×#6923)⋊C4C2×C414yes—
44C24×D61D411yescharacteristic
45C23×Dic61D411yescharacteristic
46C22×C4×D61—44no—
47C22×C4×D61C2×C411yescharacteristic
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×D61Q811yescharacteristic
57C22×C4×D61Q811yescharacteristic
58C22×C4×D61C2311yescharacteristic
59#14519735—44no—
60C2×C4⋊Dic61—21no—
61C2×C22⋊Dic61—21no—
62C2×#11758198—22no—
63C2×#11758198—22no—
64C2×C4×Dic61—22no—
65#14519684—22no—
66#14519684C2×C412yes—
67C23×C4×C61C2×C411yescharacteristic
68C2×C4⋊C4×C61—21no—
69C2×C22⋊C4×C61—21no—
70#95×C61C2×C412yes—
71C24×C61C22⋊C411yescharacteristic
72C23×D61—42no—
73C23×D61—42no—
74C23×D61—41no—
75C23×D61—41no—
76C23×D61C22⋊C411yescharacteristic
77C23×D61C22⋊C411yescharacteristic
78C23×D61C22⋊C411yescharacteristic
79C23×D61C4⋊C411yescharacteristic
80C23×D61C4⋊C411yescharacteristic
81C23×D61C2×D411yescharacteristic
82C22×#6923—24no—
83C22×C4×C61—22no—
84C22×C4×C61—42no—
85C22×C4×C61C4211yescharacteristic
86C22×C4×C61C4211yescharacteristic
87C22×C4×C61C22⋊C411yescharacteristic
88C22×C4×C61C4⋊C411yescharacteristic
89C22×C4×C61C4⋊C411yescharacteristic
90C22×C4×C61C22×C411yescharacteristic
91C22×Dic61—22no—
92C22×Dic61—42no—
93C22×Dic61C22⋊C411yescharacteristic
94C22×Dic61C22⋊C411yescharacteristic
95C22×Dic61C22⋊C411yescharacteristic
96C22×Dic61C4⋊C411yescharacteristic
97C22×Dic61C4⋊C411yescharacteristic
98C22×Dic61C2×D411yescharacteristic
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×D61C4211yescharacteristic
112C2×C4×D61C4211yescharacteristic
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×D61C22×C411yescharacteristic
124C2×C4×D61C22×C411yescharacteristic
125C2×C4×D61C2×D411yescharacteristic
126C2×C4×D61C2×Q811yescharacteristic
127C22⋊#6923—42no—
128C22⋊#6923—42no—
129C22⋊#6923—44no—
130C22⋊#6923—44no—
131#11758217—44no—
132C2×#92420—24no—
133C4⋊#6923—44no—
134C4×#6923—44no—
135#11758213—44no—
136D61⋊C8—44no—
137C4⋊C4×C61—42no—
138C22⋊C4×C61—42no—
139C22⋊Dic61—42no—
140#11758198—44no—
141#11758198—44no—
142C4⋊Dic61—42no—
143C4×Dic61—44no—
144C23×C61—21no—
145C23×C61—21no—
146C23×C61—41no—
147C23×C61—41no—
148C23×C61#9511yescharacteristic
149C23×C61#9511yescharacteristic
150C23×C61C2×C22⋊C411yescharacteristic
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—21no—
154C22×D61—21no—
155C22×D61—22no—
156C22×D61—22no—
157C22×D61—22no—
158C22×D61—22no—
159C22×D61—22no—
160C22×D61—22no—
161C22×D61—41no—
162C22×D61—41no—
163C22×D61—41no—
164C22×D61—41no—
165C22×D61—41no—
166C22×D61—41no—
167C22×D61—41no—
168C22×D61—41no—
169C22×D61—41no—
170C22×D61—41no—
171C22×D61—48no—
172C22×D61—48no—
173C22×D61#9511yescharacteristic
174C22×D61#9511yescharacteristic
175C22×D61C2×C22⋊C411yescharacteristic
176C22×D61C2×C4⋊C411yescharacteristic
177C2×#6923—44no—
178C2×#6923—44no—
179C2×#6923—44no—
180C2×C4×C61—22no—
181C2×C4×C61—22no—
182C2×C4×C61—22no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—42no—
187C2×C4×C61—42no—
188C2×C4×C61—42no—
189C2×C4×C61#9511yescharacteristic
190C2×C4×C61#9511yescharacteristic
191C2×C4×C61C2×C4211yescharacteristic
192C2×C4×C61C2×C4⋊C411yescharacteristic
193C2×Dic61—22no—
194C2×Dic61—22no—
195C2×Dic61—22no—
196C2×Dic61—41no—
197C2×Dic61—41no—
198C2×Dic61—41no—
199C2×Dic61—42no—
200C2×Dic61—42no—
201C2×Dic61—42no—
202C2×Dic61#9511yescharacteristic
203C2×Dic61#9511yescharacteristic
204C2×Dic61C2×C22⋊C411yescharacteristic
205C2×Dic61C2×C4⋊C411yescharacteristic
206C4×D61—22no—
207C4×D61—22no—
208C4×D61—22no—
209C4×D61—22no—
210C4×D61—22no—
211C4×D61—22no—
212C4×D61—22no—
213C4×D61—22no—
214C4×D61—22no—
215C4×D61—41no—
216C4×D61—41no—
217C4×D61—41no—
218C4×D61—41no—
219C4×D61—41no—
220C4×D61—41no—
221C4×D61#9914yes—
222#92420—44no—
223#8049—611nomaximal, Sylow
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—21no—
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—42no—
233C22×C61—42no—
234C22×C61C2×#9511yescharacteristic
235C22×C61#42111yescharacteristic
236C22×C61#42111yescharacteristic
237C2×D61—21no—
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—21no—
247C2×D61—44no—
248C2×D61—42no—
249C2×D61—42no—
250C2×D61—42no—
251C2×D61—42no—
252C2×D61—44no—
253C2×D61—44no—
254C2×D61—44no—
255C2×D61#34212yes—
256C2×D61#42112yes—
257#6923—84no—
258C4×C61—21no—
259C4×C61—21no—
260C4×C61—21no—
261C4×C61—82no—
262C4×C61#34212yes—
263Dic61—21no—
264Dic61—21no—
265Dic61—21no—
266Dic61—82no—
267Dic61C2×#9912yes—
268C2×#407—611no—
269#2280—611no—
270#2280—611no—
271#1297—614no—
272C2×C61—21no—
273C2×C61—21no—
274C2×C61—41no—
275C2×C61—41no—
276C2×C61#173311yescharacteristic
277C2×C61#173311yescharacteristic
278C2×C61C2×#34211yescharacteristic
279D61—22no—
280D61—22no—
281D61—41no—
282D61—41no—
283C24×C4—611no—
284C22×M16—612no—
285C2×#117—1221no—
286C2×#117—1221no—
287#407—612no—
288#407—612no—
289#407—1221no—
290#407—1221no—
291C2×C22⋊C8—1221no—
292C2×C22⋊C8—1221no—
293#381—612no—
294#381—612no—
295#380—612no—
296#380—611no—
297#380—1221no—
298#380—1221no—
299#380#692311yescharacteristic, complemented
300#379—1221no—
301#379—1221no—
302C4×C22⋊C4—612no—
303C4×C22⋊C4—612no—
304C4×C22⋊C4—1221no—
305C4×C22⋊C4—1221no—
306C61#804911yescharacteristic, complemented, Sylow
307C25—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—611no—
320C23×C4—611no—
321C23×C4—2444no—
322C23×C4C2×#692311yescharacteristic
323C2×M16—614no—
324C2×M16—1222no—
325C2×M16—2444no—
326C22×C8—1222no—
327#117—2444no—
328#117—2444no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—1222no—
331C2×C4⋊C4—1221no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—1222no—
334C2×C22⋊C4—1222no—
335C2×C22⋊C4—1222no—
336C2×C22⋊C4—1222no—
337C2×C22⋊C4—1222no—
338C2×C22⋊C4—1221no—
339C2×C42—1222no—
340C2×C42—1222no—
341C22⋊C8—1222no—
342C22⋊C8—1222no—
343C22⋊C8—1222no—
344C22⋊C8—1222no—
345#95—614no—
346#95—612no—
347#95—1222no—
348#95—1222no—
349#95C2×#692312yes—
350C24—611no—
351C24—611no—
352C24—611no—
353C24—611no—
354C24—611no—
355C24—611no—
356C24—2441no—
357C24—2441no—
358C24—2442no—
359C24—2442no—
360C24C22⋊#692311yescharacteristic
361C22×C4—22no—
362C22×C4—42no—
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—611no—
385C22×C4—1224no—
386C22×C4—1224no—
387C22×C4—1224no—
388C22×C4—1224no—
389C22×C4—1222no—
390C22×C4—2442no—
391C22×C4—2442no—
392C22×C4—2442no—
393C22×C4—2442no—
394C22×C4—2442no—
395C22×C4—2442no—
396C22×C4—2442no—
397C22×C4—2442no—
398C22×C4—2442no—
399C22×C4—2442no—
400C22×C4C4×#692311yescharacteristic
401C22×C4C4×#692311yescharacteristic
402C22×C4C4⋊#692311yescharacteristic
403C22×C4C4⋊#692311yescharacteristic
404C22×C4C22⋊#692311yescharacteristic
405C22×C4C22×#692311yescharacteristic
406M16—2444no—
407M16—2444no—
408C2×C8—1224no—
409C2×C8—2444no—
410C4⋊C4—42no—
411C4⋊C4—2442no—
412C4⋊C4—2444no—
413C22⋊C4—42no—
414C22⋊C4—2444no—
415C22⋊C4—2444no—
416C22⋊C4—2442no—
417C22⋊C4—2444no—
418C22⋊C4—2444no—
419C22⋊C4—2442no—
420C22⋊C4—2442no—
421C42—2444no—
422C42—2444no—
423C23—21no—
424C23—21no—
425C23—41no—
426C23—41no—
427C23—611no—
428C23—611no—
429C23—611no—
430C23—611no—
431C23—1222no—
432C23—1222no—
433C23—1222no—
434C23—1222no—
435C23—1222no—
436C23—1222no—
437C23—1221no—
438C23—1221no—
439C23—1221no—
440C23—1221no—
441C23—2441no—
442C23—2441no—
443C23—2441no—
444C23—2441no—
445C23—2441no—
446C23—2441no—
447C23—2441no—
448C23—2441no—
449C23—2441no—
450C23—2441no—
451C23—2448no—
452C23—2448no—
453C23(C2×#6923)⋊C411yescharacteristic
454C23(C2×#6923)⋊C411yescharacteristic
455C23C2×C22⋊#692311yescharacteristic
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—611no—
466C2×C4—614no—
467C2×C4—611no—
468C2×C4—611no—
469C2×C4—611no—
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—1222no—
481C2×C4—1222no—
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—2441no—
491C2×C4—2442no—
492C2×C4—2442no—
493C2×C4—2444no—
494C2×C4—2444no—
495C2×C4—2444no—
496C2×C4—2442no—
497C2×C4(C2×#6923)⋊C411yescharacteristic
498C2×C4(C2×#6923)⋊C411yescharacteristic
499C2×C4C2×C4×#692311yescharacteristic
500C2×C4C2×C4⋊#692311yescharacteristic
501C8—2444no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—42no—
511C22—42no—
512C22—612no—
513C22—612no—
514C22—1221no—
515C22—1221no—
516C22—1221no—
517C22—1221no—
518C22—1221no—
519C22—1221no—
520C22—1221no—
521C22—1221no—
522C22—1221no—
523C22—1221no—
524C22—2442no—
525C22—2442no—
526C22—2442no—
527C22—2442no—
528C22—2444no—
529C22—2444no—
530C22—2444no—
531C22—2444no—
532C22C2×(C2×#6923)⋊C411yescharacteristic
533C22#1684076011yescharacteristic
534C22#1684076111yescharacteristic
535C4—21no—
536C4—21no—
537C4—21no—
538C4—82no—
539C4—612no—
540C4—1221no—
541C4—1221no—
542C4—1221no—
543C4—4882no—
544C4—4884no—
545C4#1684063912yes—
546C2—21no—
547C2—21no—
548C2—41no—
549C2—41no—
550C2—1222no—
551C2—1222no—
552C2—2441no—
553C2—2441no—
554C2#2146149811yescharacteristic
555C2#2146150011yescharacteristic
556C2C2×#1684063911yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC22×C61C2×#95
prime radicalC24×D61D4
cosocleC22×C4×D61C23
hypercenter#380#6923
hypocenterC61#8049
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #21460700C2semidirect
5. C2×D61⋊M16C4semidirect
8. #16840733C4semidirect
13. #16840705C4semidirect
15. #16840704C4semidirect
21. #16839624C4semidirect
22. #16839622C4semidirect
27. C61×#380C4semidirect
299. #380#6923semidirect
306. C61#8049semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4072
#214622632
#214607002
#214482012
#804961