Finite Group Databasebeta

← #30597267

Subgroups — #30597267

Order 15616.

986 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840733C211yesmaximal, characteristic
2C2×#16840704C211yesmaximal, characteristic
3#21460719C214yesmaximal, complemented
4#407×D61C211yesmaximal, characteristic
5C22×#11758213—21no—
6C22×C4⋊#6923—21no—
7C22×C22⋊#6923C412yes—
8#16840733—21no—
9#16840733—21no—
10#16840733C412yescomplemented
11#16840733C2212yes—
12C2×#14519834—21no—
13C2×C22⋊#92420C412yescomplemented
14#16840704—21no—
15#16840704—21no—
16#16840704C412yes—
17#16840704C2212yes—
18C2×(C2×#6923)⋊C4—21no—
19C23×C4×D61C2211yescharacteristic
20C2×M16×D61C412yescomplemented
21#16839726C411yescharacteristic, complemented
22#16839725C2212yes—
23#16839724—21no—
24#16839724—21no—
25C22⋊C8×D61—21no—
26C22⋊C8×D61—21no—
27C61×#407C411yescharacteristic, complemented
28C23×#6923—22no—
29C2×#11758213—22no—
30C2×#11758213—22no—
31C2×#11758213—44no—
32C22×#92420—22no—
33C2×C4⋊#6923—22no—
34C2×C4⋊#6923—22no—
35C2×C4⋊#6923—44no—
36C2×C22⋊#6923—22no—
37C2×C22⋊#6923—44no—
38C2×C22⋊#6923C2×C414yes—
39#14519834—22no—
40#14519834—22no—
41C22⋊#92420—22no—
42C22⋊#92420C2×C414yescomplemented
43(C2×#6923)⋊C4—22no—
44(C2×#6923)⋊C4—22no—
45C24×D61C2×C411yescharacteristic
46C23×Dic61C2×C411yescharacteristic
47C22×C4×D61—44no—
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
59C22×C4×D61C2311yescharacteristic
60C2×#11758194C2×C412yescomplemented
61C2×#11758189—22no—
62M16×D61—44no—
63C2×C8×D61—22no—
64C22⋊#92418—21no—
65C22⋊#92418—21no—
66#14519689—22no—
67#14519689—22no—
68C23×C4×C61C2×C411yescharacteristic
69C2×M16×C61C2×C412yescomplemented
70C22⋊C8×C61—21no—
71C22⋊C8×C61—21no—
72C24×C61C4211yescharacteristic
73C23×D61—22no—
74C23×D61—22no—
75C23×D61—42no—
76C23×D61—42no—
77C23×D61C4211yescharacteristic
78C23×D61C22⋊C411yescharacteristic
79C23×D61C22⋊C411yescharacteristic
80C23×D61C4⋊C411yescharacteristic
81C23×D61C4⋊C411yescharacteristic
82C23×D61C22×C411yescharacteristic
83C22×#6923—24no—
84C22×#6923—44no—
85C22×#6923—44no—
86C22×#6923—44no—
87C22×C4×C61—42no—
88C22×C4×C61C4211yescharacteristic
89C22×C4×C61C22⋊C411yescharacteristic
90C22×C4×C61C22⋊C411yescharacteristic
91C22×C4×C61C4⋊C411yescharacteristic
92C22×C4×C61C4⋊C411yescharacteristic
93C22×C4×C61C22×C411yescharacteristic
94C22×Dic61—42no—
95C22×Dic61C4211yescharacteristic
96C22×Dic61C22⋊C411yescharacteristic
97C22×Dic61C22⋊C411yescharacteristic
98C22×Dic61C4⋊C411yescharacteristic
99C22×Dic61C4⋊C411yescharacteristic
100C22×Dic61C22×C411yescharacteristic
101C2×C4×D61—24no—
102C2×C4×D61—24no—
103C2×C4×D61—24no—
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—42no—
112C2×C4×D61—42no—
113C2×C4×D61C22⋊C411yescharacteristic
114C2×C4×D61C22⋊C411yescharacteristic
115C2×C4×D61C22⋊C411yescharacteristic
116C2×C4×D61C22⋊C411yescharacteristic
117C2×C4×D61C22⋊C411yescharacteristic
118C2×C4×D61C22⋊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
125C2×C4×D61C2×D411yescharacteristic
126C2×C4×D61C2×D411yescharacteristic
127C2×C4×D61C2×D411yescharacteristic
128C2×C4×D61C2×Q811yescharacteristic
129C22⋊#6923—44no—
130C22⋊#6923—44no—
131C2×#92420—24no—
132C2×#92420—44no—
133C4⋊#6923—44no—
134C4⋊#6923—44no—
135#11758213—44no—
136#11758213—44no—
137M16×C61—42no—
138C2×C8×C61—22no—
139#11758194—42no—
140C2×#92418—22no—
141#11758189—44no—
142C8×D61—44no—
143C23×C61—22no—
144C23×C61—22no—
145C23×C61—41no—
146C23×C61#9511yescharacteristic
147C23×C61#9511yescharacteristic
148C23×C61C2×C4211yescharacteristic
149C22×D61—22no—
150C22×D61—22no—
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—21no—
160C22×D61—21no—
161C22×D61—41no—
162C22×D61—41no—
163C22×D61—41no—
164C22×D61—41no—
165C22×D61—41no—
166C22×D61—41no—
167C22×D61—41no—
168C22×D61—48no—
169C22×D61—48no—
170C22×D61#9511yescharacteristic
171C22×D61#9511yescharacteristic
172C22×D61#10012yes—
173C22×D61#10112yes—
174C22×D61C2×C22⋊C411yescharacteristic
175C22×D61C2×C4⋊C411yescharacteristic
176C2×#6923—44no—
177C2×#6923—44no—
178C2×#6923—44no—
179C2×#6923—88no—
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#9511yescharacteristic
187C2×C4×C61#9511yescharacteristic
188C2×C4×C61C2×C22⋊C411yescharacteristic
189C2×C4×C61C2×C4⋊C411yescharacteristic
190C2×Dic61—22no—
191C2×Dic61—22no—
192C2×Dic61—22no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—41no—
196C2×Dic61#9511yescharacteristic
197C2×Dic61#9511yescharacteristic
198C2×Dic61C2×C22⋊C411yescharacteristic
199C2×Dic61C2×C4⋊C411yescharacteristic
200C4×D61—22no—
201C4×D61—22no—
202C4×D61—22no—
203C4×D61—22no—
204C4×D61—22no—
205C4×D61—22no—
206C4×D61—22no—
207C4×D61—22no—
208C4×D61—22no—
209C4×D61—41no—
210C4×D61—41no—
211C4×D61—41no—
212C4×D61—41no—
213C4×D61—41no—
214C4×D61—41no—
215C4×D61#9914yes—
216#92420—44no—
217C8×C61—42no—
218#92418—42no—
219#8107—611nomaximal, Sylow
220C22×C61—21no—
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—21no—
227C22×C61—44no—
228C22×C61#34312yes—
229C22×C61#34412yes—
230C22×C61C2×#9511yescharacteristic
231C2×D61—24no—
232C2×D61—24no—
233C2×D61—21no—
234C2×D61—21no—
235C2×D61—21no—
236C2×D61—21no—
237C2×D61—21no—
238C2×D61—21no—
239C2×D61—21no—
240C2×D61—21no—
241C2×D61—21no—
242C2×D61—42no—
243C2×D61—42no—
244C2×D61—44no—
245C2×D61—44no—
246C2×D61—44no—
247C2×D61—42no—
248C2×D61—42no—
249C2×D61#34212yes—
250C2×D61#34312yes—
251C2×D61C2×#10011yescharacteristic
252C2×D61C2×#10111yescharacteristic
253#6923—84no—
254C4×C61—21no—
255C4×C61—21no—
256C4×C61—21no—
257C4×C61C2×#9912yes—
258Dic61—21no—
259Dic61—21no—
260Dic61—21no—
261Dic61#34212yes—
262C2×#407—611no—
263C2×#407—611no—
264C2×#380—611no—
265#1305—614no—
266C2×C61—22no—
267C2×C61—22no—
268C2×C61—41no—
269C2×C61C2×#34211yescharacteristic
270C2×C61C2×#34311yescharacteristic
271C2×C61C2×#34411yescharacteristic
272D61—21no—
273D61—22no—
274D61—21no—
275D61—22no—
276D61—41no—
277C24×C4—611no—
278C22×M16—612no—
279C22×M16—1221no—
280C22×C4⋊C4—1221no—
281C22×C22⋊C4—612no—
282#407—612no—
283#407—612no—
284#407—611no—
285#407—612no—
286#407—1221no—
287#407—1221no—
288#407—1221no—
289#407—1221no—
290#407#692311yescharacteristic, complemented
291C2×C22⋊C8—612no—
292C2×C22⋊C8—1221no—
293C2×C22⋊C8—1221no—
294C2×C22⋊C8—1221no—
295#380—612no—
296#380—612no—
297#380—1221no—
298#380—1221no—
299C2×#95—1221no—
300C61#810711yescharacteristic, complemented, Sylow
301C25—611no—
302C23×C4—611no—
303C23×C4—611no—
304C23×C4—611no—
305C23×C4—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—1222no—
316C23×C4—2444no—
317C23×C4C2×#692311yescharacteristic
318C2×M16—612no—
319C2×M16—1222no—
320C2×M16—1222no—
321C2×M16—1222no—
322C2×M16—2444no—
323C2×M16—2444no—
324C2×M16C2×#692312yescomplemented
325C22×C8—1222no—
326C22×C8—1222no—
327C2×C4⋊C4—1222no—
328C2×C4⋊C4—1222no—
329C2×C4⋊C4—2444no—
330C2×C22⋊C4—614no—
331C2×C22⋊C4—1222no—
332C2×C22⋊C4—2444no—
333C22⋊C8—21no—
334C22⋊C8—21no—
335C22⋊C8—614no—
336C22⋊C8—1222no—
337C22⋊C8—1222no—
338C22⋊C8—1222no—
339C22⋊C8—1222no—
340C22⋊C8—1222no—
341C22⋊C8—1221no—
342C22⋊C8—1221no—
343#95—1222no—
344#95—1222no—
345C24—611no—
346C24—611no—
347C24—611no—
348C24—611no—
349C24—611no—
350C24—611no—
351C24—1222no—
352C24—1222no—
353C24—2442no—
354C24—2442no—
355C24C4×#692311yescharacteristic
356C22×C4—42no—
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—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—1224no—
380C22×C4—1224no—
381C22×C4—1224no—
382C22×C4—1224no—
383C22×C4—2442no—
384C22×C4—2442no—
385C22×C4—2442no—
386C22×C4—2442no—
387C22×C4—2442no—
388C22×C4—2442no—
389C22×C4—2442no—
390C22×C4—2442no—
391C22×C4—2442no—
392C22×C4—2442no—
393C22×C4—2444no—
394C22×C4—2444no—
395C22×C4—2444no—
396C22×C4C4×#692311yescharacteristic
397C22×C4C4⋊#692311yescharacteristic
398C22×C4C4⋊#692311yescharacteristic
399C22×C4C22⋊#692311yescharacteristic
400C22×C4C22⋊#692311yescharacteristic
401C22×C4C22×#692311yescharacteristic
402M16—42no—
403M16—2444no—
404M16—2444no—
405M16—2444no—
406M16—2442no—
407C2×C8—22no—
408C2×C8—1224no—
409C2×C8—1222no—
410C2×C8—2444no—
411C2×C8—2444no—
412C4⋊C4—2444no—
413C4⋊C4—2444no—
414C22⋊C4—2444no—
415C22⋊C4—2444no—
416C23—22no—
417C23—22no—
418C23—41no—
419C23—611no—
420C23—611no—
421C23—611no—
422C23—612no—
423C23—612no—
424C23—611no—
425C23—1222no—
426C23—1221no—
427C23—1221no—
428C23—1221no—
429C23—1222no—
430C23—1222no—
431C23—1222no—
432C23—1222no—
433C23—1221no—
434C23—1222no—
435C23—1222no—
436C23—1222no—
437C23—2441no—
438C23—2441no—
439C23—2441no—
440C23—2441no—
441C23—2441no—
442C23—2441no—
443C23—2441no—
444C23—2448no—
445C23—2448no—
446C23(C2×#6923)⋊C411yescharacteristic
447C23(C2×#6923)⋊C411yescharacteristic
448C23C2×C4×#692311yescharacteristic
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—611no—
456C2×C4—614no—
457C2×C4—611no—
458C2×C4—611no—
459C2×C4—611no—
460C2×C4—1222no—
461C2×C4—1222no—
462C2×C4—1222no—
463C2×C4—1222no—
464C2×C4—1222no—
465C2×C4—1222no—
466C2×C4—1222no—
467C2×C4—1222no—
468C2×C4—1222no—
469C2×C4—1222no—
470C2×C4—1222no—
471C2×C4—1222no—
472C2×C4—4888no—
473C2×C4—2441no—
474C2×C4—2441no—
475C2×C4—2441no—
476C2×C4—2441no—
477C2×C4—2441no—
478C2×C4—2441no—
479C2×C4—2441no—
480C2×C4—2441no—
481C2×C4—2441no—
482C2×C4—2444no—
483C2×C4—2444no—
484C2×C4—2444no—
485C2×C4(C2×#6923)⋊C411yescharacteristic
486C2×C4(C2×#6923)⋊C411yescharacteristic
487C2×C4C2×C22⋊#692311yescharacteristic
488C2×C4C2×C4⋊#692311yescharacteristic
489C8—42no—
490C8—2444no—
491C8—2442no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—44no—
500C22—612no—
501C22—611no—
502C22—612no—
503C22—611no—
504C22—1224no—
505C22—1224no—
506C22—1221no—
507C22—1221no—
508C22—1221no—
509C22—1221no—
510C22—1221no—
511C22—1221no—
512C22—1221no—
513C22—1221no—
514C22—1221no—
515C22—2442no—
516C22—2442no—
517C22—2444no—
518C22—2444no—
519C22—2444no—
520C22—2442no—
521C22—2442no—
522C22#1684064112yes—
523C22#1684064512yes—
524C22C2×(C2×#6923)⋊C411yescharacteristic
525C4—21no—
526C4—21no—
527C4—21no—
528C4—612no—
529C4—1221no—
530C4—1221no—
531C4—1221no—
532C4—4884no—
533C4D61⋊#9912yes—
534C2—22no—
535C2—22no—
536C2—41no—
537C2—1221no—
538C2—1222no—
539C2—1221no—
540C2—1222no—
541C2—2441no—
542C2#2146151611yescharacteristic
543C2C2×#1684064111yescharacteristic
544C2C2×#1684064511yescharacteristic
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#8107
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. #21460719C2semidirect
10. #16840733C4semidirect
13. C2×C22⋊#92420C4semidirect
20. C2×M16×D61C4semidirect
21. #16839726C4semidirect
27. C61×#407C4semidirect
42. C22⋊#92420C2×C4semidirect
60. C2×#11758194C2×C4semidirect
69. C2×M16×C61C2×C4semidirect
290. #407#6923semidirect
300. C61#8107semidirect
324. C2×M16C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407332
C2×#168407042
#214607192
#407×D612
#810761