Finite Group Databasebeta

← #30596331

Subgroups — #30596331

Order 15616.

954 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×D61⋊(C22⋊C8)C211yesmaximal, characteristic
3#21460662C214yesmaximal, complemented
4#21448201C211yesmaximal, characteristic
5C22×#11758213—21no—
6C22×D61⋊C8C412yescomplemented
7#16840733—21no—
8#16840733—21no—
9#16840733C412yescomplemented
10#16840733C412yescomplemented
11C2×#14519834—21no—
12C2×#14519834C412yescomplemented
13D61⋊(C22⋊C8)—21no—
14D61⋊(C22⋊C8)—21no—
15D61⋊(C22⋊C8)—21no—
16D61⋊(C22⋊C8)—21no—
17C2×C22⋊#92420C2212yes—
18C2×C22⋊#92420C2212yes—
19C23×C4×D61C2211yescharacteristic
20C2×#14519735—21no—
21#16839624—21no—
22#16839622C411yescharacteristic
23#16839619—21no—
24#16839617C412yes—
25C22⋊C4×Dic61C2212yes—
26#16839609—21no—
27C61×#380C411yescharacteristic
28C2×#11758213—22no—
29C2×#11758213—22no—
30C2×#11758213—44no—
31C2×D61⋊C8—22no—
32C2×D61⋊C8—22no—
33C2×D61⋊C8—44no—
34C22×#92420—22no—
35C22×#92420C2×C414yes—
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#14519735—44no—
60C2×C4⋊Dic61—21no—
61C2×C22⋊Dic61C2×C412yes—
62C2×#11758198—22no—
63C2×#11758198—22no—
64C2×C4×Dic61—22no—
65#14519684—21no—
66#14519684—22no—
67C23×C4×C61C2×C411yescharacteristic
68C2×C4⋊C4×C61—21no—
69C2×C22⋊C4×C61C2×C412yes—
70#95×C61—21no—
71C24×C61C22×C411yescharacteristic
72C23×D61—22no—
73C23×D61—22no—
74C23×D61—42no—
75C23×D61—42no—
76C23×D61C4211yescharacteristic
77C23×D61C4211yescharacteristic
78C23×D61C22⋊C411yescharacteristic
79C23×D61C22⋊C411yescharacteristic
80C23×D61C4⋊C411yescharacteristic
81C23×D61C4⋊C411yescharacteristic
82C22×C4×C61—22no—
83C22×C4×C61—42no—
84C22×C4×C61C4211yescharacteristic
85C22×C4×C61C4211yescharacteristic
86C22×C4×C61C22⋊C411yescharacteristic
87C22×C4×C61C22⋊C411yescharacteristic
88C22×C4×C61C4⋊C411yescharacteristic
89C22×C4×C61C4⋊C411yescharacteristic
90C22×Dic61—22no—
91C22×Dic61—42no—
92C22×Dic61C22×C411yescharacteristic
93C22×Dic61C22×C411yescharacteristic
94C22×Dic61C2×D411yescharacteristic
95C22×Dic61C2×D411yescharacteristic
96C22×Dic61C2×D411yescharacteristic
97C22×Dic61C2×Q811yescharacteristic
98C2×C4×D61—24no—
99C2×C4×D61—24no—
100C2×C4×D61—24no—
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×D61—42no—
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×D61C22⋊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
125C2×C4×D61C4⋊C411yescharacteristic
126C2×#92420—24no—
127C2×#92420—24no—
128C2×#92420—44no—
129C2×#92420—44no—
130#11758213—44no—
131#11758213—44no—
132D61⋊C8—44no—
133D61⋊C8—44no—
134C4⋊C4×C61—42no—
135C22⋊C4×C61—24no—
136C22⋊Dic61—24no—
137#11758198—44no—
138#11758198—44no—
139C4⋊Dic61—42no—
140C4×Dic61—44no—
141C23×C61—41no—
142C23×C61—41no—
143C23×C61C2×C4211yescharacteristic
144C23×C61C2×C22⋊C411yescharacteristic
145C23×C61C2×C4⋊C411yescharacteristic
146C23×C61#13112yes—
147C23×C61#13112yes—
148C22×D61—22no—
149C22×D61—22no—
150C22×D61—22no—
151C22×D61—22no—
152C22×D61—21no—
153C22×D61—21no—
154C22×D61—21no—
155C22×D61—21no—
156C22×D61—22no—
157C22×D61—22no—
158C22×D61—22no—
159C22×D61—22no—
160C22×D61—22no—
161C22×D61—22no—
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#9511yescharacteristic
173C22×D61#9511yescharacteristic
174C2×C4×C61—22no—
175C2×C4×C61—22no—
176C2×C4×C61—22no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—42no—
181C2×C4×C61—42no—
182C2×C4×C61—42no—
183C2×C4×C61#9511yescharacteristic
184C2×C4×C61#9511yescharacteristic
185C2×C4×C61#9511yescharacteristic
186C2×C4×C61#9511yescharacteristic
187C2×Dic61—22no—
188C2×Dic61—22no—
189C2×Dic61—22no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—42no—
194C2×Dic61—42no—
195C2×Dic61—42no—
196C2×Dic61C2×C22⋊C411yescharacteristic
197C2×Dic61C2×C22⋊C411yescharacteristic
198C2×Dic61C2×C4⋊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—
217#92420—44no—
218#7927—611nomaximal, Sylow
219C22×C61—21no—
220C22×C61—21no—
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—21no—
225C22×C61—42no—
226C22×C61—42no—
227C22×C61C2×#9511yescharacteristic
228C22×C61#40512yes—
229C22×C61#40811yescharacteristic
230C22×C61#40811yescharacteristic
231C22×C61#42412yes—
232C2×D61—28no—
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—21no—
243C2×D61—42no—
244C2×D61—42no—
245C2×D61—44no—
246C2×D61—42no—
247C2×D61—42no—
248C2×D61—44no—
249C2×D61—44no—
250C2×D61#34212yes—
251C2×D61#34412yes—
252C4×C61—21no—
253C4×C61—21no—
254C4×C61—21no—
255C4×C61—82no—
256C4×C61#34212yes—
257Dic61—21no—
258Dic61—21no—
259Dic61—21no—
260Dic61—82no—
261Dic61C2×#9912yes—
262C2×#407—611no—
263C22×C22⋊C8—611no—
264#2280—611no—
265#1282—614no—
266C2×C61—21no—
267C2×C61—21no—
268C2×C61—22no—
269C2×C61—22no—
270C2×C61#172911yescharacteristic
271C2×C61C2×#34211yescharacteristic
272C2×C61C2×#34411yescharacteristic
273D61—22no—
274D61—22no—
275D61—41no—
276D61—41no—
277C24×C4—611no—
278C22×M16—1221no—
279C23×C8—612no—
280C2×#117—1221no—
281#407—612no—
282#407—612no—
283#407—1221no—
284#407—1221no—
285C2×C22⋊C8—612no—
286C2×C22⋊C8—612no—
287C2×C22⋊C8—612no—
288C2×C22⋊C8—1221no—
289C2×C22⋊C8—1221no—
290C2×C22⋊C8—1221no—
291C2×C22⋊C8—1221no—
292C2×C22⋊C8—1221no—
293#381—1221no—
294#380—611no—
295#380—1221no—
296#380#692311yescharacteristic
297#379—612no—
298C4×C22⋊C4—612no—
299C4×C22⋊C4—1221no—
300C61#792711yescharacteristic, 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—2444no—
316C23×C4C2×#692311yescharacteristic
317C2×M16—1222no—
318C2×M16—1222no—
319C2×M16—2444no—
320C22×C8—614no—
321C22×C8—1222no—
322C22×C8—1222no—
323C22×C8—1222no—
324C22×C8—2444no—
325#117—2444no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—1221no—
328C2×C22⋊C4—612no—
329C2×C22⋊C4—1222no—
330C2×C22⋊C4—1222no—
331C2×C22⋊C4C2×#692312yes—
332C2×C42—1222no—
333C22⋊C8—614no—
334C22⋊C8—1222no—
335C22⋊C8—1222no—
336C22⋊C8—1222no—
337C22⋊C8—1222no—
338C22⋊C8—1222no—
339C22⋊C8—1222no—
340C22⋊C8—1222no—
341#95—21no—
342#95—1222no—
343#95—1221no—
344C24—611no—
345C24—611no—
346C24—611no—
347C24—611no—
348C24—611no—
349C24—611no—
350C24—1222no—
351C24—1222no—
352C24—2442no—
353C24—2442no—
354C24C22×#692311yescharacteristic
355C22×C4—22no—
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—1222no—
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×C4C4×#692311yescharacteristic
394C22×C4C4×#692311yescharacteristic
395C22×C4C4⋊#692311yescharacteristic
396C22×C4C4⋊#692311yescharacteristic
397C22×C4C22⋊#692311yescharacteristic
398C22×C4C22⋊#692311yescharacteristic
399M16—2444no—
400M16—2444no—
401C2×C8—1224no—
402C2×C8—1224no—
403C2×C8—2444no—
404C2×C8—2444no—
405C2×C8—2444no—
406C2×C8—2444no—
407C4⋊C4—42no—
408C4⋊C4—2442no—
409C22⋊C4—24no—
410C22⋊C4—1224no—
411C22⋊C4—2444no—
412C22⋊C4—2444no—
413C42—2444no—
414C23—41no—
415C23—41no—
416C23—611no—
417C23—611no—
418C23—611no—
419C23—611no—
420C23—1222no—
421C23—1222no—
422C23—1222no—
423C23—1222no—
424C23—1222no—
425C23—1222no—
426C23—1222no—
427C23—1222no—
428C23—1221no—
429C23—1221no—
430C23—1221no—
431C23—1221no—
432C23—1222no—
433C23—1222no—
434C23—2441no—
435C23—2441no—
436C23—2441no—
437C23—2441no—
438C23—2441no—
439C23—2441no—
440C23—2448no—
441C23—2448no—
442C23C2×C4×#692311yescharacteristic
443C23C2×C22⋊#692311yescharacteristic
444C23C2×C4⋊#692311yescharacteristic
445C23#1451986412yes—
446C23#1451986512yes—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—611no—
457C2×C4—614no—
458C2×C4—611no—
459C2×C4—611no—
460C2×C4—611no—
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—1222no—
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—2442no—
483C2×C4—2442no—
484C2×C4—2442no—
485C2×C4(C2×#6923)⋊C411yescharacteristic
486C2×C4(C2×#6923)⋊C411yescharacteristic
487C2×C4(C2×#6923)⋊C411yescharacteristic
488C2×C4(C2×#6923)⋊C411yescharacteristic
489C8—2444no—
490C8—2444no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—42no—
498C22—42no—
499C22—612no—
500C22—612no—
501C22—1228no—
502C22—1221no—
503C22—1221no—
504C22—1221no—
505C22—1221no—
506C22—1221no—
507C22—1221no—
508C22—1221no—
509C22—1221no—
510C22—1221no—
511C22—1221no—
512C22—2442no—
513C22—2442no—
514C22—2442no—
515C22—2442no—
516C22—2444no—
517C22—2444no—
518C22—2444no—
519C22C2×(C2×#6923)⋊C411yescharacteristic
520C22#1684072712yes—
521C22#1684073611yescharacteristic
522C22#1684073711yescharacteristic
523C22#1684076912yes—
524C4—21no—
525C4—21no—
526C4—21no—
527C4—82no—
528C4—612no—
529C4—1221no—
530C4—1221no—
531C4—1221no—
532C4—4882no—
533C4#1684063912yes—
534C2—21no—
535C2—21no—
536C2—22no—
537C2—22no—
538C2—1222no—
539C2—1222no—
540C2—2441no—
541C2—2441no—
542C2#2146148611yescharacteristic
543C2C2×#1684063911yescharacteristic
544C2#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#7927
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #21460662C2semidirect
6. C22×D61⋊C8C4semidirect
9. #16840733C4semidirect
10. #16840733C4semidirect
12. C2×#14519834C4semidirect
300. C61#7927semidirect

Maximal subgroups

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

subgroupindex
C2×#168407332
C2×D61⋊(C22⋊C8)2
#214606622
#214482012
#792761