Finite Group Databasebeta

← #30596267

Subgroups — #30596267

Order 15616.

1026 conjugacy classes of subgroups.

The subgroup lattice has 510 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#21460657C214yesmaximal, complemented
4C2×#16839619C211yesmaximal, characteristic
5C22×#11758213—21no—
6C22×D61⋊C8—21no—
7#16840733—22no—
8#16840733C414yescomplemented
9C2×#14519834—21no—
10C2×#14519834—21no—
11D61⋊(C22⋊C8)—22no—
12D61⋊(C22⋊C8)C414yescomplemented
13C2×C22⋊#92420C2212yes—
14C2×C22⋊#92420C2212yes—
15C23×C4×D61C2211yescharacteristic
16C22×C4⋊Dic61C411yescharacteristic
17C22×#11758198C412yes—
18#16839619—21no—
19#16839619—21no—
20#16839619—21no—
21#16839619—21no—
22C2×#14519684C2212yes—
23C22×C4⋊C4×C61C411yescharacteristic
24C2×#11758213—24no—
25C2×#11758213—42no—
26C2×#11758213—42no—
27C2×D61⋊C8—24no—
28C2×D61⋊C8—42no—
29C2×D61⋊C8—42no—
30C22×#92420—22no—
31C22×#92420—22no—
32#14519834—24no—
33#14519834—24no—
34C22⋊#92420—22no—
35C22⋊#92420—22no—
36C22⋊#92420C2×C414yes—
37C22⋊#92420C2×C414yes—
38C24×D61C2×C411yescharacteristic
39C23×Dic61C2×C412yes—
40C23×Dic61C2311yescharacteristic
41C22×C4×D61—42no—
42C22×C4×D61—42no—
43C22×C4×D61C2×C412yes—
44C22×C4×D61C2×C412yes—
45C22×C4×D61D411yescharacteristic
46C22×C4×D61D411yescharacteristic
47C22×C4×D61D412yes—
48C22×C4×D61D411yescharacteristic
49C22×C4×D61D411yescharacteristic
50C22×C4×D61Q812yes—
51C2×C4⋊Dic61—21no—
52C2×C4⋊Dic61—21no—
53C2×C4⋊Dic61—42no—
54C2×#11758198—22no—
55C2×#11758198—22no—
56C2×#11758198—44no—
57#14519684—22no—
58#14519684—22no—
59C23×C4×C61C2×C412yes—
60C23×C4×C61C2×C411yescharacteristic
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61—42no—
64C24×C61C22×C411yescharacteristic
65C23×D61—22no—
66C23×D61—22no—
67C23×D61—22no—
68C23×D61—22no—
69C23×D61—41no—
70C23×D61—41no—
71C23×D61C4212yes—
72C23×D61C22⋊C411yescharacteristic
73C23×D61C22⋊C411yescharacteristic
74C23×D61C4⋊C412yes—
75C22×C4×C61—22no—
76C22×C4×C61—22no—
77C22×C4×C61—22no—
78C22×C4×C61—24no—
79C22×C4×C61—42no—
80C22×C4×C61—42no—
81C22×C4×C61C4212yes—
82C22×C4×C61C22⋊C411yescharacteristic
83C22×C4×C61C22⋊C411yescharacteristic
84C22×C4×C61C4⋊C412yes—
85C22×Dic61—22no—
86C22×Dic61—24no—
87C22×Dic61—41no—
88C22×Dic61—41no—
89C22×Dic61—42no—
90C22×Dic61—42no—
91C22×Dic61C22×C411yescharacteristic
92C22×Dic61C22×C411yescharacteristic
93C22×Dic61C2×D411yescharacteristic
94C22×Dic61C2×D411yescharacteristic
95C22×Dic61C2×D411yescharacteristic
96C22×Dic61C2×Q811yescharacteristic
97C2×C4×D61—22no—
98C2×C4×D61—22no—
99C2×C4×D61—22no—
100C2×C4×D61—22no—
101C2×C4×D61—44no—
102C2×C4×D61—44no—
103C2×C4×D61—44no—
104C2×C4×D61—44no—
105C2×C4×D61—41no—
106C2×C4×D61—41no—
107C2×C4×D61—41no—
108C2×C4×D61—41no—
109C2×C4×D61C22⋊C412yes—
110C2×C4×D61C22⋊C412yes—
111C2×C4×D61C22⋊C412yes—
112C2×C4×D61C22⋊C412yes—
113C2×C4×D61C4⋊C412yes—
114C2×C4×D61C4⋊C412yes—
115C2×C4×D61C4⋊C412yes—
116C2×C4×D61C4⋊C412yes—
117C2×#92420—24no—
118C2×#92420—24no—
119C2×#92420—42no—
120C2×#92420—42no—
121C2×#92420—42no—
122C2×#92420—42no—
123#11758213—48no—
124D61⋊C8—48no—
125C4⋊C4×C61—42no—
126C4⋊C4×C61—42no—
127#11758198—44no—
128#11758198—44no—
129C4⋊Dic61—42no—
130C4⋊Dic61—42no—
131C23×C61—21no—
132C23×C61—21no—
133C23×C61—21no—
134C23×C61—21no—
135C23×C61C2×C4211yescharacteristic
136C23×C61C2×C22⋊C411yescharacteristic
137C23×C61C2×C4⋊C411yescharacteristic
138C23×C61#13112yes—
139C23×C61#13112yes—
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—21no—
143C22×D61—21no—
144C22×D61—24no—
145C22×D61—21no—
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—21no—
149C22×D61—21no—
150C22×D61—21no—
151C22×D61—24no—
152C22×D61—24no—
153C22×D61—24no—
154C22×D61—42no—
155C22×D61—42no—
156C22×D61—44no—
157C22×D61—44no—
158C22×D61—44no—
159C22×D61—44no—
160C22×D61#9512yes—
161C22×D61#9512yes—
162C22×D61#10012yes—
163C22×D61#10112yes—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—24no—
167C2×C4×C61—24no—
168C2×C4×C61—42no—
169C2×C4×C61—42no—
170C2×C4×C61—42no—
171C2×C4×C61—84no—
172C2×C4×C61#9512yes—
173C2×C4×C61#9512yes—
174C2×C4×C61#9912yes—
175C2×C4×C61#9912yes—
176C2×Dic61—21no—
177C2×Dic61—21no—
178C2×Dic61—21no—
179C2×Dic61—21no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—42no—
185C2×Dic61—42no—
186C2×Dic61—42no—
187C2×Dic61—84no—
188C2×Dic61C2×C22⋊C411yescharacteristic
189C2×Dic61C2×C22⋊C411yescharacteristic
190C2×Dic61C2×C4⋊C411yescharacteristic
191C2×Dic61C2×C4⋊C411yescharacteristic
192C4×D61—24no—
193C4×D61—24no—
194C4×D61—24no—
195C4×D61—24no—
196C4×D61—42no—
197C4×D61—42no—
198C4×D61—42no—
199C4×D61—42no—
200#92420—44no—
201#92420—44no—
202#7915—611nomaximal, Sylow
203C22×C61—22no—
204C22×C61—22no—
205C22×C61—22no—
206C22×C61—22no—
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—21no—
211C22×C61C2×#9511yescharacteristic
212C22×C61#40512yes—
213C22×C61#40811yescharacteristic
214C22×C61#40811yescharacteristic
215C22×C61C2×#9911yescharacteristic
216C22×C61C2×#9911yescharacteristic
217C22×C61C2×#10011yescharacteristic
218C22×C61C2×#10111yescharacteristic
219C22×C61#42412yes—
220C2×D61—22no—
221C2×D61—22no—
222C2×D61—22no—
223C2×D61—22no—
224C2×D61—22no—
225C2×D61—22no—
226C2×D61—22no—
227C2×D61—22no—
228C2×D61—22no—
229C2×D61—48no—
230C2×D61—48no—
231C2×D61—41no—
232C2×D61—41no—
233C2×D61—41no—
234C2×D61—41no—
235C2×D61#34314yes—
236C4×C61—22no—
237C4×C61—82no—
238C4×C61#34214yes—
239Dic61—21no—
240Dic61—21no—
241Dic61—21no—
242Dic61—21no—
243Dic61—82no—
244C2×#407—611no—
245C22×C22⋊C8—611no—
246C2×#380—611no—
247#1280—614no—
248C2×C61—22no—
249C2×C61—22no—
250C2×C61#147111yescharacteristic
251C2×C61#147111yescharacteristic
252C2×C61#147211yescharacteristic
253C2×C61#147211yescharacteristic
254C2×C61#172911yescharacteristic
255C2×C61C2×#34211yescharacteristic
256C2×C61C2×#34311yescharacteristic
257D61—24no—
258D61—42no—
259C24×C4—611no—
260C22×M16—1221no—
261C23×C8—1221no—
262C22×C4⋊C4—611no—
263C22×C4⋊C4#692311yescharacteristic
264C22×C22⋊C4—612no—
265#407—614no—
266#407—1222no—
267C2×C22⋊C8—612no—
268C2×C22⋊C8—612no—
269C2×C22⋊C8—614no—
270C2×C22⋊C8—1222no—
271C2×C22⋊C8—1221no—
272C2×C22⋊C8—1221no—
273#380—1221no—
274#380—1221no—
275#380—1221no—
276#380—1221no—
277C2×#95—612no—
278C61#791511yescharacteristic, complemented, Sylow
279C25—611no—
280C23×C4—611no—
281C23×C4—611no—
282C23×C4—611no—
283C23×C4—612no—
284C23×C4—612no—
285C23×C4—612no—
286C23×C4—612no—
287C23×C4—611no—
288C23×C4—611no—
289C23×C4—612no—
290C23×C4—2442no—
291C23×C4—2442no—
292C23×C4C2×#692312yes—
293C23×C4C2×#692311yescharacteristic
294C2×M16—1224no—
295C2×M16—2442no—
296C2×M16—2442no—
297C22×C8—1222no—
298C22×C8—1222no—
299C22×C8—1224no—
300C22×C8—2442no—
301C22×C8—2442no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—1221no—
306C2×C4⋊C4—1221no—
307C2×C4⋊C4—2442no—
308C2×C22⋊C4—1222no—
309C2×C22⋊C4—1222no—
310C2×C22⋊C4—2444no—
311C22⋊C8—614no—
312C22⋊C8—614no—
313C22⋊C8—1222no—
314C22⋊C8—1222no—
315C22⋊C8—1224no—
316C22⋊C8—1224no—
317#95—1222no—
318#95—1222no—
319C24—611no—
320C24—611no—
321C24—612no—
322C24—612no—
323C24—1222no—
324C24—1222no—
325C24—1222no—
326C24—1222no—
327C24—2441no—
328C24—2441no—
329C24C22×#692311yescharacteristic
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—24no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—611no—
337C22×C4—611no—
338C22×C4—611no—
339C22×C4—611no—
340C22×C4—611no—
341C22×C4—611no—
342C22×C4—612no—
343C22×C4—612no—
344C22×C4—612no—
345C22×C4—612no—
346C22×C4—612no—
347C22×C4—612no—
348C22×C4—612no—
349C22×C4—612no—
350C22×C4—1222no—
351C22×C4—1222no—
352C22×C4—1222no—
353C22×C4—1222no—
354C22×C4—1224no—
355C22×C4—1222no—
356C22×C4—2444no—
357C22×C4—2444no—
358C22×C4—2444no—
359C22×C4—2444no—
360C22×C4—2441no—
361C22×C4—2441no—
362C22×C4—2441no—
363C22×C4—2441no—
364C22×C4—2441no—
365C22×C4—2441no—
366C22×C4—2442no—
367C22×C4—2442no—
368C22×C4C4×#692312yes—
369C22×C4C4⋊#692312yes—
370C22×C4C22⋊#692311yescharacteristic
371C22×C4C22⋊#692311yescharacteristic
372M16—2448no—
373C2×C8—1224no—
374C2×C8—1224no—
375C2×C8—2448no—
376C2×C8—2442no—
377C2×C8—2442no—
378C2×C8—2442no—
379C2×C8—2442no—
380C4⋊C4—42no—
381C4⋊C4—42no—
382C4⋊C4—2442no—
383C4⋊C4—2442no—
384C22⋊C4—2444no—
385C22⋊C4—2444no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—612no—
391C23—612no—
392C23—612no—
393C23—612no—
394C23—1224no—
395C23—1224no—
396C23—1221no—
397C23—1221no—
398C23—1221no—
399C23—1221no—
400C23—1224no—
401C23—1221no—
402C23—1221no—
403C23—1221no—
404C23—1221no—
405C23—1221no—
406C23—1221no—
407C23—1224no—
408C23—2442no—
409C23—2442no—
410C23—2444no—
411C23—2444no—
412C23—2444no—
413C23—2444no—
414C23C2×C4×#692311yescharacteristic
415C23C2×C22⋊#692311yescharacteristic
416C23C2×C4⋊#692311yescharacteristic
417C23#1451986412yes—
418C23#1451986512yes—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—84no—
427C2×C4—611no—
428C2×C4—611no—
429C2×C4—611no—
430C2×C4—611no—
431C2×C4—1221no—
432C2×C4—1221no—
433C2×C4—1221no—
434C2×C4—1221no—
435C2×C4—1224no—
436C2×C4—1224no—
437C2×C4—1224no—
438C2×C4—1224no—
439C2×C4—4884no—
440C2×C4—2442no—
441C2×C4—2442no—
442C2×C4—2442no—
443C2×C4—2442no—
444C2×C4—2441no—
445C2×C4—2441no—
446C2×C4—2441no—
447C2×C4—2441no—
448C2×C4—2442no—
449C2×C4—2442no—
450C2×C4—2442no—
451C2×C4(C2×#6923)⋊C412yes—
452C2×C4(C2×#6923)⋊C412yes—
453C2×C4#1451983512yes—
454C2×C4#1451983612yes—
455C8—2444no—
456C8—2444no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—614no—
466C22—1222no—
467C22—1222no—
468C22—1222no—
469C22—1222no—
470C22—1222no—
471C22—1222no—
472C22—1222no—
473C22—1222no—
474C22—1222no—
475C22—2448no—
476C22—2448no—
477C22—2441no—
478C22—2441no—
479C22—2441no—
480C22—2441no—
481C22C2×(C2×#6923)⋊C411yescharacteristic
482C22#1684072712yes—
483C22#1684073611yescharacteristic
484C22#1684073711yescharacteristic
485C22C2×#1451983511yescharacteristic
486C22C2×#1451983611yescharacteristic
487C22D61⋊#10011yescharacteristic
488C22D61⋊#10111yescharacteristic
489C22#1684076912yes—
490C4—22no—
491C4—82no—
492C4—1221no—
493C4—1221no—
494C4—1221no—
495C4—1221no—
496C4—4882no—
497C4#1684064014yes—
498C2—22no—
499C2—22no—
500C2—1224no—
501C2—2442no—
502C2#2146109411yescharacteristic
503C2#2146109611yescharacteristic
504C2#2146109711yescharacteristic
505C2#2146109911yescharacteristic
506C2#2146148611yescharacteristic
507C2C2×#1684064011yescharacteristic
508C2#2146152211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC23×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#7915
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460657C2semidirect
8. #16840733C4semidirect
12. D61⋊(C22⋊C8)C4semidirect
278. C61#7915semidirect

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
#214606572
C2×#168396192
#791561