Finite Group Databasebeta

← #30610333

Subgroups — #30610333

Order 15616.

1022 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462680C212yesmaximal, complemented
2#21461093C212yesmaximal, complemented
3#21461087C214yesmaximal, complemented
4#21461078C211yesmaximal, characteristic, complemented
5#21461074C212yesmaximal, complemented
6#21461058C211yesmaximal, characteristic, complemented
7#21461054C212yesmaximal, complemented
8C2×#16840460C211yesmaximal, characteristic
9#16840796—22no—
10#16840792—24no—
11#16840790—22no—
12#16840783C2212yes—
13#16840779C2212yes—
14#16840733C2214yes—
15D61⋊(C22⋊C8)C2214yes—
16#16840608C2214yes—
17#16840608C2214yes—
18#16840606C2212yes—
19#16840606C2212yes—
20#16840605C2211yescharacteristic
21#16840605C2212yes—
22#16840605C2211yescharacteristic
23#16840460—22no—
24#16840460—24no—
25#16840460—22no—
26C2×#14519772C412yes—
27C2×#14519768C2211yescharacteristic
28C2×#14519762C2212yes—
29C2×#14519752C411yescharacteristic
30C2×#14519751C412yes—
31C2×#14519751C411yescharacteristic
32C2×#14519739C2211yescharacteristic
33C2×C4×C22⋊D61C2211yescharacteristic
34C2×C4×C22⋊D61C2212yes—
35C2×#14519735C411yescharacteristic
36C22×C4⋊C4×C61C411yescharacteristic
37C2×#11758213—24no—
38C2×D61⋊C8—24no—
39#14519844—22no—
40C4⋊#92420—22no—
41#14519834—24no—
42#14519834—24no—
43C22⋊#92420C2312yes—
44C22⋊#92420C2314yes—
45C22⋊#92420C2312yes—
46#14519832—22no—
47C4×#92420—22no—
48C22×D244C2×C412yes—
49C22×D244C2×C411yescharacteristic
50C22×C22⋊D61C2×C412yes—
51C22×C22⋊D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2312yes—
54#14519772—24no—
55#14519772—24no—
56#14519768—22no—
57#14519768—22no—
58#14519762—24no—
59#14519762—24no—
60#14519752—22no—
61#14519752—22no—
62#14519751—22no—
63#14519751—22no—
64#14519751—24no—
65#14519751—24no—
66#14519739D412yes—
67#14519739D414yes—
68#14519739D412yes—
69C4×C22⋊D61—24no—
70C4×C22⋊D61—24no—
71C4×C22⋊D61—22no—
72C4×C22⋊D61—22no—
73#14519735—22no—
74#14519735—21no—
75#14519735—21no—
76C2×C4⋊Dic61C2×C411yescharacteristic
77C2×C4⋊Dic61C2×C412yes—
78C2×#11758196C2×C411yescharacteristic
79C2×#11758196C2312yes—
80C2×C22⋊Dic61C2311yescharacteristic
81C2×#11758198C2×C412yes—
82C2×#11758198C2×C412yes—
83C2×#11758198C2×C412yes—
84C2×#11758198C2×C412yes—
85C2×#11758198C2311yescharacteristic
86C2×C4×Dic61C2×C412yes—
87C2×C4×Dic61C2311yescharacteristic
88C23×C4×C61C2×C411yescharacteristic
89C23×C4×C61C2×C412yes—
90C2×C4⋊C4×C61—22no—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61C2×C411yescharacteristic
94C2×C4⋊C4×C61C2×C412yes—
95C2×C4⋊C4×C61C2×C411yescharacteristic
96C24×C61C22×C411yescharacteristic
97C23×D61C22×C411yescharacteristic
98C23×D61C22×C412yes—
99C22×C4×C61—21no—
100C22×C4×C61—21no—
101C22×C4×C61—22no—
102C22×C4×C61—22no—
103C22×C4×C61—42no—
104C22×C4×C61—82no—
105C22×C4×C61C22×C411yescharacteristic
106C22×C4×C61C22×C412yes—
107C22×C4×C61C22×C411yescharacteristic
108C22×C4×C61C22×C412yes—
109C2×C22⋊D61—22no—
110C2×C22⋊D61—24no—
111C2×C22⋊D61—24no—
112C2×C22⋊D61—22no—
113C2×C22⋊D61—41no—
114C2×C22⋊D61—42no—
115C22×Dic61C22×C412yes—
116C22×Dic61C22×C411yescharacteristic
117C22×Dic61C22×C411yescharacteristic
118C22×Dic61C2411yescharacteristic
119C2×D244—24no—
120C2×D244—42no—
121C2×D244—82no—
122C2×D244C22⋊C412yes—
123C2×D244C22⋊C412yes—
124C2×C4×D61—21no—
125C2×C4×D61—21no—
126C2×C4×D61—42no—
127C2×C4×D61—82no—
128C2×C4×D61C2×D414yes—
129C2×C4×D61C2×D414yes—
130C2×#92420—22no—
131C2×#92420—22no—
132C2×#92420—24no—
133#11758213—84no—
134D61⋊C8—84no—
135C4⋊C4×C61—21no—
136C4⋊C4×C61—21no—
137C4⋊C4×C61—22no—
138C4⋊C4×C61—22no—
139C4⋊C4×C61C22⋊C412yes—
140C4⋊C4×C61C22⋊C411yescharacteristic
141C4⋊C4×C61C22⋊C411yescharacteristic
142C22⋊Dic61—22no—
143#11758198—24no—
144#11758198—24no—
145#11758198—22no—
146#11758198—22no—
147#11758198—22no—
148#11758198C22⋊C414yes—
149#11758198C22⋊C414yes—
150C4⋊Dic61—21no—
151C4⋊Dic61—21no—
152C4⋊Dic61—24no—
153#11758196—22no—
154#11758196—24no—
155C4×Dic61—22no—
156C4×Dic61—22no—
157C4×Dic61C2×D412yes—
158C4×Dic61C2×D412yes—
159C23×C61—21no—
160C23×C61—21no—
161C23×C61—41no—
162C23×C61—41no—
163C23×C61#13112yes—
164C23×C61C23×C411yescharacteristic
165C22×D61—22no—
166C22×D61—22no—
167C22×D61—21no—
168C22×D61—21no—
169C22×D61—21no—
170C22×D61—42no—
171C22×D61—42no—
172C22×D61—41no—
173C22×D61—41no—
174C22×D61C2×C22⋊C414yes—
175C2×C4×C61—22no—
176C2×C4×C61—22no—
177C2×C4×C61—21no—
178C2×C4×C61—42no—
179C2×C4×C61—42no—
180C2×C4×C61—42no—
181C2×C4×C61—42no—
182C2×C4×C61—41no—
183C2×C4×C61—82no—
184C2×C4×C61—82no—
185C2×C4×C61C2×C22⋊C412yes—
186C2×C4×C61C2×C22⋊C412yes—
187C2×C4×C61C2×C22⋊C411yescharacteristic
188C2×C4×C61C2×C22⋊C411yescharacteristic
189C22⋊D61—44no—
190C22⋊D61—48no—
191C2×Dic61—21no—
192C2×Dic61—21no—
193C2×Dic61—21no—
194C2×Dic61—22no—
195C2×Dic61—22no—
196C2×Dic61—22no—
197C2×Dic61—41no—
198C2×Dic61—41no—
199C2×Dic61C2×C22⋊C412yes—
200C2×Dic61C22×D412yes—
201D244—24no—
202D244—42no—
203D244—84no—
204C4×D61—44no—
205C4×D61—44no—
206C4×D61—42no—
207C4×D61—42no—
208#92420—42no—
209#92420—44no—
210#92420—42no—
211#17424—611nomaximal, Sylow
212C22×C61—21no—
213C22×C61—21no—
214C22×C61—22no—
215C22×C61—42no—
216C22×C61—42no—
217C22×C61—41no—
218C22×C61—41no—
219C22×C61C22×C22⋊C411yescharacteristic
220C22×C61C2×#13111yescharacteristic
221C22×C61#56811yescharacteristic
222C2×D61—24no—
223C2×D61—24no—
224C2×D61—24no—
225C2×D61—41no—
226C2×D61—41no—
227C2×D61—41no—
228C2×D61—82no—
229C2×D61—82no—
230C2×D61—81no—
231C2×D61—81no—
232C4×C61—22no—
233C4×C61—22no—
234C4×C61—21no—
235C4×C61—42no—
236C4×C61—41no—
237C4×C61#41312yes—
238Dic61—22no—
239Dic61—22no—
240Dic61—42no—
241Dic61—41no—
242C2×#553—611no—
243#2974—612no—
244#1470—612no—
245#1468—614no—
246#1466—611no—
247#1465—612no—
248#1460—611no—
249#1459—612no—
250C2×C61—21no—
251C2×C61—21no—
252C2×C61—42no—
253C2×C61#288011yescharacteristic
254C2×C61#288311yescharacteristic
255C2×C61C2×#41311yescharacteristic
256D61—44no—
257D61—81no—
258#553—1222no—
259#553—1224no—
260#553—1222no—
261C2×#126—612no—
262C2×#125—611no—
263C2×#123—612no—
264C2×#121—612no—
265C2×#121—611no—
266C2×#121—611no—
267C2×C4×D4—612no—
268C2×C4×D4—611no—
269C2×C4×D4—611no—
270C2×#117—611no—
271C22×C4⋊C4#692311yescharacteristic
272#436—1222no—
273#435—1224no—
274C8×D4—1222no—
275#432—612no—
276#431—612no—
277#407—614no—
278C2×C22⋊C8—614no—
279#324—614no—
280#324—614no—
281#323—611no—
282#323—612no—
283#323—611no—
284#323—612no—
285#323—612no—
286C61#1742411yescharacteristic, complemented, Sylow
287C22×D4—611no—
288C22×D4—612no—
289C22×D4—611no—
290C22×D4—612no—
291C23×C4—612no—
292C23×C4—611no—
293C23×C4C2×#692311yescharacteristic
294C23×C4C2×#692312yes—
295C2×M16—1224no—
296C22×C8—1224no—
297#126—1224no—
298#126—1224no—
299#125—1222no—
300#125—1222no—
301#123—1224no—
302#123—1224no—
303#121—1224no—
304#121—1224no—
305#121—1222no—
306#121—1222no—
307#121—1222no—
308#121—1222no—
309C4×D4—612no—
310C4×D4—614no—
311C4×D4—612no—
312C4×D4—1222no—
313C4×D4—1222no—
314C4×D4—1224no—
315C4×D4—1224no—
316#117—1222no—
317#117—1221no—
318#117—1221no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—611no—
323C2×C4⋊C4—612no—
324C2×C4⋊C4—611no—
325C2×C4⋊C4—612no—
326C2×C4⋊C4C2×#692311yescharacteristic
327C2×C4⋊C4C2×#692312yes—
328C2×C4⋊C4C2×#692311yescharacteristic
329C2×C22⋊C4—612no—
330C2×C22⋊C4—611no—
331C2×C22⋊C4—612no—
332C2×C22⋊C4—612no—
333C2×C22⋊C4—611no—
334C2×C22⋊C4—612no—
335C2×C42—611no—
336C2×C42—612no—
337C4⋊C8—1222no—
338C4⋊C8—1222no—
339C22⋊C8—612no—
340C22⋊C8—614no—
341C22⋊C8—612no—
342C22⋊C8—1224no—
343C22⋊C8—1224no—
344#97—1222no—
345C4×C8—1222no—
346C24—612no—
347C24—611no—
348C24C22×#692311yescharacteristic
349C2×D4—612no—
350C2×D4—612no—
351C2×D4—1224no—
352C2×D4—1222no—
353C2×D4—1224no—
354C2×D4—1222no—
355C2×D4—1224no—
356C2×D4—4882no—
357C2×D4—2442no—
358C2×D4—2441no—
359C2×D4—2442no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—42no—
365C22×C4—82no—
366C22×C4—611no—
367C22×C4—611no—
368C22×C4—614no—
369C22×C4—614no—
370C22×C4—612no—
371C22×C4—611no—
372C22×C4—1221no—
373C22×C4—1221no—
374C22×C4—4882no—
375C22×C4—2442no—
376C22×C4C22×#692311yescharacteristic
377C22×C4C22×#692311yescharacteristic
378C22×C4C22×#692312yes—
379C22×C4C22×#692312yes—
380M16—4884no—
381C2×C8—1222no—
382C2×C8—1222no—
383C2×C8—1224no—
384C2×C8—4884no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—1224no—
390C4⋊C4—1222no—
391C4⋊C4—1224no—
392C4⋊C4—1221no—
393C4⋊C4—1221no—
394C4⋊C4C22⋊#692312yes—
395C4⋊C4C22⋊#692311yescharacteristic
396C4⋊C4C22⋊#692311yescharacteristic
397C22⋊C4—614no—
398C22⋊C4—614no—
399C22⋊C4—1222no—
400C22⋊C4—1224no—
401C22⋊C4—1224no—
402C22⋊C4—1222no—
403C22⋊C4—1222no—
404C22⋊C4—1222no—
405C42—612no—
406C42—612no—
407C42—1222no—
408C42—1222no—
409C23—21no—
410C23—21no—
411C23—41no—
412C23—41no—
413C23—614no—
414C23—1222no—
415C23—1222no—
416C23—1221no—
417C23—1221no—
418C23—1221no—
419C23—2442no—
420C23—2442no—
421C23—2441no—
422C23—2441no—
423C23#1451986512yes—
424C23C23×#692311yescharacteristic
425D4—1224no—
426D4—4884no—
427D4—2442no—
428D4—2444no—
429D4—2448no—
430C2×C4—22no—
431C2×C4—21no—
432C2×C4—22no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—82no—
439C2×C4—82no—
440C2×C4—612no—
441C2×C4—612no—
442C2×C4—1221no—
443C2×C4—1221no—
444C2×C4—1221no—
445C2×C4—1222no—
446C2×C4—1222no—
447C2×C4—1222no—
448C2×C4—2444no—
449C2×C4—2444no—
450C2×C4—2442no—
451C2×C4—2441no—
452C2×C4—2442no—
453C2×C4—2441no—
454C2×C4C2×C22⋊#692311yescharacteristic
455C2×C4C2×C22⋊#692312yes—
456C2×C4C2×C22⋊#692312yes—
457C2×C4C2×C22⋊#692311yescharacteristic
458C8—2442no—
459C8—2444no—
460C8—2442no—
461C22—21no—
462C22—21no—
463C22—22no—
464C22—42no—
465C22—42no—
466C22—41no—
467C22—41no—
468C22—1224no—
469C22—1224no—
470C22—1224no—
471C22—4881no—
472C22—4881no—
473C22—4882no—
474C22—4882no—
475C22—2441no—
476C22—2441no—
477C22—2441no—
478C22C22×C22⋊#692311yescharacteristic
479C22C2×#1451986511yescharacteristic
480C22#1684084211yescharacteristic
481C4—22no—
482C4—22no—
483C4—21no—
484C4—42no—
485C4—41no—
486C4—1222no—
487C4—1222no—
488C4—2442no—
489C4—2441no—
490C4#1684074812yes—
491C2—21no—
492C2—21no—
493C2—42no—
494C2—4881no—
495C2—2444no—
496C2#2146240811yescharacteristic
497C2#2146241811yescharacteristic
498C2C2×#1684074811yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C4⋊C4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840460C2
cosocleC22×Dic61C24
hypercenterC22×C4⋊C4#6923
hypocenterC61#17424
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #21462680C2semidirect
2. #21461093C2semidirect
3. #21461087C2semidirect
4. #21461078C2semidirect
5. #21461074C2semidirect
6. #21461058C2semidirect
7. #21461054C2semidirect
286. C61#17424semidirect

Maximal subgroups

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

subgroupindex
#214626802
#214610932
#214610872
#214610782
#214610742
#214610582
#214610542
C2×#168404602
#1742461