Finite Group Databasebeta

← C2×#21461074 #30609954

Subgroups — C2×#21461074 #30609954

Order 15616.

1738 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840733C212yesmaximal, complemented
2#21461074C218yesmaximal, direct product factor
3C2×#16840608C212yesmaximal, complemented
4C2×#16840605C212yesmaximal, complemented
5C22×C4×C22⋊D61C211yesmaximal, characteristic
6C22×#11758213—22no—
7#16840733—24no—
8#16840733C2218yescomplemented
9C2×#14519834—22no—
10C2×C22⋊#92420C2214yes—
11#16840608C2218yescomplemented
12#16840605C2218yescomplemented
13C23×C22⋊D61C411yescharacteristic
14C23×C4×D61C2211yescharacteristic
15C2×C4×C22⋊D61—22no—
16C2×C4×C22⋊D61—22no—
17C2×C4×C22⋊D61—24no—
18C2×C4×C22⋊D61C414yes—
19C2×C4×C22⋊D61C2214yes—
20C22×#11758196C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×#11758198C411yescharacteristic
23C22×C4×Dic61C411yescharacteristic
24C24×C4×C61C411yescharacteristic
25C2×#11758213—28no—
26C2×#11758213—48no—
27C22×#92420—24no—
28#14519834—28no—
29C22⋊#92420—24no—
30C22⋊#92420C2318yes—
31C24×D61C2×C411yescharacteristic
32C22×C22⋊D61—24no—
33C22×C22⋊D61—22no—
34C22×C22⋊D61—22no—
35C22×C22⋊D61—24no—
36C22×C22⋊D61C2×C414yes—
37C23×Dic61C2×C411yescharacteristic
38C23×Dic61C2×C411yescharacteristic
39C23×Dic61C2311yescharacteristic
40C22×C4×D61—44no—
41C22×C4×D61C2×C412yes—
42C22×C4×D61D412yes—
43C22×C4×D61D412yes—
44C22×C4×D61D414yes—
45C22×C4×D61C2312yes—
46C4×C22⋊D61—28no—
47C4×C22⋊D61—28no—
48C4×C22⋊D61—28no—
49C4×C22⋊D61—28no—
50C2×#11758196—22no—
51C2×#11758196—22no—
52C2×#11758196C2×C412yes—
53C2×#11758196C2312yes—
54C2×C22⋊Dic61—22no—
55C2×C22⋊Dic61—22no—
56C2×C22⋊Dic61C2×C412yes—
57C2×C22⋊Dic61C2312yes—
58C2×#11758198—22no—
59C2×#11758198—22no—
60C2×#11758198C2×C414yes—
61C2×C4×Dic61—22no—
62C2×C4×Dic61—21no—
63C2×C4×Dic61—21no—
64C2×C4×Dic61C2×C414yes—
65C25×C61C2×C411yescharacteristic
66C23×C4×C61—22no—
67C23×C4×C61—21no—
68C23×C4×C61—21no—
69C23×C4×C61—44no—
70C23×C4×C61C2×C411yescharacteristic
71C23×C4×C61C2×C414yes—
72C23×C4×C61C2×C411yescharacteristic
73C24×C61—21no—
74C24×C61—21no—
75C24×C61—22no—
76C24×C61—42no—
77C24×C61—42no—
78C24×C61M1614yescomplemented
79C24×C61C22×C411yescharacteristic
80C24×C61C22×C412yes—
81C23×D61—22no—
82C23×D61—22no—
83C23×D61—42no—
84C23×D61—42no—
85C23×D61C22⋊C412yes—
86C23×D61C22⋊C412yes—
87C23×D61C22×C412yes—
88C22×C4×C61—24no—
89C22×C4×C61—21no—
90C22×C4×C61—21no—
91C22×C4×C61—24no—
92C22×C4×C61—24no—
93C22×C4×C61—44no—
94C22×C4×C61—48no—
95C22×C4×C61—48no—
96C22×C4×C61—44no—
97C22×C4×C61—42no—
98C22×C4×C61C22⋊C411yescharacteristic
99C22×C4×C61C22⋊C412yes—
100C22×C4×C61C22⋊C411yescharacteristic
101C22×C4×C61C22×C412yes—
102C22×C4×C61C22×C412yes—
103C2×C22⋊D61—216no—
104C2×C22⋊D61—216no—
105C2×C22⋊D61—28no—
106C2×C22⋊D61—28no—
107C2×C22⋊D61—28no—
108C22×Dic61—21no—
109C22×Dic61—21no—
110C22×Dic61—22no—
111C22×Dic61—21no—
112C22×Dic61—21no—
113C22×Dic61—42no—
114C22×Dic61—42no—
115C22×Dic61M1614yescomplemented
116C22×Dic61C22×C412yes—
117C22×Dic61C22×C412yes—
118C22×Dic61C22×C411yescharacteristic
119C22×Dic61C2×D412yes—
120C22×Dic61C2×D412yes—
121C22×Dic61C2411yescharacteristic
122C2×C4×D61—28no—
123C2×C4×D61—44no—
124C2×C4×D61—48no—
125C2×C4×D61—44no—
126C2×C4×D61—44no—
127C2×C4×D61C22⋊C414yes—
128C2×C4×D61C22⋊C414yes—
129C2×C4×D61C2×D414yes—
130C2×C4×D61C2×D414yes—
131C2×#92420—28no—
132C2×#92420—48no—
133#11758213—416no—
134C22⋊Dic61—24no—
135C22⋊Dic61—24no—
136#11758198—28no—
137#11758196—24no—
138#11758196—24no—
139C4×Dic61—24no—
140C4×Dic61—24no—
141C23×C61—22no—
142C23×C61—22no—
143C23×C61—22no—
144C23×C61—22no—
145C23×C61—24no—
146C23×C61—24no—
147C23×C61—42no—
148C23×C61—42no—
149C23×C61—48no—
150C23×C61—42no—
151C23×C61—48no—
152C23×C61—42no—
153C23×C61—42no—
154C23×C61—42no—
155C23×C61C2×C22⋊C411yescharacteristic
156C23×C61C2×C22⋊C411yescharacteristic
157C23×C61C2×M1612yes—
158C23×C61C2×M1612yes—
159C23×C61C2×M1614yescomplemented
160C23×C61C23×C411yescharacteristic
161C22×D61—22no—
162C22×D61—22no—
163C22×D61—24no—
164C22×D61—24no—
165C22×D61—24no—
166C22×D61—24no—
167C22×D61—42no—
168C22×D61—42no—
169C22×D61—42no—
170C22×D61—42no—
171C22×D61—48no—
172C22×D61—48no—
173C22×D61C2×C22⋊C414yes—
174C2×C4×C61—22no—
175C2×C4×C61—24no—
176C2×C4×C61—24no—
177C2×C4×C61—22no—
178C2×C4×C61—48no—
179C2×C4×C61—42no—
180C2×C4×C61—42no—
181C2×C4×C61—48no—
182C2×C4×C61—42no—
183C2×C4×C61#9914yes—
184C2×C4×C61C2×C22⋊C412yes—
185C2×C4×C61C2×C22⋊C412yes—
186C22⋊D61—232no—
187C2×Dic61—22no—
188C2×Dic61—22no—
189C2×Dic61—24no—
190C2×Dic61—24no—
191C2×Dic61—24no—
192C2×Dic61—22no—
193C2×Dic61—41no—
194C2×Dic61—42no—
195C2×Dic61—41no—
196C2×Dic61—42no—
197C2×Dic61—42no—
198C2×Dic61—42no—
199C2×Dic61C2×C22⋊C412yes—
200C2×Dic61C2×M1614yescomplemented
201C2×Dic61C22×D412yes—
202C4×D61—28no—
203C4×D61—28no—
204C4×D61—44no—
205C4×D61—44no—
206#92420—48no—
207C2×#1465—611nomaximal, Sylow
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—21no—
212C22×C61—24no—
213C22×C61—24no—
214C22×C61—24no—
215C22×C61—44no—
216C22×C61—44no—
217C22×C61—48no—
218C22×C61—42no—
219C22×C61—42no—
220C22×C61—48no—
221C22×C61#40712yes—
222C22×C61#40712yes—
223C22×C61C2×#9912yes—
224C22×C61#41312yes—
225C22×C61C22×C22⋊C411yescharacteristic
226C22×C61C22×M1611yescharacteristic
227C22×C61C22×M1611yescharacteristic
228C2×D61—24no—
229C2×D61—24no—
230C2×D61—24no—
231C2×D61—44no—
232C2×D61—44no—
233C2×D61—48no—
234C2×D61—48no—
235C4×C61—22no—
236C4×C61—42no—
237C4×C61C2×#9914yes—
238Dic61—24no—
239Dic61—22no—
240Dic61—22no—
241Dic61—42no—
242C22×C4×D4—611no—
243C2×#407—612no—
244#1465—618no—
245C2×#324—612no—
246C2×#323—612no—
247C2×C61—21no—
248C2×C61—21no—
249C2×C61—22no—
250C2×C61—44no—
251C2×C61#146514yescomplemented
252C2×C61C2×#40711yescharacteristic
253C2×C61C22×#9911yescharacteristic
254C2×C61C2×#41311yescharacteristic
255D61—44no—
256C23×D4—611no—
257C24×C4—611no—
258C24×C4#692311yescharacteristic
259C22×M16—1222no—
260C2×C4×D4—614no—
261C2×C4×D4—614no—
262C2×C4×D4—1222no—
263C2×C4×D4—1222no—
264C2×C4×D4—1224no—
265C22×C4⋊C4—611no—
266C22×C22⋊C4—611no—
267C22×C22⋊C4—611no—
268C22×C42—611no—
269#407—618no—
270#407—1224no—
271C2×C22⋊C8—614no—
272C2×C22⋊C8—1222no—
273#324—618no—
274#323—618no—
275C61C2×#146511yescharacteristic, complemented, Sylow
276C25—611no—
277C25C2×#692311yescharacteristic
278C22×D4—614no—
279C22×D4—1224no—
280C22×D4—1222no—
281C22×D4—1222no—
282C22×D4—1224no—
283C23×C4—22no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—44no—
287C23×C4—611no—
288C23×C4—611no—
289C23×C4—612no—
290C23×C4—612no—
291C23×C4—614no—
292C23×C4—612no—
293C23×C4—612no—
294C23×C4—611no—
295C23×C4—2444no—
296C23×C4C2×#692311yescharacteristic
297C23×C4C2×#692314yes—
298C23×C4C2×#692311yescharacteristic
299C2×M16—1228no—
300C2×M16—2448no—
301C22×C8—1224no—
302C4×D4—1228no—
303C4×D4—1228no—
304C4×D4—1228no—
305C4×D4—1228no—
306C2×C4⋊C4—612no—
307C2×C4⋊C4—612no—
308C2×C4⋊C4—1222no—
309C2×C4⋊C4—1222no—
310C2×C22⋊C4—612no—
311C2×C22⋊C4—612no—
312C2×C22⋊C4—614no—
313C2×C22⋊C4—1222no—
314C2×C22⋊C4—1222no—
315C2×C22⋊C4—1222no—
316C2×C22⋊C4—1222no—
317C2×C42—614no—
318C2×C42—1222no—
319C2×C42—1221no—
320C2×C42—1221no—
321C22⋊C8—618no—
322C22⋊C8—1224no—
323C22⋊C8—1228no—
324C24—21no—
325C24—21no—
326C24—22no—
327C24—42no—
328C24—42no—
329C24—612no—
330C24—612no—
331C24—612no—
332C24—1222no—
333C24—1222no—
334C24—2442no—
335C24—2442no—
336C24#1175821314yescomplemented
337C24C22×#692311yescharacteristic
338C24C22×#692312yes—
339C2×D4—1228no—
340C2×D4—1228no—
341C2×D4—12216no—
342C2×D4—12216no—
343C2×D4—1228no—
344C22×C4—24no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—44no—
350C22×C4—48no—
351C22×C4—48no—
352C22×C4—44no—
353C22×C4—42no—
354C22×C4—612no—
355C22×C4—614no—
356C22×C4—612no—
357C22×C4—612no—
358C22×C4—611no—
359C22×C4—611no—
360C22×C4—614no—
361C22×C4—614no—
362C22×C4—614no—
363C22×C4—614no—
364C22×C4—612no—
365C22×C4—1221no—
366C22×C4—1221no—
367C22×C4—1222no—
368C22×C4—1228no—
369C22×C4—1221no—
370C22×C4—1221no—
371C22×C4—2448no—
372C22×C4—2444no—
373C22×C4—2444no—
374C22×C4—2444no—
375C22×C4—2442no—
376C22×C4—2442no—
377C22×C4C22⋊#692312yes—
378C22×C4C22⋊#692311yescharacteristic
379C22×C4C22⋊#692311yescharacteristic
380C22×C4C22×#692312yes—
381C22×C4C22×#692312yes—
382M16—24416no—
383C2×C8—1228no—
384C2×C8—2448no—
385C4⋊C4—1224no—
386C4⋊C4—1224no—
387C22⋊C4—1228no—
388C22⋊C4—1224no—
389C22⋊C4—1224no—
390C42—1224no—
391C42—1224no—
392C23—22no—
393C23—22no—
394C23—24no—
395C23—24no—
396C23—22no—
397C23—22no—
398C23—42no—
399C23—48no—
400C23—42no—
401C23—42no—
402C23—48no—
403C23—42no—
404C23—42no—
405C23—42no—
406C23—614no—
407C23—1224no—
408C23—1224no—
409C23—1224no—
410C23—1224no—
411C23—1222no—
412C23—1222no—
413C23—2442no—
414C23—2442no—
415C23—2442no—
416C23—2442no—
417C23—2448no—
418C23—2448no—
419C23C2×C22⋊#692311yescharacteristic
420C23C2×C22⋊#692311yescharacteristic
421C23D61⋊M1612yes—
422C23C2×#1175821312yes—
423C23C2×#1175821314yescomplemented
424C23C23×#692311yescharacteristic
425D4—12232no—
426C2×C4—22no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—22no—
430C2×C4—48no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—48no—
434C2×C4—42no—
435C2×C4—612no—
436C2×C4—612no—
437C2×C4—614no—
438C2×C4—1224no—
439C2×C4—1224no—
440C2×C4—1224no—
441C2×C4—1222no—
442C2×C4—1222no—
443C2×C4—1228no—
444C2×C4—1228no—
445C2×C4—1222no—
446C2×C4—2444no—
447C2×C4—2444no—
448C2×C4—2441no—
449C2×C4—2442no—
450C2×C4—2441no—
451C2×C4—2442no—
452C2×C4—2442no—
453C2×C4—2442no—
454C2×C4#1451983514yes—
455C2×C4C2×C22⋊#692312yes—
456C2×C4C2×C22⋊#692312yes—
457C8—2448no—
458C22—24no—
459C22—24no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—24no—
465C22—44no—
466C22—48no—
467C22—44no—
468C22—48no—
469C22—42no—
470C22—42no—
471C22—1224no—
472C22—1224no—
473C22—1224no—
474C22—2448no—
475C22—2444no—
476C22—2444no—
477C22—2448no—
478C22#1684073312yes—
479C22#1684073312yes—
480C22C2×#1451983512yes—
481C22#1684074812yes—
482C22C22×C22⋊#692311yescharacteristic
483C22C2×D61⋊M1611yescharacteristic
484C22C22×#1175821311yescharacteristic
485C4—22no—
486C4—42no—
487C4—1224no—
488C4—1222no—
489C4—1222no—
490C4—2442no—
491C4C2×#1451983514yes—
492C2—22no—
493C2—21no—
494C2—21no—
495C2—44no—
496C2—2444no—
497C2#2146107414yesdirect product factor
498C2C2×#1684073311yescharacteristic
499C2C22×#1451983511yescharacteristic
500C2C2×#1684074811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC24×C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×C22⋊D61C4
cosocleC22×Dic61C24
hypercenterC24×C4#6923
hypocenterC61C2×#1465
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
1. C2×#16840733C2semidirect
2. #21461074C2direct (N × H)
3. C2×#16840608C2semidirect
4. C2×#16840605C2semidirect
8. #16840733C22semidirect
11. #16840608C22semidirect
12. #16840605C22semidirect
78. C24×C61M16semidirect
115. C22×Dic61M16semidirect
159. C23×C61C2×M16semidirect
200. C2×Dic61C2×M16semidirect
251. C2×C61#1465semidirect
275. C61C2×#1465semidirect
336. C24#11758213semidirect
423. C23C2×#11758213semidirect
497. C2#21461074direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407332
#214610742
C2×#168406082
C2×#168406052
C22×C4×C22⋊D612
C2×#146561