Finite Group Databasebeta

← C2×#21461056 #30609899

Subgroups — C2×#21461056 #30609899

Order 15616.

1826 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×D61⋊(C22⋊C8)C212yesmaximal, complemented
2#21461056C218yesmaximal, direct product factor
3C2×#16840607C212yesmaximal, complemented
4C2×#16840606C212yesmaximal, complemented
5C22×C4×D244C211yesmaximal, characteristic
6C22×D61⋊C8—22no—
7C2×#14519834—22no—
8D61⋊(C22⋊C8)—24no—
9D61⋊(C22⋊C8)C2218yescomplemented
10C2×C22⋊#92420C2214yes—
11#16840607C2218yescomplemented
12#16840606C2218yescomplemented
13C23×D244C411yescharacteristic
14C23×C4×D61C411yescharacteristic
15C23×C4×D61C2211yescharacteristic
16C2×C4×D244—22no—
17C2×C4×D244—24no—
18C2×C4×D244—22no—
19C2×C4×D244C414yes—
20C2×C4×D244C2214yes—
21C22×C4⋊Dic61C2211yescharacteristic
22C22×#11758198C411yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×C42×C61C411yescharacteristic
25C2×D61⋊C8—28no—
26C2×D61⋊C8—48no—
27C22×#92420—24no—
28#14519834—28no—
29C22⋊#92420—24no—
30C22⋊#92420C2318yes—
31C24×D61C2×C411yescharacteristic
32C24×D61C2×C411yescharacteristic
33C22×D244—22no—
34C22×D244—22no—
35C22×D244—24no—
36C22×D244C818yescomplemented
37C22×D244C2×C414yes—
38C23×Dic61C2×C411yescharacteristic
39C23×Dic61C2311yescharacteristic
40C22×C4×D61—21no—
41C22×C4×D61—22no—
42C22×C4×D61—21no—
43C22×C4×D61—44no—
44C22×C4×D61—44no—
45C22×C4×D61C2×C414yes—
46C22×C4×D61C2×C412yes—
47C22×C4×D61D412yes—
48C22×C4×D61D414yes—
49C22×C4×D61D412yes—
50C22×C4×D61C2312yes—
51C4×D244—28no—
52C4×D244—28no—
53C4×D244—28no—
54C4×D244—28no—
55C2×C4⋊Dic61—22no—
56C2×C4⋊Dic61—22no—
57C2×C4⋊Dic61C2×C412yes—
58C2×C4⋊Dic61C2312yes—
59C2×#11758198—22no—
60C2×#11758198—22no—
61C2×#11758198—22no—
62C2×#11758198—22no—
63C2×#11758198C2×C414yes—
64C2×#11758198C2×C412yes—
65C2×#11758198C2312yes—
66C23×C4×C61C2×C411yescharacteristic
67C23×C4×C61C2×C411yescharacteristic
68C23×C4×C61C2×C411yescharacteristic
69C2×C42×C61—21no—
70C2×C42×C61—22no—
71C2×C42×C61—21no—
72C2×C42×C61C2×C414yes—
73C24×C61C22×C411yescharacteristic
74C23×D61—21no—
75C23×D61—21no—
76C23×D61—22no—
77C23×D61—42no—
78C23×D61—42no—
79C23×D61—42no—
80C23×D61—42no—
81C23×D61C22⋊C412yes—
82C23×D61C22⋊C412yes—
83C23×D61C2×C814yes—
84C23×D61C2×C814yescomplemented
85C23×D61M1614yes—
86C23×D61C22×C412yes—
87C23×D61C22×C412yes—
88C22×C4×C61—21no—
89C22×C4×C61—21no—
90C22×C4×C61—22no—
91C22×C4×C61—24no—
92C22×C4×C61—21no—
93C22×C4×C61—21no—
94C22×C4×C61—42no—
95C22×C4×C61C22⋊C411yescharacteristic
96C22×C4×C61C22⋊C412yes—
97C22×C4×C61C22⋊C411yescharacteristic
98C22×C4×C61C2×C814yescomplemented
99C22×C4×C61C22×C412yes—
100C22×C4×C61C22×C412yes—
101C22×C4×C61C22×C412yes—
102C22×Dic61—21no—
103C22×Dic61—21no—
104C22×Dic61—42no—
105C22×Dic61—42no—
106C22×Dic61C22×C412yes—
107C22×Dic61C22×C411yescharacteristic
108C22×Dic61C2×D412yes—
109C22×Dic61C2×D412yes—
110C22×Dic61C2411yescharacteristic
111C2×D244—216no—
112C2×D244—216no—
113C2×D244—28no—
114C2×D244—28no—
115C2×D244C2×C8116yescomplemented
116C2×C4×D61—28no—
117C2×C4×D61—24no—
118C2×C4×D61—24no—
119C2×C4×D61—44no—
120C2×C4×D61—48no—
121C2×C4×D61—44no—
122C2×C4×D61—44no—
123C2×C4×D61—44no—
124C2×C4×D61—48no—
125C2×C4×D61—44no—
126C2×C4×D61—48no—
127C2×C4×D61C22⋊C414yes—
128C2×C4×D61C22⋊C414yes—
129C2×C4×D61C2×D414yes—
130C2×C4×D61C2×D414yes—
131C2×#92420—28no—
132C2×#92420—48no—
133D61⋊C8—416no—
134C42×C61—24no—
135C42×C61—24no—
136#11758198—28no—
137#11758198—24no—
138#11758198—24no—
139C4⋊Dic61—24no—
140C4⋊Dic61—24no—
141C23×C61—22no—
142C23×C61—22no—
143C23×C61C2×C22⋊C411yescharacteristic
144C23×C61C2×C22⋊C411yescharacteristic
145C23×C61C22×C812yes—
146C23×C61C2×M1612yes—
147C23×C61C23×C411yescharacteristic
148C22×D61—24no—
149C22×D61—24no—
150C22×D61—22no—
151C22×D61—22no—
152C22×D61—24no—
153C22×D61—24no—
154C22×D61—42no—
155C22×D61—42no—
156C22×D61—42no—
157C22×D61—48no—
158C22×D61—48no—
159C22×D61—42no—
160C22×D61—42no—
161C22×D61—42no—
162C22×D61—48no—
163C22×D61—42no—
164C22×D61—42no—
165C22×D61—42no—
166C22×D61—48no—
167C22×D61—42no—
168C22×D61C22⋊C818yes—
169C22×D61C22⋊C818yes—
170C22×D61C2×C22⋊C414yes—
171C22×D61C22×C814yes—
172C22×D61C22×C814yescomplemented
173C22×D61C2×M1614yes—
174C2×C4×C61—22no—
175C2×C4×C61—22no—
176C2×C4×C61—24no—
177C2×C4×C61—24no—
178C2×C4×C61—22no—
179C2×C4×C61—24no—
180C2×C4×C61—24no—
181C2×C4×C61—22no—
182C2×C4×C61—42no—
183C2×C4×C61—42no—
184C2×C4×C61—42no—
185C2×C4×C61#9914yes—
186C2×C4×C61C2×C22⋊C412yes—
187C2×C4×C61C2×C22⋊C412yes—
188C2×C4×C61C22×C814yescomplemented
189C2×Dic61—24no—
190C2×Dic61—22no—
191C2×Dic61—41no—
192C2×Dic61—42no—
193C2×Dic61—41no—
194C2×Dic61—42no—
195C2×Dic61—42no—
196C2×Dic61—42no—
197C2×Dic61C2×C22⋊C412yes—
198C2×Dic61C22×D412yes—
199D244—232no—
200C4×D61—28no—
201C4×D61—28no—
202C4×D61—44no—
203C4×D61—44no—
204C4×D61—48no—
205C4×D61—48no—
206#92420—48no—
207C2×#1459—611nomaximal, Sylow
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—21no—
212C22×C61—24no—
213C22×C61—24no—
214C22×C61C2×C22⋊C812yes—
215C22×C61C2×C22⋊C812yes—
216C22×C61C2×#9912yes—
217C22×C61#41312yes—
218C22×C61C22×C22⋊C411yescharacteristic
219C22×C61C23×C811yescharacteristic
220C22×C61C22×M1611yescharacteristic
221C2×D61—24no—
222C2×D61—24no—
223C2×D61—216no—
224C2×D61—24no—
225C2×D61—48no—
226C2×D61—44no—
227C2×D61—44no—
228C2×D61—44no—
229C2×D61—48no—
230C2×D61—42no—
231C2×D61—42no—
232C2×D61—48no—
233C2×D61—44no—
234C2×D61C2×C22⋊C818yes—
235C4×C61—24no—
236C4×C61—22no—
237C4×C61—42no—
238C4×C61C2×#9914yes—
239Dic61—22no—
240Dic61—22no—
241Dic61—42no—
242C22×C4×D4—611no—
243C22×C22⋊C8—612no—
244#1459—618no—
245C2×#324—612no—
246C2×#323—612no—
247C2×C61—21no—
248C2×C61—21no—
249C2×C61—22no—
250C2×C61#145914yescomplemented
251C2×C61C22×C22⋊C811yescharacteristic
252C2×C61C22×#9911yescharacteristic
253C2×C61C2×#41311yescharacteristic
254D61—28no—
255D61—44no—
256C23×D4—611no—
257C24×C4—611no—
258C24×C4—611no—
259C23×C8—1222no—
260C2×C4×D4—614no—
261C2×C4×D4—614no—
262C2×C4×D4—1222no—
263C2×C4×D4—1224no—
264C2×C4×D4—1222no—
265C22×C4⋊C4—611no—
266C22×C22⋊C4—611no—
267C22×C22⋊C4—611no—
268C22×C42#692311yescharacteristic
269C2×C22⋊C8—614no—
270C2×C22⋊C8—618no—
271C2×C22⋊C8—1224no—
272C2×C22⋊C8—1222no—
273#324—618no—
274#323—618no—
275C61C2×#145911yescharacteristic, complemented, Sylow
276C25—611no—
277C25—611no—
278C22×D4—618no—
279C22×D4—614no—
280C22×D4—1222no—
281C22×D4—1222no—
282C22×D4—1224no—
283C23×C4—611no—
284C23×C4—612no—
285C23×C4—612no—
286C23×C4—614no—
287C23×C4—612no—
288C23×C4—612no—
289C23×C4—611no—
290C23×C4—614no—
291C23×C4—1222no—
292C23×C4—1221no—
293C23×C4—1221no—
294C23×C4—2444no—
295C23×C4—2444no—
296C23×C4C2×#692311yescharacteristic
297C23×C4C2×#692311yescharacteristic
298C23×C4C2×#692311yescharacteristic
299C22×C8—1224no—
300C22×C8—1228no—
301C22×C8—2448no—
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—21no—
318C2×C42—22no—
319C2×C42—21no—
320C2×C42C2×#692314yes—
321C22⋊C8—618no—
322C22⋊C8—1224no—
323C22⋊C8—1228no—
324C24—612no—
325C24—612no—
326C24—614no—
327C24—614no—
328C24—612no—
329C24—614no—
330C24—612no—
331C24—1221no—
332C24—1221no—
333C24—1222no—
334C24—2442no—
335C24—2442no—
336C24—2442no—
337C24—2442no—
338C24C22×#692311yescharacteristic
339C2×D4—6116no—
340C2×D4—1228no—
341C2×D4—12216no—
342C2×D4—12216no—
343C2×D4—1228no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—22no—
347C22×C4—24no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—42no—
351C22×C4—612no—
352C22×C4—612no—
353C22×C4—611no—
354C22×C4—611no—
355C22×C4—614no—
356C22×C4—614no—
357C22×C4—614no—
358C22×C4—614no—
359C22×C4—612no—
360C22×C4—1228no—
361C22×C4—1221no—
362C22×C4—1221no—
363C22×C4—1224no—
364C22×C4—1224no—
365C22×C4—2448no—
366C22×C4—2444no—
367C22×C4—2444no—
368C22×C4—2444no—
369C22×C4—2444no—
370C22×C4—2448no—
371C22×C4—2448no—
372C22×C4—2442no—
373C22×C4—2444no—
374C22×C4—2442no—
375C22×C4D61⋊C814yescomplemented
376C22×C4C22⋊#692311yescharacteristic
377C22×C4C22⋊#692312yes—
378C22×C4C22⋊#692311yescharacteristic
379C22×C4C22×#692312yes—
380C22×C4C22×#692312yes—
381C22×C4C22×#692312yes—
382C2×C8—1228no—
383C2×C8—24416no—
384C2×C8—2448no—
385C4⋊C4—1224no—
386C4⋊C4—1224no—
387C22⋊C4—1224no—
388C22⋊C4—1224no—
389C22⋊C4—1228no—
390C42—24no—
391C42—24no—
392C23—22no—
393C23—22no—
394C23—618no—
395C23—614no—
396C23—618no—
397C23—614no—
398C23—614no—
399C23—614no—
400C23—1224no—
401C23—1224no—
402C23—1224no—
403C23—1224no—
404C23—1222no—
405C23—1222no—
406C23—2442no—
407C23—2442no—
408C23—2448no—
409C23—2448no—
410C23—2442no—
411C23—2442no—
412C23—2442no—
413C23—2448no—
414C23—2442no—
415C23—2442no—
416C23—2448no—
417C23—2442no—
418C23—2442no—
419C23—2442no—
420C23C2×C22⋊#692311yescharacteristic
421C23C2×C22⋊#692311yescharacteristic
422C23C2×D61⋊C812yes—
423C23D61⋊M1612yes—
424C23C23×#692311yescharacteristic
425D4—12232no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—22no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—612no—
438C2×C4—612no—
439C2×C4—1224no—
440C2×C4—1228no—
441C2×C4—1228no—
442C2×C4—1222no—
443C2×C4—2444no—
444C2×C4—2444no—
445C2×C4—2448no—
446C2×C4—2441no—
447C2×C4—2442no—
448C2×C4—2441no—
449C2×C4—2442no—
450C2×C4—2442no—
451C2×C4—2448no—
452C2×C4—2442no—
453C2×C4#1451983614yes—
454C2×C4C2×C22⋊#692312yes—
455C2×C4C2×C22⋊#692312yes—
456C2×C4C2×D61⋊C814yescomplemented
457C8—2448no—
458C22—24no—
459C22—24no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—618no—
465C22—12216no—
466C22—1224no—
467C22—1224no—
468C22—1224no—
469C22—2448no—
470C22—2444no—
471C22—2444no—
472C22—2444no—
473C22—2448no—
474C22—2444no—
475C22—2448no—
476C22—2442no—
477C22—2442no—
478C22D61⋊(C22⋊C8)12yes—
479C22D61⋊(C22⋊C8)12yes—
480C22C2×#1451983612yes—
481C22#1684074812yes—
482C22C22×C22⋊#692311yescharacteristic
483C22C22×D61⋊C811yescharacteristic
484C22C2×D61⋊M1611yescharacteristic
485C4—24no—
486C4—22no—
487C4—42no—
488C4—1222no—
489C4—1222no—
490C4—2442no—
491C4C2×#1451983614yes—
492C2—22no—
493C2—21no—
494C2—21no—
495C2—1228no—
496C2—2444no—
497C2#2146105614yesdirect product factor
498C2C2×D61⋊(C22⋊C8)11yescharacteristic
499C2C22×#1451983611yescharacteristic
500C2C2×#1684074811yescharacteristic
subgroupG/H
centerC22×C4C22⋊#6923
commutatorC22×C61C23×C8
FrattiniC23C23×#6923
FittingC22×C42×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D244C4
cosocleC22×Dic61C24
hypercenterC22×C42#6923
hypocenterC61C2×#1459
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. C2×D61⋊(C22⋊C8)C2semidirect
2. #21461056C2direct (N × H)
3. C2×#16840607C2semidirect
4. C2×#16840606C2semidirect
9. D61⋊(C22⋊C8)C22semidirect
11. #16840607C22semidirect
12. #16840606C22semidirect
36. C22×D244C8semidirect
84. C23×D61C2×C8semidirect
98. C22×C4×C61C2×C8semidirect
115. C2×D244C2×C8semidirect
172. C22×D61C22×C8semidirect
188. C2×C4×C61C22×C8semidirect
250. C2×C61#1459semidirect
275. C61C2×#1459semidirect
375. C22×C4D61⋊C8semidirect
456. C2×C4C2×D61⋊C8semidirect
497. C2#21461056direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D61⋊(C22⋊C8)2
#214610562
C2×#168406072
C2×#168406062
C22×C4×D2442
C2×#145961