Finite Group Databasebeta

← C2×#21462112 #30624005

Subgroups — C2×#21462112 #30624005

Order 15616.

1306 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840748C212yesmaximal, complemented
2#21462112C218yesmaximal, direct product factor
3C2×#16840673C212yesmaximal, complemented
4C2×#16840671C212yesmaximal, complemented
5C2×#16840312C211yesmaximal, characteristic
6C2×D61⋊M16—22no—
7#16840748—24no—
8#16840748C2218yescomplemented
9C2×#14519838C2214yes—
10C2×#14519837—22no—
11#16840673C2218yescomplemented
12#16840671C2218yescomplemented
13C22×#11758222C411yescharacteristic
14C22×#11758222C2211yescharacteristic
15#16840312—24no—
16#16840312C414yes—
17#16840312C2214yes—
18C2×#14519777C2211yescharacteristic
19C2×#14519774C411yescharacteristic
20C2×#14519765C411yescharacteristic
21C2×#14519765C2211yescharacteristic
22C2×#14519751—22no—
23C2×C4×D244—22no—
24C22×C42×C61C411yescharacteristic
25C2×#11758213—42no—
26D61⋊M16—28no—
27D61⋊M16—44no—
28C2×#11758217—24no—
29C2×D61⋊C8—42no—
30#14519838—24no—
31#14519838C2318yes—
32#14519837—28no—
33C2×#11758222—22no—
34C2×#11758222—41no—
35C2×#11758222—42no—
36C2×#11758222—41no—
37C2×#11758222—42no—
38C2×#11758222—41no—
39C2×#11758222—41no—
40C2×#11758222C2×C414yes—
41C2×#11758222C2×C412yes—
42C2×#11758222D414yes—
43C2×#11758222C2312yes—
44C22×Dic122C2×C411yescharacteristic
45C22×Dic122C2311yescharacteristic
46C22×D244—22no—
47C22×D244C2×C411yescharacteristic
48C22×D244C2×C411yescharacteristic
49C22×C22⋊D61—21no—
50C22×C22⋊D61D412yes—
51C22×C4×D61—21no—
52C22×C4×D61D412yes—
53#14519777—22no—
54#14519777C2×C412yes—
55#14519777C2312yes—
56#14519774—22no—
57#14519774C2×C414yes—
58#14519765—22no—
59#14519765—22no—
60#14519765C2×C414yes—
61#14519765C2×C412yes—
62#14519765C2312yes—
63#14519751—28no—
64#14519751—28no—
65C4×D244—28no—
66C4×D244—28no—
67C2×C4⋊Dic61—22no—
68C2×#11758198—22no—
69C2×#11758198—22no—
70C23×C4×C61—21no—
71C23×C4×C61C2×C411yescharacteristic
72C2×C42×C61—21no—
73C2×C42×C61—22no—
74C2×C42×C61C2×C411yescharacteristic
75C2×C42×C61C2×C411yescharacteristic
76C2×C42×C61C2×C414yes—
77C24×C61C22⋊C411yescharacteristic
78C23×D61—21no—
79C23×D61C22⋊C412yes—
80C22×C4×C61—21no—
81C22×C4×C61—22no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—24no—
86C22×C4×C61—44no—
87C22×C4×C61C22⋊C412yes—
88C22×C4×C61C22⋊C411yescharacteristic
89C22×C4×C61C22×C411yescharacteristic
90C22×C4×C61C22×C412yes—
91C2×C22⋊D61—24no—
92C2×C22⋊D61—42no—
93C2×C22⋊D61—42no—
94C2×C22⋊D61—42no—
95C2×C22⋊D61—42no—
96C2×C22⋊D61C22⋊C414yes—
97C2×C22⋊D61C2×D414yes—
98C22×Dic61—21no—
99C22×Dic61C2×D412yes—
100#11758222—42no—
101#11758222—42no—
102#11758222—44no—
103#11758222—44no—
104#11758222—42no—
105#11758222—42no—
106#11758222—44no—
107#11758222—44no—
108#11758222—44no—
109#11758222—44no—
110C2×D244—28no—
111C2×D244—21no—
112C2×D244—41no—
113C2×D244—41no—
114C2×D244—48no—
115C2×D244—41no—
116C2×D244—41no—
117C2×D244C22⋊C412yes—
118C2×D244C22×C412yes—
119C2×D244C22×C412yes—
120C2×C4×D61—22no—
121C2×C4×D61—24no—
122C2×C4×D61—22no—
123C2×C4×D61—24no—
124C2×C4×D61—42no—
125C2×C4×D61—41no—
126C2×C4×D61—41no—
127C2×C4×D61C22⋊C414yes—
128C2×C4×D61C2×D414yes—
129C2×Dic122—21no—
130C2×Dic122—41no—
131C2×Dic122—41no—
132C2×Dic122—41no—
133C2×Dic122—41no—
134C2×Dic122C22×C412yes—
135C2×Dic122C22×C411yescharacteristic
136C2×Dic122C2×D412yes—
137C2×Dic122C2411yescharacteristic
138#11758217—28no—
139#11758217—44no—
140C2×#92420—44no—
141#11758213—48no—
142D61⋊C8—48no—
143C42×C61—24no—
144C42×C61—21no—
145C42×C61—21no—
146C42×C61C22×C412yes—
147C42×C61C22×C412yes—
148#11758198—28no—
149#11758198—24no—
150#11758198—24no—
151C4⋊Dic61—24no—
152C4⋊Dic61—24no—
153C23×C61—21no—
154C23×C61—21no—
155C23×C61—42no—
156C23×C61C2×C22⋊C411yescharacteristic
157C23×C61C2×C22⋊C412yes—
158C22×D61—22no—
159C22×D61—22no—
160C22×D61—22no—
161C22×D61—44no—
162C22×D61—44no—
163C22×D61—41no—
164C22×D61—41no—
165C22×D61C2×C22⋊C414yes—
166C2×C4×C61—24no—
167C2×C4×C61—22no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—22no—
171C2×C4×C61—22no—
172C2×C4×C61—22no—
173C2×C4×C61—22no—
174C2×C4×C61—22no—
175C2×C4×C61—48no—
176C2×C4×C61—42no—
177C2×C4×C61#9912yes—
178C2×C4×C61#9911yescharacteristic
179C2×C4×C61#9911yescharacteristic
180C2×C4×C61C2×C22⋊C411yescharacteristic
181C2×C4×C61C2×C22⋊C412yes—
182C2×C4×C61C23×C411yescharacteristic
183C22⋊D61—44no—
184C22⋊D61—44no—
185C22⋊D61—48no—
186C2×Dic61—22no—
187C2×Dic61—22no—
188C2×Dic61—22no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61C2×C22⋊C412yes—
192C2×Dic61C22×D412yes—
193D244—42no—
194D244—42no—
195D244—42no—
196D244—416no—
197D244—42no—
198C4×D61—24no—
199C4×D61—24no—
200C4×D61—24no—
201C4×D61—24no—
202C4×D61—44no—
203C4×D61—44no—
204Dic122—41no—
205Dic122—42no—
206Dic122—41no—
207Dic122—42no—
208Dic122—42no—
209#92420—48no—
210C2×#2132—611nomaximal, Sylow
211C22×C61—22no—
212C22×C61—22no—
213C22×C61—42no—
214C22×C61—42no—
215C22×C61—42no—
216C22×C61C2×#9911yescharacteristic
217C22×C61C2×#9911yescharacteristic
218C22×C61C22×C22⋊C411yescharacteristic
219C2×D61—24no—
220C2×D61—44no—
221C2×D61—44no—
222C2×D61—44no—
223C2×D61—42no—
224C2×D61—82no—
225C2×D61—82no—
226C2×D61—82no—
227C4×C61—24no—
228C4×C61—21no—
229C4×C61—21no—
230C4×C61—42no—
231C4×C61C2×#9912yes—
232C4×C61C2×#9912yes—
233Dic61—22no—
234Dic61—22no—
235Dic61—42no—
236C2×#532—611no—
237C2×#413—612no—
238#2132—618no—
239C2×#356—612no—
240C2×#355—612no—
241C2×C61—21no—
242C2×C61—21no—
243C2×C61—42no—
244C2×C61#213212yescomplemented
245C2×C61C22×#9911yescharacteristic
246D61—44no—
247D61—82no—
248C22×#41—611no—
249C22×#41—611no—
250C22×M16—1222no—
251#532—614no—
252#532—614no—
253#532—1224no—
254C2×C4⋊Q8—611no—
255C2×#127—611no—
256C2×#124—611no—
257C2×#124—611no—
258C2×#121—1222no—
259C2×C4×D4—1222no—
260C22×C42#692311yescharacteristic
261#413—618no—
262#413—1224no—
263C2×#101—614no—
264C2×#100—1222no—
265#356—618no—
266#355—618no—
267C61C2×#213211yescharacteristic, complemented, Sylow
268C2×#41—614no—
269C2×#41—612no—
270C2×#41—612no—
271C2×#41—614no—
272C2×#41—1222no—
273C2×#41—2441no—
274C2×#41—2442no—
275C2×#41—2441no—
276C2×#41—2442no—
277C2×#41—2441no—
278C2×#41—2441no—
279C22×Q8—611no—
280C22×Q8—611no—
281C22×D4—612no—
282C22×D4—611no—
283C22×D4—611no—
284C22×D4—1222no—
285C22×D4—1221no—
286C23×C4—21no—
287C23×C4—612no—
288C23×C4—1221no—
289C23×C4C2×#692311yescharacteristic
290C2×M16—1224no—
291C2×M16—1228no—
292C2×M16—2444no—
293C2×M16—2442no—
294C22×C8—2442no—
295C4⋊Q8—612no—
296C4⋊Q8—612no—
297C4⋊Q8—1222no—
298#127—614no—
299#127—1222no—
300#124—612no—
301#124—612no—
302#124—614no—
303#124—1222no—
304#124—1222no—
305#121—1228no—
306#121—1228no—
307C4×D4—1228no—
308C4×D4—1228no—
309C2×C4⋊C4—1222no—
310C2×C22⋊C4—1222no—
311C2×C22⋊C4—1222no—
312C2×C42—22no—
313C2×C42—21no—
314C2×C42C2×#692311yescharacteristic
315C2×C42C2×#692311yescharacteristic
316C2×C42C2×#692314yes—
317#101—618no—
318#101—1224no—
319#100—1228no—
320C24—612no—
321C24—1221no—
322C24C22⋊#692311yescharacteristic
323#41—2444no—
324#41—2444no—
325#41—2442no—
326#41—2442no—
327#41—2442no—
328#41—2442no—
329#41—2444no—
330#41—2444no—
331#41—2444no—
332#41—2444no—
333C2×Q8—612no—
334C2×Q8—611no—
335C2×Q8—611no—
336C2×Q8—612no—
337C2×Q8—1221no—
338C2×Q8—2441no—
339C2×Q8—2441no—
340C2×Q8—2441no—
341C2×Q8—2441no—
342C2×D4—614no—
343C2×D4—614no—
344C2×D4—612no—
345C2×D4—612no—
346C2×D4—612no—
347C2×D4—1228no—
348C2×D4—1224no—
349C2×D4—1221no—
350C2×D4—2441no—
351C2×D4—2441no—
352C2×D4—2441no—
353C2×D4—2441no—
354C2×D4—2448no—
355C2×D4—2442no—
356C2×D4—2442no—
357C2×D4—2442no—
358C2×D4—2442no—
359C22×C4—21no—
360C22×C4—22no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—24no—
365C22×C4—44no—
366C22×C4—612no—
367C22×C4—614no—
368C22×C4—614no—
369C22×C4—1222no—
370C22×C4—1224no—
371C22×C4—1222no—
372C22×C4—1221no—
373C22×C4—1224no—
374C22×C4—2442no—
375C22×C4—2441no—
376C22×C4—2441no—
377C22×C4C22⋊#692312yes—
378C22×C4C22⋊#692311yescharacteristic
379C22×C4C22×#692311yescharacteristic
380C22×C4C22×#692312yes—
381M16—1228no—
382M16—2448no—
383M16—2444no—
384C2×C8—2448no—
385C2×C8—2444no—
386C4⋊C4—1224no—
387C4⋊C4—1224no—
388C22⋊C4—1224no—
389C22⋊C4—1224no—
390C22⋊C4—1228no—
391C42—24no—
392C42—21no—
393C42—21no—
394C42C22×#692312yes—
395C42C22×#692312yes—
396C23—21no—
397C23—21no—
398C23—42no—
399C23—614no—
400C23—1222no—
401C23—1222no—
402C23—1222no—
403C23—2444no—
404C23—2444no—
405C23—2441no—
406C23—2441no—
407C23C2×C22⋊#692311yescharacteristic
408C23C2×C22⋊#692312yes—
409Q8—2442no—
410Q8—2441no—
411Q8—2441no—
412Q8—2442no—
413Q8—2442no—
414D4—2442no—
415D4—2442no—
416D4—2442no—
417D4—24416no—
418D4—2442no—
419D4—2444no—
420D4—2444no—
421D4—2448no—
422C2×C4—24no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—48no—
432C2×C4—42no—
433C2×C4—612no—
434C2×C4—612no—
435C2×C4—1222no—
436C2×C4—1222no—
437C2×C4—1224no—
438C2×C4—1224no—
439C2×C4—1224no—
440C2×C4—1224no—
441C2×C4—1222no—
442C2×C4—2441no—
443C2×C4—2441no—
444C2×C4—2444no—
445C2×C4—2444no—
446C2×C4#1451983611yescharacteristic
447C2×C4#1451983612yes—
448C2×C4#1451983611yescharacteristic
449C2×C4C2×C22⋊#692311yescharacteristic
450C2×C4C2×C22⋊#692312yes—
451C2×C4C23×#692311yescharacteristic
452C8—2448no—
453C22—22no—
454C22—22no—
455C22—42no—
456C22—42no—
457C22—42no—
458C22—1224no—
459C22—4882no—
460C22—4882no—
461C22—4882no—
462C22—2444no—
463C22—2444no—
464C22—2442no—
465C22—2444no—
466C22C2×#1451983611yescharacteristic
467C22C2×#1451983611yescharacteristic
468C22C22×C22⋊#692311yescharacteristic
469C4—24no—
470C4—21no—
471C4—21no—
472C4—42no—
473C4—1222no—
474C4—1222no—
475C4—2442no—
476C4C2×#1451983612yes—
477C4C2×#1451983612yes—
478C2—21no—
479C2—21no—
480C2—42no—
481C2—4882no—
482C2—2444no—
483C2#2146211212yesdirect product factor
484C2C22×#1451983611yescharacteristic
subgroupG/H
centerC2×C4#14519836
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC22×C42×C61C4
socleC22×C61C2×#99
prime radicalC2×#16840312C2
cosocleC2×Dic122C24
hypercenterC22×C42#6923
hypocenterC61C2×#2132
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. C2×#16840748C2semidirect
2. #21462112C2direct (N × H)
3. C2×#16840673C2semidirect
4. C2×#16840671C2semidirect
8. #16840748C22semidirect
11. #16840673C22semidirect
12. #16840671C22semidirect
244. C2×C61#2132semidirect
267. C61C2×#2132semidirect
483. C2#21462112direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407482
#214621122
C2×#168406732
C2×#168406712
C2×#168403122
C2×#213261