Finite Group Databasebeta

← C2×#21461198 #30610909

Subgroups — C2×#21461198 #30610909

Order 15616.

1474 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840780C211yesmaximal, characteristic, complemented
2C2×C4×C4⋊#6923C211yesmaximal, characteristic, complemented
3#21461198C218yesmaximal, direct product factor
4C2×#16840614C212yesmaximal, complemented
5C2×#16840613C212yesmaximal, complemented
6C2×#16840309C211yesmaximal, characteristic
7C22×C4⋊#6923—21no—
8C22×C4×#6923—21no—
9#16840780—22no—
10#16840780C2214yescomplemented
11C2×#14519844—21no—
12C2×#14519834C2212yes—
13C2×C4×#92420—21no—
14C4×C4⋊#6923—22no—
15C4×C4⋊#6923C2214yescomplemented
16C2×(C2×#6923)⋊C4C2212yes—
17#16840614C2218yescomplemented
18#16840613C2218yescomplemented
19C22×#11758222—21no—
20#16840309—22no—
21#16840309—22no—
22#16840309C414yescomplemented
23#16840309C2214yes—
24C2×#14519776C411yescharacteristic, complemented
25C2×#14519773C411yescharacteristic, complemented
26C2×#14519763—21no—
27C2×#14519752C2211yescharacteristic
28C2×#14519750—21no—
29C2×#14519748C2211yescharacteristic
30C2×C4×D244C411yescharacteristic, complemented
31C2×C4×C22⋊D61—21no—
32C2×C42×D61C2211yescharacteristic
33C2×C4×D4×C61C411yescharacteristic, complemented
34C23×#6923—22no—
35C22×#92420—22no—
36C2×C4⋊#6923—28no—
37C2×C4⋊#6923—24no—
38C2×C4×#6923—24no—
39C2×C4×#6923—44no—
40#14519844—24no—
41#14519834—22no—
42#14519834C2314yes—
43C4×#92420—24no—
44(C2×#6923)⋊C4—22no—
45(C2×#6923)⋊C4C2314yes—
46C2×#11758222—24no—
47C2×#11758222—24no—
48C2×#11758222—44no—
49C2×#11758222—44no—
50C22×Dic122—21no—
51C22×D244—21no—
52C22×D244C2×C411yescharacteristic
53C22×C22⋊D61—21no—
54C22×C22⋊D61—21no—
55C22×C22⋊D61—21no—
56C22×C4×D61—21no—
57C22×C4×D61D411yescharacteristic
58C22×C4×D61D411yescharacteristic
59C22×C4×D61C2311yescharacteristic
60#14519776—22no—
61#14519776C2×C414yescomplemented
62#14519773—22no—
63#14519773C2×C414yescomplemented
64#14519763—24no—
65#14519763—24no—
66#14519752—21no—
67#14519752—21no—
68#14519752C2×C412yes—
69#14519752C2312yes—
70#14519750—24no—
71#14519750—24no—
72#14519748—21no—
73#14519748—21no—
74#14519748C2×C412yes—
75#14519748C2312yes—
76C4×D244—22no—
77C4×D244C2×C414yescomplemented
78C4×C22⋊D61—24no—
79C4×C22⋊D61—24no—
80C2×C4⋊Dic61C2×C411yescharacteristic
81C2×#11758196—21no—
82C2×C22⋊Dic61—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×C4×Dic61C2×C411yescharacteristic
86C2×C4×Dic61D411yescharacteristic
87C2×C4×Dic61D411yescharacteristic
88C42×D61C2×C412yes—
89C42×D61D412yes—
90C42×D61D412yes—
91C42×D61C2312yes—
92C22×D4×C61C2×C411yescharacteristic
93C23×C4×C61—21no—
94C4×D4×C61—22no—
95C4×D4×C61C2×C414yescomplemented
96C2×C4⋊C4×C61C2×C411yescharacteristic
97C2×C22⋊C4×C61—21no—
98C2×C42×C61C2×C411yescharacteristic
99C24×C61—21no—
100C23×D61—21no—
101C23×D61C2×D411yescharacteristic
102C22×#6923—28no—
103C22×#6923—24no—
104C22×#6923—44no—
105C22×#6923—44no—
106C2×D4×C61—21no—
107C2×D4×C61—42no—
108C2×D4×C61C22×C412yes—
109C22×C4×C61—21no—
110C22×C4×C61—24no—
111C22×C4×C61—44no—
112C22×C4×C61C22⋊C411yescharacteristic
113C22×C4×C61C22⋊C411yescharacteristic
114C22×C4×C61C22×C411yescharacteristic
115C2×C22⋊D61—22no—
116C2×C22⋊D61—22no—
117C2×C22⋊D61—24no—
118C2×C22⋊D61—24no—
119C2×C22⋊D61—42no—
120C2×C22⋊D61—42no—
121C2×C22⋊D61—44no—
122C2×C22⋊D61—44no—
123C22×Dic61—21no—
124C22×Dic61C22⋊C411yescharacteristic
125C22×Dic61C22⋊C411yescharacteristic
126C22×Dic61C2×D411yescharacteristic
127#11758222—416no—
128#11758222—48no—
129#11758222—48no—
130C2×D244—22no—
131C2×D244—22no—
132C2×D244—21no—
133C2×D244—42no—
134C2×D244—42no—
135C2×D244—42no—
136C2×D244C22×C412yes—
137C2×C4×D61—24no—
138C2×C4×D61—24no—
139C2×C4×D61—42no—
140C2×C4×D61—44no—
141C2×C4×D61C22⋊C412yes—
142C2×C4×D61C22⋊C412yes—
143C2×C4×D61D814yes—
144C2×C4×D61SD1614yes—
145C2×C4×D61C22×C411yescharacteristic
146C2×C4×D61C2×D412yes—
147C2×C4×D61C2×D411yescharacteristic
148C2×C4×D61C2×D411yescharacteristic
149C2×C4×D61C2×D412yes—
150C2×C4×D61C2411yescharacteristic
151C2×Dic122—24no—
152C2×Dic122—44no—
153C2×#92420—24no—
154C2×#92420—44no—
155C4⋊#6923—216no—
156C4×#6923—48no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61C22×C412yes—
159C22⋊C4×C61—24no—
160C42×C61C22⋊C412yes—
161C42×C61C22×C412yes—
162C22⋊Dic61—22no—
163C22⋊Dic61—22no—
164#11758198—24no—
165#11758198—22no—
166#11758198—22no—
167C4⋊Dic61—21no—
168C4⋊Dic61C22×C412yes—
169#11758196—24no—
170C4×Dic61C22⋊C412yes—
171C4×Dic61C22⋊C412yes—
172C4×Dic61C22⋊C412yes—
173C4×Dic61C22×C412yes—
174C4×Dic61C2×D412yes—
175C4×Dic61C2×D412yes—
176C23×C61—22no—
177C23×C61—42no—
178C23×C61—42no—
179C23×C61—42no—
180C23×C61C2×C22⋊C411yescharacteristic
181C22×D61—22no—
182C22×D61—22no—
183C22×D61—22no—
184C22×D61—42no—
185C22×D61—42no—
186C22×D61—42no—
187C22×D61C2×C22⋊C411yescharacteristic
188C22×D61C2×D812yes—
189C22×D61C2×SD1612yes—
190C22×D61C22×D411yescharacteristic
191C2×#6923—28no—
192C2×#6923—44no—
193C2×#6923—416no—
194C2×#6923—44no—
195D4×C61—42no—
196D4×C61—42no—
197C2×C4×C61—22no—
198C2×C4×C61—22no—
199C2×C4×C61—22no—
200C2×C4×C61—42no—
201C2×C4×C61—48no—
202C2×C4×C61#10214yes—
203C2×C4×C61C2×C22⋊C411yescharacteristic
204C2×C4×C61C2×C22⋊C412yes—
205C2×C4×C61C2×C22⋊C412yes—
206C2×C4×C61C23×C411yescharacteristic
207C22⋊D61—42no—
208C22⋊D61—42no—
209C22⋊D61—44no—
210C22⋊D61—48no—
211C22⋊D61—48no—
212C2×Dic61—22no—
213C2×Dic61—22no—
214C2×Dic61—42no—
215C2×Dic61#10214yes—
216C2×Dic61#10414yes—
217C2×Dic61C2×C22⋊C411yescharacteristic
218C2×Dic61C2×C22⋊C412yes—
219C2×Dic61C2×C22⋊C412yes—
220C2×Dic61C22×D411yescharacteristic
221D244—42no—
222D244—42no—
223D244—42no—
224D244—42no—
225D244—44no—
226C4×D61—24no—
227C4×D61—24no—
228C4×D61—41no—
229C4×D61—41no—
230C4×D61—41no—
231C4×D61—41no—
232C4×D61—48no—
233C4×D61#10218yes—
234C4×D61C2×D814yes—
235C4×D61C2×SD1614yes—
236Dic122—48no—
237#92420—44no—
238C2×#1502—611nomaximal, Sylow
239C22×C61—42no—
240C22×C61—42no—
241C22×C61—42no—
242C22×C61—84no—
243C22×C61#41012yes—
244C22×C61C2×#10212yes—
245C22×C61C2×#10412yes—
246C22×C61C22×C22⋊C411yescharacteristic
247C2×D61—21no—
248C2×D61—21no—
249C2×D61—21no—
250C2×D61—21no—
251C2×D61—24no—
252C2×D61—24no—
253C2×D61—42no—
254C2×D61—42no—
255C2×D61—42no—
256C2×D61—84no—
257C2×D61C2×#10212yes—
258C2×D61C22×D811yescharacteristic
259C2×D61C22×SD1611yescharacteristic
260#6923—48no—
261C4×C61—21no—
262C4×C61—21no—
263C4×C61—22no—
264C4×C61—42no—
265C4×C61C2×#10214yes—
266Dic61—21no—
267Dic61—21no—
268Dic61—42no—
269Dic61C2×#10214yes—
270Dic61C2×#10414yes—
271C2×#532—611no—
272C2×#431—611no—
273C2×C4×C4⋊C4—611no—
274#1502—618no—
275C2×#327—612no—
276C2×#327—612no—
277C2×C61—82no—
278C2×C61#150214yescomplemented
279C2×C61C2×#41011yescharacteristic
280C2×C61C22×#10211yescharacteristic
281C2×C61C22×#10411yescharacteristic
282D61—21no—
283D61—21no—
284D61—22no—
285D61—82no—
286C22×#41—1221no—
287#532—614no—
288#532—614no—
289#532—1222no—
290#532—1222no—
291C2×C4⋊Q8—611no—
292C2×#127—611no—
293C2×#124—1221no—
294C2×#121—611no—
295C2×#121—611no—
296C2×#121—1221no—
297C2×C4×D4—611no—
298C2×C4×D4—1221no—
299C2×C4×D4#692311yescharacteristic, complemented
300C22×C4⋊C4—1221no—
301C22×C42—611no—
302C22×C42—1221no—
303#431—614no—
304#431—1222no—
305C2×C4⋊C8—1221no—
306C2×C22⋊C8—612no—
307C2×C4×C8—1221no—
308C4×C4⋊C4—614no—
309C4×C4⋊C4—1222no—
310C2×#95—612no—
311#327—618no—
312#327—618no—
313C61C2×#150211yescharacteristic, complemented, Sylow
314C2×#41—1224no—
315C2×#41—1224no—
316C2×#41—2444no—
317C2×#41—2444no—
318C22×Q8—1221no—
319C22×D4—611no—
320C22×D4—1221no—
321C22×D4—1221no—
322C22×D4—1221no—
323C22×D4—1221no—
324C22×D4C2×#692311yescharacteristic
325C23×C4—21no—
326C23×C4—611no—
327C23×C4—611no—
328C23×C4—611no—
329C23×C4—1222no—
330C23×C4—1221no—
331C22×C8—1222no—
332C4⋊Q8—614no—
333C4⋊Q8—1222no—
334#127—614no—
335#127—1222no—
336#124—1224no—
337#124—1224no—
338#121—612no—
339#121—612no—
340#121—612no—
341#121—612no—
342#121—1224no—
343#121—1224no—
344#121—1221no—
345#121—1221no—
346#121—1221no—
347#121—1221no—
348C4×D4—22no—
349C4×D4—614no—
350C4×D4—1224no—
351C4×D4—1224no—
352C4×D4—1222no—
353C4×D4C2×#692314yescomplemented
354C2×C4⋊C4—611no—
355C2×C4⋊C4—1221no—
356C2×C4⋊C4—1224no—
357C2×C4⋊C4—1228no—
358C2×C4⋊C4C2×#692311yescharacteristic
359C2×C22⋊C4—21no—
360C2×C22⋊C4—1221no—
361C2×C22⋊C4—1221no—
362C2×C22⋊C4—1221no—
363C2×C42—611no—
364C2×C42—611no—
365C2×C42—611no—
366C2×C42—612no—
367C2×C42—612no—
368C2×C42—612no—
369C2×C42—612no—
370C2×C42—1224no—
371C2×C42—2444no—
372C2×C42C2×#692311yescharacteristic
373C4⋊C8—1224no—
374C22⋊C8—614no—
375C22⋊C8—1222no—
376C4×C8—1224no—
377#95—614no—
378#95—1222no—
379C24—21no—
380C24—611no—
381C24—1221no—
382#41—24416no—
383#41—2448no—
384#41—2448no—
385C2×Q8—1224no—
386C2×Q8—2444no—
387C2×D4—21no—
388C2×D4—42no—
389C2×D4—612no—
390C2×D4—1222no—
391C2×D4—1222no—
392C2×D4—1224no—
393C2×D4—1224no—
394C2×D4—1222no—
395C2×D4—1222no—
396C2×D4—1221no—
397C2×D4—2442no—
398C2×D4—2442no—
399C2×D4—2442no—
400C2×D4—2444no—
401C2×D4—2444no—
402C2×D4—2442no—
403C2×D4—2442no—
404C2×D4C22×#692312yes—
405C22×C4—21no—
406C22×C4—24no—
407C22×C4—44no—
408C22×C4—611no—
409C22×C4—611no—
410C22×C4—614no—
411C22×C4—614no—
412C22×C4—612no—
413C22×C4—612no—
414C22×C4—611no—
415C22×C4—612no—
416C22×C4—612no—
417C22×C4—611no—
418C22×C4—611no—
419C22×C4—611no—
420C22×C4—611no—
421C22×C4—1224no—
422C22×C4—1224no—
423C22×C4—1228no—
424C22×C4—1221no—
425C22×C4—1224no—
426C22×C4—2442no—
427C22×C4—2444no—
428C22×C4—2444no—
429C22×C4—2444no—
430C22×C4C22⋊#692311yescharacteristic
431C22×C4C22⋊#692311yescharacteristic
432C22×C4C22×#692311yescharacteristic
433C2×C8—1224no—
434C2×C8—2444no—
435C4⋊C4—21no—
436C4⋊C4—612no—
437C4⋊C4—1224no—
438C4⋊C4—12216no—
439C4⋊C4—1221no—
440C4⋊C4C22×#692312yes—
441C22⋊C4—24no—
442C22⋊C4—1222no—
443C22⋊C4—1222no—
444C22⋊C4—1222no—
445C22⋊C4—1222no—
446C22⋊C4—1224no—
447C42—612no—
448C42—612no—
449C42—612no—
450C42—612no—
451C42—612no—
452C42—612no—
453C42—2448no—
454C42C22⋊#692312yes—
455C42C22×#692312yes—
456C23—22no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—612no—
461C23—612no—
462C23—611no—
463C23—611no—
464C23—1222no—
465C23—1222no—
466C23—1222no—
467C23—2442no—
468C23—2442no—
469C23—2442no—
470C23C2×C22⋊#692311yescharacteristic
471Q8—2448no—
472D4—42no—
473D4—42no—
474D4—2442no—
475D4—2442no—
476D4—2442no—
477D4—2442no—
478D4—2444no—
479D4—2448no—
480D4—2448no—
481D4—2442no—
482D4—2442no—
483D4—2444no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—42no—
488C2×C4—48no—
489C2×C4—614no—
490C2×C4—614no—
491C2×C4—612no—
492C2×C4—612no—
493C2×C4—618no—
494C2×C4—614no—
495C2×C4—614no—
496C2×C4—611no—
497C2×C4—611no—
498C2×C4—1224no—
499C2×C4—1224no—
500C2×C4—1222no—
501C2×C4—1228no—
502C2×C4—1222no—
503C2×C4—2441no—
504C2×C4—2441no—
505C2×C4—2441no—
506C2×C4—2441no—
507C2×C4—2444no—
508C2×C4—2444no—
509C2×C4—24416no—
510C2×C4—2442no—
511C2×C4—2448no—
512C2×C4#1451983914yes—
513C2×C4C2×C22⋊#692311yescharacteristic
514C2×C4C2×C22⋊#692312yes—
515C2×C4C2×C22⋊#692312yes—
516C2×C4C23×#692311yescharacteristic
517C8—2444no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—84no—
522C22—611no—
523C22—611no—
524C22—612no—
525C22—1221no—
526C22—1221no—
527C22—1221no—
528C22—1221no—
529C22—1224no—
530C22—1224no—
531C22—4884no—
532C22—2442no—
533C22—2442no—
534C22—2442no—
535C22#1684074112yes—
536C22C2×#1451983912yes—
537C22D61⋊#10412yes—
538C22C22×C22⋊#692311yescharacteristic
539C4—21no—
540C4—21no—
541C4—22no—
542C4—42no—
543C4—614no—
544C4—614no—
545C4—1221no—
546C4—1221no—
547C4—2448no—
548C4—2442no—
549C4C2×#1451983914yes—
550C2—82no—
551C2—1221no—
552C2—1221no—
553C2—1222no—
554C2—4882no—
555C2#2146119814yesdirect product factor
556C2C2×#1684074111yescharacteristic
557C2C22×#1451983911yescharacteristic
558C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC22×C4C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4×D4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#16840309C2
cosocleC2×C4×D61C24
hypercenterC2×C4×D4#6923
hypocenterC61C2×#1502
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#16840780C2semidirect
2. C2×C4×C4⋊#6923C2semidirect
3. #21461198C2direct (N × H)
4. C2×#16840614C2semidirect
5. C2×#16840613C2semidirect
10. #16840780C22semidirect
15. C4×C4⋊#6923C22semidirect
17. #16840614C22semidirect
18. #16840613C22semidirect
22. #16840309C4semidirect
24. C2×#14519776C4semidirect
25. C2×#14519773C4semidirect
30. C2×C4×D244C4semidirect
33. C2×C4×D4×C61C4semidirect
61. #14519776C2×C4semidirect
63. #14519773C2×C4semidirect
77. C4×D244C2×C4semidirect
95. C4×D4×C61C2×C4semidirect
278. C2×C61#1502semidirect
299. C2×C4×D4#6923semidirect
313. C61C2×#1502semidirect
353. C4×D4C2×#6923semidirect
555. C2#21461198direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407802
C2×C4×C4⋊#69232
#214611982
C2×#168406142
C2×#168406132
C2×#168403092
C2×#150261