Finite Group Databasebeta

← C2×#21458514 #30559636

Subgroups — C2×#21458514 #30559636

Order 15616.

1894 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840497C211yesmaximal, characteristic
2C2×#16840487C211yesmaximal, characteristic, complemented
3#21458514C2116yesmaximal, direct product factor
4C2×#16840118C212yesmaximal, complemented
5C2×#16840110C211yesmaximal, characteristic
6C2×#16840061C212yesmaximal, complemented
7C2×#16839987C212yesmaximal, complemented
8C2×#16839963C211yesmaximal, characteristic
9C2×#16839886C211yesmaximal, characteristic, complemented
10C2×C4×#11758202C211yesmaximal, characteristic, complemented
11C2×#16839849C212yesmaximal, complemented
12C2×C61×#475C211yesmaximal, characteristic, complemented
13C22×#11758202C2211yescharacteristic
14C22×#11758190C2212yes—
15#16840497—24no—
16#16840497C2218yes—
17#16840487—24no—
18#16840487C2218yescomplemented
19C2×#14519775—21no—
20C2×#14519774C2211yescharacteristic
21C2×#14519768C2212yes—
22C2×#14519767—22no—
23C2×#14519766C2212yes—
24C2×#14519765—21no—
25C2×#14519762—22no—
26C2×Q8×Dic61—21no—
27C2×C4×Dic122C2211yescharacteristic
28C2×C4×Dic122C2211yescharacteristic
29C2×#14519742C2212yes—
30C2×C4×D244—21no—
31C2×#14519739C2212yes—
32#16840118C22116yescomplemented
33#16840110C2218yes—
34#16840061C22116yescomplemented
35#16839987C22116yescomplemented
36#16839963C2218yes—
37#16839886C2218yescomplemented
38C4×#11758202C2218yescomplemented
39#16839849C22116yescomplemented
40C2×#14519710C2211yescharacteristic
41C2×#14519706C2212yes—
42C2×#14519701C2211yescharacteristic
43C2×#14519700C2211yescharacteristic
44C2×#14519699C2212yes—
45C2×#14519697C2212yes—
46C2×#14519697C2212yes—
47C2×C4×#92418C2211yescharacteristic
48C2×C8×Dic61C2212yes—
49C2×C4⋊Q8×C61C2211yescharacteristic
50C2×C4×Q8×C61C2211yescharacteristic
51C61×#475C2218yescomplemented
52C2×#106×C61C2212yes—
53C2×C4⋊C8×C61C2211yescharacteristic
54C2×#103×C61C2212yes—
55C22×Dic122D411yescharacteristic
56C22×Dic122C2311yescharacteristic
57C22×D244—21no—
58C22×D244—21no—
59C22×D244C2312yes—
60C22×C4×D61—22no—
61C2×#11758202—24no—
62C2×#11758202C2314yes—
63C2×#11758190—28no—
64C2×#11758190C2318yes—
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67#14519775—28no—
68#14519774—22no—
69#14519774C2314yes—
70#14519768—24no—
71#14519768C2318yes—
72#14519767—216no—
73#14519766—24no—
74#14519766C2318yes—
75#14519765—28no—
76#14519762—216no—
77Q8×Dic61—28no—
78C4×Dic122—22no—
79C4×Dic122D414yes—
80C4×Dic122C2314yes—
81C4×Dic122C2314yes—
82#14519742—24no—
83#14519742C2318yes—
84C4×D244—28no—
85#14519739—24no—
86#14519739C2318yes—
87C2×C4⋊Dic61—22no—
88C2×C4⋊Dic61D411yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×#11758196—21no—
91C2×#11758196—22no—
92C2×#11758196—22no—
93C2×#11758196D412yes—
94C2×#11758198—22no—
95C2×#11758198—22no—
96C2×#11758198—22no—
97C2×C4×Dic61—21no—
98C2×C4×Dic61—22no—
99C2×C4×Dic61C2312yes—
100#14519710C2314yes—
101#14519706C2318yes—
102#14519701C2314yes—
103#14519700C2314yes—
104#14519699C2318yes—
105#14519697C2318yes—
106#14519697C2318yes—
107C4×#92418C2314yes—
108C8×Dic61C2318yes—
109C22×Q8×C61—21no—
110C22×Q8×C61C2311yescharacteristic
111C22×C8×C61C2312yes—
112C4⋊Q8×C61—22no—
113C4⋊Q8×C61C2314yes—
114C4×Q8×C61—22no—
115C4×Q8×C61C2314yes—
116C2×C4⋊C4×C61—21no—
117C2×C4⋊C4×C61—21no—
118C2×C4⋊C4×C61C2312yes—
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C42×C61—21no—
121C2×C42×C61C2311yescharacteristic
122#106×C61C2318yes—
123C4⋊C8×C61C2314yes—
124#103×C61C2318yes—
125C23×D61—22no—
126C2×Q8×C61—21no—
127C2×Q8×C61—24no—
128C2×Q8×C61—22no—
129C2×Q8×C61—22no—
130C2×Q8×C61—44no—
131C2×Q8×C61C2412yes—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—22no—
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2411yescharacteristic
138C22×Dic61—21no—
139C22×Dic61—21no—
140C22×Dic61C2×D412yes—
141C22×Dic61C2×D412yes—
142C2×D244—24no—
143C2×D244—24no—
144C2×D244—24no—
145C2×D244—22no—
146C2×D244—24no—
147C2×D244—44no—
148C2×D244—82no—
149C2×D244C2414yes—
150C2×C4×D61—28no—
151C2×C4×D61—84no—
152C2×Dic122—24no—
153C2×Dic122—21no—
154C2×Dic122—22no—
155C2×Dic122C2×D414yes—
156C2×Dic122#4114yes—
157C2×Dic122C2412yes—
158C2×C8×C61—24no—
159C2×C8×C61C2414yes—
160C4⋊C4×C61—24no—
161C4⋊C4×C61—24no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—22no—
164C4⋊C4×C61C2414yes—
165C4⋊C4×C61C2412yes—
166C42×C61—24no—
167C42×C61C2×D412yes—
168C42×C61C2412yes—
169#11758202—28no—
170#11758198—28no—
171#11758198—28no—
172#11758198—28no—
173C4⋊Dic61—21no—
174C4⋊Dic61—28no—
175C4⋊Dic61C2×D414yes—
176C4⋊Dic61C2412yes—
177#11758196—24no—
178#11758196—28no—
179#11758196—28no—
180#11758196C2×D418yes—
181C4×Dic61—24no—
182C4×Dic61—28no—
183C4×Dic61C2×D414yes—
184C4×Dic61C2414yes—
185C2×#92418—22no—
186C2×#92418—22no—
187C2×#92418C2412yes—
188C2×#92418C2412yes—
189#11758190—216no—
190C23×C61C22×D411yescharacteristic
191C22×D61—24no—
192C22×D61—44no—
193C22×D61—44no—
194C22×D61—44no—
195Q8×C61—22no—
196Q8×C61—22no—
197Q8×C61—42no—
198Q8×C61—48no—
199C2×C4×C61—22no—
200C2×C4×C61—24no—
201C2×C4×C61—22no—
202C2×C4×C61—22no—
203C2×C4×C61—42no—
204C2×C4×C61—44no—
205C2×C4×C61—42no—
206C2×C4×C61#13514yes—
207C2×C4×C61C22×D412yes—
208C2×C4×C61C22×D411yescharacteristic
209C2×C4×C61C22×D412yes—
210C2×C4×C61C2×#4112yes—
211C2×C4×C612−1+412yes—
212C2×C4×C61C2511yescharacteristic
213C2×Dic61—24no—
214C2×Dic61—24no—
215C2×Dic61—24no—
216C2×Dic61—22no—
217C2×Dic61—22no—
218C2×Dic61—42no—
219C2×Dic61C22×D414yes—
220C2×Dic61C22×D414yes—
221D244—24no—
222D244—24no—
223D244—44no—
224D244—48no—
225D244—84no—
226C4×D61—88no—
227Dic122—24no—
228Dic122—28no—
229Dic122—22no—
230Dic122C2×#4114yes—
231C8×C61—24no—
232#92418—22no—
233#92418—22no—
234C2×#3365—611nomaximal, Sylow
235C22×C61#54812yes—
236C22×C61C2×#13512yes—
237C22×C61#57712yes—
238C22×C61C23×D411yescharacteristic
239C2×D61—44no—
240C2×D61—44no—
241C2×D61—44no—
242C2×D61—88no—
243C4×C61—22no—
244C4×C61—42no—
245C4×C61—44no—
246C4×C61—42no—
247C4×C61#54812yes—
248C4×C61C2×#13514yes—
249C4×C61C22×#4111yescharacteristic
250C4×C61C2×2−1+411yescharacteristic
251Dic61—24no—
252Dic61—24no—
253Dic61—24no—
254Dic61—42no—
255C2×#559—611no—
256C2×#557—611no—
257#3365—6116no—
258C2×#488—612no—
259C2×#486—611no—
260C2×#475D6111yescharacteristic, complemented
261C2×#478—612no—
262C2×#464—612no—
263C2×#460—611no—
264C2×C8×Q8—611no—
265C2×C4×Q16—611no—
266C2×C4×SD16—612no—
267C2×C61#336514yescomplemented
268C2×C61C2×#54811yescharacteristic
269C2×C61C22×#13511yescharacteristic
270C2×C61C2×#57711yescharacteristic
271D61—84no—
272C22×Q16—611no—
273C22×SD16—612no—
274#559—618no—
275#559—1224no—
276#557—618no—
277#557—1224no—
278C2×C4⋊Q8—1221no—
279C2×C4⋊Q8C2×D6111yescharacteristic
280C2×#127—611no—
281C2×#125—612no—
282C2×#125—1222no—
283C2×#124—612no—
284C2×#124—1221no—
285C2×#123—1222no—
286C2×C4×Q8—611no—
287C2×C4×Q8—612no—
288C2×C4×Q8—611no—
289C2×C4×Q8—1221no—
290C2×C4×Q8C2×D6111yescharacteristic
291C2×C4×D4—612no—
292C2×C4×D4—1221no—
293#488—6116no—
294#486—618no—
295#478—6116no—
296#475C2×D6118yescomplemented
297#464—6116no—
298#460—618no—
299C8×Q8—618no—
300C4×Q16—618no—
301C4×SD16—6116no—
302C2×#107—611no—
303C2×#106C2×D6112yes—
304C2×C4⋊C8—612no—
305C2×C4⋊C8C2×D6111yescharacteristic
306C2×#103—611no—
307C2×#103—611no—
308C2×#103C2×D6112yes—
309C2×#102—612no—
310C2×#102—612no—
311C2×#102—612no—
312C2×C4×C8—612no—
313C2×C4×C8—611no—
314C61C2×#336511yescharacteristic, complemented, Sylow
315C22×Q8—21no—
316C22×Q8—611no—
317C22×Q8—611no—
318C22×Q8C22×D6111yescharacteristic
319C22×D4—612no—
320C22×D4—1221no—
321C22×D4—1221no—
322C23×C4—1222no—
323C2×Q16—614no—
324C2×Q16—1224no—
325C2×SD16—618no—
326C2×SD16—1228no—
327C22×C8—611no—
328C22×C8—611no—
329C22×C8C22×D6112yes—
330C4⋊Q8—22no—
331C4⋊Q8—1228no—
332C4⋊Q8C22×D6114yes—
333#127—614no—
334#127—1222no—
335#125—618no—
336#125—1224no—
337#125—12216no—
338#124—618no—
339#124—1228no—
340#124—1224no—
341#123—12216no—
342C4×Q8—22no—
343C4×Q8—614no—
344C4×Q8—614no—
345C4×Q8—618no—
346C4×Q8—614no—
347C4×Q8—1224no—
348C4×Q8—1228no—
349C4×Q8—1222no—
350C4×Q8C22×D6114yes—
351C4×D4—618no—
352C4×D4—1228no—
353C4×D4—1224no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—611no—
357C2×C4⋊C4—612no—
358C2×C4⋊C4—611no—
359C2×C4⋊C4—1222no—
360C2×C4⋊C4—1222no—
361C2×C4⋊C4—1222no—
362C2×C4⋊C4—1221no—
363C2×C4⋊C4C22×D6111yescharacteristic
364C2×C4⋊C4C22×D6112yes—
365C2×C22⋊C4—1222no—
366C2×C22⋊C4—1222no—
367C2×C22⋊C4—1222no—
368C2×C42—21no—
369C2×C42—612no—
370C2×C42—1222no—
371C2×C42—1221no—
372C2×C42C22×D6111yescharacteristic
373#107—614no—
374#106C22×D6118yes—
375C4⋊C8—618no—
376C4⋊C8C22×D6114yes—
377#103—614no—
378#103—614no—
379#103C22×D6118yes—
380#102—618no—
381#102—618no—
382#102—618no—
383C4×C8—618no—
384C4×C8—614no—
385C24—1222no—
386C2×Q8—21no—
387C2×Q8—24no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—44no—
391C2×Q8—614no—
392C2×Q8—614no—
393C2×Q8—612no—
394C2×Q8—1221no—
395C2×Q8—1222no—
396C2×Q8—1224no—
397C2×Q8C23×D6112yes—
398C2×D4—614no—
399C2×D4—1224no—
400C2×D4—1224no—
401C2×D4—1222no—
402C2×D4—1224no—
403C2×D4—1224no—
404C2×D4—4882no—
405C2×D4—2444no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—612no—
410C22×C4—612no—
411C22×C4—1228no—
412C22×C4—1221no—
413C22×C4—1221no—
414C22×C4—4884no—
415C22×C4D4×D6111yescharacteristic
416C22×C4D4×D6111yescharacteristic
417C22×C4C23×D6111yescharacteristic
418Q16—1228no—
419SD16—12216no—
420C2×C8—24no—
421C2×C8—612no—
422C2×C8—612no—
423C2×C8—1222no—
424C2×C8—1222no—
425C2×C8C23×D6114yes—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—618no—
431C4⋊C4—614no—
432C4⋊C4—612no—
433C4⋊C4—1228no—
434C4⋊C4—1228no—
435C4⋊C4—1228no—
436C4⋊C4—1221no—
437C4⋊C4—1224no—
438C4⋊C4C23×D6114yes—
439C4⋊C4C23×D6112yes—
440C22⋊C4—1228no—
441C22⋊C4—1228no—
442C22⋊C4—1228no—
443C42—24no—
444C42—614no—
445C42—614no—
446C42—1228no—
447C42—1224no—
448C42D4×D6112yes—
449C42C23×D6112yes—
450C23—1224no—
451C23—2444no—
452C23—2444no—
453C23—2444no—
454C23C2×D4×D6111yescharacteristic
455Q8—22no—
456Q8—22no—
457Q8—48no—
458Q8—42no—
459Q8—614no—
460Q8—1228no—
461Q8—1222no—
462Q8—1224no—
463D4—1224no—
464D4—1224no—
465D4—4884no—
466D4—2448no—
467D4—2444no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—24no—
472C2×C4—44no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—614no—
476C2×C4—614no—
477C2×C4—1224no—
478C2×C4—1224no—
479C2×C4—1222no—
480C2×C4—1224no—
481C2×C4—1222no—
482C2×C4—4888no—
483C2×C4—2442no—
484C2×C4#1451979814yes—
485C2×C4C2×D4×D6112yes—
486C2×C4C2×D4×D6112yes—
487C2×C4C2×D4×D6111yescharacteristic
488C2×C4#41×D6112yes—
489C2×C4#1451982512yes—
490C2×C4C24×D6111yescharacteristic
491C8—24no—
492C8—1222no—
493C8—1222no—
494C22—4888no—
495C22—2444no—
496C22—2444no—
497C22—2444no—
498C22#1684042212yes—
499C22C2×#1451979812yes—
500C22#1684057112yes—
501C22C22×D4×D6111yescharacteristic
502C4—22no—
503C4—44no—
504C4—42no—
505C4—42no—
506C4—1224no—
507C4—1224no—
508C4—1224no—
509C4—2442no—
510C4#1684042212yes—
511C4C2×#1451979814yes—
512C4C2×#41×D6111yescharacteristic
513C4C2×#1451982511yescharacteristic
514C2—4884no—
515C2#2145851414yesdirect product factor
516C2C2×#1684042211yescharacteristic
517C2C22×#1451979811yescharacteristic
518C2C2×#1684057111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#475C2
socleC23×C61C22×D4
prime radicalC2×#14519774C22
hypercenterC2×#475D61
hypocenterC61C2×#3365
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
2. C2×#16840487C2semidirect
3. #21458514C2direct (N × H)
4. C2×#16840118C2semidirect
6. C2×#16840061C2semidirect
7. C2×#16839987C2semidirect
9. C2×#16839886C2semidirect
10. C2×C4×#11758202C2semidirect
11. C2×#16839849C2semidirect
12. C2×C61×#475C2semidirect
18. #16840487C22semidirect
32. #16840118C22semidirect
34. #16840061C22semidirect
35. #16839987C22semidirect
37. #16839886C22semidirect
38. C4×#11758202C22semidirect
39. #16839849C22semidirect
51. C61×#475C22semidirect
260. C2×#475D61semidirect
267. C2×C61#3365semidirect
296. #475C2×D61semidirect
314. C61C2×#3365semidirect
515. C2#21458514direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404972
C2×#168404872
#214585142
C2×#168401182
C2×#168401102
C2×#168400612
C2×#168399872
C2×#168399632
C2×#168398862
C2×C4×#117582022
C2×#168398492
C2×C61×#4752
C2×#336561