Finite Group Databasebeta

← C2×#21458632 #30559747

Subgroups — C2×#21458632 #30559747

Order 15616.

1906 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840497C211yesmaximal, characteristic
2C2×#16840492C211yesmaximal, characteristic, complemented
3#21458632C2116yesmaximal, direct product factor
4C2×#16840123C212yesmaximal, complemented
5C2×#16840110C211yesmaximal, characteristic
6C2×#16840041C212yesmaximal, complemented
7C2×#16839987C212yesmaximal, complemented
8C2×#16839963C211yesmaximal, characteristic
9C2×#16839889C211yesmaximal, characteristic, complemented
10C2×#16839861C212yesmaximal, complemented
11C2×C4×#11758202C211yesmaximal, characteristic, complemented
12C2×C61×#477C211yesmaximal, characteristic, complemented
13C22×#11758202C2211yescharacteristic
14C22×#11758190C2212yes—
15#16840497—24no—
16#16840497C2218yes—
17#16840492—24no—
18#16840492C2218yescomplemented
19C2×#14519776—21no—
20C2×#14519776C2212yes—
21C2×#14519775—22no—
22C2×#14519774C2211yescharacteristic
23C2×#14519766C2212yes—
24C2×#14519765—21no—
25C2×#14519762—22no—
26C2×C4×Dic122C2211yescharacteristic
27C2×C4×Dic122C2211yescharacteristic
28C2×#14519742—21no—
29C2×#14519742C2212yes—
30C2×C4×D244—21no—
31C2×#14519739C2212yes—
32#16840123C22116yescomplemented
33#16840110C2218yes—
34#16840041C22116yescomplemented
35#16839987C22116yescomplemented
36#16839963C2218yes—
37#16839889C2218yescomplemented
38#16839861C22116yescomplemented
39C4×#11758202C2218yescomplemented
40C2×#14519710C2211yescharacteristic
41C2×#14519706C2212yes—
42C2×#14519701C2211yescharacteristic
43C2×#14519700C2211yescharacteristic
44C2×#14519699C2212yes—
45C2×#14519697C2212yes—
46C2×#14519697C2212yes—
47C2×#14519687C2212yes—
48C2×C4×#92418C2211yescharacteristic
49C2×C4⋊Q8×C61C2211yescharacteristic
50C2×C4×Q8×C61C2211yescharacteristic
51C61×#477C2218yescomplemented
52C2×#107×C61C2212yes—
53C2×C4⋊C8×C61C2211yescharacteristic
54C2×#103×C61C2212yes—
55C22×Dic122—22no—
56C22×Dic122D411yescharacteristic
57C22×Dic122C2311yescharacteristic
58C22×D244—21no—
59C22×D244—21no—
60C22×D244C2312yes—
61C22×C4×D61—22no—
62C2×#11758202—24no—
63C2×#11758202C2314yes—
64C2×#11758190—28no—
65C2×#11758190C2318yes—
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68#14519776—28no—
69#14519776—24no—
70#14519776C2318yes—
71#14519775—216no—
72#14519774—22no—
73#14519774C2314yes—
74#14519766—24no—
75#14519766C2318yes—
76#14519765—28no—
77#14519762—216no—
78C4×Dic122—22no—
79C4×Dic122D414yes—
80C4×Dic122C2314yes—
81C4×Dic122C2314yes—
82#14519742—28no—
83#14519742—24no—
84#14519742C2318yes—
85C4×D244—28no—
86#14519739—24no—
87#14519739C2318yes—
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—
107#14519687C2318yes—
108C4×#92418C2314yes—
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#107×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—82no—
131C2×Q8×C61C2412yes—
132C22×C4×C61—21no—
133C22×C4×C61—22no—
134C22×C4×C61—21no—
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×Dic122—28no—
156C2×Dic122—84no—
157C2×Dic122C2×D414yes—
158C2×Dic122#4114yes—
159C2×Dic122C2412yes—
160C2×C8×C61—24no—
161C2×C8×C61C2414yes—
162C4⋊C4×C61—24no—
163C4⋊C4×C61—24no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—22no—
166C4⋊C4×C61C2414yes—
167C4⋊C4×C61C2412yes—
168C42×C61—24no—
169C42×C61C2×D412yes—
170C42×C61C2412yes—
171#11758202—28no—
172#11758198—28no—
173#11758198—28no—
174#11758198—28no—
175C4⋊Dic61—21no—
176C4⋊Dic61C2×D414yes—
177C4⋊Dic61C2412yes—
178#11758196—24no—
179#11758196—28no—
180#11758196—28no—
181#11758196C2×D418yes—
182C4×Dic61—24no—
183C4×Dic61—28no—
184C4×Dic61C2×D414yes—
185C4×Dic61C2414yes—
186C2×#92418—22no—
187C2×#92418—22no—
188C2×#92418C2412yes—
189C2×#92418C2412yes—
190#11758190—216no—
191C23×C61C22×D411yescharacteristic
192C22×D61—24no—
193C22×D61—44no—
194C22×D61—44no—
195C22×D61—44no—
196Q8×C61—22no—
197Q8×C61—22no—
198Q8×C61—42no—
199Q8×C61—84no—
200C2×C4×C61—22no—
201C2×C4×C61—24no—
202C2×C4×C61—22no—
203C2×C4×C61—22no—
204C2×C4×C61—42no—
205C2×C4×C61—44no—
206C2×C4×C61—42no—
207C2×C4×C61#13714yes—
208C2×C4×C61C22×D412yes—
209C2×C4×C61C22×D411yescharacteristic
210C2×C4×C61C22×D412yes—
211C2×C4×C61C2×#4112yes—
212C2×C4×C612−1+412yes—
213C2×C4×C61C2511yescharacteristic
214C2×Dic61—24no—
215C2×Dic61—24no—
216C2×Dic61—24no—
217C2×Dic61—22no—
218C2×Dic61—22no—
219C2×Dic61—42no—
220C2×Dic61C22×D414yes—
221C2×Dic61C22×D414yes—
222D244—24no—
223D244—24no—
224D244—44no—
225D244—48no—
226D244—84no—
227C4×D61—88no—
228Dic122—24no—
229Dic122—28no—
230Dic122—22no—
231Dic122—88no—
232Dic122C2×#4114yes—
233C8×C61—24no—
234#92418—22no—
235#92418—22no—
236C2×#3375—611nomaximal, Sylow
237C22×C61#54812yes—
238C22×C61C2×#13712yes—
239C22×C61#57612yes—
240C22×C61C23×D411yescharacteristic
241C2×D61—44no—
242C2×D61—44no—
243C2×D61—44no—
244C2×D61—88no—
245C4×C61—22no—
246C4×C61—42no—
247C4×C61—44no—
248C4×C61—42no—
249C4×C61#54812yes—
250C4×C61C2×#13714yes—
251C4×C61C22×#4111yescharacteristic
252C4×C61C2×2−1+411yescharacteristic
253Dic61—24no—
254Dic61—24no—
255Dic61—24no—
256Dic61—42no—
257C2×#559—611no—
258C2×Q82—611no—
259#3375—6116no—
260C2×#489—612no—
261C2×#486—611no—
262C2×#477D6111yescharacteristic, complemented
263C2×#474—612no—
264C2×#464—612no—
265C2×#460—611no—
266C2×#446—611no—
267C2×#440—612no—
268C2×C4×Q16—611no—
269C2×C61#337514yescomplemented
270C2×C61C2×#54811yescharacteristic
271C2×C61C22×#13711yescharacteristic
272C2×C61C2×#57611yescharacteristic
273D61—84no—
274C22×Q16—611no—
275C22×SD16—612no—
276#559—618no—
277#559—1224no—
278Q82—618no—
279Q82—1224no—
280C2×C4⋊Q8—612no—
281C2×C4⋊Q8—1221no—
282C2×C4⋊Q8—1222no—
283C2×C4⋊Q8C2×D6111yescharacteristic
284C2×#127—611no—
285C2×#124—612no—
286C2×#124—1221no—
287C2×#123—1222no—
288C2×C4×Q8—611no—
289C2×C4×Q8—612no—
290C2×C4×Q8—611no—
291C2×C4×Q8—1221no—
292C2×C4×Q8C2×D6111yescharacteristic
293C2×C4×D4—612no—
294C2×C4×D4—1221no—
295#489—6116no—
296#486—618no—
297#477C2×D6118yescomplemented
298#474—6116no—
299#464—6116no—
300#460—618no—
301#446—618no—
302#440—6116no—
303C4×Q16—618no—
304C2×#107—611no—
305C2×#107C2×D6112yes—
306C2×C4⋊C8—612no—
307C2×C4⋊C8C2×D6111yescharacteristic
308C2×#103—611no—
309C2×#103—611no—
310C2×#103C2×D6112yes—
311C2×#102—612no—
312C2×#102—612no—
313C2×#102—612no—
314C2×#97—612no—
315C2×C4×C8—611no—
316C61C2×#337511yescharacteristic, complemented, Sylow
317C22×Q8—21no—
318C22×Q8—611no—
319C22×Q8—611no—
320C22×Q8—1222no—
321C22×Q8C22×D6111yescharacteristic
322C22×D4—612no—
323C22×D4—1221no—
324C22×D4—1221no—
325C23×C4—1222no—
326C2×Q16—614no—
327C2×Q16—1224no—
328C2×SD16—618no—
329C2×SD16—1228no—
330C22×C8—611no—
331C22×C8—611no—
332C22×C8C22×D6112yes—
333C4⋊Q8—22no—
334C4⋊Q8—618no—
335C4⋊Q8—1224no—
336C4⋊Q8—1228no—
337C4⋊Q8—12216no—
338C4⋊Q8C22×D6114yes—
339#127—614no—
340#127—1222no—
341#124—618no—
342#124—1228no—
343#124—1224no—
344#123—12216no—
345C4×Q8—22no—
346C4×Q8—614no—
347C4×Q8—614no—
348C4×Q8—618no—
349C4×Q8—614no—
350C4×Q8—1224no—
351C4×Q8—1228no—
352C4×Q8—1222no—
353C4×Q8C22×D6114yes—
354C4×D4—618no—
355C4×D4—1228no—
356C4×D4—1224no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—611no—
360C2×C4⋊C4—612no—
361C2×C4⋊C4—611no—
362C2×C4⋊C4—1222no—
363C2×C4⋊C4—1222no—
364C2×C4⋊C4—1221no—
365C2×C4⋊C4C22×D6111yescharacteristic
366C2×C4⋊C4C22×D6112yes—
367C2×C22⋊C4—1222no—
368C2×C22⋊C4—1222no—
369C2×C22⋊C4—1222no—
370C2×C42—21no—
371C2×C42—612no—
372C2×C42—1222no—
373C2×C42—1221no—
374C2×C42C22×D6111yescharacteristic
375#107—614no—
376#107C22×D6118yes—
377C4⋊C8—618no—
378C4⋊C8C22×D6114yes—
379#103—614no—
380#103—614no—
381#103C22×D6118yes—
382#102—618no—
383#102—618no—
384#102—618no—
385#97—618no—
386C4×C8—614no—
387C24—1222no—
388C2×Q8—21no—
389C2×Q8—24no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—82no—
393C2×Q8—614no—
394C2×Q8—614no—
395C2×Q8—612no—
396C2×Q8—1228no—
397C2×Q8—1224no—
398C2×Q8—1221no—
399C2×Q8—1222no—
400C2×Q8—4884no—
401C2×Q8C23×D6112yes—
402C2×D4—614no—
403C2×D4—1224no—
404C2×D4—1224no—
405C2×D4—1222no—
406C2×D4—1224no—
407C2×D4—1224no—
408C2×D4—4882no—
409C2×D4—2444no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—612no—
414C22×C4—612no—
415C22×C4—1228no—
416C22×C4—1221no—
417C22×C4—1221no—
418C22×C4—4884no—
419C22×C4D4×D6111yescharacteristic
420C22×C4D4×D6111yescharacteristic
421C22×C4C23×D6111yescharacteristic
422Q16—1228no—
423SD16—12216no—
424C2×C8—24no—
425C2×C8—612no—
426C2×C8—612no—
427C2×C8—1222no—
428C2×C8—1222no—
429C2×C8C23×D6114yes—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—21no—
433C4⋊C4—22no—
434C4⋊C4—618no—
435C4⋊C4—614no—
436C4⋊C4—612no—
437C4⋊C4—1228no—
438C4⋊C4—1228no—
439C4⋊C4—1221no—
440C4⋊C4—1224no—
441C4⋊C4C23×D6114yes—
442C4⋊C4C23×D6112yes—
443C22⋊C4—1228no—
444C22⋊C4—1228no—
445C22⋊C4—1228no—
446C42—24no—
447C42—614no—
448C42—614no—
449C42—1228no—
450C42—1224no—
451C42D4×D6112yes—
452C42C23×D6112yes—
453C23—1224no—
454C23—2444no—
455C23—2444no—
456C23—2444no—
457C23C2×D4×D6111yescharacteristic
458Q8—22no—
459Q8—22no—
460Q8—42no—
461Q8—84no—
462Q8—614no—
463Q8—1228no—
464Q8—1222no—
465Q8—1224no—
466Q8—4888no—
467D4—1224no—
468D4—1224no—
469D4—4884no—
470D4—2448no—
471D4—2444no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—42no—
477C2×C4—44no—
478C2×C4—42no—
479C2×C4—614no—
480C2×C4—614no—
481C2×C4—1224no—
482C2×C4—1224no—
483C2×C4—1222no—
484C2×C4—1224no—
485C2×C4—1222no—
486C2×C4—4888no—
487C2×C4—2442no—
488C2×C4#1451980914yes—
489C2×C4C2×D4×D6112yes—
490C2×C4C2×D4×D6112yes—
491C2×C4C2×D4×D6111yescharacteristic
492C2×C4#41×D6112yes—
493C2×C4#1451982512yes—
494C2×C4C24×D6111yescharacteristic
495C8—24no—
496C8—1222no—
497C8—1222no—
498C22—4888no—
499C22—2444no—
500C22—2444no—
501C22—2444no—
502C22#1684042212yes—
503C22C2×#1451980912yes—
504C22#1684056612yes—
505C22C22×D4×D6111yescharacteristic
506C4—22no—
507C4—42no—
508C4—42no—
509C4—44no—
510C4—1224no—
511C4—1224no—
512C4—1224no—
513C4—2442no—
514C4#1684042212yes—
515C4C2×#1451980914yes—
516C4C2×#41×D6111yescharacteristic
517C4C2×#1451982511yescharacteristic
518C2—4884no—
519C2#2145863214yesdirect product factor
520C2C2×#1684042211yescharacteristic
521C2C22×#1451980911yescharacteristic
522C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#477C2
socleC23×C61C22×D4
prime radicalC2×#14519774C22
hypercenterC2×#477D61
hypocenterC61C2×#3375
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
2. C2×#16840492C2semidirect
3. #21458632C2direct (N × H)
4. C2×#16840123C2semidirect
6. C2×#16840041C2semidirect
7. C2×#16839987C2semidirect
9. C2×#16839889C2semidirect
10. C2×#16839861C2semidirect
11. C2×C4×#11758202C2semidirect
12. C2×C61×#477C2semidirect
18. #16840492C22semidirect
32. #16840123C22semidirect
34. #16840041C22semidirect
35. #16839987C22semidirect
37. #16839889C22semidirect
38. #16839861C22semidirect
39. C4×#11758202C22semidirect
51. C61×#477C22semidirect
262. C2×#477D61semidirect
269. C2×C61#3375semidirect
297. #477C2×D61semidirect
316. C61C2×#3375semidirect
519. C2#21458632direct (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×#168404922
#214586322
C2×#168401232
C2×#168401102
C2×#168400412
C2×#168399872
C2×#168399632
C2×#168398892
C2×#168398612
C2×C4×#117582022
C2×C61×#4772
C2×#337561