Finite Group Databasebeta

← C2×#21458210 #30558473

Subgroups — C2×#21458210 #30558473

Order 15616.

1942 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×#16840473C211yesmaximal, characteristic
2C2×#16840472C211yesmaximal, characteristic
3#21458210C2116yesmaximal, direct product factor
4C2×#16840165C211yesmaximal, characteristic, complemented
5C2×#16840099C212yesmaximal, complemented
6C2×#16840096C212yesmaximal, complemented
7C2×#16840058C211yesmaximal, characteristic, complemented
8C2×#16840002C212yesmaximal, complemented
9C2×C4×#11758202C211yesmaximal, characteristic, complemented
10C2×#16839827C211yesmaximal, characteristic
11C2×#107×D61C212yesmaximal, complemented
12C2×C61×#477C211yesmaximal, characteristic, complemented
13C22×#11758202C2211yescharacteristic
14C22×C8×D61C2212yes—
15#16840473—24no—
16#16840473C2218yes—
17#16840472—24no—
18#16840472C2218yes—
19C2×#14519777C2211yescharacteristic
20C2×#14519769—21no—
21C2×#14519768—21no—
22C2×#14519757C2212yes—
23C2×#14519755—22no—
24C2×#14519753—22no—
25C2×#14519753C2212yes—
26C2×C4×Dic122C2211yescharacteristic
27C2×C4×D244—21no—
28C2×C4×D244C2211yescharacteristic
29C2×#14519739—21no—
30C2×C4⋊C4×D61C2212yes—
31C2×C4⋊C4×D61C2212yes—
32#16840165C2218yescomplemented
33#16840099C22116yescomplemented
34#16840096C22116yescomplemented
35#16840058C2218yescomplemented
36#16840002C22116yescomplemented
37C4×#11758202C2218yescomplemented
38#16839827C2218yes—
39C2×#14519711C2212yes—
40C2×#14519710C2212yes—
41C2×#14519710C2211yescharacteristic
42C2×#14519710C2212yes—
43#107×D61C22116yescomplemented
44C2×#14519702C2212yes—
45C2×#14519701C2211yescharacteristic
46C2×#14519700C2211yescharacteristic
47C2×#14519689C2212yes—
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—21no—
56C22×Dic122C2311yescharacteristic
57C22×D244D411yescharacteristic
58C22×C4×D61—22no—
59C22×C4×D61—22no—
60C22×C4×D61C2312yes—
61C2×#11758202—24no—
62C2×#11758202C2314yes—
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C2×C8×D61—28no—
66C2×C8×D61C2318yes—
67#14519777—22no—
68#14519777C2314yes—
69#14519769—28no—
70#14519768—28no—
71#14519757—24no—
72#14519757C2318yes—
73#14519755—216no—
74#14519753—24no—
75#14519753—216no—
76#14519753C2318yes—
77C4×Dic122—22no—
78C4×Dic122C2314yes—
79C4×D244—28no—
80C4×D244D414yes—
81C4×D244C2314yes—
82#14519739—28no—
83C2×C4⋊Dic61—21no—
84C2×C4⋊Dic61—22no—
85C2×C4⋊Dic61D411yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2312yes—
88C2×#11758196—21no—
89C2×#11758196—22no—
90C2×#11758196—22no—
91C2×#11758196—22no—
92C4⋊C4×D61—24no—
93C4⋊C4×D61—24no—
94C4⋊C4×D61C2318yes—
95C4⋊C4×D61C2318yes—
96C2×#11758198—22no—
97C2×#11758198—22no—
98C2×#11758198D412yes—
99C2×C4×Dic61—21no—
100#14519711C2318yes—
101#14519710C2318yes—
102#14519710C2314yes—
103#14519710C2318yes—
104#14519702C2318yes—
105#14519701C2314yes—
106#14519700C2314yes—
107#14519689C2318yes—
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×D61C2×D412yes—
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—22no—
140C22×Dic61—21no—
141C22×Dic61C2×D412yes—
142C2×D244Q1618yescomplemented
143C2×D244C2×D414yes—
144C2×C4×D61—24no—
145C2×C4×D61—24no—
146C2×C4×D61—28no—
147C2×C4×D61—28no—
148C2×C4×D61—84no—
149C2×C4×D61—84no—
150C2×C4×D61C2×D414yes—
151C2×C4×D61C2414yes—
152C2×Dic122—22no—
153C2×Dic122—22no—
154C2×Dic122—21no—
155C2×Dic122—24no—
156C2×Dic122—82no—
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#11758198C2×D418yes—
173C4⋊Dic61—21no—
174C4⋊Dic61—22no—
175C4⋊Dic61—24no—
176C4⋊Dic61—28no—
177C4⋊Dic61C2×D414yes—
178C4⋊Dic61C2412yes—
179C4⋊Dic61C2414yes—
180#11758196—24no—
181#11758196—28no—
182#11758196—28no—
183#11758196—28no—
184C4×Dic61—24no—
185C2×#92418—22no—
186C2×#92418#4114yes—
187C2×#92418C2412yes—
188C2×#92418C2412yes—
189C8×D61—216no—
190C23×C61C22×D411yescharacteristic
191C22×D61—24no—
192C22×D61—24no—
193C22×D61C2×Q1618yes—
194C22×D61C22×D414yes—
195Q8×C61—22no—
196Q8×C61—22no—
197Q8×C61—42no—
198Q8×C61—84no—
199C2×C4×C61—22no—
200C2×C4×C61—22no—
201C2×C4×C61—22no—
202C2×C4×C61—24no—
203C2×C4×C61—42no—
204C2×C4×C61—42no—
205C2×C4×C61—44no—
206C2×C4×C61C2×Q1614yes—
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—22no—
215C2×Dic61—22no—
216C2×Dic61—24no—
217C2×Dic61—42no—
218C2×Dic61—44no—
219C2×Dic61—42no—
220C2×Dic61C22×D414yes—
221D244C2×Q16116yescomplemented
222C4×D61—28no—
223C4×D61—24no—
224C4×D61—24no—
225C4×D61—88no—
226C4×D61—88no—
227Dic122—22no—
228Dic122—22no—
229Dic122—42no—
230Dic122—84no—
231C8×C61—24no—
232#92418—22no—
233#92418C2×#4114yes—
234C2×#3338—611nomaximal, Sylow
235C22×C61#54712yes—
236C22×C61C22×Q1612yes—
237C22×C61#57612yes—
238C22×C61C23×D411yescharacteristic
239C2×D61—216no—
240C2×D61—24no—
241C2×D61—24no—
242C2×D61C22×Q1618yes—
243C4×C61—22no—
244C4×C61—42no—
245C4×C61—42no—
246C4×C61—44no—
247C4×C61#54712yes—
248C4×C61C22×Q1614yes—
249C4×C61C22×#4111yescharacteristic
250C4×C61C2×2−1+411yescharacteristic
251Dic61—24no—
252Dic61—42no—
253Dic61—44no—
254Dic61—42no—
255C2×#554—611no—
256C2×#554—611no—
257#3338—6116no—
258C2×#500—611no—
259C2×#484—612no—
260C2×#484—612no—
261C2×#477—611no—
262C2×#477D6111yescharacteristic, complemented
263C2×#467—612no—
264C2×C4×Q16—611no—
265C2×C8×D4—611no—
266C22×#107—612no—
267C2×C61#333814yescomplemented
268C2×C61C2×#54711yescharacteristic
269C2×C61C23×Q1611yescharacteristic
270C2×C61C2×#57611yescharacteristic
271D61—28no—
272C22×Q16—611no—
273C23×C8—612no—
274#554—618no—
275#554—618no—
276#554—1224no—
277#554—1224no—
278C2×C4⋊Q8—611no—
279C2×C4⋊Q8C2×D6111yescharacteristic
280C2×#125—1221no—
281C2×#125—1221no—
282C2×C22⋊Q8—612no—
283C2×C22⋊Q8—612no—
284C2×C22⋊Q8—1222no—
285C2×C22⋊Q8—1222no—
286C2×C4×Q8—611no—
287C2×C4×Q8C2×D6111yescharacteristic
288C2×C4×D4—611no—
289C2×C4×D4—1221no—
290C2×C4×D4—1221no—
291C22×C4⋊C4—612no—
292C22×C4⋊C4—612no—
293#500—618no—
294#484—6116no—
295#484—6116no—
296#477—618no—
297#477C2×D6118yescomplemented
298#467—6116no—
299C4×Q16—618no—
300C8×D4—618no—
301C2×#107—612no—
302C2×#107—612no—
303C2×#107—612no—
304C2×#107—611no—
305C2×#107—6116no—
306C2×#107C2×D6112yes—
307C2×C4⋊C8C2×D6111yescharacteristic
308C2×#103—611no—
309C2×#103—612no—
310C2×#103—611no—
311C2×#103C2×D6112yes—
312C2×C22⋊C8—612no—
313C2×C4×C8—611no—
314C61C2×#333811yescharacteristic, complemented, Sylow
315C22×Q8—21no—
316C22×Q8—611no—
317C22×Q8—1221no—
318C22×Q8C22×D6111yescharacteristic
319C22×D4—611no—
320C23×C4—612no—
321C23×C4—1222no—
322C23×C4—1222no—
323C2×Q16—614no—
324C2×Q16—1224no—
325C22×C8—611no—
326C22×C8—611no—
327C22×C8—618no—
328C22×C8—1228no—
329C22×C8C22×D6112yes—
330C4⋊Q8—22no—
331C4⋊Q8—614no—
332C4⋊Q8—1222no—
333C4⋊Q8C22×D6114yes—
334#125—1228no—
335#125—1228no—
336C22⋊Q8—618no—
337C22⋊Q8—618no—
338C22⋊Q8—12216no—
339C22⋊Q8—12216no—
340C22⋊Q8—1224no—
341C22⋊Q8—1224no—
342C4×Q8—22no—
343C4×Q8—614no—
344C4×Q8—1222no—
345C4×Q8C22×D6114yes—
346C4×D4—614no—
347C4×D4—614no—
348C4×D4—1228no—
349C4×D4—1228no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—611no—
353C2×C4⋊C4—611no—
354C2×C4⋊C4—612no—
355C2×C4⋊C4—618no—
356C2×C4⋊C4—618no—
357C2×C4⋊C4—1224no—
358C2×C4⋊C4—1224no—
359C2×C4⋊C4—1222no—
360C2×C4⋊C4—1222no—
361C2×C4⋊C4—1222no—
362C2×C4⋊C4—1222no—
363C2×C4⋊C4—1221no—
364C2×C4⋊C4—1221no—
365C2×C4⋊C4C22×D6111yescharacteristic
366C2×C4⋊C4C22×D6112yes—
367C2×C22⋊C4—612no—
368C2×C22⋊C4—1222no—
369C2×C22⋊C4—1222no—
370C2×C42—21no—
371C2×C42—1221no—
372C2×C42C22×D6111yescharacteristic
373#107—618no—
374#107—614no—
375#107—618no—
376#107—618no—
377#107C22×D6118yes—
378C4⋊C8C22×D6114yes—
379#103—614no—
380#103—618no—
381#103—614no—
382#103C22×D6118yes—
383C22⋊C8—618no—
384C4×C8—614no—
385C24—612no—
386C2×Q8—21no—
387C2×Q8—24no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—82no—
391C2×Q8—612no—
392C2×Q8—1224no—
393C2×Q8—1221no—
394C2×Q8—1222no—
395C2×Q8—1222no—
396C2×Q8—4882no—
397C2×Q8C23×D6112yes—
398C2×D4—614no—
399C2×D4—618no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—612no—
404C22×C4—614no—
405C22×C4—614no—
406C22×C4—1228no—
407C22×C4—1228no—
408C22×C4—1224no—
409C22×C4—1224no—
410C22×C4—1221no—
411C22×C4—1221no—
412C22×C4—1222no—
413C22×C4—4884no—
414C22×C4—4884no—
415C22×C4D4×D6111yescharacteristic
416C22×C4D4×D6111yescharacteristic
417C22×C4C23×D6111yescharacteristic
418Q16—1228no—
419C2×C8—24no—
420C2×C8—614no—
421C2×C8—612no—
422C2×C8—612no—
423C2×C8—12216no—
424C2×C8—1222no—
425C2×C8C23×D6114yes—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—614no—
431C4⋊C4—612no—
432C4⋊C4—614no—
433C4⋊C4—1228no—
434C4⋊C4—1228no—
435C4⋊C4—1228no—
436C4⋊C4—1228no—
437C4⋊C4—1221no—
438C4⋊C4—1222no—
439C4⋊C4—1224no—
440C4⋊C4—1224no—
441C4⋊C4C23×D6112yes—
442C4⋊C4C23×D6114yes—
443C22⋊C4—618no—
444C22⋊C4—1228no—
445C22⋊C4—1228no—
446C42—24no—
447C42—1224no—
448C42D4×D6112yes—
449C42C23×D6112yes—
450C23—618no—
451C23—614no—
452C23—1224no—
453C23—1224no—
454C23C2×D4×D6111yescharacteristic
455Q8—22no—
456Q8—22no—
457Q8—42no—
458Q8—84no—
459Q8—1222no—
460Q8—1222no—
461Q8—4884no—
462Q8—2442no—
463D4—6116no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—42no—
469C2×C4—44no—
470C2×C4—42no—
471C2×C4—614no—
472C2×C4—1224no—
473C2×C4—1224no—
474C2×C4—1224no—
475C2×C4—1228no—
476C2×C4—1222no—
477C2×C4—1222no—
478C2×C4—1224no—
479C2×C4—4888no—
480C2×C4—4888no—
481C2×C4—2442no—
482C2×C4—2444no—
483C2×C4—2442no—
484C2×C4Q16×D6114yes—
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—614no—
493C8—1222no—
494C22—618no—
495C22—12216no—
496C22—1224no—
497C22—1224no—
498C22#1684041412yes—
499C22C2×Q16×D6112yes—
500C22#1684056612yes—
501C22C22×D4×D6111yescharacteristic
502C4—22no—
503C4—42no—
504C4—42no—
505C4—44no—
506C4—1224no—
507C4—2442no—
508C4—2442no—
509C4—2444no—
510C4#1684041412yes—
511C4C2×Q16×D6114yes—
512C4C2×#41×D6111yescharacteristic
513C4C2×#1451982511yescharacteristic
514C2—1228no—
515C2#2145821014yesdirect product factor
516C2C2×#1684041411yescharacteristic
517C2C22×Q16×D6111yescharacteristic
518C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#477C2
socleC23×C61C22×D4
prime radicalC22×D244D4
hypercenterC2×#477D61
hypocenterC61C2×#3338
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
3. #21458210C2direct (N × H)
4. C2×#16840165C2semidirect
5. C2×#16840099C2semidirect
6. C2×#16840096C2semidirect
7. C2×#16840058C2semidirect
8. C2×#16840002C2semidirect
9. C2×C4×#11758202C2semidirect
11. C2×#107×D61C2semidirect
12. C2×C61×#477C2semidirect
32. #16840165C22semidirect
33. #16840099C22semidirect
34. #16840096C22semidirect
35. #16840058C22semidirect
36. #16840002C22semidirect
37. C4×#11758202C22semidirect
43. #107×D61C22semidirect
51. C61×#477C22semidirect
142. C2×D244Q16semidirect
221. D244C2×Q16semidirect
262. C2×#477D61semidirect
267. C2×C61#3338semidirect
297. #477C2×D61semidirect
314. C61C2×#3338semidirect
515. C2#21458210direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404732
C2×#168404722
#214582102
C2×#168401652
C2×#168400992
C2×#168400962
C2×#168400582
C2×#168400022
C2×C4×#117582022
C2×#168398272
C2×#107×D612
C2×C61×#4772
C2×#333861