Finite Group Databasebeta

← C2×#21458733 #30560506

Subgroups — C2×#21458733 #30560506

Order 15616.

1854 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840492C211yesmaximal, characteristic, complemented
2C2×#16840469C211yesmaximal, characteristic
3#21458733C2116yesmaximal, direct product factor
4C2×#16840169C212yesmaximal, complemented
5C2×#16840165C211yesmaximal, characteristic, complemented
6C2×#16840072C212yesmaximal, complemented
7C2×#16840058C211yesmaximal, characteristic, complemented
8C2×#16840040C212yesmaximal
9C2×#16839889C211yesmaximal, characteristic, complemented
10C2×#16839859C212yesmaximal
11C2×C4×#11758200C211yesmaximal, characteristic
12C2×C61×#476C211yesmaximal, characteristic
13C22×#11758200C2211yescharacteristic
14#16840492—24no—
15#16840492C2218yescomplemented
16#16840469—24no—
17#16840469C2218yes—
18C2×#14519777C2211yescharacteristic
19C2×#14519776—21no—
20C2×#14519776C2212yes—
21C2×#14519775—22no—
22C2×#14519768C2212yes—
23C2×#14519756—21no—
24C2×#14519754—22no—
25C2×C4×Dic122C2211yescharacteristic
26C2×C4×Dic122C2211yescharacteristic
27C2×#14519742—21no—
28C2×#14519742C2212yes—
29C2×D4×Dic61C2212yes—
30C22×C4⋊Dic61—21no—
31#16840169C22116yescomplemented
32#16840165C2218yescomplemented
33#16840072C22116yescomplemented
34#16840058C2218yescomplemented
35#16840040C22116yes—
36#16839889C2218yescomplemented
37#16839859C22116yes—
38C4×#11758200C2218yes—
39C2×#14519711C2212yes—
40C2×#14519710C2212yes—
41C2×#14519710C2212yes—
42C2×#14519708C2211yescharacteristic
43C2×#14519706C2212yes—
44C2×#14519702C2212yes—
45C2×#14519700C2211yescharacteristic
46C2×#14519698C2211yescharacteristic
47C2×#14519687C2212yes—
48C2×C4×#92418C2211yescharacteristic
49C2×C4⋊Q8×C61C2211yescharacteristic
50C2×C4×D4×C61C2211yescharacteristic
51C61×#476C2218yes—
52C2×#106×C61C2212yes—
53C2×C4⋊C8×C61C2211yescharacteristic
54C2×#102×C61C2212yes—
55C22×Dic122—21no—
56C22×Dic122—22no—
57C22×Dic122D411yescharacteristic
58C22×Dic122C2311yescharacteristic
59C23×Dic61—22no—
60C2×#11758200Q818yescomplemented
61C2×#11758200C2314yes—
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64#14519777—22no—
65#14519777C2314yes—
66#14519776—28no—
67#14519776—24no—
68#14519776C2318yes—
69#14519775—216no—
70#14519768—24no—
71#14519768C2318yes—
72#14519756—28no—
73#14519754—216no—
74C4×Dic122—22no—
75C4×Dic122D414yes—
76C4×Dic122C2314yes—
77C4×Dic122C2314yes—
78#14519742—28no—
79#14519742—24no—
80#14519742C2318yes—
81D4×Dic61—24no—
82D4×Dic61C2318yes—
83C2×C4⋊Dic61—21no—
84C2×C4⋊Dic61—22no—
85C2×C4⋊Dic61—28no—
86C2×C4⋊Dic61D411yescharacteristic
87C2×C4⋊Dic61C2312yes—
88C2×C4⋊Dic61C2311yescharacteristic
89C2×#11758196—21no—
90C2×#11758196—22no—
91C2×#11758196—22no—
92C2×#11758196—22no—
93C2×#11758196D412yes—
94C2×C22⋊Dic61—22no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61—22no—
97C2×C4×Dic61C2312yes—
98#14519711C2318yes—
99#14519710C2318yes—
100#14519710C2318yes—
101#14519708C2314yes—
102#14519706C2318yes—
103#14519702C2318yes—
104#14519700C2314yes—
105#14519698C2314yes—
106#14519687C2318yes—
107C4×#92418C2314yes—
108C22×Q8×C61—21no—
109C22×D4×C61C2311yescharacteristic
110C23×C4×C61—21no—
111C22×C8×C61C2312yes—
112C4⋊Q8×C61—22no—
113C4⋊Q8×C61C2314yes—
114C4×D4×C61—22no—
115C4×D4×C61C2314yes—
116C2×C4⋊C4×C61—21no—
117C2×C4⋊C4×C61C2312yes—
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C22⋊C4×C61—21no—
120C2×C42×C61C2311yescharacteristic
121#106×C61C2318yes—
122C4⋊C8×C61C2314yes—
123#102×C61C2318yes—
124C24×C61—21no—
125C2×Q8×C61—24no—
126C2×Q8×C61—82no—
127C2×D4×C61—21no—
128C2×D4×C61—22no—
129C2×D4×C61C2×Q814yes—
130C2×D4×C61C2412yes—
131C22×C4×C61—22no—
132C22×C4×C61—21no—
133C22×C4×C61—24no—
134C22×C4×C61—44no—
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2411yescharacteristic
138C22×Dic61—21no—
139C22×Dic61—22no—
140C22×Dic61—21no—
141C22×Dic61—28no—
142C22×Dic61—84no—
143C22×Dic61C2×D412yes—
144C22×Dic61C2×D412yes—
145C2×Dic122—24no—
146C2×Dic122—21no—
147C2×Dic122—22no—
148C2×Dic122—24no—
149C2×Dic122—28no—
150C2×Dic122—84no—
151C2×Dic122—82no—
152C2×Dic122C2×D414yes—
153C2×Dic122C2×Q814yes—
154C2×Dic122C2412yes—
155C2×C8×C61—24no—
156C2×C8×C61C2414yes—
157C4⋊C4×C61—24no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—22no—
160C4⋊C4×C61C2414yes—
161C4⋊C4×C61C2412yes—
162C22⋊C4×C61—24no—
163C42×C61C2×D412yes—
164C42×C61C2412yes—
165C22⋊Dic61—28no—
166#11758200C2×Q8116yescomplemented
167C4⋊Dic61—24no—
168C4⋊Dic61—22no—
169C4⋊Dic61—21no—
170C4⋊Dic61—28no—
171C4⋊Dic61C2×D414yes—
172C4⋊Dic61C2412yes—
173C4⋊Dic61C2414yes—
174#11758196—24no—
175#11758196—28no—
176#11758196—28no—
177#11758196—28no—
178#11758196C2×D418yes—
179C4×Dic61—24no—
180C4×Dic61—28no—
181C4×Dic61C2×D414yes—
182C4×Dic61C2414yes—
183C2×#92418—22no—
184C2×#92418C2×Q814yes—
185C2×#92418C2412yes—
186C2×#92418C2412yes—
187C23×C61—24no—
188C23×C61—22no—
189C23×C61—42no—
190C23×C61—42no—
191C23×C61C22×D411yescharacteristic
192Q8×C61—84no—
193D4×C61—24no—
194D4×C61—22no—
195D4×C61C22×Q814yes—
196C2×C4×C61—22no—
197C2×C4×C61—24no—
198C2×C4×C61—22no—
199C2×C4×C61—42no—
200C2×C4×C61—44no—
201C2×C4×C61—48no—
202C2×C4×C61#13714yes—
203C2×C4×C61C22×D412yes—
204C2×C4×C61C22×D411yescharacteristic
205C2×C4×C61C22×D412yes—
206C2×C4×C61C22×Q812yes—
207C2×C4×C612−1+412yes—
208C2×C4×C61C2511yescharacteristic
209C2×Dic61—24no—
210C2×Dic61—24no—
211C2×Dic61—24no—
212C2×Dic61—22no—
213C2×Dic61—22no—
214C2×Dic61—24no—
215C2×Dic61—42no—
216C2×Dic61—44no—
217C2×Dic61—88no—
218C2×Dic61C22×D414yes—
219C2×Dic61C22×D414yes—
220Dic122—24no—
221Dic122—28no—
222Dic122—22no—
223Dic122—88no—
224Dic122—84no—
225Dic122C22×Q814yes—
226C8×C61—24no—
227#92418—22no—
228#92418C22×Q814yes—
229C2×#3385—611nomaximal, Sylow
230C22×C61—24no—
231C22×C61—48no—
232C22×C61—42no—
233C22×C61—42no—
234C22×C61D4×Q812yes—
235C22×C61C2×#13712yes—
236C22×C61#57612yes—
237C22×C61C23×D411yescharacteristic
238C4×C61—22no—
239C4×C61—42no—
240C4×C61—44no—
241C4×C61D4×Q812yes—
242C4×C61C2×#13714yes—
243C4×C61C23×Q811yescharacteristic
244C4×C61C2×2−1+411yescharacteristic
245Dic61—24no—
246Dic61—24no—
247Dic61—24no—
248Dic61—42no—
249Dic61—44no—
250C2×Q82—611no—
251C2×#554—611no—
252#3385—6116no—
253C2×#501—612no—
254C2×#500—611no—
255C2×#479—612no—
256C2×#477—611no—
257C2×#476D6111yescharacteristic
258C2×#474—612no—
259C2×#446—611no—
260C2×#440—612no—
261C2×C4×SD16—611no—
262C2×C61—44no—
263C2×C61#338514yescomplemented
264C2×C61C2×D4×Q811yescharacteristic
265C2×C61C22×#13711yescharacteristic
266C2×C61C2×#57611yescharacteristic
267C22×SD16—611no—
268Q82—618no—
269Q82—1224no—
270#554—618no—
271#554—1224no—
272C2×C4⋊Q8—612no—
273C2×C4⋊Q8—611no—
274C2×C4⋊Q8—1221no—
275C2×C4⋊Q8—1222no—
276C2×C4⋊Q8C2×D6111yescharacteristic
277C2×#125—612no—
278C2×C22⋊Q8—1222no—
279C2×C22⋊Q8—1221no—
280C2×C4×Q8—611no—
281C2×C4×Q8—612no—
282C2×C4×Q8—611no—
283C2×C4×Q8—1221no—
284C2×C4×D4—612no—
285C2×C4×D4C2×D6111yescharacteristic
286C22×C4⋊C4—1221no—
287#501—6116no—
288#500—618no—
289#479—6116no—
290#477—618no—
291#476C2×D6118yes—
292#474—6116no—
293#446—618no—
294#440—6116no—
295C4×SD16—618no—
296C2×#107—612no—
297C2×#107—612no—
298C2×#107—612no—
299C2×#106—611no—
300C2×#106C2×D6112yes—
301C2×C4⋊C8—612no—
302C2×C4⋊C8C2×D6111yescharacteristic
303C2×#103—612no—
304C2×#103—611no—
305C2×#102—611no—
306C2×#102C2×D6112yes—
307C2×#97—612no—
308C2×C4×C8—611no—
309C61C2×#338511yescharacteristic, complemented, Sylow
310C22×Q8—21no—
311C22×Q8—611no—
312C22×Q8—611no—
313C22×Q8—1222no—
314C22×Q8—1221no—
315C22×D4C22×D6111yescharacteristic
316C23×C4—21no—
317C23×C4—1222no—
318C2×SD16—618no—
319C2×SD16—614no—
320C22×C8—611no—
321C22×C8—611no—
322C22×C8C22×D6112yes—
323C4⋊Q8—22no—
324C4⋊Q8—618no—
325C4⋊Q8—614no—
326C4⋊Q8—1224no—
327C4⋊Q8—1228no—
328C4⋊Q8—12216no—
329C4⋊Q8—1222no—
330C4⋊Q8C22×D6114yes—
331#125—618no—
332#125—1224no—
333C22⋊Q8—12216no—
334C22⋊Q8—1228no—
335C4×Q8—614no—
336C4×Q8—614no—
337C4×Q8—618no—
338C4×Q8—614no—
339C4×Q8—1224no—
340C4×Q8—1228no—
341C4×Q8—1222no—
342C4×D4—22no—
343C4×D4—618no—
344C4×D4—1224no—
345C4×D4C22×D6114yes—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—611no—
348C2×C4⋊C4—612no—
349C2×C4⋊C4—612no—
350C2×C4⋊C4—611no—
351C2×C4⋊C4—1228no—
352C2×C4⋊C4—1222no—
353C2×C4⋊C4—1222no—
354C2×C4⋊C4—1222no—
355C2×C4⋊C4—1222no—
356C2×C4⋊C4—1221no—
357C2×C4⋊C4—1221no—
358C2×C4⋊C4C22×D6111yescharacteristic
359C2×C4⋊C4C22×D6112yes—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—1222no—
362C2×C42—612no—
363C2×C42—1222no—
364C2×C42—1221no—
365C2×C42C22×D6111yescharacteristic
366#107—618no—
367#107—618no—
368#107—618no—
369#106—614no—
370#106C22×D6118yes—
371C4⋊C8—618no—
372C4⋊C8C22×D6114yes—
373#103—618no—
374#103—614no—
375#102—614no—
376#102C22×D6118yes—
377#97—618no—
378C4×C8—614no—
379C24—21no—
380C2×Q8—24no—
381C2×Q8—82no—
382C2×Q8—614no—
383C2×Q8—614no—
384C2×Q8—612no—
385C2×Q8—1228no—
386C2×Q8—1221no—
387C2×Q8—1224no—
388C2×Q8—1222no—
389C2×Q8—1224no—
390C2×Q8—4882no—
391C2×Q8—4884no—
392C2×D4—21no—
393C2×D4—22no—
394C2×D4Q8×D6114yes—
395C2×D4C23×D6112yes—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—24no—
399C22×C4—44no—
400C22×C4—612no—
401C22×C4—612no—
402C22×C4—1228no—
403C22×C4—1221no—
404C22×C4—1221no—
405C22×C4—1222no—
406C22×C4—4884no—
407C22×C4D4×D6111yescharacteristic
408C22×C4D4×D6111yescharacteristic
409C22×C4C23×D6111yescharacteristic
410SD16—6116no—
411C2×C8—24no—
412C2×C8—614no—
413C2×C8—612no—
414C2×C8—612no—
415C2×C8—1222no—
416C2×C8C23×D6114yes—
417C4⋊C4—24no—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—614no—
421C4⋊C4—618no—
422C4⋊C4—612no—
423C4⋊C4—614no—
424C4⋊C4—1228no—
425C4⋊C4—1228no—
426C4⋊C4—1228no—
427C4⋊C4—1228no—
428C4⋊C4—1222no—
429C4⋊C4—1221no—
430C4⋊C4—1224no—
431C4⋊C4—1224no—
432C4⋊C4C23×D6114yes—
433C4⋊C4C23×D6112yes—
434C22⋊C4—24no—
435C22⋊C4—1228no—
436C42—614no—
437C42—614no—
438C42—1228no—
439C42—1224no—
440C42D4×D6112yes—
441C42C23×D6112yes—
442C23—22no—
443C23—24no—
444C23—42no—
445C23—42no—
446C23C2×D4×D6111yescharacteristic
447Q8—84no—
448Q8—614no—
449Q8—1228no—
450Q8—1222no—
451Q8—1224no—
452Q8—4884no—
453Q8—4888no—
454D4—22no—
455D4—24no—
456D4C2×Q8×D6114yes—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—42no—
461C2×C4—44no—
462C2×C4—48no—
463C2×C4—614no—
464C2×C4—614no—
465C2×C4—1224no—
466C2×C4—1224no—
467C2×C4—1222no—
468C2×C4—1224no—
469C2×C4—1222no—
470C2×C4—1224no—
471C2×C4—4888no—
472C2×C4—2444no—
473C2×C4—2442no—
474C2×C4#1451980614yes—
475C2×C4C2×D4×D6112yes—
476C2×C4C2×D4×D6112yes—
477C2×C4C2×D4×D6111yescharacteristic
478C2×C4C2×Q8×D6112yes—
479C2×C4#1451982412yes—
480C2×C4C24×D6111yescharacteristic
481C8—24no—
482C8—614no—
483C8—1222no—
484C22—24no—
485C22—48no—
486C22—42no—
487C22—42no—
488C22#1684042512yes—
489C22C2×#1451980612yes—
490C22#1684056612yes—
491C22C22×D4×D6111yescharacteristic
492C4—22no—
493C4—42no—
494C4—44no—
495C4—1224no—
496C4—1224no—
497C4—1224no—
498C4—2444no—
499C4—2442no—
500C4#1684042512yes—
501C4C2×#1451980614yes—
502C4C22×Q8×D6111yescharacteristic
503C4C2×#1451982411yescharacteristic
504C2—44no—
505C2#2145873314yesdirect product factor
506C2C2×#1684042511yescharacteristic
507C2C22×#1451980611yescharacteristic
508C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#476C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
hypercenterC2×#476D61
hypocenterC61C2×#3385
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#16840492C2semidirect
3. #21458733C2direct (N × H)
4. C2×#16840169C2semidirect
5. C2×#16840165C2semidirect
6. C2×#16840072C2semidirect
7. C2×#16840058C2semidirect
9. C2×#16839889C2semidirect
15. #16840492C22semidirect
31. #16840169C22semidirect
32. #16840165C22semidirect
33. #16840072C22semidirect
34. #16840058C22semidirect
36. #16839889C22semidirect
60. C2×#11758200Q8semidirect
166. #11758200C2×Q8semidirect
263. C2×C61#3385semidirect
309. C61C2×#3385semidirect
505. C2#21458733direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404922
C2×#168404692
#214587332
C2×#168401692
C2×#168401652
C2×#168400722
C2×#168400582
C2×#168400402
C2×#168398892
C2×#168398592
C2×C4×#117582002
C2×C61×#4762
C2×#338561