Finite Group Databasebeta

← C2×#21458728 #30560501

Subgroups — C2×#21458728 #30560501

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×Q8×Dic122C211yesmaximal, characteristic, complemented
2C2×#16840473C211yesmaximal, characteristic
3#21458728C2116yesmaximal, direct product factor
4C2×#16840170C212yesmaximal, complemented
5C2×#16840165C211yesmaximal, characteristic, complemented
6C2×#16840067C212yesmaximal, complemented
7C2×#16840053C211yesmaximal, characteristic
8C2×#16840041C212yesmaximal
9C2×#16839889C211yesmaximal, characteristic, complemented
10C2×#16839865C212yesmaximal
11C2×C4×#11758201C211yesmaximal, characteristic
12C2×C61×#477C211yesmaximal, characteristic, complemented
13C22×#11758201C2211yescharacteristic
14Q8×Dic122—24no—
15Q8×Dic122C2218yescomplemented
16#16840473—24no—
17#16840473C2218yes—
18C2×#14519777—21no—
19C2×#14519777C2211yescharacteristic
20C2×#14519776—22no—
21C2×#14519776C2212yes—
22C2×#14519768C2212yes—
23C2×#14519757—21no—
24C2×#14519753—22no—
25C2×Q8×Dic61C2212yes—
26C2×C4×Dic122—21no—
27C2×C4×Dic122C2211yescharacteristic
28C2×C4×D244C2211yescharacteristic
29C2×#14519739C2212yes—
30C2×C4⋊C4×D61—21no—
31#16840170C22116yescomplemented
32#16840165C2218yescomplemented
33#16840067C22116yescomplemented
34#16840053C2218yes—
35#16840041C22116yes—
36#16839889C2218yescomplemented
37#16839865C22116yes—
38C4×#11758201C2218yes—
39C2×#14519710C2212yes—
40C2×#14519710C2212yes—
41C2×#14519709C2212yes—
42C2×#14519708C2211yescharacteristic
43C2×#14519706C2212yes—
44C2×#14519701C2211yescharacteristic
45C2×#14519699C2212yes—
46C2×#14519697C2211yescharacteristic
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—21no—
56C22×Dic122—22no—
57C22×Dic122D411yescharacteristic
58C22×D244C2311yescharacteristic
59C22×C4×D61—21no—
60C22×C4×D61—22no—
61C2×#11758201Q818yescomplemented
62C2×#11758201C2314yes—
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65#14519777—22no—
66#14519777—28no—
67#14519777C2314yes—
68#14519776—216no—
69#14519776—24no—
70#14519776C2318yes—
71#14519768—24no—
72#14519768C2318yes—
73#14519757—28no—
74#14519753—216no—
75Q8×Dic61—24no—
76Q8×Dic61C2318yes—
77C4×Dic122—28no—
78C4×Dic122D414yes—
79C4×Dic122C2314yes—
80C4×D244—22no—
81C4×D244C2314yes—
82#14519739—24no—
83#14519739C2318yes—
84C2×C4⋊Dic61—21no—
85C2×C4⋊Dic61—22no—
86C2×C4⋊Dic61—22no—
87C2×C4⋊Dic61D411yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2312yes—
90C2×#11758196—22no—
91C2×#11758196—22no—
92C2×#11758196D412yes—
93C4⋊C4×D61—28no—
94C2×#11758198—21no—
95C2×#11758198—22no—
96C2×C4×Dic61—22no—
97C2×C4×Dic61C2312yes—
98#14519710C2318yes—
99#14519710C2318yes—
100#14519709C2318yes—
101#14519708C2314yes—
102#14519706C2318yes—
103#14519701C2314yes—
104#14519699C2318yes—
105#14519697C2314yes—
106#14519687C2318yes—
107C4×#92418C2314yes—
108C22×Q8×C61—21no—
109C22×Q8×C61C2311yescharacteristic
110C22×C8×C61C2312yes—
111C4⋊Q8×C61—22no—
112C4⋊Q8×C61C2314yes—
113C4×Q8×C61—22no—
114C4×Q8×C61C2314yes—
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61—21no—
117C2×C4⋊C4×C61C2312yes—
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C42×C61—21no—
120C2×C42×C61C2311yescharacteristic
121#107×C61C2318yes—
122C4⋊C8×C61C2314yes—
123#103×C61C2318yes—
124C23×D61—21no—
125C2×Q8×C61—21no—
126C2×Q8×C61—24no—
127C2×Q8×C61—22no—
128C2×Q8×C61—82no—
129C2×Q8×C61C2×Q814yes—
130C2×Q8×C61C2412yes—
131C22×C4×C61—21no—
132C22×C4×C61—22no—
133C22×C4×C61—21no—
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2411yescharacteristic
137C22×Dic61—21no—
138C22×Dic61—22no—
139C22×Dic61C2×D412yes—
140C22×Dic61C2×D412yes—
141C2×D244—21no—
142C2×D244—22no—
143C2×D244C2×Q814yes—
144C2×D244C2412yes—
145C2×C4×D61—24no—
146C2×C4×D61—28no—
147C2×C4×D61—44no—
148C2×C4×D61—84no—
149C2×Dic122—24no—
150C2×Dic122—24no—
151C2×Dic122—28no—
152C2×Dic122—84no—
153C2×Dic122—82no—
154C2×Dic122C2×D414yes—
155C2×C8×C61—24no—
156C2×C8×C61C2414yes—
157C4⋊C4×C61—24no—
158C4⋊C4×C61—24no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—22no—
161C4⋊C4×C61C2414yes—
162C4⋊C4×C61C2412yes—
163C42×C61—24no—
164C42×C61C2×D412yes—
165C42×C61C2412yes—
166#11758201C2×Q8116yescomplemented
167#11758198—24no—
168#11758198—28no—
169C4⋊Dic61—24no—
170C4⋊Dic61—21no—
171C4⋊Dic61—22no—
172C4⋊Dic61—28no—
173C4⋊Dic61—28no—
174C4⋊Dic61C2×D414yes—
175C4⋊Dic61C2414yes—
176C4⋊Dic61C2412yes—
177#11758196—28no—
178#11758196—28no—
179#11758196C2×D418yes—
180C4×Dic61—28no—
181C4×Dic61C2×D414yes—
182C4×Dic61C2414yes—
183C2×#92418—22no—
184C2×#92418C2×Q814yes—
185C2×#92418C2412yes—
186C2×#92418C2412yes—
187C23×C61C22×D411yescharacteristic
188C22×D61—24no—
189C22×D61—22no—
190C22×D61—42no—
191C22×D61—42no—
192Q8×C61—24no—
193Q8×C61—22no—
194Q8×C61—84no—
195Q8×C61C22×Q814yes—
196C2×C4×C61—24no—
197C2×C4×C61—22no—
198C2×C4×C61—22no—
199C2×C4×C61—22no—
200C2×C4×C61—24no—
201C2×C4×C61—42no—
202C2×C4×C61—44no—
203C2×C4×C61#13714yes—
204C2×C4×C61C22×D412yes—
205C2×C4×C61C22×D411yescharacteristic
206C2×C4×C61C22×D412yes—
207C2×C4×C61C22×Q812yes—
208C2×C4×C612−1+412yes—
209C2×C4×C61C2511yescharacteristic
210C2×Dic61—24no—
211C2×Dic61—24no—
212C2×Dic61—24no—
213C2×Dic61—22no—
214C2×Dic61—42no—
215C2×Dic61—44no—
216C2×Dic61C22×D414yes—
217C2×Dic61C22×D414yes—
218D244—24no—
219D244—22no—
220D244C22×Q814yes—
221C4×D61—48no—
222C4×D61—88no—
223Dic122—28no—
224Dic122—88no—
225Dic122—84no—
226C8×C61—24no—
227#92418—22no—
228#92418C22×Q814yes—
229C2×#3385—611nomaximal, Sylow
230C22×C61D4×Q812yes—
231C22×C61C2×#13712yes—
232C22×C61#57612yes—
233C22×C61C23×D411yescharacteristic
234C2×D61—24no—
235C2×D61—48no—
236C2×D61—42no—
237C2×D61—42no—
238C4×C61—24no—
239C4×C61—22no—
240C4×C61—42no—
241C4×C61—44no—
242C4×C61D4×Q812yes—
243C4×C61C2×#13714yes—
244C4×C61C23×Q811yescharacteristic
245C4×C61C2×2−1+411yescharacteristic
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×#477D6111yescharacteristic, complemented
257C2×#476—611no—
258C2×#474—612no—
259C2×#446—611no—
260C2×#440—612no—
261C2×C4×SD16—611no—
262C2×C61#338514yescomplemented
263C2×C61C2×D4×Q811yescharacteristic
264C2×C61C22×#13711yescharacteristic
265C2×C61C2×#57611yescharacteristic
266D61—44no—
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—1221no—
279C2×C22⋊Q8—1222no—
280C2×C4×Q8—611no—
281C2×C4×Q8—612no—
282C2×C4×Q8—1221no—
283C2×C4×Q8C2×D6111yescharacteristic
284C2×C4×D4—612no—
285C2×C4×D4—611no—
286C22×C4⋊C4—1221no—
287#501—6116no—
288#500—618no—
289#479—6116no—
290#477C2×D6118yescomplemented
291#476—618no—
292#474—6116no—
293#446—618no—
294#440—6116no—
295C4×SD16—618no—
296C2×#107—612no—
297C2×#107—612no—
298C2×#107C2×D6112yes—
299C2×#106—612no—
300C2×#106—611no—
301C2×C4⋊C8—612no—
302C2×C4⋊C8C2×D6111yescharacteristic
303C2×#103—611no—
304C2×#103C2×D6112yes—
305C2×#102—612no—
306C2×#102—611no—
307C2×#97—612no—
308C2×C4×C8—611no—
309C61C2×#338511yescharacteristic, complemented, Sylow
310C22×Q8—21no—
311C22×Q8—611no—
312C22×Q8—1222no—
313C22×Q8—1221no—
314C22×Q8C22×D6111yescharacteristic
315C22×D4—611no—
316C23×C4—1222no—
317C23×C4—1221no—
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—1228no—
327C4⋊Q8—1224no—
328C4⋊Q8—12216no—
329C4⋊Q8—1222no—
330C4⋊Q8C22×D6114yes—
331#125—618no—
332#125—1224no—
333C22⋊Q8—1228no—
334C22⋊Q8—12216no—
335C4×Q8—22no—
336C4×Q8—614no—
337C4×Q8—614no—
338C4×Q8—618no—
339C4×Q8—1228no—
340C4×Q8—1224no—
341C4×Q8C22×D6114yes—
342C4×D4—618no—
343C4×D4—614no—
344C4×D4—1224no—
345C4×D4—1222no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—611no—
349C2×C4⋊C4—612no—
350C2×C4⋊C4—611no—
351C2×C4⋊C4—612no—
352C2×C4⋊C4—1228no—
353C2×C4⋊C4—1222no—
354C2×C4⋊C4—1222no—
355C2×C4⋊C4—1222no—
356C2×C4⋊C4—1222no—
357C2×C4⋊C4—1221no—
358C2×C4⋊C4C22×D6112yes—
359C2×C4⋊C4C22×D6111yescharacteristic
360C2×C22⋊C4—1222no—
361C2×C22⋊C4—1221no—
362C2×C42—21no—
363C2×C42—612no—
364C2×C42—1222no—
365C2×C42C22×D6111yescharacteristic
366#107—618no—
367#107—618no—
368#107C22×D6118yes—
369#106—618no—
370#106—614no—
371C4⋊C8—618no—
372C4⋊C8C22×D6114yes—
373#103—614no—
374#103C22×D6118yes—
375#102—618no—
376#102—614no—
377#97—618no—
378C4×C8—614no—
379C24—1221no—
380C2×Q8—21no—
381C2×Q8—24no—
382C2×Q8—22no—
383C2×Q8—82no—
384C2×Q8—614no—
385C2×Q8—1228no—
386C2×Q8—1224no—
387C2×Q8—1224no—
388C2×Q8—4882no—
389C2×Q8—4884no—
390C2×Q8Q8×D6114yes—
391C2×Q8C23×D6112yes—
392C2×D4—614no—
393C2×D4—612no—
394C2×D4—1221no—
395C2×D4—1222no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—612no—
400C22×C4—612no—
401C22×C4—1228no—
402C22×C4—1222no—
403C22×C4—1221no—
404C22×C4—1224no—
405C22×C4—4884no—
406C22×C4—2444no—
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—24no—
419C4⋊C4—22no—
420C4⋊C4—21no—
421C4⋊C4—614no—
422C4⋊C4—618no—
423C4⋊C4—614no—
424C4⋊C4—612no—
425C4⋊C4—1228no—
426C4⋊C4—1228no—
427C4⋊C4—1228no—
428C4⋊C4—1228no—
429C4⋊C4—1221no—
430C4⋊C4—1222no—
431C4⋊C4—1224no—
432C4⋊C4C23×D6112yes—
433C4⋊C4C23×D6114yes—
434C22⋊C4—1228no—
435C22⋊C4—1224no—
436C42—24no—
437C42—614no—
438C42—614no—
439C42—1228no—
440C42D4×D6112yes—
441C42C23×D6112yes—
442C23—1222no—
443C23—1224no—
444C23—2442no—
445C23—2442no—
446C23C2×D4×D6111yescharacteristic
447Q8—22no—
448Q8—24no—
449Q8—84no—
450Q8—1228no—
451Q8—4884no—
452Q8—4888no—
453Q8C2×Q8×D6114yes—
454D4—614no—
455D4—1222no—
456D4—1224no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—44no—
463C2×C4—42no—
464C2×C4—614no—
465C2×C4—614no—
466C2×C4—1224no—
467C2×C4—1224no—
468C2×C4—1224no—
469C2×C4—1222no—
470C2×C4—4888no—
471C2×C4—2442no—
472C2×C4—2444no—
473C2×C4—2448no—
474C2×C4#1451980914yes—
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—1224no—
485C22—2448no—
486C22—2442no—
487C22—2442no—
488C22#1684042512yes—
489C22C2×#1451980912yes—
490C22#1684056612yes—
491C22C22×D4×D6111yescharacteristic
492C4—24no—
493C4—22no—
494C4—44no—
495C4—42no—
496C4—1224no—
497C4—1224no—
498C4—2442no—
499C4—2444no—
500C4#1684042512yes—
501C4C2×#1451980914yes—
502C4C22×Q8×D6111yescharacteristic
503C4C2×#1451982411yescharacteristic
504C2—2444no—
505C2#2145872814yesdirect product factor
506C2C2×#1684042511yescharacteristic
507C2C22×#1451980911yescharacteristic
508C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#477C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenterC2×#477D61
hypocenterC61C2×#3385
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
1. C2×Q8×Dic122C2semidirect
3. #21458728C2direct (N × H)
4. C2×#16840170C2semidirect
5. C2×#16840165C2semidirect
6. C2×#16840067C2semidirect
9. C2×#16839889C2semidirect
12. C2×C61×#477C2semidirect
15. Q8×Dic122C22semidirect
31. #16840170C22semidirect
32. #16840165C22semidirect
33. #16840067C22semidirect
36. #16839889C22semidirect
51. C61×#477C22semidirect
61. C2×#11758201Q8semidirect
166. #11758201C2×Q8semidirect
256. C2×#477D61semidirect
262. C2×C61#3385semidirect
290. #477C2×D61semidirect
309. C61C2×#3385semidirect
505. C2#21458728direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×Dic1222
C2×#168404732
#214587282
C2×#168401702
C2×#168401652
C2×#168400672
C2×#168400532
C2×#168400412
C2×#168398892
C2×#168398652
C2×C4×#117582012
C2×C61×#4772
C2×#338561