Finite Group Databasebeta

← C2×#21455685 #30547610

Subgroups — C2×#21455685 #30547610

Order 15616.

2094 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840393C211yesmaximal, characteristic, complemented
2C2×#16840245C211yesmaximal, characteristic
3#21455685C2116yesmaximal, direct product factor
4C2×#16840071C212yesmaximal, complemented
5C2×#16840045C212yesmaximal, complemented
6C2×#16840060C212yesmaximal, complemented
7C2×#16840050C212yesmaximal, complemented
8C2×#16839804C211yesmaximal, characteristic, complemented
9C22×#14519708C211yesmaximal, characteristic, complemented
10C2×#16839790C211yesmaximal, characteristic, complemented
11C2×#16839758C211yesmaximal, characteristic
12C2×C61×#417C211yesmaximal, characteristic
13C23×#92418C2211yescharacteristic
14#16840393—24no—
15#16840393C2218yescomplemented
16C2×#14519776—21no—
17C2×#14519776C2212yes—
18C2×#14519768—21no—
19C2×#14519768C2212yes—
20C2×#14519756—22no—
21#16840245—24no—
22#16840245C2218yes—
23C2×Q8×Dic61C2212yes—
24C2×D4×Dic61—22no—
25C2×D4×Dic61C2212yes—
26C2×#14519736—21no—
27C2×#14519736C2211yescharacteristic
28C2×#14519736C2211yescharacteristic
29C22×C4⋊Dic61—21no—
30C22×C4⋊Dic61C2211yescharacteristic
31#16840071C22116yescomplemented
32#16840060C22116yescomplemented
33#16840050C22116yescomplemented
34#16840045C22116yescomplemented
35#16839804C2218yescomplemented
36C2×#14519711C2212yes—
37C2×#14519709C2212yes—
38C2×#14519708C2212yes—
39C2×#14519708C2212yes—
40C2×#14519708C2218yescomplemented
41#16839790C2218yescomplemented
42C2×#14519706C2212yes—
43C2×#14519706C2212yes—
44#16839758C2218yes—
45C2×#14519701C2211yescharacteristic
46C2×#14519701C2211yescharacteristic
47C2×#14519698C2211yescharacteristic
48C2×#14519698C2211yescharacteristic
49C22×#41×C61C2211yescharacteristic
50C22×M16×C61C2211yescharacteristic
51C22×C4⋊C4×C61C2211yescharacteristic
52C61×#417C2218yes—
53C2×#103×C61C2212yes—
54C2×#102×C61C2212yes—
55C22×Dic122—22no—
56C23×Dic61—21no—
57C23×Dic61—22no—
58C22×#92418—24no—
59C22×#92418C2311yescharacteristic
60C22×#92418C2311yescharacteristic
61C22×#92418C2314yes—
62#14519776—28no—
63#14519776—24no—
64#14519776C2318yes—
65#14519768—28no—
66#14519768—24no—
67#14519768C2318yes—
68#14519756—216no—
69Q8×Dic61—24no—
70Q8×Dic61C2318yes—
71D4×Dic61—216no—
72D4×Dic61—24no—
73D4×Dic61C2318yes—
74#14519736—22no—
75#14519736—28no—
76#14519736D414yes—
77#14519736C2314yes—
78#14519736C2314yes—
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61—22no—
81C2×C4⋊Dic61—22no—
82C2×C4⋊Dic61—22no—
83C2×C4⋊Dic61—28no—
84C2×C4⋊Dic61D411yescharacteristic
85C2×C4⋊Dic61D411yescharacteristic
86C2×C4⋊Dic61C2312yes—
87C2×C4⋊Dic61C2314yes—
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×#11758196—22no—
91C2×#11758196—22no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—22no—
94C2×C22⋊Dic61D412yes—
95C2×C4×Dic61—21no—
96C2×C4×Dic61—22no—
97C2×C4×Dic61C2312yes—
98#14519711C2318yes—
99#14519709C2318yes—
100#14519708C2318yes—
101#14519708C2318yes—
102#14519706C2318yes—
103#14519706C2318yes—
104#14519701C2314yes—
105#14519701C2314yes—
106#14519698C2314yes—
107#14519698C2314yes—
108C2×#41×C61—22no—
109C2×#41×C61—24no—
110C2×#41×C61Q818yescomplemented
111C2×#41×C61C2314yes—
112C22×Q8×C61C2311yescharacteristic
113C22×D4×C61—21no—
114C22×D4×C61C2311yescharacteristic
115C23×C4×C61—21no—
116C23×C4×C61—21no—
117C23×C4×C61C2311yescharacteristic
118C2×M16×C61—24no—
119C2×M16×C61C2314yes—
120C22×C8×C61C2312yes—
121C2×C4⋊C4×C61—21no—
122C2×C4⋊C4×C61—22no—
123C2×C4⋊C4×C61C2312yes—
124C2×C4⋊C4×C61C2314yes—
125#103×C61C2318yes—
126#102×C61C2318yes—
127C24×C61—21no—
128C24×C61C2×D411yescharacteristic
129#41×C61—216no—
130#41×C61—28no—
131#41×C61C2×Q8116yescomplemented
132C2×Q8×C61—21no—
133C2×Q8×C61—22no—
134C2×Q8×C61C2×Q814yes—
135C2×Q8×C61C2412yes—
136C2×D4×C61—28no—
137C2×D4×C61—24no—
138C2×D4×C61—21no—
139C2×D4×C61—22no—
140C2×D4×C61C2×Q814yes—
141C2×D4×C61C2412yes—
142C22×C4×C61—21no—
143C22×C4×C61—28no—
144C22×C4×C61—24no—
145C22×C4×C61—22no—
146C22×C4×C61—24no—
147C22×C4×C61—82no—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D412yes—
150C22×C4×C61C2×Q814yes—
151C22×C4×C61#4114yes—
152C22×C4×C61C2411yescharacteristic
153C22×C4×C61C2412yes—
154C22×Dic61—22no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—24no—
158C22×Dic61—28no—
159C22×Dic61—84no—
160C22×Dic61—82no—
161C22×Dic61C2×D412yes—
162C22×Dic61C2×D412yes—
163C2×Dic122—28no—
164C2×Dic122—84no—
165M16×C61—28no—
166C2×C8×C61—24no—
167C2×C8×C61C2414yes—
168C4⋊C4×C61—24no—
169C4⋊C4×C61—22no—
170C4⋊C4×C61C2414yes—
171C22⋊Dic61—24no—
172C22⋊Dic61—28no—
173C22⋊Dic61C2×D418yes—
174C4⋊Dic61—24no—
175C4⋊Dic61—22no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—28no—
179C4⋊Dic61—28no—
180C4⋊Dic61C2×D414yes—
181C4⋊Dic61C2×D414yes—
182C4⋊Dic61C2412yes—
183C4⋊Dic61C2412yes—
184C4⋊Dic61C2414yes—
185#11758196—28no—
186#11758196—28no—
187C4×Dic61—24no—
188C4×Dic61—28no—
189C4×Dic61C2×D414yes—
190C4×Dic61C2414yes—
191C2×#92418—22no—
192C2×#92418—22no—
193C2×#92418—28no—
194C2×#92418C2412yes—
195C2×#92418C2412yes—
196C23×C61—22no—
197C23×C61—22no—
198C23×C61—24no—
199C23×C61—22no—
200C23×C61—42no—
201C23×C61—42no—
202C23×C61C22⋊Q814yes—
203C23×C61C22×D412yes—
204C23×C61C22×D411yescharacteristic
205Q8×C61—24no—
206Q8×C61—22no—
207Q8×C61C22×Q814yes—
208D4×C61—216no—
209D4×C61—24no—
210D4×C61—22no—
211D4×C61C22×Q814yes—
212C2×C4×C61—24no—
213C2×C4×C61—22no—
214C2×C4×C61—216no—
215C2×C4×C61—24no—
216C2×C4×C61—44no—
217C2×C4×C61—84no—
218C2×C4×C61C22⋊Q814yes—
219C2×C4×C61C22⋊Q818yes—
220C2×C4×C61C22×D412yes—
221C2×C4×C61C22×D411yescharacteristic
222C2×C4×C61C22×Q812yes—
223C2×C4×C61C22×Q814yes—
224C2×C4×C61C2×#4112yes—
225C2×C4×C61C2×#4114yes—
226C2×C4×C61C2511yescharacteristic
227C2×Dic61—24no—
228C2×Dic61—24no—
229C2×Dic61—22no—
230C2×Dic61—22no—
231C2×Dic61—24no—
232C2×Dic61—42no—
233C2×Dic61—42no—
234C2×Dic61—44no—
235C2×Dic61—88no—
236C2×Dic61—84no—
237C2×Dic61C22×D414yes—
238C2×Dic61C22×D414yes—
239Dic122—88no—
240C8×C61—24no—
241#92418—22no—
242#92418—22no—
243C2×#3084—611nomaximal, Sylow
244C22×C61—28no—
245C22×C61—22no—
246C22×C61—22no—
247C22×C61—24no—
248C22×C61—48no—
249C22×C61—42no—
250C22×C61—42no—
251C22×C61C2×C22⋊Q814yes—
252C22×C61C2×C22⋊Q812yes—
253C22×C61#57712yes—
254C22×C61#57712yes—
255C22×C61C23×D411yescharacteristic
256C4×C61—24no—
257C4×C61—44no—
258C4×C61C2×C22⋊Q814yes—
259C4×C61C2×C22⋊Q812yes—
260C4×C61C23×Q811yescharacteristic
261C4×C61C22×#4111yescharacteristic
262Dic61—24no—
263Dic61—24no—
264Dic61—42no—
265Dic61—42no—
266Dic61—44no—
267C2×#544—611no—
268C2×#520—611no—
269#3084—6116no—
270C2×#479—612no—
271C2×#475—612no—
272C2×#478—612no—
273C2×#476—612no—
274C2×#428—611no—
275C22×#106—611no—
276C2×#424—611no—
277C2×#417D6111yescharacteristic
278C2×#416—611no—
279C2×C61—24no—
280C2×C61—44no—
281C2×C61#308414yescomplemented
282C2×C61C22×C22⋊Q811yescharacteristic
283C2×C61C2×#57711yescharacteristic
284C2×C61C2×#57711yescharacteristic
285C22×#41C2×D6111yescharacteristic
286C22×M16C2×D6111yescharacteristic
287C23×C8—611no—
288#544—618no—
289#544—1224no—
290C2×C4⋊Q8—612no—
291C2×C4⋊Q8—1221no—
292C2×#125—612no—
293C2×#125—1221no—
294C2×C22⋊Q8—1222no—
295#520—618no—
296#520—1224no—
297C2×C4×Q8—612no—
298C2×C4×D4—612no—
299C2×C4×D4—1222no—
300C2×#117—611no—
301C2×#117—611no—
302C2×#117—1221no—
303C22×C4⋊C4—611no—
304C22×C4⋊C4—1221no—
305C22×C4⋊C4C2×D6111yescharacteristic
306#479—6116no—
307#478—6116no—
308#476—6116no—
309#475—6116no—
310#428—618no—
311C2×#107—612no—
312C2×#106—612no—
313C2×#106—612no—
314C2×#106—612no—
315C2×#106—618no—
316#424—618no—
317C2×C4⋊C8—612no—
318C2×C4⋊C8—612no—
319#417C2×D6118yes—
320#416—618no—
321C2×#103—611no—
322C2×#103—611no—
323C2×#103C2×D6112yes—
324C2×#102—611no—
325C2×#102—611no—
326C2×#102C2×D6112yes—
327C61C2×#308411yescharacteristic, complemented, Sylow
328C2×#41—22no—
329C2×#41—24no—
330C2×#41Dic12218yescomplemented
331C2×#41C22×D6114yes—
332C22×Q8—1222no—
333C22×Q8C22×D6111yescharacteristic
334C22×D4—21no—
335C22×D4C22×D6111yescharacteristic
336C23×C4—21no—
337C23×C4—21no—
338C23×C4—1222no—
339C23×C4—1221no—
340C23×C4C22×D6111yescharacteristic
341C2×M16—24no—
342C2×M16C22×D6114yes—
343C22×C8—611no—
344C22×C8—611no—
345C22×C8—614no—
346C22×C8—1224no—
347C22×C8C22×D6112yes—
348C4⋊Q8—618no—
349C4⋊Q8—1224no—
350C4⋊Q8—1228no—
351#125—618no—
352#125—1224no—
353#125—1228no—
354C22⋊Q8—12216no—
355C4×Q8—618no—
356C4×Q8—1224no—
357C4×D4—618no—
358C4×D4—1224no—
359C4×D4—12216no—
360#117—614no—
361#117—614no—
362#117—614no—
363#117—1228no—
364#117—1222no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—611no—
368C2×C4⋊C4—611no—
369C2×C4⋊C4—612no—
370C2×C4⋊C4—614no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—1228no—
374C2×C4⋊C4—1222no—
375C2×C4⋊C4—1222no—
376C2×C4⋊C4—1222no—
377C2×C4⋊C4—1222no—
378C2×C4⋊C4—1221no—
379C2×C4⋊C4—1222no—
380C2×C4⋊C4C22×D6112yes—
381C2×C4⋊C4C22×D6114yes—
382C2×C22⋊C4—612no—
383C2×C22⋊C4—1222no—
384C2×C22⋊C4—1221no—
385C2×C42—612no—
386C2×C42—1222no—
387C2×C42—1221no—
388#107—618no—
389#106—618no—
390#106—618no—
391#106—618no—
392C4⋊C8—618no—
393C4⋊C8—618no—
394#103—614no—
395#103—614no—
396#103C22×D6118yes—
397#102—614no—
398#102—614no—
399#102C22×D6118yes—
400C24—21no—
401C24D4×D6111yescharacteristic
402#41—28no—
403#41—216no—
404#41C2×Dic122116yescomplemented
405C2×Q8—21no—
406C2×Q8—22no—
407C2×Q8—1228no—
408C2×Q8—4884no—
409C2×Q8C2×Dic12214yes—
410C2×Q8C23×D6112yes—
411C2×D4—24no—
412C2×D4—28no—
413C2×D4—21no—
414C2×D4—22no—
415C2×D4C2×Dic12214yes—
416C2×D4C23×D6112yes—
417C22×C4—21no—
418C22×C4—24no—
419C22×C4—28no—
420C22×C4—22no—
421C22×C4—24no—
422C22×C4—82no—
423C22×C4—612no—
424C22×C4—612no—
425C22×C4—1228no—
426C22×C4—1224no—
427C22×C4—1221no—
428C22×C4—1222no—
429C22×C4—1221no—
430C22×C4—4884no—
431C22×C4—4882no—
432C22×C4C2×Dic12214yes—
433C22×C4D4×D6112yes—
434C22×C4D4×D6111yescharacteristic
435C22×C4#1175822414yes—
436C22×C4C23×D6112yes—
437C22×C4C23×D6111yescharacteristic
438M16—28no—
439C2×C8—24no—
440C2×C8—612no—
441C2×C8—612no—
442C2×C8—1222no—
443C2×C8—1222no—
444C2×C8—1228no—
445C2×C8C23×D6114yes—
446C4⋊C4—22no—
447C4⋊C4—24no—
448C4⋊C4—614no—
449C4⋊C4—614no—
450C4⋊C4—612no—
451C4⋊C4—612no—
452C4⋊C4—614no—
453C4⋊C4—1228no—
454C4⋊C4—1228no—
455C4⋊C4—1228no—
456C4⋊C4—1228no—
457C4⋊C4—1224no—
458C4⋊C4—1222no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C4⋊C4C23×D6114yes—
462C22⋊C4—618no—
463C22⋊C4—1228no—
464C22⋊C4—1224no—
465C42—614no—
466C42—614no—
467C42—1228no—
468C42—1224no—
469C23—22no—
470C23—22no—
471C23—24no—
472C23—22no—
473C23—42no—
474C23—42no—
475C23#1451975414yes—
476C23C2×D4×D6112yes—
477C23C2×D4×D6111yescharacteristic
478Q8—24no—
479Q8—22no—
480Q8—4888no—
481Q8C22×Dic12214yes—
482D4—216no—
483D4—24no—
484D4—22no—
485D4C22×Dic12214yes—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—216no—
489C2×C4—24no—
490C2×C4—44no—
491C2×C4—84no—
492C2×C4—614no—
493C2×C4—614no—
494C2×C4—1224no—
495C2×C4—1224no—
496C2×C4—1222no—
497C2×C4—1224no—
498C2×C4—1222no—
499C2×C4—4888no—
500C2×C4—4884no—
501C2×C4—2442no—
502C2×C4—2444no—
503C2×C4—2442no—
504C2×C4#1451975414yes—
505C2×C4#1451975418yes—
506C2×C4C2×D4×D6111yescharacteristic
507C2×C4C2×D4×D6112yes—
508C2×C4C22×Dic12212yes—
509C2×C4C22×Dic12214yes—
510C2×C4C2×#1175822412yes—
511C2×C4C2×#1175822414yes—
512C2×C4C24×D6111yescharacteristic
513C8—24no—
514C8—1222no—
515C8—1222no—
516C22—28no—
517C22—22no—
518C22—22no—
519C22—24no—
520C22—48no—
521C22—42no—
522C22—42no—
523C22C2×#1451975414yes—
524C22C2×#1451975412yes—
525C22#1684057112yes—
526C22#1684057212yes—
527C22C22×D4×D6111yescharacteristic
528C4—24no—
529C4—44no—
530C4—1224no—
531C4—1224no—
532C4—2444no—
533C4—2442no—
534C4—2442no—
535C4C2×#1451975414yes—
536C4C2×#1451975412yes—
537C4C23×Dic12211yescharacteristic
538C4C22×#1175822411yescharacteristic
539C2—24no—
540C2—44no—
541C2#2145568514yesdirect product factor
542C2C22×#1451975411yescharacteristic
543C2C2×#1684057111yescharacteristic
544C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#417C2
socleC23×C61C22×D4
prime radicalC22×#41×C61C22
hypercenterC2×#417D61
hypocenterC61C2×#3084
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#16840393C2semidirect
3. #21455685C2direct (N × H)
4. C2×#16840071C2semidirect
5. C2×#16840045C2semidirect
6. C2×#16840060C2semidirect
7. C2×#16840050C2semidirect
8. C2×#16839804C2semidirect
9. C22×#14519708C2semidirect
10. C2×#16839790C2semidirect
15. #16840393C22semidirect
31. #16840071C22semidirect
32. #16840060C22semidirect
33. #16840050C22semidirect
34. #16840045C22semidirect
35. #16839804C22semidirect
40. C2×#14519708C22semidirect
41. #16839790C22semidirect
110. C2×#41×C61Q8semidirect
131. #41×C61C2×Q8semidirect
281. C2×C61#3084semidirect
327. C61C2×#3084semidirect
330. C2×#41Dic122semidirect
404. #41C2×Dic122semidirect
541. C2#21455685direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403932
C2×#168402452
#214556852
C2×#168400712
C2×#168400452
C2×#168400602
C2×#168400502
C2×#168398042
C22×#145197082
C2×#168397902
C2×#168397582
C2×C61×#4172
C2×#308461