Finite Group Databasebeta

← C2×#21455669 #30547593

Subgroups — C2×#21455669 #30547593

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×#16840390C211yesmaximal, characteristic, complemented
2C2×#16840243C211yesmaximal, characteristic
3#21455669C2116yesmaximal, direct product factor
4C2×#16840072C212yesmaximal, complemented
5C2×#16840056C212yesmaximal, complemented
6C2×#16840061C212yesmaximal, complemented
7C2×#16840041C212yesmaximal, complemented
8C22×#14519710C211yesmaximal, characteristic, complemented
9C2×#16839790C211yesmaximal, characteristic, complemented
10C2×#16839764C211yesmaximal, characteristic
11C2×#16839756C211yesmaximal, characteristic
12C2×C61×#428C211yesmaximal, characteristic, complemented
13C22×#11758222C2211yescharacteristic
14C23×#92418C2211yescharacteristic
15#16840390—24no—
16#16840390C2218yescomplemented
17C2×#14519777—21no—
18C2×#14519776C2212yes—
19C2×#14519769—21no—
20C2×#14519768C2212yes—
21C2×#14519754—22no—
22#16840243—24no—
23#16840243C2218yes—
24C2×#14519742C2212yes—
25C2×#14519739C2212yes—
26C2×C4×C22⋊D61—22no—
27C2×#14519736C2211yescharacteristic
28C2×#14519735—21no—
29C22×C4⋊Dic61C2211yescharacteristic
30C2×C4⋊C4×D61—21no—
31#16840072C22116yescomplemented
32#16840061C22116yescomplemented
33#16840056C22116yescomplemented
34#16840041C22116yescomplemented
35C2×#14519710C2212yes—
36C2×#14519710C2212yes—
37C2×#14519710C2218yescomplemented
38#16839790C2218yescomplemented
39C2×#14519706C2212yes—
40C2×#14519706C2212yes—
41#16839764C2218yes—
42#16839756C2218yes—
43C2×#14519702C2212yes—
44C2×#14519700C2211yescharacteristic
45C2×#14519700C2211yescharacteristic
46C2×#14519699C2212yes—
47C2×#14519697C2211yescharacteristic
48C2×#14519697C2211yescharacteristic
49C22×M16×C61C2211yescharacteristic
50C2×#117×C61C2211yescharacteristic
51C22×C4⋊C4×C61C2211yescharacteristic
52C61×#428C2218yescomplemented
53C2×#107×C61C2212yes—
54C2×#106×C61C2212yes—
55C2×#11758222—22no—
56C2×#11758222—24no—
57C2×#11758222Q818yescomplemented
58C2×#11758222C2314yes—
59C22×Dic122—22no—
60C22×Dic122C2311yescharacteristic
61C22×D244C2311yescharacteristic
62C22×C22⋊D61—21no—
63C23×Dic61—21no—
64C22×C4×D61—21no—
65C22×C4×D61—22no—
66C22×#92418—24no—
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2314yes—
70#14519777—28no—
71#14519776—24no—
72#14519776C2318yes—
73#14519769—28no—
74#14519768—24no—
75#14519768C2318yes—
76#14519754—216no—
77#14519742—24no—
78#14519742C2318yes—
79#14519739—24no—
80#14519739C2318yes—
81C4×C22⋊D61—216no—
82#14519736D414yes—
83#14519736C2314yes—
84#14519735—28no—
85C2×C4⋊Dic61—21no—
86C2×C4⋊Dic61—22no—
87C2×C4⋊Dic61—22no—
88C2×C4⋊Dic61D411yescharacteristic
89C2×C4⋊Dic61D411yescharacteristic
90C2×C4⋊Dic61C2312yes—
91C2×C4⋊Dic61C2314yes—
92C2×#11758196—22no—
93C2×#11758196—22no—
94C2×#11758196—22no—
95C4⋊C4×D61—28no—
96C2×C22⋊Dic61D412yes—
97C2×#11758198—22no—
98C2×C4×Dic61—22no—
99C2×C4×Dic61C2312yes—
100#14519710C2318yes—
101#14519710C2318yes—
102#14519706C2318yes—
103#14519706C2318yes—
104#14519702C2318yes—
105#14519700C2314yes—
106#14519700C2314yes—
107#14519699C2318yes—
108#14519697C2314yes—
109#14519697C2314yes—
110C23×C4×C61—21no—
111C23×C4×C61C2311yescharacteristic
112C2×M16×C61—24no—
113C2×M16×C61C2314yes—
114C22×C8×C61C2312yes—
115#117×C61—22no—
116#117×C61C2314yes—
117C2×C4⋊C4×C61—21no—
118C2×C4⋊C4×C61—22no—
119C2×C4⋊C4×C61C2312yes—
120C2×C4⋊C4×C61C2314yes—
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C22⋊C4×C61—21no—
124C2×C42×C61—21no—
125#107×C61C2318yes—
126#106×C61C2318yes—
127C24×C61C2×D411yescharacteristic
128C23×D61—21no—
129C22×C4×C61—22no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—24no—
133C22×C4×C61—82no—
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D412yes—
136C22×C4×C61C2×Q814yes—
137C22×C4×C61#4114yes—
138C22×C4×C61C2411yescharacteristic
139C22×C4×C61C2412yes—
140C2×C22⋊D61—28no—
141C2×C22⋊D61—24no—
142C22×Dic61—21no—
143C22×Dic61—22no—
144C22×Dic61—24no—
145C22×Dic61—82no—
146C22×Dic61C2×D412yes—
147C22×Dic61C2×D412yes—
148#11758222—216no—
149#11758222—28no—
150#11758222C2×Q8116yescomplemented
151C2×D244—21no—
152C2×D244—22no—
153C2×D244C2×Q814yes—
154C2×D244C2412yes—
155C2×C4×D61—28no—
156C2×C4×D61—24no—
157C2×C4×D61—28no—
158C2×C4×D61—84no—
159C2×Dic122—21no—
160C2×Dic122—22no—
161C2×Dic122—28no—
162C2×Dic122—84no—
163C2×Dic122C2×Q814yes—
164C2×Dic122C2412yes—
165M16×C61—28no—
166C2×C8×C61—24no—
167C2×C8×C61C2414yes—
168C4⋊C4×C61—24no—
169C4⋊C4×C61—22no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61C2412yes—
173C4⋊C4×C61C2414yes—
174C4⋊C4×C61C2412yes—
175C22⋊C4×C61—24no—
176C42×C61—24no—
177C22⋊Dic61C2×D418yes—
178#11758198—28no—
179C4⋊Dic61—22no—
180C4⋊Dic61—24no—
181C4⋊Dic61—28no—
182C4⋊Dic61C2×D414yes—
183C4⋊Dic61C2×D414yes—
184C4⋊Dic61C2414yes—
185#11758196—28no—
186#11758196—28no—
187#11758196—28no—
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×C61C22⋊Q814yes—
199C23×C61C22×D412yes—
200C23×C61C22×D411yescharacteristic
201C22×D61—24no—
202C22×D61—22no—
203C22×D61—42no—
204C22×D61—42no—
205C2×C4×C61—24no—
206C2×C4×C61—22no—
207C2×C4×C61—22no—
208C2×C4×C61—42no—
209C2×C4×C61—44no—
210C2×C4×C61—42no—
211C2×C4×C61—84no—
212C2×C4×C61C22⋊Q814yes—
213C2×C4×C61C22⋊Q818yes—
214C2×C4×C61C22×D411yescharacteristic
215C2×C4×C61C22×D412yes—
216C2×C4×C61C22×Q812yes—
217C2×C4×C61C22×Q814yes—
218C2×C4×C61C2×#4112yes—
219C2×C4×C61C2×#4114yes—
220C2×C4×C61C2511yescharacteristic
221C22⋊D61—216no—
222C2×Dic61—24no—
223C2×Dic61—24no—
224C2×Dic61—24no—
225C2×Dic61—22no—
226C2×Dic61—24no—
227C2×Dic61—44no—
228C2×Dic61—84no—
229C2×Dic61C22×D414yes—
230C2×Dic61C22×D414yes—
231D244—24no—
232D244—22no—
233D244C22×Q814yes—
234C4×D61—216no—
235C4×D61—88no—
236Dic122—24no—
237Dic122—22no—
238Dic122—88no—
239Dic122C22×Q814yes—
240C8×C61—24no—
241#92418—22no—
242#92418—22no—
243C2×#3083—611nomaximal, Sylow
244C22×C61—28no—
245C22×C61—22no—
246C22×C61—22no—
247C22×C61C2×C22⋊Q814yes—
248C22×C61C2×C22⋊Q812yes—
249C22×C61#57612yes—
250C22×C61#57812yes—
251C22×C61C23×D411yescharacteristic
252C2×D61—24no—
253C2×D61—48no—
254C2×D61—42no—
255C2×D61—42no—
256C4×C61—42no—
257C4×C61—44no—
258C4×C61—42no—
259C4×C61C2×C22⋊Q812yes—
260C4×C61C2×C22⋊Q814yes—
261C4×C61C23×Q811yescharacteristic
262C4×C61C22×#4111yescharacteristic
263Dic61—24no—
264Dic61—24no—
265Dic61—24no—
266Dic61—44no—
267C2×#544—611no—
268C2×#520—611no—
269#3083—6116no—
270C2×#479—612no—
271C2×#477—612no—
272C2×#478—612no—
273C2×#474—612no—
274C2×#428D6111yescharacteristic, complemented
275C22×#107—611no—
276C2×#424—611no—
277C2×#417—611no—
278C2×#416—611no—
279C2×C61—24no—
280C2×C61#308314yescomplemented
281C2×C61C22×C22⋊Q811yescharacteristic
282C2×C61C2×#57611yescharacteristic
283C2×C61C2×#57811yescharacteristic
284D61—44no—
285C22×#41—611no—
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—1221no—
302C2×#117C2×D6111yescharacteristic
303C22×C4⋊C4—611no—
304C22×C4⋊C4—1221no—
305C22×C4⋊C4C2×D6111yescharacteristic
306#479—6116no—
307#478—6116no—
308#477—6116no—
309#474—6116no—
310#428C2×D6118yescomplemented
311C2×#107—612no—
312C2×#107—612no—
313C2×#107—618no—
314C2×#107C2×D6112yes—
315C2×#106C2×D6112yes—
316#424—618no—
317C2×C4⋊C8—612no—
318C2×C4⋊C8—612no—
319#417—618no—
320#416—618no—
321C2×#103—612no—
322C2×#103—611no—
323C2×#103—611no—
324C2×#102—612no—
325C2×#102—611no—
326C2×#102—611no—
327C61C2×#308311yescharacteristic, complemented, Sylow
328C2×#41—618no—
329C2×#41—614no—
330C2×#41—1224no—
331C2×#41—1222no—
332C22×Q8—611no—
333C22×Q8—1222no—
334C22×D4—611no—
335C22×D4—1221no—
336C23×C4—21no—
337C23×C4—1222no—
338C23×C4—1221no—
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—1228no—
350C4⋊Q8—1224no—
351#125—618no—
352#125—1228no—
353#125—1224no—
354C22⋊Q8—12216no—
355C4×Q8—618no—
356C4×Q8—1224no—
357C4×D4—618no—
358C4×D4—1224no—
359C4×D4—12216no—
360#117—22no—
361#117—614no—
362#117—614no—
363#117—1228no—
364#117C22×D6114yes—
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—1228no—
372C2×C4⋊C4—1222no—
373C2×C4⋊C4—1222no—
374C2×C4⋊C4—1222no—
375C2×C4⋊C4—1222no—
376C2×C4⋊C4—1221no—
377C2×C4⋊C4—1222no—
378C2×C4⋊C4C22×D6112yes—
379C2×C4⋊C4C22×D6114yes—
380C2×C4⋊C4C22×D6111yescharacteristic
381C2×C4⋊C4C22×D6111yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—612no—
384C2×C22⋊C4—1222no—
385C2×C42—21no—
386C2×C42—612no—
387C2×C42—1222no—
388#107—618no—
389#107—618no—
390#107C22×D6118yes—
391#106C22×D6118yes—
392C4⋊C8—618no—
393C4⋊C8—618no—
394#103—618no—
395#103—614no—
396#103—614no—
397#102—618no—
398#102—614no—
399#102—614no—
400C24—1221no—
401C24D4×D6111yescharacteristic
402#41—6116no—
403#41—1228no—
404#41—12216no—
405C2×Q8—614no—
406C2×Q8—612no—
407C2×Q8—1228no—
408C2×Q8—1221no—
409C2×Q8—1222no—
410C2×Q8—4884no—
411C2×D4—614no—
412C2×D4—612no—
413C2×D4—1224no—
414C2×D4—1228no—
415C2×D4—1221no—
416C2×D4—1222no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—24no—
421C22×C4—82no—
422C22×C4—612no—
423C22×C4—612no—
424C22×C4—1228no—
425C22×C4—1221no—
426C22×C4—1224no—
427C22×C4—1228no—
428C22×C4—1224no—
429C22×C4—1222no—
430C22×C4—4884no—
431C22×C4—4882no—
432C22×C4#1175822214yes—
433C22×C4D4×D6112yes—
434C22×C4D4×D6111yescharacteristic
435C22×C4Q8×D6114yes—
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—24no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—614no—
451C4⋊C4—614no—
452C4⋊C4—614no—
453C4⋊C4—1228no—
454C4⋊C4—1228no—
455C4⋊C4—1228no—
456C4⋊C4—1228no—
457C4⋊C4—1224no—
458C4⋊C4—1222no—
459C4⋊C4C23×D6112yes—
460C4⋊C4C23×D6112yes—
461C4⋊C4C23×D6114yes—
462C22⋊C4—24no—
463C22⋊C4—618no—
464C22⋊C4—1228no—
465C42—24no—
466C42—614no—
467C42—614no—
468C42—1228no—
469C23—22no—
470C23—22no—
471C23—1224no—
472C23—1222no—
473C23—2442no—
474C23—2442no—
475C23#1451975514yes—
476C23C2×D4×D6112yes—
477C23C2×D4×D6111yescharacteristic
478Q8—614no—
479Q8—1224no—
480Q8—1222no—
481Q8—4888no—
482D4—614no—
483D4—12216no—
484D4—1224no—
485D4—1222no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—44no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—84no—
493C2×C4—614no—
494C2×C4—614no—
495C2×C4—1224no—
496C2×C4—1224no—
497C2×C4—1224no—
498C2×C4—1222no—
499C2×C4—12216no—
500C2×C4—1224no—
501C2×C4—4888no—
502C2×C4—4884no—
503C2×C4—2444no—
504C2×C4#1451975514yes—
505C2×C4#1451975518yes—
506C2×C4C2×D4×D6112yes—
507C2×C4C2×D4×D6111yescharacteristic
508C2×C4C2×Q8×D6112yes—
509C2×C4C2×Q8×D6114yes—
510C2×C4C2×#1175822212yes—
511C2×C4C2×#1175822214yes—
512C2×C4C24×D6111yescharacteristic
513C8—24no—
514C8—1222no—
515C8—1222no—
516C22—28no—
517C22—22no—
518C22—22no—
519C22—1224no—
520C22—2448no—
521C22—2442no—
522C22—2442no—
523C22C2×#1451975514yes—
524C22C2×#1451975512yes—
525C22#1684056612yes—
526C22#1684057812yes—
527C22C22×D4×D6111yescharacteristic
528C4—44no—
529C4—42no—
530C4—42no—
531C4—1224no—
532C4—1224no—
533C4—1224no—
534C4—2444no—
535C4C2×#1451975514yes—
536C4C2×#1451975512yes—
537C4C22×Q8×D6111yescharacteristic
538C4C22×#1175822211yescharacteristic
539C2—24no—
540C2—2444no—
541C2#2145566914yesdirect product factor
542C2C22×#1451975511yescharacteristic
543C2C2×#1684056611yescharacteristic
544C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#428C2
socleC23×C61C22×D4
prime radicalC22×#11758222C22
hypercenterC2×#428D61
hypocenterC61C2×#3083
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#16840390C2semidirect
3. #21455669C2direct (N × H)
4. C2×#16840072C2semidirect
5. C2×#16840056C2semidirect
6. C2×#16840061C2semidirect
7. C2×#16840041C2semidirect
8. C22×#14519710C2semidirect
9. C2×#16839790C2semidirect
12. C2×C61×#428C2semidirect
16. #16840390C22semidirect
31. #16840072C22semidirect
32. #16840061C22semidirect
33. #16840056C22semidirect
34. #16840041C22semidirect
37. C2×#14519710C22semidirect
38. #16839790C22semidirect
52. C61×#428C22semidirect
57. C2×#11758222Q8semidirect
150. #11758222C2×Q8semidirect
274. C2×#428D61semidirect
280. C2×C61#3083semidirect
310. #428C2×D61semidirect
327. C61C2×#3083semidirect
541. C2#21455669direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403902
C2×#168402432
#214556692
C2×#168400722
C2×#168400562
C2×#168400612
C2×#168400412
C22×#145197102
C2×#168397902
C2×#168397642
C2×#168397562
C2×C61×#4282
C2×#308361