Finite Group Databasebeta

← C2×#21446008 #29680719

Subgroups — C2×#21446008 #29680719

Order 15616.

1966 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D61C211yesmaximal, characteristic
2C22×#14519711C211yesmaximal, characteristic, complemented
3C22×#14519710C211yesmaximal, characteristic, complemented
4C22×#14519689C211yesmaximal, characteristic
5C2×#16839619C211yesmaximal, characteristic
6#21446008C218yesmaximal, direct product factor
7C2×#16839524C211yesmaximal, characteristic, complemented
8C2×C61×#340C211yesmaximal, characteristic, complemented
9C23×C4×D61—21no—
10C23×C4×D61C2211yescharacteristic
11C23×#92418C2211yescharacteristic
12C22×C4⋊Dic61C2211yescharacteristic
13C22×C4⋊Dic61C2211yescharacteristic
14C22×#11758196—21no—
15C2×C4⋊C4×D61—24no—
16C2×C4⋊C4×D61—24no—
17C2×C4⋊C4×D61—22no—
18C2×C4⋊C4×D61C2214yes—
19C22×#11758198—21no—
20C2×#14519711—24no—
21C2×#14519711C2214yescomplemented
22C2×#14519710—24no—
23C2×#14519710C2214yescomplemented
24C2×#14519689C418yescomplemented
25C2×#14519689C2214yes—
26#16839619—22no—
27#16839619C2214yes—
28C2×#14519684—21no—
29#16839524C2214yescomplemented
30C23×C8×C61C2211yescharacteristic
31C22×C4⋊C4×C61C2211yescharacteristic
32C22×C4⋊C4×C61C2211yescharacteristic
33C61×#340C2214yescomplemented
34C24×D61D411yescharacteristic
35C23×Dic61—21no—
36C23×Dic61—21no—
37C23×Dic61D411yescharacteristic
38C22×C4×D61—22no—
39C22×C4×D61—22no—
40C22×C4×D61—22no—
41C22×C4×D61—22no—
42C22×C4×D61—28no—
43C22×C4×D61—24no—
44C22×C4×D61—44no—
45C22×C4×D61—44no—
46C22×C4×D61C2×C414yes—
47C22×C4×D61D412yes—
48C22×C4×D61Q814yes—
49C22×C4×D61C2312yes—
50C22×#92418—22no—
51C22×#92418—22no—
52C22×#92418C2×C414yescomplemented
53C22×#92418C2312yes—
54C2×C4⋊Dic61—22no—
55C2×C4⋊Dic61—21no—
56C2×C4⋊Dic61—22no—
57C2×C4⋊Dic61—22no—
58C2×C4⋊Dic61—21no—
59C2×C4⋊Dic61D414yes—
60C2×C4⋊Dic61C2312yes—
61C2×C4⋊Dic61C2312yes—
62C2×#11758196—28no—
63C2×#11758196—24no—
64C4⋊C4×D61—216no—
65C4⋊C4×D61—28no—
66C4⋊C4×D61—28no—
67C2×#11758198—24no—
68C2×#11758198—44no—
69#14519711—28no—
70#14519710—28no—
71#14519689C2×C4116yescomplemented
72#14519684—24no—
73C23×C4×C61—21no—
74C23×C4×C61—21no—
75C23×C4×C61C2311yescharacteristic
76C22×C8×C61—22no—
77C22×C8×C61—22no—
78C22×C8×C61C2×C414yescomplemented
79C22×C8×C61C2312yes—
80C2×C4⋊C4×C61—21no—
81C2×C4⋊C4×C61—22no—
82C2×C4⋊C4×C61—22no—
83C2×C4⋊C4×C61—22no—
84C2×C4⋊C4×C61—21no—
85C2×C4⋊C4×C61D414yes—
86C2×C4⋊C4×C61C2312yes—
87C2×C4⋊C4×C61C2312yes—
88C24×C61C2×D411yescharacteristic
89C23×D61—22no—
90C23×D61—22no—
91C23×D61—22no—
92C23×D61—22no—
93C23×D61C4⋊C414yes—
94C23×D61D814yes—
95C23×D61Q1614yes—
96C23×D61C2×D412yes—
97C22×C4×C61—24no—
98C22×C4×C61—22no—
99C22×C4×C61—22no—
100C22×C4×C61—42no—
101C22×C4×C61—42no—
102C22×C4×C61—42no—
103C22×C4×C61—42no—
104C22×C4×C61—42no—
105C22×C4×C61C22×C412yes—
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D412yes—
108C22×C4×C61C2×D412yes—
109C22×C4×C61C2×Q812yes—
110C22×C4×C61#4112yes—
111C22×C4×C61#4112yes—
112C22×C4×C61C2411yescharacteristic
113C22×Dic61—22no—
114C22×Dic61—22no—
115C22×Dic61—24no—
116C22×Dic61—22no—
117C22×Dic61—22no—
118C22×Dic61—42no—
119C22×Dic61—42no—
120C22×Dic61—42no—
121C22×Dic61—42no—
122C22×Dic61—42no—
123C22×Dic61C4⋊C414yes—
124C22×Dic61C2×D412yes—
125C2×C4×D61—28no—
126C2×C4×D61—28no—
127C2×C4×D61—24no—
128C2×C4×D61—28no—
129C2×C4×D61—28no—
130C2×C4×D61—24no—
131C2×C4×D61—22no—
132C2×C4×D61—22no—
133C2×C4×D61—22no—
134C2×C4×D61—22no—
135C2×C4×D61—216no—
136C2×C4×D61—48no—
137C2×C4×D61—432no—
138C2×C4×D61—48no—
139C2×C4×D61C4⋊C418yes—
140C2×C4×D61C22×C414yes—
141C2×C4×D61C2×Q814yes—
142C2×C8×C61—28no—
143C2×C8×C61—22no—
144C2×C8×C61—22no—
145C2×C8×C61C22×C414yescomplemented
146C4⋊C4×C61—24no—
147C4⋊C4×C61—22no—
148C4⋊C4×C61—22no—
149C4⋊C4×C61—22no—
150C4⋊C4×C61—42no—
151C4⋊C4×C61C2×D414yes—
152#11758198—48no—
153C4⋊Dic61—24no—
154C4⋊Dic61—22no—
155C4⋊Dic61—22no—
156C4⋊Dic61—22no—
157C4⋊Dic61—42no—
158C4⋊Dic61C2×D414yes—
159#11758196—216no—
160C2×#92418—28no—
161C2×#92418—22no—
162C2×#92418—22no—
163C2×#92418C22×C414yescomplemented
164C23×C61C2×C4⋊C412yes—
165C23×C61#12012yes—
166C23×C61#12312yes—
167C23×C61C2×D812yes—
168C23×C61C2×Q1612yes—
169C23×C61AGL(1,ℤ/8)12yes—
170C23×C61#13712yes—
171C23×C61C22×D411yescharacteristic
172C22×D61—22no—
173C22×D61—22no—
174C22×D61—22no—
175C22×D61—22no—
176C22×D61—28no—
177C22×D61—28no—
178C22×D61—28no—
179C22×D61—28no—
180C22×D61—28no—
181C22×D61—28no—
182C22×D61#107116yescomplemented
183C22×D61C2×C4⋊C414yes—
184C22×D61C2×D814yes—
185C22×D61C2×Q1614yes—
186C2×C4×C61—24no—
187C2×C4×C61—42no—
188C2×C4×C61—42no—
189C2×C4×C61—48no—
190C2×C4×C61—42no—
191C2×C4×C61—42no—
192C2×C4×C61—42no—
193C2×C4×C61—84no—
194C2×C4×C61C2×C4⋊C412yes—
195C2×C4×C61C4×D414yes—
196C2×C4×C61C4×D414yes—
197C2×C4×C61#12012yes—
198C2×C4×C61C22⋊Q814yes—
199C2×C4×C61C22⋊Q814yes—
200C2×C4×C61#12312yes—
201C2×C4×C61C23×C411yescharacteristic
202C2×C4×C61C22×D411yescharacteristic
203C2×C4×C61C22×D411yescharacteristic
204C2×C4×C61C22×Q811yescharacteristic
205C2×C4×C61C2×#4111yescharacteristic
206C2×C4×C61C2×#4111yescharacteristic
207C2×Dic61—22no—
208C2×Dic61—22no—
209C2×Dic61—28no—
210C2×Dic61—24no—
211C2×Dic61—42no—
212C2×Dic61—42no—
213C2×Dic61—48no—
214C2×Dic61—42no—
215C2×Dic61—42no—
216C2×Dic61—42no—
217C2×Dic61—84no—
218C2×Dic61C2×C4⋊C414yes—
219C4×D61—24no—
220C4×D61—24no—
221C4×D61—24no—
222C4×D61—24no—
223C4×D61—216no—
224C4×D61—432no—
225C8×C61—24no—
226#92418—24no—
227C2×#1852—611nomaximal, Sylow
228C22×C61#38514yes—
229C22×C61C2×#10714yes—
230C22×C61#42814yes—
231C22×C61#44714yes—
232C22×C61#45114yes—
233C22×C61#48014yes—
234C22×C61#48414yes—
235C22×C61C22×C4⋊C411yescharacteristic
236C22×C61C2×#12011yescharacteristic
237C22×C61C2×#12311yescharacteristic
238C22×C61C22×D811yescharacteristic
239C22×C61C22×Q1611yescharacteristic
240C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
241C22×C61C2×#13711yescharacteristic
242C2×D61—24no—
243C2×D61—24no—
244C2×D61—232no—
245C2×D61—24no—
246C2×D61—24no—
247C2×D61—24no—
248C2×D61—24no—
249C2×D61C2×#10718yescomplemented
250C4×C61—44no—
251C4×C61—82no—
252C4×C61#38514yes—
253C4×C61C2×C4×D411yescharacteristic
254C4×C61C2×C4×D411yescharacteristic
255C4×C61C2×C22⋊Q811yescharacteristic
256C4×C61C2×C22⋊Q811yescharacteristic
257Dic61—24no—
258Dic61—44no—
259Dic61—82no—
260C23×C4⋊C4—611no—
261C22×#107—611no—
262C22×#107—611no—
263C22×C22⋊C8—611no—
264C2×#380—611no—
265#1852—618no—
266C2×#340—611no—
267C2×#340D6111yescharacteristic, complemented
268C2×C61#185218yescomplemented
269C2×C61C2×#38511yescharacteristic
270C2×C61C22×#10711yescharacteristic
271C2×C61C2×#42811yescharacteristic
272C2×C61C2×#44711yescharacteristic
273C2×C61C2×#45111yescharacteristic
274C2×C61C2×#48011yescharacteristic
275C2×C61C2×#48411yescharacteristic
276D61—28no—
277C24×C4—611no—
278C24×C4—1221no—
279C23×C8—611no—
280C23×C8C2×D6111yescharacteristic
281C22×C4⋊C4—611no—
282C22×C4⋊C4—611no—
283C22×C4⋊C4—614no—
284C22×C4⋊C4—1224no—
285C22×C4⋊C4—1222no—
286C22×C4⋊C4—1221no—
287C22×C4⋊C4—1224no—
288C22×C4⋊C4C2×D6111yescharacteristic
289C22×C4⋊C4C2×D6111yescharacteristic
290C22×C22⋊C4—1221no—
291C2×#107—614no—
292C2×#107—614no—
293C2×#107—1224no—
294C2×#107—1224no—
295C2×C22⋊C8—618no—
296C2×C22⋊C8—614no—
297#380—614no—
298#380—1222no—
299C2×#95—1221no—
300#340—614no—
301#340C2×D6114yescomplemented
302C61C2×#185211yescharacteristic, complemented, Sylow
303C25—611no—
304C23×C4—21no—
305C23×C4—21no—
306C23×C4—611no—
307C23×C4—614no—
308C23×C4—612no—
309C23×C4—614no—
310C23×C4—612no—
311C23×C4—1224no—
312C23×C4—1228no—
313C23×C4—1222no—
314C23×C4—1222no—
315C23×C4—1222no—
316C23×C4—1222no—
317C23×C4—1221no—
318C23×C4—1221no—
319C23×C4—2444no—
320C23×C4—2444no—
321C23×C4C22×D6111yescharacteristic
322C22×C8—22no—
323C22×C8—22no—
324C22×C8—614no—
325C22×C8—612no—
326C22×C8—1222no—
327C22×C8—1222no—
328C22×C8C4×D6114yescomplemented
329C22×C8C22×D6112yes—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—614no—
336C2×C4⋊C4—612no—
337C2×C4⋊C4—612no—
338C2×C4⋊C4—1228no—
339C2×C4⋊C4—12216no—
340C2×C4⋊C4—1224no—
341C2×C4⋊C4—1228no—
342C2×C4⋊C4—1222no—
343C2×C4⋊C4—1221no—
344C2×C4⋊C4—1228no—
345C2×C4⋊C4—1222no—
346C2×C4⋊C4—1222no—
347C2×C4⋊C4—1221no—
348C2×C4⋊C4D24414yes—
349C2×C4⋊C4C22×D6112yes—
350C2×C4⋊C4C22×D6112yes—
351C2×C22⋊C4—1224no—
352C2×C22⋊C4—2444no—
353#107—1228no—
354#107—1228no—
355C22⋊C8—6116no—
356#95—1224no—
357C24—612no—
358C24—614no—
359C24—614no—
360C24—614no—
361C24—1222no—
362C24—1222no—
363C24—1222no—
364C24—1222no—
365C24D4×D6111yescharacteristic
366C22×C4—22no—
367C22×C4—24no—
368C22×C4—22no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—612no—
375C22×C4—614no—
376C22×C4—614no—
377C22×C4—614no—
378C22×C4—618no—
379C22×C4—12216no—
380C22×C4—1222no—
381C22×C4—1222no—
382C22×C4—1222no—
383C22×C4—1222no—
384C22×C4—1222no—
385C22×C4—1222no—
386C22×C4—1228no—
387C22×C4—1228no—
388C22×C4—1224no—
389C22×C4—1228no—
390C22×C4—1228no—
391C22×C4—1224no—
392C22×C4—1222no—
393C22×C4—1224no—
394C22×C4—1222no—
395C22×C4—2448no—
396C22×C4—2448no—
397C22×C4—24432no—
398C22×C4—2442no—
399C22×C4—2442no—
400C22×C4—2442no—
401C22×C4—2442no—
402C22×C4—2442no—
403C22×C4C2×C4×D6112yes—
404C22×C4C2×D24412yes—
405C22×C4#1175822212yes—
406C22×C4D4×D6112yes—
407C22×C4D4×D6111yescharacteristic
408C22×C4#1175822412yes—
409C22×C4Q8×D6112yes—
410C22×C4C23×D6111yescharacteristic
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—28no—
414C2×C8—614no—
415C2×C8—1222no—
416C2×C8—1222no—
417C2×C8—1228no—
418C2×C8C2×C4×D6114yescomplemented
419C4⋊C4—22no—
420C4⋊C4—24no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—42no—
424C4⋊C4—614no—
425C4⋊C4—12216no—
426C4⋊C4—1222no—
427C4⋊C4—1224no—
428C4⋊C4—1222no—
429C4⋊C4—1222no—
430C4⋊C4—2442no—
431C4⋊C4C2×D24414yes—
432C22⋊C4—2448no—
433C23—614no—
434C23—614no—
435C23—614no—
436C23—6116no—
437C23—1222no—
438C23—1222no—
439C23—1222no—
440C23—1222no—
441C23—1228no—
442C23—1228no—
443C23—1228no—
444C23—1228no—
445C23—1228no—
446C23—1228no—
447C23C4⋊C4×D6112yes—
448C23#1451974712yes—
449C23#1451975912yes—
450C23D8×D6112yes—
451C23Q16×D6112yes—
452C23#1451980412yes—
453C23#1451980612yes—
454C23C2×D4×D6111yescharacteristic
455C2×C4—24no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—48no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—84no—
463C2×C4—614no—
464C2×C4—1222no—
465C2×C4—1222no—
466C2×C4—1228no—
467C2×C4—1224no—
468C2×C4—1224no—
469C2×C4—1224no—
470C2×C4—1224no—
471C2×C4—12216no—
472C2×C4—1224no—
473C2×C4—4884no—
474C2×C4—24432no—
475C2×C4—2442no—
476C2×C4—2442no—
477C2×C4—2442no—
478C2×C4—2442no—
479C2×C4—2442no—
480C2×C4—2448no—
481C2×C4C4⋊C4×D6112yes—
482C2×C4#1451973714yes—
483C2×C4C4×D24414yes—
484C2×C4#1451974712yes—
485C2×C4#1451975514yes—
486C2×C4#1451975714yes—
487C2×C4#1451975912yes—
488C2×C4C22×C4×D6111yescharacteristic
489C2×C4C2×D4×D6111yescharacteristic
490C2×C4C22×D24411yescharacteristic
491C2×C4C2×Q8×D6111yescharacteristic
492C2×C4C2×#1175822411yescharacteristic
493C2×C4C2×#1175822211yescharacteristic
494C8—24no—
495C8—1224no—
496C22—618no—
497C22—1224no—
498C22—1224no—
499C22—1224no—
500C22—1224no—
501C22—12232no—
502C22—1224no—
503C22—1224no—
504C22#1683963614yes—
505C22#107×D6114yes—
506C22#1683980114yes—
507C22#1683989714yes—
508C22#1683991914yes—
509C22#1684007414yes—
510C22#1684009614yes—
511C22C2×C4⋊C4×D6111yescharacteristic
512C22C2×#1451974711yescharacteristic
513C22C2×#1451975911yescharacteristic
514C22C2×D8×D6111yescharacteristic
515C22C2×Q16×D6111yescharacteristic
516C22C2×#1451980411yescharacteristic
517C22C2×#1451980611yescharacteristic
518C4—44no—
519C4—82no—
520C4—1224no—
521C4—4882no—
522C4—2444no—
523C4#1683963614yes—
524C4C2×#1451973711yescharacteristic
525C4C2×C4×D24411yescharacteristic
526C4C2×#1451975511yescharacteristic
527C4C2×#1451975711yescharacteristic
528C2—1228no—
529C2#2144600818yesdirect product factor
530C2C2×#1683963611yescharacteristic
531C2C2×#107×D6111yescharacteristic
532C2C2×#1683980111yescharacteristic
533C2C2×#1683989711yescharacteristic
534C2C2×#1683991911yescharacteristic
535C2C2×#1684007411yescharacteristic
536C2C2×#1684009611yescharacteristic
subgroupG/H
centerC24D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#340C2
socleC24×C61C2×D4
prime radicalC24×D61D4
cosocleC22×C4×C61C24
hypercenterC2×#340D61
hypocenterC61C2×#1852
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C22×#14519711C2semidirect
3. C22×#14519710C2semidirect
6. #21446008C2direct (N × H)
7. C2×#16839524C2semidirect
8. C2×C61×#340C2semidirect
21. C2×#14519711C22semidirect
23. C2×#14519710C22semidirect
24. C2×#14519689C4semidirect
29. #16839524C22semidirect
33. C61×#340C22semidirect
52. C22×#92418C2×C4semidirect
71. #14519689C2×C4semidirect
78. C22×C8×C61C2×C4semidirect
145. C2×C8×C61C22×C4semidirect
163. C2×#92418C22×C4semidirect
182. C22×D61#107semidirect
249. C2×D61C2×#107semidirect
267. C2×#340D61semidirect
268. C2×C61#1852semidirect
301. #340C2×D61semidirect
302. C61C2×#1852semidirect
328. C22×C8C4×D61semidirect
418. C2×C8C2×C4×D61semidirect
529. C2#21446008direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D612
C22×#145197112
C22×#145197102
C22×#145196892
C2×#168396192
#214460082
C2×#168395242
C2×C61×#3402
C2×#185261