Finite Group Databasebeta

← C2×#21444934 #29655622

Subgroups — C2×#21444934 #29655622

Order 15616.

1722 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×D244C211yesmaximal, characteristic
2C2×#16840136C211yesmaximal, characteristic, complemented
3C2×#16840049C211yesmaximal, characteristic, complemented
4#21444934C218yesmaximal, direct product factor
5C2×#16839505C211yesmaximal, characteristic, complemented
6C2×D4⋊#92418C211yesmaximal, characteristic, complemented
7C2×#16839489C211yesmaximal, characteristic, complemented
8C2×C61×#476C211yesmaximal, characteristic, complemented
9C23×D244—21no—
10C22×D4×D61—21no—
11C22×#11758201—22no—
12D4×D244—22no—
13D4×D244—22no—
14D4×D244—22no—
15D4×D244C2214yes—
16C2×#14519774C2211yescharacteristic
17C2×#14519752—21no—
18C2×#14519751—21no—
19C2×#14519747—22no—
20C2×C4×D244C2211yescharacteristic
21#16840136—22no—
22#16840136C2214yescomplemented
23#16840049—22no—
24#16840049C2214yescomplemented
25C2×#14519708—21no—
26C2×C4⋊#92418C2211yescharacteristic, complemented
27C2×#14519697—21no—
28C2×C4×#92418C2211yescharacteristic, complemented
29#16839505C2214yescomplemented
30D4⋊#92418C2214yescomplemented
31#16839489C2214yescomplemented
32C2×C4⋊Q8×C61C2211yescharacteristic, complemented
33C2×C4×D4×C61C2211yescharacteristic
34C61×#476—22no—
35C61×#476C2214yescomplemented
36C2×#106×C61—21no—
37C2×C4⋊C8×C61C2211yescharacteristic, complemented
38C2×#102×C61—21no—
39C24×D61—22no—
40C22×D244—22no—
41C22×D244—24no—
42C22×D244—21no—
43C22×D244—21no—
44C22×D244—24no—
45C22×D244—44no—
46C22×D244—44no—
47C22×D244D411yescharacteristic
48C22×D244D412yes—
49C22×C22⋊D61—22no—
50C2×D4×D61—24no—
51C2×D4×D61—24no—
52C2×D4×D61—44no—
53C2×D4×D61—44no—
54C22×C4×D61—21no—
55C2×#11758201—28no—
56C2×#11758201—48no—
57C22×#92418—21no—
58C22×#92418—21no—
59#14519774—21no—
60#14519774—21no—
61#14519774D412yes—
62#14519774C2312yes—
63#14519752—24no—
64#14519752—24no—
65#14519751—24no—
66#14519751—24no—
67#14519747—28no—
68#14519747—28no—
69C4×D244—21no—
70C4×D244—21no—
71C4×D244D412yes—
72C4×D244C2312yes—
73C2×C4⋊Dic61D411yescharacteristic
74C2×#11758198—22no—
75C2×#11758198—21no—
76#14519708—24no—
77C4⋊#92418—21no—
78C4⋊#92418C2312yescomplemented
79#14519697—24no—
80C4×#92418—21no—
81C4×#92418C2312yescomplemented
82C22×Q8×C61—21no—
83C22×D4×C61D411yescharacteristic
84C23×C4×C61—21no—
85C22×C8×C61—21no—
86C4⋊Q8×C61—21no—
87C4⋊Q8×C61—21no—
88C4⋊Q8×C61—21no—
89C4⋊Q8×C61C2312yescomplemented
90C4×D4×C61—21no—
91C4×D4×C61—21no—
92C4×D4×C61D412yes—
93C4×D4×C61C2312yes—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61D411yescharacteristic
97C2×C22⋊C4×C61—21no—
98C2×C42×C61C2311yescharacteristic
99#106×C61—24no—
100C4⋊C8×C61—21no—
101C4⋊C8×C61C2312yescomplemented
102#102×C61—24no—
103C24×C61—21no—
104C23×D61—21no—
105C23×D61—22no—
106C23×D61—28no—
107C23×D61—48no—
108C23×D61—48no—
109C23×D61—84no—
110C2×Q8×C61—22no—
111C2×Q8×C61—44no—
112C2×Q8×C61—41no—
113C2×D4×C61—21no—
114C2×D4×C61—22no—
115C2×D4×C61SD1614yescomplemented
116C2×D4×C61C2×D412yes—
117C22×C4×C61—21no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—42no—
121C22×C4×C61—42no—
122C22×C4×C61—41no—
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C2×C22⋊D61—28no—
127C2×C22⋊D61—48no—
128C22×Dic61—21no—
129D4×D61—48no—
130D4×D61—416no—
131D4×D61—48no—
132C2×D244—21no—
133C2×D244—22no—
134C2×D244—28no—
135C2×D244—22no—
136C2×D244—22no—
137C2×D244—22no—
138C2×D244—22no—
139C2×D244—22no—
140C2×D244—48no—
141C2×D244—416no—
142C2×D244—48no—
143C2×D244—42no—
144C2×D244—42no—
145C2×D244—42no—
146C2×D244—42no—
147C2×D244—48no—
148C2×D244—44no—
149C2×D244SD1614yescomplemented
150C2×D244C2×D412yes—
151C2×D244C2×D414yes—
152C2×C4×D61—22no—
153C2×C4×D61—22no—
154C2×C4×D61—42no—
155C2×C4×D61—42no—
156C2×C8×C61—22no—
157C2×C8×C61—42no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—22no—
160C4⋊C4×C61—22no—
161C4⋊C4×C61—41no—
162C4⋊C4×C61—41no—
163C4⋊C4×C61C2×D412yes—
164C22⋊C4×C61—22no—
165C22⋊C4×C61—22no—
166C42×C61C2×D411yescharacteristic
167C42×C61C2×D411yescharacteristic
168C42×C61C2×D411yescharacteristic
169C42×C61C2411yescharacteristic
170#11758201—416no—
171#11758198—28no—
172#11758198—22no—
173#11758198—22no—
174C4⋊Dic61—21no—
175C4⋊Dic61C2×D412yes—
176C2×#92418—24no—
177C2×#92418—22no—
178C2×#92418—22no—
179C2×#92418—42no—
180C23×C61—22no—
181C23×C61—24no—
182C23×C61—42no—
183C23×C61—42no—
184C23×C61#12011yescharacteristic
185C22×D61—22no—
186C22×D61—24no—
187C22×D61—24no—
188C22×D61—416no—
189C22×D61—42no—
190C22×D61—42no—
191C22×D61—416no—
192C22×D61—44no—
193C22×D61—44no—
194C22×D61—44no—
195C22×D61—88no—
196C22×D61—832no—
197Q8×C61—44no—
198Q8×C61—82no—
199D4×C61—22no—
200D4×C61—24no—
201D4×C61C2×SD1614yescomplemented
202C2×C4×C61—22no—
203C2×C4×C61—22no—
204C2×C4×C61—42no—
205C2×C4×C61—42no—
206C2×C4×C61—42no—
207C2×C4×C61—44no—
208C2×C4×C61—42no—
209C2×C4×C61—82no—
210C2×C4×C61#12011yescharacteristic
211C2×C4×C61#12011yescharacteristic
212C2×C4×C61#12011yescharacteristic
213C2×C4×C61C2×SD1612yes—
214C2×C4×C61C2×SD1612yes—
215C2×C4×C61AGL(1,ℤ/8)12yes—
216C2×C4×C61AGL(1,ℤ/8)12yes—
217C2×C4×C61C22×D411yescharacteristic
218C2×C4×C61C22×D411yescharacteristic
219C2×C4×C61C22×D411yescharacteristic
220C22⋊D61—416no—
221C2×Dic61—22no—
222C2×Dic61—42no—
223D244—22no—
224D244—24no—
225D244—44no—
226D244—416no—
227D244—42no—
228D244—42no—
229D244—42no—
230D244—42no—
231D244—44no—
232D244—44no—
233D244—82no—
234D244C2×SD1614yescomplemented
235C4×D61—42no—
236C4×D61—42no—
237C4×D61—44no—
238C8×C61—42no—
239#92418—24no—
240#92418—42no—
241C2×#1629—611nomaximal, Sylow
242C22×C61—24no—
243C22×C61—48no—
244C22×C61—42no—
245C22×C61—42no—
246C22×C61#45012yes—
247C22×C61#45012yes—
248C22×C61#45312yes—
249C22×C61C2×#12011yescharacteristic
250C2×D61—24no—
251C2×D61—48no—
252C2×D61—42no—
253C2×D61—42no—
254C2×D61—44no—
255C2×D61—44no—
256C2×D61—44no—
257C2×D61—832no—
258C2×D61—88no—
259C4×C61—21no—
260C4×C61—21no—
261C4×C61—42no—
262C4×C61—82no—
263C4×C61#45012yes—
264C4×C61#45012yes—
265C4×C61C22×SD1611yescharacteristic
266C4×C61C22×SD1611yescharacteristic
267C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
268C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
269Dic61—42no—
270C2×D42—611no—
271C2×#492—611no—
272C2×#476—611no—
273C2×#476D6111yescharacteristic, complemented
274#1629—618no—
275C2×#331—611no—
276C2×D4⋊C8—611no—
277C2×D4⋊C8—611no—
278C2×C61—44no—
279C2×C61#162914yescomplemented
280C2×C61C2×#45011yescharacteristic
281C2×C61C2×#45011yescharacteristic
282C2×C61C2×#45311yescharacteristic
283D61—44no—
284D61—84no—
285C23×D4—1221no—
286C23×D4—1221no—
287C22×SD16—1222no—
288D42—614no—
289D42—1222no—
290D42—1222no—
291D42—1222no—
292C2×C4⋊Q8C2×D6111yescharacteristic, complemented
293C2×#127—611no—
294C2×#121—1221no—
295C2×#121—1221no—
296C2×#120—1222no—
297C2×C4×D4—611no—
298C2×C4×D4C2×D6111yescharacteristic
299#492—614no—
300#492—1222no—
301#476—22no—
302#476—614no—
303#476—1222no—
304#476C2×D6114yescomplemented
305C2×#106—21no—
306C2×#106—1221no—
307C2×C4⋊C8—611no—
308C2×C4⋊C8C2×D6111yescharacteristic, complemented
309C2×#102—21no—
310C2×#102—1221no—
311C2×C4×C8—611no—
312#331—614no—
313D4⋊C8—614no—
314D4⋊C8—614no—
315C61C2×#162911yescharacteristic, complemented, Sylow
316C25—1222no—
317C22×Q8—21no—
318C22×D4—611no—
319C22×D4—612no—
320C22×D4—1224no—
321C22×D4—1222no—
322C22×D4—1224no—
323C22×D4—1224no—
324C22×D4—1222no—
325C22×D4—1224no—
326C22×D4—1221no—
327C22×D4—1221no—
328C22×D4—2444no—
329C22×D4—2444no—
330C22×D4—2444no—
331C22×D4—2444no—
332C22×D4C22⋊D6111yescharacteristic
333C23×C4—21no—
334C23×C4—1221no—
335C2×SD16—1228no—
336C2×SD16—2448no—
337C22×C8—21no—
338C22×C8—1221no—
339C22×C8—1221no—
340C4⋊Q8—21no—
341C4⋊Q8—21no—
342C4⋊Q8—21no—
343C4⋊Q8C22×D6112yescomplemented
344#127—612no—
345#127—612no—
346#127—1221no—
347#127—1221no—
348#121—1224no—
349#121—1224no—
350#121—1224no—
351#121—1224no—
352#120—1228no—
353#120—1228no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4—612no—
357C4×D4—612no—
358C4×D4—1221no—
359C4×D4—1221no—
360C4×D4C22⋊D6112yes—
361C4×D4C22×D6112yes—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—611no—
365C2×C4⋊C4C22⋊D6111yescharacteristic
366C2×C22⋊C4—21no—
367C2×C22⋊C4—1222no—
368C2×C22⋊C4—1221no—
369C2×C42C22×D6111yescharacteristic
370#106—24no—
371#106—1224no—
372C4⋊C8—21no—
373C4⋊C8—612no—
374C4⋊C8—1221no—
375C4⋊C8C22×D6112yescomplemented
376#102—24no—
377#102—1224no—
378C4×C8—612no—
379C4×C8—1221no—
380C24—21no—
381C24—1228no—
382C24—1221no—
383C24—1222no—
384C24—4884no—
385C24—2448no—
386C24—2448no—
387C2×Q8—22no—
388C2×Q8—44no—
389C2×Q8—41no—
390C2×D4—21no—
391C2×D4—22no—
392C2×D4—612no—
393C2×D4—614no—
394C2×D4—614no—
395C2×D4—1228no—
396C2×D4—1228no—
397C2×D4—1222no—
398C2×D4—1222no—
399C2×D4—1221no—
400C2×D4—1222no—
401C2×D4—1222no—
402C2×D4—1222no—
403C2×D4—1222no—
404C2×D4—2444no—
405C2×D4—2448no—
406C2×D4—2448no—
407C2×D4—24416no—
408C2×D4—2448no—
409C2×D4—2448no—
410C2×D4—24416no—
411C2×D4—2448no—
412C2×D4—2448no—
413C2×D4—2442no—
414C2×D4—2442no—
415C2×D4—2442no—
416C2×D4—2442no—
417C2×D4#1175820114yescomplemented
418C2×D4C2×C22⋊D6112yes—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—41no—
425C22×C4—1221no—
426C22×C4—1222no—
427C22×C4—1222no—
428C22×C4—2442no—
429C22×C4—2442no—
430C22×C4D4×D6111yescharacteristic
431C22×C4D4×D6111yescharacteristic
432C22×C4C2×C22⋊D6111yescharacteristic
433SD16—24416no—
434C2×C8—22no—
435C2×C8—42no—
436C2×C8—1224no—
437C2×C8—1222no—
438C2×C8—1222no—
439C2×C8—2442no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—41no—
444C4⋊C4—41no—
445C4⋊C4—612no—
446C4⋊C4—1221no—
447C4⋊C4C2×C22⋊D6112yes—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—1228no—
451C22⋊C4—1222no—
452C22⋊C4—1222no—
453C42D4×D6111yescharacteristic
454C42D4×D6111yescharacteristic
455C42C2×C22⋊D6111yescharacteristic
456C42C23×D6111yescharacteristic
457C23—22no—
458C23—24no—
459C23—42no—
460C23—42no—
461C23—1222no—
462C23—1224no—
463C23—1224no—
464C23—48832no—
465C23—4888no—
466C23—24416no—
467C23—24416no—
468C23—2444no—
469C23—2444no—
470C23—2444no—
471C23—2442no—
472C23—2442no—
473C23#1451974511yescharacteristic
474Q8—44no—
475Q8—82no—
476D4—22no—
477D4—24no—
478D4—614no—
479D4—1222no—
480D4—1224no—
481D4—4882no—
482D4—2444no—
483D4—24416no—
484D4—24416no—
485D4—2442no—
486D4—2442no—
487D4—2442no—
488D4—2442no—
489D4—2444no—
490D4—2444no—
491D4C2×#1175820114yescomplemented
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—44no—
498C2×C4—42no—
499C2×C4—82no—
500C2×C4—1222no—
501C2×C4—2442no—
502C2×C4—2442no—
503C2×C4—2442no—
504C2×C4—2444no—
505C2×C4#1451974511yescharacteristic
506C2×C4#1451974511yescharacteristic
507C2×C4#1451974511yescharacteristic
508C2×C4SD16×D6112yes—
509C2×C4C2×#1175820112yes—
510C2×C4#1451980212yes—
511C2×C4#1451980412yes—
512C2×C4C2×D4×D6111yescharacteristic
513C2×C4C2×D4×D6111yescharacteristic
514C2×C4C22×C22⋊D6111yescharacteristic
515C8—42no—
516C8—1224no—
517C8—2442no—
518C22—24no—
519C22—42no—
520C22—48no—
521C22—42no—
522C22—1224no—
523C22—48832no—
524C22—4888no—
525C22—2444no—
526C22—2444no—
527C22—2444no—
528C22—2442no—
529C22—2448no—
530C22—2442no—
531C22#1683991112yes—
532C22#1683991212yes—
533C22#1683992812yes—
534C22C2×#1451974511yescharacteristic
535C4—21no—
536C4—21no—
537C4—42no—
538C4—82no—
539C4—2442no—
540C4#1683991112yes—
541C4#1683991212yes—
542C4C2×SD16×D6111yescharacteristic
543C4C22×#1175820111yescharacteristic
544C4C2×#1451980211yescharacteristic
545C4C2×#1451980411yescharacteristic
546C2—44no—
547C2—4884no—
548C2—2444no—
549C2#2144493414yesdirect product factor
550C2C2×#1683991111yescharacteristic
551C2C2×#1683991211yescharacteristic
552C2C2×#1683992811yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#476C2
socleC23×C61#120
prime radicalC2×D4×D244C2
hypercenterC2×#476D61
hypocenterC61C2×#1629
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
2. C2×#16840136C2semidirect
3. C2×#16840049C2semidirect
4. #21444934C2direct (N × H)
5. C2×#16839505C2semidirect
6. C2×D4⋊#92418C2semidirect
7. C2×#16839489C2semidirect
8. C2×C61×#476C2semidirect
22. #16840136C22semidirect
24. #16840049C22semidirect
26. C2×C4⋊#92418C22semidirect
28. C2×C4×#92418C22semidirect
29. #16839505C22semidirect
30. D4⋊#92418C22semidirect
31. #16839489C22semidirect
32. C2×C4⋊Q8×C61C22semidirect
35. C61×#476C22semidirect
37. C2×C4⋊C8×C61C22semidirect
78. C4⋊#92418C23semidirect
81. C4×#92418C23semidirect
89. C4⋊Q8×C61C23semidirect
101. C4⋊C8×C61C23semidirect
115. C2×D4×C61SD16semidirect
149. C2×D244SD16semidirect
201. D4×C61C2×SD16semidirect
234. D244C2×SD16semidirect
273. C2×#476D61semidirect
279. C2×C61#1629semidirect
292. C2×C4⋊Q8C2×D61semidirect
304. #476C2×D61semidirect
308. C2×C4⋊C8C2×D61semidirect
315. C61C2×#1629semidirect
343. C4⋊Q8C22×D61semidirect
375. C4⋊C8C22×D61semidirect
417. C2×D4#11758201semidirect
491. D4C2×#11758201semidirect
549. C2#21444934direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×D2442
C2×#168401362
C2×#168400492
#214449342
C2×#168395052
C2×D4⋊#924182
C2×#168394892
C2×C61×#4762
C2×#162961