Finite Group Databasebeta

← C2×#21447803 #29834014

Subgroups — C2×#21447803 #29834014

Order 15616.

1956 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 1956 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839948C212yesmaximal, complemented
2C2×#16839929C211yesmaximal, characteristic, complemented
3#21447803C218yesmaximal, direct product factor
4C2×#16839555C211yesmaximal, characteristic, complemented
5C2×#16839549C212yesmaximal, complemented
6C2×D42×C61C211yesmaximal, characteristic, complemented
7C2×#14519822C2211yescharacteristic, complemented
8C2×#14519803—21no—
9C2×#14519746—22no—
10#16839948—24no—
11#16839948C2218yescomplemented
12#16839929—22no—
13#16839929C2214yescomplemented
14C2×#14519705—21no—
15C2×#14519694C2211yescharacteristic, complemented
16C2×#14519692C2212yescomplemented
17C2×#14519691—22no—
18#16839555C2214yescomplemented
19#16839549C2218yescomplemented
20C23×D4×C61—22no—
21D42×C61—22no—
22D42×C61—24no—
23D42×C61C2214yescomplemented
24C2×#127×C61C2211yescharacteristic
25C2×#121×C61—22no—
26C2×#120×C61—21no—
27C2×#120×C61C2212yes—
28C2×C4×D4×C61—21no—
29#14519822—21no—
30#14519822—22no—
31#14519822—42no—
32#14519822C2312yescomplemented
33C2×#11758222—21no—
34C2×#11758224—41no—
35C22×C22⋊D61—22no—
36C22×C22⋊D61—42no—
37C2×D4×D61—41no—
38#14519803—24no—
39#14519803—42no—
40C2×#11758200—41no—
41C2×#11758199—41no—
42C2×#11758194—21no—
43#14519746—28no—
44#14519746—44no—
45C2×C22⋊Dic61—22no—
46C2×C22⋊Dic61—42no—
47#14519705—24no—
48#14519694—21no—
49#14519694C2312yescomplemented
50#14519692—22no—
51#14519692C2314yescomplemented
52#14519691—28no—
53C25×C61—21no—
54C25×C61D412yescomplemented
55C22×D4×C61—21no—
56C22×D4×C61—28no—
57C22×D4×C61—22no—
58C22×D4×C61—22no—
59C22×D4×C61—22no—
60C22×D4×C61—28no—
61C22×D4×C61—416no—
62C22×D4×C61D411yescharacteristic, complemented
63C22×D4×C61C2311yescharacteristic
64C23×C4×C61—22no—
65#127×C61—22no—
66#127×C61D412yescomplemented
67#127×C61C2312yes—
68#121×C61—28no—
69#121×C61—28no—
70#120×C61—24no—
71#120×C61—22no—
72#120×C61—22no—
73#120×C61—24no—
74#120×C61D414yescomplemented
75#120×C61C2314yes—
76C4×D4×C61—24no—
77C4×D4×C61—24no—
78C2×C4⋊C4×C61—21no—
79C2×C22⋊C4×C61—21no—
80C2×C22⋊C4×C61—22no—
81C2×C22⋊C4×C61D412yescomplemented
82C2×C42×C61D411yescharacteristic, complemented
83C24×C61—22no—
84C24×C61—24no—
85C24×C61—21no—
86C24×C61—22no—
87C24×C61—42no—
88C24×C61—48no—
89C24×C61—48no—
90C24×C61—42no—
91C24×C61—81no—
92C24×C61—81no—
93C24×C61C2×D412yes—
94C24×C61C2×D414yescomplemented
95C23×D61—22no—
96C2×D4×C61—24no—
97C2×D4×C61—28no—
98C2×D4×C61—28no—
99C2×D4×C61—24no—
100C2×D4×C61—24no—
101C2×D4×C61—24no—
102C2×D4×C61—24no—
103C2×D4×C61—21no—
104C2×D4×C61—41no—
105C2×D4×C61—41no—
106C2×D4×C61—48no—
107C2×D4×C61—41no—
108C2×D4×C61—41no—
109C2×D4×C61—432no—
110C2×D4×C61—432no—
111C2×D4×C61—48no—
112C2×D4×C61—48no—
113C2×D4×C61C2×D412yes—
114C2×D4×C61C2×D411yescharacteristic
115C2×D4×C61C2×D412yescomplemented
116C2×D4×C61C2411yescharacteristic
117C22×C4×C61—21no—
118C22×C4×C61—28no—
119C22×C4×C61—22no—
120C22×C4×C61—48no—
121C22×C4×C61C2×D411yescharacteristic
122C2×C22⋊D61—24no—
123C2×C22⋊D61—24no—
124C2×C22⋊D61—42no—
125C2×C22⋊D61—42no—
126C2×C22⋊D61—41no—
127C2×C22⋊D61—42no—
128C2×C22⋊D61—48no—
129C2×C22⋊D61—88no—
130C22×Dic61—22no—
131C22×Dic61—42no—
132#11758224—42no—
133#11758224—42no—
134#11758224—44no—
135D4×D61—42no—
136D4×D61—42no—
137D4×D61—44no—
138#11758222—22no—
139#11758222—22no—
140#11758222—41no—
141#11758222—41no—
142C2×D244—21no—
143C2×C4×D61—41no—
144C2×Dic122—21no—
145C4⋊C4×C61—24no—
146C22⋊C4×C61—24no—
147C22⋊C4×C61—22no—
148C22⋊C4×C61—24no—
149C22⋊C4×C61—24no—
150C22⋊C4×C61C2×D414yescomplemented
151C42×C61—21no—
152C42×C61C2×D412yescomplemented
153C22⋊Dic61—24no—
154C22⋊Dic61—48no—
155C22⋊Dic61—42no—
156#11758200—44no—
157#11758199—44no—
158#11758194—22no—
159#11758194—41no—
160C2×#92418—41no—
161C23×C61—28no—
162C23×C61—24no—
163C23×C61—22no—
164C23×C61—22no—
165C23×C61—22no—
166C23×C61—44no—
167C23×C61—44no—
168C23×C61—44no—
169C23×C61—48no—
170C23×C61—44no—
171C23×C61—48no—
172C23×C61—416no—
173C23×C61—42no—
174C23×C61—42no—
175C23×C61—48no—
176C23×C61—41no—
177C23×C61—41no—
178C23×C61—82no—
179C23×C61—84no—
180C23×C61—88no—
181C23×C61—84no—
182C23×C61—88no—
183C23×C61—88no—
184C23×C61#12011yescharacteristic
185C23×C61#12012yes—
186C23×C61C22×D412yes—
187C22×D61—24no—
188C22×D61—41no—
189C22×D61—42no—
190C22×D61—84no—
191D4×C61—216no—
192D4×C61—41no—
193D4×C61—42no—
194D4×C61—41no—
195D4×C61—42no—
196D4×C61—48no—
197D4×C61—48no—
198D4×C61—48no—
199D4×C61—48no—
200D4×C61—416no—
201D4×C61—81no—
202C2×C4×C61—24no—
203C2×C4×C61—22no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—24no—
207C2×C4×C61—416no—
208C2×C4×C61—44no—
209C2×C4×C61#12011yescharacteristic
210C2×C4×C61C22×D411yescharacteristic
211C22⋊D61—44no—
212C22⋊D61—44no—
213C22⋊D61—42no—
214C22⋊D61—42no—
215C22⋊D61—816no—
216C2×Dic61—24no—
217C2×Dic61—42no—
218C2×Dic61—41no—
219C2×Dic61—44no—
220C2×Dic61—84no—
221D244—22no—
222D244—41no—
223C4×D61—42no—
224C4×D61—42no—
225Dic122—22no—
226Dic122—41no—
227#92418—42no—
228C2×#2196—611nomaximal, Sylow
229C22×C61—22no—
230C22×C61—28no—
231C22×C61—22no—
232C22×C61—22no—
233C22×C61—42no—
234C22×C61—42no—
235C22×C61—44no—
236C22×C61—48no—
237C22×C61—44no—
238C22×C61—48no—
239C22×C61—44no—
240C22×C61—48no—
241C22×C61—44no—
242C22×C61—42no—
243C22×C61—82no—
244C22×C61—82no—
245C22×C61—84no—
246C22×C61—88no—
247C22×C61—816no—
248C22×C61—82no—
249C22×C61B(4,𝔽2)11yescharacteristic
250C22×C61B(4,𝔽2)11yescharacteristic
251C22×C61C2×#12011yescharacteristic
252C2×D61—42no—
253C2×D61—82no—
254C2×D61—84no—
255C2×D61—162no—
256C4×C61—24no—
257C4×C61—21no—
258C4×C61—21no—
259C4×C61—44no—
260Dic61—42no—
261Dic61—84no—
262C2×D42D6111yescharacteristic, complemented
263C2×B(4,𝔽2)—612no—
264C2×#453—611no—
265#2196—618no—
266C2×#353—611no—
267C2×AΣL(1,𝔽16)—612no—
268C2×C61—21no—
269C2×C61—21no—
270C2×C61—42no—
271C2×C61—42no—
272C2×C61—48no—
273C2×C61—82no—
274C2×C61#219612yescomplemented
275C2×C61C2×B(4,𝔽2)11yescharacteristic
276D61—82no—
277C2×H(5,𝔽2)—611no—
278C23×D4—22no—
279C2×AGL(1,ℤ/8)—1221no—
280D42—22no—
281D42—24no—
282D42C2×D6114yescomplemented
283C2×#127C2×D6111yescharacteristic
284C2×#121—22no—
285C2×#120—21no—
286C2×#120—1222no—
287C2×#120C2×D6112yes—
288C2×C4×D4—21no—
289B(4,𝔽2)—618no—
290B(4,𝔽2)—1224no—
291#453—614no—
292#453—1222no—
293C2×#104—1221no—
294C2×#100—611no—
295C2×#99—612no—
296C2×#99—1222no—
297#353—614no—
298AΣL(1,𝔽16)—618no—
299C61C2×#219611yescharacteristic, complemented, Sylow
300C25—21no—
301C25C22⋊D6112yescomplemented
302H(5,𝔽2)—612no—
303H(5,𝔽2)—1222no—
304H(5,𝔽2)—1221no—
305H(5,𝔽2)—2442no—
306C2×#41—1221no—
307C2×#41—2441no—
308C22×D4—21no—
309C22×D4—22no—
310C22×D4—28no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—28no—
314C22×D4—416no—
315C22×D4—1222no—
316C22×D4—2441no—
317C22×D4—2442no—
318C22×D4C22⋊D6111yescharacteristic, complemented
319C22×D4C22×D6111yescharacteristic
320C23×C4—22no—
321AGL(1,ℤ/8)—1224no—
322AGL(1,ℤ/8)—2442no—
323C2×SD16—2441no—
324C2×D8—2441no—
325C2×M16—1221no—
326#127—22no—
327#127C22⋊D6112yescomplemented
328#127C22×D6112yes—
329#121—28no—
330#121—28no—
331#120—24no—
332#120—22no—
333#120—22no—
334#120—24no—
335#120—1228no—
336#120—2444no—
337#120C22⋊D6114yescomplemented
338#120C22×D6114yes—
339C4×D4—24no—
340C4×D4—24no—
341C2×C4⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—1222no—
345C2×C22⋊C4—2442no—
346C2×C22⋊C4C22⋊D6112yescomplemented
347C2×C42C22⋊D6111yescharacteristic, complemented
348#104—1224no—
349#100—612no—
350#100—1221no—
351#99—614no—
352#99—1222no—
353#99—1228no—
354C24—22no—
355C24—24no—
356C24—21no—
357C24—22no—
358C24—42no—
359C24—48no—
360C24—48no—
361C24—42no—
362C24—81no—
363C24—81no—
364C24—1222no—
365C24C2×C22⋊D6112yes—
366C24C2×C22⋊D6114yescomplemented
367#41—1222no—
368#41—1222no—
369#41—2441no—
370#41—2442no—
371#41—2444no—
372#41—2442no—
373#41—2441no—
374C2×Q8—1221no—
375C2×D4—24no—
376C2×D4—28no—
377C2×D4—28no—
378C2×D4—24no—
379C2×D4—24no—
380C2×D4—24no—
381C2×D4—24no—
382C2×D4—21no—
383C2×D4—41no—
384C2×D4—41no—
385C2×D4—48no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—432no—
389C2×D4—432no—
390C2×D4—48no—
391C2×D4—48no—
392C2×D4—1221no—
393C2×D4—1224no—
394C2×D4—1224no—
395C2×D4—4888no—
396C2×D4—2442no—
397C2×D4—2442no—
398C2×D4—2444no—
399C2×D4—2448no—
400C2×D4—2442no—
401C2×D4—2442no—
402C2×D4—2442no—
403C2×D4—2441no—
404C2×D4C2×C22⋊D6111yescharacteristic
405C2×D4C2×C22⋊D6112yes—
406C2×D4C2×C22⋊D6112yescomplemented
407C2×D4C23×D6111yescharacteristic
408C22×C4—21no—
409C22×C4—28no—
410C22×C4—22no—
411C22×C4—48no—
412C22×C4—1222no—
413C22×C4—2441no—
414C22×C4—2442no—
415C22×C4C2×C22⋊D6111yescharacteristic
416SD16—2444no—
417D8—2444no—
418M16—1222no—
419M16—2441no—
420C2×C8—2441no—
421C4⋊C4—24no—
422C22⋊C4—24no—
423C22⋊C4—22no—
424C22⋊C4—24no—
425C22⋊C4—24no—
426C22⋊C4—1224no—
427C22⋊C4—2448no—
428C22⋊C4—2442no—
429C22⋊C4C2×C22⋊D6114yescomplemented
430C42—21no—
431C42C2×C22⋊D6112yescomplemented
432C23—28no—
433C23—22no—
434C23—24no—
435C23—22no—
436C23—22no—
437C23—44no—
438C23—44no—
439C23—44no—
440C23—48no—
441C23—44no—
442C23—48no—
443C23—416no—
444C23—42no—
445C23—42no—
446C23—48no—
447C23—41no—
448C23—41no—
449C23—82no—
450C23—84no—
451C23—88no—
452C23—84no—
453C23—88no—
454C23—88no—
455C23—1224no—
456C23—4884no—
457C23—2442no—
458C23—2441no—
459C23#1451974612yes—
460C23#1451974611yescharacteristic
461C23C22×C22⋊D6112yes—
462Q8—1222no—
463Q8—2441no—
464D4—216no—
465D4—41no—
466D4—42no—
467D4—41no—
468D4—42no—
469D4—48no—
470D4—48no—
471D4—48no—
472D4—48no—
473D4—416no—
474D4—81no—
475D4—1222no—
476D4—48816no—
477D4—2441no—
478D4—2444no—
479D4—2444no—
480D4—2442no—
481D4—2442no—
482C2×C4—24no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—416no—
488C2×C4—44no—
489C2×C4—1224no—
490C2×C4—4884no—
491C2×C4—2442no—
492C2×C4—2442no—
493C2×C4—2444no—
494C2×C4—2442no—
495C2×C4—2441no—
496C2×C4#1451974611yescharacteristic
497C2×C4C22×C22⋊D6111yescharacteristic
498C8—2442no—
499C22—22no—
500C22—28no—
501C22—22no—
502C22—22no—
503C22—42no—
504C22—42no—
505C22—44no—
506C22—48no—
507C22—44no—
508C22—48no—
509C22—44no—
510C22—44no—
511C22—48no—
512C22—42no—
513C22—82no—
514C22—82no—
515C22—84no—
516C22—88no—
517C22—816no—
518C22—82no—
519C22—9762no—
520C22—4884no—
521C22—4882no—
522C22—2442no—
523C22#1683994911yescharacteristic
524C22#1683994911yescharacteristic
525C22C2×#1451974611yescharacteristic
526C4—24no—
527C4—21no—
528C4—21no—
529C4—44no—
530C4—4884no—
531C4—2442no—
532C2—21no—
533C2—21no—
534C2—42no—
535C2—48no—
536C2—42no—
537C2—82no—
538C2—4882no—
539C2#2144780312yesdirect product factor
540C2C2×#1683994911yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×D4×C61C24
FrattiniC2×D4C23×D61
FittingC2×D42×C61C2
socleC22×C61B(4,𝔽2)
hypercenterC2×D42D61
hypocenterC61C2×#2196
LCSG ▷ C2×D4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. C2×#16839948C2semidirect
2. C2×#16839929C2semidirect
3. #21447803C2direct (N × H)
4. C2×#16839555C2semidirect
5. C2×#16839549C2semidirect
6. C2×D42×C61C2semidirect
7. C2×#14519822C22semidirect
11. #16839948C22semidirect
13. #16839929C22semidirect
15. C2×#14519694C22semidirect
16. C2×#14519692C22semidirect
18. #16839555C22semidirect
19. #16839549C22semidirect
23. D42×C61C22semidirect
32. #14519822C23semidirect
49. #14519694C23semidirect
51. #14519692C23semidirect
54. C25×C61D4semidirect
62. C22×D4×C61D4semidirect
66. #127×C61D4semidirect
74. #120×C61D4semidirect
81. C2×C22⋊C4×C61D4semidirect
82. C2×C42×C61D4semidirect
94. C24×C61C2×D4semidirect
115. C2×D4×C61C2×D4semidirect
150. C22⋊C4×C61C2×D4semidirect
152. C42×C61C2×D4semidirect
262. C2×D42D61semidirect
274. C2×C61#2196semidirect
282. D42C2×D61semidirect
299. C61C2×#2196semidirect
301. C25C22⋊D61semidirect
318. C22×D4C22⋊D61semidirect
327. #127C22⋊D61semidirect
337. #120C22⋊D61semidirect
346. C2×C22⋊C4C22⋊D61semidirect
347. C2×C42C22⋊D61semidirect
366. C24C2×C22⋊D61semidirect
406. C2×D4C2×C22⋊D61semidirect
429. C22⋊C4C2×C22⋊D61semidirect
431. C42C2×C22⋊D61semidirect
539. C2#21447803direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168399482
C2×#168399292
#214478032
C2×#168395552
C2×#168395492
C2×D42×C612
C2×#219661