Finite Group Databasebeta

← C2×#21444884 #29655868

Subgroups — C2×#21444884 #29655868

Order 15616.

1438 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840138C211yesmaximal, characteristic, complemented
2C2×#16839962C211yesmaximal, characteristic, complemented
3C2×#16839957C211yesmaximal, characteristic, complemented
4#21444884C218yesmaximal, direct product factor
5C2×#16839506C211yesmaximal, characteristic, complemented
6C2×Q8⋊#92418C211yesmaximal, characteristic, complemented
7C2×D4⋊#92418C211yesmaximal, characteristic, complemented
8C2×C61×#550C211yesmaximal, characteristic, complemented
9C22×#11758201—21no—
10C22×#11758199—22no—
11C22×#11758199—21no—
12C2×#14519774C2211yescharacteristic
13#16840138—22no—
14#16840138C2214yescomplemented
15#16839962—22no—
16#16839962C2214yescomplemented
17#16839957—22no—
18#16839957C2214yescomplemented
19C2×C4⋊#92418C2211yescharacteristic
20C2×C4⋊#92418C2211yescharacteristic
21C2×#14519697—21no—
22C2×#14519697—21no—
23C2×C4×#92418C2211yescharacteristic
24#16839506C2214yescomplemented
25Q8⋊#92418C2214yescomplemented
26D4⋊#92418C2214yescomplemented
27C22×#41×C61—21no—
28C61×#550—22no—
29C61×#550—22no—
30C61×#550—22no—
31C61×#550C2214yescomplemented
32C2×#127×C61—21no—
33C2×#127×C61C2211yescharacteristic
34C2×#121×C61—22no—
35C2×#121×C61—21no—
36C2×C4×Q8×C61C2211yescharacteristic
37C2×C4×D4×C61—21no—
38C2×C4×D4×C61C2211yescharacteristic
39C22×D244—21no—
40C22×D244—21no—
41C22×D244—21no—
42C2×#11758201—24no—
43C2×#11758201—44no—
44C2×#11758199—24no—
45C2×#11758199—28no—
46C2×#11758199—48no—
47C2×#11758199—44no—
48C22×#92418—21no—
49C22×#92418—21no—
50C22×#92418—21no—
51#14519774—21no—
52#14519774—21no—
53#14519774—21no—
54#14519774C2312yes—
55C4⋊#92418—21no—
56C4⋊#92418—21no—
57C4⋊#92418C2312yes—
58C4⋊#92418C2312yes—
59#14519697—24no—
60#14519697—24no—
61C4×#92418—21no—
62C4×#92418C2312yes—
63C2×#41×C61—24no—
64C2×#41×C61—24no—
65C2×#41×C61—44no—
66C2×#41×C61—44no—
67C22×Q8×C61D411yescharacteristic
68C22×D4×C61—22no—
69C22×D4×C61—22no—
70C22×D4×C61—21no—
71C22×D4×C61—21no—
72C22×D4×C61D411yescharacteristic
73C22×D4×C61D412yes—
74C23×C4×C61—22no—
75C23×C4×C61—21no—
76#127×C61—24no—
77#127×C61—24no—
78#127×C61—21no—
79#127×C61—21no—
80#127×C61D412yes—
81#127×C61C2312yes—
82#121×C61—24no—
83#121×C61—28no—
84#121×C61—28no—
85#121×C61—24no—
86C4×Q8×C61—21no—
87C4×Q8×C61—21no—
88C4×Q8×C61D412yes—
89C4×Q8×C61C2312yes—
90C4×D4×C61—24no—
91C4×D4×C61—24no—
92C4×D4×C61—21no—
93C4×D4×C61—21no—
94C4×D4×C61D412yes—
95C4×D4×C61C2312yes—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61D411yescharacteristic
98C2×C4⋊C4×C61D411yescharacteristic
99C2×C22⋊C4×C61—22no—
100C2×C22⋊C4×C61—21no—
101C2×C42×C61—21no—
102C2×C42×C61C2311yescharacteristic
103C24×C61—21no—
104C24×C61—22no—
105C23×D61—41no—
106#41×C61—48no—
107#41×C61—416no—
108#41×C61—48no—
109C2×Q8×C61—21no—
110C2×Q8×C61—22no—
111C2×Q8×C61D814yescomplemented
112C2×Q8×C61C2×D412yes—
113C2×D4×C61—28no—
114C2×D4×C61—28no—
115C2×D4×C61—21no—
116C2×D4×C61—22no—
117C2×D4×C61—22no—
118C2×D4×C61—22no—
119C2×D4×C61—22no—
120C2×D4×C61—22no—
121C2×D4×C61—22no—
122C2×D4×C61—22no—
123C2×D4×C61—48no—
124C2×D4×C61—44no—
125C2×D4×C61—42no—
126C2×D4×C61—42no—
127C2×D4×C61—42no—
128C2×D4×C61—42no—
129C2×D4×C61—84no—
130C2×D4×C61C2×D412yes—
131C2×D4×C61C2×D414yes—
132C22×C4×C61—21no—
133C22×C4×C61—28no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—48no—
139C22×C4×C61—42no—
140C22×C4×C61—42no—
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C2×D244—22no—
145C2×D244—22no—
146C2×D244—22no—
147C2×D244—44no—
148C2×D244—42no—
149C2×D244—42no—
150C2×D244—42no—
151C2×D244—42no—
152C2×D244—41no—
153C2×D244—41no—
154C2×D244—41no—
155C4⋊C4×C61—22no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—22no—
159C4⋊C4×C61C2×D412yes—
160C4⋊C4×C61C2×D412yes—
161C22⋊C4×C61—28no—
162C22⋊C4×C61—22no—
163C22⋊C4×C61—22no—
164C42×C61—22no—
165C42×C61—22no—
166C42×C61C2×D411yescharacteristic
167C42×C61C2×D411yescharacteristic
168C42×C61C2×D411yescharacteristic
169C42×C61C2411yescharacteristic
170#11758201—48no—
171#11758199—416no—
172#11758199—48no—
173C2×#92418—24no—
174C2×#92418—22no—
175C2×#92418—22no—
176C2×#92418—22no—
177C2×#92418—42no—
178C2×#92418—42no—
179C23×C61—22no—
180C23×C61—24no—
181C23×C61—44no—
182C23×C61—42no—
183C23×C61—42no—
184C23×C61—44no—
185C23×C61—44no—
186C23×C61—42no—
187C23×C61#12011yescharacteristic
188C22×D61—42no—
189C22×D61—82no—
190C22×D61—82no—
191C22×D61—82no—
192Q8×C61—22no—
193Q8×C61—24no—
194Q8×C61C2×D814yescomplemented
195D4×C61—22no—
196D4×C61—22no—
197D4×C61—44no—
198D4×C61—416no—
199D4×C61—42no—
200D4×C61—42no—
201D4×C61—42no—
202D4×C61—42no—
203D4×C61—44no—
204D4×C61—42no—
205D4×C61—44no—
206D4×C61—82no—
207D4×C61—88no—
208C2×C4×C61—22no—
209C2×C4×C61—24no—
210C2×C4×C61—22no—
211C2×C4×C61—22no—
212C2×C4×C61—22no—
213C2×C4×C61—416no—
214C2×C4×C61—42no—
215C2×C4×C61—42no—
216C2×C4×C61—42no—
217C2×C4×C61—42no—
218C2×C4×C61—44no—
219C2×C4×C61#12011yescharacteristic
220C2×C4×C61#12011yescharacteristic
221C2×C4×C61#12011yescharacteristic
222C2×C4×C61C2×D812yes—
223C2×C4×C61#13512yes—
224C2×C4×C61AGL(1,ℤ/8)12yes—
225C2×C4×C61AGL(1,ℤ/8)12yes—
226C2×C4×C61C22×D411yescharacteristic
227C2×C4×C61C22×D411yescharacteristic
228C2×C4×C61C22×D411yescharacteristic
229D244—44no—
230D244—42no—
231D244—42no—
232D244—42no—
233D244—42no—
234D244—82no—
235D244—82no—
236D244—82no—
237#92418—24no—
238#92418—42no—
239#92418—42no—
240C2×#1621—611nomaximal, Sylow
241C22×C61—44no—
242C22×C61—42no—
243C22×C61—42no—
244C22×C61—44no—
245C22×C61—44no—
246C22×C61—42no—
247C22×C61—84no—
248C22×C61—88no—
249C22×C61#44712yes—
250C22×C61#44912yes—
251C22×C61#45312yes—
252C22×C61C2×#12011yescharacteristic
253C2×D61—82no—
254C2×D61—82no—
255C2×D61—82no—
256C2×D61—164no—
257C4×C61—24no—
258C4×C61—21no—
259C4×C61—21no—
260C4×C61—42no—
261C4×C61—42no—
262C4×C61#44712yes—
263C4×C61#44912yes—
264C4×C61C22×D811yescharacteristic
265C4×C61C2×#13511yescharacteristic
266C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
267C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
268C2×#550D6111yescharacteristic, complemented
269C2×#493—611no—
270C2×#460—611no—
271C2×#459—611no—
272#1621—618no—
273C2×#331—611no—
274C2×Q8⋊C8—611no—
275C2×D4⋊C8—611no—
276C2×C61—82no—
277C2×C61—84no—
278C2×C61#162114yescomplemented
279C2×C61C2×#44711yescharacteristic
280C2×C61C2×#44911yescharacteristic
281C2×C61C2×#45311yescharacteristic
282D61—162no—
283C22×#41—21no—
284C22×SD16—1221no—
285C22×D8—1222no—
286C22×D8—1221no—
287#550—22no—
288#550—22no—
289#550—22no—
290#550C2×D6114yescomplemented
291C2×#127—21no—
292C2×#127—611no—
293C2×#127C2×D6111yescharacteristic
294C2×#121—22no—
295C2×#121—21no—
296C2×C4×Q8C2×D6111yescharacteristic
297C2×C4×D4—21no—
298C2×C4×D4C2×D6111yescharacteristic
299#493—614no—
300#493—1222no—
301#460—614no—
302#460—1222no—
303#459—614no—
304#459—1222no—
305C2×C4⋊C8—611no—
306C2×C4⋊C8—611no—
307C2×#102—1221no—
308C2×#102—1221no—
309C2×C4×C8—611no—
310#331—614no—
311Q8⋊C8—614no—
312D4⋊C8—614no—
313C61C2×#162111yescharacteristic, complemented, Sylow
314C2×#41—24no—
315C2×#41—24no—
316C2×#41—44no—
317C2×#41—44no—
318C22×Q8C22⋊D6111yescharacteristic
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—21no—
322C22×D4—21no—
323C22×D4—1221no—
324C22×D4—1221no—
325C22×D4—1221no—
326C22×D4C22⋊D6111yescharacteristic
327C22×D4C22⋊D6112yes—
328C23×C4—22no—
329C23×C4—21no—
330C2×SD16—1224no—
331C2×SD16—2444no—
332C2×D8—1224no—
333C2×D8—1228no—
334C2×D8—2448no—
335C2×D8—2444no—
336C22×C8—1221no—
337C22×C8—1221no—
338C22×C8—1221no—
339#127—24no—
340#127—24no—
341#127—21no—
342#127—21no—
343#127—612no—
344#127—1221no—
345#127—1221no—
346#127—1221no—
347#127C22⋊D6112yes—
348#127C22×D6112yes—
349#121—24no—
350#121—28no—
351#121—28no—
352#121—24no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8C22⋊D6112yes—
356C4×Q8C22×D6112yes—
357C4×D4—24no—
358C4×D4—24no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4C22⋊D6112yes—
362C4×D4C22×D6112yes—
363C2×C4⋊C4—21no—
364C2×C4⋊C4C22⋊D6111yescharacteristic
365C2×C4⋊C4C22⋊D6111yescharacteristic
366C2×C22⋊C4—22no—
367C2×C22⋊C4—21no—
368C2×C42—21no—
369C2×C42C22×D6111yescharacteristic
370C4⋊C8—612no—
371C4⋊C8—612no—
372C4⋊C8—1221no—
373C4⋊C8—1221no—
374#102—1224no—
375#102—1224no—
376C4×C8—612no—
377C4×C8—1221no—
378C24—21no—
379C24—22no—
380C24—2441no—
381#41—48no—
382#41—416no—
383#41—48no—
384C2×Q8—21no—
385C2×Q8—22no—
386C2×Q8#1175819914yescomplemented
387C2×Q8C2×C22⋊D6112yes—
388C2×D4—28no—
389C2×D4—28no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—21no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—48no—
399C2×D4—44no—
400C2×D4—42no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—42no—
404C2×D4—84no—
405C2×D4—1222no—
406C2×D4—1222no—
407C2×D4—1222no—
408C2×D4—2444no—
409C2×D4—2441no—
410C2×D4—2441no—
411C2×D4—2441no—
412C2×D4—2442no—
413C2×D4—2442no—
414C2×D4—2442no—
415C2×D4—2442no—
416C2×D4C2×C22⋊D6112yes—
417C2×D4C2×C22⋊D6114yes—
418C22×C4—21no—
419C22×C4—28no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—48no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4C2×C22⋊D6111yescharacteristic
428C22×C4C2×C22⋊D6111yescharacteristic
429C22×C4C2×C22⋊D6111yescharacteristic
430SD16—2448no—
431D8—24416no—
432D8—2448no—
433C2×C8—1224no—
434C2×C8—1222no—
435C2×C8—1222no—
436C2×C8—1222no—
437C2×C8—2442no—
438C2×C8—2442no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4C2×C22⋊D6112yes—
444C4⋊C4C2×C22⋊D6112yes—
445C22⋊C4—28no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C42—22no—
449C42—22no—
450C42C2×C22⋊D6111yescharacteristic
451C42C2×C22⋊D6111yescharacteristic
452C42C2×C22⋊D6111yescharacteristic
453C42C23×D6111yescharacteristic
454C23—24no—
455C23—22no—
456C23—44no—
457C23—42no—
458C23—42no—
459C23—44no—
460C23—44no—
461C23—42no—
462C23—4882no—
463C23—4882no—
464C23—4882no—
465C23—2442no—
466C23#1451974611yescharacteristic
467Q8—22no—
468Q8—24no—
469Q8C2×#1175819914yescomplemented
470D4—22no—
471D4—22no—
472D4—44no—
473D4—416no—
474D4—42no—
475D4—42no—
476D4—42no—
477D4—42no—
478D4—44no—
479D4—42no—
480D4—44no—
481D4—82no—
482D4—88no—
483D4—4882no—
484D4—4882no—
485D4—4882no—
486D4—2444no—
487D4—2442no—
488D4—2442no—
489D4—2442no—
490D4—2442no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—416no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—44no—
502C2×C4#1451974611yescharacteristic
503C2×C4#1451974611yescharacteristic
504C2×C4#1451974611yescharacteristic
505C2×C4C2×#1175819912yes—
506C2×C4#1451979712yes—
507C2×C4#1451980212yes—
508C2×C4#1451980312yes—
509C2×C4C22×C22⋊D6111yescharacteristic
510C2×C4C22×C22⋊D6111yescharacteristic
511C2×C4C22×C22⋊D6111yescharacteristic
512C8—1224no—
513C8—2442no—
514C8—2442no—
515C22—44no—
516C22—42no—
517C22—44no—
518C22—42no—
519C22—42no—
520C22—44no—
521C22—84no—
522C22—88no—
523C22—9764no—
524C22—4882no—
525C22—4882no—
526C22—4882no—
527C22#1683989612yes—
528C22#1683990712yes—
529C22#1683993012yes—
530C22C2×#1451974611yescharacteristic
531C4—21no—
532C4—21no—
533C4—24no—
534C4—42no—
535C4—42no—
536C4#1683989612yes—
537C4#1683990712yes—
538C4C22×#1175819911yescharacteristic
539C4C2×#1451979711yescharacteristic
540C4C2×#1451980211yescharacteristic
541C4C2×#1451980311yescharacteristic
542C2—84no—
543C2—82no—
544C2—9762no—
545C2#2144488414yesdirect product factor
546C2C2×#1683989611yescharacteristic
547C2C2×#1683990711yescharacteristic
548C2C2×#1683993011yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#550C2
socleC23×C61#120
hypercenterC2×#550D61
hypocenterC61C2×#1621
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#16840138C2semidirect
2. C2×#16839962C2semidirect
3. C2×#16839957C2semidirect
4. #21444884C2direct (N × H)
5. C2×#16839506C2semidirect
6. C2×Q8⋊#92418C2semidirect
7. C2×D4⋊#92418C2semidirect
8. C2×C61×#550C2semidirect
14. #16840138C22semidirect
16. #16839962C22semidirect
18. #16839957C22semidirect
24. #16839506C22semidirect
25. Q8⋊#92418C22semidirect
26. D4⋊#92418C22semidirect
31. C61×#550C22semidirect
111. C2×Q8×C61D8semidirect
194. Q8×C61C2×D8semidirect
268. C2×#550D61semidirect
278. C2×C61#1621semidirect
290. #550C2×D61semidirect
313. C61C2×#1621semidirect
386. C2×Q8#11758199semidirect
469. Q8C2×#11758199semidirect
545. C2#21444884direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168401382
C2×#168399622
C2×#168399572
#214448842
C2×#168395062
C2×Q8⋊#924182
C2×D4⋊#924182
C2×C61×#5502
C2×#162161