Finite Group Databasebeta

← C4×#19127696 #35402154

Subgroups — C4×#19127696 #35402154

Order 21248.

1670 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#13050591C211yesmaximal, characteristic
2C2×#19127696C212yesmaximal
3C2×C4×C8×D83C211yesmaximal, characteristic, complemented
4C4×#14581750C211yesmaximal, characteristic, complemented
5#103×Dic83C212yesmaximal, complemented
6C4×#14581716C211yesmaximal, characteristic, complemented
7C4×#14581712C211yesmaximal, characteristic, complemented
8C4×#14581714C211yesmaximal, characteristic, complemented
9#24907277C212yesmaximal, complemented
10#24907178C212yesmaximal, complemented
11C4×#103×C83C211yesmaximal, characteristic, complemented
12C22×#13050591C2211yescharacteristic
13C22×C8×D83C2212yes—
14C4×#13050591—24no—
15C4×#13050591C418yescomplemented
16C2×Q8×Dic83C2211yescharacteristic
17C2×C4×D332—21no—
18C2×C4×D332C2211yescharacteristic
19C2×#14581754—21no—
20C2×#14581754C2211yescharacteristic
21C2×#14581750—21no—
22C2×#14581750C2211yescharacteristic
23C2×#14581750C2212yes—
24C2×C42×D83—21no—
25C2×C42×D83C2211yescharacteristic
26#19127696C4116yesdirect product factor
27C2×#14581716C2212yes—
28C2×#14581714C2212yes—
29C2×#14581712C2212yes—
30C2×C4×C83⋊C8C2211yescharacteristic
31C2×C8×Dic83C2212yes—
32C4×C8×D83—24no—
33C4⋊C4×Dic83C2212yes—
34C4×C4⋊Dic83C2211yescharacteristic
35C4×(C2×D83)⋊C4—21no—
36#19127548—21no—
37#19127546—21no—
38C42×Dic83—21no—
39#19127464C2212yes—
40#19127463C2212yes—
41#19127463C2212yes—
42C2×C4×Q8×C83C2211yescharacteristic
43C2×#103×C83C2212yes—
44C2×C4×C8×C83C2211yescharacteristic
45C4×C4⋊C4×C83C2211yescharacteristic
46#340×C83C2212yes—
47C2×#13050591—22no—
48C2×#13050591—24no—
49C2×#13050591C2×C414yes—
50C2×#13050591C2×C418yes—
51C22×D332—21no—
52C22×D332C2311yescharacteristic
53C22×C4×D83—21no—
54C22×C4×D83—21no—
55C22×C4×D83—21no—
56C22×C4×D83D411yescharacteristic
57C22×C4×D83D411yescharacteristic
58C22×C4×D83C2311yescharacteristic
59C22×C83⋊C8C2312yes—
60C2×C8×D83—24no—
61C2×C8×D83—24no—
62C2×C8×D83C2×C418yescomplemented
63Q8×Dic83—22no—
64Q8×Dic83C2×C414yes—
65C4×D332—28no—
66C4×D332—22no—
67C4×D332C2×C414yes—
68#14581754—28no—
69#14581754—22no—
70#14581754C2×C414yes—
71#14581750—22no—
72#14581750—24no—
73#14581750—28no—
74#14581750C2×C414yes—
75#14581750C2×C418yescomplemented
76C2×C4⋊Dic83—21no—
77C2×C4⋊Dic83C2312yes—
78C2×C4⋊Dic83C2311yescharacteristic
79C2×(C2×D83)⋊C4—21no—
80C2×(C2×D83)⋊C4—22no—
81C2×(C2×D83)⋊C4—21no—
82C2×(C2×D83)⋊C4—21no—
83C2×C4×Dic83—21no—
84C2×C4×Dic83—21no—
85C2×C4×Dic83—22no—
86C2×C4×Dic83—22no—
87C2×C4×Dic83—21no—
88C2×C4×Dic83D411yescharacteristic
89C2×C4×Dic83D411yescharacteristic
90C2×C4×Dic83C2311yescharacteristic
91C42×D83—28no—
92C42×D83C2×C414yes—
93C42×D83D414yes—
94#14581716C2×C418yescomplemented
95#14581714C2×C418yescomplemented
96#14581712C2×C418yescomplemented
97C4×C83⋊C8—22no—
98C8×Dic83—24no—
99C83⋊#95—22no—
100C83⋊#95—21no—
101C22×Q8×C83C2311yescharacteristic
102C22×C8×C83C2312yes—
103C4×Q8×C83—22no—
104C4×Q8×C83C2×C414yes—
105C2×C4⋊C4×C83—21no—
106C2×C4⋊C4×C83C2312yes—
107C2×C4⋊C4×C83C2311yescharacteristic
108C2×C42×C83—21no—
109C2×C42×C83—21no—
110C2×C42×C83C2311yescharacteristic
111#103×C83C2×C418yescomplemented
112C4×C8×C83—22no—
113#95×C83—21no—
114C23×D83—21no—
115C23×D83C2×D411yescharacteristic
116#13050591—28no—
117#13050591—216no—
118#13050591C42116yescomplemented
119C2×D332—24no—
120C2×D332—28no—
121C2×D332—21no—
122C2×D332—22no—
123C2×D332C22×C414yes—
124C2×D332C22×C412yes—
125C22×Dic83—21no—
126C22×Dic83—22no—
127C22×Dic83C2×D411yescharacteristic
128C22×Dic83C2×D411yescharacteristic
129C22×Dic83C2×D411yescharacteristic
130C2×C4×D83—22no—
131C2×C4×D83—22no—
132C2×C4×D83—24no—
133C2×C4×D83—28no—
134C2×C4×D83—24no—
135C2×C4×D83—24no—
136C2×C4×D83—24no—
137C2×C4×D83—42no—
138C2×C4×D83—42no—
139C2×C4×D83—44no—
140C2×C4×D83C22⋊C414yes—
141C2×C4×D83C22⋊C414yes—
142C2×C4×D83C22×C412yes—
143C2×C4×D83C22×C414yes—
144C2×C4×D83C2×D412yes—
145C2×C4×D83#4114yes—
146C2×C83⋊C8—22no—
147C2×C83⋊C8—22no—
148C2×C83⋊C8C22×C414yes—
149C8×D83—216no—
150C4⋊Dic83—21no—
151C4⋊Dic83—22no—
152C4⋊Dic83—24no—
153C4⋊Dic83C22×C414yes—
154C4⋊Dic83C22×C412yes—
155(C2×D83)⋊C4—24no—
156(C2×D83)⋊C4—28no—
157(C2×D83)⋊C4—24no—
158(C2×D83)⋊C4—24no—
159C4×Dic83—24no—
160C4×Dic83—24no—
161C4×Dic83—28no—
162C4×Dic83—42no—
163C4×Dic83—44no—
164C4×Dic83C22⋊C414yes—
165C4×Dic83C22⋊C414yes—
166C4×Dic83C22×C412yes—
167C4×Dic83C2×D412yes—
168C2×Q8×C83—21no—
169C2×Q8×C83—22no—
170C2×Q8×C83C22×C414yes—
171C2×Q8×C83C22×C412yes—
172C22×C4×C83—21no—
173C22×C4×C83—21no—
174C22×C4×C83—22no—
175C22×C4×C83C2×D411yescharacteristic
176C22×C4×C83C2×D411yescharacteristic
177C22×C4×C83C2411yescharacteristic
178C2×C8×C83—22no—
179C2×C8×C83—22no—
180C2×C8×C83C22×C414yes—
181C4⋊C4×C83—24no—
182C4⋊C4×C83—21no—
183C4⋊C4×C83—22no—
184C4⋊C4×C83C22×C414yes—
185C4⋊C4×C83C22×C412yes—
186C42×C83—24no—
187C42×C83—42no—
188C42×C83C22×C412yes—
189C42×C83C2×D412yes—
190C23×C83C22×D411yescharacteristic
191C22×D83—22no—
192C22×D83—21no—
193C22×D83—21no—
194C22×D83—22no—
195C22×D83—24no—
196C22×D83—42no—
197C22×D83—41no—
198C22×D83—41no—
199C22×D83C2×C22⋊C412yes—
200C22×D83C4×D414yes—
201Q8×C83—22no—
202Q8×C83—24no—
203Q8×C83C2×C4214yes—
204C2×C4×C83—22no—
205C2×C4×C83—24no—
206C2×C4×C83—22no—
207C2×C4×C83—22no—
208C2×C4×C83—24no—
209C2×C4×C83—42no—
210C2×C4×C83—42no—
211C2×C4×C83—42no—
212C2×C4×C83C2×C22⋊C412yes—
213C2×C4×C83C2×C22⋊C412yes—
214C2×C4×C83#13512yes—
215C2×C4×C83#13512yes—
216C2×C4×C83C23×C411yescharacteristic
217C2×C4×C83C23×C412yes—
218C2×C4×C83C22×D411yescharacteristic
219C2×C4×C83C2×#4112yes—
220C2×Dic83—21no—
221C2×Dic83—21no—
222C2×Dic83—22no—
223C2×Dic83—24no—
224C2×Dic83—42no—
225C2×Dic83—42no—
226C2×Dic83—41no—
227C2×Dic83—41no—
228C2×Dic83C2×C22⋊C412yes—
229C2×Dic83C2×C22⋊C412yes—
230C2×Dic83C2×C22⋊C412yes—
231C2×Dic83C4×D414yes—
232C2×Dic83#13514yes—
233D332—216no—
234D332—22no—
235D332—24no—
236D332C2×C4214yes—
237C4×D83—28no—
238C4×D83—216no—
239C4×D83—28no—
240C4×D83—48no—
241C4×D83—48no—
242C4×D83C2×C4214yes—
243C4×D83#11714yes—
244C4×D83C4×D418yes—
245C8×C83—24no—
246C83⋊C8—24no—
247C22×C83C22×C22⋊C411yescharacteristic
248C22×C83C2×C4×D412yes—
249C22×C83C2×#13512yes—
250C22×C83C2×#13511yescharacteristic
251C22×C83C2×#13511yescharacteristic
252C2×D83—22no—
253C2×D83—22no—
254C2×D83—24no—
255C2×D83—24no—
256C2×D83—24no—
257C2×D83—42no—
258C2×D83—42no—
259C2×D83—44no—
260C2×D83—44no—
261C2×D83C4×C22⋊C414yes—
262C4×C83—22no—
263C4×C83—24no—
264C4×C83—42no—
265C4×C83—44no—
266C4×C83#41614yescomplemented
267C4×C83C22×C4211yescharacteristic
268C4×C83C2×#11711yescharacteristic
269C4×C83C2×C4×D412yes—
270Dic83—22no—
271Dic83—42no—
272Dic83—44no—
273Dic83C4×C22⋊C414yes—
274Dic83#41614yescomplemented
275C4×#416—831nomaximal, Sylow
276C2×C83C2×C4×C22⋊C411yescharacteristic
277C2×C83C2×#41611yescharacteristic
278C2×C83C2×#41611yescharacteristic
279C2×C83C4×#13512yes—
280C2×C83C4×#13512yes—
281D83—24no—
282D83—44no—
283C2×C4×#41—831no—
284C2×#416—832no—
285C22×C4×C8—831no—
286C4×#117—831no—
287C4×#103—832no—
288C4×#103—831no—
289C4×#103D8311yescharacteristic, complemented
290C4×#102—831no—
291C4×#102—831no—
292C4×#102—832no—
293#1735—832no—
294C83C4×#41611yescharacteristic, complemented, Sylow
295C22×#41—831no—
296C23×C8—832no—
297C4×#41—838no—
298C4×#41—1664no—
299C2×C4×Q8—831no—
300C2×C4×Q8C2×D8311yescharacteristic
301C2×C4×D4—831no—
302C2×C4×D4—831no—
303C2×C4×D4—1661no—
304C2×C4×D4—1661no—
305C2×#117—832no—
306C2×#117—831no—
307C2×#117—1661no—
308C22×C42—831no—
309C22×C42—1661no—
310#416—8316no—
311C2×#103—832no—
312C2×#103C2×D8312yes—
313C2×#102—832no—
314C2×#102—832no—
315C2×C4×C8—832no—
316C2×C4×C8—831no—
317C2×C4×C8—1664no—
318C2×C4×C8C2×D8311yescharacteristic
319C4×C4⋊C4—832no—
320C4×C4⋊C4—831no—
321C4×C4⋊C4C2×D8311yescharacteristic
322C4×C22⋊C4—1661no—
323C4×C22⋊C4—1661no—
324#376—1661no—
325C43—1661no—
326#340—832no—
327#340—832no—
328#340—832no—
329#340C2×D8312yes—
330C2×#41—834no—
331C2×#41—838no—
332C2×#41—1662no—
333C2×#41—1664no—
334C22×Q8C22×D8311yescharacteristic
335C22×D4—831no—
336C22×D4—1661no—
337C23×C4—831no—
338C23×C4—831no—
339C23×C4—831no—
340C23×C4—1661no—
341C23×C4—1661no—
342C23×C4—1661no—
343C22×C8—832no—
344C22×C8—838no—
345C22×C8—1664no—
346C22×C8—1664no—
347C22×C8C22×D8312yes—
348C4×Q8—22no—
349C4×Q8—834no—
350C4×Q8—1662no—
351C4×Q8C4×D8314yes—
352C4×D4—834no—
353C4×D4—834no—
354C4×D4—1668no—
355C4×D4—1662no—
356C4×D4—1668no—
357C4×D4—1662no—
358#117—834no—
359#117—838no—
360#117—1668no—
361#117—1662no—
362#117—1664no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—831no—
365C2×C4⋊C4—832no—
366C2×C4⋊C4—1661no—
367C2×C4⋊C4C22×D8311yescharacteristic
368C2×C4⋊C4C22×D8312yes—
369C2×C22⋊C4—1661no—
370C2×C22⋊C4—1661no—
371C2×C22⋊C4—1662no—
372C2×C22⋊C4—1661no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—831no—
376C2×C42—831no—
377C2×C42—831no—
378C2×C42—834no—
379C2×C42—834no—
380C2×C42—1668no—
381C2×C42—1662no—
382C2×C42—1661no—
383C2×C42—1661no—
384C2×C42—1662no—
385C2×C42—1661no—
386C2×C42C22×D8311yescharacteristic
387#103—838no—
388#103C4×D8318yescomplemented
389#102—838no—
390#102—838no—
391C4×C8—22no—
392C4×C8—1664no—
393C4×C8—1662no—
394#95—21no—
395#95—1662no—
396#95—1661no—
397C24—831no—
398C24—1661no—
399#41—8316no—
400#41—1668no—
401#41—16616no—
402C2×Q8—21no—
403C2×Q8—22no—
404C2×Q8C2×C4×D8314yes—
405C2×Q8C2×C4×D8312yes—
406C2×D4—834no—
407C2×D4—832no—
408C2×D4—1664no—
409C2×D4—1668no—
410C2×D4—1661no—
411C2×D4—1662no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—3324no—
416C22×C4—3322no—
417C22×C4—3322no—
418C22×C4—831no—
419C22×C4—831no—
420C22×C4—832no—
421C22×C4—834no—
422C22×C4—832no—
423C22×C4—834no—
424C22×C4—831no—
425C22×C4—834no—
426C22×C4—834no—
427C22×C4—1664no—
428C22×C4—1664no—
429C22×C4—1664no—
430C22×C4—1668no—
431C22×C4—1662no—
432C22×C4—1661no—
433C22×C4—1664no—
434C22×C4—1662no—
435C22×C4—1662no—
436C22×C4D4×D8311yescharacteristic
437C22×C4D4×D8311yescharacteristic
438C22×C4C23×D8311yescharacteristic
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—834no—
442C2×C8—16616no—
443C2×C8—1662no—
444C2×C8—1662no—
445C2×C8C2×C4×D8314yes—
446C4⋊C4—21no—
447C4⋊C4—22no—
448C4⋊C4—24no—
449C4⋊C4—834no—
450C4⋊C4—832no—
451C4⋊C4—1664no—
452C4⋊C4—1661no—
453C4⋊C4—1662no—
454C4⋊C4C2×C4×D8314yes—
455C4⋊C4C2×C4×D8312yes—
456C22⋊C4—1664no—
457C22⋊C4—1664no—
458C22⋊C4—1668no—
459C22⋊C4—1664no—
460C42—24no—
461C42—42no—
462C42—3324no—
463C42—3322no—
464C42—832no—
465C42—832no—
466C42—834no—
467C42—834no—
468C42—1664no—
469C42—1664no—
470C42—1668no—
471C42C2×C4×D8312yes—
472C42D4×D8312yes—
473C23—3322no—
474C23—3321no—
475C23—3321no—
476C23—832no—
477C23—834no—
478C23—1662no—
479C23—1664no—
480C23—1662no—
481C23—1661no—
482C23—1661no—
483C23C2×D4×D8311yescharacteristic
484Q8—22no—
485Q8—24no—
486Q8C42×D8314yes—
487D4—834no—
488D4—16616no—
489D4—1662no—
490D4—1664no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—3328no—
500C2×C4—3322no—
501C2×C4—3321no—
502C2×C4—3322no—
503C2×C4—3321no—
504C2×C4—3328no—
505C2×C4—832no—
506C2×C4—832no—
507C2×C4—834no—
508C2×C4—834no—
509C2×C4—834no—
510C2×C4—834no—
511C2×C4—838no—
512C2×C4—832no—
513C2×C4—1668no—
514C2×C4—16616no—
515C2×C4—1662no—
516C2×C4—1664no—
517C2×C4—1661no—
518C2×C4—1661no—
519C2×C4—1668no—
520C2×C4C22⋊C4×D8312yes—
521C2×C4C22⋊C4×D8312yes—
522C2×C4#1458181312yes—
523C2×C4#1458181512yes—
524C2×C4C22×C4×D8311yescharacteristic
525C2×C4C22×C4×D8312yes—
526C2×C4C2×D4×D8311yescharacteristic
527C2×C4#41×D8312yes—
528C8—24no—
529C8—1664no—
530C22—3324no—
531C22—3324no—
532C22—3322no—
533C22—3322no—
534C22—834no—
535C22—1664no—
536C22—1664no—
537C22—1664no—
538C22—1662no—
539C22—1662no—
540C22C2×C22⋊C4×D8311yescharacteristic
541C22C4×D4×D8312yes—
542C22#135×D8312yes—
543C22C2×#1458181311yescharacteristic
544C22C2×#1458181511yescharacteristic
545C4—24no—
546C4—22no—
547C4—44no—
548C4—42no—
549C4—3324no—
550C4—3322no—
551C4—834no—
552C4—834no—
553C4—1662no—
554C4#1912769614yesdirect product factor
555C4C2×C42×D8311yescharacteristic
556C4#117×D8311yescharacteristic
557C4C4×D4×D8312yes—
558C2—3324no—
559C2—1664no—
560C2C4×C22⋊C4×D8311yescharacteristic
561C2#416×D8311yescharacteristic
562C2C2×#1912769611yescharacteristic
563C2C4×#1458181312yes—
564C2C4×#1458181512yes—
subgroupG/H
centerC22×C4D4×D83
commutatorC4×C83C22×C42
FrattiniC22×C4C23×D83
FittingC4×#103×C83C2
socleC23×C83C22×D4
prime radicalC22×#13050591C22
cosocleC22×C4×C83C24
hypercenterC4×#103D83
hypocenterC83C4×#416
LCSG ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
3. C2×C4×C8×D83C2semidirect
4. C4×#14581750C2semidirect
5. #103×Dic83C2semidirect
6. C4×#14581716C2semidirect
7. C4×#14581712C2semidirect
8. C4×#14581714C2semidirect
9. #24907277C2semidirect
10. #24907178C2semidirect
11. C4×#103×C83C2semidirect
15. C4×#13050591C4semidirect
26. #19127696C4direct (N × H)
62. C2×C8×D83C2×C4semidirect
75. #14581750C2×C4semidirect
94. #14581716C2×C4semidirect
95. #14581714C2×C4semidirect
96. #14581712C2×C4semidirect
111. #103×C83C2×C4semidirect
118. #13050591C42semidirect
266. C4×C83#416semidirect
274. Dic83#416semidirect
289. C4×#103D83semidirect
294. C83C4×#416semidirect
388. #103C4×D83semidirect
554. C4#19127696direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#130505912
C2×#191276962
C2×C4×C8×D832
C4×#145817502
#103×Dic832
C4×#145817162
C4×#145817122
C4×#145817142
#249072772
#249071782
C4×#103×C832
C4×#41683