Finite Group Databasebeta

← C4×#11719108 #16797431

Subgroups — C4×#11719108 #16797431

Order 3328.

1022 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719108C212yesmaximal
2C4×#88240C211yesmaximal, characteristic, complemented
3C4×#88238C211yesmaximal, characteristic, complemented
4C4×#88104C211yesmaximal, characteristic, complemented
5#13130644C212yesmaximal, complemented
6#13130617C212yesmaximal, complemented
7#13130615C212yesmaximal, complemented
8C4×#88118C211yesmaximal, characteristic, complemented
9C4×#88116C211yesmaximal, characteristic, complemented
10C4×#88100C211yesmaximal, characteristic, complemented
11C4×#88170C211yesmaximal, characteristic
12C2×#88240C2212yes—
13C2×#88238C2212yes—
14C2×#88170C2211yescharacteristic
15C4×#6131C2211yescharacteristic
16C4×#6129C2211yescharacteristic
17C2×#88118C2212yes—
18C2×#88116C2212yes—
19C4×#6122—21no—
20C2×C4×#1057—21no—
21#11719108C4116yesdirect product factor
22C2×#88104C2212yes—
23C2×#88100C2212yes—
24C2×#88100C2212yes—
25#11719072—22no—
26#11719072C2212yes—
27#11719072C2212yes—
28#11719062—22no—
29C42×#261C2211yescharacteristic
30C4×#6118—21no—
31C4×#6118C2211yescharacteristic
32C4×#6118C2211yescharacteristic
33C4×D13⋊C8—21no—
34C4×D13⋊C8C2211yescharacteristic
35C4×C13×SD16C411yescharacteristic, complemented
36SD16×Dic13C411yescharacteristic, complemented
37C4×#6107C411yescharacteristic, complemented
38C4×#6104C411yescharacteristic, complemented
39#11718521C2211yescharacteristic
40#11718513C411yescharacteristic, complemented
41#11718465C2211yescharacteristic
42#11718451C411yescharacteristic, complemented
43#11718433C2211yescharacteristic
44#11718417C411yescharacteristic, complemented
45C4×#6095C411yescharacteristic, complemented
46C4×C8×D13C2211yescharacteristic
47#11718268C2212yes—
48#11718247C2212yes—
49#11718247C2212yes—
50C2×#6131C2311yescharacteristic
51C2×#6129C2311yescharacteristic
52C2×#6122—22no—
53C22×#1057—22no—
54#88240—24no—
55#88240C2×C418yescomplemented
56#88238—24no—
57#88238C2×C418yescomplemented
58C2×C4×#261—21no—
59C2×C4×#261—21no—
60C2×C4×#261C2312yes—
61C2×#6118—22no—
62C2×#6118C2312yes—
63C2×#6118C2312yes—
64C2×D13⋊C8—22no—
65C2×D13⋊C8C2312yes—
66C2×C13×SD16C2×C411yescharacteristic
67C4×Q8×C13C2×C411yescharacteristic
68C4×D4×C13C2×C411yescharacteristic
69Q8×Dic13C2×C411yescharacteristic
70C2×#6107C2×C411yescharacteristic
71D4×Dic13C2×C411yescharacteristic
72C2×#6104C2×C411yescharacteristic
73C4×C22⋊D13—21no—
74C2×C4×Dic13—21no—
75#88170C2×C418yes—
76C2×#6095C2×C411yescharacteristic
77C2×C8×D13C2311yescharacteristic
78C2×C8×D13C2311yescharacteristic
79#88147—21no—
80#88147C2×C411yescharacteristic
81#88146—21no—
82#88146C2311yescharacteristic
83#88146C2311yescharacteristic
84#88141C2×C411yescharacteristic
85#88135—21no—
86#88131—21no—
87C4×D52—21no—
88C4×D52C2×C411yescharacteristic
89C42×D13—21no—
90C42×D13C2311yescharacteristic
91C4×Dic26C2×C411yescharacteristic
92#88118C2×C418yescomplemented
93#88116C2×C418yescomplemented
94#88110—22no—
95#88110—22no—
96#88110—21no—
97#88110—21no—
98C4×#1057—22no—
99C4×#1057—22no—
100C4×#1057—21no—
101C4×#1057—21no—
102C4×#1057D411yescharacteristic
103C4×#1057D411yescharacteristic
104C4×#1057D412yes—
105#88104C2×C418yescomplemented
106#88100—24no—
107#88100C2×C418yescomplemented
108C13×#106C2×C411yescharacteristic
109C13×#103C2×C411yescharacteristic
110C13×#102C2×C411yescharacteristic
111C4×C8×C13C2×C411yescharacteristic
112#88075C2×C411yescharacteristic
113#88072C2×C411yescharacteristic
114#88061C2×C411yescharacteristic
115#88057C2×C411yescharacteristic
116#88056C2×C411yescharacteristic
117C8×Dic13C2×C411yescharacteristic
118C8×Dic13C2×C411yescharacteristic
119#88050C2×C411yescharacteristic
120#88049C2×C411yescharacteristic
121#88047C2×C411yescharacteristic
122#88047C2×C411yescharacteristic
123C4×#1055C2×C411yescharacteristic
124C4×#444—131nomaximal, Sylow
125C22×#261—22no—
126C2×Q8×C13C22×C411yescharacteristic
127C2×D4×C13C22×C411yescharacteristic
128C22×C4×C13—21no—
129C2×C22⋊D13—21no—
130C22×Dic13—21no—
131C22×Dic13—21no—
132#6131—22no—
133#6131C22×C414yes—
134#6129—22no—
135#6129C22×C414yes—
136C2×D52—21no—
137C2×D52C22×C411yescharacteristic
138C2×C4×D13—21no—
139C2×C4×D13—21no—
140C2×C4×D13—21no—
141C2×C4×D13#4111yescharacteristic
142C2×C4×D13#4111yescharacteristic
143C2×C4×D13C2411yescharacteristic
144C2×Dic26C22×C411yescharacteristic
145#6122—28no—
146C2×#1057—22no—
147C2×#1057—22no—
148C2×#1057—28no—
149C2×#1057C2×D412yes—
150C2×#1057C2×D412yes—
151C4×#261—22no—
152C4×#261—42no—
153C4×#261—42no—
154C4×#261C22×C414yes—
155#6118—22no—
156#6118—22no—
157#6118—28no—
158#6118C22×C414yes—
159#6118C22×C414yes—
160D13⋊C8—28no—
161D13⋊C8C22×C414yes—
162D13⋊C8#4114yes—
163C13×SD16C4214yescomplemented
164C2×C8×C13C22×C411yescharacteristic
165C2×C8×C13C22×C411yescharacteristic
166C13×C4⋊C4—21no—
167C13×C4⋊C4C22×C411yescharacteristic
168C13×C4⋊C4C22×C411yescharacteristic
169C13×C22⋊C4—21no—
170C42×C13—21no—
171C42×C13C22×C411yescharacteristic
172C22⋊Dic13—21no—
173#6107C4214yescomplemented
174#6104C4214yescomplemented
175#6103—21no—
176#6103—21no—
177#6103—21no—
178#6103—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13C22×C411yescharacteristic
181C4⋊Dic13C22×C411yescharacteristic
182#6101—21no—
183#6101—21no—
184C4×Dic13—21no—
185C4×Dic13—21no—
186C4×Dic13—21no—
187C4×Dic13—21no—
188C4×Dic13—21no—
189C4×Dic13C22×C411yescharacteristic
190C4×Dic13C2×D411yescharacteristic
191C4×Dic13C2×D411yescharacteristic
192C2×#1055C22×C411yescharacteristic
193C2×#1055C22×C411yescharacteristic
194#6095C4214yescomplemented
195C8×D13—22no—
196C8×D13C22×C414yes—
197C2×#444—132no—
198C4×#135—131no—
199C4×#131—131no—
200C4×#131—131no—
201C4×#108—131no—
202#1773—132no—
203#1765—132no—
204#1765—132no—
205C4×#104—131no—
206C4×#104—131no—
207C4×#97—131no—
208C23×C13—21no—
209C22×D13—21no—
210C22×D13C2×#4111yescharacteristic
211C2×#261—24no—
212C2×#261—42no—
213C2×#261—42no—
214Q8×C13—21no—
215Q8×C13C2×C4212yes—
216D4×C13—21no—
217D4×C13C2×C4212yes—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—42no—
222C2×C4×C13C4×D411yescharacteristic
223C2×C4×C13C4×D411yescharacteristic
224C2×C4×C13C23×C411yescharacteristic
225C22⋊D13—24no—
226C2×Dic13—21no—
227C2×Dic13—24no—
228C2×Dic13—21no—
229C2×Dic13—21no—
230C2×Dic13—42no—
231C2×Dic13C4×D411yescharacteristic
232C2×Dic13C4×D411yescharacteristic
233C2×Dic13C22×D411yescharacteristic
234D52—24no—
235D52—21no—
236D52C2×C4212yes—
237C4×D13—22no—
238C4×D13—24no—
239C4×D13—22no—
240C4×D13—42no—
241C4×D13—42no—
242C4×D13C23×C412yes—
243C4×D13C2×#4112yes—
244Dic26—21no—
245Dic26C2×C4212yes—
246#1057—24no—
247#1057—24no—
248#1057C4×D414yes—
249#1057C4×D414yes—
250C8×C13—21no—
251C8×C13C2×C4212yes—
252#1055—21no—
253#1055C2×C4212yes—
254C2×#135—131no—
255C2×#131—132no—
256C2×#131—132no—
257C4×#41—131no—
258C4×#41—131no—
259#444—1316no—
260C4×Q16—131no—
261C4×Q16—131no—
262C4×SD16—131no—
263C4×SD16—131no—
264C4×SD16—131no—
265C4×SD16#26111yescharacteristic, complemented
266C4×D8—131no—
267C4×D8—131no—
268C2×#108—132no—
269#427—131no—
270C2×#104—132no—
271C2×#104—132no—
272#416—131no—
273#416—131no—
274#405—132no—
275#405—132no—
276#405—262no—
277#405—262no—
278C4×M16—131no—
279C4×M16—131no—
280C4×M16—261no—
281C4×M16—261no—
282C2×#97—132no—
283C2×#97—132no—
284C2×C4×C8—131no—
285C2×C4×C8—131no—
286C2×C4×C8—261no—
287C2×C4×C8—261no—
288C43—131no—
289#341—132no—
290#339—132no—
291#339—132no—
292C22×C13—22no—
293C22×C13—41no—
294C22×C13—41no—
295C22×C13C2×C4×D411yescharacteristic
296C2×D13—21no—
297C2×D13—21no—
298C2×D13—22no—
299C2×D13—41no—
300C2×D13—41no—
301C2×D13C4×#4112yes—
302#261—44no—
303C4×C13—21no—
304C4×C13—22no—
305C4×C13—41no—
306C4×C13—41no—
307C4×C13#44412yescomplemented
308C4×C13C22×C4211yescharacteristic
309C4×C13C4×#4111yescharacteristic
310Dic13—21no—
311Dic13—22no—
312Dic13—41no—
313Dic13—41no—
314Dic13#44412yescomplemented
315Dic13C2×C4×D412yes—
316C2×#41—131no—
317C2×#41—131no—
318#135—138no—
319C2×Q16—131no—
320C2×SD16—131no—
321C2×SD16C2×#26111yescharacteristic
322C2×D8—131no—
323#131—138no—
324#131—138no—
325#131—264no—
326#131—264no—
327C2×M16—132no—
328C2×M16—132no—
329C2×M16—262no—
330C2×M16—262no—
331C22×C8—132no—
332C22×C8—131no—
333C22×C8—131no—
334C22×C8—262no—
335C22×C8—262no—
336C4×Q8—131no—
337C4×Q8—131no—
338C4×Q8—131no—
339C4×Q8C2×#26111yescharacteristic
340C4×D4—131no—
341C4×D4—131no—
342C4×D4—131no—
343C4×D4—261no—
344C4×D4—261no—
345C4×D4—261no—
346C4×D4—261no—
347C4×D4C2×#26111yescharacteristic
348#117—131no—
349#117—131no—
350#117—261no—
351#117—261no—
352C2×C42—131no—
353C2×C42—132no—
354C2×C42—261no—
355C2×C42—261no—
356C2×C42—261no—
357C2×C42—261no—
358#108—138no—
359#107—131no—
360#107—131no—
361#106—131no—
362#106C2×#26111yescharacteristic
363#104—138no—
364#104—138no—
365#103—131no—
366#103—131no—
367#103—131no—
368#103C2×#26111yescharacteristic
369#102—131no—
370#102—131no—
371#102—131no—
372#102C2×#26111yescharacteristic
373#97—138no—
374#97—261no—
375#97—261no—
376#97—264no—
377#97—262no—
378#97—262no—
379C4×C8—131no—
380C4×C8—131no—
381C4×C8—132no—
382C4×C8—131no—
383C4×C8—131no—
384C4×C8—131no—
385C4×C8—261no—
386C4×C8—261no—
387C4×C8—262no—
388C4×C8—262no—
389C4×C8C2×#26111yescharacteristic
390C2×C13—42no—
391C2×C13C42×D411yescharacteristic
392C2×C13C2×#44411yescharacteristic
393C2×C13C2×#44411yescharacteristic
394D13—22no—
395D13—42no—
396#41—134no—
397#41—134no—
398#41—262no—
399#41—262no—
400C2×Q8—131no—
401C2×Q8C22×#26111yescharacteristic
402C2×D4—131no—
403C2×D4—261no—
404C2×D4—261no—
405C2×D4C22×#26111yescharacteristic
406C22×C4—21no—
407C22×C4—131no—
408C22×C4—131no—
409C22×C4—131no—
410C22×C4—261no—
411C22×C4—261no—
412C22×C4—261no—
413C22×C4—261no—
414C22×C4—262no—
415C22×C4—261no—
416Q16—134no—
417SD16—134no—
418SD16C4×#26114yescomplemented
419D8—134no—
420M16—134no—
421M16—134no—
422M16—268no—
423M16—268no—
424M16—262no—
425M16—262no—
426C2×C8—132no—
427C2×C8—132no—
428C2×C8—134no—
429C2×C8—134no—
430C2×C8—131no—
431C2×C8—134no—
432C2×C8—131no—
433C2×C8—262no—
434C2×C8—268no—
435C2×C8—268no—
436C2×C8—262no—
437C2×C8—262no—
438C2×C8C22×#26111yescharacteristic
439C2×C8C22×#26111yescharacteristic
440C4⋊C4—21no—
441C4⋊C4—131no—
442C4⋊C4—131no—
443C4⋊C4—261no—
444C4⋊C4—261no—
445C4⋊C4—261no—
446C4⋊C4C22×#26111yescharacteristic
447C4⋊C4C22×#26111yescharacteristic
448C22⋊C4—21no—
449C22⋊C4—261no—
450C22⋊C4—261no—
451C22⋊C4—261no—
452C22⋊C4—261no—
453C22⋊C4—261no—
454C42—21no—
455C42—131no—
456C42—131no—
457C42—131no—
458C42—134no—
459C42—261no—
460C42—261no—
461C42—261no—
462C42—261no—
463C42—262no—
464C42—261no—
465C42—522no—
466C42—522no—
467C42C22×#26111yescharacteristic
468C13C4×#44411yescharacteristic, complemented, Sylow
469C23—21no—
470C23—131no—
471C23—261no—
472Q8—21no—
473Q8—132no—
474Q8—261no—
475Q8C2×C4×#26112yes—
476D4—21no—
477D4—132no—
478D4—264no—
479D4—264no—
480D4—261no—
481D4C2×C4×#26112yes—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—42no—
486C2×C4—131no—
487C2×C4—131no—
488C2×C4—132no—
489C2×C4—132no—
490C2×C4—131no—
491C2×C4—262no—
492C2×C4—264no—
493C2×C4—264no—
494C2×C4—261no—
495C2×C4—262no—
496C2×C4—264no—
497C2×C4—261no—
498C2×C4—261no—
499C2×C4—522no—
500C2×C4—522no—
501C2×C4—522no—
502C2×C4—522no—
503C2×C4—522no—
504C2×C4D4×#26111yescharacteristic
505C2×C4D4×#26111yescharacteristic
506C2×C4C23×#26111yescharacteristic
507C8—21no—
508C8—134no—
509C8—134no—
510C8—132no—
511C8—264no—
512C8—264no—
513C8—261no—
514C8C2×C4×#26112yes—
515C22—22no—
516C22—41no—
517C22—41no—
518C22—132no—
519C22—261no—
520C22—261no—
521C22—262no—
522C22—521no—
523C22—521no—
524C22C2×D4×#26111yescharacteristic
525C4—22no—
526C4—21no—
527C4—41no—
528C4—41no—
529C4—132no—
530C4—132no—
531C4—262no—
532C4—261no—
533C4—524no—
534C4—521no—
535C4—521no—
536C4#1171910812yesdirect product factor
537C4C22×C4×#26111yescharacteristic
538C4#41×#26111yescharacteristic
539C2—42no—
540C2—262no—
541C2—522no—
542C2C4×D4×#26111yescharacteristic
543C2C2×#1171910811yescharacteristic
544C2D13⋊#44411yescharacteristic
subgroupG/H
centerC2×C4D4×#261
commutatorC4×C13C22×C42
FrattiniC2×C4C23×#261
FittingC4×C13×SD16C4
socleC22×C13C2×C4×D4
prime radicalC2×#88170C22
cosocleC2×C4×D13C24
hypercenterC4×SD16#261
hypocenterC13C4×#444
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. C4×#88240C2semidirect
3. C4×#88238C2semidirect
4. C4×#88104C2semidirect
5. #13130644C2semidirect
6. #13130617C2semidirect
7. #13130615C2semidirect
8. C4×#88118C2semidirect
9. C4×#88116C2semidirect
10. C4×#88100C2semidirect
21. #11719108C4direct (N × H)
35. C4×C13×SD16C4semidirect
36. SD16×Dic13C4semidirect
37. C4×#6107C4semidirect
38. C4×#6104C4semidirect
40. #11718513C4semidirect
42. #11718451C4semidirect
44. #11718417C4semidirect
45. C4×#6095C4semidirect
55. #88240C2×C4semidirect
57. #88238C2×C4semidirect
92. #88118C2×C4semidirect
93. #88116C2×C4semidirect
105. #88104C2×C4semidirect
107. #88100C2×C4semidirect
163. C13×SD16C42semidirect
173. #6107C42semidirect
174. #6104C42semidirect
194. #6095C42semidirect
265. C4×SD16#261semidirect
307. C4×C13#444semidirect
314. Dic13#444semidirect
418. SD16C4×#261semidirect
468. C13C4×#444semidirect
536. C4#11719108direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117191082
C4×#882402
C4×#882382
C4×#881042
#131306442
#131306172
#131306152
C4×#881182
C4×#881162
C4×#881002
C4×#881702
C4×#44413