Finite Group Databasebeta

← C4×#16810895 #27390977

Subgroups — C4×#16810895 #27390977

Order 13568.

882 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810895C211yesmaximal, characteristic
2C4×#13133248C212yesmaximal
3C4×#13133223C211yesmaximal, characteristic
4#20275631C211yesmaximal, characteristic, complemented
5#20275498C211yesmaximal, characteristic, complemented
6#20275367C212yesmaximal, complemented
7#20275233C212yesmaximal
8#20274780C211yesmaximal, characteristic
9C4×#13133153C211yesmaximal, characteristic, complemented
10C4×#13133136C212yesmaximal, complemented
11C2×C4×Q16×C53C211yesmaximal, characteristic, complemented
12C2×#13133248C2212yes—
13C2×#13133223C2211yescharacteristic
14C2×#13133223C2211yescharacteristic
15C4×#11719945C2211yescharacteristic
16#16810895C418yesdirect product factor
17#16810728—22no—
18#16810721—22no—
19C4×#11719925—22no—
20C4×#11719924—22no—
21C2×#13133153C2211yescharacteristic
22C2×#13133153C2211yescharacteristic
23#16810663C2212yes—
24#16810632C2212yes—
25#16810622C2212yes—
26C2×#13133136C2212yes—
27C2×#13133136C2212yes—
28#16810578C2211yescharacteristic
29#16810578C2211yescharacteristic
30#16810577—21no—
31#16810577—21no—
32C4×#11719917C2211yescharacteristic
33C4×#11719917C2212yes—
34C4×#11719912—21no—
35C4×C8×D53—21no—
36#16810392C2212yes—
37#16810392C2212yes—
38#16810388C2212yes—
39C22×Q16×C53C2211yescharacteristic
40C2×C4×Q8×C53C2212yes—
41C4×Q16×C53—21no—
42C4×Q16×C53—21no—
43C4×Q16×C53—21no—
44C4×Q16×C53—21no—
45C2×#107×C53C2211yescharacteristic
46C2×#103×C53C2212yes—
47C2×C4×C8×C53C2211yescharacteristic
48C2×#11719945C2311yescharacteristic
49#13133248—24no—
50#13133248C2×C418yes—
51C2×#11719925—22no—
52C2×#11719924—22no—
53#13133223—22no—
54#13133223—22no—
55#13133223—22no—
56#13133223C2×C414yes—
57C2×#11719917C2312yes—
58C2×#11719917C2311yescharacteristic
59C2×#11719917C2312yes—
60C2×#11719917C2311yescharacteristic
61C2×#11719912—21no—
62C2×#11719912—21no—
63C2×C8×D53—21no—
64C2×C8×D53—21no—
65C4×Dic106D411yescharacteristic
66C4×Dic106D411yescharacteristic
67C4×D212D411yescharacteristic
68C4×D212D411yescharacteristic
69C4×C22⋊D53—21no—
70C4×C22⋊D53—21no—
71#13133176C2311yescharacteristic
72#13133174—21no—
73C42×D53—21no—
74#13133153—22no—
75#13133153C2×C414yescomplemented
76#13133150—22no—
77#13133148—22no—
78#13133141—22no—
79#13133141—22no—
80#13133140—22no—
81#13133137—22no—
82#13133136—24no—
83#13133136C2×C418yescomplemented
84#13133128—21no—
85#13133128—22no—
86#13133127—21no—
87#13133127—21no—
88C4×#88322—21no—
89C4×#88322—22no—
90C8×Dic53—21no—
91C8×Dic53—21no—
92C22×Q8×C53C2312yes—
93C2×Q16×C53—21no—
94C2×Q16×C53—21no—
95C2×Q16×C53—22no—
96C2×Q16×C53C2×C414yescomplemented
97C22×C8×C53C2311yescharacteristic
98C22×C8×C53C2311yescharacteristic
99C4×Q8×C53—22no—
100C4×Q8×C53—22no—
101C4×Q8×C53—22no—
102C4×Q8×C53—22no—
103C2×C4⋊C4×C53—22no—
104C2×C4⋊C4×C53C2312yes—
105C2×C42×C53—22no—
106C2×C42×C53C2311yescharacteristic
107#107×C53—21no—
108#107×C53—21no—
109#103×C53—22no—
110#103×C53—22no—
111C4×C8×C53D411yescharacteristic
112C4×C8×C53D411yescharacteristic
113C4×C8×C53D411yescharacteristic
114C4×C8×C53D411yescharacteristic
115C2×Q8×C53—22no—
116C2×Q8×C53—22no—
117C2×Q8×C53—22no—
118C2×Q8×C53—22no—
119C2×Q8×C53—22no—
120C2×Q8×C53C22×C414yes—
121C22×C4×C53—22no—
122C22×C4×C53—22no—
123C22×C4×C53#4111yescharacteristic
124C22×C4×C53#4111yescharacteristic
125C22×C4×C53C2411yescharacteristic
126C2×C22⋊D53—21no—
127#11719945—21no—
128#11719945—21no—
129#11719945C22×C412yes—
130#11719945#4112yes—
131C2×D212C2×D411yescharacteristic
132C2×C4×D53—21no—
133C2×C4×D53—21no—
134C2×C4×D53—21no—
135C2×Dic106C2×D411yescharacteristic
136Q16×C53—24no—
137Q16×C53—24no—
138C2×C8×C53—21no—
139C2×C8×C53—21no—
140C2×C8×C53C22×C412yes—
141C2×C8×C53C2×D411yescharacteristic
142C2×C8×C53C2×D411yescharacteristic
143C2×C8×C53C2×D411yescharacteristic
144C2×C8×C53C2×D411yescharacteristic
145C2×C8×C53#4112yes—
146C4⋊C4×C53—22no—
147C4⋊C4×C53—22no—
148C4⋊C4×C53—42no—
149C4⋊C4×C53—42no—
150C42×C53—42no—
151C42×C53—42no—
152C42×C53C2×D411yescharacteristic
153C42×C53C2×D411yescharacteristic
154C42×C53C2×D411yescharacteristic
155C42×C53C2×D411yescharacteristic
156C22⋊Dic53—21no—
157#11719925—28no—
158#11719924—28no—
159#11719921—21no—
160#11719921—21no—
161C4⋊Dic53C2×D411yescharacteristic
162C4⋊Dic53C2×D411yescharacteristic
163#11719919—21no—
164#11719919—21no—
165C4×Dic53—21no—
166C4×Dic53—21no—
167C4×Dic53—21no—
168#11719917—21no—
169#11719917—21no—
170#11719917—22no—
171#11719917—22no—
172#11719917—22no—
173#11719917C22×C412yes—
174#11719917C22×C414yes—
175#11719917#4112yes—
176C2×#88322—21no—
177C2×#88322—21no—
178C2×#88322—22no—
179C2×#88322—22no—
180#11719912—24no—
181#11719912—24no—
182C8×D53—24no—
183C8×D53—24no—
184C23×C53C2×#4111yescharacteristic
185C22×D53—21no—
186Q8×C53—24no—
187Q8×C53—24no—
188Q8×C53—42no—
189Q8×C53—42no—
190C2×C4×C53—22no—
191C2×C4×C53—24no—
192C2×C4×C53—41no—
193C2×C4×C53—42no—
194C2×C4×C53—42no—
195C2×C4×C53—42no—
196C2×C4×C53—82no—
197C2×C4×C53#12111yescharacteristic
198C2×C4×C53#12111yescharacteristic
199C2×C4×C53#12111yescharacteristic
200C2×C4×C53#12111yescharacteristic
201C2×C4×C53C23×C411yescharacteristic
202C2×C4×C53C22×D411yescharacteristic
203C2×C4×C53C22×D411yescharacteristic
204C2×C4×C53C2×#4111yescharacteristic
205C2×C4×C53C2×#4111yescharacteristic
206C2×C4×C53C2×#4111yescharacteristic
207C22⋊D53—22no—
208C22⋊D53—22no—
209C2×Dic53—21no—
210C2×Dic53—21no—
211C2×Dic53—21no—
212D212—21no—
213D212C4×D412yes—
214C4×D53—22no—
215C4×D53—22no—
216C4×D53—42no—
217C4×D53—42no—
218Dic106—21no—
219Dic106C4×D412yes—
220C8×C53—21no—
221C8×C53—21no—
222C8×C53C4×D412yes—
223C8×C53C4×D412yes—
224#88322—22no—
225#88322—24no—
226#88322—22no—
227#88322—42no—
228C4×#473—531nomaximal, Sylow
229C22×C53—21no—
230C22×C53—21no—
231C22×C53C4×#4111yescharacteristic
232C22×C53C2×#12111yescharacteristic
233C22×C53#52911yescharacteristic
234C2×D53—22no—
235C2×D53—41no—
236C2×D53—41no—
237C4×C53—21no—
238C4×C53—21no—
239C4×C53—21no—
240C4×C53—44no—
241C4×C53—82no—
242C4×C53#47312yescomplemented
243C4×C53C2×C4×D411yescharacteristic
244C4×C53C2×C4×D411yescharacteristic
245C4×C53#52511yescharacteristic
246C4×C53#53211yescharacteristic
247Dic53—22no—
248Dic53—41no—
249Dic53—41no—
250C2×#473—531no—
251C4×#137—532no—
252C2×C4×Q16D5311yescharacteristic, complemented
253C4×#131—531no—
254#1979—531no—
255#1952—531no—
256#1930—532no—
257#1908—532no—
258#1816—531no—
259C4×#108—531no—
260C4×#101—532no—
261C2×C53—21no—
262C2×C53—21no—
263C2×C53C4×#12111yescharacteristic
264C2×C53C2×#47311yescharacteristic
265C2×C53#306711yescharacteristic
266D53—42no—
267C2×#137—532no—
268C22×Q16C2×D5311yescharacteristic
269C2×#131—531no—
270C2×#131—531no—
271C4×#41—531no—
272C2×C4×Q8C2×D5312yes—
273#473—538no—
274#441—1062no—
275#440—1062no—
276C4×Q16—21no—
277C4×Q16—21no—
278C4×Q16—21no—
279C4×Q16—21no—
280C4×Q16—1062no—
281C4×SD16—1062no—
282C2×#108—531no—
283C2×#108—531no—
284#428—532no—
285C2×#107C2×D5311yescharacteristic
286#419—532no—
287#417—532no—
288C2×#103C2×D5312yes—
289C2×#101—532no—
290C2×#101—532no—
291#405—531no—
292#405—531no—
293#405—1061no—
294#405—1061no—
295C4×M16—531no—
296C4×M16—532no—
297C4×M16—1061no—
298C2×C4×C8—1061no—
299C2×C4×C8C2×D5311yescharacteristic
300#343—532no—
301#343—532no—
302#341—532no—
303C53C4×#47311yescharacteristic, complemented, Sylow
304C2×#41—531no—
305C22×Q8C22×D5312yes—
306#137—538no—
307#137—1064no—
308C2×Q16—22no—
309C2×Q16—21no—
310C2×Q16—21no—
311C2×Q16—1062no—
312C2×Q16C4×D5314yescomplemented
313C2×SD16—1062no—
314#131—534no—
315#131—1062no—
316#131—1062no—
317#131—1062no—
318C2×M16—531no—
319C2×M16—531no—
320C2×M16—532no—
321C2×M16—532no—
322C2×M16—1061no—
323C2×M16—1061no—
324C22×C8—1061no—
325C22×C8—1061no—
326C22×C8C22×D5311yescharacteristic
327C22×C8C22×D5311yescharacteristic
328C4×Q8—22no—
329C4×Q8—22no—
330C4×Q8—22no—
331C4×Q8—22no—
332C4×Q8—531no—
333C4×Q8—531no—
334C4×D4—531no—
335C4×D4—531no—
336C4×D4—1061no—
337C4×D4—1061no—
338#117—531no—
339#117—1061no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4C22×D5312yes—
342C2×C42—22no—
343C2×C42—1061no—
344C2×C42C22×D5311yescharacteristic
345#108—534no—
346#108—1062no—
347#107—21no—
348#107—21no—
349#107—1062no—
350#106—1062no—
351#103—22no—
352#103—22no—
353#103—1062no—
354#103—1062no—
355#103—1062no—
356#102—1062no—
357#101—538no—
358#101—1064no—
359#97—1061no—
360#97—1061no—
361#97—1062no—
362#97—1061no—
363C4×C8—1061no—
364C4×C8—1061no—
365C4×C8—1062no—
366C4×C8—1061no—
367C4×C8C22⋊D5311yescharacteristic
368C4×C8C22⋊D5311yescharacteristic
369C4×C8C22⋊D5311yescharacteristic
370C4×C8C22⋊D5311yescharacteristic
371#41—532no—
372#41—532no—
373#41—1061no—
374#41—1061no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—531no—
381C2×Q8C2×C4×D5314yes—
382C2×D4—531no—
383C2×D4—1061no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—1061no—
387C22×C4—1061no—
388C22×C4—1061no—
389C22×C4#1171994711yescharacteristic
390C22×C4#1171994711yescharacteristic
391C22×C4C23×D5311yescharacteristic
392Q16—24no—
393Q16—24no—
394Q16—1068no—
395SD16—1068no—
396M16—532no—
397M16—534no—
398M16—532no—
399M16—1064no—
400M16—1061no—
401M16—1062no—
402M16—1061no—
403M16—1064no—
404M16—1062no—
405M16—1062no—
406C2×C8—21no—
407C2×C8—21no—
408C2×C8—1064no—
409C2×C8—1062no—
410C2×C8—1061no—
411C2×C8—1061no—
412C2×C8—1064no—
413C2×C8—1062no—
414C2×C8C2×C4×D5312yes—
415C2×C8#1171994512yes—
416C2×C8C2×C22⋊D5311yescharacteristic
417C2×C8C2×C22⋊D5311yescharacteristic
418C2×C8C2×C22⋊D5311yescharacteristic
419C2×C8C2×C22⋊D5311yescharacteristic
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—42no—
423C4⋊C4—42no—
424C4⋊C4—531no—
425C4⋊C4—531no—
426C4⋊C4—1061no—
427C4⋊C4—1061no—
428C22⋊C4—1061no—
429C22⋊C4—1061no—
430C22⋊C4—1061no—
431C42—42no—
432C42—42no—
433C42—1061no—
434C42—1061no—
435C42—1061no—
436C42D4×D5311yescharacteristic
437C42D4×D5311yescharacteristic
438C42C2×C22⋊D5311yescharacteristic
439C42C2×C22⋊D5311yescharacteristic
440C23—1061no—
441C23C2×#1171994711yescharacteristic
442Q8—24no—
443Q8—24no—
444Q8—42no—
445Q8—42no—
446Q8—532no—
447Q8—1061no—
448D4—532no—
449D4—1062no—
450D4—1062no—
451D4—1061no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—82no—
459C2×C4—1061no—
460C2×C4—1062no—
461C2×C4—1062no—
462C2×C4—1061no—
463C2×C4—1061no—
464C2×C4—2122no—
465C2×C4—2122no—
466C2×C4#1313318811yescharacteristic
467C2×C4#1313318811yescharacteristic
468C2×C4#1313318811yescharacteristic
469C2×C4#1313318811yescharacteristic
470C2×C4C22×C4×D5311yescharacteristic
471C2×C4C2×D4×D5311yescharacteristic
472C2×C4C22×C22⋊D5311yescharacteristic
473C2×C4#41×D5311yescharacteristic
474C2×C4#41×D5311yescharacteristic
475C2×C4C2×#1171994511yescharacteristic
476C8—21no—
477C8—21no—
478C8—1064no—
479C8—1062no—
480C8—1062no—
481C8—2122no—
482C8C4×C22⋊D5312yes—
483C8C4×C22⋊D5312yes—
484C22—21no—
485C22—21no—
486C22—1062no—
487C22—2121no—
488C22—2121no—
489C22C4×#1171994711yescharacteristic
490C22C2×#1313318811yescharacteristic
491C22#1681115511yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—44no—
496C4—82no—
497C4—1062no—
498C4—2121no—
499C4—2121no—
500C4#1681089512yesdirect product factor
501C4C4×D4×D5311yescharacteristic
502C4C2×C4×C22⋊D5311yescharacteristic
503C4#1681113011yescharacteristic
504C4#1681117011yescharacteristic
505C2—21no—
506C2—21no—
507C2—2122no—
508C2C4×#1313318811yescharacteristic
509C2C2×#1681089511yescharacteristic
510C2#2028443111yescharacteristic
subgroupG/H
centerC2×C4#13133188
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C4×Q16×C53C2
socleC22×C53C2×#121
prime radicalC2×#11719945C23
cosocleC22×C4×C53C24
hypercenterC2×C4×Q16D53
hypocenterC53C4×#473
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
4. #20275631C2semidirect
5. #20275498C2semidirect
6. #20275367C2semidirect
9. C4×#13133153C2semidirect
10. C4×#13133136C2semidirect
11. C2×C4×Q16×C53C2semidirect
16. #16810895C4direct (N × H)
75. #13133153C2×C4semidirect
83. #13133136C2×C4semidirect
96. C2×Q16×C53C2×C4semidirect
242. C4×C53#473semidirect
252. C2×C4×Q16D53semidirect
303. C53C4×#473semidirect
312. C2×Q16C4×D53semidirect
500. C4#16810895direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168108952
C4×#131332482
C4×#131332232
#202756312
#202754982
#202753672
#202752332
#202747802
C4×#131331532
C4×#131331362
C2×C4×Q16×C532
C4×#47353